text stringlengths 14 5.77M | meta dict | __index_level_0__ int64 0 9.97k ⌀ |
|---|---|---|
Dale Hackle retires after long, accomplished career at NFCC; honored for 40 years of service.
Dale Hackle Retires After 40 Years of Service
Dale Hackle retires after long, accomplished career
MADISON, FL– North Florida Community College recently honored Dale Hackle for 40-years of dedicated service and
outstanding commitment to his job, the NFCC family and our community. Dale was born in South Florida and moved to Madison in 1977. In March 1978, he began working at NFCC (then North Florida Junior College) as a maintenance carpenter under the direction of then Maintenance Supervisor Ralph Williams. Dale assumed leadership of the department in 1984 and served as Director of Physical Plant at NFCC through December 2017.
"It's been a pleasure working with everyone over the years," said Dale. "It sure has been a challenging and rewarding experience."
Throughout his career, Dale says he most enjoyed working with all the new construction and maintenance projects and is proud of the campus improvements made over the years. The majority of NFCC buildings have either been remodeled or were built during his tenure.
Dale played an instrumental role in helping get campus facilities and grounds functioning and repaired after an EF3 category tornado hit NFCC in 1988, destroying and damaging buildings and uprooting trees along its path through campus. "It was quite the challenge to get building roofs dried in and to have debris removed to be able to have classes going again. We were closed for four days before we reopened."
He also had the privilege of working for eight of NFCC's nine presidents during his years of service. Beginning early in his career and still, Dale is praised for doing an admirable job, for being a fair and strong leader, and for his outstanding dedication to NFCC, the campus and his colleagues.
"Dale has been an amazing steward of NFCC's campus for decades," said NFCC President John Grosskopf. "His dedication to the College and the students we serve are a model for the rest of us who serve."
Dale is married to Gail Hackle who currently works as a senior staff assistant in the NFCC Public Safety Academy. They have been married 42 years, have two sons and three grandchildren. Dale said he was looking forward to spending more time with his family and doing more woodworking, fishing and camping in retirement. He officially passed his NFCC "tool belt" on to current NFCC Director of Physical Plant Glenn Strickland at the end of the year.
"I have enjoyed working with everyone over the years," said Dale. "I wish the College and its employees the best in the future."
PHOTO: NFCC President John Grosskopf, left, and NFCC retiree Dale Hackle, right, on Dec. 11 during Hackle's retirement reception. | {
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<?php
namespace App\Controller;
use Slim\App;
use Psr\Log\LoggerInterface;
use Psr\Http\Message\RequestInterface;
use Psr\Http\Message\ResponseInterface;
abstract class PurchaseController
{
public $logger;
public $renderer;
public $translator;
public $router;
public $cfg;
public function __construct($container)
{
$this->router = $container['router'];
$this->logger = $container['logger'];
$this->renderer = $container['renderer'];
$this->translator = $container['translator'];
$this->cookie = $container['cookie'];
$this->cfg = $container['cfg'];
}
/*
!!! Obligatoire dans ControllerSpé !!!
Renvoi la première page du type de paiement
*/
public function firstPage(){}
public function manageError($code){
if(isset($code)) {
switch ($code) {
case 310 : $message = 'REG_error_VoucherUnknown'; break;
case 311 : $message = 'REG_error_VoucherUsed'; break;
case 312 : $message = 'REG_error_VoucherExpired'; break;
case 314 : $message = 'REG_error_VoucherWrong'; break;
case 320 : $message = 'TEFPP_error_PINInvalid'; break;
case 2110 : $message = 'TEFPP_error_PINNotMatch'; break;
case 322 :
case 2111 : $message = 'TEFPP_error_PINExpired';break;
case 323 :
case 2112 : $message = 'TEFPP_error_PINInactive';break;
case 2113 : $message = 'TEFPP_error_PINMaxAttemptReached';break;
case 2101 :
case 330 : $message = 'TEFPP_error_MSISDNInvalid'; break;
case 2502 :
case 332 :
case 341 : $message = 'TEFPP_error_MSISDNAlreadySubscriber'; break;
case 371 : $message = 'TEFPP_error_PasswordNotMatch'; break;
case 325 :
case 2200 : $message = 'TEFPP_error_MSISDNBlacklisted'; break;
case 2404 : $message = 'TEFPP_error_InsufficientCredit'; break;
case 2201 : $message = 'CNX_notice_NoVivoClient'; break;
case 2202 : $message = 'TEFPP_error_MSISDNOtherCarrier'; break;
case 2203 : $message = 'REG_error_NotForPrePaid'; break;
default : $message = 'ERR_alert_ErrorOccurred';
}
return $this->translator->trans($message);
}
}
public function YourMobileCtrl(){
echo 'test';
var_dump($this->router->pathFor('root'));die();
}
} | {
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Diversity Action Group
Related Policies:
Employee Standard of Conduct
BC Human Rights Code
RRU Elders Circle
RRU International
RRU Proud
Our Diversity Statement:
Diversity enriches community, expands learning, and advances knowledge.
Royal Roads University acknowledges and celebrates the diversity of our community, which is shaped by our complex identities, life experiences, and perspectives.
We strive to increase understanding, appreciation, and engagement with each other, thereby making us more compassionate human beings and strengthening the fabric of our communities.
To achieve this, we commit to:
facilitating educational experiences, research opportunities, and a workplace environment that reflect and benefit from the diversity of our communities; and
fostering an environment that is open, inclusive, safe, respectful, and fair, and in which a diversity of ideas are able to flourish.
Our expectation is that we will support one another in fulfilling these commitments, thereby cultivating a whole, thriving community that is greater than the sum of its parts.
Contact us to become involved with Royal Roads' Diversity Action Group. Feedback is always welcome. | {
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{"url":"https:\/\/www.physicsforums.com\/threads\/zeta-function-in-the-critical-strip.279831\/","text":"# Zeta function in the critical strip\n\n1. Dec 15, 2008\n\n### TheOogy\n\nhow do i calculate values of the riemann zeta function in the critical strip? because if you only know zeta as a series:\n\n$$\\zeta(s) = \\sum 1\/n^s$$\n\nand the functional equation\n\n$$\\zeta(s) = 2^s\\pi^{s-1}\\sin\\left(\\frac{\\pi s}{2}\\right)\\Gamma(1-s)\\zeta(1-s) \\!$$\n\nyou can only calculate values that have real part bigger then 1 or smaller then 0.\ni know i can use a math software to calculate it but i want to understand the process.\n\n2. Dec 15, 2008\n\n### rscosa\n\nHi!,\nthere are many other representations (wikipedia or www.mathworld.com) but maybe non of them will be enough helpfull.\n\n3. Dec 19, 2008\n\n### Santa1\n\nUse the dirichlet eta function relation.\n\n4. Dec 19, 2008\n\n### TheOogy\n\ncan we express the eta function as a product of primes?\n\n5. Dec 19, 2008\n\n### Santa1\n\nin 0< re s <1 ?\n\n6. Dec 20, 2008\n\n### TheOogy\n\nyes.\n\n7. Dec 20, 2008\n\n### TheOogy\n\nor, is there a way to calculate values in the critical strip with out using an alternating series?\n\n8. Dec 20, 2008\n\n### Santa1\n\nWell, you can use the relation to zeta and use its euler product. But I'm not sure as far as the convergence goes.\n\nedit1: And yes, you can (amongst other ways) express $$\\eta(s)\\Gamma(s)$$ as an integral,\n\n$$\\eta(s)\\Gamma(s)=\\int_0^\\infty \\frac{x^{s-1}}{e^x+1}\\mathrm{d}x$$, valid for re s > 0.\n\nand then use the zeta relation again.\n\nYou could also use the $$\\zeta(s)\\Gamma(s)$$ integral form, and deform the contour as riemann originally did.\n\nLast edited: Dec 20, 2008\n9. Dec 20, 2008\n\n### TheOogy\n\ni tried using the euler product but it didn't work, but thanks for the eta-gamma integral, can you show me the zeta-gamma integral two and save me the search?\n\n10. Dec 21, 2008\n\n### Santa1\n\nJust go to almost any gamma or zeta function online encyclopedia site for more info, but beware the original form only works for re s > 1 (the eta form works for re s>0), if you are not somewhat familiar with complex analysis you won't get much of it.\n\nThe eta gamma + relation gives,\n\n$$\\zeta(s) = \\frac{1}{(1-2^{1-s})\\Gamma(s)}\\int_0^\\infty \\frac{x^{s-1}}{e^x+1}\\mathrm{d}x$$, edit($$\\Re s > 0, s \\not= 1$$)\n\n11. Dec 22, 2008\n\nThanks!!","date":"2017-11-18 18:50:46","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\": 0.9050747752189636, \"perplexity\": 1573.0162444403102}, \"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-2017-47\/segments\/1510934805008.39\/warc\/CC-MAIN-20171118171235-20171118191235-00125.warc.gz\"}"} | null | null |
Q: TensorFlow: improve accuracy on training data I am experimenting with TensorFlow. One of my first tries consists on learning one of the features based on the data. Let's say my data is composed on the following values:
35, 2, 3, 4, 19, 31, 7, 9, 34, 10, 33, 12, 59, 6, 14, 31, 13
...
35, 4, 7, 14, 9, 3, 17, 19, 42, 11, 3, 1, 53, 12, 17, 30, 15
I would like to predict the value of the last feature, in the example it is going to be the values 13 for the first row and 15 for the last row.
I have around 10000 rows of data. I've written the following model using TensorFlow(I'm following this tutorial):
W0 = tf.Variable(tf.zeros([nb_attributes, 25]))
B0 = tf.Variable(tf.zeros([25]))
W1 = tf.Variable(tf.truncated_normal([25, 30], stddev=0.1))
B1 = tf.Variable(tf.zeros([30]))
W2 = tf.Variable(tf.truncated_normal([30, 70], stddev=0.1))
B2 = tf.Variable(tf.zeros([70]))
W3 = tf.Variable(tf.truncated_normal([70, 150], stddev=0.1))
B3 = tf.Variable(tf.zeros([150]))
W4 = tf.Variable(tf.truncated_normal([150, 75], stddev=0.1))
B4 = tf.Variable(tf.zeros([75]))
W5 = tf.Variable(tf.truncated_normal([75, 54], stddev=0.1))
B5 = tf.Variable(tf.zeros([54]))
# placeholder for input and output
x = tf.placeholder("float", [None, nb_attributes])
Y_ = tf.placeholder("float", [None,54])
XX = tf.reshape(x, [-1, nb_attributes])
Y1 = tf.nn.sigmoid(tf.matmul(XX, W0) + B0)
Y2 = tf.nn.sigmoid(tf.matmul(Y1, W1) + B1)
Y3 = tf.nn.sigmoid(tf.matmul(Y2, W2) + B2)
Y4 = tf.nn.sigmoid(tf.matmul(Y3, W3) + B3)
Y5 = tf.nn.sigmoid(tf.matmul(Y4, W4) + B4)
# learned output
Ylogits = tf.matmul(Y5, W5) + B5
Y = tf.nn.softmax(Ylogits)
cross_entropy = tf.nn.softmax_cross_entropy_with_logits(logits=Ylogits, labels=Y_)
cross_entropy = tf.reduce_mean(cross_entropy)*100
train_step = tf.train.ProximalGradientDescentOptimizer(0.01).minimize(cross_entropy)
The train step is as follows:
for i in range(100):
batch_xs, batch_ys = get_train_events()
sess.run(train_step, feed_dict={x: batch_xs, Y_: batch_ys})
correct_prediction = tf.equal(tf.argmax(Y,1), tf.argmax(Y_,1))
accuracy = tf.reduce_mean(tf.cast(correct_prediction, "float"))
test_data_evs, test_data_out = batch_xs, batch_ys
current_accuracy = sess.run(accuracy, feed_dict={x: test_data_evs, Y_: test_data_out})
print 'Current Accuracy {}'.format(current_accuracy)
Please, note that I am using the same data for training than for testing. I am aware that it is not the approach to follow but I am doing on this way because I've found that the accuracy on the test data was so bad that I decided to know what was the accuracy on the training data. As far as I understand it is supposed that the accuracy on the training data after testing must be close to 100%, isn't it?
However, I cannot improve the accuracy to more the 60%. I tried the following:
*
*Give the data using different strategies
*Using different training optimizer from here
*Change the net architecture
*Using dropout approach
The only step that shown some progress has been to provide testing data randomly in batch of size N. In such case, I managed to move the accuracy from 60 to 64%. I was wondering whether I am applying a wrong approach or committing some stupid or naive error. Any thought in respect of the issue is going to very much appreciated.
Thanks a lot in advance!
EDIT 1: For the sake of completing the question I managed to solve quite well the problem by using the k-neighbour algorithm. This code have helped in my case.
| {
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} | 7,630 |
Robledo de Chavela é um município da Espanha na província e comunidade autónoma de Madrid, de área 94,1 km² com população de 3599 habitantes (2007) e densidade populacional de 35,72 hab/km².
Demografia
Municípios da Comunidade de Madrid
Municípios da Espanha por nome
Localidades da Espanha
Localidades da Comunidade de Madrid | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,094 |
{"url":"http:\/\/icpc.njust.edu.cn\/Problem\/Hdu\/2838\/","text":"# Cow Sorting\n\nTime Limit: 2000\/1000 MS (Java\/Others)\n\nMemory Limit: 32768\/32768 K (Java\/Others)\n\n## Description\n\nSherlock's N (1 \u2264 N \u2264 100,000) cows are lined up to be milked in the evening. Each cow has a unique \"grumpiness\" level in the range 1...100,000. Since grumpy cows are more likely to damage Sherlock's milking equipment, Sherlock would like to reorder the cows in line so they are lined up in increasing order of grumpiness. During this process, the places of any two cows (necessarily adjacent) can be interchanged. Since grumpy cows are harder to move, it takes Sherlock a total of X + Y units of time to exchange two cows whose grumpiness levels are X and Y.\n\nPlease help Sherlock calculate the minimal time required to reorder the cows.\n\n## Input\n\nLine 1: A single integer: N\nLines 2..N + 1: Each line contains a single integer: line i + 1 describes the grumpiness of cow i.\n\n## Output\n\nLine 1: A single line with the minimal time required to reorder the cows in increasing order of grumpiness.\n\n## Sample Input\n\n3\n2\n3\n1\n\n## Sample Output\n\n7\n\nHint\nInput Details\n\nThree cows are standing in line with respective grumpiness levels 2, 3, and 1.\nOutput Details\n\n2 3 1 : Initial order.\n2 1 3 : After interchanging cows with grumpiness 3 and 1 (time=1+3=4).\n1 2 3 : After interchanging cows with grumpiness 1 and 2 (time=2+1=3).\n\n\ngaojie\n\n## Source\n\n2009 Multi-University Training Contest 3 -","date":"2020-08-13 20:49:50","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\": 0.3427054286003113, \"perplexity\": 5080.243207972415}, \"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-2020-34\/segments\/1596439739073.12\/warc\/CC-MAIN-20200813191256-20200813221256-00374.warc.gz\"}"} | null | null |
{"url":"https:\/\/academy.vertabelo.com\/course\/ms-sql-basics\/set-operations\/introduction\/cycling-continued","text":"Introduction\n4. Get to know the tables (continued)\nUNION\nINTERSECT\nEXCEPT\n\nInstruction\n\nNow, why don't you check the contents of the other table we're going to work on? This time, we'll deal with speed skating medalists.\n\nExercise\n\nDisplay the contents of the Skating table.\n\nStuck? Here's a hint!\n\nType:\n\nSELECT\n*\nFROM Skating;","date":"2019-02-21 13:41:48","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\": 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\": 0.7279232144355774, \"perplexity\": 2827.0160724145203}, \"config\": {\"markdown_headings\": false, \"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-2019-09\/segments\/1550247504790.66\/warc\/CC-MAIN-20190221132217-20190221154217-00502.warc.gz\"}"} | null | null |
Q: Are WPF binding properties Path and XPath mutually exclusive? Suppose I have a UserControl whose DataContext is set to an object that has an XmlDataProvider property. I would like to bind to this property in my control's XAML, and specify some XPath. I tried this:
<TreeView ItemsSource="{Binding Path=PropertyName, XPath=/items/item/*}">
At runtime I get the exception "BindingExpression with XPath cannot bind to non-XML object". Removing the Path property and setting the TreeView's DataContext to the XmlPropertyName directly works fine.
What gives? Are Path and XPath mutually exclusive?
A: They are not mutually exclusive, as briefly mentioned in the Data Binding Overview under the Specifying the Path to the Value section.
The XPath expression will be executed before the Path property, but is sometimes desirable to use as Bea Stollnitz explains here and here.
"Removing the Path property and setting the TreeView's DataContext to the XmlPropertyName directly works fine."
Since you mentioned this, it seems to me like you are expecting the Path property to be evaluated before the XPath expression, which would be why you are getting an error, the XPath expression is evaluating on whatever your current context is, and the path is being evaluated after that.
error explanation
| {
"redpajama_set_name": "RedPajamaStackExchange"
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Announcements, a run-through of the day's calendar or maybe the Pledge of Allegiance.
Ulmer's Facebook page, Special Books by Special Kids, was created because he has been trying, unsuccessfully, to get a book published about the kids. "I have 50 rejection letters on my fridge to keep me motivated," he said. The book focuses on the story of each of the kids in his classroom and is collaboratively told by the child, his or her parents, and from Ulmer's perspective as their teacher.
Ulmer said the change has been remarkable in his students, whose diagnoses range fromautism to traumatic brain injury to speech apraxia to agenesis of corpus callosum.
"They all came from a segregated environment [from general education students]. Now they're participating in school activities, dancing in front of hundreds of other kids and in the debate club." And while Ulmer agrees academics are important, he thought it even more important to reverse the psychological damage that came from being made to feel like outcasts. | {
"redpajama_set_name": "RedPajamaC4"
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML>
<HEAD>
<TITLE> Interface <I>NamedNodeMap</I></TITLE>
<META NAME="GENERATOR" CONTENT="DOC++ 3.4.10">
</HEAD>
<BODY BGCOLOR="#ffffff">
<H2> <A HREF="#DOC.DOCU">Interface <I>NamedNodeMap</I></A></H2></H2><A NAME="DOC.DOCU"></A>
<BLOCKQUOTE>A <B>NamedNodeMap</B> object represents a list of objects that can be
accessed by name. A <B>NamedNodeMap</B> maintains the objects in
no particular order. The <B>Node</B> interface uses a <B>NamedNodeMap</B>
to maintain the attributes of a node.</BLOCKQUOTE>
<HR>
<DL>
<DT>
<IMG ALT="o" BORDER=0 SRC=icon1.gif><A NAME="ixmlNamedNodeMap_getLength"></A>
<A HREF=ixmlNamedNodeMap_getLength.html><B>ixmlNamedNodeMap_getLength</B></A><DD><I>Returns the number of items contained in this <B>NamedNodeMap</B>.</I>
<DT>
<IMG ALT="o" BORDER=0 SRC=icon1.gif><A NAME="ixmlNamedNodeMap_getNamedItem"></A>
<A HREF=ixmlNamedNodeMap_getNamedItem.html><B>ixmlNamedNodeMap_getNamedItem</B></A><DD><I>Retrieves a <B>Node</B> from the <B>NamedNodeMap</B> by name.</I>
<DT>
<IMG ALT="o" BORDER=0 SRC=icon1.gif><A NAME="ixmlNamedNodeMap_setNamedItem"></A>
<A HREF=ixmlNamedNodeMap_setNamedItem.html><B>ixmlNamedNodeMap_setNamedItem</B></A><DD><I>Adds a new <B>Node</B> to the <B>NamedNodeMap</B> using the <B>Node</B> name attribute.</I>
<DT>
<IMG ALT="o" BORDER=0 SRC=icon1.gif><A NAME="ixmlNamedNodeMap_removeNamedItem"></A>
<A HREF=ixmlNamedNodeMap_removeNamedItem.html><B>ixmlNamedNodeMap_removeNamedItem</B></A><DD><I>Removes a <B>Node</B> from a <B>NamedNodeMap</B> specified by name.</I>
<DT>
<IMG ALT="o" BORDER=0 SRC=icon1.gif><A NAME="ixmlNamedNodeMap_item"></A>
<A HREF=ixmlNamedNodeMap_item.html><B>ixmlNamedNodeMap_item</B></A><DD><I>Retrieves a <B>Node</B> from a <B>NamedNodeMap</B> specified by a numerical index.</I>
<DT>
<IMG ALT="o" BORDER=0 SRC=icon1.gif><A NAME="ixmlNamedNodeMap_getNamedItemNS"></A>
<A HREF=ixmlNamedNodeMap_getNamedItemNS.html><B>ixmlNamedNodeMap_getNamedItemNS</B></A><DD><I>Retrieves a <B>Node</B> from a <B>NamedNodeMap</B> specified by namespace URI and local name.</I>
<DT>
<IMG ALT="o" BORDER=0 SRC=icon1.gif><A NAME="ixmlNamedNodeMap_setNamedItemNS"></A>
<A HREF=ixmlNamedNodeMap_setNamedItemNS.html><B>ixmlNamedNodeMap_setNamedItemNS</B></A><DD><I>Adds a new <B>Node</B> to the <B>NamedNodeMap</B> using the <B>Node</B> local name and namespace URI attributes.</I>
<DT>
<IMG ALT="o" BORDER=0 SRC=icon1.gif><A NAME="ixmlNamedNodeMap_removeNamedItemNS"></A>
<A HREF=ixmlNamedNodeMap_removeNamedItemNS.html><B>ixmlNamedNodeMap_removeNamedItemNS</B></A><DD><I>Removes a <B>Node</B> from a <B>NamedNodeMap</B> specified by namespace URI and local name.</I>
<DT>
<IMG ALT="o" BORDER=0 SRC=icon1.gif><A NAME="ixmlNamedNodeMap_free"></A>
<A HREF=ixmlNamedNodeMap_free.html><B>ixmlNamedNodeMap_free</B></A><DD><I>Frees a <B>NamedNodeMap</B>.</I>
</DL>
<DL><DT><DD></DL><P><P><I><A HREF="index.html">Alphabetic index</A></I></P><HR>
<BR>
This page was generated with the help of <A HREF="http://docpp.sourceforge.net">DOC++</A>.
</BODY>
</HTML>
| {
"redpajama_set_name": "RedPajamaGithub"
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Dibrivka (în ) este un sat în comuna Suhovolea din raionul Volodarsk-Volînskîi, regiunea Jîtomîr, Ucraina.
Note
Dibrivka, Suhovolea, Volodarsk-Volînskîi, Jîtomîr
Dibrivka, Suhovolea, Volodarsk-Volînskîi, Jîtomîr
Dibrivka, Suhovolea, Volodarsk-Volînskîi, Jîtomîr | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,284 |
Terra Nova är en kommun i Brasilien. Den ligger i delstaten Bahia, i den östra delen av landet, km öster om huvudstaden Brasília. Antalet invånare är .
Omgivningarna runt Terra Nova är huvudsakligen savann. Runt Terra Nova är det ganska tätbefolkat, med invånare per kvadratkilometer. Savannklimat råder i trakten. Årsmedeltemperaturen i trakten är °C. Den varmaste månaden är februari, då medeltemperaturen är °C, och den kallaste är juni, med °C. Genomsnittlig årsnederbörd är millimeter. Den regnigaste månaden är maj, med i genomsnitt mm nederbörd, och den torraste är januari, med mm nederbörd.
Källor
Indelningar i Bahia | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,078 |
De marathon van Hongkong 2006 werd gelopen op 12 februari 2006 in Hongkong.
De wedstrijd werd bij de mannen gewonnen door de Keniaan Simon Bor. Hij had een ruime minuut voorsprong op zijn landgenoot Stephen Ndungu. Bij de vrouwen zegevierde de Ethiopische Dire Tune met een voorsprong van bijna zes minuten in 2:35.15.
In totaal finishten er 3317 lopers, waarvan 3040 mannen en 277 vrouwen.
Uitslagen
Mannen
Vrouwen
2006
Hongkong | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,097 |
{"url":"https:\/\/nomicon.io\/RuntimeSpec\/Fees\/","text":"# Runtime Fees\n\nRuntime fees are measured in Gas. Gas price will be discussed separately.\n\nWhen a transaction is converted into a receipt, the signer account is charged for the full cost of the transaction. This cost consists of extra attached gas, attached deposits and the transaction fee.\n\nThe total transaction fee is the sum of the following:\n\n\u2022 A fee for creation of the receipt\n\u2022 A fee for every action\n\nEvery Fee consists of 3 values measured in gas:\n\n\u2022 send_sir and send_not_sir - the gas burned when the action is being created to be sent to a receiver.\n\u2022 send_sir is used when current_account_id == receiver_id (current_account_id is a signer_id for a signed transaction).\n\u2022 send_not_sir is used when current_account_id != receiver_id\n\u2022 execution - the gas burned when the action is being executed on the receiver's account.\n\n## Receipt creation cost\u200b\n\nThere are 2 types of receipts:\n\nA transaction is converted into an ActionReceipt. Data receipts are used for data dependencies and will be discussed separately.\n\nThe Fee for an action receipt creation is described in the config action_receipt_creation_config.\n\nExample: when a signed transaction is being converted into a receipt, the gas for action_receipt_creation_config.send is being burned immediately, while the gas for action_receipt_creation_config.execution is only charged, but not burned. It'll be burned when the newly created receipt is executed on the receiver's account.\n\n## Fees for actions\u200b\n\nEvery Action has a corresponding Fee(s) described in the config action_creation_config. Similar to a receipt creation costs, the send gas is burned when an action is added to a receipt to be sent, and the execution gas is only charged, but not burned.\n\nFees are either a base fee or a fee per byte of some data within the action.\n\nHere is the list of actions and their corresponding fees:\n\n## Gas tracking\u200b\n\nIn Runtime, gas is tracked in the following fields of ActionResult struct:\n\n\u2022 gas_burnt - irreversible amount of gas spent on computations.\n\u2022 gas_used - includes burnt gas and gas attached to the new ActionReceipts created during the method execution.\n\u2022 gas_burnt_for_function_call - stores gas burnt during function call execution. Later, contract account gets 30% of it as a reward for a possibility to invoke the function.\n\nInitially runtime charges gas_used from the account. Some gas may be refunded later, see Refunds.\n\nAt first, we charge fees related to conversion from SignedTransaction to ActionReceipt and future execution of this receipt:\n\n\u2022 costs of all SignedTransactions passed to Runtime::apply are computed in tx_cost function during validation;\n\u2022 total_cost is deducted from signer, which is a sum of:\n\u2022 gas_to_balance(gas_burnt) where gas_burnt is action receipt send fee + total_send_fees(transaction.actions));\n\u2022 gas_to_balance(gas_remaining) where gas_remaining is action receipt exec fee + total_prepaid_exec_fees(transaction.actions) to pay all remaining fees caused by transaction;\n\u2022 total_deposit(transaction.actions);\n\u2022 each transaction is converted to receipt and passed to Runtime::process_receipt.\n\nThen each ActionReceipt is passed to Runtime::apply_action_receipt where gas is tracked as follows:\n\n\u2022 ActionResult is created with ActionReceipt execution fee;\n\u2022 all actions inside ActionReceipt are passed to Runtime::apply_action;\n\u2022 ActionResult with charged base execution fees is created there;\n\u2022 if action execution leads to new ActionReceipts creation, corresponding action_[action_name] function adds new fees to the ActionResult. E.g. action_delete_account also charges the following fees:\n\u2022 gas_burnt: send fee for new ActionReceipt creation + complex send fee for Transfer to beneficiary account\n\u2022 gas_used: gas_burnt + exec fee for created ActionReceipt + complex exec fee for Transfer\n\u2022 all computed ActionResults are merged into one, where all gas values are summed up;\n\u2022 unused gas is refunded in generate_refund_receipts.\n\nInside VMLogic, the fees are tracked in the GasCounter struct. The VM itself is called in the action_function_call inside Runtime. When all actions are processed, the result is returned as a VMOutcome, which is later merged with ActionResult.\n\n# Example\n\nLet's say we have the following transaction:\n\nTransaction { signer_id: \"alice.near\", public_key: \"2onVGYTFwyaGetWckywk92ngBiZeNpBeEjuzSznEdhRE\", nonce: 23, receiver_id: \"lockup.alice.near\", block_hash: \"3CwEMonK6MmKgjKePiFYgydbAvxhhqCPHKuDMnUcGGTK\", actions: [ Action::CreateAccount(CreateAccountAction {}), Action::Transfer(TransferAction { deposit: 100000000000000000000000000, }), Action::DeployContract(DeployContractAction { code: vec![\/*<...128000 bytes...>*\/], }), Action::FunctionCall(FunctionCallAction { method_name: \"new\", args: b\"{\\\"owner_id\\\": \\\"alice.near\\\"}\".to_vec(), gas: 25000000000000, deposit: 0, }), ],}\n\nIt has signer_id != receiver_id so it will use send_not_sir for send fees.\n\nIt contains 4 actions with 2 actions that requires to compute number of bytes. We assume code in DeployContractAction contains 128000 bytes. And FunctionCallAction has method_name with length of 3 and args length of 26, so total of 29.\n\nFirst let's compute the the amount that will be burned immediately for sending a receipt.\n\nburnt_gas = \\ config.action_receipt_creation_config.send_not_sir + \\ config.action_creation_config.create_account_cost.send_not_sir + \\ config.action_creation_config.transfer_cost.send_not_sir + \\ config.action_creation_config.deploy_contract_cost.send_not_sir + \\ 128000 * config.action_creation_config.deploy_contract_cost_per_byte.send_not_sir + \\ config.action_creation_config.function_call_cost.send_not_sir + \\ 29 * config.action_creation_config.function_call_cost_per_byte.send_not_sir\n\nNow, by using burnt_gas, we can calculate the total transaction fee\n\ntotal_transaction_fee = burnt_gas + \\ config.action_receipt_creation_config.execution + \\ config.action_creation_config.create_account_cost.execution + \\ config.action_creation_config.transfer_cost.execution + \\ config.action_creation_config.deploy_contract_cost.execution + \\ 128000 * config.action_creation_config.deploy_contract_cost_per_byte.execution + \\ config.action_creation_config.function_call_cost.execution + \\ 29 * config.action_creation_config.function_call_cost_per_byte.execution\n\nThis total_transaction_fee is the amount of gas required to create a new receipt from the transaction.\n\nNOTE: There are extra amounts required to prepay for deposit in TransferAction and gas in FunctionCallAction, but this is not part of the total transaction fee.","date":"2022-09-28 07:30:27","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\": 0.27564752101898193, \"perplexity\": 10022.419927588042}, \"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-2022-40\/segments\/1664030335124.77\/warc\/CC-MAIN-20220928051515-20220928081515-00342.warc.gz\"}"} | null | null |
open source innovators
Why Don't we £Value Open Source Software Assets?
By Malcolm Newbury | April 7, 2015
Developers and software providers love open source software (OSS) for its capability, maturity, accessibility and transparency. So why isn't there more promotion of the use of open source software and why do procurement professionals find it so difficult to grasp the value of open source software? One of the key reasons may lie in the genuine lack of clarity that surrounds the accounting of open source software, which has zero license cost. The ubiquitous use of open source throughout the technology sector coupled with the lack of accounting policy clarity surrounding the acts of creating and open source software, is undervaluing the assets of software intensive sectors like finance and healthcare and of large institutions like the National Health Service (NHS). | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,567 |
Klukwan és una concentració de població designada pel cens dels Estats Units a l'estat d'Alaska. Segons el cens del 2000 tenia una població de 139 habitants.
Demografia
Segons el cens del 2000, Klukwan tenia 139 habitants, 44 habitatges, i 31 famílies La densitat de població era de 43,3 habitants/km².
Dels 44 habitatges en un 54,5% hi vivien nens de menys de 18 anys, en un 45,5% hi vivien parelles casades, en un 15,9% dones solteres, i en un 27,3% no eren unitats familiars. En el 25% dels habitatges hi vivien persones soles el 6,8% de les quals corresponia a persones de 65 anys o més que vivien soles. El nombre mitjà de persones vivint en cada habitatge era de 3,16 i el nombre mitjà de persones que vivien en cada família era de 3,75.
Per edats la població es repartia de la següent manera: un 33,1% tenia menys de 18 anys, un 13,7% entre 18 i 24, un 23,7% entre 25 i 44, un 23% de 45 a 60 i un 6,5% 65 anys o més.
L'edat mediana era de 27 anys. Per cada 100 dones hi havia 104,4 homes. Per cada 100 dones de 18 o més anys hi havia 121,4 homes.
La renda mediana per habitatge era de 30.714 $ i la renda mediana per família de 31.563 $. Els homes tenien una renda mediana de 26.250 $ mentre que les dones 26.250 $. La renda per capita de la població era d'11.612 $. Cap de les famílies i l'1,5% de la població estaven per davall del llindar de pobresa.
Poblacions més properes
El següent diagrama mostra les poblacions més properes.
Referències
Concentracions de població designades pel cens d'Alaska
Borough de Haines
Àrea censal de Hoonah-Angoon | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,552 |
{"url":"https:\/\/stats.stackexchange.com\/questions\/357443\/lda-implementaion-in-pymc3?noredirect=1","text":"# LDA implementaion in pymc3\n\nI am implementing LDA with pymc3 using the referred code for pymc from the post\n\nLatent Dirichlet Allocation in PyMC\n\nI am trying to use it for pymc3 bt having problems defining\n\nw\n\nimport numpy as np\nimport pymc3 as pm, theano, theano.tensor as t\n\nK = 2 # number of topics\nV = 4 # number of words\nD = 3 # number of documents\n\ndata = np.array([[1, 1, 1, 1], [1, 1, 1, 1], [0, 0, 0, 0]])\n\nalpha = np.ones(K)\nbeta = np.ones(V)\nmodel = pm.Model()\nWd = [len(doc) for doc in data]\n(D, W) = data.shape\n\npi = []\ndef dist_over_words(z,phi):\n# Phi = theano.shared(np.array(phi))\n# print(phi[1])\n\nfor d in range(D):\nfor i in range(W):\nzi = z[d][i]\npi.append(phi[zi])\n\nwith model:\ntheta = [pm.Dirichlet(\"pthetax_%s\" % i, a=alpha, shape=K) for i in range(D)]\nphi =[pm.Dirichlet(\"pphix_%s\" % k, a=beta,shape=V) for k in range(K)]\n\nz = [pm.Categorical('zx_%i' % d,\np = theta[d],\nshape=Wd[d])\nfor d in range(D)]\n\nw = pm.Categorical(\"wx_d_i\",p = dist_over_words(z,phi), observed = data)\n\nwith model:\nstep1 = pm.Metroplolis(vars = [theta,phi,z,w])\ntr = step1.sample(1000,step = [step1])\n\npm.plots.traceplot(tr, ['theta', 'phi', 'z','w']);\n\n\nI am getting the error :\n\npi.append(phi[zi])\n\nTypeError: list indices must be integers or slices, not TensorVariable\n\nHow can I model for w since phi is a list and z[d][i] will always be a tensor?\n\nHelp much appreciated","date":"2020-01-21 02:10:20","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\": 0.5320704579353333, \"perplexity\": 14400.13074575634}, \"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-2020-05\/segments\/1579250601241.42\/warc\/CC-MAIN-20200121014531-20200121043531-00046.warc.gz\"}"} | null | null |
Hoyer (VI.) von Mansfeld (* 1484; † 9. Januar 1540) war Graf von Mansfeld, Ritter vom Goldenen Vlies und Teil der Vorderortlinie des gleichnamigen Adelsgeschlechts. Neben ihm gehörten auch die beiden jüngeren Söhne seines Vaters Albrecht V. von Mansfeld († 3. Dezember 1484) dieser Linie an: Günther IV. († 1526) und Ernst II. († 1531 oder 1532)
Leben
Unter Hoyer wurde von 1509 bis 1518 Schloss Mansfeld um Schloss Vorderort erweitert sowie die Schlosskirche um ein Sakramentshaus, das aus Holz geschnitzt wurde. Zudem war er der Schutzherr des Klosters Helfta.
Hoyer besuchte den Reichstag zu Augsburg im Jahr 1500, den Reichstag zu Köln 1505 und war bei den Reichsabschieden in Konstanz 1507 (siehe Reichstag-Tagungsorte) der erste Unterzeichner für Mansfeld.
Unter Kaiser Maximilian I. zog er 1508 gegen Venedig und verhandelte 1510 als Diplomat in dessen Namen mit dem Schwäbischen Bund, als dieser in die Revolte in Erfurt eingreifen wollte. 1512 führte er bereits den Titel Rat und oberster Stabelmeister. Er erwarb für alle Grafen von Mansfeld das Rotwachsprivileg, das Recht, mit rotem Wachs zu siegeln, und sich auch von der Reichskanzlei Wohlgeboren nennen zu lassen. Von Seiten des Erzbischofs war dies bereits seit 1440, von Sachsen aus seit 1442 praktiziert worden. Gleichzeitig versprach Maximilian für die Mansfelder den Schutz als Reichsgrafen. Während eines Aufenthalts bei Maximilian in Augsburg ab Herbst 1518 erteilte ihm dieser ein Recht auf Berufungsverhandlungen von Gerichtsurteilen vor dem Kaiser und dem Reichskammergericht sowie die exklusive Lizenz zum Bergbau auf dem mansfeldischen Territorium, ohne dass dies jemand besteuern durfte.
Hoyer begleitete 1515 den Kaiser nach Wien zu dessen Treffen mit den Königen Vladislav II. (Böhmen und Ungarn) und Sigismund I. (Polen). Von 1517 bis 1518 führte ihn ein Auftrag zum damaligen spanischen König Karl V. in die Niederlande und nach Spanien. Karl hatte ihn bereits im Jahr 1516 auf dem Ordenskapitel in Brüssel zum Ritter vom Goldenen Vlies gemacht. Als Karl 1520 in Aachen als Maximilians Nachfolger zum Kaiser gekrönt wurde, stand Hoyer in seinen Diensten. Auf dem Reichstag zu Worms im Jahr 1521 und dem Landtag 1525 zeigte sich Hoyer ebenso wie 1530 auf dem zu Augsburg, den er als verordneter kaiserlicher Rat besuchte. 1534 wurde er zum sächsischen Rat auf Lebenszeit. Konzentrierte sich Karl auf die Außenpolitik, erhielt Hoyer seine Aufträge von dessen Bruder Ferdinand, dem späteren Kaiser. Als Feldherr unter Karl ging Hoyer während der Türkenkriege nach Wien und Ungarn. Zum Preis von 500 Gulden pro Jahr war Hoyer auch als Feldhauptmann für den Erzbischof tätig.
Auch unter Karl gelang es Hoyer, mehrere Schutzbriefe zu erwirken, mit denen er sich gegen die Wettiner und ihre weltlichen Interessen an der Grafschaft durchsetzen konnte. Die Mansfelder erhielten zu Hoyers Lebzeiten noch weitere Marktrechte und Gunstbriefe.
Nach dem Tod des kinderlosen und unverheirateten Hoyer war die Stütze dieses privilegierten Standes allerdings verschwunden. Er wurde in der Andreaskirche zu Eisleben bestattet, die von beiden Konfessionen genutzt wurde. Auf seiner Tumba befindet sich ein Bronzeportrait des Grafen, das bereits 1541 von Hans Schlegel geschaffen wurde.
Hoyer setzte sich, im Gegensatz zu seinem Vetter Albrecht VII. von Mansfeld, stark für die römisch-katholische Kirche und gegen die Reformation ein. Kurz nach seinem Tod wurde sie allerdings in der Grafschaft eingeführt, und seine Nachfolger bekannten sich dazu.
Auszeichnungen
Hoyer wurde unter den beiden Kaisern über zwanzig Mal durch Verleihungen und Bestätigungen belohnt.
Literatur
Renate Seidel: Die Grafen von Mansfeld – Geschichte und Geschichten eines deutschen Adelsgeschlechts. Fouqué Literaturverlag, Engelsbach 1998, ISBN 3-8267-4230-3.
Erich Hempel: Die Stellung der Grafen von Mansfeld zum Reich und zum Landesfürstentum (bis zur Sequestration) – eine verfassungsgeschichtliche Untersuchung. Gebauer-Schwetschke, Halle 1917.
Weblinks
Einzelnachweise
Person (Mansfeld)
Familienmitglied des Hauses Mansfeld zweiten Stammes
Mansfeld
Geboren 1484
Gestorben 1540
Mann | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,375 |
I found this really cool October challenge list from a fellow blogger! I am going to try my best to blog everyday in October. Today's challenge is to list my October goals, so here goes nothing.
This sounds like a good challenge. Good luck I may join you.
This is awesome! 🙂 you have some great goals lined up for October. Do you mind if i steal this? Id love to do one also!
3. Encourage one person a day.
This is great! I'm totally going to join you! | {
"redpajama_set_name": "RedPajamaC4"
} | 850 |
Q: Connect Firebase with React Native I'm trying to connect React Native with Firebase. I'm using the following method to connect Firebase.
import * as firebase from 'firebase';
// Initialize Firebase
const firebaseConfig = {
apiKey: "<YOUR-API-KEY>",
authDomain: "<YOUR-AUTH-DOMAIN>",
databaseURL: "<YOUR-DATABASE-URL>",
storageBucket: "<YOUR-STORAGE-BUCKET>"
};
firebase.initializeApp(firebaseConfig);
app.authWithPassword({
"email": "abc@abc.com",
"password": "abc1234"
}, (error, user_data) => {
if (error) {
alert('Login Failed. Please try again');
} else {
AsyncStorage.setItem('user_data', JSON.stringify(user_data));
}
});
But it returns the following error:
app.authWithPassword is not a function.
I'm using Firebase 3.4 and React Native 0.32.
A: From the Firebase documentation:
firebase.auth().signInWithEmailAndPassword(email, password).catch(function(error) {
// Handle Errors here.
var errorCode = error.code;
var errorMessage = error.message;
// ...
});
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,656 |
\section{Introduction}
~~~Periodically driven dynamical systems play one of the central role in
classical and quantum chaos theory \ci{chir}-\ci{buch02}.
An important feature of periodically driven dynamical systems is the
chaotization of the motion under certain conditions (resonances, exceeding
critical value of the external field strength etc.).
This chaotization leads to the exponential divergence of neighboring
trajectories in the phase space and diffusive growth of the energy of the given system \ci{chir}-\ci{cas79}.
Comprehensive theoretical \ci{chir}-\ci{buch02} and experimental \ci{moor95}
study of the simplest periodically driven systems kicked rotor shows that for higher enough values of the kicking
force the average energy of the system grows linearly in time. Depending on the kicking strength dynamics of the
system can be mixed or chaotic \ci{chir}-\ci{buch02}.
In this paper we study particle motion in closed and open square billiards in the presence of external
periodic perturbation with the aim to explore the effect of confinement on periodically driven dynamics.
The motion of a particle in confined geometries is a paradigm for the study of
nonlinear dynamics and chaos in theoretical \ci{buch02}-\ci{gutk86} and
experimental contexts \ci{stei92}-\ci{demb01} in case of time-dependent
systems. Up to now much progress is done in the study of billiards with static
boundaries. {\it Also, classical dynamics of the billiards with time-dependent boundaries have been extensively studies in the context of
Fermi acceleration \ci{losk}-\ci{koil}. In particular, possibility of Fermi acceleration in Sinai \ci{losk}, stadium \ci{Losk02} and
elliptical \ci{flor07,flor08} billiards has been shown.}
Dynamics of unperturbed billiard is governed by the geometry of its boundaries, while kicked billiard has additional
factors which allows to manipulate by the dynamics. Those are perturbation parameters
such as coupling constant and frequency of the kick.
We explore the kicked billiard particle dynamics by calculating time dependence of the energy both for
a single trajectory and ensemble of the trajectories. In addition, we treat momentum transfer distribution for this system
and compare it with that of kicked rotor.
Our study shows that depending on the type of the kick potential,
localization and strength of the perturbation force the dynamics can
be different. In particular, the motion of the particle can be localized (trapped) in the kicking area.
The 'life time' of such trap depends on the perturbation strength
(coupling constant) and initial energy of the particle.
It is found that the average energy of the kicked particle grows diffusively as a function of time,
as does the kicked rotor average energy. However, this growth is more rapid than that of kicked rotor.
Also, we study particle transport in kicked billiard by considering open billiards with one and three holes.
We explore time-dependence of the escape rate and transmission and reflection coefficients.
We note that classical dynamics of unperturbed open billiards have been studied for integrable and chaotic geometries by many authors
(see, e.g., Refs.~\ci{bau90}-\ci{sti07}). In particular, it was found that the number of (non-interacting) particles in
non-integrable open billiard decreases exponentially, while
in case of regular billiard it decreases according to power law \ci{bau90}-\ci{vic01}. In this paper we extent these studies for the case
when non-interacting particles in an open billiard subjected into the influence of delta-kicking force.
The motivation for the study of periodically driven billiards is caused by several reasons. In many systems with confinement
(e.g. quantum dots, graphene, MIT bag model) in real situations a confined system is subjected to the action of external time-dependent fields.
For example, hadrons in quark-gluon plasma can be considered as driven confined system. In quantum dots or in graphene, external time-periodic
perturbation can be used for manipulating by particle transport in these systems.
This paper is organized as follows. In the next section we will give formulation of the problem for the kicked square
billiard and its detailed solution. Section III extends the results of section II for the case of
kicked open billiard with one and three holes. Last section provides some concluding remarks.
\section{Kicked billiard vs Kicked rotor}
In this work, we examine a system consisting of a particle moving inside a two-dimensional square billiard
with an additional kicking source located at the center of the billiard. The kicking potential (see Fig. \ref{fig1}) is given by
\begin{eqnarray} \label{eq1}
V(x,y,t)= \begin{cases} \alpha \cos(\frac{8\pi \rho}{a})\sum_n\delta(t-nT) \quad &\rho\le R \\
0 & \rho>R \\ \end{cases}
\end{eqnarray}
with
$$
\rho=\sqrt{\left(x-\frac{a}{2}\right)^2+\left(y-\frac{a}{2}\right)^2},
$$
where $\alpha, T$, $a$ and $R$ are the coupling constant, the kicking period, the side length of the square and
the radius of kicking area, respectively. Furthermore we fix $R=a/4$.
The Hamiltonian of the system can be written as
\begin{equation}
H=H_0+V(\rho,t),
\label{eq2}
\end{equation}
with $H_0$ being the Hamiltonian of the particle moving in the square billiard without any kicking. Since particles move balistically
in between collision with the billiard boundary as well as in between kicks, a discrete mapping is used to solve the corresponding equations of motion.
At collisions with the billiard boundary the particles undergo elastic reflections, whereas if the particles are at $t=nT, \, n=1,2,3, \dots$ inside the
kicking area, their momenta changes according to
\begin{equation}
\vec{p'}= \vec{p} - \vec{\nabla} V(x,y,t),
\end{equation}
where $\vec{p}$ and $\vec{p'}$ are the momenta just before and right after the kick respectively.
\begin{figure}[htb]
\centerline{\includegraphics[width=6.5cm]{f1c.eps}}
\caption{(Color online) Three-dimensional plot of the kicking potential for $\alpha =1.0$.}
\label{fig1}
\end{figure}
\begin{figure}[htb]
\centerline{\includegraphics[width=6.5cm]{f2c.eps}}
\caption{(Color online) Time-dependence of the energy for a typical particle in the kicked billiard ($\alpha =0.2$, $T=0.01$). Inset: rapid oscillations
of the energy, the particle is trapped for a certain time inside the kicking area.}
\label{fig2}
\end{figure}
\begin{figure}[htb]
\centerline{\includegraphics[width=6.5cm]{f3c.eps}}
\caption{(Color online) Distribution of constant energy time intervals. Circles are the results of direct numerical calculations,
solid line is the linear regression}
\label{fig3}
\end{figure}
In Fig.~\ref{fig2}, the energy $E(t)$ as a function of time for a typical trajectory is shown. The curve can be decomposed in characteristic segments,
each corresponding to a representative dynamics of the particle: Firstly, parts with rapid oscillations of the energy can be seen, see the inset of Fig.~\ref{fig2}.
During such phases, the particle is trapped for certain time inside the kicking area and experiences successive kicks, leading to the typical oscillations of
the energy shown in the inset of Fig.~\ref{fig2}. Secondly, single vertical lines in the curve of Fig.~\ref{fig2} correspond to single kicks, the energy of
the particle is either increased or decreased, depending on where the kick happens. Finally, parts of the curve where the energy remains constant. During such
times, the particle moves outside the kicking area (quasiperiodic orbits) or crosses the kicking area without getting a kick, the latter means it is in a way not synchronized with the kicking period.
To understand the kicked billiard dynamics more deeply we need to explore distribution, $N(t)$ of the time intervals during
which the energy remains constant, i.e. constant-energy-time intervals.
Fig. 3 presents the plot of such distribution in double logarithmic scale obtained using direct numerical computation.
In addition, this figure compares also $N(t)$ with the curve
$N(t)$ obtained from the linear regression.
Such power law (with the exponent equal to $-3$) behavior of $N(t)$ can be explained as follows: appearing constant energy intervals is caused by two factors.
One of them corresponds to the situation when
billiard particle moves along the quasiperiodic orbits which initially doesn't cross the kicking area. For this case one can obtain the estimate
$N(t)\sim t^{-1}$. However, we found that the probability for appearing such orbits in our system is quite small.
Therefore such regime of motion doesn't make contribution to the above distribution of constant-energy-time intervals. Second type of motion corresponds
to the above mentioned synchronized motion. It is easy to show that the distribution for the constant energy time intervals for this case behaves as $N(t)\sim t^{-3}$.
\begin{figure}[htb]
\centerline{\includegraphics[width=6.5cm]{schem.eps}}
\caption{Schematic picture}
\label{sch}
\end{figure}
To explain this we note that in the synchronized regime billiard particle returns to its initial position during the kicking period. If in each initial
condition we will shift its initial position to a infinitesimally small distance $\delta L$ (see Fig.~\ref{sch}) its final (after one kicking period) position
shifts to the same distance $\delta L$ becoming closer to the kicking area.
Then time $t$ after which particle reaches the kicking area can be found from the following relation:
\begin{equation}
\frac{L}{\delta L}=\frac{t}{T}
\label{eq:tT}
\end{equation}
where $L$ is the distance between the particle's initial position and the kicking area.
Thus the number of initial conditions is related to the quantity $\delta L$ as
\begin{equation}
N(\delta L)=\int^{\delta L}_{0}\rho(q)d(q)
\label{eq:ndl}
\end{equation}
where $\rho$ is the density of particles.
Since particles are uniformly distributed, $\rho$ depends on $q$ as
\begin{equation}
\rho(q)=\gamma q^2
\end{equation}
where $\gamma$ is coefficient of proportionality.
Therefore it follows from the eq. \eqref{eq:ndl} that
\begin{equation}
N(\delta L)=\gamma_1 (\delta L)^3
\end{equation}
or, combining with the eq.\eqref{eq:tT} we get finally:
\begin{equation}
N(t)\sim N(\delta L)=\gamma_2 t^{-3}
\end{equation}
When considering not only a single trajectory, but rather an ensemble of particles, a diffusive growth of the ensemble averaged energy
$\langle E_b(t) \rangle$ (averaged of 1000 trajectories) can be observed, see Fig.~\ref{fig4}. More precisely, the energy growth linearly
(normal diffusion) with the time $t$. The proportionality constant is naturally just the diffusion coefficient $D_b(\alpha, T)$, so that
$\langle E_b(t) \rangle = D_b(\alpha, T) \cdot t$. As indicated, $D_b$ depends on the coupling constant $\alpha$ and the kicking period $T$.
$D_b$ increases monotonically with increasing $\alpha$ and decreases monotonically with increasing $T$, see Fig.~\ref{fig6}.
\begin{figure}[htb]
\centerline{\includegraphics[width=6.5cm]{f4.eps}}
\caption{Comparison of the time-dependence of the ensemble averaged energy of the kicked billiard and kicked rotor for $\alpha =5.0$, $T=1.0$.}
\label{fig4}
\end{figure}
It is reasonable to compare the diffusive growth of the ensemble averaged energy $\langle E_b(t) \rangle = D_b(\alpha, T) \cdot t$ of the
kicked billiard with the evolution of energy $\langle E_r(t) \rangle$ of the kicked rotor (again with $\alpha$ being the coupling constant
and $T$ being the period between two successive kicks). From Fig~\ref{fig4}, it can be seen that $\langle E_r(t) \rangle =D_r(\alpha, T) \cdot t$,
but with $D_r(\alpha, T) \ll D_b(\alpha, T)$, so the energy growths much faster in the case of the kicked billiard. We note that in the case
of the kicked rotor the dynamics is effectively governed by a single parameter $K_r=\alpha T$ only, see e.g \cite{Izr90}. The energy of the
kicked rotor as a function of the dimensionless time $n=t/T$ can than for $K_r\gtrsim5$ be written as $E_r(n)= K_r^2/4 \cdot n$, so
\begin{equation}
\label{eq:Dr}
D_r(\alpha, T) = D_r(K_r) = K_r^2/4.
\end{equation}
In the kicked billiard the situation is different, the dynamics depends on $\alpha$ and $T$ individually, thus there is no simple representation
for $D_b(\alpha, T)$ as in Eq. \eqref{eq:Dr} possible. The dependence of $D_b(\alpha, T)$ on $\alpha$ and $T$ is shown in Fig. ~\ref{fig4},
whereas $D_r(\alpha, T)$ is shown in Fig.~\ref{fig5}. The large deviation between $D_b$ and $D_r$ becomes immediately clear when considering
the maximum momentum transfer $\Delta P_{max}$ at a single kick. In the case of the kicked billiard, $\Delta P_{max}=8\pi\alpha/a$, whereas
for the kicked rotor, $\Delta P_{max}= \alpha$.
\begin{figure}[htb]
\centerline{\includegraphics[width=6.5cm]{f5c.eps}}
\caption{(Color online) The dependence of the diffusion coefficient $D_b$ on $\alpha$ and $T$ for the kicked
billiard.}
\label{fig5}
\end{figure}
\begin{figure}[htb]
\centerline{\includegraphics[width=6.5cm]{f6c.eps}}
\caption{(Color online) The dependence of the diffusion coefficient $D_r$ on $\alpha$ and $T$ for the kicked
rotor.}
\label{fig6}
\end{figure}
The corresponding distributions $N_r(\Delta P)$ and $N_b(\Delta P)$ (1000 initial conditions iterated until $t=10^6 T$) are shown in
Figs.~\ref{fig7},~\ref{fig8} (the subscripts $r$ and $b$ denote the kicked rotor, the kicked billiard respectively). Clearly, the available
range in $\Delta P$ increases with increase of $\alpha$ in the case of the kicked billiard, and for a fixed $\alpha$ this range is much larger
than in the case of the kicked rotor. Unlike the $N_r(\Delta P)$, the distribution $N_b(\Delta P)$ has a jump at $\Delta P=0$, this can be
explained as following.
The momentum transfer in the case of kicked rotor can be found from 2-D standard map as $\Delta P_r=K_r\sin(\theta)$.
For the kicked billiard the momentum transfer can be written as:
\begin{equation}
\Delta P=|\vec {P'}-\vec P|=K_b\sin(b\rho)
\label{vb}
\end{equation}
where $\vec P$ and $\vec{P'}$, which are the momenta before and after the kick, respectively and $b=8\pi/a$, $K_b=b\alpha$.
Hence, for the momentum transfer distribution we get
\begin{equation}
N_b(\Delta P)\sim N(\rho) \left(\arcsin(\frac{\Delta P+\Delta \delta P}{K})-\arcsin(\frac{\Delta P}{K})\right)
\end{equation}
In the case of kicked rotor we have $N_r(\theta)=const$, for $K_r\gtrsim5$ (chaotic regime), while for kicked billiard
as it was mentioned above, we have equally distributed kick occurrence over $x,y$. Therefore, the dependence of this distribution
on $\rho$ is given by $N_(\rho)=const_1+const_2\rho$. It follows from the eq.(\ref{vb}) that $\Delta P=0$ for $\rho=0$
and for $\rho=a/4$. However, the kick numbers at these two points are not equal, number of kicks at $\rho=a/4$ points
is maximal, while for $\rho=0$ it is minimal that explains the difference between the shape of $N(\Delta P)$ in Figs.
\ref{fig7} and \ref{fig8}.\\
\begin{figure}[htb]
\centerline{\includegraphics[width=6.5cm]{f7c.eps}}
\caption{(Color online) Distributions of momentum transfers $\Delta P$ for the kicked billiard for $\alpha=5.0$ and for $T=1.0$;}
\label{fig7}
\end{figure}
\begin{figure}[htb]
\centerline{\includegraphics[width=6.5cm]{f8c.eps}}
\caption{(Color online) Distributions of momentum transfers $\Delta P$ for the kicked rotor for $\alpha =5.0$ , $T=1.0$.}
\label{fig8}
\end{figure}
\begin{figure}[htb]
\centerline{\includegraphics[width=6.5cm]{f9.eps}}
\caption{Time-dependence of the ensemble averaged energy for different localizations of
the center of the kicking source in the billiard ($\alpha =5$, $T=1$):
The central localization is compared to the case, when kicking
source is shifted to the left (position of the center at $(0.6; 0.5)$) and when it is shifted along the
diagonal of billiard (center at $(0.6; 0.6)$).}
\label{fig9}
\end{figure}
In Fig. \ref{fig9}, the time-dependence of the average energy $\langle E(t) \rangle$ is plotted for different localizations of the kicking
source and compared to the one when kicking source is located at the center of the billiard. The shift of the kick source leads to minor changes
in $\langle E(t) \rangle$ only, so the dynamics is rather robust against this shift. We tested this for other delocalizations as well, with similar
results, thus there are not shown here.
So far, we have considered the kicked billiard with a potential which is very similar to the one of the kicked rotor, in particular with the same
minimum and maximum values of the kicking potential. Despite this, however, the acceleration in the kicked billiard is much more pronounced compared
to the kicked rotor, which is of course due to the fact that much larger $\Delta P$ are possible upon single kicks in the billiard. To make the two
systems better comparable in terms of the momentum transfer, we modify the potential given in Eq. \eqref{eq1} slightly and obtain:
\begin{figure}[htb]
\centerline{\includegraphics[width=6.5cm]{f10.eps}}
\caption{Comparison of the time-dependence of the ensemble averaged energy of the kicked billiard and the kicked rotor with $\alpha =5.0$, $T=1.0$.}
\label{fig10}
\end{figure}
\begin{eqnarray} \label{eq:potential2}
V(x,y,t)= \begin{cases} \frac{\alpha a}{8\pi}\alpha \cos(\frac{8\pi \rho}{a})\sum_n\delta(t-nT) \quad &\rho\le R \\
0 & \rho>R \\ \end{cases}
\end{eqnarray}
This potential leads to the same maximum and minimum momentum transfer as in the kicked rotor. Now, the energy of the kicked rotor growth faster
than the one the kicked billiard, see Figs.~\ref{fig10}. These reasons are the following:
\begin{figure}[htb]
\centerline{\includegraphics[width=6.5cm]{f11c.eps}}
\caption{(Color online) The dependence of the diffusion coefficient $D_b$ on $\alpha$ and $T$ for the kicked
billiard.}
\label{fig11}
\end{figure}
Firstly, in the kicked rotor at every $t= nT, \, n=1,2,3,\dots$ the particle experiences a kick, a certain amount of momentum is transferred.
In the kicked billiard this is not the case, a particle gets a kick only if is at $t= nT, \, n=1,2,3,\dots$ inside the kicking area, see Fig.~\ref{fig1}.
Consequently, particles will experience fewer kicks during a certain time interval compared to the kicked rotor.
{\it We note that the above considered kicked billiard to some extent is equivalent to time-dependent
Sinai scattering billiard. However, unlike usual Sinai billiard the scatterer is not static and switches on
periodically. In addition, in kicked billiard collision with the scatterer is inelastic, while in Sinai billiard
collision with the scatterer is elastic. Here we mention that time-dependent Sinai billiard has been studied earlier
in the context of Fermi acceleration \ci{losk,Losk02,Peter1}. However, these studies deal with the
billiards whose boundaries are time-dependent, while in our system the boundaries of the billiard are static.
Therefore exploring of such time-dependent billiards requires solving the classical equations
of motion with time-dependent boundary conditions.
Time-dependence in our system is caused by the kicking source and we do not need to consider time-dependent boundary conditions
in the equations of motion.
Also, as it was shown, under certain conditions particle motion in the kicked billiard can be
localized (trapping of particle into the kicking source) in the kicking area. Such a trapping is not possible for usual
time-dependent Sinai billiard.
Finally, it should be noted that particle acceleration in kicked billiard can be considered as a kind of Fermi acceleration.
In usual Fermi acceleration the growth of the kinetic energy of a billiard particle is caused by the motion of billiard walls,
while in our case the energy grows due to the interaction with the kicking source.
The latter mechanism is close to the kicked rotor rather than to the billiard with time-dependent boundaries.
Detailed study of Fermi acceleration in billiard geometries showed that the acceleration is possible
for non-integrable billiards only \ci{losk,Losk02}. However, the above studied kicked square billiard has integrable boundaries. Despite this
acceleration is possible in this system. This is the main difference between the above kicked billiard and other time-dependent billiards
(with time-changing boundaries).}
\section{Open billiard}
\begin{figure}[htb]
\centerline{\includegraphics[width=6.5cm]{alph1com.eps}}
\caption{(Color online) Time-dependence of the number of survived particles $N(t)$ for the value $\alpha=1.0$
and calculated using eq.~\re{sur:eq}. $\sigma=0.001 \times a, N_0=10^6, p_0=1.0$.
The inset: Distribution of the escaped particle momenta.}
\label{a1c}
\end{figure}
\begin{figure}[htb]
\centerline{\includegraphics[width=6.5cm]{nmulti.eps}}
\caption{(Color online) Time-dependence of the number of survived particles $N(t)$ for different values of the delta-kick strength
$\alpha$.$\sigma=0.001 \times a, N_0=10^6, p_0=1.0$.}
\label{multi}
\end{figure}
In this section we study particle transport in a kicked open billiard.
The first system we will consider is a square billiard having one small hole with the size $\sigma$.
The type and location of the kicking source is the same as in the previous section.
Simulation of the system is performed for $N_0$ {\it non-interacting} particles with randomly distributed initial positions, $(x_0, y_0)$,
and directions of the initial velocities, $\phi$. The initial momenta of all particles are assumed to be equal $p_0$.
Classical dynamics of unperturbed open billiards has been extensively
studied both for integrable and chaotic geometries \ci{bau90}-\ci{sti07}.
In particular, it was found in the Refs.~\ci{bau90}-\ci{vic01} that for the case of ergodic particle motion in
an open billiard the particle's escape rate decreases exponentially, while for a non-chaotic
system it decreases according to power law.
In this work we explore behavior of the escape rate for the kicked open billiard.
The quantity we want to calculate is the number of particles in billiard at the time t, $N(t)$.
The escape rate is related to $N(t)$ as
$$
\rho(t) = 1-N(t)/N_0 ,
$$
where $N_0$ is the number of particles at $t = 0$.
As it was shown recently \cite{bau90,alt96}, for chaotic billiards time-dependence of survival probability
can be written as
\begin{equation}
\frac{N(t)}{N_0}= \exp(-\zeta t),
\label{sur:eq}
\end{equation}
where
$$
\zeta=\frac{p \sigma}{\pi S}.
$$
with $p$ being the absolute value of the billiard particle's momentum, $S$ is the area of the billiard.
Intuitively, one may expect similar decay in the case of kicked billiard (which is chaotic for arbitrary geometry of billiard boundaries).
However, in this case momenta of billiard particles are not equal and $p$ in eq. ~\re{sur:eq}
can be replaced by $p'$, most probable value of the
escape momentum. In Fig.~\ref{a1c} we compare $N(t)$ computed: \\
i) using eq.~\re{sur:eq} and \\
ii) by numerical modeling for three values of the kicking strength, $\alpha =1.0$. \\
As it can be seen from these plots, increasing of the kicking force leads
to decreasing of $N(t)$ which is equivalent to increasing of the number of escaped particles.
Such behavior can be explained
by the fact that according to the previous section, for higher values of the kicking force the energy of the billiard particles
growth linearly in time.
Also, the plots in Fig.~\ref{multi} show that the results of simulation are in good agreement with the results obtained using
eq.~\re{sur:eq}.
To study transport properties of the kicked billiard system we consider square billiard having three holes
with attached one incoming and two outgoing leads Fig.~\ref{leads}. Particles are assumed to come into
the billiard from incoming lead, while their escape from the billiard is possible from all three leads. Reflection coefficient
$R$ is calculated as the escape rate from the incoming lead, while transmission coefficients $T_1$ and $T_2$ are the escape rates from the outgoing leads.
\begin{figure}[htb]
\centerline{\includegraphics[width=6.5cm]{dot.eps}}
\caption{(Color online) Kicked square billiard with three holes}
\label{leads}
\end{figure}
In Fig.~\ref{fig13} these coefficients are plotted as a function of kicking strength. As it can be seen from these plots, the
reflection coefficient is much smaller compared to transmission coefficients for the leads 1 and 2.
This implies that such system can be used as a conductance amplifier. All the
coefficients become $\alpha-$independent for the values of $\alpha$ larger than $0.5$.
\begin{figure}[htb]
\centerline{\includegraphics[width=6.5cm]{t_r.eps}}
\caption{Transmission ($T$) and reflection ($R$) coefficients versus kicking force $\alpha$.
$\sigma=0.001 \times a, N_0=10^6, p_0=1.0$}
\label{fig13}
\end{figure}
\section{Summary}
In this work we studied classical dynamics of a kicked particle whose motion is confined in a square billiard.
The kick potential is considered as localized inside the billiard with central symmetric spatial distribution.
It is found that for this type of kick potential the average energy of the particle as a function of time grows faster than that of kicked free particle.
This implies that the above explored system is more attractive from the view point of acceleration.
Unlike the kicked free particle (kicked rotor) dynamics of the kicked billiard particle depends of perturbation parameters $\alpha$ and $T$ separately.
It also depends on the geometry of billiard and localization of the kick source.
In addition, the case of the kick potential that gives the same maximum and minimum values of momentum transfer as those for kicked rotor is considered.
It is found that in this system the acceleration is much weaker compared to the first system and even compared to kicked rotor.
Also, we have studied particle transport in kicked open billiard with one and three holes. In particular, we calculated escape rate, transmission
and reflection coefficients. The latter quantities are calculated for a billiard with one incoming and two outgoing holes.
Exponential decay {\it (i.e., decreasing the number of billiard particle according to exponential law)} of the system is found
for the case of one-hole open billiard. It is shown for such billiard that increasing
of the kicking force leads to rapid decay of the system. Transmission and reflection probabilities are studied for the case of a kicked billiard with
three wholes. For this system injection of particles into the billiard occurs from one hole, while escape of particles occurs from all three holes.
It is shown that for such system transmission and reflection coefficients depend on the kick strength, $\alpha$ until we increase $\alpha$
up to certain value. Further increasing of $\alpha$ does not lead to changes in $T$ and $R$.
{\it Finally, we note that the above considered kicked billiard is a kind of time-dependent billiards whose dynamics are
completely different than that of static billiards. Recently billiards with time-dependent boundaries have been extensively studied
\ci{losk} -\ci{koil} in the context of Fermi acceleration. In such billiards the dynamics is governed by the
time-changing law of the boundaries. This time-dependence requires solving of classical equations of motion with time-dependent boundary conditions.
Unlike these billiards, the kicked billiard is perturbed by the kicking source located inside the billiard
and the walls of the billiard are static. This fact causes the main difference in the dynamics of the kicked billiards and
the billiards with moving walls.}
The importance of the above study is caused by its perspective relevance to the particle transport
in various mesoscopic systems (e.g. as quantum dots, ratchets, nanotubes etc.).
Time-dependent external field can be used in these systems as an additional tool for manipulating by particle dynamics and
transport. In this context an important issue should be the extension of the above study for the case of corresponding
quantum system. Such a study is currently in progress.
\begin{acknowledgments}
This work is supported in part by the grants of the Uzbek Academy of Sciences (FA-F2-084, FA-F2-082)
and the grant of Volkswagen Foundation (Nr I/80 136).
\end{acknowledgments}
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<script type="text/javascript">
google.load("visualization", "1", {packages:["corechart"]});
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{% endblock %}
{% block header_time %}{% endblock %}
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import iam = require('@aws-cdk/aws-iam');
import cdk = require('@aws-cdk/cdk');
import { Alarm, ComparisonOperator, TreatMissingData } from './alarm';
export declare type DimensionHash = {
[dim: string]: any;
};
/**
* Properties for a metric
*/
export interface MetricProps {
/**
* Dimensions of the metric
*
* @default No dimensions
*/
dimensions?: DimensionHash;
/**
* Namespace of the metric.
*/
namespace: string;
/**
* Name of the metric.
*/
metricName: string;
/**
* The period over which the specified statistic is applied.
*
* Specify time in seconds, in multiples of 60.
*
* @default 300
*/
periodSec?: number;
/**
* What function to use for aggregating.
*
* Can be one of the following (case insensitive)
*
* - "minimum" | "min"
* - "maximum" | "max"
* - "average" | "avg"
* - "sum"
* - "samplecount | "n"
* - "pNN.NN"
*
* @default Average
*/
statistic?: string;
/**
* Unit for the metric that is associated with the alarm
*/
unit?: Unit;
/**
* Label for this metric when added to a Graph in a Dashboard
*/
label?: string;
/**
* Color for this metric when added to a Graph in a Dashboard
*/
color?: string;
}
/**
* A metric emitted by a service
*
* The metric is a combination of a metric identifier (namespace, name and dimensions)
* and an aggregation function (statistic, period and unit).
*
* It also contains metadata which is used only in graphs, such as color and label.
* It makes sense to embed this in here, so that compound constructs can attach
* that metadata to metrics they expose.
*
* This class does not represent a resource, so hence is not a construct. Instead,
* Metric is an abstraction that makes it easy to specify metrics for use in both
* alarms and graphs.
*/
export declare class Metric {
/**
* Grant permissions to the given identity to write metrics.
*
* @param identity The IAM identity to give permissions to.
*/
static grantPutMetricData(identity?: iam.IIdentityResource): void;
readonly dimensions?: DimensionHash;
readonly namespace: string;
readonly metricName: string;
readonly periodSec: number;
readonly statistic: string;
readonly unit?: Unit;
readonly label?: string;
readonly color?: string;
constructor(props: MetricProps);
/**
* Return a copy of Metric with properties changed.
*
* All properties except namespace and metricName can be changed.
*
* @param props The set of properties to change.
*/
with(props: MetricCustomization): Metric;
/**
* Make a new Alarm for this metric
*
* Combines both properties that may adjust the metric (aggregation) as well
* as alarm properties.
*/
newAlarm(parent: cdk.Construct, name: string, props: NewAlarmProps): Alarm;
/**
* Return the dimensions of this Metric as a list of Dimension.
*/
dimensionsAsList(): Dimension[];
}
/**
* Metric dimension
*/
export interface Dimension {
/**
* Name of the dimension
*/
name: string;
/**
* Value of the dimension
*/
value: any;
}
/**
* Statistic to use over the aggregation period
*/
export declare enum Statistic {
SampleCount = "SampleCount",
Average = "Average",
Sum = "Sum",
Minimum = "Minimum",
Maximum = "Maximum"
}
/**
* Unit for metric
*/
export declare enum Unit {
Seconds = "Seconds",
Microseconds = "Microseconds",
Milliseconds = "Milliseconds",
Bytes_ = "Bytes",
Kilobytes = "Kilobytes",
Megabytes = "Megabytes",
Gigabytes = "Gigabytes",
Terabytes = "Terabytes",
Bits = "Bits",
Kilobits = "Kilobits",
Megabits = "Megabits",
Gigabits = "Gigabits",
Terabits = "Terabits",
Percent = "Percent",
Count = "Count",
BytesPerSecond = "Bytes/Second",
KilobytesPerSecond = "Kilobytes/Second",
MegabytesPerSecond = "Megabytes/Second",
GigabytesPerSecond = "Gigabytes/Second",
TerabytesPerSecond = "Terabytes/Second",
BitsPerSecond = "Bits/Second",
KilobitsPerSecond = "Kilobits/Second",
MegabitsPerSecond = "Megabits/Second",
GigabitsPerSecond = "Gigabits/Second",
TerabitsPerSecond = "Terabits/Second",
CountPerSecond = "Count/Second",
None = "None"
}
/**
* Properties of a metric that can be changed
*/
export interface MetricCustomization {
/**
* Dimensions of the metric
*
* @default No dimensions
*/
dimensions?: DimensionHash;
/**
* The period over which the specified statistic is applied.
*
* Specify time in seconds, in multiples of 60.
*
* @default 300
*/
periodSec?: number;
/**
* What function to use for aggregating.
*
* Can be one of the following:
*
* - "Minimum" | "min"
* - "Maximum" | "max"
* - "Average" | "avg"
* - "Sum" | "sum"
* - "SampleCount | "n"
* - "pNN.NN"
*
* @default Average
*/
statistic?: string;
/**
* Unit for the metric that is associated with the alarm
*/
unit?: Unit;
/**
* Label for this metric when added to a Graph in a Dashboard
*/
label?: string;
/**
* Color for this metric when added to a Graph in a Dashboard
*/
color?: string;
}
/**
* Properties to make an alarm from a metric
*/
export interface NewAlarmProps {
/**
* The period over which the specified statistic is applied.
*
* Specify time in seconds, in multiples of 60.
*
* @default 300
*/
periodSec?: number;
/**
* What function to use for aggregating.
*
* Can be one of the following:
*
* - "Minimum" | "min"
* - "Maximum" | "max"
* - "Average" | "avg"
* - "Sum" | "sum"
* - "SampleCount | "n"
* - "pNN.NN"
*
* @default Average
*/
statistic?: string;
/**
* Name of the alarm
*
* @default Automatically generated name
*/
alarmName?: string;
/**
* Description for the alarm
*
* @default No description
*/
alarmDescription?: string;
/**
* Comparison to use to check if metric is breaching
*
* @default GreaterThanOrEqualToThreshold
*/
comparisonOperator?: ComparisonOperator;
/**
* The value against which the specified statistic is compared.
*/
threshold: number;
/**
* The number of periods over which data is compared to the specified threshold.
*/
evaluationPeriods: number;
/**
* Specifies whether to evaluate the data and potentially change the alarm state if there are too few data points to be statistically significant.
*
* Used only for alarms that are based on percentiles.
*/
evaluateLowSampleCountPercentile?: string;
/**
* Sets how this alarm is to handle missing data points.
*
* @default TreatMissingData.Missing
*/
treatMissingData?: TreatMissingData;
/**
* Whether the actions for this alarm are enabled
*
* @default true
*/
actionsEnabled?: boolean;
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,993 |
from model.contact import Contact
testdata = [
Contact(lastname="Doe", firstname="John", nickname="Vanya", title="tester", company="Yandex", address="489 Wateer Oal, NY",
email="Doe.John@yandex.ru", email2="Doe.John@google.ru", email3="Doe.John@google.com",
homephone="+1768387593", mobilephone="(707)5783737", workphone="(898)879-7865",
secondaryphone="7086787609"),
Contact(lastname="Ivanon", firstname="Pert", nickname="Petka", title="tester", company="Google", address="1600 Amphitheatre Parkway,Mountain View, CA 94043",
email="Ivanon.Pert@yandex.ru", email2="Ivanon.Pert@google.ru", email3="Ivanon.Pert@google.com",
homephone="+1547786737593", mobilephone="(707)47368736", workphone="(898)434-4345",
secondaryphone="548782987")
]
| {
"redpajama_set_name": "RedPajamaGithub"
} | 567 |
layout: post
title: "Association Rule Mining"
categories: discover
date: 2015-02-19 21:46:04
---
A popular application of association rules involves examining products that were bought together. Consider the following four sets of items (itemsets) bought together:
1. {bread, diapers, milk}
2. {beer, diapers, butter}
3. {bread, beer, diapers, butter}
4. {beer, butter}
Definition: Support of itemset A, denoted sup(A) or $$\vert A \vert$$ = the number of records (purchase transactions) containing A.
Definition: Let A and B be two itemsets. An association rule A->B asserts that if a transaction contains A, it is also likely to contain B.
Definition: The support of an association rule A->B is $$ \vert AB \vert $$
Definition: The confidence of an association rule A->B is $$\frac{ \vert AB \vert }{ \vert A \vert }$$
For example, the support of beer->diapers is 2 and its confidence is 2/3.
In practice, we want to find association rules that have sufficiently high support (perhaps at least 1% of the dataset) and sufficiently high confidence (perhaps 90% or 95%). For examples of business insight that can be obtained from association rules, see Tan, Steinbach & Kumar, chapter 1 slides 23-25.
Since the number of possible association rules can be very large, we need an efficient algorithm. The APRIORI algorithm can efficiently find association rules with a desired support threshold, call it s, and a desired confidence threshold, call it c. It exploits the following properties:
1. Let A, B and C be three itemsets. The support of the following association rules is the same: AB->C, AC->B, BA->C, BC->A, A->BC, B->AC, C->BA. So, one way to solve the association rule mining problem is to first find all the FREQUENT ITEMSETS, i.e., those with support >= s. Then we construct possible association rules from the frequent itemsets and return those with confidence >= c
2. For any two itemsets A and B, $$\vert A \vert >= \vert AB \vert $$. So, if we find that $$ \vert A \vert $$ < s, we don't have to consider any supersets of A since we already know that their support will be < s.
The APRIORI algorithm first finds frequent itemsets of size one (one item each), then uses them to build frequent itemsets of size 2, and so on. After finding the frequent itemsets. Recall the above dataset and suppose s=2 and c=95%.
Step 1: examine all itemsets of size 1 and compute their support
|bread|=2, |diapers|=3, |milk|=1, |butter|=3, |beer|=3
Since |milk| < 2, from now on we never consider any itemsets with milk as a subset because we know they cannot have support >=2
Step 2: examine only those itemsets of size 2 where all of their subsets have support >= 2
|bread,diapers|=2, |bread,butter|=1, |bread,beer|=1, |diapers,butter|=2, |diapers,beer|=2, |butter,beer|=3
Note: none of these include milk
From now on, never consider any itemsetes with milk, or {bread,butter} or {bread,beer} as a subset.
Step 3: examine only those itemsets of size 3 where all of their subsets have support >= 2
|diapers,butter,beer|=2
This is the only itemset of size 3 all of whose subsets have support >=2, as per the previous steps
Step 4: examine only those itemsets of size 4 where all of their subsets have support >=2
Nothing to examine since there is only one frequent itemset of size 3
Stop.
Answer: the frequent itemsets are: {bread}, {diapers}, {butter}, {beer}, {bread,diapers}, {diapers,butter}, {diapers,beer}, {butter,beer}, {diapers,butter,beer}.
Next step: construct possible association rules from the above frequent itemsets and return those which have confidence >= c
Final answer: bread->diapers, butter->beer, beer->butter, diapers,butter->beer, diapers,beer->butter
Note: association rules are not limited to itemset data. See, e.g., Frank&Whitten, chapter 4 slides 61-67
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,374 |
{"url":"http:\/\/twotrees.s1.brinkdev.com\/ebooks\/category\/arithmetic\/page\/4","text":"## Contemporary's Number Power 6: Word Problems\n\nFormat: Paperback\n\nLanguage: English\n\nFormat: PDF \/ Kindle \/ ePub\n\nSize: 10.55 MB\n\nIn this frame of thought, explains the mental discipline as an educational goal that is achieved through a keen intellectual work around those disciplines that are considered most suitable for training the mind. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or Copyright Act, without either the prior written permission of the Publisher, or Elementary numerical analysis I Kendall Atkinson and Weimin Han.-3rd ed.\n\n## ANALYTISCHE GEOMETRIE DER KEGELSCHNITTE\n\nFormat: Paperback\n\nLanguage: English\n\nFormat: PDF \/ Kindle \/ ePub\n\nSize: 8.05 MB\n\nAlso, the inverse element of addition (the additive inverse ) is the opposite of any number, that is, adding the opposite of any number to the number itself yields the additive identity,\u00a00. How many days would it take a person to traverse it, going at the rate of 125 miles a day? At a jump, a Fourier series is the half-sum of its left and right limits. Such numbers are the only real numbers which do not have a unique decimal representation, as they can also be written as a representation that has a recurring 9, for instance 1 = 0.99999..., 1\/2 = 0.499999..., etc.\n\n## New Elementary Arithmetic\n\nFormat: Paperback\n\nLanguage: English\n\nFormat: PDF \/ Kindle \/ ePub\n\nSize: 11.99 MB\n\nIt determines the side of the cube of a given volume. Poor student performance is seen as a failure of the education system and numerous state and national mandates have been put in place to assure equal access to a quality education for all children. It can be very difficult for parents to find productive and worthwhile activities for children on the Internet; however fun online math games do offer a wonderful alternative. Common fractions are used most often when the denominator is relatively small.\n\n## Kids Math for Kids : Multiplication for Kids (Interactive) 4\n\nFormat: Print Length\n\nLanguage: English\n\nFormat: PDF \/ Kindle \/ ePub\n\nSize: 13.73 MB\n\nModern climate change has a strong potential to shift earth systems and biological communities into novel states that have no present-day analog, leaving ecologists with no observational basis to predict the likely biotic effects. \\leq \\binom{n-1}{r-1}with equality holding if and only if all the sets share a common element. National Board for Professional Teaching Standards, http:\/\/www.nbpts.org\/\n\n## WALDY in the English language (WALDY is a children's picture\n\nFormat: Print Length\n\nLanguage: English\n\nFormat: PDF \/ Kindle \/ ePub\n\nSize: 11.01 MB\n\nIf you choose option A, On the other hand, if you choose option B, No doubt now you can see clearly that option B is the best option. This led to cooler temperatures, decreased vapor pressure deficit, and increased surface soil moisture in higher diversity communities. On April 18, 1977 President Carter told the American people, \"And in each of these decades (the 1950s and 1960s), more oil was consumed than in all of man's previous history combined.\" The company also has \"overhead costs\" (machinery or rent or whatever) of \\$3000.\n\n## Algebra: An Elementary Text Book for the Higher Classes of\n\nFormat: Paperback\n\nLanguage: English\n\nFormat: PDF \/ Kindle \/ ePub\n\nSize: 8.86 MB\n\nTo divide 1 into fourths, cut the line three times. Jeff Miller gathered the following information: Slope. Although I'll admit not everyone accepts it as such. Count forward or backward to or from any given number up to 120. The plus-minus sign (\u00b1) is a mathematical symbol with multiple meanings. \u2022 In mathematics, it generally indicates a choice of exactly two possible values, one of which is the negation of \u2022 In experimental sciences, the sign commonly indicates the con\ufb01dence interval or error in a measurement, often \u2022 In engineering the sign indicates the tolerance, which is the range of values that are considered to be acceptable, safe, or which comply with some standard, or with a contract.* [2] \u2022 In chemistry the sign is used to indicate a racemic mixture. \u2022 In chess, the sign indicates a clear advantage for the white player; the complementary sign \u2213 indicates the same A version of the sign, including also the French word\u201cou\u201d(meaning\u201cor\u201d) was used in its mathematical meaning by symbols, allowing the formula to represent two values or two equations.\n\n## The Numberlies : Number Three\n\nFormat: Paperback\n\nLanguage: English\n\nFormat: PDF \/ Kindle \/ ePub\n\nSize: 6.10 MB\n\nDST My School [Powerpoint] (English) DST My School [Powerpoint] (Spanish) The wizard wants to take a vacation but needs help deciding where to go! Number Maze focuses on helping the user improve math skills through practice. Now we are stuck again for a way to write one hundred. In 1791, Americans added a list of rights to the Constitution. Shortest Connectivity: An Introduction with Applications in Phylogeny. The evolution of the vortex and minimum temperatures during 1998-99 was remarkably similar to that during 1987-88, the only previous year when a major warming was observed before the end of Dec.\n\n## Elements of Arithmetic, Theoretical and Practical: Adapted\n\nFormat: Paperback\n\nLanguage: English\n\nFormat: PDF \/ Kindle \/ ePub\n\nSize: 12.52 MB\n\nThe earliest known material use of zero as a decimal \ufb01gure. Through the Advanced Search Page, you can find items by searching specific terms such as Title, Author, Subject, ISBN, etc or you can narrow your focus using our amazing set of criteria parameters. The warming trend, however, is unlikely to strongly affect the physical stability of the lake, which depends primarily on salinity gradient. Every natural number except zero has a predecessor.\n\n## A New Complete Arithmetic: Uniting Oral and Written\n\nFormat: Hardcover\n\nLanguage: English\n\nFormat: PDF \/ Kindle \/ ePub\n\nSize: 13.73 MB\n\nYou can only upload a photo (png, jpg, jpeg) or a video (3gp, 3gpp, mp4, mov, avi, mpg, mpeg, rm). Van der Waerden's theorem: Long monochromatic arithmetic progressions. Prentice-Hall. pp. 67\u201368. [5] Kendall & Stuart 1969, Example 14.4. [6] Kendall & Stuart 1969, Example 14.5. [7] Kendall & Stuart 1969, Example 14.12. \u2022 Dodge, Y. (2003). Anh Hoang Luyen Eng96-016 Richard Compean Ph. Writing Assignment #3 \u2013 Rewrite October 21th, 13 Pieces of April...\n\n## Practical Mathematics\n\nFormat: Hardcover\n\nLanguage: English\n\nFormat: PDF \/ Kindle \/ ePub\n\nSize: 5.14 MB","date":"2017-05-28 12:23:55","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\": 0.3293588161468506, \"perplexity\": 3880.0077287800746}, \"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-2017-22\/segments\/1495463609817.29\/warc\/CC-MAIN-20170528120617-20170528140617-00369.warc.gz\"}"} | null | null |
module AdvancedSearches
class Variant
include Base
def initialize(params)
@params = params
@presentation_class = VariantWithStateParamsPresenter
end
def model_class
::Variant
end
private
def handler_for_field(field)
default_handler = method(:default_handler).to_proc
@handlers ||= {
'id' => default_handler.curry['variants.id'],
'name' => default_handler.curry['variants.name'],
'description' => default_handler.curry['variants.description'],
'variant_group' => default_handler.curry['variant_groups.name'],
'ensembl_version' => default_handler.curry['variants.ensembl_version'],
'reference_build' => method(:handle_reference_build),
'reference_bases' => default_handler.curry['variants.reference_bases'],
'variant_bases' => default_handler.curry['variants.variant_bases'],
'chromosome' => default_handler.curry['variants.chromosome'],
'start' => default_handler.curry['variants.start'],
'stop' => default_handler.curry['variants.stop'],
'representative_transcript' => default_handler.curry['variants.representative_transcript'],
'chromosome2' => default_handler.curry['variants.chromosome2'],
'start2' => default_handler.curry['variants.start2'],
'stop2' => default_handler.curry['variants.stop2'],
'representative_transcript2' => default_handler.curry['variants.representative_transcript2'],
'variant_types' => default_handler.curry['variant_types.display_name'],
'hgvs_expressions' => default_handler.curry['hgvs_expressions.expression'],
'variant_alias' => default_handler.curry['variant_aliases.name'],
'gene' => default_handler.curry[['genes.name', 'secondary_genes_variants.name']],
'suggested_changes_count' => method(:handle_suggested_changes_count),
'evidence_item_count' => method(:handle_evidence_item_count),
'civic_actionability_score' => default_handler.curry['variants.civic_actionability_score'],
}
@handlers[field]
end
def handle_reference_build(operation_type, parameters)
[
[comparison(operation_type, 'variants.reference_build')],
::Variant.reference_builds[parameters.first]
]
end
def handle_suggested_changes_count(operation_type, parameters)
sanitized_status = ActiveRecord::Base.sanitize(parameters.shift)
having_clause = comparison(operation_type, 'COUNT(DISTINCT(suggested_changes.id))')
condition = ::Variant.select('variants.id')
.joins("LEFT OUTER JOIN suggested_changes ON suggested_changes.moderated_id = variants.id AND suggested_changes.status = #{sanitized_status} AND suggested_changes.moderated_type = 'Variant'")
.group('variants.id')
.having(having_clause, *parameters.map(&:to_i)).to_sql
[
["variants.id IN (#{condition})"],
[]
]
end
def handle_evidence_item_count(operation_type, parameters)
status = parameters.shift
conditional_clause = case status
when 'not rejected'
"AND evidence_items.status != 'rejected'"
when 'any'
''
else
"AND evidence_items.status = #{ActiveRecord::Base.sanitize(status)}"
end
having_clause = comparison(operation_type, 'COUNT(DISTINCT(evidence_items.id))')
condition = ::Variant.select('variants.id')
.joins("INNER JOIN evidence_items ON evidence_items.variant_id = variants.id #{conditional_clause}")
.group('variants.id')
.having(having_clause, *parameters.map(&:to_i)).to_sql
[
["variants.id IN (#{condition})"],
[]
]
end
end
end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,282 |
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what information we need to: best provide you with products and services; manage your relationship with us; meet our statutory obligations; develop our products and services; and meet our customers' and previous customers reasonable expectations. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,073 |
using System.Collections.Generic;
using System.Linq;
using Mono.Cecil;
namespace Stratis.SmartContracts.CLR.Validation
{
/// <summary>
/// Validates whether a type defines any fields
/// </summary>
public class FieldDefinitionValidator : ITypeDefinitionValidator
{
public IEnumerable<ValidationResult> Validate(TypeDefinition type)
{
// Don't apply to nested enums or structs
if (type.IsNested && type.IsValueType)
return Enumerable.Empty<TypeDefinitionValidationResult>();
var errors = new List<TypeDefinitionValidationResult>();
foreach (FieldDefinition field in type.Fields)
{
if (field.HasConstant) continue;
errors.Add(new FieldDefinitionValidationResult(
"",
"Field usage",
$"Non-constant field {field.Name} defined in Type \"{type.Name}\". Fields are not persisted and may change values between calls."
));
}
return errors;
}
public class FieldDefinitionValidationResult : TypeDefinitionValidationResult
{
public FieldDefinitionValidationResult(TypeDefinition type, FieldDefinition field)
: base("", "Field usage", $"Non-constant field {field.Name} defined in Type \"{type.Name}\". Fields are not persisted and may change values between calls.")
{
}
public FieldDefinitionValidationResult(string subjectName, string validationType, string message)
: base(subjectName, validationType, message)
{
}
}
}
} | {
"redpajama_set_name": "RedPajamaGithub"
} | 6,209 |
valgrind --tool=memcheck --leak-check=yes --track-origins=yes --log-file=valgrind.log ./rps
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,203 |
Another Environmental Suit Threatens 26 Northwest Dams
In the latest in what has seemingly been and endless stream of litigation, yet another environmental group is suing the government over allegations that several dozen Northwest dams threaten bull trout habitats.
State Wants to Breach Access Path to Bateman Island
Technically Bateman Island isn't really a true island, it's joined to the shore of the Columbia River, just south of the merger between the Yakima and Columbia Rivers. There's a narrow causeway, or path, that allows people to access the area. But a plan to breach the causeway to help …
Don't Fret Over All those Dead Salmon Seen on Banks of Columbia
If it seems like there's a lot more dead salmon littering the banks of the Columbia River in and around the Tri-Cities, it's actually normal, and perhaps a good thing. (Photo courtesy of KNDU-TV)
Now Is a Good Time to See Fish at McNary Dam Near Umatilla!
I stopped at McNary Dam on Saturday to see the fish ladder and it was the best fish viewing experience I've ever had.
Greg DeLange
Verdict: Consultant Says Vista Field Could Succeed With Investment
It will likely come down to the opinion of Kennewick residents.
The Bird & Fish Apocalypse – Everything You Need to Know So Far
What started with a bunch of fallen birds has escalated into an eerie string of animal deaths across the globe, with many people asking, "apocalypse now?" After the jump, a run-down of everything you need to know about "Birdpocalypse" thus far:
The Brad | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,288 |
import logging
import unittest
from framework.filters import FilterSystem
class FilterableTestSuite(unittest.TestSuite):
""" Pre-processes added test methods and filter items that need to be
excluded based on the user-defined inclusion and/or exclusion rules
"""
_filters = None
def __init__(self, tests=()):
self._logger = logging.getLogger(__name__)
super().__init__(tests)
@classmethod
def set_filters(cls, filters: FilterSystem):
""" Provide the filter system so that all suite instances can access
the filter rules during test registration
"""
cls._filters = filters
def addTest(self, test):
""" Registers a TestCase in the TestSuite
Filtration of test functions based on the configuration is done here by marking the
excluded test cases for skipping. All excluded tests will explicitly log their skip
status in the test report
:param test: Test case containing tests to be pre-processed for queuing
:type: unittest.TestCase (or derivative)
:return:
"""
assert FilterableTestSuite._filters, 'Filter system not configured'
if isinstance(test, unittest.TestCase):
test_methods = [func for func in dir(test) if callable(getattr(test, func)) and func.startswith("test_")]
for method_name in test_methods:
method = getattr(test, method_name)
tags = getattr(method, 'tags', None)
if self._filters.filter_by_product(test, method, tags):
continue
if self._filters.filter_by_priority(test, method, tags):
continue
if self._filters.filter_by_blacklist(test, method, tags):
continue
if self._filters.filter_by_whitelist(test, method, tags):
continue
super().addTest(test)
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,769 |
\section{Introduction}
Supervised sequence learning is a regression task where the objective is to learn a mapping function from the input sequence $\mathbf x$ to the corresponding output sequence $\mathbf z$ for all $(\mathbf x, \mathbf z) \in S$ with the given training set $S$, where $\mathbf x$ and $\mathbf z$ can have different lengths. When combined with recurrent neural networks (RNNs), supervised sequence learning has shown great success in many applications including machine translation \citep{bahdanau2014neural, sutskever2014sequence, cho2014learning}, speech recognition \citep{graves2013speech, graves2014towards, hannun2014deepspeech, bahdanau2015end, chorowski2015attention, chan2015listen}, and handwritten character recognition \citep{graves2008unconstrained, frinken2012novel}. Although several attention-based models have been introduced recently, connectionist temporal classification (CTC) \citep{graves2006connectionist} is still one of the most successful techniques in practice, especially for end-to-end speech and character recognition tasks \citep{graves2014towards, hannun2014deepspeech, graves2008unconstrained, frinken2012novel}.
The CTC based sequence training is usually applied to bidirectional RNNs \citep{graves2005framewise}, where both the past and the future information is considered for generating the output at each frame. However, the output of the bidirectional RNNs is available after all of the frames in the input sequence are fed into the RNNs because the future information is backward propagated from the end of the sequence. Therefore, the bidirectional RNNs are not suitable for realtime applications such as incremental speech recognition \citep{fink1998incremental}, that require low-latency output from the RNN. On the other hand, unidirectional RNNs only make use of the past information with some performance sacrifice and are suitable for the low-latency applications. Moreover, the CTC-trained unidirectional RNNs do not need to be unrolled (or unfolded) at the test time. It is shown by \citet{graves2012supervised} that CTC can also be employed for sequence training of unidirectional RNNs on a phoneme recognition task. In this case, the unidirectional RNN also learns the suitable amount of the output delay that is required to accurately process the input sequence.
For the CTC training of both unidirectional and bidirectional RNNs, it is required to unroll the RNNs by the length of the input sequence. By unrolling an RNN $N$ times, every activations of the neurons inside the network are replicated $N$ times, which consumes a huge amount of memory especially when the sequence is very long. This hinders a small footprint implementation of online learning or adaptation. Also, this ``full unrolling'' makes a parallel training with multiple sequences inefficient on shared memory models such as graphics processing units (GPUs), since the length of training sequences is usually not uniform, and thus a load imbalance problem occurs. For unidirectional RNNs, this problem can be addressed by concatenating sequences to make a very long stream of sequences, and training the RNNs with synchronized fixed-length unroll-windows over multiple training streams \citep{chen2014efficient, hwang2015single}. However, it is not straightforward to apply this approach to the CTC training, since the standard CTC algorithm requires full unrolling for the backward variable propagation, which starts from the end of the sequence.
In this paper, we propose an expectation-maximization (EM) based online CTC algorithm for sequence training of unidirectional RNNs. The algorithm allows training sequences to be longer than the amount of the network unroll. Moreover, it can be applied to infinitely long input streams with roughly segmented target sequences (e.g. only with the utterance boundaries and the corresponding transcriptions for training an end-to-end speech recognition RNN). Then, the resulting RNN can run continuously without pre-segmentation or external reset. Due to the fixed unroll amount, the proposed algorithm is suitable for online learning or adaptation systems with constrained hardware resource. Furthermore, the approach can directly be combined with the GPU based parallel RNN training algorithm described in \citet{hwang2015single}. For evaluation, we present examples of end-to-end speech recognition on the Wall Street Journal (WSJ) corpus \citep{paul1992design} with continuously running RNNs.\footnote{Further experiments are performed on TIMIT \citep{garofolo1993darpa} in Appendix~\ref{sec:timit}.} Experimental results show that the proposed online CTC algorithm performs comparable to the almost fully unrolled CTC training even with the small unroll amount that is shorter than the average length of the sequences in the training set. Also, the reduced amount of unroll allows more parallel sequences to be trained concurrently with the same memory use, which results in greatly improved training speed on a GPU.
The paper is organized as follows. In Section~\ref{sec:ctc}, the standard CTC algorithm is explained. Section~\ref{sec:online_ctc} contains the definition of the online sequence training problem and proposes the online CTC algorithm. In Section~\ref{sec:continuous}, the algorithm is extended for the continuously running RNNs, which is followed by its parallelization in Section~\ref{sec:parallel}. In Section~\ref{sec:experiments}, the proposed algorithm is evaluated with speech recognition examples. Concluding remarks follow in Section~\ref{sec:conclusion}.
\section{Connectionist temporal classification (CTC)}
\label{sec:ctc}
\begin{figure}[h]
\begin{center}
\includegraphics[height=1.35in]{ctc-dog}%
\end{center}
\caption{CTC forward-backward example for the target sequence ``DOG'', where the black and white dots represent the labels and blanks, respectively. The arrows indicate the allowed transitions.}
\label{fig:ctc-dog}
\end{figure}
The CTC algorithm \citep{graves2006connectionist, graves2012supervised} considers the order of the output labels of RNNs with ignoring the alignments or timings by introducing an additional blank label, $b$. For the set of target labels, $L$, and its extended set with the additional CTC blank label, $L' = L \cup \{b\}$, the path, $\pi$, is defined as a sequence over $L'$, that is, $\pi \in L'^{T}$, where $T$ is the length of the input sequence, $\mathbf x$. Then, the output sequence, $\mathbf z \in L^{\leq T}$, is represented by $\mathbf z = \mathcal F(\pi)$ with the sequence to sequence mapping function $\mathcal F$. $\mathcal F$ maps any path $\pi$ with the length $T$ into the shorter sequence of the label, $\mathbf z$, by first merging the consecutive same labels into one and then removing the blank labels. Therefore, any sequence of the raw RNN outputs with the length $T$ can be decoded into the shorter labeling sequence, $\mathbf z$, with ignoring timings. This enables the RNNs to learn the sequence mapping, $\mathbf z = \mathcal G(\mathbf x)$, where $\mathbf x$ is the input sequence and $\mathbf z$ is the corresponding target labeling for all $(\mathbf x, \mathbf z)$ in the training set, $S$. More specifically, the gradient of the loss function $\mathcal L(\mathbf x, \mathbf z) = -\ln p(\mathbf z | \mathbf x)$ is computed and fed to the RNN through the softmax layer \citep{bridle1990probabilistic}, of which the size is $|L'|$.
As depicted in \figurename~\ref{fig:ctc-dog}, the CTC algorithm employs the forward-backward algorithm for computing the gradient of the loss function, $\mathcal L(\mathbf x, \mathbf z)$. Let $\mathbf z'$ be the sequence over $L'$ with the length of $2 |\mathbf z| + 1$, where $z'_u=b$ for odd $u$ and $z'_u=z_{u/2}$ for even $u$. Then, the forward variable, $\alpha$, and the backward variable, $\beta$, are initialized by
\begin{align}
\alpha(1, u) =
\begin{cases}
y_b^1 & \text{if } u = 1 \\
y_{z_1}^1 & \text{if } u = 2 \\
0 & \text{otherwise}
\end{cases} \; , \quad
\beta(T, u) =
\begin{cases}
1 & \text{if } u = |\mathbf z'|, |\mathbf z'| - 1 \\
0 & \text{otherwise}
\end{cases},
\label{eq:CTC_init}
\end{align}
where $y_k^t$ is the softmax output of the label $k \in L'$ at time $t$.
The variables are forward and backward propagated as
\begin{align}
\alpha(t, u) = y_{z_u'}^ t \sum_{i=f(u)}^u \alpha(t - 1, i) \; , \quad
\beta(t, u) = \sum_{i=u}^{g(u)} \beta(t + 1, i) y_{z'_i}^{t+i},
\label{eq:recursion}
\end{align}
where
\begin{align}
f(u) =
\begin{cases}
u - 1&\text{if } z'_u=b\text{ or } z'_{u-2}=z'_u\\
u - 2&\text{otherwise}
\end{cases} \; , \quad
g(u) =
\begin{cases}
u + 1&\text{if } z'_u=b\text{ or } z'_{u+2}=z'_u\\
u + 2&\text{otherwise}
\end{cases}
\end{align}
with the boundary conditions:
\begin{align}
\alpha(t, 0) = 0, \; \forall t \; , \quad
\beta(t, |\mathbf z'|+1) = 0, \; \forall t .
\end{align}
Then, the error gradient with respect to the input of the softmax layer at time $t$, $a_k^t$, is computed as
\begin{align}
\frac {\partial \mathcal L(\mathbf x, \mathbf z)} {\partial a_k^t} = y_k^t - \frac {1}{p(\mathbf z | \mathbf x)} \sum_{u \in B(\mathbf z, k)} {\alpha(t, u) \beta(t, u)},
\label{eq:CTC_gradient}
\end{align}
where
$ B(\mathbf z, k) = \{ u : \mathbf z'_u = k\} $ and
$ p(\mathbf z | \mathbf x) = \alpha(T, |\mathbf z'|) + \alpha(T, |\mathbf z'| - 1)
$.
\section{Online sequence training}
\label{sec:online_ctc}
\subsection{Problem definition}
Throughout the paper, the online sequence training problem is defined as follows.
\begin{itemize}
\item The training set $S$ consists of pairs of the input sequence $\mathbf x$ and the corresponding target sequence $\mathbf z$, that is, $(\mathbf x, \mathbf z) \in S$.
\item The estimation model $\mathcal M$ learns the general mapping $\mathbf z = \mathcal G (\mathbf x)$, where the training sequences $(\mathbf x, \mathbf z) \in S$ are sequentially given.
\item For each $(\mathbf x, \mathbf z) \in S$ and at time $t$, only the fraction of the input sequence up to time $t$, $\mathbf x_{1:t}$, and the entire target sequence, $\mathbf z$, are given, where $1 \leq t \leq |\mathbf x|$. The length of the input sequence, $|\mathbf x|$, is unknown except when $t=|\mathbf x|$.
\item The parameters of the estimation model $\mathcal M$ is updated in the manner of online learning, that is, they can be frequently updated even before seeing the entire input sequence $\mathbf x$.
\end{itemize}
This online learning problem usually occurs in real world when a human learns a language from texts and the corresponding audio. For example, when watching movies with subtitles, we are given the entire target sequence (subtitle for the current utterance) and the input sequence (the corresponding audio) up to the current time, $t$. We cannot access the future audio and even do not know exactly when the utterance will end (at $t=|\mathbf x|$).
When RNNs are trained with the standard CTC algorithm, it is difficult to determine how much amount of unrolling is needed before the entire sequence $\mathbf x$ is given, since the length of $\mathbf x$ is unknown at time $t < |\mathbf x|$. Also, it is not easy to learn the sequences that are longer than the unroll amount, which is often constrained by the hardware resources.
\subsection{Overview of the proposed approach}
\begin{figure}[h]
\begin{center}
\includegraphics[width=5.0in]{online}%
\end{center}
\caption{Online CTC($2h'$;~$h'$) algorithm depicted for a single sequence that is longer than the RNN unroll amount. The shaded areas indicate the range of the RNN unrolling at each iteration.}
\label{fig:online}
\end{figure}
We propose an online CTC algorithm where the RNN can learn the sequences longer than the unroll amount, $h$. The algorithm is based on the truncated backpropagation through time (BPTT) algorithm \citep{werbos1990backpropagation} with the forward step size of $h'$ and the unroll amount of $h$, which is called BPTT($h$;~$h'$), as proposed in \citet{williams1990efficient}. Algorithm~\ref{algo:BPTT} describes the BPTT($h$;~$h'$) algorithm combined with the CTC loss, where $T$ is the length of the training sequence, $\mathbf x$
\begin{algorithm}
\caption{Online CTC training with BPTT($h$;~$h'$) for a single sequence}\label{algo:BPTT}
\begin{algorithmic}[1]
\Procedure{BPTT($h$;~$h'$)}{}
\State $\tau_0 \gets 0$
\State $n \gets 1$
\While {$\tau_{n-1} < T$}
\State $\tau'_n \gets \max\{1, nh' - h + 1\}$ \Comment{Start index of unrolling}
\State $\tau_n \gets \min\{nh', T\}$ \Comment{End index of unrolling}
\State RNN forward activation from $t=\tau_{n-1} + 1$ to $\tau_n$
\State CTC($h$;~$h'$) error computation on the softmax output layer \Comment{Algorithm~\ref{algo:onlineCTC}}
\State RNN backward error propagation from $t=\tau_{n}$ to $\tau'_{n}$
\State RNN gradient computation and weight update
\State $n \gets n + 1$
\EndWhile
\EndProcedure
\end{algorithmic}
\end{algorithm}
However, although BPTT($h$;~$h'$) is designed for online training of RNNs, employing the standard CTC loss function requires full unrolling of the networks. Therefore, we propose the CTC($h$;~$h'$) algorithm for computing the CTC loss in the online manner as in BPTT($h$;~$h'$) as in Algorithm~\ref{algo:onlineCTC}. The algorithm is also depicted in \figurename~\ref{fig:online} with the example in which the length of the sequence, $T = |\mathbf x|$, is 2.5 times as long as the unroll amount.
\begin{algorithm}
\caption{CTC($h$;~$h'$) error computation at the iteration $n$}\label{algo:onlineCTC}
\begin{algorithmic}[1]
\Procedure{CTC($h$;~$h'$)}{}
\State $\tau_{n-1} \gets (n-1)h'$
\State $\tau'_n \gets \max\{1, nh' - h + 1\}$
\State $\tau'_{n+1} \gets \max\{1, (n+1)h' - h + 1\}$
\State $\tau_n \gets \min\{nh', T\}$
\If {$n = 1$}
\State Initialize the CTC forward variable, $\alpha$, at $t=1$ \Comment{\eqref{eq:CTC_init}}
\EndIf
\State CTC forward propagation of $\alpha$ from $t=\tau_{n-1} + 1$ to $\tau_n$ \Comment{\eqref{eq:recursion}}
\If {$\tau_n = T$} \Comment{CTC-TR in Section~\ref{ssec:ctc-tr}}
\State Initialize the CTC-TR backward variable, $\beta$, at $t=T$ \Comment{\eqref{eq:CTC_init}}
\State CTC-TR backward propagation of $\beta$ from $t=T$ to $\tau'_n$ \Comment{\eqref{eq:recursion}}
\State CTC-TR error computation with $\alpha$ and $\beta$ on $t \in [\tau'_n, T]$ \Comment{\eqref{eq:CTC_gradient}}
\Else \Comment{CTC-EM in Section~\ref{ssec:ctc-em}}
\State Initialize the CTC-EM backward variable, $\beta_{\tau_{n}}$, at $t=\tau_{n}$ \Comment{\eqref{eq:CTC-EM_init}}
\State CTC-EM backward propagation of $\beta_{\tau_{n}}$ from $t=\tau_{n}$ to $\tau'_n$ \Comment{\eqref{eq:recursion}}
\State CTC-EM error computation with $\alpha$ and $\beta_{\tau_{n}}$ on $t \in [\tau'_n, \tau'_{n+1}-1]$ \Comment{\eqref{eq:CTC_gradient}}
\State Set error to zero on $t \in [\tau'_{n+1}, \tau_{n}]$
\EndIf
\EndProcedure
\end{algorithmic}
\end{algorithm}
CTC($h$;~$h'$) consists of two CTC algorithms. The first one is the truncated CTC (CTC-TR), which is basically the standard CTC algorithm applied at the last iteration with truncation. In the other iterations, the generalized EM based CTC algorithm (CTC-EM) is employed from $t=\max\{1, nh' - h + 1\}$ to $\max\{0, (n + 1)h' - h\}$ with the modified backward variable, $\beta_\tau$. The CTC-TR and CTC-EM algorithms are explained in Section~\ref{ssec:ctc-tr} and Section~\ref{ssec:ctc-em}, respectively. Note that simply setting $h=2h'$ works well in practice. In this setting, we denote the algorithm as CTC($2h'$;~$h'$).
\subsection{CTC-TR: Standard CTC with truncation}
\label{ssec:ctc-tr}
With the standard CTC algorithm, it is not possible to compute the backward variables when $\tau_n < T$, as the future information beyond $\tau_n$ cannot be accessed. Therefore, we only compute the CTC errors at the last iteration, where $\tau_n = T$ as in Algorithm~\ref{algo:onlineCTC}. In this case, however, the gradients are only available in the unroll range. Since the backward propagation is truncated at the beginning of the unroll range, we call the CTC algorithm in this range as truncated CTC, or CTC-TR. Also, we call the range that is covered by the CTC-TR algorithm as the CTC-TR coverage.
The RNN can be trained only with CTC-TR if there are sufficient labels that occur within the CTC-TR coverage. However, the CTC-TR coverage decreases by making the unroll amount smaller. Then, the percentage of the effective training frames, which actually generate the output errors, goes down, and the efficiency of training decreases. Also, the effective size of the training set gets smaller, which results in the loss of the generalization performance of the RNN. Therefore, for maintaining the training performance while reducing the unroll amount, it is critical to make use of the full training frames by employing the CTC-EM algorithm, which is described in Section~\ref{ssec:ctc-em}.
\subsection{CTC-EM: Online CTC with expectation-maximization (EM)}
\label{ssec:ctc-em}
\begin{figure}[h]
\begin{center}
\includegraphics[height=1.35in]{online-dog}%
\end{center}
\caption{Forward-backward algorithm of CTC-EM for the target sequence ``DOG'', where the black and white dots represent the labels and CTC blanks, respectively. The arrows represent the paths with allowed transitions.}
\label{fig:online-dog}
\end{figure}
Assume that only the fraction of the input sequence, $\mathbf x_{1:\tau}$, is available. Then, as shown in the \figurename~\ref{fig:online-dog}, there are $|\mathbf z| + 1$ possible partial labelings.\footnote{Although $\mathbf z_{1:m}$ is not possible by the standard CTC formulation when $m > \tau$, we can still say that $\mathbf z_{1:m}$ is a possible labeling with a probability of zero without loss of generality.} Let $\mathbf z_{1:m}$ be the subsequence of $\mathbf z$ with the first $m$ labels. Also we define $Z$ as the set that consists of these labeling sequences:
\begin{align}
Z = \{\mathbf z_{1:m} : 0 \leq m \leq |\mathbf z|\}.
\end{align}
One of the most simple approach for training the network under this condition is to choose the most likely partial alignment from $Z$ and compute the standard CTC error by regarding the partial alignment as the ground truth labeling. For example, we can select $\mathbf z_{1:m'}$ where $m'=\operatornamewithlimits{arg\,max}_m \alpha(\tau, m)$ since $\alpha(\tau, m)$ is a posterior probability $p(\mathbf z_{1:m} | \mathbf x_{1:\tau}, \mathbf w^{(n)})$ with the current network parameter $\mathbf w^{(n)}$. This is a well-known hard-EM approach. This simple idea can easily be extended to the more sophisticated soft-EM approach as follows. First, select one of the partial labelings in $Z$ with the probability $p(\mathbf z_{1:m} | Z, \mathbf x_{1:\tau}, \mathbf w^{(n)})$ estimated by the RNN with current parameters (E-step). Then, maximize the probability of that labeling by adjusting the parameters (M-step).
This optimization problem is readily reduced into the generalized EM algorithm. Specifically, the expectation step is represented as
\begin{align}
Q_\tau(\mathbf w | \mathbf x, \mathbf z, \mathbf w^{(n)}) &=
\mathbb{E}_{\mathbf z_{1:m} | Z, \mathbf x_{1:\tau}, \mathbf w^{(n)}}
\left[ \ln p(\mathbf z_{1:m} | \mathbf x_{1:\tau}, \mathbf w) \right] \\
&=
\sum_{m=0}^{|\mathbf z|}
p(\mathbf z_{1:m} | Z, \mathbf x_{1:\tau}, \mathbf w^{(n)})
\ln p(\mathbf z_{1:m} | \mathbf x_{1:\tau}, \mathbf w),
\end{align}
where $\mathbf w^{(n)}$ is the set of the network parameters at the current iteration, $n$. In the maximization step of the generalized EM approach, we try to maximize $Q_\tau$ by finding new parameters $\mathbf w^{(n+1)}$ that satisfies $Q_\tau(\mathbf w^{(n+1)} | \mathbf x, \mathbf z, \mathbf w^{(n)}) \geq Q_\tau(\mathbf w^{(n)} | \mathbf x, \mathbf z, \mathbf w^{(n)})$. As proved in Appendix~\ref{sec:ctc-em_derivation}, this is equivalent to the optimization problem where the objective is to minimize the loss function defined as $\mathcal{L_\tau (\mathbf x, \mathbf z)} = -\ln p(Z | \mathbf x_{1:\tau})$. Then, the gradient of the loss function with respect to the input of the softmax layer is
\begin{align}
\frac{ \partial \mathcal{L_\tau (\mathbf x, \mathbf z)}}
{\partial a_k^t}
=
y_k^t - \frac {1}{p(Z | \mathbf x_{1:\tau})} \sum_{u \in B(\mathbf z, k)} {\alpha(t, u) \beta_\tau(t, u)},
\end{align}
where $p(Z | \mathbf x_{1:\tau})$ can be computed by
\begin{align}
p(Z | \mathbf x_{1:\tau})=
\sum_{u=1}^{|\mathbf z'|}
\alpha(\tau, u)
\end{align}
and the backward variable, $\beta_\tau (t, u)$, is initialized as
\begin{align}
\beta_{\tau}(\tau, u) = 1, \; \forall u .
\label{eq:CTC-EM_init}
\end{align}
The new backward variable is backward propagated using the same recursion in \eqref{eq:recursion}, and the error gradients are computed with \eqref{eq:CTC_gradient} as in the standard CTC algorithm. See Appendix~\ref{sec:ctc-em_derivation} for the derivation of the above equations.
\section{Training continuously running RNNs}
\label{sec:continuous}
\begin{figure}[h]
\begin{center}
\includegraphics[width=5.0in]{online-cont}%
\end{center}
\caption{Online CTC training with a continuous stream of sequences. The shaded areas indicate the range of RNN unrolling at each iteration.}
\label{fig:online-cont}
\end{figure}
In this section, the proposed online CTC algorithm in Section~\ref{sec:online_ctc} is extended for training infinitely long streams. The training stream can be naturally very long with the target sequence boundaries, or can be generated by concatenating training sequences in a certain order. When trained on this training stream without external reset of the RNN at the sequence boundaries, the resulting RNN can also continuously process infinitely long input streams without pre-segmentation or external reset. This property is useful for realtime speech recognition or keyword spotting (spoken term detection) systems since we can remove the frontend voice activity detector \citep{sohn1999statistical} for detecting and pre-segmenting utterances.
The CTC($h$;~$h'$) algorithm can directly be applied to the infinitely long training streams as shown in \figurename~\ref{fig:online-cont}. When the sequence boundaries are reached during the forward activation, we perform CTC-TR, initialize the forward variable, and process the next sequence with some frame offset. Also, care should be taken on the transition of CTC labels at the boundary. Assume that the last label of the sequence $n$ and the first label of the sequence $n+1$ are the same. Then, a CTC blank label should be inserted between two sequences since the same labels that occur consecutively in the decoding path are folded into one label. In practice, this folding can easily be prevented by forcing the blank label at the first frame of each sequence by modifying the initialization of the forward variable as follows:
\begin{align}
\alpha_c(1, u) =
\begin{cases}
y_b^1 & \text{if } u = 1 \\
0 & \text{otherwise}
\end{cases},
\end{align}
where the subscript $c$ indicates the continuous CTC training.
\section{Parallel training}
\label{sec:parallel}
In a massively parallel shared memory model such as a GPU, efficient parallel training is achieved by making use of the memory hierarchy. For example, computing multiple frames together reduces the number of read operations of the network parameters from the slow off-chip memory by temporarily storing them on the on-chip cache memory and reuse them multiple times. For training RNNs on a GPU, this parallelism can be explored by employing multiple training sequences concurrently \citep{hwang2015single}.
The continuous CTC($h$;~$h'$) algorithm in Section~\ref{sec:continuous} can be directly extended for parallel training with multiple streams. Since the forward step size and the unroll amount is fixed, the RNN forward, backward, gradient computation, and weight update steps can be synchronized over multiple training streams. Thus, the GPU based parallelization approach in \citet{hwang2015single} can be employed for the RNN training. Although the computations in the CTC($h$;~$h'$) algorithm are relatively fewer than those of the RNN, further speed-up can be achieved by parallelizing the CTC algorithm similarly.
\section{Experiments}
\label{sec:experiments}
\subsection{End-to-end speech recognition with RNNs}
For the evaluation of the proposed approach, we present examples of character-level speech recognition with end-to-end trained RNNs without external language models. The speech recognition RNN is similar to the one in \citet{graves2014towards} except that our model employs unidirectional long short-term memory (LSTM) network \citep{hochreiter1997long} trained with the online CTC algorithm on the continuous stream of speech, instead of the bidirectional LSTM network with the sentence-wise CTC training.
Specifically, the experiments are performed with the deep unidirectional LSTM network with 3 LSTM layers, where each layer has 768 LSTM cells. The output layer is a 31-dimensional softmax layer. Each unit of the softmax layer represents one of the posterior probabilities of 26 alphabet characters, two special characters (. and '), a whitespace character, the end of sentence (EOS) symbol, and the CTC blank label. The input of the network is a 123-dimensional vector that consists of a 40-dimensional log Mel-frequency filterbank feature vector plus energy, and their delta and delta-delta values. The feature vectors are extracted from the speech waveform in every 10 ms with 25 ms Hamming window using HTK \citep{young1997htk}. Before being fed into the RNN, feature vectors are element-wisely normalized to the zero mean and the unit standard deviation, where the statistics are extracted from the training set.
\subsection{Wall Street Journal (WSJ) corpus}
\begin{figure}[h]
\centering
\centerline{%
\begin{tikzpicture}
\begin{axis}
[
width=\columnwidth,
height=0.32\columnwidth,
bar width=0.03\columnwidth,
compat=1.3,
xmin=0,
ymin=0,
xmax=2000,
ymax=5000,
label style={font=\footnotesize},
xlabel={Length of the sequence (frames)},
ylabel={Number of sequences},
xlabel shift=-2pt,
ylabel shift=-2pt,
ybar legend,
legend style={font=\scriptsize,at={(0.98,0.94)},anchor=north east},
tick label style={font=\scriptsize},
ymajorgrids,
minor x tick num=4,
minor y tick num=4,
xtick pos=both,
xtick align=inside,
major tick style={line width=0.010cm, black},
major tick length=0.10c
]%
\legend{WSJ SI-284 (NVP)};
\addplot[ybar, fill=cyan]
file{data/hist_si284.txt};
\end{axis}%
\end{tikzpicture}%
}%
\caption{Histogram of the length of the sequences in the WSJ SI-284 training set, where only the utterances with non-verbalized punctuations (NVPs) are considered. The feature frames are extracted with the period of 10 ms.}
\label{fig:hist_wsj}
\end{figure}
The experiments are performed on the Wall Street Journal (WSJ) \citep{paul1992design} corpus. For the training, the subset of the WSJ SI-284 set is used, where only the utterances with non-verbalized punctuations (NVPs) are included, resulting in about 71 hours of utterances. The histogram of the length of the sequences in the training set is shown in \figurename~\ref{fig:hist_wsj}. Note that the average length of the sequences is 772.5 frames. If we unroll the network over $N$ frames, the sequences longer than $N$ frames will not be fully covered by CTC-TR.
\begin{figure}[h]
\centering
\centerline{%
\begin{tikzpicture}
\begin{axis}
[
width=\columnwidth,
height=0.32\columnwidth,
compat=1.3,
bar width=0.018\columnwidth,
xmin=0,
ymin=0,
xmax=2000,
ymax=4e6,
label style={font=\footnotesize},
xlabel={Length of the sequence (frames)},
ylabel={Coverage (frames)},
xlabel shift=-2pt,
ylabel shift=-2pt,
ybar legend,
legend style={font=\scriptsize,at={(0.98,0.94)},anchor=north east},
tick label style={font=\scriptsize},
domain=1:512,
ymajorgrids,
minor x tick num=4,
minor y tick num=4,
xtick pos=both,
xtick align=inside,
major tick style={line width=0.010cm, black},
major tick length=0.10c
]%
\legend{CTC-TR + CTC-EM, CTC-TR max. ({1,024}), CTC-TR avg. ({1,024}), CTC-TR max. (512), CTC-TR avg. (512)};
\addplot[ybar, fill=black!70, xshift=-0.008\columnwidth]
file{data/hist_si284_frames.txt};
\addplot[ybar, fill=cyan!40, xshift=0]
file{data/hist_si284_frames_tr1024.txt};
\addplot[ybar, fill=cyan, xshift=0]
file{data/hist_si284_frames_tr1024_avg.txt};
\addplot[ybar, fill=magenta!40, xshift=0.008\columnwidth]
file{data/hist_si284_frames_tr512.txt};
\addplot[ybar, fill=magenta, xshift=0.008\columnwidth]
file{data/hist_si284_frames_tr512_avg.txt};
\end{axis}%
\end{tikzpicture}%
}%
\caption{Coverage of the trainable frames with respect to the length of the sequences in the WSJ SI-284 (NVP) training set. The average and maximum coverages of CTC-TR on continuous training streams are visualized for the unroll amount of 512 and 1,024 when CTC($2h'$;~$h'$) is applied. Note that the proposed online CTC algorithm (CTC-TR + CTC-EM) covers the entire training frames.}
\label{fig:coverage_wsj}
\end{figure}
In \figurename~\ref{fig:coverage_wsj}, the CTC-TR coverage is further analyzed with respect to the length of the sequence and the unroll amount. When the stream of sequences are trained with the continuos CTC algorithm, the CTC-TR coverage varies depending on the frame offsets of CTC($h$;~$h'$). The average coverage is calculated assuming that the offset is uniformly distributed. If the probability that a certain frame is included in the coverage is greater than zero, then the frame is included in the maximum coverage. For the experiments, we only consider CTC($2h'$;~$h'$), that is, the unroll amount is twice as much as the forward step size. Then, unrolling the network 1,024 times results in the CTC-TR coverage of 79.48 \% on average and 95.69 \% at maximum. On the other hand, when the unroll amount is 512, CTC-TR only covers 48.16 \% on average and 63.27 \% at maximum. Note that the full coverage is achieved when CTC-TR is combined with CTC-EM.
The WSJ Nov'93 20K development set and the WSJ Nov'92 20K evaluation set are used as the development (validation) set and the test (evaluation) set, respectively. For the final evaluation of the network after training, a single test stream is used that is generated by concatenating all of the 333~utterances in the test set.
\subsection{Training procedure}
The networks are trained on a GPU as in Section~\ref{sec:parallel} with the memory usage constraint. To maintain the memory usage same while changing the unroll amount, we fixed the total amount of unrolling over multiple training streams to 16,384. For example, the number of parallel streams become 8 with the unroll amount of 2,048 and 32 with 512 times of unrolling. The total amount of GPU memory usage is about 9.5 GiB in our implementation based on \citet{hwang2015single}.
The performance evaluation of the network is performed at every 10,485,760 training frames (i.e. $N$ continuous training streams with the length of $10,485,760/N$ each) in terms of word error rate (WER) on the 128 parallel development streams of which length is 16,384 each. For this intermediate evaluation, best path decoding \citep{graves2006connectionist} is employed for fast computation.
For the online update of the RNN parameters, the stochastic gradient descent (SGD) method is employed and accelerated by the Nesterov momentum of 0.9 \citep{nesterov1983method, bengio2013advances}. Also, the network is annealed by combining the early stopping technique as follows. If the network performance based on the intermediate evaluation is not improved for 11 consecutive times (10 times of retry), the learning rate is reduced by the factor of 10 and the training is resumed from the second best network. The training starts from the learning rate of $10^{-5}$ and finishes when the learning rate becomes less than $10^{-7}$.
The pre-trained network is used for CTC-TR and CTC-EM combined training because the expectation step of CTC-EM requires the RNN to align the target labels in a certain level. The pre-trained networks are obtained by early stopping the CTC-TR training of the networks when the performance is not improved during 6 consecutive intermediate evaluations using the learning rate of $10^{-5}$. For the CTC-TR and CTC-EM combined training with the unroll amount of 512, 1,024, and 2,048, the training starts from the pre-trained network that is trained with the same amount of unrolling. Otherwise, for the combined training with the unrolling less than 512 times, we use the pre-trained network with the unroll amount of 512.
\subsection{Evaluation}
\begin{figure}[h]
\centering
\centerline{%
\begin{tikzpicture}
\begin{axis}
[
width=\columnwidth,
height=0.4\columnwidth,
compat=1.3,
xmin=0.0e9,
ymin=0.4,
xmax=2.0e9,
ymax=0.8,
label style={font=\footnotesize},
xlabel={Number of frames trained},
ylabel={WER},
xlabel shift=-2pt,
ylabel shift=-2pt,
legend style={font=\scriptsize,at={(0.98,0.94)},anchor=north east},
tick label style={font=\scriptsize},
domain=1:512,
ymajorgrids,
minor x tick num=4,
minor y tick num=4,
log basis x={10},
xtick pos=both,
xtick align=inside,
major tick style={line width=0.010cm, black},
major tick length=0.10c
]%
\legend{CTC-TR (512)\hphantom{,0}, CTC-TR ({1,024}), CTC-TR ({2,048}), CTC-TR + CTC-EM (256), CTC-TR + CTC-EM (512)};
\addplot[color=black, solid, mark=square, mark size=1.5, mark repeat=10,mark options=solid]
file{data/512_tr_1e-05.txt};
\addplot[color=cyan, solid, mark=triangle, mark size=2, mark repeat=10,mark options=solid]
file{data/1024_tr_1e-05.txt};
\addplot[color=orange, solid, mark=o, mark size=1.5, mark repeat=10,mark options=solid]
file{data/2048_tr_1e-05.txt};
\addplot[color=blue, solid, mark=x, mark size=2, mark repeat=10,mark options=solid]
file{data/256_online_1e-05.txt};
\addplot[color=red, solid, mark=diamond, mark size=2, mark repeat=10,mark options=solid]
file{data/512_online_1e-05.txt};
\end{axis}%
\end{tikzpicture}%
}%
\caption{Convergence curves in terms of WER on the development set with the various unroll amounts of 256, 512, 1,024, and 2,048, and the fixed learning rate of $10^{-5}$.}
\label{fig:convergence}
\end{figure}
\figurename~\ref{fig:convergence} shows the convergence curves in terms of WER on the development set with various unroll amounts and training algorithms, where the unroll amount is twice the forward step size. The convergence speed of the CTC-TR only training decreases when the unroll amount becomes smaller. This is because the percentage of the effective training frames become smaller due to the reduced CTC-TR coverage. Also, it can be observed that the performance of the CTC-TR only trained network with 512 times of unrolling converges to the worse WER than those of the other networks due to the reduced size of the effective training set. On the other hand, the convergence curves of the CTC-TR and CTC-EM combined training with the unroll amounts of 256 and 512 are similar to that of the CTC-TR only training with 2,048 times of unrolling. Considering that the average sequence length of the training set is 772.5 frames, the results are quite encouraging.
The evidence of the similar convergence curves with the different unroll amounts implies that the training can be accelerated under the memory usage constraint by employing more parallel training streams with less unrolling. To examine how much speed-up can be achieved on a GPU, further experiments are performed as in \tablename~\ref{tbl:wsj_wer}. The training speed is measured on the system equipped with NVIDIA GeForce Titan X GPU and Intel Xeon E5-2620 CPU. For the final character error rate (CER) and WER report on the test set, the output of the RNN is decoded by the CTC beam search \citep{graves2014towards} without language models. As shown in the table, we can achieve a great amount of speedup without sacrificing much WERs. Also, it is possible to train a network with only 64 times of unrolling, which corresponds to 640 ms window, at the cost of 4.5\% relative WER. See Appendix~\ref{sec:timit} for further experiments on TIMIT \citep{garofolo1993darpa}.
\begin{table}[t]
\caption{Comparison of the CTC-TR coverages, the CER and WERs on the test set, and the training speeds on the GPU with the varying amounts of unrolling}
\label{tbl:wsj_wer}
\begin{center}
\begin{tabular}{l|cc|cc|cc}
\multicolumn{1}{c|}{\bf \# Streams} &\multicolumn{2}{c|}{\bf CTC-TR coverage (\%)} &\multicolumn{2}{c|}{\bf CER / WER (\%)} &\multicolumn{2}{c}{\bf Speed (frames/s)} \\
\multicolumn{1}{c|}{\bf $\times$ \# Unroll}&\multicolumn{1}{c}{Average} &\multicolumn{1}{c|}{Maximum} &\multicolumn{1}{c}{CTC-TR} &\multicolumn{1}{c|}{+ CTC-EM} &\multicolumn{1}{c}{CTC-TR} &\multicolumn{1}{c}{+ CTC-EM}
\\ \hline\hline \rule{0pt}{2.5ex}%
\hphantom{00}8 $\times$ 2,048 &97.84 &\hphantom{0}99.995 &- &10.6 / 38.4 &\hphantom{0}3.81 k &\hphantom{0}3.80 k \\
\hphantom{0}16 $\times$ 1,024 &79.48 &95.69 &11.2 / 39.1 &10.9 / 38.6 &\hphantom{0}6.79 k &\hphantom{0}6.60 k \\
\hphantom{0}32 $\times$ 512 &48.16 &63.27 &13.9 / 47.2 &10.9 / 38.8 &12.58 k &11.70 k \\
\hphantom{0}64 $\times$ 256 &24.82 &33.06 &- &11.2 / 39.7 &18.03 k &15.99 k \\
128 $\times$ 128 &12.43 &16.57 &- &11.3 / 40.0 &23.64 k &20.54 k \\
256 $\times$ 64 &\hphantom{0}6.21 &\hphantom{0}8.29 &- &11.4 / 40.1 &26.98 k &22.24 k
\end{tabular}
\end{center}
\end{table}
\section{Concluding remarks}
\label{sec:conclusion}
Throughout the paper, the online CTC($h$;~$h'$) algorithm is proposed for online sequence training of unidirectional RNNs. The algorithm consists of CTC-TR and CTC-EM. CTC-TR is the standard CTC algorithm with truncation and CTC-EM is the generalized EM based algorithm that covers the training frames that CTC-TR cannot be applied. The proposed algorithm requires the unroll amount less than the length of the training sequence and is suitable for small footprint online learning systems or massively parallel implementation on a shared memory model such as a GPU. Also, the online CTC algorithm is extended for training continuously running RNNs without external reset, and evaluated in the TIMIT experiments with a continuous input speech. On the WSJ corpus, the experimental results indicate that when the memory capacity is constrained, the proposed approach achieves significant speed-up on a GPU without sacrificing the performance of the resulting RNN much. We expect that further acceleration of training will be possible with lower performance loss when different unroll amounts are used in the pre-training, main training, and annealing stages.
\subsubsection*{Acknowledgments}
This work was supported in part by the Brain Korea 21 Plus Project and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No.~2015R1A2A1A10056051).
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{"url":"https:\/\/gamedev.stackexchange.com\/questions\/146255\/why-arent-my-2d-primitives-visible-using-a-custom-effect","text":"# Why aren't my 2D primitives visible using a custom effect?\n\nI'm working with Monogame and rendering a triangle using the following code.\n\nvertices = new []\n{\nnew VertexPositionColor(new Vector3(100, 200, 0), Color.White),\nnew VertexPositionColor(new Vector3(200, 100, 0), Color.White),\nnew VertexPositionColor(new Vector3(300, 200, 0), Color.White),\n};\n\ngraphicsDevice.DrawUserPrimitives(PrimitiveType.TriangleList, vertices, 0, 1);\n\n\nOrdinarily I'd apply a BasicEffect before the draw call, but this time I'm using a custom effect. For testing, I wrote the following shader code to return solid green for each pixel within the triangle.\n\nstruct VertexShaderInput\n{\nfloat4 Position : POSITION;\nfloat4 Color : COLOR;\n};\n\n{\nfloat4 Position : POSITION;\nfloat4 Color : COLOR;\n};\n\n{\noutput.Color = input.Color;\noutput.Position = input.Position;\n\nreturn output;\n}\n\n{\nreturn float4(0, 1, 0, 1);\n}\n\ntechnique Technique0\n{\npass Pass0\n{\n}\n};\n\n\nThe problem is that, although the shader compiles successfully, nothing shows up.\n\nWhy is my triangle invisible using this shader?\n\nBased on my understanding of vertex and pixel shaders, the above HLSL code should work correctly. In the vertex shader, since (for the moment) I'm working in strictly 2D without a camera, no transformations need to be done on the vertices (i.e. they're already in screen space). From there, the pixel shader simply returns solid green for each pixel. I've also ruled out potential backface culling issues by swapping the order of vertices, and I've tried using different semantics on my HLSL structure variables. No luck.\n\nShaders still feel uncomfortable to me, but I feel my logic is correct based on what I've read. If that's the case, there must be some weird quirk I'm not aware of in having these HLSL shaders work at all, apart from the logic. What am I missing? Is there a better way to debug these problems short of changing random variables and hoping for the best?\n\nThe problem you are having is that 'no transform' coordinates are not in pixels. They are in normalized device coordinates which range from -1 to 1. If you want to specify your vertices in pixel coordinates, you need a transformation which converts that to normalized device coordinates with a scale and offset.\n\nFor example in DirectX Tool Kit's SpriteBatch, this function computes a matrix to do just that:\n\n\/\/ Generates a viewport transform matrix for rendering sprites using x-right y-down screen pixel coordinates.\nXMMATRIX SpriteBatch::Impl::GetViewportTransform(_In_ ID3D11DeviceContext* deviceContext, DXGI_MODE_ROTATION rotation )\n{\n\/\/ Look up the current viewport.\nif ( !mSetViewport )\n{\nUINT viewportCount = 1;\n\ndeviceContext->RSGetViewports(&viewportCount, &mViewPort);\n\nif (viewportCount != 1)\nthrow std::exception(\"No viewport is set\");\n}\n\n\/\/ Compute the matrix.\nfloat xScale = (mViewPort.Width > 0) ? 2.0f \/ mViewPort.Width : 0.0f;\nfloat yScale = (mViewPort.Height > 0) ? 2.0f \/ mViewPort.Height : 0.0f;\n\nswitch( rotation )\n{\ncase DXGI_MODE_ROTATION_ROTATE90:\nreturn XMMATRIX\n(\n0, -yScale, 0, 0,\n-xScale, 0, 0, 0,\n0, 0, 1, 0,\n1, 1, 0, 1\n);\n\ncase DXGI_MODE_ROTATION_ROTATE270:\nreturn XMMATRIX\n(\n0, yScale, 0, 0,\nxScale, 0, 0, 0,\n0, 0, 1, 0,\n-1, -1, 0, 1\n);\n\ncase DXGI_MODE_ROTATION_ROTATE180:\nreturn XMMATRIX\n(\n-xScale, 0, 0, 0,\n0, yScale, 0, 0,\n0, 0, 1, 0,\n1, -1, 0, 1\n);\n\ndefault:\nreturn XMMATRIX\n(\nxScale, 0, 0, 0,\n0, -yScale, 0, 0,\n0, 0, 1, 0,\n-1, 1, 0, 1\n);\n}\n}\n\n\u2022 Thank you for the help. I knew that texture coordinates were normalized, but didn't realize that positions were normalized too. \u2013\u00a0Grimelios Jul 31 '17 at 20:18","date":"2021-08-02 22:40:30","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\": 0.3450774848461151, \"perplexity\": 5052.564801722184}, \"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-2021-31\/segments\/1627046154385.24\/warc\/CC-MAIN-20210802203434-20210802233434-00528.warc.gz\"}"} | null | null |
\section{Introduction}
\label{sec:intro}
High-dimensional inference problems come up naturally in many fields of science and engineering including computational biology and genomics, natural language processing, medical imaging and remote sensing. A well-known example is the standard linear regression problem where one is given data items $\veca_1,\veca_2,\ldots,\veca_{\slrrows} \in \mathbb{R}^\slrcolumns$ and responses $b_1,\ldots,b_{\slrrows} \in \mathbb{R}$ where each $b_i \approx \langle \veca_i, \vecx^*\rangle$ for a hidden parameter vector $\vecx^* \in \mathbb{R}^\slrcolumns$. When $\slrcolumns \gg \slrrows$, the model is unidentifiable; however, in various application domains (such as the ones above), it makes sense to require that $\vecx^*$ is sparse, that is, it has only a few non-zero coordinates. The resulting problem is called {\em sparse linear regression} which can be formulated as finding
$$ \widehat{\vecx} \in \argmin_{\vecx\in \mathbb{R}^\slrcolumns} \|\vecb-\matA\vecx\|_2 \hspace{.2in}\mbox{ such that } \|\vecx\|_0 \leq k$$
where $\matA \in \mathbb{R}^{\slrrows \times \slrcolumns}$ is the design matrix with $\veca_i$ as its rows, $\vecb \in \mathbb{R}^{\slrrows\times 1}$ is the response vector consisting of the $b_i$'s as entries, and $k$ is the sparsity parameter.
This problem is non-convex and finding an exact as well as approximate solution is known to be $\mathcal{NP}$-hard~\cite{natarajan1995sparse, davis1997adaptive, foster2015variable}.
Despite this negative result, when the design matrix $\matA$ is particularly well-conditioned, polynomial-time algorithms based on $\ell_1$-relaxation, such as basis pursuit and Lasso estimators~\cite{tibshirani,CDS98} as well as the Dantzig selector~\cite{CT07} have been shown to meet the minimax-optimal lower bound for sparse linear regression. This is also the setting of compressed sensing, which has seen much exciting work in the last two decades.
However, in several high-dimensional regression problems in data science, there is no such guarantee on the design matrix $\matA$, as the features could be correlated. As a result, the problem formulation with general design matrices is also of great interest, and is the main focus of this paper.
On the one hand, the NP-hardness of this problem \cite{natarajan1995sparse, davis1997adaptive, foster2015variable} rules out algorithms that run in time polynomial in $\slrrows, \slrcolumns$ and $k$. On the other hand, the best known algorithm for this problem is trivial brute-force search that runs in time $O(\slrcolumns^{k})$. Concretely, one can enumerate over all possible $\binom{\slrcolumns}{k}$ supports, and run an ordinary least squares regression with an $\slrrows \times k$ design matrix, which results in a $\slrcolumns^k (\slrrows + k)^{O(1)}$ time algorithm \cite{har2016approximate}. \anote{Say that we do not care about the $M$ and $k$ factors.} Improving this to, say, $O(\slrcolumns^{0.999k})$ or even a modest $O(\slrcolumns^{k-1})$ seems out of reach. This state of affairs motivates our question:
\begin{quote}
Can $k$-sparse linear regression be solved in time $\slrcolumns^{(1-\epsilon)k}$ for {\em some} constant $\epsilon>0$?
\end{quote}
Our main result in this paper shows that the answer is ``no'' assuming popular conjectures from the field of fine-grained algorithms and complexity~\cite{williams2018some}.
First, we show that it is hard to solve $k$-SLR in the $\ell_2$ norm faster than $O(\slrcolumns^{k-\epsilon})$ for any constant $\epsilon>0$, assuming either the min-weight $k$-clique hypothesis~\cite{williams2018some} or the conjectured hardness of the lattice closest vector problem~\cite{bennett2017quantitative}.
The min-weight $k$-clique problem asks to find a clique with $k$ vertices with the smallest total edge weight, in a weighted undirected graph. The best known algorithm is exhaustive search which runs in time $O(\slrcolumns^k)$ on $N$-node graphs~\cite{williams2018some}. The closest vector problem is a long-studied problem in the geometry of numbers~\cite{Minkowski,MGbook}, which asks to find the closest lattice point to a given target vector, given an arbitrary $n$-dimensional integer lattice. The best known algorithm runs in time $O(2^n)$~\cite{ADS15}, and improving it is a long-standing challenge with considerable impact in the area of combinatorial optimization and lattice-based cryptography~\cite{bennett2017quantitative}.
(For a more formal description of these problems, we refer the reader to Section~\ref{sec:defs}).
Secondly, we show that it is hard to solve $k$-SLR in $\ell_p$ norms (including $p=1$ and odd $p>2$) faster than $O(\slrcolumns^{(1-\epsilon)k})$ under the strong exponential-time hypothesis (SETH)~\cite{impagliazzo2001complexity}. The strong exponential-time hypothesis, formulated by Impagliazzo and Paturi, conjectures that the satisfiability problem (SAT), the cornerstone of computer science, cannot be sped up significantly. More precisely, SETH states that for every $\epsilon>0$, there is an $k\in \mathbb{N}$ such that $k$-SAT on $n$ variables cannot be solved in time $2^{(1-\epsilon)n}$.
These results together settle the exact complexity of the $k$-sparse linear regression problem in the worst-case, assuming popular conjectures in fine-grained complexity and the geometry of numbers. Under these conjectures, there are {\em no better-than-brute-force} algorithms for sparse linear regression.
\paragraph{A Window into our Techniques: Translating Integrality into Sparsity.}
The hardness of problems such as the closest vector problem are closely connected to integer linear programming, where hardness arises from the fact that one has to come up with {\em integer solutions} to an optimization problem. On the other hand, there is no such integrality condition in $k$-sparse linear regression; rather, the hardness seems to arise from the fact that we insist on {\em sparse} solutions. Thus, a key technical contribution of our work is showing several ways to map two apparently different sources of hardness, namely integrality and sparsity.
In the rest of the paper, we provide a self-contained exposition of our results. We start with definitions in Section~\ref{sec:defs}, and proceed to show the reduction from the min-weight $k$-clique problem to sparse linear regression in Section~\ref{sec:min-k-clique-slr} and the reduction from the lattice closest vector problem in Section~\ref{sec:cvp-slr}. Finally, in Section~\ref{sec:seth2slr}, we also show that there are no sub-quadratic $\slrcolumns^{2-\epsilon}$-time algorithms for $k$-SLR when $k=2$, assuming the strong exponential-time hypothesis.
\subsection{Related work}\label{sec:related-work}
\paragraph{Lower bounds.} Natarajan~\cite{natarajan1995sparse} showed the $\mathcal{NP}$-hardness of solving sparse linear regression, which rules out $(\slrcolumns k)^c$-time algorithms for any absolute constant $c$. Har-Peled, Indyk and Mahabadi~\cite{har2016approximate} showed the hardness of solving $k$-SLR faster than $O(\slrcolumns^{k/2})$ time, under the well-known $k$-SUM conjecture from fine-grained complexity. However, both results left a gap between the best known upper bound which is brute-force search that runs in $\slrcolumns^k$ time, and a lower bound of $\slrcolumns^{k/2}$.
\paragraph{Algorithms.}
Har-Peled, Indyk and Mahabadi~\cite{har2016approximate} also give an algorithm for {\em approximate} sparse linear regression {\em with pre-processing} that runs in time slightly better than brute force, namely in time $\tilde{O}(\slrcolumns^{k-1})$. Gupte and Lu~\cite{guptelu2020fine-grained} showed a slight improvement to the standard $k$-SLR problem in the {\em noiseless} setting, namely they showed an $O(\slrcolumns^{k-1})$ time algorithm. They also give a $\slrcolumns^{\Omega(k)}$-time lower bound in the noiseless setting, under the Exponential Time Hypothesis. In contrast to both these works, our result shows that even such a modest improvement is impossible to achieve for the standard and well-studied $k$-SLR problem. That is, we show that $k$-SLR cannot be solved in time $O(\slrcolumns^{k-\epsilon})$ for any constant $\epsilon > 0$, under the popular min-weight $k$-clique conjecture~\cite{williams2018some} from fine-grained complexity.
\paragraph{Compressed Sensing and the LASSO.}
While the focus of this paper is the worst-case complexity of sparse linear regression, its {\em average-case} complexity has been the object of much study. Methods based on $\ell_1$-relaxation, such as basis pursuit and Lasso estimators~\cite{tibshirani,CDS98} as well as the Dantzig selector~\cite{CT07} have been shown to meet the minimax-optimal lower bound in some cases. In particular, they focus on the setting where $\vecb = \matA \vecx + \vecw$ where the noise vector $\vecw \sim \mathcal{N}(0,\sigma^2)$ comes from a Gaussian distribution. While these methods perform well when the design matrix $\matA$ is well-conditioned in an appropriate sense, Zhang, Wainwright and Jordan~\cite{zhang2014lower} show that such a condition is necessary unless $\mathcal{NP} \subseteq \mathcal{P}/\mathsf{poly}$. Recently, and concurrently with this work, Kelner et al~\cite{kelnerpreconditioning} show random-design instances of sparse linear regression that are hard for a particular class of algorithms, namely preconditioned Lasso. In contrast, we show hardness for {\em worst-case} design matrices, but with respect to {\em any algorithm} that runs faster than trivial brute force search.
\medskip\noindent
Further afield, the areas of fine-grained complexity and the geometry of numbers (or the study of integer lattices) have recently been shown to have interesting connections to statistical problems. For example, Backurs, Indyk and Schmidt~\cite{BIS17} show that certain empirical risk minimization (ERM) problems cannot be solved in sub-quadratic time, under the SETH conjecture. In another result, Backurs and Tzamos~\cite{backurs2017improving} showed that the classical Viterbi algorithm for finding the most likely path in a Hidden Markov Model is in fact optimal under the min-weight $k$-clique hypothesis which we rely on in this work. Bruna, Regev, Song and Tang~\cite{BRST20} recently showed the hardness of problems in robust statistics and learning mixtures of Gaussians, assuming the hardness of lattice problems.
\section{Preliminaries and definitions}\label{sec:defs}
\paragraph{Notations.} Bold lower-case letters, such as $\vecx$, denote (column) vectors. Bold uppercase letters, such as $\matA$, denote matrices. $\mathbb{R}$ stands for the set of real numbers, $\mathbb{Z}$ for the set of integers, and $\mathbb{R}^+$ (resp. $\mathbb{Z}^+$) for the set of non-negative real numbers (resp. integers). We will let $\|\vecx\|_p$ denote the $\ell_p$ norm of $\vecx \in \mathbb{R}^\slrcolumns$, that is, $\|\vecx\|_p = \big( \sum_{i\in [\slrcolumns]} |x_i|^p \big)^{1/p}$. The Hamming weight of $\vecx$, also called its $\ell_0$ norm, is simply the number of non-zero coordinates of $\vecx$. A vector $\vecx \in \R^\slrcolumns$ is called $k$-sparse if its Hamming weight is at most $k$, that is, if $\| \vecx\|_0 \leq k$.
\subsection{Sparse linear regression}
We now define the sparse linear regression problem.
\begin{definition}[$k$-SLR$_p$]
For any integer $k \ge 2$ and $1 \le p \le \infty$, the $k$-sparse linear regression problem with respect to the $\ell_p$ norm is defined as follows.
Given a matrix $\matA \in \R^{\slrrows \times \slrcolumns}$, a target vector $\vecb \in \R^{\slrrows}$, and a number $\delta > 0$, distinguish between:
\begin{itemize}
\item a {\em \textbf{YES}} instance, where there is some $k$-sparse $\vecx \in \R^\slrcolumns$ such that $\| \matA \vecx - \vecb \|_p \le \delta$; and
\item a {\em \textbf{NO}} instance, where for all $k$-sparse $\vecx \in \R^\slrcolumns$, $\| \matA \vecx - \vecb \|_p > \delta$.
\end{itemize}
\end{definition}
$k$-sparse linear regression can be trivially solved in time $\slrcolumns^{k}$. In this work, we are interested in determining if there are significantly faster algorithms. We will sometimes also give the algorithms more power, by allowing them unbounded time to preprocess the design matrix $\matA$ in an ``offline'' phase, and require them to be fast only in an ``online'' phase where they are given $\vecb$. We call this variant {\em sparse linear regression with preprocessing}.
\subsection{Fine-grained complexity and its hypotheses}\label{sec:assumptions}
Fine-grained complexity is the study of exact runtimes of algorithms for various problems. We present the relevant problems and results here, and refer the reader to the survey by Vassilevska-Williams \cite{williams2018some} for a detailed exposition.
\paragraph{$k$-SAT and the SETH Hypothesis.}
A central problem in fine-grained complexity is the study of the satisfiability problem, and the associated strong exponential-time hypothesis.
Given a CNF-SAT formula on $n$ variables with each clause having size at most $k$, the $k$-SAT problem asks to determine whether the formula is satisfiable or not.
Impagliazzo and Paturi \cite{impagliazzo2001complexity} introduced the strong exponential time hypothesis, conjecturing the fine-grained hardness of $k$-SAT.
\begin{definition}[Strong Exponential Time Hypothesis (SETH)]
For every $\eps > 0$ there exists an integer $k \ge 3$ such that no (randomized) algorithm can solve $k$-SAT on $n$ variables in $2^{(1 - \eps) n}$ time.
\end{definition}
We also use the non-uniform version of SETH to show hardness of sparse linear regression with preprocessing.
\begin{definition}[Non-uniform SETH]
For every $\eps > 0$ there exists an integer $k \ge 3$ such that no family of circuits of size $2^{(1 - \eps)n}$ solves $k$-SAT on $n$ variables.
\end{definition}
\paragraph{The Weighted $k$-Clique Conjecture.}
Suppose we are given an undirected graph $G = (V, E)$ with $|V| = \slrcolumns$ nodes. For a constant $k \ge 3$, a $k$-clique of $G$ is a fully connected subgraph of $G$ of size $k$. The $k$-clique problem asks to distinguish between \textbf{YES} instances, where $G$ contains a $k$-clique, and \textbf{NO} instances, where $G$ does not contain any $k$-clique. Given an {\em edge-weighted} graph and a threshold weight $W$, the Min-Weight $k$-Clique problem asks to distinguish between $\textbf{YES}$ instances which are graphs $G$ that contain a $k$-Clique of weight at most $W$, and \textbf{NO} instances where $G$ does not contain any $k$-clique of weight at most $W$.
\begin{definition}[Min-weight-$k$-clique]
Given a graph $G$ with integer edge weights and a weight threshold $W$, determine whether $G$ has a $k$-clique with weight at most $W$ or not.
\end{definition}
The naive algorithm for both problems requires enumerating all $\binom{\slrcolumns}{k}$ subsets of vertices of size $k$, and this takes time $O(\slrcolumns^k)$. In the case of the $k$-clique conjecture, slightly faster algorithms that run in time $O(\slrcolumns^{\omega k/3})$ are known \cite{nevsetvril1985complexity}, where $\omega < 2.373$ is the matrix multiplication constant.
However, no non-trivial algorithms are known for the weighted $k$-clique problem. It is conjectured that the problem of finding the minimum weight $k$-clique requires time $\slrcolumns^{k - o(1)}$ \cite{williams2018some}.
Under the min-weight $k$-clique hypothesis, Backurs and Tzamos~\cite{backurs2017improving} showed that the classical Viterbi algorithm for finding the most likely path in a Hidden Markov Model is in fact optimal. Under this hypothesis, tight lower bounds are also known for the the local alignment problem \cite{abboud2014consequences} from computational biology and the Maximum Weight Rectangle problem \cite{backurs2016tight} from computational geometry.
\begin{definition}[Min-weight $k$-clique hypothesis]
The Min-Weight $k$-Clique problem on $\slrcolumns$ node graphs with edge weights in $\{-\slrcolumns^{100k}, \ldots, \slrcolumns^{100k} \}$ requires (randomized) $\slrcolumns^{k - o(1)}$ time.
\end{definition}
We note that the following variants of the min-weight $k$-clique problem are as hard as the original one. First, we can assume that the edges are non-negative and in the range $\{1, \ldots, 2\slrcolumns^{100k} + 1\}$. To see this, let $w^*$ be the minimum weight of the edges in a graph. Create a new graph $G'$ with the same vertex and edge sets. The edge weights of $G'$ are obtained by adding $|w^*| + 1$ to the weight of the corresponding edge in $G$. Then $G'$ has a $k$-clique of weight at most $W + \binom{k}{2} (|w^*| + 1)$, if and only if $G$ has a $k$-clique of weight at most $W$.
Secondly, we can assume that there is a partition of the vertex set into $k$ subsets such that the $k$-clique has one vertex from each subset.
To see this, suppose there is a $k$-clique $K$ in $G$ with weight at most $W$. Then, we claim that we can assume that the vertex set $V$ is partitioned into $k$ subsets $V = V_1 \cup \ldots, V_k$ such $|K \cap V_i| = 1$ for all $i \in \{1, \ldots, k\}$.
To see this, randomly partition the vertices into $k$ subsets, by assigning each vertex to a subset uniformly and independently at random. Then, for any given $k$-clique (and in particular, the min-weight one), the probability that it has exactly one vertex in each subset is $\prod_{i=0}^{k-1} \left( \frac{k - i}{k} \right) = \frac{k!}{k^k}$, which is at least $\sqrt{2 \pi k} \cdot e^{-k} \cdot e^{\frac{1}{12k + 1}} > e^{-k}$ by Stirling's formula. Repeating this $O(e^k)$ many times completes the argument. Note that although the number of repetitions is exponential in $k$, it is independent of $\slrcolumns$, and so is sufficient for our purposes.
\subsection{The closest vector problem}
A lattice $\mathcal L$ is the set of the integer linear combinations of a set of linearly independent vectors (a basis) $\matB = (\vecb_1, \vecb_2, \ldots, \vecb_{\cvpcolumns})$ where each $ \vecb_i \in \R^{\cvprows}$:
\[\mathcal L = \mathcal L(\matB) = \left\{ \matB \vecz \mid \vecz \in \Z^{\cvpcolumns} \right\}.\]
Given a lattice basis $\matB$, and a target vector $\vect$, define $\dist_p(\mathcal L(\matB), \vect) = \min_{\vecx \in \mathcal L(\matB)} \|\vecx - \vect \|_p$ to be the minimum $\ell_p$ distance from $\vect$ to $\mathcal L = \mathcal L(\matB)$.
We follow \cite{bennett2017quantitative} for definitions of lattice problems.
\begin{definition}[$\gamma$-approximate Closest Vector Problem with respect to the $\ell_p$ norm ($\gamma$-$\CVP_p$)]
For any $\gamma \ge 1$ and $1 \le p \le \infty$, given a lattice $\mathcal L$ (specified by its basis $\matB \in \R^{\cvprows \times \cvpcolumns}$), a target vector $\vect \in \R^n$ and a number $r > 0$, distinguish between a \textbf{YES} instance, where $\dist_p(\mathcal L, \vect) \le r$ and a \textbf{NO} instance, where $\dist_p(\mathcal L, \vect) > \gamma r$.
\end{definition}
We refer to the exact version of the problem, when $\gamma = 1$, as $\CVP_p$.
The best known algorithm for exact CVP$_2$ runs in time $2^{\cvpcolumns + o(\cvpcolumns)}$ time \cite{ADS15}. However, for $p \neq 2$, the best known algorithms for CVP$_p$ are slower, i.e., they run in time $\cvpcolumns^{O(\cvpcolumns)}$ \cite{Kannan83, micciancio2014fast}.
Bennett, Golovnev and Stephens-Davidowitz~\cite{bennett2017quantitative} proved an SETH-based hardness bound for the Closest Vector Problem. In particular, for many $p$, including odd integers $p \ge 1$ and $p = \infty$, they show that $\CVP_p$ cannot be solved in time $2^{(1 - \eps) \cvpcolumns}$ for any $\eps > 0$, unless the Strong Exponential Time Hypothesis (SETH) is false.
\begin{theorem}[SETH-hardness of CVP$_p$ \cite{bennett2017quantitative}]\label{thm:sethcvp}
For every $\eps > 0$ and every integer $p \ge 1, p \notin 2\Z$ there is no $2^{(1 - \eps)\cvpcolumns}$ algorithm for CVP$_p$, unless SETH is false.
\end{theorem}
CVP with preprocessing (CVPP) refers to algorithms for the closest vector problem which are allowed an unbounded-time offline preprocessing phase where they get the basis $\matB$, and are required to be fast only in an online phase where they receive the target vector $\mathbf{t}$ and the distance threshold $r$. Aggarwal, Bennett, Golovnev and Stephens-Davidowitz show the following hardness results for CVPP$_p$.
\begin{theorem}[\cite{aggarwal2021fine}]
For every $\eps > 0$ and every integer $p \ge 1, p \notin 2\Z$ there is no $2^{(1 - \eps)\cvpcolumns}$ algorithm for CVPP$_p$, unless non-uniform SETH is false.
\end{theorem}
Examining their proof more carefully, we notice that they prove a stronger result. In particular, they show SETH-hardness of the following problem, which we refer to as $(0,1)$-$\CVP_p$.
\begin{definition}[$(0,1)$-$\CVP_p$]
For any $1 \le p \le \infty$, the $(0,1)$-Closest Vector Problem with respect to the $\ell_p$ norm is the following promise problem. Given a lattice $\mathcal L$ specified by a basis $\vec B \in \R^{\cvprows \times \cvpcolumns}$, a target vector $\vec t \in \R^\cvprows$ and two numbers $r, \tau > 0$, distinguish between the following two cases:
\begin{itemize}
\item \textbf{YES} instances, where there exists some $\vec {y}^* \in \{0, 1\}^\cvpcolumns$ such that $\|\vec{B} \vec{y}^* - \vec {t}\| \le r$; and
\item \textbf{NO} instances, where for all $\vec y \in \Z^\cvpcolumns$, $\| \vec B \vec y - \vec t\| \ge r + \tau.$
\end{itemize}
\end{definition}
Their method does not show hardness of $\CVP_2$ (or $(0,1)$-$\CVP_2$). On the other hand, to the best of our knowledge, there is no $2^{(1- \epsilon) \cvpcolumns}$-time algorithm for $(0, 1)$-CVP$_2$ for any $\epsilon > 0$. Indeed, as we observe in Section~\ref{sec:max-cut}, such an algorithm would imply a better algorithm for Weighted Max-Cut.
\section{Optimal worst-case hardness of sparse linear regression under the min-weight $k$-clique hypothesis}\label{sec:min-k-clique-slr}
The main result of this section is the theorem below, which shows that there are no {\em better-than-brute-force} algorithms for worst-case sparse linear regression, unless the Min-weight $k$-clique conjecture is false.
\begin{theorem}\label{thm:weightedclique}
For any integer $k \ge 4$, the $k$-SLR problem in the Euclidean ($\ell_2$) norm requires $\slrcolumns^{k - o(1)}$ (randomized) time, unless the Min-Weight $k$-clique conjecture is false.
\end{theorem}
\begin{proof}
We give a reduction from any Min-weight $k$-clique instance $G = (V, E)$ with positive edge weights to a $k$-SLR$_2$ instance $(\matA, \vecb, \delta)$ as follows.
First, we set large numbers $\alpha$ and $\beta$, whose significance will be clear in the sequel:
\[\alpha = \sqrt{\max \left\{ 1, \sum_{e \in E} w_e + 8W \right\}}, \quad \beta = \sqrt{\sum_{e \in E} w_e + 8W + \alpha^2 Z} \cdot \max\left\{8 Z, 50 \left(\alpha^2 Z +\sum_{e \in E} w_e \right) \right\},\]
where we define $Z = \left| \{ (u, v) \notin E \mid u, v \in V \} \right|$ to be the number of non-edges in the graph $G$.
We enumerate the unordered pairs of vertices $(u_{i_1}, u_{i_2})$ with index $i \in \left[ \binom{\slrcolumns}{2} \right]$ where $u_{i_1}, u_{i_2} \in V$. Let edge $e$ have weight $w_e$.
We first describe how we construct $\matA, \vecb$ which have the following structure:
\[
\matA =
\begin{pmatrix}
\matC\\
\matD
\end{pmatrix}, \quad
\vecb =
\begin{pmatrix}
\vecc\\
\vecd
\end{pmatrix}
\]
The submatrix $\matC \in \R^{\binom{\slrcolumns}{2} \times \slrcolumns}$ contains one row for each unordered pair of vertices and one column for each vertex in $V$. This submatrix $\matC$, along with the target subvector $\vecc \in \R^{\binom{\slrcolumns}{2}}$, encodes the $k$-clique instance. The submatrix $\matD \in \R^{k \times \slrcolumns}$ and its corresponding target vector $\vecd \in \R^k$ ensure that any solution must have exactly $k$ non-zero entries, all of which are close to $1$.
For each unordered pair of vertices $(u_{i_1}, u_{i_2}) \notin E$ corresponding to a non-edge, we add a row to the matrix $\matC$, and a corresponding entry in the target vector $\vecc$.
\[
\matC_{i, j} =
\begin{dcases}
2 \alpha & \mbox{for } j \in \{i_1, i_2\}\\
0 &\text{otherwise}
\end{dcases}
, \quad
\vecc_i = \alpha
\]
where the large number $\alpha$ is defined above.
For each $e_i = (u_{i_1}, u_{i_2})$ with weight $w_{e_i} > 0$, we add a row to $\matC$ and a corresponding entry in the target subvector $\vecc$.
\[
\matC_{i, j} =
\begin{dcases}
2 \sqrt{w_{e_i}} & \mbox{for } j \in \{i_1, i_2\}\\
0 &\text{otherwise}
\end{dcases}
, \quad
\vecc_i = \sqrt{w_{e_i}}
\]
As described in Section~\ref{sec:assumptions}, we can assume that we know a partition of the $\slrcolumns$ vertices into $k$ blocks of size $\slrcolumns/k$ such that if a $k$-clique with weight at most $W$ exists, then there is such a $k$-clique with exactly one vertex in each block.
We order the vertices such that the first $\slrcolumns/k$ vertices belong to the first block, the second $\slrcolumns/k$ vertices belong to the second block, and so one.
Let $\vec{1} \in \R^{\slrcolumns/k}$ to be the all $1$'s row vector. Then, we construct $\matD$ and $\vecd$ to each have $k$ rows.
\[
\matD =
\begin{pmatrix}
\beta \vec{1} & \vec{0} & \ldots & \vec{0}\\
\vec{0} & \beta \vec{1} & \ldots & \vec{0}\\
\vec{0} & \vec{0} & \ldots & \beta \vec{1}
\end{pmatrix}, \quad
\vecd =
\begin{pmatrix}
\beta\\
\vdots\\
\beta
\end{pmatrix}
\]
Finally, set $\delta > 0$ such that $\delta = \sqrt{\sum_{e \in E} w_e + 8W + \alpha^2 Z}$.
We first prove completeness. In other words, if there is a $k$-clique of weight at most $W$, then we construct a vector $\vecx \in \R^\slrcolumns$ such that $\|\matA \vecx - \vecb \|_2 \le \delta$. We index entries of $\vecx$ by the vertices in $G$ that they correspond to.
Suppose $G$ contains a $k$-clique $\widetilde{K}$ of weight $\widetilde{W} \le W$. Set $x_u = 1$ if vertex $u \in K$, and otherwise set $x_u = 0$.
From this definition, we see that for each non-edge, the contribution of the corresponding row to the error $\|\matA \vecx - \vecb \|^2_2$ is $\alpha^2$, since $\widetilde{K}$ cannot contain both endpoints of any non-edge. For each edge $e \in E$ such that $e$ is not in the clique $\widetilde{K}$, the contribution is $w_e$. For each edge $e$ in $\widetilde{K}$, the contribution is $(4\sqrt{w_e} - \sqrt{w_e})^2 = 9 w_e$.
Since $\widetilde{K}$ is a $k$-clique with one vertex in each of the $k$ blocks, $\|\matD \vecx - \vecd\|_2 = 0$. This gives that
\begin{align*}
\|\matA \vecx - \vecb \|^2_2 = \sum_{e \notin \widetilde{K}} w_e + \sum_{e \in \widetilde{K}} 9 w_e + \alpha^2 Z
& = \sum_{e\in E} w_e + \sum_{e \in \widetilde{K}} 8 w_e + \alpha^2 Z \\
& = \sum_{e\in E} w_e + 8\widetilde{W} + \alpha^2 Z
\le \delta^2
\end{align*}
Now, we show soundness.
In other words, if there is some $\vecx^*$ such that $\| \matA\vecx^* - \vecb \|_2 \le \delta$, then there must be a $k$-clique in $G$ of weight at most $W$.
We show that the only possible such $\vecx^*$ are those that have exactly $k$ non-zero entries, one in each block of $\vecx^*$, with each non-zero entry being very close to $1$.
Suppose for contradiction that one block of $\vecx^*$ does not have any non-zero entries. Then by the choice of $\beta$, we know that $\|\matA \vecx^* - \vecb\|_2 \ge \beta > \delta$. Since $\vecx^*$ is $k$-sparse, this implies that each block has exactly one non-zero entry.
Now, suppose for contradiction that $\vecx^*$ has some non-zero entry $x^*_u$ outside the interval $\left[1 - 2 \delta/\beta, 1 + 2 \delta/\beta \right]$, then
\[\| \matA \vecx^* - \vecb \|_2 \ge |\beta (x^*_u - 1)| \ge 2 \delta > \delta.\]
So all non-zero entries of $\vecx^*$ have to be in $\left[1 - 2 \delta/\beta, 1 + 2 \delta/\beta \right]$.
Now we claim that these $k$ non-zero entries have to correspond to a $k$-clique in the graph.
Suppose for contradiction that there are two non-zero entries $x^*_u, x^*_v$ such that $(u, v) \notin E$.
Then, counting the error term from rows corresponding to the other $Z - 1$ non-edges as well,
\begin{align*}
\|\matA \vecx^* - \vecb\|^2_2 &\ge (2 \alpha x^*_u + 2 \alpha x^*_v - \alpha)^2 + \left( 2 \alpha (1 - 2 \delta/\beta) - \alpha \right)^2 (Z - 1)\\
&\ge \alpha^2 \left( 4 \left( 1 - 2 \delta/\beta \right) - 1 \right)^2 + \alpha^2 \left( 2 (1 - 2 \delta/\beta) - 1 \right)^2 (Z - 1)\\
&= \alpha^2 \left[ \left(1 - \frac{4 \delta}{\beta} \right)^2 (Z - 1) + \left( 3 - \frac{8 \delta}{\beta} \right)^2 \right]\\
&\ge \alpha^2 \left[ \left( 9 - \frac{48\delta}{\beta} \right) + \left( 1 - \frac{8 \delta}{\beta} \right)(Z- 1) \right]\\
&\ge \alpha^2 \left[Z + 8 - \frac{8 \delta Z}{\beta} - \frac{48 \delta }{\beta} \right] \ge \alpha^2 (Z + 6) > \delta^2
\end{align*}
Finally, we show that the clique $\widetilde{K}$ so obtained has weight at most $W$. We can give upper and lower bounds to $\widetilde{\delta}^2 \coloneqq \| \matA \vecx^* - \vecb \|^2_2$ as follows. By assumption,
$\widetilde{\delta}^2 \le \delta^2 = \sum_{e \in E} w_e + 8 W + \alpha^2 Z$.
Now, to give a lower bound, consider the contribution to the error $\widetilde{\delta}^2$ from each type of row.
For non-edges, each corresponding row contributes at least $\left( 2\alpha (1 - 2 \delta/\beta) - \alpha \right)^2$.
For each edge $e \notin \widetilde{K}$, the corresponding row contributes at least $\left( 2 (1 - 2\delta/\beta) - 1 \right)^2 w_e$.
For each edge $e \in \widetilde{K}$, the corresponding row contributes at least $\left( 4 (1 - 2 \delta/\beta) - 1 \right)^2 w_e$.
From this, we get
\begin{align*}
\widetilde{\delta}^2 &\ge \left( 2\alpha (1 - 2 \delta/\beta) - \alpha \right)^2 Z + \sum_{e \notin \widetilde{K}} \left( 2 (1 - 2\delta/\beta) - 1 \right)^2 w_e + \sum_{e \in \widetilde{K}} \left( 4 (1 - 2 \delta/\beta) - 1 \right)^2 w_e\\
&= \left( \alpha^2 Z + \sum_{e \notin \widetilde{K}} w_e \right) \left( 1 - \frac{4 \delta}{\beta} \right)^2 + \sum_{e \in \widetilde{K}} w_e \left( 3 - \frac{8 \delta}{\beta} \right)^2\\
&\ge \left( \alpha^2 Z + \sum_{e \notin \widetilde{K}} w_e \right) \left( 1 - \frac{8 \delta}{\beta} \right) + \sum_{e \in \widetilde{K}} w_e \left( 9 - \frac{48 \delta}{\beta} \right)\\
&\ge \left( \alpha^2 Z + \sum_{e \in E} w_e \right) \left( 1 - \frac{48 \delta}{\beta} \right) + 8 \sum_{e \notin \widetilde{K}} w_e
\end{align*}
From these two bounds we get that
\[\frac{48 \delta}{\beta} \left( \alpha^2 Z + \sum_{e \in E} w_e \right) + 8W \ge 8\sum_{e \in \widetilde{K}} w_e \]
Since $\beta \ge 50 \delta \left(\alpha^2 Z + \sum_{e \in E} w_e \right)$, and the edge weights and the threshold $W$ are all integers, we get that
\[W \ge \sum_{e \in \widetilde K} w_e\]
The runtime of this reduction is $O(\slrcolumns^3)$, so if there is an algorithm that solves $k$-sparse linear regression in the $2$-norm in time $\slrcolumns^{k - \epsilon}$ for some $\epsilon > 0$,
then this reduction gives an algorithm that runs in time $\slrcolumns^3 + \slrcolumns^{k - \epsilon} = O(\slrcolumns^{k - \epsilon})$ for Min-weight $k$-clique when $k \ge 4$.
This completes the proof.
\end{proof}
\section{Optimal worst-case hardness of sparse linear regression under the hardness of lattice problems}\label{sec:cvp-slr}
Our main theorem in this section is a fine-grained reduction from the closest vector problem (CVP) in any norm to sparse linear regression (SLR) over the same norm. Using Theorem~\ref{thm:sethcvp}, a corollary is that unless the strong exponential hypothesis (SETH) is false, there is no algorithm for $k$-$\SLR_p$ (defined on odd norms) that runs in time better than $\slrcolumns^{(1-\epsilon) k}$ for any constant $\epsilon>0$.
While CVP and SLR look similar at a high level, our reduction has to bridge a significant difference between the problems: $\SLR$ refers to {\em sparse} solutions over $\mathbb{R}$, whereas CVP refers to {\em unrestricted} solutions over $\mathbb{Z}$.
\begin{theorem}\label{thm:cvp-slr}
For any integer $k \ge 2$ and $ 1 \le p \le \infty$, there is an efficient reduction from $(0,1)$-$\CVP_p$ on a lattice with rank $\cvpcolumns$ and ambient dimension $\cvprows$ to $k$-$\SLR_p$ on a matrix of dimensions $(\cvprows + k) \times k \cdot 2^{\cvpcolumns/k}$.
It follows that if, for any $\epsilon > 0$, there is a $\slrcolumns^{(1 - \epsilon)k}$-time algorithm for $k$-$\SLR_p$ then there is a $2^{(1 - \epsilon)\cvpcolumns}$-time algorithm for $(0, 1)$-$\CVP_p$.
\end{theorem}
\begin{proof}
Given a $(0, 1)$-$\CVP_p$ instance consisting of a lattice basis $\vec B \in \R^{\cvprows \times \cvpcolumns}$, a target vector $\vec{y} \in \R^\cvprows$, and two numbers $r, \tau > 0$, we construct the $k$-$\SLR_p$ instance $(\vec{A}, \vec{b}, \delta)$ as follows.
We set $\delta = r$ and
partition the columns of $\vec B$ into $k$ groups $\vec{B}_1, \ldots, \vec{B}_k$, each of size at most $\ceil{n/k}$.
\[\vec B =
\begin{pmatrix}
\vec{B}_1 &\ldots &\vec{B}_k
\end{pmatrix}\]
Construct $\vec{A}_i \in \R^{\cvprows \times 2^{\cvpcolumns/k}}$ for $i = 1$ to $k$ such that the columns of $\vec{A}_i$ are formed by summing all possible $2^{\cvpcolumns/k}$ subsets of the columns in $\vec{B}_i$.
Define $\vec{1} \in \R^{1\times 2^{\cvpcolumns/k}}$ to be the row vector of all $1$'s, and let $\alpha \in \R$ be some large number to be determined.
\[
\matA =
\begin{pmatrix}
\vec{A}_1 & \vec{A}_2 & \ldots &\vec{A}_k\\
\alpha\vec{1} & \vec{0} & \ldots &\vec{0}\\
\vec{0} & \alpha\vec{1} & \ldots & \vec{0} \\
\vec{0} & \vec{0} & \ldots & \alpha \vec{1}
\end{pmatrix}
, \quad
\vec b =
\begin{pmatrix}
\vec t\\
\alpha\\
\vdots\\
\alpha
\end{pmatrix}
\]
Suppose the $(0, 1)$-$\CVP_p$ instance is a \textbf{YES} instance, that is, there is some $\vec{y}^* \in \{0, 1\}^n$ such that $\| \vec B \vec {y}^* - \vec t\|_p \le r$. Then there is a $k$-sparse $\vec{x}^*$ that can be directly computed from $\vec{y}^*$ as follows.
\[
x^*_S =
\begin{dcases}
1 &\mbox{if } y^*_i = 1 \text{ for all } i \in S \mbox{ and } y^*_i = 0 \text{ for all } i \notin S \\
0 &\text{ otherwise}
\end{dcases}
\]
Here we have indexed the entries in $\vec x^*$ by the subset $S \subset [(i-1)\cvpcolumns/k + 1, in/k]$ of columns it corresponds to in $\vec B$, where $i$ is the block number. The $\vecx_S^*$ makes the $k$-SLR instance a YES instance since
\[\|\vec A \vecx^* - \vec b\|_p = \| \vec B \vec{y}^* - \vec t\|_p \le r = \delta\]
Now, suppose that the $k$-$\SLR_p$ instance we reduced to is a \textbf{YES} instance. That is, there is some $\vec{x}^*$ such that $\|\vec A \vecx^* - \vec b\|_p \le \delta$. We show that the only possible such solutions are those which have exactly $k$ non-zero entries, one in each block of $\vec{x}^*$, and that these non-zero entries have to be close to $1$.
Suppose for contradiction that one block of $\vec{x}^*$ does not have any non-zero entries, so it is the all-zero vector. Then
$\|\vec A \vecx^* - \vec b\|_p \ge \alpha > \delta$. So by the $k$-sparsity of $\vec{x}^*$, each of its blocks has exactly one non-zero entry.
Now suppose there is some non-zero entry ${x}^*_i$ of $\vec{x}^*$ that is outside the interval $\left[1 - \frac{2 \delta}{\alpha}, 1 + \frac{2 \delta}{\alpha} \right]$. Then
\[\|\vec A \vec{x}^* - \vec b\|_p \ge |\alpha (x^*_i - 1)| \ge 2 \delta > \delta.\]
Therefore we need to consider only the case where each non-zero entry of $\vec{x}^*$ is within the interval $\left[1 - \frac{2 \delta}{\alpha}, 1 + \frac{2 \delta}{\alpha} \right]$.
Consider the vector ${\overline{\vecx}}^*$ obtained by rounding the entries of $\vec{x}^*$ to either $0$ or $1$.
\[
{\overline{x}}^*_i =
\begin{dcases}
1 &{x}^*_i \neq 0\\
0 &{x}^*_i = 0
\end{dcases}
\]
We can construct a solution $\vec{y}^*$ to the $(0, 1)$-CVP$_p$ instance as follows.
\[
{y}^*_i =
\begin{dcases}
1 &\text{there is some }S\text{ such that } \overline{x}^*_S = 1\\
0 &\text{otherwise}
\end{dcases}
\]
\begin{align*}
\|\vec B \vec{y}^* - \vec{t}\|_p &= \| \vec A {\overline{\vecx}}^* - \vec b \|_p\\
&\le \| \vec{A} {\overline{\vecx}}^* - \vec{A} \vec{x}^* \|_p + \| \vec{A} \vec{x}^* - \vec b \|_p\\
&\le \| \vec{A} \|_p \cdot k \cdot \frac{2 \delta}{\alpha} + \delta \\
& \leq \| \vec{B} \|_p \cdot n \cdot \frac{2 \delta}{\alpha} + \delta \\
& < r + \tau
\end{align*}
for any value of $\tau$, by setting $\alpha = \frac{4 \delta}{\tau} \cdot \|\vec B\|_p \cdot n$ to be large enough.
Here, $\|\vec{B}\|_p := \max_{i\in [\cvpcolumns]} \|\vec{b}_i\|_p$, where $\vec{b}_i$ are the columns of $\matB$.
Since $\|\matB \vecy^* - \mathbf{t}\|_p < r+\tau$, by the promise of the $(0,1)$-CVP problem,
it must be the case that
\[\|\vec B \vec{y}^* - \vec{t}\|_p \le r,\]
making $(\matB,\vect,\delta)$ a \textbf{YES} instance of the CVP problem.
This reduction takes time $O \left( d\cdot k \cdot 2^{\cvpcolumns/k} \right)$, and so if there is an algorithm that solves $k$-SLR$_p$ in time $\slrcolumns^{(1 - \epsilon)k}$, then this reduction gives us an algorithm for $(0,1)$-CVP$_p$ that runs in time $(k \cdot 2^{\cvpcolumns/k})^{(1 - \epsilon)k} = O(2^{(1 - \epsilon)\cvpcolumns})$. This completes the proof.
\end{proof}
The same reduction, combined with the result by Aggarwal et al. \cite{aggarwal2021fine}, gives the following hardness result for sparse linear regression in the $p$-norm with pre-processing.
\begin{corollary}
If there is an algorithm that solves $k$-SLR$_p$ for odd norms $p$ with preprocessing in time better than $\slrcolumns^{(1 - \epsilon)k}$ for some $\epsilon > 0$, then SETH is false.
\end{corollary}
\section{SETH-hardness of $2$-SLR}\label{sec:seth2slr}
Here we define the Orthogonal Vectors problem (OV), and show that a subquadratic algorithm for $2$-sparse linear regression in the $2$-norm violates the Orthogonal Vectors Hypothesis and, by a result of \cite{williams2004new}, the strong exponential time hypothesis.
Let $d = \omega(n)$. Given two sets $U, V$ of $d$-dimensional vectors with $0,1$ entries, where $|U| = |V| = n$, distinguish between:
\begin{itemize}
\item \textbf{YES} instances, where there are vectors $\vecu \in U$ and $\vecv \in V$ s.t. $\langle \vecu, \vecv \rangle := \sum_{i=1}^d \vecu[i] \vecv[i] = 0$; and
\item \textbf{NO} instances, where no such pair of vectors exists.
\end{itemize}
The naive brute force algorithm runs in time $O(n^2 d)$ time, and no algorithm that runs in time $n^{2 - \epsilon} \poly(d)$ is known, for any $\epsilon > 0$. The OV Hypothesis states that this algorithm is essentially optimal, and is implied by both SETH and the Min-Weight $k$-Clique conjecture \cite{williams2004new,abboud2018more}.
\begin{definition}[Orthogonal Vectors Hypothesis]
No randomized algorithm can solve OV on instances of size $n$ in
$n^{2 - \epsilon} \poly(d)$ time for constant $\epsilon > 0$.
\end{definition}
The Orthogonal Vectors Hypothesis is implied by the strong exponential time hypothesis, as the following theorem states.
\begin{theorem}[SETH-hardness of Orthogonal Vectors \cite{williams2014finding}]
If there is an algorithm that solves OV in $n^{2 - \epsilon} \poly(d)$ time, for some $\epsilon > 0$ then SETH is false.
\end{theorem}
With this background, we are ready to state our main result of this section, and its corollary, which guarantees the hardness of $2$-sparse linear regression under SETH or the weaker Orthogonal Vectors Hypothesis.
\begin{proposition}\label{prop:ov-2-slr}
There is an efficient reduction from Orthogonal Vectors with $2$ sets of $n$ vectors from $\{0,1\}^d$ to $2$-sparse linear regression in the $2$-norm, with a $(d + 2) \times 2n$ design matrix.
\end{proposition}
\begin{corollary}
Suppose there is an algorithm that can solve $2$-sparse linear regression in time $n^{2 - \epsilon}\poly(d)$ for some $\epsilon > 0$. Then, the Orthogonal Vectors Hypothesis and SETH are false.
\end{corollary}
\paragraph{Other Results.} In Appendix~\ref{sec:max-cut}, we recall a folklore fine-grained reduction from the max-cut problem on weighted undirected graphs to the CVP problem in the $\ell_2$ norm \cite{aggarwal2021fine}. %
In turn, this shows that solving $k$-SLR in $\slrcolumns^{(1-\epsilon)k}$ time implies a corresponding speedup for the weighted max-cut problem, which is believed to be hard~\cite{williams2004new}.
\paragraph{An Open Problem.} It remains open to show that $k$-SLR in the $\ell_2$ norm is optimally hard assuming the strong exponential hypothesis (SETH).
\paragraph{Acknowledgements.}
The first author would like to thank David Jerison, Frederic Koehler, Kerri Lu and Ankur Moitra for discussions on the problem of sparse linear regression. We thank Noah Stephens-Davidowitz for pointing us to the connection between maxcut and CVP~\cite{aggarwal2021fine} and for his comments on the manuscript.
\bibliographystyle{alpha}
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namespace Klampt {
class GLUTGUI : public GenericGUIBase, public GLUTProgramBase
{
public:
GLUTGUI(GenericBackendBase* backend=NULL,int w=800,int h=600);
virtual ~GLUTGUI() {}
//if you want to set up the window title, it must be called before Run()
void SetWindowTitle(const char* title) { window_title = title; }
//if you want to set up the display mode, it must be called before Run()
void SetDisplayMode(int mode) { displayMode = mode; }
///Subclasses: put GL initialization code here
virtual bool Initialize();
virtual void Handle_Display();
virtual void Handle_Reshape(int w,int h);
virtual void Handle_Keypress(unsigned char key,int x,int y);
virtual void Handle_KeypressUp(unsigned char key,int x,int y);
virtual void Handle_Special(int key,int x,int y);
virtual void Handle_SpecialUp(int key,int x,int y);
virtual void Handle_Click(int button,int state,int x,int y);
virtual void Handle_Drag(int x,int y);
virtual void Handle_Motion(int x,int y);
virtual void Handle_Idle();
virtual void Run();
virtual bool OnQuit();
virtual bool OnNotify(const string& text,const string& msglevel);
virtual bool OnPauseIdle(double secs);
virtual bool OnRefresh();
virtual bool OnDrawText(double x, double y, double z, const std::string &text, int height);
virtual bool OnDrawText(int x, int y, const std::string &text, int height);
string window_title;
unsigned int displayMode;
};
} //namespace Klampt
#endif
| {
"redpajama_set_name": "RedPajamaGithub"
} | 850 |
Als Fossa canina bezeichnet man die Eckzahngrube im Gesichtsschädel. Sie ist größer und tiefer ausgeprägt als die vergleichbaren prägnanten Fossae incisivi, den Frontzahneinziehungen, und wird von diesen durch einen senkrechten Grat, die Eckzahn-Eminenz getrennt, die mit der langen Wurzel des Eckzahns korrespondiert. Die Fossa canina ist der Ursprung des Musculus levator anguli oris. Sie liegt unterhalb des Foramen infraorbitale.
Entzündungen, die von den Wurzeln der oberen Schneidezähne ausgehen, können einen Fossa-canina-Abszess verursachen.
Die Caldwell-Luc-Operation wird von der Fossa canina aus vorgenommen.
Literatur
N. Schwenzer, M. Ehrenfeld,
Schädel
Zahnmedizin | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,518 |
{"url":"https:\/\/www.esaral.com\/q\/define-value-of-polynomial-at-a-point-39208\/","text":"Define value of polynomial at a point.\nQuestion:\n\nDefine value of polynomial at a point.\n\nSolution:\n\nIf $f(x)$ is a polynomial and $\\alpha$ is any real number, then the real number obtained by replacing $x$ by $\\alpha$ in $f(x)$, is called the value of $f(x)$ at $x=\\alpha$ and is denoted by $f(\\alpha)$","date":"2022-08-10 13:13:27","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\": 0.941032886505127, \"perplexity\": 84.39985346543655}, \"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\/1659882571190.0\/warc\/CC-MAIN-20220810131127-20220810161127-00406.warc.gz\"}"} | null | null |
\section{\bf Introduction}
\bigskip
The Riemann zeta function $\zeta(s)$ plays a crucial role in mathematics. The Laurent series expansion of $\zeta(s)$ around $s=1$ (see \cite{chowla}) can be written as
\begin{equation*}
\zeta(s) = \frac{1}{s-1} + \gamma + \sum_{k=1}^{\infty} \frac{{(-1)}^k}{k!} \, \gamma_k \, {(s-1)}^k,
\end{equation*}
where
\begin{equation*}
\gamma_k := \lim_{N \rightarrow \infty} \bigg\{ \sum_{n=1}^N \bigg( \frac{\log^k n}{n} \bigg) - \frac{\log^{(k+1)} N}{k+1} \bigg\}
\end{equation*}
are called Stieltjes constants and $\gamma$ is the well known Euler-Mascheroni constant. Even though these constants are important ingredients of the theory of the Riemann zeta function and appear in many contexts, it is unknown whether they are rational or irrational although they are expected to be transcendental. As a generalization of this question to arithmetic progressions, Knopfmacher \cite{knopf} defined
\begin{equation*}
\gamma_k(a,q) := \lim_{x \rightarrow \infty} \bigg\{ \sum_{\substack{n \leq x, \\ n \equiv a \bmod q}} \bigg( \frac{\log^k n}{n} \bigg) - \frac{\log^{(k+1)}x}{q(k+1)} \bigg\},
\end{equation*}
for natural numbers $a$ and $q$. The case $k=0$ was studied earlier by D. H. Lehmer \cite{lehmer} in 1975. We refer to these constants as \textit{generalized Stieltjes constants}.
\par
The motivation for studying these constants emanates from our desire
to understand special values of $L$-series. More precisely,
when $f$ is an arithmetical function, with period $q$, the
Dirichlet series
$$L(s,f):= \sum_{n=1}^\infty {f(n) \over n^s}, $$
has been the focus of intense study (see for example the
survey article by Tijdeman \cite{tijdeman} as well as \cite{tmp}, \cite{gmr}
and \cite{ram-saradha}). However, these papers studied the special
value $L(1,f)$ whenever it is defined. Interestingly, this special
value can be studied using Baker's theory of linear forms in logarithms.
In this paper, our focus will be on the derivative $L'(1,f)$.
This problem has received scant attention. For example, there is the
curious result of Murty and Murty \cite{murty-murty} which states
that if there is some squarefree $D>0$ and $\chi_D$ is the quadratic
character attached to ${\mathbb Q}(\sqrt{-D})$ is such that $L'(1,\chi_D)=0$,
then, $e^\gamma$ is transcendental. An analogous question of non-vanishing
seems to occur in other contexts as well (see for example, \cite{scourfield}).
These are not unrelated to the Euler-Kronecker constants
studied in \cite{ihara-murty} and \cite{mourtada-murty}.
\par
Many arithmetic properties and computational aspects of these constants have been studied in \cite{dilcher} but the only known result about their transcendental nature is a theorem due to M. Ram Murty and N. Saradha \cite[Theorem 1]{ram-saradha}, where they tackle the case $k=0$. In this paper, we concentrate on the arithmetic nature of these constants when $k=1$.
The nature of values of the gamma function at rational arguments and relations among them has been the subject of research for a long time. In light of this, a conjecture put forth by S. Gun, M. Ram Murty and P. Rath \cite{gmr} will be useful towards a partial solution to our question. The conjecture is the following.
\begin{conjecture}\label{conj}
For any positive integer $q > 2$, let $\overline{V_{\Gamma}(q)}$ be the $\overline{\mathbb{Q}}$-vector space spanned by the real numbers
\begin{equation*}
\log\Gamma \bigg(\frac{a}{q}\bigg), \hspace{1mm} 1 \leq a \leq q, \hspace{1mm} (a,q) = 1.
\end{equation*}
Then the dimension of $\overline{V_{\Gamma}(q)}$ is $\phi(q)$.
\end{conjecture}
This conjecture was inspired by a conjecture of Rohrlich (see \cite{waldschmidt}) regarding the possible relations among the special values of the $\Gamma$-function.
We note that the conjecture is equivalent to the numbers $\{ \log\Gamma(a/q) : 1 \leq a \leq q, (a,q) = 1\}$ being $\overline{\mathbb{Q}}$-linearly independent for $q>2$. This is a major unsolved problem in number theory and is believed to be outside the scope of current mathematical tools.
For a natural number $q$, a function $f$ defined on the integers which is periodic with period $q$ is said to be {\sl odd} if $f(q-n) = - f(n)$ for all natural numbers $n$.
It is said to be {\sl even} if $f(q-n)=f(n)$ for all natural numbers $n$.
As noted earlier, the $L$-series attached to $f$ is defined as
\begin{equation*}
L(s,f) := \sum_{n=1}^{\infty} \frac{f(n)}{n^s},
\end{equation*}
for $\Re(s)>1$. Using the theory of the Hurwitz zeta function, $L(s,f)$ can be extended to an entire function as long as $\sum_{a=1}^q f(a) = 0$. Given a function $f$ which is periodic mod $q$, we define the Fourier transform of $f$ as
\begin{equation}\label{fourier-def}
\hat{f}(b) := \frac{1}{q} \sum_{a=1}^q f(a) \zeta_q^{-ab},
\end{equation}
where $\zeta_q = e^{2 \pi i/q}$.
This can be inverted using the identity
\begin{equation*}\label{fourier-inversion}
f(n) = \sum_{b=1}^q \hat{f}(b) \zeta_q^{bn}.
\end{equation*}
Thus, the condition for convergence of $L(1,f)$, i.e, $\sum_{a=1}^q f(a) = 0$ can be interpreted as $\hat{f}(q) = 0$. An arithmetical function periodic with period $q$ is said to be of \textit{Dirichlet type} if
\begin{equation*}
f(n) = 0, \hspace{1mm} \text{whenever} \quad (n,q) > 1.
\end{equation*}
Another important notion is that of the linear independence of arithmetical functions. A set of arithmetical functions $\{f_1,f_2, \cdots, f_m\}$ is said to be linearly independent over $\overline{\mathbb{Q}}$ if
\begin{equation*}
\sum_{j=1}^m \alpha_j f_j = 0, \text{ with } \alpha_j \in \overline{\mathbb{Q}} \Rightarrow \alpha_j = 0 \hspace{1mm} \text{ for all } 1 \leq j \leq m.
\end{equation*}
Again, using the theory of the Hurwitz zeta function, one can derive
formulas (as we will see below) for $L'(1,f)$ in terms of the Stieltjes
constants.
With this discussion in place, we state the main theorems of this paper.
\begin{theorem}\label{main-theorem-1}
Let $p$ be a prime greater than $7$. Define
\begin{equation*}
\mathfrak{F}_p := \bigg\{ f : \mathbb{Z} \rightarrow \overline{\mathbb{Q}} \hspace{1mm} |
\, \hspace{1mm} f \text{ is periodic with period } p, \, f \text{ is odd}, \, \widehat{f}(p) = 0, \, L(1,f) \neq 0 \bigg\}.
\end{equation*}
For $r > 2$, let $f_1, f_2, \cdots, f_r $ be $\overline{\mathbb{Q}}$-linearly independent elements of $\mathfrak{F}_p$. Then Conjecture \ref{conj} implies that at most three of the numbers
\begin{equation*}
\bigg\{ L'(1,f_j) = - \sum_{a=1}^p f_j(a) \gamma_1(a,p) \hspace{1mm} | \hspace{1mm} 1 \leq j \leq r \bigg\}
\end{equation*}
are algebraic.
\end{theorem}
We also handle the case for arithmetical functions periodic with period $p$ and $L(1,f)=0$ in the theorem below.
\begin{theorem}\label{main-theorem-2}
Let $p$ be a prime number greater than 5. Define
\begin{equation*}
\mathfrak{G}_p := \bigg\{ f: \mathbb{Z} \rightarrow \overline{\mathbb{Q}} \hspace{1mm} | \hspace{1mm}
f \text{ is periodic with period } p, \, f \text{ is odd}, \, \widehat{f}(p) = 0, \, L(1,f) = 0 \bigg\}.
\end{equation*}
For $r \geq 2$, let $f_1, \cdots, f_r$ be $\overline{\mathbb{Q}}$-linearly independent elements of $\mathfrak{G}_p$. Then under Conjecture \ref{conj}, we conclude that at most one of the numbers
\begin{equation*}
\bigg\{ L'(1, f_j ) = - \sum_{a=1}^p f_j(a) \gamma_1(a,p) \hspace{1mm} | \hspace{1mm} 1 \leq j \leq r \bigg\}
\end{equation*}
is algebraic.
\end{theorem}
\begin{remark*}
Both the above theorems also hold when the period of the functions under consideration is a composite number $q$, provided that the Fourier transforms of the functions are of Dirichlet type. This restriction comes from the nature of Conjecture \ref{conj}. Indeed, we will prove that Theorem \ref{main-theorem-1} holds for the general set of functions
\begin{equation*}
\begin{split}
\mathfrak{F}_q := \bigg\{ f: \mathbb{Z} \rightarrow \overline{\mathbb{Q}} \hspace{1mm} | & \hspace{1mm}
f \text{ is periodic with period } q, \, f \text{ is odd}, \\
& \widehat{f} \text{ is of Dirichlet type}, \, L(1,f) \neq 0 \bigg\},
\end{split}
\end{equation*}
and Theorem \ref{main-theorem-2} holds for
\begin{equation*}
\begin{split}
\mathfrak{G}_q := \bigg\{ f: \mathbb{Z} \rightarrow \overline{\mathbb{Q}} \hspace{1mm} | & \hspace{1mm}
f \text{ is periodic with period } q, \, f \text{ is odd}, \\
& \widehat{f} \text{ is of Dirichlet type}, \, L(1,f) = 0 \bigg\},
\end{split}
\end{equation*}
where $q$ is not necessarily prime.
\end{remark*}
We note that the above defined set $\mathfrak{F}_q$ is non-empty since odd primitive Dirichlet characters modulo $q$ are in $\mathfrak{F}_q$. We will see this in the course of proof of the following corollary.
\begin{corollary}\label{coro-1}
Let $q$ be a natural number greater than $7$. Then assuming Conjecture \ref{conj}, we deduce that at most three of the following numbers are algebraic:
\begin{equation*}
\bigg\{ L'(1,\chi) = - \sum_{a=1}^q \chi(a) \gamma_1(a,q) \hspace{1mm}| \hspace{1mm} \chi \text{ is an odd primitive Dirichlet character mod } q \bigg\}.
\end{equation*}
\end{corollary}
Applying Theorem \ref{main-theorem-1} to the scenario when $q = p$, an odd prime greater than $7$ and
\begin{equation*}
f_j(n) :=
\begin{cases}
1 & \text{ if } n \equiv j \bmod p, \\
-1 & \text{ if } n \equiv -j \bmod p, \\
0 & \text{ otherwise,}
\end{cases}
\end{equation*}
for $1 \leq j \leq (p-1)/2$, we infer the following:
\begin{corollary}\label{coro-2}
For an odd prime $p$ greater than $7$, Conjecture \ref{conj} implies that at least $(p-7)/2$ of the numbers
\begin{equation*}
\big\{ \gamma_1(a,p) \hspace{1mm} | \hspace{1mm} 1 \leq a \leq p-1 \big\}
\end{equation*}
are transcendental.
\end{corollary}
\section{\bf Preliminaries}
\bigskip
The aim of this section is to introduce notation and some fundamental results that will be used in the later part of the paper. Let $q$ be a fixed positive integer. Consider $f : \mathbb{N} \to \overline{\mathbb{Q}}$, periodic with period $q$. Define
\begin{equation*}
L(s,f) = \sum_{n=1}^{\infty} \frac{f(n)}{n^s}.
\end{equation*}
Observe that $L(s,f)$ converges absolutely for $\Re(s) > 1$. Since $f$ is periodic,
\begin{align}
L(s,f) & = \sum_{a=1}^q f(a)\sum_{k=0}^{\infty} \frac{1}{{(a + kq)}^s} \nonumber \\
& = \frac{1}{q^s} \sum_{a=1}^q f(a) \zeta(s, a/q), \label{l-zeta}
\end{align}
where $\zeta(s,x)$ is the Hurwitz zeta function. For $\Re(s) > 1$ and $0 < x \leq 1$, the Hurwitz zeta function is defined as
\begin{equation*}
\zeta(s,x) = \sum_{n=0}^{\infty} \frac{1}{{(n+x)}^s}.
\end{equation*}
In 1882, Hurwitz \cite[Chapter 12, Section 5]{apostol} proved that $\zeta(s,x)$ has an analytic continuation to the entire complex plane except for a simple pole at $s=1$ with residue $1$. Using this, we conclude that $L(s,f)$ can be extended analytically to the entire complex plane except for a simple pole at $ s=1 $ with residue $ \frac {1} {q} \sum_{a=1}^q f(a)$. Thus,
it is easy to deduce that
$\sum_{n=1}^\infty \frac {f(n)} {n}$ converges whenever $\sum_{a=1}^q f(a) = 0$. Hence, $f(q) = \hat{f}(q) = 0$ implies that both $L(s,f)$ as well as $L(s, \hat{f})$ are entire.\\
Before proceeding, we prove a few lemmas for arithmetical functions periodic with period $q$.
\begin{lemma}\label{lemma-1}
Let $f$ be an arithmetical function periodic with period $q$. Then,
\begin{equation*}
L(1-s,f) = 2 \, \Gamma(s) {\bigg(\frac{q}{2 \pi}\bigg)}^s \cos\bigg( \frac{s\pi}{2}\bigg) L(s,\hat{f}),
\end{equation*}
when $f$ is even (i.e., f(q-n) = f(n) for all $n$) and
\begin{equation*}
L(1-s,f) = 2\,i \, \Gamma(s) {\bigg(\frac{q}{2 \pi}\bigg)}^s \sin\bigg( \frac{s\pi}{2}\bigg) L(s,\hat{f}),
\end{equation*}
when $f$ is odd (i.e, f(q-n) = -f(n) for all $n$).
\end{lemma}
\begin{proof}
We refer the reader to \cite[Chapter XIV, Theorem 2.1]{lang}.
\end{proof}
In analogy with the notation of generalized Bernoulli numbers associated to Dirichlet characters, we define
\begin{equation*}
B_{1,f} := \sum_{a=1}^q a \, f(a),
\end{equation*}
where $f$ is an odd arithmetical function periodic with period $q$. We make another important observation.
\begin{lemma}\label{lemma-2}
For any arithmetical function $f$ periodic with period $q$,
\begin{equation*}
L'(0,f) = \frac{\log q}{q} \, B_{1,f} + \sum_{b=1}^q f(b) \log\Gamma \bigg( \frac{b}{q} \bigg).
\end{equation*}
\end{lemma}
\begin{proof}
By differentiating \eqref{l-zeta} with respect to $s$, we have
\begin{equation*}
L'(s,f) = \frac{- \log q}{q^s} \bigg[ \sum_{a=1}^q f(a) \, \zeta \bigg(s, \frac{a}{q} \bigg) \bigg] + \bigg[ \frac{1}{q^s} \sum_{a=1}^q f(a) \, \zeta' \bigg(s, \frac{a}{q} \bigg) \bigg].
\end{equation*}
Substituting $s=0$, we have
\begin{equation*}
L'(0,f) = - \log q \bigg[ \sum_{a=1}^q f(a)\,\zeta \bigg(0, \frac{a}{q} \bigg) \bigg] + \bigg[ \sum_{a=1}^q f(a) \zeta' \bigg(0, \frac{a}{q} \bigg)\bigg].
\end{equation*}
The values of the Hurwitz zeta function and its derivative at $s=0$ are given by
\begin{equation*}
\zeta(0,x) = 1 + \zeta(0) - x, \hspace{1mm} \zeta'(0,x) = \log\Gamma(x) + \zeta'(0),
\end{equation*}
where $\zeta(s)$ is the Riemann zeta function. A proof of the above fact can be found in \cite{deninger}. Substituting these values in the expression obtained earlier, we get
\begin{align*}
L'(0,f) & = - \log q \, \big(1 + \zeta(0)\big) \bigg[ \sum_{a=1}^q f(a) \bigg] + \frac{\log q}{q} \sum_{a=1}^q f(a)\, a \\
& + \zeta'(0) \bigg[ \sum_{a=1}^q f(a) \bigg] + \sum_{a=1}^q f(a) \log\Gamma\bigg( \frac{a}{q} \bigg) \\
& = \frac{\log q}{q} \sum_{a=1}^q f(a) \, a + \sum_{a=1}^q f(a) \log\Gamma\bigg( \frac{a}{q} \bigg),
\end{align*}
since $\sum_{a=1}^q f(a) = 0$. This proves the lemma.
\end{proof}
The functional equation obtained in Lemma \ref{lemma-1} gives an expression for the value of $L'(1,f)$ when $f$ is an odd periodic function as below.
\begin{lemma} \label{lemma-3}
Let $f$ be an odd periodic arithmetical function with period $q$ satisfying $f(q) = \hat{f}(q) = 0$. Then,
\begin{equation*}
L'(1,f) = \frac{i \pi}{q} \bigg\{ \bigg( \bigg( 1 + \frac{1}{q} \bigg) \log q - \log 2 \pi - \gamma \bigg) B_{1,\hat{f}} + \sum_{b=1}^q \hat{f}(b) \log \Gamma \bigg( \frac{b}{q} \bigg) \bigg\},
\end{equation*}
where $B_{1,g} := \sum_{a=1}^q a g(a) $ for any odd arithmetical function periodic with period $q$.
\end{lemma}
\begin{proof}
Note that if $f$ is an odd periodic arithmetical function, then so is $\hat{f}$. Thus, differentiating the functional equation for $L(s,\hat{f})$ from Lemma \ref{lemma-1} gives
\begin{multline*}
- L'(1-s,\hat{f}) = 2 \, \Gamma'(s) {\bigg(\frac{q}{2 \pi}\bigg)}^s \sin\bigg( \frac{s\pi}{2}\bigg) L(s,f) \\
+ 2 \, \Gamma(s) {\bigg(\frac{q}{2 \pi}\bigg)}^s \log \bigg( \frac{q}{2 \pi} \bigg) \sin\bigg( \frac{s\pi}{2}\bigg) L(s,f) \\
+ 2 \, \Gamma(s) {\bigg(\frac{q}{2 \pi}\bigg)}^s \, \frac{\pi}{2} \cos\bigg( \frac{s\pi}{2}\bigg) L(s,f) \\
+ 2 \, \Gamma(s) {\bigg(\frac{q}{2 \pi}\bigg)}^s \sin\bigg( \frac{s\pi}{2}\bigg) L'(s,f).
\end{multline*}
Since $f(q) = \hat{f}(q) = 0$, both $L(s,f)$ and $L(s,\hat{f})$ are entire. Taking limit as $s$ tends to 1 in the above expression, we have
\begin{align*}
- L'(0,\hat{f}) & = 2 \, i \, \Gamma(1) \frac{q}{2\pi} \sin \bigg( \frac{\pi}{2} \bigg) \bigg\{ \bigg(\frac{\Gamma'}{\Gamma}(1) + \log \bigg( \frac{q}{2 \pi} \bigg) \bigg) L(1,f) + L'(1,f) \bigg\} \\
& = \frac{i q}{\pi} \bigg\{ L'(1,f) + L(1,f) \bigg( \log\bigg( \frac{q}{2\pi} \bigg) - \gamma \bigg) \bigg\},
\end{align*}
as $\Gamma'(1)/ \Gamma (1) = - \gamma$. By rearrangement, we get
\begin{equation*}
L'(1,f) = \frac{i \pi}{q} L'(0,\hat{f}) - \bigg( \log \bigg(\frac{q}{2 \pi} \bigg) - \gamma \bigg) L(1,f).
\end{equation*}
The value $L(1,f)$ for periodic arithmetical functions is well-understood (for example, see \cite[Theorem 3.1]{tmp}). In particular, when $f$ is odd,
\begin{equation}\label{L(1,f)-odd}
L(1,f) = \frac{- i \pi}{q} \sum_{a=1}^q \hat{f}(a) \, a = \frac{- i \pi}{q} \, B_{1,\hat{f}},
\end{equation}
where $\hat{f}$ denotes the Fourier transform of $f$. This evaluation, together with Lemma \ref{lemma-2} gives
\begin{align*}
L'(1,f) & = \frac{i \pi}{q} \bigg\{ \frac{\log q}{q} B_{1,\hat{f}} + \sum_{b=1}^q \hat{f}(b) \log\Gamma \bigg( \frac{b}{q} \bigg) + \bigg( \log \bigg(\frac{q}{2 \pi} \bigg) - \gamma \bigg) B_{1,\hat{f}} \bigg\},\\
& = \frac{i \pi}{q} \bigg\{ \bigg( \frac{\log q}{q} + \log q - \log 2 \pi - \gamma \bigg) B_{1,\hat{f}} + \sum_{b=1}^q \hat{f}(b) \log\Gamma \bigg( \frac{b}{q} \bigg) \bigg\},
\end{align*}
from which the lemma is immediate.
\end{proof}
A useful connection between value of derivatives of $L$-functions, attached to periodic functions at $s=1$ and generalized Stieltjes constants is illustrated in the following lemma. We include its proof for the sake of exposition (see \cite[Proposition 3.2]{knopf}).
\begin{lemma}\label{identity-lemma}
For an arithmetical function $f$ which is periodic with period $q$ and satisfies $\hat{f}(q) = 0$, we have
\begin{equation*}
{L}^{(k)}(1,f) = {(-1)}^k \sum_{a=1}^q f(a) \gamma_k(a,q),
\end{equation*}
where $\gamma_k(a,q)$ are generalized Stieltjes constants as defined earlier.
\end{lemma}
\begin{proof}
In view of brevity, let
\begin{equation*}
H_k(x,a,q) := \sum_{\substack{n \leq x, \\ n \equiv a \bmod q}} \frac{\log^k n}{n},
\end{equation*}
for any positive real number $x$. Observe that
\begin{align*}
\sum_{n \leq x} f(n) \, \frac{\log^k n}{n} & = \sum_{a=1}^q f(a) H_k(x,a,q) \\
& = \sum_{a=1}^q f(a) \bigg( H_k(x,a,q) - \frac{\log^{k+1 x}}{q(k+1)}\bigg),
\end{align*}
since $q \, \hat{f}(q) = \sum_{a=1}^q f(a) = 0$. Taking limit as $x$ tends to infinity on both sides gives the result.
\end{proof}
As mentioned earlier, the special value $L(1,f)$ has been extensively studied and is important in the context of our theorems. The following result of Baker, Birch and Wirsing \cite{bbw} will be particularly useful.
\begin{theorem}\label{bbw-thm}
If $f$ is a non-vanishing function defined on the integers with algebraic values and period $q$ such that (i) $f(n) = 0$ whenever $1 < (n,q) < q$ and (ii) the $q^{th}$ cyclotomic polynomial $\Phi_q$ is irreducible over $\mathbb{Q} (f(1), f(2), \cdots , f(q))$, then
\begin{equation*}
\sum_{n=1}^\infty \frac{f(n)} {n} \neq 0.
\end{equation*}
\end{theorem}
We also observe that if $f_1, \cdots, f_r$ are arithmetical functions periodic with period $q$, then
\begin{equation}\label{lin-ind-f-hat}
\sum_{j=1}^r \alpha_j f_j = 0 \iff \sum_{j=1}^r \alpha_j \widehat{f_j} = 0,
\end{equation}
for any complex numbers $\alpha_j$, $1 \leq j \leq r$. This is immediate from the fact that the Fourier transform is a linear automorphism of the $\mathbb{C}$-vector space of arithmetical functions periodic with period $q$.
\section{\bf Proofs of Results}
\bigskip
\subsection{Proof of Theorem \ref{main-theorem-1}}
For convenience of notation, let
\begin{equation*}
\mathscr{C} := \bigg( 1 + \frac{1}{q} \bigg) \log q - \log 2 \pi - \gamma.
\end{equation*}
Thus, Lemma \ref{lemma-3} gives
\begin{equation*}
L'(1,f_j) = \frac{i \pi}{q} \bigg\{ \mathscr{C} B_{1,\hat{f_j}} + \sum_{b=1}^q \hat{f_j}(b) \log\Gamma \bigg( \frac{b}{q} \bigg) \bigg\},
\end{equation*}
for all $1 \leq j \leq r$. By \eqref{L(1,f)-odd}, the hypothesis $L(1,f_j) \neq 0$ implies that $B_{1,\hat{f_j}} \neq 0$. \\
For $1 \leq k < l \leq r$, define
\begin{equation*}
d_{k,l} := B_{1,\hat{f_l}} L'(1,f_k) - B_{1,\hat{f_k}} L'(1,f_l).
\end{equation*}
We claim that $d_{k,l} \neq 0$. Indeed, if $d_{k,l} = 0$, then we get that
\begin{align*}
0 & = B_{1,\hat{f_l}} L'(1,f_k) - B_{1,\hat{f_k}} L'(1,f_l) \\
& = \frac{i \pi}{q} \bigg\{ \mathscr{C} \bigg( B_{1,\hat{f_l}} B_{1,\hat{f_k}} - B_{1,\hat{f_k}} B_{1, \hat{f_l}} \bigg) + \sum_{b=1}^q \bigg[ B_{1,\hat{f_l}} \hat{f_k}(b) - B_{1, \hat{f_K}} \hat{f_l}(b) \bigg] \log\Gamma\bigg( \frac{b}{q}\bigg) \bigg\} \\
& = \sum_{b=1}^q \bigg[ B_{1,\hat{f_l}} \hat{f_k}(b) - B_{1, \hat{f_K}} \hat{f_l}(b) \bigg] \log\Gamma\bigg( \frac{b}{q}\bigg),
\end{align*}
which is a $\overline{\mathbb{Q}}$-linear relation among the values of the
log gamma function as $B_{1,\hat{f_j}} \in \overline{\mathbb{Q}}$ for all $1 \leq j \leq r$. Therefore, Conjecture \ref{conj} gives that
\begin{equation*}
B_{1,\hat{f_l}} \hat{f_k} - B_{1,\hat{f_k}} \hat{f_l} = 0
\end{equation*}
on all natural numbers. This implies $\overline{\mathbb{Q}}$-linear dependence of $\hat{f_k}$ and $\hat{f_l}$ and thus, contradicts the $\overline{\mathbb{Q}}$-linearly independence of $f_k$ and $f_l$ by \eqref{lin-ind-f-hat}. Hence, $d_{k,l}$ is not zero.
We now consider the ratio $d_{k,l}/d_{u,v}$ for $1 \leq k,u < l,v \leq r$ and $(k,l) \neq (u,v)$. If this ratio is algebraic, i.e.,
\begin{equation*}
\frac{d_{k,l}}{d_{u,v}} = \eta \hspace{1mm} \in \overline{\mathbb{Q}},
\end{equation*}
then we are led to argue that
\begin{align*}
0 & = d_{k,l} - \eta d_{u,v} \\
& = \sum_{b=1}^q \bigg[ B_{1,\hat{f_l}} \hat{f_k}(b) - B_{1,\hat{f_k}} \hat{f_l}(b) - \eta B_{1,\hat{f_w}} \hat{f_u}(b) + \eta B_{1, \hat{f_u}} \hat{f_w}(b) \bigg] \log\Gamma \bigg(\frac{b}{q} \bigg),
\end{align*}
which is a $\overline{\mathbb{Q}}$-linear relation among log gamma values. Hence, by Conjecture \ref{conj}, we have
\begin{equation*}
B_{1,\hat{f_l}} \hat{f_k} - B_{1,\hat{f_k}} \hat{f_l} - \eta B_{1,\hat{f_w}} \hat{f_u} + \eta B_{1, \hat{f_u}} \hat{f_w} = 0
\end{equation*}
on all natural numbers. Since $B_{1,\hat{f_j}}$ are non-zero algebraic numbers, we obtain a non-trivial $\overline{\mathbb{Q}}$-linear relation among $\hat{f}_k , \hat{f_l}, \hat{f_u}$ and $\hat{f_w}$. The fact \eqref{lin-ind-f-hat} transports this to $\overline{\mathbb{Q}}$-linear dependence of $f_k$, $f_l$, $f_u$ and $f_w$, which contradicts our hypothesis. Thus, at most one of the $d_{k,l}$'s can be algebraic for $1 \leq k < l \leq r$.
As a result, if four numbers, namely, $L'(1,f_k), L'(1,f_l), L'(1,f_u)$ and $L'(1,f_w)$ are algebraic for $(k,l) \neq (u,w)$, then $d_{k,l}/d_{u,w}$ would be algebraic leading to a contradiction. Hence, the theorem follows.
$\hfill\ensuremath{\square}$
\subsection{Proof of Theorem \ref{main-theorem-2}}
Using the hypothesis that $L(1,f) = 0$ for all $f \in \mathfrak{G_q}$ and \eqref{L(1,f)-odd}, we know that
\begin{equation*}
B_{1,\hat{f_j}} = 0,
\end{equation*}
for all $1 \leq j \leq r$. Hence, Lemma \ref{lemma-3} gives
\begin{equation*}
L'(1,f_j) = \frac{i \pi}{q} \bigg\{ \sum_{b=1}^q \hat{f_j}(b) \log\Gamma \bigg( \frac{b}{q} \bigg) \bigg\},
\end{equation*}
for all $1 \leq j \leq r$. Suppose that for $1 \leq k < l \leq r$,
\begin{equation*}
\frac{L'(1,f_k)}{L'(1,f_l)} = \xi \in \overline{\mathbb{Q}}.
\end{equation*}
Then simplifying the above expression gives
\begin{equation*}
\sum_{b=1}^q \bigg[ \hat{f_k}(b) - \xi \hat{f_l}(b) \bigg] \log\Gamma\bigg( \frac{b}{q}\bigg) = 0,
\end{equation*}
which is an algebraic linear relation among the log gamma values. Therefore, by Conjecture \ref{conj}, we get that
\begin{equation*}
\hat{f_k} - \xi \hat{f_l} = 0
\end{equation*}
on all natural numbers. This implies the $\overline{\mathbb{Q}}$-linear dependence of the functions $\hat{f_k}$ and $\hat{f_l}$ and thus, contradicts the $\overline{\mathbb{Q}}$-linear independence of $f_k$ and $f_l$ by \eqref{lin-ind-f-hat}. Hence, the quotient $L'(1,f_k)/L'(1,f_l)$ is transcendental for all $1 \leq k < l \leq r$, which in turn leads us to conclude that at most one of the numbers under consideration is algebraic.
$\hfill\ensuremath{\square}$
\subsection{Proof of Corollary \ref{coro-1}}
Let $q$ be any natural number greater than $7$ and $\chi$ be an odd primitive Dirichlet character modulo $q$. It suffices to show that $\chi \in \mathfrak{F_q}$ i.e, that $\hat{\chi}$ is of Dirichlet type and that $L(1,\chi) \neq 0$. The latter follows from the famous theorem of Dirichlet \cite[Theorem 6.20 and Section 7.3]{apostol}. The former is also from \cite[Chapter 8, Theorem 8.19]{apostol} since
\begin{equation*}
\hat{\chi}(n) = \frac{1}{q} \sum_{a=1}^q \chi(a) \zeta_q^{-an}.
\end{equation*}
This completes the proof of the corollary.
$\hfill\ensuremath{\square}$
\subsection{Proof of Corollary \ref{coro-2}}
We begin the proof by observing that the functions $f_j$ defined below are in $\mathfrak{F_p}$. For $1 \leq j \leq (p-1)/2$,
\begin{equation*}
f_j(n) :=
\begin{cases}
1 & \text{ if } n \equiv j \bmod p, \\
-1 & \text{ if } n \equiv -j \bmod p, \\
0 & \text{ otherwise}.
\end{cases}
\end{equation*}
Clearly, each $f_j$ is periodic with odd prime period $p$, $f_j$ is odd and $f_j(p) = 0$. Moreover, $\sum_{a=1}^p f_j(a) = 0$ and by Theorem \ref{bbw-thm}, $L(1,f_j) \neq 0$ for all $1 \leq j \leq r$. Thus, $f_j \in \mathfrak{F_p}$ for all $1 \leq j \leq r$. Also note that the functions $\{ f_j : 1 \leq j \leq (p-1)/2\}$ are $\overline{\mathbb{Q}}$-linearly independent. Therefore, Theorem \ref{main-theorem-1} implies that at least $\frac{(p-1)}{2} - 3$ of the numbers
\begin{equation*}
\big\{ \gamma_1(a,p) - \gamma_1(p-a,p) : 1 \leq a \leq (p-1)/2 \big\}
\end{equation*}
are transcendental. Since the difference of two numbers being transcendental implies that at least one of them is transcendental, the result follows. $\hfill\ensuremath{\square}$
\section{\bf Concluding Remarks}
\bigskip
Our work here represents a modest beginning into the arithmetic nature of generalized Stieltjes constants. These constants have emerged in other contexts. Most notably, they appear in Li's criterion for the Riemann hypothesis (see for example \cite{coffey}). It is quite possible that the study of these
constants can lead us to the holy grail of mathematics.
\section*{Acknowledgments}
We thank the referee and P. Rath for valuable comments on an earlier version of this paper.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 252 |
# **BECOMING VEGAN**
**EXPRESS EDITION**
**the everyday guide to plant-based nutrition**
Brenda Davis, RD
Vesanto Melina, MS, RD
**BOOK PUBLISHING COMPANY
_Summertown, Tennessee_**
Library of Congress Cataloging-in-Publication Data
Davis, Brenda, 1959-
Becoming vegan express edition / Brenda Davis, RD, Vesanto Melina, MS, RD.
pages cm
Includes bibliographical references and index.
ISBN 978-1-57067-295-8 (pbk.) — ISBN 978-1-57067-903-2 (e-book)
1. Vegetarianism—Health aspects 2. Vegetarianism. 3. Vegetarian cooking. I. Melina, Vesanto, 1942– II. Title.
RM236.D36 2013
641.5'636—dc23
2013023875
_To the visionaries before us and beside us, who have dedicated their lives to making this world a kinder, gentler place:_
Donald Watson, Dr. Frey Ellis, and the founders of the vegan movement
Jay and Freya Dinshah and others who started vegan organizations throughout the world
Bob and Cynthia Holzapfel and the hundreds of courageous plant-based pioneers at The Farm
Albert Schweitzer, John Robbins, Jane Goodall, and all those who have guided our paths to compassion
Michael Klaper, Neal Barnard, Michael Greger, and the many physicians who have dedicated their lives to guiding others toward healthful vegan lifestyles
Virginia Messina, Reed Mangels, Sue Havala, Jack Norris, George Eisman, and the countless dietitians who laid the foundations of vegan dietary wisdom
Cover art: Julia Ruffles
Cover and interior design: John Wincek
© 2013 Brenda Davis and Vesanto Melina
All rights reserved. No portion of this book may be reproduced by any means whatsoever, except for brief quotations in reviews, without written permission from the publisher.
Printed in Canada
Book Publishing Company
P.O. Box 99
Summertown, TN 38483
888-260-8458
bookpubco.com
ISBN 13: 978-1-57067-295-8
19 18 17 16 15 14 13 1 2 3 4 5 6 7 8 9
Printed on recycled paper
Book Publishing Co. is a member of Green Press Initiative. We chose to print this title on paper with postconsumer recycled content, processed without chlorine, which saved the following natural resources:
112 trees
3,509 pounds of solid waste
52,408 gallons of water
9,663 pounds of greenhouse gases
50 million BTU of energy
For more information, visit greenpressinitiative.org.
Paper calculations from Environmental Defense
Paper Calculator, edf.org/papercalculator.
## **CONTENTS**
ACKNOWLEDGMENTS
**CHAPTER 1 Widening the Circle of Compassion**
**CHAPTER 2 The Great Vegan Advantage**
**CHAPTER 3 Protein Power from Plants**
**CHAPTER 4 Fat Matters**
**CHAPTER 5 The Two Faces of Carbohydrates**
**CHAPTER 6 Valuing Vitamins**
**CHAPTER 7 Minding Your Minerals**
**CHAPTER 8 Clean Vegan Eating**
**CHAPTER 9 Triumph over Weight**
**CHAPTER 10 Overcoming Underweight**
**CHAPTER 11 From Pregnancy On: Nourishing Strong Children**
**CHAPTER 12 The Prime of Life: Vegan Nutrition for Seniors**
**CHAPTER 13 The Fit Vegan**
**CHAPTER 14 The Vegan Food Guide**
APPENDIX
RESOURCES
INDEX
## **ACKNOWLEDGMENTS**
We are most grateful for our brilliant and dedicated colleagues at the Book Publishing Company, including publisher Bob Holzapfel; editors Cynthia Holzapfel, Carol Lorente, and Jasmine Star; and the marketing and support team, Anna Pope, Thomas Hupp, and Liz Murray.
Our deepest thanks go to the insightful vegan professionals who provided invaluable feedback on sections or chapters: Michael Greger, Reed Mangels, Jack Norris, Ginny Messina, Paul Shapiro, Mark Rivkin, Andrea Frisque, Heather Waxman, and James Chicalo.
We are indebted to colleagues and friends who took the time to offer support, inspiration, or thoughtful commentary: Margie Roswell, Carolyn Johnston, Margie Colclough, Daneen Agecoutey, and Angelina Rogon.
We appreciate the supportive energy of our research assistants: Renee Webb-Pelchat, Deanna Ibbitson, Carole Douglas, Katherine Jassman, Hana Tahae, and Cory Davis (Brenda's cherished son).
Many thanks for the time and expertise of our gracious advisors: Dr. Luciana Baroni, Dr. Winston Craig, Dr. Michael Klaper, Dr. Paul Appleby, Dr. Joe Millward, Dr. Melvin H. Williams, Dr. Ricardo Uauy, Dr. Ailsa Welch, Dr. Jagoda Ambroszkiewicz, Dr. Undurti N. Das, John Davis, and Freya Dinshah. We also thank Vesanto's son Xoph Crawford for his insights about food and healing. Thanks to young parents Kavyo Crawford (Vesanto's dear daughter), Stefan Shielke, Stephanie Weisner, Ian Hubbard, Kayla Vierling, and Aimée and Daniel Lindenberger.
Boundless love and gratitude to our partners, Paul Davis and Cam Doré, for their continued dedication and support. Special thanks to Cam for his brilliant and ongoing assistance with technical challenges.
Photographic credits and appreciation to Kevin Trowbridge (kevintrowbridge.com) and his assistant Katherine Trowbridge.
We are also grateful to those who generously shared their excellent products for recipe testing: Kelly Saunderson of Manitoba Harvest (hempseeds), Omega Nutrition (quality oils), Nature's Path Foods, and Adeline Cheong of LeSaffre Yeast Corporation (Red Star Vegetarian Support Formula nutritional yeast). We also thank ESHA Research for their fine nutritional analysis program, the Food Processor.
## **CHAPTER 1**
## **Widening the Circle of Compassion**
It takes immense inner strength and courage to oppose the status quo. Yet if people hadn't risen up against social injustice, women wouldn't have the vote, the poor would have remained uneducated, and slavery would be legal. What does social justice have to do with a vegan lifestyle? Nothing, if you regard animals as resources; everything, if you recognize them as sentient beings.
It is possible that the greatest social injustice of our time is committed not against our fellow human beings but against our fellow _non_ human beings. Becoming vegan is about taking a stand against this injustice.
### **Vegan Awakenings**
The seeds of vegan ethics were sown by philosophers and spiritual leaders in the East and spread in the West by the sixth-century Greek philosopher and mathematician Pythagoras, who shunned the consumption of animal flesh and directed his followers to do the same. While many other legendary thinkers, including Plato, Plutarch, Seneca, Ovid, and Socrates, followed suit, it wasn't until the mid-1800s that the moral roots of vegetarianism were firmly established in Western culture. The epicenter was England, and the driving forces were moral leaders of select Christian churches. While the movement was becoming wellgrounded in the West, its influence was limited when contrasted with the practices and teachings of the East, where Buddhism, Jainism, and Hinduism emphasized compassion toward animals and vegetarianism as a part of their core doctrines.
The word _vegetarian_ was coined by the founders of the British Vegetarian Society in 1842. The word has nothing to do with vegetables and actually comes from the Latin word _vegetus_ , which means "lively, fresh, and vigorous." The ethics of consuming dairy products were hotly debated within the burgeoning UK vegetarian movement, but there is good evidence that the first people to call themselves vegetarians were actually what we now call vegans. Eventually, a small, like-minded group of individuals decided to branch off and promote an entirely new breed of vegetarians, then called nondairy vegetarians.
The father of the contemporary vegan movement, Donald Watson, and his British compatriots recognized that the flesh food industry and dairy product industry were inextricably linked. They contended that the case against the dairy industry rivaled that against the meat industry, and that the use of dairy products was no longer justifiable for ethical vegetarians. Their intent was to eliminate the exploitation of both animals and humans and move closer to a truly humane society. Together, they founded the first vegan society in 1944 with only twenty-five members. Watson coined the word _vegan_ (pronounced "VEE-gun") to describe vegetarians who exclude all animal products from their diet and lifestyle. In the 1950s, London physician Frey Ellis joined their ranks, significantly strengthening the scientific understanding of vegan health.
In 1948, Dr. Catherine Nimmo and Rubin Abramowitz established the first vegan society in the United States in Oceano, California. The group continued until 1960, when a national organization, the American Vegan Society (AVS), was founded by H. Jay Dinshah. The society has consistently encouraged the active practice of _ahimsa_ —a Sanskrit word meaning "dynamic harmlessness"—as a part of a vegan lifestyle. Ahimsa, which is embraced by AVS as an urgent, worldwide necessity, advocates six pillars, one for each letter of the word:
Abstinence from animal products
Harmlessness, with reverence for life
Integrity of thought, word, and deed
Mastery over oneself
Service to humanity, nature, and creation
Advancement of understanding and truth
In 1987, veganism was catapulted into the mainstream by author John Robbins with the release of his groundbreaking book _Diet for a New America_. Robbins's book provided the first hard-hitting exposé of the consequences of factory farming on food animals, the environment, and human health. Today, vegan groups and societies exist in more than fifty countries.
### More Than Diet
Many people believe that being vegan is about eschewing hamburgers and ice cream. It is not. Being vegan is about making an ethical decision to widen your circle of compassion and take a stand against deeply rooted customs and traditions—customs that are often strongly held by people we love, respect, and admire. For most of us, this triggers a long, hard battle with our conscience in which our conscience ultimately prevails.
Being vegan is about including those who are commonly excluded, be they human animals or nonhuman animals. It's about understanding that our choices have consequences for ourselves and beyond ourselves and recognizing that eating animals and animal products is both unnecessary and potentially harmful. Being vegan is about making choices that are a true reflection of our ethical and moral principles.
So how does a philosophy of reverence for life and compassion for all living things translate to diet and lifestyle? In terms of diet, the primary approach is excluding meat, poultry, fish, dairy products, eggs, gelatin, and other foods of animal origin, while allowing all foods of plant origin, including vegetables, fruits, legumes, grains, nuts, and seeds. But a vegan _lifestyle_ takes it a few steps further.
A vegan lifestyle also excludes—as far as possible and practical—animal exploitation. A vegan avoids all products derived from animals—not just meat, eggs, and dairy products, but also certain consumer products. A vegan doesn't wear clothing produced from fur, leather, wool, or silk or use personal care or cleaning products that contain animal-derived ingredients. A vegan also avoids products and activities that involve the mistreatment or misuse of animals, including research conducted on animals and entertainment that exploits animals.
There are degrees of veganism. A _pure vegetarian_ or _dietary vegan_ is someone who consumes a vegan diet but doesn't lead a vegan lifestyle. Pure vegetarians may use animal products, support the use of animals in research, wear leather shoes or wool clothing, or have no objection to the exploitation of animals for entertainment. They are generally motivated by personal health concerns rather than by ethical objections. Some may adopt a more vegan lifestyle as they are exposed to vegan philosophy.
You may wonder how vegan you have to be to call yourself a vegan. Essentially, if you identify as a vegan and strive to avoid animal products and activities that exploit animals, you are vegan, even if you slip on occasion. There are no vegan police scrutinizing your diet and lifestyle habits. Being vegan isn't about personal purity or moral superiority. It's about making a conscious choice to widen your circle of compassion by avoiding animal exploitation as much as possible and practical.
In today's world, it is virtually impossible to be 100 percent cruelty-free. Traces of animal products lurk almost everywhere—as red dye in candy, as filters in the processing of wine, and in phones, matches, sandpaper, theatrical lighting, photographic film, cars, bicycles, planes, computers, and the list goes on. Our efforts to live with compassion far exceed our ability to eliminate the trace amounts of animal products that permeate our marketplace. Besides, there are instances in which the use of a nonvegan product can result in a reduction in animal suffering. Think back to the time before digital cameras. Had we avoided photography because film utilizes animal products, thousands of people moved by graphic images of exploited animals would have continued to exploit them. The vegan lifestyle is a means to an end—which is to reduce animal suffering—and not the end itself.
### Their Plight, Our Power
Some people view everything on this planet as a resource that is here for the taking. To them, animals exist only to serve humans. This logic is used to defend the exploitation of animals for fashion, entertainment, experimentation, research, and food. There is often controversy about how animals should be treated in the process, but the actual use of animals is generally not a point of contention for the majority of people in our society.
Perspectives on the appropriate treatment of animals can vary widely from culture to culture. In America, kittens and puppies are beloved pets. In China, they may be skinned and boiled alive for dinner. While the very thought may disgust Americans, they don't give a second thought about dining on lobster. Some people would argue that dogs and cats are more intelligent than lobsters so they deserve to be treated more kindly, yet our treatment of pigs, which are more intelligent than dogs, is arguably worse than our treatment of lobsters.
The industry responsible for the overwhelming majority of animal suffering is the food industry. More than 95 percent of all animals purposefully killed by people are killed to be eaten.
### The Making of Meat Machines
Forget the bucolic scenes from your favorite childhood storybooks. The lives of today's farm animals bear no resemblance to those fairy tales.
In 1900, 41 percent of Americans lived on farms; one hundred years later, that figure had dropped to 1.9 percent. With the rising consumption of animal products, how is it possible to supply sufficient meat and milk to satisfy so many people with so few farmers? In a word, agribusiness. In terms of animal products, the goal of agribusiness is to transform animals into production units, generating the greatest amount of meat, milk, or eggs for the least amount of money. The most efficient way to accomplish this is to bring the animals from the fields to factories and do whatever it takes to minimize the time it takes to get them to slaughter.
This quest has become a science in and of itself. Among the most timehonored techniques are keeping animals in small spaces, giving them hormones so they gain more weight more quickly, stimulating their appetite, breeding them for rapid growth, feeding them antibiotics to control disease, and using cheap feed. The result is what the industry terms "concentrated animal feeding operations" (CAFOs), more commonly known as factory farms.
Every year in North America, approximately eleven billion land animals are slaughtered for food. Of these, almost 80 percent of cattle and almost all chickens, laying hens, turkeys, and pigs are raised in factory farms. These animals, so vigilantly hidden from view, endure unspeakable suffering, but the average consumer is so far removed from the animals' lives that they easily forget that the meat at the grocery store is the flesh of an animal.
#### **A PIG'S LIFE**
When living in their natural environment, pigs live in groups of six to thirty. They are remarkably clean and particular, having separate sites for eating, sleeping, grooming, and elimination. Pigs are playful and protective and have complex social systems. They love to bathe in water, and while they do roll in mud, this behavior is necessary for temperature regulation since they lack sweat glands and are prone to heat stress. The mud also protects them from insects and sunburn. Pigs have been shown to be more intelligent than dogs or even threeyear-old children. They have remarkably long memories and can learn to play simple games every bit as quickly as primates. They can even be highly skilled at video games, learning to play with a joystick designed for them.
The natural life span of a pig is ten to fifteen years, but pigs raised for food in the United States live only about six months. Breeder sows live until their reproductive ability wanes, generally three to four years. Most of this time is spent in crates with insufficient room for them to turn around. Although piglets are usually weaned at about fifteen weeks, in intensive farming they are removed from their mothers for fattening after only two to four weeks of nursing, and the sows are then impregnated again.
Weanlings spend the next six weeks in "nurseries," which are generally wire cages stacked one on top of the other. Piglets who don't grow fast enough are typically "euthanized" by three weeks of age. Although there are a variety of methods for killing them, the most common is blunt trauma to the head, often by picking them up by their hind legs, swinging them, and slamming their heads onto a concrete floor.
Healthy piglets receive medication to prevent the diarrhea that results from eating solid foods, which they are too young to properly digest. Most undergo a variety of mutilations, including castration for males, ear notching, tail docking, and tooth clipping. These agonizing procedures, done primarily to reduce stressrelated behaviors, are performed without painkillers.
The animals destined for meat production are transferred to cramped pens until they reach a slaughter weight of 240 to 300 pounds. The pigs are crammed together in single stalls or groups, with no room for rooting, exploring, nesting, or other natural social behaviors. The floors are commonly metal grid systems that allow urine, feces, and vomit to fall into a huge pit below. The air inside these facilities is riddled with dust, dander, ammonia, and other noxious gases. Not surprisingly, respiratory diseases are endemic. Pig factories are fertile breeding grounds for communicable diseases. In order to ensure the animals' survival until the time of slaughter, antibiotics, hormones, and other drugs are routinely added to their feed.
The only time many of these animals see the light of day is during the trip from their pens to the truck that transports them to the slaughterhouse. It is estimated that one million US pigs die en route to slaughter each year from crushing, freezing, dehydration, or disease. If animals are frightened and resist loading, unloading, or moving forward in slaughterhouse chutes, they are prodded with high-voltage electric rods. Sometimes animals are beaten with metal pipes or kicked by frustrated handlers.
The first step in pig slaughter is stunning the animal with electricity or CO2 to render it unconscious. The pig is then dragged upside down using chains or ropes around the back feet. Unfortunately, electrical stunning isn't always effective, and reports of animals squealing and kicking wildly are not uncommon. Next comes the "sticker," the person who slits the pig's throat. If the sticker is unsuccessful, the pig continues along the line to the scalding tank, where it is boiled alive to remove its hair. All of this is done quickly, at line speeds of more than one thousand pigs per hour.
Consumers provide a resounding stamp of approval and a financial incentive to continue these practices every time they buy a pound of bacon or a few slices of ham from a grocery store. In the United States, an estimated 110 million pigs were slaughtered for food in 2010. Globally, 1.3 billion pigs per year end up on dinner plates.
#### LITTLE RED HENS
Chickens are sociable animals that live communally in flocks. Each flock has a well-established "pecking order" in which dominant individuals receive priority in regard to food and nesting areas. Each individual knows its place in the flock and remembers the faces and ranks of up to ninety other birds.
Chickens are far more intelligent than most humans give them credit for. Chicks learn by observation. They can count, and they have self-control and a sense of time and object permanence—a skill human babies don't acquire until they're six or seven months old. Chickens can also anticipate events and predict outcomes. One research team set up a reward system for chickens using colored buttons. If the birds waited two to three seconds to peck on the buttons, they would receive a small amount of food, but if they held out for twenty-two seconds, they were rewarded with a jackpot of food. After learning the rules, more than 90 percent of the time the chickens held out for the jackpot.
More than nine billion chickens, turkeys, ducks, geese, pheasants, quail, and other fowl are slaughtered in North America every year for food, the vast majority being chickens. And more than 95 percent of chickens raised for food in North America are raised in total confinement from birth to death. They are either raised for meat (broilers) or eggs (layers). (For "free-range" conditions, see "The Problem with 'Cruelty-Free,'" on page 12.)
#### **Broilers**
Broiler chickens, also called broiler-fryers, are generally raised on open floors in huge metal sheds that often house 20,000 or more birds per shed, with 150,000 to 300,000 birds per operation. The average space per animal is less than one square foot. This overcrowding causes extreme stress and escalates the risk of injury and disease.
Because of the popularity of breast meat, broilers are selectively bred to have bigger breasts and are almost twice as heavy at slaughter as their ancestors from the 1950s. This selective breeding causes muscle growth to surpass bone growth, resulting in deformities, fractures, tears, and ruptures. Many birds are literally crippled under their own weight. Some starve to death because they can't physically access food or water because of their deformities, and some die of heart attacks or organ failure.
At only six or seven weeks of age, the birds reach market weight. A single catcher will grab the legs of three or four birds per hand and load 1,000 to 1,500 birds per hour into crates for transport to slaughter. The process is highly stressful and commonly associated with serious and sometimes fatal injuries. At the slaughterhouse, chickens are dumped onto conveyor belts and hung upside down on a moving rack. There is no requirement for stunning prior to slaughter because chickens are exempt from the Humane Slaughter Act. Instead, they are subjected to an electric water bath that paralyzes them but doesn't always render them unconscious. If they aren't unconscious, their throats are slit so they can die prior to being plunged into scalding water to loosen their feathers. For some unfortunate birds, this process is also unsuccessful, so they drown in scalding hot water.
#### **Layers**
Egg-laying hens are packed into wire battery cages so tightly that they are afforded less than half the space of broilers, only about 67 square inches per bird. This is slightly more than half the size of a standard sheet of paper. For perspective, a hen needs about 72 square inches of space to be able to stand up straight, 178 square inches to preen, and 291 square inches to flap her wings. This degree of overcrowding makes it impossible for the birds to carry out natural behaviors such as nesting, perching, roosting, foraging, taking a dust bath, preening, or exploring. In order to manage the aberrant behavior resulting from these conditions, about one-third to one-half of the beak is seared off with a heated blade to prevent birds from pecking one another to death. This amputation is conducted without anesthetic and causes severe nerve injury and acute and even chronic pain.
Many egg factories also subject their birds to the practice of forced molting in an effort to induce another egg-laying cycle. During this time, food is either completely withheld or restricted for ten to fourteen days, causing weight losses of up to 35 percent of body weight.
The entire system, from feeding and watering to egg collection, is typically fully automated. The cage floors slope forward so that eggs roll onto a conveyor belt that transports them directly to the cleaning stations. Layers are productive for one to two years, after which time egg production drops below the level necessary to provide an economic return. These "spent" hens are genetically selected for efficient egg production, and they don't have much meat on them. Because a great deal of calcium is required for egg production, they also have very fragile bones that break easily during handling. These two factors make these birds of little value to processors. Traditionally, spent hens were used for soup and school lunch programs, but with the large supply of broilers available there is little demand for these smaller birds, so they are gassed to death and then incinerated or ground up and fed to other animals, including other chickens.
Of course, in order to keep the industry going, new layers must constantly be produced. At one day old, chicks are sexed to determine their fate. A total of 260 million male chicks born each year in the United States have no economic value because they can't lay eggs and are poor meat producers, so they are immediately disposed of in several grisly manners: ground up alive, gassed, suffocated, electrocuted, even put through a wood chipper.
#### CATTLE, DAIRY COWS, AND CALVES
Today's domestic cattle provide humans with about half of their red meat, about 80 percent of their leather, and 95 percent of their milk. Although they are subjected to branding, dehorning, and, for males, castration, all without painkillers, their lives seem rather enviable when compared with pigs or chickens.
#### Beef Cattle
Beef cattle are among the few food animals that spend their lives outdoors, with their first seven to nine months in pasture. When they reach about 650 pounds, cattle are taken to a feedlot for "finishing." Most finishing facilities house more than 1,000 head of cattle, and larger operations accommodate 30,000 to 150,000 animals. At the feedlot, they receive a high-energy, grain-based diet designed to pack on about 400 pounds in three to four months. Of course, adding about 100 pounds per month by feeding the animals an unnatural diet has consequences for the animals' health. Cattle are perfectly designed to eat a diet that is foraged, extremely high in fiber, and low in starch. A grain-based diet causes a variety of health problems and, in severe cases, can lead to liver abscesses, acidosis, and bloat.
Feed is routinely laced with antibiotics to help promote growth and reduce the risk of diseases induced by these intensive feeding systems. Livestock now receive an estimated 70 percent of all the antibiotics used in the United States, which contributes to the increasing problem of antibiotic-resistant bacteria. But the antibiotics don't seem to be doing the job: One study showed that almost half of 136 samples of meat and poultry taken from twenty-six grocery stores in five US cities tested positive for the disease-causing bacteria _Staphylococcus aureus_. Almost all of the staph bacteria tested were resistant to at least one antibiotic, and at least half were resistant to three or more.
Cattle producers have used growth hormones since the 1950s to make the animals grow larger more quickly on less feed. This reduces cost and produces leaner meat, which is more in line with consumer preferences. Currently, approximately two-thirds of all cattle and about 90 percent of feedlot cattle receive growth hormones. In large commercial feedlots, they are used in almost 100 percent of the animals.
Hormone residues that remain in beef may act as endocrine disruptors in humans, interfering with the actions of natural hormones in the body. They may also affect fertility, age of onset of puberty, and the risk of certain cancers in people who eat the meat. In addition, hormones wind up in feedlot waste and often contaminate local water sources.
The final journey for cattle is to the slaughterhouse, where 300 head per hour file one by one up a ramp to be stunned and hoisted into the air, and then have their throats slit and make their way down the disassembly line.
Not surprisingly, slaughterhouses are among the most dangerous workplaces in North America. At one time, most slaughterhouse workers were unionized and had good pay and stable jobs. Line speeds were slower, and the work was relatively safe. Today, most slaughterhouses are nonunionized, the pay is low, and workers are largely immigrants. Line speeds have escalated, and accidents have multiplied. Because meatpacking plants receive fines for high injury rates, plant managers and owners have been caught keeping records that misrepresent the actual occurrence of injury and illness by as much as 1,000 percent.
#### **Dairy Cows and Veal**
Some vegetarians believe drinking milk and eating eggs are reasonable choices because the animals don't have to die for us to take their milk or eggs. While animals don't _have_ to die to produce these items, they're almost always sent to slaughter once their efficiency wanes. The current intensive methods of milk and egg production result in suffering and death on par with that in meat production, and in the case of eggs, probably more.
In the early 1900s, the average dairy cow produced about 3,000 pounds of milk per year. By 1950, annual milk production per cow had almost doubled, and today each animal produces an astounding 17,000 pounds of milk per year—almost a sixfold increase in milk production in one century.
In the 1950s, most farm families had at least two dairy cows to ensure yearround dairy products for their family. Typical dairy farms had about a dozen cows, and the very largest farms boasted 50 to 100 cows. Today, standard dairy farms exceed 100 cows, with many large facilities housing 700 to 1,000 animals and the largest accommodating several thousand animals.
Every aspect of dairy farming is designed to maximize production and profit. Dairy cows begin their cycle of milk production by being impregnated, generally by artificial insemination, at about thirteen to sixteen months of age. They are then impregnated once a year to ensure a steady production of milk. In most cases, calves are separated from their mothers within a day of birth. Although the separation is extremely traumatic for both mother and calf, allowing more time together would strengthen their bond and increase the stress of separation.
Female calves are raised to replace the "spent" cows, but male calves, of course, are of no use to the dairy industry, except for the few that are used for breeding. Among the remainder, the more fortunate males are funneled into the beef industry. The rest become veal calves. In the United States, this generally means "special-fed veal," also called "white veal" or "milk-fed veal," terms that reflect the market's desire for light-colored meat. This is achieved by feeding the calves an iron-deficient milk replacement, and the tenderness of their flesh is assured by tethering them in small stalls so they can't move and develop their muscles.
Most veal calves are slaughtered at the age of sixteen to eighteen weeks. That may seem young, but the remaining 15 percent of US veal, called "bob veal," comes from calves ranging from two days to three weeks of age.
More than 80 percent of dairy cows are confined in primarily indoor systems, with some having access to barnyards. Fewer than 10 percent are raised on pasture. Some are reared in stalls where they are tethered at the neck, while others are permitted to roam within the barn.
These methods of rearing trigger two key conditions: lameness and mastitis. Lameness occurs in an estimated 14 to 25 percent of cows and is caused primarily by hoof lesions associated with concrete flooring and insufficient physical activity. This painful condition is the leading cause of dairy cow deaths. Extremely high milk production and bacterial infections caused by poor sanitation can trigger a painful swelling and infection of the mammary glands called mastitis, the most common medical condition among dairy cows and the second leading cause of their death. One factor that is strongly associated with both lameness and mastitis is the use of recombinant bovine somatotropin, also known as rBst or recombinant bovine growth hormone (rBGH), a genetically engineered hormone that increases milk yields. By the age of four, most US Holstein cows have produced milk for about 729 days and are no longer of use to the industry, so they are slaughtered. Their natural life span would have been more than twenty years.
#### SOMETHING FISHY
Until recently, science didn't pay much attention to fish as sentient beings. Few believed that fish had much capacity to think, and even fewer believed that they had the capacity to feel. Since the 1990s, however, a steady stream of studies has forced us to rethink this position. We now know that fish form relationships, recognize other individuals, pass on knowledge and skills, have long-term memory, solve problems, collaborate in hunting, use tools, strategize, experience fear and distress, and avoid risky situations. There is no longer any doubt that fish feel pain, although it is difficult for us to weigh the extent of their suffering against that of mammals because it is expressed differently.
Health authorities advocate eating more fish to reduce the risk of disease, but concerns about exploitation of these creatures and the impacts of fishing practices grow by the year. The commercial fishing industry is divided into two sectors, each harvesting roughly half of the seven billion fish (excluding shellfish) killed per year: commercial, or capture fisheries, and aquaculture, or fish farms.
#### Capture Fisheries
The consequences of our current fishing practices for marine ecosystems are incalculable. More than half of all monitored fish stocks are now fully exploited, meaning that we have reached our limit for catching this species and capturing any more will threaten its survival. Another quarter is overexploited, depleted, or slowly recovering. More than 90 percent of the global predatory fish population has been wiped out, yet consumers continue to be urged to eat more fish. If current trends in fishing continue, all stocks could collapse by 2048, meaning it would be unlikely that endangered fish species could make a comeback.
Capture fisheries use a wide range of catching techniques, many of them highly malicious, such as dynamiting coral reefs, exceedingly efficient bottom trawling, longlining, gillnetting, and purse seining. In addition, poisons are routinely used to paralyze or stun fish for aquariums or live-fish restaurants, killing reefs in the process. Less ecologically destructive systems are also commonly used. Sharks, for example, are caught using hooks. Their fins are cut off and the living animal is then returned to the ocean, where it slowly suffocates because water must be moving over its gills in order for it to breathe, yet it no longer has fins for swimming—all because shark fins, a delicacy in Asian cuisine, fetch a premium price.
The depths of the oceans are among the most pristine ecosystems remaining on our planet. They are the homes of yet unnamed species that may well become extinct before they have even been identified. It's estimated that 95 percent of damage to these ecosystems results from deep-sea bottom trawling. Huge nets with metal plates at each end and metal wheels along the bottom are dragged along the ocean floor like giant underwater bulldozers, demolishing seafloor ecosystems. This is the underwater equivalent of clear-cutting. As the nets are brought to the surface, fish and sea animals caught in the nets experience extreme decompression, causing vital organs to rupture. Among the worst offenders are shrimp trawlers, which "unintentionally" kill up to 20 pounds of marine life for every pound of shrimp plucked from the net. This "bycatch," as it's known, includes sea turtles, dolphins, sharks, and numerous other fish and nonfish species that are simply tossed overboard.
Longlining uses one or more main lines with short attached lines with hooks at the ends. The main lines can be as long as 75 miles, holding hundreds or thousands of baited hooks. They are set at varying depths in the water depending on the target species. Fish captured by longlines can by dragged behind a boat for hours or even days. The longline industry is notorious for killing millions of marine mammals, including birds, dolphins, sharks, and turtles. It is, however, less destructive to the ocean floor than bottom trawling.
Gillnetting is a method that uses huge nets measuring hundreds of feet to over a mile long to snare target fish. Fish attempt to swim through the openings in the mesh nets, but their gills become trapped, so they can't escape. Other species may be small enough to swim through or large enough that their gills aren't snagged. Gill nets are often left unmonitored for long periods, so the trapped fish slowly suffocate.
Purse seining is another type of fishing that employs large nets. The purse seine gets its name from its structure: a rope passes through a series of rings that run along the bottom of the net, which can be pulled to completely close the net at the bottom, like a giant drawstring bag. Purse seining is the preferred method of capturing fish that congregate in schools near the surface of the water. One of the primary concerns about purse seining is that dolphins are commonly trapped in the nets. Fish are often still alive when they are pulled on deck and are conscious when they are slit and gutted.
#### **Aquaculture**
The imminent global collapse of wild fish stocks is driving a massive shift from capture fisheries to fish farming. Aquaculture or aquafarming, popularly called fish farming, is the fastest growing animal-based food sector in the world. In 2008, an estimated 46 percent of fish consumed worldwide were raised on farms, up from only 9 percent in 1980. Some fish farms are based on land, using ponds, pools, tanks, or man-made waterways. Others are created near ocean shorelines, with the fish being held in the water in huge nets, pens, or cages. All are intensive operations, similar to factory farms for land animals.
The goal of fish farming is no different than that of factory farming: to generate the greatest amount of meat for the least amount of money. Fish farms maintain a density of animals that seldom occurs in the wild. As a result, fish can become sick or infected, and the usual response is antibiotics, antimicrobials, and other pharmaceuticals.
The consequences of these intensive operations are widespread and severe, although we can only speculate how severe for the individual animal. Crowding, an inappropriate physical environment, polluted water, and disease outbreaks can cause stress, fear, discomfort, and pain in fish. But the most pressing concerns are the welfare of all sea creatures, the negative effects on the environment, and the toll on wild fish.
Waste, food pellets, and drug residues from fish farms seriously threaten ecologically sensitive areas, such as mangrove swamps, coastal estuaries, and salmon migration routes. Untreated waste goes directly into the ocean, where it affects sea life and water quality. Aquaculture operations also fuel harmful algal blooms, a proliferation of toxin-producing algae that that can cause massive die-offs of fish, shellfish, marine mammals, seabirds, and the animals that consume them.
The strongest argument used to justify fish farming has been that it protects wild fish. Paradoxically, for carnivorous sea animals, fish farming could do the opposite, because a farmed carnivorous fish has to eat 2.5 to 5 pounds of wild fish to produce 1 pound of flesh. In addition, farmed fish can escape, infecting wild fish with diseases, sea lice, and other parasites. When nonnative species escape into nearby waters, they can devastate native fish populations by competing for food and habitat.
In addition, the fish industry hasn't escaped genetic engineering. While not yet approved for market sales, salmon, prawns, and abalone are currently being genetically altered. Atlantic salmon, for example, have been modified with genes from Chinook salmon so they reach market size in half the time. Genetically modified fish that escape into the wild, as many fish farmed in open systems do, pose a significant threat to related native species if they interbreed.
### **The Problem with "Cruelty-Free"**
People often wonder what could possibly be wrong with eating meat from free-range animals that are raised on organic feed and treated well. This brings up an important distinction in ethical perspectives.
Vegans are ethically opposed to the exploitation of animals. Vegans don't view animals as ours to use and therefore reject the notion that if animals are treated well, we are justified in killing and eating them. While most people agree that animals raised for food should be treated humanely, only a rather small percentage seem to be willing to actually pay more for meat, milk, and eggs from such animals. In addition, consumers who say they prefer products from humanely treated animals often make concessions when eating out or if they can't find those foods at the store.
Although a small percentage of consumers go directly to small local farmers to buy "humane" products, most shop at grocery stores, where consumers must rely on catchphrases on food labels, such as "free-range," "cage-free," "grass-fed," and "humanely raised," to determine whether the product came from an animal treated in an acceptable manner. Unfortunately, there is no independent inspection or verification to ensure that farmers are living up to consumer expectations. These animals are still generally bred by the thousands, kept in crowded conditions, and removed from their mothers shortly after birth. Chickens are usually still debeaked, and the male offspring are still disposed of. Even in facilities that offer "access to the outdoors," the access can be a small opening to an outdoor enclosure that is inaccessible to many of the animals crowded into the building.
Of course, in the end, all food animals meet the same fate, regardless of how they are raised. While a few are slaughtered on small farms, most are killed in the same facilities that slaughter animals raised on factory farms. The fact that they may have suffered less than most other farm animals doesn't justify their exploitation in the first place.
We have just scratched the surface of the animal rights argument for veganism. We encourage you to dig deeper and learn more about these issues. For a list of recommended books and films, see nutrispeak.com/resources or the resources link at brendadavisrd.com.
### Paying the Price with Our Planet
The human species is consuming the earth's resources more rapidly than they can be replenished, and our food choices may be the greatest contributor to this depletion. If we all ate the average American diet, it would take 3.74 earths to sustain our current population of about 7 billion people. By 2050, there will be an estimated 9.2 billion people on the planet; at that point, even if every individual minimized their carbon footprint by using 95 percent renewable energy and consumed a plant-rich diet, we would still need the equivalent of 1.3 planets to sustain the population. Celebrated environmentalist Paul Hawken notes that if every single company on earth were to adopt the highest environmental standards and policies, we still couldn't forestall the environmental collapse of our planet.
The earth has a limited capacity to produce precious resources on which our lives depend, from oxygen and algae to soil and trees. When we use more than what is produced and the earth can't keep pace, our manner of living is no longer sustainable for future generations. The global population is growing by a staggering 250,000 people per day, or 166 people per minute. Our fragile planet is ill-equipped to handle an exponentially increasing population of human beings. The ecological crisis we face is a reflection of sheer numbers, and perhaps sheer greed.
Humans have essentially attempted to outwit Mother Nature, but we are slowly coming to realize that the laws of nature are not up for grabs. Our tireless effort to reinvent the natural order to suit our own species only puts us at greater risk. The network of life depends on a complex food web. The lowest level of the food web sustains plants, which in turn sustain animals, with both plants and animals constantly recycling nutrients back into the soil. Humans have altered the food web to such an extent that many species and entire ecosystems must adapt or perish. But eventually the toll will become so great that the entire system will collapse. While some believe that we already are beyond the point of no return, we must do what we can—if not for ourselves, for our children, and if not for our children, then for all other species, whose future we hold in our hands. Our greatest hope lies _within_ the laws of Mother Nature. She has beckoned us for years, and we have largely ignored her. Now her patience is wearing thin.
When considering human impacts on the environment, most people focus on the use of fossil fuels, but another activity has an equal impact: raising livestock. Many experts have already suggested that a global shift toward a vegan diet can protect the world from increased hunger and poverty and the worst impacts of climate change. There is no question that intensive animal agriculture is among the most notorious polluters of air, water, and soil, and one of the greatest contributors to deforestation, desertification, and the extinction of species. The shift toward a vegan diet may well be the most powerful step an individual can take toward the preservation of this planet, and at this point, it may be an ecological imperative.
#### **GLOBAL WARMING**
These days, when people think about going green with their diet, the focus is usually on eating local. The idea is that fewer miles in transport trucks cuts the use of fossil fuels. They may not realize that the majority of food-related greenhouse gas emissions are due to food _production_ rather than food _miles_.
According to a United Nations Food and Agriculture Organization (FAO) report called Livestock's Long Shadow, livestock are responsible for 18 percent of greenhouse gas emissions—more than all forms of transportation combined. Efforts to curb global warming, both nationally and internationally, have concentrated largely on reducing or capping CO2 emissions. When we clear forests to make room for food animals, run farm machinery, bring in feed, or transport animals, CO2 is released. Fertilizers generate nitrous oxide, and manure releases methane (as do cow burps and flatulence). One-fifth of human-generated greenhouse gas emissions—9 percent of the CO2, 37 percent of the methane, and 65 percent of the nitrous oxide—comes from livestock production. When compared to CO2, the global warming effects of methane are 23 times greater, and those of nitrous oxide are 296 times greater.
Transportation accounts for only 11 percent of food-related greenhouse gas emissions, and final delivery from the producer to retail stores is responsible for one-third of that (4 percent of all emissions). The other two-thirds of transportation-related emissions originate from production (feed for animals, fertilizer for vegetables, resources for processing, and so on). Within the category of food production, 44 percent of greenhouse gases are CO2, 32 percent are nitrous oxide, 23 percent are methane, and 1 percent are other gases. So the impact of food on climate change is due mainly to greenhouse gases other than CO2. Nitrous oxide and methane emissions are most strongly linked to the red meat and dairy industries.
The bottom line is that livestock animals consume far more food than they yield. It takes about 15 pounds of feed to make 1 pound of beef, 6 pounds of feed for 1 pound of pork, and 5 pounds of feed for 1 pound of chicken. Consumers are always being told to use alternative energy sources, select fuel-efficient appliances, and drive low-emission vehicles, but how many have heard that they should eat veggie burgers instead of hamburgers? Ultimately, the average consumer could reduce his carbon footprint more effectively by eating 100 percent vegan _one_ day a week than by eating 100 percent local _seven_ days a week. If everyone in the United States were to do this, the effect would be equivalent to taking 31.5 million cars off the road.
#### **WATER**
Water is intrinsically tied to our food supply and to the maintenance of our ecosystems. More than one billion people worldwide are experiencing water shortages, and water pollution affects many more. In addition to threatening human food supplies, water shortages and water pollution severely reduce biodiversity and boost rates of infectious diseases.
In 2009, approximately 45 percent of freshwater in the United States was deemed unfit for drinking or recreational use because of contamination by dangerous microorganisms, pesticides, and fertilizers. A year later, an assessment by the World Wildlife Fund's _Living Planet Report 2010_ found that the global freshwater Living Planet Index (LPI), a measure of the earth's biodiversity and a solid indication of humanity's demands on the earth's resources, declined by 35 percent between 1970 and 2007, and the tropical freshwater LPI declined by almost 70 percent.
Animal agriculture is one of the leading threats to our water systems. It takes 43 times more water to produce 1 pound of beef than to produce 1 pound of grain—about 5,160 gallons of water per pound of beef (43,000 per kg) and about 120 gallons per pound (1,000 liters per kg) of grains. According to the US Environmental Protection Agency (EPA), the agricultural industry is "the leading contributor" to the pollution of US waterways. On the global scale, an estimated 70 percent of freshwater consumption is for agricultural production.
In the United States, factory farms produce approximately 500 million tons of raw waste every year, about triple that of the human population. A farm with 2,500 dairy cows produces about the same amount of waste as an entire city of 411,000 people. Human waste must be treated before finding its way into our water systems, yet no such requirements exist for animal waste.
On factory farms, animal manure is stored in open pits or huge holding tanks before being spread on fields as fertilizer. But concrete manure pits can crack, and if laid in sand or gravel, manure can leak out and work its way into groundwater. Tanks can also overflow and pollute nearby surface water. If the waste is applied to fields at a rate greater than the ability of the soil and crops to absorb and utilize it, the excess can release toxic gases into the environment and contaminate waterways with pathogenic bacteria, carbon compounds, nitrates, phosphorous, antibiotics, hormones, sediments, heavy metals, and ammonia. Pathogenic bacteria can end up in nearby rivers and streams, which may in turn be used to irrigate vegetable crops; most vegetable-related food-borne disease outbreaks can be traced back to contamination from nearby factory farms.
Carbon compounds, which are the primary constituents in manure, can contribute to oxygen depletion in water. In addition, water runoff from contaminated farms and fields contains nitrogen and phosphorus—about half to two-thirds of it from poultry farms—which cause dead zones in water systems where algal blooms deplete oxygen from the water and choke out aquatic life.
Antibiotics and both natural and synthetic hormones also make their way into surface water and groundwater when released in manure. According to the EPA, as much as 80 percent of antibiotics administered orally to livestock end up in manure _unchanged_. This poses a significant concern for human health, since the routine use of antibiotics in animals can lead to antibiotic resistance in pathogenic bacteria and reduce the effectiveness of antibiotics in people who become infected with these organisms. There are also serious concerns about the health consequences of hormone use in livestock production, which has been directly linked to increased rates of breast, prostate, and testicular cancer.
#### **LAND**
The livestock industry is by far the largest user of land on earth, utilizing 30 percent of the land surface of the planet and 70 percent of all agricultural land. Therefore, it has a massive impact on both the quality and quantity of available soil, generally damaging and depleting it. Plus, intensive farming and monocrop agriculture deplete the soil of nutrients and cause erosion, and overuse of fertilizers and pesticides causes serious contamination.
Every year, US cropland loses soil at a rate thirteen times higher than what is considered sustainable, and ranges and pastures lose soil at a rate six times higher than is sustainable. An estimated 60 percent of US pastureland is overgrazed. In a 2006 report to the US Senate, the Nutrition Security Institute stated that if soil loss continues at present rates, it is estimated that there are only fortyeight years of topsoil left on the planet. By 2054, the earth's farmable topsoil will be gone, as will our ability to provide food to the nine billion people who are expected to occupy this planet. Soil forms at a rate of about 1 inch every 381 to 1,270 years, so waiting for soil regeneration is not an option.
Raising livestock is among the leading causes of deforestation globally, particularly in rain forests such as the Amazon. An estimated 91 percent of these deforested areas are used for livestock production. Deforestation is responsible for 15 percent of annual global CO2 emissions and also threatens millions of plant and animal species, causing the global loss of an estimated 50,000 species a year or 137 species a day. Many of these species haven't even been identified yet. If we continue to destroy the rain forest, we could eventually reach a point where the entire ecosystem collapses. While the human race can recover within a few generations from economic hardships, natural disasters, and even wars, species extinction is permanent. As the rate of extinction accelerates, our own safety net disappears.
Livestock production also can result in desertification, the conversion of usable, semiarid land into nonproductive deserts. Desertification decimates plant diversity and causes soil erosion. Overgrazing strips away plants that anchor topsoil, leading to irreversible losses of soil, decreased biodiversity, and the invasion of alien species.
#### **AIR**
Factory farms stink, both figuratively and literally. While their horrific stench has long been viewed as merely an inconvenience in the eyes of the industry and the courts, evidence suggests that the impact is far more insidious.
**_The Real Costs_**
A typical fast-food burger costs about $2, but experts suggest that, in the absence of government subsidies, the real cost would be closer to $200. (If we subsidize anything, it should be kale—that would make sense.) Each passing day brings us a little closer to the realization of an old Cree proverb: "When all the trees have been cut down, when all the animals have been hunted, when all the waters are polluted, when all the air is unsafe to breathe, only then will you discover you cannot eat money."
Whether animal waste is stored or spread on fields, it decomposes, and noxious fumes are released into the air. Odors from factory farms are associated with numerous respiratory and health conditions, including mood disturbances, depression, and severe respiratory problems. Nearly 70 percent of workers employed in concentrated swine facilities report at least one respiratory symptom, and 58 percent have chronic bronchitis. Manure pits are especially problematic, posing confined-space hazards due to oxygen deficiency and toxic gases. Farmworkers are advised to never enter a manure pit without wearing a self-contained breathing apparatus.
### **Beyond Vegan**
Becoming vegan is the biggest step you can take to lighten the ecological footprint of your diet, but it isn't the only step. Here are a few tips for further fine-tuning your planet-friendly habits.
**Choose organic food.** Organic foods are farmed in a manner that is more ecologically sustainable than conventionally produced food, avoiding the use of synthetic fertilizers, pesticides, and genetically modified organisms. Organic farming preserves the soil, decreases water pollution, and helps store carbon dioxide, minimizing the harm to air, water, and soil. Compared to conventional farming, organic farming has been found to reduce carbon dioxide emissions by 49 to 66 percent.
**Opt for local, seasonal plant foods.** By some estimates, the average North American meal travels about 1,500 miles (2,400 km) from field to plate and contains ingredients from five other countries, beyond the United States. If a typical family bought 100 percent local for a year, their greenhouse gas emissions would be reduced by 4 to 5 percent. Also consider growing your own food, even if it's just a few herbs or tomatoes on your balcony. Purchase directly from farmers or farmers' markets, and frequent stores that feature local products. Buy in season when possible to reduce the energy required for food preservation, storage, and transportation. Also purchase unprocessed or minimally processed food.
**Avoid products with excessive packaging.** All that plastic, paper, and aluminum contributes to environmental degradation. Besides, foods that are overpackaged tend to be rife with sugar, salt, and fat. Shop in places that don't overpackage food: farms, farmers' markets, produce markets, bulk stores, and food co-ops. Opt for the most reusable or recyclable items available, such as products in glass containers. Join a community-supported agriculture (CSA) enterprise or sign up for regular deliveries of farm-fresh produce and other local goods.
**Reduce food waste.** Rotting food releases methane and contributes to greenhouse gas emissions. Plus, all of the resources that went into producing the food are wasted. Using food before it goes bad will help the environment—and your pocketbook. Plan your meals in advance, then buy only as much food as you need and prepare only what you'll eat. Store food properly, and keep track of what's in your fridge. Get creative with leftovers. Freeze foods that tend to go rancid or spoil quickly, such as nuts, seeds, and bread. If you do have to throw food away, compost it rather than sending it to a landfill.
**Compost your food scraps.** Composting not only minimizes the amount of garbage you produce, it also enriches your garden. If you live in an apartment or don't have a yard, consider worm composting, called vermicomposting. It can be done indoors, it's odor-free, and it doesn't take much space. Many cities also offer a compost pickup system; check with your city for details, and if they don't have such a program available, request that they start one.
**Walk, bike, or use public transportation.** Transportation contributes an estimated 13.5 percent to greenhouse gas emissions. When purchasing food or eating out, try to select markets and restaurants within walking or biking distance. In addition to saving money, you'll also stay fit. If the distance is too long or your cargo too heavy, take public transit, carpool, or limit shopping trips to once a week. If a motorized vehicle is a necessity, consider a motorcycle, scooter, or small fuel-efficient car.
**BYOB.** Bring your own bag, that is. Plastics find their way into oceans, breaking down into tiny suspended particles and acting like sponges for water-borne carcinogens such as PCBs and pesticides. They work their way into the food chain, poisoning fish and killing marine mammals that mistake the plastic for food. In the ocean, plastics and other wastes often become trapped in rotating currents called gyres, forming massive mats of garbage. Opt for reusable cloth bags instead of plastic, and try to use glass storage containers and jars whenever possible.
### **Vegan Goes Mainstream**
Up until the early 1980s, the word _vegan_ conjured up images of cultish extremists who were essentially wasting away on diets of roots and shoots. If you inquired about vegan options in a restaurant, you usually received a blank stare in response. The only place the word _vegan_ ever appeared on a product label was in a natural food store. If you happened to mention your vegan diet to a doctor or dietitian, they would probably try to "educate" you about the risks of eliminating what were considered two essential food groups: meat and dairy. University textbooks warned soon-to-be doctors and dietitians that vegan diets were downright dangerous. Fortunately, the tables have turned.
In 2010, _Business Week_ featured an article called "Power Vegan." The first paragraph completely obliterated the old vegan stereotype: "It used to be easy for moguls to flaunt their power. All they had to do was renovate the chalet in St. Moritz, buy the latest Gulfstream jet, lay off 5,000 employees, or marry a much younger Asian woman. By now, though, they've used up all the easy ways to distinguish themselves from the rest of us—which may be why a growing number of America's most powerful bosses have become vegan. Steve Wynn, Mort Zuckerman, Russell Simmons, and Bill Clinton are now using tempeh to assert their superiority. As are Ford Executive Chairman of the Board Bill Ford, Twitter co-founder Biz Stone, venture capitalist Joi Ito, Whole Foods Market Chief Executive Officer John Mackey, and Mike Tyson. Yes, Mike Tyson, a man who once chewed on human ear, is now vegan."
There is no denying it: vegan is on the radar of mainstream America. It has arrived because of the moguls and other pioneers who have defied the stereotypes and made vegan attractive to the masses. Vegan bodybuilders have won international titles and blown away images of skinny weakling vegans. Elite endurance athletes are gaining a competitive edge by fueling their bodies with plant-based foods. (See chapter 14). Executive chefs are dazzling judges with extraordinarily colorful and creative vegan masterpieces. Movie stars, musicians, and models are strutting their vegan stuff. Doctors and dietitians are endorsing plant-based diets as ideal for the prevention and treatment of lifestyle-induced chronic diseases.
Not surprisingly, the market is responding. Vegan restaurants are popping up everywhere, and conventional restaurants are adding vegan options to their menus. Products featured in mainstream grocery stores are using the word _vegan_ on labels as a marketing tool. A proliferation of documentary films with noticeably vegan messages are making a splash at the box office. Vegan lifestyles are topics of conversation on wildly popular talk shows. Vegan books, shoes, cosmetics, and specialty products are proliferating in the marketplace. Peer-reviewed articles examining the therapeutic value of vegan diets are making headlines. Internet sites dedicated to veganism and support services are emerging daily.
In 2011, the Vegetarian Resource Group (VRG) commissioned a Harris Interactive poll to estimate the number of Americans consuming a vegetarian or vegan diet or regularly eating vegetarian meals. An estimated 5 percent of Americans consume a vegetarian diet, and about half of the vegetarians consume a vegan diet. This is almost double the rate reported in a 2009 poll (1 percent vegan and 3 percent vegetarian). About 17 percent of Americans avoid meat, poultry, and fish at up to half of their meals, and 16 percent avoid these foods at more than half of their meals. These numbers suggest that about one-third of Americans are choosing vegetarian meals on a regular basis.
In a National Restaurant Association poll, "What's Hot in 2011," more than half of the 1,500 chefs polled included vegan entrées as a hot trend. Of six hundred participants surveyed in a research report from Context Marketing, 21 percent said vegetarian is important or very important to them, and 14 percent said vegan is important or very important to them. Almost 70 percent said that they would be willing to pay more for food produced using higher ethical standards. Eating mostly vegetarian—now known as flexitarian—was one of the top ten consumer food trends in 2011.
Close to half of the US population is trying to reduce its meat consumption. People are interested in eating foods that are produced sustainably, responsibly, and ethically. They want to buy local, fresh, organic, whole foods, as well as foods with minimal or biodegradable packaging. They are drawn to a way of eating that can reduce obesity, diet-induced diseases, and health care costs. Whereas two or three decades ago, the word _vegan_ was associated with dangerous nutritional deficiencies, today it is the one word that's instantly recognized as being consistent with the personal, ethical, and ecological objectives of conscious consumers. The shift in public thinking is palpable, and the future is hopeful.
Of course, challenges remain. Businesses that earn hefty profits from animal exploitation wield a great deal of power. These industries have tremendous influence on government policy and are key recipients of agricultural subsidies. Consumers are constantly bombarded with advertising that makes leather, suede, silk, steak, and lobster seem attractive, sexy, sophisticated, and highly desirable. Fortunately, we have a choice. We can fall into a hypnotic consumer trance, or we can honor our inner moral compass. By doing so, we restore the Golden Rule: "Do unto others as you would have others do unto you."
The Golden Rule has long served as a moral foundation for humanity. Our shared vegan vision is one that would have humankind expand the definition of "others" to include our nonhuman brethren. In July 2012, _Reader's Digest_ featured a cover article titled "Why Whales Are People Too." The piece described the work of a group of scientists who presented the "Declaration of Rights for Cetaceans" at the annual meeting of the American Association for the Advancement of Science in Vancouver, British Columbia, in February of 2012. The declaration essentially protects whales and dolphins as nonhuman "persons" and protects their right to life, liberty, and well-being. If the declaration were binding, these animals could not be slaughtered, held in captivity, or owned. The scientists plan to bring the declaration before the United Nations to have it legally endorsed. There is a push to extend this sort of protection to other animals that exhibit "person" traits of self-awareness, creativity, communication, and intentionality.
Perhaps as we gain a greater understanding of nonhuman animals, we will come to the conclusion that simply being a sentient being, able to think, feel, and suffer, is enough to warrant compassion from human animals.
The advantages of being vegan are associated with compassion not only for animals and the earth, but also for ourselves and for our health. Let's learn how a vegan diet can provide everything we need to help lower our risks for disease.
## **CHAPTER 2**
## **The Great Vegan Advantage**
You may have decided to adopt a vegan diet in an effort to lose weight, reduce disease risk, or even reverse an existing condition. Rest assured that you are on the right track. The evidence for the benefits of vegan diets to prevent many chronic conditions is accumulating by the minute. While you may encounter naysayers who warn about malnutrition, in truth, you are more likely to be malnourished on a standard American diet than on a well-planned vegan diet.
While we generally associate the word _malnutrition_ with undernutrition, or hunger, there are actually more people in the world who suffer from overnutrition, or overconsumption of food, and that too is a form of malnutrition. In the year 2010, for the first time in history the number of people suffering from overnutrition worldwide exceeded the number of people suffering from undernutrition.
Vegan diets rarely lead to undernutrition or overnutrition in adults. Research has consistently demonstrated a greater prevalence of overnutrition, overweight, and obesity within the general population than within the vegan community. In the United States, an estimated 68 percent of the general population suffers from overnutrition and the associated problems of overweight and obesity. This increases the risk of type 2 diabetes, coronary artery disease, stroke, hypertension, and many other serious health conditions.
A third type of malnutrition, called micronutrient deficiency, is common across all dietary groups. It can appear in both vegans and omnivores and in both undernutrition and overnutrition as a result of insufficient access to high-quality food, poor variety in the diet, or an excess of fat and sugar. In vegans, micronutrient deficiencies, especially deficiencies of vitamin B12, are more prevalent in those who overly restrict their diets.
### Where Do We Stand?
Scientific evidence about vegan diets has been flowing into scientific journals since 1976, thanks in large part to Seventh-day Adventists. Members of this Protestant denomination have adopted healthful lifestyles as part of their faith. Most don't drink alcohol or coffee, and many are vegetarian or vegan. Two key studies have provided a wealth of data: The Adventist Health Study-1, which followed 34,198 members of the church between 1974 and 1988, resulting in dozens of research papers, and the Adventist Health Study-2, which began in 2002, and is ongoing. Of the 96,000 participants in the latter study, 28 percent are vegetarian and 8 percent are vegan.
Another large population study is the European Prospective Investigation into Cancer and Nutrition (EPIC). It is the largest study of the diet and health of a group of people to date, with approximately 520,000 participants from ten European countries. EPIC-Oxford, which is one of twenty-three EPIC centers, purposefully recruited as many vegetarians and vegans as possible. Of the 65,500 people enrolled, approximately 29 percent are vegetarian and 4 percent are vegan. Other smaller but significant studies have also been conducted in the United Kingdom and Germany.
These studies have found that well-planned vegan diets supply adequate nutrition. However, vegans are not a homogeneous group. While they tend to eat more vegetables and fewer processed foods than the general population, there are vegans who live on tea and toast, pasta and bagels, or soda and French fries, and research doesn't always tease out these kinds of crucial diet details. Finally, the methods of obtaining dietary information are far from foolproof. Often, participants are asked to recall their diets or to fill out questionnaires, and these provide only very rough estimates of food intake. In addition, participants may not be followed for a long enough time to obtain sufficient information about changes in their nutritional status.
While properly designed vegan diets provide ample nutrients, poorly planned vegan diets can fall short—as can poorly planned omnivorous diets. When vegan diets are poorly designed, the nutrients most commonly lacking are vitamin B12, calcium, and vitamin D. Other nutrients that are potentially deficient for some vegans are protein, essential fatty acids, riboflavin, zinc, selenium, and iodine. Still, although intake of some of these nutrients may be below recommended levels, in most cases they are close to the recommended amount, and the overall health of vegan subjects is good. Plus, vegans as a group tend to be leaner than people following any other type of diet, and their diets consistently provide better levels of fiber, vitamin C, vitamin E, thiamin, folate, iron, copper, and magnesium.
The nutrition challenges commonly faced by vegans are relatively easy to overcome. In fact, many foods popular with vegans, such as nondairy milks, meat substitutes, and breakfast cereals, are fortified with nutrients such as calcium, vitamin B12, vitamin D, riboflavin, and zinc. The bottom line? You don't need animal products to have a healthful and nutritionally adequate diet.
### **Vegans on Trial**
Prior to the 1990s, chronic diseases such as cardiovascular disease, diabetes, cancer, and lung disease were commonly known as "diseases of affluence" because they occurred among people who had the luxuries of eating too much and exercising too little. The term has since become obsolete as rates of these diseases are rising most rapidly in poorer countries. In 2008, 63 percent of deaths worldwide were due to such conditions. It's estimated that, by 2020, lifestylerelated chronic diseases will be responsible for almost three-quarters of deaths globally. This shift has created a major public health threat with catastrophic implications for struggling economies throughout the world. The four primary causes of this epidemic, according to the World Health Organization, are poor diet, lack of exercise, smoking, and alcohol consumption. Simply put, the majority of deaths globally are self-inflicted.
Governments, health organizations, and nutrition authorities are acutely aware of the connection between diet, lifestyle, and chronic disease, and of the health benefits associated with plant-based diets. Nutrition education materials consistently reflect this knowledge. For instance, in 2010 the Dietary Guidelines Advisory Committee recommended four steps to help reduce the risk of chronic disease. In simple terms, they advised consumers to eat less, exercise more, eat a more plant-based diet, and eat fewer refined grains and foods with added sugar, solid fats, and salt.
The 2010 Dietary Guidelines for Americans state that vegetarian diets are associated with lower levels of obesity, reduced risk of cardiovascular disease, lower blood pressure, and lower total mortality. According to the guidelines, vegetarians typically eat less fat, fewer calories, and more fiber, potassium, and vitamin C than nonvegetarians.
But here's the rub: Although health authorities agree that eating mostly whole plant foods makes good sense, few suggest eating _only_ plant foods. Many who urge a shift toward a more plant-centered diet also advocate increases in what are considered "healthful animal products," such as fish and low-fat dairy products. The healthiest, longest-living populations on the planet consume whole-foods, plant-based, or mostly plant-based diets, but none of these groups is entirely vegan. Vegan diets are essentially on trial in the eyes of the world. Fortunately, as the evidence unfolds, vegan diets are not only being vindicated, they are increasingly being recognized as rising stars in the arsenal against many chronic diseases.
Based on current evidence, vegans come closer to meeting recommendations for intake (or avoidance) of total fat, saturated fat, cholesterol, trans-fatty acids, and fiber than people of other dietary persuasions. In addition to being low in saturated fat, free of cholesterol, and high in fiber, well-planned vegan diets provide abundant antioxidants and protective phytochemicals, so they may be useful in the prevention and treatment of numerous chronic diseases, including asthma, cancer, cardiovascular disease, cataracts, diverticular disease, fibromyalgia, gallbladder disease, gastrointestinal disorders, kidney disease, overweight and obesity, rheumatoid arthritis, and type 2 diabetes.
Let's take a look at some of these diseases and see just how helpful a vegan diet can be in preventing or reducing the risk of certain chronic illnesses.
### **Cardiovascular Disease**
Cardiovascular disease (CVD) refers to diseases of the heart and circulatory system, including coronary artery disease, hypertension, congestive heart failure, congenital cardiovascular defects, and cerebrovascular disease, or stroke. As the leading cause of death worldwide, CVD accounted for 30 percent of all deaths in 2005. In the United States the toll is higher: 34.3 percent of all deaths in 2006 were due to CVD—that's one of every three deaths, or about one death every thirty-eight seconds.
Recently, CVD has been increasing in low- and middle-income countries due to increased smoking, decreased physical activity, and increased intake of meat and high-calorie foods laden with fat, oil, sodium, and sugar. In China, for instance, meat consumption jumped 246 percent between 1980 and 2003. This trend has been directly linked to rising cholesterol levels, which one study found to be responsible for 77 percent of the increased risk of CVD.
There is no question that meat eaters have more risk factors for cardiovascular disease than vegans. Unfortunately, few studies have separated out data on vegans because the number of vegan participants in these studies is generally small. In 1978, however, a very preliminary report of the Adventist Mortality Study found that, among vegan men older than thirty-five, death rates due to coronary artery disease were only 14 percent that of the general population. In a 1999 analysis, the death rate for vegans from ischemic heart disease was 26 percent lower than for meat eaters, compared to 34 percent lower for both the vegetarians and the fish eaters. The vegans' risk for stroke was 30 percent lower, compared to 13 percent lower for vegetarians and 4 percent higher for fish eaters, although these findings were not statistically significant.
A 2013 report from EPIC-Oxford found that vegetarians and vegans had a 32 percent lower risk of ischemic heart disease compared to meat eaters and fish eaters. Surprisingly, fish eaters didn't enjoy an advantage over meat eaters. Although the reason for this finding isn't clear, it is possible that fried fish, a favorite in the UK, could have predominated in the fish eaters' diets.
It may seem surprising that vegans don't have a greater advantage where heart disease is concerned than the evidence has shown. This may be because vegan diets favorably affect some CVD risk factors while negatively affecting others. It's important for vegans to be aware of any potential pitfalls that may increase risk and take steps to avoid them, so let's take a look at the CVD risk factors that are potentially affected by a vegan diet.
#### **CHOLESTEROL**
Cholesterol is an essential component of cell membranes, but an excess can increase the risk of CVD. Cholesterol is a large, fat-soluble molecule that's carried in the blood by lipoproteins. The two main lipoproteins, low-density lipoprotein (LDL) and high-density lipoprotein (HDL), are essentially cholesterol carriers. Although LDL transports cholesterol to various tissues for cell building, it also dumps excess cholesterol in artery walls, contributing to the formation of plaque, hence its nickname: "bad cholesterol." HDL is referred to as "good cholesterol" because it transports excess cholesterol to the liver for removal.
Elevated LDL is a major risk factor for coronary artery disease. The higher the LDL, the higher the risk. However, the higher the HDL, the lower the risk. Although HDL tends to be slightly lower in vegans, the balance of LDL to HDL is more favorable, and therefore CVD risk is reduced.
In addition to lower cholesterol levels, vegans also appear to be at an advantage when it comes to cholesterol metabolism. A healthy blood cholesterol level is considered to be no higher than 200 mg/dl (5.2 mmol/l), and based on the results of twenty-four studies of vegan populations over about thirty years, vegan cholesterol levels average about 150 mg/dl (3.9 mmol/l)—lowest of any dietary group. A cholesterol level of 150 mg/dl (3.9 mmol/l) is a bit of a magic number in the medical world. People with cholesterol levels lower than that have the lowest risk of heart disease. Indeed, in the first fifty years of the famous Framingham Heart Study, only five patients with cholesterol levels less than 150 developed coronary artery disease.
Vegans have significantly lower LDL levels as well, averaging 85 mg/dl (2.2 mmol/l), compared to 105 mg/dl (2.7 mmol/l) for lacto-ovo vegetarians and 119 mg/dl (3.1 mmol/l) for nonvegetarians. The differences in HDL were small, however: HDL levels of vegans averaged 49 mg/dl (1.27 mmol/l), compared to 52 mg/dl (1.34 mmol/l) for lacto-ovo vegetarians and 54 mg/dl (1.4 mmol/l) for nonvegetarians. It's important to note that the participants in most of these studies—regardless of their dietary group—were from health-conscious populations, so even the nonvegetarians had death rates close to half that of the general population.
Intake levels of saturated fats, trans-fatty acids, and, to a lesser extent, cholesterol are all associated with elevated cholesterol levels. There is good evidence that replacing saturated fat with polyunsaturated fat significantly reduces CVD risk, and that replacing saturated fat with refined carbohydrates—white flour products, white rice, and sugar-sweetened beverages and treats—may actually elevate CVD risk.
Vegans consume no cholesterol and typically have the lowest saturated fat intake of all dietary groups and a lower intake of trans fats. They average 6.3 percent of calories from saturated fat, compared to 10.6 percent for lacto-ovo vegetarians and 12 percent for nonvegetarians. Although only a few studies have assessed trans fat intakes in vegans, they consistently show lower levels compared with lacto-ovo vegetarians and nonvegetarians. Vegans also tend to opt for unrefined carbohydrates rather than refined, and their diets maximize intake of cholesterol-lowering food components, such as soluble fiber, plant proteins, phytosterols (beneficial plant sterols and stanols), polyunsaturated fats, and phytochemicals, all of which are found exclusively or predominately in plant foods.
Research suggests that the most damaging form of cholesterol is oxidized cholesterol, or oxycholesterol. Oxidized cholesterol hastens the formation of plaque and hardening of the arteries, reducing their elasticity and increasing the risk for CVD. Cholesterol can oxidize in the body when people don't eat well, and this is particularly likely to occur with the consumption of fried foods, fast foods, and other processed foods.
Within the body, cholesterol can become oxidized if you eat too much cholesterol and not enough antioxidants, such as vitamins C and E, carotenoids, flavonoids, and polyphenolic compounds. Just as their name implies, antioxidants block oxidation. Since antioxidants come primarily from whole plant foods, vegans tend to eat more of them than typical omnivores do. A vegan or other plant-based diet improves antioxidant intake and decreases cholesterol oxidation.
In addition, high intakes of heme iron—the type from meat, as opposed to nonheme iron from plants—may also increase LDL oxidation and atherosclerosis. Since vegans don't consume heme iron, they may be further protected against CVD.
#### **TRIGLYCERIDES**
Triglycerides are a type of fat in your blood synthesized from the food you eat. Elevated triglycerides—considered to be more than 150 mg/dl (1.7 mmol/l)—can increase your risk for heart disease and for metabolic syndrome, a condition that can lead to diabetes.
If you eat more calories than you need, particularly too much fat, cholesterol, sugar, refined carbohydrates, or alcohol, your liver converts the excess into triglycerides and packages them in a molecule called very low-density lipoprotein (VLDL). VLDL transports triglycerides through the bloodstream to fat tissue, also called adipose tissue, to store it for later use. If you make a habit of eating more than your body uses, your VLDL will increase in order to manage all of the excess triglycerides. After the VLDL dumps its triglyceride load into your fat tissue, it turns into LDL, the bad cholesterol—a lose-lose situation.
One common criticism of plant-based diets has been that they increase triglycerides. This can happen to vegans if they eat too much fat, sugar, or refined carbs, but those who focus on whole, high-fiber foods generally have low triglycerides. Vegans have been shown to have the lowest triglyceride levels of all dietary groups, with an average of 83.5 mg/dl (0.94 mmol/l), compared to 107 mg/dl (1.2 mmol/l) for lacto-ovo vegetarians and 95.5 mg/dl (1.1 mmol/l) for meat eaters.
#### **HIGH BLOOD PRESSURE**
Vegans are less likely than other dietary groups to have to worry about high blood pressure. This is probably because vegans are, for the most part, fairly lean, and body mass index (BMI) is a strong indicator of blood pressure. About half of the variations in hypertension between dietary groups can be attributed to BMI, with the remainder being due to differences in fiber, fat, sodium, alcohol intakes, and nondietary factors, such as physical activity.
#### **INFLAMMATION**
CVD has been solidly linked to inflammation, from the earliest stages of atherosclerotic plaque formation to the sudden rupture of established plaques and the ensuing heart attack. A widely available lab test called high-sensitivity C-reactive protein (hs-CRP) can predict cardiac risk by measuring levels of C-reactive protein, which is produced in response to inflammation. Generally, lifestyle factors such as smoking, inactivity, being overweight, and poor food choices cause the inflammation that results in elevated CRP levels.
Four of five studies of vegetarians showed significantly lower inflammation levels compared with omnivores. The only study assessing CRP levels in vegans found markedly lower levels of inflammation compared to endurance athletes and people who ate a standard Western diet. In this study, the vegans consumed raw diets.
#### **HOMOCYSTEINE**
Homocysteine is a by-product of the metabolism of the essential amino acid methionine. Low levels of vitamins B12, vitamin B6, and folate can cause homocysteine levels to rise. Elevated homocysteine damages blood vessel walls, triggering oxidation, inflammation, and the formation of blood clots. High homocysteine levels can be predictive of CVD and coronary problems. It is estimated that for every 5 mmol/L increase in homocysteine, risk for CVD jumps 20 to 23 percent and risk of death from CVD increases up to 50 percent (or up to 60 percent in people with type 2 diabetes).
Elevated homocysteine is usually treated with folic acid, vitamin B6, and vitamin B12, which may reduce the risk of stroke. However, this treatment may not reduce heart disease in patients with CVD.
Vegans generally have excellent folate and vitamin B6 status, but their B12 tends to be low, and numerous studies have reported elevated homocysteine in vegans who don't supplement with B12. Poor homocysteine status in vegans may therefore counteract some of the cardioprotective benefits of a vegan diet. While we don't know precisely how low B12 levels must go to affect homocysteine, limited evidence suggests that it needs to stay above 300 pg/ml, and that 400 pg/ml may be better still. If you're concerned about your B12 intake, consider having your B12 and homocysteine levels tested.
#### **ABNORMAL BLOOD COAGULATION**
Many serious cardiovascular events begin with the formation of a blood clot, or thrombus, that blocks the flow of blood in the blood vessels. Heart attacks occur when arteries to the heart are blocked; strokes occur when arteries to the brain are blocked. The initial stage of thrombus formation is when blood platelets clump together, called platelet aggregation. Injuries to the blood vessel walls or rupture of a plaque accelerates platelet aggregation.
Unfortunately, few studies have assessed platelet aggregation in vegans, but those that have been done suggest vegetarians and vegans may actually be at a slight disadvantage compared to nonvegetarians. These negative findings are a surprise, since many dietary factors associated with increased platelet aggregation, such as consumption of saturated fat and cholesterol, are low in most vegetarian and vegan diets. Plus, vegetarians and vegans consume more of the dietary compounds known to diminish platelet aggregation, such as phytochemicals from vegetables, fruits, and herbs. The most likely explanation for the increased platelet aggregation seen in these studies is that the vegetarians and vegans had poor omega-3 fatty acid status. Vegetarians, especially vegans, can usually benefit from boosting intakes of omega-3 fatty acids and improving the balance of omega-3s and omega-6s. (See page 66, for more on omega-3 and omega-6 fatty acids.)
**_What Does "Percent-Fat Diet" Mean?_**
_Percent fat_ refers to the percentage of calories in the diet obtained from fat. A 10-percent-fat diet, for example, means that 10 percent of the calories eaten that day were derived from fat. (Also see page 53.)
#### **EMERGING RISK FACTORS**
Although research has shown that antioxidants provide some protective benefits, their impact on CVD risk remains unclear. People consuming vegan, raw vegan, and vegetarian diets have better antioxidant status than nonvegetarians, but the associated benefits may be limited. One thing we do know is that obtaining antioxidants from food appears to be more protective than getting them from supplements.
Thicker, stiffer arteries also increase CVD risk, as do diets high in meat and low in fiber, so it's no surprise that vegans, near-vegans, and vegetarians have been shown to have healthier arteries than nonvegetarians and even many endurance athletes.
Low vitamin D status also could be a significant CVD risk factor, and this could be a problem for vegans, who usually have less than optimal vitamin D levels (although this isn't an inevitable result of being vegan).
Vegans who eat a whole-foods diet low in saturated fat and high in fiber, antioxidants, and protective phytochemicals, and who include reliable sources of vitamin B12, vitamin D, and essential fatty acids, have a reduced risk for CVD. But vegans who eat a diet of refined, processed foods may actually increase their risk.
#### **THE VEGAN FIX FOR CVD**
Vegan and near-vegan diets have been used in a variety of medical trials to improve blood fat or lipid levels and blood pressure and as a treatment for severe coronary artery disease. Even though lacto-ovo vegetarian diets reduce total lipid and LDL levels by 10 to 15 percent, a vegan diet can do even better, resulting in a 15 to 25 percent decrease in total cholesterol and LDL levels. Vegan diets rich in specific protective components, such as phytosterols, soluble or viscous fiber, soy protein, and nuts, can reduce levels even more: from 20 to 35 percent.
Two researchers have demonstrated that very low-fat vegan or near-vegan diets can effectively reverse established coronary artery disease (CAD): Dean Ornish and Caldwell Esselstyn.
In 1983, Dean Ornish, MD, used a near-vegan diet with only 10 percent of calories from fat, along with exercise, smoking cessation, and stress management, to treat twenty-three CAD patients for twenty-four days. At the end of the trial, patients had better heart muscle function and cholesterol levels and could exercise for longer periods of time, and 91 percent of them had a reduction in angina episodes.
In 1990, Ornish published the results of his landmark study, the Lifestyle Heart Trial. In this study, twenty-eight participants used a lifestyle intervention program similar to his 1983 study, while twenty participants were assigned to a control group. Coronary blockages actually regressed, or became smaller, in 82 percent of the participants in the lifestyle intervention group, compared with 53 percent in the control group. The frequency of angina, in which an inadequate blood supply to the heart causes chest pains, fell 91 percent in the lifestyle intervention group, compared to a 165 percent jump in the control group. LDL levels dropped approximately 37 percent in the lifestyle intervention group compared to 6 percent in the control group. In a five-year follow-up, arterial blockages had regressed even further among those in the lifestyle intervention group, and they had experienced 60 percent fewer cardiac events than the control group.
Caldwell Esselstyn, MD, also used a very low-fat, near-vegan diet, plus cholesterol-lowering medications if necessary, to treat twenty-four patients with severe CAD. Most participants were debilitated by angina and other symptoms of their disease, and several had such advanced heart disease that traditional interventions such as bypass surgery could no longer be offered. Of these, eighteen patients adhered to the program long term.
At the five-year follow-up, none of the participants had experienced a cardiac event. Blockages in eleven of the eighteen participants stopped growing, and in eight of the eleven the blockages had regressed. Interestingly, the six patients who returned to standard care experienced thirteen new cardiac events in the first five years. Twelve years later, the mean total cholesterol of the seventeen remaining patients on Esselstyn's program was 145 mg/dl (3.8 mmol/l). Not one person who stayed with the program experienced disease progression, a cardiac event, or cardiac interventions.
Although we don't have studies on changes in artery lesions and blockages using higher-fat vegan or near-vegan diets, we have considerable evidence for dramatic lipid reductions and improved cardiovascular markers with higher-fat, whole-food vegan diets. Vegan diets are associated with improvements in blood lipids, blood pressure, blood viscosity, and inflammation, whether low or higher in fat. The bioactive compounds and nutrients in higher-fat vegan foods such as nuts, seeds, and avocados have been shown to favorably affect the markers of cardiovascular disease. While we don't know if higher-fat vegan diets would prove as effective as low-fat vegan diets in improving artery lesions and blockages, we do know that whole-foods vegan diets are powerful allies in the battle against the world's leading killer.
### Cancer
Cancer, the most dreaded of all chronic diseases, is currently the second-most-common cause of death globally, and the incidence is rising. While perhaps less predictable than heart disease or type 2 diabetes, cancer generally isn't an indiscriminate killer. Consider the striking differences in cancer rates between populations throughout the world. For example, the prevalence of colon, breast, and prostate cancers is several times higher in North America and northern Europe than in rural Asia. While it is tempting to assume that rural Asians are genetically protected against these cancers, risk increases tremendously within a generation or two after Asians migrate to the West.
Contrary to what many people believe, only 5 to 10 percent of cancers are determined by genetics. The remaining 90 to 95 percent of cancers are a product of the environment, and what we eat is the linchpin, accounting for an estimated 30 to 35 percent of all cancers. As shown in table 2.1, the impact of diet varies with the type of cancer; it's particularly high in the hormone-related and colorectal cancers that are prevalent among those consuming Western diets.
Beyond diet, an estimated 25 to 30 percent of cancers—and 87 percent of lung cancers—are due to smoking, 15 to 20 percent are linked to infections, 10 to 20 percent are triggered by obesity, and 4 to 6 percent are tied to alcohol. The balance can be attributed to radiation, stress, inadequate physical activity, and environmental contaminants.
#### **DIET AND LIFESTYLE**
While only a small percentage of cancers are the result of genetics, gene expression—the process by which genes are turned on or off—is influenced by multiple factors. Diet and lifestyle choices are the factors that cause most of the genetic mutations that lead to cancer. Mutations can occur when normal by-products of metabolism, such as free radicals, damage our genetic material. Our cells may fail to repair the damage if we've been exposed to carcinogens or if we lack certain components needed for DNA synthesis and repair, such as selenium, folate, or coenzyme Q10.
**TABLE 2.1.** Estimated contribution of diet to cancer deaths
**TYPE OF CANCER** | **PERCENT OF DEATHS LINKED TO DIET**
---|---
Prostate | 75
Colorectal | 70
Breast, endometrial, gallbladder, and pancreatic | 50
Stomach | 35
Lung, larynx, pharynx, esophagus, mouth, and bladder | 20
Other | 10
Source of data: P. Anand et al., "Cancer is a Preventable Disease that Requires Major Lifestyle Changes," _Pharmaceutical Research,_ no. 9 (2008): 2097-116.
The World Cancer Research Fund and the American Institute for Cancer Research convened two expert panels to determine the strength of the evidence linking diet and lifestyle to cancer. The resulting reports are considered the most authoritative and influential in this field to date. They found convincing evidence linking diet and lifestyle to several cancers:
* **Breast cancer.** The reports found that the best lifestyle interventions to reduce risk for breast cancer are to keep a lean body weight, avoid alcohol, and, for mothers, to breast-feed their babies.
* **Colorectal cancer.** Eating foods rich in fiber—in other words, plant foods—and engaging in physical activity can reduce the risk for colorectal cancer, as can eating garlic. Getting sufficient calcium, whether from supplements or dairy products, has also been associated with decreased risk. Eating red meat and processed meat, drinking alcohol (particularly for men), being overweight, and carrying abdominal fat can increase the risk.
* **Esophageal cancer.** Alcohol and body fatness can increase the risk of esophageal cancer. The risk can probably be decreased by eating fruits, nonstarchy vegetables, and foods high in vitamin C.
* **Lung cancer.** Fruits and foods high in carotenoids (see "Vitamin A," on page 109) can reduce the risk of lung cancer, but beta-carotene supplements and being overweight may increase the risk.
* **Prostate cancer.** Men who want to lessen their risk for prostate cancer should probably eat more foods containing lycopene and selenium (see page 138 for more on selenium) or take selenium supplements. High-calcium diets may increase the risk for prostate cancer, although the evidence against dairy products is still considered to be limited.
* **Stomach cancer.** A diet high in salt and salty foods may increase the risk of stomach cancer, while consuming plenty of fruits and nonstarchy vegetables probably decreases the risk.
#### **THE VEGAN VERDICT ON CANCER**
Well-planned vegan diets can provide impressive protection against cancer, especially cancers that are closely tied to dietary choices. While the evidence is just beginning to emerge, results are encouraging.
In 2012, the Adventist Health Study-2 (AHS-2) released results based on almost three thousand cancer cases. Compared to nonvegetarians, overall cancer risk was 16 percent lower among vegans and 8 percent lower among lacto-ovo vegetarians. In terms of female-specific cancers, vegans enjoyed a 34 percent risk reduction compared to nonvegetarians. The authors concluded that vegan diets confer lower risk for cancer overall and for female-specific cancers compared to other dietary patterns.
In the EPIC-Oxford studies, cancer rates among vegetarians and vegans were 89 percent those of health-conscious meat eaters. However, cancer rates were lower still in health-conscious pescatarians (people who are primarily vegetarian but also eat fish), at 83 percent of the rate among health-conscious meat eaters. When compared with the general British population, which is less health-conscious than the meat eaters in the study, the overall cancer rate among vegetarians and vegans was 65 percent of the rate among the general population.
Findings on colon cancer among vegetarians differed significantly in the EPIC-Oxford and AHS-2 studies. While AHS-2 found a 25 percent risk reduction for vegetarians compared to meat eaters, EPIC-Oxford actually reported an increased risk among vegetarians. The reason for this discrepancy is unknown; however, it's possible that the British vegetarians were consuming diets higher in refined carbohydrates and processed fats and lower in whole plant foods. Whatever the reason, switching to a vegetarian diet doesn't automatically guarantee protection from colon cancer—or any other cancer for that matter. As always, the quality of the diet is a key factor.
#### **DOES A RAW VEGAN DIET PROTECT AGAINST CANCER?**
It remains unclear what type of plant-based diet affords the greatest protection against cancer, but it does appear that whole plant foods are an important part of an anticancer diet, and that raw vegetables offer several advantages over cooked vegetables.
More than two dozen studies have examined the relationship between raw and cooked vegetables and cancer risk. These studies were not done on people consuming raw vegan diets; rather they focused on the possible advantages of specific foods or components of foods. While most studies have shown that cancer risk decreases as vegetable intake increases, findings have been more consistent for raw vegetables than for cooked vegetables. Studies have also shown that the more raw vegetables you eat, the more benefits you get.
Researchers have suggested several reasons why raw vegetables provide greater protection against cancer:
* Several protective substances, such as vitamin C and phytochemicals, are water-soluble and heat sensitive and can be destroyed or leached out during cooking.
* Cooking disables enzymes that are responsible for converting certain phytochemicals into their active forms, so they can lose their powerful anticancer effects (see "Enzymes," on page 148).
* Cooking changes the physical structure of the food and its physiologic effects. For example, it can destroy insoluble fiber, reducing the body's ability to bind and excrete cancer-causing substances.
* Cooking at high temperatures can form compounds that damage DNA.
It's also well established that raw diets can favorably alter intestinal bacteria, which can reduce levels of toxins that may increase cancer risk. In addition, some raw food preparation techniques can enhance the protective substances in food. For example, juicing removes plant cell walls, and with them the phytate compounds that can inhibit the absorption of nutrients and phytochemicals. Sprouting increases the nutrient and phytochemical content of seeds, grains, beans, and nuts.
On the other hand, cooking can kill many potentially harmful organisms, improve the bioavailability of some nutrients, destroy compounds that interfere with nutrient absorption, and improve the digestibility of some foods, such as legumes. To minimize harmful products of oxidation from cooking, use moist preparation methods, such as steaming, stewing, or poaching.
#### **VEGAN TREATMENTS FOR CANCER**
There isn't a lot of evidence that a vegan diet helps treat cancer, but in a US study published in 2005, an intervention consisting of vegan diet, exercise, stress management, and group therapy apparently reduced the progression of prostate cancer. After one year on this lifestyle program, the levels of prostate-specific antigen (PSA), a protein that's elevated in prostate cancer, decreased 4 percent in the lifestyle-intervention group but increased 6 percent in the control group. In addition, prostate cancer cell growth was inhibited nearly eight times more in the vegan lifestyle group than in the control group. Further research is needed to see if such interventions could produce similar benefits in patients with other forms of cancer.
Metabolic markers for cancer, such as PSA, are less clear-cut than those for heart disease or diabetes, but they do provide worthwhile information. Vegans tend to show more favorable test results for these markers than vegetarians, non-vegetarians, and even endurance athletes. In several studies, vegans, particularly raw-food vegans, have shown lower levels of tumor promoters, less DNA damage or better protection against damage, and fewer toxins known to promote cancer. Several studies have confirmed the positive effects of a mostly raw vegan diet on intestinal bacteria and other factors that may prove beneficial in cancer risk reduction.
In addition, a number of metabolic changes that occur with vegetarian and vegan diets may provide further protection against cancer:
* **Lower estrogen levels.** A lower lifetime exposure to estrogen is associated with a reduced risk of breast cancer.
* **Fewer bad bacteria.** Vegans and vegetarians apparently have fewer of the intestinal bacteria that convert bile acids into a more carcinogenic form. Plus, they have a less acidic colon, which reduces the activity of the enzymes responsible for this conversion.
* **A healthier gut.** Larger, heavier, softer stools and more frequent bowel movements mean potential carcinogens have less time to harm the intestinal lining. In addition, fecal mutagens—substances that damage DNA—have less opportunity to damage DNA, possibly reducing the risk for colon cancer.
* **More antioxidants and less oxidation.** Increased antioxidant intake and the resulting lower levels of oxidation can protect against DNA damage, potentially reducing cancer risk.
#### **THE SOY-CANCER DEBATE**
Soybeans are unique among legumes because they contain high levels of isoflavones, a type of phytoestrogen (plant estrogen). These compounds can bind to human estrogen receptor sites, but they are generally much weaker in their activity and more selective than human estrogens in the receptors they bind to. Plus, the type of estrogen receptor they bind to determines whether the isoflavones have weak estrogen-like effects or antiestrogen effects. Also see page 62.
Soy intake has been associated with a reduced risk of prostate cancer and reduced prostate cancer cell growth. Recent research suggests that in reproductive cells, such as breast and uterus tissue, isoflavones act more like antiestrogens, while in bone-forming cells they behave as weak estrogens, in both cases with beneficial effects. The evidence to date suggests that lifetime soy consumption may actually help protect against breast cancer and improve breast cancer prognosis. Here are the results of some of the more promising studies:
* Soy consumption during childhood and adolescence reduces lifetime breast cancer risk.
* Among Asian women, the more soy a woman consumes, the lower her risk for breast cancer, but so far this association hasn't been found in Western women. This could be because Asians appear to metabolize isoflavones in a way that produces more of a compound called S-equol, which may provide added protection; however, the research on this topic is limited. Interestingly, one study reported that vegetarians were 4.25 times more likely to produce S-equol than nonvegetarians.
* Most studies show that the risk of recurrence or death from breast cancer is either reduced or unaffected by isoflavones. A pooled analysis of both Chinese and American women found that those with the highest intakes (10 mg isoflavones or more) were 17 percent less likely to die from breast cancer and 25 percent less likely to have a recurrence of breast cancer. The protective effect of soyfoods appears to be due to their isoflavone content.
The weight of evidence suggests that soy is protective against breast cancer, breast cancer recurrence, and death due to breast cancer, although some studies suggest that it doesn't affect risk either way. The strongest evidence exists for moderate intake (about two servings a day) of traditional soy foods, such as tofu and soy milk.
#### **ANTICANCER TIPS FOR VEGANS**
Based on the evidence currently available, vegans are at an advantage where cancer risk is concerned. Still, there are steps you can take to maximize the benefits of a vegan diet:
* Eat mostly whole plant foods. Choose organic whenever possible. Try to meet most if not all of your nutritional needs through diet rather than through supplements.
* Eat at least nine servings of vegetables and fruits every day. Eat plenty of dark, leafy greens, and select produce in all the colors of the rainbow.
* Aim for at least 35 grams of fiber each day from a variety of plant foods (see page 89).
* Don't eat foods that contain trans-fatty acids.
* Limit your consumption of processed foods, particularly those containing refined carbohydrates and those that are energy dense. (Energy density refers to the number of calories per weight of food.) Processed foods with high energy density are associated with weight gain, which increases cancer risk. The worst offenders are sugary drinks, fruit juices, fast foods, and processed foods with added fat and sugar.
* Make pure, clean water your beverage of choice. Other healthful beverages include fresh vegetable juices and antioxidant-rich teas, such as green tea.
* Rely on foods such as nuts, seeds, and avocados for most of your fat, and ensure you're obtaining sufficient essential fatty acids (see chapter 4).
* Eat raw foods daily. Eat more sprouted foods.
* If you cook your food, try to stick mainly to moist cooking methods, such as steaming.
* Flavor foods with immune-boosting herbs and spices, such as turmeric, ginger, garlic, basil, oregano, rosemary, and coriander.
* Be lean. Try to keep your body weight at the low end of the normal range for your height and build. Too much body fat can cause insulin resistance and inflammation, which may trigger cancers of the esophagus, colon, rectum, pancreas, breast (postmenopause), kidney, gallbladder, and liver.
* Be physically active. Do moderate exercise—the equivalent of brisk walking—for at least one hour a day, or vigorous exercise for thirty minutes daily. Activity provides protection from colon and endometrial cancers and, after menopause, breast cancer. Inactivity has been linked to lung and pancreatic cancers.
* Limit your intake of alcohol. Alcohol increases your risk for several cancers, and there is no apparent safe intake level. Two drinks per day for men and one for women is considered the absolute maximum.
* Keep your salt intake to no more than 2,300 mg per day, and limit your consumption of smoked, pickled, and salted foods.
### Type 2 Diabetes
Diabetes has become a twenty-first-century plague, crippling rich and poor nations alike. In the United States, the rate of diabetes has climbed more than 900 percent in fifty years, from 0.9 percent in the late 1950s to 8.3 percent in 2010. According to the Centers for Disease Control and Prevention, one in ten US adults had diabetes in 2010. If the current trend continues, it's estimated that as many as one in three adults will have diabetes by 2050. Statistically, diabetes is the seventh-leading cause of death in the United States, but this figure belies the fact that most people with diabetes don't die of diabetes; they die of heart disease, kidney failure, and other complications of the disease.
#### **WHAT IS DIABETES?**
Glucose is the primary source of energy for the body, and in order for glucose to enter the cells, a "gatekeeper" called insulin must let it in. Diabetes is a metabolic disorder that diminishes the body's ability to move glucose into cells so it can be used for energy. People with diabetes either don't produce insulin, don't produce enough insulin, or have become resistant to the insulin they produce. This means insulin can't do its job, so levels of blood glucose, or blood sugar, rise. When blood glucose is elevated over time, body tissues become awash in it, and health tumbles down a predictable slippery slope.
There are two main types of diabetes. Type 1, previously known as juvenile-onset diabetes, occurs suddenly and most often affects children and adolescents. It is characterized by a lack of insulin production by the pancreas and is generally regarded as an autoimmune disease. In type 2 diabetes, once called adult-onset diabetes because it rarely occurred in people younger than fifty, the body continues to produce insulin but the cells have become resistant to the action of this hormone. Insulin resistance causes a rise in blood glucose, so the body responds by pumping out more insulin. Eventually the pancreas can wear out and insulin production declines. Today, type 2 diabetes is seen in young adults, teens, and even children. Untreated or poorly controlled type 2 diabetes is a leading cause of blindness, premature heart attack and stroke, kidney failure, nerve damage, and amputations.
Essentially the product of diet and lifestyle, type 2 diabetes is an insidious disease, often going undetected for many years. Globally, type 2 accounts for more than 90 percent of all diabetes, and the rise in the disease runs roughly parallel with the rise in overweight and obesity. If you're overweight, your risk of developing the disease is double that of a person of normal weight. If you're obese, your risk is tripled.
Although excess body fat plays a strong role in this disease, the way the fat is distributed is perhaps even more significant. Weight concentrated around the abdomen and in the upper part of the body, resulting in an apple shape, increases risk far more than weight that settles around the legs and hips, resulting in a pear shape. Fat that collects in and around vital organs, called visceral fat, is far more damaging than fat that accumulates close to the skin's surface, or subcutaneous fat.
Diabetes is defined as a fasting blood glucose level of at least 126 mg/dl (7 mmol/l), but problems can begin at lower levels. When fasting blood glucose reaches 100 mg/dl (6 mmol/l), the condition is called prediabetes or impaired glucose tolerance. Often, prediabetes appears as part of metabolic syndrome, a cluster of risk factors characterized by elevated blood glucose, abdominal fat, elevated blood pressure and triglycerides, and low levels of HDL. These conditions often escalate to full-blown type 2 diabetes.
#### **LUCK OF THE DRAW?**
Some people believe that type 2 diabetes is more a matter of bad genes than bad habits. While it is true that some populations have a greater susceptibility to the disease, you might think of genes as a loaded gun. It is almost always diet and lifestyle that pull the trigger. Eating animal products and processed foods—red meat, processed meat, high-fat dairy products, foods containing trans fats, fried foods, soft drinks, and refined carbohydrates, such as white flour and sugar—almost always increases the risk. In contrast, eating a fiber-rich diet of vegetables, fruits, whole grains, and legumes almost always decreases the risk. Lean, physically active people who eat diets consisting primarily of whole plant foods, such as those in poor, rural populations in Africa and Asia, have the lowest rates of type 2 diabetes in the world. However, as soon as people adopt Western eating patterns and become sedentary and overweight, their diabetes rates escalate.
Rates of diabetes among vegans have been reported to be less than 3 percent, compared to about 8 percent for nonvegetarians. A study following sixty thousand Americans reported that vegans developed diabetes about half as often as lacto-ovo vegetarians and 25 percent as often as nonvegetarians. Vegans were only 62 percent as likely to develop diabetes as nonvegetarians.
#### **METABOLIC MARKERS OF DIABETES IN VEGANS**
Vegans have fewer metabolic markers for diabetes. They are typically leaner, have lower blood glucose levels, more efficient insulin production, and lower levels of intramyocellular lipids, the fat inside cells that interferes with insulin action.
Research also suggests that blood glucose levels are much less likely to rise quickly after a vegan meal than after a nonvegetarian meal. Finally, a study on raw vegans reported reduced fasting glucose, fasting insulin, insulin resistance, and inflammation compared with endurance athletes or people eating standard Western diets.
#### **TREATING DIABETES**
In addition to reducing the risk of diabetes, a vegan diet can also successfully treat and even reverse the disease, as evidenced by several lifestyle programs. Although the vegan programs that have been found effective vary in the amount of starch, fat, and raw food they contain, all are built on whole plant foods. The most effective diets are consistently rich in fiber, phytochemicals, and antioxidants while also being low in saturated fat and free of trans-fatty acids and cholesterol.
Although many programs focus on very low-fat vegan diets, evidence suggests that higher-fat plant foods, especially nuts and seeds, may be beneficial for people with diabetes. In the Nurses' Health Study, the relative risk of developing diabetes dropped 27 percent for those eating five or more servings of nuts per week, compared to those never or almost never eating nuts.
Vegan diets also have been shown to significantly reduce nerve damage, fasting glucose levels, and the need for insulin. One research team showed that people with diabetes could lose weight on low-fat vegan diets without restricting calories or portion sizes. In these studies, people with diabetes improved more dramatically on a vegan diet than on a diet that followed the guidelines of the American Diabetes Association.
#### **A WORD OF CAUTION**
Not getting enough vitamin D, vitamin B12, and omega-3 fatty acids can accelerate the progression of diabetes. Recent evidence suggests that many people with diabetes or prediabetes don't get enough vitamin D. Vitamin B12 was found to be an effective treatment for diabetic peripheral neuropathy—perhaps even more effective than standard medications. Low levels of omega-3 fatty acids increase the risk of depression in people with diabetes, and preliminary evidence suggests that plant sources of omega-3s may reduce diabetes risk.
#### **THE TAKE-HOME MESSAGE ON DIABETES**
Currently, whole-foods vegan diets appear to be more effective than conventional therapy in preventing and treating type 2 diabetes. Well-designed vegan diets can even reverse the disease in some people. But to maximize this potential, the diet must be based on whole plant foods—vegetables, fruits, legumes, nuts, seeds, and whole grains—and it must ensure adequate intakes of all nutrients, especially vitamin D, vitamin B12, and omega-3 fatty acids.
### Osteoporosis
To most consumers, the popular advertising slogan "Got Milk?" is synonymous with "Got Bones?" The dairy industry's party line is straightforward: osteoporosis is a calcium-deficiency disease, and dairy products are the best sources of calcium. However, that argument quickly falls apart if you examine global differences in calcium intakes. High dairy consumption doesn't always result in lower rates of osteoporosis. As it turns out, those who consume the most calcium (and also the most dairy products) have _higher_ , not lower, rates of osteoporosis than populations that consume far less calcium.
While some consider this proof that dairy products contribute to osteoporosis, the evidence doesn't bear that out either. There are plenty of studies of people who have similar diets and lifestyles but varying dairy intakes. In such cases, those who consume dairy tend to have better bone density than those who don't. So what's going on?
To put it simply, osteoporosis isn't a dairy-deficiency disease; it isn't even a calcium-deficiency disease. It's a disease that involves a complex interplay of factors. While calcium is important to bone health, its impact can be significantly mitigated by other diet and lifestyle choices. No one would argue that cow's milk is a rich source of calcium; it provides about 300 mg per cup (250 ml). But that doesn't make it any more essential for people than moose or deer milk, which, incidentally, both contain about twice as much calcium as cow milk. It's estimated that during the Paleolithic era, when humans didn't have access to the milk of other mammals, calcium intake averaged 2,000 mg per day or more, predominantly from wild leafy greens. Some came from other plants or mineral ash, but none came from dairy.
#### **WHAT IS OSTEOPOROSIS?**
Bones are strong, somewhat flexible, living tissues that are constantly being remodeled by tearing down old bone and building up new. Up to the age of about thirty, the balance favors the cells that build bone, and bone density continues to rise until peak bone mass is reached. After age thirty or so, the body is able to balance the two processes for a while, but eventually the demolition crew begins to overtake the builders, and bone mineral density begins to diminish.
In some people, especially those who failed to achieve good peak bone mass during their early years, a condition of weakened bones known as osteopenia results. If the imbalance between bone breakdown and formation further accelerates, it can lead to the more serious osteoporosis, characterized by fragile, porous, and often brittle bones. In medical terms, osteoporosis sets in when 30 to 40 percent of existing bone has demineralized. Many people are unaware that their bones are losing minerals until a relatively minor fall, a bump, a hug, or even a cough causes a fracture.
Approximately 80 percent of osteoporosis occurs in women. Men are also at risk, but they tend to have greater bone mass, and the hormonal changes that negatively affect men's bone density occur almost a decade later than those that affect women. It's estimated that one in four North American women will develop osteoporosis. Postmenopausal women are at the greatest risk because bone is an estrogen-dependent tissue, and estrogen levels decline dramatically at menopause. The key to preventing osteoporosis is to accumulate as much bone as possible before age thirty and then make diet and lifestyle choices that minimize losses thereafter.
#### **DEM VEGAN BONES**
When Brenda was in her early forties, her doctor ordered a complete bone mineral density test because he believed she was at high risk for osteoporosis. He went through all of the strikes against her: she was a slim Caucasian female, she had stopped menstruating for two years in her late teens, and her mother was diagnosed with osteoporosis in her fifties. The fact that Brenda hadn't consumed dairy in more than a decade indicated to him that Brenda was at high risk.
As it turned out, he was stunned by the results of her test. It indicated that her bone mineral density was far greater than expected for her age. In fact, her bones were even stronger than what would have been expected at age thirty, when she had reached peak bone mass. Her doctor said, "I don't know what you are doing, but whatever it is, just keep doing it. Your bones are made of steel." The moral of the story is not that a vegan diet guarantees strong bones, but rather that a vegan diet doesn't preclude strong bones. It's possible to maintain excellent bone health without a single drop of cow's milk if your diet is well planned. On the other hand, a poorly planned vegan diet provides no advantage in terms of bone health and could potentially increase your risk.
Research on vegan bone health to date is somewhat limited, and the data isn't particularly encouraging. Although six studies found little or no significant differences in the bone health of vegans compared to other dietary groups, eight others reported that average bone mineral densities of vegans were about 10 to 20 percent lower than those of lacto-ovo vegetarians or nonvegetarians. One study showed increased fracture rates in vegans and one showed increased fracture risk.
No studies have reported significantly better bone health in vegans compared with lacto-ovo vegetarians or nonvegetarians. It is important to note, however, that the bone health of older adults reflects lifelong habits of diet, sun exposure, and exercise. The vegan diets consumed by the participants in these studies generally included few foods fortified with calcium or vitamin D. Today, vegan products fortified with calcium and vitamin D, such as nondairy milks, are far more readily available and most vegans consume them often. This can be expected to improve the results of future studies.
#### **BONE BUDDIES AND BULLIES**
Osteoporosis risk is increased by two groups of factors. The first are things we can't change: genetics, family history, advanced age, female gender, and Caucasian or Asian descent. In addition, we have limited ability to change low estrogen levels in women and low testosterone levels in men. The second group includes things we can change: smoking, heavy alcohol use, physical inactivity, minimal sun exposure, and poorly planned diets. All of these choices can have a profound impact on both the quality and the quantity of bone we produce and maintain. Physical activity, particularly weight-bearing exercise, sends a message to the bones to intensify bone-building efforts, helping increase bone density during childhood and adolescence and maintain bone density as we age.
The association between diet and bone health is complex, and research findings are inconsistent. We know that diets that supply sufficient calcium, magnesium, manganese, copper, boron, iron, zinc, fluoride, vitamin D, vitamin K, and vitamin C contribute to bone health, and that fruits, vegetables, and soy inhibit bone breakdown. Phosphorus is an important structural mineral for bones, but too much phosphorus and not enough calcium can weaken bones. While protein has generally been found to be protective and is an important component of bones, eating very high amounts of protein may be detrimental if you're not getting enough calcium.
Other dietary factors that are known to adversely affect bone health include the following:
* **Alcohol.** Chronic, excessive alcohol consumption reduces calcium and vitamin D absorption and can injure the liver, impairing the ability to activate vitamin D. Alcohol also can lower estrogen production, eroding the capacity to build bone.
* **Caffeine.** Caffeine appears to reduce the absorption of calcium; however, the effect is completely mitigated by a small increase in calcium intake. For example, adding milk to coffee compensates for the modest reduction in calcium absorption caused by the caffeine content. Fortified soy milk might be expected to do the same.
* **Sodium.** High sodium intake increases the excretion of calcium through urine and perspiration.
* **Vitamin A.** While preformed vitamin A, or retinol, which is present in animal products and some supplements, is necessary for bone growth, very high intakes can increase bone breakdown and interfere with the efforts of vitamin D to help the body absorb calcium. Carotenoids that can be converted to vitamin A, such as beta-carotene from plants, don't have this effect.
Numerous dietary factors benefit bone health, and vegan diets provide many of them. Vegans generally don't consume retinol and generally have lower intakes of sodium, alcohol, and caffeine (though not always). On the other hand, vegans tend to have lower intakes of calcium, vitamin D, and protein—nutrients that are critical to bone health—so you need to plan menus with these in mind.
#### **THE CALCIUM CONUNDRUM**
There is no controversy regarding the importance of calcium for bone health. Calcium is the structural mineral that predominates in bones, and it's necessary for both building and maintaining bone tissue. However, calcium also plays an important role in the functioning of the heart and nervous system. If dietary calcium is insufficient to maintain the levels necessary in the blood, calcium is quickly drawn from the bones to avert disaster.
A somewhat ambiguous and unpredictable relationship exists between calcium and bone health. While the evidence generally supports a positive association between calcium intake and bone health, some populations who eat less than 400 mg of calcium per day have lower rates of osteoporosis than populations who consume more than 1,000 mg per day. This is because calcium _balance_ is more critical than calcium _intake._
Calcium balance is determined by a complex interplay of intake, absorption, and excretion. When you retain enough calcium, you don't have to draw upon body reserves; you are in calcium balance. So if you eat foods that compromise calcium absorption and increase calcium excretion, you need to consume more calcium to compensate for the loss. On the other hand, if your diet maximizes calcium absorption and minimizes calcium excretion, your requirements would be considerably lower.
How much calcium do vegans need? It depends on how well designed the diet is and other lifestyle factors, such as physical activity. There is good evidence that intakes less than 525 mg per day increase risk. Until more definitive research is released, it's a good idea to make sure you get the recommended amount (1,000 mg per day for adults younger than fifty and 1,200 mg for those fifty and older). While foods, including those that are fortified with calcium, are the best option, take a supplement if your dietary calcium intake falls short. (For more information on calcium, see page 129.)
#### **THE VITAMIN D DEBACLE**
Vitamin D is no minor player in bone health. When blood levels of calcium begin to drop, the body converts vitamin D into its active form and puts it to work enhancing calcium absorption and reducing losses. Considering how absorption and excretion of calcium are involved in overall calcium balance, it's easy to see why vitamin D is every bit as relevant to bone health as calcium.
The problem for vegans is that they consistently consume less vitamin D than nonvegetarians. The reason is simple. Historically, humans derived vitamin D from sunshine, not food. Apart from fatty fish, very few foods were reliable sources of vitamin D. As humans migrated farther away from the equator, covered themselves in clothing, protected themselves against the elements by staying indoors, and began to live in smog-filled cities, vitamin D deficiency became widespread. Health authorities responded by adding vitamin D to a basic staple: cow's milk. Today, nondairy milks with added vitamin D are also widely available, although few people get enough vitamin D from either dairy or nondairy milk.
As a result of recent research, many experts believe that we should consider getting 25 mcg (1,000 IU) or more of vitamin D per day. In view of the reduced vitamin D status of many vegans, it is especially important that they get at least that much vitamin D per day, particularly if their exposure to sunshine is limited. (For more information on vitamin D, see page 104.)
#### **THE PROTEIN PARADOX**
For many years, a common belief among vegans was that avoiding animal protein provided protection from osteoporosis. This belief was supported by the fact that osteoporosis rates are higher in developed nations with high consumption of animal protein, even when intakes of calcium are high.
This theory held that a high intake of animal protein leads to bone loss and osteoporosis. The standard explanation went something like this: Animal protein is rich in amino acids that raise the acidity of the blood. In order to neutralize this acid, the body draws from its huge store of calcium—specifically, the calcium in our bones. Once the calcium does its job, it's excreted in urine. Given this association between animal protein consumption and calcium loss, the thinking was that vegans were protected against osteoporosis and also required less dietary calcium than meat eaters. Although the theory makes logical sense, it hasn't been supported by science. As it turns out, the connection between protein and bone health is a little more complicated than had been thought. In addition, the data on the bone health of vegans isn't as favorable as would be expected if the animal protein hypothesis were true.
Protein is involved in various metabolic activities, and some are beneficial to bone health, whereas others are detrimental. High protein intake causes calcium loss in the urine. However, the loss isn't as great when protein is consumed as part of a whole-foods diet rather than when it's consumed as a protein supplement. Acid-forming diets may also suppress bone-building activity and stimulate bone breakdown. While these activities can be detrimental, protein does have a flattering flip side. It has been shown to increase calcium absorption and enhance bone building.
Considering all of these factors together, it appears that protein generally offers modest protection to bones, particularly if you eat enough calcium and lots of fruits and vegetables. For vegans, getting sufficient protein appears to be an important piece of the bone health puzzle. In one study, vegetarians who ate the most protein-rich plant foods, such as legumes, meat analogs, and nuts, had the lowest risk for wrist fracture. Those who ate fewer than three servings of those foods per week had the highest risk. (For more information on protein, see chapter 3.)
#### **THE TAKE-HOME MESSAGE ON OSTEOPOROSIS**
Vegans do need to be concerned about long-term bone health. Although a well-planned vegan diet can help protect against osteoporosis, one that's poorly planned can compromise bone health. There are several steps you can take to build and maintain strong bones:
* Follow the recommendations in chapter 14, The Vegan Food Guide, to ensure ample intake of calcium, vitamin D, protein, vitamin K, potassium, and other bone-building nutrients.
* Aim for nine or more servings of vegetables and fruits each day.
* Include soy foods such as tofu, tempeh, and soy milk.
* Consume only moderate amounts of alcohol and caffeine or avoid them altogether.
* Don't smoke.
* Keep sodium intake below 2,300 mg/day, or 1,500 mg/day if you're over fifty, have high blood pressure, or are African-American.
* Aim for an hour of weight-bearing exercise most days.
### Other Diseases
Vegan diets have been shown to reduce risk or provide effective treatment for cataracts, diverticular disease, gallstones, kidney disease, and rheumatoid arthritis. The risk of dementia may increase or decrease with vegan diets, depending on several factors. Here are findings from some of the studies on the effects of a vegan diet on disease.
#### **CATARACTS**
Vegans may have the lowest incidence of cataracts of all dietary groups. In a large, fifteen-year study, the incidence of cataracts was highest in meat eaters and lowest in vegans, who had a 40 percent reduction in risk for the condition. This study doesn't prove that meat eating causes cataracts, but it certainly suggests an association that warrants further investigation.
#### **DEMENTIA**
Poor vitamin B12 status is a well-recognized contributor to memory loss and brain dysfunction. (However, supplementing with B12 doesn't appear to benefit those who already have dementia or Alzheimer's disease and aren't deficient in vitamin B12.) Vitamin B12 in animal products is bound to protein, and as we age, we get less efficient at cleaving the B12 off the protein. For this reason, everyone is advised to rely on B12 supplements or eat foods fortified with B12. This is especially important for vegans, as B12 status is often lower in this population. Then again, there's reasonable evidence to suggest that the risk is actually decreased for vegans who ensure adequate B12 intakes, because other components in plant-based diets are protective.
In addition to vitamin B12, folate and vitamin B6 are important; however, these two nutrients are abundant in most vegan diets. As an added bonus, vegans tend to have high intakes of antioxidants and phytochemicals, which appear to protect brain health. Of course, vegans who are physically active, get sufficient rest, avoid smoking and excessive alcohol, and keep their brains active and challenged further reduce their risk.
#### **DIVERTICULAR DISEASE**
Diverticular disease is endemic in the Western world but rare in areas where diets are high in unprocessed high-fiber foods. An impressive body of evidence supports the theory that diverticular disease is essentially a result of fiber deficiency. We know that vegans typically consume twice the fiber of nonvegetarians.
Vegans' risk for diverticular disease is 72 percent lower than that of meat eaters, according to a recent report from Epic-Oxford that included more than forty-seven thousand participants. A high-fiber vegan diet was thought to be largely responsible, but it's possible that the absence of meat also provided protection. This is because meat can negatively affect gut flora, reducing the integrity of the colon wall, and increasing the risk of diverticular disease.
#### **GALLSTONES**
To date, no studies have examined rates of gallstone formation in vegans. However, there is good evidence to suggest that vegetarians are at lower risk than nonvegetarians and that the factors that afford this protection may be stronger among vegans. Obesity and overweight are strongly linked to increased risk, and eating sufficient fiber, fruits, vegetables, vegetable protein, and unsaturated fat is related to decreased risk for gallstones. Eating lots of saturated fat, trans-fatty acids, cholesterol, and refined carbohydrates may increase the chance of getting gallstones. Vegans have the lowest risk of overweight and obesity, the lowest in-takes of saturated fat and cholesterol, and the highest intakes of fiber, vegetable protein, and fruits and vegetables. Therefore, it would be reasonable to assume that the risk of gallstones in vegans would be even lower than it is among lactoovo vegetarians.
#### **KIDNEY DISEASE**
Although excessive consumption of either animal protein or vegetable protein can cause renal injury and accelerate kidney disease, plant-based diets don't promote renal decline to the same extent as diets rich in protein from meat. Experts now believe a vegan diet may be a suitable replacement for the conventional low-protein diets prescribed to patients with mild chronic renal failure. (As a bonus, patients say the vegan diet is cheaper and tastes better.)
#### **RHEUMATOID ARTHRITIS**
Vegan diets appear to offer significant benefits for some people suffering from rheumatoid arthritis, a chronic inflammatory disease. Limited evidence suggests that raw or living-food diets can be especially effective. Vegan diets are generally replete with vegetables, fruits, and other whole plant foods, and these are the key sources of protective anti-inflammatory and antioxidant compounds. Vegan diets are also free of animal products, such as red meat and processed meats, and typically are low in processed foods, all of which promote inflammation. Phytochemicals beneficial in the treatment of rheumatoid arthritis have been reported to be ten times more abundant in vegan diets than in nonvegetarian diets. In addition, a vegan diet can reduce gut bacteria that produce harmful byproducts associated with inflammation.
Some experts argue that the benefits conferred by vegan diets are due to the removal of allergenic foods or foods that people tend to be sensitive to. Common triggers for food allergies and sensitivities, such as dairy products and eggs, aren't part of a vegan diet, and some vegan and raw diets often also exclude wheat and other gluten-containing grains.
### Our Evolving Concepts
Just a few short decades ago, vegan diets were viewed as downright dangerous. As evidence accumulated, vegan diets were recognized as nutritionally adequate as long as they were well planned. Today, vegan diets are acclaimed for their ability to prevent and even reverse chronic disease. Although this attitude shift is palpable, especially in relation to chronic disease, many people have lingering doubts about the nutritional adequacy of vegan diets. They still question the quality of plant protein and the quantities of vitamins and minerals supplied by plants.
In the next chapters, we address these concerns and provide information to help you construct a diet that provides everything your body needs to achieve optimal health. Let's start with protein.
## **CHAPTER 3**
## **Protein Power from Plants**
If you're already vegan, you've probably been asked, more than once, where you get your protein. If you're contemplating becoming vegan, maybe you're wondering about the very same thing. It is reassuring to know that plant foods can supply both the optimal quantity and quality of protein to meet all of our body's needs.
Most people equate protein with meat, seafood, eggs, and cheese so they assume a vegan diet is bound to be insufficient. That's probably because two-thirds of the protein in diets in North America and in many developed countries comes from animal products, and just 32 percent comes from plant foods. But worldwide, these numbers are quite different: plants contribute 65 percent of the protein in human diets globally, with about 47 percent coming from grains; 8 percent from legumes, nuts, and seeds; 1 percent from fruit; and the remaining 9 percent from vegetables.
These days, many vegans, including some influential speakers and writers, take for granted that protein intake is automatically sufficient on any vegan diet. After all, they reason, every plant contains protein. But this line of reason isn't entirely accurate either. It's true that all vegetables, legumes, seeds, nuts, and grains contain protein, and even fruit has a little. But a vegan diet can be short of protein if people eat mostly fruit (as some people on raw food diets do), if you don't eat enough calories (for weight loss or other reasons), if you eat a lot of junk food, or if you don't eat enough legumes (beans, peas, lentils, or peanuts).
### What Is Protein?
Proteins, like carbohydrates and fats, are macronutrients, meaning they can be used as sources of energy for the body, with carbohydrates being the body's preferred source. While protein can be used for energy, it's most important for a variety of other crucial functions. As a component of muscle and bone, protein is essential for the body's structure and movement. We also require protein for protection (as antibodies), to accomplish reactions (as enzymes), for coordinating body functions (as hormones), and as carriers (to move oxygen and electrons). In addition, we need protein for routine maintenance and the replacement of cells.
### How Much Protein Do We Need?
The recommended dietary allowance for protein, meaning the amount a person needs each day, is stated in grams of protein per kilogram (2.2 lb) of body weight per day, or g/kg/d. Both vegetarians and nonvegetarians are advised to get 0.8 g/kg/d, but some studies suggest vegans should aim for at least 0.9 g/kg/d, and 1 g per kg body weight is a reasonable and simple goal.
Table 3.1 lists the grams of protein needed by adult vegans of various weights, based on 0.9 g/kg/d. Note that extra body fat requires little protein, so if you're overweight, base your protein intake on what your ideal or healthy body weight would be.
#### **FACTORS AFFECTING PROTEIN NEEDS**
The amount of protein required varies depending on age and physical factors. For example, infants and children, who are building muscle and bone, have high protein needs per kilogram (2.2 lb) of body weight. In the first year of life, infants require almost twice as much protein per kilogram (2.2 lb) of body weight as adults. To be clear, that doesn't mean they require twice as much protein—only twice as much per kilogram (2.2 lb) of body weight. Because their bodies are small, the actual amounts of protein they need are small, typically about 11 grams of protein per day for infants ages six to twelve months and 19 grams per day for children ages four to eight. The amounts of protein required per kilogram (2.2 lb) of body weight gradually decrease until adulthood. (Menus that meet and exceed protein requirements during pregnancy, lactation, infancy, and childhood can be found in chapter 11.)
**TABLE 3.1.** Recommended protein intake for vegan adults
**BODY WEIGHT (lb)** | **BODY WEIGHT (kg)** | **RECOMMENDED PROTEIN (g)**
---|---|---
120 | 54 | 49
135 | 61 | 55
150 | 68 | 61
165 | 75 | 68
180 | 82 | 74
195 | 88 | 79
Sources of data are listed in _Becoming Vegan: Comprehensive Edition,_ by Brenda Davis and Vesanto Melina (Book Publishing Company, 2014).
After age sixty, the body's ability to use protein becomes less efficient. Vegan seniors need 1 to 1.1 g/kg/d, and getting enough protein can be a challenge without some planning. (For more information, see chapter 12.)
Vegans who are moderately involved in sports and exercise generally don't need more than 0.9 g/kg/d. They may need more carbohydrates than sedentary folks, since carbs are the ideal energy source for active people, but not more protein. On the other hand, endurance athletes may need more protein, particularly in the early stages of training and muscle building. Expert opinions vary, with recommended amounts ranging between 1.2 and 1.6 g/kg/d. Strength athletes also require extra protein, typically from 1.2 to 2.0 g/kg/d. For more on sports nutrition, see chapter 13, and for menus at several calorie levels that provide abundant protein, see chapter 14.
### Protein Quality
Two factors determine the quality of a protein: digestibility and amino acid content. Digestibility is a measure of how much protein is absorbed by the body, a process affected by the amount of fiber in the food. Plants contain fiber, and we don't digest some forms of fiber. These forms of fiber pass through the intestinal tract, taking a small amount of protein with them. Animal products contain no fiber. Refined plant foods contain only a fraction of the fiber of the original food, ranking them about even with animal protein in digestibility.
Food preparation methods can also affect protein digestibility. For example, soaking or sprouting legumes, seeds, and grains increases their digestibility. As their cells take up water, some of the proteins fragment, making them easier for the body to absorb. Soaking also may activate plant enzymes that begin the digestion process. Compounds that can inhibit digestion, such as phytates, also are broken down by soaking, which enhances digestibility. As a further benefit, sprouting beans for six days was shown to remove 70 to 100 percent of their oligosaccharides, compounds that sometimes cause flatulence. Note that beans larger than lentils and mung beans should always be cooked after sprouting. Sprouting can further improve protein quality by slightly increasing amounts of amino acids that may be in short supply.
Foods can be rated according to the digestibility of their protein. If we absorb 96 percent of the nitrogen (representing protein) and 4 percent passes out through the intestine, the protein digestibility rating of that food is 96 percent. Overall, protein in the American diet and the Chinese diet is rated as 96 percent digestible; Brazilian and East Indian diets of grains and beans are rated as 78 percent digestible.
**TABLE 3.2.** Digestibility of protein in various foods
**PLANT FOODS** | **DIGESTIBILITY (%)**
---|---
Refined white flour or white bread | 96
Soy protein isolate | 95
Peanut butter | 95
Tofu | 93
Whole wheat flour or bread | 92
Rolled oats | 86
Lentils | 84
Black, kidney, and pinto beans and chickpeas | 72–89
**ANIMAL PRODUCTS**
|
Eggs | 97
Milk and cheese | 95
Beef and fish | 94
Sources of data are listed in: _Becoming Vegan: Comprehensive Edition,_ by Brenda Davis and Vesanto Melina (Book Publishing Company, 2014).
Based on a glance at table 3.2, you might assume that you should choose white bread rather than whole wheat bread for your peanut butter sandwich, or highly processed soy protein isolate rather than tofu or cooked beans, due to their highly digestible protein. Yet the choice isn't so simple. While processing foods increases the digestibility of their protein by removing fiber and other materials, it can strip the foods of valuable vitamins, minerals, and phytochemicals. In fact, consuming some refined food can be a wise choice at times to help make a diet less bulky for small children or seniors, or for those with high energy needs.
The second factor that determines the quality of protein is its amino acid content. Amino acids are the building blocks of protein. They are made of carbon, hydrogen, oxygen, and nitrogen. Each protein molecule is an intricate structure that consists of amino acids (typically hundreds of them) in specific sequences and arrangements.
Nine of the twenty amino acids are known as indispensable amino acids, formerly called essential amino acids: phenylalanine, valine, threonine, tryptophan, isoleucine, methionine, leucine, lysine, and histadine. They are called indispensable because we have to get them from food. We can build the other eleven amino acids from them. Fortunately, every one of these indispensable amino acids is present in both plant foods and animal products.
### Noteworthy Amino Acids for Vegans
Although all indispensable amino acids are readily available from plant foods, it's important for vegans to eat a wide variety of plant foods to ensure adequate intakes of each (not to be confused with protein complementing, discussed below). In addition, two of these, lysine and tryptophan, are of special interest, as well as one amino acid that has become a popular supplement, carnitine.
#### **LYSINE**
The indispensable amino acid lysine is in relatively short supply in many diets worldwide, especially in diets centered on foods such as corn, wheat, rice, and most other grains, which tend to be low in lysine. Lysine is required for growth, and low intakes of calories, protein, and lysine specifically are the reasons for the small stature of some people in regions where dietary choices are limited.
The adult recommended intake for lysine is 38 mg/kg/d. Three servings of legumes will generally provide half of the recommended intake of protein and two-thirds of the lysine for the day. Since ½ cup (125 ml) of cooked legumes is considered a serving, this could be met, for example, with ½ cup (125 ml) of beans in a salad at lunch, plus 1 cup (250 ml) of lentils in a soup at supper. Or you could start the day with a smoothie that includes pea or soy protein powder or soy milk, snack on peanuts or a peanut butter sandwich, and have beans or tofu at supper. Including beans, peas, and lentils as staples on a daily basis goes a long way toward ensuring an adequate vegan diet. A little dab of hummus on a cracker or a celery stick just won't cut it.
People on raw vegan diets tend to eat few if any beans. If you're in that category, you can get your lysine from fresh green peas or sprouted lentils, peas, and mung beans. As a bonus, sprouting increases lysine content.
#### **TRYPTOPHAN**
After the growth spurt of early childhood, we need to turn our attention to another indispensable amino acid, tryptophan, which is important for maintenance. Again, beans, especially soy, and peanuts contain abundant tryptophan. Wheat, oats, millet, and buckwheat provide moderate amounts. Those on raw vegan diets can emphasize spinach, peas, sesame and other seeds, and nuts.
#### **CARNITINE**
Carnitine isn't indispensable; our bodies can synthesize it from other amino acids—in this case, lysine or methionine, both of which are present in vegan diets. Carnitine helps the body convert fat into energy by carrying fatty acids into the energy production centers in cells (mitochondria) and removing waste products. It's promoted as a supplement for weight loss and improved sports performance, although research hasn't found evidence that it performs as claimed. In fact, carnitine has been linked to heart disease and prostate cancer, so lower intakes of carnitine by vegans may turn out to be a considerable health advantage. The body typically makes sufficient carnitine to meet the needs of most people, with the exception of preterm infants and people on diets deficient in protein.
Carnitine is found in beef and in lesser amounts in other animal products. It is present in a few plant foods in very small amounts. Whereas ½ cup (125 ml) of cow's milk provides 4 mg of carnitine, ½ cup (125 ml) of asparagus contains only 0.2 mg, and a peanut butter sandwich contains 0.3 mg.
Although vegans obviously don't eat beef, they still tend to have normal plasma carnitine levels because their bodies make it from the lysine in legumes and the methionine in grains and vegetables. The synthesis of carnitine is dependent on vitamin C, niacin, vitamin B6, and iron, all of which are abundant in balanced vegan diets.
A small proportion of people (on any diet, vegan or otherwise) have found that taking supplemental carnitine helped reduce migraine headaches, hypoglycemia, or muscle weakness. Over-the-counter acetyl-L-carnitine supplements in veggie caps, which are vegan, are available in the United States, but in Canada they are only available by prescription. Amounts as high as 500 mg per day are generally regarded as safe, though research is limited. Taking larger amounts, such as 4 grams per day, can have side effects, including nausea, diarrhea, and a fishy body odor, and may significantly increase your risk of chronic disease. Don't take carnitine if you're pregnant, have thyroid problems, or have a history of seizures.
### Protein Complementing
Plant protein has gotten a bad rap for years. It's been dismissed as "incomplete," and vegans were told to be careful to combine foods at each meal to ensure intake of "complete" protein. This idea stemmed from the belief that many plant foods lacked some of the amino acids or contained very little. Vegans were advised to eat certain plant foods together to get the complete spectrum of indispensable amino acids. We now know that all amino acids are present in every whole plant food, and that eating a variety of healthful vegan foods every day usually provides all the needed amino acids.
The theory does have a grain of truth in it. Different foods and food groups contain different amounts of amino acids. Most legumes and seeds provide abundant lysine but are somewhat short in methionine, whereas grains tend to be good sources of methionine but low in lysine. As a result, eating a mixed diet that includes legumes, seeds, grains, and vegetables within a twenty-four-hour period easily provides adequate amounts of every amino acid that we require.
All over the world, legumes and whole grains provide the optimum mix of amino acids. In Southeast Asia, meals are centered on tofu and rice. In the southern United States, a favorite combination is black-eyed peas and cornbread, or the ubiquitous peanut butter sandwich. Ethiopians appreciate lentils and teff. The Scots have long enjoyed white bean soup and oatcakes. In Egypt, menus feature fava beans and millet. The French and French-Canadians appreciate split pea soup with freshly baked bread, and Boston is known for baked beans and brown bread. Latin Americans enjoy colorful meals of black beans with quinoa, rice, or tortillas made from wheat or corn.
_Balancing Macronutrients_
For a balanced diet, aim for 10 to 20 percent of calories from protein, 50 to 75 percent of calories from carbohydrate, and 15 to 30 percent of calories from fat.
### Percent of Calories
W hen the body converts fat, protein, and carbohydrate to calories, we derive 9 calories from each gram of fat and 4 calories from each gram of protein or carbohydrate. Table 3.3 (page 54) lists the amount of protein in foods plus the percentage of calories from protein, fat, and carbohydrates.
Every unrefined or whole plant food supplies small or moderate amounts of protein. Calories from protein in green vegetables and in legumes are typically in the range of 10 to 37 percent. Tofu is somewhat higher in protein, and veggie meats are higher still. Calories from protein in most nuts, seeds, and grains typically range from 9 to 17 percent. Fruits are at the low end of the spectrum, with just 2 to 10 percent of calories coming from protein.
**Protein.** In your overall diet, you should try to get 10 to 20 percent of your calories from protein. Most people get 10 to 15 percent of calories from protein, and vegan diets typically fall within this range. Those who don't consume many calories, such as the elderly or those who are trying to lose weight, should aim toward the upper end of the 10 to 20 percent range. When people consume insufficient calories, as they intentionally do on a weight-loss diet, the percentage of total calories from protein should be about 15 to 20 percent of calories, otherwise they'll lose not only weight but also muscle mass.
**Carbohydrates.** Carbohydrates should provide 50 to 75 percent of your calories. Raw vegan diets may provide a little less carbohydrate and still be healthful. (For more on carbohydrates, see chapter 5.)
**Fat.** Fat should provide 15 to 30 percent of your calories, though people on special therapeutic diets for reversal of chronic diseases such as cardiovascular disease can benefit from a diet with as little as 10 percent of calories from fat. As you can see in table 3.3, lettuce and other leafy greens provide 8 to 13 percent of calories from fat (without a drop of salad dressing). Some raw vegan diets with abundant nuts, seeds, and avocados have a higher proportion of calories from fat but are still considered healthful. (For more on fat, see chapter 4.)
TABLE 3.3. Calories, protein, and percentage of calories from protein, fat, and carbohydrates in selected foods
Sources of data: US Department of Agriculture, Agricultural Research Service, USDA National Nutrient Database for Standard Reference, Release 25 (2012), ndb.nal.usda.gov. ESHA Research, The Food Processor software, version 10.12.0.
Key: c = cup; g = gram; oz = ounce; tbsp = tablespoon.
*Check labels for product-specific information.
**Laboratory analysis by Cantest Lab, arranged by authors.
Meat, eggs, and cheese are significant protein sources, with 24 to 36 percent of their calories coming from protein. However, what is truly distinctive about these animal products is their high levels of fat and cholesterol. Meat, eggs, and cheese could be viewed primarily as sources of fat, rather than protein, since 60 to 75 percent of their calories are derived from fat. As you can see in table 3.3, many plant foods provide 25 to 35 percent of calories from protein, and veggie meat analogs go even higher—but without cholesterol, and typically with much less fat.
### The Soy Controversy
Soy is well-known for its top-quality protein and the protection it offers against certain chronic diseases. At the same time, there may be more controversy surrounding soy than any other food. The roots of the controversy lie in both good science and bad science, and perhaps in the fact that soy poses a threat to the animal products industry. Also see "The Soy-Cancer Debate" on page 34.
Research has established that the components in soy known as isoflavones have certain protective effects, including reducing hot flashes and perhaps wrinkles. They bind to estrogen receptors in women and girls, and one or two servings per day over a lifetime can protect women against breast cancer, but that protective effect appears to be linked to consumption of soy in childhood and/or adolescence. For women who have had breast cancer, soy and its isoflavones decrease the risk of recurrence and death from breast cancer. Soy also provides health benefits to men. Among men who regularly consume soy foods risk of prostate cancer is reduced by an estimated 26 percent. In addition, significant evidence indicates that eating one or two servings of soy foods per day can lower levels of LDL (bad cholesterol).
However, people with thyroid problems should limit soy, which can affect the thyroid in people who are subject to hypothyroidism and in those who are deficient in iodine. Solutions involve adjusting the dosage of thyroid hormone for those with hypothyroidism and consuming adequate iodine to avert deficiency. (For more on iodine, see page 135.) For these individuals, it makes sense to limit soy consumption until the thyroid problem is corrected.
The bottom line is that, although soy isn't an essential part of a vegan diet, including some soy foods in the diet is an excellent and often easy way for adults and particularly for children to achieve recommended intakes of protein. Edamame, or young whole soybeans, are a natural, unprocessed form that's generally easier to digest. Tofu and soy milk are versatile soy foods with proven nutritional and health benefits, as evidenced over centuries of use across Asia. Tempeh is similar, and the fermentation process it undergoes enhances its digestibility and increases the availability of its minerals. Soy protein isolate (aka isolated soy protein) is highly refined but also provides concentrated, high-quality protein in a convenient form as veggie meats or protein powder. Rather than judging one of these forms of soy as better than another, it makes sense to regard them as variations that are suited to various uses, occasions, or dietary preferences. Be sure to choose organic soy foods.
### The Final Word on Protein
Getting enough protein is easily accomplished on a plant-based diet, especially once you learn simple and tasty ways to include beans, peas, lentils, and soy foods in your diet. As a bonus, these high-protein ingredients also deliver iron, zinc, lysine, tryptophan, and many other nutrients. They also help stabilize blood sugar levels. For these reasons, this book emphasizes the use of legumes, and its companion volume, _Cooking Vegan_ , by V. Melina and J. Forest (Book Publishing Company, 2012), provides recipes for delicious protein-rich dips, spreads, soups, entrées, and desserts. Beyond legumes, many vegetables, seeds, nuts, and grains contain plenty of protein.
An advantage of the many high-protein plant foods is that they tend to be low in fat, and the fat tends to be the kind our bodies need. In the next chapter, we will learn that fat isn't always the pariah that it's made out to be. There's good fat, and then there's bad fat. Know the difference.
## **CHAPTER 4**
## **Fat Matters**
For years, the lack of animal fat and cholesterol was the trump card that set vegan diets apart and attracted people afflicted with chronic diet-related diseases or who wanted to prevent them. Today, however, there's controversy over whether fat is the bogeyman we were led to believe, or whether refined carbohydrates bear more of the responsibility for so many diseases. And if fat is the culprit, are all fats bad? In this chapter, we'll cut through the confusion, starting with some basic definitions.
### A Primer in Fats
Fat is one of the three macronutrients. Like protein and carbohydrates, fat provides energy for the body. Fat supplies 9 calories per gram, more than twice the energy of protein or carbohydrate. However calorie for calorie, fat is less filling, which may partially explain the link between high-fat diets and weight gain.
In addition to providing energy, fat is also an essential component of cell membranes and is used to make hormones and hormonelike substances that help control many body systems. In digestion, it aids in the absorption of phytochemicals and some vitamins. In addition, fat provides physical padding and insulation that shields the body from extreme temperatures. It also serves as a shock absorber for vital organs, allowing us to take part in high-impact physical activities. Fat is also important for healthy skin, hair, and bones.
#### **GOOD FATS VERSUS BAD FATS**
While fats are essential to life, they are not all equal: some are good, some are bad, and others are downright ugly.
The good fats are those in whole plant foods. They come neatly packaged with protein, unrefined carbohydrate, fiber, phytochemicals, phytosterols, antioxidants, and a variety of vitamins and minerals. All plant foods contain some fat, but the most concentrated fat sources are nuts, seeds, avocados, coconuts, and olives. The fat in plant foods is largely unsaturated, with the exception of coconut and palm oils, which are predominately saturated. Although saturated fats are linked to increased risk of certain diseases, when consumed as a part of a whole-foods, plant-based diet, there is little evidence suggesting adverse effects.
It's best to obtain fat through whole foods, since processing exposes them to oxygen, light, and often heat and harsh chemicals, all of which can damage the fat. Plus, refining removes most of the protective components associated with the whole food. However, if properly stored, unrefined expeller-pressed oils can be a source of healthful fats.
Bad fats are so called because they are strongly linked to increases in cholesterol, insulin resistance, colorectal cancer, and lung cancer. They are found primarily in meat and dairy products and are mostly saturated.
Ugly fats are those that wreak havoc in the body and are implicated in many diseases. Trans-fatty acids and fats damaged by exposure to high heat fall into this category. Trans-fatty acids raise cholesterol levels, trigger inflammation, increase insulin resistance, and compete against essential fatty acids for incorporation into cells. Fats heated to high temperatures can be carcinogenic. Ugly fats are mostly found in deep-fried fast foods and in processed foods. In the latter case, they will be noted in the nutritional information on the package. It's best to avoid them completely.
Of course, the terms "good," "bad," and "ugly" are neither scientific nor precise. So in the sections that follow, we'll define some key terms in regard to fats.
#### **FATTY ACIDS**
Fatty acids, also sometimes referred to as lipids, are the basic components of fats and oils. All foods contain three types of fatty acids in varying amounts: monounsaturated, polyunsaturated, and saturated. Those names refer to the amount of hydrogen attached to the carbon atoms in the fatty acid. The more hydrogen, the more saturated they are.
**Monounsaturated fats.** In monounsaturated fats, one spot in the carbon chain isn't bound to hydrogen (hence "mono"). Oils rich in monounsaturated fats, such as olive oil, are generally liquid at room temperature but become cloudy and thick when refrigerated. The richest dietary sources of monounsaturated fat are olives, olive oil, canola oil, avocados, and nuts and their oils and butters, with the exception of walnuts, butternuts (also known as white walnuts), and pine nuts. Monounsaturated fat has been shown to have neutral or slightly beneficial effects on health, with modest beneficial effects on cholesterol levels. Replacing saturated fat, trans-fatty acids, or refined carbohydrates with monounsaturated fat reduces total and LDL (bad cholesterol) and slightly increases HDL (good cholesterol).
**Polyunsaturated fats.** In polyunsaturated fats, more than one spot in the carbon chain isn't bound to hydrogen. Oils high in polyunsaturated fat are liquid when refrigerated. Polyunsaturated fats generally have favorable effects on health and are present in many plant foods, especially vegetable oils, seeds, nuts, grains, and legumes. When it replaces saturated fat, trans-fatty acids, or refined carbohydrates in the diet, total and LDL cholesterol levels decrease and HDL may slightly increase.
**Saturated fats.** In saturated fats, the carbon chain is completely packed or "saturated" with hydrogen. Saturated fat is generally solid at room temperature, as is the case with butter and other animal fats. Most high-fat plant foods contain much less saturated fat than animal fats with the exception of tropical oils. Coconut fat is close to 90 percent saturated, palm kernel oil about 85 percent saturated, and palm oil is about 50 percent saturated. High intakes of saturated fat have been linked to an increased risk of coronary artery disease and insulin resistance. Despite current controversy as a result of contradictory findings in 2010, most of the scientific studies since the mid-1990s have found an association between saturated fat intake and higher risk for diabetes and cardiovascular disease. But again, when saturated fats are consumed as a part of a whole-foods, plant-based diet, there is little evidence suggesting adverse effects.
**Cholesterol.** Cholesterol is a type of fat called a sterol. It's necessary to the structure of every cell, but the body makes all the cholesterol it needs, so there's no need to eat foods containing it. Only animal foods contain cholesterol. High intakes may increase the risk of chronic diseases, especially those of the heart and blood vessels.
**Phytosterols.** Phytosterols, or plant sterols, are healthful fats and help block cholesterol absorption in the gut. All whole plant foods contain small amounts of phytosterols. The most concentrated sources are vegetable oils, seeds, nuts, avocados, wheat germ, legumes, and sprouts.
**Trans-fatty acids.** You have undoubtedly heard of trans-fatty acids, or trans fats. These are fats formed by partial hydrogenation, an industrial process that converts liquid oil into solid fat by adding hydrogen until the fat is almost, but not completely "saturated." (Trans-fatty acids also are found naturally in some animal products, but only in minute quantities.) Although partially hydrogenated vegetable oils were originally introduced as more healthful substitutes for lard and butter, they have since been found to be even more damaging to human health, strongly increasing the risk of cardiovascular diseases. Although the partially hydrogenated fats found naturally in animal products don't appear to be as damaging to the cardiovascular system, they may increase insulin resistance more than manufactured trans fats. In addition, natural trans-fatty acids reduce levels of HDL cholesterol and markedly increase lipid peroxidation, a process that leads to cell damage. In North America, efforts are underway to remove artificial trans fats from the food supply.
### Back to the Essentials
There are two distinct families of polyunsaturated fats: omega-3 fatty acids and omega-6 fatty acids. These fats are required for the synthesis of many compounds that regulate immune and inflammatory responses, are important structural components of cell membranes, and are necessary for nervous system function and vision.
Each of these families contains one essential fatty acid (EFA). They are called essential because the body cannot make them, yet they are necessary for life. The two essential fatty acids are alpha-linolenic acid (ALA), the foundation or parent of the omega-3 family, and linoleic acid (LA), the parent of the omega-6 family. The essential fatty acids can be converted into larger, long-chain fatty acids: ALA to eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA) and LA to gamma-linolenic acid (GLA) and arachidonic acid (AA). These long-chain fatty acids are used to produce hormonelike compounds that have a significant benefit on many body functions, including blood clotting, blood pressure, immune response, cell division, pain, inflammation, and numerous diseases. Vegans must rely on conversion to produce important long-chain fatty acids, as animal products are the primary dietary sources. While vegans tend to produce plenty of long-chain omega-6 fatty acids, omega-3 conversion can be more precarious. There are several steps vegans can take to maximize conversion, and to ensure good EFA status.
#### **GETTING ENOUGH OMEGA-3S**
EPA plays an important role in reducing chronic inflammation and may protect against certain mental disorders. Plus, the body can convert EPA to DHA, which is necessary for the development and maintenance of brain and eye function. On average, vegans' blood levels of EPA and DHA are about half those of omnivores. The breast milk of vegan women contains only about 38 percent of the DHA found in the breast milk of omnivores, according to one study. There's some evidence that low levels of DHA in pregnant and nursing women could lead to less visual acuity, growth, development, and cognition in babies and toddlers. However, research on the growth and development of vegan children has failed to reveal any deficiencies in visual or mental development when mothers get sufficient vitamin B12 and enough calories. In any case, it seems prudent for vegans to ensure their omega-3 status is optimal.
Begin by eating a nutritionally adequate diet. By following the food guide in chapter 14, you'll make sure you're getting sufficient protein, vitamins, and minerals to maximize your ability to convert ALA into the more biologically active EPA and DHA. Avoid trans-fatty acids and excess consumption of alcohol or caffeine, since they can reduce your ability to convert ALA.
Include good sources of ALA in your diet. The richest sources are chia seeds, ground flaxseeds, hempseeds, and walnuts. Select oils rich in omega-3s, such as cold-pressed flaxseed oil or hempseed oil, or balanced oils that include plenty of omega-3s, for use in uncooked foods and salad dressings. Try Liquid Gold salad dressing (page 105) for a boost in omega-3s. See Sources of Essential Fatty Acids (facing page) for food sources of omega-3 and omega-6 acids; then take a look at table 4.1 (page 68) for the specific amounts of these fatty acids in a variety of foods.
**_Sources of Essential Fatty Acids_**
Getting sufficient essential fatty acids, with a ratio of omega-6s to omega-3s ranging from about 2 to 1 to 4 to 1, is an important step in optimizing conversion of ALA to EPA and DHA. For most people, this means eating more omega-3 fatty acids, and in some cases, cutting back a little on omega-6s. However, as you'll see, many foods, such as soybeans, wheat germ, and walnuts are sources of both. For more precise information, see table 4.3. Also, just for the record, regular eggs contain small amounts of DHA, whereas the eggs from chickens given feed rich in omega-3s are considerably higher.
The following lists of sources of omega-3s and omega-6s can help you make better choices.
**SOURCES OF OMEGA-3 FATTY ACIDS**
**Alpha-linolenic acid (ALA)**
Canola oil
Chia seeds and chia oil
Flaxseeds and flaxseed oil
Green leafy land and sea vegetables
Soybeans and soybean oil
Walnuts and walnut oil
Wheat germ and wheat germ oil
**Eicosapentaenoic acid (EPA) and decosahexaenoic acid (DHA)**
Breast milk
Eggs
Fish and seafood, particularly cold-water, oily fish
Microalgae (not blue-green algae)
Sea vegetables (mostly EPA)
**SOURCES OF OMEGA-6 FATTY ACIDS**
**Linoleic acid (LA):**
Corn kernels and corn oil
Grapeseed oil
Hempseeds and hempseed oil
Pine nuts
Pumpkin seeds and pumpkin seed oil
Safflower oil
Sesame seeds and sesame seed oil
Soybeans and soybean oil
Sunflower seeds and sunflower seed oil
Walnuts and walnut oil
Wheat germ and wheat germ oil
**Gamma-linolenic acid (GLA)**
Black currant oil
Borage oil
Evening primrose oil
Hempseed oil
Spirulina
To ensure sufficient ALA for conversion, most vegans will need to double the RDA. This means at least 3.2 grams of ALA for men and 2.2 grams ALA for women. The higher ALA intakes help to shift the balance of essential fatty acids towards more efficient conversion. If you take daily DHA or EPA supplements, the RDA for ALA is sufficient—at least 1.6 grams per day for men and 1.1 grams for women. Table 4.2 lists the recommended daily intakes for both those who rely solely on ALA and those who also include DHA or EPA supplements. In addition to dietary factors, conversion can be adversely affected by genetics, male gender, advancing age, smoking, and chronic diseases such as diabetes, metabolic syndrome, hypertension, and high cholesterol levels.
**TABLE 4.1.** Eessential fatty acid content of selected plant foods
Sources of data: US Department of Agriculture, Agricultural Research Service, _USDA National Nutrient Database for Standard Reference_ , Release 25 (2012), ndb.nal.usda.gov. Sanders, T., and Lewis, F., "Review of Nutritional Attributes of Good Oil (Cold Pressed Hemp Seed Oil)," Nutritional Sciences Division, King's College London (2008), goodwebsite.co.uk/kingsreport.pdf.
Key: c = cup (250 ml); g = gram; ml = milliliter; tbsp = tablespoon.
**TABLE 4.2.** Adequate intake (AI) of omega-3 fatty acids and suggested intakes for vegans
**ADEQUATE INTAKE (AI)** | **DAILY AI OF ALA** | **SUGGESTED DAILY INTAKE OF ALA WITHOUT EPA/DHA SOURCES** | **SUGGESTED DAILY INTAKE OF ALA WITH EPA/DHA SOURCES**
---|---|---|---
Infants 0–12 months | 0.5 g | N/A* | Omega-3s from breast milk are adequate. If using formula, select one with DHA.
Children 1–3 years | 0.7 g | 1.4 g | Breast milk or
| | |
0.7 g ALA + 70 mg DHA
Children 4–8 years | 0.9 g | 1.8 g | 0.9 g ALA + 90 mg DHA/EPA
Boys 9–13 years | 1.2 g | 2.4 g | 1.2 g ALA + 120 mg DHA/EPA
Girls 9–13 years | 1.0 g | 2.0 g | 1.0 g ALA + 100 mg DHA/EPA
Males 14+ years | 1.6 g | 3.2 g | 1.6 g ALA + 160 mg DHA/EPA
Females 14+ years | 1.1 g | 2.2 g | 1.1 g ALA + 110 mg DHA/EPA
Pregnancy | 1.4 g | 2.8 g | 1.4 g ALA + 200–300 mg DHA
Lactation | 1.3 g | 2.6 g | 1.3 g ALA + 200–300 mg DHA
Sources of data: National Research Council, _Dietary Reference Intakes for Energy, Carbohydrate, Fiber, Fat, Fatty Acids, Cholesterol, Protein, and Amino Acids (Macronutrients)_ (Washington, DC: National Academies Press, 2005). Saunders, A., et al., "Omega-3 Polyunsaturated Fatty Acids and Vegetarian Diets," _MJA Open_ 1, no. 2 (2012): 22–25.
Key: g = gram; mg = milligram.
*Not applicable because infants get DHA from breast milk or appropriate commercial formula.
Keep tabs on your omega-6 intake. Too much omega-6 can reduce omega-3 conversion, increasing health risk. For vegans, the ideal ratio of omega-6s to omega-3s ranges between 2 to 1 and 4 to 1. For most people this means an omega-6 intake of about 9 to 13 grams daily. Getting too much omega-6 is easy, especially if you use cooking oils rich in omega-6s, such as sunflower, safflower, corn, grapeseed, or sesame oil. Many processed foods rely on oils that contain a lot of omega-6s, so try to limit those. If you use cooking oils or packaged foods containing oils, look for those that are mainly monounsaturated, such as extra-virgin olive oil, organic canola oil, or high-oleic sunflower or safflower oil. While these oils provide some omega-6s, they are present in much smaller quantities.
While it is possible to push your intake of omega-6s too high even when eating whole foods, this isn't an issue for most people. However, a sure way to keep omega-6 intake under control is to minimize use of oils rich in omega-6s and limit consumption of foods rich in omega-6s, such as pumpkin seeds, sunflower seeds, sesame seeds, and pine nuts, to about 1 ounce (30 g) per day in a 2,000-calorie diet.
It's also important to recognize that while the fats from avocados and most nuts are mainly monounsaturated, these foods do contribute omega-6s. Most nuts contain 1 to 3 grams of omega-6s per ounce (30 g), and pecans have almost 6 grams, while half an avocado provides less than 2 grams. Grains are also far higher in omega-6s than omega-3s, so including some concentrated omega-3 sources can help bring omega-6s into balance.
Consider including direct sources of DHA and EPA in your diet. While this isn't essential, there's good evidence that doing so will boost your omega-3 status. This is especially important during pregnancy and lactation, and also for people who have diabetes or hypertension, who may have difficulty with conversion.
The only vegan sources of EPA and DHA are microalgae and sea vegetables. Vegan supplements providing DHA or DHA plus EPA are widely available, but they're relatively expensive. For most people, an intake of 100 to 300 mg per day is reasonable. (For sources, do an Internet search using "vegan DHA" or "vegan DHA and EPA.") Microalgae-based DHA is also being added to some soy milks, cold-pressed oils, juices, cereals, and other foods, although the amounts are relatively small.
Blue-green algae (spirulina and _Aphanizomenon flos-aquae_ ) are low in EPA and DHA. Spirulina is rich in GLA, while about 40 to 50 percent of the fat in _Aphanizomenon flos-aquae_ is ALA. While blue-green algae isn't a significant source of EPA or DHA, some research indicates that it may promote more efficient omega-3 conversion than what is commonly seen with land plants.
To ensure sufficient omega-3 intake for infants, they should breast-feed for at least two years and beyond if possible, with mothers maintaining their intake of omega-3s. If breast-feeding stops before twelve months of age or formula is used as the primary milk, select a formula with added DHA. Once babies are weaned to fortified, full-fat soy milk (only after one year of age), they may benefit from a supplement providing 70 mg of DHA per day. For pregnant and lactating women, DHA intakes of at least 200 mg per day are recommended.
### How Much Fat Do We Need?
One of the most fiercely debated issues in nutrition is how much fat we should eat. For years, the common belief was the less, the better. But recently the low-fat mantra has fallen out of favor, yielding to a more moderate message, and research is backing the idea that quality seems to trump quantity, particularly when calorie intakes aren't excessive.
Fat intakes vary significantly among healthy populations around the world, and it appears that the percent of total calories from fat is not a critical factor in terms of health and longevity. For example, traditional diets of rural Asians commonly provide about 10 to 15 percent of calories from fat, while those of healthy Mediterranean populations frequently exceed 35 percent of calories from fat. So what do the diets of these people, renowned for longevity, have in common?
First, these populations eat mostly plant foods and seldom consume highly processed fast food and convenience foods. Meat is typically reserved for special occasions, and some people avoid it altogether. Beans, whole grains, and garden vegetables are the foundation of the diet among populations with the greatest longevity. In some regions, nuts, seeds, soy foods, antioxidant-rich spices, and red wine are also important parts of the diet.
Vegans display a similarly broad range in percent of calories from fat. At one end of the spectrum are adherents of a no-oil, very low-fat approach, and at the other are aficionados of a raw vegan diet, who may get 40 percent or more of their calories from fat because nuts and seeds are their primary sources of protein and they tend to eat fewer starchy foods, such as grains, legumes, and starchy vegetables. Yet somehow, people at both ends of the spectrum are healthy. As to what level of fat intake is best for the garden-variety vegan, it depends on many factors, including stage of life, state of health, metabolism, and the quality and types of fat consumed. The short answer is that a relatively broad range of fat intakes can be healthful, as long as the fat is good fat and calorie intake isn't excessive.
Most major health organizations agree that fat intake should range from a low of 15 to 20 percent of calories to a high of 35 percent of calories. They also agree that saturated fats, trans-fatty acids, and cholesterol should be restricted. There are no separate recommendations for vegans, and there's no reason to assume that their requirements would differ from those of nonvegans. However, limited evidence from studies on people eating a raw vegan diet suggests that higher total fat intakes can be healthful when the fat is from whole plant foods, such as nuts, seeds, and avocados.
If you're very physically active or require a lot of calories to maintain your body weight, you could probably aim toward the higher end of the range: 25 to 35 percent fat. If you're overweight, require fewer calories, or have a chronic disease, such as cardiovascular disease, it might be best to aim toward the lower end: 15 to 20 percent fat. A fat intake below 15 percent of calories can be safe and effective in the treatment and reversal of chronic disease. However, this generally isn't advised for healthy people, and it isn't suitable for children or adolescents.
Let's take a look at what those percentages translate to. Assuming a diet of 2,000 calories per day, at the lower end of the range you could eat 33 to 44 grams of fat per day, and at the higher end you could eat 66 to 77 grams. Most vegans average 30 percent of calories, compared to an average of 36 percent among people eating a standard American diet. While that 6 percent difference is significant, the sources of fat in the vegan diet are more noteworthy. Vegans eat no cholesterol and only about half as much saturated fat as omnivores. Trans-fatty acid intakes vary depending on how many convenience foods and other processed foods the person eats. However, many vegans eat negligible amounts of processed foods.
#### **PROS AND CONS OF A VERY LOW-FAT DIET**
Some of the most highly respected vegetarian and vegan health authorities recommend limiting fat in the diet to no more than 10 percent of total calories (22 grams on a diet of 2,000 calories per day) because they believe that this is the best way to protect against chronic disease. While there's little evidence to suggest that lower-fat diets are more protective against chronic disease, very lowfat diets have proven to be an effective therapeutic intervention for thousands of people with life-threatening chronic diseases. Considering the extent to which these diseases afflict Westerners, the value of that dietary approach cannot be ignored. Unfortunately, studies haven't yet compared the disease-fighting power of very low-fat vegan diets with vegan diets that provide more fat in the form of nuts, seeds, and other whole foods.
Low-fat proponents strongly advise against the use of concentrated fats and oils, yet the long-lived populations of the world use some oil in varying amounts. Many very low-fat regimens also minimize higher-fat plant foods, such as nuts, seeds, avocados, and olives, but studies examining the health effects of these foods are overwhelmingly positive. Eliminating or severely restricting higher-fat plant foods may end up being counterproductive. For example, vegan diets with fewer than 10 percent of calories from fat may not provide sufficient essential fatty acids. If you're eating a very low-fat vegan diet, make sure you at least add about 1 ounce (30 g) of hempseeds or walnuts per day to ensure you're getting enough. Alternatively, eat a combination of about 1 ounce (30 g) of flaxseeds plus pumpkin seeds, or chia seeds plus sunflower seeds.
You need some fat so your body can absorb certain phytochemicals and vitamins, such as A, D, E, and K. These nutrients are essential for health and provide protection against numerous diseases and health conditions. According to the Institute of Medicine, very low-fat diets also have been associated with inadequate intakes of zinc and some B vitamins, nutrients that are most abundant in higher-fat foods such as nuts and seeds.
Very low-fat, high-carbohydrate diets, especially those that rely on refined carbs, can cause a decline in HDL cholesterol and a rise in triglycerides, a situation associated with increased risk for coronary artery disease, metabolic syndrome, and type 2 diabetes. If you adhere to a high-carbohydrate diet, avoid foods made with white flour and sugar, and rely on whole plant foods such as legumes, vegetables, and whole grains to help keep triglyceride levels down.
While very low-fat, whole-foods vegan diets can cause a drop in HDL cholesterol, this is a natural consequence of total cholesterol reduction and may not be a health risk. The primary function of HDL is the removal of excess cholesterol from the bloodstream, so when there's less cholesterol to remove, less HDL is produced. In vegan populations, as well as other populations consuming low-fat plant-based diets, HDL levels are typically slightly lower than in the general population, yet risk for coronary artery disease is low.
Very low-fat, high-fiber diets may not provide enough calories for infants, children, and adults with high energy needs. Studies of malnutrition in vegetarians and vegans have shown that highly restrictive diets don't adequately support children's growth and development. In one study, vegan infants fourteen to sixteen months of age who had been fed diets with 17 percent of calories from fat were malnourished. Low-fat diets can also result in chronic diarrhea in children. Until we know more, vegan parents should make sure their children get enough fat: 55 percent of calories from fat up to six months of age, 30 to 40 percent of calories from fat for children between six months and three years old, and 25 to 35 percent of calories from fat for those between four and eighteen years old.
Don't make avoiding fat the highest priority when selecting foods. A fat-free sugar-based commercial salad dressing may indeed be in line with a low-fat diet, but that doesn't make it healthful. Homemade tahini dressing with lemon juice provides far greater nutritional value. Plant foods with a higher fat content—nuts, seeds, wheat germ, avocados, olives, and soy foods—are the most valuable fat sources for all vegans beyond one year of age. They provide important nutrients, including a variety of antioxidants, trace minerals, and protective phytochemicals.
#### **PROS AND CONS OF A HIGH-FAT DIET**
High-fat diets, defined as more than 35 percent of calories from fat, have long been thought to contribute to obesity and a variety of chronic diseases. However, there are some healthy populations who have long consumed diets with more than 35 percent of calories from fat, including some Mediterranean communities and many people on raw diets. Some leading health authorities promote Mediterranean diets as being optimal for health and encourage liberal use of higher-fat foods, especially olive oil.
In 1980, the well-known Seven Countries Study by biologist Ancel Keys showed a strong connection between total fat, saturated fat, and coronary artery disease. As fat intake increased, so did coronary artery disease, with one important exception: residents of the Greek island of Crete, where people averaged 37 percent of calories from fat, had the lowest rates of all the countries studied, including Japan, where average fat intake was only 11 percent of calories.
What seems to separate the people of Crete and other healthy Mediterranean populations from less healthy populations who also eat high-fat diets is the type of fat they consume. The traditional diet of Crete includes abundant plant foods and olive oil and typically includes less than 2 ounces (60 g) of meat, poultry, or fish per day. In addition, most Cretans fast during the forty days of Lent, and an unknown number also follow Greek Orthodox dietary doctrines that prescribe almost 180 days of fasting each year, which involves abstention from meat, fish, dairy products, and eggs, and even olive oil. While these practices weren't factored into the results of Keys's study, leading experts from the University of Crete believe that the regular restriction of certain foods, notably those of animal origin, have significant health benefits.
Mediterranean diets provide a compelling argument that the quality of fat trumps the quantity as a predictor of health outcomes—if you don't eat too many calories. However, even good fats may increase the risk of disease when eaten to excess. High-fat diets have been linked to chronic medical conditions, such as cardiovascular diseases, metabolic syndrome, diabetes, gallbladder disease, and some cancers. The fats implicated here are saturated fats and trans-fatty acids, and vegans tend to eat less of these, but evidence still indicates that diets very high in fat (more than 42 percent of calories from fat) can potentially increase risk for heart disease, no matter what the source of the fat.
Another issue is that concentrated fats and oils, including vegetable oils, are packed with calories—about 120 calories per tablespoon—but contribute few vitamins, minerals, and phytochemicals and no fiber. Therefore, a high-fat diet can dilute nutrient density, meaning you get fewer nutrients per calorie consumed. This makes it a challenge to eat enough to achieve sufficient intakes of many nutrients, especially trace minerals such as zinc and selenium. This is particularly problematic when the main sources of fat are concentrated, as in vegetable oils, margarine, mayonnaise-type spreads, coconut oil, and foods prepared or manufactured with these fats, as opposed to whole foods such as nuts, seeds, soybeans, avocados, and olives. Although unrefined expeller-pressed or cold-pressed oils are generally richer sources of essential fatty acids, vitamin E, and phytochemicals, most of the oils on supermarket shelves are highly refined—another reason to get your fats and nutrients from whole foods.
High-fat diets can make you fat. Because fat is a concentrated source of calories, you can get a lot of calories in a very small amount of a high-fat food, which can lead you to consume more calories than your body needs. If you have a tendency toward being overweight, try eating a diet that contains only moderate amounts of fat.
Another problem with a very high-fat diet is that it makes it difficult for the body to convert essential fatty acids to their usable form. This can increase the risk of chronic diseases and adversely affect mood and energy levels, particularly for vegans and others who don't consume direct sources of EPA and DHA. Finally, free radicals—those compounds that cause oxidative damage to body tissues—are more likely to react with the polyunsaturated fats found in oils such as corn, sunflower, safflower, and soybean. Oxidative stress has been linked to increased risk of numerous diseases, including heart disease, cancer, diabetes, arthritis, age-related diseases, and neurological disorders.
### Good Vegan Fats
As mentioned, a number of highly respected vegan health advocates have taken a hard-line view against fats of all types. Although there's evidence that very low-fat vegan diets can improve severe coronary artery disease, there's little evidence that such diets are the gold standard for healthy vegans. There are hundreds of scientific studies that have demonstrated that high-fat plant foods not only deserve a place in our diets, but that they deserve a place of honor.
#### **NUTS**
People tend to think of nuts in the same vein as potato chips: as high-fat foods that clog the arteries and lead to weight gain. It's time to put that misconception to rest, because eating nuts has consistently been shown to provide health advantages, reducing risk of chronic disease and increasing longevity. Evidence shows that people who eat nuts on a regular basis generally have a lower body mass index (BMI), smaller waist, less hypertension, higher HDL levels, lower fasting blood sugar levels, and significantly less risk for coronary heart disease. According to the Nurses Health Study, replacing dietary carbohydrates with the same amount of calories from nuts reduces the risk of coronary heart disease by about 30 percent, and replacing saturated fat with nuts may reduce the risk by about 45 percent. In addition, regular nut consumption may prevent stroke, type 2 diabetes, dementia, macular degeneration, gallstones, and all by eating just 1 to 2 ounces (30 to 60 g) of nuts per day.
Nuts are nutrient-dense foods, brimming with an array of vitamins and minerals. Most of their fat is monounsaturated. They are also rich in compounds that help preserve the elasticity and flexibility of blood vessels, enhancing blood flow. But they're also high in calories, so keep your intake moderate—sprinkle them on foods rather than eating them by the bowlful.
#### **SEEDS**
Far less research has been conducted on seeds than on nuts, and their value tends to be underestimated. Seeds are the most plentiful sources of essential fatty acids. Pumpkin seeds, sunflower seeds, poppy seeds, hempseeds, and sesame seeds are rich in omega-6s. Flaxseeds, chia seeds, hempseeds, and canola seeds are rich in omega-3s. Seeds also are among the richest sources of vitamin E and provide an impressive array of other vitamins, minerals, and phytochemicals, along with protein and fiber.
Flaxseeds are a case in point. They have a remarkably high omega-3 content, so adding them to your diet can go a long way toward correcting any imbalance in intake. They are very high in soluble fiber, which lowers cholesterol, and are one of the richest known sources of the trace mineral boron. Flaxseeds can help reduce cholesterol levels and improve a number of other markers of coronary artery disease. They also are the richest known source of lignans (not to be confused with lignins, a type of fiber), which may help reduce the growth of cancer cells. (Be sure to use ground flaxseeds, since the body can't fully digest whole flaxseeds.)
Chia seeds, both whole and sprouted, are rapidly gaining popularity in plant-based diets. They are the only food higher in omega-3s than flaxseeds. They are also packed with antioxidants and other nutrients. A mere 2 tablespoons (30 ml) of chia seeds contains 3.3 mg of iron and 142 mg of calcium.
Hempseeds also have exceptional nutritional value. About 20 percent of their calories come from easily digestible, high-quality protein, and they provide an impressive array of trace minerals, vitamins, and phytochemicals. Hempseed oil has an excellent ratio of omega-6 to omega-3 fatty acids. It is one of the few foods that provides both stearidonic acid (SDA), an omega-3 fatty acid that more readily converts to EPA than does ALA, and GLA, a beneficial omega-6 fatty acid.
#### **AVOCADOS**
Like other fat-rich plant foods, avocados offer some pleasant nutritional surprises. In addition to being rich in monounsaturated fatty acids, they possess high levels of nutrients, fiber, phytochemicals, and antioxidants. Avocados are rich in carotenoids, and vitamins C and E and contain more folate per ounce (30 g) than any other fruit, 60 percent more potassium than bananas, and 13.5 grams of fiber per average fruit.
Avocados also contain phytosterols that can inhibit cholesterol absorption, help reduce cholesterol levels, and possibly inhibit tumor growth. In one study, people who followed a diet recommended by the American Heart Association to reduce cholesterol were compared with people who ate a diet that derived 20 to 35 percent of their total calories from avocados. Total cholesterol dropped an average of 4.9 percent among those on the Heart Association diet, but total cholesterol dropped 8.2 percent among those eating the avocado-rich diet.
Eating avocados may provide benefits in cancer prevention and treatment, in certain inflammatory diseases, and in lowering the side effects of certain chemotherapy drugs. There also is preliminary evidence that avocado extract is active against _Helicobacter pylori_ , the bacteria associated with ulcers and stomach cancer, and that its anti-inflammatory effects may reduce the symptoms of knee and hip osteoarthritis.
#### **OLIVES**
Olives are an ancient food and a cherished part of the Mediterranean diet. They are good sources of copper, iron, and vitamin E, and are rich in phytosterols and a host of phytochemicals, particularly polyphenolic compounds. Oleuropein, the major polyphenol in olives, is a potent free radical scavenger, inhibiting oxidative damage and protecting heart tissue. Olives and olive oil also contain compounds with known anticancer and anti-inflammatory effects.
Raw olives are cured in order to leach out an alkaloid that makes them bitter and unpalatable. Various solutions can be used to cure olives, including water, brine, seasoned oil, or lye. Olives can also be dry cured by layering them with dry rock salt. The choice of curing agent affects the nutritional content of the olives and the sodium content.
Extra-virgin olive oil, which is obtained from the first pressing of the olives, is rich in bioactive compounds compared to more refined varieties. While olive oil has the advantage of being much lower in sodium than most types of olives, olives are whole plant foods, so they contain fiber, whereas olive oil doesn't. In addition, olive oil, like all oils, contains 120 calories per tablespoon (15 ml), whereas ten large olives contain only 50 calories.
#### **COCONUT**
There are few foods that have been simultaneously so maligned and so acclaimed as coconut and coconut oil. Some view coconut oil as a notorious health villain because it's the most concentrated food source of saturated fat—even higher than lard. Not surprisingly, it rests at the very top of the "avoid" column of mainstream heart-healthy food lists. Others view coconut oil as a fountain of youth and the greatest health discovery in decades, claiming that it can provide therapeutic benefits for everything from Alzheimer's disease to thyroid disease.
The main reason that coconut oil is so often blacklisted by nutrition experts is because almost 90 percent of its fat is saturated, and people think of saturated fat as the sole culprit in clogging arteries. However, there are actually several different types of saturated fats, each with its own effects on cholesterol levels and health. The predominant saturated fat in coconut, lauric acid, does raise total cholesterol, but it appears to also raise HDL levels even more than LDL levels, favorably altering the ratio of total cholesterol to HDL—a ratio that is widely considered a more important predictor of coronary artery disease risk than levels of total cholesterol or LDL.
**TABLE 4.3.** Fatty acid composition of selected foods
Sources of data: US Department of Agriculture, Agricultural Research Service, _USDA National Nutrient Database for Standard Reference_ , Release 25 (2012), ndb.nal.usda.gov. Manitoba Harvest, manitobaharvest.com (for hempseeds and hempseed oil).
Key: g = gram; mg = milligram; ml = milliliter; oz = ounce; tbsp = tablespoon.
In addition, lauric acid converts into a powerful antiviral, antifungal, and antiseptic compound in the body, and there is also evidence that coconut products have anti-inflammatory and antioxidant powers. While the health effects of coconut and coconut oil remain somewhat uncertain, in many parts of the world where they are principle sources of dietary fat, rates of chronic disease, including coronary artery disease, are low. There is one major caveat in regard to coconut: its benefits seem to occur only when coconut products are consumed as part of a diet that is rich in unprocessed, high-fiber plant foods.
Based on the available science, coconut oil should be regarded like any other concentrated oil: as a food that provides a lot of calories and only limited amounts of other nutrients. It's okay to use a bit of high-quality coconut oil, but as with any other oil, consumption should be minimized. On the other hand, coconut flesh should be treated in much the same way as other high-fat plant foods: enjoyed primarily as a whole food. As such, it is loaded with fiber, vitamin E, and healthful phytochemicals. As a bonus, it has powerful antimicrobial properties.
### The Take-Home Message
The science is crystal clear: a wide range of fat intake levels can support and promote excellent health. Here are the key points to keep in mind in regard to fat consumption:
* Don't overeat.
* Eat good fats. The fats in highly processed foods, fast foods, and convenience foods cause health problems, whereas the fats in whole foods, such as nuts, seeds, avocados, and olives, don't, as long as you aren't consuming excess calories.
* Don't assume that very low-fat diets are suitable for all vegans. Optimal fat intake depends on many things. Needs vary among individuals and change throughout the life cycle.
* Very low-fat diets are highly effective in treating certain chronic diseases, particularly cardiovascular disease. If you've adopted a vegan diet in an effort to treat cardiovascular disease, explore the very low-fat diet, but be sure to consume sufficient essential fatty acids.
* If you're a vegan with a healthy body weight, focus on eating a variety of nourishing plant foods, including nuts, seeds, and avocados. For most people, eating two or three servings of higher-fat plant foods daily is reasonable. One serving is half an avocado or 1 ounce (30 g) of nuts or seeds, about 3 or 4 tablespoons (45 to 60 ml).
* Limit your use of concentrated oils. To get sufficient high-quality fat without using concentrated fats and oils, eat nuts, seeds, avocados, olives, tofu, soy milk, and lower-fat plant foods such as whole grains and legumes. Be sure to include choices that contribute a healthful balance of essential fatty acids. If you use oils in salad dressings and uncooked foods, stick mainly to high-quality oils that provide omega-3s.
* If you're overweight or obese, avoid concentrated fats and oils. However, you need not avoid nuts and seeds; 1 to 2 ounces (30 to 60 g) per day probably won't interfere with healthful weight loss.
Simple, complex, refined, whole...carbohydrates come in several guises. They're the foundation of a healthful vegan diet, and knowing the difference between good carbs and not-so-good carbs is important. In the next chapter, we sort them all out for you. No worries.
## **CHAPTER 5**
## **The Two Faces of Carbohydrates**
Foods rich in carbohydrates are the human body's most valuable sources of energy. Globally, carbohydrate intake ranges from about 40 to 80 percent of calories, with people in developing countries consuming diets in the higher end of the range and Western diets falling near the lower end.
In obesity-ridden developed countries, advocates of popular low-carb diets urge people to shun carbohydrates in favor of meat-centered, protein-rich fare, claiming that carbohydrates are responsible for the obesity epidemic and chronic disease. For vegans, these allegations are disturbing. After all, plants are where carbohydrates reside. The only foods that are free of carbohydrates are meat, fish, poultry, and oil. While low-carb diets have been shown to be relatively successful in short-term weight loss efforts, they fail over time. They are also a nightmare for animals and for the planet.
This chapter cuts to the heart of carbohydrates, and clarifies what is myth and what is reality. In the process, we will sort through the questions about carbohydrates that tend to be foremost in the minds of those who cast their vote for plant foods.
### Carbohydrates 101
Like proteins and fats, carbohydrates are macronutrients—a source of energy for the body. (The only other dietary source of energy is alcohol.) Carbs are the preferred fuel for the brain, red blood cells, and nervous system. Protein can be used as a fuel, but it must first be processed by the liver and kidneys. Plus, protein is essential for building body tissues; for the production of enzymes, hormones, and antibodies; and for the regulation of fluids, electrolytes, and pH balance. To ensure that protein is used for these important tasks rather than as a source of energy, we must eat sufficient carbohydrates.
Fat is also used as a fuel, but it isn't a preferred energy source either. If the body uses fat for energy on an ongoing basis, by-products called ketones can accumulate. In extreme cases, this can cause ketoacidosis, in which the body's pH drops to dangerously low levels. And for the record, alcohol also isn't a desirable fuel source, as it is highly toxic to the body, especially the brain, liver, and pancreas. That leaves us with carbohydrates, which provide an efficient and safe source of energy for the entire body.
Carbohydrates supply approximately 4 calories per gram. Protein also provides 4 calories per gram, and fat supplies 9 calories per gram. In addition to serving as the body's preferred source of calories, carbohydrate-rich whole foods help to maintain blood sugar levels and insulin metabolism, and keep levels of cholesterol and triglycerides in check. These foods also support a healthy gastrointestinal tract by protecting against constipation and intestinal diseases and disorders.
Nutrition experts recommend consuming between 45 and 75 percent of calories from carbohydrates. On a diet of 2,000 calories per day, that would be 900 to 1,500 calories from carbs, or 225 to 375 grams. When carbohydrate intakes fall below 45 percent of energy, fat consumption can become excessive, potentially increasing the risk of chronic diseases. Not more than 10 percent of calories should come from added sugars—concentrated sugars used in processed foods and beverages or added to food at home or in restaurants. Sugars that occur naturally in whole foods such as fruits and vegetables are not added sugars.
Carbohydrate intake in the United States averages 50 percent of calories; vegans usually eat closer to 60 percent, and those on low-fat vegan diets typically get close to 75 percent of their calories from carbs. At the other end of the vegan spectrum, the carb content of a raw vegan diet, with its generous amounts of nuts, seeds, and avocados, commonly dips below 50 percent of calories.
Most of your carbohydrates should come from whole plant foods, such as vegetables, fruits, whole grains, legumes, nuts, and seeds. Animal products, with the exception of dairy products, contain few carbohydrates, if any. (The carbohydrate in dairy products is lactose, or milk sugar.) See figure 5.1 on the facing page for the average percentage of calories from carbs in various food groups.
#### **CARBOHYDRATE CONFUSION**
In populations with high rates of chronic disease, most people eat carbohydrates in their refined and processed forms. What distinguishes the world's healthiest populations—most of whom eat high-carb diets—is that they eat _unrefined_ carbohydrates. This is just one among many reasons why health experts now generally agree that processed or refined carbs can be damaging to health. This has initiated a new era in our understanding of carbohydrates, along with a confusing proliferation of terms.
For many years, carbohydrates were divided into two main categories: simple carbohydrates (sugars) and complex carbohydrates (starches). Simple carbohydrates were viewed as bad, and complex carbohydrates were considered good. As it turns out, this was more than an oversimplification; it was fundamentally inaccurate. Whether carbohydrates are simple or complex is relevant to their structure, but not so relevant to human health. Simple carbohydrates can be healthful when they come from fruits and nonstarchy vegetables, and complex carbohydrates are generally unhealthful when they come from white flour and other refined starches.
FIGURE 5.1. Average percentage of calories from carbohydrates in common foods
Source of data: US Department of Agriculture, Agricultural Research Service, _USDA National Nutrient Database for Standard Reference_ , Release 25 (2012), ndb.nal.usda.gov.
What really matters is whether the carbohydrate is in its natural state. When carbohydrates are eaten in the form of vegetables, fruits, legumes, whole grains, nuts, and seeds, they are teamed with vitamins, minerals, protein, antioxidants, phytochemicals, fiber, and essential fatty acids, and these whole plant foods are consistently associated with disease risk reduction. Because so much confusion (and scaremongering) surrounds carbohydrates, we want to make sure you're clear about the distinctions:
* **Simple carbohydrates** are molecules containing one or two units of sugar. They are found in whole foods like fruits and vegetables, in concentrated sweeteners like sugar, and in products made with those sweeteners.
* **Complex carbohydrates** are starches containing three or more units of sugar linked together. They are found in whole foods such as whole grains, starchy vegetables, legumes, nuts, and seeds, as well as flours, starches (cornstarch and potato starch), and products made with these foods.
* **Refined carbohydrates** are carbohydrate-rich foods made from processed grains (white flour), other processed starchy foods (peeled potatoes), or processed sweeteners (white or brown sugar). Refined carbohydrates may contain either complex or simple carbohydrates. Examples of foods that contain a lot of refined complex carbohydrates are white bread and white pasta. Examples of foods that contain a lot of refined simple carbohydrates are soda, candy, and jam.
* **Unrefined carbohydrates** are naturally present in whole plant foods such as vegetables, fruits, legumes, whole grains, nuts, and seeds. Unrefined carbohydrate foods may contain mainly complex or simple carbohydrates. Examples of foods that provide mainly complex carbohydrates in unrefined form are barley, quinoa, sweet potatoes, and beans. Examples of foods providing mainly simple carbohydrates in unrefined form are fruit and nonstarchy vegetables, such as cucumbers, peppers, and tomatoes.
#### **REFINING**
Why would anybody pay four dollars for a bag of potato chips when they could pay a quarter for a potato? It comes down to taste and convenience. So how does the food industry turn a twenty-five-cent commodity into a four-dollar temptress? They strip away everything that might curb its appeal; flavor it with salt, sugar, and fat; package it persuasively; and advertise it relentlessly. Unfortunately, the true cost of these "foods" far exceeds the price tag when you factor in their impact on health.
When wheat berries (and other grains) are refined into white flour, the germ and bran are removed, leaving only the endosperm, which is mainly starch and some protein. Unfortunately, the germ and bran contain about 80 percent of the vitamins, minerals, and fiber and the vast majority of the phytochemicals. (Figure 5.2 shows the amount of fiber and key nutrients that are lost when wheat berries are processed into white flour.)
**FIGURE 5.2.** Nutrients lost when wheat berries are processed into white flour
Source of data: "Grain Math: Weights, Measures, and Conversion Factors," Prairie Grains, no. 54 (June 2003)
Granted, some of the lost nutrients are added back in the process called enrichment. For example, when wheat or rice is refined, it is commonly enriched with iron and four B vitamins (thiamin, riboflavin, niacin, and folic acid). However, not all of the vitamins and minerals that were removed are added back, nor are any of the phytochemicals or the fiber.
### Fiber: Just Passing Through?
Everyone knows that fiber is good for you. It is viewed as nature's broom—the part of plants that keeps things moving smoothly and efficiently through the intestinal tract. The benefits of fiber have been universally recognized since the 1970s, when researcher Denis Burkitt discovered that people in rural Africa were free of Western diseases such as diabetes, heart disease, and obesity, as well as such intestinal disorders as colon cancer and constipation. He determined dietary fiber set Africans apart from Westerners. Fiber became the topic du jour, and it was added to everything from potato chips to ice cream.
While the benefits of fiber begin in the intestine, they extend to every part of the body. The most recognized advantages of high-fiber diets are for gastrointestinal health, cardiovascular health, blood sugar control, and weight management.
Fiber has traditionally been divided into two categories: soluble and insoluble. Soluble fiber is the type that dissolves in water; insoluble does not. For many years, experts believed soluble fiber helped improve blood sugar and cholesterol levels, and that insoluble fiber was associated with bowel regularity. More recent research suggests that the effects of soluble and insoluble fibers are more variable. The health benefits of fiber appear to be related more to the viscosity and fermentability of the fiber than to its solubility. As a result, health authorities are phasing out the terms "soluble" and "insoluble" and referring to fiber as "viscous" or "nonviscous," and "fermentable" or "nonfermentable."
Part of the confusion surrounding fiber stems from the fact that much of our fiber research has been conducted on isolated fibers rather than whole foods. While the terms "soluble" and "insoluble" are useful when referring to isolated types of specific fibers, they are less useful when talking about food, because all high-fiber foods contain a variety of both soluble and insoluble fibers. Gums, mucilages, and pectins are all soluble fibers, while celluloses and lignins are insoluble. Hemicelluloses and beta-glucans can be either or both.
Viscous fiber becomes gel-like, or thick and gummy, when mixed with water. Nonviscous fiber may absorb water, but it doesn't become thick or gummy. Viscosity is thought to be responsible for some of fiber's greatest health advantages. It helps delay stomach emptying and increase feelings of fullness after eating. It can stabilize blood sugar levels and reduce cholesterol. Examples of viscous fiber include guar gum, mucilages, and pectins. Examples of nonviscous fiber include celluloses and lignins. As is the case for these types of fiber, most viscous fiber is also soluble and most nonviscous fiber insoluble, although there are exceptions. Hemicelluloses and beta-glucans can fall into either category, although most hemicelluloses are nonviscous and most beta-glucans are highly viscous.
Fiber also serves as food for intestinal bacteria, which are able to extract energy by fermenting fiber. The types of fiber that are the most fermentable by intestinal bacteria include beta-glucans, guar gum, hemicelluloses, pectins, and oligosaccharides—small chains of carbohydrates that the body can't break down. Gums and mucilages are the most slowly fermented, while oligosaccharides are the most rapidly fermented. Less fermentable types of fiber, such as celluloses, resistant starches, and lignins, contribute to stool bulk and improve laxation. Wheat bran is an excellent example of a food rich in these less fermentable fibers. Table 5.1 lists the major types of fiber, their health effects, and food sources.
### **KEY HEALTH BENEFITS OF FIBER**
Clearly, fiber has many health benefits—too many to discuss them all in detail. In the following sections, we'll briefly discuss some of the most significant findings.
**Gastrointestinal health.** The most obvious benefits of fiber are gastrointestinal. Fiber helps prevent constipation, hemorrhoids, and diverticulosis (small sacs in the wall of the intestines). It may also protect against colorectal cancer, gallstones, and inflammatory bowel diseases such as ulcerative colitis. A high-fiber diet makes stools softer and heavier, helping them pass out of the colon more easily and rapidly. While insoluble, nonviscous, nonfermentable fibers, such as celluloses and lignins, are particularly helpful in this regard, fiber that is fermented in the colon also contributes to stool softening and bulk. Many fermentable carbohydrates serve as prebiotics, stimulating the growth of friendly bacteria. Fermentation generates by-products that can inhibit harmful substances, enhance mineral absorption, reduce food sensitivities and allergies, disable carcinogens, attack cancer cells, and favorably affect the metabolism of fats and sugars.
**TABLE 5.1.** Types of plant fiber, health effects, and common sources
**TYPE OF FIBER** | **HEALTH EFFECTS** | **COMMON SOURCES**
---|---|---
Beta-glucans | Improve blood sugar and cholesterol levels. | Oats, barley, and mushrooms
|
Soften stools, add bulk, and improve laxation, especially if insoluble.
|
Celluloses | Increase stool bulk and improve laxation. | Grains, fruits, vegetables, legumes, nuts, and seeds
Gums and mucilages | Improve blood sugar and cholesterol levels. Soften stools; smaller effect on stool bulk and laxation. | Psyllium seeds, guar gum, and sea vegetable extracts (carageenans and alginates)
Hemicelluloses | May improve blood sugar or cholesterol levels, if viscous. | Fruits, grains (especially outer husks), legumes, nuts, seeds, and vegetables
|
Increase stool bulk and improve laxation, especially if nonfermentable.
|
Lignins | Increase stool bulk and improve laxation. | Stringy vegetables and the outer layer of cereal grains
Nondigestible oligosaccharides | Soften stools, increase bulk, and improve laxation. | Fruits, grains, legumes, and vegetables
|
May act as prebiotics, stimulating the growth and activity of friendly bacteria in the colon.
|
Pectins | Improve blood sugar and cholesterol levels. Soften stools; smaller effect on stool bulk and laxation. | Berries and fruits, especially apples and citrus fruits
Resistant starches | Improve insulin sensitivity and blood sugar and cholesterol levels. | Legumes, raw potatoes, and underripe bananas
|
Some increase in stool bulk and laxation.
|
Sources of data are listed in _Becoming Vegan: Comprehensive Edition,_ by Brenda Davis and Vesanto Melina (Book Publishing Company, 2014).
**Cardiovascular health.** Diets rich in fiber have been associated with a reduced risk of cardiovascular disease. Every 10 grams of fiber added to the diet has been associated with a 14 percent decrease in risk for a coronary event and a 27 percent decrease in risk for coronary death. One study of more than forty thousand male health professionals reported that those consuming the most fiber had a 40 percent reduction in risk for coronary heart disease compared with those consuming the least fiber. One popular theory is that soluble, viscous fiber binds with cholesterol-containing bile acids to carry them out of the body. Another possibility is that people who eat lots of fiber eat fewer calories because they feel full sooner. Fiber can also reduce blood pressure, help remove blood clots, and enhance insulin sensitivity.
**Diabetes and metabolic syndrome.** Eating a high-fiber diet reduces risk for metabolic syndrome and type 2 diabetes. Soluble viscous fiber delays the absorption of fats and carbohydrates from the small intestine, which improves insulin sensitivity and blood sugar levels and helps curb appetite, possibly reducing overeating and weight gain.
**Weight.** High-fiber foods are associated with healthier body weight. Generally, high-fiber foods take more space on your plate and in your stomach, and they require more chewing time, so you may eat less. Many high-fiber foods are also less energy dense, meaning they have fewer calories for a specific volume of food. All of these factors contribute to satiety, or feelings of fullness.
#### **IDEAL FIBER INTAKE**
How much fiber do we need in a day? The Adequate Intake is 14 grams of fiber per 1,000 calories for everyone older than one year. For men, that's a daily intake of about 38 grams between the ages of nineteen and fifty, and 30 grams after age fifty. For women, it's about 25 grams between the ages of nineteen and fifty, and 21 grams after age fifty. If you are consuming the recommended amount but still struggling with constipation, you may need to eat up to 45 grams per day or more.
Western diets typically provide only about 15 to 17 grams of fiber daily, just half the recommended intake. Vegans, on the other hand, consume 35 to 50 grams per day on average. (The menus in chapter 14 provide 48 or more grams of fiber per day.)
Switching to a whole-foods vegan diet usually solves any problems with constipation. If it doesn't do the trick for you, here are some steps you can take to get things moving along:
* Eat at least ½ to 1 cup (125 to 250 ml) of legumes per day.
* Aim for nine or more servings of vegetables and fruits each day, with an emphasis on higher-fiber options. (For details on serving sizes, see table 14.1, on page 265, and for the approximate fiber content of various foods, see table 5.2, on page 89.) To boost fiber even more, eat the edible peels and consume a good portion of these foods raw. Enjoy a large raw salad every day, and if you cook your vegetables, minimize cooking time.
* When eating grains, opt for intact whole grains most of the time. Processing grains and grinding break down fiber, and the smaller particles generally contribute less to stool bulk. It's best to rely on whole grains rather than adding bran, because too much bran can inhibit the body's absorption of minerals.
* If you use processed grain products, select whole-grain options. Aim for at least 2.5 grams of fiber in a serving of bread or pasta and 5 grams from a serving of breakfast cereal.
* Seeds can be very helpful in increasing stool bulk, particularly whole flax-seeds and psyllium seeds.
* Opt for baked goods, such as bread, muffins, cookies, and crackers with high-fiber ingredients such as whole or sprouted grains, wheat germ, oat bran, flaxseeds, other nuts and seeds, and dried, fresh, or cooked fruits (applesauce, mashed bananas, prunes, dates, and raisins).
* Select high-fiber snacks, such as raw fruits and vegetables, trail mixes, popcorn, stuffed dates, and other raw treats.
* Drink at least 8 cups (2 liters) of fluid each day.
* Get your daily dose of exercise. Whether it's a brisk walk or jog, an aerobics class or yoga, swimming or a game of tennis—any physical activity will help keep your intestines working well.
#### **DEALING WITH GAS**
Gas results when bacteria ferment carbohydrates in the intestine, and also from swallowing air. Gas is actually a good thing—at least for your body—because it protects the colon against damage that can lead to cancer, dilutes carcinogens, stimulates beneficial bacterial growth, and keeps the gut at the proper pH.
On average, people pass gas twelve to twenty-five times a day. Of course, there is a point at which passing gas becomes a social liability. Some people limit their consumption of beans and high-fiber foods to help prevent the embarrassment caused by flatulence. However, these foods are extremely healthful, so we'll provide some tips on how to keep gas production tolerable:
* Eat more slowly, with your mouth closed.
* Chew your food really well.
* Avoid carbonated beverages, chewing gum, and sucking on candies.
* Eat smaller meals; stop eating when you are 80 percent full.
* Cook with asafetida, black pepper, cinnamon, cloves, garlic, ginger, and turmeric. Epazote and kombu also are commonly added to foods to neutralize gas-producing compounds.
* Take probiotic supplements or use probiotic powders or rejuvelac (a cultured grain beverage).
* Limit foods rich in added fructose or sugar alcohols (sweeteners such as mannitol, sorbitol, and xylitol). When these sugars aren't completely absorbed, they're fermented by bacteria in the colon. Even fructose from fruits can be a problem when they're eaten in excess or in certain combinations.
* Take activated charcoal right before eating problematic foods. It may reduce both the quantity and the odor of intestinal gas.
* If you wear dentures, make sure they fit properly.
* If all else fails, take a supplement containing the enzyme alpha-galactosidase, which breaks down certain gas-producing components in food that the body can't digest.
#### **THE MUSICAL FRUIT**
About one hundred varieties of legumes (beans, peas, lentils, peanuts) are commonly cultivated globally. In South America, Africa, China, the Middle East, and India, legumes have served as dietary staples for centuries; per capita consumption can top 88 pounds (40 kg) per year. Americans only consume about 6.5 pounds (3 kg) of legumes per person per year, although dietary guidelines strongly promote more.
Legumes provide many of the key nutrients found in meat, such as protein, iron, and zinc, along with protective compounds largely absent from meat, such as fiber, phytosterols, antioxidants, phytochemicals, and often other minerals, including calcium. The iron from legumes is easily absorbed by the body and may have advantages over the iron in meat. (For more on iron, see page 132.) Most legumes are low in fat and very low in saturated fat, and all are cholesterol-free. Small red beans, red kidney beans, and pinto beans are loaded with antioxidants. It's not stretching it to say that if you want to live longer, you should eat beans regularly. Research shows that risk of death drops 7 to 8 percent for every 0.7-ounce (20 g) increase in daily bean intake, probably because they can reduce the risk of diseases such as cancer, cardiovascular diseases, and diabetes, and because of their favorable effects on body weight.
As mentioned, some folks avoid eating beans because of the gas issue. Beans are among the most notorious flatulence producers because they contain nondigestible oligosaccharides, which arrive in the colon relatively unscathed and are finally broken down by bacterial fermentation, resulting in intestinal gas. But as it turns out, oligosaccharides are responsible for many of the health benefits associated with beans, in part because they act as prebiotics, promoting healthy gut flora. And again, we do have some tips to help minimize the undesirable effects associated with the "musical fruit":
* Start with small servings and gradually increase your portion size over two or three weeks. A gradual increase will give the bacteria in your body time to increase their population to digest a normal serving. Begin by adding a small amount of beans to soups, stews, and salads for a couple of weeks before digging into chili or baked beans.
* Soak beans for at least twelve hours or overnight. Then discard the soaking water, and rinse well before cooking them in fresh water. Better yet, soak them overnight, drain, add fresh water, and soak another night. Then drain and cook in fresh water. If you don't have time to soak them, boil the beans briefly in enough water to cover them. Turn off the heat and let them sit in the water for an hour or two, then drain, rinse well, and cook in fresh water.
* Cook beans thoroughly. You should be able to easily crush one between your tongue and the roof of your mouth. Undercooked beans are more difficult to digest.
* Sprout beans. Sprouting converts the oligosaccharides in beans into more easily digested sugars. To sprout beans, soak them in water for at least twelve hours, then drain them and put them in a sprouting jar or sprouter. Rinse every twelve hours until a small sprout appears. This can take three to five days for many legumes. The beans are ready to cook when they have a tiny sprout. Sprouted beans cook in half the time. Sprouted mung beans, lentils, and peas can be eaten raw. Other legumes should be cooked after sprouting.
* Use fresh beans instead of dried beans; their oligosaccharide content is much lower.
* If using canned beans, drain and rinse well before adding to recipes or eating.
* Select smaller beans, such as adzuki, lentils, split peas, and split mung beans. Generally, smaller beans are easier to digest than large beans, such as lima or kidney beans.
* Buy only as many dried beans as you will use within a few months. The longer beans are stored, the more oligosaccharides they develop.
* Use tofu and tempeh. The fermentation process used to make tempeh enhances digestibility and reduces gas.
#### **SOURCES OF DIETARY FIBER**
All whole plant foods provide fiber; it's fundamental to their structure. Animal products don't contain fiber; bones give animals their structure. Table 5.2 (facing page) outlines the approximate fiber content of various foods.
#### **TOO MUCH FIBER?**
While it's possible to eat too much fiber, it's unlikely if you are consuming whole plant foods and drinking sufficient fluids. During Paleolithic times, it's estimated that humans consumed more than 100 grams of fiber per day. Excessive fiber is more of an issue for people who consume concentrated fiber sources, such as wheat bran, in large amounts. Very high-fiber diets can be too bulky for small children and some seniors, leading them to eat insufficient calories, but this is seldom a concern in healthy adults.
**TABLE 5.2.** Fiber content of selected whole plant foods
AMOUNT OF FIBER PER SERVING | FOOD AND SERVING SIZE
---|---
Very high-fiber foods 10 to 19.9 grams | Legumes (all varieties), cooked, 1 c (250 ml)
Avocado (1 medium), 6.7 oz (200 g)
High-fiber bran cereal, ½ c (125 ml)
Artichoke (1 medium), 4 oz (120 g)
High-fiber foods 5 to 9.9 grams | Some berries (raspberries, blackberries), fresh, 1 c (250 ml)
Some fruits (Asian pear, papaya, pear), 1 medium
Dried fruit (apricots, figs, peaches, pears, prunes, raisins), ½ c (125 ml)
Coconut, fresh, shredded, ½ c (125 ml)
Flaxseeds, 2 tbsp (30 ml)
Most whole grains, cooked, 1 c (250 ml)
Potatoes, regular or sweet, baked (1 large), 7–10 oz (210–300 g)
Pasta, whole wheat, cooked, 1 c (250 ml)
Moderate-fiber foods 2 to 4.9 grams | Some berries (blueberries, strawberries), fresh, 1 c (250 ml)
Most fruits (1 medium or 2 small), 1 c (250 ml)
Most vegetables: raw, 2 c (500 ml); cooked 1 c (250 ml)
Most nuts and seeds, ¼ c (60 ml)
Some whole grains (brown rice, millet, oats), cooked, 1 c (250 ml)
Many whole-grain breads, 2 slices
Pasta, white, cooked, 1 c (250 ml)
Popcorn, 3 c (750 ml)
Lower-fiber foods 1.9 grams or less | Melon, 1 c (250 ml)
Fruit or vegetable juice (all varieties), 1 c (250 ml)
Sprouts (all varieties), 1 c (250 ml)
Lettuce, all types, 2 c (500 ml)
Cucumber (1 medium), 8 inch (20 cm)
Most refined grains, (white rice, Cream of Wheat), cooked, ½ c (125 ml)
Refined cold cereals, 1 oz (30 g)
Source of data: US Department of Agriculture, Agricultural Research Service, USDA National _Nutrient Database for Standard Reference_ , Release 25 (2012), ndb.nal.usda.gov.
Key: c = cup; cm = centimeter; g = gram; ml = milliliters; oz = ounce; tbsp = tablespoon.
Fiber can reduce absorption of calcium, iron, and zinc, although fermentation in the large intestine can release them. In addition, when compared to refined foods, high-fiber whole foods generally provide enough extra minerals to compensate for reduced absorption. That's one reason why it's best to avoid concentrated fiber, such as wheat bran or fiber supplements, and get fiber from food instead. Athletes and others who require very high caloric intakes may want to eat some foods in a refined form; their fiber intake will still be ample.
### The Goods on Grains
Grains, or, more precisely, cereal grains, are the edible seeds of grasses. These include wheat, oats, rye, barley, Kamut, spelt, rice, millet, triticale, teff, and corn. Seeds of nongrass plants that are used as grains are more accurately called pseudograins or pseudocereals. However, they are commonly included as grains in the popular press and tend to be used in the same ways, so in this book we include them when referring to grains. Examples include amaranth, quinoa, and buckwheat.
Grains are key sources of calories and protein for the majority of humans and significant sources of fiber, B vitamins, several trace minerals, phytosterols, and phytochemicals. They typically make a significant contribution to total nutrient intakes while providing little fat, no cholesterol, and plenty of fiber. In addition to being very affordable and versatile, whole grains help keep blood sugar levels stable. All of that said, they tend to be less nutrient-dense than other plant foods, so one way of approaching grains is to eat your quota of other plant foods—vegetables, fruits, legumes, nuts, and seeds—and vary your grain intake based on your energy needs. If your energy needs are moderate to high, eat more grains; if low, eat less.
There is widespread agreement that excessive consumption of refined grains contributes to overweight, obesity, and chronic disease, yet an estimated 90 percent of the grains in the typical American diet are refined. Here are just a few of the potential adverse health consequences:
* **Elevated triglycerides and decreased HDL.** Both increase the risk of cardiovascular disease and metabolic syndrome, a prediabetic condition.
* **An increase in blood pressure.** This occurs even when sodium consumption is moderate.
* **Overeating.** Refined carbohydrates are less filling than their whole-food counterparts, which can lead to eating too much.
* **Large fluctuations in blood sugar levels.** Refined carbohydrates are released into the bloodstream more rapidly after eating.
* **Increased gastrointestinal disturbances.** Refined carbohydrates contain little fiber compared to the whole foods from which they were obtained.
* **Increased risk of cancer, especially colorectal cancer.** Sugars and starches contain few of the plant nutrients and phytochemicals that protect against cancer. Refined carbs may increase the risk of colorectal and stomach cancers and possibly cancer of the pancreas.
* **Micronutrient deficiencies.** Refined carbohydrates are generally poor sources of vitamins and minerals. When these are staples of your diet, it can be a challenge to get all of the other nutrients you need.
* **Increased inflammation and oxidative stress.** Refining foods dramatically reduces their quantities of antioxidants and phytochemicals, which protect against inflammatory diseases and oxidative stress.
While there is no doubt that consumption of refined grains should be limited, these foods aren't poison. Eating a piece of pizza or a pasta dish won't sabotage your diet. It isn't a sin to throw a little sugar into your Christmas cookies. Indeed, these departures from a predominantly whole-food diet can make eating more enjoyable and sometimes easier to share with nonvegan friends. Just try to make whole grains your daily fare.
#### **THE WHOLE-GRAIN HIERARCHY**
Even within the realm of whole-grain food products, some aren't the best choices for health. For example, you might eat flaked whole-grain cereal in the morning, whole-grain bread at lunch, whole wheat pasta at dinner, and brown rice cakes as a snack. All of these products are made from whole grains, but they are still processed.
The more processed a whole grain is, the lower its nutritional value. The most nutritious form is the intact whole grain as it comes from the plant. You can further enhance your intake of nutrients and phytochemicals from intact whole grains by soaking and sprouting them. Figure 5.3 shows the whole grain hierarchy, with examples of the most healthful at the top and the least nutritious at the bottom.
Components of whole grains, such as oat bran, wheat germ, and wheat bran, aren't technically whole grains. However, they can play a useful role in the diet. For example, wheat germ can add nutritional value to baked goods made with whole wheat flour, and oat bran can provide extra viscous fiber and help control blood sugar levels or reduce cholesterol levels. (And there are times when less processed grains can be helpful to the diet, particularly for children and seniors. See chapters 11 and chapter 12.)
**FIGURE 5.3.** The whole-grain hierarchy
#### **GLUTEN**
Many people have difficulty tolerating gluten, a protein that's present in several grains, including wheat, spelt, Kamut, rye, barley, and triticale. About 1 percent of the population has an extreme reaction to gluten due to celiac disease. An estimated 10 percent have a less severe reaction, known as gluten sensitivity. People with celiac disease must eliminate all traces of gluten from their diets. People with gluten sensitivity may have to avoid gluten completely or may be able to eat minimal amounts without symptoms.
In either case, symptoms often affect the gastrointestinal system, causing abdominal pain, cramping, bloating, diarrhea, and constipation. However, adverse reactions to gluten can show up in any body system. Behavioral issues (such as depression, foggy mind, hyperactivity, and autism), iron-deficiency anemia (which causes fatigue, weakness, and lack of concentration), dementia, infertility, joint pain, muscle disorders, osteoporosis, leg numbness, migraines, and sinus problems also are commonly reported.
Celiac disease has increased fourfold in the past forty years, yet humans have been eating grains for centuries. In the August-September 2011 issue of _Living Well_ , Alessio Fasano, MD, a world-renowned expert on celiac disease, said the reasons for this surge are twofold: "First, the grains we're eating have changed dramatically. In our great-grandparents' era, wheat contained very low amounts of gluten and it was harvested once a year. Now we've engineered our grains to substantially increase yields and contain characteristics, like more elasticity, that we like. We're susceptible to the consequences of these extremely rich, gluten-containing grains. Second is the upward trend we're seeing in all autoimmune diseases. We're changing our environment faster than our bodies can adapt to it."
If you think you might be sensitive to gluten, it's important to rule out celiac disease and wheat allergy. If these tests are negative, you can still go on a gluten-free diet for two to four weeks to see if your symptoms improve. If they do, that's a strong indicator of gluten sensitivity. To double check, try eating foods that contain gluten for a day and see if your symptoms return.
Sprouting significantly reduces gluten content but doesn't eliminate it. Your sensitivity might be such that sprouting allows you to eat some grains that would normally be troublesome.
Oats may or may not be a problem. They contain a gluten-like protein that most people with celiac disease or gluten sensitivity can tolerate. However, many oats sold in North America are processed on machinery that also handles grains containing gluten, so the oats may become contaminated.
Even if gluten isn't much of an issue for you, it's wise to vary the grains you eat. Whole grains differ in their content of fiber, vitamins, minerals, and phytochemicals, so consuming a variety of grains ensures a better balance. Definitely include pseudograins such as quinoa, amaranth, and buckwheat in the mix. All are protein powerhouses, and they're also gluten-free and more concentrated in vitamins and minerals.
### The Sour Side of Sugar
Humans have a soft spot for sweets. We're born that way, and for good reason. In foods found in nature, sweetness generally signals safety, while bitterness serves as a warning flag. The sugar in plants provides a reasonable concentration of glucose to keep the human body running smoothly. It would be difficult to consume excessive sugar when eating a variety of vegetables, fruits, legumes, grains, nuts, and seeds. Unfortunately, when we process foods and concentrate their sugars, our hardwired attraction to sweets begins to work against us.
Prior to the 1500s, concentrated sweeteners were less common, with the exception of honey, for those who had access to it. It wasn't until the mid-1800s that sugar became a common part of everyday diets. By 1900, per capita annual sugar consumption in the United States averaged about 64 pounds (29 kg), one of the highest levels globally.
The use of added sugars increased more than 200 percent between 1900 and 2005, and by 19 percent between 1970 and 2005. Americans consumed an average of 30 teaspoons (126 g) of added sugars per day in 2005. That amounts to 488 calories, or almost 25 percent of your calories if you're eating 2,000 calories per day. Soft drinks and other sweetened beverages account for close to half of the added sugars Americans consume. Between 1970 and 2000, consumption of sugar-laden soft drinks increased from less than 8 fluid ounces (250 ml) per day to almost 16 fluid ounces (500 ml).
Between 1970 and 1995, the most notable change was not in the amount of sugar consumed, but the type. While the consumption of table sugar (sucrose) declined by 38 percent, intake of corn sweeteners—mainly high-fructose corn syrup—almost quadrupled. In 2007, 45 percent of all added sugars were sucrose, 41 percent were high-fructose corn syrup, and 14 percent were glucose syrup, pure glucose, and honey.
#### **HOW BAD IS SUGAR?**
Sugar isn't inherently harmful. In fact, when it's part of a whole plant food, it's a valuable and healthful source of energy. The human body prefers sugar as a fuel source and can handle it fairly well—in reasonable doses, such as the amounts naturally present in fruits and vegetables. Excess sugar is the issue, particularly when it comes from concentrated sweeteners. The adverse health effects of sugar are similar to those of refined carbs, discussed earlier in this chapter. In addition, high-sugar diets have the following adverse impacts on health:
* They increase levels of triglycerides, the fatty acids implicated in cardiovascular disease, especially when simple sugars exceed 20 percent of energy (as they typically do in Western diets).
* They raise blood sugar levels and increase insulin output and insulin resistance, which can contribute to metabolic syndrome, prediabetes, and type 2 diabetes.
* They cause cavities and impaired dental health.
* They result in nonalcoholic fatty liver disease, which increases risk of atherosclerosis and cardiovascular diseases.
* They adversely affect immunity and increase susceptibility to infection.
#### **HOW MUCH SUGAR IS OKAY?**
Clearly, sugar can be toxic when consumed in excess. The million-dollar question is how much is too much. The World Health Organization suggests a maximum of 10 percent of calories from added sugars, or no more than about 12½ teaspoons (53 g) per day in a 2,000-calorie diet. There is no question that less is better, but the upper limit suggested by World Health Organization is a reasonable maximum for most people.
Learn to read labels. Manufacturers must list total sugar (sugar naturally present in foods plus any added sugar) per serving, but they aren't required to separate out added sugars. If the food has no naturally occurring sugars, then the sugar listed is all added sugar.
If there are natural sugars from fruits, dried fruits, or vegetables such as tomatoes, then further detective work is called for. Scrutinize the ingredient list. Ingredients are listed in descending order by weight. If sugar is high on the list, this is a good clue that added sugars are high. However, if several different sweeteners have been used in the product, each will be listed separately; they may appear lower in the list, yet their cumulative amount may be substantial. You may not even recognize some of them as sugar. Any of the following ingredients are simply different forms of sugar: agave nectar, barley malt syrup, blackstrap molasses, brown rice syrup, brown sugar, cane sugar, corn syrup, crystalline fructose, dextrose, dried cane juice, evaporated cane juice, fructose, fruit juice concentrate, glucose, high-fructose corn syrup, honey, invert sugar, lactose, maltodextrin, maltose, malt syrup, maple syrup, molasses, raw sugar, rice syrup, Sucanat, sucrose, sugar, syrup, and turbinado sugar.
Also note the serving size; servings are often smaller than you might imagine. Look for the number of grams of sugar per serving. There are approximately 4.2 grams in 1 level teaspoon (5 ml) of sugar, so, if a product contains 12 grams of sugar, that's about 3 teaspoons. Table 5.3 (facing page) lists the sugar content of some common vegan foods.
#### **MORE HEALTHFUL SWEETENERS**
Most sugars provide about the same number of calories and are essentially glucose, fructose, or a combination. Glucose tends to raise blood sugar more readily than fructose, but fructose has been implicated in many health conditions. The take-home message is simple: sugar is sugar is sugar, and consumption should be limited regardless of the variety used.
Although a few sweeteners contain tiny amounts of nutrients, you would have to eat far more than you should for them to make a significant contribution to your nutritional needs. One notable exception is blackstrap molasses, which is a significant source of minerals because it contains the minerals stripped away in the process of refining sugar. For example, 2 tablespoons (30 ml) of blackstrap molasses provides 344 mg of calcium, 7 mg of iron, and 996 mg of potassium. That's more calcium than 1 cup (250 ml) of milk, more iron than an 8-ounce (240 g) steak, and more potassium than two large bananas. (Choose organic molasses, or you'll also have a significant source of pesticides.)
**TABLE 5.3.** Sugar content of common vegan foods
**FOOD** | **SERVING SIZE** | **SUGAR (g)** | **SUGAR (tsp)**
---|---|---|---
Almond milk (Silk, True Almond, original) | 1 c (250 ml) | 7 | 1.7
Almond milk (Silk, True Almond, vanilla) | 1 c (250 ml) | 15 | 3.6
Chocolate bar, 70% cacao (Greens and Black) | 1.7 oz (50 g) | 12.5 | 3
Chocolate bar, rice milk (Terra Nostra) | 1.7 oz (50 g) | 27.5 | 6.5
Coconut yogurt (So Delicious, blueberry) | 6 oz (170 g) | 20 | 4.8
Granola bar (Nature's Path, all flavors) | 1.2 oz (35 g) | 10–11 | 2.4–2.6
Granola, premium (Nature's Path, all flavors) | ½ c (125 ml) | 12 | 2.9
Granola, regular (Nature's Path, all flavors) | ½ c (125 ml) | 7–9 | 1.7–2.1
Organic soda (Blue Sky) | 12 fl oz (375 ml) | 37–44 | 8.8–10.5
Salad dressing (Annie's Raspberry Balsamic Vinaigrette) | 2 tbsp (30 ml) | 7 | 1.7
Soy ice cream (So Delicious, all flavors) | ½ c (125 ml) | 15–27 | 3.6–6.4
Soy milk (Silk, original) | 1 c (250 ml) | 6 | 1.4
Soy milk (Silk, vanilla) | 1 c (250 ml) | 8 | 1.9
Tomato sauce (Newman's Own Organic Traditional Herb) | ½ c (125 ml) | 9 | 2.1
Sources of data are listed in _Becoming Vegan: Comprehensive Edition,_ by Brenda Davis and Vesanto Melina (Book Publishing Company, 2014).
Key: fl oz = fluid ounce; g = gram; ml = milliliter; oz = ounce; tbsp = tablespoon.
Date sugar (dried and ground dates) and coconut sugar (dried nectar from the flowers of coconut palms) also contain more nutrients than many other sugars because they are derived from whole foods. Of course, the most nutritious sweeteners are fresh or dried fruits, which can be used to make fabulous desserts without adding any concentrated sugar or other sweetener.
#### **FRUCTOSE: THE SUGAR VILLAIN**
Based on scientific research to date, fructose has damaging effects on the body, particularly when consumed in excess. The body can handle small amounts of fructose, such as those that naturally occur in whole foods. However, regular consumption of significant amounts of concentrated sources of fructose—no matter the source—can quickly exceed the body's capacity to handle it.
Every cell in the human body can use glucose for energy, but fructose immediately goes to the liver, where it is rapidly converted to fatty acids. Some of the fatty acids stay in the liver, and the remainder enter the bloodstream as triglycerides. Many of the adverse effects associated with concentrated sweeteners—such as nonalcoholic fatty liver disease, high triglycerides, increased LDL cholesterol, insulin resistance, visceral fat accumulation, and elevated blood pressure—are even more pronounced with fructose. Remember, it is the dose that makes the poison. The fructose content of a serving of fruit is 2 to 8 grams, whereas the fructose content of a 12-fluid-ounce (375 ml) soda is about 25 grams—regardless of whether it is sweetened with high-fructose corn syrup or sucrose.
**_Are Sugar Substitutes Safe?_**
There are essentially two classes of sugar substitutes: sugar alcohols and noncaloric sweeteners (also called nonnutritive sweeteners). In small amounts, sugar alcohols, such as mannitol, sorbitol, and xylitol, are relatively benign, although they can cause gastrointestinal distress if you eat too much. They do raise blood sugar levels, but not as much as other carbohydrates.
Noncaloric sweeteners (also called nonnutritive sweeteners) can be further divided into two categories: artificial sweeteners and natural noncaloric sweeteners. In the United States, five artificial sweeteners are approved for use: acesulfame K, aspartame, neotame, saccharin, and sucralose. Natural noncaloric sweeteners include stevia and rebaudioside A, both of which are derived from the stevia plant.
Generally, it's best to minimize your use of sugar substitutes or avoid them. They can have negative effects on health and provide few, if any, benefits. If you must use these products, stick to sugar alcohols or natural noncaloric sweeteners.
### The Glycemic Index
The glycemic index (GI) is a measure of the effect of 50 grams of carbohydrates from a specific food on blood sugar levels. Carbohydrates that are quickly digested and release their sugars into the bloodstream rapidly have a high GI. They usually trigger an exaggerated insulin response, which adversely affects long-term blood sugar control, elevates triglyceride levels, and decreases HDL levels. Carbohydrates that are slowly digested and release their sugars into the bloodstream gradually have a low GI and may have positive effects on insulin response and triglyceride and HDL levels.
The glycemic index uses a scale of 0 to 100, with foods that cause a rapid rise in blood sugar levels having higher values. Pure glucose serves as a reference point and has a GI of 100. White bread has a GI of 75, which means the blood sugar response to the carbohydrate in white bread is 75 percent that of the response to the pure glucose. By comparison, barley has a GI of 28. A low GI is between 0 and 55, a moderate GI is between 56 and 69, and a high GI is above 69.
The GI gives us a ballpark idea of how a 50-gram serving of carbohydrates affects blood sugar levels. But we don't always eat exactly 50 grams of carbohydrate from a food. This is where the glycemic load (GL) comes in. Glycemic load factors in the serving size of the food and the actual amount of carbohydrate consumed. Foods that have a high GI aren't necessarily problematic if they don't contain much carbohydrate and have a low GL.
The GL of a food is calculated by multiplying the GI by the grams of carbohydrate in a _serving_ of the food and dividing the total by 100. So although watermelon has a GI of 72, a 120-gram (4 oz) serving of watermelon provides only 6 grams of carbohydrate and therefore has a GL of 4, which is low. (Note that this calculation is done using the weight of carbs in a serving, not the weight of the serving.) The important point is that the total amount of carbohydrate in a food is just as important as its GI in determining its impact on blood sugar. A low GL is between 0 and 10, a moderate GL is between 11 and 19, and a high GL is above 19. Table 5.4 lists some common foods and their GI and GL.
**TABLE 5.4.** Glycemic index (GI) and glycemic load (GL) of selected foods
**FOOD** | **GI** | **SERVING SIZE** | **GL**
---|---|---|---
**GRAINS**
Barley, cooked | 28 | 5 oz (150 g) | 12
Bread, white | 75 | 1 oz (30 g) | 11
Bread, whole wheat | 74 | 1 oz (30 g) | 9
Buckwheat, cooked | 54 | 5 oz (150 g) | 16
Bulgur wheat, cooked | 48 | 5 oz (150 g) | 13
Cornflakes | 81 | 1 oz (30 g) | 20
Corn tortilla | 46 | 5 oz (150 g) | 4
Millet, cooked | 71 | 5 oz (150 g) | 26
Oatmeal, instant | 79 | 8 oz (250 g) | 21
Oatmeal, made from rolled oats | 55 | 8 oz (250 g) | 13
Quinoa, cooked | 53 | 5 oz (150 g) | 13
Rice, brown, cooked | 50–87 | 5 oz (150 g) | 16–33
Rice, white, cooked | 43–109 | 5 oz (150 g) | 15–46
Rice cakes, plain | 82 | 0.9 oz (25 g) | 17
Rice crackers, plain | 91 | 1 oz (30 g) | 23
Rye crispbread | 64 | 0.9 oz (25 g) | 10
Shredded wheat cereal | 67 | 1 oz (30 g) | 13
Rye bread (pumpernickel) | 53 | 1 oz (30 g) | 6
Spaghetti, white, cooked | 49 | 6 oz (180 g) | 24
Spaghetti, whole wheat, cooked | 44 | 6 oz (180 g) | 18
**LEGUMES**
Baked beans, canned, vegetarian | 48 | 5 oz (150 g) | 7
Chickpeas, cooked | 28 | 5 oz (150 g) | 8
Kidney beans, cooked | 28 | 5 oz (150 g) | 7
Lentils, cooked | 29 | 5 oz (150 g) | 5
Mung beans, sprouted, raw | 25 | 5 oz (150 g) | 4
Navy beans, cooked | 38 | 5 oz (150 g) | 12
Peas, split, yellow | 32 | 5 oz (150 g) | 6
Soybeans, cooked | 18 | 5 oz (150 g) | 1
**NUTS**
Cashews | 22 | 1.7 oz (50 g) | 3
Mixed nuts | 24 | 1.7 oz (50 g) | 4
Peanuts | 14 | 1.7 oz (50 g) | 1
**VEGETABLES**
Beet | 64 | 2.7 oz (80 g) | 5
Carrot, raw and boiled | 47 | 2.7 oz (80 g) | 3
Corn, boiled | 52 | 2.7 oz (80 g) | 9
Parsnip, boiled | 52 | 2.7 oz (80 g) | 4
Peas, frozen, boiled | 51 | 2.7 oz (80 g) | 4
Potato, baked | 86 | 5 oz (150 g) | 22
Potato, boiled | 82 | 5 oz (150 g) | 21
Potatoes, new, boiled | 76 | 5 oz (150 g) | 16
Pumpkin, boiled | 64 | 2.7 oz (80 g) | 6
Sweet potato, raw and cooked | 70 | 5 oz (150 g) | 22
Yam, steamed and boiled | 54 | 5 oz (150 g) | 20
**FRUITS**
Apple | 38 | 4 oz (120 g) | 6
Apricot | 34 | 4 oz (120 g) | 3
Apricots, dried | 31 | 2 oz (60 g) | 7
Banana | 52 | 4 oz (120 g) | 13
Cantaloupe | 65 | 4 oz (120 g) | 4
Cherries | 22 | 4 oz (120 g) | 3
Grapes | 46 | 4 oz (120 g) | 8
Kiwi | 53 | 4 oz (120 g) | 6
Mango | 51 | 4 oz (120 g) | 9
Orange | 42 | 4 oz (120 g) | 5
Papaya | 59 | 4 oz (120 g) | 10
Peach | 42 | 4 oz (120 g) | 5
Pear | 38 | 4 oz (120 g) | 4
Pineapple | 59 | 4 oz (120 g) | 8
Plum | 39 | 4 oz (120 g) | 5
Strawberries | 40 | 4 oz (120 g) | 1
Watermelon | 72 | 4 oz (115 g) | 4
**MILKS**
Cow's milk | 31 | 1 c (250 ml) | 4
Rice milk, "original" | 86 | 1 c (250 ml) | 23
Soy milk, "original" | 34 | 1 c (250 ml) | 5
**SNACK FOODS**
Chocolate, dark | 23 | 1.7 oz (50 g) | 6
Chocolate, milk | 43 | 1.7 oz (50 g) | 12
Dates | 42 | 2 oz (60 g) | 18
Ice cream, French vanilla, (16% fat) | 38 | 1.7 oz (50 g) | 3
Popcorn | 72 | 0.7 oz (20 g) | 8
Potato chips | 54 | 1.7 oz (50 g) | 11
Pretzels | 84 | 1 oz (30 g) | 17
**SUGARS**
Agave syrup | 13 | 0.3 oz (10 g) | 1
Fructose | 15 | 0.3 oz (10 g) | 2
Glucose | 103 | 0.3 oz (10 g) | 10
Golden syrup | 63 | 0.9 oz (25 g) | 13
Honey | 61 | 0.9 oz (25 g) | 12
Maple syrup | 54 | 0.3 oz (10 g) | 10
Sucrose | 65 | 0.3 oz (10 g) | 7
Source of data: F. S. Atkinson et al., "International Tables of Glycemic Index and Glycemic Load Values: 2008," _Diabetes Care_ 31, no. 12 (2008):2281–2283.
GI - low: less than 55; medium: 55-69; high: 70 or more
GL - low: less than10; medium: 11-19; high: 20 or more
Key: c = cup; g = gram; ml = milliliter; oz = ounce.
#### **THE LIMITATIONS OF GI AND GL**
The GI and GL are sometimes seen as a key way to judge a food's healthfulness. This is a serious error. These tools determine the effect of carbohydrates on blood sugar levels, but they don't tell us anything else about the food and aren't designed to be used as the sole criteria for food selection.
First, foods that contain little if any carbohydrate have a very low GI, and a negligible GL. For example, meat has a small impact on blood sugar, but this doesn't qualify it as a healthy or "free food" for people with diabetes. The GI of potato chips is lower than that of baked potatoes, but adding salt and fat doesn't make potatoes more healthful. Other unhealthful snacks, such as candy bars, cupcakes, and ice cream, also frequently fall within the low GI range because of their high fat content. In contrast, plenty of nutritious, higher-carbohydrate whole foods, such as some fruits, starchy vegetables, and whole grains, have relatively high GIs or GLs, but that doesn't mean you should avoid them.
Despite these limitations, GI and GL can be helpful when used appropriately. Among the best ways to use these tools is to compare similar foods or foods in the same category. For instance, in table 5.4 you might compare corn tortillas with corn flakes; barley with millet (both intact grains); or soy milk with rice milk. It's also helpful to recognize that foods with higher GIs and GLs can serve as valuable fuel sources during demanding physical activity, when you need carbohydrate that's readily available.
Vegans don't necessarily have to worry about GI and GL, because vegan diets have a low overall GI compared with nonvegetarian diets and a low to moderate GL. One study examining the GI and GL of vegan diets reported an average GI of 51 and an average GL of 144—the sum of all the foods eaten during the day—which is considered low to moderate. This could provide a health advantage for vegans in terms of risks for both diabetes and cardiovascular diseases. Both the GI and GL of vegan diets compare very favorably to those of nonvegetarian diets. This could help to explain the health advantages for vegans in terms of risks for both diabetes and cardiovascular diseases.
GI and GL can be useful tools for determining the impact of food on blood sugar levels, but they don't determine the food's nutritional value. For that, we need a more complete picture. Let's start with vitamins.
## **CHAPTER 6**
## **Valuing Vitamins**
Our knowledge of specific vitamins is just a century old, with vitamin A, first in the lineup, not identified until 1913. Yet the awareness that certain foods held mysterious properties that could cure illnesses such as scurvy and rickets goes back thousands of years.
Vitamins are complex molecules that contain carbon along with other elements, including hydrogen, oxygen, and sometimes nitrogen. They have far-reaching effects in the body, governing certain aspects of growth, regulating the metabolism of minerals, protecting us from free radical damage, turning the food we eat into usable energy, and more. The list of their functions is long and impressive. Yet the total amount of vitamins we need is tiny—only about 0.5 gram per day, equal in weight to about one-sixth of a garlic clove.
Vitamins are essential to life, and the body cannot synthesize them—we have to get them from the food we eat. Vegan diets deliver most vitamins in abundance. The exceptions are vitamins B12 and D, but those are easily added.
In this chapter, we examine the roles of vitamins and explore the options for meeting recommended intakes. Let's begin with the two of greatest interest in vegan diets: vitamins B12 and D.
### Vitamin B12 (Cobalamin, Cyanocobalamin)
Throughout history, vitamin B12 was primarily available from animal products. In the past, when vegans had far less access to plant-based foods fortified with vitamin B12, the average intakes of American vegans were only about one-quarter of the recommended amount. However, shortfalls are easily averted with supplements and the B12-fortified plant foods that have proliferated in recent decades. Fortunately, responsible vegetarian societies and raw-food groups have encouraged vegans to make sure they have a reliable source of this essential nutrient.
**_Details, Details_**
For detailed information on vitamins, recommended intakes throughout every stage of life, and food sources of vitamins, see table 6.1 (facing page), table 6.2 (page 120), and the appendix (page 274).
Vitamin B12 is part of a team of nutrients that converts carbohydrates, fat, and protein into usable energy. It helps build DNA and red blood cells, particularly during times of rapid growth, and it maintains the protective sheaths around nerve fibers. In addition, it helps rid the body of homocysteine, a potentially damaging substance that can injure the delicate inner lining of artery walls and trigger heart disease. A deficiency of B12 can have severe consequences, such as gastrointestinal problems, nerve damage, and megaloblastic anemia.
Vegans who don't include a reliable source of vitamin B12 will eventually become deficient. For some, this will happen in a matter of months; for others, it could take years. The consequences of the deficiency will depend on how soon the symptoms are recognized and how quickly you begin to make up for it. The longer it takes to recognize the problem, the greater the risk of permanent damage. If you have symptoms of fatigue, weakness, mood changes, shortness of breath, or palpitations or have other reasons to suspect a B12 deficiency, arrange a lab test through your doctor. Supplementation usually works quickly to improve the deficiency conditions if the damage hasn't gone too far.
#### **RECOMMENDED INTAKES OF VITAMIN B 12**
The recommended intake for adults is 2.4 mcg, spread over the day, however many experts suggest 4 to 8 mcg. When vitamin B12 is taken in a single dose, a smaller amount of that dose is absorbed than if you took the same dose in divided portions. If you take a single daily supplement, the suggested intake is 25 to 100 mcg per day. Another option is to take 1,000 mcg twice a week.
#### **Pregnancy, Lactation, and Infancy**
Taking a reliable supplementary source of vitamin B12 is especially important for mother and child during pregnancy and breast-feeding. The recommended intake of vitamin B12 for pregnant women is 2.6 mcg, and for nursing moms it's 2.8 mcg. Again, many experts recommend more, with options shown in table 6.1.
It is essential that babies who have not yet built up their reserves of this nutrient get adequate dietary vitamin B12. Without it, an infant can develop irreversible brain damage in a few months. Fortunately, when a breast-feeding mother is getting sufficient B12, her baby gets enough through her milk. As babies are weaned from breast milk or infant formula, they should be given vitamin B12 drops.
**TABLE 6.1.** Options for meeting the recommended dietary allowance(RDA) for vitamin B12
Sources of data are listed in _Becoming Vegan: Comprehensive Edition,_ by Brenda Davis and Vesanto Melina (Book Publishing Company, 2014).
#### **Seniors**
Vitamin B12 can help treat cognitive impairment and dementia in the small number of cases where B12 deficiency exists. Vitamin B12 deficiency may also be related to depression in later life.
Seniors on any type of diet should have their B12 status tested every five years starting at age fifty. With age, the body's ability to absorb the form of vitamin B12 found in animal products diminishes. In animal products, vitamin B12 is attached to a protein, and as people get older, they start to lose the ability to cleave the B12 from the protein. The form of B12 in fortified plant foods or supplements isn't attached to protein, so they are good sources even as we age. People older than fifty, regardless of diet, should take B12 supplements or eat B12-fortified foods to meet most or all of the recommended intakes based on the amounts for adults in table 6.1, above. Vegan seniors are likely to have an advantage over nonvegetarian seniors if they've already developed the habit of taking a B12 supplement.
Some older adults (regardless of diet) also don't produce enough intrinsic factor, a compound necessary for B12 absorption. In such cases, monthly B12 injections or relatively large oral doses, such as 2,000 mcg followed by 1,000 mcg per day, have proven to be effective.
#### **GETTING ENOUGH VITAMIN B 12**
There are several ways to get enough vitamin B12. You can use one or a combination of the following approaches.
#### **Take a B 12 Supplement Daily**
Choose a vitamin or multivitamin-mineral supplement that includes 25 to 100 mcg of vitamin B12 (cyanocobalamin, the form used in most research). For optimal absorption, chew your B12 supplement. Methylcobalamin is advised for smokers and those with kidney problems; 1000 mcg daily may be needed for this form.
#### **Take a Larger B 12 Supplement Twice a Week**
Because the body retains only a small portion of vitamin B12 when a large amount is consumed, you can take a very large amount twice a week instead of a smaller daily supplement and still ensure you're absorbing the correct amount. If you go with this option, take 1,000 mcg of cyanocobalamin two or three times per week; chew for optimal absorption.
#### **Get Vitamin B 12 from Fortified Foods Daily**
Each day, eat two servings of B12-fortified foods, such as nondairy milks, vegetarian meat analogs, breakfast cereals, and nutrition bars. Check labels to make sure each serving provides 2 mcg or more, or at least 50 percent of the actual daily value per serving. Food labels use 6 mcg as 100 percent. This means a food labeled as containing 50 percent of the daily value would provide 3 mcg per serving.
Fortified foods aren't as reliable a source for vitamin B12 as supplements, because even though adequate amounts of the vitamin are added during production, amounts can vary considerably from one sample to another. If you rely on fortified foods for your B12 intake, consider including a 1,000 mcg supplement once a week to ensure optimal B12 status.
Unreliable B12 sources include fermented foods, mushrooms, sea vegetables (nori and dulse), spirulina, sprouts, and raw plant foods. Chlorella and AFA ( _Aphanizomenon flos-aquae_ ), two species of algae, have not yet proven to be reliable sources.
#### **Use Nutritional Yeast**
Nutritional yeast is grown on a vitamin B12-enriched medium, and 2 tablespoons (30 ml or 8 g) may provide 2.4 mcg, but the B12 content can vary from batch to batch, so it's best to also take a supplement from time to time. Each day, sprinkle 2 tablespoons (30 ml or 8 g) of Red Star Vegetarian Support Formula nutritional yeast on food or use it as an ingredient in salad dressings and vegan cheeses. (For delicious recipes featuring nutritional yeast, see _Cooking Vegan_ , by V. Melina and J. Forest, and _The Nutritional Yeast Cookbook_ by Jo Stepaniak.)
For additional information, see "Vitamin B12: Are You Getting It?" by Jack Norris, registered dietitian and coauthor of _Vegan for Life_ , available online at veganhealth.org/articles/vitaminb12.
### Vitamin D (Calciferol)
For centuries, the puzzling and crippling disease known as rickets prevented children's bones from hardening enough to hold up the weight of their growing bodies. The first scientific description of rickets was written around 1650, shortly after soft coal had been introduced as an energy source in England. The use of coal spread through northern European cities, accompanied by a pall of coal smoke that polluted the air and blocked out the sun. Rickets became known as the disease of the Industrial Revolution since its incidence increased when families left farms to move to smoky, smoggy, sunless cities in the United Kingdom, northern Europe, and the northern United States. By 1900, an estimated 80 percent of the children in Boston, New York, and some other industrialized cities of the northeastern United States and northern Europe had rickets.
**_Liquid Gold Dressing_**
Makes 1½ cups (375 ml)
We developed this dressing for use on salads, baked potatoes, rice, steamed broccoli, and other vegetables and gave it the name Liquid Gold because of its nutritional wealth. Just 3 tablespoons (45 ml) can provide half of your daily B12 requirement and a day's supply of omega-3 fatty acids. It's also packed with other B vitamins, and, best of all, it's very tasty.
½ cup (125 ml) flaxseed oil
½ cup (125 ml) water
⅓ cup (90 ml) freshly squeezed lemon juice
1 tablespoon (15 ml) cider, balsamic, or raspberry vinegar 2 tablespoons (30 ml) tamari or Bragg Liquid Aminos
½ cup (125 ml) Red Star Vegetarian Support Formula nutritional yeast
1 tablespoon (15 ml) ground flaxseeds 2 teaspoons (10 ml) Dijon mustard 1 teaspoon (5 ml) ground cumin, turmeric, or a combination
Put all the ingredients in a blender and process until smooth. Stored in a covered jar in the refrigerator, Liquid Gold Dressing will keep for 2 weeks.
Shortly after World War I, scientists had closed in on two effective ways to prevent rickets: ultraviolet radiation from the sun or a lamp, and a substance derived from cod liver oil that became known as vitamin D. In succeeding decades, researchers demonstrated how vitamin D could be produced in human skin when exposed to sunlight. They also learned that one of the forms of vitamin D (vitamin D2) could be produced when mushrooms, yeasts, alfalfa, or lichens were exposed to sunlight or ultraviolet light, and that the human body can convert vitamin D2 to the active form that the body uses. Identification of the vitamin prompted the fortification of cow's milk and then infant formula with vitamin D to reliably provide this nutrient to most infants and children. As a result, rickets was almost eradicated in regions that adopted fortification. Starting in the 1990s, nondairy beverages, such as soy milk, also were fortified.
Vitamin D has many important functions, including helping with the absorption of calcium and phosphorus, maintenance of critical blood levels of calcium, and limiting calcium losses through the urine. This vitamin is important at all ages, including for seniors, who tend to be at risk for osteoporosis. (For more on vitamin D and osteoporosis, see pages 234 and .) It's also important in the functioning of the muscles, heart, brain, pancreas, and thyroid. Vitamin D controls the growth and maturation of cells, including those in bone and the immune system. Through its impact on the immune system, it helps fight infectious diseases and reduce the risk of Crohn's disease, multiple sclerosis, and rheumatoid arthritis. It regulates insulin production in the pancreas and can protect against diabetes. Due to its active role in blood vessels, it helps regulate blood pressure and prevent cardiovascular disease and stroke. Low vitamin D intakes and serum vitamin D levels are associated with increased risk for colon cancer and other cancers, whereas adequate vitamin D seems to protect against the recurrence of breast cancer. Vitamin D also helps preserve cognitive function as we age, and plays a role in the functioning of the reproductive system.
Those at greatest risk for vitamin D deficiency are breast-fed infants whose mothers are low in vitamin D, people with dark skin living far from the equator, adults older than fifty (whose vitamin D production is diminished), and those who are obese, with a BMI greater than 30. (See table 9.2, Body Mass Index, on page 166).
#### **HOW VITAMIN D WORKS**
Sun shining on human skin stimulates a substance called dehydrocholesterol to become vitamin D3. Vitamin D3 enters the bloodstream and is carried to the liver, where it is converted into calcidiol, which is transported to the kidneys, where it is finally converted to its active form: calcitriol. From there, calcitriol moves to other locations in the body, including the intestine, where it stimulates calcium absorption and performs its many other functions.
The amount of vitamin D humans can produce from sunlight depends on many variables: geographic location, time of year, time of day, cloud cover, skin color, age, body weight, how much skin is exposed, length of exposure, and use of sunscreen and UVB light. For example, people who live between latitudes 37 degrees north and 37 degrees south get more of the right kind of rays. People with lighter skin need less sun than people with darker skin. Obese people need more than normal-weight people, since they are less able to produce vitamin D than leaner people. Younger people are far more efficient at vitamin D production than seniors.
Because of all these variables, it's difficult to pinpoint just how much sun will produce enough vitamin D for any given individual, and recommended intake is currently the subject of lively debate among experts. Since vegans don't use fortified cow's milk, they get less than other dietary groups unless they regularly use vitamin D supplements or consume nondairy beverages or other foods fortified with vitamin D. Vegans tend to get only a little more than half the recommended level; however, international studies have found that many adults have low in-takes and low blood levels of vitamin D, so this problem isn't specific to a vegan diet. Food fortification policies are changing, and this may help the situation.
In general, if you are in the northern hemisphere, below latitude 37—a horizontal line that divides the United States in half, roughly following the southern borders of Utah, Colorado, Kentucky, and Virginia—you can expect to make sufficient vitamin D throughout the year through sun exposure. To do so, if you're light skinned, spend ten to twenty minutes outdoors (without sunscreen) daily, getting sun on your face, arms, and legs. If you're dark skinned or elderly, you'll need to spend significantly more time in the sun.
If you live north of that latitude, you probably need to take a vitamin D supplement and eat fortified foods in the winter, in addition to spending time outdoors on sunny days in summer. To make sure you're meeting your vitamin D requirements, ask your doctor to check your blood levels of vitamin D, or use a self-testing kit. They're widely available, including through the Vitamin D Council (vitamindcouncil.zrtlab.com). By the way, the body self-regulates the production of vitamin D, so even if you spend a lot of time outdoors, you can't produce too much vitamin D.
#### **VITAMINS D 2 AND D3**
Vitamin D is commonly taken in single-vitamin supplements, in multivitamin-mineral supplements, and in supplements that contain vitamin D plus calcium and perhaps magnesium. Vitamin D2 (ergocalciferol) is vegan, and vitamin D3 (cholecalciferol) is commonly of animal origin but is now available in vegan form, made from lichen. (To find a vegan vitamin D3 supplement, do an Internet search for "vegan vitamin D3.")
Research comparing the effectiveness of vitamin D2 and D3 offers a variety of perspectives and some lively controversy. The bottom line is that both forms are effective, though it can take a little more vitamin D2 to achieve optimal vitamin D levels.
#### **RECOMMENDED INTAKES OF VITAMIN D**
The recommended vitamin D intake from birth to one year is 10 mcg (400 IU) per day; for ages one to seventy it's 15 mcg (600 IU) per day; and for ages seventy-one and older it's 20 mcg (800 IU) per day. However, many experts suggest 25 to 50 mcg (1,000 to 2,000 IU) daily for adults. Others advise even higher intakes of up to 100 mcg (4,000 IU), though this is the upper limit a person should take without medical supervision. The tolerable upper limits are lower for younger children. Obese people may have somewhat higher requirements for vitamin D because fat can absorb this vitamin D, making it unavailable to the rest of the body.
#### **Pregnancy, Lactation, and Infancy**
Breast-fed babies whose moms are low in vitamin D are among those at the greatest risk for vitamin D deficiency and rickets, particularly if they don't receive a vitamin D supplement and live outside of the zone from latitude 37 north to latitude 37 south. The American Academy of Pediatrics recommends a daily intake of 10 mcg (400 IU) of vitamin D starting from the first few days of life. Ask your pediatrician about a suitable intake for your baby, and avoid giving the baby more than the doctor suggests, as too much may cause your child's bones to harden too soon.
#### **Seniors**
The body's ability to produce vitamin D diminishes with age. For example, the skin of someone who is sixty five or older can synthesize only about 25 percent as much vitamin D as that of a young person. This has potentially severe consequences for older people, who are generally more susceptible to falls, as vitamin D deficiency is linked to muscle weakness. Research has shown that supplementation with 20 mcg (800 IU) of vitamin D reduced falls in institutionalized older patients by more than 20 percent.
#### **SOURCES OF VITAMIN D**
Few foods, whether of plant or animal origin, naturally contain vitamin D, but a growing number of vegan foods fortified with vitamin D are becoming available, including nondairy milks, juices, and breakfast cereals. Typically, 1 cup (250 ml) of soy or rice milk contains 2.5 to 3 mcg (100 to 120 IU) of vitamin D; 1 teaspoon (5 ml) of margarine contains 0.5 mcg (20 IU), and one serving of breakfast cereal contains 1 mcg (40 IU). Check food labels for exact amounts.
Mushrooms contain a compound that can be converted to vitamin D2 when they are exposed to UVB rays. Under these conditions, they can be a good source of vitamin D. Such mushrooms are becoming available in markets and are advertised as vitamin D sources. Most commercial mushrooms are grown indoors, so are not sources of vitamin D. Only wild edible mushrooms and cultivated mushrooms grown with light exposure may be reliable sources.
### The ACE Antioxidant Team
Just as oxygen can make food turn brown and metal rust, oxidation in the body can also lead to damage. When oxygen joins with certain molecules, oxidation occurs, causing chain reactions of rampaging molecules called free radicals. Free radicals damage cells and DNA, effectively aging our bodies and increasing our risk for diseases including cancer, cardiovascular disease, cataracts, macular degeneration, diseases of the nervous system (such as Alzheimer's and Parkinson's), and premature aging of skin. The body also produces free radicals during normal metabolism, but if you smoke, drink alcohol, or are exposed to pollutants or radiation, including too many UV rays from the sun, free radicals can multiply rapidly. This chain reaction can only be stopped by substances that intervene and deactivate the process. These substances are called antioxidants.
An important group of antioxidants consists of vitamin A, which the body can make from the carotenoid known as beta-carotene, and vitamins C and E. These antioxidants are team players. Each helps the others function, so we need a regular supply of all three to help prevent cell damage and disease.
#### **DIET AND DETOX**
The liver may be the busiest hub of activity in the body. One of its functions is to detoxify the body, ridding it of substances that are potentially damaging, such as caffeine, medications and other drugs, paint and exhaust fumes, pesticides, and tobacco smoke. The liver recognizes dangerous molecules and transforms them into harmless forms and then facilitates their elimination.
Liver detoxification occurs in two phases. The activities of these two phases must be well coordinated because intermediary compounds that form during phase I can be even more toxic than the original substance. If these intermediary compounds aren't quickly processed in phase II, damage such as cell injury or cancer can ensue, particularly if you smoke, drink, or eat barbecued foods, since all of these can increase the damage. This is where the teamwork of vitamins A, C, and E comes in. Other substances, such as phytochemicals, selenium, certain B vitamins, and dietary fiber also are involved in detoxification.
The important thing to know here is that individual antioxidants in pill form don't provide the same protection as the same substances in food. Diet clearly has a major impact on potential damage to cells and protection from that damage. The nutrient teamwork that's involved helps explain why a varied diet of plant foods goes far beyond supplements in keeping people healthy. In the sections that follow, we'll discuss each of the antioxidant team members in detail.
### Vitamin A (and Beta-carotene)
There are two forms of vitamin A in food: provitamin A carotenoids from plants, and preformed vitamin A from animal products. The body converts certain carotenoids, such as beta-carotene, to the active form of vitamin A, called retinol. The carotenoids provide many of the beautiful orange, red, and yellow colors in fruits and vegetables. Carotenoids are present in green vegetables too, but the color is masked by the green of chlorophyll. Other carotenoids, such as lycopene, lutein, and zeaxanthin, aren't converted to vitamin A, but they do have powerful health benefits.
Vitamin A plays an important role in cell differentiation, the process that creates different kinds of cells to carry out specific tasks. In the eye, vitamin A or certain carotenoids help us see at night, prevent cataracts and macular degeneration, and keep the cornea healthy. Vitamin A is required for immune system function and to build and preserve the integrity of the skin and mucous membranes so they can act as protective barriers against bacteria and viruses. Many carotenoids help protect us against cancer and heart disease. Vitamin A is needed for the growth of bones and teeth, for reproduction, and for the production and regulation of hormones.
#### **RECOMMENDED INTAKES OF VITAMIN A**
Vitamin A is measured both in retinol activity equivalents (RAE) and in international units (IU). Women need 700 mcg RAE (2,333 IU) of the active form of vitamin A daily, and men need 900 mcg RAE (3,000 IU) daily.
Vegan diets, with their abundance of colorful fruits and veggies, can easily provide more than enough vitamin A. Vegan vitamin A intake has been estimated at 1,500 mcg RAE (4,950 IU) for women and 1,200 RAE (3,960 IU) mcg for men per day. The key is to include lots of yellow, orange, red, and green vegetables and fruits. Consuming these with foods that are rich in plant oils, such as olives, avocados, nuts, and seeds, or with oil-based salad dressings, increases carotenoid absorption.
#### **SOURCES OF VITAMIN A**
Carotenoids are present in apricot, broccoli, cantaloupe, carrot, leafy greens, mango, nectarine, papaya, peppers (bell and chile), persimmon, plantain, prunes, pumpkin, sea vegetables, squash, sweet potato, tomato, and turnip.
You can get your recommended daily intake from ½ cup (125 ml) of carrot juice, baked sweet potato, or canned pumpkin, or from ¼ cup (60 ml) of cooked kale. We derive about 470 mcg RAE from ½ cup (125 ml) of cooked spinach or butternut squash or from ½ cantaloupe.
Cooking seems to increase the absorption of some carotenoids, as does including a little fat as part of the meal. Juicing provides even greater carotenoid absorption than cooking. We recommend eating some of these colorful vegetables cooked and others raw.
Supplements can be tremendously helpful for those who are deficient. For example, vitamin A supplements can prevent blindness in children who have little access to carotenoid-rich vegetables or fruits. However, the preferred form of this vitamin is from food. Long-term high intakes of vitamin A from supplements have been linked to hip fracture and should generally be avoided. If you take vitamin A supplements, be sure they provide amounts that are within the recommended range. Avoid high intakes without medical supervision.
### Vitamin C (Ascorbic Acid)
Scurvy was the scourge of the seas for hundreds of years. After sailing vessels developed the capability for long voyages away from land, many crew members on extended voyages became weak and developed painful joints, swollen gums, and loose teeth. Eating became impossible, and the devastated sailors could barely move. Death typically followed soon thereafter.
For centuries, Native Americans had used herbs and cranberries to cure scurvy. And although some early explorers, including Vasco de Gama's crew in 1499, discovered that citrus fruits could alleviate the condition, it took hundreds of years for European doctors to connect the dots between the disease that had killed thousands and the simple lack of fruits and vegetables. Scientists identified vitamin C in 1912, proved its relationship to scurvy in 1932, and synthesized the vitamin in 1935.
Vitamin C's role in preventing and curing scurvy is due to its ability to build collagen, an essential component of blood vessel walls, scar tissue, tendons, ligaments, cartilage, and bone. Without vitamin C, the gums and other collagen-containing tissues break down. In addition, vitamin C helps metabolize the amino acid that transports fat to the cells for energy.
Vitamin C is a highly effective antioxidant; it helps regenerate vitamin E, another antioxidant, and even small amounts can protect cells from damage. Vitamin C supports the immune system, boosting resistance to infection when under stress, and aids in the production of thyroid hormone. Vitamin C from the copious amounts of fruits and vegetables found in typical vegan diets appears to protect the body from chronic diseases, including heart disease. Vitamin C helps the body absorb iron from plant foods (see "Iron Absorption," on page 133, for more information). It also aids in the synthesis of norepinephrine, a neurotransmitter and stress hormone essential for brain function and mood regulation.
#### **RECOMMENDED INTAKES OF VITAMIN C**
The recommended intake of vitamin C is 75 mg daily for women, 90 mg daily for men. Smokers are advised to get an additional 35 mg per day (or, better yet, quit smoking). Vegetarians tend to get about 150 mg per day—50 percent more than nonvegetarians—and vegans get even more, 138 to 584 mg per day. Five servings of fruits and vegetables per day typically provide about 200 mg of vitamin C. Organic produce has been shown to provide significantly more vitamin C than conventionally grown fruits and vegetables.
#### **SOURCES OF VITAMIN C**
Good sources of vitamin C include blackberries, broccoli, Brussels sprouts, cabbage, cantaloupe, citrus fruits, green peas, guava, kiwifruit, leafy greens, mango, papaya, pineapple, raspberries, red peppers (bell and chile), strawberries, sweet potato, tomato, and vegetables in the cabbage family.
### Vitamin E (Alpha-tocopherol)
Vitamin E, the third member of the ACE antioxidant team, is actually a family of related compounds with alpha-tocopherol being the form with the greatest antioxidant activity. Vitamin E's job is to protect vitamin A, polyunsaturated fatty acids, and other fats from free radical damage. Vitamin E stabilizes cell membranes and prevents them from breaking. Through these protective actions, vitamin E plays a role in the prevention of many diseases. When vitamin E neutralizes a free radical, it loses its antioxidant function. Fortunately, vitamin C can come to the rescue and regenerate vitamin E so that it becomes an antioxidant once again.
Vitamin E is found in plant oils. It was discovered in 1922 in spinach, yet it wasn't recognized as essential until 1968. Though we might not think of leafy greens as significant sources of fat, in fact about 10 percent of the calories we derive from these greens are from oils. Since a typical serving of spinach or other greens contains few calories, this proportion of fat has little significance for people who consume greens in only limited quantities. But for many vegans, including those on raw diets, big salads are an important source of vitamin E. You can get one-third of your day's supply of vitamin E from 8 cups (2 L) of raw spinach. If you add half an avocado and 3 tablespoons (45 ml) of sunflower seeds, the salad contains 15 mg (22.5 IU) of vitamin E, which is the recommended daily intake for adults. Steamed spinach cooks down to a small volume, yet it retains this vitamin; therefore, 1 cup (250 ml) of cooked spinach provides close to 4 mg (6 IU) of vitamin E.
Most people in the United States get far less vitamin E than they need for optimal health, averaging only 6.9 mg (10.4 IU) per day. These low levels are linked with higher risk of heart disease, and possibly with the development of cataracts and other conditions. Studies indicate that vitamin E from food offers us greater protection than that from supplements.
The natural form of alpha-tocopherol, called d-alpha-tocopherol, comes from plants and is the ideal form to use. Synthetic dl-alpha-tocopherol is also available, but you need approximately 50 percent more IU of the synthetic form from dietary supplements and fortified foods to obtain the same amount you would get from the natural form in plants. The synthetic form isn't as well utilized by the body, and it can even cause health problems in high doses.
#### **RECOMMENDED INTAKES OF VITAMIN E**
Adults need 15 mg (22.5 IU) of vitamin E per day. Vegan intakes are usually between 14 and 33 mg (21 and 49.5 IU) per day.
People on very low-fat diets who get less than 15 percent of their calories from fat tend to consume insufficient amounts of vitamin E. However, a serving of fortified cereal (check the label for serving size and vitamin E content), ¼ cup (60 ml) of sunflower seeds, or 1 ounce (30 g) of almonds supplies about half of the day's recommended intake of vitamin E. Alternatively, 1 cup (250 ml) of canned, pureed tomatoes provides one-third of your vitamin E for the day, and 1 cup (250 ml) of cooked spinach provides one-quarter of the amount needed. You might also want to top off your intake with a supplement that includes natural vitamin E, such as a multivitamin listing d-alpha-tocopherol.
#### **SOURCES OF VITAMIN E**
Vitamin E can be found in almonds and other nuts, avocado, broccoli, carrot, kiwifruit, leafy green vegetables, peanuts, sunflower seeds and other seeds, wheat germ, and whole grains. The process of refining vegetable oil destroys vitamin E, so to maximize vitamin E intake, it's best to use unrefined oils.
### The Energetic B Vitamins
The body uses carbohydrates, fat, and protein as fuel, and the B vitamins play essential roles in that process. In complex sequences that resemble busy factory production lines, each of the nine B vitamins assists specific enzymes. These enzymes can't function without their particular vitamin assistant, or coenzyme.
For energy production, the body requires dietary sources of thiamin, riboflavin, niacin, pantothenic acid, vitamin B6, and biotin. Folate, vitamin B12, and choline are crucial to the formation of cells that deliver oxygen and nutrients so the energy production line can function. The B vitamins also help build genetic material, nerve impulse transmitters, certain hormones, and the fats needed in cell membranes. In the sections that follow, we'll discuss the B vitamins in detail, with the exception of vitamin B12, which we covered earlier in the chapter.
### Thiamin (Vitamin B1)
Thiamin is sometimes called the carb burner because it helps convert carbohydrates to usable energy. Thiamin deficiency results in beriberi, a disease characterized by extreme weakness and dysfunction of various physiological systems, including the nervous system. It was described as early as 2600 BC in China, where it got its name, which roughly translates to "weak, weak" or "I cannot, I cannot," clearly reflecting the feeling of weakness that results.
Beriberi was a cause of death among the poor in Asia during the 1800s when polished white rice was introduced to the diets of those who had limited access to thiamin-rich foods. Polishing removes the outer bran layer of the rice, which contains thiamin. Wealthier people tended to include other sources of thiamin in their diets, but rice was a dietary staple among the poor. At that time such diseases were thought to be linked to infection or other causes, but three physicians, one of them Japanese and two Dutch, traced the weakness and nerve disorders in beriberi to a deficient diet. Their insights played a key role in the discovery of vitamins. Now, thiamin, iron, and sometimes several other B vitamins are added to white rice.
#### **RECOMMENDED INTAKES OF THIAMIN**
Women need 1.1 mg of thiamin per day, and men need 1.2 mg per day. Thiamin requirements are linked with calorie intake, so active, high-energy people require more. Studies show that vegans generally meet recommended intakes or exceed them by 50 to 100 percent.
#### **SOURCES OF THIAMIN**
Thiamin is found in moderate amounts in many plant foods: whole and enriched grains, whole-grain products, legumes, nuts, seeds, and nutritional yeast. It is also present in avocado, carrot juice, corn, dried fruit, peas, and squash.
### Riboflavin (Vitamin B2)
While the rest of the B vitamins are busy converting carbs, fats, and protein into energy, riboflavin is busy interacting with them, providing support and protection against free radicals and toxins. Deficiency symptoms include cracks at the corners of the mouth and inflammation and redness of the tongue.
#### **RECOMMENDED INTAKE OF RIBOFLAVIN**
Women need 1.1 mg of riboflavin per day, and men need 1.3 mg per day. As with thiamin, the requirement is linked to caloric intake and activity level. Studies show that vegans usually meet the recommended intakes.
#### **SOURCES OF RIBOFLAVIN**
Just 1½ teaspoons (7 ml) of nutritional yeast provides a day's recommended in-take of riboflavin. (The ultraviolet rays of the sun or fluorescent light can destroy riboflavin, so keep nutritional yeast in an opaque container in a dark place.) Soy foods, fortified cereals, and Marmite yeast extract are excellent sources. Moderately good sources include almonds, avocado, banana, broccoli, buckwheat, cashews, enriched wheat flour, green beans, leafy greens, peas, quinoa, sea vegetables, seeds, sweet potato, and whole grains. Sprouting has been shown to increase the riboflavin content of alfalfa seeds and mung beans.
### Niacin (Vitamin B3)
Niacin assists hundreds of enzymes in producing energy and supporting the health of the skin, digestive tract, and nervous system. Niacin-deficiency disease is called _pellagra,_ an Italian word meaning "sour skin," and its symptoms are dermatitis, diarrhea, dementia, and death. Deficiency can occur in people whose diets are very low in calories and variety because if we don't get enough riboflavin, vitamin B6, or iron, we can't convert the amino acid tryptophan to niacin.
Niacin deficiency was first recorded in areas of the world where poorer people subsisted mainly on corn, or maize, a food that's low in both niacin and tryptophan. Yet at the same time, it was also recognized that people in Mexico and Central and South America, who typically relied on corn as a dietary staple, didn't get pellagra. As it turned out, the niacin in corn is in bound form, meaning the body can't absorb it unless the corn is treated with an alkali, which is exactly what cooks do in the traditional cuisines of Mexico and many other Central and South American cuisines: they treat corn with lime before cooking. (Here, lime refers to calcium hydroxide, not the fruit.) This treatment releases the bound niacin, making it easier for the body to absorb. Unfortunately, it wasn't until the early 1900s that niacin deficiency was understood to be the cause of pellagra.
#### **RECOMMENDED INTAKES OF NIACIN**
Women need 14 mg per day, and men should get 16 mg. Studies show that most vegans meet the recommended intakes. In supplements, the maximum upper intake level recommended is 35 mg. Pharmacological preparations of niacin use higher dosages as cholesterol-lowering agents in treating heart disease and may lead to side effects such as flushing of the face, chest, and arms.
#### **SOURCES OF NIACIN**
Excellent sources of niacin include many foods that are rich in protein: edamame, soybeans, peanuts, peanut butter, peas, tempeh, tofu, and other legumes. Other good sources are avocado, buckwheat, cherimoya, dried fruit, durian, enriched and whole grains, fortified cereals, Marmite yeast extract, mushrooms, nutritional yeast, nuts, quinoa, sea vegetables, seeds, tahini, and wild rice. Good sources of tryptophan include green vegetables, seeds, nuts, and legumes. The great agricultural chemist George Washington Carver's emphasis on the importance of peanuts as a good source of niacin did much to improve the diets of Southerners.
### Pantothenic Acid (Vitamin B5)
The name of pantothenic acid comes from the Greek _pantothen_ , meaning "from everywhere." It is present in all whole plant foods, so it's not likely to be lacking in vegan diets unless they are particularly low in calories.
As a coenzyme found in all living cells, pantothenic acid plays a central role in releasing energy from food. It also helps build fats, including any cholesterol that we need, steroid hormones, and other essential compounds. In addition, it supports communication between cells so they work together to our benefit.
#### **RECOMMENDED INTAKES OF PANTOTHENIC ACID**
The recommended intake for adults is 5 mg per day. Research shows that most vegans meet or exceed recommended levels.
#### **SOURCES OF PANTOTHENIC ACID**
All whole plant foods contribute pantothenic acid, at least in small amounts. Certain foods are particularly good sources: Avocado, broccoli, legumes, mushrooms, nutritional yeast, nuts, seeds, sweet potato, and whole grains. It is also possible that we absorb some of the pantothenic acid produced by intestinal bacteria.
### Vitamin B6 (Pyridoxine)
There are many stories about the powers of vitamin B6. Some are quite mysterious, and not all are substantiated by science. However, there is research showing that vitamin B6 helps improve morning sickness and could help alleviate depression in cases where the condition is linked to high levels of homocysteine.
Vitamin B6 is needed to help convert amino acids to energy and for building amino acids, fatty acids, and neurotransmitters. As one of its many functions, vitamin B6 helps the body get rid of homocysteine, a troublesome compound created during certain metabolic processes. Folate and vitamins B6 and B12 convert homocysteine to two amino acids that the body can use in building protein. When these three B vitamins are in short supply, homocysteine levels rise, which may lead to damage of arterial walls and the formation of blood clots, increasing the risk of heart disease. Vitamin B6 also helps the body access glycogen, the storage form of glucose, from the liver when energy is needed. In addition, it supports the immune system and many other essential physiological processes.
#### **RECOMMENDED INTAKES OF VITAMIN B 6**
The adult recommended intake for vitamin B6 is 1.3 mg to age fifty; after fifty, it increases to 1.5 mg for women and 1.7 mg for men. Studies show that most vegans meet the recommended intakes.
#### **SOURCES OF VITAMIN B 6**
Vitamin B6 is widely distributed among plant foods, especially fruit. For example, you can get your day's supply from three bananas. Vegan diets generally include plenty of foods rich in vitamin B6, such as avocado, legumes, nutritional yeast, nuts, seeds, spinach, whole grains, and fortified breakfast cereals.
### **Biotin (Vitamin B 7)**
Along with other B vitamins, biotin is involved in the metabolism of amino acids, fats, and carbohydrates. This vitamin doesn't hit the headlines because deficiencies are rare. Although research is limited, most people on plant-based diets seem to get sufficient biotin. Your intake of biotin is likely to be fine unless you're not eating enough calories.
#### **RECOMMENDED INTAKES OF BIOTIN**
Adults are advised to get 30 mcg of biotin per day. One study of Seventh-day Adventists found plasma levels of biotin to be higher in vegans than in lacto-ovo vegetarians and nonvegetarians.
#### **SOURCES OF BIOTIN**
The many sources of biotin include almonds, avocado, banana, carrot, cauliflower, corn, hazelnuts, legumes, nutritional yeast, peanut butter, raspberries, oatmeal, onion, tomato, walnuts, and whole grains.
### **Folate (Vitamin B 9, Folic Acid)**
Folate helps build DNA and protect it from changes that may lead to cancer. In pregnancy, adequate folate is important for proper growth of the fetus; a deficiency can cause neural tube defects and other types of birth defects. Folate can help prevent heart disease by lowering elevated levels of homocysteine. It supports fertility, and for men it's required to make healthy sperm.
High blood levels of homocysteine may indicate deficiencies of either folate (less likely in vegans) or vitamin B12 (likely in vegans who don't take B12 supplements or consume enough B12-fortified foods). Lack of these two B vitamins can also cause red blood cells to fail to mature properly, increasing in size until they're big enough to divide, but failing to divide properly and being unable to perform their oxygen-carrying function. This condition is known as macrocytic anemia, or big cell anemia. People with this condition are often weak, tired, and short of breath.
The word _folate_ has the same Latin root as _foliage_ , so you can probably guess that leafy greens are important sources of this vitamin. In 1945, folate was first isolated; the source was spinach. Since that time, numerous other green vegetables have been added to the list of excellent sources.
Folate is the form of vitamin B9 that occurs in food. The form in supplements, folic acid, is somewhat different chemically, and scientists are still exploring the similarities and differences of the two forms. Although natural folate in foods is protective against cancer, folic acid supplements in high doses may actually increase risk of asthma and various types of cancer, including breast, prostate, and colorectal, although more research is needed.
#### **RECOMMENDED INTAKES OF FOLATE AND FOLIC ACID**
The recommended intake for adults is 400 mcg per day. We don't need higher levels than these recommended intakes. It's safest to get this vitamin from food. In order to absorb folate, the body requires adequate intakes of vitamin C and iron. Studies have shown that vegan intakes of folate generally meet or exceed recommended levels.
Large amounts of folic acid can mask a B12 deficiency. Therefore, you shouldn't take more than 1,000 mcg of folic acid per day. High intakes of folic acid may also provoke seizures in people taking anticonvulsant medications. While many experts suggest that taking less than 1,000 mcg of folic acid per day is safe, others recommend getting most or all of your recommended intake for this vitamin in the form of folate from food.
#### **Pregnancy and Lactation**
Women capable of becoming pregnant are advised to consume 400 mcg of folic acid daily in order to protect against neural tube defects, which can occur in the fetus before a woman knows she is pregnant. Women who are pregnant are advised to take 600 mcg daily throughout pregnancy.
#### **SOURCES OF FOLATE AND FOLIC ACID**
Excellent sources of folate include almonds, asparagus, avocado, beet, cashews, fortified breakfast cereals, kelp, kiwifruit, legumes, mung bean sprouts, nutritional yeast, oranges, quinoa, spinach, sprouted lentils, sunflower seeds, and yeasts. Folic acid is added to enriched flour, rice, and pasta, and this policy has been credited with greatly reducing the incidence of neural tube defects in North America since 1998.
Sprouting has been shown to more than double the folate content of seeds. Folate is easily destroyed by boiling, whereas steaming has been shown to cause little or no loss of folate from broccoli or spinach.
### Choline
Choline has hopped back and forth across the line between vitamin—and therefore essential—and nonvitamin. That's because the body can produce sufficient choline unless a person's diet is short on folate, vitamin B12, and the amino acid methionine. People seem to need significantly different amounts depending on genetics and diet. Choline is present in all cell membranes of plants and animals, and in the brain as part of a fatty mixture of molecules known as lecithin. In cell membranes, choline helps transport fats and other nutrients into and out of cells. In the brain, it helps build important neurotransmitters, making it crucial for the transmission of nerve impulses. Choline also helps clear fat and cholesterol from the liver.
By the way, lecithin is a food additive that acts as an emulsifier. It may be added to a chocolate bar to keep the cocoa and cocoa butter from separating. It's also used in vegetable oil sprays. Most lecithin is derived from soy or sunflower oil and is vegan. However, it may be derived from eggs. Sometimes the source will be included on labels as, for example, "soy lecithin."
#### **RECOMMENDED INTAKES OF CHOLINE**
Women should get 425 mg of choline per day, and men should get 500 mg per day.
#### **SOURCES OF CHOLINE**
There are plenty of good sources of choline. A few that are particularly rich are beans, broccoli, peas, quinoa, and soy foods.
### Vitamin K (Phylloquinone and Menaquinone)
Vitamin K is a relative newcomer to the vitamin hall of fame. It wasn't recognized until 1974, and its functions are still being investigated. The K is derived from the German word _koagulation_ and is related to the vitamin's essential role in helping blood clot. The form of vitamin K that was first discovered, vitamin K1, or phylloquinone, is widely available in plant foods, especially greens. In addition, intestinal bacteria synthesize forms of this vitamin known collectively as vitamin K2, or the menaquinones. Vitamin K2 also is present in meat and in a fermented Japanese soy food called natto. Infants are given a vitamin K shot at birth because their intestinal production of vitamin K doesn't get rolling for a few days. Symptoms of vitamin K deficiency include defective blood clotting and hemorrhaging. There also is a synthetic form, known as vitamin K3, or menadione.
**_If You Take Blood Thinners_**
In the past, doctors often advised their patients who take anticoagulants, or blood thinners, to avoid eating greens, since vitamin K acts as a coagulant. Today, most physicians recommend that people eat about the same amount of greens from week to week. Medication is adjusted to factor in the effects of vitamin K from the vegetables. If you are taking these drugs and have questions about whether you should be eating foods rich in vitamin K, consult your doctor.
Vitamin K regulates calcium levels in the blood and plays a role in bone growth and maintaining bone mineral density. Data from the 1998 Nurses' Health Study showed that those who ate lettuce at least once a day had a significantly lower risk of hip fracture than those who ate lettuce once a week or less. Since then, studies have shown that 200 mg of vitamin K, the amount present in 1½ cups (375 ml) of raw spinach or ½ cup (125 ml) of raw or cooked kale, can reduce the risk of bone fracture.
#### **RECOMMENDED INTAKES OF VITAMIN K**
Women should get 90 mcg of vitamin K per day, and men are advised to get 120 mcg. The average intake of the US population has been estimated to be 300 to 500 mcg per day, and most vegans probably get more. A study of vegans' blood-clotting rate, an indicator of vitamin K status, indicated that intakes of vitamin K were sufficient.
If you follow popular lay health gurus on the Internet, you may wonder if you need supplemental vitamin K2, since little of this form is present in a vegan diet. At this time, there is no scientific evidence to suggest that vegans need to worry about supplementing with vitamin K2.
#### **SOURCES OF VITAMIN K**
Leafy green vegetables are vitamin K superstars. You can get your recommended daily intake from 2 tablespoons (30 ml) of parsley or kale or 2 cups (500 ml) of romaine lettuce. If you put a little dressing (not fat-free) on your salad, the oil increases absorption of this fat-soluble vitamin.
Other excellent sources are asparagus, avocado, broccoli, Brussels sprouts, cabbage, cauliflower, grapes, kiwifruit, lentils, peas, pumpkin, sea vegetables, and soybean oil. It is best not to overcook foods to help minimize losses. Natto, a fermented, bacteria-rich soy food from Japan, is a unique and concentrated source of vitamin K2.
### Vitamins in Vegan Foods
Table 6.2 shows the vitamin content in a typical portion of a variety of vegan foods. You can also find nutrient data on a variety of foods at the US Department of Agriculture website: ndb.nal.usda.gov.
**TABLE 6.2.** Vitamins in vegan foods
Sources of data: US Department of Agriculture, Agricultural Research Service, _USDA National Nutrient Database for Standard Reference_ , Release 25 (2012), ndb.nal.usda.gov. ESHA Research, The Food Processor software, version 10.12.0.
Key: c = cup; g = gram; mcg = microgram; mg = milligram; oz = ounce; tbsp = tablespoon; ... indicates that no data is available.
*For other ages, see the appendix (page 274).
**Check labels for product-specific information.
Calcium, zinc, iodine...all the minerals you need are abundant in plant-based foods. Discover how to create a magnificent vegan diet, rich in minerals, in chapter 7.
## **CHAPTER 7**
## **Minding Your Minerals**
In Western cultures, there tends to be a strong, social and industry-based bias in favor of diets that rely heavily on animal products, and this has had a big impact on how most people view dietary requirements for certain minerals. Federal departments of agriculture support and protect meat and dairy producers through a variety of financial and educational programs. In addition, the meat, dairy, and egg industries are major sponsors of conferences for dietitians, physicians, educators, and other health professionals, and the nutrition research funded by these industries is biased in favor of their products. This influences many health professionals who develop nutrition education programs for consumers. On top of all of this is a massive amount of industry-funded advertising. Therefore, it isn't surprising that our minds are imprinted with messages that link calcium and strong bones with dairy consumption or iron with meat consumption. Yet plant-based diets can provide optimal amounts of these minerals and all of the others that we need.
### Minerals, Vegetables, and Animals
Carbohydrates and fat consist of three mineral elements—carbon, hydrogen, and oxygen. Protein provides these three plus nitrogen and sulfur. Many other minerals are also required for the structure and operation of our bodies, including calcium, chromium, copper, iodine, iron, magnesium, manganese, phosphorus, potassium, selenium, sodium, and zinc.
Minerals are released from decaying matter into the soil with the help of bacteria and fungi. When dissolved in water, they are then absorbed by plants. From there, minerals are picked up by plant-eating animals and move further up the food chain into the flesh of carnivorous animals. The decomposition of plant and animal matter returns minerals to the soil.
Minerals can perform a variety of roles. In the human body, minerals are part of dynamic systems in bones, fluids, and nerves. Around the clock, the body remodels bones, builds thyroid hormones and enzymes, creates new red blood cells, and maintains a precise balance between acid and alkali in body fluids. For these purposes, you need a steady supply of building materials, including specific minerals.
In this chapter, you'll learn about those minerals and how they function. We'll also provide tips for meeting recommended intakes and increasing absorption, and discuss the wide range of tasty plant foods that can provide the minerals you need. We'll take a close look at four minerals that are of particular importance to vegans: calcium, iron, zinc, and iodine. Then we'll briefly discuss several other minerals.
For details about minerals for all stages of life, see the appendix. For recommended intakes and food sources of calcium, iron, and zinc, see table 7.2 (page 139). For food sources of iodine, see table 7.1 (page 136).
### Mineral Absorption
Several factors influence the ease with which our bodies absorb minerals, or their bioavailability. These include cooking, the presence of certain chemical compounds, and an individual's overall mineral status.
#### **COOKING**
Minerals are soluble in water and can be lost if the cooking liquid is discarded, particularly if the food has been boiled. Steaming foods, however, results in good mineral retention.
#### **PHYTATE**
In legumes, whole grains, nuts, and seeds, the phosphorus-containing compound known as phytate, or phytic acid, binds calcium, iron, magnesium, and zinc. These phytate-mineral complexes aren't completely broken down during digestion, so some of the minerals in these foods can't be absorbed. Enzymes in these foods help release the minerals when they get wet, so soaking, sprouting, juicing, and blending plant foods all help release the minerals from the phytate so the body can absorb them.
Fermentation also helps to release minerals from phytate compounds. When plant foods are fermented, as when soy is made into tempeh or miso, more than half of the phytate complexes are broken down. Leavening bread with yeast has a similar effect on the phytate in wheat.
While too much phytate can interfere with getting an adequate supply of calcium, iron, magnesium, and zinc, phytate compounds aren't all bad. Some have antioxidant powers that appear to offer protection against cancer, cardiovascular disease, and diabetes.
#### **OXALATES**
A naturally occurring plant compound called oxalic acid can combine with certain minerals and reduce their absorption during digestion. As a result, the body can't absorb most of the calcium and some of the iron and magnesium from foods such as amaranth, beet greens, cassava, chives, parsley, purslane, spinach, and Swiss chard. However, these foods still contribute a bit of calcium to the diet. For example, your body can still absorb much of the iron and about 5 percent of the calcium in spinach. And, of course, these foods still provide many other nutrients; for example, spinach provides abundant folate, vitamin K, beta-carotene, and numerous other nutrients, along with protective phytochemicals, all of which are unaffected by oxalic acid. The bottom line is, don't dismiss the nutritional value of foods just because they contain oxalic acid.
#### **NEED AND DOSE SIZE**
Mineral absorption also can be influenced by your need at that particular moment. If your body is well stocked with iron, for example, you'll absorb iron less efficiently than someone who has very little stored iron. Also, you're likely to absorb less of a mineral consumed in a large quantity at one time, such as a 1,000 mg single-dose calcium supplement, than from two doses of 500 mg each.
### Calcium
As discussed in chapter 2, bone health involves a complex interplay of many lifestyle factors, but a well-designed vegan diet will include vegetables and fruits associated with greater bone density and less bone loss. But even so, some vegan diets are low in calcium or otherwise fail to support lifelong bone health.
From advertising, we get the impression that calcium is the primary player in promoting bone health, but relying on that one mineral to prevent osteoporosis is like trying to win at baseball with only a pitcher on your team. You need other team members—seventeen in fact—on the bases, behind the plate, and in key spots in the outfield. The team has to include a mix of protein; essential fatty acids; the minerals boron, calcium, copper, fluoride, magnesium, manganese, phosphorus, and zinc; and the vitamins B12, B6, C, D, K, and folate. (For a discussion of many of the vitamins and other nutrients you need for healthy bones, see the section "Osteoporosis," on page 38.)
#### **CALCIUM IN PERSPECTIVE**
Calcium is the most common mineral in the body. It's also the fifth-most-common mineral in the earth's crust, present in marble, limestone, and chalk. You can get calcium directly from plant foods and from dairy milk. It is also abundant in breast milk. It is believed that prior to the advent of agriculture, humans in many parts of the world had dairy-free diets that were very high in calcium, providing from 1,500 to 3,000 mg per day. However, the modern versions of many fruits and other plant foods have been bred for qualities such as sweetness, rather than nutritional excellence, and therefore are far lower in calcium than the versions available to our ancestors. In nature's calcium cycle, animal bones, the shells of marine organisms, and antlers disintegrated, returning calcium to the earth that was absorbed into plants; plus, many populations cooked bones in their soup stocks.
#### **CALCIUM'S FUNCTIONS**
Calcium is best known for its structural role in hardening bones and teeth. In addition, it helps blood to clot, allows muscles to relax, helps nerves transmit messages, and regulates cell metabolism. In addition, consuming recommended levels of calcium may help prevent high blood pressure.
Calcium levels in the blood and in the fluids between cells must be kept within a specific and narrow range. If these levels drop too low, the parathyroid gland produces a hormone that activates vitamin D, which raises blood calcium levels by increasing its absorption in the intestine, decreasing urinary calcium losses, and, if necessary, breaking down some bone.
Nutrition education campaigns and dairy advertisements may tell us that we need cow's milk to meet our nutritional needs for calcium, but for most of human history, we've gotten most of the calcium we needed from plants. Dairying appears to be a relatively recent phenomenon, occurring in the last ten thousand years and only in specific areas of the world. Where dairy products contributed significantly to people's diets, a genetic adaptation occurred that allowed people to continue drinking milk after weaning from breast milk. Normally, after weaning the body produces much less of the enzyme lactase, which digests lactose, or milk sugar. In fact, as much as 70 percent of the world's population experiences diminished lactase production after weaning. In South America, Africa, and Asia, more than 50 percent of people over four years old are lactose intolerant and experience abdominal pain, bloating, flatulence, and diarrhea when they drink cow's milk. In some Asian countries, almost everyone is lactose intolerant.
#### **RECOMMENDED INTAKES OF CALCIUM**
The recommended calcium intake is 1,000 mg per day for adults younger than fifty and 1,200 mg for those fifty and older. For recommended intakes at other stages of life, see the appendix. Most people in the United States, including vegans, fall short of the recommended intake. This is particularly true of women and people older than fifty. It's important to get the recommended intake, as this reduces the risk of bone fractures, which are directly linked to low calcium levels.
#### **CALCIUM SUPPLEMENTS**
If you don't get enough calcium from your diet, you should probably take a supplement. Most calcium supplements should be taken with meals because they are absorbed better when stomach acid is present, although calcium citrate and calcium citrate malate can be taken anytime. You also can increase absorption by dividing your daily supplemental calcium into two or more doses. Vitamin D is essential for optimum calcium absorption, so be sure you also get enough vitamin D.
#### **DIETARY SOURCES OF CALCIUM**
Calcium is abundant in a wide assortment of vegetables, particularly the low-oxalate green vegetables, broccoli, bok choy, kale, napa cabbage, watercress, and collard, dandelion, mustard, and turnip greens. Other good sources are fresh and dried fruit, calcium-fortified juices, almonds, and tahini. Calcium is added to fortified nondairy milks and tofu, and in both cases, calcium absorption compares favorably with that of cow's milk. Some mineral waters are good sources; check product labels to determine which are.
#### **SOLID SOLUTIONS FOR BETTER BONES**
The following sections provide tips on how to ensure strong, healthy bones. In addition, following the recommendations in chapter 14, The Vegan Food Guide, will help ensure you get the entire team of bone-building nutrients.
**Put dark green vegetables on your daily menu.** Include broccoli, bok choy, collard greens, kale, and napa cabbage in your diet regularly. Some minerals (and vitamins) are lost in cooking water, so steam these vegetables or use the mineral-rich cooking water in soups or when cooking grains.
**Eat calcium-set tofu.** Tofu is made by coagulating soy milk in either nigari (magnesium chloride) or calcium sulfate. Obviously, the type made with a calcium salt such as sulfate is what you want if you're looking to increase your intake of calcium. Check the label; the calcium content can range from 120 mg to 600 mg per serving. Tofu is an unusually versatile food. It can be added to everything from soup to dessert, so use it often. The isoflavones in soy foods, such as tofu, tempeh, and soy milk, also are associated with reduced risk of bone fracture.
**Drink calcium-fortified beverages.** Fortified nondairy milks and juices can help boost your total calcium intake.
**Include almonds, almond butter, blackstrap molasses, figs, and tahini in your meals and snacks.** Every time you replace 2 tablespoons (30 ml) of peanut butter with an equal amount of almond butter, you increase your calcium intake by 73 mg. By replacing 1 tablespoon (15 ml) of jam with 1 tablespoon (15 ml) of molasses, you boost your intake by a surprising 168 mg of calcium. These flavorful options boost your calcium and also provide iron and zinc.
**Don't keep company with the calcium thieves.** Avoid alcohol, limit caffeine, and, of course, don't smoke. Keep your sodium intake below 2,300 mg per day. If you are salt sensitive, have high blood pressure, or are middle-aged or older, keep your sodium intake below 1,500 mg per day.
**Get some sunshine (or vitamin D).** Take the opportunity to stretch your legs and walk around the block on your lunch break. In addition to benefiting from the exercise, under the right conditions your body can manufacture your day's supply of vitamin D. (For more on vitamin D, see page 104.) Take a vitamin D supplement when sunshine isn't an option.
**Exercise.** Some form of weight-bearing exercise, such as walking, jogging, dancing, hiking, or step classes, is essential for lifelong bone health. With bones, it's a case of use 'em or lose 'em.
**Top off with a supplement.** If you think you aren't getting enough calcium and other bone-building nutrients in your diet, take them in supplement form.
### Iron
Iron is a precious metal when it comes to human health. As a part of red blood cells, it plays a central role in transporting oxygen throughout the body and carrying away carbon dioxide, a metabolic waste product. As part of many enzyme systems, iron also plays key roles in the production of energy, immune system functioning, and mental processes involved in learning and behavior.
Every day we lose tiny amounts of iron in cells that are sloughed from skin and the inner lining of the intestine. Naturally, people experiencing blood loss for any reason (such as ulcers or blood donation) have increased needs. Women have iron losses during menstruation and generally need an extra 30 to 45 mg of iron each month, making their requirements significantly higher than those of men. Growth and the building of new cells put demands on stored and dietary iron and can deplete the small reserves of infants and children. With teens, there can be the double challenges of growth and notoriously poor eating habits. Athletes have somewhat higher requirements due to increased oxygen demands. (For more on meeting the iron needs of athletes, see page 255). The body is efficient at recycling iron, but once lost, iron must be replaced in the diet, perhaps augmented by supplements.
#### **IRON IN PERSPECTIVE**
Many vegetarians have lower levels of stored iron—called serum ferritin—than nonvegetarians. This common situation doesn't affect how we feel and isn't an issue as long as you regularly eat foods containing iron so you can replace any iron you lose. In fact, a lower level of serum ferritin might be an advantage, since it may help improved insulin sensitivity and reduce risk of type 2 diabetes. In addition, high serum ferritin may be linked to coronary heart disease and colon cancer.
Even with lower iron stores, vegetarians and vegans don't experience iron-deficiency anemia more often than nonvegetarians. However, iron deficiency is the most common nutritional deficiency worldwide, especially among women of childbearing age, infants, and teens, so vegans in those categories need to be careful. When hemoglobin levels go below the normal range, problems begin. The body's capacity to deliver oxygen to the cells will diminish, and the person may look pale, have headaches, and feel exhausted, irritable, and lethargic. Iron deficiency is easily diagnosed, so if you have any doubts, have a lab test done.
#### **RECOMMENDED INTAKES OF IRON**
Because the iron from plant foods isn't absorbed as readily as the iron from meat, vegans and vegetarians should aim for 1.8 times as much iron as the recommended intake for nonvegetarians. Vegetarian women of childbearing age are advised to get 32.4 mg of iron per day, and other vegetarian adults need 14.4 mg of iron; for other ages, see the appendix and multiply the recommended intake by 1.8. However, these recommendations are based on skimpy evidence and less-than-ideal diets. Vegans who eat plenty of foods rich in vitamin C and who don't routinely use tea, coffee, or calcium supplements are likely to need somewhat less than these high levels.
An iron supplement or iron as part of a multivitamin-mineral supplement can be a valuable addition to any diet that may be somewhat low in iron, and can be helpful for people with low or marginal iron status.
#### **DIETARY SOURCES OF IRON**
Because the iron from plant foods isn't absorbed as readily as the iron from meat, the Institute of Medicine has set the recommended intake for vegetarians at 1.8 times higher than for nonvegetarians. This decision has been a point of controversy because it was based on a diet in a single study that minimized iron absorption. Vegetarian women of childbearing age are advised to get 32.4 mg iron per day and other vegetarian adults 14.4 mg (see page 275 for complete recommendations). Vegans who eat plenty of foods rich in vitamin C and who don't routinely use tea, coffee, or calcium supplements are likely to need somewhat less than these high levels.
#### **IRON ABSORPTION**
Even though the body is continually breaking down red blood cells and building new ones, it efficiently recycles the iron in old red blood cells. The body absorbs more iron when needed and less when not needed, but calcium and compounds such as phytate compounds, tannins, and polyphenols (in tea, coffee, and cocoa) decrease the amount of iron the body can absorb. If you're iron deficient or need to maximize your iron intake, avoid consuming these at the same time as your iron sources.
On the other hand, foods rich in vitamin C, such as red peppers and strawberries, or foods high in citric acid, such as citrus fruits, increase the absorption of iron. These acidic foods change the iron in plant foods into a soluble form that is readily absorbed. For example, 5 fluid ounces (150 ml) of orange juice, containing 75 mg of vitamin C, has been shown to increase the absorption of iron from foods eaten at the same time by a factor of four. Vegans typically eat plenty of fruits and vegetables and get over 150 percent more vitamin C than nonvegetarians. This is a definite advantage when it comes to iron absorption.
As previously mentioned, soaking, fermenting, leavening with yeast, and sprouting break down the phytate compounds in grains, beans, peas, and lentils, releasing iron and other minerals and making them easier to absorb. Compounds in onions and garlic also help increase the availability of iron (and zinc) from grains and legumes, so consider adding them to bean and grain dishes.
### Zinc
Zinc is essential to cell division and plays significant roles in growth during pregnancy and from infancy through adolescence. Zinc is important to the functioning of the immune system and is necessary for wound healing and nerve development. In addition, it is crucial for the functioning of a whopping three hundred enzyme systems. Our ability to taste is highly dependent on zinc. The iris and retina of the eye and the prostate, sperm, and seminal fluid contain high concentrations of zinc, and zinc may also play an important role in regulating men's serum testosterone levels.
Adequate zinc intake is particularly important during periods of growth, from gestation and birth through adolescence. Severe zinc deficiency shows up in stunted growth, reduced immune function, diarrhea, poor appetite, and an impaired ability to taste. Marginal zinc deficiency can be difficult to detect, but it's more likely than severe zinc deficiency in North America, particularly among low-income children and pregnant women, sometimes resulting in babies being born prematurely.
#### **RECOMMENDED INTAKES OF ZINC**
The recommended daily intake for zinc is 8 mg for women and 11 mg for men. However, vegan diets often include more substances that inhibit zinc absorption, so needs may actually be 50 percent higher. Vegans with low caloric intakes or who rely on refined foods may have poor zinc intakes.
In most studies to date, vegans met or exceeded the recommended intake for zinc, but in two studies, vegans' average zinc intake was about 10 percent short of the recommended amount. To be on the safe side, include foods rich in zinc every day. As with iron, soaking, fermentation, leavening with yeast, and sprouting can greatly improve the bioavailability of zinc. Garlic also promotes absorption, so consider adding garlic to hummus, cooked rice, and other legumes and grains.
#### **DIETARY SOURCES OF ZINC**
Zinc is generally present in the same vegan foods as iron: seeds, nuts (especially cashews), legumes, tofu, and whole grains, including oats and brown rice. Seeds and seed butters can be zinc superstars in a vegan diet. Therefore, hummus on whole-grain bread or crackers is a particularly zinc-rich combination. Note that diets that rely heavily on refined foods are usually low in zinc, since refining strips the zinc from food.
### Iodine
Iodine is a mineral required in only miniscule amounts, but it is absolutely critical to life and health. It is an essential part of thyroid hormones (both T3, or triiodothyronine, and T4, or thyroxine), and most of the organ systems in the body are influenced by these hormones. Iodine is essential for energy metabolism, and iodine deficiency can result in either depressed or accelerated metabolic function, known as hypothyroidism or hyperthyroidism, respectively.
Hypothyroidism can result in a growth called a goiter, in which the thyroid gland becomes greatly enlarged in its efforts to trap iodine. Other symptoms of iodine deficiency are skin problems, weight gain, and increased cholesterol levels—all of which can be reversed with sufficient iodine in the diet. Fibrocystic breast disease can also result from iodine deficiency.
Iodine deficiency during pregnancy has tragic consequences. Adequate levels of thyroid hormones are crucial while an infant's brain is developing during gestation. Insufficient iodine causes an irreversible condition known as cretinism, a completely preventable developmental disability.
#### **RECOMMENDED INTAKES OF IODINE**
Adults require 150 mcg of iodine per day. For recommended intakes at other stages of life, see the appendix. It's preferable to consume the recommended in-take of iodine in small but frequent amounts several times a week, rather than to consume a large dose less frequently. Vegans may not get enough iodine unless they use iodized salt, eat sea vegetables, or take a multivitamin-mineral supplement that contains iodine; otherwise a vegan diet is likely to provide only about 10 percent of recommended levels. That said, it's still important to monitor overall iodine intake, as excessive amounts can cause goiter, burning in the throat, and other problems.
#### **DIETARY SOURCES OF IODINE**
Much of the planet's iodine is found in ocean water. The amount of iodine in soil varies greatly from one region to another, so some crops are rich in iodine whereas others lack this mineral. Since 1924, US salt processors have voluntarily added iodine to table salt as a way to provide this essential nutrient to the general population and prevent the tragedies of iodine deficiency that used to be common in some areas. Adding iodine has proven to be powerfully effective, but it isn't mandatory everywhere. Plus, sea salt typically doesn't contain significant amounts of iodine. Be sure to check the label of the salt you buy; not all varieties contain iodine.
In the United States and Canada, about ½ teaspoon (2 ml or 2 g) of iodized salt is supposed to deliver the day's recommended intake of 150 mcg of iodine. In practice, amounts may vary from one sample of iodized salt to another. Popular salty vegan ingredients, such as tamari, soy sauce, Bragg's Liquid Aminos, and miso, aren't iodized.
Plants that are grown in iodine-rich soil can be good sources of this mineral, however iodine levels of produce generally aren't known, so it's hard to determine your intake from foods. Sea vegetables (sometimes called seaweeds), can be excellent sources of iodine; however, amounts can vary as much as eightfold from one batch to another, so it's hard to be sure how much iodine you're getting. It can also be challenging to find a supplier who provides accurate information about iodine content of their products. Although hijiki (a type of sea vegetable) is rich in minerals, it isn't a suitable choice because it commonly contains excessive amounts of arsenic, which is both toxic and carcinogenic.
Amounts of iodine also can vary depending upon how sea vegetables are dried and stored. To confirm the amounts in salts and sea vegetables, check product labels, and consider contacting manufacturers who provide iodine levels of their products. Note that levels of iodine in these products can sometimes be quite high, in which case eating large amounts of them or eating them frequently can cause you to exceed the tolerable upper limit. Supplements are carefully standardized, so the quantities of iodine in those tend to be reliable. Table 7.1 provides some guidance on iodine levels, though as we said before, actual amounts can vary significantly.
#### **SPECIAL ISSUES WITH IODINE**
Several nutritious foods, such as soy foods, flaxseeds, cruciferous vegetables (broccoli and cabbage), peanuts, pine nuts, peaches, pears, strawberries, spinach, and sweet potatoes, contain goitrogens. These are substances that can interfere with thyroid metabolism _if and only if_ a person is iodine deficient. The solution is not to avoid these foods; instead, ensure a reliable source of iodine in the daily diet. Cooking can reduce help to reduce goitrogens in foods.
Water pollutants known as perchlorates, which are by-products of solid fuels, and various minerals from fertilizers and pesticides can also amplify thyroid problems in people who are iodine deficient or whose intakes are low. Finally, selenium deficiency can worsen a marginal iodine deficiency.
**TABLE 7.1.** Iodine in salt and dried sea vegetables
**SOURCE** | **AMOUNT SUPPLYING 150 mcg OF IODINE** | **AMOUNT SUPPLYING TOLERABLE UPPER LIMIT OF IODINE (1,100 mcg)**
---|---|---
Iodized sea salt or table salt | ½ tsp (2 ml) | 4 tsp (20 ml)
Noniodized sea salt or table salt | Not a source of iodine | Not a source of iodine
Arame | ½ tsp (2 ml) | 3½ tsp (18 ml)
Dulse granules | ½ tsp (2 ml) | 3¼ tsp (16 ml)
Kelp | Less than tsp (0.3 ml) | Scant ½ tsp (1.5 ml)
Nori | 1½ sheets | 10½ sheets
Wakame | 1⅛ tsp (5.5 ml) | 2 tbsp plus 2 tsp (40 ml)
Sources of data: ESHA Research, The Food Processor software, version 10.12.0. EdenFoodsedenfoods.com. Crohn, D. M., "Perchlorate Controversy Calls for Improving Iodine Nutrition," _Vegetarian Journal_ no. 2 (2006).
Key: mcg = micrograms, ml = milliliters, tsp = teaspoons, tbsp = tablespoon
### Other Important Minerals
Here's a quick rundown of other minerals vegans may want to consider when planning a healthful diet: chromium, copper, magnesium, manganese, phosphorus, potassium, selenium, and sodium. Fortunately, most vegan diets easily meet or exceed the requirements for these.
#### **CHROMIUM**
**Adult daily recommended intake:** Women: 25 mcg to age fifty, then 20 mcg. Men: 35 mcg to age fifty, then 30 mcg.
**Functions:** Supports the action of insulin. Helps metabolize carbohydrates.
**Key plant sources:** Apple, broccoli, dark chocolate, grapefruit juice, grape juice, kiwifruit, leek, orange, and whole grains.
**Special issues:** Measurement of chromium content of food is challenging; limited data is available.
#### **COPPER**
**Adult daily recommended intake:** 900 mcg.
**Functions:** Helps form enzymes that play key roles in energy metabolism, helps protect against free radical damage, and is essential to brain and nervous system function.
**Key plant sources:** Lentils, mushrooms, nuts, seeds, and whole grains.
**Special issues:** Vegan intakes are typically more than adequate.
#### **MAGNESIUM**
**Adult daily recommended intake:** Women: 310 mg to age thirty, then 320 mg. Men: 400 mg to age thirty, then 420 mg.
**Functions:** An essential component of bones, teeth, muscles, and cell membranes. Supports transmission of nerve impulses and affects muscle contraction. Plays a role in energy production and DNA building. Good magnesium status is associated with lower blood pressure and lowered risk for diabetes, heart disease, and stroke.
**Key plant sources:** Leafy green vegetables, other vegetables, fruits, whole grains, and nuts.
**Special issues:** Vegan intakes are typically adequate.
#### **MANGANESE**
**Adult daily recommended intake:** Women: 1.8 mg. Men: 2.3 mg.
**Functions:** Supports enzyme activity. Required for bone and cartilage formation and wound healing.
**Key plant sources:** Coconut, leafy vegetables, legumes, pineapple, raspberries, tea, nuts, and whole grains.
**Special issues:** Vegan diets easily meet and exceed recommended intakes.
#### **PHOSPHORUS**
**Adult daily recommended intake:** 700 mg.
**Functions:** A structural component of bone. Involved in the production and storage of energy from food.
**Key plant sources:** Dried fruit, garlic, legumes, nuts, tomato, and whole grains.
**Special issues:** Vegan diets typically provide intakes above recommended levels. Diets high in sodas can be too high in phosphorus. Using antacids that contain aluminum can lead to phosphorus deficiency.
#### **POTASSIUM**
**Adult daily recommended intake:** 4,700 mg.
**Functions:** Essential for transmission of nerve impulses, including beating of the heart. May reduce risk of osteoporosis, strokes, high blood pressure, and kidney stones when levels are adequate.
**Key plant sources:** Banana, barley, dark leafy greens, dried fruit, legumes, papaya, parsnip, potato, pumpkin, and tomato. It is a myth that bananas are the most concentrated source; Brussels sprouts, cantaloupe, green beans, grapefruit, strawberries, and tomato all provide more potassium per calorie.
**Special issues:** Vegan diets provide far more potassium than nonvegetarian diets, yet some may not reach recommended levels. It takes plenty of fruit and vegetables to reach the recommended intake, so get your 9 servings!
#### **SELENIUM**
**Adult daily recommended intake:** 55 mcg.
**Functions:** An antioxidant that protects cells from damage by free radicals. Reduces risk of cancer and heart disease. Helps regulate thyroid function.
**Key plant sources:** Beans, Brazil nuts and other nuts, seeds, and whole grains.
**Special issues:** American and British vegans tend to meet or exceed recommended intakes.
#### **SODIUM**
**Adult daily recommended intake:** To age fifty, sodium intakes ranging from 1,500 mg to an upper limit of 2,300 mg are suggested. Intakes should range from 1,300-1,500 mg from age fifty to seventy and 1,200 to 1,500 mg after age seventy.
**Functions:** Maintains the proper amount of fluid between cells. Allows transmission of nerve impulses. Plays a role in pancreas functions. Replenishes sodium lost through perspiration, urine, and tears.
**Key plant sources:** Among North Americans, most sodium comes from processed foods; only 6 percent comes from table salt, and 5 percent is added during cooking. Whole foods provide much safer, smaller amounts than processed foods.
**Special issues:** Higher intakes can be problematic for older people, African-Americans, and people with diabetes, high blood pressure, or chronic kidney disease. For all of these groups, sodium intake should be at the lower end of the recommended range. The average American consumes almost 3,500 mg of sodium per day.
### Three Rules for Getting Enough Minerals
Making sure you get enough of the minerals you need isn't difficult, particularly for vegans. Just remember these three rules:
1. Eat _whole_ plant foods. Minerals are found in all the different food groups, but many are lost in the refining process. Follow the recommendations in chapter 14, The Vegan Food Guide.
2. Get enough calories. If you're on a weight-loss diet, take a multivitamin-mineral supplement.
3. Check food labels. Consider using some foods that are fortified with calcium, zinc, iron, and iodine.
**TABLE 7.2.** Minerals in vegan foods
Sources of data: US Department of Agriculture, Agricultural Research Service, _USDA National Nutrient Database for Standard Reference_ , Release 25 (2012), ndb.nal.usda.gov. ESHA Research, The Food Processor software, version 10.12.0.
Key: c = cup; g = gram; mcg = microgram; mg = milligram; ml = milliliter; oz = ounce; tbsp = tablespoon; ... indicates that no data is available.
*For other ages, see the appendix.
**Recommended intakes for vegetarians and vegans are set at 1.8 times greater than the recommended intakes for nonvegetarians (see page 133 for further information).†Check labels for product-specific information.
What is "clean eating?" It's a well-planned vegan diet, high in vitamins and minerals and bursting with phytochemicals. Read all about it, in chapter 8.
## CHAPTER 8
## **Clean Vegan Eating**
Sometimes it is said that food is to the human body what fuel is to cars. Healthy foods are considered premium fuel, and, like our vehicles, our bodies run best on clean fuel. Although the analogy is useful, it isn't entirely accurate. Food does serve as fuel for our bodies, but that's just one of its many roles. Food also provides the structural materials used to build, rebuild, and repair our tissues, along with the resources needed to manufacture brain cells, muscles, bones, hormones, and enzymes. You literally are what you eat or, perhaps more accurately, what you absorb.
### The Power of the Plate
As mentioned in previous chapters, plant foods are concentrated sources of antioxidants, phytochemicals, phytosterols, fiber, vitamins, and minerals. These compounds and many others work together to support all of the body's systems, turning off disease-promoting genes, reducing inflammation, maintaining insulin sensitivity, boosting immune function, balancing hormones, protecting gastrointestinal function, reducing cholesterol levels, and controlling blood sugar levels. Although you can get many of these protective substances from supplements, research continues to show that nutrients work synergistically and are best obtained from food.
In contrast to whole plant foods, highly processed foods and animal products are generally the sources of dietary components that have been linked with disease, such as sodium, refined carbohydrates, saturated fat, cholesterol, trans-fatty acids, toxins, and chemical contaminants, such as hormones, antibiotics, and persistent organic pollutants. When eaten in excess, these compounds work together to disrupt health and promote disease.
### Disease Preventers
We've covered a lot about essential nutrients: protein, fats, carbohydrates, vitamins, and minerals. Impressive as these are, plant foods continue to dazzle us with additional protective compounds, such as enzymes, phytochemicals, phytosterols, and prebiotics.
#### **ENZYMES**
The enzymes in raw plant foods help to convert specific phytochemicals into their active forms and may aid digestion. However, cooking reduces or destroys these enzymes.
To date, two plant families are known to contain enzymes that convert phytochemicals into their highly beneficial active forms. One is cruciferous vegetables, such as broccoli, broccoli sprouts, radish sprouts, Brussels sprouts, cabbage, cauliflower, kale, and turnips, and the other is allium vegetables, such as onions, garlic, and chives. By the way, sprouts are much higher in phytochemicals than the mature plants. The active phytochemicals produced in the cruciferous vegetables have remarkable detoxification effects. Most notably, they help process and eliminate carcinogens. The active phytochemicals in allium vegetables are antimicrobial and help fight bacteria, parasites, viruses, fungi, arthritis, and cancer. They can also lower cholesterol levels.
The enzymes in food may also aid digestion, though the overall contribution to digestion is very small. Enzymes start working to break down food as soon as the food is chopped, mashed, pureed, or blended—before we even begin eating it. The enzymes continue working while we chew and up until the food reaches the lower part of the stomach, where acidic conditions deactivate most of them. Food enzymes with the greatest chance of surviving stomach acid and arriving intact in the small intestine, where most digestion takes place, are those that are packaged within microorganisms, as in fermented and cultured foods.
Take-Home Message: Include many cruciferous and allium vegetables in your diet, along with a variety of sprouts. Also add cultured and fermented foods to your diet. To maximize the enzymes in vegetables and fruits, eat at least some of them raw.
#### **PHYTOCHEMICALS**
Phytochemicals are chemicals found in plants. ( _Phyto_ is Greek for "plant.") Plants produce phytochemicals for their own survival and protection. Some play a critical role in attracting pollinators and seed dispersers, and others act as an internal defense system, protecting plants from pests, pathogens, and potentially hostile environments. Phytochemicals play a big role in the colors, flavors, textures, and odors of plant foods.
When you eat plants, these phytochemicals go to work on your body's behalf. They support optimal health by reducing the risk of chronic disease and fighting existing diseases in multiple ways, such as by reducing inflammation and eradicating carcinogens.
All whole plant foods contain hundreds of thousands of phytochemicals. Choosing a wide variety of colorful vegetables, fruits, herbs, spices, legumes, nuts, seeds, and whole grains is the key to a diet rich in a broad range of phytochemicals. Of course, there are superstars that can help transform a good eating pattern into a phytochemical feast. Among the most noteworthy are dark leafy greens (kale, collard greens, spinach), cruciferous vegetables, sprouts, purple and blue fruits (blueberries, blackberries), herbs and spices, tomatoes, citrus fruits, legumes, nuts, seeds (flaxseeds, hempseeds), and cocoa beans.
Many factors can affect the quantity of phytochemicals in food and their bioavailability. Soil, water, climate, and the use of chemicals can all affect the phytochemical content as plants grow. Organic produce has an edge over conventional produce when it comes to phytochemical content, which makes sense, given that organic foods need more robust defenses. Refining can dramatically reduce the phytochemical content of food, especially when the most phytochemical-rich parts of the plants are removed—for instance, the germ and bran from wheat flour—or when the processing involves exposure to harsh chemicals, heat, or pressure. Some postharvest storage methods can also diminish phytochemical concentrations.
Most phytochemicals are more efficiently absorbed from raw foods. Chopping, pureeing, processing, milling, mashing, grating, and juicing all break down or remove fiber and other compounds that reduce the bioavailability of phytochemicals and other nutrients. Therefore, drinking vegetable juice can be a practical way to boost antioxidant and phytochemical intake without adding bulk to the diet. Sprouting and fermenting can also significantly enhance phytochemical content or bioavailability. For example, compared to broccoli, broccoli sprouts contain ten to one hundred times the amount of a phytochemical that has detoxifying, anticancer, and antibacterial properties and may improve insulin resistance in people with type 2 diabetes.
Cooking tends to decrease the amount of phytochemicals, and the higher the heat and the longer the food is cooked, the more significant the loss. Cooking method can also be a factor. For example, the loss of water-soluble phytochemicals is higher with boiling than steaming.
On the other hand, cooking softens plant cell walls, making it easier for the body to extract and absorb some types of phytochemicals, particularly carotenoids. For example, we absorb more of the carotenoid lycopene from cooked tomatoes than raw tomatoes, and more beta-carotene from cooked carrots than raw. In addition, including even a small amount of fat, from oil or from high-fat whole foods, improves absorption of carotenoids, whether the foods containing them are raw or cooked.
**Take-Home Message:** To boost phytochemical intake, eat foods with a wide range of colors within every food group. The more colorful your plate, the richer the variety and concentration of phytochemicals in your diet. Opt for organic. Eat sprouts and fermented foods, and include legumes, nuts, seeds, and whole grains in addition to vegetables and fruits.
#### **PHYTOSTEROLS**
Phytosterols, also called plant sterols or stanols, are an essential part of plant cell membranes. They are structurally similar to cholesterol, and because of this, they can inhibit our absorption of dietary cholesterol, lower total and LDL cholesterol levels, and suppress inflammation.
The diets of early humans probably provided about 1,000 mg of phytosterols a day, but the average intake these days is only about 150 to 450 mg. Vegetarian diets are generally higher in phytosterols, with vegan diets being highest. Raw vegan diets provide between 500 and 1,200 mg of phytosterols per day, and sometimes more. Consuming about 2,000 mg of phytosterols per day reduces LDL by approximately 9 to 15 percent in those with elevated cholesterol levels, but to get 2,000 mg, you'd have to take supplements or eat phytosterol-fortified foods.
Although all whole plant foods contain phytosterols, the most concentrated natural sources are seeds, nuts, wheat germ, avocados, legumes, sprouts, and vegetable oils. The food industry now fortifies a variety of food products, such as margarine, cereal, and fruit juice, with phytosterols because of their cholesterol-lowering properties. While such fortified products may provide some benefit for people with elevated cholesterol levels, it makes little sense to add an otherwise unhealthful food to your diet just to boost phytosterol intake. It would make better sense to eat more plant foods. Vegans with healthful diets needn't give these products a second thought. They eat far more sterols than people on other diets, consume no cholesterol, and usually have lower cholesterol levels.
For those who do take phytosterol supplements or use phytosterol-fortified foods, intakes exceeding 2,000 mg per day haven't been shown to provide added benefit, and for some people, it may cause more harm than good.
**Take-Home Message:** The safest and most effective way to boost phytosterol intake is to eat a whole-foods vegan diet, including higher-fat plant foods such as seeds, nuts, wheat germ, and avocados. Vegans don't need to eat phytosterol-fortified processed foods.
#### **PREBIOTICS AND PROBIOTICS**
Your intestinal tract is buzzing with trillions of bacteria collectively known as gut flora or microbiota. Although thirty to forty species account for 99 percent of these microorganisms, as many as four hundred different species are known residents. These intestinal inhabitants account for a surprising 50 percent of fecal mass.
Although the body's relationship with microbiota is largely beneficial, some of these guests are more welcome than others. Benefits of preferred strains include the following:
* Boosting nutritional status by enhancing the absorption of several nutrients, maintaining amino acids, and synthesizing certain vitamins
* Breaking down fiber that the human body can't digest, resulting in the release of more than 10 percent of our daily calorie needs, improving carbohydrate and fat metabolism, and protecting against colon cancer
* Supporting immune system function, protecting against food allergies, and maintaining healthy intestinal tissues
If friendly flora aren't adequately supported, less welcome guests—more pathogenic bad bacteria—can multiply, with several ill effects:
* Toxins that injure the gut lining, making it more permeable, or leaky
* Reduced immune function
* Chronic, low-grade inflammation
* Infections
* Impaired metabolism
* Contributions to overweight and obesity
Your food choices influence whether the balance of flora is friendly or hostile. A plant-based, high-fiber diet supports good bacteria, whereas a high-fat, low-fiber diet encourages bad bacteria. The goal is not to wipe out bad bugs—you actually need some of them—but to shift the balance from bad bugs to good bugs.
Consuming probiotics can help. Probiotics are foods or supplements that contain friendly microorganisms. They arrive in the intestinal tract in an active form and exert beneficial health effects. Another option is prebiotics: indigestible, fermentable food components that stimulate the growth or activity of beneficial bacteria, usually serving as their food supply.
Fermented or cultured vegan foods that offer probiotics include nondairy yogurt and kefir, miso (if not boiled), sauerkraut, and rejuvelac (a fermented grain beverage). Consuming these foods or taking probiotic supplements can prevent or diminish complaints associated with lactose intolerance, irritable bowel syndrome, and certain types of diarrhea. Probiotics decrease cancer-promoting enzymes and toxic by-products of bad bacteria. They also appear to protect the health of the gastrointestinal tract and reduce complications associated with inflammatory bowel diseases and infection with _Helicobacter pylori_ , the bacteria associated with ulcers. They can aid in the prevention of flu, the common cold, urogenital infections, and, among infants, allergies and skin disorders. Probiotics may also help reduce cholesterol levels, prevent cancer, protect against autoimmune diseases, and promote dental health.
Prebiotics are nondigestible sugars such as inulin and oligosaccharides that stimulate the growth and activity of beneficial bacteria in the digestive system. Prebiotics are found in asparagus, bananas, raw chicory, garlic, Jerusalem artichokes, leeks, onions, and sweet potatoes and are also available in foods fortified with prebiotics.
When purchasing a probiotic supplement, you'll notice that the label includes the genus and species of bacteria supplied. A probiotic containing a variety of Lactobacillus and Bifidobacteria strains is generally more effective than a single-strain acidophilus supplement. Also, each strain of bacteria has distinct health effects. If you're using probiotics to treat a specific condition, do some research to find out what strains are most effective for your condition.
No matter what strains you use, if the microorganisms are dead, they aren't probiotics. Check the label for the expiration date. Most probiotics need to be refrigerated. To test whether a supplement is viable, you can add a spoonful to a small bowl of soymilk; leave it at room temperature and, after a day or so, check to see whether there's any bubbling or other activity indicating a living culture. Typical dosages vary with the product, but generally higher dosages (from five to ten billion colony-forming units, or CFU, per day for children, and ten to twenty billion CFU per day for adults) are associated with better outcomes.
Be aware that heat kills beneficial bacteria. If using cultured or fermented foods as a source of probiotics, don't cook them over high heat. For example, miso should be mixed with warm water and stirred into cooked dishes, rather than being boiled in a soup.
**Take-Home Message:** High-fiber vegan diets help promote and maintain healthy gut flora. To help restore gut flora, eat plenty of raw vegetables and fruits and add some fermented or cultured foods to your diet. Consider periodic use of a multistrain probiotic.
### Disease Promoters
While focusing on whole plant foods can go a long way in promoting health and well-being, to maximize the advantages you'll also want to avoid dietary factors that can promote disease. In the sections that follow, we'll consider culprits not previously addressed.
#### **TRIGGERS FOR FOOD ALLERGIES AND SENSITIVITIES**
Although food sensitivities aren't widely recognized as playing a role in disease, adverse food reactions can contribute to disease processes. "Food sensitivity" is commonly used as an umbrella term for allergies, nonallergic food hyper-sensitivities, and intolerances. A true food allergy is a reaction to an allergen (usually a protein) that the immune system views as a foreign invader. The body produces antibodies against the allergen, triggering the release of histamine, which is responsible for allergy symptoms: hives, eczema, a runny nose, earaches, shortness of breath, swelling, inflammation, diarrhea, and so on. Eight foods account for 90 percent of true food allergies: milk, eggs, peanuts, tree nuts, shellfish, fish, wheat, and soy. Although allergies can begin at any age, most appear during early childhood, and in 90 percent of those cases, children outgrow them by age seven. The people most likely to remain allergic are those with severe, life-threatening anaphylactic reactions and those sensitive to peanuts or tree nuts.
Adverse food reactions that don't trigger an immune response are called nonallergic food hypersensitivities or intolerances. Though the symptoms can be similar, they may be less acute and less easily recognized than those of true food allergies. Lactose intolerance, the inability to digest lactose, the sugar in milk, is a good example of a food intolerance. Lactose intolerance commonly occurs after about age four, when production of the enzyme lactase declines in about 65 percent of people. Lactase is required by babies to digest lactose in breast milk, which is also present in cow's milk. If milk products are consumed in significant amounts after lactase levels decline, lactose in the large intestine remains undigested and causes gastrointestinal distress.
Pharmacological reactions are another type of nonallergic hypersensitivity. For example, monosodium glutamate (MSG), a flavor enhancer commonly used in Chinese food, may cause some people to have side effects similar to those of drugs, such as flushing, headaches, and abdominal symptoms. Other potentially problematic food components include sulfites in wine and dried fruit, tyramine in aged cheeses, theobromine in chocolate, and preservatives, flavorings, and coloring agents in processed foods.
Gastrointestinal reactions to food are the symptoms most strongly linked to chronic disease risk. When you're in good health, the lining of the gut serves as a highly selective barrier that facilitates the absorption of essential nutrients such as fatty acids, vitamins, minerals, antioxidants, and phytochemicals and prevents the absorption of potentially harmful substances. If the integrity of the gut wall is compromised, some of these can leak into the bloodstream, setting off immune reactions in various parts of the body and placing a significant burden on detoxification systems. This condition is often referred to as leaky gut syndrome. The lining of the gut can be breached when it's constantly in contact with the food components that cause inflammation or injury. Damage can also be caused by medications, environmental contaminants, radiation, stress, inflammatory conditions such as Crohn's disease, or an overgrowth of unfriendly gut microflora.
Once compounds leak from the gut into the bloodstream, they can wreak havoc in the system, contributing to a myriad of conditions:
* Anxiety or depression
* Asthma
* Autism
* Autoimmune diseases
* Cancer
* Cardiovascular diseases
* Celiac disease or gluten hypersensitivity
* Chronic fatigue
* Chronic low-grade inflammation
* Diabetes (type 1 and type 2)
* Gastrointestinal disorders such as diarrhea, bloating, irritable bowel syndrome, or ulcerative colitis
* Hormone abnormalities
* Insulin resistance or metabolic syndrome
* Joint and muscle issues such as chronic pain or rheumatoid arthritis
* Liver dysfunction
* Migraine headaches
* Overweight or obesity
* Skin problems such as itching, eczema, hives, acne, or psoriasis
In addition, if the epithelial cells lining the gut are damaged, they lose their ability to transport nutrients into circulation and malnutrition can result. While any food can be problematic, the foods most strongly associated with increased gut permeability are dairy products and those that contain gluten (a protein in wheat, barley, rye, spelt, triticale, and Kamut). (For more information on gluten, see page 92.) Diets that promote an imbalance in gut flora, such as those high in sugar, can also adversely affect the integrity of the gut. Fortunately, with improvements in diet, the intestinal lining can regenerate and heal itself. For some individuals, supplementing with L-glutamine, probiotics, zinc, and omega-3 fatty acids may be helpful.
It's important to properly identify offending foods, but traditional allergy testing isn't helpful in identifying nonallergic food hypersensitivities. Plus, all types of allergy testing have limitations, even for the diagnosis of true allergies. To confirm a food culprit, eliminate all of the suspect foods for several weeks. If the sensitivity doesn't cause an anaphylactic response, reintroduce the suspect foods one at a time, at two- or three-day intervals, checking on reactions after each. For more information on food allergies, nonallergic food hypersensitivities, gut health, and elimination diets, see _The Food Allergy Survival Guide_ , by V. Melina, D. Aronson, and J. Stepaniak (Book Publishing Company, 2004).
**Take-Home Message:** Nonallergic food hypersensitivities and allergies can be significant players in many disease processes. If you struggle with unsolved health issues, it's worth considering adverse food reactions as a potential contributor. In some cases, an elimination diet may be warranted.
#### **CHEMICAL CONTAMINANTS**
Food can be contaminated by hazardous materials that enter the food chain during the growing, harvesting, storage, processing, packaging, or preparation of food, including as a result of the use of agrochemicals. Unfortunately, the more polluted our world becomes, the greater our exposure to toxic contaminants. Many of these substances persist in the environment and work their way up the food chain. Ingesting various contaminants, such as arsenic, cadmium, lead, mercury, PCBs, DDT, pesticides, and hormones, has been associated with many health conditions, including cancer, diabetes, cardiovascular diseases, endocrine disruption, hypertension, and nervous system damage.
Common sources of chemical contaminants are processed foods, animal products, and conventionally grown produce. Meat, fish, and poultry can be high in contaminants due to their considerable presence in animal fodder. Therefore, vegans and vegetarians have lower exposure to almost all dietary contaminants except for agrochemicals used on conventionally grown produce, since they eat more produce than omnivores. But when all contaminants are taken into account, vegans eat fewer of them. Of course, vegans who eat mostly organic food have the lowest blood levels of agrochemical pesticides.
Although vegans have reduced exposure to chemical contaminants relative to others, there are several steps vegans can take to further reduce their risk:
* Eat organic food.
* Buy from local growers. Produce from farmers' markets tends to have fewer pesticides, even if it isn't organic.
* Grow your own organic produce. If you're short on yard space, use containers.
* Wash produce well before eating. Although pesticides get inside of foods and cannot be completely removed by washing, it will reduce total pesticide content. Peeling conventional produce also reduces pesticide content.
* Avoid highly processed foods. They often contain additives, preservatives, and products of oxidation, such as rancid fats.
* Moderate use of rice and rice products to reduce exposure to arsenic. Feed your baby a variety of cereals, rather than relying exclusively on rice cereals.
* Avoid hijiki. Although all sea vegetables can be contaminated by heavy metals and pollutants from the ocean, hijiki is particularly high in arsenic. If you do use it, soak it first and drain it well.
* Limit exposure to potentially dangerous packaging materials. Select glass containers instead of plastic for storing and reheating food. If using plastic, purchase products free of BPA (bisphenol A). At the very least, avoid putting hot foods into plastic containers or heating foods in plastic. Avoid imported canned foods, since the cans may contain lead, and don't store food in lead-glazed or leaded glassware.
* Use cooking methods that are less likely to create toxic compounds. Steaming, stewing, and braising produce fewer by-products than frying, barbecuing, and broiling. Minimize consumption of deep-fried foods and foods cooked at high heat for long periods of time. If you cook with high heat, don't blacken or overcook foods.
* Eat more raw foods to reduce your exposure to harmful by-products of cooking. For more information, see _Becoming Raw_ , by B. Davis and V. Melina (Book Publishing Company, 2010).
**Take-Home Message:** The primary sources of environmental contaminants are animal products, processed foods, and conventionally grown produce. Vegans have low blood levels of contaminants but can reduce these levels even more.
### Which Vegan Diet Is Best?
People of all ages, genetic makeups, physical activity levels, and states of health all share two common dietary goals: to be adequately nourished, and to avoid or reverse diet-induced chronic disease. You might wonder what type of vegan diet best meets these goals. If you asked a dozen different authorities, you might receive a dozen different answers.
Many vegan diets have been touted as healthiest: low-fat, macrobiotic, Mediterranean, nutrient-dense, raw, starch-based, whole-foods, fruitarian, and the list goes on. While there are pros and cons to each, most can be designed to be nutritionally adequate. The greater challenge is teasing out the factors that provide an advantage in terms of disease prevention or treatment.
The following sections examine some common vegan diets, outlining their strengths and weaknesses and summarizing how to make each variation work for your health.
**Diet: Conventional** (combination of cooked and raw foods; about 30% fat)
**Strengths:** It isn't difficult to achieve nutritional adequacy on a conventional vegan diet, and key foods are easily accessible. It also allows greater flexibility socially. Foods are relatively accessible.
**Weaknesses:** With poor food choices, a conventional vegan diet may be low in foods rich in protein, iron, and zinc, such as legumes, or in calcium-rich foods.
**Making it work:** Eat a balance of cooked and raw foods, and use convenience foods in moderation.
**Diet: Fast and Easy** (high use of convenience and fast foods)
**Strengths:** This diet is practical and simple, and with its reliance on prepared foods, it typically includes fortified foods that boost intakes of iron and vitamins B12 and D.
**Weaknesses:** Convenience foods are high in added fats, sugars, and sodium and lower in protective phytochemicals, antioxidants, and fiber. These foods also may be expensive.
**Making it work:** Choose foods with short ingredient lists and less sodium, fat, and sugar. Use nutritious convenience foods such as hummus, lentil soup, and fortified nondairy milks, yogurts, and breakfast cereals.
**Diet: Fruitarian**
**Strengths:** A fruitarian diet is low in calories and fat and high in phytochemicals and antioxidants. It also avoids common allergens.
**Weaknesses:** Fruit may not provide enough protein, essential fatty acids, or important vitamins and minerals. It's also unsuitable for children.
**Making it work:** Include organic greens, nuts, seeds, and sprouted or cooked legumes. Ensure that you're getting enough iodine and vitamins B12 and D.
**Diet: Low-Fat** (15% fat or less)
**Strengths:** A low-fat vegan diet minimizes harmful fats and is effective for weight loss and for treating cardiovascular diseases and type 2 diabetes.
**Weaknesses:** Such diets may be low in essential fatty acids and vitamin E, and absorption of minerals. They may also increase triglycerides if refined carbohydrates are emphasized. Absorption of some vitamins and phytochemicals may be impaired. In addition, a low-fat diet may not provide enough calories for children or those who are underweight.
**Making it work:** Eat vegetables, fruits, legumes, and whole grains and at least 1 ounce (30 g) of nuts and seeds per day, including a source of omega-3 fatty acids.
**Diet: Macrobiotic**
**Strengths:** A macrobiotic diet is focused on whole foods and low in processed foods, including flour products.
**Weaknesses:** Such diets may not provide enough iron, zinc, lysine, essential fatty acids, or vitamins B12 and D. They also have a lower nutrient density due to their heavy reliance on grains.
**Making it work:** Include generous amounts of vegetables, fruits, legumes, nuts, and seeds. Ensure that you're getting enough iodine and vitamins B12 and D.
**Diet: Mediterranean**
**Strengths:** A Mediterranean diet includes generous amounts of legumes, vegetables, fruits, whole grains, nuts and seeds and limits processed foods.
**Weaknesses:** Such diets may be too high in fat for those who are overweight or have high cholesterol. If wine is emphasized, it may increase cancer risk.
**Making it work:** Rely on nuts, seeds, avocados, and olives for fat rather than oil. Ensure that you're getting enough iodine and vitamins B12 and D.
**Diet: Nutrient-Dense**
**Strengths:** A nutrient-dense diet emphasizes vegetables and other whole foods and provides abundant vitamins and minerals while minimizing processed foods and oil.
**Weaknesses:** This diet doesn't necessarily take into account harmful factors such as environmental contaminants and free radicals.
**Making it work:** Ensure that you're getting enough iodine and vitamins B12 and D. Factor in all protective dietary components as well as the potentially harmful ones (see table 8.1).
**Diet: Raw**
**Strengths:** A raw diet minimizes processed foods and avoids common allergens. It's also low in damaging dietary components, high in protective components, and avoids problems related to cooking, such as loss of nutrients and phytochemicals and formation of carcinogens.
**Weaknesses:** If not well planned, a raw diet may fall short of recommended in-takes for protein, iron, zinc, calcium, iodine, and vitamins B12 and D. Food prep can be labor-intensive, and this diet can be expensive if you rely on specialty products. Raw diets aren't recommended for infants and children.
**Making it work:** Ensure that all of your nutritional and calorie needs are met. Eat sprouted or cooked legumes to boost protein, iron, and zinc. ("Raw-food" diets may include up to 25 percent cooked foods). Soak, sprout, juice, blend, dehydrate, and ferment foods to increase the concentration and availability of nutrients.
**Diet: Starch-Based**
**Strengths:** Starch-based diets are typically affordable and low in fat and include only moderate amounts of processed foods.
**Weaknesses:** Because grains provide fewer minerals and vitamins and less protein than vegetables or legumes, such diets have lower nutrient density. They may also be low in essential fatty acids and lysine and can be unsuitable for smaller people or those with small appetites.
**Making it work:** Eat nine servings of vegetables and fruits and at least 1 ounce (30 g) of nuts and seeds each day. Include legumes for more concentrated protein, and select nutrient-dense starches such as quinoa and yams. Ensure that you're getting enough iodine and vitamins B12 and D.
**Diet: Whole-Foods**
**Strengths:** When well planned, whole-foods diets are high in antioxidants, phytochemicals, fiber, vitamins, and minerals. Such diets are also affordable and low in sodium and added fat and sugar.
**Weaknesses:** A diet focused on whole foods may lack iodine and vitamins B12 and D. Food prep can be labor-intensive.
**Making it work:** Include some lightly processed foods (tofu, fortified nondairy milks, and nondairy yogurt) to boost nutrient intake and make prep easier. Ensure that you're getting enough iodine and vitamins B12 and D.
#### **TRANSITIONING TO A HEALTHFUL VEGAN DIET**
The transition to a healthful vegan diet can be a delightful culinary adventure. When you eliminate animal products from the menu, you open up a whole new world of delights: fresh flavors, appealing textures and colors, and intriguing international influences. As you turn your focus to healthful whole plant foods—vegetables, fruits, legumes, whole grains, nuts, and seeds—opt for the cleanest choices within each of these categories, as outlined table 8.1. Also, follow the Vegan Food Guide (see pages 263–267) to ensure all your nutrient needs are met!
**TABLE 8.1.** Clean, green food choices
**FOOD CATEGORY** | **BEST CHOICES** | **CONSIDERATIONS**
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Vegetables | All vegetables and vegetable juices, but especially dark leafy greens | Choose organic when possible. Eat greens low in oxalates (bok choy, collard, kale, napa cabbage, watercress, and collard, dandelion, mustard, and turnip greens) for calcium. Eat at least half of your veggies raw. Focus on moist cooking methods and don't overcook. Include a fat source in salad dressings. Choose orange or yellow starchy vegetables (yams, squash). Use vegetable juices as a concentrated source of antioxidants and phytochemicals.
Fruits | All fruits, fresh, frozen, and dried | Eat mainly fresh, organic fruits and juices; cooking depletes vitamin C. Use fresh or dried fruits as sweeteners. Fruit smoothies are an almost-instant meal and very nutritious, especially if you add greens.
Legumes | Beans, lentils, peas, and their sprouts, as well as soy foods, and peanuts | Aim for 3 servings each day. Soak or sprout dried legumes before cooking. Choose organic soy products. Select fortified soymilk made with whole soybeans rather than isolates. Limit veggie meats, which are highly processed.
Whole grains | Sprouted, intact, cut or rolled whole grains and "pseudograins" (amaranth, buckwheat, quinoa, wild rice) | Sprouting dramatically increases phytochemical and lysine content and reduces compounds that inhibit nutrient absorption. Pseudograins are more nutrient dense than other grains and gluten-free. Use intact grains when possible. Moderate use of flour products even if whole-grain. Limit processed products such as flaked whole grain cereals. Minimize refined grains.
Nuts | Nuts, nut butters, and nut cheeses | Soak nuts to improve digestibility, boost phytochemical content, and decrease compounds that inhibit nutrient absorption. Walnuts provide omega-3 fatty acids. Select natural nut butters. Limit intake of roasted nuts, especially when roasted in oil and salt or coated in sugar.
Seeds | Seeds and seed butters | Sprout seeds for added nutrition. Soak them to improve digestibility, increase phytochemical content, and decrease compounds that inhibit nutrient absorption. Select natural seed butters. Use omega-3-rich seeds (chia seeds, hemp-seeds, and ground flaxseeds).
Sea vegetables | All except hijiki | Sea vegetables provide essential fats and iodine, but they may be contaminated if from polluted waters. Avoid hijiki due to arsenic contamination.
Concentrated fats and oils | Mechanically pressed oils rich in omega-3s or with a good balance of omega-3s and omega-6s | Limit use of added oils. Select organic oils to minimize toxins, which are concentrated when oil is extracted, and store refrigerated. For cooking, use small amounts of organic olive, canola, coconut, or high-oleic oils. Minimize use of hard fats other than coconut oil, such as margarine.
Concentrated sweeteners | Dried fruit sugars, blackstrap molasses | Minimize use of concentrated sugars. Sugars made from whole foods such as dates are more nutritious options. Blackstrap molasses is the most nutrient-rich sweetener. Choose organic.
Sources of data are listed in _Becoming Vegan: Comprehensive Edition,_ by Brenda Davis and Vesanto Melina (Book Publishing Company, 2014).
**_The Paleo Diet: Facing the Facts_**
High-protein, low-carbohydrate diets often attract athletes, dieters, and health seekers of all stripes, and the "paleo" diet is an example. Its basic premise is simple—the diet humans ate in preagricultural, Paleolithic times is best suited for human health. While we can't blindly assume that what our relatively short-lived ancestors ate was necessarily optimal for human health, nutritional anthropologists have studied true Paleolithic diets extensively.
That diet essentially consisted of wild plants and wild animals, which varied with location, season, hunting and gathering skills, available tools, and so on. We know that preagricultural peoples didn't consume oil, sugar, salt, anything from a box or bag, or the milk of other mammals. Today's new paleo devotees attempt to copy the diet of our ancestors by eating meat, poultry, fish, vegetables, fruits, nuts, and seeds and, in most cases, avoiding processed foods, grains, legumes, and dairy products.
Followers apparently imagine that the nutrient intake of the new paleo diet approximates that of our Paleolithic ancestors, but they're wrong. As it turns out, vegan diets have more in common with true Paleolithic diets than the new paleo diets. This may sound like a bit of a stretch, so we did the math for you: We compared three days of recommended paleo menus from a popular paleo website with three days of recommended vegan menus from chapter 14 in this book. We also compared the average daily intakes offered by the diet true Paleolithic people ate. The results are summarized in table 8.2, which also provides dietary reference intakes (DRIs, the nutrient intake recommendations from the US National Academy of Sciences). The DRI values are for adult males and adult women who aren't pregnant or lactating. Nutrients and other dietary factors in the new paleo or vegan diet that are more similar to the true Paleolithic diet are highlighted in gray.
As you can see, new paleo intakes of protein, vitamin A, and zinc are closer to amounts in a true Paleolithic diet than in the vegan diet, but cholesterol intake is almost triple that of a true Paleolithic diet. However, vegan intakes of carbohydrate, fat, saturated fat, fiber, riboflavin, thiamin, vitamin C, vitamin E, iron, calcium, sodium, and potassium are all closer to levels in a true Paleolithic diet than in a new paleo diet.
More than 50 percent of calories in the new paleo diet come from fat, and 20 percent of calories come from saturated fat. In other words, today's paleo wannabes may be consuming twice the fat and more than three times the saturated fat of true Paleolithic people. Fiber intakes of the new paleo diet are about 30 grams per day in a 3,000-calorie diet, whereas the vegan menu provides about 80 grams of fiber. However, even the 100 percent plant-based vegan diet falls short when compared to the 104 grams of fiber consumed by our Paleolithic ancestors, who clearly ate plenty of plant foods.
Why does the new paleo diet fall flat on its face when compared to the true Paleolithic diet? The reason is that the meat and vegetables consumed today are very different from those eaten by true Paleolithic people. The wild animals eaten in Paleolithic times were far leaner than even the leanest domestic animals, and the wild plants were more concentrated in fiber and other nutrients than most of the crops commercially raised today. In addition, new paleo eaters tend to rely far more heavily on meat than did most of their ancestors.
**TABLE 8.2.** New paleo, true Paleolithic, and vegan diets compared
Sources of data: New paleo data is based on the average of three days (Wednesday, Thursday, and Friday) of recommended menus from the Paleo Plan website (paleoplan.com/resources/sampler-menu-meal-plan/), adjusted to 3,000 calories. True Paleolithic data is from Eaton, S. B., et al., "Paleolithic Nutrition Revisited: A Twelve-Year Retrospective on Its Nature and Implications," _European Journal of Clinical Nutrition_ 51, no. 4 (1997): 207–216. Vegan data is based on the average of three days of menus from chapter 14, adjusted to 3,000 calories.
**Bottom Line:** The new paleo diet is a very pale imitation of the diet of early humans. The focus tends to be on consuming large quantities of meat. Plus, this dietary pattern ignores the environmental crisis that makes eating lower on the food chain an ecological imperative, the ethical issues associated with an increased demand for food animals, and the numerous health risks associated with the consumption of meat. If people want to move closer to a true Paleolithic diet, they might turn their attention to becoming vegan—it's as close to a true Paleolithic diet as most modern-day people can achieve.
#### **THE OCCASIONAL INDULGENCE**
There are few foods that haven't been "veganized." Vegan peanut butter cups, chicken nuggets, croissants, pizza, cream cheese, marshmallows, ice cream bars, mayonnaise, spare ribs, and even calamari are all readily available, and their accessibility can make the transition to a vegan diet less daunting. Still, you may wonder if these convenience foods have a place in a healthful vegan diet.
For most people, the occasional treat isn't a problem. Ultimately, the answer depends on your health and energy needs. People who are healthy and active have more dietary leeway than those who are unhealthy or inactive. If you are fighting a serious disease, we recommend that your diet be as clean as possible. Remember, all body systems are interconnected, and when one system is compromised, other systems falter. Even for vegans, too many calories or too much highly processed food can compromise health and healing.
As you progress along the vegan culinary path, you'll discover that the taste of processed, prepared foods doesn't compare to the flavors of whole, fresh foods. For example, vegan ice cream is yummy, but desserts made solely from frozen fruits, such as banana and mango, are stupendous. Over time, you're likely to find that commercial products taste too sweet, too rich, and too salty and simply lose their appeal.
Next, we tackle one of the most pervasive health problems of our century: over-weight and obesity.
## **CHAPTER 9**
## **Triumph over Weight**
One of the great attractions of a vegan diet is the promise of slimness. It's an established part of the vegan stereotype. If you're an overweight vegan, mentioning your dietary preferences may elicit looks of surprise. Reactions, even if unspoken, often clearly say, "You don't look like a vegan." If you're overweight and adopt a vegan diet, not losing weight can be frustrating. And if you _gain_ weight after becoming vegan, it can be downright exasperating. But the truth is, vegans come in all shapes and sizes, and although becoming vegan can be an effective ally in an effort to shed pounds, it doesn't guarantee weight loss.
### The Costs of Overweight
Avegan diet provides remarkable protection against over-weight and obesity. Vegans are leaner, having lower body mass indexes (BMI) and percentage of body fat than any other dietary group. The average vegan has a BMI of about 22, compared to a BMI of about 28 for the average American. The United States is one of the most overweight nations, with almost 70 percent of the adult population being overweight or obese. In a large study in the United Kingdom, only 2 percent of vegans were obese, compared to more than 5 percent of health-conscious meat eaters. Still, although these statistics are reassuring, they provide little consolation for overweight and obese vegans.
Overweight and obesity come with a hefty price tag. In 2008, medical costs associated with obesity in the United States were estimated at $147 billion. Excess body fat causes harmful changes to the body's basic physiology, adversely affecting blood pressure, cholesterol, triglycerides, respiration, fertility, skin and joint health, hormones, and insulin activity. More specifically, it significantly increases risk for the following debilitating and often fatal health conditions:
* **Type 2 diabetes.** The risk of type 2 diabetes is directly linked to the amount of excess body fat, particularly when fat is carried in the abdomen. As body fat increases, insulin sensitivity declines and insulin resistance increases.
* **Heart disease and stroke.** Being overweight contributes to high blood pressure, high cholesterol and triglyceride levels, and angina and can markedly increase the chance of a heart attack, stroke, or congestive heart failure.
* **Cancer.** Overweight women suffer more breast, uterine, cervical, ovarian, gallbladder, and colon cancers, while overweight men are at elevated risk for cancers of the colon, rectum, and prostate.
* **Osteoarthritis.** Excess body weight increases the risk of osteoarthritis, probably because it puts extra pressure on the joints, which erodes the cartilage that cushions and protects joints.
* **Sleep apnea.** Sleep apnea, which involves pauses in breathing during sleep, is often marked by heavy snoring and snorting breaths following sometimes fairly prolonged lapses in breathing. Risk for sleep apnea is significantly higher among overweight people.
* **Gout.** The product of high levels of uric acid in the blood, gout causes painful swelling in the joints, usually affecting one joint at a time, most commonly the big toe. Risk for gout rises progressively with increased body weight.
* **Gallbladder disease.** Being significantly overweight increases the risk of gallbladder disease and gallstones, but rapid, significant weight loss can also increase the chance of developing gallstones. Gradual weight loss of about 1 to 2 pounds (0.4 to 0.9 kg) per week is less likely to trigger gallbladder attacks.
* **Polycystic ovarian syndrome.** A painful disorder marked by small cysts on the ovaries, menstrual irregularities, facial hair, acne, patches of dark skin on the neck, and weight gain, polycystic ovarian syndrome affects women of reproductive age. It's associated with insulin resistance and abdominal obesity and strongly increases the risk of type 2 diabetes, heart disease, and stroke.
You may wonder how problematic some excess weight is if you're eating a healthy vegan diet. While published research hasn't yet answered this question, there is evidence that healthful lifestyle habits are associated with a significant reduction in mortality for all people, whether of healthy weight, overweight, or obese, with the greatest benefits being observed in obese individuals. Because vegan diets are generally associated with reduced risk of chronic disease, it's understandable that overweight and obese vegans would enjoy some health advantages compared to overweight and obese omnivores. However, vegans who eat a lot of refined grains and processed foods with added fat, sugar, and salt will assuredly fare worse than health-conscious meat eaters.
### Healthy Body Weight
Not all people of the same height will have the same ideal weight, despite widely held beliefs to the contrary. Healthy weight depends on bone structure, muscle mass, body fat, and build. However, the following definitions, along with body mass index (BMI; outlined in table 9.1), can be helpful in determining if a person is overweight or obese.
"Overweight" is generally defined as weighing at least 10 percent more than healthy body weight. For most people, that amounts to 10 to 30 pounds more than their healthy weight. "Obese" is generally defined as weighing at least 20 percent more than healthy body weight. For most people, that amounts to 30 or more pounds above their healthy weight.
The best way to know if your weight is within a healthy range is to determine how much of your body weight is fat. A simple tool called body mass index (BMI) is commonly suggested for estimating this. As shown in table 9.1 (page 166), a BMI of 18.5 to 24.9 is in the healthy range. A BMI below 18.5 is deemed underweight, and a BMI of 25 to 29.9 is considered overweight. Obesity is generally defined as a BMI equal to or greater than 30, with a BMI of 35 or higher being severe and a BMI of 40 or more being extreme.
While BMI is a useful tool for most people, it has several significant limitations. First and foremost, it doesn't take into account differences in body composition between genders and among races, ethnic groups, or those of different ages. In addition, it's only considered to be valid for people twenty to sixty-five years old, is less precise for people less than 5 feet (1.5 meters) tall, and is of little value to bodybuilders or other people with extremely large muscles. It isn't applicable to pregnant women.
### What Your Body Shape Means
Once you've figured out your BMI and have a general idea of your degree of body fat, there's one more important factor to consider: your body shape. The most common descriptors of body shape are apple and pear. If you carry the bulk of your weight above your hips (mainly in your abdomen), you have an apple shape. People who are apple shaped sometimes have a larger waist than hips. If you have an apple shape, when you gain weight, it tends to go directly to your stomach. This body shape is more prevalent in men.
If you carry excess weight in your hips, thighs, and buttocks, you have a pear shape. People who are pear shaped generally have larger hips than waist. This body shape is more common in women.
You also can easily determine whether you have an apple or pear shape by calculating your waist to hip ratio. Simply measure your waist and hips and divide your waist measurement by your hip measurement. Ratios of 0.8 or less for women and 0.9 or less for men are considered a pear shape.
Whether you have an apple or pear shape only matters if you're carrying excess weight. If you're overweight or obese, having an apple shape puts you at much higher risk for heart disease, type 2 diabetes, hypertension, and several types of cancer. For those who naturally become apple shaped with weight gain, it's critically important to maintain a healthy body weight.
TABLE 9.1. Body mass index (BMI)
**UNDERSTANDING YOUR BMI**
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BMI less than 18.5: May indicate underweight | BMI 30–34.9: Indicates class 1 obesity
BMI 18.5–24.9: Healthy weight for most people. | BMI 35–39.9: Indicates class 2 or severe obesity
BMI 25–29.9: Indicates overweight | BMI 40 or more: Indicates class 3 or extreme obesity
There's another way to determine whether you're carrying excess weight. Simply measure your waist. A measurement greater than 32 inches (81 cm) for women and 37 inches (94 cm) for men suggests that you shouldn't gain any weight. A measurement of 35 inches (89 cm) for women and 40 inches (102 cm) for men indicates that you're overweight and weight loss could improve your health. (Note that these numbers would need to be adjusted for people with very large or very small frames.)
Being overweight or obese isn't something many people aspire to or would choose. So why are so many Americans overweight or obese? And why aren't kale-eating vegans entirely protected from this fate? Let's take a look.
### The Root of the Weight Crisis
Everyone knows that overeating and insufficient activity are at the root of the obesity epidemic. It's clearly a matter of energy balance. If you eat more than you need, you gain weight. If you eat less than you need, you lose weight.
While it sounds so simple, there are a number of factors that can throw a monkey wrench into the energy-in/energy-out theory. For years, the accepted axiom regarding weight loss was that 1 pound (0.45 kg) of fat contains 3,500 calories. So if you wanted to lose 1 pound (0.45 kg) of fat per week, you needed to decrease food intake by 3,500 calories, increase energy output by 3,500 calories, or do some combination of the two. While this works beautifully on paper, real-life results aren't nearly as predictable.
The human body is a remarkably adaptable machine, and when survival is at stake, it hangs on to energy reserves for dear life. Therefore, the 3,500-calorie rule may overestimate weight loss for most people. For example, if you cut out 500 calories per day, you might lose 1 pound (0.45 kg) per week for a few weeks, but your body would quickly adjust to the new reality and weight loss would slow or stop.
There's tremendous individual variability in this process. Two people eating the same diet and exercising the same can lose (or gain) weight at very different rates. As it turns out, for a given energy deficit (less calories consumed than used), adults with greater fat reserves can expect to lose more weight than those with fewer fat reserves. Still, even though weight loss may not be as rapid as would be expected based on the 3,500-calorie formula, small changes in energy intake can result in significant weight loss over time.
The long-held view that all calories are equal has also recently come under fire. Evidence suggests that not all calories behave the same way in the body and that some foods and food combinations promote calorie burning more effectively than others.
In addition, sleep, stress, and exposure to environmental toxins can disturb hormones that influence the storage and breakdown of fat, calorie burning, and body weight. All of these factors can weigh as heavily on vegans as nonvegans. The bottom line is, while it's true that overweight and obesity are the result of energy imbalances, the degree of imbalance is the product of a complex interplay of physical, environmental, and emotional factors.
#### **PHYSIOLOGICAL FACTORS**
Some people seem to gain weight simply by inhaling too deeply as they pass a bakery, while others can apparently devour an entire loaf of bread as an appetizer and not gain an ounce. If you fit into the former category, you might be described as metabolically efficient. Dropped on a desert island with no food, your body would preserve your fat and release its stored energy slowly to prolong your survival. The good news is that you'd probably last for weeks. The bad news is that in today's world, you're far more likely to be faced with an endless supply of energy-dense food beckoning you throughout the day. While humans are naturally drawn to this level of security, it commonly leads to weight gain and increased risk of many diseases. Those who are best able to survive famine are least able to thrive with excess. For such people, moderate food intake and vigorous physical activity are necessary.
Not surprisingly, risk of being overweight can be affected by genes, age, and gender. Men tend to burn more calories than women, and for most people, metabolism gradually declines after age forty. Very low-calorie diets and yo-yo dieting only make matters worse, as they send a strong signal to put on the metabolic brakes and conserve precious energy stores.
Less commonly, overweight and obesity can be triggered by hypothyroidism. Hypothyroidism lowers metabolic rate, triggers weight gain, and often makes people feel cold, tired, weak, and depressed. This condition can be triggered or worsened by chronic iodine deficiency, which is rare in North America due to the addition of iodine to table salt. However, those who use mostly natural, noniodized salt are at higher risk. (For more on iodine, see page 135.)
Finally, corticosteroids, antidepressants, and antiseizure medications can slow metabolism, increase appetite, or cause water retention, all of which can lead to weight gain. (Of course, if you're taking such medications, the underlying condition may be a greater health threat than excess weight. In any event, please don't discontinue these medications without the approval and guidance of your health care provider.)
#### **ENVIRONMENTAL FACTORS**
The United States is an ideal environment for overweight and obesity. Food choices are perhaps more diverse than anywhere on the planet, and food is abundant and accessible at home, at work, and everywhere in between. Unfortunately, all too often an American meal is a heaping plate of nutritionally depleted processed or fast food, loaded with fat, salt, and sugar.
Humans are hardwired to like the flavors of fat, sugar, and salt. These flavors, which are highly diluted in nature, once gave us assurance that food was safe and nourishing. But when these flavors are concentrated in processed foods such as sodas, hot fudge sundaes, double cheeseburgers, stuffed-crust pizzas, and deep-fried doughnuts, the results are disastrous. Our innate ability to control appetite becomes unhinged because foods that contain concentrated sugar, fat, and salt are physically addictive, stimulating the same pleasure centers in the brain as heroin, nicotine, and alcohol. Essentially, they provide so much pleasure that they trigger cravings. And don't fool yourself: vegan versions of such foods can be just as problematic.
Another challenge is that portion sizes keep expanding. According to the Centers for Disease Control and Prevention, the average restaurant meal is four times larger than it was in the 1950s. A serving of soda has shot up from 7 fluid ounces (210 ml) to 42 fluid ounces (1.25 L). A serving of French fries, which once was 2.4 ounces (68 g) is now 6.7 ounces (190 g). And whereas a typical burger used to be just 3.9 ounces (111 g), it is now 12 ounces (340 g). No wonder the average adult is 26 pounds (11.8 kg) heavier than sixty years ago! Not surprisingly, as portion sizes increase, people—vegan or not—eat more.
Vegan versions of almost every convenience food, snack food, and fast food are now yours for the taking. Today, the word _vegan_ is used to provide products with a halo of health. Don't be fooled. Just because the word _vegan_ is plastered on a label doesn't guarantee that a product is good for you, nor do labels of "low-calorie," "low-fat," "low-sugar," or "low" anything.
Further compounding the problem, the level of physical activity necessary in much of the world has dwindled dramatically in recent decades. Increasing numbers of people work in offices, and most drive or take public transit to and from work. Even if people want to increase their activity level, many neighborhoods lack sidewalks and safe places for outdoor exercise. People tend to devote their spare time to watching television, playing video games, surfing the Internet, and other passive activities. In addition, every possible convenience has been developed to help reduce energy expenditure: elevators, escalators, remote controls, electric mixers, bread machines, dishwashers, and even electric can openers.
Another potential trigger for weight gain—one that's less well recognized—is lack of sleep. While you might assume that less sleep means greater expenditure of calories, evidence suggests that lack of sleep promotes weight gain. This may be because people who are sleep deprived are attracted to more energy-dense foods, which can lead to overeating and weight gain. In addition, studies indicate that lack of sleep reduces insulin sensitivity, increases levels of ghrelin, a hormone that promotes hunger, and reduces levels of leptin, a hormone that curbs hunger.
### A Permanent Solution
The weight-loss industry has a remarkable track record for peddling promises, marketing miracles, and delivering disappointment. Diets are generally designed to produce a calorie deficit or ensure that people take in fewer calories than they burn so they'll lose weight. Most succeed in this task.
So, if most diets succeed in producing weight loss, why do so many fail in the long run? The answer is simple: they end. If you don't have a plan for lifelong dietary and lifestyle changes, old habits return, and with them the weight. Unfortunately, in many cases, the deprivation of a diet pushes the body into conservation mode, sending metabolism into a nosedive. As a result, you may not just regain the lost weight, but also pack on a few extra pounds. This is your body's attempt to effectively prepare for the next famine.
Weight-loss diets are generally a lesson in frustration, but this doesn't mean you have to give up on weight loss. You just need to find a more effective long-term solution. Three simple steps will help you redirect your goals so weight loss becomes a by-product of bigger and better things: make health your goal, think positively, and build healthful habits.
#### **STEP 1: MAKE HEALTH YOUR GOAL**
Dump the dieter's mentality of thinness at all costs and redirect your focus to health. Make it your top priority. The ultimate test of anything that promises to peel off pounds is one simple question: Does it support and promote optimal health? If the answer is yes, it has passed the litmus test and will be a useful ally. If the answer is no, don't even give it a second thought. If it compromises health, it's worse than useless.
Every single cell of your body is a product of the food you put in your mouth; food provides the body's basic structural materials. Resist the urge to select foods on the basis of their caloric content or perceived effectiveness as diet foods. Instead, select foods on the basis of their ability to nourish and protect your body. Before you bite into a sugar-free diet cookie made with white flour, partially hydrogenated vegetable oil, and artificial sweeteners, ask yourself whether those are the best materials for rebuilding your brain cells, or any other cells for that matter. Keep your eyes squarely on the goal.
Establish an environment that will effectively reset your metabolic machinery. Do what you can to calm inflammation and minimize your exposure to toxins (more on how these factors affect weight shortly). This will help ensure that the hormones that affect hunger, metabolism, and weight aren't compromised.
#### **STEP 2: THINK POSITIVELY**
Hold on to your dreams. No matter how far away they might seem, know that every step you take in the right direction is worth celebrating. Being on the right path, even if just inching your way to your goal, is more important than where you are on that path. Listen carefully to your body. It communicates with you constantly and honestly. Let it guide you as you gradually reclaim your health.
Fear of failure is often the greatest stumbling block, breeding negative thoughts that can effectively crush your spirit. In this journey, there are no reprisals or exams. There's nothing to fear. Take on only what you're ready and able to take on. Push out any negative thoughts with positive affirmations. Remind yourself that you will achieve what you've set your sights on and that nothing anyone else does or says can extinguish your enthusiasm.
As you work to develop positive habits, be prepared for stumbling blocks and resistance. Don't beat yourself up when things don't go according to plan. Instead, use each disappointment as a valuable lesson about what works and what doesn't.
#### **STEP 3: BUILD HEALTHFUL HABITS**
One of the greatest challenges in the quest for wellness is to break old, destructive habits and replace them with habits that truly support and promote health. Many repetitions are required to transform a behavior into a habit.
Bad habits are hard to break because they arise to fill a need. Identify that need and consider the costs and benefits of using the habit to fill that need. You may find it helpful to keep a log for a couple of weeks to make you more conscious of your behavior. If a habit doesn't serve you, it's time to replace it with something that does. Fill the need with anything that will improve your well-being and make you feel better about yourself. For example, if your diet descends into the abyss of junk food while watching television after dinner, fill your evenings with television-free activities. Create a new routine and follow it faithfully for a set period of time. One month is a good goal. If you set a time frame for yourself, it makes sticking to the routine a little easier. Once you've repeated a behavior for a month, you're well on your way to turning it into a new habit. To make your plan foolproof, be sure to surround yourself with a network of supportive friends and family.
### Preparing for the Journey
The following guidelines will help ensure your success in the journey to freedom from excess pounds and the related risk of chronic diseases.
**Get a physical exam.** Have testing done to determine your blood pressure and levels of thyroid hormones, cholesterol, triglycerides, blood sugar, vitamin B12, vitamin D, iron, and CRP (measure of inflammation). If you're on prescription medications, make sure your health care provider knows about your new health plan. As you regain your health, it's important to closely monitor your condition, as you may need to reduce or eliminate certain medications (with the guidance of your health care provider).
**Keep a three-day food and activity diary.** Keep track of everything you eat and drink for three full days. (Excellent online sites and apps can assist you in this task.) Try to include at least one weekend day. Include the following information:
* Type and amount of food consumed
* Time of day you ate
* Where you ate
* Preparation method used
* Reason for selecting the food
* Degree of physical hunger on a scale of 0 to 5 (0 being not hungry and 5 being famished)
* How you felt before eating the food
* How you felt after eating the food
In addition, note all of your activities, from gardening to grocery shopping. Include any exercise or other fitness activities and be specific about duration. Keep track of your sleeping patterns: when and where you slept, how long, and how well. Also note anything you did to take care of yourself, such as getting a massage or pedicure, prayer time, meditation, or enjoyable social activities. Finally, record of all addictive substances you used, such as cigarettes, alcohol, or recreational drugs. Simply writing these things down provides a powerful reality check.
**Set both short-term and long-term health goals.** When setting goals, be specific. They should be measurable and attainable. The primary focus shouldn't be weight loss, but rather improving your fitness level, increasing your fiber intake, eating more leafy greens, reducing your cholesterol level, and so on. Tackle goals one at a time, so you don't feel overwhelmed. Even small changes can produce big health rewards.
**Deliver yourself from temptation.** Get rid of unhealthful foods and beverages that tempt you. You don't need that kind of pressure. Take them to a food bank or homeless shelter, give them away, or throw them out. If others in your household don't want you to give these things away, explain what you're doing and why, and respectfully request their support. Be sure to express gratitude for whatever sacrifices they are willing to make.
**Restock your pantry.** Eating healthfully isn't about deprivation. Highly healthful food can be more delicious than the unhealthy food it's replacing. Go shopping for items that meet your new standards. Select recipes that you'd like to try, and gather all the ingredients required. Consider investing in some high-quality food preparation equipment if you can.
**Take a few steps outside your comfort zone.** If you've been eating a lot of junk food or fast food, you may need to learn how to prepare healthful food. Begin by making a few simple meals. Try at least one new recipe every day or two, even if it's just a salad dressing. Experiment with dehydrating, juicing, or sprouting or soaking beans and nuts.
### Reclaiming Your Health
No one else can achieve health for you. No doctor or dietitian can eat for you, exercise for you, or manage stress for you. You hold the power to transform your life and reclaim your health. Becoming vegan is an extraordinary first step. The next step is becoming a truly healthy vegan.
Before we discuss specific food choices, we think it will be helpful for you to understand why you need to make the recommended changes. Dietary choices that work against your body can compromise all body systems. While you may feel as though your body is failing you, there's a good chance that you're failing your body. Your body depends on your dietary choices for survival. Below are six health goals, each of which will help explain why food choices recommended later in this chapter are necessary.
#### **OVERCOME FOOD ADDICTIONS AND CRAVINGS**
Although it sounds a little extreme, we encourage you to think of ultraprocessed foods laden with fat, sugar, or salt as drugs. To break your addiction, you have to stop eating them. While breaking a food addiction isn't easy, replacing addictive foods with foods that are of real value to your health has amazing results. Your body can restore its balance and free you from the addiction. When you reach this point, cravings are far less likely, and your body will also be better able to handle the occasional addictive food.
To overcome a food addiction, you need to keep your blood sugar levels stable. Eat meals containing a good balance of protein, carbohydrate, and fat. For example, if you eat cereal for breakfast, top it with nuts and seeds. Use unsweetened nondairy milk. Eat legumes, tofu, or tempeh at lunch and dinner. Consider including legumes at breakfast to give you staying power through the morning. Avoid caloric beverages, sugar, and artificial sweeteners. Eliminate deep-fried foods. Steer clear of ultraprocessed foods. Also be aware of any food allergies, which are one of the less well-recognized causes of cravings. Ironically, people often crave the very foods they're allergic to, and for growing numbers of people, wheat or gluten seems to be an issue.
#### **CONTROL INFLAMMATION**
Inflammation is one of the key forces behind overweight, obesity, insulin resistance, diabetes, heart disease, dementia, and just about every other chronic disease. Dietary factors can generate inflammation in many ways. Overweight can trigger inflammation. Healthy fat cells produce a balance of proinflammatory and anti-inflammatory hormones. When fat cells become overfilled with fat, production of proinflammatory hormones increases, while production of anti-inflammatory hormones decreases. This imbalance promotes insulin resistance.
Other common contributors to inflammation are food sensitivities and allergies. Once again, gluten can be especially problematic. Environmental contaminants, chronic stress, and deficiencies of certain nutrients, particularly vitamin D and omega-3 fatty acids, can also promote inflammation. Fortunately, the abundant vegetables, fruits, legumes, whole grains, nuts, seeds, herbs, and spices in a whole-foods, high-fiber, plant-based diet don't just help prevent overweight and obesity; they also provide an array of anti-inflammatory compounds.
#### **IMPROVE DIGESTION**
An unhealthy gut can contribute to obesity and disease. There are two key issues here: leaky gut syndrome and bacterial imbalance in the intestinal tract. We'll address this issue briefly here; for more information, see "Food Sensitivities" on page 152.
The foods most commonly associated with leaky gut syndrome are gluten-containing grains (wheat, spelt, Kamut, rye, barley, and triticale), dairy products, and ultraprocessed, packaged convenience foods such as sugar and highly refined flour.
There's no question that good food feeds good bacteria and bad food feeds bad bacteria. Low-fat, high-fiber diets with plenty of vegetables help keep gut-healthy bacteria flourishing. High-quality probiotic products can help reestablish a healthy gut flora.
#### **AVOID TOXINS**
There is increasing awareness of a connection between accumulation of body fat and environmental contaminants such as BPA, heavy metals, persistent organic pollutants, and pesticides. While you can't completely eliminate your exposure to these compounds, you can minimize it. You can also reinforce the body systems that help neutralize and excrete these compounds.
Fortunately, vegans may be at an advantage on both counts. Animal products, including fish, are high on the food chain, so they contain higher concentrations of environmental toxins. These are, of course, not included in vegan diets. Eating organic foods whenever possible will further reduce exposure. Vegans also tend to eat a lot of cruciferous vegetables (broccoli, cabbage, cauliflower, and the like), which are rich in phytochemicals that support detoxification. Numerous vitamins, minerals, amino acids, phytochemicals, and antioxidants play a role in this process, so good nutritional status is important.
#### **ENHANCE YOUR NUTRITIONAL STATUS**
Although vegans tend to eat more nutrient-rich vegetables and fruits and have higher intakes of fiber and many phytochemicals, antioxidants, and other nutrients, shortfalls are not uncommon. Even if you think you're doing everything right, when you limit calories in an effort to lose weight, you can easily miss out on nutrients, particularly vitamin B12, vitamin D, and iodine. In addition, it's important to make sure you're getting enough protein, iron, zinc, calcium, magnesium, and selenium. Follow the vegan food guide, and if your diet still falls short, take supplements to meet your needs. (See chapters 3, , and for details.)
When cutting back on calories, focus on eating foods with a lot of nutrients per calorie. The best choices are vegetables (especially leafy greens), legumes, fruits, nuts, seeds, and intact whole grains (rather than grains that have been processed or ground into flour). When you fuel your body with high-quality, organic, whole plant foods, it shifts gene expression, reducing your risk for over-weight, obesity, and chronic disease.
#### **BALANCE HORMONES AND BOOST METABOLISM**
Boosting metabolism is the holy grail of seekers of slimness everywhere, but how fast your body burns calories depends on numerous factors. Optimal health and metabolism are highly dependent on the functioning of the many systems that produce and release hormones, including thyroid and stress hormones.
Thyroid hormones control metabolism and can have a significant impact on body weight. Vegans, especially those who avoid iodized salt, sea vegetables, and supplements can be low in iodine, which is needed in the production of thyroid hormones. Insufficient selenium and vitamin D can also adversely affect thyroid function.
Cortisol is a hormone that helps deliver the appropriate type and quantity of carbohydrate, fat, and protein to body tissues. Under chronic stress or calorie deprivation, cortisol levels rise and fat is shuttled into fat deposits in the abdomen. Called visceral fat, these deposits are associated with insulin resistance. Elevated cortisol is also associated with increased appetite and cravings for fat and sugar.
The keys to balancing all of these hormones and boosting metabolism is to consume a whole-foods, nutrient-dense, plant-based diet that emphasizes foods with a low glycemic load, take supplements if needed, manage stress, and get enough physical activity.
### Getting Healthy
So far in this chapter, you've learned about the roots of the overweight and obesity crisis and about the essential steps required to achieve and maintain a healthy body weight for life. Now, let's turn our attention to designing a delicious vegan diet that supports you in this process.
#### **EAT AT LEAST SIX SERVINGS OF NONSTARCHY VEGETABLES DAILY**
One serving is 1 cup (250 ml) of raw vegetables or ½ cup (125 ml) cooked. In their natural state, vegetables are the most nutrient-dense foods on the planet. Aim for every color of the rainbow: at least three servings of green vegetables, including dark leafy greens, and at least one each of red, orange-yellow, purple-blue, and white-beige each day. Eat a variety of raw vegetables daily. Cooked vegetables are most nutritious when lightly steamed rather than boiled. Limit serving sizes of starchy vegetables, such as sweet potatoes and corn, to no more than ½ cup (125 ml) once or twice a day.
#### **LEARN TO LOVE LEGUMES**
Beans, lentils, and peas are the powerhouses of the plant kingdom when it comes to protein, iron, and zinc. They are also among the richest sources of fiber, which contribute to satiety and provide staying power between meals. Lentils, split peas, or fresh peas (in or out of the pod) are great choices for people trying to slim down because they are extremely low in fat but high in nutrients and fiber. Lentils, mung beans, and dried peas are the best legumes for sprouting. Tofu and tempeh, which are made from soybeans, are also nutrient-rich choices.
Eat at least three ½-cup (125 ml) servings of legumes per day. In addition to beans, peas and lentils, options include tofu, tempeh, unsweetened soy milk, some protein powders, and some vegan meats. If need be, begin with smaller servings and gradually increase portion sizes over a couple of weeks to give your body time to adjust to the increased fiber intake. Add beans to stews, soups, and salads or use them to make patties, loaves, and spreads.
#### GO EASY ON GRAINS
Once you've met the recommended number of servings for vegetables, fruits, legumes, and nuts and seeds (see chapter 14 for details), add grains to meet your energy needs. As your calorie needs decrease (for example, as a result of aging, menopause, reduced physical activity, and so on), decrease your consumption of grains. Most people trying to lose weight should limit grains to not more than ½ cup (125 ml) per meal, but people with higher energy needs can afford to include more grains in their diets.
Focus on intact whole grains, such as quinoa, wild rice, buckwheat, oat groats, and barley. One of the most healthful ways to prepare grains is to sprout them. Add sprouted grains to salads or use them as breakfast cereal. (Add them to a bowl of fruit and nondairy yogurt and top with seeds.) Cut and rolled grains are also options, although they are less desirable than intact whole grains because processing them damages or destroys some of their nutrients. Because each stage of processing further diminishes nutrients and increases impact on blood sugar, it's best to minimize consumption of all types of ground grains and flour, even if they are whole-grain. This includes most whole-grain breads, crackers, pretzels, cookies, and other baked goods. Completely avoid highly refined grains, such as white rice and products made with white flour. Also avoid processed cereals with added sugar and salt.
If you're avoiding foods that contain gluten, don't substitute packaged gluten-free foods made with processed, refined ingredients. Instead, use gluten-free whole foods, such as cooked quinoa, millet, brown rice, wild rice, or buckwheat.
#### SATISFY YOUR SWEET TOOTH WITH FRESH FRUIT
Fruit is nature's candy—with the added bonus of vitamins, antioxidants, and fiber. Eat all of the edible parts of fruit, including skins and seeds, which often contain the highest amounts of fiber and phytochemicals.
While it may take time to get used to thinking of a piece of fruit as dessert, there are ways to make it more appealing. Simply slicing fruit and arranging it creatively on a plate makes it seem special. Make a fruit salad and top it with a bit of plain nondairy yogurt. For a delectable frozen dessert, process frozen berries, peeled bananas, and cubed pineapple and mango in a blender, food processor, or juicer until smooth. Alternatively, put frozen fruit in a blender with a little nondairy milk or yogurt and process until very smooth.
If you have high blood sugar, limit fruit to three or four servings per day. One serving is 1 cup (250 ml) of fresh fruit, 1 medium fruit, or ½ cup (125 ml) of fruit juice or cooked fruit. Limit dried fruit to ¼ cup (60 ml) per day since it's very high in natural sugars.
#### GET FATS FROM NUTS, SEEDS, AND AVOCADOS
Although nuts, seeds, and avocados are high in fat and packed with calories, they are unexpected weight-loss allies. They are loaded with phytochemicals, plant sterols, and healthy fats, and because they contain a lot of fiber, they're also highly satisfying. Still, portion sizes are important. Reasonable daily intakes for weight loss are half of a small avocado and 1 to 2 ounces (30 to 60 g) of nuts and seeds. Consuming a mixture of chia seeds, flaxseeds, hempseeds, and walnuts will ensure a good balance of essential fatty acids. Include one or two Brazil nuts to boost selenium. Soaking nuts and seeds reduces compounds that interfere with absorption of nutrients, increasing their nutritional value.
#### MAKE THE MOST OF HERBS AND SPICES
Herbs and spices are health heroes. Not only do they make foods taste better, they do so without adding sodium or fat. Several herbs and spices have shown promise as weight-loss allies due to their ability to boost metabolism, calm inflammation, or balance blood sugar levels. Among these spicy superstars are black pepper, cardamom, cayenne, cinnamon, cloves, cumin, ginger, mustard seeds, oregano, rosemary, and turmeric. Grow your own herbs on a windowsill. Most are hardy plants that may produce year-round. Herbs can also be frozen or dehydrated for later use.
#### LIMIT PROCESSED AND CONVENIENCE FOODS
Throughout this book, we've talked about how processed, convenience foods are at the bottom of the barrel when it comes to supporting health. Not all processed foods are bad news, however. Good choices include frozen herbs, low-sodium canned beans in BPA-free cans, frozen shelled edamame, some sprouted breads, organic fruit and nut bars, and some jarred tomato sauces. Read the ingredient list; if you can't pronounce the ingredients, it quite possibly isn't real food.
#### MINIMIZE CONCENTRATED SWEETENERS AND AVOID ARTIFICIAL SWEETENERS
Whether sugar comes from high-fructose corn syrup or organic dehydrated cane juice is less important than the _amount_ of sugar you eat. Regardless of the source, sugar is sugar, and it's full of empty calories.
Avoid artificial sweeteners. They won't assist you in your quest for health, and they may negatively affect metabolism and appetite control. If you must sweeten your coffee or tea, using stevia would be a reasonable option. (For more information, see "Are Sugar Substitutes Safe?" on page 96.)
#### LIMIT FATS AND AVOID PARTIALLY HYDROGENATED OILS
Although fats and oils are extracted from whole foods, processing strips them of fiber, minerals, phytochemicals, and even fat-soluble vitamins. It's best to use them sparingly. Fats and oils contain about 120 calories per tablespoon (15 ml), and per weight, they contain about 2.5 times more calories than protein or carbohydrates. Avoid margarines and other foods containing partially hydrogenated fats and oils, as they contain trans fats, which are strongly linked to many health conditions, including insulin resistance.
Mechanically pressed oils (preferably organic) are the best choices, being rich in essential fatty acids. However, they shouldn't be used for cooking because they are damaged by heat. If you use other oils, 1 tablespoon (15 ml) is the upper limit if you're trying to lose weight, and less is better.
#### AVOID SNACKING
Cut out snacks unless you're genuinely hungry. If you do snack, stick to raw vegetables, raw fruits, legumes, nuts, or seeds. Other acceptable snacks include plain popcorn and seasoned sea vegetable snacks.
#### RELY ON WATER
Water is the best thirst quencher, and it's calorie-free. If possible, use a filter that eliminates chlorine, lead, nitrates, microorganisms, and other environmental contaminants without removing minerals such as calcium and magnesium.
Herbal teas can also be healthful choices, and green tea has been shown to slightly boost metabolism and may aid in weight loss. For added nutrition with minimal calories, vegetable juice (especially green juices or tomato juice) or wheat grass juice are good options. If you want something sweet to drink, try sparkling water with a splash of pure fruit juice or have a sweet herbal tea, such as apple cinnamon.
While some beverages are good sources of nutrients, you're generally better off getting those nutrients from whole foods because they provide greater satiety, which is so helpful in weight management. If you consume nutritious higher-calorie beverages such as fresh fruit juices, fruit smoothies, and nondairy milks, think of them as food rather than drinks. They often contain 100 to 150 calories per cup (250 ml). Smoothies made from a combination of fruit, greens, and seeds, with 400 to 500 calories per 3-cup (750 ml) serving, can be healthful meal replacements, but if you use them in this way, limit it to one per day.
Beware of most other beverages. It's easy to underestimate their contribution to calories. For example, 12 fluid ounces (375 ml) of lemonade, fruit punch, or soda contains 120 to 150 calories and has little or no nutritional value; 12 fluid ounces (375 ml) of beer contains 110 to 170 calories; 1½ fluid ounces (45 ml) of distilled spirits has about 110 calories; 1½ fluid ounces (45 ml) of liqueur has 150 to 190 calories; and 4 fluid ounces (125 ml) of wine has about 80 calories. Of course, these numbers don't include any added cocktail mixes.
_Are Weight-Loss Aids Helpful?_
Weight-loss aids are designed to block the absorption of fat or carbohydrate, stimulate thermogenesis (fuel burning), increase metabolism, or suppress appetite. Research hasn't shown them to be particularly effective. Those containing stimulants, such as caffeine, ephedrine, and synephrine, can cause insomnia, irritability, restlessness, anxiety, and, in the long term, dependency and exhaustion. It's best to avoid them. Some food-based supplements, such as green tea or green tea extract and certain types of food fiber may help prevent weight gain over time and are relatively safe. Weight-loss aids are unnecessary, but if you want to use one, stick with food-based products that support health.
Also avoid calorie-free beverages containing artificial sweeteners. They can confuse your appetite control center and metabolic hormones and are of no value to health.
### Making the Most of Your Menu
Simple menus to get you started can be found in chapter 14, including a basic 1,600-calorie menu and a 2,000-calorie menu. These menus can be adjusted to suit your energy needs and food preferences. Most people should eat at least 1,600 calories per day (or 1,400 calories for those who are very small) because it can be difficult to meet all of your nutritional requirements on fewer calories.
Very low-calorie diets can also trigger the body to slam on the brakes on metabolism, making it even more difficult to shed unwanted pounds. The 1,600-calorie diet menu on page 269 provides a reasonable blueprint for most people with weight-loss goals. The 2,000-calorie diet on page 270 may be more appropriate for active individuals or larger men.
To enhance the nutritional, hormonal, and metabolic advantages of these basic diets, here are a few practical tips:
* Add extra greens or other nonstarchy vegetables, including sprouts.
* Be generous with herbs and spices such as turmeric, ginger, and garlic.
* Substitute green tea for coffee.
* Choose higher-fiber fruits, such as berries, apples, pears, and figs.
* Use unsweetened fortified nondairy milks, such as plain soy or rice milks, instead of sweetened or flavored varieties.
* When using tofu, pick a brand that's high in calcium.
* Select breads made with sprouted grains or higher-fiber breads. Better yet, substitute whole grains for bread.
* Eat fruit instead of drinking fruit juice.
* Drink plenty of water.
* Consider nutritional supplements. For most people, reasonable additions include 1,000 mcg of vitamin B12 twice a week, daily supplementation with 25 mcg (1,000 IU) of vitamin D and 150 mcg of iodine, and a high-potency probiotic taken daily for two weeks and twice weekly thereafter.
### Beyond Food
Losing weight involves more than simply restricting food intake. Certain lifestyle changes go hand in hand with a good diet to improve your health and support your efforts to achieve and maintain a healthful weight:
#### LET THE SUN SHINE IN
Strive for thirty to sixty minutes of fresh air and sunshine a day. Sunshine helps the body manufacture vitamin D and may benefit the body in other ways that haven't yet been identified. There's no doubt that the sun's rays have healing powers for both the body and soul. (For more on vitamin D, see page 104.)
#### MAKE EXERCISE A PRIORITY
Plan to exercise daily or at least five days a week, for forty-five to sixty minutes per day. The best exercise for you depends on your age, current fitness level, state of health, and personal preferences. (For more details on types of exercise and designing an exercise program, see chapter 13).
If you haven't exercised in a long time, begin with walking or an activity that you're comfortable with. Start with ten to fifteen minutes of walking two or three times a day and increase the duration gradually. As you get stronger, incorporate a balance of cardio, strength, and flexibility exercises in your program. The best choice for burning calories and for overall health is moderate aerobic activity, such as brisk walking, combined with resistance training, such as working out with light weights. Be sure to stretch well after working out. Consider adding focused stretching routines, such as yoga or Pilates, into the mix.
Ultimately, it's best to include a wide variety of activities in your exercise program: walking, jogging, biking, swimming, hiking, yoga, racket sports, aerobics classes, and so on. The more you vary the intensity, duration, and type of activity, the more fit you'll become. Also be sure to choose activities you enjoy, as you'll be far more likely to stick with them.
Try to do something physical after eating. This is one of the most effective changes you can make, because muscles at work quickly use up circulating sugar, avoiding an insulin surge. This prevents excess blood sugar from being stored as fat and keeps sugars from damaging body tissues. There's some wisdom in the old Chinese saying "Walk one hundred steps after dinner, and you'll live to be ninety-nine years old."
Also increase your activity level in general, not just through exercise. Every physical movement you make helps increase your energy expenditure. For example, gardening, walking while shopping or at work, grating carrots, cleaning the house, making your bed, bathing your dog, and so on. In fact, this type of activity can make a bigger difference in your energy expenditure than exercise. Take full advantage of every opportunity you have to move your body, especially if you have to sit much of the day.
#### GET ADEQUATE SLEEP
Insufficient sleep can result in weight gain, compromise physical and mental performance, and contribute to death and disease. Requirements for sleep vary with age, gender, lifestyle, stress, and even genetics. If you wake up spontaneously and feel refreshed and alert for the whole day, you've had a good sleep. For most adults, this requires seven to eight hours of sleep, but some people require as little as six hours, while others need nine hours. Listen to your body.
Sleeping well requires adequate preparation. Doing activities that calm and soothe you just before bedtime, such as taking a warm bath or reading, can help. (Watching the late news while sipping on an espresso probably doesn't fall into this category!) Set a regular bedtime and stick to it as much as possible. It's important that your bedroom be free of light and noise. If your neighborhood is noisy or brightly lit at night, consider investing in an eye mask, light-blocking window shades, or earplugs. Do whatever you can to make your sleeping environment peaceful and inviting.
#### MANAGE STRESS
While stress is normal and even potentially beneficial, ongoing severe stress can wreak havoc with your immune system, trigger mindless or binge eating, and increase the risk of death and disease. Incorporating stress management techniques into your daily routine will increase your ability to handle excess stress when it arises. A healthful vegan diet, exercise, adequate sleep, and getting fresh air and sunshine are all important, but attitude is the trump card when it comes to dealing with stress. For many people, a practice such as prayer, meditation, or yoga can be helpful. Building healthy relationships with friends, family, and colleagues can also help you cope with stress.
#### AVOID ADDICTIVE SUBSTANCES
Alcohol contains about 7 calories per gram—almost twice the amount in carbohydrate or protein—so, not surprisingly, it can be an important contributor to overweight and obesity. Worse, consuming any alcohol at all increases the risk of cancer, and excessive drinking can contribute to high blood pressure, liver disease, impaired immunity, and heart failure.
Of all personal choices, smoking tobacco is thought to be the greatest threat to health. Although smoking slightly increases metabolic rate, that isn't worth dying for. Surprisingly, nicotine also can significantly increase risk of overweight and obesity in infants of mothers who smoked during pregnancy.
Next, we'll discuss the flip side of the weight coin: underweight. In chapter 10, those who need to gain weight will learn how to do so healthfully on a whole-foods vegan diet.
## CHAPTER 10
## Overcoming Underweight
In a world with a burgeoning epidemic of overweight and obesity, being underweight is an anomaly. Yet for those who struggle with being too thin, it can be more challenging to gain a pound than it is for someone who's overweight to lose a pound.
Although underweight affects people of both genders, it's less often considered a problem for women, in whom thinness is prized. Men feel a different sort of pressure around body shape. While low body fat is desirable, being skinny isn't. The goal for men is a buff body, so their quest is to accumulate sufficient muscle.
If you see yourself as underweight, regardless of the reason, rest assured that a vegan diet can help you achieve a healthy body weight. Our goal in this chapter is to help you do that.
### The Downside
About 1.6 percent of Americans are underweight as defined by the World Health Organization and the Centers for Disease Control, having a body mass index (BMI) less than 18.5. (For more on the BMI, see the section "Healthy Body Weight," on page 165, and table 9.1, on page 166.) A BMI of 17 to 18.4 is considered mildly underweight, a BMI of 16 to 16.9 is considered moderate, and a BMI below 16 is considered severe. These values aren't necessarily accurate for everyone. For example, a small-boned person may not be underweight with a BMI of 18, while a large-framed person could be underweight with a BMI of 20.
The number of underweight Americans has steadily declined from about 4 percent in the early 1960s. While comparable statistics for American vegans aren't available, most vegans do have healthy body weights and BMIs in the normal range. In a culture plagued by overweight, they are generally lucky to have lower BMIs and less body fat than lacto-ovo vegetarians or the general population. However, vegans, and particularly raw-food vegans, do seem to experience higher rates of underweight compared to the general population.
While most people would rather be underweight than overweight, being under-weight is also associated with several negative health issues. The most significant is increased mortality. People who are underweight experience higher death rates than normal or overweight individuals but lower rates than obese individuals. Studies suggest a direct relationship between BMI and mortality: as BMI decreases, mortality decreases, right up to the point of being clinically underweight, at which point mortality increases as weight decreases. However, this finding is controversial because there is also evidence suggesting that people with good lifestyle habits who restrict calories live longer. While research is limited, the critical factor appears to be lifestyle and nutritional status. Being underweight is riskiest for people who smoke, are inactive, or eat few fruits and vegetables. On the other hand, the Oxford Vegetarian Study reported increased death rates from all causes except cancer in people with BMIs less than 18. Since it isn't easy to meet needs for all nutrients on low-calorie diets, it makes sense to strive to meet your body's energy needs and avoid being underweight, if possible.
Here are a few other health problems associated with being underweight:
* **Nutritional imbalances.** If you're underweight because you don't get enough calories, you may not be getting all the nutrients you need. This can lead to a weakened immune system and less protection against infection. Deficiency in just one nutrient can impair the immune response, even when the deficiency is mild. In addition, underweight people, particularly women of childbearing age, have a higher risk for iron deficiency, which results in weakness, fatigue, and irritability.
* **Hormonal imbalances.** Being underweight can influence the production and action of hormones in both men and women. In women, low body fat can prevent ovulation and menstruation, reducing fertility. If conception does occur and weight gain is insufficient, the baby is at risk and is more likely to be small for its gestational age. In underweight men, sperm count and semen quality can be significantly reduced.
* **Weakness, fatigue, and reduced muscle mass.** If you don't eat sufficient calories, the body first mobilizes energy from glycogen (the stored form of carbohydrate). When it exhausts its glycogen, it then uses body fat. When those reserves are depleted, it will try to get energy from protein, which decreases muscle mass, leading to weakness and fatigue.
* **Osteoporosis.** Underweight individuals—both men and women—are at risk for bone breakdown and decreased bone density, elevating the risk of osteoporosis.
### Determining Your State of Health
Careful consideration of the following factors will help you determine whether your low body weight poses a health risk and weight gain is warranted. In general, if you lack energy and are weak, often sick, and take a long time to recover, chances are your weight is too low. Of course, it's important to rule out any underlying disease that could be causing these symptoms. On the other hand, if you're generally in good health, energetic, seldom sick, and quick to recover from illness, you may be at a healthy body weight even though your BMI is low.
**Body frame.** If you have a small frame, your BMI may indicate that you're underweight when you actually aren't. For example, a healthy, small-boned woman who is 5 feet 4 inches (1.63 m) tall and weighs 107 pounds (52 kg) has a BMI of 18.4, which is technically underweight. However, considering her bone structure and health status, she's likely at a healthy weight. On the other hand, a large-framed woman may appear to have a healthy weight according to her BMI but actually be underweight. For example, a woman with a large bone structure who's 5 feet 4 inches (1.63 m) tall and weighs 116 pounds (56.4 kg) may be underweight even though her BMI of 20 is well within the healthy range.
**Gender.** Men tend to have larger bones and muscles than women, so at any given height, men generally weigh more than women, even when their body fat is lower. While the BMI ranges are the same for men and women, it's relatively common for men to be underweight when their BMI is between 18.5 and 20—above what is technically classified as underweight.
**Lifestyle.** If you're underweight as a result of unhealthy lifestyle practices such as substance abuse or a poor diet, you could be at risk for disease. However, if you eat a healthy plant-based diet, avoid addictive substances, and engage in regular physical activity, your weight-related health risks would be lower.
### Causes of Underweight
Underweight is relatively rare in populations with abundant food supplies. Technically, underweight is the result of not consuming enough calories for the energy expended, just as overweight is the result of too many calories for the energy expended. However, just as with overweight and obesity, the causes are far more complex than energy-in, energy-out. People become underweight for a variety of reasons, including genetics, illness, medications and other drugs, and psychological factors.
**Genetics.** Just as someone can be genetically predisposed to overweight, it's also possible to be predisposed to underweight. We all know entire families who exhibit "lean genes." If you're underweight and have a high metabolism, you require more food than other people of similar height and weight but still don't seem to gain a pound. Becoming vegan and eliminating high-calorie meat and dairy products may cause weight loss, since you'll replace those foods with others that are generally lower in fat, lower in calories, and higher in fiber. Fortunately, there are simple steps you can take to ensure a healthy weight without consuming animal products (discussed later in this chapter).
**Illness.** Many diseases can cause weight loss or result in being underweight. Gastrointestinal diseases can prevent the absorption and metabolism of foods or trigger chronic diarrhea. Metabolic and hormonal disorders can alter appetite control, metabolic rate, or energy needs, resulting in less hunger, reduced food intake, or rapid burning of calories consumed.
**Medications and chemical dependencies.** Certain medications can cause under-weight, so in a sense, this is another way in which illness can be involved. In addition, drugs, alcohol, and tobacco can reduce appetite, speed metabolism, and compromise energy intake.
**Psychological factors.** Here are some of the more common psychological factors that can contribute to underweight:
* **Depression.** Those who are overwhelmed by depression commonly lose interest in eating and sharing meals with others.
* **Eating disorders**. Anorexia nervosa results in significant, sustained, and often severe weight loss. (For an in-depth look at eating disorders, see _Becoming Vegan: Comprehensive Edition_ , by B. Davis and V. Melina, Book Publishing Company, 2014.)
* **Stress.** While some people respond to stress, anxiety, and other forms of psychological pain by eating, others have a diminished appetite and avoid food.
* **Cultural pressure.** Our society promotes thinness, especially in women. This reinforces eating behaviors that promote restrictive eating, such as skipping meals or curbing appetite by smoking, gum chewing, or other means.
* **Abuse.** One consequence of physical or emotional abuse can be withdrawal and a subconscious effort to occupy as little space as possible—to become invisible. One way to achieve that is to become as thin as possible.
#### OTHER FACTORS
* **Habits.** Skipping meals, avoiding between-meal snacks, avoiding higher-fat foods, and restricting portion sizes can all lead to insufficient intake of calories, especially in those with a high metabolic rate.
* **Hunger.** Worldwide, the most common cause of underweight is inadequate access to food or hunger. While this is less common in more affluent areas of the world, such as North America, it may be more prevalent in the West than is recognized.
* **Overactivity.** Underweight may be the product of an overactive lifestyle: too much exercise, work, volunteering, and so on. When activities demand a lot of time and energy, there may be an energy imbalance or insufficient time to eat well.
* **Social factors.** Behaviors related to food are affected by family patterns and styles of social interaction. People who like to eat with others but are usually alone for meals may eat less than they need to. If one family member chooses to drastically change his or her diet, to treat a health condition, for example, another family member might follow suit to offer support and not eat enough as a result.
### Great Gains for Vegans
Whether you decide to actively pursue weight gain may largely depend on your perception of your body. For the most part, men tend to be more highly motivated to correct underweight than women because of the way society views thinness in men versus women. However, as a vegan, you may want to broaden your goals. Your personal example is your most powerful tool to shift others toward a more compassionate and sustainable lifestyle. If you're under-weight and generally unhealthy, your example probably won't create the kind of inspiration you may have hoped for.
Perhaps it's time to renew your commitment to health and take the steps necessary to achieve a healthy weight. The most effective approach to weight gain isn't so different from that for weight loss: permanent lifestyle changes that include a combination of diet and exercise. While exercise might seem counterintuitive if you're trying to gain weight, building and maintaining lean body tissue is critical to success, so make it a priority. As you plot your course forward, consider the rest of this chapter to be your blueprint for weight gain.
### Eating to Gain
Many lifestyle factors come together to influence body weight. Fortunately, most of these factors are within your control. They fall into two main categories: diet and lifestyle. Let's begin by considering the multiple ways of adjusting your food intake to better support health and achieve your target body weight.
#### MAKE GOOD HEALTH YOUR TOP GOAL
Think of food as the raw materials with which you'll rebuild your body. The best building blocks are foods that provide not only calories but also an abundance of antioxidants, phytochemicals, and other nutrients. Even if you don't gain weight as quickly as you'd like, you'll soon notice that you have increased energy, better concentration, fewer illnesses, and improved mood.
Because you can afford to eat extra calories, it may be tempting to load up on vegan junk foods, such as chips, candy, and sweet desserts. While the occasional indulgence is fine, these foods shouldn't be dietary staples. An unhealthful diet can lead to heart attacks, strokes, cancer, and other afflictions, regardless of body weight.
#### INCREASE FOOD INTAKE
The typical formula for weight gain is that you need to add between 500 to 1,000 calories to your diet daily to gain 1 to 2 pounds (0.45 to 0.9 kg) per week. However, this is actually an underestimate for some people. Most underweight adults require about 2,500 to 4,000 calories per day to gain weight, and athletes need even more. To accomplish this, select energy-dense vegan foods, with an emphasis on whole foods, and increase your serving sizes. In chapter 14, you'll find sample high-calorie menus, one offering 2,500 to 2,800 calories per day, and another providing 4,000 calories. Table 10.1, below, presents general guidelines on daily number of servings from each food group for 2,500- and 4,000-calorie diets. In addition to boosting your intake of calories, this strategy will ensure that you get all of the nutrients you need. (See table 14.1, on page 265, for information about each food group, including serving sizes.) Ideally, these foods should be consumed throughout the day, including a bedtime snack and other snacks as desired.
#### EAT MORE OFTEN
It's difficult to take in enough calories if you eat only one or two meals a day. Aim for three meals a day, plus at least two hearty snacks. Don't skip meals or go to bed on an empty stomach. If you're likely to forget to eat, use a timer to remind yourself. If your mornings are rushed, make your lunch and snacks the night before.
Including just one additional snack of 500 calories each day could result in a weight gain of 1 pound (0.45 kg) a week. Here are a few snack options that each provide approximately 500 calories:
* ¾ cup (185 ml) trail mix (nuts, seeds, and dried fruits)
* cup (160 ml) nuts
* A smoothie (such as the Protein Power Smoothie on page 194)
* An almond butter and banana sandwich plus 1 cup (250 ml) soy milk or hot chocolate made with soy milk
* ¾ cup (185 ml) granola, 1 banana, and 1½ cups (375 ml) soy milk
* 20 crackers, 2 ounces (60 g) vegan cheese, 4 vegan deli slices, and 10 olives
**TABLE 10.1.** Suggested daily food servings* for weight gain
**FOOD GROUP** | **AVERAGE CALORIES PER SERVING** | **DAILY SERVINGS IN A 2,500-CALORIE DIET** | **DAILY SERVINGS IN A 4,000-CALORIE DIET**
---|---|---|---
Vegetables | 40 | 5 | 7
Fruits | 75 | 4 | 6
Legumes | 120 | 5 | 9
Grains | 75 | 8 | 13
Nuts and seeds | 160 | 4 | 6
Fats and oils† | 40 | 4 | 7
*See the Vegan Food Guide in Chapter 14 for serving sizes in each food group.
†1 serving = 1 teaspoon
* 1 vegan muffin or energy bar, 1 cup (250 ml) coconut yogurt, and 1 apple
* 2 ounces (60 g) baked pita chips with ½ cup (125 ml) each of salsa, refried beans, and guacamole
#### SNEAK IN EXTRA CALORIES
Whole plant foods, especially fruits and vegetables, can be high in fiber, low in fat, and relatively low in calories, filling you up without providing sufficient calories for weight gain. The following tips will help you to add calories to a whole foods diet while also boosting nutrients and flavor:
* Garnish salads with beans, nuts, seeds, tofu, or avocado, and use dressings made with high-quality oils or tahini.
* Top steamed vegetables with a creamy sauce made from tofu or nuts.
* Include tofu, nuts, or seeds in stir-fries, casseroles, and pasta dishes.
* Top diced fruits with nondairy yogurt and granola.
* Cook hot cereals, such as whole grains or oats, in nondairy milk rather than water. Add chopped nuts, seeds, and dried fruits.
* Spread nut butter on English muffins or toast.
* Use full-fat nondairy milk instead of lighter varieties.
* Top vegan ice cream with nuts, dark chocolate, and berries.
* Dip cut-up fruit in a vegan avocado-chocolate mousse.
* Add cashew cream or coconut milk to soups and sauces. To make cashew cream, puree ½ cup (125 ml) of cashews with 1 cup (250 ml) water.
#### USE BEVERAGES TO YOUR ADVANTAGE
The beverages you choose can make a significant difference in your overall energy intake. For example, 1 cup (250 ml) of fruit juice typically provides 120 to 180 calories (freshly squeezed is best); 1 cup (250 ml) of soy milk provides 100 to 120 calories; and a soy-fruit shake, 300 to 500 calories. These energy-rich beverages can be an easy way to increase calories. However, it's best to limit the liquids you consume with meals, since low-calorie soups or calorie-free beverages such as coffee and tea can fill you up. If you have difficulty eating larger portions at mealtime, try drinking beverages primarily between meals.
#### EAT HIGHER-FAT WHOLE FOODS
Vegan diets are generally higher in fiber and lower in fat than nonvegan diets, and that can interfere with gaining weight. The easiest way to add energy without adding too much fiber or volume is to increase the fat. About 20 to 30 percent of your calories should come from fat. Among the most energy-dense vegan foods are nuts, seeds, soy foods, coconut, nondairy alternatives (milk, cheese, yogurt, and so on), avocados, nutritious baked goods, and oils. Table 10.2 (page 190) shows the approximate calorie content of some high-calorie vegan foods.
**TABLE 10.2.** Calorie content of higher-fat foods
**FOOD** | **SERVING SIZE** | **CALORIES**
---|---|---
Avocado | 1 medium | 340
Carrot cake | 1 slice | 400
Hearty cookie | 2 cookies | 300
Nuts (except peanuts) | ½ c (125 ml) | 360–480
Peanuts | ½ c (125 ml) | 415
Pumpkin muffin | 1 large muffin | 400
Soy milk | 1 c (250 ml) | 120–160
Soy nuts | ½ c (125 ml) | 390
Tofu (firm) | ½ c (125 ml) | 183
Unrefined oil | 1 tbsp (15 ml) | 120
Source of data: US Department of Agriculture, Agricultural Research Service, USDA National Nutrient Database for Standard Reference, Release 25 (2012), and estimates based on popular vegan recipes for baked goods.
Key: c = cup; tbsp = tablespoon.
The following sections provide tips on how to incorporate more of these higher-fat, nutritious foods into your meals and snacks.
#### Nuts and Seeds
Try to add ½ to 1 cup (125 to 250 ml) of nuts and seeds to your daily diet. They're highly nutritious and conveniently portable. Although soy nuts are legumes, they have similar advantages and can be used in much the same way. Here are just a few ideas on how to boost your consumption of these nutritional powerhouses:
* Keep nuts and seeds wherever you spend most of your time so you can snack at will.
* Use nuts and seeds as a base for vegan cheeses or sauces.
* Add them to stir-fries, baked goods, pancakes, and waffles.
* Use them to make veggie roasts, burgers, and pâtés.
* Sprinkle them on salads.
* Eat power bars based on nuts or seeds.
* Spread nut and seed butters on bread, apple slices, or celery sticks.
* Mix nut and seed butters into salad dressings.
#### Tofu
Tofu is wonderfully versatile, low in fiber, and relatively high in fat. Here are some tips on adding tofu to your diet:
* Add soft tofu to shakes or use it in desserts, such as puddings.
* Eat scrambled tofu for breakfast.
* Use flavored tofu or tofu salads in sandwiches.
* Add cubed tofu to stir-fries, stews, curries, and soups.
* Use mashed tofu in lasagna.
* Sauté chopped, sliced, or grated tofu with a little oil, tamari, nutritional yeast, and herbs and use it as a salad topping.
* Use tofu as a base for veggie roasts, burgers, pâtés, and dips.
* Try marinated baked or barbecued tofu as a dinner entrée.
* Experiment with tofu especially in desserts. Add it to cheesecakes, cakes, muffins, and cookies.
#### Dairy Alternatives
Today, you can find vegan replacements for most dairy products. Some are based on soy, while others are made from almonds, rice, coconut, hempseeds, grains, or root vegetables. These products continue to be improved and are often tasty and nutritious. However, some contain partially hydrogenated oils, sugar, preservatives, and other unhealthful ingredients, so be sure to read ingredient lists.
A great option is to prepare some of your own nondairy foods. Many cookbooks and online resources offer recipes for almond or hempseed milk, fermented nut cheeses, fruit-based ice cream, and nondairy yogurts. If you use commercial soy milk, choose one that's full-fat and made with organic soybeans. Because nondairy foods can significantly increase your energy intake, they're well worth adding to your diet. Here are a few suggestions on how to do so:
* Use nondairy milk or yogurt in smoothies and on cereal.
* Replace water with soy milk when making puddings, pancakes, waffles, breads, muffins, and other baked goods.
* Enjoy a simple dessert of nondairy yogurt, berries, and granola or nuts.
* Use vegan sour cream as a base for dips or as a topping for soups. For an optimally healthy product, you may want to make your own using cashews or tofu.
* Add vegan mayonnaise to sandwiches and salads. Again, you can make your own using cashews or tofu.
* Experiment with nut-based cheeses.
#### Avocados
Avocados pack a lot of calories into a small and delectable fruit. Here are some delicious ways to use them:
* Dress up a salad with wedges of avocado.
* Mash avocados with lemon juice for dips, sandwich spreads, and toppings.
* Add avocado chunks to salsa.
* Use avocado slices in sandwiches and pita pockets.
* Add diced avocado to pasta or quinoa salads.
#### Sweet Treats
If you start with the right ingredients, sweet treats can make a valuable contribution to your daily calorie count. Here are some tips on how to keep sweet treats healthful:
* Go raw. Raw desserts, such as vegan cheesecakes, pies, cookies, and brownies, are outrageously delicious and usually high in healthful calories, since they're based on nuts, coconut, and dried and fresh fruits.
* Replace some or all of the fat in baked goods with nuts, seeds, or coconut or their butters.
* Try ground flaxseeds, which are a great source of omega-3 fatty acids, as an egg replacer. For each egg in a recipe, whisk together 1 tablespoon (15 ml) of ground flaxseeds and 3 tablespoons (45 ml) of water.
* Substitute cooked and mashed dried fruits for all or part of the sugar in your treat recipes.
* Use high-quality oils instead of hydrogenated fats in baking.
#### BE GENEROUS WITH CARBOHYDRATES
A high-carbohydrate diet helps muscles work harder for longer periods of time and spares protein from being used as an energy source. Between 55 and 65 percent of your daily calories should come from carbohydrates. The most concentrated sources are grains and starchy vegetables. Excellent choices are pseudograins, such as quinoa, buckwheat, and amaranth, and colorful starchy vegetables, such as yams, corn, winter squash, and purple potatoes. Here are some suggestions to stoke your creativity with carbs:
* Soak or sprout grains to use in cereals, salads, breads, and raw or baked treats and desserts.
* Use cooked whole grains in salads, stews, pilafs, and cereals.
* Add cooked yams or sweet potatoes to salads.
* For a one-two punch of grains and high-carb legumes, enjoy bread with hummus or other legume-based spreads.
* Add potatoes to curries, stews, and scrambled tofu.
* Enjoy breads, muffins, pancakes, and waffles made with whole-grain flours and wheat germ.
* Add corn to salads, soups, and stews.
#### PUSH PLANT PROTEIN
Vegan diets can fall short on protein, particularly when they include only minimal legumes, nuts, and seeds. If your muscle mass is low, build it up by eating 1.2 to 1.7 grams of protein per kilogram (2.2 lb) of body weight per day (g/kg/d). If you don't need to build muscle, 1.2 g/kg/d is sufficient. Calculate your needs based on your ideal body weight rather than your actual body weight. For example, if you weigh 120 pounds (54 kg), but your healthy weight is 145 pounds (66 kg), aim for at least 80 grams of protein per day (66 kg x 1.2 g/kg = 79.2 g).
Include a good source of protein in every meal. Table 10.3 provides simple suggestions for substituting protein-rich foods for lower-protein foods. For a comprehensive list of plant foods and the amounts of protein they contain, see table 3.3, on pages 54–60; also see table 11.3, on page 204.
#### SAVOR SMOOTHIES
Smoothies are an exceptional vehicle for adding protein, calories, and nutrients to your diet. If you're having difficulty meeting your protein needs, adding vegan protein powder to a smoothie is a great option. A wide variety of products are available with protein derived from hempseeds, peas, rice, soy, and other foods. The easiest and most delicious way to use protein powder is to add it to a smoothie.
**TABLE 10.3.** Substitutions to boost protein
**INSTEAD OF:** | **PROTEIN (g)** | **CHOOSE:** | **PROTEIN (g)**
---|---|---|---
Brown rice, 1 c (250 ml) | 5 | Quinoa, 1 c (250 ml) | 8
Corn nuts, 2 oz (60 g) | 5 | Soy nuts, 2 oz (60 g) | 24
Cornflakes, 1 c (250 ml) | 2 | Oatmeal, 1 cup (250 ml) | 6
Garden salad, 4 c (1 L), with Italian dressing, 2 tbsp (30 ml) | 4 | Kale salad, 4 c (1 L), with tahini dressing containing 1 tbsp (15 ml) tahini | 12
Margarine, 2 tbsp (30 ml) | 0 | Peanut butter, 2 tbsp (30 ml) | 8
Orange juice, 1 c (250 ml) | 2 | Protein Power Smoothie (page 194), 2½ c (625 ml) | 40
Pretzels, 1 oz (30 g) | 3 | Pumpkin seeds, 1 oz (80 g) | 9
Vegetable soup, 1 c (250 ml) | 2 | Lentil soup, 1 c (250 ml) | 9
Rice milk, 1 c (250 ml) | 1 | Soy milk, 1 c (250 ml) | 8
Tomato sandwich on whole-grain bread | 6 | Tomato sandwich on whole-grain bread with 2 oz (60 g) vegan deli slices* | 21
Tomato sauce, 1 c (250 ml) | 3 | Tomato sauce, 1 c (250 ml) with 2 oz (60 g) vegan ground round | 15
Vegan mayonnaise-based dip, ¼ c (60 ml) | 0 | Hummus, ¼ c (60 ml) | 5
Vegetable stir-fry, 3 c (750 ml) | 6 | Vegetable stir-fry, 3 c (750 ml), with ½ c (125 ml) firm tofu* | 26
Source of data: US Department of Agriculture, Agricultural Research Service, _USDA National Nutrient Database for Standard Reference_ , Release 25 (2012).
Key: c = cup; g = gram; L = liter; ml = milliliter; oz = ounce; tbsp = tablespoon.
*Check labels for product-specific information.
_Protein Power Smoothie_
Makes 2½ cups (625 ml)
If you like your smoothies ice-cold, use frozen fruit. Alternatively, add a few ice cubes before blending. This smoothie provides about 500 calories and 40 grams of protein, depending on choice of protein powder.
1 scoop protein powder
1 banana
1 cup (250 ml) berries, chopped peaches, or other fruit
1½ cups (375 ml) soy milk
Put all the ingredients in a blender and process until smooth. Serve immediately.
Be creative with smoothie boosters and variations. High-fat boosters, such as avocados, oils, and nuts and seeds and their butters add valuable calories. Foods rich in antioxidants and phytochemicals, such as kale, carob powder, cocoa powder, goji berries, and spices can help boost health. Nondairy yogurts or probiotic powders provide beneficial bacteria. Try one or more of the following to boost the protein in any smoothie, including the Protein Power Smoothie, above.
* For a green smoothie, add 2 cups (500 ml) of chopped kale, ½ small avocado, or both.
* Chocolate lovers can add 1 to 1½ tablespoons (15 to 22 ml) of cocoa or carob powder.
* For a boost in beneficial bacteria, add ½ cup (125 ml) of nondairy yogurt.
* To increase essential fatty acids, add 1 tablespoon (15 ml) of cold-pressed oil rich in omega-3s, such as flaxseed, hempseed, or chia seed oil. For optimum nutrition, choose one with added DHA. Alternatively, add 2 tablespoons (30 ml) of hempseeds, flaxseeds, or chia seeds.
* To support healthy bacteria in your intestinal tract, add ¼ teaspoon (1 ml) of powdered probiotics.
* Add healthful, flavorful herbs and spices such as cinnamon, cloves, ginger, and nutmeg to fruit smoothies, and fresh herbs, such as basil, mint, and oregano, to green smoothies.
* For added protein and healthy fat, add 1 tablespoon (15 ml) of nut butter.
* Add 2 tablespoons (30 ml) of goji berries. (Soak dried goji berries for at least four hours and drain before using.)
#### MAKE EATING A PRIORITY
If you never seem to have real food around the house and eat mainly out of boxes and bags, it's time for some lifestyle adjustments in keeping with your weight-gain goals. Making specific plans about meals will help you succeed in your quest. Here are a few things you might try:
* Make a weekly menu, prepare a shopping list, and select a weekly shopping day. (See _Cooking Vegan_ by V. Melina and J. Forest, Book Publishing Co., 2012)
* If you can't cook, take lessons. Go with a friend and make it fun.
* Make eating a social event. Eat with friends and family more often. Host a potluck, invite someone to dinner, or enjoy a meal at a vegetarian restaurant.
* Invest in simple vegan cookbooks and try a few new recipes each week.
* Buy a slow cooker. In the morning, throw in a combination of ingredients, such as grains, veggies, and beans or tofu and let it cook all day.
* Plan to spend time cooking on the weekends or whenever you have time. Make one or two main dishes, a soup, and some healthy baked goods. Prepare enough to last several days. Freeze leftovers for days when you don't have time to cook.
* Keep your pantry, fridge, and freezer well stocked with healthful foods that you enjoy eating: trail mix, power bars, muffins, healthy cookies, frozen bananas dipped in melted chocolate and rolled in nuts, vegan cheesecake... you get the picture.
* Stash a few goodies at work, in your car, in your purse or backpack, or anywhere that you spend a lot of time.
#### FUEL YOUR APPETITE
You may rarely feel hungry, perhaps because you have a small appetite or a small stomach. While appetite can be affected by mood, stress, and physical activity, some simple food and nutrition tips can help kick it into high gear:
* Increase your food intake gradually, allowing your stomach to expand over time so you'll be able to comfortably eat more.
* Focus on foods that take up less space in the stomach per calorie. Examples include nuts, seeds, dried fruits, beans, avocados, and tofu. Mashing and pureeing foods can also help reduce their volume.
* Surround yourself with tempting aromas. Bake bread or buy frozen dough and bake it at home. Simmer a few cinnamon sticks and cloves in a pot of water. Walk past food stands, bakeries, and restaurants that entice you.
* Tantalize your senses with beautiful pictures of food in magazines and cookbooks. Then try the recipes!
* Make mealtimes enjoyable. Create a low-stress atmosphere with candles, a pretty table setting, soft music, and, if possible, pleasant company.
* Use big bowls, plates, cups, and cutlery. Using larger dishes, forks, and spoons has been shown to increase total food intake.
* Eat several courses. When you include a variety of different smells and tastes, it's easier to tempt your taste buds. Instead of one big plate of food, try having four sequential courses.
* Honor your hunger. Eat when you feel the least bit hungry. If you know you should be eating something, but are not hungry, drink something. Have carrot juice, freshly squeezed orange juice, hot chocolate, or a smoothie.
* Avoid foods that cause you gastrointestinal distress. This can reduce your appetite and food intake.
#### KEEP A FOOD DIARY
You may want to log your food intake. You can even do this online; there are free sites for this. If you have a smartphone, you can also download free apps for this purpose. Keeping track of your food intake will help you understand your eating habits, likes, dislikes, and tendencies. Adjusting what you do is easier if you know where you're starting and understand the challenges.
#### BE CAUTIOUS ABOUT WEIGHT-GAIN AIDS
There are dozens of weight-gain aids in the marketplace, but most are designed for bodybuilders who aren't underweight. Do your research and know the risks and benefits before trying a new supplement.
While some may prove helpful, others are a waste of money and may even be harmful. The US Food and Drug Administration provides online information about bodybuilding products that contain ingredients considered to be unsafe.
Your health care provider may suggest appetite stimulants to support your weight-gain efforts. While these can be effective, some have undesirable side effects. It's best to use other strategies to increase food intake.
#### CONSIDER SUPPLEMENTS
If your diet hasn't been particularly healthful in the past, consider taking a multivitamin-mineral supplement until you improve your nutritional status. Select one that provides zinc, magnesium, chromium, selenium, and possibly iron. (However, it's a good idea to have your iron level tested to see if you need additional iron, since excesses can be dangerous.) We also recommend that you include supplements of vitamin B12, vitamin D (if exposure to sunshine is insufficient), and iodine (if you don't use iodized salt)—as we do for all vegans.
### Building a Bigger Body
The second piece of the weight-gain puzzle is lifestyle. Let's explore the lifestyle changes you can make to put on healthy pounds.
**Set realistic goals.** Determine a target weight. Aim to gain 1 or 2 pounds (0.45 to 0.9 kg) per week. Be realistic; if your natural body type is tall and slim, don't expect to be transformed into the Hulk overnight. While it is possible to gain muscle, your body may fight it every step of the way. You may have to work twice as hard as the average person to gain the same amount of weight. Consistency is the key to producing results, but even with regular training, most men will gain no more than 20 pounds (9 kg) of lean tissue per year, and women will gain about half that much.
**Do resistance training.** Even if you have no desire to build big muscles, moderate resistance training is the best way to promote muscle growth and ensure that the weight you gain includes a healthful balance of muscle and fat. Resistance training is often done with free weights or weight machines, but you can also use resistance bands or your own body weight, with push-ups or pull-ups, for example. Here are some tips to optimize the effectiveness of resistance training:
* Work with a professional trainer who can tailor your program to meet your personal goals and abilities and who will follow your progress.
* Train only two or three times per week to allow your muscles sufficient time to recover and grow between workouts.
* Aim for thirty- to sixty-minute workout sessions, and keep the pace moderate to intense. Begin with light weights and increase gradually as you perfect your form.
* Change your exercise routine every six to eight weeks to keep your muscles challenged (and your interest up).
* Warm up for five to ten minutes before strength training and cool down for five to ten minutes afterward.
* Drink plenty of water.
**Don't overdo aerobic exercise.** It's tough to gain weight while training for a marathon. Aerobic exercise boosts metabolism and burns calories, which can work against you when you're trying to gain weight. On the other hand, aerobic exercise improves overall health, enhances cardiovascular and respiratory function, and keeps body fat low, so don't avoid it altogether. A reasonable compromise is to do a moderate amount of aerobic activity, such as thirty to sixty minutes, two or three times a week.
**Get some R & R.** Physical and emotional stress can affect your metabolism, appetite, and hormones and prevent weight gain. Consider doing yoga, tai chi, qigong, meditation, or other relaxation therapies. Take little relaxation breaks throughout the day, and pamper yourself from time to time. Be sure to get sufficient sleep; it restores energy and allows muscles to recuperate and grow. For most adults, seven to nine hours a night is reasonable. If your life is so busy that you often forget to eat, it's time to rethink your priorities and simplify your life.
**Avoid addictive substances.** In addition to damaging health, alcohol, tobacco, and recreational drugs can alter your metabolism and interfere with appetite, especially if consumed regularly or to excess. If you struggle with addiction, it's probably a contributing factor to your weight challenges. Take a step in a positive direction and seek professional help.
**Listen to your body.** Everyone's body is unique, and people function optimally at different sizes and shapes. If you're constantly tired, you may need more sleep or more food. If you're always sore, you may be training too much. (That said, some underweight people probably shouldn't trust their instincts where food is concerned because their hunger and satiety mechanisms may be compromised. In that case, eating specific amounts at designated times each day can be very helpful.)
**Pregnancy, breast-feeding, and raising children to be healthy eaters can present special nutritional challenges. The next chapter explores the dietary issues unique to these stages of life and simple ways to adapt a vegan diet to ensure that dietary needs are met during these critical times.**
## CHAPTER 11
## From Pregnancy On: Nourishing Strong Children
As we've seen throughout this book, a well-balanced vegan diet can be an excellent path to health. But when the conversation shifts to the best diets for pregnancy, babies, and children, emotions often set in. We become vulnerable to the opinions of well-meaning people we love, and we may begin to question our decisions. A parent may wonder whether a diet that's great for the average adult will also be good for moms-to-be, babies, and children.
We assure you that eating a healthful vegan diet during pregnancy and while breast-feeding will give your baby the best possible start and will set the stage for a lifetime of good health for your entire family. This chapter discusses how a well-balanced vegan diet can contribute to a healthy pregnancy and a healthy baby, how it can help ensure an abundance of nutritious breast milk and superb health and well-being for growing children and teens.
### The Research
If you're already vegan, don't be surprised if your doctor questions your diet or doesn't know a lot about vegan diets. A physician may get only three hours of nutrition training, and the focus of that training isn't vegan nutrition. You can point out that the Academy of Nutrition and Dietetics has voiced its support for vegan diets, including during pregnancy, lactation, childhood, and adolescence. Share a copy of their position on vegetarian diets (see Resources, page 276). If health professionals, family members, or friends don't know how to put together a nutritionally adequate vegan diet, they may not be sure it's possible and advise against it. Like all pioneers, you'll need to do some research and have some facts on hand. You might also consider sharing some tasty vegan meals with doubters.
_For More on Specific Nutrients_
This chapter outlines requirements for specific nutrients at many phases of life (pregnancy, lactation, infancy, and through to adolescence). For more information on specific vitamins and minerals, and for complete details on nutritional requirements for all stages of life, see chapters 6 and and the appendix.
Studies have shown few or no significant health differences between babies born to vegetarian moms versus nonvegetarians. In fact, where differences exist, vegetarian moms are at an advantage in some regards. They are less likely to give birth to infants with health problems related to excessively high birth weights, and also less likely to develop gestational diabetes, especially if they were physically active while pregnant.
Getting enough iron is a concern during any pregnancy. However, pregnant vegetarians have been shown to have higher intakes of dietary iron than meat eaters. Nonheme iron, the type in plant foods, has been linked to better birth weights. Vegetarian moms are also more likely to take iron supplements.
The largest study to date on the health of pregnant vegans and their pregnancy outcomes was completed in 1987. It examined the maternity records of 775 vegan women from The Farm, a community in Summertown, Tennessee. Their diet was centered on soy foods, grains, fruits, and vegetables, most of which were organic and grown on The Farm. The women took prenatal supplements with iron and calcium, received regular prenatal care, and had active lifestyles. They didn't smoke cigarettes or drink alcohol, and only rarely did they drink coffee.
Two important findings emerged from this research. First, the infants were all of normal weight, and second, only one, or 0.13 percent, of the vegan moms developed preeclampsia, a dangerous condition that includes high blood pressure, fluid retention, and protein loss in the urine and can result in harm and even death to mother and baby. In the general population, preeclampsia affects 5 to 10 percent of expectant moms.
Some studies have shown less favorable pregnancy outcomes among vegan women, particularly among women on restrictive macrobiotic diets who were unwilling to take vitamin and mineral supplements, and among moms whose diets were low in calories and lacked vitamin B12. Also, earlier studies on pregnant vegans were carried out long before fortified vegan foods and nutritious vegan convenience foods became widely available. Now almost every supermarket stocks hummus, tofu, nondairy beverages fortified with calcium and vitamin D, and vegetarian meats fortified with vitamin B12.
The message we can take from all of this is that vegan diets can support healthy pregnancies as long as moms ensure they're getting enough calories and nutrients, as is the case for anyone on any diet.
### Preparing for Pregnancy
Even before you become pregnant, you need to prepare to host a new life. If you're planning to get pregnant any time in the next few years, start making the necessary changes in your diet now. By the time you're pregnant, your nutrient reserves will be in good shape and you also will have established eating patterns that are health promoting for you and your family.
One step is to get your weight where you'd like it to be _before_ you become pregnant. Check table 9.1 (page 166) to determine your body mass index (BMI). This will give you a good idea of whether your weight is in the optimal range. You don't want to be following a weight-loss diet during any stage of pregnancy. If your BMI is in the overweight or obese range (page 166), weight reduction can decrease your risk of gestational diabetes, high blood pressure, and preeclampsia. If you're underweight, gaining enough weight for a normal BMI can increase your chances of becoming pregnant and decrease your chances of having a preterm birth or an underweight infant. See chapters 9 and for tips on losing or gaining weight.
No matter what your weight, make sure your diet is rich in folate. Folate deficiency in the mother in early pregnancy can result in spina bifida and other neural tube defects in the baby. Getting enough folate shouldn't be difficult, since beans, greens, and oranges are excellent sources of this vitamin. It is extremely important that you enter pregnancy with abundant reserves of this nutrient, because they will be drawn upon frequently for nine months. See pages 117 and for more information on folate.
It may be advisable to take a prenatal multivitamin-mineral supplement or a supplement specific to pregnancy. Ask your health care provider about this. Choose a supplement that includes vitamin B12, vitamin D, choline, iodine, iron, and zinc. Avoid herbal supplements and botanical remedies unless you discuss them with your health care provider.
### Vegan Nutrition During Pregnancy
The nutrients your baby needs for growth come entirely from you. Although you need only in the range of 10 to 15 percent more calories during the second and third trimesters, your need for specific vitamins and minerals can increase significantly over your pre-pregnancy requirements (shown in the appendix, pages 274–275), in some cases doubling. Your food selections really matter. Fortunately, designing a nutritionally adequate vegan diet for pregnancy is not only possible, it's also less challenging than you might think.
Recommended intakes for certain vitamins and minerals during pregnancy and lactation are shown in table 11.1. As you can see, recommendations for some nutrients, such as calcium and vitamins D and K, don't change, whereas the need for some increases during lactation, and the need for yet others decreases during lactation. For many nutrients, simply eating greater quantities of a wide variety of healthful vegan foods will easily ensure adequate intakes. Also note that adequate intake of omega-3 fatty acids is essential, as outlined on pages 66 and . A daily DHA supplement of 200 to 300 mg is commonly recommended during pregnancy.
**TABLE 11.1.** Recommended intakes for pregnant or breast-feeding women ages nineteen to fifty
**NUTRIENT** | **RECOMMENDED INTAKE DURING PREGNANCY** | **RECOMMENDED INTAKE WHILE BREAST-FEEDING**
---|---|---
Calcium | 1,000 mg | 1,000 mg
Iodine | 220 mcg | 290 mcg
Iron* | 49 mg (27 mg) | 16 mg (9 mg)
Magnesium** | 350 or 360 mg | 210 or 320 mg
Zinc | 11 mg | 12 mg
Vitamin A (carotenoids) | (2,450 IU) 770 mcg RAE | (4,290 IU) 1,300 mcg RAE
Vitamin C | 85 mg | 120 mg
Vitamin D | (600 IU) 15 mcg | (600 IU) 15 mcg
Vitamin E | (22.5 IU) 15 mg | (28.5 IU) 19 mg
Vitamin K | 90 mcg | 90 mcg
Vitamin B12 | 2.6 mcg | 2.8 mcg
Thiamin | 1.4 mg | 1.4 mg
Riboflavin | 1.4 mg | 1.6 mg
Niacin | 18 mg | 17 mg
Pantothenic acid | 6 mg | 7 mg
Vitamin B6 | 1.9 mg | 2.0 mg
Folate | 600 mcg | 500 mcg
Sources of data: Institute of Medicine summaries. Mangels, R., _The Everything Vegan Pregnancy Book_ (Axon, MA: F+W Media, 2011). Linus Pauling Institute, Micronutrient Information Center, "Micronutrient Needs during Pregnancy and Lactation" (2012), lpi.oregonstate.edu/infocenter/lifestages/pregnancyandlactation.
*The recommended intake of iron shown here is for vegans and other vegetarians and is higher than that for nonvegetarians (shown in parentheses). However, the need for a higher intake among vegetarians and vegans is controversial, and actual need may be less.
**For magnesium, the first amount is the recommended intake for women nineteen to thirty years of age; the second is for those older than thirty.
Key: IU = International Units, mcg = microgram, mg = miligram; RAE = Retinol Activity Equivalents
#### FIRST TRIMESTER
You'll need few if any added calories during the first trimester. Average weight gain during the first trimester is 3.5 pounds (1.6 kg). Underweight women gain about 5 pounds (2.2 kg) during this time; overweight women typically gain about 2 pounds (0.9 kg). For overall weight gain recommendations, see table 11.2.
Morning sickness can be the first sign of pregnancy for many women. Fortunately, it often subsides after the first trimester. Dry, low-fat carbohydrate foods, such as crackers, seem to help morning sickness because they are digested quickly, creating less opportunity for queasiness as they rapidly pass through the stomach. Eating a few crackers upon waking seems to help some women. Eating ginger cookies or sipping ginger tea may be beneficial. Sometimes the nausea is actually due to hunger, so eat often, relying on small meals and frequent snacks. Crackers with hummus is a nutritious combination, as is lentil or bean soup with toast. If you feel too queasy to eat solid food, drink juice, water, soy milk, or miso broth. If you're unable to eat or drink adequate amounts of fluids for twenty-four hours, contact your health care provider.
**TABLE 11.2.** Weight gain in pregnancy
**FACTORS DETERMINING WEIGHT-GAIN GOALS** | **TOTAL WEIGHT GAIN RECOMMENDED** | **AVERAGE RATE OF WEIGHT GAIN PER WEEK IN SECOND AND THIRD TRIMESTERS**
---|---|---
Normal or optimal prepregnancy weight (BMI 18.5–24.9) | 25–35 lb (11.5–16 kg) | 0.8–1 lb (0.35–0.45 kg)
Underweight before pregnancy (BMI < 18.5) | 28–40 lb (12.5–18 kg) | 1–1.3 lb (0.45–0.59 kg)
Overweight before pregnancy (BMI 25–29.9) | 15–25 lb (7–11.5 kg) | 0.5–0.7 lb (0.23–0.32 kg)
Obese before pregnancy (BMI ≥ 30) | 11–20 lb (5–9 kg) | 0.5 lb (0.23 kg)
Adolescent | 30–45 lb (14–20.5 kg) | (variable)
Normal or optimal prepregnancy weight with twins | 37–54 lb (17–24 kg) | (variable)
Sources of data are listed in _Becoming Vegan: Comprehensive Edition_ , by Brenda Davis and Vesanto Melina (Book Publishing Company, 2014).
Though the recommended intake of protein doesn't increase during the first trimester, make sure you emphasize foods that are rich in protein and iron to help build the additional blood your body must create. In addition, focusing on high-protein legumes (beans, peas, and lentils) can reduce the risk of gestational diabetes, and their fiber will help with constipation. (See "How Much Protein Do We Need," on page 48, for information on protein needs, which are based on body weight.)
#### SECOND AND THIRD TRIMESTERS
By the fourth month of pregnancy, you'll need more calories. The average weight gain during this time is 1 pound (0.45 kg) per week. (See table 11.2.)You'll probably gain a little more than that if you're underweight. If you're overweight, you may gain a little less. On average, you'll need to eat an additional 340 calories per day in the second trimester, and 452 additional calories daily during the third. (See chapter 14 for menus at different calorie levels, and table 3.3, on page 54, for the number of calories in various foods.) At this important stage, choosing nutrient-rich foods is crucial.
### Specific Nutrients
In the sections that follow, we'll take a look at some of the nutrients of greatest concern during pregnancy. We'll also discuss substances to avoid and provide some suggested menus. Then our focus will shift to nutritional requirements during lactation in similar detail.
#### PROTEIN
Starting in the fourth month of pregnancy, your recommended protein intake increases by 25 grams per day. If you're expecting twins, double that amount. Table 11.3 shows various foods that provide 15 grams of protein based on the serving sizes listed in the left-hand column. (Some of these are hearty servings, but you'll probably have a growing appetite.) It makes sense to include at least one protein-rich food in each meal and most snacks, especially as these foods often provide iron, zinc, folate, and choline as well.
**TABLE 11.3.** Foods that provide 15 grams of protein per serving
Sources of data: US Department of Agriculture, Agricultural Research Service, _USDA National Nutrient Database for Standard Reference_ , Release 25 (2012), and estimates based on popular vegan recipes for baked goods.
Key: c = cup; g = gram; L = liter; ml = milliliter; tbsp = tablespoon
Although raw vegan diets can be healthful and slimming for adults, we don't advise 100 percent raw diets for pregnant women or for children. Take a look at the amount of pea pods you need for 15 grams of protein in table 11.3 on the facing page! Instead, include some cooked legumes. (For a more extensive list of foods and their protein content, see table 3.3, on page 54. You also can see replacements that increase your protein intake in table 10.3, on page 193.)
#### IRON
Whether the diet is vegan, vegetarian, or omnivorous, iron deficiency can be a concern for women. Many fail to meet the recommended intakes, especially during pregnancy, when the body's blood supply increases by 40 to 50 percent in order to deliver oxygen to the baby and supporting tissues. Iron supports neurological development and is required for the fetus to build up iron stores, especially during the third trimester. Adequate iron intakes during pregnancy are linked with reduced likelihood of preterm births and with larger birth weights.
During pregnancy, when women need more iron, nature steps in and greatly increases the ability to absorb iron from plants, especially during the second trimester. Also, the monthly losses that normally occur during menstruation obviously don't occur during pregnancy, making more iron available for mother and baby.
Pregnant women are advised to consume 27 mg of iron per day. Because some plant foods contain substances that limit iron absorption, such as phytate compounds, pregnant vegetarians are advised to get 1.8 times as much iron as nonvegetarians, which would make their recommended intake 49 mg per day. But there is some question as to whether vegans need that much, since their diets are already high in vitamin C, which greatly increases iron absorption. In any case, vegan diets tend to be high in iron, with studies repeatedly showing that vegans consume more iron than nonvegetarians.
Supplements providing 30 mg of iron are commonly prescribed for pregnant women. It's best to combine such a supplement with an iron-rich diet. Large doses of supplemental iron can be toxic, so don't exceed the amount recommended by your health care provider. Here are some suggestions for effectively meeting your requirement for iron:
* Eat iron-rich foods, such as beans, blackstrap molasses, dried fruit, leafy greens, lentils, seeds, soy foods, whole grains, and fortified grain products.
* Eat foods rich in vitamin C, such as bell peppers, citrus, and tomatoes, when you eat iron-rich foods, in order to increase absorption of the iron.
* Take a prenatal supplement that includes iron or take a daily supplement of 30 mg of iron. A good strategy is to take the supplement between meals, with orange juice.
* Avoid coffee and all types of tea (including black, green, and even some herbal teas, such as chamomile and peppermint), which can decrease the absorption of iron.
#### **ZINC**
Zinc is required for cell differentiation, in which cells change to perform particular functions in the body. This mineral is also involved in cell replication, which is fundamental to growth. Insufficient intake during pregnancy has been linked with preterm deliveries, low birth weights, prolonged labor, and other problems. Recommended daily intakes increase from 8 mg before pregnancy to 11 mg during pregnancy or 12 mg for pregnant teens. Fortunately, absorption of this mineral increases during pregnancy.
Many foods high in protein and iron, such as beans, also are rich in zinc. Other good sources include asparagus, cashews, corn, mushrooms, peanuts, peas, quinoa, seeds, tahini, tofu, and fortified cereals and veggie meats.
#### **CALCIUM**
Though a growing fetus needs calcium for bone building, a woman's recommended intake for this mineral, which is 1,000 mg between the ages of nineteen and fifty, doesn't increase during pregnancy and lactation. As with iron and zinc, the body becomes more efficient at absorbing calcium during pregnancy. However, note that most vegans don't meet recommended levels, so pay attention to your calcium intake. If you don't get enough calcium, your body will take calcium from your bones to make up the difference.
Many plant foods are excellent sources of calcium, including almonds, blackstrap molasses, bok choy, broccoli, Chinese cabbage, collard greens, figs, kale, okra, and tofu (if calcium-set). You should also include calcium-fortified foods such as orange juice, nondairy beverages, and cereals to help you meet your daily requirement.
#### **IODINE**
Iodine is an essential component of thyroid hormones. Tiny amounts of this mineral are required for normal development of the infant's brain and central nervous system and to avoid the tragedy of cretinism, a preventable form of brain damage that occurs in babies when the mother is deficient in iodine during pregnancy.
Not all prenatal supplements contain iodine, so make sure yours does. The recommended daily intake is 220 mcg per day. Most supplements contain only 150 mcg. However, if you add ¼ teaspoon (1 ml) of iodized salt over the course of the day, you'll add 70 mcg of iodine and meet the recommended intake while avoiding excessive sodium intake.
Some vegans tend to use sea vegetables as a source of iodine, but this isn't ideal, since the amount of iodine can vary so much from one batch to another. If the package has a label, check to see if it lists iodine content (many don't). Iodine drops also are a possibility and deliver a known quantity of iodine per drop. Be aware that there is an upper limit for daily iodine intake, which is 900 mcg for teens and 1,100 mcg for adults, pregnant or not.
#### **VITAMIN D**
The recommended daily intake for women for vitamin D is 15 mcg (600 IU), whether or not she is pregnant. This vitamin plays many roles, including aiding in the absorption of calcium. During pregnancy, insufficient vitamin D may increase the risk of preeclampsia. Some experts recommend that all pregnant and lactating mothers take 50 mcg (2,000 IU) of vitamin D per day through the winter months in order to maintain sufficient vitamin D levels.
#### **VITAMIN B 12**
It's essential that pregnant women get sufficient vitamin B12, whether from diet or supplements. If not, the baby has an increased risk of neural tube defects, brain damage, being born prematurely, seizures, and even death. In addition, if a mother's vitamin B12 levels are low, levels of this vitamin will be low in her breast milk, so the infant won't get enough vitamin B12.
In addition to the tragic outcomes for babies and their families, this also hurts the reputation of vegan diets, which have so much going for them. Medical associations have taken stands against vegan diets based on such tragedies. It's important to understand your B12 needs and how to meet them, and to spread the word to other women. In short, all pregnant women should take one of the following:
* A daily supplement that includes at least 25 mcg of vitamin B12.
* A supplement that contains 1,000 mcg of vitamin B12 two or three times a week.
* Three servings of food fortified with vitamin B12 each day—for example, breakfast cereals, veggie meats, or Red Star Vegetarian Support Formula nutritional yeast. Make sure each serving contains at least 4 mcg of vitamin B12, with the label showing that each serving contains at least 60 percent of the daily requirement for this vitamin.
#### **FOLATE**
Crucial for building the baby's DNA and for other aspects of growth, folate is also needed for the development of the neural tube, which develops into the brain and spinal cord. Vegans are likely to get enough folate since they eat plenty of beans, greens, and oranges. However, the recommended intake of folate for pregnant women can be complex. A pregnant woman should get 600 mcg of folate per day. The body utilizes folate from food quite readily. A pregnant vegan could get her day's supply of folate from 1 cup (250 ml) of orange juice, 3 cups (750 ml) of romaine lettuce, and 1 cup (250 ml) each of cooked quinoa and black beans.
A synthetic version of folate, called folic acid, is used in supplements and fortified foods such as breads, pasta, rice, flour, cereals, and other enriched grain products. The body converts folic acid to folate, but there's no reliable way to tell how much folate the body obtains as a result. Although it's safe to get plenty of natural folate from food, preliminary evidence suggests a link between high intakes of folic acid and some cancers. Therefore, it may be prudent to limit your intake of folic acid supplements to 600 mcg per day; the benefits of folic acid supplements in early pregnancy outweigh the possible risks. A diet that includes plenty of folate-rich plant foods can easily meet recommended intakes, but a supplement is recommended especially if your appetite is poor.
#### **OMEGA-3 FATTY ACIDS**
Essential omega-3 fatty acids are key nutrients needed before, during, and after pregnancy. The long-chain omega-3 fatty acids docosahexaenoic acid (DHA) and eicosapentaenoic acid (EPA) are critical building blocks for development of the baby's retinas, brain, and central nervous system. We all have the ability to convert ALA to EPA and DHA, but pregnant women have superpowers in this regard. Even so, vegans have lower levels of DHA and EPA, including in their breast milk, than nonvegetarians, so many experts suggest that pregnant and nursing vegans take supplemental DHA and EPA. Aim for a ratio of omega-6 to omega-3 fatty acids between 2 to 1 and 4 to 1. (For more on omega-3 and omega-6 fatty acids, see page 66.)
During pregnancy and lactation, it's essential to consume adequate alpha-linolenic acid (ALA), which the body can convert into EPA and DHA. Good sources of ALA are chia seeds, hempseeds, walnuts, ground flaxseeds, and their oils.
Certain dietary habits affect the ability to convert ALA to DHA. The body makes DHA most efficiently when we limit our intake of trans-fatty acids and oils high in omega-6 fatty acids (corn, cottonseed, safflower, sesame, and sunflower oils), and when we eliminate processed and deep-fried foods made with these oils and fats. Foods containing trans-fatty acids that inhibit DHA production include some margarines, crackers, cookies, pastries, and any food that lists "partially hydrogenated vegetable oil" on the label.
There may be a health advantage to the infant if the mother includes a direct source of vegan DHA, such as a microalgae-based DHA supplement or foods and oils that are fortified with algae-derived DHA. A combination of DHA and EPA is also suitable, as the body can convert EPA to DHA.
### Avoiding the Bad Guys
Alcohol is toxic to developing brain cells. Avoid it entirely throughout pregnancy. It passes from your blood directly through the placenta, and the baby's liver isn't mature enough to handle it. There's no point in getting stressed if you had a few drinks early in pregnancy, before you knew that you were embarking on this great adventure, but now that you know, don't use alcohol.
The same goes for tobacco and marijuana. The amount of caffeine that's safe isn't certain, but a small amount—a maximum of 200 mg per day—is commonly considered safe. Note that 1 cup (250 ml) of coffee contains 100 to 200 mg, 1 cup (250 ml) of tea has 40 to 75 mg, 12 ounces (360 ml) of cola has 40 to 60 mg, and 1 ounce (30 g) of dark chocolate has about 15 mg.
The placenta can filter out toxins of a certain size, but it can't totally protect a fetus, so do your part by not letting in toxic substances in the first place. That includes pesticides, so be sure to choose organic foods whenever possible.
### Exercise
Staying active during pregnancy has plenty of advantages. It makes you feel good, it keeps you fit and shapely (even when round), and it tones your muscles to aid in delivery. While you shouldn't ski, scuba dive, in-line skate, do gymnastics, ride horseback, or do activities where you might fall, plenty of possibilities remain. Swimming, water aerobics, prenatal yoga, and walking are all good choices. If you jogged and cycled before you were pregnant, it may be fine to continue. Aim to get at least thirty minutes of exercise daily. If you aren't accustomed to exercise, are concerned, or have a high-risk pregnancy, check with your doctor.
### Meal Ideas
Let's take a look at how you can incorporate all of the nutrients discussed above into a delicious vegan diet that's ideal for you and your baby. Each day, try to eat at least three servings of grains, three servings of legumes, five servings of vegetables, four servings of fruit, and one serving of nuts or seeds. Make sure six servings of these foods are high in calcium.
The sample menu that follows incorporates those recommendations. It also features protein-rich foods at every meal and snack, and no calories are wasted on sugar or other refined foods that don't deliver nutrients to you and your baby. Potassium, choline, and folate come from vegetables, fruits, and beans. The high fiber intake helps prevent constipation, and drinking plenty of water and exercising will also help with this. The beans, hummus, soy foods, cereal, and nuts or seeds deliver zinc and iron, but not quite as much iron as recommended during pregnancy. We recommend taking a prenatal supplement to provide vitamin B12 and additional vitamin D, iodine, and iron.
As indicated in the list of variations below the menu, you can substitute different foods and still be assured that you're meeting your nutritional requirements. Be aware that this plan doesn't leave a lot of room for soft drinks, sweets, chips, and oily snacks, so when you want to enjoy a treat, choose something based on whole foods, such as homemade ice creams made from frozen fruit, or cookies and bars made with whole-grain flour, nuts, and dried fruit.
Before you review the menu, we'd like to set the record straight on soy foods, which seem to be a magnet for rumors. To some extent, this can be traced back to messages put out by competing industries, rather than to authentic research. In some cases, studies that cast a negative light on soy used birds as research subjects. One was a report on two people who unwisely consumed twelve to fourteen servings of soy foods per day for many months. That said, if you have thyroid problems and your iodine status is low, you shouldn't eat soy until you get enough iodine and the thyroid problems are resolved; after that, soy shouldn't be a problem. In general, feel free to have one to three servings of soy foods per day during pregnancy and while breast-feeding.
#### **SAMPLE PREGNANCY MENU**
**BREAKFAST**
1 cup (250 ml) cereal with ½ cup (125 ml) blueberries or other fruit and 1 cup (250 ml) fortified soy milk
1 slice whole-wheat toast with 2 tablespoons (30 ml) almond butter or seed butter
1 cup (250 ml) freshly squeezed orange juice or fruit
**SNACK**
½ cup (125 ml) carrot sticks with ¼ cup (60 ml) hummus
**LUNCH**
Sandwich with ½ cup (125 ml) seasoned tofu and lettuce on 2 slices whole-grain bread
2 cups (500 ml) tossed salad with ½ avocado and 2 tablespoons (30 ml) Liquid Gold Dressing (page 105)
**SNACK**
2 figs or 1 piece other fresh fruit
2 tablespoons (30 ml) nuts, peanuts, or seeds
1 cup (250 ml) fortified soy milk
**DINNER**
1 cup (250 ml) beans and ½ cup (125 ml) brown rice
½ to 1 cup (125 to 250 ml) cooked kale with lemon juice
1 cup (250 ml) tomato slices
Nutritional analysis: calories: 2,135; protein: 97 g (18% of calories); fat: 85 g (34% of calories); carbohydrate: 271 g (48% of calories); dietary fiber: 60 g; calcium: 1,400 to 2,109 mg (depending on choice of tofu, nuts, and fruit); iron: 22 mg; magnesium: 791 mg; phosphorus: 1,817 mg; potassium: 4,938 mg; selenium: 94 mcg; sodium: 1,451 mg; zinc: 15 mg; thiamin: 3.2 mg; riboflavin: 3.4 mg; niacin: 23 mg; vitamin B6: 2.8 mg; folate: 754 mcg; pantothenic acid: 6.1 mg; vitamin B12: 5.1 mcg; vitamin A: 1,581 mcg RAE (5,271 IU); vitamin C: 234 mg; vitamin D: 5.5 mcg (200 IU); vitamin E: 18 mg (27 IU); vitamin K: 497 mcg; omega-6 fatty acids: 21 g; omega-3 fatty acids: 5.9 g
#### VARIATIONS
* Substitute similar items, such as different types of fruits, vegetables, and beans.
* For an equally high-protein menu without soy, use a different fortified nondairy milk, increase the hummus in the snack to ⅓ cup (160 ml), and replace the tofu with 1 cup (250 ml) of lentils.
* For an alternative source of omega-3s, replace the Liquid Gold Dressing with 2 tablespoons (30 ml) of ground flaxseeds, 2 teaspoons (10 ml) of flaxseed oil, or a handful of walnuts.
### Fueling the Milk Machine
For a multitude of reasons, breast-feeding is the best option for both babies and moms. When it isn't possible, commercial soy-based infant formula is a safe and healthful alternative.
Nature has done a superb job of designing human breast milk. It contains the perfect balance of protein, fat, and carbohydrate. It's easy for the baby to digest. The proportions of protein and sodium are ideal for the infant's kidneys. Vitamins, minerals, and protective compounds abound, as does DHA, which builds brain and eye tissues. Breast milk also contains a number of protective substances, helps the gastrointestinal system mature, and guards against gastrointestinal illness.
Breast-fed babies are less likely to develop colds, ear infections, stomach upsets, allergies, and asthma. They are also less likely to be overweight as children or adults and more likely to do well in school. They have a reduced risk of childhood leukemia, diabetes, and heart disease. In addition, the mother's body automatically adjusts the composition of the milk as the baby grows so that it always meets the baby's changing nutritional requirements from birth to toddlerhood.
The American Academy of Pediatrics and the World Health Organization recommend breast-feeding exclusively for the first six months before introducing solid food. If possible, breast-feeding should continue for at least another six months, and longer as desired by mother and baby. The natural age of weaning is between two and four years. At the age of four, lactase, the enzyme that breaks down the milk sugar lactose, naturally declines. However, even a short period of breast-feeding is beneficial, so just do the best you can given any practical considerations you face. Vegetarian and vegan moms tend to nurse their babies longer than nonvegetarians, and this is an excellent trend.
In terms of advantages for mothers, those who breast-feed lose baby weight more quickly, especially if breast-feeding lasts at least six months. Breast-feeding also reduces mothers' risk of diabetes and breast and ovarian cancers later in life. Breast-feeding is convenient. You don't have to warm bottles and cart a lot of equipment with you whenever you and your baby venture out. It also gives you superb one-on-one time with your baby, often providing some of the sweetest moments of parenting.
Vegan and vegetarian mothers offer their babies a further advantage by breast-feeding: they have fewer toxins in their milk than nonvegetarian moms. Sadly, the levels of potentially toxic environmental pollutants commonly found in breast milk would prevent its sale as a food for infants. But breast milk from vegetarian moms typically contains only a fraction of those levels. Given that, imagine the advantages of a vegan diet of _organic_ food.
Breast-feeding moms need plenty of calories, protein, and other nutrients. During the first six months of breast-feeding, you need 330 to 500 extra calories per day. (Naturally, if you have multiple infants, such as twins, you'll need even more.) If you need to lose some baby weight, stick with about 330 extra calories per day. If your weight is already back where you want it, eat about 400 extra calories per day. Of course, how much you eat depends on the baby's appetite too. If your little one is voracious, you may need more calories. After the baby begins eating solid food, you'll need fewer calories. As in pregnancy, eating small frequent meals is a good way to ensure that you're getting enough calories.
While nursing, you could continue using the same sample pregnancy menu on page 210, adding a little extra avocado or nut butter or other sources of vitamin E, and be assured that you're meeting all of your basic nutrient requirements, with two exceptions. You'll need to get more pantothenic acid and vitamin A, so we'll discuss these two nutrients first.
#### **PANTOTHENIC ACID**
Pantothenic acid is needed for building essential cell components and neurotransmitters, and for energy production. You need more while you're breast-feeding, but a good vegan diet can provide enough. Whole grains are good sources of this vitamin; in refined grains it's been stripped away. You can get the additional pantothenic acid you need for the day if you eat another half avocado, add ¾ cup (185 ml) of sweet potato or mushrooms, or eat 2 cups (500 ml) of cooked oatmeal with a big banana for breakfast. Other good sources of pantothenic acid include broccoli, legumes, mushrooms, nutritional yeast, nuts, and seeds, such as sunflower seeds.
#### **VITAMIN A**
Vitamin A allows cells to carry out specific tasks, and its effects are diverse. It's needed for the growth of bones and teeth, for reproduction, and to build and regulate hormones. Vegans get vitamin A from the carotenoids in orange, yellow, red, and green fruits and vegetables. The sample pregnancy menu on page 210 provides enough to meet your needs from carrots, kale, lettuce, tomatoes, and fortified soy milk. Carotenoids are also found in apricots, broccoli, cantaloupe, leafy greens, mangoes, nectarines, papayas, peppers, persimmons, plantains, prunes, pumpkin, squash, sweet potatoes, turnips, and sea vegetables. For other sources, see table 6.2 (page 120).
#### **VITAMIN B 12**
Babies require vitamin B12 for the normal development of brain, nerve, and blood cells. Without it, the baby's brain won't develop normally, resulting in neurological problems. This can occur even if the mother shows no symptoms of vitamin B12 deficiency, so it is critical that nursing moms get enough vitamin B12. Breast milk doesn't include vitamin B12 from the mother's stores, so nursing moms must eat foods fortified with vitamin B12 or take a B12 supplement daily or a larger supplement twice a week (see page 207). Supplements are a better choice than fortified foods because the amounts are more carefully standardized.
#### **PROTEIN**
Nursing mothers need to get as much protein as in the second and third trimesters of pregnancy. Legumes, whole grains, greens, and vegetables provide plenty of protein, along with iron, zinc, calcium, other minerals, and many B vitamins.
#### **IRON**
Women require less iron while breast-feeding than during pregnancy, since the body is no longer building its blood supply for gestation, or for menstruating. Breast milk provides adequate amounts of iron in a form that's easily absorbed by the baby. The recommended intake for nursing vegans and vegetarians is 16 mg per day.
#### **ZINC**
Mothers need slightly more zinc while breast-feeding than during pregnancy—12 mg instead of 11 mg per day. Some of the best sources of zinc are seeds, particularly pumpkin and sunflower seeds and sesame tahini; nuts, especially cashews; every kind of bean, pea, and lentil; peanuts; soy foods; whole grains, including barley, brown rice, oats, whole wheat products, and wheat germ; plus asparagus, corn, mushrooms, spinach, and dark chocolate. Some breakfast cereals, nondairy milks, veggie meats, and energy bars are fortified with zinc.
#### **CALCIUM**
Mothers need just as much calcium—1,000 mg per day—while nursing as during pregnancy. While lactating, the body goes through changes that enhance its absorption of calcium. The mother's body may also draw on calcium stores in her bones for breast milk. Consuming more calcium doesn't seem to prevent this, but fortunately, studies have shown that after weaning, the mother's bone mineral content will be restored.
#### **VITAMIN D**
Breast milk is low in vitamin D, and levels vary according to the mother's sun exposure, her dietary intake, and whether she takes a vitamin D supplement. The American Academy of Pediatrics recommends that all infants and children, including adolescents, get at least 10 mcg (400 IU) of vitamin D daily beginning soon after birth.
#### **OMEGA-3 FATTY ACIDS**
The section on omega-3s earlier in this chapter (page 208) discussed ways to enhance the body's stores of DHA. However, the most reliable way of increasing DHA in breast milk is to take supplemental DHA. Although these are commonly made using fish oil, vegan DHA supplements made from DHA-rich algae (the same place the fish get their DHA) are available. Supplementation isn't absolutely essential, but taking 200 to 300 mg of DHA per day will help boost your DHA status. Another option is to eat DHA-fortified foods and oils. In addition, because this essential fat is so important during the third trimester, premature babies should receive supplemental DHA, as they aren't yet able to synthesize DHA. Formulas for premature infants include DHA.
#### **FLUIDS**
If your body is going to make milk, you need to drink lots of liquids. You will feel thirsty often, so keep water, juice, soy milk, or smoothies on hand all day. Be sure to keep beverages near the comfortable chair that you use for nursing so you can sip while your baby nurses.
### Formula Feeding
There can be good reasons to use infant formula as your baby's primary source of nutrition or as an occasional option. The American Academy of Pediatrics recommends iron-fortified infant formula as the only acceptable substitute for breast milk during the first year because it can help prevent iron-deficiency anemia. Infants born prematurely are at highest risk for iron deficiency because their iron stores can be very low. Full-term infants are usually born with iron stores sufficient for their first six months, until solid foods are introduced. Formula contains higher levels of iron than breast milk, but the iron from breast milk is absorbed more easily. Infant formula also supplies adequate amounts of vitamins D and B12, but it lacks many of the immune-protective compounds found in breast milk.
Standard formulas are based on cow's milk or soy milk and are fortified to contain roughly the same nutrients as breast milk at similar levels. If you wish to avoid animal products, use soy formula. (However, soy formula isn't suitable for preterm infants or those with congenital thyroid problems. For more information on this, see the "Infant Formula" section of "Soy: What's the Harm?" at veganhealth.org/articles/soy_wth.)
Several of the infant formulas available in North America are close to vegan. As this book goes to press, the single nonvegan component is vitamin D3 derived from lanolin from sheep's wool. With sufficient consumer demand, more companies might choose to use vitamin D2 or vegan vitamin D3 from lichen.
Please be aware that most cases of malnutrition in vegan infants can be traced to homemade infant "formulas" that are grossly nutritionally inadequate. Never feed a baby homemade formula, and never substitute regular dairy or nondairy milk for formula or breast milk. Using regular dairy or nondairy milk or homemade formula can lead to poor child development or even tragic, disastrous health problems, _including death_. Babies need specific nutrients in certain amounts. Beverages other than breast milk and infant formula don't provide all of the nutrients they require. The only safe and nutritionally adequate types of milk for the first twelve months of life are breast milk and commercial infant formula.
**_Resources and Websites for Pregnancy and Lactation_**
Good nutrition during pregnancy and lactation is crucial to giving infants an healthy start in life, but space doesn't permit us to address this important topic in greater detail. Here are a few resources that provide more details:
* _The Everything Vegan Pregnancy Book_ , by R. Mangels (Adams Media, 2011). The title says it all.
* _Cooking Vegan_ , by V. Melina and J. Forest (Book Publishing Company, 2012). Tasty high-protein recipes, complete with nutritional analyses.
* _Raising Vegetarian Children_ , by J. Stepaniak and V. Melina (McGraw-Hill, 2003). An entirely vegan book packed with practical tips, recipes, and menus.
* "Pregnancy and the Vegan Diet" at vrg.org/nutrition/veganpregnancy.htm. An Internet resource offered by the Vegetarian Resource Group.
* "Vegetarian Diets in Pregnancy" at vegetariannutrition.net/docs/Pregnancy-Vegetarian-Nutrition.pdf. An Internet resource offered by the Academy of Nutrition and Dietetics.
For a more extensive edition of this book, fully referenced and for health professionals, see _Becoming Vegan, Comprehensive Edition: The Complete Reference to Plant-Based Nutrition_ , by B. Davis and V. Melina (Book Publishing Company, 2014).
### Food Allergies
If anyone in the baby's family has a history of allergies, seek advice from a dietitian, nurse, doctor, or clinic regarding the introduction of foods beyond breast milk. The potential to develop an allergy is an inherited characteristic. However, the tendency to react to specific foods isn't inherited. Pediatricians and allergy specialists can provide individualized guidance. Early introduction of solid foods, especially before three months of age, has been linked with the development of food allergies, and it's a primary reason experts recommend against introducing solid foods until the baby is six months old. Your baby may have a reduced risk of developing celiac disease if you wait until after six months to introduce foods with gluten. However, giving gluten- and wheat-containing foods after the six-month mark has been found to _lessen_ risk of celiac disease. Breast-feeding seems to play a protective role in reducing reactions to gluten or potential food allergens. Breast-feeding may support the immune system and the maturation of the intestinal tract so they can more effectively perform their protective functions.
For all infants, and especially those with a family history of allergies, it's wise to introduce foods one at a time and then wait at least three or four days to see if there's any reaction before introducing another new food. Mixed foods shouldn't be introduced until the individual ingredients have been consumed without reaction. Signs of food allergy can appear on the skin as red or itchy patches, which may be eczema or hives; in the respiratory tract as a stuffy nose, wheezing, or runny eyes; or in the gastrointestinal tract as colic that doesn't go away, frequent spitting up, or diarrhea. In extreme cases, the baby's lips, face, eyes, or ears may swell, and the baby may have trouble breathing. This can signal a medical emergency, so if this happens, take your baby to an emergency room immediately.
In the past, the medical community advised parents to delay the introduction of highly allergenic foods, but now that advice has come into question. Needlessly restricting the diet can be problematic and lead to nutrient shortages that are entirely unnecessary. Follow the advice of your physician.
However, we will share information on foods that are more likely to be allergenic so you can be alert to potential issues when (or if) you introduce them. These include fish, shellfish, eggs, milk, peanuts, tree nuts, soy, wheat, sesame seeds, and sulfites (for example, in dried fruit). Foods generally considered less likely to trigger allergic reactions include apple (cooked), apricot, avocado, banana, barley, beet, blueberries, broccoli, carrot, cauliflower, green beans, kale, millet, oats, parsnip, peach, pear, plum, potato, prunes, rice, quinoa, squash, sweet potato, tapioca, and yam.
Note that children who react to a particular food in raw form sometimes don't react to the same food when it's cooked.
### Introducing Solid Foods
Several decades ago, The Farm in Tennessee was the focus of another study, this time looking at the growth and development of 288 vegan children who were born and raised there. The children ate nutritious vegan foods, including full-fat, fortified soy milk. Researchers found that infants born at The Farm had normal birth weights and that their growth was typical of predominantly breast-fed children. Their average weights and heights were within normal ranges and fell between the twenty-fifth and seventy-fifth percentiles. So if well-meaning friends and relatives question the safety of raising children on a vegan diet, you can say you have solid medical science on your side.
Up to about six months of age, babies typically need only breast milk or formula, but then things start to change. The baby's intestinal tract matures, decreasing the possibility of allergic responses to foods.
In addition, the baby's supply of iron, which is stored during gestation, starts to run low. In a few cases, this happens as early as four months. By six months of age, nursing babies should receive complementary foods to provide about 1 mg of iron per kilogram (2.2 lb) of body weight per day. If insufficient iron-rich solid foods are consumed, a supplement is recommended. In most cases, formula-fed babies don't need an iron supplement, since formula is fortified with iron. Parents are generally advised to provide supplemental iron to preterm breast-fed babies and a special iron-enriched formula to those who are formula-fed, as these babies have low iron reserves. However, inappropriate iron supplementation can lead to iron overload, so these infants should be carefully monitored by their physicians.
**_What about Raw Diets for Growing Children?_**
Scientific studies haven't established the adequacy of raw diets for growing children. In fact, extremely restrictive and high-fiber diets, such as fruitarian diets, can be too low in calories, protein, and some vitamins and minerals and have been linked to cases of severe malnutrition and even infant deaths. We don't recommend raw vegan diets for infants and children, although including some raw foods is great!.
Beginning solid foods at the right stage has many benefits, including helping children avoid weight problems later on. For example, formula-fed babies who eat solid foods before four months of age are six times more likely to be obese at age three.
Babies show that they are ready for solid foods when they can sit, hold up their head, and pick up a morsel of food and put it in their mouth. Another sign is when they show interest in the foods that family members are eating. When a baby reaches this stage, don't wait too long to introduce solid foods. If you miss this period of fascination with new tastes and textures, the child may become a picky eater. However, be sure that a major component of the baby's diet remains breast milk or formula until at least age one, and perhaps age two or older.
Parents typically begin with pureed food. As babies progress beyond that stage, it's important to make sure they get enough calories. Use full-fat soy foods, such as tofu and soy yogurt. Other sources of concentrated calories and nutrients include avocados, nut and seed butters, and bean spreads. You may wish to include some refined grain products (such as pasta) in addition to whole grains.
Rely on cooked foods such as thick soups and stews, as cooking generally makes food more digestible. Cookies, muffins, puddings, and shakes can also be highly nutritious foods if you use healthful ingredients.
#### **BOOSTING BABY'S IRON STORES**
Because babies' iron stores tend to start running low at six months, when solid foods are usually introduced, be sure to include iron-rich foods early on. Iron-fortified commercial infant cereals generally are a good first choice as you introduce solid foods; two tablespoons (30 mL) dry iron-fortified oat cereal provides enough iron for the day. Vary your grains. Well-cooked, pureed whole grains such as oats, barley, or quinoa are good options, but provide less iron than fortified cereals. In the past, many people recommended against giving babies wheat early on. However, recent research shows that including wheat as a starter food for breast-fed babies may reduce their risk of celiac disease and sensitivity to wheat. Mix cereals or grains with some breast milk or formula. Iron-rich foods to try include Cream of Wheat and pureed broccoli, green beans, kale, peas, or sweet potatoes.
At around seven months, follow up with additional iron-rich foods, such as well-cooked lentils and beans, mashed tofu, soy yogurt, grated or peeled and cooked vegetables, and fruits. Prune juice is a good source of iron, and citrus fruit or a bit of citrus juice will increase absorption of dietary iron.
#### **EXPANDING THE MENU**
When babies are eight to nine months old, they begin to enjoy finger foods. Try chunks of pita bread or tortilla, teething biscuits, different shapes of pasta, unsweetened cereal, pieces of rolls or pancakes, unsalted crackers, steamed tofu cubes, and soft fruits like avocado, banana, kiwi, mango, melon, or papaya.
At nine to twelve months, most babies are ready to join family meals and can start eating what the family eats: mixed dishes, stews, grated raw carrot and apple, and veggie meats. After each new food seems well accepted, include it regularly. Soon your family can share ratatouille, stir-fries, lentil curries, chili, pasta dishes, vegan pizza, risotto, roasted veggies, and more. Just omit the salt and salty seasonings, such as Bragg Liquid Aminos, tamari, or soy sauce, from your baby's portion.
### Meals for Babies
Table 11.4 outlines sample meal plans for babies ages six to eighteen months. Babies need 3 to 4 cups (24 to 32 fl oz, or 750 ml to 1 liter) of breast milk or infant formula over the course of the day. That amount will naturally decrease between twelve and eighteen months of age. Although fortified soymilk is an acceptable milk alternative after 12 months of age, iron-fortified infant formula is preferable until age two. After six months or as the baby begins to eat more solid food, add some sips of water, especially when the weather is warm.
#### **SUPPLEMENTS AND FOOD SOURCES FROM BIRTH TO EIGHTEEN MONTHS**
The sample menus meet the recommended intakes for all nutrients, except for vitamins B12 and D, which can be obtained from fortified foods and supplements. After you introduce solid foods, regularly include well-cooked broccoli and firm tofu for calcium, avocado and seed butters for vitamin E, and plenty of fruits and vegetables for potassium, along with abundant breast milk or formula.
**TABLE 11.4.** Sample meal plans for babies six to eighteen months old
TIME | 6 TO 9 MONTHS | 9 TO 12 MONTHS | 12 TO 18 MONTHS
---|---|---|---
Early morning | Breast milk or formula | Breast milk or formula | Sleep in! (Or wish you could.)
Breakfast | ¼ to ½ c (60 to 125 ml) infant cereal mixed with breast milk, formula, or water
1 to 4 tbsp (15 to 60 ml) soft fruit in small pieces | ¼ to ½ c (60 to 125 ml) infant cereal mixed with breast milk, formula, or water
Small pieces of whole-grain toast
Soft fruit in small pieces
Breast milk or formula in a cup | 1 small pancake; toast with tahini; or ½ c (125 ml) oatmeal
½ banana or ½ c (125 ml) applesauce
Breast milk or ¾ c (185 ml) formula in a cup
Morning snack | Breast milk or formula | Breast milk or formula
Soft fruit in small pieces | Small whole wheat bun or 2 or 3 crackers, spread with 2 tbsp (30 ml) hummus
Breast milk or ½ c (125 ml) formula
Lunch | 1 to 4 tbsp (15 to 60 ml) mashed or soft vegetables
1 to 6 tbsp (15 to 90 ml) pureed well-cooked beans, lentils, or peas; steamed tofu or tempeh; or soy yogurt
Soft fruit in small pieces
Breast milk or formula | 2 to 4 tbsp (30 to 60 ml) mashed or soft vegetables or fruit
2 to 6 tbsp (30 to 90 ml) soft cooked beans, peas, or lentils; steamed tofu or tempeh; veggie burger; or soy yogurt
Breast milk or formula in a cup | ½ to ¾ c (125 to 185 ml) lentil soup
½ veggie burger or sandwich
½ cup (125 ml) berries or fruit, such as cooked peeled pear
Breast milk or ½ c (125 ml) formula in a cup
Afternoon snack | Breast milk or formula | Breast milk or formula
Soft vegetables or fruit in small pieces | ½ c (125 ml) soy yogurt with fruit
Water in a cup
Supper | 1 to 4 tbsp (15 to 60 ml) mashed or soft vegetables
1 to 6 tbsp (15 to 90 ml) pureed cooked beans, peas, or lentils
1 to 4 tbsp (15 to 60 ml) soft fruit in small pieces
Breast milk or formula | 2 to 6 tbsp (30 to 90 ml) cooked potato or pasta
2 to 6 tbsp (30 to 90 ml) pureed cooked beans, peas, or lentils; steamed tofu or tempeh; or soy yogurt
Soft vegetables or fruit in small pieces
Breast milk or formula in a cup | ¼ cup (60 ml) cooked beans, peas, or lentils, with ½ c (125 ml) rice, potato, or pasta, and ⅓c (85 ml)
stir-fried vegetaables; or 1 to 1½ c (250 to 375 ml)
family entrée
Breast milk or ½ c (125 ml) formula in a cup
Evening snack | Breast milk or formula
¼ to ½ c (60 to 125 ml) infant cereal mixed with formula, breast milk, or water | Breast milk or formula
Finger foods such as pieces of frozen fruit, cooked sweet potato, toast, vegan teething biscuits, or dry cereal flakes | Breast milk or ½ c (125 ml) formula
Favorite healthy snacks
Sources of data are listed in _Becoming Vegan: Comprehensive Edition,_ by Brenda Davis and Vesanto Melina (Book Publishing Company, 2014).
Key: c = cup; ml = milliliter; tbsp = tablespoon.
Nutritional analysis (for the "6 to 9 Months" column; based on larger amounts where there is a range, and on the first item where there is an option): calories: 1,170; protein: 32 g (11% of calories); fat: 64 g (48% of calories); carbohydrate: 126 g (41% of calories); dietary fiber: 11 g; calcium: 1,260 mg; iron: 18 mg; magnesium: 170 mg; phosphorus: 547 mg; potassium: 1,531 mg; selenium: 43 mcg; sodium: 201 mg; zinc: 5 mg; thiamin: 1.1 mg; riboflavin: 1.4 mg; niacin: 23.1 mg; vitamin B6: 0.7 mg; folate: 200 mcg; pantothenic acid: 3.9 mg; vitamin B12: 0.52 mcg; vitamin A: 2,317 IU (702 mcg RAE); vitamin C: 99 mg; vitamin D: 40 IU (1 mcg); vitamin E: 7.5 IU (5 mg); vitamin K: 60 mcg; omega-6 fatty acids: 9 g; omega-3 fatty acids: 1.3.
**_The Diet of a Good Role Model_**
Whether or not you're breast-feeding, your diet matters—and not just for your own health. Children take in every move made by Mom and Dad, and your habits can lay the foundation for lifelong patterns of your children. Habits, such as eating a lot of vegetables, tend to start early in life.
**Vitamin D.** To one year of age, breast-fed babies need 10 mcg (400 IU) of vitamin D daily as a supplement. Formula is fortified and contains sufficient vitamin D when it's the baby's main food source. From one to three years of age, the recommended intake is 15 mcg (600 IU) of vitamin D.
**Vitamin B 12.** As mentioned, breast-feeding moms need to get enough vitamin B12 so their breast milk will supply enough of this essential nutrient. Infant formula is fortified with vitamin B12 and is a reliable source. As the baby takes less milk, and after weaning, provide foods or formula fortified with vitamin B12 three times a day, or give a supplement. Recommended daily intakes are 0.5 mcg from six to twelve months of age and 0.9 mcg from one to three years of age.
**Omega-3 fatty acids.** The recommended daily intake of alpha-linolenic acid for infants six to twelve months old is 0.5 gram, and for children one to three years old, it's 0.7 gram (double to 1.4 grams when no DHA is provided). Breast-feeding moms need to get sufficient omega-3 fatty acids, since these are passed along in breast milk. If using formula, choose one with added DHA. If using a formula without DHA, one simple way to provide sufficient ALA is to give ¼ teaspoon (1 ml) of a balanced, omega-3-rich oil to babies between six and twelve months old, and then ½ teaspoon (2 ml) of the oil to children between one and three years old. For more on omega-3 fatty acids, see chapter 4.
### Toddlers and Preschoolers
When babies are standing on their own two feet and ready to head off into the world, leaving breast or bottle behind (at least some of the time), their nutrient needs change again. You can have a wonderful time exploring textures and flavors together as the baby's ability to feed himself or herself increases. However, children are often nutritionally vulnerable at this time, thanks to growth spurts and discovering the power of "No!" The key to success is to have a good dietary plan in mind while also being flexible, adjusting for your preferences and those of your child.
The Vegan Food Guide for Toddlers included in this section explains the number of servings of each food group required each day and offers guidelines on serving size. Basically, include foods from three to five of the food groups listed at every meal and from at least two food groups at snack time. Don't necessarily limit certain foods to being breakfast or supper items. Consider possibilities such as starting your child's day with breakfast burritos or soup, or offer rice and raisin pudding at any time of day. Include iron-rich foods often, such as iron-fortified cereals.
Children have small stomachs. To keep them well nourished, provide meals or snacks every two to three hours. Have nutritious foods at the ready when hunger strikes: perhaps soy yogurt, a tray of cut-up veggies with avocado or bean dip, a fruit smoothie with hempseeds, or frozen muffins, which thaw quickly.
Though children may appear to be picky eaters, diligent detective work often proves that they are managing well and even thriving. Note their food intake, energy, and growth. They may reject much of the food on their plate at mealtime but readily eat snacks. If so, it's especially important to offer highly nutritious snacks. For example, over the course of a day, if children weighing from 25 to 33 pounds (11.5 to 15 kg) consume 3 cups (750 ml) of fortified soy milk, two peanut butter sandwiches, two sliced bananas, and ½ cup (125 ml) of peas, they're getting enough calories and triple the recommended amount of protein.
#### **VEGAN FOOD GUIDE FOR TODDLERS**
**Milks and formula:** 2½ to 3 cups (20 to 24 fl oz, or 600 to 750 ml) total About three ¾- to 1-cup (6 to 8 fl oz, or 180 to 240 ml) servings of breast milk, commercial infant formula, full-fat fortified soy milk, or a combination of these
**Breads and cereals:** four to six toddler-sized servings
One toddler-sized serving:
* ½ slice bread or a similar-sized piece of tortilla or pita bread
* ¼ cup (60 ml) cooked grain or pasta
* ½ cup (125 ml) ready-to-eat cereal
* ¼ cup (60 ml) cooked cereal
**Vegetables:** two to three toddler-sized servings
One toddler-sized serving:
* ½ cup (125 ml) salad or raw vegetable pieces
* ¼ cup (60 ml) cooked vegetables
* ⅓ cup (85 ml) vegetable juice
**Fruits:** two to three toddler-sized servings
One toddler-sized serving:
* ½ to 1 fresh fruit
* ¼ cup (60 ml) cooked fruit
* ¼ cup (60 ml) fruit juice; limit to ½ cup (125 ml) per day
**Beans and alternates:** two toddler-sized servings
One toddler-sized serving:
* ¼ cup (60 ml) cooked beans, peas, or lentils
* 2 ounces (60 g) tofu
* ½ to 1 ounce (15 to 30 g) veggie meat
* 1½ tablespoons (22 ml) nut or seed butter
* 2 tablespoons (30 ml) soy yogurt
#### **NUTRIENT NOTES**
Look online or in your natural food store or pharmacy for a high-quality vegan children's multivitamin-mineral that includes adequate amounts of vitamin B12, vitamin D, and iodine, along with calcium, iron, and zinc. This can give you peace of mind, especially during times when your little one seems picky, resulting in eating habits that seem unbalanced or insufficient. (Be sure to store all supplements safely away from children.)
**Vitamin B 12.** From age one to three years, the recommended intake is 0.9 mcg per day—the amount found in 2¼ cups (18 fl oz, or 550 ml) of infant formula or fortified soy milk. (Check labels.)
**Vitamin D.** From age one until adulthood, the recommended intake is 15 mcg (600 IU). Infant formula or fortified soy milk may provide vitamin D; check labels for amounts. To get enough vitamin D from sun exposure, children need to have sun on their face and forearms between 10 a.m. and 2 p.m.: ten to fifteen minutes for light-skinned children, and twenty minutes or more for those with darker skin. This isn't an option in winter months at latitudes above 37 degrees north, so a supplement may be necessary. Avoid excess sun exposure, and don't give more than 63 mcg (2,520 IU) of supplemental vitamin D per day; excess vitamin D can be toxic.
**Omega-3 fatty acids.** From age one to three years, the recommended intake is 0.7 gram of alpha-linolenic acid if your child is still nursing or drinking formula. Otherwise, supplement with 1.4 grams of alpha-linolenic acid or 0.7 gram of alpha-linolenic acid plus 70 mg of DHA.
**Iodine.** From age one to eight, the recommended intake is 90 mcg. This can be obtained through a supplement, from iodized table salt (limit to ¼ tsp/1 ml daily) and other iodine-rich foods, or a combination. (See pages 135–136).
### Children to Age Twelve
Rapidly growing children have nutritional needs that are quite different from those of adults. At around age two, a toddler may weigh 27 pounds (12 kg) and be 34 inches (86 cm) tall. Three years later, that child might weigh 50 percent more and be 9 inches (23 cm) taller. To accomplish this amazing feat of building the body, the child's diet must be rich in protein, minerals, and numerous other nutrients. The pace of growth eases slightly during the preteen years and then picks up with new force in early adolescence. In the sections that follow, we offer some meal ideas that can help ensure adequate nutrition while also transforming meal planning and preparation from a daily burden into a rewarding shared process.
**_What's a Treat?_**
Though children will ask for unhealthful foods and beverages, you don't have to buy them. It's best to offer more nutritious choices. For example, you can make healthy soda using sparkling water and freshly squeezed orange juice or another pure fruit juice. In place of conventional ice pops, you can make your own with ice-pop molds and a combination of fruit and either fruit juice or nondairy yogurt. Splurge on fresh berries or make a healthful fruit shake.
#### **BREAKFAST**
Eating breakfast helps children pay attention, concentrate, remember, and perform better academically. Skip the sugar-laden cereals, despite the provocative marketing ads, and create appealing and nutritious breakfasts. For a change of pace, try scrambled tofu or a smoothie with hempseeds, sunflower seeds, or a smoothie booster. Many children enjoy a "breakfast bar" similar to a salad bar; keep several types of muesli, granola, or other wholesome ready-to-eat cereals near the breakfast table, along with jars of seeds, nuts, and shredded coconut. This assortment may be popular for snacks too. Cooked cereal, fresh fruit, and fortified nondairy beverages can be added in the morning.
Planning can help ensure a peaceful start to the day, even if everyone has to be out the door early. For children who are too sleepy to eat before heading to school or day care, a grab-and-go breakfast such as a nutritious homemade muffin or a nut butter sandwich might be a good solution, providing something they can eat on the ride to school or during a morning break.
If you have time for a leisurely and companionable start, perhaps on weekends, it's fun to make pancakes together and serve them topped with fruit or fruit sauce. This activity can motivate children to become good cooks later in life. For a special breakfast that's almost instant, pop vegan frozen waffles into the toaster.
#### **PACKED LUNCHES**
Assembling lunch boxes or bag lunches can be a pleasant shared task, perhaps done the evening before. Some children prefer a familiar favorite sandwich every day. For others, a packed lunch will be more appealing if the offerings change often.
Lunch should include protein-rich foods and whole grains to help supply sustained energy through the afternoon. It may seem that a vegan diet doesn't lend itself to sandwiches, since it doesn't include meat and cheese. Fortunately, that isn't the case. The possibilities are numerous and can easily accommodate anyone's preferences. Start with a grain product, such as a baguette or crusty roll, whole-grain bread, pita bread, rice cakes, or a tortilla. Spread on some vegan buttery spread, mustard, ketchup, guacamole, olive tapenade, pickle relish, or soy mayonnaise. Add a protein, such as a tofu spread or seasoned tofu slices, nondairy cheese, falafel patties, hummus, nut or seed butter, vegetarian deli slices, a veggie burger, or refried beans. Also include a layer of vegetables, such as sprouts, lettuce, sauerkraut, shredded carrot, or sliced avocado, cucumber, bell pepper, red onion, olives, or tomato.
If your child has an insulated lunch bag, other welcome choices include nondairy yogurt and hearty salads made with beans, potatoes, pasta, or grains. Leftover pizza and pasta dishes work well too and can include gluten-free options.
#### **DINNER**
Children who aren't fond of homemade soups, cooked vegetables, or stir-fries may become more open to vegetables if they help with the preparation, perhaps bringing lettuce from the garden, washing carrots, and, when capable of handing a knife safely, chopping. Most people live on six to ten favorite meals, repeated over and over. Some time-tested favorites among children are pizza, chili, veggie burgers, falafel, tacos, burritos, and spaghetti with a pasta sauce that includes well-cooked red lentils. When made with the right ingredients, these dishes can be well-balanced nutritionally, and the leftovers are often great for packed lunches.
#### **SNACKING**
When cooking grains, pasta, and entrées, make enough that you'll have leftovers to serve as snacks. Although many children don't mind cold grains or pasta, these also can be warmed with a little tomato sauce or peanut sauce. To satisfy a sweet tooth, keep fresh fruit in a bowl on the countertop and jars of dried dates, apricots, figs, or other dried fruit handy. (Brush teeth after eating dried fruit!)
#### **THE GOOD FOOD DAY**
Table 11.5 (page 226) gives examples of menus that meet the nutritional needs of children at three different weights and stages of growth. Very active children may burn more calories than the amounts supplied by these menus, in which case you can simply increase their portions or add foods to these menus. All of these menus easily meet and exceed protein recommendations. As you may note, a menu that meets recommended intakes for all nutrients leaves little room for junk food.
#### **NUTRIENT NOTES**
For children whose diets generally are good, a daily supplement isn't necessary, with the possible exceptions of vitamins B12 and D. However, do consider a supplement on days when food intake is less than adequate. Amounts of vitamins and minerals in supplements are more reliable than in fortified foods, so using a combination can be wise. See pages 274–275 for recommended intakes.
**Vitamin B 12.** In addition to supplements, fortified nondairy milks provide vitamin B12, as do some fortified veggie burgers and breakfast cereals.
**Vitamin D.** Fortified nondairy milks also provide vitamin D, but they currently don't meet the more recent, increased recommendations. Children should get ten to fifteen minutes of sun on their faces and forearms daily (without sunscreen) to top up their vitamin D. After that, be sure they use sunscreen if they'll be outside longer. For those who live at latitudes above 37 degrees north, sunlight is insufficient for vitamin D production during the winter, so supplements can be important from October or November through March or April.
**Iodine.** Sufficient iodine could be obtained through a supplement, from iodized salt (limit to ¼ tsp/1 ml daily), other iodine-rich food or a combination. (See pages 135–136).
#### **EATING AWAY FROM HOME**
Some people anticipate that a vegan diet will make life difficult for children by setting them apart. Fortunately, many parents find that this isn't such a big hurdle.
To ensure that meals away from home are nutritious, planning is essential. When traveling, check out happycow.net or vegdining.com, or do an Internet search to locate vegan-friendly restaurants. Breakfast can be as simple as oatmeal, cereals, fruit, toast, jam, peanut butter, and juices. Cereal can be eaten dry, or with nondairy milk or juice. Sometimes bringing one or two items from home can allow your family to enjoy school or restaurant meals without compromising dietary choices. For lunch and dinner, many restaurants include vegan options, if not as entrées then as side dishes, such as rice, baked potatoes, pasta, vegetables, or salad, which you can combine for a meal. Salad bars, whether in restaurants or markets, are often a good choice, as they include high-protein options such as peas, chickpeas, beans, and possibly tofu. In many cases, your best bet may be an ethnic restaurant, particularly Chinese, Indian, Middle Eastern, Japanese, or Thai.
Some children are naturally adventurous, and others want familiar foods when they venture out. For the less adventurous child, bring a favorite brand of crackers, individual boxed nondairy milk, mini portions of peanut butter, a favorite sandwich, or trail mix. For car travel, carry a big bottle of water to wash berries, cherry tomatoes, or peas in the pod, which you can purchase en route, plus a knife to cut fresh fruit or veggies.
**TABLE 11.5.** Three menus for children
Sources of data are listed in _Becoming Vegan: Comprehensive Edition,_ by Brenda Davis and Vesanto Melina (Book Publishing Company, 2014).
Key: c = cup; g = gram; kg = kilogram; ml = milliliter; tbsp = tablespoon; tsp = teaspoon.
If you hope to make positive changes in local school meals, an important first step may be to gather a few allies, such as vegetarian-friendly teachers, school food service personnel, or other parents. You're more likely to be successful if you approach school food service staff positively, offering encouragement, praise for their efforts, and helpful ideas and input. Whether your initial overtures are welcomed or rebuffed, you'll be contributing to a widespread movement to improve the healthfulness of school meals and include entirely vegetarian options for those who want them. Visit the Vegetarian Resource Group online (vrg.org) and look at information under "Teens, Family, and Kids" and "Food Service." Another helpful resource is the Physicians Committee for Responsible Medicine (pcrm.org). At their site, do a search for "school lunch."
### Teens
Vegetarian teens tend to be significantly better nourished than their nonvegetarian peers. Studies comparing teens at Adventist schools, where diets are predominantly vegetarian, with children in public schools found that BMI was lower among vegetarians, especially girls. In addition, vegetarian girls and girls who ate more soy foods started menstruating seven months later than nonvegetarian girls, on average. Later onset of menstruation is linked to longevity and lower risk of breast cancer. A study of Australian teens also found that vegetarians were leaner and had better cholesterol levels. Heights, hemoglobin levels, and activity levels were similar in the two groups. The one disadvantage noted for the predominantly vegetarian group was lower levels of vitamin B12, something that can easily be changed by taking supplements.
The teen years can be challenging—a time when kids are asserting their independence and making more of their own choices. Nutrition-related issues can become an arena for conflict, but they can also facilitate shared learning for the whole family.
Some teens become vegan within nonvegan households. Their parents may be supportive if the teen is willing to eat a nutritionally adequate vegan diet. Even more helpful is if such teens are willing to prepare entrées to complement the meals the rest of the family eats. Typically, the items needed are protein-rich beans, peas, lentils, and veggie meats.
In contrast, in some vegan families, a teenager decides to experiment with being a meat eater. It's important to let teens make their own decisions, watching over them and loving them through the process. For parents, this is a time to learn lessons about boundaries and letting go.
Here are some of the common food-related concerns that may arise during adolescence. We'll take a closer look at a few of these issues in the rest of this chapter:
* The need for increased nutrients during a major growth spurt
* Rebellion about family food guidelines
* Disinterest or being uninvolved in food preparation
* Not prioritizing good nutrition
* Distress about skin problems, premenstrual syndrome (PMS), and weight
* Development of eating disorders
* A focus on sports
#### **NOURISHING HEALTHY SKIN**
As with many aspects of appearance, skin health can be a major issue during adolescence. A surge in sex hormones can enlarge and stimulate oil glands in the skin, particularly around the nose and on the neck, chest, and back. Some people produce more oil than others, and some people's skin is less efficient at clearing away discarded cells. The result can be acne and pimples. It's important to clean the skin gently and regularly with water and mild soap, to avoid oil-based cosmetics, and to keep the skin dry. Some teens find that certain foods, such as sweets, processed foods, artificially flavored beverages, and fried foods, can result in skin reactions.
Water is an important cleanser, inside the body as well as outside. It carries away toxins that are flushed out through the kidneys. Never underestimate the effectiveness of drinking 6 to 8 cups (1.5 to 2 liters) of water daily in promoting skin health. Fruits and vegetables help keep skin clear and healthy too, in part because they contain 80 to 95 percent water by weight, and also because they contribute vitamins and phytochemicals that directly nourish the skin. Carotenoid-rich yellow, orange, red, and green vegetables and fruits give a warm glow to the skin. All of this information may help convince teenagers who are struggling with skin issues to drink more water and eat more vegetables—practices that promote health in many ways.
#### **PREMENSTRUAL SYNDROME**
Some girls experience excruciating cramps and other unpleasant symptoms at the onset of menstruation. Here are some diet-related tips that may help.
* **Eat a low-fat, high-fiber vegan diet.** A diet of whole grains, beans, vegetables, and fruits, along with a vitamin B12 supplement, can reduce PMS, menstrual pain, water retention, and monthly weight gain. These benefits may be related to the impact of diet on hormone levels.
* **Eat plant foods rich in B vitamins.** Research has shown that thiamin and riboflavin can reduce pain and improve mood, and that these B vitamins are best obtained from food, not supplements. Fortunately, they are plentiful in whole grains, fortified cereals, nutritional yeast, legumes, soy foods, seeds, and nuts.
* **Include beneficial oils.** Overall, a PMS-prevention diet should be moderately low in fat. However, it's helpful to include omega-3 fatty acids, such as 2 tablespoons (30 ml) of ground flaxseeds or ¼ cup (60 ml) of hempseeds or walnuts each day. One study found that borage oil and evening primrose oil didn't improve PMS symptoms, despite their reputation for doing so.
* **Get enough vitamin D.** A study of college-age women showed that those with better dietary intakes of vitamin D had lower rates of PMS. This may be related to improved calcium absorption and retention, or to impacts on hormones or neurotransmitters. Sunshine also might help.
* **Avoid alcohol and sugar.** According to one study, those who experience PMS tend to consume relatively high amounts of alcohol and sugar. However, the study didn't indicate whether PMS caused the pattern of consumption or the pattern of consumption caused the PMS. Anyone troubled by PMS might try avoiding alcohol and sugar for a cycle or two to see whether it has any effect.
#### **CALCIUM, VITAMIN D, AND BONE BUILDING**
The teen years are a key time for bone mineralization and achieving the healthy bone density that's crucial for helping stave off osteoporosis later in life. Unfortunately, vegan diets can be short on calcium. Good sources include fortified juices and nondairy beverages, greens with low oxalate levels (collard greens, kale, and napa cabbage), beans, blackstrap molasses, and figs. Also some corn tortillas are also high in calcium.
Outdoor activities can help teens build bone in at least two ways: First, weight-bearing exercise helps build bone. And second, sunlight helps the body produce vitamin D, which enhances calcium absorption. Higher vitamin D levels among girls aged nine to fifteen years who participate in high-impact sports are associated with fewer stress fractures.
#### **EATING TOGETHER**
Mealtimes can offer a special occasion for adolescents to share their day with other family members. Some teens spend much of their time in their bedroom listening to music, watching television, using the computer, or talking on the phone, emerging only when famished and perhaps returning to their room to eat. It's important to give teens responsibilities that keep them involved with the rest of the family, such as setting the table for dinner, washing dishes, baking, or preparing bag lunches. It's possible to largely respect their need for private time while also requiring them to spend a half hour with the family at dinner. As a bonus, studies show that teens who have regular meals with their families eat more fruits and vegetables than teens who don't.
Pregnant and nursing moms, babies, toddlers, and children all have special nutritional needs that are more than met by a well-planned, whole-foods vegan diet. People older than sixty-five comprise another group with unique dietary concerns and needs. With a little understanding of aging's effects on nutritional needs and a little tweaking of diet, vegan seniors can healthfully coast through the golden years.
## CHAPTER 12
## The Prime of Life: Vegan Nutrition for Seniors
Of Americans older than sixty-five, almost half eat at least one vegetarian meal a week. About three in one hundred never consume animal flesh, and one in one hundred is vegan. Whatever led to their dietary shift, and whether it occurred early in life or more recently, they know that a nutritious diet of plant foods is a wise choice for anyone at any age.
Seniors need fewer calories, yet their requirements for certain nutrients, such as protein, calcium, and vitamins D and vitamin B6, increase. In other words, they have to get more bang for their nutrition buck. What they eat really has to deliver.
Fortunately, a vegan diet delivers. Studies of older vegetarians, including vegans, indicate that their intakes of many minerals and vitamins are similar to or better than those of nonvegetarians. In addition, their body weight is more likely to be in the optimal range, and they're likely to live longer.
### Changes with Age
As we age, our lean muscle tissue tends to shrink while our percentage of body fat typically increases. At age sixty, women have an average of 3.5 pounds (1.6 kg) less muscle than they did at twenty. Men lose even more, with 7 pounds (3.2 kg) less muscle at age sixty. The shift from muscle to fat occurs for a variety of reasons: changes in hormones or in your metabolic rate, and, most importantly, reduced physical activity. Loss of muscle mass and strength can set in motion a cascade of consequences that includes worsening of diseases, increased disability, malnutrition, and even death.
Our energy expenditure decreases throughout our lifetime from the age of nineteen. Each decade a man expends 100 fewer calories daily and a woman, 70 calories fewer. Many adults gain about 1 pound (450 g) or so each year if they don't adjust their menus to eliminate some calories. Around the time of menopause, women often gain an extra 10 pounds (4.5 kg) and experience greater loss of muscle mass. The end result of all of these factors is that among adults older than sixty-five years of age, one in three is obese.
**_Just the Facts_**
One in eight Americans is over the age of sixty years. Since 1900, the percentage age sixty-five and older has tripled. Among sixty-five-year-olds, 39 percent are in excellent health and have an average life expectancy of 18.8 more years. Men living to age eighty-five can expect to live 5.7 additional years and women 6.8 additional years. In 2001, there were 48,000 people in the United States who were age one hundred years or more; eight years later, this number had risen to more than 64,000.
This slippery slide from muscle to fat and excess weight isn't the only option open to us. We can counteract it with a vegan diet, by eating a little less every decade, by focusing on more nutritious foods with a higher protein content, and by exercising. Increasing physical activity has numerous benefits, including allowing us to eat a bit more scrumptious vegan food without getting fat.
### Exercise and Fitness
Lack of exercise is a primary reason for needing fewer calories as we age. Fewer than 5 percent of adults get thirty minutes of daily physical activity, and even that amount declines with age. Keeping fit is as much a key to wellness as avoiding excess calories. Regular exercise promotes physical and psychological well-being and better sleep quality. It reduces the risk of disability and vulnerability to chronic diseases such as coronary heart disease, type 2 diabetes, metabolic syndrome, stroke, hypertension, loss of cognitive function, depression, and colon, breast, endometrial, and lung cancers. Regular physical activity can keep our muscles and bones strong, our metabolic rate up, and our weight in check, and it can also help prevent falls. A Texas study of adults with an average age of seventy showed that just forty-five minutes of walking on a treadmill daily improved blood flow and built muscle.
Of course, it's important to increase an exercise program gradually. With time, seniors should aim for an hour of exercise each day and include some weight-bearing exercise to maintain strong bones, such as walking, jogging, dancing, tennis, or hiking. To keep your heart strong, add swimming, water aerobics, cycling, or kayaking. To strengthen your muscles, include weight lifting, stair climbing, or everyday activities like carrying groceries or gardening. For flexibility and balance, also include yoga, tai chi, stretching, or Pilates for flexibility and balance.
Little things also help. Work on your balance to help preserve your cognitive function and prevent falls; for example, you might try standing on one foot while in the checkout line, at the bus stop, or washing dishes. Make exercise a fun and social event by inviting friends to join you on bike rides, walks, and hikes. Running around with your grandchildren and playing with the dog also count. Experiment and create an engaging fitness program that works well for you.
Keeping fit can also save you money. A California study of 424 older adults at risk for impaired mobility and diminished ability to walk safely and independently estimated that an eight-month to one-year physical activity program cost only $1,309 while preventing disability-related costs of $28,206 for the year. The program involved thirty minutes of activity a day in the gym or at home and included stretching.
### Getting Enough Nutrients
As we age and ideally eat fewer calories and exercise more, we need to make sure we still get the protein, minerals, vitamins, and fiber that we need. In the following sections, we'll provide recommendations on how you can do just that.
#### **PROTEIN**
Many seniors, vegan or not, don't meet their protein needs, and this nutrient deserves special consideration. Protein requirements for seniors are at least as high as those for younger people, perhaps slightly higher. There are currently no separate dietary reference intakes for seniors, but many experts suggest 1 or 1.1 g of protein per kilogram (2.2 lb) of body weight daily as a goal. That works out to about 61 grams per day for a 135-pound (61 kg) person, and 75 grams for a 165-pound (75 kg) person, which translates to 15 to 20 grams of protein at each meal plus a couple of protein snacks.
Vegan protein has been shown to be more than sufficient in maintaining the muscle mass of seniors, even if they get slightly less protein than nonvegetarians. In a study of men ages sixty to seventy who were doing resistance training, researchers found that a soy-rich diet was as effective as one that emphasized beef for improving muscle strength and power, without the negative effects on cholesterol associated with beef consumption.
A vegan diet may be an advantage because excess protein from meat, poultry, and fish can worsen the decline in kidney function that some seniors experience. Adding protein powders based on soy, peas, pumpkin seeds, or rice to smoothies can be a simple way to increase protein intake. (For more on vegan sources of protein, see chapter 3 and table 11.3, on page 204.)
#### **IRON**
Iron-deficiency anemia is common in seniors no matter what their diet. Low iron levels can be caused by a variety of conditions, including chronic bleeding in the gastrointestinal tract, dental problems, diminished sense of taste and smell, poor appetite, challenges in obtaining food or making meals, and poverty. Anemia can also result from chronic inflammation, chronic kidney disease, or insufficient dietary iron. Complications of anemia in the elderly include greater risk of mortality, cardiovascular disease, cognitive dysfunction, falls, fractures, longer hospitalizations, and reduced bone density.
Seniors don't need more iron than younger people. Senior women actually need less iron than women in their childbearing years, who lose iron during menstruation. The recommended intake for older vegan women and men is 14.4 mg per day, a level that isn't difficult to reach, as many plant foods are rich in iron. In fact, vegetarians and vegans tend to have higher iron intakes than nonvegetarians. Plus, their higher vitamin C intake from fruits and vegetables enhances absorption of iron.
Foods rich in iron also tend to be excellent sources of protein and zinc. These include soy foods, hummus, peas, lentils, beans, fortified breakfast cereals, meat analogs, and whole grains. Dried apricots, raisins, dark chocolate, and blackstrap molasses are also good sources of iron. (For more information on iron, see page 132.)
#### **ZINC**
A deficiency in zinc can result in poor wound healing, reduced immune function, and dermatitis in the elderly. Lack of zinc also affects our ability to taste, which can have an effect on appetite. Zinc deficiency can result from poor absorption of this mineral, physical stress, trauma, muscle wasting, and use of certain medications. Fortunately, deficiency problems seem to resolve once people get enough zinc: taste returns, dermatitis improves, and wounds heal more quickly. Zinc supplements can help, but they can interfere with the absorption of other minerals, so getting zinc from food or as part of a multivitamin-mineral supplement is preferable.
Foods high in zinc include oats, whole-grain products, fortified breakfast cereals, cashews, beans, peas, lentils, fortified meat analogs, soy foods, seeds, and seed butters. Pine nuts, pecans, wheat germ, and fresh and sun-dried tomatoes also are good sources of zinc. (For more information on zinc, see page 134.)
#### **CALCIUM AND VITAMIN D**
To maintain strong bones, we need a combination of nutrients—especially calcium, vitamin D, and protein—and we need more of these nutrients as we age.
The recommended intake for calcium increases from 1,000 to 1,200 mg per day for people older than fifty. Some experts suggest it should be increased to 1,500 mg per day after age sixty-five, since our ability to absorb calcium diminishes as we get older. Many adults find it challenging to obtain that much calcium from food. In that case, it's helpful to eat more foods fortified with calcium and take an optional supplement.
Vitamin D, which is required for the absorption of calcium, plays a role in regulating bone mass. It also plays an essential role in immune function and dental health. In addition, low levels of vitamin D are linked with excess weight gain in women sixty-five and older.
At age seventy, the recommended intake for vitamin D goes from 15 mcg (600 IU) to 20 mcg (800 IU). Many experts recommend more. Seniors with daily intakes of about 20 mcg (800 IU), along with 1,000 to 1,200 mg of calcium, have less risk of falling and fractures than those who get less. Maintaining an adequate level of vitamin D may even help you live longer.
As we age, vitamin D production in the skin, liver, and kidney becomes less efficient. At seventy, vitamin D production is only 25 percent of what it was at age twenty-five. Seniors may want to have their vitamin D level checked periodically to determine whether they should be taking supplements.
Other nutrients also help keep our bones strong. One key nutrient is vitamin K, found in leafy green vegetables. Adding just 2 tablespoons (30 ml) of kale to a smoothie or eating 1 cup (250 ml) of romaine lettuce, 2 cups (500 ml) of cabbage, or ½ cup (125 ml) of broccoli a day will help maintain the complex protein-mineral structure of your bones.
The 1,600-calorie menu on page 269 provides approximately 2,000 mg of calcium (depending on one's choice of calcium-set tofu) and the 2,000-calorie menu on page 270 provides about 1,300 mg of calcium. (For more details on osteoporosis and bone health, see the section "Osteoporosis," on page 38.)
#### **VITAMIN B 12**
Vitamin B12 keeps nerves in good repair and helps rid the body of a troublesome by-product of metabolism called homocysteine. High homocysteine levels in the blood increase the likelihood of depression, heart attack, and stroke and may heighten the risk of dementia. Vitamin B12 is needed for a healthy nervous system; confusion, disorientation, and memory loss can be symptoms of a shortage of this vitamin. In such cases, if the deficiency is recognized and reversed soon enough, these symptoms often go away.
Other signs of deficiency include fatigue, depression, irritability, mood swings, restlessness, apathy, insomnia, and perhaps poor hearing. Lack of vitamin B12 is linked to megaloblastic anemia and DNA damage that can increase susceptibility to cancer. In vegetarians whose vitamin B12 levels are below normal, supplementation has been shown to improve arterial function and reduce the risk of atherosclerosis.
Our ability to absorb B12 often decreases as we age due to decreases in stomach acid and other factors. A deficiency of this vitamin can also result from intestinal surgery, thyroid problems, use of nitrous oxide during medical procedures, or use of laxatives, antacids, or alcohol.
The recommended daily intake of vitamin B12 for adults is 2.4 mcg per day. Although you might think vegan seniors are especially at risk for deficiency, most vegans are accustomed to using supplements and foods fortified with B12 and continue to do so as they get older. The form of vitamin B12 in fortified foods is readily absorbed, even by those with diminished stomach acid. As a result, vegan seniors are able to get plenty of absorbable B12. (For more details on vitamin B12, see page 101.)
#### **ANTIOXIDANTS**
Vitamins A, C, and E and the mineral selenium provide powerful protection against free radical damage. Antioxidants are linked to a reduced risk of heart disease, cataracts, macular degeneration, various forms of cancer, and even wrinkles. The high concentrations of antioxidants in vegetables and fruits give vegans a considerable advantage. With all of the carotenoid-rich yellow, orange, red, and green plant foods in their diets, vegetarians have a significantly reduced risk of developing cataracts, and vegans have even less risk. In one study, nonvegetarians who changed to a low-fat vegan diet for fourteen or twenty-two weeks markedly improved their intakes of vitamins A and C (along with folate, magnesium, potassium, and fiber). Vitamin E intakes were better than those of people on nonvegetarian diets, although they were still slightly low, which is to be expected if a diet is low in fat. Including some higher-fat foods, such as avocado, seeds, nuts, and olives or olive oil, can help ensure adequate vitamin E intake.
Older people may have dental problems that cause them to shy away from fresh vegetables and fruits. However, soft cooked fruits, cooked vegetables, and freshly squeezed or bottled juices can take the place of foods that are more difficult to chew while still delivering plenty of protective nutrients. Baked sweet potatoes and winter squash are comforting, easy to eat, and rich in vitamin A, as are fresh or frozen mangoes and papaya. You may think of vitamin C primarily in relation to orange juice or citrus fruit, but you can get your recommended intake for the day from 1 cup (250 ml) of cooked potato plus ½ cup (125 ml) of cooked broccoli. And when it comes to selenium, you can get an adequate amount just by eating a big Brazil nut every other day. (For more details about vitamins A, C, and E, see chapter 6. For more information on selenium, see page 138.)
#### **VITAMIN B 6 (PYRIDOXINE)**
One vitamin that people need slightly more of as they age is vitamin B6. This vitamin, which is abundant in many fruits, is involved in amino acid metabolism and building hemoglobin. That's just one of several good reasons to be sure to eat four servings of fruit per day, as recommended in chapter 14. There are plenty of other vegan sources of vitamin B6, including avocado, fortified breakfast cereals, legumes, nutritional yeast, nuts, seeds, spinach, and whole grains. (For more information on vitamin B6, see page 115.)
#### **FIBER, FLUIDS, AND INTESTINAL HEALTH**
Dietary fiber comes from plant foods, so a vegan diet is a great help in avoiding constipation and staying regular. The fiber in legumes, whole grains, vegetables, and fruits keeps waste and toxins moving on and out through the intestine and helps maintain a good mix of intestinal bacteria and stable blood sugar levels. Because vegans typically consume plenty of fiber, they are advised to avoid adding wheat bran to foods, since it can compromise mineral absorption. And as healthful as whole, unprocessed plant foods are, seniors who are frail or have poor appetites may benefit from including some refined grains in the diet to help increase calorie intake.
Many seniors are susceptible to dehydration. The sense of thirst may become less acute as we get older, and infections and certain medications can also affect hydration. In addition, the kidneys become less adept at concentrating urine as people age, resulting in more frequent trips to the bathroom. Unfortunately, fear of incontinence leads some older people to drink less water and other fluids. However, it's important to keep beverages handy and sip on them often, emphasizing beverages that are calorie-free or low in added sugars, such as water, fortified nondairy milks, and herbal teas. Another way to increase hydration is by eating more fruits and vegetables; many are more than 90 percent water.
**_Raw Food for Seniors_**
The exciting world of raw vegan foods has a lot to offer seniors, particularly in terms of blended vegetable soups. See the books _Becoming Raw_ , by B. Davis and V. Melina (Book Publishing Company, 2010), or the _Raw Food Revolution Diet_ , by C. Soria, B. Davis, and V. Melina (Book Publishing Company, 2008) for a number of delicious and nutrient-rich soups, sauces, and pâtés based on pureed vegetables, seeds, and nuts.
### Planning Senior Meals
For planning meals and menus, The Vegan Plate (page 264) is a helpful guide. For many people, the minimum servings from each food group will provide enough calories. In general, emphasize legumes and vegetables for a diet rich in protein and a wide variety of vitamins and minerals. Fruit is important for its potassium content. Seniors often find that three servings from the grains group are sufficient, and this approach tends to be ideal for those who want to lose weight. Nuts, seeds, and their butters provide important minerals, and the fat they contain promotes absorption of protective phytochemicals, minerals, and fat-soluble vitamins.
Although seniors need a highly nutritious diet, certain practical factors interfere with this. Chewing, swallowing, and digesting food and absorbing nutrients may be impaired for a variety of reasons. Poor oral health, loss of teeth, ill-fitting dentures, and other dental problems can make chewing difficult. Changes in the stomach and intestinal lining can affect digestion and nutrient absorption. Fortunately, a vegan diet has advantages in these regards.
Even without intending to be vegan, some elderly people are motivated to switch from meat to tofu because tofu is easier to chew and swallow. Tofu can easily be incorporated into fruit smoothies, providing a tasty and easily consumed source of protein, iron, zinc, calcium, and numerous other nutrients. If the smoothie includes mango, orange juice, or strawberries, it will also be an excellent source of vitamins A and C. Seasoned or marinated tofu can also be the centerpiece of lunch and dinner menus.
As mentioned, despite how healthful whole grains are, for some seniors products made with refined grains, such as enriched white bread or rolls, couscous, and white rice may be a good choice because they're easier to chew. Plus, most vegan diets provide so much fiber in vegetables, fruits, legumes, nuts, and seeds that using some refined products is nutritionally acceptable, especially for seniors. That said, some whole grains are easy to chew and swallow, such as quinoa and oatmeal.
By the age of seventy, people have just 30 percent of the taste buds they had as young adults. Zinc helps maintain that sensation of taste, so seniors should be sure to consume foods that are rich in zinc, such as cashews, seeds, nut and seed butters, legumes, soy foods, and whole grains. A huge downside to loss of taste and smell is that people often pile on salt to make food more flavorful. However, excess sodium can increase the risk of hypertension and contribute to heart disease, stroke, and kidney disease. If a diminished sense of taste is an issue, flavor foods with herbs, spices, lemon juice, and other low-sodium seasonings.
**_Maintain Your Brain_**
Older adults with higher intakes of antioxidants from foods are likely to have less cognitive decline and less degenerative disease. In addition to eating antioxidant-rich foods, getting sufficient omega-3 fatty acids, exercising your body and mind, and taking supplemental vitamin B12 and DHA (docosahexaenoic acid) can help protect brain function. (For more information on omega-3 fatty acids, see chapter 4.)
#### **EASY MEALS**
Loss of appetite can be related to sensory loss, poor health, diminished cognitive status or isolation. You may have enjoyed food preparation when you could shop for interesting ingredients or when you were cooking for others but lost interest after becoming more homebound or cooking for only one. Perhaps physical disabilities, loss of mobility, or lack of transportation make it a real challenge to put together a meal. Poor eyesight can make it hard to read package directions, and limited hand strength or coordination can make opening packages a challenge. To help with these challenges, here are some meal ideas and kitchen tips that can help you put together simple, easy to chew, affordable, appealing meals that also deliver good nutrition.
BREAKFAST
* Bagel, toast, or soft bread with nut butter, sesame tahini, or blackstrap molasses, accompanied by fresh fruit
* Hot cereal or fortified ready-to-eat cereal with fruit, nuts, seeds, and fortified nondairy milk
* Scrambled tofu with sautéed onions, garlic, spinach, mushrooms, peppers, or other vegetables, seasoned with nutritional yeast, turmeric, or other seasonings, accompanied by rye toast and fresh fruit or juice
* Smoothie made with fresh or frozen blueberries, banana, hempseeds, and tofu or protein powder
LUNCH AND DINNER
* Baked potato with steamed broccoli and chickpeas, drizzled with Liquid Gold Dressing (page 105) and sprinkled with toasted sunflower or pumpkin seeds
* Baked yam with black beans and steamed kale
* Baked tofu with barbecue sauce, green salad, and steamed yam
* Canned low-sodium soup with beans, peas, or lentils, with added chopped greens of your choice
* Canned low-sodium baked beans or chili atop baked sweet potato, with a spinach salad
* Veggie burger with baked potato wedges and green beans
* Vegan pizza and green salad
* Tacos made with soft tortillas, refried beans, avocado, lettuce, and salsa
* Hummus, crackers, and raw vegetables
* Flavored rice mix with veggies, peas, beans, or edamame
* Soup with dip and raw vegetables sticks or crackers
* Marinated three-bean salad and soup
* Pasta with prepared sauce and lentils
* Pasta with prepared sauce, greens, and chickpeas
* Peanut butter or nut butter and banana sandwich
* Quinoa with chopped veggies and lima beans
* Vegetable stir-fry with seasoned or baked tofu on brown rice
* Sandwich of avocado and tomato slices and vegan meat (optional) on whole-grain bread
PREP TIPS
* Add cashews to vegetable soups and blend for a creamy texture. (Blended cashews thicken when heated.)
* Add cubes of tofu to soups to enhance nutrition; for a creamy texture, blend the tofu into the soup.
* Bake a variety of root vegetables at the same time, for example, potatoes and yams. You could also bake tofu with barbecue sauce, peanut sauce, or another sauce at the same time. Then you can quickly put together tasty meals based on these ingredients for days.
* Mix crumbled tofu with vegan mayonnaise and your favorite seasonings for a sandwich filling.
* Dried beans are economical, and soaking them for a few hours and then discarding the soaking water before cooking will reduce flatulence. Cook beans in quantity and freeze them in smaller portions. If using canned beans, be sure to rinse them well to remove some of the sodium, or just buy a low-sodium variety.
* Eat ripe soft fruits such as papayas, peaches, nectarines, mangoes, pears, bananas, melons, kiwifruit, and berries.
* Bake or stew fruit.
* Grate harder fruits, such as apples, for salads.
* Substitute quinoa for rice or other whole grains in a variety of dishes. It's higher in protein and minerals than other grains and cooks in only fifteen minutes. Be sure to rinse the quinoa before cooking.
* Invest in a good juicer. Fresh juices are an excellent way to get lots of nutrients that are easily absorbed.
* To prevent spoilage, keep bread in the freezer. Remove a slice or two at a time for toast or a sandwich.
* Keep some canned fruits and vegetables in the pantry for easy snacks and side dishes or for adding to recipes.
* Make large batches of hearty soups or stews and freeze in smaller portions.
* Mild curry paste adds a superb blend of flavors to cooked lentils and beans.
* Order Chinese take-out, such as vegetables, tofu, and rice, and get enough for leftovers.
* Red lentils, which take just fifteen to twenty minutes to cook, are a great source of iron, protein, and zinc. They can be added to tomato sauce, other sauces, and soups.
* See the 1,600-, 2,000-, and 2,500-calorie menus in chapter 14 and adapt these to your preferences.
* Slice kale into thin strips or chop it in a food processor, then add it to salads.
* Well-cooked vegetables may be easier to eat: try soft-cooked squash, yams, sweet potatoes, zucchini, eggplant, potatoes, and other veggies.
### Other Challenges
Declining health and other age-related challenges can have an impact on how well nourished an elderly person is. One issue is medications that can affect nutrient status. For example, proton pump inhibitors, which are prescribed for peptic ulcers and gastroesophageal reflux disease, are linked with deficiencies of calcium and other nutrients, and also with certain infections.
Digestive difficulties, swallowing problems, hypertension, and other disease conditions can all require dietary modifications. Unfortunately, discussion of these issues is beyond the scope of this book. However, we can recommend a few resources. A helpful book for those with diabetes or metabolic syndrome is _Defeating Diabetes_ , by B. Davis and T. Barnard, MD (Book Publishing Company, 2003). And, because 52 percent of people older than sixty-five have some form of arthritis, you may be interested to know that a raw vegan diet has proven helpful for some people with rheumatoid arthritis and some with fibromyalgia. (For more on rheumatoid arthritis, see page 45.) You might also be interested in _Bravo: Health-Promoting Meals from the TrueNorth Kitchen_ , by R. Bravo, the skilled chef at TrueNorth Health Center in California, a clinic that provides highly effective treatment for type 2 diabetes, hypertension, and rheumatoid arthritis using fasting and a vegan diet free of sugar, oil, and salt.
For healthy, delicious, and easy recipes, see the companion volume to this book, _Cooking Vegan_ , by V. Melina and J. Forest (Book Publishing Company, 2012).
### Senior Resources
Though our focus in this book is nutrition, other lifestyle factors also are key to good health in the senior years: regular exercise, loving relationships, a positive attitude, and a great sense of humor. Though these topics are outside of the nutrition realm, we'd like to share a few suggestions.
#### **VEGETARIAN ASSOCIATIONS**
More and more communities have lively vegetarian associations with members ranging from newborns to those dancing through the doors in their nineties. Those in wheelchairs are, of course, also welcome. If you're Internet-savvy, look for a local group by doing a search using the name of your town, state, or region plus the word "vegetarian" or "vegan." If you're less familiar with computers or need a little help, ask at your local library.
Vegetarian associations usually organize potluck dinners, meetings, and restaurant get-togethers on a regular basis, and sometimes put together food fairs and annual festivals. You may find these events a great place to meet like-minded people, begin new friendships, learn about cooking classes, and get involved as a volunteer. Vegetarian associations tend to be open to new ideas for outreach, including the creation of seniors support groups or local social networking.
From the comfort of your home, using a computer you can explore Meetups (meetup.com)—groups based on shared interests, such as vegan food or animal rights—and then see if you want to meet someone or a group in person. Internet dating may also be a reasonable way to meet potential partners or friends. A search using the words "vegan online dating" will quickly show you numerous vegan-friendly websites to explore.
#### **TRAVEL TIP**
Two websites that can help you find excellent vegan fare whether you are going to Paris, Prague, Portland, or Perth are happycow.net and vegdining.com. Click on the continent you plan to visit, narrow your search down to the city, and then print the restaurants there that suit your fancy. Happycow also offers an app for mobile phones.
#### **COMMUNITY SUPPORT**
If you are housebound or have difficulty getting around or preparing meals, many supermarkets and some natural foods stores offer grocery delivery services. These can include delicious vegan items from the deli department. Food delivery programs such as Meals on Wheels often have vegetarian but not vegan options, although new services offering plant-based meals are beginning to make their mark. The Vegetarian Resource Group (vrg.org) has created a four-week menu cycle specifically for Meals on Wheels that is vegan and vegetarian. Encourage your local Meals on Wheels to participate in this program.
Through state and tribal agencies, the Senior Farmers' Market Nutrition Program provides low-income seniors (over age sixty) with coupons that can be exchanged for eligible fruits, vegetables, and fresh herbs at farmers' markets, roadside stands, and community-supported agriculture programs. The US Department of Health and Human Services Administration on Aging provides funding for nutrition education and home-delivered meals to low-income seniors through the Older Americans Act and the US Department of Agriculture's SNAP program, among others. These may include vegan menu items. In some areas, other meal programs are available that allow older people to meet in a central location to enjoy a meal in the company of others, often with transportation to the site being provided.
About 29 percent of older adults live alone, and some of these seniors would prefer to have a greater sense of community while continuing to have their own home. One approach that successfully addresses the problem of isolation while retaining the best aspects of independent living is cohousing. Cohousing is a type of collaborative housing in which residents actively participate in the design and operation of their own neighborhoods. Members often share meatless meals as more vegetarians and vegans join their communities. One book on this topic is _Senior Cohousing: A Community Approach to Independent Living_ , by C. Durrett (New Society Publishers, 2009). Online information can be found at cohousing.org.
#### **FOOD IN CARE FACILITIES**
For those in search of a suitable care home for a vegan or vegetarian, whether yourself or a loved one, consider checking into those run by Seventh-day Adventists. These health-oriented folks have expertise in providing nutritious, delicious, and varied vegetarian meals. A local Seventh-day Adventist church can probably help you find a facility.
For short-term care, be aware that Seventh-day Adventist hospital cafeterias provide vegetarian and vegan meals. And in Portland, Oregon, great progress has been made in creating a hospital restaurant that is entirely vegan, the Living Well Bistro.
You may be pleasantly surprised to find that some nursing homes and assisted living facilities are willing and able to accommodate a vegan or vegetarian senior, especially if you help the busy workers figure out practical solutions to the challenge of providing suitable entrées along with their main menu. One resource on quantity cooking at care facilities is _Vegan in Volume: Vegan Quantity Recipes for Every Occasion_ , by N. Berkoff (Vegetarian Resource Group, 2000).
#### **VEGAN AND VEGETARIAN DIET SPECIALISTS**
Dietetic associations in the United States, Canada, the United Kingdom, Europe, and Australia list dietitians who specialize in vegetarian and vegan nutrition and nutritional aspects of disease. They can be contacted through the association's website. The Academy of Nutrition and Dietetics has a strong vegetarian dietary practice group (vegetariannutrition.net) with a link for "Find an RD" (registered dietitian) as well as numerous online resources.
Keeping fit is of tremendous value at any age. Whether you're a long-distance runner, an endurance athlete, or just someone who likes to go to the gym a few times a week, a vegan diet can see you through your active lifestyle. Learn how, in chapter 13.
## CHAPTER 13
## **The Fit Vegan**
Exercise generates energy and vitality. It improves brain function, boosts mood, reduces stress, strengthens bones, enhances metabolism and the production of hormones, supports immune function, and reduces the risk of chronic diseases, such as diabetes, heart disease, and cancer.
Fit vegans are among the most persuasive ambassadors of a vegan lifestyle. Without saying a single word, they tell the world that it isn't necessary to eat chickens, pigs, or cows to be fit—to run fast, jump high, or be strong. Their contributions are immeasurable because, without this reassurance, many people wouldn't give a vegan lifestyle a second thought. A fit vegan will essentially silence the naysayers.
You don't have to be an elite athlete to serve as an example; just make exercise a priority in your daily life. It doesn't matter so much what type of exercise you choose, as long as you do something. As your fitness level improves, so will your health. Those around you will notice.
In this chapter, we'll consider the ins and outs of exercise for everyone, from sedentary individuals to elite, competitive athletes. We'll examine the benefits of exercise, review the research regarding vegan fitness, provide guidelines regarding exercise for nonathletes, and then dive into the world of competitive sports and how vegans can maximize their athletic performance.
### The Endless Benefits of Exercise
Being fit allows us to live life to its fullest. Fitness dramatically improves health and gives us the freedom to pursue all of our goals.
Exercise isn't a luxury or self-indulgence. It is a necessity, just like eating, sleeping, and breathing. The human body is built to move. If you hope to achieve optimal health, exercise isn't an option; it's an imperative. If you're at all skeptical, consider the top ten benefits of exercise:
1. **Exercise reduces the risk of death and disease.** Recent research puts inactivity on par with smoking and obesity as a leading cause of death. Inactivity increases sick days, doctor's visits, hospitalizations, and use of medications. Even moderate physical activity substantially reduces the risk of heart disease, stroke, high blood pressure, type 2 diabetes, metabolic syndrome, osteoporosis, several forms of cancer, and many other medical conditions. Exercise increases insulin sensitivity, reduces bad cholesterol (LDL), boosts good cholesterol (HDL), lowers blood pressure, and improves gastrointestinal function, balance, coordination, and lung function.
2. **Exercise boosts immunity.** People who exercise regularly don't get sick as often as those who are inactive. (However, high-intensity exercise can increase the risk of infection. The theory is that the body is so busy trying to repair tissue damage caused by extreme exercise that it's less able to defend against attackers.)
3. **Exercise suppresses inflammation.** Chronic inflammation increases insulin resistance, atherosclerosis, nerve degeneration, and tumor growth. Regular moderate exercise reduces inflammation. Precisely how physical activity accomplishes this task isn't known, but exercise does increase levels of anti-inflammatory compounds in the body. It also reduces visceral fat (fat in and around vital organs), decreasing the release of proinflammatory molecules.
4. **Exercise sharpens the mind.** Physical activity, particularly aerobic exercise, may be among the most powerful protectors of the brain and nervous system. Exercise increases oxygenation and blood flow to brain tissue, boosts chemicals associated with improved cognition, and enhances growth factors responsible for the production and preservation of nerve cells. It can also augment cognitive function in seniors and reduce the risk of developing dementia and Alzheimer's disease.
5. **Exercise increases happiness.** Physical activity promotes the release of endorphins, brain chemicals that act as natural antidepressants and pain relievers—and that give people the famous runner's high. Levels of endorphins and other beneficial brain chemicals remain elevated for several days following exercise, increasing happiness and decreasing stress. Exercise may also be an effective treatment for depression.
6. **Exercise improves your sex life.** Regular physical activity stimulates blood flow, reduces the risk of erectile dysfunction, improves endurance, and boosts energy. It also incites hormonal changes that increase libido, promote relaxation, and reduce performance anxiety. Of course, being fit also boosts self-confidence and sex appeal.
7. **Exercise helps control weight.** Exercise burns calories, boosts metabolism, and promotes energy balance. Of course, this varies with the duration and intensity of physical activity. Even without an exercise program, you can increase your level of physical activity simply by taking the stairs instead of the elevator, walking more briskly, or doing simple household chores more vigorously.
8. **Exercise improves sleep.** Exercise can promote falling asleep more quickly and sleeping more deeply. While this may be because exercise is tiring, being physically active also enhances mood, reduces anxiety, and increases serotonin production—all of which promote good sleep. One caveat: For some people, exercising late in the evening or close to bedtime can be stimulating and interfere with sleep.
9. **Exercise enhances energy and endurance.** Physical activity strengthens muscles, builds bones, makes the heart work more efficiently, boosts lung capacity, and increases balance and coordination. It ensures that sufficient oxygen and nutrients are delivered to cells throughout the body. Being fit makes everything easier: shopping, housecleaning, gardening, playing with your children or grandchildren, walking with a friend or neighbor, and so much more.
10. **Exercise improves appearance and well-being.** Regardless of a person's age, gender, and physical ability, exercise tones muscles, reduces cellulite, and enhances complexion and skin health. Exercise also improves posture, strength, energy, and self-esteem. A fit body is a huge confidence booster. Fitness also decreases anxiety, making life more enjoyable.
### Getting Fit and Staying Fit
With so many obvious benefits to exercise, it seems strange that an estimated 60 percent of Americans don't do it. While it's tempting to chalk that up to laziness, inactivity is more likely about missed opportunities, the lack of social support systems, time constraints, conveniences, fears, and insecurities. If you don't exercise regularly, now is the time to make it a real priority. It doesn't matter how old you are, how coordinated you are, or how busy you are, you have the potential to get fit. In the following sections, we'll give you the information you need to get started.
#### **TYPES OF EXERCISE**
You may wonder what type of exercise is best. The answer is simple: the type of exercise you'll do consistently. Choose activities that are reasonably accessible to you and that you enjoy. You want exercise to be something you look forward to. If you have a family, select some activities that you can all enjoy together.
While all forms of exercise afford health benefits, there are three main types of exercise: aerobic activity, resistance training, and flexibility exercises. A well-rounded exercise program that features all three types is ideal for optimum fitness.
**Aerobic activity.** Aerobic, or cardio, activity is any physical activity that utilizes your large muscle groups to get your heart and lungs working harder than they do when you're sedentary. This type of exercise is especially important for endurance, circulation, and heart health. Examples include jogging, brisk walking, bicycling, swimming, skating, climbing stairs, cross-country skiing, and jumping rope.
**Resistance training.** Resistance or strength training is any physical activity that builds, strengthens, firms, and tones your muscles. This type of exercise helps improve bone density, balance, and coordination. Examples include push-ups, lunges, pull-ups, and any exercise that uses free weights or a weight machine.
**Flexibility exercises.** Flexibility exercises are activities that improve your range of motion and lengthen your muscles. They can help reduce stiffness, aches, and pains. Examples include yoga, Pilates, and stretching routines.
#### **HOW MUCH TO EXERCISE**
Any amount of exercise is better than none. However, to enjoy the maximum benefits, you need to work your way up to thirty to sixty minutes a day. The following exercise guidelines are adapted from the US government's Physical Activity Guidelines for Americans.
**Children and adolescents:** Children and adolescents need one hour or more of exercise per day. At least three days a week should include vigorous activity, and at least three days should include strength training.
**Adults (ages eighteen to sixty-four):** Adults should get 2.5 to 5 hours per week of moderate intensity activity, or 1.25 to 2.5 hours of vigorous exercise. At least two days should include strength training for all muscle groups.
**Older adults (ages sixty-five and older):** Follow the guidelines for adults if possible; if not, just be as active as your abilities allow. Include exercises that maintain or improve balance and do some resistance training with light weights.
**Disabled:** Those who are disabled should follow the guidelines for their age group as much as their disability permits.
**Pregnancy and postpartum:** Healthy pregnant women who haven't been doing vigorous exercise should get at least 2.5 hours of moderately intense aerobic exercise per week. Women who regularly engage in vigorous aerobic activity can continue during pregnancy if this is approved by their health care provider.
#### **CREATING AN EXERCISE PROGRAM**
To maintain a high level of fitness, it's best to exercise daily or almost daily. If you can't imagine setting aside thirty to sixty minutes a day for exercise, start by taking ten minutes and build from there. If you gradually increase the duration, frequency, and intensity of your workouts, your fitness goals will seem easier to achieve, and you'll also reduce your chances of injury. Table 13.1 provides a sample weekly fitness plan that meets the preferred guidelines for a healthy adult. Of course, you can substitute activities of your choice.
**TABLE 13.1.** Sample weekly fitness schedule
**DAY** | **ACTIVITY** | **DURATION** | **TYPE OF EXERCISE**
---|---|---|---
Monday | Jog or brisk walk | 30 to 60 minutes | Aerobic
|
Stretch | 10 minutes | Flexibility
Tuesday | Bike ride | 30 minutes | Aerobic
|
Free weights | 20 minutes | Resistance
|
Stretch | 10 minutes | Flexibility
Wednesday | Yoga | 60 minutes | Resistance and flexibility
Thursday | Swim | 30 minutes | Aerobic
|
Free weights | 20 minutes | Resistance
|
Stretch | 10 minutes | Flexibility
Friday | Yoga | 60 minutes | Resistance and flexibility
Saturday | Jog or brisk walk | 30 to 60 minutes | Aerobic
|
Stretch | 10 minutes | Flexibility
Sunday | Rest day | |
#### **WHEN TO EXERCISE**
When to exercise depends entirely on your body clock, your schedule, and your personal preferences. There's no universally applicable "best" time. If you wake up bright-eyed and bushy-tailed, you may enjoy exercising early in the day. If you aren't a morning person, it may be best for you to exercise in the late afternoon or early evening. Some evidence indicates that endurance and strength are at their peak in the late afternoon when body temperature is high and muscles are warm, so exercising at this time may reduce the risk of injury.
If you can't exercise when you most feel like it because of work or family commitments or other schedule issues, know that your body clock is adjustable and a different time may eventually work well for you. If your schedule is so busy that you can't spare thirty to sixty minutes for exercise, you may find that you're able to manage shorter blocks of ten to twenty minutes two or three times a day.
### The Vegan Athlete
Whether you aspire to be a world-class competitor or are a recreational athlete aiming to improve your performance, rest assured that a varied and well-planned vegan diet can provide all of the nutrients you need to meet your goals. Some people insist that vegan diets provide a competitive edge, particularly when it comes to endurance sports, while others argue that they put athletes at a disadvantage, especially when it comes to strength. Despite these strong opinions, studies suggest that plant-based diets are neither particularly beneficial nor detrimental to athletic performance. Of course, well-planned vegan diets are associated with a reduction in risk for chronic diseases, and that may translate into health advantages in the long term.
The bottom line is, vegan diets can and do support optimal performance in athletes when they are well designed. Consider just a small sampling of the world-class athletes who are vegan:
* **Patrik Baboumian.** Strongman; European champion in powerlifting, setting two world records in the 125 to 140 kg (275 to 310 pound) category. Winner of the German loglift championships; record holder for fronthold and keg lift.
* **Brendan Brazier.** Professional Ironman triathlete; winner of the Canadian 50-kilometer (31-mile) ultramarathon in 2003 and 2006.
* **Mac Danzig.** American mixed martial artist (MMA), with titles including MMA national amateur MMA champion, Gladiator Challenge lightweight champion, International Fighting Championships lightweight champion, five-time King of the Cage world lightweight champion, and _The Ultimate Fighter_ season six winner.
* **Steph Davis.** Rock climber; only woman to have free-soloed at the 5.11 + grade; featured in an extreme sport film climbing the Mineral Canyon in Utah, and appeared on the March 2013 cover of _Climbing_ magazine.
* **Ruth Heidrich.** Triathlete champion; winner of more than nine hundred gold medals for marathons, ultramarathons, other running events, and triathlons; set three world fitness records in her age group; named one of the top ten fittest women in North America in 1999 at the age of sixty-four (others were in their twenties and thirties).
* **Scott Jurek.** American ultramarathon champion; winner of multiple elite ultrarunning titles, including the US record for twenty-four-hour distance on all surfaces—165.7 miles (266.7 km), equal to 6.5 marathons in one day; the 153-mile (246 km) Spartathlon; the 100.5-mile (161.7 km) Hardrock 100; the 135-mile (217 km) Badwater Ultramarathon; the Miwok 100K; and the 100-mile (161 km) Western States Endurance Run, which he won seven times in a row; also named one of the top runners of the decade by the _Washington Times_ ; deemed a "hero of running" by _Runner's World_ ; named ultrarunner of the year three times by _Ultrarunning Magazine_.
* **Georges Laraque.** Retired Canadian professional NHL hockey player; at 6 feet 3 inches (1.9 meters) and 260 pounds (118 kg), one of the toughest guys in the league.
* **Fiona Oakes.** Marathon runner and firefighter; winner of several international marathons; personal best marathon time of 2 hours and 28 minutes.
* **John Salley.** Retired professional basketball player; first player in NBA history to win a championship with three different franchises.
### Fueling Peak Performance for Athletes
There are four main factors that drive athletic performance: genetics, training, diet, and drive. While there isn't much you can do about genetics, the other factors are largely up to you. Each of these variables can be exploited to provide a competitive edge. Diet alone can't guarantee athletic success, but enriching the fuel that sustains your physical activity will improve your efficiency. This can make a critical difference when a win or loss is determined by a split second. Of course, a deficient diet can undermine even the most consistent and determined athletic effort. The key to fueling peak performance is consuming a healthful balance of all the necessary nutrients and meeting your energy needs.
#### **ENERGY TO BURN**
There are two main sources of energy that fuel muscles: carbohydrates and fat. These fuels are readily available in the bloodstream from the foods you consume and from your body stores. Glucose, or blood sugar, is stored as glycogen and provides about 5 percent of your stored energy reserves. The lion's share of your stored fuel is fat, and most people have enough to last for many hours or even days of exercise.
The fuel of choice for your muscles depends on the type, intensity, and duration of the activity and your fitness level. During the first few minutes of exercise, the body relies almost exclusively on carbohydrates for energy. As exercise continues, more fats are used. Within about twenty or thirty minutes of activity, the body uses about half carbohydrates and half fats. If you continue with low- to moderate-intensity exercise, you'll use mostly fat for fuel. If you continue with high-intensity exercise, you'll use mostly carbs because your body can't metabolize fat fast enough to provide all the energy needed for more demanding activities.
#### **THE AEROBIC AND ANAEROBIC SYSTEMS**
Any exercise that uses large muscle groups over an extended period of time is an aerobic, or cardio, activity. Examples include running, swimming, biking, cross-country skiing, rowing, hiking, and canoeing. Aerobic refers to forms of exercise that train the heart, lungs, and cardiovascular system to process and deliver oxygen more quickly and efficiently to every part of the body. As a result, a fit person can exercise longer and more vigorously and recovers more quickly at the end of an aerobic session.
When your heart and lungs can't provide your muscles with sufficient oxygen for aerobic activities, your body switches to anaerobic metabolism to generate energy. During anaerobic metabolism, the body uses only glucose, not fat as fuel. The anaerobic system prevails in the first two or three minutes of exercise or when activity is so intense that the body's intake of oxygen can't keep up with energy demands. This occurs in speed sports, such as sprinting and other quick track events, short-distance swim races, basketball, hockey, volleyball, football, baseball, lacrosse, and speed skating. It also occurs in power sports involving sudden intense movements, such as weight lifting, bodybuilding, field events (throwing and jumping disciplines), and wrestling.
#### **MEETING ENERGY NEEDS OF ACTIVE VEGANS**
Energy needs vary depending on body size, weight, composition, metabolism, gender, age, and the amount and type of physical activity, and generally range between 2,000 and 6,000 calories a day. For casual fitness buffs who exercise a few times a week, calorie needs increase only slightly, if at all. Elite endurance athletes, on the other hand, such as ultramarathoner Scott Jurek, may need to eat 5,000 to 8,000 calories per day.
Getting enough calories is essential for optimal physical performance. The best indicators of adequate energy intake are body weight and composition. Eating more than you need increases body fat, which can compromise performance and endurance and cause injuries. If you don't eat enough calories, your body will use muscle protein for fuel, which can reduce muscle mass and endurance. Eating too little can also lower your metabolic rate, reduce the amount of energy available for exercise, and compromise your nutritional, immune, and endocrine status. This is of particular concern for women (see "The Female Athlete Triad," facing page). In young athletes, insufficient energy intake can hinder growth and development.
It's entirely possible to take in a lot of calories on a vegan diet (see chapter 14 for sample high-calorie menus.) However, plant foods tend to be high in fiber and lower in calories, so it's important that vegan athletes with increased energy needs include plenty of energy-dense vegan options. You may find it easier to meet your energy needs by eating more frequent meals and snacks, and during heavy training, you may need to take advantage of every eating opportunity, including large snacks before bed. Great choices include smoothies, sandwiches, whole-grain cereal, grain and bean salads, stir-fries, healthful baked goods, bean soups and stews, seasoned tofu, nori rolls, avocados, trail mix, toast with nut butter, vegan power bars, nondairy yogurt with fruit and granola, and pasta dishes. If you find it difficult to consume enough calories, incorporating more foods in liquid form, such as smoothies, and some refined foods, such as pasta, may be helpful. You may need to introduce higher-fiber foods, such as legumes, gradually to minimize gastrointestinal discomfort. In addition, you may find it helpful to moderate your intake of very high fiber foods, as they are filling and may reduce the volume of food you are able to consume.
#### **CARBOHYDRATES**
Carbohydrates, discussed in detail in chapter 5, provide the primary fuel for active vegans and vegan athletes. Large intakes of carbs are associated with an improved capacity for exercise and larger stores of glycogen. Vegans may be at an advantage here, since both quantity and quality of carbohydrates tend to be high in plant-based diets. If you rely on whole plant foods (whole grains, vegetables, fruits, legumes, nuts, and seeds) as your primary sources of carbohydrates, they will also provide a healthful complement of protein, fat, vitamins, minerals, and phytochemicals—all of which contribute to peak performance.
**_The Female Athlete Triad_**
The female athlete triad is a syndrome that can arise in women who participate in sports that emphasize leanness. It's characterized by disordered eating, lack of menstruation, and osteoporosis and is more common in athletes involved in endurance sports, such as distance running, and aesthetic sports, such as dancing, gymnastics, swimming, and figure skating.
Those thought to be at greatest risk are athletes who restrict calories, limit the types of foods they eat, exercise for prolonged periods, or are vegetarian. The reason vegetarian diets are associated with increased risk may be that women often choose a vegetarian diet as a means of restricting calories. In addition, vegetarian diets that are very high in fiber and low in fat may promote fecal excretion of estrogens, reducing estrogen levels in the body.
Vegan female athletes need to be sure to eat sufficient calories, protein, iron, and zinc. Very low-calorie diets—less than 1,500 calories per day—pose the greatest risk. In some cases, reducing fiber by replacing some legumes with tofu, some whole grains with refined grains, and some fruits and vegetables with fresh juices may be helpful.
Recommended carbohydrate intakes for athletes range from approximately 5 to 12 grams per kilogram (2.2 lb) of body weight per day (g/kg/d). The amount depends on training needs. Table 13.2 provides guidelines suitable for all athletes. Table 13.3 (page 252) lists a variety of foods or food combinations providing 50 grams of carbohydrates. The options that include refined foods may be more suitable as part of a pre-event meal (discussed in detail a bit later in the chapter).
**TABLE 13.2.** Carbohydrate needs for athletes
**RECOMMENDED CARBOHYDRATE INTAKE (g/kg OF BODY WEIGHT)** | **ACTIVITY LEVEL**
---|---
5–7 g/kg per day | Medium-duration, low-intensity training (60–90 minutes/day)
7–12 g/kg per day | Medium- to long-duration endurance training (1–3 hours/day)
10–12 g/kg per day | Extreme endurance training (4+ hours/day)
Source of data: International Olympic Committee, "IOC Consensus Statement on Sports Nutrition 2003" (2003), www.sfsn.ethz.ch/PDF/IOC_Conseus2003.pdf.
**TABLE 13.3.** Vegan foods providing 50 grams of carbohydrate
**FOOD** | **PORTION SIZE**
---|---
Peanut butter and banana sandwich | 2 slices bread, 2 tbsp (30 ml) peanut butter, 1 small banana (or ½ large)
Fruit smoothie | 1 banana, 1 c (250 ml) soy milk, 1 scoop protein powder,* 1 c (250 ml) strawberries
Pea, lentil, or bean soup and bread | 1¼ c (310 ml) pea, lentil, or bean soup, 1 large slice rye or other bread
Cereal, blueberries, and soy milk | 1 oz (30 g) cold cereal, ¾ c (185 ml) blueberries, 1 c (250 ml) soy milk
Almond yogurt with apple and granola | 1 c (250 ml) yogurt, 1 apple, ¼ c (60 ml) granola
Muffin with almond butter and orange juice | 1 nutritious muffin, 1 tbsp (15 ml) almond butter, ½ c (125 ml) fresh orange juice
Power bar | 1 commercial vegan power bar*
Pita bread and hummus | 1 pita bread, ½ c (125 ml) hummus*
Brown rice with tofu and vegetables | ¾ c (185 ml) rice with 2 c (500 ml) vegetables and 2 oz (60 g) tofu
Source of data: US Department of Agriculture, Agricultural Research Service, _USDA National Nutrient Database for Standard Reference_ , Release 25 (2012), ndb.nal.usda.gov.
Key: c = cup; g = gram; ml = milliliter; oz = ounce; tbsp = tablespoon.
*Check labels for product-specific information.
#### **FAT**
In addition to being an important energy source, dietary fat provides essential fatty acids and is a carrier of fat-soluble vitamins (A, D, E, and K) and protective phytochemicals. After you meet your carbohydrate and protein needs, the remainder of your calories should come from healthy fat. For athletes, that usually translates to 20 to 35 percent of calories from fat.
Reducing fat intake below 20 percent won't enhance your athletic performance and isn't generally recommended. If you eat less than 15 percent of calories from fat, you may not have enough energy when you need it during training. In addition, for women this may cause exercise-related amenorrhea (ceasing of menstruation).
On the other hand, try not to exceed 35 percent of calories from fat, as this could result in insufficient intake of carbs and protein.
Vegan athletes should rely primarily on whole plant foods for fat because they also provide protein, carbs, and valuable vitamins, minerals, and phyto-chemicals. Excellent choices include nuts and seeds (and nut and seed butters, milks, and the like), avocados, olives, and soy foods. And although concentrated oils lack many of the essential nutrients provided by high-fat whole foods, these products can help athletes with high calorie requirements meet their energy needs; just be sure to select high-quality oils.
#### PROTEIN
A common notion among athletes, coaches, and trainers is that protein is the most vital nutrient, and the more the better. Some athletes hesitate to make the switch to a vegan diet because they've always heard that plants don't provide enough protein. Although athletes do need more protein, they can get plenty from a well-designed vegan diet.
Protein plays only a very small role as a fuel source for exercise. However, adequate protein is critical for maintenance of lean body tissue and exercise performance. Current research and recommendations by sports nutrition authorities indicate that 1 g/kg/d is the minimum intake for vegan athletes. Endurance athletes should try to get 1.3 to 1.5 g/kg/d, and those who focus on strength activities should aim for 1.3 to 1.9 g/kg/d while building muscle.
The vegan athletes at greatest risk for inadequate protein intake are those who restrict their calories or eat fewer concentrated protein sources, such as legumes, tofu, tempeh, and veggie meats. It's important to consume good sources of protein at each meal. Vegans who have trouble eating enough protein may find it helpful to add vegan protein powder to smoothies. Table 13.4 lists foods that provide approximately 10 grams of protein per serving. Table 13.5 (page 254) provides suggestions for boosting protein content of meals by replacing low-protein foods with higher-protein options. (For more ideas on how to boost protein consumption, see table 10.3, on page 193, and table 11.3, on page 204.)
**TABLE 13.4.** Vegan foods providing 10 grams of protein
**FOOD** | **SERVING SIZE**
---|---
Almonds | ⅓ c (85 ml)
Black bean soup | c (160 ml)
Deli slices* | 3 slices
Firm tofu | 4 oz (120 g)
Hempseeds | 3 tbsp (45 ml)
Hummus | ½ c (125 ml)
Peanuts | ⅓ c (85 ml)
Peas, raw | 1¼ c (310 ml)
Power bar* | 1
Pumpkin seeds | ¼ c (60 ml)
Veggie burger (patty only)* | ½–1
Sources of data: US Department of Agriculture, Agricultural Research Service, _USDA National Nutrient Database for Standard Reference_ , Release 25 (2012), ndb.nal.usda.gov. Manitoba Harvest, "Nutrients: Hemp Hearts" (2012, healing-source.com/about_HempHearts_b.htm#NUTRIENTS.
Key: c = cup; g = gram; ml = milliliter; oz = ounce; tbsp = tablespoon.
*Check labels for product-specific information.
**TABLE 13.5.** Suggestions for increasing the protein content of meals
**INSTEAD OF:** | **CHOOSE:** | **PROTEIN GAINED (APPROX.)**
---|---|---
**BREAKFAST** | |
1½ c (375 ml) cornflakes, 1 c (250 ml) rice milk | 1 c (250 ml) granola, 1 c (250 ml) soy milk | 19 g
3 pancakes, 2 tbsp (30 ml) maple syrup | 3 pancakes, 3 vegan sausages, ½ c (125 ml) cooked blueberries | 14 g
**LUNCH** | |
1½ c (375 ml) vegetable soup, 2 slices whole wheat toast with 2 tsp (10 ml) margarine | 1½ c (375 ml) lentil soup, 2 slices whole wheat toast with 2 tbsp (30 ml) peanut butter | 23 g
3 c (750 ml) green salad, 2 tbsp (30 ml) Italian dressing, 2 slices garlic bread | 3 c green salad, 4 oz (120 g) grilled tofu, 2 tbsp (30 ml) tahini dressing, 2 slices multigrain Italian bread | 13 g
**DINNER** | |
2 c (500 ml) pasta, 1 c (250 ml) marinara sauce | 2 c (500 ml) pasta, 1 c (250 ml) red lentil sauce | 8 g
3 c (750 ml) vegetable curry, 1 c (250 ml) brown rice | 3 c (750 ml) chickpea and vegetable curry, 1 c (250 ml) quinoa | 15 g
**SNACK** | |
2 c (500 ml) green smoothie with banana, blueberries, kale, and water | 2 c (500 ml) green smoothie with banana, blueberries, kale, hemp protein powder, and water | 20 g
2 oz (60 g) pretzels or popcorn | 1 vegan power bar | 6–14 g*
Sources of data: US Department of Agriculture, Agricultural Research Service, _USDA National Nutrient Database for Standard Reference_ , Release 25 (2012), ndb.nal.usda.gov. Manitoba Harvest, "Nutrients: Hemp Hearts" (2012, healing-source.com/about_HempHearts_b.htm#NUTRIENTS.
Key: c = cup; g = gram; ml = milliliter; oz = ounce; tbsp = tablespoon; tsp = teaspoon.
*Check labels for product-specific information.
### Vitamins and Minerals for Vegan Athletes
Not surprisingly, athletes' needs for vitamins and minerals are often higher than those of inactive people because these micronutrients play key roles in the body's use of fuel, carbs, fats, and protein. Vitamins and minerals are also important for immune function, production of hemoglobin, minimizing oxidative damage to the body, and the synthesis, maintenance, and repair of muscle and bone tissue. In addition, mineral status can have profound effects on performance.
Many people assume that athletes need to take vitamin and mineral supplements, but most athletes get enough vitamins and minerals from dietary sources as long as they eat enough food to ensure they have sufficient energy. This is also true for vegan athletes, with the exception of vitamin B12 and possibly riboflavin, vitamin D, iron, zinc, calcium, magnesium, and electrolytes.
Although not essential for all athletes, multivitamin-mineral supplements may be useful, especially for those who restrict energy intake or are dieting, have poorly planned diets or eating disorders, are pregnant or breast-feeding, or are recovering from injury. Otherwise, single-nutrient supplements can be used to address specific medical or nutritional challenges, such as iron deficiency. (For more details on specific vitamins and food sources, see chapter 6, and for minerals see chapter 7.)
#### **VITAMIN B** 12
Because B12 is lacking in whole plant foods, all vegans, including athletes, must rely on fortified foods or supplements to ensure adequate intake of this nutrient. Some athletes take B12 shots in an effort to boost oxygen delivery to tissues and enhance performance. While B12 shots can be highly effective for vegan athletes who have a deficiency, there's no evidence that athletes with good B12 status benefit from them.
#### **RIBOFLAVIN**
The need for riboflavin increases with training due to its role in energy production. While most vegan diets provide ample riboflavin, vegan athletes who restrict caloric intake may not get enough, so it's important to include sufficient reliable sources of this nutrient, such as nutritional yeast, almonds, leafy greens, broccoli, asparagus, mushrooms, and fortified cereals.
#### **VITAMIN D**
In addition to its critical role in calcium absorption and bone health, vitamin D is directly involved in the formation and maintenance of the nervous system and skeletal muscles. Vegan athletes who consume few fortified foods, train indoors, or live in northern latitudes can probably benefit from a vitamin D supplement. Although the RDA for vitamin D is just 15 mcg (600 IU) for adults ages nineteen to forty-nine years, a growing number of experts suggests a daily intake of at least 25 mcg (1,000 IU) daily.
#### **IRON**
Insufficient iron is the most common mineral deficiency among athletes, especially female endurance athletes. Iron is required for the transport and handling of oxygen and for enzymes involved in energy production. High-impact exercise and intense endurance activity can cause iron losses, reducing the blood's ability to carry oxygen and resulting in muscle fatigue and impaired performance.
Endurance athletes' iron requirements are increased by about 70 percent. This is especially true for distance runners. For this reason, vegan athletes and long-distance runners should aim for an iron intake above 32 mg per day for women and 14 mg per day for men. All female endurance athletes need to keep tabs on their iron status.
Vegan athletes, especially women of menstruating age and endurance athletes, should eat plenty of iron-rich plant foods and iron-fortified foods, along with foods rich in vitamin C. If you're iron deficient, you may require an iron supplement. However, it's important to know your iron status before you take supplements, because excessive iron can be dangerous.
#### **ZINC**
Zinc is involved in energy production and immune function and helps heal muscle injuries. A deficiency of zinc can reduce muscle strength, cardiorespiratory function, endurance, metabolic rate, and protein use, adversely affecting performance. Insufficient zinc can also lead to weight loss, decreased endurance, increased risk of osteoporosis, and anorexia.
Intense exercise can accelerate loss of zinc. Very high-carb, low-protein, lowfat diets also elevate the likelihood of zinc deficiency, particularly in female and endurance athletes. Because vegans tend to have lower zinc intakes and reduced zinc absorption, their risk for zinc deficiency may be somewhat higher.
Vegan athletes may need as much as 50 percent more than the RDA to maintain adequate zinc levels. This would mean an intake of about 16.5 mg for men and 12 mg for women. The best plant sources of zinc include legumes, tofu, nuts, seeds, whole grains, and wheat germ. It's best to avoid single-nutrient zinc supplements, since they often exceed the tolerable upper limit of 40 mg, potentially resulting in nutritional imbalances. If intakes are low, a multi-vitamin-mineral supplement providing an extra 5 to 10 mg is usually sufficient to ensure needs are met.
### **CALCIUM**
Calcium is critical for muscle contractions, transmission of nerve impulses, and numerous other body functions. It's also essential for bone health, and poor calcium status is linked to reduced bone density and stress fractures. Some vegan athletes may be at increased risk, particularly females who don't consume enough calories, have eating disorders, or are postmenopausal or not having periods.
Vegan athletes should meet the RDA for calcium (1,000 to 1,300 mg daily). Female athletes who are at risk for osteoporosis should aim for 1,500 mg per day. To accomplish this, most vegans need to incorporate some fortified foods, such as nondairy beverages, and eat plenty of calcium-rich plant foods. If you can't meet the recommended intake with food, take a supplement.
#### **MAGNESIUM**
Magnesium has a profound effect on muscle function. Evidence suggests that even marginal magnesium deficiency diminishes performance and can cause muscle cramps.
Intense endurance activities can increase magnesium requirements by 10 to 20 percent due to losses in urine and sweat. Athletes who restrict calories are at increased risk of deficiency. Vegans generally consume enough magnesium, from nuts, legumes, greens, and whole grains. If you aren't meeting daily recommended intakes (320 mg for women; 420 mg for men), add magnesium-rich foods to your diet. Some individuals may benefit from taking a magnesium supplement.
#### **ELECTROLYTES**
Electrolytes are electrically charged minerals in our body fluids that regulate hydration, nerve and muscle function, blood pH, blood pressure, and the repair of damaged tissues. These include sodium, potassium, chloride, calcium, and magnesium.
The amounts of potassium, sodium, and chloride athletes need vary widely among athletes and depend largely on fluid losses. Vegans who eat plenty of fruit and legumes get plenty of potassium. But like all athletes, they can quickly become depleted of sodium and chloride during intense endurance sports, and insufficient levels of these nutrients can seriously impair performance. Endurance athletes commonly require significantly more sodium and chloride than the upper limit for daily intake, which is 2,300 mg for sodium and 3,600 mg for chloride. For endurance events lasting more than two hours, use beverages that contain sodium and potassium (for details, see the section "Event Food and Fluid," a bit later in this chapter).
### Eating to Excel
Compared to the general population, athletes require more energy to fuel their exercise and more fluids to compensate for losses through sweat. It's important to select meals, snacks, and beverages and the timing of consumption according to the intensity and duration of the activity and the individual needs of the athlete. Hydration is especially important, as a loss of more than 2 percent of body mass via fluids can adversely affect performance, especially in warm climates and at high altitudes. Dehydration is also associated with heat exhaustion and heat stroke. The foods and fluids you consume before, during, and after events or training sessions can make or break your performance.
#### **PRE-EVENT FOOD AND FLUID**
The purpose of a pre-event meal is to provide sufficient fuel to sustain yourself during the event. The trick is to eat just enough to maximize performance while avoiding undigested food in your stomach. Timing is everything. The closer you get to an event, the smaller your meal should be. Liquid meals may be more convenient and tolerable within one hour of an event, especially if you tend to experiences nausea, cramps, or vomiting after eating solid food.
Consuming a meal that provides 200 to 300 grams of carbohydrate three to four hours prior to an event has been shown to enhance performance (see table 13.3, on page 252, for examples of foods providing 50 g of carbohydrates). The high carbohydrate content will boost energy. The meal also should be relatively low in fat and fiber to help hasten digestion. Choose foods that you tolerate well. If you're prone to reflux, avoid caffeine, chocolate, fatty or fried foods, and carbonated beverages, which make things worse. If you frequently experience diarrhea, you may need to reduce fiber intake for about twenty-four to thirty-six hours prior to an event.
Generally, an athlete's store of glycogen in the muscles is sufficient for events that last sixty to ninety minutes. You can boost your stores twenty-four hours before the event by eating carbohydrate-rich meals and decreasing your activity level. During events longer than ninety minutes, athletes may experience extreme fatigue, hitting the wall when glycogen becomes depleted. To avoid this, thirty-six to forty-eight hours before the event, start exercising less and eating a high-carb diet, consuming about 10 g/kg/d.
Drink 1½ to 3 cups (375 to 750 ml) of water or a sport beverage (see facing page) at least four hours before training or before the event. The smaller amount is recommended for smaller people; larger people should drink in the higher range. In events that last longer than one hour and offer little opportunity for hydration, drink fifteen minutes before the start of the event.
#### **EVENT FOOD AND FLUID**
Most active individuals don't need special food or beverages for less than one hour of exercise or training. However, there is some evidence that sports drinks providing 6 to 8 percent carbohydrates—14 to 18 grams of carbohydrate per cup (250 ml)—benefit performance in intense endurance events lasting less than one hour. The additional carbohydrates help maintain blood sugar levels and can be particularly useful if the event or activity takes place in the early morning on an empty stomach. Fluids providing more than 8 percent carbohydrates (such as soda) can slow digestion and aren't recommended.
For events or activities lasting more than one hour, most athletes should eat foods containing carbohydrates at a rate of about 30 to 60 grams of carbohydrate per hour during the event. If the event lasts three hours or longer, it might be a good idea to up that to 90 grams of carbs per hour. Eating carbs every fifteen to twenty minutes, rather than all at once, is best. Eating carbs during exercise is particularly important for athletes who didn't carbo-load prior to the event, who haven't eaten a meal in three to four hours, or who have been restricting calories to lose weight.
In addition to a fuel supply, athletes need to remain hydrated. Sometimes athletes become dehydrated because their sweat rate exceeds their ability to absorb fluids from the stomach. Common signs of dehydration include muscle cramps and fatigue, low blood pressure, dizziness, and headache. And while most cases of dehydration are the result of fluid loss exceeding fluid intake, some athletes may begin an event in a dehydrated state because they have too little time between events to rehydrate or are limiting foods and fluids in an effort to make a weight class for competition.
There are two ways to replenish carbohydrates, fuel, and electrolytes during endurance events. First, you can consume water and solid foods, such as energy bars. Although this approach is very effective, it isn't always convenient during competition. The second approach is to consume beverages that provide fluid, energy, and electrolytes, such as sports drinks. Choose a beverage that provides 6 to 8 percent carbohydrates and 125 to 175 mg of sodium per cup (250 ml). With heavy sweating, more sodium may be required. Potassium status is less affected by sweating than sodium status is, so a potassium-rich diet may be sufficient to maintain levels during events. However, some authorities do suggest using sports beverages with potassium, particularly during endurance events.
**_Sports Drinks: All They're Cracked Up to Be?_**
The value of sports drinks is hotly debated within the scientific and athletic communities. Amid the confusion, one thing is very clear: sports drinks are not only useless for most consumers, they are a health scourge. The last thing the average consumer or recreational athlete needs is an infusion of calories, sugar, and salt. While use of sports drinks for serious endurance athletes is certainly more justified, water and solid food are more nutritious options for fuel and hydration.
For athletes who prefer to avoid solid food during training and events, coconut water and juices are great alternatives, and a combination of the two provides an excellent balance of carbohydrates and electrolytes. Coconut water with added fruit juice is significantly higher in carbohydrates than plain coconut water. Vegetable juices, such as carrot juice, beet juice, and green juices are also reasonable choices. Because beet juice is high in nitrates, it may enhance performance by reducing the amount of oxygen needed during exercise. However, beets aren't the only nitrate-rich vegetable. Arugula, bok choy, carrots, celery, collard greens, radishes, rhubarb, spinach, and Swiss chard also provide hefty doses. Happy juicing!
#### **POST-EVENT FOOD AND FLUID**
After an event or training session, you need to rehydrate your body, restore glycogen, and repair lean body tissue. Food and fluid needs depend on the intensity and duration of the event or training session and the timing of the next event. If you're participating in more than one event in a day, the time between events is critical. If you do a single event, the post-event protocol is less significant.
Ideally, you should start replenishing glycogen within thirty minutes of an event. Generally, eating 55 to 80 grams of carbs for a 120-pound (54 kg) person or 70 to 110 grams for a 160-pound (73 kg) person right after the event, and again 2.5 and 4.5 hours later is recommended, especially if you'll be participating in another event. This type of refueling isn't as important if you'll have rest days before your next event or training day.
Some authorities suggest consuming a 3-to-1 ratio of carbohydrates to protein to ensure sufficient protein for muscle tissue synthesis and repair. This means 100 grams of carbohydrates would be accompanied by 33 grams of protein. (See table 3.3, on page 54, for amounts of protein in foods.) Other experts simply suggest eating 15 to 25 grams of protein after workouts or events in addition to carbohydrates.
After an event or training session, athletes also need to replace fluids and sodium lost in perspiration. Generally, try to drink 6 cups (1.5 L) of fluid for every 2.2 pounds of body weight (1 kg) lost.
### Putting It All Together
The keys to peak performance, regardless of dietary pattern, are to stay well hydrated and eat sufficient quantities of a wide variety of nutrient-dense whole foods. The information and menus in chapter 14 will assist you in making healthful food choices at various levels of caloric intake. The menus are appropriate for active vegans, including competitive athletes. For most athletes, the 2,500- to 2,800-calorie or 4,000-calorie menu will be most suitable, although for athletes requiring fewer calories or trying to lose weight, the lower-calorie menus provide sufficient protein and should be nutritionally adequate.
Table 13.6 (facing page) lists suggested numbers of servings from each food group at various levels of caloric intake. Feel free to vary the number of servings to suit your eating style, being sure to get at least the minimum number of servings from each group recommended in chapter 14. Select calcium-rich foods in each category to meet the recommended intake of six to eight servings of calorie-rich foods. "Other choices" refers to foods such as added fats or added sugars and other foods that don't fit into any of the food groups. If you don't use these foods, select a greater number of servings from whatever food group you wish to roughly equal the number of calories designated for "Other choices."
#### **PRACTICAL TIPS**
Here are some tips that will help you make the most of your choices in each food group as you plan your fitness diet.
**Vegetables.** If you have difficulty eating the recommended number of servings from this group, try to include vegetables at lunch as well as dinner, and use a mixture of raw and cooked vegetables (cooking condenses vegetables and makes it easier to eat larger amounts). Keep cut-up, ready-to-eat vegetables handy for snacks. Juicing vegetables also greatly reduces their bulkiness, making it easier to eat more. Try making dehydrated vegetable chips for crunch appeal. Kale, zucchini, and sweet potatoes work especially well. You can find recipes for these on the Internet.
**Fruits.** To increase fruit consumption, add fruit to breakfast cereal, bring a few pieces of fruit to enjoy as snacks at work or school, add fruit to smoothies, and make fruit-based desserts. Fresh fruit juices are another option. Avocado can be added to smoothies.
**Legumes.** The protein powerhouses of the plant kingdom, beans and products made from beans, are important for athletes. If you have difficulty eating enough servings, get creative. Use white beans in dips and pâtés, add cooked red lentils to spaghetti sauce, and include sprouted peas in salads. Experiment with ethnic cuisines, and use a wide variety of products made from beans, such as hummus, tofu, tempeh, and vegan meats.
**TABLE 13.6.** Suggested servings from food groups at various caloric intakes
Source of data: US Department of Agriculture, Agricultural Research Service, _USDA National Nutrient Database for Standard Reference_ , Release 25 (2012), ndb.nal.usda.gov.
*Calorie estimates are based on an average of several choices, and individual items can vary considerably from these estimates. Please note:
* Starchy vegetables provide at least double the calories of other vegetables.
* The energy content of legumes varies widely. See table 3.3 for more precise calorie counts. Peanuts and peanut butter contain about 200 calories per serving (similar to nuts and seeds).
* Whole grains are heavier and slightly higher in calories than bread.
Key: c = cup; g = gram; mg = milliliter; oz = ounce; tbsp = tablespoon; tsp = teaspoon.
**Grains.** Eating the suggested amount of grains to increase your calories can seem daunting. But one serving is only ½ cup (125 ml) of grains or 1 slice of bread. It's easy for big eaters to get six servings of grains in one meal—for example, 2 cups (500 ml) of rice plus a whole-grain roll, or 2 cups (250 ml) of pasta plus 2 slices of garlic bread will provide six servings. Likewise, 2 cups (500 ml) of oatmeal with 2 slices of toast provides six servings. If you prefer to limit your intake of grains, eat more servings from all of the other groups.
**Nuts and seeds.** Nuts, seeds, and their butters are valuable nutrition allies for vegan athletes. Include them with most meals, and be sure omega-3 selections are part of the mix. Sprinkle nuts and seeds on salads and cereals, and use nut or seed butters on crackers, toast, celery, and in salad dressings. Nut-based cheeses, spreads, yogurts, and other dairy replacements are a great addition to the diet.
**Other choices.** The foods in this category are fats and oils, concentrated sweeteners such as maple syrup and blackstrap molasses, chocolate, and other sweet treats. While it isn't necessary to eat these foods, most people do, so it's important to include them in your calorie count. Plus, these foods can help boost calories if you have very high energy needs, while also adding flavor and variety to your diet.
We are nearing the end of our tour through the land of vegan nutrition. You've learned what a nourishing, health-supporting vegan diet should include. Now you just need to know how to put all of that information together into tasty menus that are designed specifically for you. Well, just turn the page and—voilà!—chapter 14, The Vegan Food Guide.
## CHAPTER 14
## The Vegan Food Guide
You may wonder how you can take all of the information in this book and boil it down into healthful daily meals for you and your family. Take heart. You are likely to discover that, as a vegan, your options actually increase as you become more familiar with the broad spectrum of plant foods. Although these choices are also available to nonvegetarians, we humans tend to not look outside of our comfort zone. When you shift your gaze in a new direction, entire worlds open up, in this case, new cuisines, new flavors, new textures, new aromas, and new food experiences. How exciting is that?
This chapter takes into account each essential nutrient and weaves all of them together into a plan that meets recommended in-takes, combining information from the rest of the book into a simple guide for daily food intake with the goal of glowing, optimal health. We call our planning tool The Vegan Plate. We provide several sample menus, each for a day's worth of delicious vegan food.
The Vegan Plate features five food groups (listed in the first column of table 14.1 on page 265). The next column gives examples of foods in each group and serving size. The next column presents calcium-rich foods from each of these groups: foods that provide 100 to 150 mg calcium per serving. Be sure to choose six to eight servings of these foods daily. The right-hand column includes notes on how to optimize nutrition with each food group. This information is followed by a brief recap of sources of a few nutrients of special interest in vegan diets: omega-3 fatty acids, vitamins B12 and D, and iodine.
It isn't essential to achieve the minimum intake of every food group every single day, though this could be your goal over time. Eating patterns can vary greatly and still meet recommended intakes on average over the course of a few days.
This guide is very versatile, applying equally to those who want a well-designed menu for weight loss, people whose energy requirements have decreased with age, those on raw foods diet, and athletes with high energy requirements. It may seem to recommend a lot of servings, but the amounts eaten at a meal can vary considerably from one person to another, and we usually eat more than one serving from a particular food group at a meal. For example, 1 cup (250 ml) of soy milk, fruit, oatmeal, pasta, or rice actually counts as two servings.
Following this guide means that most of your calories will come from wholesome, nutrient-packed foods. Although you might occasionally indulge in foods high in sugar or fat, there isn't a lot of room for such items in any diet that meets recommended intakes of nutrients, whether or not the diet is vegan.
### The Vegan Plate
"The Vegan Plate" diagram shown below is coordinated to match table 14.1 on the facing page. Here's how to use the information: Vegetables, shown to take up just over one-quarter of your plate in the diagram, should come from the listings in table 14.1; legumes, shown to take up just under a quarter of your plate, should come from that section of the table; and so on.
**TABLE 14.1.** Food groups and serving sizes
**FOOD GROUP AND SERVINGS PER DAY** | **FOODS IN THIS GROUP WITH SERVING SIZE** | **CALCIUM-RICH FOODS WITH SERVING SIZE** | **NOTES**
---|---|---|---
Vegetables: 5 or more servings | ½ c (125 ml) raw or cooked vegetables
1 c (250 ml) raw leafy vegetables
½ c (125 ml) vegetable juice | 1 c (250 ml) cooked bok choy, broccoli, collard greens, kale, mustard greens, napa cabbage, or okra 2 c (500 ml) raw bok choy, broccoli, collard greens, kale, or napa cabbage ½ c (125 ml) calcium-fortified tomato or vegetable juice | Include at least 2 daily servings of calcium-rich greens. Choose from the full rainbow of colorful vegetables: purple, blue, green, yellow, orange, red, and white.
Fruits: 4 or more servings | ½ c (125 ml) fruit or fruit juice ¼ c (60 ml) dried fruit 1 medium fruit | ½ c (125 ml) calcium-fortified fruit juice ¼ c (60 ml) dried figs 2 oranges | Fruits are excellent sources of potassium. Enjoy the full spectrum of colorful fruits, and make them your sweet treats.
Legumes: 3 or more servings | ½ c (125 ml) cooked beans, peas, lentils, tofu, or tempeh
1 c (250 ml) raw peas or sprouted lentils or peas
¼ c (60 ml) peanuts
2 tbsp (30 ml) peanut butter
1 oz (30 g) vegan meat | 1 c (250 ml) black or white beans
½ c (125 ml) fortified soy milk or soy yogurt
½ c (125 ml) calcium-set tofu (look for calcium on the ingredient list), cooked soybeans, or soy nuts | Legumes are great sources of protein, iron, and zinc with an average of 7 to 9 grams of protein per serving. Include a selection from this group at most meals.
Grains: 3 or more servings | ½ c (125 ml) cooked cereal, pasta, quinoa, rice, or other grain 1 oz (30 g) bread ½ c (125 ml) raw corn or sprouted quinoa, buckwheat, or other grain 1 oz (30 g) cold cereal | 1 oz (30 g) calcium-fortified cereal or bread
1 calcium-fortified tortilla | Select whole grains as often as possible. Adjust the number of grain servings to suit your energy needs; some need many more servings. Some fortified cereals and tortillas are particularly high in calcium.
Nuts and seeds: 1 or more servings | ¼ c (60 ml) nuts or seeds 2 tbsp (30 ml) nut or seed butter | ¼ c (60 ml) almonds 2 tbsp (30 ml) almond butter or sesame tahini | Seeds and nuts contribute copper, selenium, other minerals, vitamin E, and fat; choose some that are rich in omega-3s.
Sources of data are listed in _Becoming Vegan: Comprehensive Edition,_ by Brenda Davis and Vesanto Melina (Book Publishing Company, 2014).
Key: c = cup; g = gram; mg = milliliter; oz = ounce; tbsp = tablespoon.
### Other Essentials
Here are recommendations on a few essential nutrients of interest to vegans: omega-3 fatty acids, vitamins B12 and D, and iodine. For more on omega-3s, see chapter 4; for more on vitamins B12 and D, see chapter 6; for more on iodine, see chapter 7.
**Omega-3 fatty acids.** Include at least one of the following:
* 2 tablespoons (30 ml) of ground flaxseeds or chia seeds
* ¼ cup (60 ml) of hempseeds
* ⅓ cup (85 ml) of walnuts
* l½ teaspoons (7 ml) of flaxseed oil
* l½ tablespoons (22 ml) of hempseed oil
* 2½ tablespoons (37 ml) of canola oil
Taking a supplement of 200 to 300 mg of vegan DHA two to three times per week may be beneficial for some individuals (such as during pregnancy or for those with diabetes). A supplement that combines DHA with EPA can also be used.
Vitamin B12. Include one of the following:
* A daily supplement that provides at least 25 mcg of vitamin B12
* Twice a week, a supplement that provides at least 1,000 mcg of vitamin B12
* Three servings daily of foods fortified with vitamin B12, such as nondairy milks, vegan meats, or breakfast cereals, totaling at least 4 mcg of vitamin B12 for the day (2/3 of the Daily Value [DV] on food labels). For one of those servings, you can substitute 2 teaspoons (10 ml) of Red Star Vegetarian Support Formula nutritional yeast flakes.
**Vitamin D.** Get vitamin D in the following ways:
* Expose your face and forearms to warm sunshine for fifteen minutes every day between 10 a.m. and 2 p.m. if you have light-colored skin, twenty minutes if you're dark-skinned, and thirty minutes if you're a senior.
* If you can't get enough sun exposure—for instance, during winter, especially in northern latitudes—take a supplement or eat fortified foods. The recommended daily vitamin D intake for adults is 15 mcg (600 IU) to age seventy and 20 mcg (800 IU) after seventy. Amounts of vitamin D as high as 100 mcg (4,000 IU) are considered safe.
**Iodine.** Include one of the following:
* A multivitamin-mineral supplement that provides 150 mcg of iodine
* About ⅜ teaspoon (2 ml) of iodized salt. Note that sea salt generally isn't iodized; if it is, this will be declared on the label.
### Practical Pointers
In addition to the preceding tips, a few simple dietary approaches will help ensure optimum nutrition and well-being:
* **Eat a wide variety of foods from each food group.** Variety helps ensure you consume sufficient quantities of a broad range of nutrients, phytochemicals, and fiber. It also makes meals much more interesting.
* **Fill at least half of your plate with vegetables and fruits.**
* **Be moderate in your intake of concentrated fats, oils, and added sugars.** These foods are generally rich in calories but poor sources of nutrients. Excessive intakes of fat and sugar will crowd out foods that offer valuable nutrients. It's better to use whole foods such as seeds, nuts, avocados, and olives as your sources of fat, and fruits as your source of sugar, rather than extracted oils and sugars.
* **Watch your sodium intake.** Using ready-to-eat processed foods can make life easier, but relying excessively on canned, frozen, and other processed foods can result in excessively high sodium intakes.
* **Aim for an hour of physical activity each day.** Activity is central to energy balance and overall health. It also helps maintain muscle strength, bone density, balance, and mental well-being.
* **Drink enough water to stay hydrated.** Fluids such as water, herbal teas, and vegetable juices can help maintain good health and prevent kidney stones and urinary tract infections. Let thirst be your guide.
### Sample Menus
Following are four sample menus with varying amounts of calories. Each has been planned for specific body types or activity levels. Select the one that meets your needs as an example of a meal plan to follow, with variations, on a daily basis.
You'll find a few other sample menus in chapter 11:
* A menu for pregnant or breast-feeding women (page 210), with 2,135 calories daily and 97 g of protein
* Three menus for infants of different ages (page 219)
* Three menus for children of different weights (page 226)
There also is a
* table showing suggested daily food servings for weight gain (page 188),
* vegan food guide for toddlers (page 221),
* list of easy meals, complete with prep tips (page 238),
* table of ways to increase the protein content of meals (page 254),
* list of suggested servings from food groups at various caloric intakes (page 261).
The other four menus focus on family meals with children's favorites, simple dishes, raw foods, and holidays and celebrations. Each menu is presented at three calorie levels: 1,600 calories, 2,000 calories, and 2,500 calories.
In the menus that follow, food groups are indicated by the following letters:
C | = | calcium-rich foods
---|---|---
F | = | fruits
G | = | grains
L | = | legumes
N | = | nuts and seeds
n-3 | = | sources of omega-3s
V | = | vegetables
After each menu, we total how many foods from each group it includes and provide a nutritional analysis for the day.
**_Menus for Every Taste_**
For more menus, see the companion volume to this book, _Cooking Vegan,_ by V. Melina and J. Forest (Book Publishing Company, 2012). It includes a dozen menus with delicious recipes to support each. Eight of the menus are based on cuisines from around the world: North American, Asian Fusion, East Indian, French, Italian, Japanese, Mexican, and Middle Eastern. The other four menus focus on family meals with children's favorites, simple dishes, raw foods, and holidays and celebrations. Each menu is presented at three calorie levels: 1,600 calories, 2,000 calories, and 2,500 calories. The more than 150 recipes include nutritional analyses.
In this book you also will find a chapter on making friends with new ingredients, including healthful oils, sweeteners, thickeners, nondairy milks, soyfoods, and herbs and spices, along with specific directions for cooking grains and legumes. You will learn how to substitute vegan for nonvegan items in recipes and will have a helpful shopping list and kitchen equipment list. If you don't feel adept in the kitchen, the chef tips are designed to make your culinary experiences more pleasurable and productive.
#### **1,600-CALORIE SAMPLE MENU**
This high-protein menu is suitable for small or elderly people or people who want to lose weight. To reduce the amount of protein, replace soy milk with other fortified nondairy beverages.
**BREAKFAST**
½ cup (125 ml) cooked cereal or 1 ounce (30 g) dry cereal | 1 G
---|---
½ cup (125 ml) raspberries or other fruit | 1 F
½ cup (125 ml) fortified soy milk | 1 L, 1 C
**LUNCH**
Soup of 1 cup (250 ml) cooked lentils plus 1 cup (250 ml) cooked vegetables (onion, carrot, celery) | 2 L, 2 V
4 rye wafers or rice crackers | 1 G
2 cups (500 ml) raw vegetables (peppers, cherry tomatoes, cucumber, carrots) | 2 V
1½ cups (375 ml) watermelon or other fruit | 3 F
**SUPPER**
Stir-fry of 2 cups (500 ml) green vegetables (broccoli, napa cabbage) | 2 V, 1 C
with ½ cup (125 ml) cubed calcium-set tofu | 1 L, 1 C
and 1 teaspoon (5 ml) sesame oil, 1 teaspoon (5 ml) tamari | -
½ cup (125 ml) cooked whole grain, such as brown rice, millet, or quinoa | 1 G
½ cup (125 ml) fortified soy milk | 1 L, 1 C
**SNACK**
Chocolate shake of 1 banana, ½ cup (125 ml) blueberries, | 2 F
with 1 cup (250 ml) fortified chocolate soy milk, ¼ cup (60 ml) hempseeds | 2 L, 2 C, 1 N, 1 n-3
Total servings of food groups: Total grains 3; vegetables 6; fruits 6; legumes 7; nuts and seeds 1; calcium-rich foods 6; omega-3s 1
Vitamin B12 is supplied by three servings of fortified soy milk.
Vitamin D is supplied by fortified soy milk; add sunshine or a supplement.
_Nutritional analysis:_ calories: 1,597; protein: 80 g (19% of calories); fat: 43 g (23% of calories); carbohydrate: 241 g (58% of calories); dietary fiber: 52 g; calcium: 1,964 mg; iron: 22 mg; magnesium: 680 mg; phosphorus: 1,583 mg; potassium: 4,700 mg; sodium: 826 mg; zinc: 14 mg; thiamin: 1.7 mg; riboflavin: 10.9 mg; niacin: 23 mg; vitamin B6: 2.2 mg; folate: 904 mcg; pantothenic acid: 5.3 mg; vitamin B12: 5.4 mcg; vitamin A: 1,438 mcg RAE (4,746 IU); vitamin C: 283 mg; vitamin D: 10 mcg (400 IU); vitamin E: 13 mg (19.5 IU); omega-6 fatty acids: 13.8 g; omega-3 fatty acids: 9.7 g
#### **2,000-CALORIE SAMPLE MENU**
This menu provides enough protein for adults (including recreational athletes) weighing 168 pounds (76 kg) at a suitable level of 1 gram of protein per kilogram (2.2 lb) of body weight. Almond milk is a source of vitamin E. Blackstrap molasses and sesame tahini are a tasty combination on toast, and both are good sources of calcium. Dark chocolate is not only tasty; it's also high in iron.
**BREAKFAST**
2 slices toast (2 ounces/60 g total) | 2 G
---|---
with 2 tablespoon (30 ml) sesame tahini and 1 tablespoon (15 ml) blackstrap molasses | 1 N, 2 C
1 cup (250 ml) calcium-fortified orange juice | 2 F, 2 C
**LUNCH**
Taco: 1 tortilla and 1 cup (250 ml) black beans, pinto beans, or refried beans | 1 G, 2 L, 1 C
with 1 tomato, 1 cup (250 ml) lettuce, ¼ avocado, and salsa | 3 V
½ cup (125 ml) fortified almond milk | 1 C
**SUPPER**
½ cup (125 ml) cooked whole grain, such as brown rice or quinoa, or 1 whole-grain roll (1 ounce/30 g) | 1 G
4 cups (1 L) salad of kale, romaine lettuce, and napa cabbage | 4 V
with 2 tablespoons (30 ml) Liquid Gold Dressing (page 105) | 1 n-3
½ cup (125 ml) cubed tempeh with lemon and ginger or BBQ sauce | 1 L
**SNACKS**
¼ cup (60 ml) dried figs and 1 orange | 2 F, 1 C
¼ cup (60 ml) pumpkin seeds | 1 N
½ cup (125 ml) fortified almond milk | 1 C
1 ounce (30 g) dark chocolate | -
Total servings of food groups: grains 4; vegetables 7; fruits 4; legumes 3; nuts and seeds 2; calcium-rich foods 8; omega-3s 1
Vitamin B12 is supplied by nutritional yeast in Liquid Gold Dressing and fortified non-dairy milk.
Vitamin D is supplied by fortified juice and almond milk; add sunshine or a supplement.
_Nutritional analysis:_ calories: 1,958; protein: 76 g (15% of calories); fat: 76 g (32% of calories); carbohydrate: 268 g (53% of calories); dietary fiber: 48 g; calcium: 1,294 mg; iron: 22 mg; magnesium: 808 mg; phosphorus: 1,867 mg; potassium: 4,847 mg; sodium: 1,100 mg; zinc: 12 mg; thiamin: 3.2 mg; riboflavin: 2.2 mg; niacin: 23 mg; vitamin B6: 2.9 mg; folate: 826 mcg; pantothenic acid: 5 mg; vitamin B12: 5.6 mcg; vitamin A: 1,313 mcg RAE (4,333 IU); vitamin C: 294 mg; vitamin D: 5 mcg (200 IU); vitamin E: 15 mg (22.5 IU); omega-6 fatty acids: 20.9 g; omega-3 fatty acids: 5.8 g
#### **2,500- to 2,800-CALORIE SAMPLE MENU**
This menu provides 2,500 calories and meets the recommended intakes for adults. To increase the calories to 2,800, add a bit more food, such as a piece of fruit and two cookies. Using the Vega One nutritional shake rather than seeds boosts levels of most nutrients well above the recommended intake. Convenience foods such as vegan meats and canned baked beans or chili can be high in sodium, so check labels—or use homemade versions, which are typically lower in sodium.
**BREAKFAST**
1 bagel with 2 tablespoons (30 ml) peanut butter; or 1 cup (250 ml) whole-grain cereal with nuts | 2 G, 1 L
---|---
Fruit smoothie: 1 scoop (35.9 g) Vega One nutritional shake or ¼ cup (60 ml) sunflower seeds or hempseeds | l L, 4 C
with 1 cup (250 ml) calcium-fortified juice (or nondairy milk) | 2 F, 2 C
and ½ banana and ½ cup (125 ml) strawberries | 2 F
**LUNCH**
1½ sandwiches: 3 slices whole-grain bread (3 ounces/90 g) | 3 G
with 3 slices vegan turkey | 1.5 L
and 1 tomato and 1 cup (250 ml) lettuce | 2 V
and 1 tablespoon (15 ml) vegan mayo | -
**SUPPER**
1 cup (250 ml) baked beans or vegetarian chili | 2 L
1 cup (250 ml) baked squash or yam | 2 V
1 cup (250 ml) steamed broccoli | 2 V, 1 C
1 baked potato with 2 tablespoons (30 ml) Earth Balance buttery spread | 1 V
**SNACKS**
1 cup (250 ml) trail mix: ⅓ cup (85 ml) walnuts, ⅓ cup (85 ml) raisins, ⅓ cup (85 ml) dried apricots | 1 N, 2 F, 1 n-3
1 cup (250 ml) calcium-fortified nondairy milk | 2 C
Total servings of food groups: grains 5, vegetables 7, fruits 6, legumes 5.5, nuts and seeds 1, calcium foods 9, omega-3s 1
Vitamin B12 is supplied by the Vega One nutritional shake and fortified vegan meat, or add a supplement.
Vitamin D is supplied by fortified juice and nondairy milk and the Vega One nutritional shake; add sunshine or a supplement.
_Nutritional analysis:_ calories: 2,501; protein: 97 g (15% of calories); fat: 75 g (25% of calories); carbohydrate: 395 g (60% of calories); dietary fiber: 59 g; calcium: 1,858 mg; iron: 30 mg; magnesium: 772 mg; phosphorus: 1,793 mg; potassium: 6,841 mg; sodium: 2,200 mg; zinc: 24 mg; thiamin: 2.9 mg; riboflavin: 2.2 mg; niacin: 34 mg; vitamin B6: 4 mg; folate: 898 mcg; pantothenic acid: 11 mg; vitamin B12: 4.2 mcg; vitamin A: 988 mcg RAE (3,260 IU); vitamin C: 409 mg; vitamin D: 55 mcg (2,200 IU); vitamin E: 27 mg (40.5 IU); omega-6 fatty acids: 20 g; omega-3 fatty acids: 5.6 g
#### **4,000-CALORIE SAMPLE MENU**
This menu contains plenty of protein without substantial reliance on soy. Other protein-rich options are scrambled tofu for breakfast or soy-based veggie burgers.
**BREAKFAST**
2 cups (500 ml) granola; or 4 pancakes or waffles with maple syrup | 4 G
---|---
2 oranges or other fruit | 2 F, 1 C
2 cups (500 ml) fortified almond milk or other nondairy milk | 4 C
**LUNCH**
Burgers: 2 whole wheat hamburger buns | 4 G
with 2 fortified black bean burgers | 1 G, 1 L
and sliced tomato, red onion, chopped lettuce, and spreads | 2 V
1½ cups (375 ml) potato salad | 3 V
½ cup (125 ml) mango, or 1 apple or other fruit | 1 F
**SUPPER**
Stir-fry of 1 cup (250 ml) chickpeas and ⅓ cup (85 ml) cashews | 2 L, x1.5 N
with 2 cups (500 ml) greens (such as broccoli, okra, napa cabbage) | 4 V, 2 C
and 1 cup (250 ml) carrots or peppers | 2 V
and 1 teaspoon (5 ml) sesame oil, 1 teaspoon (5 ml) tamari | -
2 cups (500 ml) noodles or rice | 4 G
1 tablespoon (15 ml) olive oil | -
**SNACKS**
½ cup (125 ml) hummus | 1 L
8 crackers | 1 G
1 peach or other fruit | 1 F
1 cup (250 ml) fortified almond milk or other nondairy milk (or juice) | 2 C
½ cup (125 ml) walnuts | 1 N, 1 n-3
1 power bar (68 g) or dessert
|
Total servings of food groups: grains 14; vegetables 11, fruits 4, legumes 4; nuts and seeds 2.5, calcium foods 9, omega-3s 1
Vitamin B12 is supplied by the fortified nondairy milk and veggie burger, or a add supplement.
Vitamin D is supplied by fortified nondairy milk; add sunshine or a supplement.
_Nutritional analysis:_ calories: 4,002; protein: 128 g (13% of calories); fat: 152 g (32% of calories); carbohydrate: 584 g (55% of calories); dietary fiber: 88 g; calcium: 1,826 mg; iron: 37 mg; magnesium: 910 mg; phosphorus: 2,589 mg; potassium: 6,258 mg; sodium: 2,300 mg; zinc: 23 mg; thiamin: 7.4 mg; riboflavin: 2.5 mg; niacin: 38 mg; vitamin B6: 3.9 mg; folate: 1,646 mcg; pantothenic acid: 16 mg; vitamin B12: 3.8 mcg; vitamin A: 1,844 mcg RAE (6,085 IU); vitamin C: 425 mg; vitamin D: 8 mcg (317 IU); vitamin E: 52 mg (78 IU); omega-6 fatty acids: 33 g; omega-3 fatty acids: 6 g
## APPENDIX
## **Recommended Intakes of Vitamins and Minerals**
The Dietary Reference Intakes (DRIs) are a comprehensive set of reference values that indicate recommended daily intakes for vitamins, minerals, and other nutrients for healthy populations. The DRIs have been established by American and Canadian scientists through a review process overseen by the US National Academies, which is an independent, nongovernmental body, and they reflect the current state of scientific knowledge with respect to nutrient requirements. They can be used for assessing and planning diets.
The recommended dietary allowance (RDA) is the average daily dietary in-take of a nutrient that is sufficient to meet the requirement of most (97 to 98 percent) healthy persons. This number can be used as a goal for individuals and is likely to exceed the recommended intake for most people within that age or gender group. These are shown in bold type.
Adequate intake (AI) is the intake level suggested when an RDA cannot be determined due to insufficient data. The AI is more of a good guess or estimate of the amount needed to promote health. In the tables, these are shown in regular rather than bold type.
These and tolerable upper intake level (UL) are available through the Institute of Medicine of the National Academies online at iom.edu/Activities/Nutrition/SummaryDRIs/~/media/Files/Activity%20Files/Nutrition/DRIs/New%20Material/5DRI%20Values%20SummaryTables%2014.pdf or by scanning the QR code below. Alternate measures sometimes used (such as international units, or IU) can also be found at this website. For additional details and reports see the website iom.edu. The UL is the highest daily intake of a nutrient, consumed on a continuing basis, that is considered safe, in other words likely to pose no risks of adverse health effects for most individuals.
In table A.1 (page 274), "Vit" refers to vitamin. For further details on vitamins and essential minerals, see chapters 6 and and the websites lpi.oregonstate.edu/infocenter/vitamins.htmlandlpi.oregonstate.edu/infocenter/minerals.html.
US National Academies DRIs
**TABLE A.1.** Dietary Reference Intakes for Vitamins
Key: g = gram; mcg = microgram; mg = milligram
**TABLE A.2.** Dietary Reference Intakes for Minerals
## **RESOURCES**
#### **NUTRITION BOOKS**
**_Becoming Raw._** Brenda Davis and Vesanto Melina, Book Publishing Company, 2010.
**_Becoming Vegan: Comprehensive Edition. The Complete Reference to Plant-Based Nutrition._** Brenda Davis and Vesanto Melina, Book Publishing Company, 2014.
**_The Complete Idiot's Guide to Plant-Based Nutrition._** Julieanna Hever, Alpha Books, 2011.
**_Cooking Vegan_**. Vesanto Melina and Joseph Forest, Book Publishing Company, 2012. (Companion volume to **_Becoming Vegan_**. Published in Canada as **_Cooking Vegetarian._** Joseph Forest and Vesanto Melina, Harper Collins, 2011.)
**_Defeating Diabetes._** Brenda Davis and Tom Barnard, Book Publishing Company, 2000.
**_The Dietitian's Guide to Vegetarian Diets._** Reed Mangels, Virginia Messina, and Mark Messina, Jones and Bartlett Learning, 2011.
**_The Everything Vegan Pregnancy Book._** Reed Mangels, Adams Media, 2011.
**_Food Allergies: Health and Healing._** Jo Stepaniak, Vesanto Melina, and Dina Aronson, Books Alive, 2010.
**_Food Allergy Survival Guide._** Vesanto Melina, Jo Stepaniak, and Dina Aronson, Healthy Living Publications, 2004.
**_The Plant-Powered Diet._** Sharon Palmer, The Experiment, 2012.
**_Raising Vegetarian Children._** Jo Stepaniak and Vesanto Melina, McGraw-Hill, 2003.
**_Raw Food Revolution Diet._** Cherie Soria, Brenda Davis, and Vesanto Melina, Book Publishing Company, 2008.
**_Vegan for Her: The Women's Guide to Being Healthy and Fit on a Plant-Based Diet._** Ginny Messina and J. L. Fields, Da Capo Lifelong Books, 2013.
**_Vegan for Life._** Jack Norris and Virginia Messina, Da Capo Lifelong Books, 2011.
#### NUTRITION WEBSITES
**Brenda Davis.** brendadavisrd.com
**Dietary Reference Intakes.** fnic.nal.usda.gov/dietary-guidance/dietary-reference-intakes
**Linus Pauling Institute's Micronutrient Information Center.** lpi.oregonstate.edu/infocenter
**Nutrition Facts.** nutritionfacts.org
**Physicians Committee for Responsible Medicine.** pcrm.org
**USDA National Nutrient Database for Standard Reference.** ndb.nal.usda.gov
**The Plant-Based Dietitian.** plantbaseddietitian.com
**Vegan Health.** veganhealth.org
**The Vegan RD.** theveganrd.com
**Vegetarian Diets Position of the Academy of Nutrition and Dietetics.** eatright.org/About/Content.aspx?id=8357
**Vegetarian Nutrition Dietetic Practice Group of the Academy of Nutrition and Dietetics.** vegetariannutrition.net/faq
**Vesanto Melina.** nutrispeak.com
#### **VEGAN AND VEGETARIAN WEBSITES**
**American Vegan Society.** americanvegan.org
**The Compassionate Cook.** compassionatecook.com
**Happy Cow.** happycow.net
**International Vegetarian Union.** ivu.org
**North American Vegetarian Society.** navs-online.org
**One Green Planet.** onegreenplanet.org
**Vegan Outreach.** veganoutreach.org
**Vegan Society.** vegansociety.com
**VegDining.** vegdining.com
**Vegetarian Resource Group.** vrg.org
**Vegetarian Summerfest.** vegetariansummerfest.org
**VegNews.** vegnews.com
**VegSource.** vegsource.com
## **INDEX**
The index that appeared in the print version of this title was intentionally removed from the eBook. Please use the search function on your eReading device to search for terms of interest. For your reference, the terms that appear in the print index are listed below.
Abramowitz, Rubin
Academy of Nutrition and Dietetics
acesulfame K
addictive substances, avoiding
Adequate Intake (AI)
defined
for fiber
omega-3 fatty acids
Adventist Health Study-1
Adventist Health Study-2
Adventist Mortality Study
aerobic exercise
age issues. _see_ children; infants; seniors
agribusiness
_ahimsa,_ defined
air quality, food industry and
alcohol consumption
avoiding
avoiding, during pregnancy
chronic disease and
osteoporosis and
toxicity of
allergies, to foods
allium vegetables
alpha-linolenic acid (ALA)
alpha-tocopherol (vitamin E)
American Academy of Pediatrics
American Association for the Advancement of Science
American Heart Association
American Institute for Cancer Research
American Vegan Society
amino acids
anaerobic metabolism
angina
animal rights issues
antibiotics, given to animals
antioxidants
cancer and
cardiovascular disease and
for seniors
vitamin A as
vitamin C as
vitamin E as
apple shape body type
aquaculture
Aronson, D.
arteries. _see_ cardiovascular disease (CVD)
arthritis, rheumatoid
artificial sweeteners, avoiding
ascorbic acid (vitamin C)
aspartame
avocados
Baboumian, Patrik
"bad fats,"
bags, reusable
Barnard, T.
beef cattle
beriberi, preventing
Berkoff, N.
beta-carotene (vitamin A)
beverages. _see_ fluids
bifidobacteria
biotin (vitamin B7)
blackstrap molasses
blood clots
blood pressure
blood sugar. _see_ glycemic index (GI); sugar; type 2 diabetes
body frame, underweight and
body mass index (BMI) blood pressure and
overweight and
pregnancy and
underweight and
body shape
bone health. _see_ osteoporosis
brain health
dementia and
exercise for
seniors and
_Bravo: Health-Promoting Meals form the TrueNorth Kitchen_ (Bravo)
Bravo, R.
Brazier, Brendan
breakfast, for children
breast cancer
breast-feeding. _see_ lactation
British Vegetarian Society
broiler chickens
Burkitt, Denis
_Business Week,_
caffeine
avoiding, during pregnancy
osteoporosis and
calciferol (vitamin D)
calcium
benefits of
for exercise
for lactation
osteoporosis and ( _see also_ osteoporosis)
for pregnancy
for seniors
for teens
calories
from carbohydrates
energy-dense foods for weight gain
energy imbalance and weight ( _see also_ overweight; underweight)
exercise and
from fat
menus for different caloric intake levels
in Paleo diet
pregnancy and
from protein
cancer
deaths from
diet and lifestyle
generally
overweight and
prevention tips for
raw vegan diet and
soy and
treatments for
vegan diet for prevention of
capture fisheries
carbohydrates
calories from
fiber and
food for exercise
glycemic index (GI) and
grains and
importance of
refined
sugar and
types of
carbon compounds, in manure
cardiovascular disease (CVD)
abnormal blood coagulation and
cholesterol and
emerging risk factors
fiber for cardiovascular health
generally
high blood pressure and
homocysteine and
inflammation and
overweight and
triglycerides and
vegan diet for
care facilities, vegan food in
carnitine
cataracts
cattle, food industry and
celiac disease
Centers for Disease Control and Prevention
chemical contaminants, avoiding
chia seeds
chickens, food industry and
children
to age twelve
dietary fat needed by
exercise for
infants
omega-3 fatty acids for infants
protein for
teens
toddlers and preschoolers
cholesterol
cardiovascular disease and
high-density lipoprotein (HDL)
low-density lipoprotein (LDL)
oxidized cholesterol (oxycholesterol)
sterols
triglycerides
very low-density lipoprotein (VLDL)
choline
chromium
clear-cutting
coagulants, vitamin K and
cobalamin. _see_ vitamin B12
coconut oil
coconut sugar
colorectal cancer
community support, vegan food and
"complete" protein
complex carbohydrates
composting
concentrated animal feeding operations (CAFOs)
Context Marketing
conventional vegan diet, defined
_Cooking Vegan_ (Melina, Forest)
copper
cravings, overcoming
C-reactive protein (CRP)
cruciferous vegetables
"cruelty-free" meat, problem of
cyanocobalamin. _see_ vitamin B12
dairy alternatives, for weight gain
dairy industry
calcium and
cows
formula for infants
Danzig, Mac
date sugar
Davis, B.
Davis, Steph
_Defeating Diabetes_ (Davis, Barnard)
deforestation
dehydrocholesterol
dementia
desertification
diabetes. _see_ type 2 diabetes Dietary Guidelines Advisory Committee (2010)
Dietary Reference Intakes (DRIs)
defined
minerals
vitamins
dietary vegans, defined
dietetic associations
_Diet for a New America_ (Robbins)
dieting, problem of
digestion
enzymes and
improving
of protein
Dinshah, H. Jay
diverticular disease
docosahexaenoic acid (DHA)
Earth, resources of
eating disorders
eicosapentaenoic acid (EPA)
electrolytes
Ellis, Frey
energy
B vitamins and
energy-dense foods for weight gain
overweight as energy imbalance
seniors and
England, veganism in
enrichment
environmental issues
air quality
cancer and
global warming
land use
overweight and
resource depletion
water
enzymes
EPIC-Oxford
esophageal cancer
Esselstyn, Caldwell
essential fatty acids. _see also_ omega-3 fatty acids
estrogen
ethnicity
cancer and
diabetes and
fat intake and
protein complementing and
protein digestibility of different diets
European Prospective
Investigation into Cancer and Nutrition (EPIC). _see also_ EPIC-Oxford
exercise
achieving fitness
benefits of
for bone health
dietary fat needed for
eating habits and
food and activity diaries
lack of
nutrients for
overweight and
during pregnancy
as priority
protein for
recommendations
for seniors
tips for
vegan athletes
for weight gain
eye health
factory farms. _see also_ food industry
The Farm (Summertown, Tennessee)
Fasano, Alessio
fast and easy vegan diet, defined
fat (body). _see also_ overweight; underweight
body mass index (BMI)
body shape
diabetes and
of seniors
waist to hip ratio
fat (dietary)
benefits of
calories from
cardiovascular disease and
cholesterol and lipids
composition of, in selected foods
energy-dense foods for weight gain
exercise and
fatty acids, defined
fatty acids, essential
good _versus_ bad
importance of
limiting
low-fat vegan diet
requirements for
sources of
female athlete triad
fiber
Adequate Intake for
benefits of
cancer and
cardiovascular disease and
diabetes and
diverticular disease and
gas from
generally
high-fiber diet
for seniors
sources of
types of
"finishing" facilities
fish
food industry and
pescatarians
flaxseeds
flexibility exercises
flexitarians, defined
fluids
for exercise
for lactation
recommendations
for seniors
water
for weight gain
folate (vitamin B9, folic acid)
benefits of
for lactation
for pregnancy
food addiction, overcoming
_Food Allergy Survival Guide, The_ (Melina, Aronson, Stepaniak)
food and activity diaries
food industry
agribusiness and
cattle
chickens
"cruelty-free,"
fish
flesh food and dairy product industries as linked
pigs
food preparation
mineral absorption and
phytochemicals and
protein and digestibility
raw vegan diet and cancer
food sensitivities
Forest, J.
formula feeding
4,000-calorie sample menu
fowl, food industry and
free radicals
fructose
fruitarian diet, defined
gallbladder
gallstones
overweight and
gamma-linolenic acid (GLA)
gas, from fiber
gender. _see also_ lactation; pregnancy; vitamins; _individual types of cancer_
body shape and
exercise and
osteoporosis and
premenstrual syndrome
soy and
underweight and
genetic engineering, of animals
genetics
cancer and
diabetes and
underweight and
gillnetting
global warming, food industry and
glucose
diabetes and ( _see also_ glycemic index (GI); type 2 diabetes)
exercise and
generally
glycogen
sweeteners
gluten
glycemic index (GI)
generally
GI and glycemic load (GL) of selected foods
limitations
goals, setting
"good fats,"
gout
grains
for exercise
generally
gluten in
limiting
whole-grain hierarchy
greenhouse gas emissions
happiness, exercise and
Harris Interactive poll
Hawken, Paul
heart attack. _see also_ cardiovascular disease (CVD)
Heidrich, Ruth
_Helicobacter pylori,_
_Helio,_
hempseeds
herbs
high-density lipoprotein (HDL)
high-fat diet
high-fiber diet
high-sensitivity C-reactive protein (hs-CRP)
histadine
homocysteine
hormones
balancing
given to animals
skin of teens and
Humane Slaughter Act
hydrogenated oils
hypertension
hypothyroidism
infants
breast feeding
food allergies in
formula feeding
menus for
protein requirements and
scientific evidence about vegan diet during pregnancy ( _see also_ pregnancy)
solid foods for
inflammation
cardiovascular disease and
controlling
exercise for
insoluble fiber
Institute of Medicine
insulin. _see also_ type 2 diabetes
intestinal health
bacteria for
fiber and
leaky gut
prebiotics and probiotics
for seniors
inulin
iodine
benefits of
children to age twelve
for pregnancy
recommendations
for toddlers and preschoolers
iron
benefits of
for exercise
infants and
for lactation
for pregnancy
for seniors
isoflavones
isoleucine
juicing
Jurek, Scott
ketones
Keys, Ancel
kidney disease
lactation
formula feeding compared to
generally
nutrients for
resources for
lactobaccilus
lacto-ovo vegetarian diet
land use, food industry and
Laraque, Georges
lauric acid
layers (chickens)
leaky gut syndrome
legumes
benefits of
for exercise
fiber from
leucine
Lifestyle Heart Trial
linoleic acid (LA)
Liquid Gold Dressing (recipe)
liver detoxification
livestock industry
Livestock's Long Shadow (United Nations Food and Agriculture Organization)
_Living Planet Report 2010_ (World Wildlife Fund)
_Living Well_ (Fasano)
longevity
longlining
low-density lipoprotein (LDL)
low-fat vegan diet, defined
lunch, for children
lung cancer
lysine
macrobiotic diet
defined
pregnancy and
macronutrients
balancing
carbohydrates as
fat as
protein as
magnesium
malnutrition
manganese
manure
marijuana
meal planning
away from home
for children to age twelve
for exercise
family time and
for infants
meal frequency
menus for different caloric intake levels
for pregnancy
as priority
for seniors
Mediterranean diet
Melina, V.
menaquinone (vitamin K)
metablism, boosting
metabolic markers
for cancer
for diabetes
metabolic syndrome
methane
methionine
micronutrient deficiency
minerals
absorption of
calcium
chromium
copper
for exercise
generally
iodine
iron
magnesium
manganese
phosphorus
potassium
for pregnancy
recommended intakes
selenium
for seniors
sodium
in vegan foods
zinc
molasses
monosodium glutamate (MSG)
monounsaturated fats
morning sickness
muscle mass, reduced
National Restaurant Association
neotame
niacin (vitamin B3)
Nimmo, Catherine
nitrous oxide
noncaloric sweeteners
nonviscous fiber
Nurses' Health Study
nutrient-dense vegan diet, defined
nutrients. _see_ fat (dietary); fiber; minerals; protein; vitamins
nutritional yeast
Nutrition Security Institute
nuts
exercise and
fat in
omega-3 fatty acids in
weight gain and
Oakes, Fiona
oats, gluten and
obesity, defined. _see also_ overweight
oligosaccharides
olives
omega-3 fatty acids
for cardiovascular health
for infants
for lactation
for pregnancy
recommendations
sources of
for toddlers and preschoolers
omega-6 fatty acids
organic foods, advantages of
Ornish, Dean
osteoporosis
bone health and
calcium and
preventing
protein and
risk factors and
underweight and
vitamin D and
overnutrition
overweight
adopting vegan diet for health
body mass index (BMI) and
body shape and
defined
as energy imbalance
environmental factors of
exercise and
healthy lifestyle habits for
physiological factors of
pregnancy and
problems of
weight loss and
oxalates
oxidized cholesterol (oxycholesterol)
packaging
Paleo diet, vegan diet compared to
pantothenic acid (vitamin B5)
pear shape body type
pellagra, preventing
percent fat
pescatarians
phenylalanine
phosphorus
phylloquinone (vitamin K)
physical exams, need for
phytate
phytochemicals
phytosterols
pigs, food industry and
platelet aggregation
polycystic ovarian syndrome
polyunsaturated fats
portion size
positive thinking, weight and
potassium
"Power Vegan" _(Business Week),_
prebiotics
pregnancy. _see also_ children; infants; lactation
exercise during
folate (vitamin B9, folic acid) for
meal planning for
nutrients needed during
preparing for
resources for
scientific evidence on vegan nutrition for
substances to avoid during
vitamins for
premenstrual syndrome
preschoolers, vegan foods for
probiotics
processed foods, limiting
prostate cancer
protein
amino acids and
for bone health
calories from
complementing
defined
digestibility of
for exercise
importance of
for lactation
osteoporosis and
for pregnancy
requirements for
for seniors
from soy
for weight gain
Protein Power Smoothie (recipe)
pure vegetarians, defined
purse seining
pyridoxine (vitamin B6)
Pythagoras
raw vegan diet
cancer and
defined
lysine and
for seniors
_Reader's Digest,_
rebaudioside A
recipes
Liquid Gold Dressing
Protein Power Smoothie
recombinant bovine growth hormone (rBGH)
recommended dietary allowances (RDA)
defined
omega-3 fatty acids
protein
refined carbohydrates
renal failure
resistance training
resource depletion, food industry and
resources, lists of
retinol. _see_ vitamin A
rheumatoid arthritis
riboflavin (vitamin B2)
rickets, preventing
Robbins, John
saccharin
Salley, John
saturated fats
school-aged children, vegan foods for
scurvy, preventing
seasonal foods, advantages of
seeds
for dietary fat
for exercise
omega-3 fatty acids in
for weight gain
selenium
seniors
brain health of
challenges of
exercise for
meals for
nutrients for
physical changes of
protein requirements and
raw vegan diet for
resources for
vitamin B12 for
vitamin D for
S-equol
serum ferritin
Seven Countries Study
Seventh-Day Adventists care facilities of
studies
sex life, exercise and
simple carbohydrates
1,600-calorie sample menu
skin, of teens
slaughterhouses. _see also_ food industry
sleep
apnea
exercise and
importance of
smoothies
snacks
avoiding
for children
fruit as dessert
healthful
soaking, for digestibility
sodium
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{"url":"http:\/\/mathhelpforum.com\/advanced-algebra\/218329-inverse-matrix-eigenvalues-eigenvectors-proof-needed.html","text":"# Thread: Inverse Matrix - Eigenvalues & Eigenvectors (Proof Needed)\n\n1. ## Inverse Matrix - Eigenvalues & Eigenvectors (Proof Needed)\n\nHello,\n\nOne of the questions I was presented in a tutorial the other day really stumped me and I am unsure as to how to prove it.\nThe question is:\n\n\"Suppose that A is an invertible matrix and that x is an eigenvector for A with eigenvalue 'lambda cannot equal 0'. Show that x is an eigenvector for the inverse matrix of A with eigenvalue 'lambda-1'.\n\nI have been shown a similar question where you had to prove that the matrix A2 had an eigenvalue of lambda2 through the manipulation of the equation Ax = (lambda)x as below:\n\nAx = (lambda)x\nA(Ax) = A(lambda)x\nA2x = (lambda)Ax\nA2x = (lambda)(lambda)x\nA2x = (lambda)2x\n\nIs the solution to this question reached through the same steps, or is there a step I need to do differently?\n\nAny help would be greatly appreciated\n\n2. ## Re: Inverse Matrix - Eigenvalues & Eigenvectors (Proof Needed)\n\nPerhaps you should attempt this question before asking for help. Don't be afraid to try.\n\n$Ax=\\lambda x \\iff A^{-1}Ax=A^{-1}\\lambda x \\iff x=\\lambda A^{-1}x$\n\n3. ## Re: Inverse Matrix - Eigenvalues & Eigenvectors (Proof Needed)\n\nLet $A$ be a matrix with eigenvalue $\\lambda$ and eigenvector $x$.\n\nThen $Ax = \\lambda x$\n\nSince $A$ is invertible, we can multiply both sides by $A^{-1}$.\n\n$A^{-1} Ax = A^{-1}\\lambda x$\n$x = A^{-1} \\lambda x$\n\nSolve for $A^{-1} x$.\n\nThus, $A^{-1} x = \\frac{1}{\\lambda} x$","date":"2016-09-25 06:38:32","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\": 0, \"img_math\": 0, \"codecogs_latex\": 11, \"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\": 0.8852044343948364, \"perplexity\": 567.4901831340208}, \"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-2016-40\/segments\/1474738659865.46\/warc\/CC-MAIN-20160924173739-00251-ip-10-143-35-109.ec2.internal.warc.gz\"}"} | null | null |
\section{Introduction}
Since the pioneering works of Zhou and his colleagues (\cite{zho93};
\cite{zho94}; \cite{zho95}), observational signatures of infall motion
in the early phase of star formation have been discovered towards many
young stellar objects (YSOs).
They are mainly based on the spectral features that an opaque molecular
line has a self-absorption with the blue peak stronger than the red one
(hereafter the blue asymmetry), while an optically thin line of single
peak is located between the two peaks of the opaque one.
In an attempt to search for infalling YSOs, surveys of class 0 and I
sources have been undertaken using the transitions of, e.g., CS, H$_2$CO,
and HCO$^+$.
However, only a few sources like B335 and IRAS 16293--2422 seem to provide
compelling evidence of collapse motion (\cite{zho93}; \cite{zho95};
\cite{nar98}). Line profiles of some sources exhibit different asymmetry
from one molecular species to another as well as from transition to
transition in a molecule (\cite{mar97}; \cite{leh97}; \cite{gre97}).
It is likely that the infall motion is not so simple or monotonic as one
expects. Not only outflow motion but also aspherical geometry make
the problem more complex.
Thus, previous studies have always come to a conservative conclusion that
class 0 objects seem to undergo infall phase in a statistical sense only
and it is unclear for class I objects (\cite{mar97}; \cite{gre97}).
In order to have a comprehensive view on the internal motion of YSOs, one
needs to make observations with various molecules and transitions using
both single dish and interferometer.
As a complement to the previous single dish observations by Mardones et al.
(1997) and by Gregersen et al. (1997), we have carried out an HCN $J$=1--0
survey of class 0 and I YSOs.
We can probe denser regions with HCN $J$=1--0 lines than with CS $J$=2--1
one, the most popular density tracer. The $J$=1--0 transition of HCN has
three hyperfine lines ($F$=1--0, 1--1, and 2--1) whose optical depths are
scaled to $1:3:5$ in the LTE condition.
The hyperfine lines enable us to investigate how the line shape changes
with their optical depths.
Moreover, molecular abundance and spatial resolutions are the same for
the three hyperfine components. This is an advantage over using other
combinations of molecules or transitions with different beam sizes or
abundances.
Recently, it is known that the HCN emission peak of each Bok globule is
coincident with the position of embedded source within 6$''$ and the
detection rate of HCN lines is higher in class I and probably class 0
sources than in starless cores and class II sources (\cite{afo98}).
Thus HCN may be a good tracer of class 0 and I objects.
The main goal of this study is to provide another set of line profiles
of YSOs. Based on the data set, we investigate the tendency of line
asymmetry among three hyperfine components, compare the asymmetry
with that of other molecular lines, and probe the internal structure
and kinematics of the cores.
Probing with various molecular species may also be helpful in
investigating molecular chemistry in the protostellar cores
(\cite{raw96}).
After presenting observation and data reduction procedure (section~2),
we describes observational results in section~3. A simple radiative
transfer model of L483 is detailed in section~4.
Discussions on the relevant molecular chemistry and hyperfine line
ratios of HCN are given in section~5.
Finally, we summarize results in section~6.
\section{Observations}
The sources listed in Table~1 have been selected based on the data set
in Mardones et al. (1997) and Gregersen et al. (1997). We detected
HCN hyperfine lines toward 22 of 24 with an rms level of a few tens of
mK.
Observations were carried out with a radome-enclosed 14 meter telescope
in Taeduk Radio Astronomy Observatory, Korea, during April and May 1997.
We used an SIS receiver and an autocorrelation spectrometer with 20 KHz
(0.068 km s$^{-1}$ at HCN $F$=2--1 frequency) resolution. System
temperatures were typically $400-600$ K (SSB) and pointing was good to an
accuracy of 10$''$ in both directions of azimuth and elevation.
The spectra were Hanning-smoothed, calibrated by a standard chopper wheel
method, and presented in an antenna temperature ($T_A^*$) scale.
The rest frequency of $F$=2--1 transition is 88.631847 GHz, and the
separations of $F$=1--1 and $F$=0--1 lines with respect to $F$=2--1 are
4.84 and $-7.07$ km s$^{-1}$, respectively (\cite{lov92}).
Measured FWHM beam size and beam efficiency are 61$''$ and 40\%,
respectively, at this frequency.
We used frequency switching mode with $\Delta f = 6$ MHz and obtained the
spectra with the S/N ratios better than 15.
\section{Results}
\subsection{Line profiles}
Observed line profiles are presented in Fig.~1 (a-d), where we see
spectral features like self-absorption, asymmetry, and broad wings.
The hyperfine lines are well separated except for a few cases. Line
asymmetries of many sources seem to grow as the optical depth increases.
All three hyperfine lines appear to be optically thin for L146, Serp SMM3,
L673A, and L1152, whereas they all are optically thick for NGC1333-4A,
L483, and B335.
The line wings of many sources are generally weaker than those in other
studies (\cite{mar97}; \cite{gre97}), which may result from a larger
telescope beam of this study.
\subsection{Individual sources}
We outline the characteristics of HCN line profiles of the sources and,
when available, compare them with those of CS 2--1, H$_2$CO 2$_{12}$--1$_{11}$,
and N$_2$H$^+$ 1--0 in Mardones et al. (1997) and with HCO$^+$ 4--3
and 3--2 in Gregersen et al. (1997).
Mainly sources with dissimilarities in line shapes among molecular
species are discussed.
It should be noted that the two surveys are made with FWHM beam
size of $\stackrel{<}{_{\sim}}20''$, while ours are with 61$''$.
\noindent
L1448-IRS3: $F$=2--1 line looks similar to CS line, whereas $F$=0--1 line
to N$_2$H$^+$ line. HCO$^+$ 3--2 line is significantly shifted to the red.
\noindent
L1448mm: All HCN hyperfine components show the blue asymmetry like CS
spectrum. On the other hand, all transitions of H$_2$CO and HCO$^+$ have
the red asymmetry.
\noindent
NGC1333-2: All three lines differ from those of CS and H$_2$CO in their
shapes. Instead, they are similar to N$_2$H$^+$ line, which seems to be
also optically thick.
\noindent
L43: It shows how the absorption dip grows as the optical depth increases.
The line shape of $F$=2--1 transition is quite similar to that of CS.
$F$=0--1 line is relatively strong compared to the other two hyperfine
lines.
\noindent
L146: The shape of line profiles are closer to that of H$_2$CO. Lines are
gradually shifted to the red, as the transition becomes optically thick.
As in L43, $F$=0--1 line is brighter than $F$=1--1 line. $F$=2--1 line is
quite narrow.
\noindent
L483: This is a good example showing how the line shape varies with the
optical depth. It seems to be consistent with a Shu (1977) type infall
motion; the red shoulder in the least opaque $F$=0--1 transition changes
into the absorption dip in the most opaque $F$=2--1 one.
$F$=2--1 lines are more asymmetric than those of CS and H$_2$CO. However,
the asymmetry is reversed to the red in the 20$''$ beam observation of
HCO$^+$. It is interesting to note that $F$=0--1 line is the brightest
among three components. The depression of $F$=2--1 line can not be
explained by self-absorption only (see section~4).
\noindent
S68N: $F$=2--1 line has a deep self-absorption with a wider blue component.
The general shape of HCN resembles that of CS, though the blue wing of HCN
is weaker. By contrast, H$_2$CO has a clear blue asymmetry.
\noindent
FIRS1: This is a typical object demonstrating diverse asymmetries of
different molecular transitions. $F$=2--1 component of HCN shows a
prominent blue asymmetry like CS, H$_2$CO line does the red one, and
HCO$^+$ lines are nearly symmetric.
\noindent
SMM4: This shows a progressive blue shift of HCN lines and deviation
from symmetry with an increasing optical depth. However, the shift
may not result from infall, but from outflow motion, judged from long
tail to the blue.
The opaque lines are similar in shape to both CS and H$_2$CO lines.
HCO$^+$ lines with the central absorption dips have the same asymmetry,
but do not have any long tail to the blue.
\noindent
SMM3: All three HCN components are fitted well with Gaussian. Other
transitions of CS, H$_2$CO, and HCO$^+$ are also symmetric. Relative
intensities are quite close to the values of optically thin limit under
the LTE condition.
\noindent
B335: The asymmetry of HCN lines seems to change from the blue to the red
as we move from $F$=0--1 line to $F$=2--1 one, although the S/N ratio is
not so high.
B335 core has been well known as a prototype of YSOs with convincing
evidence of core collapse, and thus well studied (\cite{zho93}, 1994;
\cite{zho95}; \cite{cho95}). However, our observation contradicts most
existing observations (cf. \cite{kam85}), except CCS observations
(\cite{vel95}). DC 303.8-14.2 is another example showing a reversal
of asymmetry among HCN hyperfine lines (\cite{leh97}). Most observations
suggestive of collapse motion have been made with a beam of
$\stackrel{<}{_{\sim}} 20''$, while observations of this study and
Velusamy et al. (1995) are with $\sim 1'$ beam. Line profiles obtained
with larger beams may be contaminated by outflow motion.
However, we can not rule out a possibility that the outer part of B335 is
slowly expanding (\cite{leh97}).
\noindent
L1157: $F$=2--1 and 1--1 lines have long tails to the blue with single
peaks, while $F$=0--1 line is almost symmetric. Both CS and H$_2$CO lines
show the blue asymmetry as well. On the contrary, HCO$^+$ lines have
rather strange spectral features, the blue asymmetry in $J$=3--2 and the
red one in $J$=4--3 transition.
\noindent
L1251B: Shoulders in the red of $F$=2--1 and 1--1 transitions coincide
with that of CS. H$_2$CO has the blue asymmetry like HCN and CS, but its
self-absorption is much deeper than those of HCN and CS.
In summary, for a large fraction of sources, the asymmetries are the same
in all the transitions of HCN, CS, H$_2$CO, and HCO$^+$. However, for
several sources, it depends on the molecular species and, particularly
for B335 and L1157, it varies from transition to transition of a molecule.
It should be pointed out that the asymmetry of HCN is relatively more
similar to that of CS than to that of H$_2$CO, which will be quantified
in next subsection.
\subsection{Correlations}
For more detailed investigation of line profiles, one needs to quantify
the line velocity associated with internal motion. We use a parameter
defined by Mardones et al. (1997).
At first, we measure $V_{\rm G}$($i$--$j$), the Gaussian peak velocity
in the $F$=$i$--$j$ transition of HCN after fitting the three hyperfine
lines with three Gaussians.
Fitting procedure is straightforward for the lines of simple shape.
For lines having another weak peak or a shoulder, we fit the profile after
masking such features. If intensities of two peaks differ by less than
$2 \sigma$, where $\sigma$ is the rms noise of spectrum, the whole velocity
span is taken into account.
The resulting $V_{\rm G}$($i$--$j$) and its standard deviation of each
hyperfine component are listed in Table~1. The standard deviation is
usually less than one channel width of the spectrometer.
Since some hyperfine transitions of S68N, Serp FIRS1, and Serp SMM5 are
blended each other, their $V_{\rm G}$($i$--$j$)s are not included in the
table.
The measure of velocity shift or degree of asymmetry $\delta V$ is
then defined as
\begin{equation}
\delta V = (V_{\rm G} - V_{\rm thin})/\Delta V_{\rm thin}.
\end{equation}
We use the line velocity and FWHM of N$_2$H$^+$ for $V_{\rm thin}$
and $\Delta V_{\rm thin}$, respectively, in Mardones et al. (1997).
We plot relations between $\delta V$(HCN) and $\delta V$(CS), and between
$\delta V$(HCN) and $\delta V$(H$_2$CO) in Fig.~2.
The velocity shifts of CS and H$_2$CO molecules are also from Mardones
et al. (1997). It is found that $\delta V$(0--1) correlates well with
$\delta V$(CS). And we do not find any significant differences in their
relations between class 0 and I. The close relation itself implies that
HCN $F$=0--1 transition probes as similar kinematics as CS molecule does.
It would be possible only if the distribution of HCN molecule is similar
to that of CS inside the core.
However, the slope of 0.47 suggests that $F$=0--1 transition is moderately
optically thick; if the transition is as thin as that of N$_2$H$^+$, the
slope should be around zero.
It would not be so optically thick, since their line shapes are usually
simple and show a single peak. The slope significantly less than unity
may also be due to a difference in the beam size of two surveys; our
larger telescope beam, which covers more volume of static envelope,
may lessen the slope.
As going toward the $F$=2--1 transition, we notice the worse correlation
as well as the gradual increase of the slope.
The increase of the slope up to around unity implys that the most opaque
line of HCN is as sensitive to the internal motion of the core as the CS,
again suggesting similar spatial distributions of both HCN and CS molecules.
General similarity in the line shapes between HCN $F$=2--1 and CS $J$=2--1,
as shown in the previous subsection, supports this argument. An increasing
scatter can be interpreted in terms of the opacity of the transition;
since the opaque line is formed where the optical depth is about one,
it does not reflect a global property, but does a local one. Thus small
differences in excitation conditions and chemistry between HCN and CS would
result in large differences in their line profiles.
In the lower panel of Fig.~2, we plot the relations between $\delta V$(HCN)
and $\delta V$(H$_2$CO). The correlation between them is not so good as
the case of $\delta V$(HCN) and $\delta V$(CS); we can hardly find a
linear relationship between $\delta V$(0--1) and $\delta V$(H$_2$CO).
Their distributions mimic the relation between $\delta V$(CS) and
$\delta V$(H$_2$CO) illustrated in Fig~3, which is drawn from data set
of Mardones et al. (1997).
However, if we confine ourselves to the sources of $\delta V$(HCN)$<0$
and $\delta V$(H$_2$CO)$<0$, then we can see as similar trend
as in the upper panel -- the concomitant increase of the slope to unity
with the optical depth.
Good correlations of $\delta V$s between HCN and CS indicate a similar
distribution of both molecular species in the core. It is intriguing
that, in spite of the larger beam size of our HCN observation, the slope
is roughly unity for both pairs of $\delta V$(HCN)--$\delta V$(CS) and
$\delta V$(HCN)--$\delta V$(H$_2$CO) for the most opaque transition of
HCN. It appears that HCN is even more sensitive to the internal motion
of the core.
The critical density of HCN $J$=1--0, $2.5\times 10^6$ cm$^{-3}$,
is larger than those of CS and H$_2$CO, $5.7\times 10^5$ cm$^{-3}$ and
$1.1\times 10^6$ cm$^{-3}$, respectively.
Thus HCN molecule traces deeper and denser regions of YSOs than CS or
H$_2$CO. If HCN lines are observed with as similar beam size as that
of CS or H$_2$CO ($\sim 20''$), we may be able to see more clearly
the internal motion of the cores.
Fig.~4 quantifies the $\delta V$(HCN) of individual sources as a function
of relative optical depth. If there is any systematic internal motion,
we may expect gradual increase or decrease of $\delta V$ (\cite{mye95};
\cite{zha98}).
It was not so easy to find such a relation from combinations of different
molecules or transitions often sparsely distributed in frequency space,
since the chemistry and beam size are different from each other.
Most YSOs exhibit a monotonic increase or decrease of $\delta V$ with
respect to the optical depth. Seven sources (L1448mm, NGC1333-4A, L483,
Serp SMM4, L1157, L1172, and L1251B) suggest infall motion, while three
sources (L43, L146, and B335) do outward motion.
A few YSOs (L1448-IRS3, serp SMM3, and 18331-0035) seem to be static.
A few large blobs or clumps may also give rise to such a systematic
velocity shift. This possibility is, however, ruled out by the
smoothness of optically thin N$_2$H$^+$ lines which are almost symmetric.
\section{Radiative Transfer Model of L483}
Line profiles of L483 in Fig.~1 demonstrate clearly how the absorption
dip develops under inward velocity field as the optical depth increases.
Line intensity ratios among hyperfine transitions significantly deviate
from the `standard hyperfine ratios' (see section~5).
Thus, synthesizing them with radiative transfer code will be useful in
understanding the infall motion as well as structure of L483.
We do not try to reproduce detailed features of the observed line profiles,
but focus on quantitative comparisons between observed and synthesized
lines.
The radiative transfer of HCN is complicated due to line overlap
caused by hyperfine splitting of energy levels. In the case of cold
cores like L483, the hyperfine lines do not overlap each other in
$J$=1--0 transition, but they do in the transitions of higher $J$s,
which affects the excitation condition of $J$=1--0 transition. The
problem of the line overlap has been successfully treated by the Monte
Carlo method (\cite{gon93}; \cite{lap89}) as well as by a conventional
one (\cite{tur97}). We will use the former scheme and impose the condition
of infall motion. Levels up to $J$=4 are taken into account, which
include 13 individual energy levels and 21 radiative transitions among
them. The Einstein $A$ coefficients and line frequencies are provided
by Gonz\'{a}les-Alfonso (1998) and by Turner (1998), and the collisional
rate coefficients by Monteiro \& Stutzki (1986). With those molecular
constants, we made a model of one dimensional radiative transfer, and
confirmed its performance, by reproducing results of Gonz\'{a}les-Alfonso
\& Cernicharo (1993).
The Shu model (\cite{shu77}) could be a start point for the distributions
of gas density and motion inside the core. Based on the observation of
high density tracing molecules, HC$_3$N and NH$_3$ (\cite{ful93}), we fix
the size of the core as $1.\!\!'72$ or $R=0.10$ pc at a distance
of 200 pc.
The core is divided into 30 concentric shells with radii running as
$r_i \propto i^{0.7} (i=0,...,30)$. Since temperature is found to be
12 K near the {\it IRAS} source and fall to 9 K in the outer region
(\cite{ful93}; \cite{par91}), $T_k$ is assumed to be constant at 10 K
in the first set of calculations. The sound speed is then 0.2 km s$^{-1}$.
An e-folding non-thermal turbulence of $v_{\rm turb}=0.4$ km s$^{-1}$
is found from Myers et al. (1995), and the abundance of HCN relative to
H$_2$, $5\times 10^{-9}$ is from Turner et al. (1997) and from
Gonz\'{a}les-Alfonso \& Cernicharo (1993).
Model calculations are then carried out and resulting line profiles are
convolved with the telescope beam.
In order to compare the synthetic line profile with the observed one
in brightness temperature unit, we divided the latter one by 0.5, a
compromise between the main beam efficiency (0.4) and the forward beam
coupling efficiency (0.7).
The Shu model is completely described by an infall radius, $r_{\rm inf}$
or an elapsed time after the onset of infall. Fig.~5 shows synthesized
line profiles for $r_{\rm inf} = 0, 0.4 R$, and $0.8 R$, respectively.
From the synthesized lines (top in Fig.~5), we find that
i) the asymmetry is negligible in three hyperfine lines,
ii) the synthesized lines are weaker than the observed ones,
and iii) the line intensity ratios are maintained as
$I(F=0-1):I(F=1-1):I(F=2-1) = 1:(1.3-2):(2-3)$. Then we applied the
kinetic temperature varying as $T_k(r)=10 (R/r)^{0.4}$ K, where the
$r^{-0.4}$ dependence is based on the distribution of dust temperature
(\cite{mye95}; \cite{wan95}).
The sound speed was accordingly changed to 0.25 km s$^{-1}$. In fact,
the Shu model assumes `isothermal' cloud, and thus the model with
kinetic temperature decreasing outward is far from consistency.
However, we need to assume `constant' sound speed in order to use his
simple expression of density and velocity field. With this
new temperature distribution, the synthetic lines (middle in Fig.~5)
become stronger and more asymmetric. However, the $F$=0--1 line is
still weaker than the observed one, and the hyperfine ratios differ from
observation.
It appears that the inside-out collapse model can not produce the
observational features well.
One viable option is to increase the density of Shu model core and to
introduce an extended diffuse envelope, as proposed by Wang et al.
(1995) and by Gonz\'{a}les-Alfonso \& Cernicharo (1993).
The role of the diffuse envelope is to attenuate the optically thicker
line more. A large turbulence in the envelope is required for
rather uniform attenuation across the line.
If the envelope is sufficiently opaque, the line core of $F$=2--1
component may be formed in the envelope. The general weakening of
lines is then compensated by an augmentation of density in the core.
A successful fit after several trial and errors is shown in the
bottom of Fig.~5. The resulting model is that a core with
$r_{\rm inf}=R=0.1$ pc and $v_{\rm turb}=0.3$ km s$^{-1}$ is embedded in
a static envelope with $R=0.3$ pc, $n({\rm H}_2)=5\times 10^3$ cm$^{-3}$,
$v_{\rm turb}=1$ km s$^{-1}$, and $T_k=10$ K. In the core, the density
increases by a factor of 6 and the infall velocity decreases by a factor
of 2 with respect to those of the Shu model, respectively.
The line center optical depths of $F$=0--1, 1--1, and 2--1 transitions
towards the center of core are 3, 8, and 11, respectively, which are not
beam averaged. The difference in peak brightness temperature is, of
course, due to different excitation temperatures of the transitions.
The red shift of absorption dip shown in Fig.~1b justifies rather large
infall radius; without the inward motion of outer layer, the absorption
dip will be located at the velocity of optically thin line.
The size and density of envelope may change in such a way that its
optical depth is kept constant. Different combinations, however, give
rise to deeper or shallower absorption dips due to different excitation
conditions of HCN in the envelope.
Thus, we come to a model different from that of Shu (1977), as invoked
already by Wang et al. (1995). In fact, higher density and slower infall
speed are characteristic features of a magnetically supported core model,
where the contraction occurs quasi-statically and the density of envelope
increases as the core evolves (\cite{cio94}, 1995).
Obviously, the real structure of L483 seems to be more complex than our
model. It is shown that a near IR image exhibits an elongated structure
in the East-West direction and the axis of CO molecular outflow is also
aligned in this direction (\cite{par91}; \cite{lad91}; \cite{ful95}).
Gregersen et al. (1997) noticed that HCO$^+$ $J$=3--2 and 4--3 lines
show the red asymmetry, contrary to ours. However, the possibility of
outward motion suggested by HCO$^+$ near the center is ruled out by the
recent VLA observation of NH$_3$ indicating inward motion down to
$\sim 0.\!\!'2$ scale (\cite{ful99}).
Reasons for different asymmetry of HCO$^+$ may be attributable to
differences in molecular chemistry and excitation conditions (see
section~5).
\section{Discussions}
The similarity of line shapes between CS and HCN and the dissimilarity
between HCO$^+$ and HCN were already mentioned in section~3. We further
examine the line asymmetries of 9 class 0 objects which have been
observed in all transitions of four molecular species (CS, H$_2$CO, HCN,
and HCO$^+$).
As summarized in Table~2, only one source each shows the reversal of
asymmetry between CS and HCN, and between HCO$^+$ and H$_2$CO.
On the other hand, three sources change their asymmetries between HCN
and HCO$^+$. Thus, though the number of samples is not large, it seems
that the line asymmetry is similar within each pair of CS--HCN and
HCO$^+$--H$_2$CO, but different between two pairs.
It is interesting to note that CS and probably HCN seem to prefer the
blue asymmetry compared with HCO$^+$.
Why do the two pairs show different asymmetry? Let us first consider
if the critical densities of four molecules are grouped in the same way
as their line shapes. A sequence of transitions is, however,
CS 2--1, H$_2$CO 2$_{12}$--1$_{11}$, HCN 1--0, and HCO$^+$ 3--2 \&
4--3 in an order of increasing critical density (The critical densities
of HCO$^+$ 3--2 and 4--3 are $0.5\times 10^7$ and $1.3\times 10^7$
cm $^{-3}$, respectively; \cite{mon85}), suggesting that excitation
condition is of little importance.
Then molecular chemistry such as depletion in the innermost region and
enhancement in the outflow may play important roles in the line formation.
It is known that HCN as well as CS may freeze out onto grains in cold
dense region (\cite{ber95}; \cite{bla92}; \cite{mcm94}), whereas HCO$^+$
will not, since it has a small dipole moment and there is no chemical
reaction route to consume it in this region (\cite{raw96}; \cite{van98}).
However, there seems to be little observational evidence of significantly
depleted CS or HCN.
If so, the blue asymmetry would be more frequent in HCO$^+$ than in CS
or HCN, provided that motion is more like inside-out collapse, which is
usually confined to the central region of core.
However, this is not the case, as shown in Table~2.
Outflows prevalent in these sources may make certain molecules more
abundant. L1157 is one of the examples which shows dramatic enhancements
of various kinds of molecules (\cite{bac97}), where four molecules of our
concern, CS, H$_2$CO, HCN, and HCO$^+$ are all enhanced.
In the interferometric observations of 9 class 0 objects, HCO$^+$ and
HCN show so different sensitivity to the envelope and outflow from source
to source that one could not find any general tendency (\cite{cho99}).
Recent BIMA observation of L483 suggests that HCO$^+$ traces outflow, while
HCN does thick disk or envelope (\cite{par99}).
The molecular chemistry is very complicated in this way, if both outflow
and infalling envelope coexist; even in the case that the outflow occupies
a small fraction of volume, the line shape will be significantly affected,
if the abundance increases drastically (e.g., $>100$) in the flow region.
The chemistry may also be related with the evolution of YSOs. Observations
with high spatial resolution and more elaborated time-dependent chemistry
models are required for further understanding of line formation and
molecular chemistry in YSOs (\cite{mun95}).
We noted in section~3 that hyperfine line intensities of Serp SMM4
and SMM3 are scaled to the relative LTE optical depth.
It is also interesting to note that, despite of their strong
self-absorptions, the intensity ratios of three sources, S68N,
Serp FIRS1, and SMM5, are also close to $1:3:5$, an optically thin
limit in the LTE condition.
In Fig.~6, excluding these three sources, we plot the hyperfine line
ratios, $R_{02}$ and $R_{12}$, defined by,
\begin{eqnarray}
R_{02} = {T_{\rm max}(F=0-1) \over T_{\rm max}(F=2-1)}, \ \ \ \ \
R_{12} = {T_{\rm max}(F=1-1) \over T_{\rm max}(F=2-1)}.
\end{eqnarray}
It is found that $R_{12}$ lies between 0.4 and 0.7, except one source,
while $R_{02}$ spans from 0.2 to 1.0. Similar distributions have been
known for quiescent dark clouds (\cite{har89}; \cite{gon93}) and for
small translucent cores (\cite{tur97}), though their physical conditions
are quite different each other. The parameter space with
$R_{12}\stackrel{<}{_{\sim}}1$ and $R_{02}\stackrel{<}{_{\sim}}0.8$ can
be explained in terms of radiative transfer effect on the clouds/cores
which are either static or under systematic motion (\cite{gon93};
\cite{tur97}). However, the region of
$R_{12}\stackrel{>}{_{\sim}}1$ or $R_{02}\stackrel{>}{_{\sim}}0.8$,
where the $F$=2--1 component is significantly suppressed with respect
to the $F$=0--1 and $F$=1--1 components, seems to invoke the existence
of diffuse envelope, as we have shown in section~4.
Recently, Afonso et al. (1998) carried out an HCN $J$=1--0 survey
towards YSOs in Bok globules. They found that HCN is detected with a
higher probability in class I and probably class 0 objects than in
starless cores and class II sources. Because there is only one class 0
source in their survey, such a preference for class 0 was uncertain.
Our study implies the high detection rate of almost unity for both class 0
and I sources. Thus there seems to be a unique phase of class 0 and I
in the evolution of YSOs when a dense envelope of $\sim 1'$ ($0.05-0.1$
pc at the distances of $150-300$ pc) in size is formed.
\section{Summary}
We have carried out a survey of HCN $J$=1--0 hyperfine lines for 24
objects identified as class 0 and I with a spectral resolution of
0.068 km s$^{-1}$. 22 sources are detected with around 30 mK rms level
in $T_A^*$ unit.
It is found that three hyperfine components show a variety of spectral
features such as deep self-absorption, asymmetry, and broad wings which
are more prominent in the optically thicker lines.
Moreover, for a large fraction of sources, HCN hyperfine lines
show a progressive shift to the blue, as the optical depth increases.
Only a few sources show a gradual shift to the red, which implies that
an inward motion is predominant in the core embedding YSOs.
When compared with previous CS and H$_2$CO surveys, the velocity shifts
of HCN correlate better with those of CS than with those of H$_2$CO.
Little difference in the correlation is noted between class 0 and I.
L483 is confirmed as a candidate infalling source on $\sim 0.1$ pc scale,
from a growing degree of asymmetry and self-absorption with an increasing
optical depth.
We synthesized its hyperfine lines, by solving radiative transfer in a
collapsing core model with the Monte Carlo method.
The synthetic lines based on the Shu (1977) model do not fit the observed
ones. We reproduced the observed ones successfully with the modification
of the Shu model, an overall increase of gas density by a factor of 6 and
the decrease of infall velocity by a factor of 2.
Furthermore, in order to explain the line intensity ratios, a diffuse,
static, and geometrically thick envelope surrounding the modified Shu core
is essential.
\acknowledgments
Authors are grateful to Dr. C.W. Lee and Dr. E. Gonz\'{a}les-Alfonso for
helpful discussions. This study was supported by Korea Astronomy
Observatory through KAO grant 97-5400-000.
| {
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The Ministerial Council on Energy (MCE) was established as a committee of the Council of Australian Governments in June 2001. It was superseded by the Standing Council on Energy and Resources in June 2011.
During its time, it was responsible for a range of initiatives including:
Equipment Energy Efficiency Program
National Framework for Energy Efficiency
Reform of Energy Markets - issued 11 December 2003
See also
Australian Energy Regulator
Australian Energy Market Commission
References
Energy policy of Australia
2001 establishments in Australia
2011 disestablishments in Australia
Council of Australian Governments | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 952 |
Tineola är ett släkte av fjärilar som beskrevs av Herrich-Schäffer 1853. Tineola ingår i familjen äkta malar.
Kladogram enligt Catalogue of Life och Dyntaxa:
Bildgalleri
Källor
Externa länkar
Äkta malar
Tineola | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,263 |
{"url":"https:\/\/tidymodels.github.io\/tidyposterior\/reference\/perf_mod.html","text":"Bayesian analysis used here to answer the question: \"when looking at resampling results, are the differences between models 'real?'\" To answer this, a model can be created were the outcome is the resampling statistics (e.g. accuracy or RMSE). These values are explained by the model types. In doing this, we can get parameter estimates for each model's affect on performance and make statistical (and practical) comparisons between models.\n\nperf_mod(object, ...)\n\n# S3 method for rset\nperf_mod(object, transform = no_trans,\nhetero_var = FALSE, ...)\n\n# S3 method for vfold_cv\nperf_mod(object, transform = no_trans,\nhetero_var = FALSE, ...)\n\n# S3 method for resamples\nperf_mod(object, transform = no_trans,\nhetero_var = FALSE, metric = object\\$metrics[1], ...)\n\n# S3 method for data.frame\nperf_mod(object, transform = no_trans,\nhetero_var = FALSE, ...)\n\n## Arguments\n\nobject A data frame or an rset object (such as rsample::vfold_cv()) containing the id column(s) and at least two numeric columns of model performance statistics (e.g. accuracy). Additionally, an object from caret::resamples can be used. Additonal arguments to pass to rstanarm::stan_glmer() such as verbose, prior, seed, family, etc. An named list of transformation and inverse transformation fuctions. See logit_trans() as an example. A logical; if TRUE, then different variances are estimated for each model group. Otherwise, the same variance is used for each group. Estimating heterogeneous variances may slow or prevent convergence. A single character value for the statstic from the resamples object that should be analyzed.\n\n## Value\n\nAn object of class perf_mod.\n\n## Details\n\nThese functions can be used to process and analyze matched resampling statistics from different models using a Bayesian generalized linear model with effects for the model and the resamples.\n\nBy default, a generalized linear model with Gaussian error and an identity link is fit to the data and has terms for the predictive model grouping variable. In this way, the performance metrics can be compared between models.\n\nAdditionally, random effect terms are also used. For most resampling methods (except repeated V-fold cross-validation), a simple random intercept model its used with an exchangeable (i.e. compound-symmetric) variance structure. In the case of repeated cross-validation, two random intercept terms are used; one for the repeat and another for the fold within repeat. These also have exchangeable correlation structures.\n\nThe above model specification assumes that the variance in the performance metrics is the same across models. However, this is unlikely to be true in some cases. For example, for simple binomial accuracy, it well know that the variance is highest when the accuracy is near 50 percent. When the argument hetero_var = TRUE, the variance structure uses random intercepts for each model term. This may produce more realistic posterior distributions but may take more time to converge.\n\nAlso, as shown in the package vignettes, the Gaussian assumption make be unrealistic. In this case, there are at least two approaches that can be used. First, the outcome statistics can be transformed prior to fitting the model. For example, for accuracy, the logit transformation can be used to convert the outcome values to be on the real line and a model is fit to these data. Once the posterior distributions are computed, the inverse transformation can be used to put them back into the original units. The transform argument can be used to do this.\n\nThe second approach would be to use a different error distribution from the exponential family. For RMSE values, the Gamma distribution may produce better results at the expense of model computational complexity. This can be achieved by passing the family argument to perf_mod as one might with the glm function.\n\n## Examples\n\n# Example objects from the \"Getting Started\" vignette at\n# https:\/\/topepo.github.io\/tidyposterior\/articles\/Getting_Started.html\n\n# File for pre-run model is at\nex_dat <- \"https:\/\/bit.ly\/2OJdvl1\"\n\n# Summary method shows the underlying stan model\n# summary(roc_model)","date":"2019-03-23 06:13:33","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\": 0.5125170946121216, \"perplexity\": 1427.4062427331708}, \"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-2019-13\/segments\/1552912202728.21\/warc\/CC-MAIN-20190323060839-20190323082839-00311.warc.gz\"}"} | null | null |
Q: Time complexity of T(n) = T(n - 1) + (n - 1)^2 I am wondering what is the time complexity of this recurrence relation.
A: T(n) = T(n-1) + f(n)
Means
T(n) = T(0) + Sum_from_i=1_to_n_of( f(i) )
In your case, that's:
T(n) = T(0) + 02 + 12 + 22 ... (n-1)2
If you don't know immediately from discrete calculus that the sum comes out to O(n3), you can notice that there are n terms, with the largest being (n-1)2, and there more than (n/3) terms that are >= (n/2)2.
A: Sorry if I'm writing with images, but I needed to include some math:
| {
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<?xml version="1.0" encoding="UTF-8"?>
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~
~ This file is part of easyrec.
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~ easyrec is free software: you can redistribute it and/or modify
~ it under the terms of the GNU General Public License as published by
~ the Free Software Foundation, either version 3 of the License, or
~ (at your option) any later version.
~
~ easyrec is distributed in the hope that it will be useful,
~ but WITHOUT ANY WARRANTY; without even the implied warranty of
~ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
~ GNU General Public License for more details.
~
~ You should have received a copy of the GNU General Public License
~ along with easyrec. If not, see <http://www.gnu.org/licenses/>.
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{"url":"http:\/\/www.alexejgossmann.com\/code\/","text":"# Code\n\n\u2022 grpSLOPEMC \u2014 This is an extension package to the R package grpSLOPE. It contains Monte Carlo based methods for the estimation of the regularizing sequence. github\n\n\u2022 grpSLOPE \u2014 Group SLOPE is a penalized linear regression method that is used for adaptive selection of groups of significant predictors in a high-dimensional linear model. A unique feature of the Group SLOPE method is that it offers (group) false discovery rate control (i.e., control of the expected proportion of irrelevant groups among the total number of groups of predictors selected by the Group SLOPE method). github gh-pages CRAN\n\n\u2022 mixed_models \u2014 Fit statistical (linear) models with fixed and mixed (random) effects in Ruby. The package supports the formula language of the R package lme4 for model specification (a pain to implement), many types of hypotheses tests and confidence intervals for the fixed and random effects coefficients, methods for prediction and prediction intervals, etc. It is my Google Summer Of Code 2015 project. github rubygems\n\n\u2022 spitzy \u2014 Spitzy is the name of a cute Pomeranian. Spitzy reads backwards as yztips, which translates into: Your Zappy-Tappy Initial and boundary value Partial (and ordinary) differential equation Solver. It is my collection of numerical methods for differential equations written in Ruby. github gh-pages rubygems\n\n\u2022 When I have some free time, I like to contribute code to open source software projects (mostly, related to mathematics, statistics or machine learning). Visit my github page for the projects that I contribute to.","date":"2017-09-23 16:33:41","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\": 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\": 0.2797348201274872, \"perplexity\": 1900.942995254781}, \"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-2017-39\/segments\/1505818689752.21\/warc\/CC-MAIN-20170923160736-20170923180736-00077.warc.gz\"}"} | null | null |
DELUXE DIGITAL GAUGE: This dual configurable LCD screen gauge allows to you check all the vital information about your snowmobile and more. 14 different readings to be exact. There's an odometer, speedometer, max RPM, 2 trip meters, engine hours, low oil light, coolant temperature, exhaust temperature, intake air temperature, battery voltage, fuel level, clock, reverse indicator, hand warmer and thumb warmer.
Estimated Dry - 438 lb.
153 x 15 x 3.00in. | {
"redpajama_set_name": "RedPajamaC4"
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Anosia bataviana är en fjärilsart som beskrevs av Moore 1883. Anosia bataviana ingår i släktet Anosia och familjen praktfjärilar. Inga underarter finns listade i Catalogue of Life.
Källor
Praktfjärilar
bataviana | {
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\section{INTRODUCTION}
The first detection of an exoplanetary atmosphere was accomplished via measuring the sodium doublet transit signal of HD 209458b \citep{Charbonneau}.
The atmosphere of HD~189733b\ has also been detected by Ly$\alpha$\ transit \citep{Lecavelier,Bourrier2013}.
The species O$_{\rm\,I}$, Na$_{\rm ~I}$, and possibly K$_{\rm ~I}$\ \citep{Pont,Jensen11} were detected by the Hubble Space Telescope (HST) \citep{Ben-Jaffel, Huitson, Pont}.
An indication of an extended atmosphere was also found in X-ray by Chandra \citep{Poppenhaeger}.
The H$\alpha$, H$\beta$, and H$\gamma$\ hydrogen lines, and absorption lines from Na$_{\rm ~I}$\ and possibly Mg$_{\rm ~I}$\ were detected in HD~189733b's atmosphere \citep{Jensen11, Jensen, Cauley2015, Cauley2016, Redfield, Wyttenbach, Khala}, which shows the promise of ground based telescopes in studying exoplanet atmospheres.
An H$_2$O feature has been identified at 3.2$\mu$m during the secondary transit \citep{Birkby}.
The atmosphere of HD 209458b has been modeled in order to compare to the observed H Ly$\alpha$, O, Si $_{\rm III}$, and Na$_{\rm ~I}$\ lines \citep{Fortney, KoskinenI, KoskinenII, Lavvas}.
For the purpose of studying the Ly$\alpha$\ emission spectrum, \citet{Menager} calculated the Ly$\alpha$\ resonant scattering process in the atmosphere of HD 209458b, based on the atmospheric structure model in \citet{KoskinenI}, and HD~189733b\ based on an unpublished model \citep{Koskinen2011}. A simulation of HD~189733b 's escaping atmosphere has been performed by \citet{Salz}.
As the hot gas in the upper thermosphere is more weakly bound to the planet, conditions there set the boundary condition for the rate of gas escape \citep{Yelle,Garcia,Murray-Clay} .
Among detected species, H$\alpha$\ is a sensitive probe of the planet's upper atmosphere because the excitation and de-excitation processes for H(2$\ell$), the absorber of H$\alpha$, are strongly dependent on the local particle densities, temperature, and radiation field. In addition, unlike Ly$\alpha$, the interstellar medium is transparent to H$\alpha$\ and this optical line can be observed with large ground based telescopes. Therefore, the H$\alpha$\ transmission spectrum is a powerful and economical method to probe the structure of the planet's upper atmosphere.
As this work shows, the temperature, and hence scale height, in the region optically thick to H$\alpha$\ is (approximately) set by a balance of photoelectric heating and line cooling by metal species, mainly Mg$_{\rm ~I}$\ and Na$_{\rm ~I}$. If only photoelectric heating and line cooling from hydrogen were included, the atmosphere would be hotter by $\simeq 2000-3000\ \rm K$ \citep{Christie}, giving transit depths far too large in comparison to observations. Furthermore, several studies \citep{Garcia,KoskinenI,Lavvas} suggested that the transition from atomic to molecule hydrogen occurs at pressures $P \simeq 10~\mu$bar. These studies included detailed heating and cooling physics in the molecular layer. But transmission spectra for the Na D doublet and Mg lines may in principle provide further constraints on atmosphere models around this transition altitude.
In addition, the atmospheric temperature of HD~189733b\ derived from the Na doublet transmission spectrum by \citet{Huitson} and \citet{Wyttenbach} is significantly lower than the modeled upper atmosphere temperature found in \citet{Salz} and \citet{Christie}.
A model of the Na transmission spectrum is required to understand these contradictory results.
Both the HD~189733b\ H$\alpha$\ transmission spectrum observed by \citet{Cauley2016} and the Na D transmission spectrum presented by \citet{Wyttenbach} have the spectral resolution to resolve the line core. The line center transit depths of both observations are about 1-1.5\%, which means the line core absorption features of both species are mostly contributed by the same region in the atmosphere.
Since the temperature of the molecular layer is below 3000 K, and the molecular hydrogen has a large absorption cross section to Ly$\alpha$\ photon \citep{Black1987}, both the collisional excitation rate and radiative excitation rate are too small to create enough H(2$\ell$) to absorb the H$\alpha$\ in the molecular layer.
These results suggest that the absorption features of both H$\alpha$\ and Na near line center are tracing the atomic layer in the HD~189733b\ atmosphere.
The HD~189733b\ H$\alpha$\ transmission spectrum was modeled by \citet{Christie}, who constructed a hydrostatic atmosphere model similar to the one considered here. In that work, a detailed treatment of Ly$\alpha$\ radiation transfer was not included, and hence the role of Ly$\alpha$\ excitation deep in the atmosphere was not appreciated. \citet{Christie} showed that if collisional excitation dominates, it would lead to a fairly constant H(2s) density within the atomic layer, because of the combination of increasing temperature and decreasing H(1s) density with radius.
In attempting to improve on their model, it was found that Ly$\alpha$, especially from recombinations occurring within the atmosphere, could give radiative excitation rate to H(2p) much larger than the collisional excitation rate, and that this excitation could occur deeper in the atmosphere where the H(1s) density is higher, even though the temperature is much lower there. This key insight motivated the detailed Ly$\alpha$\ radiative transfer treatment in the present work.
\section{ analytic estimates }
\label{sec:analytic}
\begin{table}
\centering
\caption{Adopted values for the orbital and physical parameters of HD~189733 and HD~189733b}
\begin{tabular}{cc}
\hline \hline
Stellar type & K2V \\
Star mass & $M_\star = 1.60\times 10^{33}\, \rm g$ \\
Star radius & $R_\star = 5.60\times 10^{10}\, \rm cm$ \\
Semi-major axis & $a = 0.031\, \rm AU$ \\
Planet mass & $M_p = 2.17\times 10^{30}\, \rm g$ \\
Planet radius & $R_p = 8.137 \times 10^9\, \rm cm$ \\
Planet surface gravity & $g_p = GM_p/R_p^2 = 2.2\times 10^3\, \rm cm\ s^{-2}$ \\
\hline
\end{tabular}
\tablecomments{ Source: exoplanets.org}
\label{tab:param}
\end{table}
Observations of the H$\alpha$\, transmission spectrum for HD~189733b\ show a $\sim 1 \%$ line center transit depth, and a half-width of $\sim 0.4 \rm~\AA$ (e.g. \citet{Cauley2015}). \citet{Wyttenbach} measured a nearly $\sim 1\%$ transit depth for both Na D lines, among which the Na$_{\rm ~I}$\ 5890~\AA\ is slightly deeper. This section contains analytic estimates for the conditions in the atmosphere required to generate the observed H$\alpha$\ and Na D absorption lines.
The outermost reaches of HD 189733b's atmosphere are highly ionized by stellar photons. Moving inward, the radiative recombination rate eventually increases to the point that the atmosphere is dominated by atomic hydrogen, at a pressure level $P \simeq 10^{-3}\, {\rm \mu bar}$. The temperature near the transition from ionized to atomic is regulated to be near $T\simeq 10,000\, \rm K$, which is far too hot for molecular hydrogen to form, and hence there must be a layer of atomic hydrogen extending over the temperature range $T \simeq 2,500-10,000\, \rm K$. In the hydrostatic model presented in this paper, the temperature in the atomic layer is set by a balance of photoelectric heating and atomic line cooling, for which H$_2$ will dominate at $P \ga 10\, \mu\, \rm bar$. In terms of size, the atomic hydrogen layer extends over $\sim 10$ pressure scale heights, has a mean molecular weight $\mu \simeq 1.3$ and mean temperature $T \simeq 5,000\, \rm K$. As compared to the underlying molecular layer, with mean molecular weight $\mu \simeq 2.3$ and temperature $T \simeq 1,000\, {\rm K}$, the scale height in the atomic layer is larger by a factor of $\sim 10$ compared to the molecular layer, and hence can give rise to absorption to much larger altitudes.
The origin of the H(2$\ell$) population requires a detailed level population calculation. In the present model of the atomic layer, it is found that radiative excitation by Ly$\alpha$\, creates a nearly constant H(2$\ell$) density over $\sim 6$ pressure scale heights near the base of the atomic layer. This is the cause of the H$\alpha$\, absorption.
The underlying molecular layer is expected to be optically thin to H$\alpha$\, for two reasons.
First, the density of atomic hydrogen drops rapidly into the molecular layer (e.g. \citealt{Lavvas}), as compared to the base of the atomic layer, due to the much lower temperature there.
Second, the mean free path to true absorption of Ly$\alpha$\, by H$_2$ \citep{Black1987} rapidly decreases as the H$_2$ density increases, and hence the Ly$\alpha$\, intensity is expected to drop rapidly in the molecular layer, with an associated decrease in excitation to the n=2 state.
The measured line center transit depth $\Delta F/F \sim 1 \%$ requires a certain area to be optically thick. The scale height in the atomic layer is
\begin{eqnarray}
H & = & \frac{k_B T}{\mu m_p g} = 1500\, {\rm km} \left( \frac{T}{5000\, \rm K} \right),
\end{eqnarray}
where the mean molecular weight has been assumed to be $\mu=1.3$.
If N scale heights are optically thick, as compared to the neighboring continuum radiation, this gives an extra absorption depth
\begin{eqnarray}
\frac{\Delta F}{F} & \simeq & N \frac{2\pi R_p H}{\pi R_\star^2} = 8 \times 10^{-4} N \left( \frac{T}{5000\, \rm K} \right)
\nonumber \\ & = & 0.5\% \ \left( \frac{N}{6} \right)
\left( \frac{T}{5000\, \rm K} \right).
\end{eqnarray}
Hence the measured line center depth can only be explained by a layer extending many pressure scale heights, and with high temperature $T \ga 5,000\, \rm K$.
The line center optical depth must be greater than unity over the above annulus.
As will be shown, $n_{2\ell}$ is nearly constant over a large pressure range.
Then for an effective path length $2\sqrt{2 N R_p H} \simeq 7\times 10^9\ {\rm cm}\ (N/6)^{1/2}(T/5,000\rm K)^{1/2}$
and H$\alpha$\, line center cross section $\sigma_0=5 \times 10^{-13}\ {\rm cm^2}\ (5,000\rm K/T)^{1/2}$, the maximum line center optical depth is
\begin{eqnarray}
\tau_0 & \simeq & 35 \times \left( \frac{ n_{2\ell} }{ 10^4\ \rm cm^{-3} } \right)
\end{eqnarray}
for the fiducial value $n_{2\ell} = 10^4\ \rm cm^{-3} $.
The line width is mainly set by the temperature and the maximum line center optical depth. For sightlines optically thick to H$\alpha$\, at a line center, the optical depth at distance $x=(\nu-\nu_0)/\Delta \nu_D$ from line center is $\tau(x) = \tau_0 \exp(-x^2)$, when Doppler broadening dominates. All frequencies out to $x \simeq \sqrt{ \ln (\tau_0) }$ are then optically thick. In velocity units, the
line width is then
\begin{eqnarray}
\Delta v & = & \left( \frac{2k_BT}{m_p} \right)^{1/2} \left( \ln \tau_0 \right)^{1/2} = 9.1\, {\rm km\ s^{-1}}\left( \ln \tau_0 \right)^{1/2}
\end{eqnarray}
or in wavelength units
\begin{eqnarray}
\Delta \lambda & = & 0.2\rm~\AA\, \left( \ln \tau_0 \right)^{1/2}.
\end{eqnarray}
Since $\tau_0 \gg 1$ for H$\alpha$\, over a large region, the width will be larger than the thermal width.
If Ly$\alpha$\ excitation is balanced by radiative de-excitation, and $\ell$-mixing populates the 2s state, the abundances relative to the ground state are
\begin{eqnarray}
\frac{ n_{2p} }{ n_{1s} } & \simeq & 3 \frac{ n_{2s} }{ n_{1s} } = \frac{ J_{12} B_{12}}{A_{21}}
\nonumber \\ & \simeq &
10^{-8}\, \left( \frac{J_{12}}{10^{-9}\rm ~erg~cm^{-2}~s^{-1}~Hz^{-1}} \right),
\end{eqnarray}
where $A_{21}$ and $B_{12}$ are the Einstein A and B (absorption) coefficient respectively, following the definition in \citet{Rybicki}.
The peak Ly$\alpha$\, intensity $J_{12} \simeq 0.1 F_{\rm LyC} / \Delta \nu_D \simeq 10^{-8} \rm ~erg~cm^{-2}~s^{-1}~Hz^{-1}$ is found near the peak in photoionization of ${\rm H}(1s)$ near $P \simeq 10^{-3}\, \rm \mu bar$. Here, $F_{\rm LyC} \simeq 10^4\, \rm ~erg~cm^{-2}~s^{-1}$ is the LyC flux deposited in that region, and it is assumed that each ionization is balanced by a recombination producing a Ly$\alpha$\, photon. While the ratio of excited state to ground state is high near the peak in Ly$\alpha$, the H(1s) density there is too small for significant H(2$\ell$) density.
The key question for the H(2$\ell$) population is how fast the Ly$\alpha$\, intensity decreases moving deeper into the atmosphere. If Ly$\alpha$\, intensity does not drop off too fast, the rapid increase in H(1s) density with depth will lead to higher H(2$\ell$) density deeper in the atmosphere. One can imagine two limits to answer this question. In the first limit, there is a shallow source of Ly$\alpha$\, at optical depth $\tau_s$ and the intensity $J_\nu(x,\tau)$ is desired at $\tau \gg \tau_s$. An analytic solution based on the Fokker-Planck equation given in \citet{Harrington} is
\begin{eqnarray}
J_\nu(x,\tau) & \simeq & 0.1 \left( \frac{ F_0 }{ \Delta \nu_D} \right) \left( \frac{\tau_s}{\tau} \right).
\end{eqnarray}
This expression is valid in the plateau of the intensity near line center.
Since Ly$\alpha$\, optical depth $\tau \propto n_{1s}$, this scaling for $J_\nu$ would give $n_{2\ell} \propto n_{1s} J_\nu \simeq \rm constant$ with depth.
The second limit to imagine is where radiation is emitted and absorbed locally, which is appropriate deep in the atmosphere where $\tau \sim 10^8$ scatterings are required to escape the atmosphere.
For a constant, frequency-integrated source function $S$, and true absorption by metal species, the frequency-integrated photon energy equation becomes $S \simeq n_m \sigma_m J$, where $J$ is the frequency-integrated intensity, $n_m$ is the metal number density and $\sigma_m$ is the metal photoionization cross section at Ly$\alpha$. For a constant mixing ratio, $n_m \propto n_{1s}$,
and again $n_{2\ell} \simeq \rm constant$. While the scaling found by these two estimates, constant 2$\ell$ density, is the same, it is found that the local balance of sources and sinks is the applicable limit in the present atmosphere model.
Up to this point, the estimates have been concerned with the H$\alpha$\ transmission line, however, the center of each line in the Na doublet may also be formed in the atomic layer.
Because the cross section of Na$_{\rm ~I}$\ 5890 is larger than Na$_{\rm ~I}$\ 5896 by a factor of 2, the difference in transit radius between the two resolved line centers corresponds to $\ln (2) H$, assuming a constant Na$_{\rm ~I}$\ number fraction.
Keeping in mind the error bars in the measurement, according to \citet{Wyttenbach}, the difference in transit radius between the Na D lines is $\sim 3000$ km, which gives a local scale height $H\simeq 4300 ~\rm km$. Plugging in the transit radius $R({\rm Na})=9.4 \times 10^9~\rm cm$ to compute the gravity, assuming $\mu=1.3$, the temperature derived from the line centers is $T\simeq 11,000~\rm K$. In order to explain this scale height with a molecular gas, the temperature has to be higher by a factor of 2. But this high temperature is inconsistent with the gas being in molecular form.
\section{hydrogen level population}
\label{sec:level}
Balmer line photons are absorbed by the 2$\ell$ excited states of H. Due to ionization and the subsequent recombination cascades, and a radiation excitation temperature different from the gas temperature, the level populations are not set by the Boltzmann distribution at the local gas temperature.
Therefore, a study of the H level population over the range of densities, temperatures, and intensities found in hot Jupiter atmosphere is required. The following processes are considered.
\begin{enumerate}
\item Hydrogen radiative (de-)excitation of all possible electric dipole transitions between multiplets up to $n=6$ ~\citep{Wiese};
\item Electron collisional (de-)excitation for transitions from $1s$ to each sub-state $\ell$ up to $n=5$, from $2s$ to each sub-state $\ell$ up to n=5, and from $2p$ to each sub-state $\ell$ up to n=3 (CHIANTI database, \citet{Chianti,Chianti8});
\item Electron collisional $\ell$-mixing between $2s$ and $2p$~\citep{Seaton55};
\item Proton collisional $\ell$-mixing between $2s$ and $2p$~\citep{Seaton55}, and $\ell$-mixing for levels $3\leq n\leq 6$~\citep{Vrinceanu};
\item Electron collisional ionization and three-body recombination for each sub-state $\ell$ up to n=4 and total ($\ell$-unresolved) rates for $n=$5 and 6~\citep{Janev}. The cross sections are assumed to be equal for all sub-states in the same level for $n=$5 and 6;
\item Photoionization of each sub-state $\ell$ up to n=6~\citep{TOP}. The corresponding recombination rate can be calculated using the Milne relation.
\end{enumerate}
\begin{figure}
\begin{center}
\includegraphics[width=0.5\textwidth]{Muscles_sm.pdf}
\caption{Stellar energy flux spectrum ($F_\lambda$) against wavelength ($\lambda$) used in the model at orbital distance of HD 189733b.}
\label{spec}
\end{center}
\end{figure}
The stellar spectrum of $\epsilon$ Eri, another K2V star, given by the MUSCLES treasury survey version 2.1 \citep{France,Yongblood,Loyd} is applied in the model. Its energy flux ($F_\lambda$) is normalized to the distance $a=0.031\ \rm AU$ of HD 189733b from its parent star, shown in Figure~\ref{spec}.
The Ly$\alpha$\ fluxes are combined with models of solar active regions \citep{Fontenla} to estimate the EUV luminosity in the wavelength region 100 -- 1170\rm~\AA\ in 100\rm~\AA\ bins.
The stellar flux attenuation due to bound-bound transitions is not included in this calculation because it is relatively unimportant in setting the level populations, and performing radiation transfer calculations in addition to Ly$\alpha$\ would greatly complicate the analysis.
Bound-bound transitions due to Ly$\beta$, Ly$\gamma$ etc. are ignored as it is assumed that these photons rapidly down-convert into a Ly$\alpha$\ photon and lower series photons at the large optical depths of interest for these lines.
The level population is determined by the kinetic equilibrium between production and loss processes. The equation of rate equilibrium for the state $j$ is
\begin{multline}
\alpha_{j} n_e n_p + \beta_{j}n_e^2n_p + \sum_{k}C_{k\to j}^{(e)}n_en_{k} \\
+ \sum_{k}C_{k\to j}^{(p)}n_pn_k + \sum_{k>j}A_{k\to j}n_k + \sum_{k<j}B_{k \to j}\bar{J}_{k \to j}n_k \\
= \Big(\Gamma_{j} + \sum_{k}C_{j \to k}^{(e)}n_e + \sum_{k}C_{j \to k}^{(p)}n_p\\
+ C_{j\to \infty}^{(e)}n_e + \sum_{k>j}B_{j \to k}\bar{J}_{j \to k} + \sum_{k<j}A_{j\to k} \Big) n_{j},
\label{eq:levelpopeqn}
\end{multline}
where $\alpha_{j}$ and $\beta_{j}$ denote radiative and three-body recombination rate coefficients for state $j$, respectively. Case B recombination with $\alpha_{1s}\equiv 0$ is employed. The $n_k$ is the number density of hydrogen in sub-state $k$.
The inequality $k>j$ denotes a downward transition from a state with principle quantum number of state $k$ larger than that of state $j$. The rate coefficients
$C_{j\to k}^{(e/p)}$ are for electron/proton impacts causing a transition from state $j$ to state $k$, and the state $\infty$ represents ionization. The rate for proton collisions is only included for the $\ell$-mixing transitions at fixed principal quantum number. The spontaneous radiative decay rates are $A_{j\to k}$.
The photoionization rate from state $j$ is denoted $\Gamma_{j}$, and attenuation from the overlying gas is included in the ground state photoionization calculation. The optical depth for ionizing photons is computed as
\begin{equation}
\tau_{{\rm att},\nu}=\sigma_{1s}(\nu)N_{1s}+\sum_{m} \sigma_{m}(\nu) N_{m},
\end{equation}
where $N_{k}(r)=\int_r^\infty {\rm d} r' n_{k}(r')$ is the column of species $k$ above the layer under consideration. The sum over the subscript $m$ stands for all metal species considered. As discussed in Section \ref{hydro}, this is $m=$neutral and first ionized C, O, Mg, Si, and S, and neutral Na and K.
Including the attenuation factor $e^{-\tau_{\rm att},\nu}$, the photoionization rate is
\begin{equation}
\label{eq:12}
\Gamma_{j,\rm pi}=\int_{\nu_{j,\rm th}}^\infty \sigma_{j,\rm pi}(\nu)\frac{F_{\nu}}{h\nu}e^{-\tau_{{\rm att},\nu}}{\rm d} \nu,
\end{equation}
where $\nu_{\rm th}$ is the corresponding photoionization threshold frequency. The photoionization rates and photoelectric heating rates (see Equation~\ref{eq:7} and~\ref{eq:8}) at $\tau_{\rm att}=0$ are listed in Table~\ref{tab:pi_rates}.
The H(1s) state can also undergo ``secondary ionization" by photoelectrons generated when a photon with much higher energy than the ionization threshold ionizes a hydrogen or metal atom. If $n_e/n_{1s}$ is small, photoelectrons can cause H(1s) collisional ionization and excitation before sharing their energy with other electrons through Coulomb collisions, which would increase the photoionization rate and reduce the photoelectron heating efficiency.
Different from the treatment of constant efficiency applied in \citet{Yelle} and \citet{Murray-Clay}, or the ionization fraction $x_e=n_e/n_{1s}$ independent efficiency applied in \citet{KoskinenI}, an efficiency dependent on local $x_e$ and photoelectron energy $E=h(\nu-\nu_{\rm th})$ is used here. Given the incoming photon frequency $\nu$ and ionization threshold energy $E_{\rm th}$, \citet{Draine} gives the number of secondary ionizations per ionizing photon, in the case of $E>50 \text{ eV} \text{ and } x_e<1.2$, to be
\begin{equation}\label{ke}
k_e(E)=\left(\frac{E-15{\rm\ eV}}{35{\rm\ eV}}\right)\left( \frac{1-x_e/1.2}{1+18x_e^{0.8}/\ln(E/35{~\rm eV})}\right).
\end{equation}
After correcting for the secondary ionizations, the form for the H(1s) ionization rate which is used in the rate equations becomes
\begin{align}
\Gamma_{1s} & =\Gamma_{1s}^{\rm 1st }+\Gamma_{1s}^{\rm 2nd} \nonumber \\
& =\int_{\nu_{\rm th}}^\infty \sigma_{1s}(\nu)(1+k_e)\frac{F_\nu}{h\nu}e^{-\tau_{{\rm att},\nu}}{\rm d} \nu,
\label{eq:Gamma1s}
\end{align}
where $\Gamma_{1s}^{\rm 1st }$ and $\Gamma_{1s}^{\rm 2nd}$ stand for primary and secondary photoionization rate from H(1s) respectively.
Secondary photoionization becomes an important consideration at pressures $P \ga 0.1\, \mu$bar, where the initially more abundant lower energy photons have already been absorbed higher in the atmosphere, and the dominant photons being absorbed can induce at least one secondary ionization on average.
\begin{table}
\caption{Photoionization rates and photoelectric heating rates}
\begin{center}
\begin{tabular}{ccc}
\hline \hline
Species & $\Gamma_{\rm pi} $ (s$^{-1}$) & $Q_{\rm pi}$ (erg s$^{-1}$) \\
\hline
H($1s$) & $1.61\times 10^{-3}$ & $5.91\times 10^{-15}$ \\
H($2s$) & 25.7 & $1.42\times 10^{-11}$ \\
H($2p$) & 21.5 & $1.13\times 10^{-11}$ \\
O$_{\rm ~I}$ & $3.06\times 10^{-3}$ & $6.14\times 10^{-14}$ \\
O$_{\rm ~II}$ & $7.10\times 10^{-4}$ & $1.51\times 10^{-14}$ \\
C$_{\rm ~I}$ & $7.43\times 10^{-3}$ & $5.91\times 10^{-14}$ \\
C$_{\rm ~II}$ & $3.90\times 10^{-4}$ & $1.07\times 10^{-14}$ \\
Mg$_{\rm ~I}$ & $6.12\times 10^{-4}$ & $2.96\times 10^{-14}$ \\
Mg$_{\rm ~II}$ & $2.23\times 10^{-4}$ & $2.14\times 10^{-14}$ \\
Si$_{\rm ~I}$ & $2.18\times 10^{-2}$ & $1.02\times 10^{-14}$ \\
Si$_{\rm ~II}$ & $2.07\times 10^{-4}$ & $1.07\times 10^{-14}$ \\
S$_{\rm ~I}$ & $2.21\times 10^{-2}$ & $1.56\times 10^{-13}$ \\
S$_{\rm ~II}$ & $2.30\times 10^{-4}$ & $1.04\times 10^{-14}$ \\
Na$_{\rm ~I}$ & $9.92\times 10^{-4}$ & $5.36\times 10^{-14}$ \\
K$_{\rm ~I}$ & $2.08\times 10^{-3}$ & $2.60\times 10^{-14}$ \\
\hline
\end{tabular}
\end{center}
\tablecomments{ Atmospheric attenuation, secondary ionization effect and the contribution by Ly$\alpha$\ photon are not included.}
\label{tab:pi_rates}
\end{table}
Lastly, the bound-bound radiative excitation rates are given by
\begin{equation}
B_{l \to u}\bar{J}_{l \to u}=\frac{g_u}{g_l} \frac{c^2 A_{u\rightarrow l}}{2 h \nu^3} \int {\rm d} \nu J_\nu \phi(\nu),
\end{equation}
where $\bar{J}_{l \to u}$ is line profile weighted mean intensity and $\phi(\nu)$ is the Voigt profile.
\begin{table}
\caption{Rate which may be important to $n_{2p}$ population and de-population}
\centering
\begin{tabular}{*2c}
\hline \hline
Process & Rates ($\rm cm^{-3}s^{-1}$) \\
\hline
Radiative excitation $1s \to 2p$ & $1.7 \times 10^{11} (n_{1s}/10^{10}~\rm cm^{-3})$ \\
Collisional excitation $1s \to 2p$ & $8.4\times 10^{4} (n_e n_{1s} /10^{19}~\rm cm^{-6})$ \\
Radiative recombination to $2p$ & $6.2\times 10^{4} (n_e n_{p} /10^{18}~\rm cm^{-6})$ \\
Spontaneous decay $2p \to 1s$ & $6.3\times 10^{11} (n_{2p} /10^{3}~\rm cm^{-3})$ \\
$p$ collisional $\ell$-mixing $2p \to 2s$ & $1.9 \times 10^{8} (n_{2p}n_p/10^{12}~\rm cm^{-6})$ \\
Photoionization from $2p$ & $2.2\times 10^{4} (n_{2p} /10^{3}~\rm cm^{-3})$ \\
Collisional de-excitation $2p \to 1s$ & $7.4\times 10^{3} (n_{2p} n_e/10^{12}~\rm cm^{-6})$ \\
Collisional ionization from $2p$ & $7.4\times 10^{2} (n_{2p} n_e/10^{12}~\rm cm^{-6})$ \\
\hline
\end{tabular}
\tablecomments{In the table, $\bar{J}_{Ly\alpha}=2\times 10^{-9}\rm ~erg~cm^{-2}~s^{-1}~Hz^{-1}$ and $T$=8000 K are applied. The reference numbers are $n_{1s}=10^{10}~\rm cm^{-3}$, $n_e=n_p=10^{9}~\rm cm^{-3}$ and $n_{2p}=10^{3}~\rm cm^{-3}$.}
\label{tab:n2p_rates}
\end{table}
Equation \ref{eq:levelpopeqn} is evaluated for all $0 \leq \ell \leq n-1$ and $1 \leq n \leq 6$, resulting in a linear system of 21 equations in total for the number density of each $(n,\ell)$ state, $n_{n\ell}$. The quantities $n_e$, $n_p$, and $T$ are treated as given parameters in the equations. The linear system is solving using Gauss-Jordan elimination~\citep{Recipes}.
The rates of important processes related to the $2p$ state population are listed in Table~\ref{tab:n2p_rates}. The rates related to higher excited states are not listed in the table because they cannot have a large net effect on $2p$ in steady state, unless the higher state itself has a large source or sink, which is not the case. The stellar Ly$\alpha$\ mean intensity (see Section~\ref{MC}) is applied for the estimate. The table shows that all other rates except the $\ell$-mixing rates between $2s$ and $2p$ are negligible compared to the radiative rates between $2p$ and $1s$. The proton collisional $\ell$-mixing rate is much larger than the electron rate. The $\ell$-mixing rates between $2s$ and $2p$ nearly cancel each other and $2\ell$ states are in collisional equilibrium due to the large $\ell$-mixing rates at the densities of interest. Thus, $A_{2p\to 1s}n_{2p}$ and $B_{1s\to 2p}\bar{J}_{Ly\alpha}n_{1s}$ completely dominate the $2p$ generation and destruction rate, and the n=2 state number densities are simply set by $\bar{J}_{Ly\alpha}$, so we have,
\begin{equation}
\label{eq:6}
n_{2p}\approx 3n_{2s}\approx n_{1s} \frac{g_u}{g_l}\frac{c^2\bar{J}_{Ly\alpha}}{2h\nu^3}.
\end{equation}
In Section~\ref{sec:fiducial}, it will be shown that this is a good approximation for the whole simulation region. To obtain the intensity of Ly$\alpha$, a resonant scattering study of Ly$\alpha$\ photon will be discussed in Section~\ref{MC}.
\section{the atmosphere model}\label{hydro}
\subsection{Basic Structure}
Following \citet{Christie}, a spherically-symmetric, hydrostatic atmosphere model is constructed for the region composed of ionized and atomic gas sitting above the molecular atmosphere.
The transit radius measured in broadband optical wavelengths is $R_p$, and the base of the atomic layer is at radius $R_b > R_p$. The thickness of the molecular layer below the atomic layer is then $R_b-R_p$. Assuming an isothermal molecular layer with equilibrium temperature $T=T_{\rm eq}=1140{\rm~K}$ \citep{Wyttenbach}, the thickness is
\begin{equation}
R_b-R_p\approx \frac{k_{\rm B} T_{\rm eq} R_p^2}{\mu m_{\rm H}GM_p}\ln \left( \frac{P_p}{P_b}\right),
\end{equation}
where $\mu \approx 2.3$ is the mean molecular weight, $P_p=1\, $bar is the pressure of the optical photosphere suggested by~\citet{Sharp}. It is assumed that the pressure at the base of the atomic layer is $P_b=10\, \mu$bar. It will be shown that the temperature in the atomic layer becomes small enough for molecular hydrogen to dominate there, for the assumptions used here.
\subsection{Differential Equations}
Given the temperature and number density of each species at one level in the atmosphere, the equation of hydrostatic balance and equations for the column of each species must be integrated inward to find pressure and columns at the next step inward.
The hydrostatic balance equation is
\begin{align}
\frac{{\rm d} P}{{\rm d} r} & =-\frac{\rho GM_p}{r^2}
\label{eq:hb}
\end{align}
and the columns are integrated as
\begin{align}
\frac{{\rm d} N_i}{{\rm d} r} & = -n_i.
\label{eq:Ni}
\end{align}
The subscript $i$ stands for each species, including H(1s) and the individual neutral and first ionized metal element considered.
The ideal gas law for the gas pressure is
\begin{equation}
P=(n_e+(n_p+n_{\rm H})(1+f_z+f_{\rm He}))k_{\rm B}T,
\label{eq:P}
\end{equation}
where $f_z=\sum f_m$ is the sum of metal species relative number density abundance to hydrogen, and $f_{\rm He}$ is the fraction of He by number assuming solar abundance \citep{Asplund}. Ionization of He is ignored in this paper.
The gas density is written
\begin{equation}
\rho=(n_p+n_{\rm H})(1+4f_{\rm He}+\sum m_mf_m)m_p,
\end{equation}
where $m_m$ is the metal atomic mass in atomic units.
The pressure and the column density are integrated inward, with a starting value $P_{\rm top}=5\times 10^{-5}\mu$bar on the outside, where the atmosphere above becomes optically thin to Ly$\alpha$. The starting value of each $N_i=0$. The solution is integrated inward from a starting radius $R_{\rm top}$ and pressure $P_{\rm top}$, until the base radius $R_b$ is reached. The boundary condition imposed there is that $P=P_b$. This boundary condition is satisfied in practice by varying the starting radius $R_{\rm top}$ until $P(R_b) = P_b$, the desired value, using Brent's method~\citep{Recipes}.
The hydrostatic model will be inaccurate near the outer boundary, as a number of physical effects have been neglected, such as: outflowing gas from the planet, interaction with the stellar wind, strong magnetic forces, radiation pressure, and stellar tidal forces. The region where these effects may be appreciable will be estimated in Section~\ref{sec:ad_cool}. However, in the region where this model shows the dominant absorption by H(2$\ell$), the density is so high that these effects are negligible. Hence the hydrostatic model is sufficient for the purposes of this study.
\subsection{Ionization State and Temperature}
At each level of the atmosphere, the pressure $P$ and columns $N_i$ are given by the boundary conditions or the integration of Equations \ref{eq:hb} and \ref{eq:Ni}. The temperature and particle densities must then be updated to continue the integration.
Since the gas is not in local thermodynamic equilibrium (LTE), these quantities must be determined by solving rate equilibrium equations for ionization/recombination, heating/cooling, a charge balance equation, and the equation of state. The equations used are as following. Terms related to metal species will be discussed in more detail in Section~\ref{metal}.
The charge balance equation is
\begin{equation}
n_p+\sum n_{\rm M_{\,II}} + 2\sum n_{\rm M_{\,III}}=n_e,
\label{eq:number}
\end{equation}
where $n_{\rm M_{\,II}}$ and $n_{\rm M_{\,III}}$ are the number density of first ionized and second ionized metal species respectively. Higher ionization states are ignored as their abundance would be negligible for the given ionizing flux and particle densities.
The hydrogen ionization and recombination balance equation is
\begin{multline}
(\alpha_Bn_e+k^{(\rm O)}_{\rm ion}n_{\rm O\,I})n_p=n_{1s}(\Gamma_{1s}+C_{1s \to \infty}^{(e)}n_e+k^{(\rm O)}_{\rm rec}n_{\rm O\,II})\\
+C_{2 \to \infty}^{(e)}n_en_2+\Gamma_{2p}n_{2p}+\Gamma_{2s}n_{2s}+\sum_{m}\Gamma_{m}^{\rm 2nd}n_{m},
\label{eq:Hp}
\end{multline}
where $\alpha_B$ is the case B recombination rate, which is a good approximation for region deeper than $3\times 10^{-3}~\rm \mu bar$ where the atmosphere is optically thick to Lyman continuum photons near the ionization threshold. $k^{(\rm O)}_{\rm ion}$ and $k^{(\rm O)}_{\rm rec}$ are rates of whichoxygen ionizes and recombines through charge exchange with hydrogen respectively. The n=2 state has separate contributions from H(2s) and H(2p) as
\begin{equation}
C_{2 \to k}^{(e)}n_en_2=C_{2s \to k}^{(e)}n_en_{2s}+C_{2p \to k}^{(e)}n_en_{2p}.
\end{equation}
The last term in Equation \ref{eq:Hp} represents ionization from the H(1s) state due to photoelectrons created by metal ionization.
Hence high energy photoelectrons created through ionization of metal species can have the same secondary ionization effect as Equation~\ref{ke}. The secondary ionization rate due to metal species is then
\begin{equation}
\label{eq:2nd}
\Gamma_{m}^{\rm 2nd}=\int_{\nu_{\rm th}}^\infty \sigma_{m,\rm pi}(\nu)k_e \frac{F_\nu}{h\nu}e^{-\tau_{{\rm att},\nu}}{\rm d} \nu,
\end{equation}
where $\sigma_{m,\rm pi}(\nu)$ is the metal photoionization cross section.
When evaluating the excited state H abundance in Equation \ref{eq:Hp}, the approximation in Equation~\ref{eq:6} is applied.
The heating and cooling balance equation is
\begin{align}
\label{eq:heat}
\Big[ \big(13.6\, &\text{eV}C_{1s \to \infty}^{(e)}+10.2\, \text{eV}C_{1s \to 2}^{(e)}\big)n_{1s}\nonumber\\
&+3.4\, \text{eV}C_{2 \to \infty}^{(e)}n_{2}+\sum_m \Lambda_mn_m+\Lambda_{ff}n_p\nonumber\\
&+\langle E_{rr}\rangle\alpha_Bn_p + k_{\rm B}T\sum_m\alpha_mn_m^{\rm ion}\Big]n_e\\
=n_{1s}&Q_{1s}(N_{1s})+Q_{2p}n_{2p}+Q_{2s}n_{2s}\nonumber\\
&+10.2\text{ eV}~ n_e n_2 C_{2 \to 1}^{(e)}+\sum_mQ_mn_m\nonumber,
\end{align}
where $\Lambda$ stands for cooling function. \citet{AGN2} give the free free cooling rate
\begin{equation}
\Lambda_{ff}=1.85\times10^{-27} ~T^{1/2}(\rm ~erg~cm^3~s^{-1}),
\end{equation}
where $T$ is in units of Kelvin.
The mean kinetic energy of the recombining electrons is~\citep{Draine}
\begin{equation}
\langle E_{rr}\rangle=[0.684-0.0416\ln(T_4)]k_{\rm B}T,
\end{equation}
where $T_4=T/10^4\ \rm K$.
In Equation \ref{eq:heat}, the symbol $Q$ represents the photoelectric heating rate, per photoionization, corrected for the secondary ionization effect. \citet{Dalgarno} find that secondary electrons give rise to approximately the same number of ionizations as 1s$\rightarrow$2p excitations, so the heat deposited into the atmosphere by one photoelectron with energy $E$ is taken to be
\begin{equation}
\eta(E)=E-(13.6{\rm eV} + 10.2{\rm eV})k_e,
\end{equation}
where the second term represents the energy lost by the photoelectron to ionizations and Ly$\alpha$\ excitations.
Thus, the net photoelectric heating rate is
\begin{equation}
Q =\int_{\nu_{\rm th}}^\infty \eta\sigma_{pi}(\nu)\frac{F_\nu}{h\nu}e^{-\tau_{{\rm att},\nu}}{\rm d} \nu.
\label{eq:7}
\end{equation}
Given $P$ and the columns $N_i$, Equations \ref{eq:P}, \ref{eq:number}, \ref{eq:Hp}, and \ref{eq:heat} give four algebraic equations to solve for $T$, $n_e$, $n_p$, and $n_{1s}$ at this level in the atmosphere. A globally convergent Newton's method \citep{Recipes} is applied to solve the set of equations.
\subsection{Radiative Cooling Due to Metal Species}\label{metal}
Although H and He are by far the most abundant elements, their electron-impact line cooling rates are heavily suppressed at temperatures $T \la 10^4\ \rm K$ due to the high excitation energies. Metal line cooling due to electron impact followed by radiative de-excitation is an important coolant, especially near the base of the atmosphere at $T \la 8000\ \rm K$.
The ionization/recombination rate equilibrium equation is included to determine the relative abundance of each ionization state. Transitions yielding large cooling rates are chosen from abundant elements, and by striking a balance between low excitation energies, $\Delta E$, and large radiative decay rate $A_{ul}$. Solar abundance is assumed \citep{Asplund}. The elements considered are O, C, Mg, Si, S, Na, and K. Although Mg was not a priori expected to be abundant in the upper atmosphere due to condensation \citep{Visscher, KoskinenII}, Mg$_{\rm\,I}$ is in fact detected in HD 209458b \citep{Vidal-Madjar13} and marginally detected in HD~189733b\ \citep{Cauley2016}.
The abundance of each ionization state is set by solving for rate equilibrium between ionization and recombination. Only neutral, first, and second-ionized atoms are included.
As a special case, rather than photoionization, collisional, and radiative recombination, the ionization state of oxygen is determined by charge exchange with hydrogen. Considering that $n_{\rm H}\gtrsim 10^5~\rm cm^{-3}$ everywhere in the model, the charge exchange rates in the high-density limit in \citet{Draine} are applied. The energy differences between three fine-structure levels of neutral oxygen are ignored because they are much smaller than $k_{\rm B}T$.
The rate equilibrium equations are
\begin{align}
(\Gamma_{\rm M_{\,I}}+C_{\rm M_{\,I},\infty}^{(e)}n_e+k^{(\rm O)}_{\rm ion}n_p)n_{\rm M_{\,I}}&=(\alpha_{\rm M_{\,II}}n_e+k^{(\rm O)}_{\rm rec}n_{\rm 1s})n_{\rm M_{\,II}} \nonumber\\
\Gamma_{\rm M_{\,II}}n_{\rm M_{\,II}}&=\alpha_{\rm M_{\,III}}n_en_{\rm M_{\,III}} \\
n_{\rm M_{\,I}}+n_{\rm M_{\,II}}+n_{\rm M_{\,III}}&=(n_{\rm H}+n_p)f_m, \nonumber
\end{align}
where $C_{\rm M_{\,I},\infty}^{(e)}$ is the electron collisional ionization rate, which is only considered for Na and K atoms.
The collisional ionization of other metal species are ignored because of the much higher ionization potential.
The secondary ionization states of Na and K are ignored. The photoionization rates of all species from \citet{Verner95, Verner96ion}. The Na and K collisional ionization rates are given by \citet{Lennon}.
The rates of \citet{Pequignot1991} are used to describe the recombination of C and O, of \citet{Shull} for that of Mg, Si, and S, of \citet{Verner96recomb} and \citet{Landini} for that of Na and K respectively.
Because the ionization potentials of Mg$_{\rm ~I}$, Si$_{\rm ~I}$, Na$_{\rm ~I}$, and K$_{\rm ~I}$\ are smaller than the Ly$\alpha$\ energy, both continuum and Ly$\alpha$\ photons contribute to their photoionization and photoelectric heating rates. The metal species photoionization rate is
\begin{multline}
\Gamma_{m,\rm pi}=\int_{\nu_{\rm th}}^\infty \sigma_{m,\rm pi}(\nu)\frac{F_\nu}{h\nu}e^{-\tau_{{\rm att},\nu}}{\rm d} \nu \\
+ \frac{ 4\pi\sigma_{m,\rm pi}(\nu_{\rm Ly \alpha}) }{h\nu_{\rm Ly \alpha}}\int J_\nu{\rm d}\nu,
\end{multline}
where the first integral excludes the stellar flux contribution near the Ly$\alpha$\ line, and the metal species photoelectric heating rate
\begin{multline}
Q_{m,\rm pi}=\int_{\nu_{\rm th}}^\infty \eta\sigma_{m,\rm pi}(\nu)\frac{F_\nu}{h\nu}e^{-\tau_{{\rm att},\nu}}{\rm d} \nu \\
+ 4\pi \sigma_{m,\rm pi}(\nu_{\rm Ly \alpha})\frac{\nu_{\rm Ly \alpha}-\nu_{\rm th}} {\nu_{\rm Ly \alpha}}\int J_\nu{\rm d}\nu,
\label{eq:8}
\end{multline}
where $\sigma_{m,\rm pi}(\nu_{\rm Ly \alpha})$ is only nonzero for Mg$_{\rm ~I}$, Si$_{\rm ~I}$, Na$_{\rm ~I}$, and K$_{\rm ~I}$. The mean intensity $J_\nu$ in these formulas denotes the intensity in the vicinity of the Ly$\alpha$\ line, found as a result of the resonant scattering calculation in Section \ref{MC}.
The metal line cooling rates require a model for the excited state densities.
For a two-level system, rate equilibrium between upward and downward rates gives
\begin{equation}
n_l(n_eC_{lu}^{(e)}+B_{lu}\bar{J}_{lu})=n_u(A_{ul}+n_eC_{ul}^{(e)}).
\end{equation}
Stimulated emission is ignored due to dilution of the stellar flux.
Collisional excitation is a sink of thermal translation energy while collisional de-excitation is a source. Thus the cooling rate of this two levels system is
\begin{multline}
\Delta E\, n_e(C_{lu}^{(e)}n_l-C_{ul}^{(e)}n_u)\\
= n_e n_l \ \Delta E\ C_{lu}^{(e)}\left(\frac{A_{ul}-B_{lu}\bar{J}_{lu}(n_l/n_u)_{\rm eq}}{A_{ul}+n_eC_{ul}^{(e)}}\right)
\equiv \Lambda n_e n_l,
\label{eq:coolingfunc}
\end{multline}
where $(n_l/n_u)_{\rm eq}=g_l/g_u\exp(\Delta E/(k_{\rm B}T))$, and the last equality defines $\Lambda(T)$, the cooling function.
Permitted transitions in the optical and near UV bands are always associated with strong absorption features in the stellar spectrum, which lead to a very small radiative excitation rate $B_{lu}\bar{J}_{lu}(n_l/n_u)_{\rm eq}$ for the transitions used. In the case of forbidden transitions, to compensate for the small $A_{ul}$, only small $\Delta E$ transitions give rise to significant cooling. At the long wavelength end, the dilution of radiation flux due to the solid angle of the star overcomes the effect of higher brightness temperature of the star. As a result, radiative excitation is negligible in Equation \ref{eq:coolingfunc} for both permitted and forbidden transitions.
For forbidden transitions, the electron number density $n_e$ is much larger than the critical density $n_{\rm crit}$ above which collisional de-excitation dominates radiative de-excitation. In this limit, the level population is given by the Boltzmann distribution, and the cooling rate becomes
\begin{equation}
\label{eq:11}
\Lambda n_e n_l=\Delta En_lA_{ul}\left(\frac{n_u}{n_l} \right)_{\rm eq},
\end{equation}
which is independent of $n_e$ and collisional rates.
The emitted metal line photons are assumed to escape freely from the atmosphere. In reality, the atmosphere may be optically thick to permitted emissions near the base of the atomic layer.
The major cooling processes are listed in Table~\ref{cooling}, while Table~\ref{tab:cooling_minor} in the appendix contains addition transitions from O, C, S, and Si lines which are included in the model but only have a minor effect on the temperature. The lower state of some transitions may not be the ground state. In this case, the lower state is assumed to reach collisional equilibrium with ground state in the cooling rate calculation.
Mg$_{\rm ~I}$\ 5184~\AA\ is another line that may contribute to cooling. The lower state of this transition is not the ground state, and the upper state is associated with the ground state of the strong resonance line Mg$_{\rm ~I}$\ 2852~\AA.
A Mg level population calculation and Mg$_{\rm ~I}$\ 2852~\AA\ radiation transfer study are required to accurately model the cooling effect, which is beyond the scope of this work. Mg$_{\rm ~I}$\ 5184~\AA\ is not included in this work as a result.
\begin{table*}
\begin{center}
\caption{List of major metal cooling transitions}\label{cooling}
\begin{tabular}{cccccc}
\hline \hline
Transition & $\Delta E$ & $A_{ul}$\footnote{\citet{NIST}} & $n_{\rm crit}$ \footnote{$n_{\rm crit}=A_{ul}/C_{ul}^{(e)}(4000\rm~K)$} & $\Lambda$ & Source of \\
& (eV) & ($\rm s^{-1}$) & ($\rm cm^{-3}$) & ($\rm ~erg~cm^3~s^{-1}$) & collision rate \\
\hline
Mg$_{\rm ~I}$\ 2852 & 4.35 & $4.91\times 10^8$ & $6.7\times 10^{15}$ & $3.4\times 10^{-19}T^{0.18} e^{-5.04/T_4}\ $\footnote{$T_4=T/10^4{\rm~K}$} & Van Regemorter formula \footnote{\citet{vanRegemorter}}\\
Mg$_{\rm ~I}$\ 4571 & 2.712 & 254 & $8.5\times 10^9$ & $1.0\times 10^{-16} e^{-3.15/T_4}/(254+3.0\times 10^{-8}n_e)$ & \citet{Osorio}\\
Mg$_{\rm ~II}$\ 2803 & 4.422 & $2.57\times 10^8$ & $8.6\times 10^{14}$ & $7.1\times 10^{-12} C_{lu}^{(e)}$ & CHIANTI \footnote{~\citet{Chianti,Chianti8}}\\
Mg$_{\rm ~II}$\ 2796 & 4.434 & $2.60\times 10^8$ & $2.2\times 10^{14}$ & $7.1\times 10^{-12} C_{lu}^{(e)}$ & CHIANTI\\
Na$_{\rm ~I}$\ 5890+5896 & 2.104 & $6.16\times 10^7$ & $4.4\times 10^{14}$ & $3.4\times 10^{-12} C_{lu}^{(e)}$ & \citet{Igenbergs} \\
K$_{\rm ~I}$\ 7665+7699 & 1.615 & $3.78\times 10^7$ & $1.8\times 10^{14}$ & $3.7\times 10^{-19}T^{0.18} e^{-1.87/T_4}$ & Van Regemorter formula \\
\hline
\end{tabular}
\end{center}
\end{table*}
\subsection{Molecular Hydrogen}\label{sec:H2}
Near the base of the atomic layer, where the temperature drops below $T \sim 2000-3000\ \rm K$, it is expected that the density of molecules will increase rapidly and come to dominate over the atomic species. This is the base of the atomic layer and the top of the molecular layer. The atomic-to-molecular transition is not self-consistently modeled in this work, as the rate equations to determine molecular densities (e.g. \citealt{Yelle,Garcia}), and the strong effect of molecular coolants from e.g. H$_2$O rotation-vibration bands, are not taken into account.
Although the details of molecule formation are beyond the scope of this paper, a rough estimate of the H$_2$ number density is made to verify that the temperature does indeed become low enough to form molecules as the base is approached. \citet{Lenzuni} noted that for a wide range of radiation intensity, that dissociation of H$_2$ is due to collisional processes, rather than photo-dissociation. \citet{Yelle} found the same result for a model for the thermosphere of HD 209458b. In this limit, an estimate of the H$_2$ density can be found using the Saha equation. Applying the H$_2$ partition function from \citet{Borysow}, the H$_2$ number density, $n_{\rm H_2}$ can be computed from the atomic hydrogen density, $n_{\rm H}$, and the temperature $T$.
The buildup of a significant column of H$_2$ will shield the lower atmosphere from stellar UV, and allow the formation of other molecules, e.g. CO and H$_2$O which may be important coolants. Another effect more relevant to this work is that H$_2$ may act as a strong absorber of Ly$\alpha$\ photons, effectively setting a lower boundary to the region of the atmosphere that may have a large Ly$\alpha$\ intensity. \citet{Black1987} discussed numerous ``accidental resonances" between Ly$\alpha$\ and electronic transitions in H$_2$. The strongest of these can have oscillator strength $f \sim 10^{-2}$, implying that a column $N_{\rm H_2} \simeq 10^{14}\ \rm cm^{-2}$ is required to give unit optical depth for these transitions. For a scale height $H \simeq 10^8\ \rm cm$, this gives a critical number density $n_{\rm H_2} \simeq 10^6\ \rm cm^{-3}$ for true absorption optical depth unity over a scale height. In practice, Ly$\alpha$\ photons near the optically-thick base of the atomic layer would require a large number of scatterings to escape the atmosphere, implying a total distance traversed even larger than a scale height. This will effectively set an absorbing lower boundary for the atomic layer in the radiation transfer described in Section~\ref{MC}.
\section{Ly$\alpha$\ radiation transfer}\label{MC}
Ly$\alpha$\ photons can excite hydrogen from the 1s to the 2p state, providing a population of absorbers that may be detected in Balmer line transmission spectra. Ly$\alpha$\ may also play a role in the heating/cooling and ionization/recombination balance, so a detailed Ly$\alpha$\ radiation transfer calculation is crucial.
Two sources of Ly$\alpha$\ are included in the model, the stellar Ly$\alpha$\ incident through the top of the planet's atmosphere, and also Ly$\alpha$\ generated within the planet's atmosphere by electron impact excitation or a recombination cascade. The results of particle densities and temperature versus radius from the hydrostatic model in Section \ref{hydro} are used to specify the Ly$\alpha$\ source function, as well as the mean free paths to scattering and true absorption.
In the transfer calculation it is convenient to use Ly$\alpha$\ line center optical depth, $\tau$, as the vertical coordinate.
A plot of pressure P and radius r versus $\tau$ will be shown in Figure~\ref{fig:T}.
A major simplifying assumption is to use plane-parallel geometry, so that mean intensity $J_\nu(r)$ is tabulated as a function of altitude. The radius in the hydrostatic model varies by a factor of 2 from base to top, and by a factor of $\simeq20$\% near the base of the layer where the H$\alpha$\ line is formed. The plane-parallel assumption simplifies the calculation, and is consistent with uniform irradiation assumed in the hydrostatic model.
At the outer boundary ($\tau=0$), the unpolarized stellar Ly$\alpha$\ intensity enters the slab vertically. The line is parameterized by a double Gaussian line profile with width (in velocity units) $\sigma = 49\ {\rm km\ s^{-1}}$ and centers at $\mu = \pm 74\ {\rm km\ s^{-1}}$ \citep{Gladstone, Curdt, Tian}. Instead of using the value of $\epsilon$ Eri from MUSCLES, the integrated line flux at the top of the HD~189733b's atmosphere given by \citet{Linsky}, $F_0 = 2.0 \times 10^4\rm ~erg~cm^{-2}~s^{-1}$, is applied. Outgoing photons can escape from the top boundary freely.
An absorption bottom boundary is applied at the base of the slab, which represents the base of the atomic layer.
Physically, this boundary condition is imposed to represent the short mean free path to true absorption of Ly$\alpha$\ on H$_2$ \citep{Shull1978,Black1987} and H$_2$O \citep{Miguel}. Since $n_{\rm H_2}$ increases inward much faster than $n_{\rm H}$, the mean free path to resonant scattering will become longer than that to true absorption in the molecular layer, greatly decreasing the Ly$\alpha$\ intensity compared to the atomic layer. As will be shown, even in the atomic layer, the intensity falls rapidly toward the base.
Ly$\alpha$\ generated inside the atmosphere by collisional excitation or a recombination cascade is assumed to be unpolarized and have an initial frequency distribution given by a Gaussian distribution with the Doppler width set by the local temperature. In practice, this initial distribution is much narrower than the resultant mean intensity, so it is the same effect as initializing photons at line center.
The source function inside the atmosphere is
\begin{multline}
S_\nu=\frac{10.2{\rm~eV}}{4\pi}\Big(\alpha_Bn_pn_e + C_{1s\to 2}^{(e)}n_{1s}n_e\\
+\Gamma_{1s}^{\rm 2nd}n_{1s}+\sum_m \Gamma_{m}^{\rm 2nd}n_m\Big)\phi_\nu,
\label{eq:sourcefunc}
\end{multline}
where $\phi_\nu$ is the Doppler profile evaluated at the local temperature. The first term in Equation \ref{eq:sourcefunc} represents recombinations, each of which is assumed to produce one Ly$\alpha$\ photon. The following three terms represent collisional excitation by thermal electrons, photoelectrons from ionizing H(1s), and photoelectrons generated from ionizing metals. Recombination and collisional excitation to H(2s) are also included because H(2s) and H(2p) are well coupled by the $\ell$-mixing.
The line center optical depth to scattering reaches values as large as $\tau \simeq 10^8$ near the base of the model, and photons will scatter $\sim \tau$ times before exiting the atmosphere \citep{Harrington} if no other process intervenes. Ly$\alpha$\ photons can leave this scattering cycle by two categories of processes. First, the radiative excitation may not be followed by radiative de-excitation of a Ly$\alpha$\ photon some fraction $\epsilon$ of the time.
The dominant processes are: photoionization from the n=2 state by stellar Balmer continuum emission; collisional de-excitation; and two photon decay from 2s$\rightarrow$1s. The former two processes also contribute to ionizing and heating rates. The second kind of process is ``true absorption", in which a Ly$\alpha$\ photon is absorbed by some other species besides H(1s), for example by photoionizing an atom with low ionization potential less than 10.2eV.
Ly$\alpha$\ photons can also leave this scattering cycle by the $\ell$-mixing or radiative excitation processes from the 2p state. Because it will be followed by the reverse process immediately, these processes are equivalent to Ly$\alpha$\ photon redistribution that put the line wing photons frequently back to the line center and stop the photons from escaping.
These processes are not included in this model because a careful consideration required the H$\alpha$\ mean intensity in the atmosphere, which is not available right now.
The plane-parallel transfer equation including resonant scattering, true absorption, the source function for photon creation, and excitation followed by de-excitation a fraction $1-\epsilon$ of the time is
\begin{multline}
\mu\frac{{\rm d} I_\nu(z,{\bm n})}{{\rm d} z}=-(\alpha_{\rm sc}+\alpha_{\rm abs})I_\nu(z,{\bm n})+ S_\nu(z) \\
+(1-\epsilon)4\pi \frac{\alpha_{\rm sc}}{\phi_\nu}\int R(\nu,{\bm n};\nu',{\bm n'}) I_{\nu'}(z,{\bm n'}) {\rm d} \Omega' {\rm d} \nu',
\end{multline}
where $\mu=\cos\theta$, $\phi_\nu$ is the Voigt line profile, $\alpha_{\rm sc}$ is resonant scattering coefficient, $\alpha_{\rm abs}$ is true absorption coefficient, and $R$ is the \citet{Hummer} case II-B redistribution function, with dipole angular dependence.
The redistribution function $R$ gives the probability that the photon is scattered from incident frequency $\nu'$ and direction ${\bm n'}$ to frequency $\nu$ and direction ${\bm n}$. Case II-B redistribution assumes that, in the rest frame of the atom, the line profile for absorption of the photon (excitation) is a Lorentzian profile, and that in the rest frame the outgoing photon has the same energy as the ingoing photon. \citet{Hummer} presents formulae for the resulting redistribution function thermally averaged over a Boltzmann distribution of atom velocities. Case II-B with dipole angular dependence results for resonant scattering when the initial and final states are the H(1s) state, and the finite lifetime of the intermediate H(2p) state is included. Fine structure splitting of the excited state is ignored. This is a good approximation in the present application where the mean intensity is much broader than the fine structure separation of the $J=1/2$ and $3/2$ states.
The transfer equation is solved numerically with the Monte Carlo method (e.g. \citealt{2011BASI...39..101W}).
First, unpolarized photon packets are initialized at a point randomly generated from the source function (see Equation~\ref{eq:sourcefunc}) and with a randomly chosen direction.
Second, the optical depth $\tau$ that the photon will travel through before it is scattered or absorbed is randomly generated with a probability density $e^{-\tau}$. The spatial location of the scattering or ``true absorption'' at optical depth $\tau$ from the point of emission is then determined with the knowledge of the densities and temperature, and cross sections of $n_{\rm H}$, $n_{\rm Mg I}$, $n_{\rm Si I}$, $n_{\rm Na I}$, $n_{\rm KI}$.
The Lucy method~\citep{Lucy} is used to tabulate intensity and flux from the motion of the photon packets. This was crucial in optically thick regions, and worked much better than accumulating photon statistics only when they pass through the face of a cell.
Based on the radiative excitation and absorption optical depth, the rejection method is used to determine whether the photon is absorbed. Whether the H(2p) emits another Ly$\alpha$\ photon is determined by comparing a random number with $1-\epsilon$.
Third, at each scattering, the outgoing photon direction is chosen including polarization accumulated during prior scatterings. The Stokes matrix for Rayleigh scattering is used. However, rather than using the Stokes matrix in scattering-plane coordinates, as discussed in ~\citet{Chandra}, a scattering matrix was derived in terms of the incoming and outgoing photon direction without reference to the scattering plane, which was found to be more convenient for numerical calculations.
Then, the velocity of scatterers along the direction of the incident photon is randomly generated by the method described in \citet{Zheng}, with small modifications to improve the efficiency. Recoil is included in computing the new frequency of the photon after scattering. The process of propagation and scattering is repeated until the photon escapes the modeled system or leaves the scattering cycle.
By knowing the $n_{1s}$ from the hydrostatic atmosphere model and $\bar{J}_{Ly\alpha}$ from the Ly$\alpha$\ radiation transfer calculation, the $n_{2\ell}$ population is given by Equation~\ref{eq:6}.
Note that the ionization, heating, and cooling rates in the atmosphere depend on the $n_{2\ell}$ and Ly$\alpha$\ mean intensity.
Therefore, the hydrostatic model and radiation transfer calculation are performed iteratively, until the $n_{2\ell}$ converged, which takes typically $\sim 8$ iterations.
\section{the fiducial atmosphere model}
\label{sec:fiducial}
\begin{figure}
\centering
\includegraphics[width=0.5\textwidth]{spectrum.pdf}
\caption[mean intensity]{Ly$\alpha$\ mean intensity spectrum $(J_{\nu})$ at six different depths in the atmosphere. At line center the spectrum is flat, much wider than the thermal line width, and becomes broader with depth. The intensity decreases rapidly on the line wing. The fluctuations in the spectra are due to the statistical noise in the Monte Carlo simulation.}
\label{fig:Jnu}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=0.5\textwidth]{T_P.pdf}
\caption[Temperature]{Temperature ($T$) and Ly$\alpha$\ line center optical depth ($\tau$) versus pressure ($P$, bottom axis) and radius ($r$, top axis).}
\label{fig:T}
\end{figure}
\begin{figure*}
\centering
\includegraphics[width=\textwidth]{H_C.pdf}
\caption[Cooling rate]{Major heating ($Qn$, solid lines) and cooling ($\Lambda n_e n$) rates versus pressure ($P$). The line cooling profiles (dashed lines) present the radiative cooling of Ly$\alpha$\ and the metal lines listed in Table~\ref{cooling}.}
\label{fig:cooling}
\end{figure*}
\begin{figure*}
\centering
\includegraphics[width=\textwidth]{n_P.pdf}
\caption[number density]{Number density ($n$) of main species against the pressure ($P$). The solid lines present the profiles for neutral atoms and the dashed lines for first ionized ions. The combination of large Ly$\alpha$\ intensity $\bar{J}_{Ly\alpha} \propto P^{-1}$ and increasing H(1s) density with depth give rise to an approximately flat H(2$\ell$) density around $10^4~\rm cm^{-3}$ over two decades in pressure near the base of thermosphere. The number densities of Na$_{\rm ~I}$\ and H(2$\ell$) are comparable in the pressure region between $10^{-2} \mu$bar and $10^{-1} \mu$bar, where the line center optical depths of H$\alpha$\ and Na D are near unity (see Figure~\ref{tau_b}). }
\label{fig:n_P}
\end{figure*}
In this section, results are presented for the fiducial model with solar abundance for all species and extreme ultraviolet (EUV) and X-ray flux set by the day-side value. The Ly$\alpha$\ mean intensity spectrum in the atmosphere is shown in Figure~\ref{fig:Jnu}. Temperature versus height for the fiducial model is shown in Figure~\ref{fig:T}. The heating and cooling rates per unit volume are given in Figure~\ref{fig:cooling}, and the number densities of each species are given in Figure~\ref{fig:n_P}. Figure~\ref{fig:source} shows the Ly$\alpha$\ photon sources, sinks, and H ionization rates per unit volume. Line profile weighted Ly$\alpha$\ mean intensity $\bar{J}_{Ly\alpha}$ of the fiducial model are given in Figure~\ref{fig:Jbar}.
Figure~\ref{fig:Jnu} shows the Ly$\alpha$\ mean intensity at six different depths in the atmosphere. The line center of the resonant scattering spectrum has a flat part with width $\sim (a\tau)^{1/3}\nu_D$~\citep{Harrington}. The dip at line center near the surface arises because the photons have to diffuse away from line center in order to escape from the slab, due to the extremely short mean free path at line center. The mean intensity near line center has a peak around $\tau\sim 10^4$, where the H($1s$) photoionization, as well as the subsequent recombination, which is the major Ly$\alpha$\ photon source, is the strongest. The spectrum decreases rapidly on the line wing. The fluctuations in the spectra are due to the statistical noise in the Monte Carlo simulation. Since the number densities of H(2$\ell$) are proportional to the $\bar{J}_{Ly\alpha}$, this fluctuation also appears in the H(2$\ell$) number densities curve, and other curves such as heating rates.
At the top of the model, for pressures $P<3\times 10^{-3}\, \mu$bar, the gas is fully ionized and the contribution to the number density of electrons by metal species is negligible. The gas is optically thin to LyC photons, thus the ionization rate and heating rate per particle are nearly constant. In this region $n_{1s}\approx n_e^2\alpha_B/\Gamma_{1s}\propto P^2$. The gas temperature is set by the balance of H($1s$) photoelectric heating and line cooling by \ion{Mg}{2} for solar Mg abundance or Ly$\alpha$\ for low Mg abundance. The cooling rate $n_{\rm Mg II}n_e\Lambda_{\rm Mg}\approx n_{1s}Q_{1s}\propto P^2$. Because the $n_{\rm Mg II}$ increases faster than $P$ (see Figure~\ref{fig:n_P}), the gas temperature is regulated to $T\propto 1/\log P$ near temperatures $T=9000 \-- 13,000$ K, shown in Figure~\ref{fig:T}.
Note that the ionized region of the hydrostatic model at $P\lesssim 3\times 10^{-4}\, \mu$bar may have an unphysically high temperature, as the inclusion of a hydrodynamic outflow and adiabatic cooling may be important in this region, as in the well-studied case of HD 209458b (e.g. \citealt{Yelle}). However, inspection of Figure \ref{fig:n_P} shows that the H(2$\ell$) and Na$_{\rm ~I}$\ densities are negligible in this region, and hence errors in the temperature profile there will not affect the H$\alpha$\ and Na transit depth.
H(1s) is the main absorber of the stellar LyC flux over the majority of the energy range. Besides H(1s), the 2s-shell of O$_{\rm ~I}$\ absorbs most photons with energy above 538 eV, and C and Si are the main absorbers of the photons below 13.6 eV in the atomic layer.
The atmosphere becomes optically thick to 400\rm~\AA\ photons at the pressure of $\sim 5 \times 10^{-3}~\rm \mu bar$.
The strong stellar flux between 100 and 400\rm~\AA\ causes the local maximum in the $T-P$ profile.
Photoelectric heating from ionization of H(1s) contributes the large peak in Figure \ref{fig:cooling} over the pressure range $P=10^{-3}-10^{-1}\, \mu$bar. Below that, it continues to be an important source of heating, with absorption of successively higher energy photons with depth, and ionization by secondary electrons becoming important. There is a narrow region near $P\sim 1\, \mu$bar where heating due to electron impact de-excitation of H(2$\ell$) dominates. Ultimately the heating in this region is due to the Ly$\alpha$\ radiation, which excites the atoms to the n=2 state. Near the base, at $P=1-10\, \mu$bar, metal photoelectric heating from ionization of Si, O, and C dominates the heating.
Na line cooling is the dominant coolant below $P=0.5\, \mu$bar. Above that, assuming solar Mg abundance, Mg line cooling dominates, among which \ion{Mg}{1} 4571 contributes most at $P>0.4~\rm \mu bar $ while \ion{Mg}{2} contributes most above. Ly$\alpha$\ line would be the major coolant instead if the Mg abundance is low.
Hence near the base of the model, both heating and cooling are controlled by metal species, and the temperature is not sensitive to an overall shift in metallicity. Above $P=1\, \mu$bar, the temperature is sensitive to metallicity, and eliminating a single important coolant could make a difference, with Mg and Na-poor atmospheres expected to be hotter and more extended. Since this region is important for the H$\alpha$\, and Na transmission spectrum, the temperature, with it's dependence on the metallicity, may be an important parameter in understanding the transmission spectrum.
Ly$\alpha$\ line center optical depth versus height for the fiducial model is also shown in Figure~\ref{fig:T}. Near the base of the atomic layer, $\tau \propto P \propto n(H(1s))$, since ground state hydrogen is the dominant species. However, above $P=2\times 10^{-3}\, \mu$bar, hydrogen is predominantly ionized, and the optical depth decreases outward approximately as $\tau \propto n(H(1s)) \propto n_p^2 \propto P^2$ in ionization equilibrium. At the outer boundary of the model, $\tau$ drops abruptly to zero due to the $\tau=0$ boundary condition there.
The most abundant species in Figure \ref{fig:n_P} are electrons and protons above $P=5\times 10^{-3}\, \mu$bar, and H(1s) below. Recall that ionization of He is ignored in this paper, and that He is assumed to be neutral and have solar abundance.
The electron number density stays nearly constant in the deeper part of the atomic layer because both the ionization and the recombination rates are insensitive to altitude and temperature. The ionization is dominated by the photoionization from H(2$\ell$) in this region and a flat H(2$\ell$) number densities lead to a flat ionization rate (see Figure~\ref{fig:source}).
From the near equality $n_e \simeq n_p$, ionization of hydrogen supplies most of the electrons down to $1\, \mu$bar, and first ionized Mg and Si are important below. The ionization state of O closely follows that of H because of the very large O and H charge exchange rate.
The atmosphere becomes opaque to the stellar flux above 10.4 eV due to the absorption by S$_{\rm ~I}$\ and C$_{\rm ~I}$. The atmosphere is transparent to stellar flux below the S$_{\rm ~I}$\ ionization threshold throughout the model.
The ionization of Na$_{\rm ~I}$\ and K$_{\rm ~I}$\ is dominated by collisional ionization at the level above $0.1 \rm~\mu bar$.
Near the base of the model, the density of H$_2$ rises rapidly, and is only slightly less abundant than H(1s). In a more complete model it is expected that the inclusion of strong molecular cooling due to e.g. H$_3^+$ and H$_2$O would cause the temperature near the base to be even lower and $n_{\rm H_2}$ to be even larger.
The combination of large Ly$\alpha$\ intensity $\bar{J}_{Ly\alpha} \propto P^{-1}$ (see Figure~\ref{fig:Jbar}) and increasing H(1s) density with depth gives rise to an approximately flat H(2$\ell$) densities around $10^4~\rm cm^{-3}$ over two decades in pressure near the base of atomic layer.
The number densities of Na$_{\rm ~I}$\ and H(2$\ell$) are similar in the pressure region between $10^{-2} \mu$bar and $10^{-1} \mu$bar. In Section \ref{sec:transit}, it will be shown that $\tau \sim 1$ for Na D and H$\alpha$\ in this pressure region. This leads to similar transit depths for the H$\alpha$\ and Na D transmission lines, in agreement with the observations of \citet{Cauley2016} and \citet{Wyttenbach}.
Shown in Figure~\ref{fig:source}, the photoionization rate from H($1s$) dominates the H ionization rate in the top layer of the atmosphere, and becomes constant after the atmosphere becomes optically thick to the LyC photons. The photoionization from H(2$\ell$) takes over for the region $P\gtrsim10^{-1}~\rm \mu bar$. The rate of charge exchange between O and H can be very high, but they almost cancel each other and leave a small net effect. The collisional ionization by secondary $e$ generated by the photoionization of metals ($\sum_m \Gamma_{m}^{\rm 2nd}n_m$) becomes large at $P>1~\rm \mu bar$.
The H radiative recombination cascade process dominates the Ly$\alpha$\ photon production throughout the simulation domain. The radiative decay after a thermal $e$ collisional excitation from $1s$ state has a narrow peak in creating Ly$\alpha$\ photon near $10^{-2}~\rm \mu bar$. The collisional excitation by $e$ generated by the photoionization of H($1s$) ($\Gamma_{1s}^{\rm 2nd}n_{1s}$) and metals ($\sum_m \Gamma_{m}^{\rm 2nd}n_m$) becomes important in creating Ly$\alpha$\ photons near the top and base of the atomic layer respectively.
The stellar Ly$\alpha$\ photons incident through the surface and the photons generated above $10^{-2}~\rm \mu bar$ can mostly escape through the top boundary. In contrast, the photons emitted below $0.1~\rm \mu bar$ are mostly absorbed during the resonant scattering processes due to the high optical depth. The Ly$\alpha$\ flux at the bottom boundary is about $40\rm ~erg~cm^{-2}~s^{-1}$.
The total LyC flux absorbed inside the simulation domain, is $F_{\rm LyC}=2.6 \times 10^4 \rm ~erg~cm^{-2}~s^{-1}$. Besides the $2.0 \times 10^4 \rm ~erg~cm^{-2}~s^{-1}$ stellar Ly$\alpha$\ flux that mostly reflects back out, a net $9.6\times 10^3 \rm ~erg~cm^{-2}~s^{-1}$ flux leaving the atmosphere originated from the Ly$\alpha$\ emission inside the atmosphere. In comparison, integrating the source function in Equation~\ref{eq:sourcefunc} over height, solid angle and frequency, the total column Ly$\alpha$\ internal emission is $1.6 \times 10^4 \rm ~erg~cm^{-2}~s^{-1}$. And the flux of Ly$\alpha$\ that hits the bottom boundary is $44 \rm ~erg~cm^{-2}~s^{-1}$.
Because the photoionization of an H(2$\ell$) is followed by a radiative recombination cascade, emitting another Ly$\alpha$\ photon, these two processes taken together can be thought of not as sources or sinks, but as a redistribution in photon energy. The absorption of a photon on the wing, and its subsequent re-emission at line center make it harder for the photon to escape the atmosphere. The most important remaining ``real'' photon sources are excitation by secondary $e$, and radiative recombination cascade of a $p$ which was collisionally ionized by high energy photoelectron. The ``real'' photon sinks are collisional de-excitation, photoionization of metals by Ly$\alpha$, and 2 photon decay.
A breakdown of line profile weighted mean intensity, $\bar{J}_{Ly\alpha}$, in terms of the different sources is given in Figure~\ref{fig:Jbar}. The external Ly$\alpha$\ directly from star stays nearly constant above $0.05~\rm \mu bar$. Because the incident stellar Ly$\alpha$\ is peaked at the frequency that is more than 5 Doppler widths away from the line center, the cross section to these photons in the Lorentzian wing is about $10^5$ smaller than the cross section in the line center. Most stellar Ly$\alpha$\ photons can directly penetrate to the $P\sim 10^{-2}\mu$bar level, which leads to a nearly constant intensity above this layer.
Radiative recombination cascades are important at $10^{-3} \-- 10^{-2}~\rm \mu bar$ and below 0.1 $\mu$bar, with secondary $e$ excitation becoming the second largest source deeper than $1~\rm \mu bar$.
The Ly$\alpha$\ mean intensity near the base can be estimated by assuming a local balance of frequency-integrated sources and sinks, giving $J \simeq S L$. Here $J$ is the frequency integrated mean intensity, $S$ is the frequency integrated source function, and $L$ is the total path length traversed by the photon before it is destroyed. The photon source is insensitive to altitude as shown in Figure~\ref{fig:source}.
For a sink given by true absorption due to photoionization of metals, the mean intensity is
\begin{equation}
\label{eq:2}
J \simeq S L = \frac{S} {n_m \sigma_{m,\rm pi}(\nu_{Ly\alpha})}.
\end{equation}
The photoionization cross section of metals by Ly$\alpha$\ photons, $\sigma_{m,\rm pi}(\nu_{Ly\alpha})$, is independent of altitude and frequency. The number densities of Mg$_{\rm ~I}$, Si$_{\rm ~I}$, Na$_{\rm ~I}$, and K$_{\rm ~I}$\ scale proportional or slightly steeper than $P$. As a result, the $J \propto P^{-1}$.
Next consider collisional de-excitation and 2 photon decay, for which
\begin{align}
\label{eq:3}
J &\simeq S \epsilon^{-1} l_{\rm mfp} \nonumber \\
&= S \left(\frac{3 A_{2p\to 1s}}{4 n_eC_{2\to 1s}(T)+A_{2s\to 1s}}\right)\left(\frac{1}{n_{1s}\sigma_{1s}(\nu_0)}\right),
\end{align}
where $\epsilon$ is the probability of excitation not followed by de-excitation, and $l_{\rm mfp}$ is the line center mean free path. Because $n_e$, $C_{2\to 1s}(T)$ are insensitive to altitude, $J \propto P^{-1}$ in this case also.
To show the reliability of the approximations given in Equation~\ref{eq:6}, which are used in the hydrostatic model, the results for the H($1s$) number density and temperature were plugged back to the full hydrogen level population code described in Section~\ref{sec:level}. Figure~\ref{fig:pop} compares the approximate result and the full calculation for the $n_e$, $n_{2s}$, and $n_{2p}$. The approximation holds for the whole simulation region. The $n_{2s}$ and $n_{2p}$ obtained from both methods are almost identical except the approximate method slightly underestimates the $n_{2s}$ at the very top of the atmosphere, due to the fact that the contribution from recombination and collisional excitation is not completely negligible there. The $n_e$ obtained from the hydrogen level population calculation is slightly larger in the majority of the regions except the part that is close to the inner boundary. It is because that, in the hydrogen level population calculation, the secondary ionization due to metal species (see Equation~\ref{eq:2nd}) is not included, and the recombinations are only included up to $n=6$, while the case B recombination rate used in the hydrostatic model sums over all levels.
The number density of H($n=3$) obtained from the level population is also shown in the Figure~\ref{fig:pop}. Because an optically thin stellar H$\alpha$\ intensity is applied and Ly$\beta$ radiation transfer is not carefully considered, the number density of H($n=3$) shown here is only a rough estimate. Nevertheless, the low number density indicates that the Paschen series absorption features are unlikely to be observed.
\begin{figure*}
\centering
\includegraphics[width=\textwidth]{Source_Sink.pdf}
\caption[Source&Sink]{Ly$\alpha$\ photon sources, sinks, and H ionization rates per unit volume as a function of pressure ($P$). Each Ly$\alpha$\ photon source in Equation~\ref{eq:sourcefunc} is plotted with a solid line. The secondary $e$ excitation stands for the collisional excitation by $e$ generated by the photoionization of H($1s$) ($\Gamma_{1s}^{\rm 2nd}n_{1s}$) and metals ($\sum_m \Gamma_{m}^{\rm 2nd}n_m$). The sink rates are the output from the Ly$\alpha$\ Monte Carlo simulation. The process that a Ly$\alpha$\ photon photoionizes a low ionization potential metal atom is referred as the photoionization of metals under the Ly$\alpha$\ photon sinks section. A breakdown of the H radiative recombination cascade rate into individual H ionization processes based on Equation~\ref{eq:Hp} is also plotted. The output rate of photoionization of H(2$\ell$) in the Ly$\alpha$\ Monte Carlo simulation as a photon sink recovers the rate of the same process as a H ionization given by the ionization equation. O charge exchange stands for the difference between recombination of an O$_{\rm ~II}$\ and ionization an O$_{\rm ~I}$\ by charge exchange with H ($k^{(\rm O)}_{\rm rec}n_{\rm O\,II}n_{1s}-k^{(\rm O)}_{\rm ion}n_{\rm O\,I}n_p$). The photoionization of metals listed here stands for the H collisional ionization by $e$ generated by the photoionization of metals ($\sum_m \Gamma_{m}^{\rm 2nd}n_m$). }
\label{fig:source}
\end{figure*}
\begin{figure}
\centering
\includegraphics[width=0.5\textwidth]{Jbar.pdf}
\caption[weighted mean intensity]{Line profile weighted mean intensity $\bar{J}_{Ly\alpha}$ from different initial Ly$\alpha$\ photon generation mechanisms against the pressure ($P$). The large $\bar{J}_{Ly\alpha}$ stays nearly constant deep into the atmosphere and $\bar{J}_{Ly\alpha} \propto P^{-1}$ near the base of the atomic layer. Both Ly$\alpha$\ photons created inside the atmosphere and incident from the star are important in the H$\alpha$\ line formation region. }
\label{fig:Jbar}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=0.5\textwidth]{n_P_pop.pdf}
\caption{Comparison of the hydrogen sub-states and electron number densities ($n$) obtained from the full hydrogen level population code (solid line) and the approximation in Equation~\ref{eq:6} (dashed line), which mostly overlaps with the solid lines. A rough estimate of the H($n=3$) number density is also shown in green.}
\label{fig:pop}
\end{figure}
\section{TRANSMISSION SPECTRUM}
\label{sec:transit}
For a planet at distance $d$ from the observer, with uniform intensity $I_\nu$ over the stellar disk, the measured flux is
\begin{equation}
F_\nu = \frac{2\pi I_\nu}{d^2} \int_0^{R_\star} e^{-\tau_\nu(b)} b {\rm d} b ,
\end{equation}
where $\tau_\nu(b)$ is the optical depth along a trajectory associated with the impact parameter $b$. The optical depth can be divided into a continuum part, $\tau_c(b)$, which is independent of frequency over the line, and the line opacity part due to absorption by H(2$\ell$),
\begin{equation}
\tau_{l,\nu}(b)=2\int_0^{\sqrt{R_{\rm top}^2-b^2}}(n_{\rm 2s}\sigma_{\rm 2s}+n_{\rm 2p}\sigma_{\rm 2p}){\rm d} s,
\end{equation}
where $s$ is the line of sight distance.
The continuum absorption is then approximated as complete for $b<R_p$ and zero for $b>R_p$. The continuum integral then becomes as
\begin{align}
F^{(c)}_{\nu} &\equiv F_\nu-F_\nu^{(c)} \nonumber \\
&= \frac{2\pi I_\nu}{d^2} \int_0^{R_\star} e^{-\tau_c} b {\rm d} b = I_{\nu} \frac{\pi (R_\star^2-R_p^2)}{d^2},
\end{align}
where $R_p$ is the radius of the planet due to the continuum opacity. The difference in flux due to total opacity and continuum opacity is then
\begin{equation}
\Delta F_\nu = \frac{2\pi I_\nu}{d^2} \int_0^{R_\star} \left( e^{-\tau_c(b)-\tau_{l,\nu}(b)} - e^{-\tau_c(b)} \right) b {\rm d} b.
\end{equation}
The contribution from both terms is zero for $b<R_p$ due to the continuum opacity, and there is no continuum absorption outside that range, and so this expression can be rewritten
\begin{equation}
\label{eq:10}
\Delta F_\nu = \frac{2\pi I_\nu}{d^2} \int_{R_p}^{R_\star} \left( e^{-\tau_{l,\nu}(b)} - 1 \right) b {\rm d} b.
\end{equation}
Equivalent to the transmission spectrum defined in the observations (e.g. \citet{Cauley2015}), the fractional change in flux, relative to the continuum integral at the same frequency, is then
\begin{align}
\frac{\Delta F}{F}(\nu) &\equiv \frac{\Delta F_\nu}{F^{(c)}_{\nu}} \nonumber \\
&= \frac{2}{R_\star^2-R_p^2} \int_{R_p}^{R_\star} \left(e^{-\tau_{l,\nu}(b)} - 1 \right) b {\rm d} b.
\end{align}
The ratio $\Delta F/F$ will be referred to as the model transmission spectrum.
\subsection{{\rm H$\alpha$} and {\rm H$\beta$} Transmission Spectrum}
\label{sec:ha}
\begin{figure}
\begin{center}
\includegraphics[width=0.5\textwidth]{Halpha.pdf}
\caption{H$\alpha$\ transmission spectrum. The black solid line shows the transmission spectrum of the fiducial model. The blue solid line shows the model with atomic layer base pressure $P_b=1~\mu$bar. Black and red dashed lines show the model with stellar LyC multiplier factor $\xi=1/4$ and $\xi=4$ respectively. The red solid line shows the model without Mg. Circles in the plot are observational data from \citet{Cauley2015, Cauley2016}.}\label{Halpha}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[width=0.5\textwidth]{Hbeta.pdf}
\caption{Comparison of the H$\beta$\ transmission spectrum observed by \citet{Cauley2015} and \citet{Cauley2016}, to the calculated transmission spectrum of the fiducial model, as well as models with different LyC boost factor $\xi$ and Mg abundance.}\label{Hbeta}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[width=0.5\textwidth]{tau_b.pdf}
\caption{H$\alpha$, H$\beta$, Na D doublet, and \ion{Mg}{2} 2795 line center optical depth ($\tau_0$) versus impact parameter ($b$). The vertical solid lines show the location of pressure levels $10~\mu$bar, $1~\mu$bar, $0.1~\mu$bar, $0.01~\mu$bar, and $0.001~\mu$bar from left to right.}\label{tau_b}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[width=0.5\textwidth]{dWdb.pdf}
\caption{H$\alpha$\ and Na D transmission spectrum equivalent width per unit impact parameter (${\rm d} W_\lambda/{\rm d} b$) (defined in Equation~\ref{eq:4}) versus b.
The contribution to $W_\lambda$ by Na D doublet are summed together.
The vertical solid lines show the location of $10~\mu$bar, $1~\mu$bar, $0.1~\mu$bar, $0.01~\mu$bar, and $0.001~\mu$bar from left to right.}\label{dWdb}
\end{center}
\end{figure}
From the discussion in Section~\ref{MC}, the Ly$\alpha$\ intensity is small in the molecular layer at $r<R_b$. As a result, the H(2$\ell$) density there is small, and the region between $R_p$ and $R_b$ is transparent to H$\alpha$.
Figure~\ref{Halpha} shows the model H$\alpha$\ transmission spectrum and the data from \citet{Cauley2015, Cauley2016}.
We do not include the results of \citet{Jensen} since these observations were not performed across a single transit.
The fiducial model discussed in Section~\ref{sec:fiducial} is given by the black line labeled ``$\xi=1, P_{\rm b}=10\, \mu$bar". Given the noise in the data, the fiducial model is in broad agreement for both the line center absorption depth and the line width.
The double-peak feature in \citet{Cauley2016}'s observations, whose amplitude is similar to the fluctuation in the continuum wavelength, cannot be explained by the model.
The wavelengths have been corrected for the index of refraction of air at ``standard condition'', $n_{\rm H\alpha}=1.0002762$, according to \citet{Refractive}. The plot also shows the effect of a different LyC flux, as denoted by lines with a different value of the factor $\xi$ and the metallicity, which will be discussed in the Section~\ref{sec:euv} and \ref{sec:z}, respectively.
The base pressure, $P_{\rm b}$, is not self-consistently determined in this study. In order to investigate the dependence of the transmission spectrum on this parameter, the blue solid line labeled ``$\xi=1, P_{\rm b}=1\, \mu$bar" shows a model with the base of the atomic layer at $P_b=1~\rm \mu bar$. The line center transit depth is smaller by $\simeq 20\%$ for $P_b=1~\rm \mu bar$. Changing this boundary causes only small changes the atmosphere properties, so the H$\alpha$\ becomes optically thick at approximately the same pressure.
However, because the scale height between $1~\rm \mu bar$ and $10~\rm \mu bar$ significantly decreases after switching to lower temperature and larger mean molecular weight, the radius in the atomic layer that corresponds to the same pressure becomes smaller, which leads to a smaller transit depth. Although we do not expect the transition from atomic layer to molecular layer to be as high up as $1~\rm \mu bar$ based on Figure~\ref{fig:n_P}, a more physical molecular model is required to produce a more precise transmission spectrum.
Figure~\ref{Hbeta} shows the model H$\beta$\ transmission spectrum and the data from \citet{Cauley2015, Cauley2016}.
While the model roughly agrees with the observation, there is an extra absorption on the blue side of the line, which cannot explained by the model.
Because of the smaller cross section, H$\beta$\ line probes a deeper region in the atmosphere compared to H$\alpha$.
The lower temperature there leads to a narrower line width.
Compared to H$\alpha$, the H$\beta$\ observations have larger uncertainty and less significant transit depth variation.
Figure~\ref{tau_b} shows the line center optical depth of the fiducial model versus impact parameter $b$. The H$\alpha$\ line center optical depth reaches the maximum value $\sim 70$ for $b=R_{\rm b}$, the base of the atomic layer. Although the optical depth of H$\alpha$\ slightly decreases inward, due to the (assumed) transparent molecular layer, the optical depth is still much larger than 1 all the way to the continuum radius $b=R_{\rm p}$. \citet{Lecavelier08} showed that the optical depth at the effective radius is $\tau_{eq} \simeq 0.56$\footnote{With the approximation of the uniform mixing ratio and isothermal thin atmosphere, the integral in Equation~\ref{eq:10} may be expanded in a series as $\int_0^\infty {\rm d} u \left( 1 - e^{-\beta e^{-u}} \right) \simeq \ln(\beta) + \gamma + {\cal O} (\beta^{-2})$, where $\gamma \simeq 0.577$ is the Euler-Mascheroni constant and $\beta \simeq n(R_p)\sigma\sqrt{2\pi R_pH}$. This formula is valid for $\beta \gg 1$. This expansion then gives $\tau_{\rm eq}=e^{-\gamma} \simeq 0.561$, in good agreement with \citet{Lecavelier08}.},
and is not sensitive to the details of the atmospheric structure. In the fiducial model, the effective radius is $9.93\times 10^9~\rm cm$, corresponding to an H$\alpha$\ optical depth $\tau=0.55$ and pressure $P=5.2\times 10^{-3}~\rm \mu bar$. The optical depth drops to below $\sim 10^{-2}$ at a pressure $10^{-3}~\rm \mu bar$, which means the contribution to H$\alpha$\ absorption from the atmosphere above this level is small.
Determined by the ratio of oscillator strength and wavelength, the ratio between the optical depth of H$\alpha$\ and H$\beta$\ is 7.3.
To indicate the vertical distribution of H$\alpha$\ and Na D absorption by the atmosphere, Figure~\ref{dWdb} shows the equivalent width contributed by an annulus of atmosphere with radius $b$, defined as
\begin{equation}
\label{eq:4}
\frac{{\rm d} W_\lambda}{{\rm d} b}=\frac{2b}{R_\star^2-R_p^2}\int \left(1-e^{-\tau_{l,\nu}(b)}\right){\rm d} \lambda.
\end{equation}
For impact parameters in the range $R_{\rm p} < b < R_{\rm b}$, which go through the molecular layer, the H$\alpha$\ line center optical depth is $\simeq 70$, and the absorption in the Lorentzian damping wing is negligible. Therefore, the base of the atomic layer is in the flat portion of the curve of growth~\citep{Draine}. The contribution to the equivalent width decreases slowly inward in this part of the atmosphere because of the smaller annulus radius and the lower temperature.
It is shown that the atomic layer of the atmosphere has an approximately uniform contribution to H$\alpha$\ absorption, while the absorption of H$\beta$\ is dominated by the region of $P\gtrsim 0.1~\rm \mu bar$.
In principle, high quality H$\alpha$\ and H$\beta$\ observations can be a good tracer for the vertical structure of the atomic layer.
\subsection{{\rm Na D} Transmission Spectrum}
\begin{figure}
\begin{center}
\includegraphics[width=0.5\textwidth]{Huitson.pdf}
\caption{Comparison of the Na D doublet transmission spectrum observed by \citet{Huitson} to the transmission spectrum of the fiducial model ($\xi=1, P_b=10~\mu$bar). The histogram shown as a black line is the modeled spectrum binned to the instrument resolution. The blue curve shows the result of the modeled spectrum convolved with a Gaussian profile with FWHM matching the instrument resolution.}\label{Huitson}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[width=0.5\textwidth]{Wyttenbach.pdf}
\caption{Comparison of the Na D doublet transmission spectrum observed by \citet{Wyttenbach} binned by $5\times$, to the calculated transmission spectrum of the fiducial model, as well as models with different atomic layer base pressures $P_b$, LyC boost factor $\xi$ and metallicity. Note the break in the x-axis. The spectra of the three models with $P_b=10\rm~\mu bar$ and solar abundance are nearly overlap on each other.}
\label{Wyttenbach}
\end{center}
\end{figure}
Unlike H$\alpha$, the Na D doublet lines are absorbed by ground state Na, which has high density deep in the atmosphere. The molecular layer is not treated in detail here, rather a simple model with constant (solar abundance) mixing ratio and temperature $T=1140$ K is used. Because Na and Mg are extremely optically thick in the molecular layer, their number density is not important in determining the line profile.
For simplicity, number density of Na and Mg are assumed to be equal to the value at the very base layer of the model. Similar to Ly$\alpha$, Na D photons undergo a resonant scattering process in the atmosphere, at least at pressures sufficiently low that collisional de-excitation and collisional broadening are negligible. An accurate model of the Na D transmission spectrum requires treatment of resonant scattering by Na$_{\rm ~I}$, as well as true absorption and emission by the atmosphere, which is beyond the scope of this paper. Instead, as was done for H$\alpha$\ in this work, a simple $e^{-\tau_{l,\nu}(b)}$ absorption will be used to compute the transmission spectrum. Because the line wings of the Na D doublet are overlapping, $\tau_{l,\nu}(b)$ uses the sum of the cross sections for each line of the doublet, evaluated at frequency $\nu$.
Figure~\ref{tau_b} shows that the optical depths of the Na D doublet lines reach $\tau \sim 0.5$ at $P\sim 10^{-2}~\rm \mu bar$, comparable to that of H$\alpha$, agreeing with the inference made previously based on the similar transit depth of H$\alpha$\ and Na D.
At this altitude, the temperature is $\sim 8500$ K, comparable to the analytic estimate using the difference between the Na D doublet transit depths discussed in Section~\ref{sec:analytic}.
The optical depth of the Na D doublet become much larger than unity below $1~\mu$bar. Thus Na D absorption by the atmosphere near the base of the atomic layer is in the damped portion of the curve of growth, which explains the large contribution to the equivalent width shown in Figure~\ref{dWdb}.
However, because of the slow transit depth variation with frequency on the damping wing, it is difficult to distinguish the Na D damping wings from possible additional sources of continuum opacity or observational error bars. The presence of clouds or hazes would further complicate the detection of this lower portion of the atmosphere, in spite of its large equivalent width contribution.
The portion of the curve that is deeper than $10~\mu$bar has no practical meaning because the value is limited by the wavelength integration range of the equivalent width.
Figure~\ref{Huitson} compares the observed Na D transmission spectrum from \citet{Huitson} and the fiducial model. The wavelength has been corrected for the index of refraction of air, $n_{\rm Na D}=1.0002771$ according to \citet{Refractive}. The spectral resolution of the Space Telescope Imaging Spectrograph (STIS) G750M grating aboard the HST used in this observation is $\sim 6$ times broader than the full width at half maximum (FWHM) of each line in the Na D doublet. Two methods are used to compare the model spectrum with the low spectral resolution observation. The first method is described in \citet{Huitson}, and is shown as a black histogram. The model spectrum is binned to the STIS instrument resolution, 2 pixels, since the G750M grating gives a resolution $\sim$2 pixels at 5893~\AA. Care is required since the absorption depth of the binned spectrum near each line center depends on the wavelength range used for binning. In view of this, the second method, shown as a blue solid curve, convolves the model spectrum with a Gaussian profile with FWHM matching the instrument resolution (2 pixel widths). For both methods, to imitate the process of normalization to the continuum outside the regions of interest which been done in observational data reducing, the Na absorption depth at 5912~\AA\ is subtracted out and treated as the continuum.
Figure~\ref{Wyttenbach} compares the high resolution Na D transmission spectrum observed by \citet{Wyttenbach} with the fiducial model, as well as models with different atomic layer base pressures $P_b$, $\xi$ and metallicity, equivalent to the models shown in Figure~\ref{Halpha}. In comparing to the H$\alpha$\ transmission spectrum, recall that the line width of Na is narrower as compared to H$\alpha$\ due to the larger mean atomic weight of Na.
To reduce the noise, the data plotted are binned by 5$\times$. The resulting $0.05 \rm~\AA$ bin width is equal to the FWHM of the average spectrograph line spread function, and is $\sim 3$ times narrower than the Na D FWHM.
On top of the $2.3 \rm ~km~s^{-1}$ shift to the red which accounts for the systemic velocity, the data were shifted by $10 \rm ~km~s^{-1}$ to the red to cancel the observed blueshift from an unknown source described in \citet{Wyttenbach}. Similar to the treatment in Figure~\ref{Huitson}, the correction from the index of refraction and continuum flux are made to the simulated spectrum. No binning or convolving is required because the spectral features are well resolved.
The line center absorption depths generated by the models agree with the Na D spectrum in both observations roughly to the level of the observational error bars. Note that there is a strong absorption feature on the red side of the line center which cannot be explained by the model.
\subsection{Retrieval of the Temperature Profile from {\rm Na D} Transmission Spectra}
\label{sec:retr-temp}
To measure the temperature versus altitude profile from the Na D transmission spectrum, $r(\lambda)$, \citet{Lecavelier08} applied the analytic model
\begin{equation}
\label{eq:5}
r(\lambda)=H\ln(\sigma(\lambda))+\text{constant},
\end{equation}
which is derived for a plane-parallel isothermal atmosphere with uniform mixing ratio of Na$_{\rm ~I}$\ and scale height $H=k_{\rm B}T/\mu m_p g$.
Here $\sigma(\lambda)$ is the summed cross section from each line of the Na D doublet, and a Voigt profile at the local temperature is used. The wavelength-independent constant term is determined by the radius at continuum wavelengths.
If the temperature and abundance vary slowly with altitude, an approximate scale height $H$ of the atmosphere at a certain radius can be derived from $H=({\rm d} r/{\rm d} \lambda)/({\rm d} \ln \sigma/{\rm d} \lambda)$.
Then, applying a mean molecular weight $\mu$, the local temperature $T(r)$ at $r(\lambda)$ can be computed from the fitted value of $H$.
Methods similar to this were applied by \citet{Huitson} and \citet{Wyttenbach} to measure the upper atmosphere temperature from their observed Na transmission spectra.
The atmosphere was assumed to be molecular with $\mu=2.3$ in both studies.
To decrease the uncertainty of the temperature measurement due to noise in the observed $r(\lambda)$ profile, \citet{Huitson} broke the spectrum into small wavelength intervals, and fit $r(\lambda)$ in each interval by varying $H$ and the constant.
\citet{Wyttenbach} also broke the spectrum into intervals, and fit for $H$ in each spectral region, but with a fixed value for the constant term in Equation~\ref{eq:5} in each interval.
As a result, if connecting the fitting curves from separate wavelength ranges together, the joined curve is not continuous in both the slope and value of the transit depth at the boundary between adjacent wavelength ranges.
The measured temperatures near line center in both studies are more than a factor of 2 lower than the model temperature here (see Figure~\ref{Retrieve}) over the relevant region of the atmosphere.
This is in spite of their using a mean molecular weight $\mu=2.3$, which assumes molecular hydrogen, while here the mean molecular weight in the atomic layer is closer to $\mu \simeq 1.3$, smaller by a factor of 2.
Such a large difference in temperature cannot be explained by the abundance variations due to ionization seen in Figure \ref{fig:n_P}.
\begin{figure}
\begin{center}
\includegraphics[width=0.5\textwidth]{fitNa.pdf}
\caption{Comparison of the fiducial model transmission spectrum and two different fits at a single point (circled) using the isothermal transit radius approximation in Equation \ref{eq:5}. The black line shows the transit radius of the Na$_{\rm ~I}$\ 5890 line for the fiducial ``$\xi=1, P_{\rm b}=10\mu\, \rm bar$" model (see Figures~\ref{Huitson} and \ref{Wyttenbach}). The red curve is chosen to agree with the value of the transit radius at $r(\lambda)=1.057R_p$, and with the continuum $r(\lambda)$ on the line wing. This requires a temperature $T=2830$ K, assuming $\mu=2.3$. The blue curve is chosen to have the same slope as the black curve at the circled point, which requires $T=6010$ K for $\mu=2.3$. }
\label{Fitting}
\end{center}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[width=0.5\textwidth]{Tfit.pdf}
\caption{Retrieved temperature profile using two different fitting strategies shown in Figure~\ref{Fitting}. Temperature profile fitted from the observed Na D transmission spectrum obtained by \citet{Wyttenbach} is shown with red circles. }
\label{Retrieve}
\end{center}
\end{figure}
One indication that higher temperatures than found in \citet{Huitson} and \citet{Wyttenbach} are required comes from the inferred range of density between line center and line wing. A lower temperature means a larger density difference between the base of the atmosphere, where the continuum forms, and higher altitudes where the line center forms. An underestimate of this density decrease can be found by using the highest fitted temperature used in \citet{Wyttenbach}, $T=3270$ K, and mean molecular weight $\mu=2.3$. Assuming the pressure is large, 1 bar at the continuum altitude, also errs on the side of high density higher in the atmosphere. With these two assumptions, an isothermal atmosphere gives the pressure $5\times 10^{-5}~\rm \mu bar$ at the line center altitude $1.27\times 10^4$ km.
To be optically thick to the Na$_{\rm ~I}$\ 5890 line, the ground state density must be $n_{\rm Na_I} \ga (\sigma_{\rm Na D2}\sqrt{2\pi r H})^{-1} \simeq 10^2 \rm~cm^{-3}$, where $\sigma_{\rm Na D2}$ is the line center cross section of Na$_{\rm ~I}$\ 5890.
This requires a $\sim 10^{-6}$ mixing ratio of Na$_{\rm ~I}$\, which means Na has to be mostly neutral at this altitude if the atmosphere is in solar abundance.
However, because the atmosphere is optically thin to the stellar flux at this pressure, Na is significantly ionized (see the left hand side of Figure \ref{fig:n_P}).
Therefore, the highest temperature measured in \citet{Wyttenbach} may underestimate the line center temperature formed high in the atmosphere.
For sufficiently high spectral resolution data, $r(\lambda)$, with high signal to noise for each data point, and for an atmosphere which is nearly isothermal and with small abundance gradients, the temperature of the atmosphere will be accurately recovered using Equation~\ref{eq:5} in the plane-parallel limit.
However, in an atmosphere where temperature increases upward rapidly, this method tends to underestimate the temperature \citep{Wyttenbach}. The problem is exacerbated when the opacity is provided by the line's Doppler core at the altitudes of interest.
To better understand the retrieval of a temperature profile for the non-isothermal, non-constant abundance case, an example is given here to fit the fiducial model $r(\lambda)$ (see Figures~\ref{Huitson} and \ref{Wyttenbach}) with the isothermal profile in Equation~\ref{eq:5}. This eliminates measurement errors in the data, and a fine enough grid of points is used so that numerical error is negligible. The black curve in Figure~\ref{Fitting} shows the fiducial model for the Na$_{\rm ~I}$\ 5890 absorption profile, the same as in Figure~\ref{Wyttenbach}. Two methods are used to fit Equation~\ref{eq:5} to the fiducial model.
``Method 1" is equivalent to that in \citet{Wyttenbach}. The constant term in Equation~\ref{eq:5} is chosen in order that the absorption depth is 0 at 5912~\AA, on the line wing.
The temperature $T(r)$ at each radius $r(\lambda)$ is determined by matching the value of the transit radius using Equation~\ref{eq:5} to the fiducial model.
A mean molecular weight $\mu=2.3$ is used, as in \citet{Wyttenbach}.
Figure~\ref{Fitting} shows an example of a Method 1 fit with $T=2830$ K, which matches the value of the absorption depth at $R=1.057R_p$. When the value is fitted, the slope will be smaller than that of the fiducial model.
``Method 2" is equivalent to that in \citet{Huitson}.
By adjusting $H$ and the constant term at each $r(\lambda)$, Equation~\ref{eq:5} is used to match the slope of the fiducial model transit radius.
Again $\mu=2.3$ is used.
Figure~\ref{Fitting} shows an example of a Method 2 fit with $T=6010$ that is tangent to the fiducial model $r(\lambda)$ curve at $R=1.057R_p$.
The retrieved temperature profiles for Method 1 and Method 2 are compared to the fiducial model temperature profile in Figure~\ref{Retrieve}.
For comparison, the Method 1 temperature profile estimated from the data by \citet{Wyttenbach} is shown as the points with error bars. Given that there is no numerical noise in this example, as the isothermal $r(\lambda)$ is fit to a theoretical model, the disagreement between the Method 1 and Method 2 fits and the true temperature profile is quite large. The disagreement would be even larger if the more appropriate $\mu \simeq 1.3$ was used near line center.
Method 1 can reasonably retrieve the temperature in the molecular layer, where the fiducial model temperature is constant and $\mu=2.3$.
However, the retrieved temperature in the atomic layer is lower than the fiducial model where the temperature increases outward.
Although the retrieved temperature is still higher than the points from \citet{Wyttenbach}, this example partially explains the lower inferred temperature in that work as compared to the fiducial model in this work.
Retrieving the temperature from a high resolution spectrum using Method 2 will significantly overestimate the temperature. In the Doppler core, Equation \ref{eq:5} gives
\begin{eqnarray}
r(\lambda) - r(\lambda_0) & =& - H \left( \frac{\Delta \nu}{\Delta \nu_D} \right)^2 \nonumber \\
&\simeq &- 6000\, {\rm km} \left( \frac{\Delta \lambda}{0.1\rm~\AA}
\right)^2 ,
\label{eq:isolinecenter}
\end{eqnarray}
independent of temperature.
Equation \ref{eq:isolinecenter} shows that the slope gets steeper further from line center.
This continues until the damping wing is reached, where the slope becomes more shallow.
Therefore, Equation~\ref{eq:isolinecenter}, evaluated near the core-wing boundary, gives the maximum slope of transit radius with $\Delta \lambda$ for the isothermal profile.
By contrast, the fiducial model $r(\lambda)$ is steeper than Equation \ref{eq:isolinecenter} in the line core because the absorption by a higher and hotter atmosphere layer produces a broader absorption than if the temperature is constant.
As the result, the slope of a section of the fiducial model near the line core is too steep and Equation \ref{eq:5} cannot produce such a steep slope for any temperature.
In addition, near the line core, the slope of $r(\lambda)$ for the fiducial model also depends on the Na$_{\rm ~I}$\ abundance gradient.
Collisional ionization by thermal electrons and Ly$\alpha$\ photoionization decrease the Na ionization fraction at level above $0.1 \rm~\mu bar$ (see Figure \ref{fig:n_P}), which can decrease the slope near the line center.
These results suggest that the isothermal model may not accurately retrieve a rapidly rising temperature profile (see also \citet{Heng}). In comparison, fitting the whole wavelength range with an atmosphere model contains several isothermal layers, or a single layer with a continuous temperature profile may better constrain the atmosphere temperature.
\subsection{{\rm Mg} Transmission Spectrum}
\begin{figure}
\begin{center}
\includegraphics[width=0.5\textwidth]{MgII.pdf}
\caption{The calculated \ion{Mg}{2} 2795 transmission spectrum of the fiducial model, as well as models with different LyC boost factor $\xi$ and Mg abundance.}\label{MgII}
\end{center}
\end{figure}
Figure~\ref{MgII} shows the model predicted transmission spectrum of \ion{Mg}{2} 2795, one of the \ion{Mg}{2} doublets. No correction of index of refraction has been applied.
Assuming solar metalicity, almost the entire atmosphere in the simulation region is optically thick to Mg lines at the line center, because of the high abundance and shallower dependence on pressure (see Figure~\ref{fig:n_P}).
In this case, the line center transit depth is $\sim 5\%$, 3 times larger than the planet transit depth in continuum.
In contrast, assuming the abundance of Mg is $10^{-4}$ of the solar value, the transit depth is $\sim 0.8\%$.
The model predicts very similar transmission spectra for \ion{Mg}{2} 2803 and \ion{Mg}{1} 2852 line.
Because of the probable large transit depth and its strong impact on the physical properties of the atmosphere, the transmission spectra of Mg resonant lines in middle UV might be a good target to constrain the hot Jupiter upper atmosphere.
\subsection{Impact of LyC Flux on Transit Depth}
\label{sec:euv}
HD 189733 is known to be an active star \citep{Boisse, Pillitteri2014, Pillitteri2015}. To show the dependence of the transmission spectrum on the stellar EUV/X-ray flux, two more models with an extra LyC flux multiplier factor $\xi=1/4$ and $\xi=4$ are applied.
Figure~\ref{Halpha} and \ref{Hbeta} show that a stronger LyC flux will make the H$\alpha$\ and H$\beta$\ transit depth deeper.
This is consistent with the conclusion in \citet{Cauley2017} that the H$\alpha$\ transit showing the largest absorption value occurs when the star is the most active.
In comparison, Figure~\ref{Wyttenbach} shows that LyC flux has no effect on the NaD transmission spectrum.
The reason of this difference is that the Na D transmission spectrum depends on the temperature or scale height of the atmosphere as well as Na ionization fraction below $10^{-2}~\rm \mu bar$.
Above the level of $10^{-1}~\rm \mu bar$, collisional ionization dominate Na ionization.
Although the temperature of the atmosphere increases with the $\xi$, the effect of increasing scale height is canceled by the Na higher ionization fraction.
In contrast, the ionization of H is not sensitive to the temperature.
Instead, Balmer lines depend on the Ly$\alpha$\ intensity in this region, which is larger for a strong LyC flux environment.
The Balmer lines transmission spectra also become slightly broader in the strong LyC flux case, because the lines become optically thick at higher and hotter part of the atmosphere in this case.
This indicates that Balmer lines are the better tracer of atmosphere temperature compared to Na doublets.
Comparing the variability of the transit depths of the H$\alpha$\ and Na D lines is a possible method to break the degeneracy between the transit depth variability due to blocking an active region on the star surface and the change in the atmosphere due to stellar activity.
\subsection{Impact of Metallicity on Transit Depth}
\label{sec:z}
The metallicity is crucial in the model presented in this paper, but its value is uncertain. Since Mg is the dominant coolant in the model, a model that reduces the Mg abundance to $10^{-4}$ of the solar value is calculated to assess the effect of metallicity on the transmission spectrum. Because the atmosphere is warmer and more extended without Mg cooling, the transit depths of H$\alpha$\ and H$\beta$\ become deeper, as shown in Figures~\ref{Halpha} and \ref{Hbeta}. The transit depth of Na is insensitive to the Mg abundance because of the trade off between atmosphere scale height and ionization fraction discussed in~\ref{sec:euv}. The relatively large transit depth difference between two models with and without Mg indicates that high precision Balmer and Mg transmission spectrum measurements can constrain the metallicity in the upper atmosphere.
\section{DISCUSSION}\label{discussion}
\subsection{Other Possible Cooling Mechanisms}
\label{sec:ad_cool}
Adiabatic cooling is another potential cooling mechanism discussed in the literature. \citet{KoskinenI} constructed an atmosphere model for a similar hot Jupiter HD 209458b. In their model, the stellar heating is mainly balanced by adiabatic cooling. Compared with HD~189733b\ system, the LyC flux of HD 209458 is weaker and the orbit of HD 209458b is further away from the star. They also introduced a factor of 1/4 reduction on stellar flux to account for uniform day-night heat redistribution. As a result of these differences, the heating rate of \citet{KoskinenI} HD 209458b atmosphere model is more than $20$ times smaller than the rate in our HD~189733b\ model. On the other hand, the adiabatic cooling does not differ much in two systems because of the similar mass loss rate~\citep{Murray-Clay}. Therefore, the adiabatic cooling is unlikely to be the answer in the case of HD 189733b.
The effect of the adiabatic cooling of the model here can be estimated with an assumed mass loss rate. Including the adiabatic cooling in the pressure coordinate system according to \citet{Bildsten}, the entropy equation takes the following form,
\begin{equation}
\label{eq:9}
\sum H - \sum C = \frac{C_p \dot{M} T \rho g_p}{4\pi R_p^2 P}\left(\nabla_{\rm ad}-\frac{{\rm d} \ln T}{{\rm d} \ln P}\right),
\end{equation}
where $\sum H$ and $\sum C$ stand for the sum of heating and cooling rates respectively as shown in the right and left hand side of Equation~\ref{eq:heat}, $\nabla_{\rm ad}=({\rm d} \ln T/{\rm d} \ln P)_S$ is the adiabatic temperature gradient at constant entropy, $\dot{M}$ is the mass loss rate, and $C_p$ is the specific heat per unit mass at constant pressure.
In the fiducial model, the temperature gradient is about ${\rm d} T/{\rm d} r=5\times 10^{-7}~\rm K~cm^{-1}$ at the radius that 13.6 eV photon becomes optically thick, where most LyC photons get absorbed. Applying the mass-loss rate $\dot{M}=4\times 10^9 \rm~g~s^{-1}$ suggested by \citet{Salz} using a hydrodynamic escaping atmosphere model, the adiabatic cooling rate is $1.1\times 10^{-8} \rm ~erg~cm^{-3}~s^{-1}$ and the first term in the Equation~\ref{eq:9} is the dominant source.
Compared to the heating and cooling rates shown in Figure~\ref{fig:cooling}, the adiabatic cooling is more than two orders of magnitude smaller in the region where H$\alpha$\ mostly absorbed, and may only become important in the region above $P\sim 3\times 10^{-4}\rm~\mu bar$. The mass-loss rate may be model dependent. An upper bound for the mass loss rate can be found using the energy-limited escape rate \citep{Murray-Clay}, which assumes all LyC flux converts to unbinding the atmosphere.
The LyC flux $F_{\rm LyC}=2.6 \times 10^4 \rm ~erg~cm^{-2}~s^{-1}$ corresponds to the energy-limited mass-loss rate $\dot{M}=3\times 10^{11} \rm~g~s^{-1}$. In this case, the adiabatic cooling rate is $8\times 10^{-7} \rm ~erg~cm^{-3}~s^{-1}$ and still has a less than 15\% effect in the region mainly concerned.
\subsection{Comparing with Other Hot Jupiter Upper Atmosphere Models}
\paragraph{\citet{Christie}}
The present study agrees with the conclusion in \citet{Christie} that the $2p$ occupation is set by radiative excitation and de-excitation, and as an improvement, we include a Ly$\alpha$\ radiation transfer inside the atmosphere instead of applying a constant solar Ly$\alpha$\ intensity. Because of the $\sim 30$ times stronger stellar Ly$\alpha$\ intensity of HD 189733 comparing to the Sun and considering the Ly$\alpha$\ photons generated inside the atmosphere due to collisional excitation and recombination cascades, the Ly$\alpha$\ mean intensity should be $\sim 100$ times larger for the majority of the atomic layer. In addition, because \citet{Christie} underestimates the $n_{2p}$ by a factor of 20 due to a math error, the $n_{2p}$ should be significantly larger in the whole simulation domain, and thus the atmosphere is optically thick to H$\alpha$\ mainly due to the absorption of H($2p$). The observed H$\alpha$\ absorption width agrees well with an optically thick atmosphere model.
Because of the much larger $n_{2\ell}$, the photoionization of H(2$\ell$) is larger compared to photoionization of the ground state in the atomic layer. Hence the $n_e$ and $n_p$ in this work is $\sim 10$ times larger.
Considering the proton collisional $\ell$-mixing process with rate $\sim 10$ times larger than electron collisional process, as well as the large H(2p) population, the creation of 2s hydrogen is dominated by $\ell$-mixing rather than collisional excitation considered in \citet{Christie}. As a result, $2s$ and $2p$ reach collisional equilibrium.
In addition, it is shown that the metal lines are crucial in cooling the atmosphere. Assuming solar abundance, lines of Mg and Na can cool the atomic layer by $\simeq 2000-3000$ K.
\paragraph{\citet{Menager}}
\citet{Menager} investigate the Ly$\alpha$\ emission and reflection by the atmosphere of HD~189733b. The temperature and electron, hydrogen, and helium number density profiles of HD~189733b\ from the \citet{Koskinen2011} unpublished model were applied. The temperature, $n_e$, $n_p$, and $n_{\rm H}$ are in broad agreement with the profiles presented in this paper in the corresponding pressure range. According to a similar model of HD 209458b presented in \citet{KoskinenI}, it should be a one-dimensional hydrodynamic model of the upper atmosphere considering hydrogen and helium constructed on top of a full photochemical model of the lower atmosphere. They chose the average solar flux as their stellar spectrum, which is $\sim10$ times smaller than the synthetic spectrum from MUSCLES. Different from the photoelectron heating efficiency $\eta(E)$ calculated at the fixed ionization fraction $x_e=0.1$ throughout the model, or a constant $\eta$ applied in the \citet{KoskinenI}, a $\eta$ based on the local $x_e$ is used in this work.
The temperature in the HD~189733b\ model of \citet{Koskinen2011} reachs a peak of about 13000 K at a pressure of $3\times 10^{-4}~\rm \mu bar$. The adiabatic cooling lowers the temperature at higher altitude. Their temperature at pressure range $10^{-3}$ to 1 $\mu$bar is higher by about 3000 K. Two possible reasons of this difference are \citet{KoskinenI} do not consider metal lines cooling, which are the dominant cooling mechanisms in our model, and conduction is not included in this work, which is a net heating in this pressure range according to their result. Their temperature decreases much faster with pressure above 1 $\mu$bar comparing to Figure~\ref{fig:T}. The lack of molecular cooling in this work is the possible reason. Their $n_e$ decreases slowly with pressure in the atomic layer and is $\sim 10$ times smaller at 10 $\mu$bar compared to this work. This difference is the result of missing the photoionization from H($2s$), which is the dominant ionization mechanism in this region.
In the Ly$\alpha$\ radiation transfer simulation of \citet{Menager}, the Ly$\alpha$\ photons emitted by the star and by the planetary atmosphere are considered. However, when considering the Ly$\alpha$\ photon emitted by the planetary atmosphere, the Ly$\alpha$\ photon created through recombination cascades is not included. In order to calculate the Ly$\alpha$\ thermal excitation in the atmosphere, the number densities of $2s$ and $2p$ states hydrogen are modeled with a level population study. In the $2p$ state level equation, Ly$\alpha$\ excitation, which completely dominates the $2p$ state, is not included. In addition, because the $p$ collisional $\ell$-mixing process is missing in their model, the 2$\ell$ state number densities result shown are affected.
\citet{Menager} claimed that the thermal emission of HD~189733b\ contributes to 6\% of the total intensity of the Ly$\alpha$\ line.
In the fiducial model of this work, this ratio is $9.6\times 10^3\rm ~erg~cm^{-2}~s^{-1} / (2.0\times 10^4 \rm ~erg~cm^{-2}~s^{-1} + 9.6\times 10^3\rm ~erg~cm^{-2}~s^{-1}) = 32\%$. This ratio strongly depends on the metallicity as well as the stellar LyC to Ly$\alpha$\ flux ratio.
\section{CONCLUSION}
A detailed one-dimensional hydrostatic atmosphere model is constructed over the region dominated by atomic hydrogen and comparison of model transmission spectra to the data has been made.
An atomic hydrogen level population calculation and a Monte-Carlo Ly$\alpha$\ radiation transfer are done to model the abundance of 2$\ell$ state hydrogen. The model transmission spectra of H$\alpha$, H$\beta$, and Na are in broad agreement with the HD 189733b data for both the line center absorption depth and the line width, although the comparison is complicated by the observed variability.
The Ly$\alpha$\ radiation transfer shows that the Ly$\alpha$\ has a very broad line width with a flat top due to the resonant scattering process.
The line profile weighted mean intensity $\bar{J}_{Ly\alpha}$ is large and approximately constant down to the $P=0.1~\rm \mu bar$ level of the atmosphere.
Ly$\alpha$\ photons created inside the atmosphere and incident from the star are both important. The Ly$\alpha$\ source function extends deep into the atmosphere due to ionization from progressively higher energy stellar LyC photons. The stellar Ly$\alpha$\ photon can penetrate into very large line center optical depth because the stellar Ly$\alpha$\ intensity is much boarder than the Doppler width inside the atmosphere. The stellar Ly$\alpha$\ photons incident through the surface and the photons generated above $10^{-2}~\rm \mu bar$ can mostly escape through the top boundary. In contrast, the photons emitted below $0.1~\rm \mu bar$ are mostly absorbed during the resonant scattering processes due to the high optical depth. For $P\gtrsim 0.1~\rm \mu bar$, $\bar{J}_{Ly\alpha}\propto P^{-1}$.
The $n_{2p}$ is determined by the radiative rates between $1s$ and $2p$ throughout the simulation domain because of the large Ly$\alpha$\ intensity. The $2s$ and $2p$ states reach collisional equilibrium by the large $p$ collisional $\ell$-mixing rate, which was overlooked in this context. The combination of the decreasing Ly$\alpha$\ excitation rates and the increasing hydrogen density gives rise to a nearly flat $n_{2\ell}$ over two decades in pressure. This layer is optically thick to H$\alpha$, and the temperature is in the range $T \simeq 3000-8500\, \rm K$. Both H$\alpha$\ and NaD are optically thick up to the level $P\sim 10^{-2}~\rm \mu bar$, which corresponds to the atomic layer of the atmosphere. Assuming solar abundance, radiative cooling due to metal species dominates over the entire model, with Mg and Na being the two most important species. The model shows that \ion{Mg}{2} may have a very large transit depth assuming solar abundance, which might be a good target to constrain the atmospheric properties.
Additional models computed for a range of the stellar LyC flux find transit depth of H$\alpha$\ changes with LyC level, suggesting that the variability in H$\alpha$\ transit depth may be due to variability in the stellar LyC. In contrast, the Na absorption profile is insensitive to the LyC level. Since metal lines provide the dominant cooling of this part of the atmosphere, the atmosphere structure is sensitive to the density of species such as Mg and Na, which may themselves be constrained by observations. Lastly, since the H$\alpha$\ and Na D lines have comparable absorption depths for the same spectral resolution, we argue that the center of the Na D lines are also formed in the atomic layer where the H$\alpha$\ line is formed.
The present model is in agreement with the observed Na D transmission spectrum by \citet{Huitson} and \citet{Wyttenbach}, although the inferred atmospheric temperature is significantly larger than that found assuming an isothermal profile and molecular composition.
It is shown that the temperature achieved by fitting each wavelength interval in the observed transmission spectrum with an isothermal atmosphere model may not accurately retrieve the original temperature profile, if the temperature increases rapidly with the altitude.
\section{ACKNOWLEDGMENTS}
We are grateful to Wilson Cauley and Aur\'elien Wyttenbach for kindly providing the data. We thank Wilson Cauley, Seth Redfield, and Adam Jansen for useful discussions regarding H$\alpha$\ observations. We also thank the helpful conversations with Ira Wasserman, Craig Sarazin, Shane Davis, Roger Chevalier, and Remy Indebetouw regarding the model construction, and the help from Katherine Holcomb in improving the code efficiency. The simulations in this work were carried out on the Rivanna computer cluster at the University of Virginia. We also thank the referee for providing constructive comments and suggestions, especially in suggesting use of the MUSCLES spectrum. This research was supported by NASA grants NNX14AE16G, NNX10AH29G, and NNX15AE05G.
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{"url":"https:\/\/math.stackexchange.com\/questions\/1491755\/prove-the-following-set-is-an-ideal-of-the-ring-zx","text":"# Prove the following set is an ideal of the ring $Z[x]$\n\nShow that the set of all polynomials whose constant term is a multiple of 3 is an ideal of the ring $Z[x]$.\n\nAttempt: Suppose then we need to show\n\nif $p(x), q(x) \\in I$ then $p(x) + q(x) \\in I$ and if $r(x) \\in Z[x]$ , then $p(x)r(x) \\in I$ and $r(x)p(x) \\in I$.\n\nAnd $0 \\in Z$, then $0 \\in I$.\n\nThen let\n\n$I =$ {$a_nx^n + a_{n-1}x^{n-1} + ...+a_1x + a_0$ | $a_i \\in Z$, $a_0\\in 3Z$}\n\n$p(x) = a_nx^n + a_{n-1}x^{n-1} + ...+a_1x + 3a$\n\nand $q(x) = b_mx^n + b_{m-1}x^{n-1} + ...+b_1x + 3b$\n\nHere we do not assume that $p(x)$ and $q(x)$ have the same degree. Then $p(x) + q(x) = [a_nx^n + a_{n-1}x^{n-1} + ...+a_1x + 3a] + [b_mx^n + b_{m-1}x^{n-1} + ...+b_1x + 3b] = 3(a + b) + (a_1 + b_1)x + ....+ (a_n + b_m)x^n$.\n\nso $p(x) + q(x) \\in I$\n\nAnd $0 \\in Z$ is also in $I$, since for $p(x) = 0x^n + ....+ 3(0) = 0$.\n\nAnd let $r(x)= c_nx^n + ...+3c \\in Z[x]$.\n\nThen $r(x)p(x) = 3(3ac) + (3b_1 + 3a_1) + ....+ a_nb_mx^{2n}$\n\nSo $r(x)p(x) \\in I$.\n\nCan someone please help? I am not really sure how to prove this. I am getting confused with the underscrips Any help or better approach would really help. Thanks in advance!\n\nAnother way is to take the ring homomorphism $\\Bbb Z[x]\\to\\Bbb F_3$ by $f\\mapsto f(0)\\pmod3$. Its kernel is clearly the set in question.\nA better approach would be to prove that the set of polynomials with constant term a multiple of 3 is the ideal generated by $X$ and $3$. Namely it is $\\{Xf(X)+3g(X) \\ \\vert \\ f,g \\in \\mathbb{Z}[X]\\}$, which is more easily proven to be an ideal.\nIf you believe that $(x)=x\\Bbb Z[x]$ and $(3)=3\\Bbb Z[x]$ and that the sum of two ideals is an ideal, you could show your set is equal to the sum of the two ideals I just mentioned.\nMuch like Lubin's solution, you can again use the evaluation homomorphism where you evaluate at $0$. This sends a $f(x)\\in \\mathbb{Z}[x]$ to $f(0)$. This will just give the constant term. Then the set you are interested in is the preimage of the ideal $(3)$ in $\\mathbb{Z}$ and the preimage of an ideal is an ideal.","date":"2019-08-25 00:38:09","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\": 0.9769310355186462, \"perplexity\": 49.21309745766748}, \"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\/1566027322160.92\/warc\/CC-MAIN-20190825000550-20190825022550-00286.warc.gz\"}"} | null | null |
{"url":"https:\/\/www.iacr.org\/news\/legacy.php?p=detail&id=5049","text":"International Association for Cryptologic Research\n\n# IACR News Central\n\nYou can also access the full news archive.\n\nFurther sources to find out about changes are CryptoDB, ePrint RSS, ePrint Web, Event calender (iCal).\n\n2015-04-19\n21:17 [Pub][ePrint]\n\nIn authenticated encryption schemes, there are two techniques for handling long ciphertexts while working within the constraints of a low buffer size: Releasing unverified plaintext (RUP) or Producing intermediate tags (PIT). In this paper, in addition to the two techniques, we propose another way to handle a long ciphertext with a low buffer size by storing and releasing only one (generally, or only few) intermediate state without releasing or storing any part of an unverified plaintext and without need of generating any intermediate tag.\n\nIn this paper we explain this generalized technique using our new construction sp-AELM. sp-AELM is a sponge based authenticated encryption scheme that provides support for limited memory devices. We also provide its security proof for privacy and authenticity in an ideal permutation model, using a code based game playing framework. Furthermore, we also present two more variants of sp-AELM that serve the same purpose and are more efficient than sp-AELM.\n\nThe ongoing CAESAR competition has 9 submissions which are based on the Sponge construction. We apply our generalized technique of storing single intermediate state to all these submissions, to determine their suitability with a Crypto module having limited memory. Our findings show that only ASCON and one of the PRIMATE\\'s mode(namely GIBBON) satisifes the limited memory constraint using this technique, while the remaining 8 schemes (namely, Artemia, ICEPOLE, Ketje, Keyak, NORX, $\\\\pi$-Cipher, STRIBOB and two of the PRIMATEs mode: APE \\\\& HANUMAN) are not suitable for this scenario directly.\n\n21:17 [Pub][ePrint]\n\nAbstract: Broadcast or multicast is one of the most fundamental\n\nconcepts in data communication and distributed cryptography. A\n\ncentral entity wishes to broadcast a secret data stream to a\n\ndynamically changing privileged subset of recipients in such a\n\nway that non-members of the privileged class cannot learn the\n\nAlgorithm (ASBA) based on threats analytics and case based\n\nreasoning. It defines the security intelligence of an adaptively\n\nsecure broadcast comprehensively with a novel concept. It\n\nrecommends a set of intelligent model checking moves for the\n\nverification of security intelligence of broadcasting mechanism.\n\nThe algorithm is analyzed from the perspectives of security\n\nintelligence, communication complexity, computational\n\nintelligence and efficiency of mechanism. The computational\n\nintelligence is associated with the complexity of broadcast\n\nscheduling, verification of security intelligence of broadcasting\n\nsystem, key management strategies and payment function\n\ncomputation. The cost of communication depends on number of\n\nagents and subgroups in the broadcasting group and complexity of\n\ndata. The algorithm is applicable to the analysis of intelligent\n\nmechanisms in static and dynamic networks, auction or\n\ncombinatorial auction for e-market, digital content distribution\n\n21:17 [Pub][ePrint]\n\nThe problem of verifiable data streaming (VDS) considers a client with limited computational and storage capacities that streams an a-priori unknown number of elements to an untrusted server.\n\nThe client may retrieve and update any outsourced element. Other parties may verify each outsourced element\\'s integrity using the client\\'s public-key.\n\nAll previous VDS constructions incur a bandwidth and computational overhead on both client and server side, which is at least logarithmic in the number of transmitted elements.\n\nWe propose two novel, fundamentally different approaches to constructing VDS.\n\nThe first scheme is based on a new cryptographic primitive called Chameleon Vector Commitment (CVC).\n\nA CVC is a trapdoor commitment scheme to a vector of messages where both commitments and openings have constant size.\n\nUsing CVCs we construct a tree-based VDS protocol that has constant computational and bandwidth overhead on the client side.\n\nThe second scheme shifts the workload to the server side by combining signature schemes with cryptographic accumulators.\n\nHere, all computations are constant, except for queries, where the computational cost of the server is linear in the total number of updates.\n\n21:17 [Pub][ePrint]\n\nA family of hash functions is called correlation intractable\\'\\' if it is hard to find, given a random function in the family, an input-output pair that satisfies any sparse\\'\\' relation, namely any relation that is hard to satisfy for truly random functions. Correlation intractability captures a strong and natural Random Oracle-like property. However, it is widely considered to be unobtainable. Indeed, it was shown that correlation intractable functions do not exist for some length parameters [Canetti, Goldreich and Halevi, J.ACM 04]. Furthermore, no candidate constructions have been proposed in the literature for any setting of the parameters.\n\nWe construct a correlation intractable function ensemble that withstands all relations with a priori bounded polynomial complexity. We assume the existence of sub-exponentially secure indistinguishability obfuscators, puncturable pseudorandom functions, and input-hiding obfuscators for evasive circuits. The existence of the latter is implied by Virtual-Grey-Box obfuscation for evasive circuits [Bitansky et al, CRYPTO 14].\n\n21:17 [Pub][ePrint]\n\nSecurity models for two-party authenticated key exchange (AKE) protocols have developed over time to capture the security of AKE protocols even when the adversary learns certain secret values. Increased granularity of security can be modelled by considering partial leakage of secrets in the manner of models for leakage-resilient cryptography, designed to capture side-channel attacks. In this work, we use the strongest known partial-leakage-based security model for key exchange protocols, namely continuous after-the-fact leakage eCK (CAFL-eCK) model. We resolve an open problem by constructing the first concrete two-pass leakage-resilient key exchange protocol that is secure in the CAFL-eCK model.\n\n21:17 [Pub][ePrint]\n\nWe study the possibility of computing cryptographic primitives in a fully-black-box arithmetic model over a finite field $\\\\F$. In this model, the input to a cryptographic primitive (e.g., encryption scheme) is given as a sequence of field elements, the honest parties are implemented by arithmetic circuits which make only a black-box use of the underlying field, and the adversary has a full (non-black-box) access to the field. This model captures many standard information-theoretic constructions.\n\nWe prove several positive and negative results in this model for various cryptographic tasks. On the positive side, we show that, under reasonable assumptions, computational primitives like commitment schemes, public-key encryption, oblivious transfer, and general secure two-party computation can be implemented in this model. On the negative side, we prove that garbled circuits, multiplicative-homomorphic encryption, and secure computation with low online complexity cannot be achieved in this model. Our results reveal a qualitative difference between the standard Boolean model and the arithmetic model, and explain, in retrospect, some of the limitations of previous constructions.\n\n21:17 [Pub][ePrint]\n\nWe present a hardware architecture for all building blocks required in polynomial ring based fully homomorphic schemes and use it to instantiate the somewhat homomorphic encryption scheme YASHE. Our implementation is the first FPGA implementation that is designed for evaluating functions on homomorphically encrypted data (up to a certain multiplicative depth) and we illustrate this capability by evaluating the SIMON-64\/128 symmetric key cipher in the encrypted domain. Our implementation provides a fast polynomial operations unit using CRT and NTT for multiplication combined with an optimized memory access scheme; a fast Barrett like polynomial reduction method that allows all possible polynomial moduli; an efficient divide and round unit required in the multiplication of ciphertexts and an efficient CRT unit. These building blocks can be easily reused to instantiate any other polynomial ring based fully homomorphic scheme, including the ones designed for SIMD operations, since no restricting assumptions have been made. These building blocks are integrated in a coprocessor with instructions to execute YASHE, which can be controlled by a computer for evaluating arbitrary functions (up to the multiplicative depth 44 and 128-bit security level). Our architecture was compiled (place-and-route analysis) for a single Xilinx Virtex-7 XC7V1140T FPGA, where it consumes 23\\\\,\\\\% of registers, 50\\\\,\\\\% of LUTs, 53\\\\,\\\\% of DSP slices, and 38\\\\,\\\\% of BlockRAM memory. The implementation evaluates SIMON-64\/128 in approximately 157.7\\\\,s (at 143\\\\,MHz) and it processes 2048 ciphertexts at once giving a relative time of only 77\\\\,ms per block. This is 26.6 times faster than the leading software implementation on a 4-core Intel Core-i7 processor running at 3.4\\\\,GHz.\n\n21:17 [Pub][ePrint]\n\nThe aim of this paper is to present an attack upon the protocol of Diaz et al. \\\\cite{Diaz}, which goal is to introduce a fair anonymity in the Tor network. This attack allows an attacker to impersonate Tor users with the complicity of an exit node.\n\n2015-04-17\n16:49 [Job][New]\n\nThe Cryptology Group and the Embedded Security Group at Ruhr-University Bochum (Horst-Goertz Institute) are seeking to recruit two Marie Sklodowska-Curie Research Fellows in Cryptography to start in September 2015, as part of the ECRYPT-NET project.\n\nECRYPT-NET is a research network of six universities and two companies that intends to develop advanced cryptographic techniques for the Internet of Things and the Cloud, and to create efficient and secure implementations of those techniques on a broad range of platforms. ECRYPT-NET is funded by a prestigious Marie Sklodowska-Curie ITN (Integrated Training Network) grant. The network will educate a group of 15 PhD students with a set of interdisciplinary skills in the areas of mathematics, computer science and electrical engineering. The training will be provided in an international context that include Summer Schools, workshops and internships. Participants are expected to spend at least six months abroad with a network partner or in one of the seven associated companies. We are looking for highly motivated candidates, ideally with background on cryptology and with proven research abilities.\n\nTwo of the ECRYPT-NET ESR (Early Stage Researcher) positions will be based at Ruhr-University Bochum, to work on the following projects:\n\n\u2022 Fully Homomorphic Encryption - Design and Analysis\n\u2022 Post-Quantum Cryptosystems on Embedded Platforms\n\nMarie Curie ITN eligibility criteria apply to both of these positions.\n\nFounded in 2001, the Horst-G\u00f6rtz Institute at Ruhr-University Bochum is a world-leading interdisciplinary research center dedicated to research and education covering all aspects of IT security, with an excellent record of research in cryptography. The Horst-G\u00f6rtz Institute has 15 professors and over 80 PhD students. It hosts the only German Research Training Group for Doctoral students in Cryptology.\n\n2015-04-16\n16:20 [Job][New]\n\nWe are looking for postdoc fellow with expertise on Cryptographic Protocols (UC-security, multi-party computations), Information Security, Cloud Computing and Big Data Analytics. The candidates should have PhD in Cryptography and Information Security or Cloud Computing or Database Engineering with track record of strong R&D capability.","date":"2017-09-19 20:32:18","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\": 1, \"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\": 0.3278820216655731, \"perplexity\": 2585.114446304723}, \"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-2017-39\/segments\/1505818686034.31\/warc\/CC-MAIN-20170919202211-20170919222211-00197.warc.gz\"}"} | null | null |
Nat Geo's 'Killing Reagan' Ditches Bill O'Reilly's Controversial Post-Assassination Theory – TCA
Lisa de Moraes
TV Columnist
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Nat Geo's adaptation of Bill O'Reilly's Killing Reagan will dodge the controversy spawned by the book's suggestion that Ronald Reagan suffered intellectual decline after an assassination attempt on his life. "We deal with the assassination attempt in a limited way," screenwriter Eric Simonson told TV critics at TCA. The "limited way" doesn't include O'Reilly's depiction of Reagan's dementia.
"One of the decisions Eric had to make is what do we not include from the book," director Rod Lurie chimed in. O'Reilly's book, he explained, deals with the post-assassination controversy, as well as Reagan's childhood, his affairs, and his relationship with Soviet Union leader Mikhail Gorbachev. "We made the decision to confine it to this six-month period, so a lot of things you're talking about did not need to be dealt with."
O'Reilly's book was "very successful" and "very entertaining," Lurie said, adding "but I was telling the story that Eric gave to me. I'm more working on Simonson's Killing Reagan than O'Reilly's."
With this week's news that Reagan's would-be assassination John Hinckley will soon be released from a Washington psychiatric hospital, to live full-time with his 90-year-old mother in Williamsburg, Virginia, panelists naturally got asked for their thoughts. (A judge this week said that Hinckley can leave the hospital next month with restrictions.
"He's not coming to the premiere. I can tell you that," Lurie snarked.
"Nancy wouldn't like it," said Cynthia Nixon, who plays the former First Lady in the project.
Lurie also noted that while some Reagan family members aren't happy, the original judge 34 year ago said Hinckley should remain confined "until such time as no longer mentally ill and no longer a danger. And in this country we don't extend confinements, willy-nilly, because he shot an American President."
Kyle S. More, who plays Hinckley in the project, added that Secret Service has said "he's never going to be really free; they're always going to have one eye out."
In early May, Deadline reported that Tim Matheson had been cast as President Ronald Reagan and Cynthia Nixon as Nancy Reagan in the Nat Geo adaptation.
Killing Reagan is scheduled to premiere on National Geographic Channel in the U.S. and in 171 countries in 45 languages, including Nat Geo Mundo.
More than a decade ago, CBS wound up not airing its much ballyhooed Reagan miniseries after the project raised eyebrows in various quarters for such elements as the casting of Barbara Streisand's husband James Brolin as Ronald Reagan (Judy Davis played Nancy Reagan).
More recently, this past April the hue and cry went up when reports surfaced that Will Ferrell, who played George W. Bush on Saturday Night Live and on Broadway, might be playing Reagan on the big screen in an adaptation of The Black List Reagan script from Mike Rosolio. The 40th President's son Michael Reagan and daughter Patti Davis both expressed outrage over the project. Announced in December in the 11th edition of the most-liked un-produced screenplays, Rosolio's Reagan is set at the end of 1984 when Reagan had just been re-elected in a landslide. In the script, he is suffering from dementia, and an intern, who's hoping to move up, is tasked with trying to convince the former SAG leader he is in a movie in which he is playing the President.
Michael Reagan tweeted, "#Alzheimers is not a comedy to the 5 million people who are suffering with the decease, it first robs you of your mind and then it kills you."
Among those who blasted Bill O'Reilly's book, USA Today called it a "misfire" in that it "deals more with Reagan's gradual descent into dementia, the result of his fight with Alzheimer's disease" and "asserts Reagan exhibited signs of the illness during his presidency." The book also has been dinged for delving into Reagan's affairs in Hollywood, parenting, and disputes with Nancy.
Killing Reagan
Rod Lurie
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Q: java and python gives different result in logical operator I am trying to get broadcast ip address coding in Java and Python for practice. Here is my code in java which gives me correct output:
public IPv4Address getBroadcastAddress() throws IllegalArgumentException {
long bits = 0;
bits = this.address.decimalIP() ^ (~(0xffffffff ^ (1L << 32 - getMaskLength()) - 1));
IPv4Address broadcast = new IPv4Address(bits);
return broadcast;
}
Here decimalIP is the number representing IP address, getMaskLength - number representing its mask. Here I got expected broadcast address.
By in python using the same logic I got unexpected results:
def broadcastaddress(self):
return IPv4Address(self.address.decimalip ^ (~(0xffffffff ^ (1 << 32 - self.mask) - 1)))
Here all components represent the same entries as in java. After debugging I got that number (~(0xffffffff ^ (1 << 32 - self.mask) - 1)) is negative. In documents operator ~ gives inversion in bits but I don't understand why this number is negative in Python and not in Java?
A: Python integers are not bounded and are not signed, so ~ creates a negative number:
>>> hex(~(0xffffffff ^ (1 << 32 - 24) - 1))
'-0xffffff01'
>>> ~(0xffffffff ^ (1 << 32 - 24) - 1)
-4294967041
However, ~ in Java would give you the two's complement, while the operation on the subnet mask requires a one's complement, which can be achieved by using XOR on the netmask. Since that'd undo the other XOR operation you already applied, you don't need to use the 1's complement here at all:
return IPv4Address(self.address.decimalip ^ ((1 << 32 - self.mask) - 1))
I suspect that you could just use IPv4Network.broadcast_address here:
network = IPv4Network('{}/{}'.format(self.address.decimalip, self.mask)
return network.broadcast_address`
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\section{The Peak Patch Picture and the Cosmic Web Theory of Filaments}
We approach the connected ideas we loosely call Cosmic Web theory
(Bond, Kofman and Pogosyan 1996, BKP) and the Peak Patch Picture (Bond
and Myers 1996, BM, refer here for pre-1995 work) through a historical path
that includes an outline of the relevant terminology. In 1965, Lin,
Mestel \& Shu showed that a cold triaxial collapse implied an oblate
``pancake'' would form. In 1970, Zeldovich developed his famous
approximation and argued that pancakes would be the first structures
that would form in the adiabatic baryon-dominated universes popular at
that time. Generally for a cold medium, there is a full non-linear
map: ${\bf x} ({\bf r} , t) \equiv {\bf r}-{\bf s} ({\bf r} , t)$,
from Lagrangian (initial state) space, ${\bf r}$, to Eulerian (final
state) space, ${\bf x}$. The map becomes multivalued as nonlinearity
develops in the medium. It is conceptually useful to split the
displacement field, ${\bf s} = {\bf s}_b + {\bf s}_f$, into a smooth
quasilinear long wavelength piece ${\bf s}_b$ and a residual highly
nonlinear fluctuating field ${\bf s}_f$. If the {\it rms} density
fluctuations smoothed on scale $R_b$, $\sigma_\rho (R_b)$, are $<
{\cal O}(1/2)$, the ${\bf s}_b$-map is one-to-one (single-stream)
except at the rarest high density spots. In the peak patch approach,
$R_b$ is adaptive, allowing for dynamically hot regions like
protoclusters to have large smoothing and cool regions like voids to
have small smoothing. If $D(t)$ is the linear growth factor, then
${\bf s}_b =D(t) {\bf s}_b ({\bf r} ,0 )$ describes Lagrangian linear
perturbation theory, {\it i.e.} the Zeldovich approximation. The large
scale peculiar velocity is ${\bf V}_{Pb} = -\bar{a}(t) \dot{{\bf
s}}_b({\bf r}, t)$. What is important for us is the strain field (or
deformation tensor): { \small
\begin{eqnarray}
&& e_{b,ij} ({\bf r})\equiv - {1\over 2} \big({\partial s_{bi} \over
\partial r_j}+ {\partial s_{bj} \over \partial r_i}\big) ({\bf r} ) =
-\sum_{A=1}^3 \lambda_{vA} {\hat n}_{vA}^{i} {\hat n}_{vA}^{j},{\rm~where}\nonumber
\label{eq:eb}\\ && \
\lambda_{v3}={\delta_{Lb}\over 3}(1+3 e_v + p_v),\
\lambda_{v2}={\delta_{Lb}\over 3}(1-2 p_v),\
\lambda_{v1}={\delta_{Lb}\over 3}(1+3 e_v - p_v), \nonumber
\end{eqnarray}}and $\delta_{Lb}=-e_{b,i}^i$ is the smoothed linear
overdensity, which we often express in terms of the height relative to
the {\it rms} fluctuation level $\sigma_\rho (R_b)$, $\nu_b \equiv
\delta_{Lb}/\sigma_\rho (R_b)$. The deformation eigenvalues are
ordered according to $\lambda_{v3}\ge \lambda_{v2} \ge \lambda_{v1}$
and ${\hat n}_{vA}$ denote the unit vectors of the principal axes. In
that system, $x_A=r_A (1-\lambda_{vA} ({\bf r} , t))$ describes the
local evolution. The Zeldovich-mapped overdensity is $
(1+\delta_Z)({\bf r} ,t )= \vert {(1-D(t)\lambda_{v3}
)(1-D(t)\lambda_{v2} )(1-D(t)\lambda_{v1})}\vert^{-1}$, exploding when
the largest eigenvalue $D(t)\lambda_{v3}$ reaches unity (fold caustic
formation). In a Zeldovich map a pancake developes along the surface
${\hat n}_{v3} \cdot \nabla_{{\bf r}} \lambda_{v3} =0$.
The strain tensor is related to the peculiar linear tidal tensor by
${\partial^2 \Phi_P \over \partial x^i \partial x^j} = - 4\pi G {\bar
\rho}_{nr}\bar{a}^2\, e_{b,ij}$, where $\Phi_P$ = peculiar
gravitational potential, and to the linear shear tensor by ${\dot
e}_{b, ij}$. The anisotropic
part of the shear tensor has two independent parameters, the
ellipticity $e_v$ (always positive) and the prolaticity $p_v$.
Doroshkevich (1973) and later Doroshkevich \& Shandarin (1978) were
among the first to apply the statistics of Gaussian random fields to
cosmology, in particular of $\lambda_{vA}$, at random points in the
medium. Arnold, Shandarin and Zeldovich (1982) made the important step
of applying the catastrophe theory of caustics to structure
formation. This work suggested the following formation sequence:
pancakes first, followed by filaments and then clusters. This should
be compared to the BKP Web picture formation sequence: clusters first,
followed by filaments and then walls. BKP also showed that filaments
are really ribbons, walls are webbing between filaments in cluster
complexes, and that walls are not really classical pancakes. For the
Universe at $z\sim 3$, massive galaxies play the role of clusters, and
for the Universe at $z\sim 5$ more modest dwarf galaxies take on that
role.
The Web story relies heavily upon the theory of Gaussian random fields
as applied to the rare ``events'' in the medium, {\it e.g.}, high density
peaks. Salient steps in this development begin with Bardeen {\it et
al.} (1986, BBKS), where the statistics of peaks were applied to
clusters and galaxies, {\it e.g., } the calculation of the peak-peak
correlation function, $\xi_{pk,pk}$. In a series of papers, Bond
(1986-90) and Bond \& Myers (1990-93) developed the theory so that it
could calculate the mass function, $n(M)dM$. It was also applied to
the study of how shear affects cluster alignments ({\it e.g., } the
Binggeli effect), and to Ly$\alpha$ clouds, `Great Attractors', giant
`cluster-patches', galaxy, group and cluster distributions, dusty PGs,
CMB maps and quasars. This culminated in the BM ``Peak-Patch Picture
of Cosmic Catalogues''.
We briefly describe the BM peak patch method and how it is applied to
initial conditions for simulations; an example is shown in
Fig.~\ref{dotplot}. We identify candidate peak points using a
hierarchy of smoothing operations on the linear density field
$\delta_{L}$. To determine patch size and mass we use an ellipsoid
model for the internal patch dynamics, which are very sensitive to the
external tidal field. A byproduct is the internal (binding) energy of
the patch and the orientation of the principal axes of the tidal
tensor. We apply an exclusion algorithm to prevent peak-patch
overlap. For the external dynamics of the patch, we use a
Zeldovich-map with a locally adaptive filter ($R_{pk}$) to find the
velocity ${\bf V}_{pk}$ (with quadratic corrections sometimes
needed). The peaks are rank-ordered by mass (or internal
energy). Thus, for any given region, we have a list of the most
important peaks. By using the negative of the density field, we can
also get void-patches. Some of the virtues of the method are: it
represents a natural generalization of the Press-Schechter method to
include non-local effects;\footnote{The hugely popular,
trivial-to-implement, Press-Schechter (1976) method for determining
$n(M)$ has been the principal competitor to the peaks theory over the
years, but it has no real physical basis and disagrees strongly with
the spatial distribution (Bond {\it et.al.} 1991); thus the amazement,
and delight, in the community that $n(M)$ fits that of $N$-body group
catalogues so well.} is a natural generalization of BBKS
single-filter peaks theory to allow a mass spectrum and solve the
cloud-in-cloud ({\it i.e.}, peak-in-peak) problem; allows efficient
Monte Carlo constructions of 3D catalogues; gives very good agreement
with $N$-body groups; has an accurate analytic theory with which to
estimate peak properties, ({\it e.g., } mass and binding energy from
mean-profiles, using $\delta_{L,crit}(e_v)$, $\langle{e_v \vert
\nu_{pk}\rangle}$); and handles merging, with high redshift peaks
being absorbed into low redshift ones.
BKP concentrated on the impact the peak-patches would have on their
environment and how this can be used to understand the web. They
showed that the final-state filament-dominated web is present in the
initial conditions in the $\delta_{Lb}$ pattern, a pattern
largely determined by the position and primordial tidal fields of
rare events. BKP also showed how 2-point rare-event constraints define
filament sizes (see their Fig. 2). The strongest filaments are
between close peaks whose tidal tensors are nearly aligned. Strong
filaments extend only over a few Lagrangian radii of the peaks they
connect. They are so visually impressive in Eulerian space because the
peaks have collapsed by about 5 in radius, leaving the long bridge
between them, whose transverse dimensions have also decreased. This is
illustrated by the lower right panel of Fig.~\ref{dotplot} in which
the aligned galaxy peaks are connected by strong filaments. Strong
vertical filaments are a product of the vertical alignment of the
peaks' tidal tensors, which simultaneously acts to prevent a strong
horizontal filament between the top two peaks. The reason for this
phenomenon is that the high degree of constructive interference of the
density waves required to make the rare peak-patches, and to
preferentially orient them along the 1-axis, leads to a slower
decoherence along the 1-axis than along the others, and thus a higher
density. 3-point and higher rare-event constraints of nearby peaks
determine the nature of the webbing between the filaments, also
evident in Fig.~\ref{dotplot}.
\begin{figure}
\centerline{
\epsfxsize=2.5in\epsfbox{galpksz5Ppullback.ps}
\hspace{0.0in}
\epsfxsize=2.5in\epsfbox{lyapksz5D+Pr026350.ps}}
\vspace{0.0in}
\centerline{
\epsfxsize=2.5in\epsfbox{galpksz5D+P.ps}
\hspace{0.0in}
\epsfxsize=2.5in\epsfbox{lyapksz5D+P.ps}}
\caption{\small These plots show the reconstruction of a galaxy-galaxy
filament present in our 40\,Mpc ``galaxy'' simulation. The cosmology
is a standard initially scale-invariant $\Omega_{nr}$=1 CDM model with
$\Omega_{B}$=0.05, ${\rm h}$=0.5, normalized to $\sigma_8$=0.67. We
use the cosmological SPH+P$^3$MultiGrid code described in WB. We
identified the peak-patches that should collapse by $z=4$ in the
initial conditions (IC), as shown in the top left panel (which is
10\,$h^{-1}$Mpc across, comoving). For each patch, the outer ellipsoid
represents the alignment of the shear tensor and the inner sphere is
an estimate of the final object size. In the lower left panel, we zoom
in on the central filamentary web structure and overlay dark matter
from a simulation of these IC (panel 2.5\,$h^{-1}$Mpc across). The
five peak patches (at $z=4$ with overdensity 180) and two voids that
define this region were used as constraints for a new higher
resolution IC (12.8\,Mpc), which we also evolved numerically. These
peaks are shown overlaid with dark matter from the new simulation in
the right hand panels. The top right panel is a different orientation
to the others that shows the filament more clearly, also shown in
$n_{HI}$ in Fig.~2. These panels demonstrate that peaks represent an
excellent way to compress the essential information about large scale
filamentary behaviour. }
\label{dotplot}
\end{figure}
\section{Crafting High Resolution $N$-body/Hydrodynamical Simulations}
Although it is usual to evolve ambient ``random'' patches of the
Universe in cosmology, there are obvious advantages in spending one's
computational effort on the regions of most interest. Single peak
constraints are very useful if cluster or galaxy formation is the
focus, while multiple peak constraints are more useful if
superclusters, or cluster substructure, or filaments and walls are the
focus. We have seen that the essential features at a given epoch of
the filamentary structure and the wall-like webbing between the
filaments is largely defined by the dominant collapsed structures, and
the peak patches that gave rise to them. A general method for building
peak environments is suggested: construct random field initial
conditions that require the field to have prescribed values of the
peak shear (smoothed over the peak size at the peak position), for a
subset from the size-ordered list of peaks that will have a strong
impact on the patch to be simulated. Only a handful $N_{pk}$ of peaks
and/or voids is usually needed to determine the large scale features,
effectively compressing the information needed to $(3+1+6)N_{pk}$
numbers (${\bf r}_{pk}, M_{pk}, e_{pk,ij}$); peak velocities and the
peak constraint are also usually added but these are not as important.
To illustrate how this works, we created a random (unconstrained)
initial state for a CDM model in a 40\,Mpc box, our ``galaxy''
simulation. We found peak patches according to the method described in
BM and focussed on a specific subregion exhibiting a strong filament,
choosing the peaks and voids that were expected to exert strong tidal
influences within and upon the patch, as described in
Fig.~\ref{dotplot}. The region chosen was just above the large central
cluster of peaks in the top left panel of Fig.~\ref{dotplot}. We
constructed a higher resolution set of ``Ly$\alpha$ cloud'' initial
conditions for this patch, which the ``galaxy'' initial condition
simulation could not resolve well enough to address the low column
depth Ly$\alpha$ forest of interest to us.
By compressing the initial data in our target region to just the
positions and shears of a few large peak patches, then forming a
constrained realization and applying different random waves
(optimally-sampled for the smaller region) than the original $40 Mpc$
initial condition used, we know we will get high frequency structure
wrong. But clearly the large scale features are the same. This is in
spite of the tremendously complex filamentary structure just below our
chosen sub-region. The peaks we chose were on the basis of rareness
(size) and proximity to the patch (using an algorithm roughly based on
correlation function falloff from each peak). The five peak-patches
used for this companion Ly$\alpha$ simulation had the following masses
(in units of $10^{11}{\rm\,M_\odot}$) and halo velocity dispersion (in
units of $km\,s^{-1}$) as determined from the binding energy: $3.6,
77$; $3.5, 80$; $1.4, 57$; $0.85,48$; $0.51, 40$. These accord well
with what our group finder finds in the simulation at this
redshift. The two void-patches used had Lagrangian masses of $2.4$ and
$0.72$, and were outside the high resolution interior. The
approximate alignments of the shear tensors for the peak patches
inside ensure that a strong filament exists. Fig.~\ref{ray} shows how
the filament looks in HI column density.
\begin{figure}
\epsfxsize=\hsize
\centerline{
\epsfxsize=5.0in\epsfbox{double.ps}}
\caption{ \small Left: A pseudo ray-traced rendering of the HI density
for a region at $z$=4 constrained by the complex pattern of
galaxy-scale peak and void shear-fields described in the text,
encoding the main large scale structure features, and which ensures
strong filamentary webbing arises in the patch. The colour scale codes
the temperature variation, with the darker shades in the centre of
objects representing high column cold gas. The region is
$2.5\,h^{-1}Mpc$ across, comoving, and corresponds to the top right
panel of fig.~1. Right: $n_{HI}$ for an ambient patch of the Universe
at $z$=3 with control parameter $\nu_b$=0, simulation as described in
WB. Note the filament dominance in both cases.}
\label{ray}
\end{figure}
To do such complex regions, the standard periodic box approach to
cosmological simulations is obviously not appropriate. Advantages of
focussed non-periodic simulations include: (1) good mass resolution,
allowing us to concentrate on the scale needed to adequately treat the
objects that form ({\it e.g.} dwarf galaxies,
$a_L=a_{Lattice,High\,Res}=100$\,kpc), and corresponding high
numerical resolution ($h_{sph,min}$, $h_{grav}$ $\sim 1$ {\rm\,kpc}),
can be achieved; (2) good $k$-space sampling is also possible. The
competing demands of $k$-space sampling and resolution are further
described in Fig.~\ref{probes}. Our method allows high resolution
without compromising our long wave coverage by going beyond grid based
FFTs, with a FastFT for high $k$ (which kicks out well before the
fundamental mode is reached) that is superseded by two direct FTs,
power-law then log $k$ sampling, with transitions among them
determined by minimizing the volume per mode in
$k$-space. Well-sampled $k$-space is especially important for
Ly$\alpha$ cloud and galaxy formation as opposed to cluster
formation because the density power spectrum for viable hierarchical
theories has nearly equal power per decade (approaching flatness in
Fig.~\ref{probes}): if just the FFT is used, as is often the case in
cosmology even for non-periodic calculations, because there is only
one fundamental $k$-mode along each box axis, the large scale
structure in the simulation will be poorly modelled, and this can also
have a deleterious effect on small scale structure.
There is no point adding long waves without maintaining accurate large
scale tides and shearing fields during the calculation. We achieve
this with a high resolution region of interest (grid spacing $a_L$,
$50^3$ sphere) that sits within a medium resolution region ($2\,a_L$,
$40^3$), in turn within a low resolution region ($4\,a_L$,
$32^3$). The influence of ultra long waves is included by measuring
the mean external tide acting on the low resolution region in the
initial conditions, adopting simple models for the ultra-long wave
dynamics based on that measurement ({\it e.g.} linear, Zeldovich, or
homogeneous ellipsoid, as in BM) and applying it as an ``external
force'' throughout the simulation. For this simulation, linear ultra
long wave dynamics were adequate.
\begin{figure}
\vspace{-.5in}
\centerline{\epsfxsize=5.in\epsfbox{halifax96pow.eps}}
\vspace{-.5in}
\caption{\small The two (linear) power spectra shown (scaled to
redshift 3) were used in the simulations here and in WB. The upper
curve at high $k$ is the standard untilted CDM model, but normalized
to cluster abundances, $\sigma_8=0.67$. The other has the same
cosmological age (13 Gyr) and $\Omega_B{\rm h}^2$ (0.0125) but
$H_0=70$ with $\Omega_\Lambda = 0.67$, slightly tilted to be
COBE-normalized ($n_s=0.94$). (Also shown is a COBE-normalized CDM
model, which misses the solid data point in the cluster-band
(constraint from $dn_{cl}/dT_X$).) The bands in comoving wavenumber
probed by various simulations are contrasted. Periodic simulations may
use the entire volume, but the $k$-space restriction to lie between
the fundamental mode (low-$k$ boundary line) and the Nyquist
wavenumber (high-$k$ boundary line) in the IC can severely curtail the
rare events in the medium that observations especially probe, and
prevents tidal distortions of the simulation volume. We use 3
$k$-space sampling procedures (FFT and two direct FTs) with the
boundaries defined by which has the smallest volume per $k$-mode. Even
though a $256^3$ Fourier transform was used, notice how early the
direct sampling takes over (with only 10000 modes). Using an FFT with
the very flat spectra in the dwarf galaxy (dG) band can give
misleading results. The 3 low-$k$ lines shown for our Ly$\alpha$ and
galaxy simulations correspond to the high, medium and low resolution
fundamental modes. We actually include modes in the entire hatched
region, with the tidal fields associated with the longer waves
included by a self-consistent uniform tide on the LR simulation
volume. $h_m$ denotes our best resolution. $a_{Lp}$ denotes the
physical (best) lattice spacing for the grid-based Eulerian hydro
codes of Cen and Zhang {\it et.al.} ($z=3$). $k$-space domains for two
large scale structure ($z=0$) simulations are also shown, a Klypin
$256^3$ $PM$ calculation and a Couchman ({\it hugh}) $128^3$ $P^3M$
simulation. }
\label{probes}
\end{figure}
In WB, instead of complex multipeak constraints for individual
regions, we use {\it importance sampling} of {\bf shearing patches}
(patches with the smoothed shear tensor $e_{b,ij}(0)$ prescribed at
the centre) to maximize the statistical information we can get from a
crafted set of relatively modest constrained-field SPH calculations,
defined by a set of control parameters, here the central $\nu_b$,
$e_v$, $p_v$ smoothed over a galactic-scale $R_b$. This allows us to
sample rare peak and void patches, difficult to sample even in large
box simulations, especially if FFTs are used. These are in addition to
patches with more typical {\it rms} density contrasts. We then
combine the results to get the frequency distribution of, say,
$N_{HI}$ for a random patch of the Universe using Bayes theorem, which
decomposes it into the frequency distribution for $N_{HI}$ for our
constrained patches given the control parameters, measured from the
simulations, and the known probability distribution of the control
parameters: schematically,
\noindent
{\small $P({{\tt random-patch}} ) = \int P( {\tt constr-patch} \vert
{\tt control} ) \ P({\it \tt control} ) \ d {\it \tt control-param}$}.
\noindent
Shearing patches with low $\vert \nu_b \vert $ $
{{\raisebox{-.7ex}{$<$}}\atop{\raisebox{+.2ex}{$\sim$}}} 2$ often have
relatively large shear ellipticity, $\langle e_v \, \vert \nu_b
\rangle \approx 0.54\vert \nu_b \vert^{-1}$, which can give strongly
asymmetric collapses for $\nu_b > 0$, amplifying the smaller scale
filamentary webbing by concentrating it in larger scale filaments or
walls (which depends upon $p_v$). Fig.~\ref{ray} shows that a
$\nu_b=0$ shearing patch has its $n_{HI}$ filaments more spread out
than the multipeak case we have described here, which is reminiscent
of, but even more concentrated than, a $\nu_b=1.4$ calculation shown
in WB.
Simulating a large number of controlled patches in parallel is a form
of adaptive refinement, of which there is much discussion in these
proceedings. In refined regions, the initial conditions are almost
never modified with higher frequency waves, so the Lagrangian ({\it
i.e.} mass) resolution remains fixed even though the Eulerian
resolution may be superb. (This is especially vexing for voids.) When
we refine a region by creating a high resolution realization with the
information contained in peak patches, we {\it optimally} resample
$k$-space to generate a new set of high frequency waves. It is clear
that the cosmological codes of the future will have to simultaneously
adapt in Eulerian and $k$ space, and the techniques explored here
offer a promising path towards this goal.
\acknowledgments
Support from the Canadian Institute for Advanced Research and NSERC is
gratefully acknowledged. We thank Lev Kofman, Steve Myers and Dmitry
Pogosyan for much fun peak-patch/web interaction.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,760 |
\section{Introduction}
Monocular 3D face reconstruction has been widely applied in many fields such as VR/AR applications (e.g., movies, sports, games), video editing, and virtual avatars. Reconstructing human faces from monocular RGB data is a well-explored field and most of the approaches can be categorized into optimization-based methods \cite{Blanz1999,booth2018large,ganfit} or regression-based methods \cite{zhu20153ddfa,feng2018joint,deng2020retinaface,deng2019accurate}.
For the optimization-based methods, a prior of face shape and appearance \cite{Blanz1999,booth2018large} is used. The pioneer work 3D Morphable Model (3DMM) \cite{Blanz1999} represents the face shape and appearance in a PCA-based compact space and the fitting is then based on the principle of analysis-by-synthesis. In \cite{booth2018large}, an in-the-wild texture model is employed to greatly simplify the fitting procedure without optimization on the illumination parameters. To model textures in high fidelity, GANFit \cite{ganfit} harnesses Generative Adversarial Networks (GANs) to train a very powerful generator of facial texture in UV space and constrains the latent parameter by state-of-the-art face recognition model~\cite{deng2019arcface,arcface,deng2021variational,an2022killing,zhu2021webface260m,zhu2022webface260m}. However, the iterative optimization in these methods is not efficient for real-time inference.
For the regression-based methods, a series of methods are based on synthetic renderings of human faces \cite{genova2018unsupervised,wood20223d} or 3DMM fitted data \cite{zhu20153ddfa} to perform a supervised training of a regressor that predicts the latent representation of a prior face model (e.g., 3DMM~\cite{tran2016regressing}, GCN~\cite{zhou2019dense}, CNN~\cite{tran2018nonlinear}) or 3D vertices in different representation formats~\cite{jackson2017large,gueler2017densereg,feng2018joint,deng2020retinaface}. Genova et al.~\cite{genova2018unsupervised} propose a 3DMM parameter regression technique that is based on synthetic renderings and Tran et al.~\cite{tran2016regressing} directly regress 3DMM parameters using a CNN trained on fitted 3DMM data. Zhu et al.~\cite{zhu20153ddfa} propose 3D Dense Face Alignment (3DDFA) by taking advantage of Projected Normalized Coordinate Code (PNCC). In \cite{zhou2019dense}, joint shape and texture auto-encoder using direct mesh convolutions is proposed based on Graph Convolutional Network (GCN).
In \cite{tran2018nonlinear}, CNN-based shape and texture decoders are trained on unwrapped UV space for non-linear 3D morphable face modelling. Jackson et al.~\cite{jackson2017large} propose a model-free approach that reconstructs a voxel-based representation of the human face. DenseReg~\cite{gueler2017densereg} regresses horizontal and vertical tessellation which is obtained by unwrapping the template shape and transferring it to the image domain.
PRN~\cite{feng2018joint} predicts a position map in the UV space of a template mesh. RetinaFace~\cite{deng2020retinaface} directly predicts projected vertices on the image plane within the face detector. Besides these supervised regression methods, there are also self-supervised regression approaches. Deng et al.~\cite{deng2019accurate} train a 3DMM parameter regressor based on photometric reconstruction loss with skin attention masks, a perception loss based on FaceNet~\cite{facenet}, and multi-image consistency losses. DECA~\cite{deca} robustly produces a UV displacement map from a low-dimensional latent representation.
Although the above studies have achieved good face reconstruction results, existing methods mainly use orthogonal projection to simplify the projection process of the face. When the face is close to the camera, the distortion caused by perspective projection can not be ignored \cite{kao2022single,zielonka2022towards}. Due to the use of orthogonal projection, existing methods can not well explain the facial distortion caused by perspective projection, leading to poor performance.
To this end, we propose a joint 3D mesh and 2D landmark regression method in this paper. Monocular 3D face reconstruction usually includes two tasks: 3D face geometric reconstruction and face pose estimation. However, we avoid explicit face pose estimation as in RetinaFace~\cite{deng2020retinaface} and DenseLandmark~\cite{wood20223d}. The insight behind this strategy is that the evaluation metric for face reconstruction is usually in the camera space and the regression error on 6DoF parameters will repeat to every vertex. Even though dense vertex or landmark regression seems redundant, the regression error of each point is individual. Most important, explicit pose parameter regression can result in drift-alignment problem \cite{chaudhuri2019joint}, which will make the 2D visualization of face reconstruction unsatisfying.
By contrast, the 6 Degrees of Freedom (6DoF) face pose can be easily estimated by the PnP solver based on our predicted 3D vertices and 2D landmarks.
To summarize, the main contributions of this work are:
\begin{itemize}
\item We propose a Joint Mesh and Landmark Regression (JMLR) method to reconstruct 3D face shape under perspective projection, and the 6DoF face pose can be further estimated by PnP.
\item The proposed JMLR achieves first place on the leader-board of the ECCV 2022 WCPA challenge.
\item The visualization results show that the proposed JMLR is robust under different identities, exaggerated expressions and extreme poses.
\end{itemize}
\section{Our Method}
\subsection{3D Face Geometric Reconstruction}
\begin{figure}[t]
\centering
\includegraphics[width=1.0\linewidth]{image/framework.png}
\caption{Straightforward solutions for perspective face reconstruction. (a) direct 3D vertices regression, (b) two-stream 3D vertices regression and 6DoF prediction, and (c) our proposed Joint Mesh and Landmark Regression (JMLR).}
\label{fig:mesh}
\vspace{-4mm}
\end{figure}
In Fig.~\ref{fig:mesh}, we show three straightforward solutions for perspective face reconstruction. The simplest solution as shown in Fig.~\ref{fig:mesh} (a) is to directly regress the 3D vertices and 6DoF (i.e., Euler angles and translation vector) from the original image (i.e., $800\times800$), however, the performance of this method is very limited as mentioned by the challenge organizer. Another improved solution as illustrated in Fig.~\ref{fig:mesh} (b) is that the face shape should be predicted from the local facial region while the 6DoF can be obtained from the global image. Therefore, the local facial region is cropped and resized into $256\times256$, and then this face patch is fed into the ResNet \cite{he2016deep} to predict the 1,220 vertices. To predict 6DOF information, the region outside the face is blackened and the original $800\times800$ image is then resized into $256\times256$ as the input of another ResNet.
In RetinaFace \cite{deng2020retinaface}, explicit pose estimation is avoided by direct mesh regression on the image plane as direct pose parameter regression can result in misalignment under challenging scenarios. However, RetinaFace only considered orthographic face reconstruction. In this paper, we slightly change the regression target of RetinaFace, but still employ the insight behind RetinaFace, that is, avoiding direct pose parameter regression. More specifically, we directly regress 3D facial mesh in the world space as well as projected 2D facial landmarks on the image plane as illustrated in Fig.~\ref{fig:mesh} (c).
For 3D facial mesh regression in the world space, we predict a fixed number of $N=1,220$ vertices ($ \mathbf{V} =[v_{x}^0, v_{y}^0, v_{z}^0; \cdots; v_{x}^{N-1}, v_{y}^{N-1}, v_{x}^{N-1}]$) on a pre-defined topological triangle context (i.e., 2,304 triangles). These corresponding vertices share the same semantic meaning across different faces. With the fixed triangle topology, every pixel on the face can be indexed by the barycentric coordinates and the triangle index, thus there exists a pixel-wise correspondence with the 3D face. In \cite{wood20223d}, 703 dense landmarks covering the entire head, including ears, eyes, and teeth, are proved to be effective and efficient to encode facial identity and subtle expressions for 3D face reconstruction. Therefore, 1K-level dense vertices/landmarks are a good balance between accuracy and efficiency for face reconstruction.
As each 3D face is represented by concatenating its $N$ vertex coordinates, we employ the following vertex loss to constrain the location of vertices:
\begin{eqnarray}\label{eq:verticsloss}
\mathcal{L}_{vert} {=} \frac{1}{N}\sum_{i=1}^{N} ||v_i(x,y,z)-v^{*}_i(x,y,z)||_{1},
\vspace{-4mm}
\end{eqnarray}
where $N=1,220$ is the number of vertices, $v$ is the prediction of our model and $v^{*}$ is the ground-truth.
By taking advantage of the 3D triangulation topology, we consider the edge length loss~\cite{deng2020retinaface}:
\begin{eqnarray}\label{eq:edgeloss}
\mathcal{L}_{edge} {=} \frac{1}{3M}\sum_{i=1}^{M} ||e_i-e^{*}_i||_{1},
\vspace{-4mm}
\end{eqnarray}
where $M=2,304$ is the number of triangles, $e$ is the edge length calculated from the prediction and $e^{*}$ is the edge length calculated from the ground truth. The edge graph is a fixed topology as shown in Fig.~\ref{fig:mesh} (c).
For projected 2D landmark regression, we also employ distance loss to constrain predicted landmarks close to the projected landmarks from ground-truth:
\begin{eqnarray}\label{eq:landloss}
\mathcal{L}_{land} {=} \frac{1}{N}\sum_{i=1}^{N} ||p_i(x,y)-p^{*}_i(x,y)||_{1},
\vspace{-4mm}
\end{eqnarray}
where $N=1,220$ is the number of vertices, $p$ is the prediction of our model and $p^{*}$ is the ground-truth generated by perspective projection.
By combining the vertex loss and the edge loss for 3D mesh regression and the landmark loss for 2D projected landmark regression, we define the following prospective face reconstruction loss:
\begin{eqnarray}\label{eq:totalloss}
\mathcal{L} {=} \mathcal{L}_{vert} + \lambda_0 \mathcal{L}_{edge} + \lambda_1 \mathcal{L}_{land},
\vspace{-4mm}
\end{eqnarray}
where $\lambda_0$ is set to $0.25$ and $\lambda_1$ is set to $2$ according to our experimental experience.
\subsection{6DoF Estimation}
Based on the predicted 3D vertices in the world space, projected 2D landmarks on the image plane, and the camera intrinsic parameters, we can easily employ the Perspective-n-Point (PnP) algorithm \cite{marchand2015pose} to compute the 6D facial pose parameters (i.e., the rotation of roll, pitch, and yaw as well as the 3D translation of the camera with respect to the world).
Even though directly regressing 6DoF pose parameters from a single image by CNN (Fig.~\ref{fig:mesh} (a)) is also feasible, it achieves much worse performance than our
method due to the non-linearity of the rotation space.
In perspective projection, 3D face shape $V_{world}$ is transformed from the world coordinate system to the camera coordinate system by using 6DoF face pose (i.e., the rotation matrix $R\in \mathbb{R}^{3\times3}$ and the translation vector $T\in \mathbb{R}^{1\times3}$) with known intrinsic camera parameters $K$,
\begin{eqnarray}\label{eq:pnp}
V_{camera} = K (V_{world}R+T),
\vspace{-4mm}
\end{eqnarray}
where $K$ is related to (1) the coordinates of the principal point (the intersection of the optical axes with the image plane) and (2) the ratio between the focal length and the size of the pixel. The intrinsic parameters $K$ can be easily obtained through an
off-line calibration step. Knowing 2D-3D point correspondences as well as the intrinsic parameters, pose estimation is straightforward by calling \emph{cv.solvePnP().}
\section{Experimental Results}
\subsection{Dataset}
In the perspective face reconstruction challenge,
250 volunteers were invited to record the training and test dataset. These volunteers sit in a random environment, and the 3D acquisition equipment (i.e., iPhone 11) is fixed in front of them, with a distance ranging from about 0.3 to 0.9 meters. Each subject is asked to perform 33 specific expressions with two head movements (from looking left to looking right / from looking up to looking down). The triangle mesh and head pose information of the RGB image is obtained by the built-in ARKit toolbox. Then, the original data are pre-processed to unify the image size and camera intrinsic, as well as eliminate the shifting of the principal point of the camera.
In this challenge, 200 subjects with 356,640 instances are used as the training set, and 50 subjects with 90,545 instances are used as the test set. Note that there is only one face in each image and the location of each face is provided by the face-alignment toolkit \cite{bulat2017far}.
The ground truth of 3D vertices and pose transform matrix of the training set is provided. The unit of 3D ground-truth is in meters. The facial triangle mesh is made up of 1,220 vertices and 2,304 triangles. The indices of 68 landmarks \cite{deng2019menpo} from 1,220 vertices are also provided.
\subsection{Evaluation Metrics}
For each test image, the challenger should predict the 1,220 3D vertices in world space (i.e., $V_{world}\in \mathbb{R}^{1220\times3}$) and the pose transform matrix (i.e., the rotation matrix $R\in \mathbb{R}^{3\times3}$ and the translation vector $T\in \mathbb{R}^{1\times3}$) from world space to camera space.
$V_{world}=
\begin{bmatrix}
v_x^0 & v_y^0 & v_z^0 \\
v_x^1 & v_y^1 & v_z^1 \\
\vdots & \vdots & \vdots \\
v_x^{1219} & v_y^{1219} & v_z^{1219}
\end{bmatrix}$,
$R=\begin{bmatrix}
r_{00} & r_{01} & r_{02} \\
r_{10} & r_{11} & r_{12} \\
r_{20} & r_{21} & r_{22}
\end{bmatrix}$,
$T = \begin{bmatrix}
t_x & t_y & t_z
\end{bmatrix}$.
Then, we can compute the transformed vertices in camera space by $V_{camera} = V_{world}R+T$.
In this challenge, the error of 3D vertices and face pose is measured in camera space. Four transformed sets of vertices are computed as follows:
\begin{flalign}
V_1 & = V^{gt}R^{gt}+T^{gt},
V_2 = V^{pred}R^{pred}+T^{pred},\\ \nonumber
V_3 & = V^{gt}R^{pred}+T^{pred},
V_4 = V^{pred}R^{gt}+T^{gt}.
\end{flalign}
Finally, $L_2$ distance between pair $(V_1, V_2), (V_1, V_3), (V_1, V_4)$ are calculated and combined into the final distance error:
\begin{equation}
L_{error}=\left \|V_1-V_2 \right \|_2 +\left \|V_1-V_3 \right \|_2 + 10 \left \|V_1-V_4 \right \|_2,
\end{equation}
where geometry accuracy across different identities and expressions is emphasized by $\times 10$.
On the challenge leader-board, the distance error is multiplied by 1,000, thus the distance error is in millimeters instead of meters.
\subsection{Implementation Details}
\noindent{\bf Input.} We employ five facial landmarks predicted by RetinaFace \cite{deng2020retinaface} for normalized face cropping at the resolution of $256 \times 256$. Colour jitter and flip data augmentation are also used during our training.
\begin{figure}
\centering
\subfigure[ResNet 34]{
\label{fig:backbonebasline}
\includegraphics[height=0.3\textwidth]{figure/WCPAR34Baseline.pdf}}
\subfigure[Searched ResNet]{
\label{fig:searchedresnet}
\includegraphics[height=0.3\textwidth]{figure/WCPAR34.pdf}}
\vspace{-2mm}
\caption{Computation redistribution for the backbone. (a) the default ResNet-34 design. (b) our searched ResNet structure for perspective face reconstruction.}
\vspace{-4mm}
\label{fig:backbone}
\end{figure}
\noindent{\bf Backbone.} We employ the ResNet \cite{he2016deep} as our backbone. In addition, we refer to SCRFD \cite{guo2021sample} to optimize the computation distribution over the backbone. For the ResNet design, there are four stages (i.e., C2, C3, C4 and C5) operating at progressively reduced resolution, with each stage consisting of a sequence of identical blocks. For each stage $i$, the degrees of freedom include the number of blocks $d_i$ (i.e., network depth) and the block width $w_i$ (i.e, number of channels). Therefore, the backbone search space has 8 degrees of freedom as there are 4 stages and each stage $i$ has 2 parameters: the number of blocks $d_i$ and block width $w_i$. Following RegNet \cite{radosavovic2020designing}, we perform uniform sampling of $d_i\leq 24$ and $w_i\leq 512$ ($w_i$ is divisible by 8). As state-of-the-art backbones have increasing widths, we also constrain the search space, according to the principle of $w_{i+1}\ge w_i$. The searched ResNet structure for perspective face reconstruction is illustrated in Fig~\ref{fig:searchedresnet}.
\noindent{\bf Loss optimization.} We train the proposed joint mesh and landmark regression method for 40 epochs with the SGD optimizer. We set the learning rate as $0.1$ and the batch size is set to $64\times 8$. The training is warmed up by 1,000 steps and then the Poly learning scheduler is used.
\subsection{Ablation Study}
In Table~\ref{table_ablationstudy}, we run several experiments to validate the effectiveness of the proposed augmentation, network structure, and loss. We split the training data into 80\% subjects for training and 20\% subjects for validation. From Table~\ref{table_ablationstudy}, we have the following observations: (1) flipping augmentation can decrease the reconstruction error by 0.45 as we check experiments 1 and 2, (2) the capacity of ResNet-34 is well matched to the dataset as we compare the performance between different network structures (e.g., ResNet-18, ResNet-34, and ResNet-50), (3) searched ResNet with similar computation cost as ResNet-34 can slightly decrease the reconstruction error by 0.18, (4) without the topology regularization by the proposed edge loss, the reconstruction error increase by 0.29, confirming the effectiveness of mesh regression proposed in RetinaFace \cite{deng2020retinaface}, (5) by the model ensemble, the reconstruction error significantly reduces by 0.92.
\begin{table}[t]
\centering
\caption{Ablation study regarding augmentation, network structure, and loss. The results are reported on 40 subjects from the training set and the rest 160 subjects are used for training.} \label{table_ablationstudy}
\begin{tabular}{|c|c|c|c|c|}
\hline
Aug& Network & Loss & Flops & Score \\
\hline
Flip & ResNet34 & $\mathcal{L}$ & 5.12G & 34.31 \\
No Flip & ResNet34 & $\mathcal{L}$ & 5.12G & 34.76 \\
Flip & ResNet18 & $\mathcal{L}$ & 3.42G & 34.95 \\
Flip & ResNet50 & $\mathcal{L}$ & 5.71G & 34.70 \\
Flip & Searched ResNet & $\mathcal{L}$ & 5.13G & 34.13 \\
Flip & ResNet34 & $\mathcal{L}_{vert}$+$\mathcal{L}_{land}$ & 5.12G & 34.60 \\
Flip & ResNet34 \& Searched ResNet & $\mathcal{L}$ & 10.25 G & 33.39 \\
\hline
\end{tabular}
\vspace{-2mm}
\end{table}
\subsection{Benchmark Results}
For the submission of the challenge, we employ all of the 200 training subjects and combine all the above-mentioned training tricks (e.g. flip augmentation, searched ResNet, joint mesh and landmark regression, and model ensemble). As shown in Table~\ref{table_benchmark}, we rank first on the challenge leader-board and our method outperforms the runner-up by 0.07.
\begin{table}[t]
\centering
\caption{Leaderboard results. The proposed JMLR achieves best overall score compared to other methods.} \label{table_benchmark}
\begin{tabular}{|l|c|c|c|c|c|}
\hline
Rank & Team & Score & $ \left \|V_1-V_2 \right \|_2$ & $\left \|V_1-V_3 \right \|_2$ & $10 \left \|V_1-V_4 \right \|_2$\\
\hline
1st (JMLR)& EldenRing &\textbf{32.811318} & \textbf{8.596190} & \textbf{8.662822} & 15.552306\\
2nd & faceavata & 32.884849 & 8.833569 & 8.876343 & \textbf{15.174936}\\
3rd & raccoon\&bird & 33.841992 & 8.880053 & 8.937624 & 16.024315\\
\hline
\end{tabular}
\vspace{-4mm}
\end{table}
\subsection{Result Visualization}
In this section, we display qualitative results for perspective face reconstruction on the test dataset. As we care about the accuracy of geometric face reconstruction and 6DoF estimation, we visualize the projected 3D vertices on the image space both in the formats of vertex mesh and rendered mesh. As shown in Fig.~\ref{img_id}, the proposed method shows accurate mesh regression results across 50 different test subjects (i.e., genders and ages). In Fig.~\ref{img_exp6159} and Fig.~\ref{img_exp239749}, we select two subjects under 33 different expressions. The proposed method demonstrates precise mesh regression results across different expressions (i.e., blinking and mouth opening). In Fig.~\ref{img_pose1}, Fig.~\ref{img_pose3}, and Fig.~\ref{img_pose4}, we show the mesh regression results under extreme poses (e.g., large yaw and pitch variations). The proposed method can easily handle profile cases as well as large pitch angles. From these visualization results, we can see that our method is effective under different identities, expressions and large poses.
\begin{figure}
\centering
\includegraphics[width=1.0\textwidth]{figure/id.jpg}
\caption{Predicted meshes on 50 test subjects. 68 landmarks are also indexed for better visualization. The proposed method shows stable and accurate mesh regression results across different subjects (i.e., genders and ages).}
\label{img_id}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=1.0\textwidth]{figure/6159exp.jpg}
\caption{Predicted meshes of ID-6159 under 33 different expressions. 68 landmarks are also indexed for better visualization. The proposed method shows stable and accurate mesh regression results across different expressions (i.e., blinking and mouth opening).}
\label{img_exp6159}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=1.0\textwidth]{figure/239749exp.jpg}
\caption{Predicted meshes of ID-239749 under 33 different expressions. 68 landmarks are also indexed for better visualization. The proposed method shows stable and accurate mesh regression results across different expressions (i.e., blinking and mouth opening).}
\label{img_exp239749}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=1.0\textwidth]{figure/pose1.jpg}
\caption{Predicted meshes of different identities under different poses. 68 landmarks are also indexed for better visualization. The proposed method shows stable and accurate mesh regression results across different facial poses (i.e., yaw and pitch).}
\label{img_pose1}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=1.0\textwidth]{figure/pose3.jpg}
\caption{Predicted meshes of different identities under different poses. 68 landmarks are also indexed for better visualization. The proposed method shows stable and accurate mesh regression results across different facial poses (i.e., yaw and pitch).}
\label{img_pose3}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=1.0\textwidth]{figure/pose4.jpg}
\caption{Predicted meshes of different identities under different poses. 68 landmarks are also indexed for better visualization. The proposed method shows stable and accurate mesh regression results across different facial poses (i.e., yaw and pitch).}
\label{img_pose4}
\end{figure}
\section{Conclusion}
In this paper, we explore 3D face reconstruction under perspective projection from a single RGB image. We implement a straightforward algorithm, in which joint face 3D mesh and 2D landmark regression are proposed for perspective 3D face reconstruction. We avoid explicit 6DoF prediction but employ a PnP solver for 6DoF face pose estimation given the predicted 3D vertices in the world space and predicted 2D landmarks on the image space. Both quantitative and qualitative experimental results demonstrate the effectiveness of our approach for perspective 3D face reconstruction and 6DoF pose estimation. Our submission to the ECCV 2022 WCPA challenge ranks first on the leader-board and the training code and pre-trained models are released to facilitate future research in this direction.
\clearpage
\bibliographystyle{splncs04}
| {
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Also known as The Bonnie Lass Of Fyvie, Peggy-O, Pretty Peggy.
The Bonnie Lass O' Fyvie has been added to 8 tune sets.
The Bonnie Lass O' Fyvie has been added to 25 tunebooks.
# Added by Red Menace 8 years ago .
I've submitted this because it's such a well-known Scottish tune and I think it ought to be on here, and because I really love playing it on the whistle. I play it lively with lots of snap. It also works as a march and is played by pipe bands.
This was hideously butchered by folkies in the 60s. If you've heard Bob Dylan or Simon & Garfunkel or the Grateful Dead singing Peggy-O, you haven't really heard this tune. They were playing an American variant, which sadly seemed to have all the life sucked out of it along with the syncopation.
yup, can't deny it, but this rendition from the chad mitchell trio was my first hearing of it, and it has stayed with me now for nearly fifty years. gotta say it still stirs, though i appreciate the dubliners' rougher sound. i certainly understand the story better in the mitchell trio's setting.
# Posted by 'tinamatt 6 years ago .
This was used as entrance music for legendary pro wrestler Rowdy Roddy Piper in the 80's and 90's in the WWF (as it was).
The version was what I guess you would call, 'strident', it was forceful and because of the character who used it, the tune usually meant, "oh, here we go, now it's all going to kick off…"
Interestingly, the version they used switched to Scotland The Brave mdi-tune. This is my earliest recollection of bagpipe music and still sends shivers down my spine when I hear the WWF-recorded version.
I will look for a link later and post here.
# Posted by dcef 5 years ago .
I think that's the most amazing link to a tune ever.
Doesn't seem to be the version with Scotland The Brave.
Lass of Fyvie - Strathspey???
I first head this played as a march by the Royal Scots Dragoon Guards Military Band & Pipes and Drums in front of Munich Town Hall in Summer 1979. They were introducced as being on both British and German Pop Charts with Amazing Grace.
On that day they did not play Amazing Grace, but they did play the Lass of Fyvie as a march.
I didn't know it could be a Strathspey!
It's not a strathspey, - [although it could be played as such ] - it's a march, but for various reasons explained elsewhere, there is no "march" category on this website. Consequently, marches are sometimes posted here under the "strathspey" category, and this is one instance.
It's the first tune I learned on the Highland Pipes.
# Posted by polkadown one year ago . | {
"redpajama_set_name": "RedPajamaC4"
} | 5,371 |
{"url":"https:\/\/zbmath.org\/?q=rf%3A1187531","text":"## Found 3 Documents (Results 1\u20133)\n\n100\nMathJax\n\n### Some relationships between the geometry of the tangent bundle and the geometry of the Riemannian base manifold. (English)Zbl\u00a01247.53034\n\nMSC:\u00a0 53C20 53B21 53A55\nFull Text:\n\n### Natural tensor fields of type $$(0,2)$$ on the tangent and cotangent bundles of a semi-Riemannian manifold. (English)Zbl\u00a01056.53043\n\nMSC:\u00a0 53C50 58A32\nFull Text:","date":"2022-05-17 02:24:09","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\": 0.2593785524368286, \"perplexity\": 1315.752471106809}, \"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-2022-21\/segments\/1652662515466.5\/warc\/CC-MAIN-20220516235937-20220517025937-00199.warc.gz\"}"} | null | null |
Q: Regex remove repeated characters from a string by javascript I have found a way to remove repeated characters from a string using regular expressions.
function RemoveDuplicates() {
var str = "aaabbbccc";
var filtered = str.replace(/[^\w\s]|(.)\1/gi, "");
alert(filtered);
}
Output: abc
this is working fine.
But if str = "aaabbbccccabbbbcccccc" then output is abcabc.
Is there any way to get only unique characters or remove all duplicates one?
Please let me know if there is any way.
A: A lookahead like "this, followed by something and this":
var str = "aaabbbccccabbbbcccccc";
console.log(str.replace(/(.)(?=.*\1)/g, "")); // "abc"
Note that this preserves the last occurrence of each character:
var str = "aabbccxccbbaa";
console.log(str.replace(/(.)(?=.*\1)/g, "")); // "xcba"
Without regexes, preserving order:
var str = "aabbccxccbbaa";
console.log(str.split("").filter(function(x, n, s) {
return s.indexOf(x) == n
}).join("")); // "abcx"
A: This is an old question, but in ES6 we can use Sets. The code looks like this:
var test = 'aaabbbcccaabbbcccaaaaaaaasa';
var result = Array.from(new Set(test)).join('');
console.log(result);
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Q: If you had one wish for SubSonic what would it be? I know this question seems subjective but it's really pretty simple. As a long term user, and part time contributor to SubSonic I'm interested in what the community thinks would be the single best way to improve it.
So what's your opinion, how would you make SubSonic even better? What one thing would make you more likely to use/recommend/evangelise/stop complaining about it?
As I said I know this is a bit subjective and may get closed but as SO is the main support forum for SubSonic I think this could be a useful way to solicit opinion and/or contributions.
To keep this from turning into a general discussion here's the rules:
*
*No omnibus wishes
*No duplicate wishes
*Up-vote those you agree with rather than re-posting them
A: Ability to run in MediumTrust out of the box
A: In all honesty the biggest thing thats lacking is solid documentation and HowTo's
Its got better but I think it needs a lot more.
A: Ability to automatically map collections of other objects, like Fluent NHibernate does.
A: When SubSonic throws an exception that isn't clear, I'd like to be able to use Google or some other mechanism to discover more information about how to keep my development effort moving forward. Right now it's too easy to get into a situation where you have to go spelunking into the SubSonic source code since SubSonic doesn't seem to be very proactive when the user goes off the "happy path".
This critique is hardly specific to SubSonic. Many (most?) software products suffer from this same problem. I have not really had this problem with NHibernate though, which is SubSonic's most clear competitor.
A: Faster and higher quality releases
A: Binary types for SimpleRepository (Images)
A: Left Outer Joins
A: Support more database-independent code generation...
What I mean by this is that it is truly a real pain if your application wants to talk to different databases (e.g. SQL Server and Oracle) and you want to only have one set of generated DAL objects. I would love it if you had the option of specifying that any SQL code that gets sent to the DB would be as compatible with most engines as possible, since right now if you generated your objects targeting SQL Server then all queries will be of the form:
SELECT [schema].[table_name] FROM ....
Sadly, this does not work in Oracle, so basically you're out of luck there.
Perhaps this isn't a huge concern for most of you, but I'm currently writing a commercial app that touts one of its main features as being able to run on various database engines just by changing its configuration and I chose SubSonic because I thought it could handle the job pretty easily, but I'm honestly having second thoughts now because of all the hoops I may have to jump through just to get this to work correctly under different environments.
A: Support MS Access ,Postgres and FireBird database :)....
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{"url":"https:\/\/www.rocketryforum.com\/threads\/what-is-everyone-using-for-a-gps.159172\/","text":"What is everyone using for a GPS?\n\nHelp Support The Rocketry Forum:\n\nMbuzz49\n\nNew Member\nHi all!!\nI am currently looking for a \"cheaper\" GPS system for my model rockets. I have seen plenty of \"cheap\" trackers on amazon however, they all require a monthly service fee which I want to stay clear from. The ones that don't have a service fee cost hundreds of dollars.. I am looking for one around $50 -$100 that has no monthly fees. Any suggestions??\nMy best - Buzz\n\nArsenal78\n\nWell-Known Member\nThere are things not to cheap out on and GPS is one of them. I've seen a lot of those cheap Amazon trackers fail. One of the best GPS systems on the market atm for rocketry is the Featherweight. It's small, compact, and the receiver links to your phone to give you directions. A good GPS system does cost a good bit of coin but it's worth it. Eggfinders are only good if you want to spend eternity trying to figure out which arrow does what on their analog screen (and being able to remember it).\n\nwatheyak\n\nBarnstormer\nTRF Supporter\nI definitely second the Featherweight tracker suggestion. I've used BigRedBee, Telemetrum, various beacons and the Featherweight is my favorite by far.\n\nIt does not meet your price requirements, unfortunately.\n\nrharshberger\n\nWell-Known Member\nThere are things not to cheap out on and GPS is one of them. I've seen a lot of those cheap Amazon trackers fail. One of the best GPS systems on the market atm for rocketry is the Featherweight. It's small, compact, and the receiver links to your phone to give you directions. A good GPS system does cost a good bit of coin but it's worth it. Eggfinders are only good if you want to spend eternity trying to figure out which arrow does what on their analog screen (and being able to remember it).\nNot true of Eggfinders, yes if you use the LCD only it has a learning curve, if you use the bluetooth and link it to a tablet or phone you can walk right up to the rocket. I have done it both ways, for the money the Eggfinder gets the job done, I have seen other more expensive units lose rockets too. The only thing about Eggtimer products is they are kits and you have to assemble them.\n\nMbuzz49\n\nNew Member\nThank you, looks like I will be looking into expanding my budget if it's that big of a difference! Many thanks again!\n\nVoyager1\n\nWell-Known Member\nTRF Supporter\nEggfinders are hard to beat for value if you\u2019re OK with a soldering iron. Featherweigh Tracker, Missile Works T3 and TeleMega are others that I use.\n\nHVArcas\n\nWell-Known Member\nIn my experience, high altitude \/ harsh terrain, TeleGPS is the best.\n\nAnd BRB is the worrrrrrrrrrst - by a mile (or if the BRB is measuring the distance, several miles)\n\nPhilip Tiberius D.\n\nOld Fashioned 2.5oz Rye\/H2O 8 drops Orange Bitters\nI used a cube from Sprint which worked as long as the area had cell coverage. Last time let me walk right up underneath it, dangling about 90 ft above me in the only, tallest, not climbable Sycamore tree around. I checked back for months until one time it was gone. Looked all around & Aura had my contact info. Lost JLCR & Alt3 as well. I have a yet untested MW-RRC3 Altimeter (came with Fusion). I\u2019m on the hook for a Eggtimer \u201cWhole Enchilada\u201d and looked seriously at Apogee\u2019s tracker (B-day in June), but think I'll go with Eggtimer.\n\nLast edited:\n\nksaves2\n\nUse what works for you. I suggest a dedicated system designed for Rocketry. I even bought an old used GPS setup for the ARTS II (used of course) that was one of the only unlicensed systems 15 years ago at close to a grand. Like an oversized EggFinder. The Ham Radio licensees had access to other trackers on the 2 meter and 70cm bands and I\u2019ve had great results with the Beeline products. Beeline APRS was the only thing out there when I started out 15 years ago and provided the impetus for me to get a General Ham license. The cost ratio was skewed toward amateur radio APRS back then. Plus any APRS tracking program can be used.\nI still fly the Beeline APRS with a Kenwood D74A APRS handitalkie interfaced into a Garmin 60CsX so I get a map in hand. Used a D72A in the beginning but the two used ones I had went out of spec and are not worth getting fixed. If a Ham wants a 2 meter tracker, the AP510 with one watt output (which can be cut to 500mW) is pretty cheap but needs a 3 or 4 inch nosecone to stuff it in and keep it away from the eBay.\nI jumped on board with the EggFinders and built a pile of Cris\u2019s products. Dorked a couple in the building process too. Have a TRS and LCD kit on 70cm I can\u2019t wait to build. Flown the 900Mhz one and it works nicely. Wished he did a 70cm Eggfinder.\nI suspect there may be a bit better packet recovery on 70cm\nHave come to the conclusion they and the other 900Mhz products, (got a Missleworks too) are mighty fine for finding rockets. Don\u2019t expect to get every single position packet as with the dynamic flight of a rocket leads to very challenging reception issues. I hacked Ham radio APRS software to track the flights on a live map as opposed to using GPS Rocket Locator so I can see and save all the position data in real time.\nDuring the \u201cupside\u201d and even past apogee one might not see anything coming in. After drogue and main deployment is when things settle down and positions start coming in. I try to blow the main as high up as the flying venue allows as that\u2019s when reception is at its best. Altitude will give more hang time and allow a drift pattern to be seen if using a live map. Of course it depends upon how high a main deployment a flying site can \u201chandle\u201d. For a totally sight unseen flight, having a drift pattern visualized on a map can be very helpful if one gets to the last known position of the rocket and nothing is seen nor received. Just proceed in the direction the drift pattern suggests and hopefully a signal will be picked up to lead one to the final resting place. Also look down. I had a core sample and the last known position took me to the fincan sticking out of the ground. Of course the tracker (Eggfinder) died in the process but the last position sent while up in the air was right underneath the resting place. Gotta get ready for work. I can talk about this stuff ad nauseum.\nKurt\n\nHVArcas\n\nWell-Known Member\nmaybe you should! great review\n\ncerving\n\nOwner, Eggtimer Rocketry\nTRF Supporter\n...Eggfinders are only good if you want to spend eternity trying to figure out which arrow does what on their analog screen (and being able to remember it).\nPM me with your suggestions on how to make the interface better... we're always open to suggestions.\n\nTobor\n\nTRF Supporter\nI used a cube from Sprint which worked as long as the area had cell coverage. Last time let me walk right up underneath it, dangling about 90 ft above me in the only, tallest, not climbable Sycamore tree around. I checked back for months until one time it was gone. Looked all around & Aura had my contact info. Lost JLCR & Alt3 as well. I have a yet untested MW-RRC3 Altimeter (came with Fusion). I\u2019m on the hook for a Eggtimer \u201cWhole Enchilada\u201d and looked seriously at Apogee\u2019s tracker (B-day in June), but think I'll go with Eggtimer.\nLast fall at QCRS, a guy had a brand new Apogee unit. About two blinks after launch the base unit lost the TX signal and never reacquired....\nThat lone event sets me against recommending Apogee's product.\n\nMy EggFinder (Rev. B4d) works very well.\n\nksaves2\n\nLast fall at QCRS, a guy had a brand new Apogee unit. About two blinks after launch the base unit lost the TX signal and never reacquired....\nThat lone event sets me against recommending Apogee's product.\n\nMy EggFinder (Rev. B4d) works very well.\nI would be suspicious about two things: 1. Lost battery power to the tracker. 2. Lousy antenna system and\/or flier did not do an adequate range test on the ground to see what the range was.\n\nI was guilty of number 2 myself and was lucky a visual was had of the L powered rocket under chute in descent and recovered nominally. I didn't do a range test and the metallic paint shielded the Rf from getting out of the rocket. Up close and on the pad, had a signal. After launch, lost it. I looked at the Apogee product out of curiosity as I have several GPS trackers already. I would have leaned more towards the Featherweight tracker because of the kudos I've read on it. Just get a used Apple phone\/device and good to go. One doesn't have to have a sim card installed in the phone to use. Also only $351.00 as opposed to the$415 of the apogee device. The apogee product tracker\/transmitter looks like an EggFinder clone anyways. Kurt\n\nBuckeye\n\nWell-Known Member\nTRF Supporter\nIn my experience, high altitude \/ harsh terrain, TeleGPS is the best.\n\nAnd BRB is the worrrrrrrrrrst - by a mile (or if the BRB is measuring the distance, several miles)\nIf you are getting errors measured in miles, then you are doing something wrong. Or, the unit is damaged in some way.\n\ncerving\n\nOwner, Eggtimer Rocketry\nTRF Supporter\nIf you are getting errors measured in miles, then you are doing something wrong. Or, the unit is damaged in some way.\nOr you're using the wrong units, i.e. DMS instead of Degrees-decimals. Check your navigation app... the units must match.\n\nPhilip Tiberius D.\n\nOld Fashioned 2.5oz Rye\/H2O 8 drops Orange Bitters\nI would be suspicious about two things: 1. Lost battery power to the tracker. 2. Lousy antenna system and\/or flier did not do an adequate range test on the ground to see what the range was.\n\nI was guilty of number 2 myself and was lucky a visual was had of the L powered rocket under chute in descent and recovered nominally. I didn't do a range test and the metallic paint shielded the Rf from getting out of the rocket. Up close and on the pad, had a signal. After launch, lost it. I looked at the Apogee product out of curiosity as I have several GPS trackers already. I would have leaned more towards the Featherweight tracker because of the kudos I've read on it. Just get a used Apple phone\/device and good to go. One doesn't have to have a sim card installed in the phone to use. Also only $351.00 as opposed to the$415 of the apogee device. The apogee product tracker\/transmitter looks like an EggFinder clone anyways. Kurt\nPicked up a Missile RTx for a SONG - so going to check that out. Still thinking about Egg Timer. I have a retired iPhone7 and older Samsung phone I can use. Now if I can just steer clear of 90 ft trees\n\nBuckeye\n\nWell-Known Member\nTRF Supporter\nOr you're using the wrong units, i.e. DMS instead of Degrees-decimals. Check your navigation app... the units must match.\nYes, user error.\n\nOne time, I punched in East longitude instead of West longitude and my rocket was thought to be in China.\n\nksaves2\n\nIf you are getting errors measured in miles, then you are doing something wrong. Or, the unit is damaged in some way.\nI agree, I\u2019ve had great performance of my BRB 70cm GPS trackers, low and higher powered. Like everything else, there is a learning curve on getting stuff to work.\n\nLike Cris says, one has to make sure the units match with the receiving APRS hardware or they will be off on a wild goose chase.\n\nI remember being at a launch and a fellow was doing some outta\u2019 sight flights and had a BRB 70cm band GPS tracker, a Kenwood D72A APRS handi-talkie and a handheld Garmin 60CsX mapping GPS. His plan was to input the last known position into the Garmin and walk to the rocket. Well you guessed it. He had the units wrong in the Garmin and was off on a wild goose chase. Found his rocket by chance after about an hour.\n\nAt that time, I was already flying the same system except I was using a Garmin 60Cs handheld mapping GPS. I didn\u2019t have my system there with me that day but the difference was I had a $20.00 serial interface cable that plugs into the round port of the Garmin 60Cs and goes to the Kenwood D72A and reads incoming positions live and paints them on the map. I told the fellow what he did wrong (he didn\u2019t realize it) and gave him some sources for the serial cable and told him by email how to set it up. He was a happy camper after that. Neat thing about this setup is one can have the altitude screen pulled up on the Kenwood and read off the GPS derived above ground level altitude and the rocket is being painted live on the map in the Garmin. You can see where this is headed. As long as one has a \u201cnavigator brain\u201d they know exactly where to look to see if they can catch a visual of the main chute event. Can\u2019t beat a good visual if it can be had! They can do the simple math and with a live altitude readout, can have their head pointed in the right direction to see if they can get the \u201cvisual\u201d. Sometimes with a small rocket that flies far and high, the main event is too small to be seen. There again though, with the live altitude readout (that other systems out there now also have) the descent rate slows quite a bit so they know their recovery was nominal even though they only saw the upside of the flight. GPS tracking gets addicting plus the recovery takes less time and one can go on and fly the next rocket. That\u2019s the big one. Saves time getting the rocket back and can burn more motor money! Kurt ksaves2 Lifetime Supporter TRF Lifetime Supporter Picked up a Missile RTx for a SONG - so going to check that out. Still thinking about Egg Timer. I have a retired iPhone7 and older Samsung phone I can use. Now if I can just steer clear of 90 ft trees Remember, Eggfinder you or someone else has to build. I don\u2019t believe the EF and MW products are compatible. i.e. each has its own receiver. (I have both) Fly your Missileworks first and see if you like it. If you want to go with a tunable system, consider the EggFinder with the LCD receiver. Put B\/T in the LCD receiver and you can port the NMEA packets to a mapping program. Most use GPS Rocket Locator even though it can be quirky at times. Believe me, I\u2019ve suffered through a lot of quirks!! I\u2019ve hacked the APRSIS32 Ham APRS program to read the incoming NMEA streams from the rocket and the base station position but didn\u2019t get the rocket position recovery I wanted to see. I suspected it was an internal communication problem with two instances of the program running at once. I thought of the remedy to fix that after I went on hiatus that is really simple. I get my base location where I\u2019m standing to paint just once on the map. Then I turn that datastream off. Let the rocket fly and avoid internal position collisions and turn on \u201cmy position\u201d once the rocket is down so I can paint my position relative to the rocket when its lying on the ground. Since the rocket isn\u2019t moving much, internal position loss isn\u2019t much of a problem since we are both moving slowly. Can\u2019t wait to try the new protocol out and see if it works. Incidentally, when I drive around in the car with both the Eggfinder GPS tracker, the LCD\/GPS receiver with B\/T along with a Windoze tablet running APRSIS32, the two positions hop-scotch together at the relatively slow driving speed and of course there aren\u2019t the vagaries of high speed flight and increasing range of a rocket launch. On a real rocket flight, I don\u2019t see as many positions recovered I\u2019d like to see but there is enough to recover. Yes I know what happens to a GPS at high speed. I have a couple of \u201ctracker dog\u201d rockets with nosecone mounted EggFinders I use for testing. Single deploy and use a chute release for pseudo dual deploy. Good gosh, I like those things. Kurt Nytrunner Pop lugs, not drugs TRF Supporter Missileworks T3 with the rocket locator app has been good to me as long as I secure the batteries properly and take a calm minute to get it paired HVArcas Well-Known Member Yes, user error. One time, I punched in East longitude instead of West longitude and my rocket was thought to be in China. it aint user error when it stops transmitting for an hour at a time, springing back into life well after the rocket was found visually we could have gotten a bad unit but in our experience its reliability is a fraction of that of other transmitters. dlb Sky Pyrate... TeleGPS. works like a champ, 7 Mile Max range so far. TeleBT receiver and arrow antenna. With a Android tablet, I can find them anywhere, even use Rssi for tracking assistance. ksaves2 Lifetime Supporter TRF Lifetime Supporter TeleGPS. works like a champ, 7 Mile Max range so far. TeleBT receiver and arrow antenna. With a Android tablet, I can find them anywhere, even use Rssi for tracking assistance. I have one I haven't flown yet but you're right. For a Ham band unit, it's small size is a plus and their software is really great. I've been impressed with my ground testing I've done with the unit. Kurt swatkat Down these mean skies, a kat must fly! T3 has been great for me. Only had to use it up to 10800 foot range, but worked flawlessly. swatkat Down these mean skies, a kat must fly! tiny too. fits in 38mm BT rockets. Attachments \u2022 64.1 KB Views: 23 \u2022 55.6 KB Views: 22 GlueckAuf Well-Known Member I have one of these, as well as one of its indentical cousin, the Trackimo. Yes, Tracki is a subscription-based service, but hold on...you can sign up for as little as one month at a time for$20. If you only need a tracker a few times a year, this is good fit. I'm very impressed by its accuracy and dependability. The best feature, in my view, is that if you cato, submerge, or tree your rocket irretrievably, you're out less than $40 Yes, it is dependent on the 3G GSM mobile phone network. So if you fly exclusively on the salt flats of Bonneville or deep into the Mojave Desert, this is probably not a viable solution. But for what most rocketeers need a tracker to deliver 99% of the time, it's a simple, economical solution. The identical (but with a different business model) Trackimo, on the other hand, has a steep admission price of nearly$200. The subscription price, though, can be as low as $5 per month for one year. But if you hang this one atop a 100-year-old Michigan oak tree, you're out the whole$200 plus the unused portion of your subscription.\n\nThe Tracki I just received and have not flown it yet. The identical Trackimo I have owned for over three years, and with very few exceptions, it has always delivered the landing spot of my rocket on my mobile phone via an elegant Google maps-based interface.\n\nOnly twice in three years has my rocket landed in a low spot on a field adjacent to our Michigan International Speedway range, and the Trackimo couldn't report its position. When I found the bird in the traditional way and lifted it out of a depression that prevented it from connecting to a cell phone tower, Trackimo immediately connected and reported its location like normal.\n\nTracki and Trackimo are a simple, economical, and reliable solution for basic tracking. And they work anywhere on the mobile-phone connected parts of the planet.\n\nGood skies,\n\nGlueck Auf\n\nWell-Known Member\nI don't know what service Tracki\/Trackimo use but AT&T has said that they'll fully decommission 3G by 2022. I imagine the other services wont be too far off that date.\n\nMotocrossman24\n\nWell-Known Member\nIv got to give a recommendation to the featherweight gps tracker...I haven\u2019t flown it yet in any of my rockets, but we flew it in my friends 4\u201d competitor to almost 15,000 feet, and it tracked the rocket all the way to apogee, speaking out altitude over iPhone the entire flight. And while we saw where the rocket landed, we still tracked it via gps and it got us within a foot of the rocket. It\u2019s a highly impressive system if you are an iOS user, has great features, and is incredibly easy to use, and small( I\u2019d assume you could easily fit it in a 29mm airframe. It\u2019s not the cheapest option, but is in a good price point compared to other offerings. Iv also seen the eggfinder gps units work well, and if you can solder smd components, or have someone who can, it\u2019s hard to beat eggtimer pricing. I\u2019m getting a hot air rework station soon to build some eggtimer altimeters and trackers, as with smaller builds, the eggfinder trs altimeter\/tracker combo is too nice to pass up.\n\nMotocrossman24\n\nWell-Known Member\nPM me with your suggestions on how to make the interface better... we're always open to suggestions.\nkind of off topic, but while your here, have you considered offering an accelerometer based flight controller with 2 or4 channels that has no WiFi? Iv been in the search for an accelerometer altimeter for a little while for my minimum diameter project, and was considering the proton, altho it\u2019s way more channels then I need, and with Tripoli\u2019s new WiFi rules, I personally don\u2019t feel like bothering with WiFi. The build is also likely above my current skill set also.\n\nJimJarvis50\n\nWell-Known Member\nIn my experience, high altitude \/ harsh terrain, TeleGPS is the best.\n\nAnd BRB is the worrrrrrrrrrst - by a mile (or if the BRB is measuring the distance, several miles)\nCertainly not my experience with BRB. I've had multiple flights with regular hits from over 30 miles.\n\nJim","date":"2021-03-04 13:24:33","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\": 0.30475690960884094, \"perplexity\": 3144.6403235381536}, \"config\": {\"markdown_headings\": false, \"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-2021-10\/segments\/1614178369054.89\/warc\/CC-MAIN-20210304113205-20210304143205-00534.warc.gz\"}"} | null | null |
Q: How to retrieve all attributes of an anytree Node? For an anytree Node, how can I get all the attributes and their values?
For example, if I do:
>>> from anytree import Node
>>> root = Node("root")
>>> s0 = Node("sub0", parent=root, foo="10", bar="ggg")
how can I get something like [("foo", "10"), ("bar", "ggg")]?
I can think of a route via the following:
>>> s1=Node("dummy", parent=root)
>>> set(dir(s0))-set(dir(s1))
{'foo', 'bar'}
but I hope there is a more concise way.
A: This is working in your case:
s0.__dict__.items()
However, beware that this method relies on the inner implementation of anytree (and it's always a bad idea to rely on a specific implementation). Also, the __dict__ attribute contains also the name, parent and (optionally) children (and you might want to get rid of these).
[(k, v) for k, v in s0.__dict__.items() if k not in ('name', 'parent', 'children')]
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,727 |
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</ul>
</div>
<h2 data-device-preview="../docs-demos/navbar-layout.html">Navbar layout</h2>
<p>Navbar layout is pretty simple and self explaining:</p>
<pre><code><div class="navbar">
<div class="navbar-inner">
<div class="left">Left</div>
<div class="center">Center</div>
<div class="right">Right</div>
</div>
</div></code></pre>
<div class="important-note">
<p>Note that Navbar's Center element has lowest width priority, and when window screen will not fit all three elements during window resize, then Center part will be cuted. </p>
</div>
<p>So if you use plain text in Center part it will have ellipsis (...) on the end when cuted. But you need to take care about it if you have some custom elements there.</p>
<h3 data-device-preview="../docs-demos/navbar-links.html">Navbar with links</h3>
<p>To add links in Left or Right part you just need to add the plain <code><a></code> tag with additional <code>link</code> class:</p>
<pre><code><div class="navbar">
<div class="navbar-inner">
<div class="left">
<a href="#" class="link">Left Link</a>
</div>
<div class="center">Center</div>
<div class="right">
<a href="#" class="link">Right Link</a>
</div>
</div>
</div> </code></pre>
<p>Additional <code>link</code> class is not required but recommended, because it adds required link sizes and "active" opacity effect</p>
<h3 data-device-preview="../docs-demos/navbar-multiple-links.html">Multiple links</h3>
<p>Nothing extraordinary. Just add more <code><a class="link"</code> to the required part:</p>
<pre><code><div class="navbar">
<div class="navbar-inner">
<div class="left">
<a href="#" class="link">Left 1</a>
<a href="#" class="link">Left 2</a>
</div>
<div class="center">Center</div>
<div class="right">
<a href="#" class="link">Right 1</a>
</div>
</div>
</div></code></pre>
<h3 data-device-preview="../docs-demos/navbar-links-icons.html">Links with icons + text</h3>
<p>Here comes a little difference. In this case we need to <strong>wrap link's text with</strong> <code><span></code> element. It is required for correct spacing between icon and "word", and for animation:</p>
<pre><code><div class="navbar">
<div class="navbar-inner">
<div class="left">
<a href="#" class="link">
<i class="icon icon-back"></i>
<span>Back</span>
</a>
</div>
<div class="center">Center</div>
<div class="right">
<a href="#" class="link">
<i class="icon icon-bars"></i>
<span>Menu</span>
</a>
</div>
</div>
</div></code></pre>
<h3 data-device-preview="../docs-demos/navbar-only-icons.html">Links with icons only</h3>
<p>If need links with icons and without text we need to additional <strong>"icon-only"</strong> class to links. With this class link will have fixed 44x44 px size so we can't miss it with finger:</p>
<pre><code><div class="navbar">
<div class="navbar-inner">
<div class="left">
<a href="#" class="link icon-only">
<i class="icon icon-back"></i>
</a>
</div>
<div class="center">Center</div>
<div class="right">
<a href="#" class="link icon-only">
<i class="icon icon-bars"></i>
</a>
</div>
</div>
</div> </code></pre>
<h2 data-device-preview="../docs-demos/navbar-hide.html">Related App and View methods</h2>
<p>If we have <a href="views.html">initialized View</a> we can use following methods available for Navbar:</p>
<table class="methods-table">
<tbody>
<tr>
<td>myApp.hideNavbar(<span>navbar</span>)</td>
<td>Hide specified toolbar.<br><code>navbar</code> - <span class="parameter-type">HTMLElement</span> or <span class="parameter-type">string</span> (with CSS Selector) of required navbar. Required.</td>
</tr>
<tr>
<td>myApp.showNavbar(<span>navbar</span>)</td>
<td>Show specified toolbar.<br><code>navbar</code> - <span class="parameter-type">HTMLElement</span> or <span class="parameter-type">string</span> (with CSS Selector) of required navbar. Required.</td>
</tr>
<tr>
<td>view.hideNavbar()</td>
<td>Hide navbar in this View</td>
</tr>
<tr>
<td>view.showNavbar()</td>
<td>Show navbar in this View</td>
</tr>
<tr>
<td>myApp.sizeNavbars(<span>viewContainer</span>)</td>
<td>
<p> <code>viewContainer</code> - CSS Selector <span class="parameter-type">string</span> or <span class="parameter-type">HTMLElement</span>. URL of page to load</p>
<p>Call this method to recalculate positional styles for Navbar in selected View. For example: <b>myApp.sizeNavbars('.view-main')</b></p>
<p>It could be useful after you change some of Navbar elements dynamically.</p>
<p><span class="ios-only">Used only by iOS theme</span></p>
</td>
</tr>
</tbody>
</table>
<p>And the following example:</p>
<pre><code>var myApp = new Framework7();
var $ = Framework7.$;
var mainView = myApp.addView('.view-main');
$('.hide-navbar').on('click', function () {
mainView.hideNavbar();
});
$('.show-navbar').on('click', function () {
mainView.showNavbar();
});</code></pre>
<h2 data-device-preview="../docs-demos/navbar-hide-auto.html">Hide Navbar automatically</h2>
<p>Framework7 allows you to hide/show navbar automatically for some Ajax loaded pages where you may not need Navbar. It is useful only when you use through-type layout.</p>
<p>To make it work all you need is to add <srong>"no-navbar"</srong> class to loaded page (<code><div class="page no-navbar"></code>) and put there empty Navbar:</p>
<pre><code><!-- Empty Navbar -->
<div class="navbar">
<div class="navbar-inner">
</div>
</div>
<!-- Page has additional "no-navbar" class -->
<div data-page="about" class="page no-navbar">
<div class="page-content">
<div class="content-block">
<p><a href="#" class="back button">Go Back</a></p>
...
</div>
</div>
</div></code></pre>
<div style="height:150px" class="device-spacer"></div>
<div class="full-width stop-scroll-device">
<h2>Dynamic Navbar Events</h2>
<p>If you use <a href="dynamic-navbar.html">Dynamic Navbar</a> in your app then it will also have useful <a href="dynamic-navbar.html#dynamic-navbar-events">special events</a>.</p>
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As more and more consumers make searching for discounts a part of their shopping routine either you or your competitor will reap the rewards for your one time effort. This new customer may not find you because you have a coupon or discount code but rather choose to finalize their purchase with your company because you offer a discount.
Just how big is this marketing opportunity? From 2007 to 2008 online coupon usage grew by more than 130%. The savings from online coupons reached more than $850 million for 2009, a 170% increase over 2008. If you have an e-commerce store or you are looking for walk in customers originating from the Internet, discount codes and coupons should be a part of your marketing mix.
The buying behavior of the customer who searches to find a store off-line might use the newspaper ads or the yellow pages for their search. A business will advertise and offer coupons in those advertising channels to attract the buyer to visit their store and make a purchase. The online shopper however takes an opposite approach. First the buyer searches to find what they want to purchase and then performs a second search to see if there is a discount available before they finalize their purchase or decision to visit a local store.
It's not very difficult for you to offer a discount. If you're a local business, Google Places is where you want to start. It's free and not only does it put you in Google maps but you can enter your business hours, add photos and video to your listing. You can also include a simple printable coupon. Google then makes it easy for the online searcher to find your business and your coupon.
Several web sites offer listings for discount codes. Tjoos.com has over 1,000,000 unique visitors per month. Add your website to their listings and online shoppers can enter that discount code into your online shopping cart.
To find other coupon factory type sites and list your discount codes, just search for "coupon discount codes" and visit the sites to see which are appropriate for you.
If you're not using a discount or coupon code you may want to make it part of your online marketing plan. Offering discount coupon codes can easily bring additional revenue for your business and help you to be found on the Web. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,966 |
{"url":"https:\/\/www.nature.com\/articles\/s41598-019-44765-4?error=cookies_not_supported&code=786edd88-8a38-471c-b2ef-933ce9d6b1e9","text":"## Introduction\n\nAmyotrophic lateral sclerosis (ALS) is a fatal neurodegenerative disease characterised by the rapidly progressive loss of the upper and lower motor neurons. Disease onset commonly occurs in middle to late age1 and typically results in death within three to five years. Existing treatments are of limited effect, and despite intensive effort, the pathogenic mechanisms underlying disease are still poorly understood. A recognised family history (familial ALS, FALS) is seen in approximately 10% of cases while the remainder are considered sporadic (SALS)2. The familial and sporadic forms of the disease are clinically and pathologically indistinguishable3. To date, the only proven cause of ALS are gene mutations leading to motor neuron death. Pathogenic repeat expansions in the C9orf72 gene and missense mutations in the SOD1 gene are the most frequent known causes of ALS worldwide, yet no cause has been identified for the majority of patients (>80%2). Even in those individuals with a proven causal gene mutation, inter- and intra-familial phenotypic heterogeneity is commonly observed1,4. Age of disease onset may vary by more than 60 years and disease duration may be measured in months or in decades. Affected individuals, particularly those with a C9orf72 repeat expansion, may present with ALS or frontotemporal dementia (FTD), or a mixed phenotype. Causal mutations may show incomplete penetrance4 and indeed monozygotic twins are more commonly discordant for ALS than concordant5. Taken together, this phenotypic variability suggests a significant contribution from modifying factors in disease manifestation.\n\nEpigenetic and transcriptional profiling have implicated differential DNA methylation and\/or gene expression in ALS. C9orf72 has been shown to have increased methylation6,7 and decreased transcription8,9 in ALS\/FTD patients with the pathogenic repeat expansion. Other major ALS genes, however, including SOD1, FUS and TARDBP, are generally unmethylated and show no differences between patients and controls10,11,12. Nevertheless, changes in expression of some ALS genes is apparent in sporadic disease13. Whole methylome and transcriptome studies in spinal cord and blood tissue have found global changes10,14,15 and implicated various genes, pathways and several overlapping themes including changes that affect immune response14,16,17 and cellular transport18,19.\n\nDisease discordant monozygotic (MZ) twins hold great potential for studies that seek to identify epigenetic and transcriptomic factors that modify the phenotype of complex human diseases. Identical twin studies can account for confounding factors such as genetic variation and the early development environment. Such studies have informed understanding of phenotypic variation in Parkinson\u2019s disease20, Alzheimer\u2019s disease21, systemic lupus erythematosus22, and depression23, among others. Previous DNA methylation studies of known causal ALS genes in ALS-discordant MZ twins found no aberrant methylation between twins24,25, while twin-based methylome-wide studies suggested a different epigenetic age in affected twins25,26 and identified potentially altered GABA signalling25 and immune response27. Nevertheless, further studies are required because the differentially methylated sites implicated in initial screens have often failed to be validated in targeted studies using bisulphite pyrosequencing26. Similarly, candidate molecular pathways have shown limited overlap between twin sets25 and changes in methylation are yet to be linked to changes in transcription. It remains unclear which of the observed differences in either DNA methylation or gene expression reflect ALS discordance between co-twins. It is also unclear whether these differences in DNA methylation correlate with differential gene expression on a transcriptome-wide scale.\n\nIn this study, we undertook comprehensive methylome- and transcriptome-wide analysis of a longitudinal ALS-discordant cohort comprising MZ triplets and twins, representing the three most common types of ALS: C9orf72-linked ALS, SOD1-linked ALS and sporadic ALS. We analysed methylome- and transcriptome-wide data, independently and in combination, in an attempt to identify disease-relevant methylation changes and their downstream impact. Co-twin analyses indicated a significant interaction effect between age and disease status on DNA methylation age, with older twins showing a consistent difference between ALS-affected and unaffected co-twins in a longitudinal series. Furthermore, we identified several genes likely to contribute to ALS through integration of longitudinal twin genome-wide DNA methylation and transcription data, further assessed in a large sporadic ALS case-control cohort.\n\n## Results\n\n### ALS-discordant and control twin\/triplet sets\n\nClinical and sample information for the three discordant MZ twin sets, one discordant MZ triplet set and two control twin sets are included in Table\u00a01. Pedigrees and extended pedigrees are shown in Fig.\u00a01. All individuals with ALS have been screened for causal mutations in known ALS genes. The FALS twin set has a pathogenic hexanucleotide repeat expansion in C9orf72. The FALS triplet set harbours a SOD1 p.I114T mutation.\n\n### Targeted analysis of methylation in mutation-known MZ sets\n\nTo assess whether differential methylation of the C9orf72 or SOD1 CpG islands were associated with the disease discordance we observe in the C9orf72 twin set and SOD1 triplets, we investigated the status of CpG methylation of the C9orf72 and SOD1 CpG islands. To perform a high-density, targeted analysis, we used EpiTYPER, with additional support from a number of Infinium HumanMethylation450K CpG sites present in the same region.\n\n#### SOD1 methylation in the SOD1 MZ triplet set shows a consistent methylation pattern\n\nWe used EpiTYPER to quantify methylation of the upstream SOD1 CpG island encompassing the SOD1 promoter region and exon 1 in the discordant MZ triplets carrying the SOD1 p.I114T mutation and a pair of control twins from another SOD1 p.I114T family that were negative for the SOD1 mutation. Additionally, five SOD1 CpG sites present in the Infinium HumanMethylation450K data set were located within the CpG island (Fig.\u00a02A). Neither the 23 CpG units within the CpG island, nor the five 450K SOD1 CpG sites, showed any consistent methylation differences between ALS affected and ALS unaffected MZ triplets, nor control twins (Fig.\u00a02A).\n\n#### No differences were observed in C9orf72 methylation in the C9orf72 MZ twin set\n\nThe quantitative methylation status of two CpG islands associated with C9orf72 was determined using EpiTYPER. The amplicons covered the entirety of both CpG islands, the promoter region and adjacent intronic\/intergenic regions. The intronic pathogenic (GGGGCC)n repeat expansion (indicated with a black diamond in Fig.\u00a02B) is flanked by the two CpG islands. In the disease discordant FALS twin set harbouring a C9orf72 expansion, methylation across the GpG island (CGI) measured by the EpiTYPER assay are highly concordant and generally unmethylated (Fig.\u00a02B). Similarly, in the four 450K probes associated with C9orf72, none of the CpG sites show a clear difference in methylation between the co-twins (Fig.\u00a02B).\n\n### Whole methylome analysis of disease discordant MZ twins\/triplets\n\n#### Co-twin\/triplet differences in DNA methylation age (DNAm) reflects an age-dependant effect\n\nHorvath\u2019s DNA methylation age algorithm28 used methylation levels of 353 CpG sites to predict the epigenetic age from each twin\/triplet sample in Table\u00a01. DNA methylation age has a high correlation with chronological age across multiple tissue types, thus enabling calculation of the biological age of an individual. We tested the association of methylation age with disease status and chronological age in a mixed model while controlling for sex. The effect of disease status on methylation age was found to be highly dependent upon chronological age (p\u2009=\u20091.3E-5, Fig.\u00a03A). Briefly, with increasing age, asymptomatic co-twins were estimated to have a younger epigenetic age than their ALS-affected twin. This result was most evident in the approximately 20-year difference in methylation age between twins in the oldest disease discordant twin set of this cohort (Fig.\u00a03A).\n\n#### Global methylation and cell type proportions do not show any effect of disease status\n\nGlobal methylation was calculated as the mean methylation across all Infinium HumanMethylation450K CpG sites passing data processing (n\u2009=\u2009386183). No significant effect of disease on global methylation was found when controlling for sex and age at sample collection (p\u2009=\u20090.08, Fig.\u00a03B). To better reflect influence on transcription, CpG sites were classified according to CpG density: high density CpG islands, intermediate density in islands, island shores, and low CpG density. Mean methylation within each of these four levels of CpG density does not show any effect of disease status (HC, p\u2009=\u20090.93; IC, p\u2009=\u20090.99; ICshore, p\u2009=\u20090.82; LC, p\u2009=\u20090.093, Supplementary Fig.\u00a0S2). Full blood count data were unavailable from twin\/triplet sets at time of sample collection. Therefore, blood cell proportions for each twin\/triplet sample were estimated from methylation data using Houseman et al.\u2019s algorithm29 and the six cell types were assessed for association with disease status. Disease status did not have a significant effect on any of the cell types when controlling for age at sample collection and sex (all p\u2009>\u20090.2, Fig.\u00a03C).\n\n#### Differentially methylated probes were identified across discordant MZ twins\/triplets\n\nThe established DNA methylation twin-study method of statistical significance and the magnitude of pairwise methylation differences were combined to detect differentially methylated probes in discordant MZ twin studies. 59 probes were identified as differentially methylated across twin\/triplet sets (full list in Supplementary Table\u00a0S5, 9 top-ranked probes shown in Fig.\u00a04A). All 59 probes were used for hierarchical clustering and principal components analysis (PCA) of the longitudinal MZ cohort to investigate the presence of a disease signature. Both hierarchical clustering and PCA did not indicate that samples cluster by disease status, but rather approximately by twin set and individual, where longitudinal samples were available (Fig.\u00a04B,C). The 59 probes were subsequently investigated in our large case-control 450K methylation extended data set (n\u2009=\u2009646 SALS cases and 533 unrelated controls). After FDR correction, 2 of the 59 probes showed significantly differential methylation between cases and controls when controlling for age and sex (RAD9B, cg00278366, p\u2009=\u20092.5E-5; C8orf46, cg15444185, p\u2009=\u20090.049, Fig.\u00a04D; full results for all 59 CpGs in Supplementary Table\u00a0S6). As observed in the MZ cohort, hierarchical clustering and PCA of this probe list in the case-control cohort does not indicate any power to discriminate between ALS and control samples (Fig.\u00a04E,F), nor sex or age group.\n\n#### Differentially methylated probes (DMPs) identified within discordant MZ twin\/triplet sets implicates new genes and existing ALS genes\n\nGiven the clinical heterogeneity in our twin\/triplet cohort, within-twin-set differential methylation was also investigated. Using a threshold of a difference in \u03b2-methylation \u22650.25 between co-twins or the affected triplet and the mean of the unaffected triplets, we identified 0 DMPs in female SALS twins, 6 in C9orf72 twins, 58 in SOD1 triplets, 2689 in male SALS, and 29 in control twins (Supplementary Fig.\u00a0S3A\u2013E). Up to 11 probes were annotated per gene in the male SALS twin list of DMPs, for a total of 1829 genes identified. The 506 genes to which multiple male SALS twin probes annotate are given in Supplementary Table\u00a0S7, which includes two genes previously associated with ALS, DPP6 (Dipeptidyl Peptidase Like 6) and RAMP3 (Receptor Activity Modifying Protein 3) (Fig.\u00a05A). No other discordant twin\/triplet set had multiple probes annotated to the same gene. Across all discordant twin\/triplet sets, 2 probes (Fig.\u00a05B) and 13 genes (BDKRB2, CHRD, DYSF, HOXD11, IRX4, ISL1, JOSD1, mir_44, NKX2-5, NXN, OTX1, POU4F2, RFX4, Fig.\u00a05C) were identified in multiple twin\/triplet sets. None of these probes or genes were also identified in the control twin set. Each of the male SALS twins\u2019 DMPs, C9orf72 twins\u2019 DMPs and SOD1 triplets\u2019 DMPs showed minimal overlap with the control twins DMPs (5, 1, and 1 DMPs, respectively, Fig.\u00a05B, Supplementary Table\u00a0S8). Similarly, minimal overlapping genes-annotated-to-DMPs were identified between the control and discordant twins\/triplets, with 9, 1, and 1 genes respectively (Fig.\u00a05C, Supplementary Table\u00a0S8).\n\n### Transcriptome-wide analysis of disease discordant MZ siblings\n\n#### Differentially expressed genes within male SALS twins implicates immune function and cell signalling functional pathways in sporadic ALS\n\nUsing limma voom to detect genes differentially expressed between male SALS twins while controlling for repeated sampling, we identified 4179 genes as significant following FDR correction (p\u2009<\u20090.05). Of these, 750 genes also had a fold change of 1.5 or greater (Fig.\u00a06A, top genes shown in Fig.\u00a06C, full list in Supplementary Table\u00a0S9). Notably, CCNF and CCS, both known ALS genes, were identified as significantly downregulated in the ALS twin compared to their unaffected co-twin (CCNF: logFC\u2009=\u20090.70, t\u2009=\u20093.99, FDR\u2009=\u20090.027; CCS: logFC\u2009=\u20090.70, t\u2009=\u20096.42, FDR\u2009=\u20090.008, Fig.\u00a06B). Gene Ontology (GO) analysis of these 750 genes identified 74 terms significantly enriched in this list. Over-representation of genes was seen in 25 terms associated with immune function and cell signalling, while there was an under-representation of genes associated with 45 terms, largely related to transcription and protein modification (Fig.\u00a07, Supplementary Table\u00a0S10).\n\n#### Validation of twin differentially expressed genes in a case-control cohort\n\nWithin the validation RNAseq data set of SALS and controls, 379 of the 750 genes identified in the male SALS twins were present. When analysed with limma while controlling for sex, 213 of the 379 genes were differentially expressed between cases and controls, yet none also showed a minimum fold change of 1.5 (top 8 of 213 genes shown in Fig.\u00a08A, 213 genes in Supplementary Table\u00a0S11). CCNF was not present in the case-control data set, while CCS was not validated (log FC\u2009=\u20090.13, t\u2009=\u20091.99, FDR\u2009=\u20090.075). Hierarchical clustering and PCA of the 379 genes did not identify clusters representing disease status (Fig.\u00a08B,C).\n\n### Integration of genome-wide methylation and transcriptome data sets identifies 12 genes both differentially methylated and differentially expressed\n\nTo increase the likelihood of detecting biologically meaningful disease-related alterations, RNA-Seq and Infinium HumanMethylation450K data sets were combined for the male SALS twins. Of 506 genes having at least one differentially methylated CpG probe annotated to them in the male SALS twins, 123 are also identified in the entire post-processing RNA-Seq data set of 13718 genes. Conversely, of the 750 genes present in our top DEG list, 642 also have at least one CpG probe mapped to the same gene in the full post-processing 450K set of 24073 genes. When comparing the gene lists of the 123 differentially methylated genes and the 642 differentially expressed genes from the same twin set, 12 genes (C11orf49, CD8A, COL7A1, EOMES, GATA6, GZMM, HOXA4, KANK3, OLIG2, QPRT, SMPD3, SNED1) were present in both gene lists (Fig.\u00a09A\u2013C).\n\n## Discussion\n\nUsing a longitudinal cohort of MZ twins and triplets that are discordant for ALS, we have conducted both a targeted and genome-wide DNA methylation study in conjunction with a sample-matched transcriptomic study. Our cohort is representative of the clinical heterogeneity (age of disease onset, disease duration) frequently observed in ALS cohorts. We have shown that DNA methylation age is the most consistently altered epigenetic signature in ALS. In addition, we observed a higher frequency of unique peripheral blood methylation changes within twin\/triplet sets compared to shared methylation changes across twin\/triplet sets. However, combined analysis of peripheral blood methylation and transcription detected ALS-relevant changes. These data suggest that the epigenetic and transcriptomic landscape of ALS may be highly complex with numerous small perturbations and various pathways, only some of which are common, contributing to disease.\n\nEpigenetic age was significantly associated with disease in an age-dependent manner, such that affected twins\/triplets have an older DNA methylation age than their unaffected co-twins\/-triplets while no such effect was observed in young discordant twins. A clear and consistent difference was apparent between the oldest twins in the study, and to a lesser extent, within both middle-aged twin\/triplet sets. This pattern of increased methylation age in ALS affected twins is consistent with previous studies of SOD1, C9orf72 and SALS disease-discordant twins25,26,30. Increased DNA methylation age has been linked to increased mortality31 and age has been shown to be a major risk and prognostic factor for ALS32. Our results also reflect a contribution of ageing to disease risk. Methylation age has also been previously linked to age of onset in ALS patients with a C9orf72 repeat expansion30, while we observed a similar phenomenon in our sporadic ALS twin sets, with a much greater between-co-twin difference in DNA methylation age in our late onset twin set compared to our early onset twin set. Further investigation in extended ALS cohorts, specifically mutation-known FALS and SALS would be worthwhile to confirm the contribution of increased DNA methylation age to ALS.\n\nWhen assessing genome-wide DNA methylation using a magnitude and statistical ranking method, we identified 59 probes differentially methylated in all ALS twins\/triplets compared to their unaffected co-twin\/-triplets. These 59 probes were selected from high CpG density regions of the genome, therefore considered biologically relevant as they are more likely to affect gene expression. Annotation of the probes to the closest gene transcription site and subsequent gene ontology analysis implicated developmental processes. However, clustering of these 59 DMPs were unable to discriminate between affected and healthy twins, or sporadic cases and controls. Yet, two of these probes were confirmed as significantly differentially methylated in the case-control analysis. C8orf46\u2019s Xenopus homolog gene vexin is involved in neurogenesis and highly expressed in the brain33, while RAD9B responds to DNA damage by moving to the nucleus and contributes to control of the cell cycle34. There is a growing body of evidence that DNA damage response is a significant factor in ALS35.\n\nWe conducted within-twin\/triplet-set comparisons to show the SOD1 triplet set, C9orf72 twin set and the male SALS twin set each have a moderate number of probes with large differences in methylation (6, 58, and 2689 probes respectively with |\u0394\u03b2|\u2009\u2265\u20090.25). In contrast, the female SALS twin set showed highly consistent methylation across all >386,000 probes (max |\u0394\u03b2|\u2009=\u20090.11). Following annotation of these probes to genes, limited overlap of differentially methylated genes was observed between disease discordant twin sets, consistent with other genome-wide methylation studies in ALS-discordant SALS twin sets25,27. This may be reflective of the heterogenous nature of sporadic ALS, or the different methodologies and strategies used to determine differential methylation. A meta-analysis incorporating these studies would be worthwhile to give a broader picture of the methylation signature of sporadic ALS.\n\nIt is noteworthy that the four twin sets used in this study represent two distinct genetic forms of disease (SOD1 and C9orf72), along with two cases at extreme age-of-disease-onset ends of the clinical spectrum of sporadic ALS, suggesting again that there may be various epigenetic pathways impacting the phenotype. Some proportion of the observed differences unique to a twin set may result from epigenetic drift36, especially as the greatest number of unique differentially methylated probes was identified in the oldest twin set and the least in the youngest twin set. It is therefore likely that disease, as well as age, is contributing to the differential methylation observed. The metabolism and nutritional status of an individual with ALS, compared to their unaffected co-twin, may also influence methylation status37,38, and therefore potentially contribute to the differential methylation observed. However, detailed dietary data is not available for the individuals included in this study and therefore could not be assessed. Nevertheless, we identified multiple differentially methylated probes annotated to two genes previously associated with ALS, DPP639 and RAMP340 in our oldest twin set, the male SALS twins. DPP6 was the first gene to be associated with sporadic ALS41. It has roles regulating dendritic excitability, with membrane hyperexcitability observed in ALS42,43. It has also been associated with multiple sclerosis44 and spinal muscular atrophy45, and as such is worthy of further investigation in broader ALS.\n\nAnalysis of transcriptome-wide gene expression in a subset of our disease discordant MZ cohort, the male SALS twins, found 750 differentially expressed genes. 379 of these genes were assessed in our validation sporadic case-control cohort, and 213 were confirmed to be significantly differentially expressed in sporadic ALS. Gene Ontology analysis implicated primarily upregulation of the immune system, which has been previously identified as dysregulated in ALS14,16,17,27. Interestingly, CCNF and CCS were downregulated in the ALS-affected twin. CCNF has been identified as a causal ALS and FTD gene in several international cohorts46. While transient overexpression has been shown to have deleterious effects in CCNF zebrafish models47, this is the first report of altered CCNF mRNA expression in ALS. CCS has been previously linked to SOD1 in its implication in ALS48. Little is known about the effects of altered expression of CCS in ALS, but its overexpression in the G93A-SOD1 ALS mouse model has been linked to accelerated neurological deficits and worsened mitochondrial pathology49. It is interesting that we observed lower expression in the ALS twin than their unaffected co-twin, given that overexpression has been linked to disease in both genes. It was an unfortunate limitation of this study that neither gene featured in our post-processing HumanMethylation450K dataset, and that so few of the genes identified had data available in our case-control data set. As such, it would be worthwhile to further investigate disease-dependent expression of the remaining 371 genes.\n\nComparison of transcriptional and DNA methylation changes in ALS-discordant twin\/triplet set(s) indicated that despite many genes being present in only one data set, there was overlap between the two datasets. Of the 750 differentially expressed genes identified in the male SALS twins, 642 had methylation data available, while of the 506 genes to which multiple of the 1366 differentially methylated probes annotated, only 123 were also represented in our gene expression data. When we compared these 642 expression-derived genes and 123 methylation-derived genes, we identified twelve genes: C11orf49, CD8A, COL7A1, EOMES, GATA6, GZMM, HOXA4, KANK3, OLIG2, QPRT, SMPD3, SNED1. Notably, the ALS genes identified from DMPs in the male SALS twin set, RAMP3 and DPP6, were not present in the post-processing male SALS twins RNA-Seq data set. C8orf46 and RAD9B were identified across all twin sets to have a single probe differentially methylated, which was confirmed in our sporadic case-control cohort, however, neither gene was present in our RNA-Seq data set. While CCNF and CCS were differentially expressed in the male SALS twins, neither gene was present in the methylation dataset. While none of the twelve genes have previously been directly linked to ALS, some indirect links exist. COL7A1, as part of the collagen gene family, is related to COL6A1, which has been linked to neurodegeneration through impaired autophagy and induction of apoptosis50. Additionally, collagen has also been identified as a significant gene ontology term in analysis of DNA methylation in sporadic ALS11. GZMM, granzyme M, is 1 of 4 gene products from the granzyme family. Granzymes A and B are elevated in ALS serum, with granzyme B correlated to ALS severity51. Granzyme B has been further implicated in inducing apoptosis in human ALS motor neurons52. SMPD3, neutral Sphingomyelinase II, is associated with apoptosis and cell cycle regulation, which have been previously linked to ALS53,54. KANK3 has been suggested as a possible gene contributing to an ALS-linked region on chromosome 1755. QPRT is involved in the kynurenine pathway, which has been implicated in ALS56. These twelve genes, identified when combining DNA methylation and gene expression data, may thus contribute to disease, and warrant further investigation.\n\nAssessment of global methylation and blood cell composition showed no difference between ALS and healthy co-twins. Although a lack of global changes in methylation is consistent with five other sets of ALS-discordant twins25, not all studies agree10,14,15. It is also interesting that blood cell composition, as determined from whole blood methylation, was not found to vary between affected and unaffected twins, given that upregulation of the immune system and changes in white blood cell populations have previously been demonstrated in ALS57,58. This lack of effect in white blood cell estimates may be partly attributable to shared genetic background59,60, although a prior study reported differing methylation-derived cell proportion estimates in one ALS-discordant twin pair27.\n\nHigh-density quantitative targeted analysis of the C9orf72 and SOD1 gene-associated CpG islands and gene promotors did not identify any differences in methylation status between ALS-discordant MZ twins\/triplets carrying mutations in these genes. The general consistency observed in SOD1 methylation between carriers of SOD1 mutations suggests DNA methylation of the SOD1 promoter itself is not likely to be a major mechanism contributing to differences in penetrance in SOD1-linked ALS, in line with previous reports10. Methylation of C9orf72 was low in a twin set carrying the C9orf72 repeat expansion. Methylation of the C9orf72 promoter and\/or the repeat expansion has been reported in the brain and blood of repeat expansion carriers6,9,61,62,63,64,65, in some cases with similar low levels of methylation as that observed here. Interestingly, neither of the two prior C9orf72 twin studies, one ALS concordant and one discordant, detected methylation of C9orf7224,66, suggesting that C9orf72 methylation is just one part of the epigenetic story in ALS.\n\nIn conclusion, our disease-discordant twin study, utilising longitudinal samples throughout disease progression, demonstrated significant association of DNA methylation age with disease in an age dependent manner. We have also identified an important set of DMPs and DEGs, and associated functional pathways, that may be involved in either ALS pathogenesis or protection from disease. These genes and pathways offer potential targets for future therapeutic treatment for ALS patients.\n\n## Methods\n\n### Participants\n\nThe cohort of 1806 total participants used in this study is summarised below. This study was approved by the human research ethics committees of Macquarie University (5201600387) and Sydney South West Area Health Service. Samples from ALS patients, family members, and unrelated controls were obtained from the Macquarie University Neurodegenerative Diseases Biobank, Molecular Medicine Laboratory at Concord Hospital, and the Australian MND DNA bank. Written informed consent was obtained from all study subjects and all methods were performed in accordance with the relevant guidelines and regulations. Most participants were of European descent and patients were clinically diagnosed with definite or probable ALS based on El Escorial criteria67. Genomic DNA was extracted from peripheral blood using standard protocols. RNA was extracted from peripheral blood with the QIAsymphony PAXgene blood RNA kit (Qiagen, Hilden, Germany).\n\n#### Twin\/triplet cohort\n\nThree ALS discordant monozygotic twin pairs, one ALS discordant MZ triplet set and two control MZ twin pairs were included in this study (Fig.\u00a01 and Table\u00a01). Monozygosity for each twin\/triplet set was confirmed using STR fragment analysis and\/or SNP microarrays. Longitudinal samples were available from two twin sets (male and female sporadic ALS (SALS) twin sets in Fig.\u00a01). The four discordant twin\/triplet sets had previously undergone mutation analysis for known ALS genes and whole genome analysis for novel and\/or rare de novo variants.\n\n#### Data processing and extended cohorts\n\nAdditional samples were used in this study for data processing (Illumina HumanMethylation 450K, EpiTYPER methylation assays, and RNA-Seq) and for examination of significant findings (Illumina HumanMethylation 450K assay and RNA-Seq). Demographic characteristics between cases and controls in extended cohorts were assessed with t-tests for age and \u03c72 tests for sex.\n\nFor quality control and processing of the EpiTYPER data, 279 samples with C9orf72 EpiTYPER data (158 familial ALS\/FTD samples, 56 asymptomatic samples (individuals harbouring a causal gene mutation but currently unaffected), and 65 control samples), and 261 samples with SOD1 EpiTYPER data (123 familial ALS, 65 asymptomatic, and 73 control samples) were used.\n\nFor the Infinium HumanMethylation 450K BeadChip, 1658 samples were used in data processing and normalisation. This comprised 889 individuals with sporadic or familial ALS, 92 asymptomatic and 668 controls. The familial ALS and asymptomatic cases largely overlap with the EpiTYPER cohort. The extended cohort subset comprised 650 sporadic ALS individuals and 539 unrelated controls.\n\nOne hundred and ninety samples were used for data processing and normalisation of the RNA-Seq data, comprising 114 individuals with ALS (99 sporadic ALS, 15 familial ALS) and 76 unrelated controls. The validation subset comprised of 96 sporadic cases and 69 controls. The majority of the 96 validation sporadic ALS cases were also present in the HumanMethylation 450K BeadChip SALS\/control cohort.\n\n### Methylation assays and data processing\n\nAll quality control and data processing steps were carried out in R v 3.4.468.\n\n#### EpiTYPER assay\n\nCustom EpiTYPER assays (Sequenom, San Diego, USA) were used to quantify CpG methylation of 56 and 39 CpG units respectively of the two gene-associated CpG islands for C9orf72 and the gene-associated CpG island upstream of SOD1. EpiTYPER uses base-specific cleavage of bisulphite-converted DNA and matrix-assisted laser desorption\/ionization time-of-flight mass spectrometry (MADL-TOF MS) to quantify DNA methylation69. Primers for overlapping amplicons were designed with Sequenom\u2019s EpiDesigner software to target the CpG island regions, and therefore the promoter regions, as shown in Supplementary Fig.\u00a0S1. Primer and assay details are available in Supplementary Table\u00a0S1. Samples were assayed in one or two batches, and either in duplicate or as singletons (Supplementary Table\u00a0S1). Sample processing was performed by Agena Bioscience (Brisbane, Queensland, Australia). As each gene assay was run across several plates of samples, the highly methylated DNA control was used to calculate the between-plate coefficient of variation, determined to be 4.9% and 2.3% for SOD1 and C9orf72 plates, respectively. CpG methylation was quantified as the percentage of methylated cytosines for each CpG unit, where CpG units consist of one or more CpG sites. For units with multiple CpG sites, methylation percentages were normalised by averaging across the number of sites.\n\n#### EpiTYPER data processing\n\nEpiTYPER data processing was adapted from a previously established method70. Twin samples were processed together with the full familial cohorts to leverage the increased sample size. In brief, CpG units that failed to meet assay reliability standards were discarded and samples in duplicate were averaged for the remaining CpG units. Given the relatively small number of CpG units remaining after removal of those determined to be unreliable and the relatively high failure rate of samples and units, a two-step sample\/unit filtering process was used. First, failed samples, with \u226590% of CpG unit readings missing, were removed, followed by CpG units which were missing data for \u226590% of samples. Second, samples with a low detection success (missing data for \u226515% of units) were removed, and the same threshold applied to remove CpG units with low detection success (units missing data for \u226515% of samples). Finally, any remaining missing values were imputed with the mean for that unit. Following data processing and filtering, 28 of 56 and 23 of 39 CpG units (for C9orf72 and SOD1, respectively) remained for analysis.\n\n#### Infinium Human Methylation 450K v1.2 BeadChip array\n\nGenome-wide methylation was investigated using the Infinium HumanMethylation 450K v1.2 BeadChip (Illumina, San Diego, USA). This microarray provides qualitative methylation values for approximately 480,000 CpG sites distributed throughout the genome. Bisulphite-converted DNA was hybridised to the Infinium HumanMethylation 450K BeadChip. Fluorescence imaging of the BeadChip using an Illumina HiScan SQ scanner successfully generated raw Intensity Data files (.idat) for all samples.\n\n#### 450K data processing\n\nData processing of the .idat files was adapted from the method presented by71. Twin samples were processed together with the full cohort to leverage larger sample sizes. All default settings were used except where otherwise specified. In brief, samples with less than 99% of CpGs detected were removed. shinyMethyl (v. 1.12.072) was used to visually identify possible outliers, with confirmation of sex queries using RnBeads (v. 1.0.0.73). Samples with any possibility of incorrect identification were removed. Data were normalised with the dasen function from wateRmelon (v. 1.20.374). Probes that had failed to be detected (threshold p\u2009>\u20090.05) with the minfi (v. 1.22.175) function detectionP were removed (n\u2009=\u200910270 probes). Normalised data were submitted to Horvath\u2019s online DNAm age calculator28. Samples that did not strongly correlate (r\u2009<\u20090.85) with the DNAm age results gold standard were removed. Leveraging technical replicate\/duplicate samples (n\u2009=\u200930), both 1) in the form of multiple blood collections at the same time and resulting independent DNA extractions (technical replicates) and 2) multiple aliquots of single DNA extractions (duplicates), a custom filtering step was included to identify and remove highly variable probes. Any probe identified to have multiple pairs of technical replicate or duplicate samples with differences greater than three standard deviations from the probe\u2019s mean difference was discarded (n\u2009=\u200938697). Of the remaining probes, any known to cross hybridise, be located on sex chromosomes, or bind to SNPs, were removed (n\u2009=\u200950362)76.\n\nFollowing raw data processing, quantitative CpG methylation values for 1215 samples (including 34 twin samples from Table\u00a01 and 1179 case\/control extended cohort samples outlined in Supplementary Table\u00a0S2) and 386183 probes remained for analysis and examination. Comparison of the case-control extended cohort (Supplementary Table\u00a0S2) showed that sex ($${\\chi }_{(1,{\\rm{n}}=1179)}^{2}$$\u2009=\u200933.8, p\u2009<\u20090.01) and age (t1174\u2009=\u20094.20, p\u2009<\u20090.01) were significantly different between ALS cases and controls.\n\n### Analysis of methylation data\n\nAll statistical analyses were carried out in R v. 3.4.468.\n\n#### Gene-specific targeted methylation analysis of SOD1 and C9orf72 in the FALS twin\/triplet sets\n\nMethylation of SOD1 or C9orf72, as quantified by both EpiTYPER and 450K assays, was visualised in the relevant monozygotic disease discordant twin\/triplets. Four and five 450K CpGs were available in the post processing data set in the targeted region of C9orf72 (cg05990720, cg11613875, cg14363787, cg23074747) and SOD1 (cg16086310, cg17253939, cg18126791, cg19948014, cg26893544), respectively. Since only one twin set and one triplet set are available in our cohort for each respective variant, results are descriptive only.\n\n#### Observed differences in DNA methylation age, blood cell composition and global methylation within a twin\/triplet set\n\nDNA methylation age was determined from 450K methylation data using the method of Horvath28. Blood cell proportions in whole blood derived methylation was estimated from 450K methylation data with the minfi implementation of Houseman et al.\u2019s algorithm29. Global methylation levels were determined as the mean methylation estimate across all post-processing 450K CpG sites per sample. CpG sites were also divided into one of four categories based on HIL CpG classes (high-density CpG island (HC), intermediate-density CpG island (IC) and non-island (LC); ICshore, intermediate-density CpG island shore that borders HCs)77,78 and the mean methylation for each was calculated.\n\n#### Methylome-wide analysis in MZ sets to identify differentially methylated probes\n\nThe list of differentially methylated probes (DMP) across all MZ sets was identified using an established ranked magnitude-significance method79. In brief, statistical significance per CpG site was determined using a paired t-test on methylation M-values, using the per-patient mean of longitudinal samples and unaffected triplets. The magnitude of the difference in methylation was calculated as the mean difference in \u03b2-methylation between co-twins. Both methods were used to rank all CpGs, and a final ranked list was determined from the mean of these two ranking methods. Top DMPs were the subset of all CpG probes that met the following two criteria, 1) they were in high CpG density regions of the genome and 2) the ranked list of high-density probes was truncated immediately prior to the first probe to show a difference in the direction of change across the four discordant MZ sets. The ability of these probes to discriminate between ALS and healthy individuals was assessed by hierarchical clustering and principal components analysis of all twin\/triplet sets.\n\nWithin-twin\/triplet set DMPs were also identified. A CpG probe was considered to be differentially methylated within a twin\/triplet set where there was an absolute difference in \u03b2-methylation \u22650.25 between the affected twin and their unaffected co-twin\/triplet.\n\n#### Examination of identified twin DMPs in a sporadic ALS cohort\n\nTwin\/triplet DMPs were examined in the larger sporadic case-control cohort. Differences between cases and controls for each of the identified probes were analysed, along with the ability of the DMP list to cluster cases and controls separately.\n\n### Gene expression\n\n#### RNA sequencing\n\nRaw sequencing reads in fastq format were generated for male SALS twins (based on longitudinal sample availability) and the sporadic case-control validation cohort as outlined in Supplementary Table\u00a0S3.\n\n#### RNA-Seq data processing\n\nThe quality of raw sequencing reads was evaluated using fastQC (v 0.11.780) for both datasets. Trimming and alignment was performed as outlined in Table\u00a01 using either Trimmomatic (v. 0.3681) or Cutadapt (version 1.8.182) and HISAT2 (v2.0.583). All subsequent data processing and analysis was completed in R (v. 3.4.4), using BioConductor packages edgeR (v. 3.18.184) and limma (v. 3.32.1085). A standard edgeR TMM normalisation and filtering pipeline was used in data processing, with only those genes where expression was greater than 0.3 counts per million in a minimum of 3 samples (male SALS twins) or 2 counts per million in a minimum of 75 samples (case-control cohort) retained for analysis, which is equivalent to approximately 12\u201315 raw counts in the smallest library size for each dataset. For the male SALS twins RNA-Seq data, of the 27685 human genes present in the per-gene read counts generated by HTSeq86, 13718 genes remained following raw data processing using edgeR84. Whereas in the case-control cohort, of the 23368 human genes present in the per-gene read counts generated by HTSeq86, 7354 genes remained following raw data processing using edgeR84. MDS (multi-dimensional scaling) indicated the presence of three outliers in the case-control cohort, 1 control and 2 SALS samples. All three were removed and final clinical details for the cohort can be found in Supplementary Table\u00a0S4. Comparison of the RNA-Seq case-control validation cohort (Supplementary Table\u00a0S4) showed that there were no significant differences in age (t157.9\u2009=\u20091.74, p\u2009=\u20090.08) between the ALS cases and controls, but a difference was observed in sex between cases and controls ($${\\chi }_{(1,{\\rm{n}}=165)}^{2}$$\u2009=\u20096.5, p\u2009=\u20090.01).\n\n#### Differentially expressed genes in MZ twins\n\nTo identify differentially expressed genes (DEGs) using the paired longitudinal RNA-Seq samples from the ALS-discordant male SALS twins (Table\u00a01), read count data was analysed using limma85, including model terms for longitudinal sample collection and disease status. Voom87 transformation was applied prior to modelling. Multiple testing correction using the BH-FDR method88 was applied to the full list of post-processing genes.\n\n#### Validation of twin DEGs in a sporadic cohort\n\nGenes identified in twin analyses were investigated for an effect of disease in the full case-control cohort with limma, including sex as a covariate. Data were voom transformed, given the highly variable library sizes. Multiple testing corrections using the BH-FDR method was applied only on the subset of genes identified as differentially expressed in twins. Hierarchical clustering and principal components analysis of the expression of these DEGs in the case-control cohort was assessed.\n\n### Combined methylation and expression analysis\n\n#### Intersect of top CpGs and genes\n\nTo identify genes most likely to be altered in disease, results from independent analysis of genome-wide methylation and expression data sets were integrated. Longitudinal RNA-Seq data is only available for one male SALS twin set, therefore we first identified the overlap between top DEGs and the genes annotated to the most differentially methylated probes within that twin set. We extended this analysis by overlapping the same list of DEGs with the genes annotated to the top differentially methylated probes across all combined twin sets.\n\n### Gene Ontology analysis\n\nGene Ontology enrichment analysis89,90 for biological processes was applied to the genes identified as differentially expressed in male SALS twins. The gene list was analysed with PANTHER overrepresentation tests (GO Ontology database release 2018-08-0991). Enrichment was tested relative to all genes detected in the appropriate post-processing data set. Fisher\u2019s exact test with FDR correction was used.\n\n### Statistics\n\nAll analyses were carried out in R (v. 3.4.4)68. Linear mixed effects models were used to analyse DNAm age, blood cell type proportions and global mean M-methylation. Modelling was carried out using the lmer function in the package lme4 (v. 1.1.1492) for DNAm age and mean methylation, while a mixed effects beta regression for cell type proportions was applied with the glmmTMB function from the glmmTMB package (v. 0.2.2.093). Blood cell type proportions were increased by 0.001 to all estimates to avoid taking the log of zero. All mixed models assessed the effect of disease status while controlling for age at sample collection and sex. When analysing DNAm age, the interaction of disease and age at collection was also tested. Random effects were introduced for repeated sampling within co-twins, and a random intercept per twin\/triplet set. When modelling cell types, due to convergence issues, the random slope for repeated sampling was dropped, leaving random intercepts for each co-twin and twin set. Likelihood ratio tests were used to determine significance of model terms. Linear models were used for case-control examination of probes identified in the MZ cohort, with the same fixed effect terms of age at sample collection and sex as described for mixed models. Hierarchical clustering utilised the package cluster (v. 2.0.6), with Manhattan distance and ward clustering methods for 450K data94, and Spearman correlation distance and average linkage clustering for log-transformed RNA-Seq count data95. 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Measuring the 'cold freon' effect – Copley Scientific's new PTT 1000 takes the temperature of inhaled aerosols
27 September 2012; Nottingham, UK: Copley Scientific has launched the Plume Temperature Tester PTT 1000, a high precision instrument for measuring the plume temperature of Metered-Dose Inhalers (MDIs) and nasal sprays. The PTT 1000 is the first instrument on the market that can reliably measure plume temperature during dose delivery, to support determination of the 'cold freon' effect – the chilling sensation that inhaler users often experience. Since this effect can directly impact the consistency and efficiency of drug delivery, the new tester is particularly useful for those seeking to demonstrate therapeutic equivalence or to develop softer, warmer plumes with improved patient compliance rates.
The widely recognised 'cold freon' effect is due to the high velocity blast and subsequent evaporation of liquid propellant that impact the back of the user's throat during drug delivery. Since the effect is a function of both aerosol spray force and plume temperature, Copley Scientific offers the PTT 1000 alongside the Spray Force Tester 1000, an instrument that measures the impaction force of delivery. Together these provide a combined solution for complete quantification.
In certain instances the 'cold freon' effect can result in the patient aborting the inhalation process and is therefore a significant cause of inconsistent drug delivery. As a result, this effect is specifically given as an example of a criteria that might be required to substantiate in vitro therapeutic equivalence in EMA guidelines for orally inhaled products (OIP) (January 2009).
With an internal geometry identical to that of the standard USP induction port used for all orally inhaled product testing, the PTT 1000 incorporates a series of four thermocouples that measure a precise temperature profile of the plume at different distances from the actuator. A data acquisition system under the control of an associated PC ensures efficient data capture and display, and the thermocouples are easily removed for cleaning. The new tester can be directly connected to a Waste Shot collector or Dose Uniformity Sampling Apparatus for streamlined integration within existing test set-ups.
For further information on the new the Copley Plume Temperature Tester PTT 1000 please go to: http://bit.ly/COPCSC
CAPTION: Plume Temperature Tester PTT 1000
Copley Scientific's pharmaceutical product range includes test equipment for: delivered dose uniformity and aerodynamic particle size measurement of metered-dose inhalers, dry powder inhalers, nebulizers and nasal sprays; as well as tablets (dissolution, disintegration, friability and hardness) capsules, powders, suppositories and transdermals.
Copley Scientific has offices in the UK and Switzerland. The company works in partnership with aerosol particle science experts MSP Corporation in North America, and also distributes MSP Corporation's air sampling and aerosol characterisation products throughout Europe.
Serving the pharmaceutical and associated industries, Copley Scientific offers an extensive range of equipment for research, development and quality control, as well as full validation and aftersales services. This broad range of products is supplied and supported worldwide through a network of specialist distributors. www.copleyscientific.com | {
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{"url":"http:\/\/rinfix.com\/cannot-execute\/valgrind-cannot-execute-binary-file-mac-os-x.html","text":"Home > Cannot Execute > Valgrind Cannot Execute Binary File Mac Os X\n\n# Valgrind Cannot Execute Binary File Mac Os X\n\n## Contents\n\nCan you be more specific about \"can't make valgrind work\"? \u2013barbaz Jun 17 '11 at 14:05 2 Valgrind works by itself, but when I try to analyze my application running So... All postings and use of the content on this site are subject to the Apple Support Communities Terms of Use. \u00ef\u00a3\u00bf Apple Support Communities More ways to shop: Visit an Apple Missing } inserted. \\int dx = x + C & What is the meaning of ''cry oneself\"? weblink\n\nFor me also neither the macports build worked, nor did the build that i created my self from the vanilla tar.gz file from the valgrind page. You need to be able to link to the Intel libraries on your G4 and it may not be doing that. Is there an actual army in 1984? Once I fixed that, Hudson is successfully able to drive the minicom sesson.\n\nIt's a silent command. \u2013Ben Richards Jun 12 '12 at 21:57 | show 4 more comments 5 Answers 5 active oldest votes up vote 45 down vote accepted Usually that error A bash script on Server B invokes minicom with the runscript script along with some companion actions. Could anyone help? $file um um: ELF 64-bit LSB executable, x86-64, version 1 (SYSV), dynamically linked (uses shared libs), for GNU\/Linux 2.6.9, not stripped files executable binary fortran share|improve this Not the answer you're looking for? \u2022 Server B (FC 12) builds the tests that actually run on the target, and can ssh to Server A. \u2022 Mar 31, 2008 12:41 PM Helpful (0) Reply options Link to this post by Charles Minow, Charles Minow Mar 31, 2008 6:45 PM in response to vortexfive Level 6 (9,180 points) \u2022 This is why different OS software need different binaries, even if both operating systems use the same processor. \u2022 http:\/\/stackoverflow.com\/questions\/6082808\/run-valgrind-in-32-bit-mode-on-mac-10-6\/6303692#6303692)I use the one from Fink and it works fine. \u2022 And I uninstalled MacPorts version before installing Homebrew version. \u2013Ryan Jun 17 '11 at 14:02 2 Then you are experiencing another problem. \u2022 Will I get the same result if I use 18-55mm lens at 55mm (full zoom) and 55-200mm lens at 55mm (no zoom), if not, then why? I build Valgrind with: svn co -r 11094 \"svn:\/\/svn.valgrind.org\/valgrind\/trunk\" valgrind cd valgrind svn up -r 1964 VEX\/ # explicitly fetch the corresponding VEX revision patch -p0 -i ..\/limits.patch sh autogen.sh && Logged caleb9 Jr. Single word for the act of being susceptible? Bash Cannot Execute Binary File Exec Format Error Mar 31, 2008 12:14 PM Helpful (0) Reply options Link to this post by Mihalis Tsoukalos, Mihalis Tsoukalos Mar 31, 2008 12:31 PM in response to vortexfive Level 4 (2,015 points) Join Date Apr 2012 Location Detroit, MI USA Beans 62 DistroUbuntu 12.04 Precise Pangolin Re: Error: \"cannot execute binary file\" Just taking a shot in the dark here, trying running the Bash Cannot Execute Binary File Linux At first I also got the PAGE_ZERO error for unknown reason but after recompiling the executable again it all seems to work fine. Apple disclaims any and all liability for the acts, omissions and conduct of any third parties in connection with or related to your use of the site. Member Posts: 51 Re: Valgrind, Lazarus and Lion \u00ab Reply #4 on: September 28, 2011, 01:19:29 pm \u00bb Yup I know, if you look at the compiler options I used for Linux arnavisca-System-Product-Name 3.2.0-24-generic-pae #39-Ubuntu SMP Mon May 21 18:54:21 UTC 2012 i686 i686 i386 GNU\/Linux 2. Cannot Execute Binary File Bash share|improve this answer answered Jun 13 '12 at 3:07 LawrenceC 47.2k677146 6 \"if you try to run x86 executables on an ARM CPU, this message comes up.\" That was EXACTLY Both provide a system and a \"language\" that allows for more complex components of the computer to complete tasks for the end user. Tango Icons \u00a9 Tango Desktop Project. ## Bash Cannot Execute Binary File Linux Not the answer you're looking for? You can use objdump (from binutils) to check architecture of binaries. Bash Cannot Execute Binary File Mac I'll skip compiling with -Px86_64 since my main goal is to debug a Lazarus app, so I have to stick to 32 bits for now. Cannot Execute Binary File Java However, when Hudson tries to do the same thing, over in the minicom session it complains about a line in the \"yet another bash script\" that invokes the C executable, .\/executable, If I try to execute .\/MyAppName.app, the error would be the same, only path would differ... \u2013Ryan Jun 17 '11 at 14:19 add a comment| up vote 4 down vote Just have a peek at these guys GCC is no longer distributed as the compiler of choice on OS X.$ sh large-h.sh 350 && gcc large.cc -o large $valgrind --tool=none .\/large ==50438== Nulgrind, the minimal Valgrind Does an Eldritch Knight's war magic allow Extra Attacks? If anyone knows what can I do to use it with FPC, I'd be grateful for some hints :]. \u00ab Last Edit: September 29, 2011, 10:55:22 am by caleb9 \u00bb Logged Cannot Execute Binary File Exec Format Error Ubuntu chunk=a filename=large.h if [ \"$1\" == \"\" ] then megs=136 else megs=$1 fi counter=20 # 1 Mb while [$counter -gt 0 ] do chunk=$chunk$chunk let counter=counter-1 done chunk=\"\\\"\"$chunk\"\\\"\" mchunk=$chunk\\\\ echo more stack exchange communities company blog Stack Exchange Inbox Reputation and Badges sign up log in tour help Tour Start here for a quick overview of the site Help Center Detailed share|improve this answer edited Jun 17 '11 at 12:42 answered Jun 17 '11 at 12:37 barbaz 5611619 Thank you for the answer, Barbaz! check over here I wonder if there could be a difference in the way the target boots (perhaps a race condition).\n\nThe only things I've changed were Project Options -> Compiler Options \/ Linking where I toggled 'Generate Debugging Info For GDB' and 'Generate code for valgrind (-gv)', and in Code generation Cannot Execute Binary File Ubuntu share|improve this answer answered Jun 12 '12 at 22:29 acoh Facha 1674 add a comment| Your Answer draft saved draft discarded Sign up or log in Sign up using Google This leads to a conclusion: Dissimilar computers \"talk\" in different tongues.\n\n## If so, what?\n\nI'll help you solve the compilation errors, just comment the answer! move back and forth between the processor instruction set compatible with will usually work well, if they are not compatible CPU will not be able to understand instructions. You should get something like this (this is 64bit, but similar): # file .\/splunk .\/splunk: ELF 64-bit LSB executable, AMD x86-64, version 1 (SYSV), for GNU\/Linux 2.4.0, dynamically linked (uses shared Cannot Execute Binary File Centos Valgrind supports both.\n\nYou will receive 10 karma points upon successful completion! Can a president win the electoral college and lose the popular vote Find the \"unwrapped size\" of a list How do you enchant items with Lapis Luzuli? I'm downvoting this post because: * This will be publicly posted as a comment to help the poster and Splunk community learn more and improve. http:\/\/rinfix.com\/cannot-execute\/usr-bin-gcc-cannot-execute-binary-file.html share|improve this answer answered Jul 28 '11 at 10:29 Ryan 54111034 add a comment| Your Answer draft saved draft discarded Sign up or log in Sign up using Google Sign\n\nLogged Jonas Maebe Hero Member Posts: 527 Re: Valgrind, Lazarus and Lion \u00ab Reply #10 on: September 28, 2011, 02:33:11 pm \u00bb a) neither of those messages shows an actual crashb) That sounds like a good clue to look at. Is calling a function with local side-effects twice in the same expression undefined behavior? I don't have 10.7.The \"file\" command simply tells you that the C binary is a 64 bit one and the FPC binary is a 32 bit one.\n\nBrowse other questions tagged c++ osx unix gcc valgrind or ask your own question. share|improve this answer edited Sep 1 '15 at 4:02 Ravan 3,091113156 answered Sep 1 '15 at 1:06 Onurhan 215 add a comment| up vote 0 down vote Please post how did Can I solve the problem in this way. Even the simplest Lazarus project crashes valgrind.\n\nIt's 30Mb in .tgz ...","date":"2018-01-18 01:58:37","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\": 0.17016829550266266, \"perplexity\": 5950.656557038617}, \"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-2018-05\/segments\/1516084887054.15\/warc\/CC-MAIN-20180118012249-20180118032249-00296.warc.gz\"}"} | null | null |
{"url":"https:\/\/realnfo.com\/ee\/Electrical-Circuit-Analysis\/The-Laplace-Transform\/Application-of-The-Laplace-Transform-to-the-Network-Synthesis","text":"# Application of The Laplace Transform to the Network Synthesis\n\nNetwork synthesis may be regarded as the process of obtaining an appropriate network to represent a given transfer function. Network synthesis is easier in the $s$ domain than in the time domain.\nIn network analysis, we find the transfer function of a given network. In network synthesis, we reverse the approach: given a transfer function, we are required to find a suitable network.\nNetwork synthesis is finding a network that represents a given transfer function.\nKeep in mind that in synthesis, there may be many different answers-or possibly no answers - because there are many circuits that can be used to represent the same transfer function; in network analysis, there is only one answer.\nNetwork synthesis is an exciting field of prime engineering importance. Being able to look at a transfer function and come up with the type of circuit it represents is a great asset to a circuit designer. Although network synthesis constitutes a whole course by itself and requires some experience, the following examples are meant to whet your appetite.\nExample 1: Given the transfer function\n$$H(s)=\\frac{V_{o}(s)}{V_{i}(s)}=\\frac{10}{s^{2}+3 s+10}$$\nrealize the function using the circuit in Fig. 1(a).\n(a) Select $R=5 \\Omega$, and find $L$ and $C$.\n(b) Select $R=1 \\Omega$, and find $L$ and $C$.\nFig. 1: Example 1.\nSolution: The $s$-domain equivalent of the circuit in Fig. 1(a) is shown in Fig. 1(b). The parallel combination of $R$ and $C$ gives\n$$R \\| \\frac{1}{s C}=\\frac{R \/ s C}{R+1 \/ s C}=\\frac{R}{1+s R C}$$\nUsing the voltage division principle,\n$$V_{o}=\\frac{R \/(1+s R C)}{s L+R \/(1+s R C)} V_{i}=\\frac{R}{s L(1+s R C)+R} V_{i}$$\nor\n$$\\frac{V_{o}}{V_{i}}=\\frac{R}{s^{2} R L C+s L+R}=\\frac{1 \/ L C}{s^{2}+s \/ R C+1 \/ L C}$$\nComparing this with the given transfer function $H(s)$ reveals that\n$$\\frac{1}{L C}=10, \\quad \\frac{1}{R C}=3$$\nThere are several values of $R, L$, and $C$ that satisfy these requirements. This is the reason for specifying one element value so that others can be determined.\n(a) If we select $R=5 \\Omega$, then\n$$C=\\frac{1}{3 R}=66.67 \\mathrm{mF}, \\quad L=\\frac{1}{10 C}=1.5 \\mathrm{H}$$\n(b) If we select $R=1 \\Omega$, then\n$$C=\\frac{1}{3 R}=0.333 \\mathrm{~F}, \\quad L=\\frac{1}{10 C}=0.3 \\mathrm{H}$$\nMaking $R=1 \\Omega$ can be regarded as normalizing the design.\nIn this example we have used passive elements to realize the given transfer function. The same goal can be achieved by using active elements, as the next example demonstrates.\nExample 2: Synthesize the function\n$$T(s)=\\frac{V_{o}(s)}{V_{s}(s)}=\\frac{10^{6}}{s^{2}+100 s+10^{6}}$$\nusing the topology in Fig. 2.\nFig. 2: Example 2.\nSolution:\nWe apply nodal analysis to nodes 1 and 2 . At node 1 ,\n$$\\left(V_{s}-V_{1}\\right) Y_{1}=\\left(V_{1}-V_{o}\\right) Y_{2}+\\left(V_{1}-V_{2}\\right) Y_{3}$$\nAt node 2,\n$$\\left(V_{1}-V_{2}\\right) Y_{3}=\\left(V_{2}-0\\right) Y_{4}$$\nBut $V_{2}=V_{o}$, so Eq. (15.26.1) becomes\n$$Y_{1} V_{s}=\\left(Y_{1}+Y_{2}+Y_{3}\\right) V_{1}-\\left(Y_{2}+Y_{3}\\right) V_{o}$$\nand Eq. (15.26.2) becomes\n$$V_{1} Y_{3}=\\left(Y_{3}+Y_{4}\\right) V_{o}$$\nor\n$$V_{1}=\\frac{1}{Y_{3}}\\left(Y_{3}+Y_{4}\\right) V_{o}$$\nSubstituting Eq. (15.26.4) into Eq. (15.26.3) gives\n$$Y_{1} V_{s}=\\left(Y_{1}+Y_{2}+Y_{3}\\right) \\frac{1}{Y_{3}}\\left(Y_{3}+Y_{4}\\right) V_{o}-\\left(Y_{2}+Y_{3}\\right) V_{o}$$\nor\n$$Y_{1} Y_{3} V_{s}=\\left[Y_{1} Y_{3}+Y_{4}\\left(Y_{1}+Y_{2}+Y_{3}\\right)\\right] V_{o}$$\nThus,\n$$\\frac{V_{o}}{V_{s}}=\\frac{Y_{1} Y_{3}}{Y_{1} Y_{3}+Y_{4}\\left(Y_{1}+Y_{2}+Y_{3}\\right)}$$\nTo synthesize the given transfer function $T(s)$, compare it with the one in Eq. (15.26.5). Notice two things: (1) $Y_{1} Y_{3}$ must not involve $s$ because the numerator of $T(s)$ is constant; (2) the given transfer function is second-order, which implies that we must have two capacitors. Therefore, we must make $Y_{1}$ and $Y_{3}$ resistive, while $Y_{2}$ and $Y_{4}$ are capacitive. So we select\n$$Y_{1}=\\frac{1}{R_{1}}, \\quad Y_{2}=s C_{1}, \\quad Y_{3}=\\frac{1}{R_{2}}, \\quad Y_{4}=sC_2$$\nSubstituting Eq. (15.26.6) into Eq. (15.26 .5) gives\n$$\\begin{split} \\frac {V_{0}}{V_{s}}&=\\frac {1 \/ \\left(R_{1} R_{2} \\right)}{1 \/\\left(R_{1} R_{2}\\right)+s C_{2}\\left(1 \/ R_{1}+1 \/ R_{2}+s C_{1}\\right)} \\\\ &=\\frac{1 \/\\left(R_{1} R_{2} C_{1} C_{2}\\right)}{s^{2}+s\\left(R_{1}+R_{2}\\right) \/\\left(R_{1} R_{2} C_{1}\\right)+1 \/\\left(R_{1} R_{2} C_{1} C_{2}\\right)} \\end{split}$$\nComparing this with the given transfer function $T(s)$, we notice that\n$$\\frac{1}{R_{1} R_{2} C_{1} C_{2}}=10^{6}, \\quad \\frac{R_{1}+R_{2}}{R_{1} R_{2} C_{1}}=100$$\nIf we select $R_{1}=R_{2}=10 \\mathrm{k} \\Omega$, then\n$$\\begin{array}{c}C_{1}=\\frac{R_{1}+R_{2}}{100 R_{1} R_{2}}=\\frac{20 \\times 10^{3}}{100 \\times 100 \\times 10^{6}}=2 \\mu \\mathrm{F} \\\\C_{2}=\\frac{10^{-6}}{R_{1} R_{2} C_{1}}=\\frac{10^{-6}}{100 \\times 10^{6} \\times 2 \\times 10^{-6}}=5 \\mathrm{nF}\\end{array}$$\nThus, the given transfer function is realized using the circuit shown in Fig. 3.\nFig. 3: For Example 1.","date":"2023-03-28 08:48:50","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\": 0.6283173561096191, \"perplexity\": 582.060643210868}, \"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-2023-14\/segments\/1679296948817.15\/warc\/CC-MAIN-20230328073515-20230328103515-00792.warc.gz\"}"} | null | null |
Description The communications copied into the volume are letters sent from December 15, 1808, to November 12, 1810, during the administration of Henry Dearborn and William Eustis. Most of the letters were written by the Secretaries, but some were by their chief clerk. Also copied in the volume are two proclamations of President James Madison. | {
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\section{Introduction}
The Pyramid of Khnum-Khufu, also known as the Great Pyramid of Giza or Cheops, is the oldest and largest of the three main pyramids that are part of the necropolis of Giza (Egypt). The infrastructure is built with blocks of granite, weighing approximately 2.5 tons each. To complete the work is estimated to have taken at least two and a half million blocks, put in place with millimeter precision in a short period of time, estimated at around 15 or 30 years \cite{lehner1997complete}.
The pyramids of Egypt, despite being one of the oldest and largest monuments on Earth, to date there is still no common and scientifically established idea on how they were built \cite{hawass1998pyramid,smith2018great}.
The Red Sea was the most important Harbor Facilities at the time of King Khufu \cite{tallet2016harbor}, where an exceptionally well-preserved harbor complex from the Early Old Kingdom at Wadi al-Jarf along the Egyptian coast of the Red Sea has been excavated.
In studying the origin of the pyramids, we believe we should not overlook the existence of ancient mythological writings.
A study concerning the myths and folklore of the ancient peoples of the world, highlighting all the similarities between them, was made in \cite{bhatt2019subcontinent}. The argument that myths are insignificant, often considered mere stories passed on through generations has been challenged. The authors are open to the possibility that a technologically more advanced civilization existed before a known timeline, where the existence of various glacial ages \cite{kump2005foreshadowing} prevented the passing down of history. Focusing on the mythical cities mentioned in ancient Indian texts, describing how that subcontinent was an integral part of this \cite{bergendorff2019social,noc2015analyse}.
However, how the Egyptian Pyramids were built has remained an enduring mystery\cite{houdin2007construction,baud2015djeser,dodson2000layer}. A theory that the pyramids were cast of cement-like conglomerate made directly in-situ using granular limestone aggregates and an alkali-silicate binder, is proposed in \cite{barsoum2006microstructural}, and evidences are also discussed in \cite{harrell1993great, smyth1877our}.
In order to obtain an accurate perception of how the pyramids were constructed, various engineering hypotheses were evaluated in \cite{tasellari2013great}, noting that in their current form they lay the foundations for new theories.
At present the general academic consensus is that pyramids served as funerary monuments and burial sites for the pharaohs. However, it is also widely
theorized that such infrastructures may have been built for another purpose. On an aseptic panoramic view, many connections can be found between the pyramids, vibrations and many mechanical devices reminiscent of hydraulic systems, resonance chambers and acoustic filters \cite{malanga1997cheope,hancock2011fingerprints}. The energy to
make the pyramids vibrate can be provided by natural environment and the Earth's atmosphere infrasound vibrations may provide the source of such energy \cite{bedard2000atmospheric}. This provides a basis for the discussion of special classes of waves, including mountain Lee-waves, infrasound, progressive waves in the lower atmosphere, and waves in the upper atmosphere and ionosphere \cite{gossard1975waves}. Atmospheric sound models and extended to the combination effects of both finite depth ocean and source directivity in both elevation and azimuth angles is studied in \cite{de2020atmospheric}.
Acoustic waves are widely used in the field of archaeology. The acoustics of three important World Heritage sites such as the five caves in Spain, the Stonehenge stone circle in England and the Paphos Theatre in Cyprus are studied in \cite{till2019sound}. Groundwater can influence the geomagnetic field measured in the subsurface. The level of water in the rock determines its electrical conductivity, and thus changes the magnitude of the telluric currents induced in the rock by the change in magnetic fields generated in the ionosphere. This can be studied by using several magnetometers at different points in the subsurface. Geomagnetic signals using two magnetometers were successfully monitored in \cite{henry2014monitoring} by setting an optimal electrokinetic magnitude signal upper-bound.
A methodology used for self-potential and seismic-electromagnetic measurements, both for on-site and laboratory experiments as well as for modeling is extensively described in \cite{jouniaux2012electrokinetics}. The research also provides the bibliography on studies carried out in hydrology to remotely detect water flows, to deduce their thickness, and to predict their hydraulic conductivity. The observation method discussed also proposes the detection of fractures in wells, which is also useful in trying to study earthquakes.
Recent theoretical and experimental studies have produced several unusual and interesting results on the cold fusion of matter experienced on dense lithium \cite{guillaume2011cold}. The existence of this exciting propriety of matter relates to zero-point energy estimates that suggest quantum effects play a significant role in shaping the phase diagram of lithium.
The vibration-induced property change in the melting and solidifying process of silver nanoparticles with the use of molecular dynamics simulation was found in \cite{zheng2017vibration}.
The general problem of acoustic wave propagation through parallel paths is addressed by the information theory of two-port telecommunication networks. This allows any mechanical system to be considered as a single element with two gates. Such a circuit is schematically represented with concentrated elements by admittance that have a value compared to the sum of the corresponding instantaneous admittance existing along the parallel paths. In order to calculate all parameters including those representing transmission losses (e.g. the standing wave ratio), in the case of a non-adaptive paths, the theory of transmission lines is well applicable. A Quincke-tube acoustic filter therefore uses two parallel paths. In order to optimize the maximum wave propagation through the system, the Quincke-tube must be adapted and, through the choice of length and thickness of the ducts, can produce a selective transmission loss, so that it can operate as an acoustic filter. In \cite{hixson1963quincke}, the transmission loss characteristics of several other variations in duct sizes and lengths are presented, together with some very limited experimental data. The phenomenon of pressure pulsations in pipeline systems caused by centrifugal pumps or reciprocating compressors are known to have detrimental effects on industrial applications. An experimental investigation of the attenuation mechanism of a Herschel-Quincke device and its effectiveness in damping pressure pulsations when applied to a resonant piping system had been presented in \cite{lato2019passive}.
The development of mechanical engineering in ancient Egypt through the stone industry was
described in \cite{hassaan2016mechanical}, covering the period from the Predynastic to the Old Kingdom. The characteristics and innovations of stone vessels available in these periods were analyzed.
Conventional sound absorbers can hardly possess the good performance of low-frequency and broadband absorption simultaneously. In order to combine these two functions into one kind of absorbers, the gradually perforated porous materials backed with Helmholtz resonant cavity are proposed in \cite{liu2021gradually}.
A strategy to design three-dimensional elastic periodic structures endowed with complete band-gaps, the first of which is ultra-wide, where the top limits of the first two band-gaps are overstepped in terms of wave transmission in the finite structure is proposed in \cite{d2017mechanical}. Thus, subsequent band-gaps are merged, approaching the behavior of a three-dimensional low-pass mechanical filter.
The debate on how the granite blocks could have been transported up the full height of the pyramids is still an open one. To this end, the theory of in-situ formation of the blocks by means of a cement mixture has also been formulated. Most synthetic stones can be made from re-agglomerated materials. Starting with a mineral substance such as granite rock or naturally eroded, disintegrated or not-aggregated limestone, it is given a compact structure using a binder, such as a geological glue that agglomerates to bond the mineral particles to each other. The result is a new rock with the same mechanical characteristics as a natural equivalent. Such a technique is supposed to have been used to build the pyramid of Khnum-Khufu \cite{davidovits2009pharaohs, barsoum2006microstructural}.
It has been also studied that the generation of waves of any nature can be also correlated with the brain waves of the living creatures. Previous correlations between geomagnetic activity and quantitative changes in electroencephalographic power revealed interesting associations with the right parietal lobe, compatible with theta activity, and the right frontal region for activity in gamma frequencies. During the experiment \cite{mulligan2012experimental}, subjects were exposed to no magnetic field first, then they were exposed to a purely magnetic field of 20 nT or 70 nT, at a frequency of 7 Hz, with amplitude-modulated signals for 30 minutes. Quantitative electroencephalographic (QEEG) measurements were taken before, during and after exposure and results support the thesis that magnetic field fluctuations are primarily responsible for the significant geomagnetic-QEEG correlations reported in several studies. Studying the effects of weak complex magnetic fields on the neuroplasticity of rats, following the induction of early epilepsy, an unprecedented increase in post-crisis mortality (76\%) was observed in young rats that had been exposed perinatally to magnetic fields of 7 Hz with a maximum intensity of about 5 nT. Rats exposed to fields less intense or more intense than this frequency did not show this magnitude of significant mortality \cite{st2007enhanced,whissell2007developmental}.
Back to the pyramid of Khnum-Khufu, for over a century it has been known that the beams forming the ceiling of the King's Chamber and those of the first and second Relieving Chambers in the Great Pyramid are cracked. However, the temporal origin of these cracks is still unknown. The results of a 3D virtual reality computer simulation designed to determine precisely when the beams cracked are reported in \cite{10.2307/24555438}.
Several 3D imaging techniques applied on the Khnum-Khufu pyramid are developed in \cite{bui2011imaging}. Among all the theories formulated to try to explain how the pyramid of Khnum-Khufu was built, there is also the hypothesis of the existence of an internal ramp that goes around the pyramid several times. This theory could prove the fact that the pyramid could have been built in twenty years \cite{lheureux2010analyse}.
Microgravity surveys of the Khnum-Khufu pyramid have shown, considering also the general structure of the pyramid. A new interpretation technique for endoscopy of large finite bodies has been developed in \cite{bui1988application}.
In order to carry out non-invasive internal scans of the pyramid \cite{ivashov2021proposed}, using electromagnetic waves, it is necessary to use special georadar \cite{yoshimura1987non}, which however have the limitation of having little penetration inside the granite.
The study of ancient Egyptian monuments attracted the attention of experts all over the world. A recent event that confirms this is the discovery, using muon sensors \cite{bross2022tomographic,aly2022simulation}, of the presence of a previously unknown cavity located inside the pyramid of Khnum-Khufu. Since this discovery cannot be directly confirmed by drilling, another independent non-destructive method is needed to confirm this discovery and provide an accurate determination of the location and shape of the cavity. A possible holographic radar simulation framework for the detection of openings or other unknown structures of interest is analyzed in \cite{ivashov2021proposed}.
Research \cite{alvarez1970search} for the first time investigated the possibility to use cosmic-ray detectors involved their ability to measure the angle of arrival of penetrating cosmic rays muons with great precision over a large sensitive area. In \cite{morishima2017discovery} authors reported the discovery of a large void (with a cross-section similar to that of the Grand Gallery and a minimum length of 30 metres)
situated above the Grand Gallery.
The investigation of the microgravimetric measurements on the side of a pyramid could also map the recently discovered "muon chamber" in the Great Pyramid of Khnum-Khufu in Egypt. In\cite{pavsteka2022discovery} the exploitation of technical capabilities of modern gravimeters, is used to perform three-dimensional model calculations with realistic model parameters. A gradiometer survey has been carried out in \cite{odah2005gradiometer} over a surface area of 100m $\times$ 100m to achieve the purpose and the magnetic data were processed using Geoplot software in order to obtain high quality images of hidden structures inside the Khnum-Khufu pyramid. The results obtained show the presence of interconnected large tomb structures composed of mud-bricks; some other ancient rooms and walls are also present.
A climbing robot called "Djedi" has been designed, constructed, and deployed in \cite{richardson2013djedi} to explore shafts of the Queen's chamber within the Great Pyramid. The Djedi robot is based on the concept of inchworm motion and is capable of carrying a long reach drill or snake camera. The robot successfully climbed the southern shaft of the Great Pyramid, deployed its snake camera, and revealed writing not seen for thousands of years. Robot design, including climbing steps in the shaft and lessons learned from experimental deployment, has been designed in \cite{richardson2013djedi}.
Satellite remote sensing is widely used in the field of archaeology \cite{evans2006use,chen2017overview}. Data from the use of SAR to survey the southern Maya plains suggest that large areas were continuously drained by ancient canals that may have been used for intensive cultivation. In agreement with the authors of \cite{adams1981radar}, SAR remote sensing confirmed the existence of the canals. Through excavations and in-situ ground surveys, they provided sufficient comparative information. Correlating all the data, it was concluded that the Maya civilization, of the Late Classic period, was firmly based on intensive and large-scale cultivation of marshy areas.
Research \cite{brichieri2020spurred} found an ideal model configuration, associated with spiral ramps, demonstrating how Egyptians could have built the pyramids.
In the past, Synthetic Aperture Radar (SAR) vibrations have been very useful in estimating key vessel characteristics. Research \cite{filippo2019cosmo,biondi2019micro} propose a novel strategy to estimate the micro-motion (mm) of ships from SAR images. The proposed approach is for mm estimation of ships, occupying thousands of pixels, processes the information generated during the coregistration of several re-synthesized time-domain and not overlapped Doppler sub-apertures of COSMO-SkyMed satellite single-look complex (SLC) data.
Authors of \cite{Pia_1} propose a new procedure to monitor critical infrastructures like the Mosul dam, processing COSMO-SkyMed data. The proposed procedure is an in-depth modal assessment based on the mm estimation, through a Doppler sub-apertures tracking and a multi-chromatic analysis.
The procedure described above was made available to perform a comprehensive survey of large road bridges, according to \cite{chen2018structural}. The authors of \cite{biondi2020perspectives,9224142,8714049} successfully formulated a comprehensive procedure to perform structural health monitoring using SAR. The technique allows to successfully estimate the position and shape of cracks on bridges in order to prevent their collapse.
In this paper we use a new method based on the tomographic reconstruction of mm, with the aim to perform imaging of the principal targets that make up visible the main internal structure of the pyramid. We use the similar methods already experimented in \cite{Pia_1} to search for cracks in large infrastructures, but not for tomography. The physical principle we use is that of estimating the vibrations captured by the Khnum-Khufu pyramid during the SAR observation time interval. The vibration estimation is done by evaluating the Doppler centroid anomalies, an indispensable parameter that is used during the SAR azimuth focusing process. We use Doppler sub-apertures to estimate the vibrations present on the pyramid. The vibration energy is generated from many sources such as wind. Great contribution in terms of vibration energy, is also generated by the city of Cairo, which is located closely to the pyramid of Khnum-Khufu and by the presence of Nile river.
We processed several SAR images observed in the Vertical-Vertical (VV) polarization, and the estimated mm allows us to visualize the principal internal components present in the pyramid.
We can state that the experimental results we propose definitively solve one of the oldest mysteries of human existence, the complete solution of the internal structure of Khnum-Khufu.
To this end, in order to provide a more complete contribution to our work, we have firstly investigated the details of the external structure of all the pyramids belonging to the Giza Plateau (Khufu, Kefren and Menkaure), then we concentrated on studying the internal structure of the pyramid of Khnum-Khufu alone, providing a complete and detailed 3D reconstruction of all the known and unknown chambers, based on tomographic SAR measurements.
In the paper, we provide a complete list of the internal structures measured by tomography, each of them marked with a unique sequential number.
\begin{figure}
\centering
\includegraphics[width=12.0cm,height=7.5cm]{Figures/GIZA-Plateau_3.png}
\caption{Electro-optical satellite representation of the Giza plateau. The pyramidal infrastructure is visible, oriented to the North.}
\label{GIZA-Plateau_3}
\end{figure}
\begin{figure}
\centering
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/Knum_Khufu_1.png}
\caption{Khnum-Khufu scheme of the known internal structures.}\label{Knum_Khufu_1}
\end{figure}
\begin{table}[tb!]
\caption{Characteristics of the SAR acquisitions.}
\begin{center}
\begin{tabular}{ p{3cm} p{3cm}}
\hline
SAR parametrer & Value\\
\hline
Chirp bandwidth& 250 MHz\\
PRF& 2 kHz\\
PRT& 0.23 ms\\
Antenna length & 6 m\\
Type of acquisition & Stripmap\\
Polarization & HH\\
Acquisition duration & 5 s\\
Platform velocity & 7 km/s\\
Observation height & 650000 m\\
\hline
\end{tabular}
\label{Table_1}
\end{center}
\end{table}
\section{Giza Plateau Presentation and Description}
The pyramid of Khnum-Khufu is a monumental structure built mainly of granite blocks, its orientation is almost perfectly aligned to the North. The monumental complex of the Giza plateau is represented in Figure \ref{GIZA-Plateau_3}. The three pyramids, Khnum-Khufu (top right), Kefren (located in the center) and Menkaure (the last on the bottom left) can be observed. In this context our work focuses on visualizing the vibrational tomographic profile of the pyramid of Khnum-Khufu. The Figure \ref{Knum_Khufu_1} (a) is the schematic representation of the North-south central section of the infrastructure. The figure represents the schematic of what is known and the main parts of the infrastructure are numbered sequentially from 1 to 11. The object consists of the Zed and the King's chamber, with its sarcophagus inside. The Zed, the details of which can be seen in Figure \ref{Knum_Khufu_1} (b) and (c), is a large monument made entirely of granite, consisting of an upper roof made of two oblique granite slabs, and five parallel stone slabs, spaced at varying distances from each other. Each stone has its upper face not smooth, so each surface has a pronounced roughness. On the contrary, each of its lower faces is extremely smooth. Below this monument is the King's room. Boh the Zed and the king's room are off-axis with respect to the apex of the pyramid and are located toward the south on the north-south symmetry plane. Object 2 of Figure \ref{Knum_Khufu_1} (a), is the Queen's room, a smaller volume object located on the axis of the pyramid and below the King's room. As can be seen from the figure \ref{Knum_Khufu_1} (a), Object 2, unlike the King's room, is located exactly under the apex of the pyramid. The last room is Object 3 which is also off-axis of the pyramid, it is also shifted to the south, but in this case, it is located underground. It is usually called the unfinished room. Object 4 represents a large corridor that connects the King's room with the Queen's room, it is called the Grand Gallery. Objects 5, and 6 are air ducts, while the remaining ducts 8, 9, and 10 connect the Grand Gallery with the Queen's room and the unfinished room (the one located below ground). Object 7 is the entrance to the pyramid, and finally, line 11 indicates the surface on which the pyramid sits.
\begin{figure}
\centering
\centering
\includegraphics[width=8.0cm,height=6.0cm]{Figures/Geometry_1.png}
\caption{SAR acquisition geometry.}\label{Geometry_1}
\end{figure}
\section{Methodology}\label{Methodology}
In this work, the m-m technique is used to perform sonic imaging by processing a single synthetic aperture radar (SAR) image in the single-look-complex (SLC) configuration. The technique involves the m-m estimation belonging to the Khnum-Khufu pyramid and is generated by the background ripple underground seismic activity that reflects superficial vibrations. The m-m estimation is done through MCA, performed in the Doppler direction. Multiple Doppler sub-apertures, SAR images with lower azimuth resolution, are generated to estimate the vibrational trend of some pixels of interest. The infra-chromatic displacement is calculated through the pixel tracking technique \cite{filippo2019cosmo,biondi2019micro}, using high-performance sub-pixel coregistration \cite{biondi2020monitoring,biondi2020perspectives}. Vibrations observed along the tomographic view-direction, embedded into the multi-chromatic Doppler diversity, are focused along the height (or depth) dimension, and developing high-resolution tomographic underground imaging.
The SAR synthesizes the electromagnetic image through a ''side looking'' acquisition, according to the observation geometry shown in Figure \ref{Geometry_1}, where:
\begin{itemize}
\item $r$ is the zero-Doppler distance (constant);
\item $R$ is the slant-range;
\item $R_0$ is the reference range at $t=0$;
\item $d_a$ is the physical antenna aperture length;
\item $V$ is the platform velocity;
\item $d$ is the distance between two range acquisitions;
\item $G_{sa}$ is the total synthetic aperture length;
\item $t$ is the acquisition time variable;
\item $T$ is the observation duration;
\item $t=0$ and $t=T$ are the start and stop time acquisition respectively;
\item $L=\frac{\lambda r}{d_a}$ is the azimuth electromagnetic footprint width;
\item $\theta$ is the incidence angle of the electromagnetic radiation pattern.
\end{itemize}
All the above parameters are related to the staring-spotlight SAR acquisition that is adopted in this work. The SAR data belonging to the electromagnetic image are formed through the focusing process that involves the application of a two-dimensional matched filter acting in the range direction and in the azimuth direction.
The SLC signal resulting from compression is given by \cite{john1991synthetic}:
\begin {eqnarray}\label{Eq_6}
\begin{split}
&s_{SLC}(k,x)=2N\tau \exp\left[-\jmath\frac{4\pi}{\lambda}r\right] \textrm{sinc}\left[\pi B_{c_r}\left(k-\frac{2R}{c}\right)\right] \textrm{sinc}\left[\pi B_{c_D}x\right] \\
&\textrm{for} \ x=kt, \ k=\{0,1,\dots,N-1\} , \ x=\{0,1,\dots,M-1\}, \ \textrm{with} \ N,M \ \in \mathbb{N}.
\end{split}
\end {eqnarray}
Equation \eqref{Eq_6} represents the focused SAR signal generated by the back-scattered electromagnetic energy of a point target supposed to be stationary. The terms $ B_{c_r}$, and $B_{c_D}=\frac{4 Nd}{\lambda r}$ are the total chirp and Doppler bandwidths respectively. The total synthetic aperture is equal to $L_{sa}=2Nd$ and the azimuth resolution $\delta_D\approx \frac{1}{B_{c_D}}=\frac{\lambda R}{2L_{sa}}$.
In \eqref{Eq_6} the $\frac{2\vec{\boldsymbol{R}}}{c}$ parameter identifies the position in range where the maximum of the sinc function is positioned, while in azimuth it is centered around ''zero''.
In the case where the peak of the sinc function has a nonzero coordinate along the azimuth dimension, Equation \eqref{Eq_6} can be recast as:
\begin {eqnarray}\label{Eq_8}
\begin{split}
&s_{SLC}(k,x)=2N\tau \exp\left[-\jmath\frac{4\pi r}{\lambda}\right] \textrm{sinc}\left[\pi B_{c_r}\left(k-L_{c_g}\right)\right] \textrm{sinc}\left[\pi B_{c_D}\left(x-L_{D_h}\right)\right] \\
&\textrm{for} \ L_{c_g}, \ L_{D_h} \ \in \mathbb{N},
\end{split}
\end {eqnarray}
where the DFT is equal to:
\begin {eqnarray}\label{Eq_8_DFT}
\begin{split}
S_{SLC_{F}}(n,q)&=DFT2\left\lbrace2N\tau \exp\left[-\jmath\frac{4\pi r}{\lambda}\right] \textrm{sinc}\left[\pi B_{c_{r}}k\right] \textrm{sinc}\left[\pi B_{c_D}x\right]\right\rbrace \\
&=2N \tau\exp\left[-\jmath\frac{4\pi r}{\lambda}\right]\sum_{k=0}^{N-1}\sum_{x=0}^{M-1} \textrm{sinc}\left[\pi B_{c_{r}}n\right] \textrm{sinc}\left[\pi B_{c_D}q\right]\\
&\exp\left(-\jmath\frac{2\pi k n}{N}\right)\exp\left(-\jmath\frac{2\pi x q}{M}\right)\\
&=2N \tau\exp\left[-\jmath\frac{4\pi r}{\lambda}\right]\frac{1}{\pi B_{c_{r}}}\textrm{rect}\left[\frac{n}{\pi B_{c_{r}}}\right]\frac{1}{\pi B_{c_D}} \textrm{rect}\left[\frac{q}{\pi B_{c_D}} \right]\\
&\exp\left(-\jmath 2 \pi n L_{c_g}\right)\exp\left(-\jmath 2 \pi q L_{D_h}\right),
\end{split}
\end {eqnarray}
which has a rectangular shape.
\subsection{Doppler Sub-Apertures Model}\label{Doppler_Sub_Apertures}
In this paper we experiment a strategy that employs Doppler sub-apertures, that are generated to measure target motion. Figure \ref{Bandwidth_Strategy_1} represents the used bandwidth allocation strategy. From the single SAR image we calculate the 2D digital Fourier Transform (DFT) which, according to \eqref{Eq_8_DFT}, has a rectangular shape. As can be seen from Figure \ref{Bandwidth_Strategy_1}, $B_{C_D}$ is the total Doppler band synthesized with the SAR observation, while $B_{D_L}=\frac{B_{C_D}}{2}$ is the bandwidth we left out from the matched-filter boundaries, to obtain a sufficient sensitivity to estimate target motions. In this context formula \ref{Eq_8_DFT} is the focused SAR spectrum, at maximum resolution, thus exploiting the whole band $\{B_{c_r},B_{C_D}\}$, in accordance with the frequency allocation strategy shown in Figure \ref{Bandwidth_Strategy_1}, the following range-Doppler sub-apertures large-matrix is constructed for the Master multi-dimensional information:
\begin {eqnarray}\label{Eq_8_matrix}
\begin{split}
&S_{SLC}(k,x)_{M}= \begin{bmatrix}
S_{SLC}(k,x)_{M_{\{1,1\}}} & S_{SLC}(k,x)_{M_{\{1,2\}}} & S_{SLC}(k,x)_{M_{\{1,3\}}} & \dots & S_{SLC}(k,x)_{M_{\{1,N_D\}}}
\end{bmatrix}\\
&\textrm{for} \ N_D \ \in \mathbb{N},
\end{split}
\end {eqnarray}
and for the slave, the following large-matrix is presented:
\begin {eqnarray}\label{Eq_9_matrix}
\begin{split}
&S_{SLC}(k,x)_{S}= \begin{bmatrix}
S_{SLC}(k,x)_{S_{\{1,1\}}} & S_{SLC}(k,x)_{S_{\{1,2\}}} & S_{SLC}(k,x)_{S_{\{1,3\}}} & \dots & S_{SLC}(k,x)_{S_{\{1,N_D\}}}
\end{bmatrix}\\
&\textrm{for} \ N_D \ \in \mathbb{N},
\end{split}
\end {eqnarray}
\begin{figure}
\centering
\begin{subfigure}
\centering
\includegraphics[width=15.0cm,height=4.0cm]{Figures/Bandwidth_Strategy_1.png}
\end{subfigure}\quad
\caption{Doppler sub-aperture strategy.}\label{Bandwidth_Strategy_1}
\end{figure}
The explanation of the chirp-Doppler sub-aperture strategy, represented in Figure \ref{Bandwidth_Strategy_1} is the following: We consider Figure \ref{Bandwidth_Strategy_1}, where Master and slave sub-bands are generated by focusing the SAR image, where the matched-filter is set to exploit a range-azimuth bandwidth equal to ${B_{c_r},B_{c_D}-B_{D_L}}$. The not-processed bandwidths $B_{D_L}$ are divided into $N_D$ equally-distributed bandwidths steps respectively. At this point $N_c$ rigid shifts of the master-slave system are made along the azimuth bandwidth domain, this is made to populate the entire row of \ref{Eq_8_matrix}, and \ref{Eq_9_matrix}. The process is repeated $N_D$ times for each shift in azimuth, in fact, Figures \ref{Bandwidth_Strategy_1} (1), (2) and (3), represent the azimuth frequency variation strategy when the Doppler bandwidth is located at $N_D$. At each Doppler frequency shift $\frac{B_{c_D}-B_{D_L}}{N_D}$ every element of \ref{Eq_8_matrix}, and \ref{Eq_9_matrix} is populated.
\subsection{Doppler Sub-Aperture Strategy}
The decomposition of the SAR data into Doppler sub apertures is formalized in this subsection, which is performed starting from the spectral representation of the focused SAR data.
To this end, notice that the generic $i-$th chirp sub-aperture 2-dimensional DFT of \eqref{Eq_8} is given by:
\begin {eqnarray}\label{Eq_9}
\begin{split}
&S_{SLC_{F_i}}(n,q)=DFT2\left\lbrace2N\tau \exp\left[-\jmath\frac{4\pi r}{\lambda}\right] \textrm{sinc}\left[\pi B_{c_{r_i}}\left(k-L_{c_g}\right)\right] \textrm{sinc}\left[\pi B_{c_D}\left(x-L_{D_h}\right)\right]\right\rbrace \\
&=2N \tau\exp\left[-\jmath\frac{4\pi r}{\lambda}\right]\sum_{k=0}^{N-1}\sum_{x=0}^{M-1} \textrm{sinc}\left[\pi B_{c_{r_i}}\left(n-L_{c_g}\right)\right] \textrm{sinc}\left[\pi B_{c_D}\left(q-L_{D_h}\right)\right]\\
&\exp\left(-\jmath\frac{2\pi k n}{N}\right)\exp\left(-\jmath\frac{2\pi x q}{M}\right)\\
&=2N \tau\exp\left[-\jmath\frac{4\pi r}{\lambda}\right]\frac{1}{\pi B_{c_{r_i}}}\textrm{rect}\left[\frac{n}{\pi B_{c_{r_i}}} \right]\frac{1}{\pi B_{c_D}} \textrm{rect}\left[\frac{q}{\pi B_{c_D}} \right] \exp\left(-\jmath 2 \pi n L_{c_g}\right)\exp\left(-\jmath 2 \pi q L_{D_h}\right).
\end{split}
\end {eqnarray}
From the last equation, it turns out that a single point stationary target has a two-dimensional rectangular nature with total length proportional to the range-azimuth bandwidths respectively. The phase term $\exp\left(-\jmath 2 \pi n L_{c_g}\right)\exp\left(-\jmath 2 \pi q L_{D_h}\right)$ is due to the sinc function dislocation in range and azimuth when the SLC SAR data are considered.
In the SAR, the movement of a point target with velocity in both range and azimuth direction is immediately warned by the focusing process, resulting in the following anomalies:
\begin{itemize}
\item azimuth displacement in the presence of target constant range velocity;
\item azimuth smearing in the presence of target azimuth velocity or target range accelerations;
\item range-walking phenomenon, visible as range defocusing, in the presence of target range speed, backscattered energy can be detected over one or more range resolution cells.
\end{itemize}
In practical cases, the backscattered energy from moving targets is distributed over several range-azimuth resolution cells.
As a matter of fact, considering the point-like target $T_1$ (of Figure \ref{Geometry_1}) that is moving with velocity $\vec{\boldsymbol{v}}_t$ whose range-azimuth and acceleration components are $\{v_r,v_a\}$, and $\{a_r,a_a\}$, respectively, then we can write
\begin {eqnarray}\label{Eq_10}
\begin{split}
&R^2(t)=(V t-S_a)^2+(R_0-S_r)^2 \ \textrm{with} \ S_r=v_r t+\frac{1}{2}a_r t^2 \ \textrm{and} \ S_a=v_a t+\frac{1}{2}a_a t^2 \\
&\left|R(t)\right|=\left|R_0-S_r\right|\left\lbrace 1+\frac{\left(Vt-S_a\right)^2}{\left(R_0-S_r\right)^2} \right\rbrace^\frac{1}{2}.\\
\end{split}
\end {eqnarray}
Considering the following Taylor expansion:
\begin {eqnarray}\label{Eq_11}
\begin{split}
&\left(1+x\right)^\beta\approx1+\beta x\\
\end{split}
\end {eqnarray}
and that $R_0-S_r\approx R_0$, and $\left(V_t-S_a\right)^2 \approx V^2 t^2 - 2V t S_a$, \eqref{Eq_10} can be written in the following form:
\begin {eqnarray}\label{Eq_12}
\begin{split}
&\left| R(t) \right| = \left\lbrace \left| R_0-S_r \right| + \frac{1}{2}\frac{\left(Vt-S_a\right)^2}{\left(R_0-S_r\right)} \right\rbrace = |R_0-S_r|+\frac{V^2t^2}{2R_0} \left( 1-\frac{2S_a}{Vt} \right)
\end{split}
\end {eqnarray}
\begin {eqnarray}\label{Eq_13}
\begin{split}
&=R_0-S_r+\frac{V^2t^2}{2R_0}-\frac{V t S_a}{R_0} \\
&=R_0 - v_r t-\frac{1}{2}a_r t^2+\frac{V^2t^2}{2R_0}-\frac{V t \left(v_a t+\frac{1}{2}a_a t^2\right)}{R_0}\\
&=R_0 - v_r t-\frac{1}{2}a_r t^2+\frac{V^2t^2}{2R_0}-\frac{V v_a t^2}{R_0}-\frac{V a_a t^3}{2R_0}.
\end{split}
\end {eqnarray}
The term $\frac{V a_a t^3}{2R_0}$ can be neglected and by approximating $\left(V^2-2Vv_a\right)\approx\left(V-v_a\right)^2$ Equation \eqref{Eq_13} can be written like:
\begin {eqnarray}\label{Eq_14}
\begin{split}
&\left|R(Vt)\right|=R_0-v_r t + \frac{t^2}{2R_0} \left[ \left( V-v_a \right)^2 -R_0 a_r\right].
\end{split}
\end {eqnarray}
recasting \eqref{Eq_14} in terms of $x=Vt$, we obtain \cite{4103740}:
\begin {eqnarray}\label{Eq_15}
\begin{split}
&\left|R(x)\right|=R_0-\epsilon_{r_1}x+ \left[ \left( 1-\epsilon_{c_1} \right)^2 - \epsilon_{r_2} \right] \frac{x^2}{2R_0}, \ x=Vt.
\end{split}
\end {eqnarray}
where:
\begin{itemize}
\item $\epsilon_{r_1}=\frac{v_r}{V}$ (due to range velocity);
\item $\epsilon_{r_2}=\frac{a_rR_0}{V^2}$ (due to range acceleration);
\item $\epsilon_{c_1}=\frac{v_c}{V}$ (due to azimuth velocity).
\end{itemize}
Thus, the above terms modify the received signal, as shown in \cite{4103740}, and should be taken into account in Equation \eqref{Eq_9} .
\section{Tomographic Model}\label{Methods}
Considering a single SLC image from which we applied the MCA according to the frequency allocation strategy depicted in Figure \ref{Bandwidth_Strategy_1}, the tomogram represented by the line of contiguous pixels shown in Figure \ref{Tomo_1} is calculated. The vibrations present on the tomographic plane extending from the Earth's surface to a depth of a few kilometres is assessed. The figure represents a series of harmonic oscillators anchored on each pixel of the tomographic line, symbolically represented as a spring linked to a mass and oscillating due to the application of harmonic vibrations. Each wave generated by each harmonic oscillator bounces off the surface of the Earth as there is an abrupt variation in the density of the medium (the ground-air boundary). On each pixel a vibrational phasor is observed in time applying Doppler MCA \cite{biondi2020monitoring,biondi2020perspectives}.
Through the orbital change of view (which is performed in azimuth), an effective subsurface in-depth vibrational scan of the Earth is achieved.
\begin{figure}
\centering
\begin{subfigure}
\centering
\includegraphics[width=15.0cm,height=4.5cm]{Figures/Tomo_1.png}
\end{subfigure}\quad
\caption{Tomographic acquisition geometry.}\label{Tomo_1}
\end{figure}
\subsection{Vibrational Model of the Earth}\label{Vibrational_Model_of_cables}
The proposed vibrational model of the Earth surface is schematically shown in Figure \ref{Tomo_1} (a), and (b). The geometrical reference system for both sub-pictures is the range, azimuth and altitude three-dimensional space. For the present case, the vertical dimension represents the depth below the topographic level, (for this specific case the medium boundary is represented by the green plane). The tomographic line of interest is constituted of the series of contiguous pixels laying on the green plane. As can be seen from Figure \ref{Tomo_1} (a) on each pixel belonging to the tomographic line, a mass is hanging using a spring. This system is now induced to oscillate harmonically, helped by the Earth magma instability. These oscillations are schematized as the vibration energy function visible in Figure \ref{Tomo_1} (b). In this context the radar instantaneously perceives this coherent harmonic oscillation. In a mathematical point of view, the Earth displacement is perceived as a complex shift belonging on each pixel of interest. Each instantaneously displacement is estimated between the master image with respect to the slave, where oversimplification shifts are estimated through the pixel tracking technique \cite{biondi2020monitoring,biondi2020perspectives}. The number of tomographic independent looks (depending on the total number of Doppler sub-apertures) are defined by the parameter $k$.
We suppose now the spring being perturbed by an impulsed force. According to this perturbation the rope begins to vibrate describing an harmonic motion (in this context we are not considering any form of friction). Resulting perturbation moves the rope through the space-time in the form of a sinusoidal function. The seismic wave will then reach a constraint end that will cause it to reflect in the opposite direction. The reflected wave will then reach the opposite constraint that will make it reflect in the original direction and returning in the initial location, maintaining the same frequency and amplitude. According to Classical Physics principles, the rebounding wave is superimposed on the arriving wave, and the interference of two sine waves with the same amplitude and frequency propagating in opposite directions leads to the generation of an ideal and perpetual standing wave on the spring. Each vibrational channel is now considered when the spring is able to oscillate into the three-dimensional space, according to specific perturbation nature. When the Earth vibrates, it happens that the length of the spring must also fluctuate. This phenomenon causes oscillations in the tension domain of the spring. It is clear that these oscillations (i.e. the longitudinal ones) propagate through a frequency approximately twice as high as the frequency value of the transverse vibrations. The coupling between the transverse and longitudinal oscillations of the spring can essentially be modeled through non-linear phenomena.
\begin{figure}
\centering
\includegraphics[width=16.0cm,height=6.5cm]{Figures/Interferometric_Phase_1.png}
\caption{SAR image representing the interferometric repeat-pass phase of the Giza plateau.}
\label{Interferometric_Phase_1}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=16.0cm,height=6.0cm]{Figures/Interferometric_Coherence_1.png}
\caption{SAR image representing the interferometric repeat-pass coherence of the Giza plateau.}
\label{Interferometric_Coherence_1}
\end{figure}
{\color{black}Figure \ref{Tomo_1} (c, d) illustrates the oscillating model in the Euclidean space-time coordinates (x,y,z,t), where the satellite motion has been purified from any orbital distortions, so that the geometric parameters used to perform the tomographic focusing can be rigorously understood.} From Figure \ref{Tomo_1} (c), $L$ is the length of the spring when it is at its maximum tension while $L_0$ is its length when no mass is present. Finally the spring has been considered to have an elastic constant equal to $\xi$. The vibrational force applied to the mass $m1$ of Figure \ref{Tomo_1} (c) is equal to \cite{tufillaro1989nonlinear}:
\begin {eqnarray}\label{Eq_16}
\begin{split}
&F=-4 \xi \mathbf{r} \left(1-\frac{L_0}{\sqrt{L^2+4\mathbf{r}^2}}\right).
\end{split}
\end {eqnarray}
If $\mathbf{r}\ll L$, \eqref{Eq_16} is expanded in the following series:
\begin {eqnarray}\label{Eq_16_Bis}
\begin{split}
&F=-4 \xi \mathbf{r}(L-L_0)\left(\frac{\mathbf{r}}{L}\right)-8 \xi L_0 \left[\left(\frac{\mathbf{r}}{L}\right)^3-\left(\frac{\mathbf{r}}{L}\right)^5+\dots\right],
\end{split}
\end {eqnarray}
where a precise approximation of \eqref{Eq_16_Bis} is the following cubic restoring force:
\begin {eqnarray}\label{Eq_18}
\begin{split}
&F=m\ddot{\mathbf{r}}\approx-4 \xi \mathbf{r}(L-L_0)\left(\frac{\mathbf{r}}{L}\right) \left[1+\frac{2L_0}{(L-L_0)}\left(\frac{\mathbf{r}}{L}\right)^2\right].
\end{split}
\end {eqnarray}
Considering \eqref{Eq_18}, the non-linearity dominates when $L \approx L_0$.
If we define:
\begin {eqnarray}\label{Eq_19}
\begin{split}
&\omega_0=\frac{4 \xi}{m}\left[\frac{\left(L-L_0\right)}{L}\right],
\end{split}
\end {eqnarray}
and
\begin {eqnarray}\label{Eq_20}
\begin{split}
&\xi=\frac{2L_0}{L^2}\left(L-L_0\right).
\end{split}
\end {eqnarray}
Considering \eqref{Eq_18} we have:
\begin {eqnarray}\label{Eq_21}
\begin{split}
&\ddot{\mathbf{r}}+\omega^2 \mathbf{r} \left(1+ \xi\mathbf{r}^2\right)=0.
\end{split}
\end {eqnarray}
If we consider damping and forcing \eqref{Eq_21} is modified as:
\begin {eqnarray}\label{Eq_24}
\begin{split}
&\ddot{\mathbf{r}}+\lambda\dot{\mathbf{r}}+\omega^2\left(1+\xi\mathbf{r}^2\right) \mathbf{r}=\mathbf{f}(\omega t),
\end{split}
\end {eqnarray}
where $\mathbf{f}(\omega t)$ is the forcing term and $\lambda$ is the damping coefficient.
If non-linearity of \eqref{Eq_24} is sufficiently low, it can be reduced into the following two-degree-of-freedom linear harmonic oscillator:
\begin {eqnarray}\label{Eq_23}
\begin{split}
&\mathbf{r}(t)=\left(a \cos\omega_0 t, b\sin \omega_0 t\right)\exp\left(\frac{-\lambda t}{2}\right).
\end{split}
\end {eqnarray}
In \ref{Eq_23} $\{a,b\}$ are the instantaneous shifts estimated by the coregistrator. The harmonic oscillator \eqref{Eq_23} is the displacement parameters ${\epsilon_{r_1}, \epsilon_{r_2}, \epsilon_{c_1}}$ estimated by \eqref{Eq_15}.
According to Figure \ref{Tomo_1} (d) the vector representation of $k$ samples of the time-domain function \eqref{Eq_23} consisting in the following multi-frequency data input is considered:
\begin {eqnarray}\label{eq_2}
\mathbf{Y} =\left[\mathbf{y}(1),\dots ,\mathbf{y}(k)\right],\in \mathbf{C}^{k\times 1}.
\end {eqnarray}
The steering matrix $\mathbf{A}(z)=\left[\mathbf{a}(z_{min}),\dots,\mathbf{a}(z_{MAX})\right]$, $\in \mathbf{C}^{k\times F}$ contains the phase information of to the Doppler frequency variation of the sub-aperture strategy, associated to a source located at the elevation position $\mathbf{z} \in \{z_{min},z_{MAX}\}$,
\begin{eqnarray}\label{Eq_31}
\mathbf{A}(\mathbf{K}_z,\mathbf{z})= \begin{bmatrix}
1,\exp(\jmath 2\pi k_{z_2} t z_0),\dots,\exp(\jmath 2\pi k_{z_{k-1}} t z_0) \\
1,\exp(\jmath 2\pi k_{z_2} t z_1),\dots,\exp(\jmath 2\pi k_{z_{k-1}} t z_1) \\
\dots \\
1,\exp(\jmath 2\pi k_{z_2} t z_{F-1}),\dots,\exp(\jmath 2\pi k_{z_{k-1}} t z_{F-1})
\end{bmatrix},
\end{eqnarray}
where $\mathbf{K}_z= \frac{4\pi B_{\perp}}{\lambda \mathbf{r}_i \sin \theta}$, $i=1,\dots,k$, $B_\perp$ is the $i-$th orthogonal baseline which is visible in Figure \ref{Tomo_1} (d), and $\mathbf{r}_i$ is the $i-$th slant-range distance. The standard sonic tomographic model is given by the following relation:
\begin{eqnarray}\label{Eq_35}
\mathbf{Y}&=\mathbf{A}(\mathbf{K}_z,\mathbf{z}) {\mathbf{h}}(\mathbf{z}).
\end{eqnarray}
where in \eqref{Eq_35} ${\mathbf{h}}(\mathbf{z}) \in \mathbf{C}^{1 \times F}$, inverting \eqref{Eq_35} I finally find the following tomographic solution:
\begin{eqnarray}\label{Eq_34}
{\mathbf{h}}(\mathbf{z})&=\mathbf{A}(\mathbf{K}_z,\mathbf{z})^\dagger \mathbf{Y}.
\end{eqnarray}
In the \eqref{Eq_34} the steering matrix $\mathbf{A}(\mathbf{K}_z,\mathbf{z})$ represents the best approximation of a matrix operator performing the digital Fourier transform (DFT) of $\mathbf{Y}$. The tomographic image $\mathbf{h}(\mathbf{z})$, which represents the spectrum of $\mathbf{A}(\mathbf{K}_z,\mathbf{z})$, is obtained by doing pulse compression.
The tomographic resolution is equal to $\delta_T=\frac{\lambda R}{2 A}$, where $\lambda$ is the sound wavelength over the Earth, $R$ is the slant range, and $A$ is the orbit aperture considered in the tomographic synthesis, in other words, consists to the Doppler bandwidth used to synthesize the sub-apertures. The maximum tomographic resolution obtainable using this SLC data, synthesized at 24 kHz, is as follows. Considering an average speed of propagation of the seismic waves of about $v \approx 6000 \frac{m}{s}$, a frequency of investigation set by us equal to 12500 Hz, the wavelength of these vibrations is equal to about $\lambda=\frac{v}{f}\approx \frac{6000}{12500} \approx 0.48 m$. Considering the above parameters, extending the tomography to the maximum orbital aperture equal to half the total length of the orbit, therefore about $42000$ m, with $R=650000 m$ the tomographic resolution is equal to $\delta_z=\frac{\lambda R}{2 A}= \frac{0.48 \cdot 650000}{2 \cdot 42000} \approx 3.71 m$. This is the tomographic resolution set to calculate all the experimental parts shown in section \ref{Experimental_Rasults_All}.
\begin{figure}
\centering
\includegraphics[width=16.0cm,height=4.5cm]{Figures/Interferometric_Phase_Cut_1_All.png}
\caption{Electro-optical satellite representation of the Giza plateau. The pyramidal infrastructure is visible, oriented to the North.}
\label{Interferometric_Phase_Cut_1_All}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=16.0cm,height=4.5cm]{Figures/Intererogramma_3_Khufu_Nord_2.png}
\caption{Representation in particular of the pyramid of Khnum-Khufu. Interferometric phases. (a): North side. (b,c,d): magnification of interferometric fringe 1,2, and 3.}
\label{Intererogramma_3_Khufu_Nord_2}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=16.0cm,height=3.5cm]{Figures/Intererogramma_3_Khufu_All_Ovest.png}
\caption{Representation in particular of the pyramid of Khnum-Khufu. Interferometric phases. (a): East side. (b,c,d): magnification of interferometric fringe 1,2, and 3.}
\label{Intererogramma_3_Khufu_All_Ovest}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=16.0cm,height=4.0cm]{Figures/Intererogramma_3_Khufu_All_Est.png}
\caption{Representation in particular of the pyramid of Khnum-Khufu. Interferometric phases. (a): West side. (b,c,d): magnification of interferometric fringe 1,2, and 3.}
\label{Intererogramma_3_Khufu_All_Est}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=16.0cm,height=4.0cm]{Figures/Chefren_Nord_All.png}
\caption{Representation in particular of the pyramid of Kefren. Interferometric phases. (a): North side. (b,c,d): magnification of interferometric fringe 1,2, and 3.}
\label{Chefren_Nord_All}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=16.0cm,height=4.0cm]{Figures/Chefren_Est_All.png}
\caption{Representation in particular of the pyramid of Kefren. Interferometric phases. (a): Est side. (b,c,d): magnification of interferometric fringe 1,2, and 3.}
\label{Chefren_Est_All}
\end{figure}
\section{Experimental Results}\label{Experimental_Rasults_All}
In this section we will show all the experimental results that have been made and have been divided into external, and internal, experimental results. In the first case, we show the results provided by SAR interferometry (InSAR). These consist of the evaluation of radar interferometric fringes to demonstrate the actual shapes of the outer facades of all pyramids in the Giza Plateau. The detailed explanation is provided in the subsection \ref{Experimental_Rasults_External}. Similarly the results for the internal vibrational tomography analysis of Khnum-Khufu alone, are discussed in detail in subsection \ref{Experimental_Rasults_Internal}.
\section{External Experimental Results}\label{Experimental_Rasults_External}
This subsection shows and discusses all the results obtained with the aim of revealing new features of the external appearance of all pyramids residing on the Giza Plateau. In order to achieve this goal, we employed the InSAR technique and evaluated the nature of the interferometric fringes and discovered, through the measurement of their inclination, that all pyramids do not each consist of four faces but of eight faces. We found that each face of each pyramid had an inwards bow that became more relevant closer to the ground much like a trough. Figures \ref{Interferometric_Phase_1} show the interferometric fringes generated by two SAR repeat-pass acquisitions, with a suitable spatial baseline in order to generate a series of well-estimated interferometric fringes imprinted on the faces of the pyramids. The interferometric acquisition was performed along a time baseline equal to the complete orbital cycle of the single CSG satellite, which coincides with 16 days. In spite of the substantial number of waiting days, the interferometric acquisition appears not to be very noisy and this quality is confirmed through the evaluation of the coherence parameter whose map is represented in Figure \ref{Interferometric_Coherence_1}. This result appears very good, as a large part of the figure, removing all the areas where the radar shadow is present, maintains coherence levels very close to 1.
The Figure \ref{Interferometric_Phase_Cut_1_All} (a) represent the details of the InSAR fringes measured on the three pyramids (Khufu, Kefren, and Menkaure), while Figure \ref{Interferometric_Phase_Cut_1_All} (b) is the detail of the pyramid of Khnum-Khufu, and finally Figure \ref{Interferometric_Phase_Cut_1_All} (c) is the pyramid of Kefren. Figure \ref{Intererogramma_3_Khufu_Nord_2} (a), (b), (c) and (d), are the particular representations of the SAR interferometric fringes observed on the North face of the Pyramid of Khnum-Khufu (in box (a)). The remaining boxes (b), (c) and (d), represent the first, second and third interferometric fringes observed on the North face of the same pyramid, starting from the bottom. The inclination of the entire face of the pyramid is clearly observed, having symmetry along the height of the geometric figure. The east face of the Khnum-Khufu pyramid is depicted in Figure \ref{Intererogramma_3_Khufu_All_Ovest} (a), while the details of the first, second and third fringe (starting from the ground plane) are shown in Figure \ref{Intererogramma_3_Khufu_All_Ovest} (b), (c) and (d) respectively. Here again, the same effect is observed whereby the single face is divided into two indented half-faces. The West face also presents the same architectural feature, in fact, Figure \ref{Intererogramma_3_Khufu_All_Est} (a), depicts the extension of the interferometric fringes extended over the entire West face, while the details of the first, second and third fringes (always starting from the ground plane), are shown in Figure \ref{Intererogramma_3_Khufu_All_Est} (b), (c) and (d) respectively.
We now move to the pyramid of Kefren to repeat the same experiments where the same qualitative evaluation of the SAR interferometric fringes present on the three facets of it, except for the South one, will be carried out, reaching the identical conclusions made for the pyramid of Khufu. Figure \ref{Chefren_Nord_All} (a), (b), (c) and (d), are the particular representation of the SAR interferometric fringes observed on the North face of the Pyramid of Kefren (in box (a)). The remaining boxes (b), (c) and (d), represent the first, second and third interferometric fringes observed on the North face of the same pyramid, starting from the bottom. The East Front of the second Kefren pyramid is analyzed in Figure \ref{Chefren_Est_All} (a), depicting the extent of the interferometric fringes as a whole, while the details of the first, second and third fringes (starting from the ground plane) are shown in Figure \ref{Chefren_Est_All} (b), (c) and (d) respectively. The West Façade is also studied in Figure \ref{Chefren_Ovest_All} (a), along with its first, second and third fringe details (starting from the ground plane), which are shown in Figure \ref{Chefren_Ovest_All} (b), (c) and (d) respectively.
\begin{figure}
\centering
\includegraphics[width=16.0cm,height=4.0cm]{Figures/Chefren_Ovest_All.png}
\caption{Representation in particular of the pyramid of Kefren. Interferometric phases. (a): West side. (b,c,d): magnification of interferometric fringe 1,2, and 3.}
\label{Chefren_Ovest_All}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=16.0cm,height=4.0cm]{Figures/Micerino_All.png}
\caption{Representation in particular of the pyramid of Menkaure. Interferometric phases. (a): Menkaure pyramid. (b): East-side interferometric fringe particular. (c): West-side interferometric fringe particular. (d): North-side interferometric fringe particular.}
\label{Micerino_All}
\end{figure}
Although much smaller, the pyramid of Menkaure is also well represented by the interferometric radar. As a matter of fact, Figures (a), (b), (c) and (d) depict the entire pyramid (in Figures (a)), while Figures (b), (c) and (d) depict the first fringe starting from the ground plane of the East, West, and North faces respectively. Surprisingly, the pyramid of Menkaure also consists of eight facets and not four (while maintaining the fact that the south face could not be observed because in radar shadow).
This subsection, which focused on presenting the results of external measurements alone, ends by rigorously demonstrating, through radar measurements, the eight-sided nature of the three pyramids of Khufu, Kefren and Menkaure. In the next subsection, the internal measurements that were made from space will be detailed, in order to carry out for the first time the complete internal mapping of all structures belonging to the pyramid of Khnum-Khufu alone.
\begin{figure}
\centering
\includegraphics[width=10.0cm,height=8.0cm]{Figures/Fully_3D_2_1.jpeg}
\caption{(a): SLC SAR image in magnitude representation of Khnum-Khufu. (b): Schematic representation of Khnum-Khufu.}
\label{Fully_3D_1}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=15.0cm,height=6.5cm]{Figures/Knum-Khufu_NS_Merged_1.png}
\caption{(a): Tomographic map of Khnum-Khufu overlapped to its schematic representation. (b): Tomographic map of Khnum-Khufu.}
\label{Merged_0}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=15.0cm,height=6.5cm]{Figures/Tomografia_Principale_3.jpg}
\caption{Schematic representation of the Khufu pyramid.}
\label{Merged_1}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=15.0cm,height=4.5cm]{Figures/Zed_1.jpg}
\caption{Imagine SAR of the pyramid of Khnum-Khufu. The V-shaped plot represents the tomographic line for which the vibrations were calculated, so that the inner section of the pyramid can be represented.}
\label{SLC_3}
\end{figure}
\section{Internal Experimental Results of Khnum-Khufu}\label{Experimental_Rasults_Internal}
Data analysis obtained using te SAR tomographic Doppler imaging technique was able to provide clear objective elements to understand the internal structure of the pyramid of Khnum-Khufu. When proposing our results, we start by describing the well-known structures and then move on to the description of all the unknown structures.
The internal imaging obtained from multiple angles, allow us to obtain an accurate 3D model that gave us the possibility, like never before, to take a look inside one of the most important and mysterious megalithic monuments in the world.
This subsection describes all the tomographic measurements and the entire internal architecture of Khnum-Khufu has been redesigned, which we propose in Figure \ref{Fully_3D_1}. The complete list of rooms, corridors and tunnels that had never been inventoried until now is shown in Tab. \ref{Tab_1}. Each structure (simple or complex) was assigned to a unique tag numbered from 1 to 20, according to Figure \ref{Fully_3D_1}. For this work, we have not used any kind of simulated data or predictive mathematical model, but rather we report in a scientific manner what the CSG satellite has brought to our attention. Here we list the explanation of all the results obtained respecting the order given in Tab. \ref{Tab_1}. Each structure listed in Tab. \ref{Tab_1} will be described in detail, identified in the tomography and reconstructed within a Computer-Aided Design and Drafting (CAD) environment where all measurements will be provided.
\begin{figure}
\centering
\includegraphics[width=15.0cm,height=3.5cm]{Figures/Regina_1.jpg}
\caption{(a): Schematic representation of the ZED (box 1 details of Figure \ref{Merged_1} (b)). (b): (b): Schematic representation of the ZED (box 1 details of Figure \ref{Merged_1} (b)) partially overlapped to tomographic result. (c): Figure \ref{Merged_1} (b) box 1 details Tomographic result.}
\label{SLC_4}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/Connessione_Reg_Sotto_2.png}
\caption{(a): Schematic representation of Figure \ref{Merged_1} (b) box 3 details partially overlapped with tomographic result. (b): tomographic result of Figure \ref{Merged_1} (b) box 3 details.}
\label{Connessione_Reg_Sotto}
\end{figure}
\subsection{Imaging of known structures}
Before describing what has been discovered (what is still unknown) we propose the imaging of the known objects, in particular the King's room, the Zed, the Queen's room, the Grand Gallery, the grotto, and the so-called unfinished room. The SAR image of the pyramid is shown in Figure \ref{Merged_0} (a), while the internal diagram of the pyramid, oriented towards the North (the Northern direction goes from left to right) is shown in Figure \ref{Merged_0} (b). The first tomographic result is presented in Figure \ref{Merged_1} (a) and (b). This result is illustrated in Figure \ref{Merged_0} (a) by means of two yellow lines (identified by the number 1) that extend from the ground towards the pyramid apex. By estimating the vibrations, the pyramid is transparent like a crystal due to their penetration characteristics within the solid rock, and its internal structures can be observed in Figure {\ref{Merged_1} (a) and (b). Figure \ref{Merged_1} (a) represents the sonic tomography partially overlapped with the picture in Figure \ref{Merged_0} (b), while Figure \ref{Merged_0} (b) shows the non-overlapped tomography where three areas of interest are shown, and details are below studied. Figure \ref{SLC_3} (a), (b) and (c) is the detailed representation of the ZED, located inside box number 1 of Figure \ref{Merged_1}(b), where \ref{SLC_3} (a) is the schematic representation, while Figures \ref{SLC_3} (b) and (c) are the partially overlapped, and not-overlapped tomography magnitude images respectively. The Queen's chamber particular is depicted in Figure \ref{SLC_4} (a), (b) and (c), here we use the same representation strategy where \ref{SLC_4} (a) is the room scheme and Figures \ref{SLC_4} (b) and (c) are the partially overlapped and not-overlapped tomography respectively. Figure \ref{Connessione_Reg_Sotto} (a) and (b) is the detailed image contained within the red box 3 of Figure \ref{Merged_1} (b) and the void commonly referred to as 'the Grotto' is clearly visible. The lower chamber, the one commonly referred to as 'the unfinished room', is detected by radar, although with a weak signal, within the white box number 2. The Queen's room appears to be connected through a corridor connecting the grotto to the room below. This corridor, although it appears to be abruptly interrupted, is detected through a radar signature, which is marked by the white arrow number 3. It is assumed that this corridor follows the trajectory indicated by the red line, also pointed out by the white arrow number 3. Figure \ref{Knum_Khufu_1} (b) and (c) show the detailed figure of the ZED, the colossal monument located at the heart of the pyramid (visible in Figure \ref{Merged_1} (a)). Figure \ref{Knum_Khufu_1} (b) is its representation along the West-East direction, while Figure \ref{Knum_Khufu_1} (c) shows its pattern along the South-North direction. Concluding this section we propose in Figure \ref{ZED_12} (a) and (b) the partially and not-overlapped tomography of the Zed respectively, where also the King's chamber is visible.
Here we show in sequence all the tomographies we have calculated, whereby for each of them the subpicture (a) represents the SAR image in magnitude, whereby the tomographic line of investigation is visible (indicated with a yellow line marked with the number 1), while subpicture (b) represents the tomogram (again in magnitude). In order to be more clear, we report the aforementioned figures in Table \ref{Tab_2}:
\begin{figure}
\centering
\includegraphics[width=15.0cm,height=7.0cm]{Figures/ZED_NEW_2.png}
\caption{Schematic representation of the Zed and the King chamber.}
\label{ZED_12}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=15.0cm,height=5.0cm]{Figures/Paper_Ingresso_Principale_3}
\caption{Entrance on Khnum-Khufu. (a): Optical image. (b): Tomographic map (magnitude).}
\label{Paper_Ingresso_Principale_3}
\end{figure}
\begin{figure}[htp]
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/Mask_6.png}
\caption{SAR images. (a): SLC SAR image (magnetude). (b): Tomographic result (magnetude).}
\label{Mask_6}
\end{figure}
\begin{figure}[htp]
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/Mask_7.png}
\caption{SAR images. (a): SLC SAR image (magnetude). (b): Tomographic result (magnetude).}
\label{Mask_7}
\end{figure}
\begin{figure}[htp]
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/Linea_Tomografica_2_2_2.png}
\caption{SAR images. (a): SLC SAR image (magnetude). (b): Tomographic result (magnetude).}
\label{Mask_7_1}
\end{figure}
\begin{figure}[htp]
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/SLC_2.png}
\caption{SAR images. (a): SLC SAR image (magnetude). (b): Tomographic result (magnetude).}
\label{SLC_2_1}
\end{figure}
\begin{figure}[htp]
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/Linea_Tomografica_3.png}
\caption{SAR images. (a): SLC SAR image (magnetude). (b): Tomographic result (magnetude).}
\label{Linea_Tomografica_3}
\end{figure}
\begin{figure}[htp]
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/Linea_Tomografica_2_1.png}
\caption{SAR images. (a): SLC SAR image (magnetude). (b): Tomographic result (magnetude).}
\label{Linea_Tomografica_2}
\end{figure}
\begin{figure}[htp]
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/Linea_Tomografica_2.png}
\caption{SAR images. (a): SLC SAR image (magnetude). (b): Tomographic result (magnetude).}
\label{Linea_Tomografica_2_1}
\end{figure}
\begin{figure}[htp]
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/SLC_3.png}
\caption{SAR images. (a): SLC SAR image (magnetude). (b): Tomographic result (magnetude).}
\label{SLC_3_1}
\end{figure}
\begin{figure}[htp]
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/Tomo_1_bis.png}
\caption{SAR images. (a): SLC SAR image (magnetude). (b): Tomographic result (magnetude).}
\label{Tomo_1_1}
\end{figure}
\begin{figure}[htp]
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/Tomo_1_1.png}
\caption{SAR images. (a): SLC SAR image (magnetude). (b): Tomographic result (magnetude).}
\label{Tomo_1_2}
\end{figure}
\subsection{Eastern and Western ascending ramps (tag 1, tag 2)}
Two inclined and diverging ramps (identified with the numbers 1 and 2 in the 3D reconstruction depicted in Figure \ref{Fully_3D_1}), characterized by an approximate slope of about 42 degrees, located inside the West and East sides. For both ramps, the lower part starts from the ground level on the North side and reaches half the height of the pyramid on the south side. The reference images are Figure \ref{Tag_1_4_7} (a), (b), for the Eastern side, and Figure \ref{Tag_1_9} (a), (b), for the Western side, where the 3D models are compared to measured tomograms. From the figures, tags number 1,2,3,4 5,7 and 9 are recognized.
\begin{figure}
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/Tag_1_4_7.jpg}
\caption{Tags association from tomography to 3D model. (a): 3D model of Khnum-Khufu. (b): Tomographic reconstruction (magnitude).}
\label{Tag_1_4_7}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/Tag_1_9.jpg}
\caption{Tags association from tomography to 3D model. (a): 3D model of Khnum-Khufu. (b): Tomographic reconstruction (magnitude).}
\label{Tag_1_9}
\end{figure}
\subsection{Southern Corridor, (tag 3)}
The ascending corridors are connected to each other by means of a horizontal structure placed at a height of about 90 meters and located near the south side of the pyramid (identified with the number 3 in Figure \ref{Fully_3D_1}). The corridor is recognized in Figure \ref{Tags_Generic_4} (b), where the 3D reconstruction can be seen in Figure \ref{Tags_Generic_4} (b).
\begin{figure}
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/Tags_Generic_4.jpg}
\caption{Tags association from tomography to 3D model. (a): 3D model of Khnum-Khufu. (b): Tomographic reconstruction (magnitude).}
\label{Tags_Generic_4}
\end{figure}
\subsection{Eastern and Western descending ramps, (tag 4, tag 5)}
Two ramps that, both connected to the previous ones, parallel to each other and also to the East and West base sides that run through a descending underground section with variable slope (numbers 4 and 5 in the 3D model). Figures \ref{Tag_4_5} (a) and \ref{Tag_4_5_2} (a) are the 3D reconstruction models showing the descending corridors from two different view angles, while Figures \ref{Tag_4_5} (b) and \ref{Tag_4_5_2} (b) corresponds to tomographic measurements of the same tags, corresponding to the same descending corridors.
\begin{figure}
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/Tag_4_5.jpg}
\caption{Tags association from tomography to 3D model. (a): 3D model of Khnum-Khufu. (b): Tomographic reconstruction (magnitude).}
\label{Tag_4_5}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/Tag_4_5_2.jpg}
\caption{Tags association from tomography to 3D model. (a): 3D model of Khnum-Khufu. (b): Tomographic reconstruction (magnitude).}
\label{Tag_4_5_2}
\end{figure}
\subsection{Northern underground corridor, (tag 6) and Northern-East and Northern-West underground corridors (tag 7, tag 8)}
At the point where descending ramps (tags 4 and 5) increase slope they appear connected with the Northern underground corridor (tag number 6 structure), parallel to the North side of the pyramid. The Northern underground corridor is characterized by two extrusions, which are still located underground. Figure \ref{Tag_6_7_8} (a) is the 3D reconstruction model showing the structures tagged by numbers 6, 7 and 8, while \ref{Tag_6_7_8} (b) corresponds to tomographic measurements of the same tags, corresponding to the same descending corridors. The section of this structure is deducted on the tomogram of Figure \ref{Tags_Generic_2} (b), while the corresponding 3D model is showed in Figure \ref{Tags_Generic_2} (a).
\begin{figure}
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/Tag_6_7_8.jpg}
\caption{Tags association from tomography to 3D model. (a): 3D model of Khnum-Khufu. (b): Tomographic reconstruction (magnitude).}
\label{Tag_6_7_8}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/Tags_Generic_2.jpg}
\caption{Tags association from tomography to 3D model. (a): 3D model of Khnum-Khufu. (b): Tomographic reconstruction (magnitude).}
\label{Tags_Generic_2}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=16.0cm,height=4.0cm]{Figures/Tomo_Orizzontali_1.png}
\caption{SLC SAR image (magnitude).}
\label{Tomografia_Orizzontale_1}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/Tag_9.jpg}
\caption{Tags association from tomography to 3D model. (a): 3D model of Khnum-Khufu. (b): Tomographic reconstruction (magnitude).}
\label{Tag_9}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/Tags_Generic_1.jpg}
\caption{Tags association from tomography to 3D model. (a): 3D model of Khnum-Khufu. (b): Tomographic reconstruction (magnitude).}
\label{Tags_Generic_1}
\end{figure}
\subsection{Northern underground complex-structure (tag 9)}
Immediately below the base of the pyramid structure, at the North side, a complex structure appears consisting of a horizontal body from which several identical bodies branch off, extruded perpendicularly to the main structure and characterized by a geometry, also present in other Egyptian pyramids, such as the pyramid of Zawyet El-Aryan \cite{dodson2000layer,noc2015analyse,bergendorff2019social} and the Sekhemkhet pyramid \cite{baud2015djeser} . This complex structure (Number 9 in the 3D model) is characterized by a small conduit placed in a central position that runs a short distance in a vertical direction, in analogy with the presence of a similar building also in El-Aryan \cite{dodson2000layer,noc2015analyse,bergendorff2019social} and Saqqara \cite{baud2015djeser}. The reference tomography is shown in Figure \ref{Tag_9} (b), while the 3D model is depicted in Figure \ref{Tag_9} (a).
\subsection{ZED complex-structure (tag 10)}
A complex square structure (identified with the number 10 tag), which connects itself to the structure number 11, belonging to the structure of passage number 3. The structure 10 develops around the Zed, approximately at the height of the lowest room (Davison's Chamber) \cite{hancock2011fingerprints}. The reference tomography is shown in Figure \ref{Tags_Generic_2} (b), while the 3D model is depicted in Figure \ref{Tags_Generic_2} (a). The structure is also detected through different tomograms depicted in Figure \ref{Tomografia_Orizzontale_1} (b), (c), where the reference SLC image is showed in Figure \ref{Tomografia_Orizzontale_1} (a), and the tomographic lines 1 and 2 are showed on the northern and southern pyramid surfaces respectively.
\begin{figure}
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/Tags_Generic_5.jpg}
\caption{Tags association from tomography to 3D model. (a): 3D model of Khnum-Khufu. (b): Tomographic reconstruction (magnitude).}
\label{Tags_Generic_5}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/Tags_Generic_6.jpg}
\caption{Tags association from tomography to 3D model. (a): 3D model of Khnum-Khufu. (b): Tomographic reconstruction (magnitude).}
\label{Tags_Generic_6}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/Tag_Front_Corrider.jpg}
\caption{Tags association from tomography to 3D model. (a): 3D model of Khnum-Khufu. (b): Tomographic reconstruction (magnitude).}
\label{Tag_Front_Corrider}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/IMG_2065.jpg}
\caption{Tags association from tomography to 3D model. (a): 3D model of Khnum-Khufu. (b): Tomographic reconstruction (magnitude).}
\label{IMG_2065}
\end{figure}
\subsection{Eastern and western sarcophagus passages facility (tag 11 and tag 12)}
Structure number 3 also seems to contain two sub-structures, identified with the numbers 11 and 12, connected, through corridor 13, to the King's room, through a passage that seems located under the floor of the latter. The reference tomography is shown in Figure \ref{Tags_Generic_5} (b), while the 3D model is depicted in Figure \ref{Tags_Generic_5} (a).
\subsection{Bottom sarcophagus room facility (tag 13)}
A room located below structures 11 and 12, connecting facilities 3 to 13. The reference tomography is shown in Figure \ref{Tags_Generic_6} (b), while the 3D model is depicted in Figure \ref{Tags_Generic_6} (a). The reference tomography is shown in Figure \ref{IMG_2065} (b), while the 3D model is depicted in Figure \ref{IMG_2065} (a).
\subsection{Queen's bottom room (tag 14)}
A further structure (identified with the number 14 in the 3D model), located below the Queen's chamber and connected to it through a small conduit. From space number 14 the conduit seems to continue, bonding a similar path which, from the room known as "Grotto", leads to the underground room called unfinished". The reference tomography is shown in Figure \ref{IMG_2065} (b), while the 3D model is depicted in Figure \ref{IMG_2065} (a).
\subsection{Southern bottom room (tag 15)}
A room located on the bottom of structures 11 and 12. The reference tomography is shown in Figure \ref{IMG_2065} (b), while the 3D model is depicted in Figure \ref{IMG_2065} (a).
\subsection{Southern Connection (tag 16)}
A further conduit (number 16 of the 3D model) joins the structure 14 to a structure, placed almost at ground level (number 15 of the 3D model). This facility has been discovered through tomographic result depicted in Figure \ref{IMG_2065} (b), where a particular of the 3D model is visible in Figure \ref{IMG_2065} (a).
\subsection{Little-void (tag 17)}
A void that can be located immediately behind the original entrance of the pyramid, not easily identificable in shape and size (number 17 of the 3D model), from which a horizontal conduit (number 18 of the 3D model) starts and which seems to end at the foot of the Grand Gallery, but not directly connected to it.
This is a void located in front of the Northern entrance of the pyramid \cite{morishima2017discovery}. The room is clearly visible in Figure \ref{Paper_Ingresso_Principale_3} (b), precisely located above the corridor identified by the structure with tag 18. It possible to observe the little-void also on Figure \ref{Tag_Front_Little-Void} (b), there the reference 2D model is reported in Figure \ref{Tag_Front_Little-Void} (a).
\begin{figure}
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/Tag_Front_Little_Void.jpg}
\caption{Tags association from tomography to 3D model. (a): 3D model of Khnum-Khufu. (b): Tomographic reconstruction (magnitude).}
\label{Tag_Front_Little-Void}
\end{figure}
\subsection{Front corridor (tag 18)}
A corridor-like structure clearly visible in Figure \ref{Paper_Ingresso_Principale_3} (b) located just behind the external V-shaped structure depicted in Figure \ref{Paper_Ingresso_Principale_3} (a). The corridor is detected and its tomographic representation il depicted in Figure \ref{Paper_Ingresso_Principale_3} (b).
\subsection{Big-void (tag 19)}
A large structure whose shape resembles a parallelepiped (number 19 of the 3D model). This object appears to be connected to structure 10 by means of a double horizontal connection (number 20 of the 3D model). The reference tomography images are shown in Figures \ref{IMG_2108} (b) \ref{IMG_2053} (b) and , while the 3D models are depicted in Figure \ref{IMG_2108} (a) and \ref{IMG_2053} (a). The large red target 1 visible in Figure \ref{IMG_2053} (b) is a false alarm, generated by the south-west ascending angle of the pyramid \cite{li2021stress}.
\begin{figure}
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/IMG_2108.jpg}
\caption{Tags association from tomography to 3D model. (a): 3D model of Khnum-Khufu. (b): Tomographic reconstruction (magnitude).}
\label{IMG_2108}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=15.0cm,height=6.0cm]{Figures/IMG_2053.jpg}
\caption{Tags association from tomography to 3D model. (a): 3D model of Khnum-Khufu. (b): Tomographic reconstruction (magnitude).}
\label{IMG_2053}
\end{figure}
\subsection{ZED-Big-void double connection (tag 20)}
Structure 19 (big-void) is connected to the large corridor 3 to the south, at the height of the big-void, via two oblique corridors. The reference tomography is that shown in Figure \ref{Tags_Generic_4} (b), while the reference 3D model is that in Figure \ref{Tags_Generic_5} (a).
\subsection{Metric determination}
The final objective of this study is to provide approximate measurements of the structures detected using the Doppler SAR tomography technique. The measurements that we propose are expressed in metres and are affected by an error that we have estimated to be very low, with respect to the actual measurement of the structures, according to the particular methodology we used. The dimensions are proposed in Figures \ref{Cad_con_Misure_1}, \ref{Cad_con_Misure_2} and \ref{Cad_con_Misure_3}. The measurements we suggest also include the thickness of the material used to construct them and are not to be intended as mere empty space. With regard to obtaining only empty space, research is currently underway in order to improve the technique and find a way to distinguish solid spaces from hollow spaces. The measures reported are evaluated by using Tape Measuring Wall Area software (http://www.pictureenginecompany.com/MeasureEngine/Promo.html) emploing as internal standard the pyramid's base lenght and are in accordance whith the results afforded by Sar data.
\begin{figure}[htp]
\centering
\includegraphics[width=12.0cm,height=10.0cm]{Figures/Cad_con_Misure_6.jpeg}
\caption{Measurements of the detected facilities of the pyramid. The numbers shown after the comma can not be significant.}
\label{Cad_con_Misure_1}
\end{figure}
\section{Discussion}\label{Discussion}
\subsection{Data analysis}
Here we proceed to data analysis, while being aware that some aspects of the internal structure of the pyramid of Khnum-Khufu still need to be clarified, it is possible, in our opinion, to attribute a meaning to the internal structures of the monument, taking into account all the data relating to previous research in this field.
It is possible to underline how our 3D reconstruction, even if for now it does not claim to indicate the true measurements of the objects shown, (even if the SAR technique can accurately evaluate this parameter), is following some facts exposed in previous research.
Some researchers have shown how on the North edge of the East side of the pyramid at ground level, there is a thermal anomaly that suggests the presence of a room and a corridor located a few meters from the external wall of the monument \cite{ivashov2021proposed,marini2018real,bross2022tomographic,aly2022simulation}.
These data are in agreement with our analyses which predict, at that point, the presence of a room as a link between the two ramps 1 and 4 of our 3D model.
The microgravimetry data, carried out on the pyramid by different research groups \cite{ivashov2021proposed,yoshimura1987non,lheureux2010analyse,bui2011imaging}, can show us how, under the floor of the King's room, there is a lack of homogeneity possibly attributable to structures such as those hypothesized by us (see points 12 and 13 of the 3D model). The presence of rooms located under the King's room is also amply documented by many photographic finds on the Web.
The presence of ramps, placed inside the pyramid and which we highlight with certainty for the first time (numbers 1, 2, 3, and 4 of the 3D model), had already been postulated \cite{tasellari2013great} and partly detected by electrogravitic measurements carried out in 1998 \cite{bui1988application}.
The presence of further rooms located near the Queen's room had already been postulated in the past by some researchers \cite{bui1988application,blindenberg3d}, based on intuitions not confirmed, however, by objective evidence.
Authors of \cite{blindenberg3d} also postulated the presence of a horizontal passage placed between the original entrance of the pyramid and the Great Gallery, in place of structure number 17 which we highlight in this work; moreover, in this work, the presence of a room located immediately after the entrance to the great pyramid is highlighted. This void also seemed to be confirmed by muon spectroscopy \cite{houdin2007construction} carried out by researchers at the University of Nagoya in 2017 and indicated with the name of "Small Void".
It must be strongly emphasized that, while the analyses used up to now in the attempt to describe the objects inside the pyramid, gave only the possibility of making indirect hypotheses, the SAR methodology visibly produces direct evidence of the geometries inside the objects that can be analyzed. In contrast, the muon spectroscopy used in 2017 \cite{houdin2007construction} would not have been deemed reliable by the Egyptian Supreme Council of Antiquities, providing controversial data \cite{morishima2017discovery}.
No trace of the presence of a structure identified as a Big Void, put in evidence by muonic spectroscopy \cite{houdin2007construction}, was in our hands detected by SAR.
On the other hand, the SAR technique, allows us of making more observations using different starting geometries, thus being able to see the same structures inside the pyramid, from different points of view, and the only possibility of mistake lies in the visual interpretation of the data obtained but does not invalidate the presence or absence of specific structural elements.
The geometries of the objects highlighted by the SAR in this paper, also make us reasonably exclude any errors due to the possible non-homogeneity of the materials employed during the construction of the pyramid interiors.
\begin{figure}[htp]
\centering
\includegraphics[width=15.0cm,height=12.0cm]{Figures/Cad_con_Misure_5.jpeg}
\caption{Measurements of the detected facilities of the pyramid. The numbers shown after the comma can not be significant.}
\label{Cad_con_Misure_2}
\end{figure}
\subsection{Data interpretation}
On the basis of the above, it appears necessary to provide a plausible explanation as a key to understanding the function of the structures found inside the pyramid, taking into account that this interpretation is only intended to be a starting point for further interpretative ideas that could arise from a serene discussion at the level of the scientific community.
The authors' vision starts from what we have already previously published in \cite{WinNT} and widely discussed \cite{malanga1997cheope,whissell2007developmental,st2007enhanced,mulligan2012experimental,hassaan2016mechanical,henry2014monitoring,jouniaux2012electrokinetics,davidovits2009pharaohs,barsoum2006microstructural}.
Starting from the observation of the outside of the three pyramids of the Giza plateau, for the first time, we were able to establish that the three pyramids of Khnum-Khufu, Kefren and Menkaure have eight sides. This feature, known only for the larger pyramid, is now extended to the other two. According to the authors of \cite{morishima2017discovery}, the idea that the pyramids of the Giza plateau had this characteristic is due to the need to convey, in an orderly manner, the water that flowed along the faces of the pyramidal structures.
In the case of the pyramid of Khnum-Khufu, which we have analyzed in depth, it can be assumed, in analogy with other authors \cite{bhatt2019subcontinent,zheng2017vibration,jana2007great}, that it was surrounded by an enormous basin full of water, which allowed the circulation of some boats. These boats were used by some attendants with the task of bringing the water to about 90 meters high, pouring it into the South shaft by using many rotating stones probably similar to the Sabu diorite stone \cite{hassaan2016mechanical}.
The SAR tecnique allows us to put in evidence that the shape of this monument do not resemble a perfect pyramidic form because the presence of a double changing in slope: the first of which of 14.5 ca. degrees at approximately 20 meters of high and the second one of 6 degrees ca. at approximately 100 meters of high.
The Nile river's water should have filled the basin up to the height of the first change of slope of the pyramid, thus allowing the Egyptian boats not to get stuck with the keel on the side of the pyramid itself
The water would have invaded the King's chamber but having reached the height of the granite basin inside the chamber (often referred to as the sarcophagus), it would not have exceeded that level in height and would have instead risen in the North shaft, whose entrance is placed at the same height as the basin, creating an air seal that effectively airlocked the room. The King's chamber in fact hermetically sealed would have caused excess water to rise up the North shaft.
The Queen's chamber would also be filled with water, up to the height of the shafts, by means of two connections to the shafts of the King's chamber, probably located in rooms 19 and 11, building a closed circuit, called Quincke's tube \cite{hixson1963quincke}.
As also proposed by other authors \cite{WinNT_2}, the pyramid, with its megalithic structure was placed in vibration by the wind and the low frequencies thus developed, which acted as a low pass filter allowing only low frequencies to bounce back on the roof of the Zed towards the King's chamber \cite{malanga1997cheope}.
Such a room would behave like an air-filled bottle of Helmholtz \cite{liu2021gradually}, in which the granite basin acted as a bottleneck. The walls of the basin, vibrating at low and precise frequencies, linked to the internal and external measurements of the basin itself, proportional to multiples of $\pi$ and the Golden Ratio $\phi$ \cite{malanga1997cheope}, would have caused the water contained in the Quincke's circuit to vibrate.
These frequencies, traveling through the closed circuit of Quincke's tube, at about 1400 m/sec, (speed of sound in the water), reached the Queen's chamber, where the height of the water could not exceed the height of shafts from the floor. A particular frequency could be developed, suitably amplified by the correct dimensions of the niche present in the West wall, which acted as a sound box for a musical instrument, releasing into the air a sound frequency that was able to interact with a cylindrical container, placed on the floor of the room, traces of which are still visible \cite{smyth1877our}.
This cylindrical container, probably made of wood, was put into resonance by the obtained low frequency.
Two individuals were placed both in the basin of the King's chamber and in the cylindrical container, in the Queen's chamber and appropriately treated with this low sound frequency for curative and religious purposes \cite{till2019sound}.
At the end of the procedure, the King's chamber was emptied by letting the water out of the Great Gallery and conveying it towards the room called "Grotto" towards the "Unfinished" chamber which brought the water back through a path in the floor, now occluded by debris, to the Nile.
Subsequently, the Queen's chamber was emptied in two steps: first a granite "plug" in the corridor leading to the room was removed: (this passage actually has a slight hydraulic slope towards the Great Gallery) and the water was made to flow out. At the floor of the Great Gallery, where it was conveyed towards the "Grotto". Subsequently, a plug placed in the floor was removed to finish the emptying of the room.
The water thus conveyed through the hole in the floor, highlighted in a book published in 1877 \cite{smyth1877our}, allowed the liquid to enter the room which, in our 3D reconstruction, corresponds to the number 14, eventually reaching the "Unfinished" room. and returning to the Nile.
The "Grotto" and room 14 are, in our opinion, necessary to stop the fall of water by slowing down its speed, with a mechanism similar to a common water jet pump used in laboratories to create vacuum in equipment, called Venturi's tube.
The evident traces of erosion due to water inside the pyramid rooms are in support of our interpretative hypothesis.
The three boulders that today are wedged at the beginning of the oblique corridor leading to the Great Gallery, would have been used as "plugs" to block the access of water to the exit of the pyramid or from the Queen's chamber by making them flow in different positions as needed.
The existence of a passage 18 seems to be related with a little open room, never described by anyone but well tracked by numerous photographic evidences, that appears located at the top of the entrance of the Great Gallery, probably employed as security exit.
The entire system of the ramps highlighted by the SAR could be interpreted as a gigantic resonant structure, having the purpose of equalizing any differences in vibration between the North and South part of the pyramid, with the aim of making the square structure reach number 10, placed around the Zed, an equalized vibrational signal.
Similarly, the complex structure number 9 identified immediately below the plane on which the pyramid rests, has a shape similar to structures used to absorb the effects of mechanical vibrations that are transmitted through the ground \cite{d2017mechanical}.
\begin{figure}[htp]
\centering
\includegraphics[width=15.0cm,height=9.0cm]{Figures/Cad_con_Misure_3.jpeg}
\caption{Measurements of the detected facilities of the pyramid. The numbers shown after the comma can not be significant.}
\label{Cad_con_Misure_3}
\end{figure}
\begin{table}[tb!]
\caption{List of the principal tomographic images.}
\begin{center}
\begin{tabular}{ |p{2cm}||p{4cm}|p{4cm}| }
\hline
Picture& Tomographic looking-direction & Tomographic line orientation \\
\hline
Figure \ref{Mask_6} & Eastern-side & Vertical \\
Figure \ref{Mask_7} & Northern-side & Horizontal \\
Figure \ref{Mask_7_1} & Western-side & Horizontal \\
Figure \ref{SLC_2_1} & Eastern-side & Horizontal \\
Figure \ref{Linea_Tomografica_3} & Western-side & Horizontal \\
Figure \ref{Linea_Tomografica_2} & Northern-side & Horizontal \\
Figure \ref{Linea_Tomografica_2_1} & Western-side & Vertical \\
Figure \ref{SLC_3_1} & Eastern-side & Vertical investigation \\
Figure \ref{Tomo_1_1} & Northern-Southern-side & Vertical \\
Figure \ref{Tomo_1_2} & Southern-side & Horizontal \\
\hline
\end{tabular}
\label{Tab_2}
\end{center}
\end{table}
\begin{table}[tb!]
\caption{Characteristics of the SAR acquisitions.}
\begin{center}
\begin{tabular}{ |p{2cm}||p{4cm}|p{7cm}| }
\hline
Structure number& Structure type & Structure name \\
\hline
1 & Corridor & Eastern ascending ramp \\
2 & Corridor & Western ascending ramp \\
3 & Corridor & Southern Corridor \\
4 & Corridor & Eastern descending ramp \\
5 & Corridor & Western descending ramp \\
6 & Corridor & Northern underground corridor\\
7 & Corridor & Northern-East underground corridor\\
8 & Corridor & Northern-West underground corridor\\
9 & Complex structure & Northern underground complex-structure\\
10 & Complex structure & ZED complex-structure \\
11 & Room & Eastern sarcophagus passage facility\\
12 & Room & Western sarcophagus passage facility\\
13 & Room & Bottom sarcophagus room facility\\
14 & Room & Queen's bottom room\\
15 & Room & Southern bottom room\\
16 & Corridor & Southern Connection \\
17 & Room & Little-void \\
18 & Corridor & Front corridor \\
19 & Room & Big-void\\
20 & Complex structure & ZED-Big-void double connection\\
\hline
\end{tabular}
\label{Tab_1}
\end{center}
\end{table}
\section{Acknowledgments}\label{Acknowledgements}
We would like to thank Prof. Daniele Perissin for making the SARPROZ software available, through which many calculations were carried out more easily and quickly. We also thank the Italian Space Agency for providing the SAR data. We would also like to thank Dr. Riccardo Garzelli for conducting a deep revision of the English language and for having made crucial revisions to the entire article's structure and layout. The signal processing technique presented in this work has been submitted patent application in 04 July 2022, to Commerce Department of Malta, Industrial Property Registrations Directorate, patent application number 4451.
\section{Author contributions statement}
The authors contributed to all parts of this work
\section{Conclusions}\label{Conclusions}
In this paper we have shown how it is possible to use SAR micro-motion Doppler tomography in an advantageous, economical, non-invasive and rapid way to make a valid contribution in the study of the structure of ancient megalithic monuments such as the pyramid of Khnum-Khufu. We are aware that only by confirmation on the field of our findings can we validate our hypothesis. However it seemed logical to provide a hypothetical interpretation based on the data we collected that could serve as a starting point for future research. In the near future we would like to extend the SAR methodology to the investigation of the internal structure of other important monuments of the Giza plateau.}
\bibliographystyle{unsrt}
\section{Introduction}
\lipsum[2]
\lipsum[3]
\section{Headings: first level}
\label{sec:headings}
\lipsum[4] See Section \ref{sec:headings}.
\subsection{Headings: second level}
\lipsum[5]
\begin{equation}
\xi _{ij}(t)=P(x_{t}=i,x_{t+1}=j|y,v,w;\theta)= {\frac {\alpha _{i}(t)a^{w_t}_{ij}\beta _{j}(t+1)b^{v_{t+1}}_{j}(y_{t+1})}{\sum _{i=1}^{N} \sum _{j=1}^{N} \alpha _{i}(t)a^{w_t}_{ij}\beta _{j}(t+1)b^{v_{t+1}}_{j}(y_{t+1})}}
\end{equation}
\subsubsection{Headings: third level}
\lipsum[6]
\paragraph{Paragraph}
\lipsum[7]
\section{Examples of citations, figures, tables, references}
\label{sec:others}
\lipsum[8] \cite{kour2014real,kour2014fast} and see \cite{hadash2018estimate}.
The documentation for \verb+natbib+ may be found at
\begin{center}
\url{http://mirrors.ctan.org/macros/latex/contrib/natbib/natnotes.pdf}
\end{center}
Of note is the command \verb+\citet+, which produces citations
appropriate for use in inline text. For example,
\begin{verbatim}
\citet{hasselmo} investigated\dots
\end{verbatim}
produces
\begin{quote}
Hasselmo, et al.\ (1995) investigated\dots
\end{quote}
\begin{center}
\url{https://www.ctan.org/pkg/booktabs}
\end{center}
\subsection{Figures}
\lipsum[10]
See Figure \ref{fig:fig1}. Here is how you add footnotes. \footnote{Sample of the first footnote.}
\lipsum[11]
\begin{figure}
\centering
\fbox{\rule[-.5cm]{4cm}{4cm} \rule[-.5cm]{4cm}{0cm}}
\caption{Sample figure caption.}
\label{fig:fig1}
\end{figure}
\subsection{Tables}
\lipsum[12]
See awesome Table~\ref{tab:table}.
\begin{table}
\caption{Sample table title}
\centering
\begin{tabular}{lll}
\toprule
\multicolumn{2}{c}{Part} \\
\cmidrule(r){1-2}
Name & Description & Size ($\mu$m) \\
\midrule
Dendrite & Input terminal & $\sim$100 \\
Axon & Output terminal & $\sim$10 \\
Soma & Cell body & up to $10^6$ \\
\bottomrule
\end{tabular}
\label{tab:table}
\end{table}
\subsection{Lists}
\begin{itemize}
\item Lorem ipsum dolor sit amet
\item consectetur adipiscing elit.
\item Aliquam dignissim blandit est, in dictum tortor gravida eget. In ac rutrum magna.
\end{itemize}
\section{Conclusion}
Your conclusion here
\section*{Acknowledgments}
This was was supported in part by......
\bibliographystyle{unsrt}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,272 |
Families re-embracing our Anishinabe traditions; working together to nurture healthy holistic lifestyles.
The Manager of Health and Social Services administers 13 health programs focussed on prevention as well as provides up to date health information and liason services to members.
The programs offers a variety of services that were developed to meet and address our member's needs to ensure healthy lives.
Nimino Ayaa Health Committee is comprised of community members who are actively involved within the Health department and provides guidance to meet the health needs of the membership of Animbiigoo Zaagi'igan Anishinaabek.
For additional information on AZA Health Services and Programs please contact our Health Coordinator Lynda Lynch. | {
"redpajama_set_name": "RedPajamaC4"
} | 8,482 |
Saint Julian the Hospitaller with Christ the Redeemer is a fresco by Andrea del Castagno in the Feroni Chapel of Santissima Annunziata, Florence. Usually hidden behind an altarpiece by Carlo Loth since 1692, it was painted in 1451 on the construction of the church's five chapels. The Altarpiece was removed carelessly in 1857, damaging the bottom of the fresco, probably consisting of scenes from Julian the Hospitaller's life described in Vasari's Lives of the Artists as executed "with a good number of figures and an escaped dog, which was highly praised".
References
1451 paintings
Paintings depicting Jesus
Paintings of Julian the Hospitaller
Paintings by Andrea del Castagno
Church frescos in Florence | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,100 |
Belief is synonymous with faith to which I have none as it pertains to the government.
Now since that's a fact, (and remember my faithless position concerning government), are you seriously that naive to think RFID chips will only apply to passports???
Another question, what's with the RFID in the first place? Why are they needed?
it provides for state to state access to existing databases. It is not creating anything new.
You're right, it's only expanding an existing database.
Okay so we got a source other than Youtube clip?
in at least 9 states, passport will be required even for a flight within USA.. apparently cause those sates have not met real-ID requirements of Fed.
plus by 2020, all ID must be chipped. gosh, what's the next deadlne at this rapid rate?
Been wondering when this would come along.
This will get rolled out in all the slave states of the US govt including my country within a short period.
Its just part of the ever increasing surveillance of individuals and to get them comfortable with being stopped and therefore accepting of carrying their identity on them every where they go.
When we travel by plane internationally, we get our identity checked at both ends. This new move will ensure this happens at each end of domestic travel too.
Moreover, it will slowly extend to motor vehicle, train, ferry and bus journeys as well. I reckon it will eventually extend to having to show them at the door of cinemas, concerts, sporting venues etc.
Restrictions on Travel - Not everybody should be free to travel the way they do now in the United States. Travel is a privilege. Travel then would become very restricted. People would need permission to travel and they would need a good reason to travel. If you didn't have a good reason for your travel you would not be allowed to travel.
Everyone would need ID. This would at first be an ID card you would carry on your person and you must show when you are asked for it. It was already planned that later on some sort of device would be developed to be implanted under the skin that would be coded specifically to identify the individual. This would eliminate the possibility of false ID and also eliminate the possibility of people saying, "Well, I lost my ID."
I don't fly much... but how much is this gona cost ?
It looks like in my local area a passport can cost approx $200.
That is not affordable for me right now.
Will prices drop if they require everyone to obtain a passport ?
I may not need one anyways... but ya never know.
Passengers would be wise to wear DEPENDS as well. I heard that airplane bathrooms are increasingly being closed for maintenance.
I wont fly so long as there is a TSA.
not sure on first time application fees for u.s passport these days . but for renewal its u.s 110.00 and they touchy as hell on the pics just got told today at embassy that have to go retake the damn pic because it didnt meet their standards after having it taken at the place they said to . suspect they getting kickback from the photo studio for sending them people . also if your outside the u.s and ever need help from embassy your basically screwed as unless you have an appointment bastards wont even let you past the gate so make sure to schedule any travel emergencies in advance . | {
"redpajama_set_name": "RedPajamaC4"
} | 245 |
Q: How do I get a sound file's total time in Java? How do I get a sound file's total time in Java?
--UPDATE
Looks like this code does de work:
long audioFileLength = audioFile.length();
recordedTimeInSec = audioFileLength / (frameSize * frameRate);
I know how to get the file length, but I'm not finding how to get the sound file's frame rate and frame size... Any idea or link?
-- UPDATE
One more working code (using @mdma's hints):
AudioInputStream audioInputStream = AudioSystem.getAudioInputStream(file);
AudioFormat format = audioInputStream.getFormat();
long audioFileLength = file.length();
int frameSize = format.getFrameSize();
float frameRate = format.getFrameRate();
float durationInSeconds = (audioFileLength / (frameSize * frameRate));
A: Given a File you can write
File file = ...;
AudioInputStream audioInputStream = AudioSystem.getAudioInputStream(file);
AudioFormat format = audioInputStream.getFormat();
long frames = audioInputStream.getFrameLength();
double durationInSeconds = (frames+0.0) / format.getFrameRate();
A: This is a easy way:
FileInputStream fileInputStream = null;
long duration = 0;
try {
fileInputStream = new FileInputStream(pathToFile);
} catch (FileNotFoundException e) {
e.printStackTrace();
}
try {
duration = Objects.requireNonNull(fileInputStream).getChannel().size() / 128;
} catch (IOException e) {
e.printStackTrace();
}
System.out.println(duration)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,954 |
\section{Introduction and Statement of Results}\label{Intro}
Consider the semilinear heat equation
\begin{equation}\label{prob}
\begin{aligned}
&u_t=\Delta u-Vu +u^p\ \text{in}\ R^n\times(0,T); \\
&u(x,0)=\phi(x)\gneq0 \ \text{in}\ R^n,
\end{aligned}
\end{equation}
where $p>1$, $n\ge1$ and $T\in(0,\infty]$.
In this paper, when we speak of a \it solution\rm\ to the above equation, or to any of the other equations appearing later on, we mean
\it a classical solution $u$ satisfying $||u(\cdot,t)||_\infty<\infty$, for $0<t<T$.\rm\
This allows us to employ comparison principles.
A solution to \eqref{prob} is called global if $T=\infty$.
In the case that $V\equiv0$,
$p^*\equiv1+\frac2n$ is the critical exponent, the so-called \it
Fujita exponent\rm, and one has the following dichotomy:
if $p>p^*$, then for sufficiently small
initial data $\phi$, the solution to \eqref{prob} is global, whereas
if $1<p\le p^*$, then \eqref{prob} has no global solution---every solution blows up in
finite time.
This
result goes back to Fujita \cite{F} in the case $p\neq p^*$.
Various proofs of blow-up in the borderline case $p=p^*$ can be
found in \cite{AW}, \cite{KST}, \cite{P97}.
More recently, Zhang \cite{Z01} considered \eqref{prob} with $n\ge3$ for potentials $V$ behaving like $\frac{\omega}{1+|x|^b}$, for $b>0$ and $\omega\neq0$.
He proved the following result.
\begin{Z} Let $n\ge3$.
\noindent i. If
$0\le V(x)\le\frac \omega{1+|x|^b}$, for some $b>2$ and $\omega>0$, then $p^*=1+\frac2n$ and consequently the potential does not
affect the critical exponent;
\noindent ii. If $V(x)\ge\frac \omega{1+|x|^b}$, for some $b\in(0,2)$ and $\omega>0$, then $p^*=1$ and there exist global solutions for all $p>1$;
\noindent iii. If $ \frac \omega{1+|x|^b}\le V(x)\le 0$, for some $b>2$ and $\omega<0$ with $|\omega|$ sufficiently small, then
$p^*=1+\frac2n$ and consequently the potential does not affect the critical exponent;
\noindent iv. If $V(x)\le\frac \omega{1+|x|^b}$, for some $b\in(0,2)$ and $\omega<0$, then $p^*=\infty$ and there are no global solutions for any $p>1$.
\end{Z}
Note that
wherever the statement of the result is that there exist global solutions,
Zhang either does not allow for negative $V$ or else requires that $|V|$ be sufficiently small. The reason for this will
become clear from Theorem \ref{spectral} below.
Zhang noted that it seemed difficult to specify the exact value of the critical exponent in the case
of quadratic decay; that is in the case that $V(x)\sim\frac \omega{|x|^2}$ as $|x|\to\infty$. He also noted that it is unclear
whether or not $p^*$ is finite in the case that $V(x)\sim\frac \omega{|x|^2}$, with $\omega<0$.
Very recently, Ishige \cite{I} treated \eqref{prob} for $n\ge3$ in
the case $V(x)\sim\frac \omega{|x|^2}$ with $\omega>0$.
Let $\alpha=\alpha(\omega,n)$ denote the larger root of the equation
$\alpha(\alpha+n-2)=\omega$; that is
\begin{equation}\label{root}
\alpha(\omega,n)=\frac{2-n+\sqrt{(n-2)^2+4\omega}}2.
\end{equation}
Since we are assuming here that $\omega>0$, one has $\alpha(\omega,n)>0$.
Define
\begin{equation}\label{pomega}
p^*(\omega)=1+\frac 2{n+\alpha(\omega,n)}.
\end{equation}
\begin{I}
Let $n\ge3$ and assume that $V\ge0$. Let $\omega>0$.
\noindent i. If
$V(x)\ge \frac \omega{|x|^2}$ for large $|x|$, then for $p>p^*(\omega)$
there exist global solutions to \eqref{prob};
\noindent ii. If $V(x)\le\frac\omega{|x|^2}$ for large $|x|$, then for $1<p\le p^*(\omega)$
every solution to \eqref{prob} blows up in finite time.
\end{I}
Note that Ishige assumes from the outset that $V\ge0$. The delicacy between having global solutions and allowing
$V$ to take negative values will be explained by Theorem \ref{spectral} below.
Ishige's proof involved comparison with a solution to the radially symmetric linear equation
$v_t=\Delta v-\hat V(|x|) v$, where $\hat V(r)\sim\frac\omega{r^2}$ as $r\to\infty$. The large time behavior of this
linear equation, which is needed for the comparison, was recently obtained by Ishige and Kawakami \cite{IK}.
In this paper, our main focus is the study of the remaining case, $V(x)\sim\frac\omega{|x|^2}$, with $\omega<0$.
In fact we treat the following more general problem:
\begin{equation}\label{probextra}
\begin{aligned}
&u_t=\Delta u-Vu +au^p \ \text{in}\ R^n\times (0,T);\\
&u(x,0)=\phi(x)\gneq0,\ \text{in}\ R^n,
\end{aligned}
\end{equation}
where $p>1$, $n\ge2$, $T\in(0,\infty]$, $\phi$ is bounded and continuous,
$0\lneq a\in C^\alpha(R^n)$ and
$V\in C^\alpha(R^n-\{0\})$ $\alpha\in(0,1]$.
We also require that $\liminf_{x\to0}V(x)>-\infty$ so that $V$ is locally bounded from below.
Our methods, which are completely different from the method employed by Ishige, also allow one to obtain weaker versions of Ishige's results for the case
$\omega>0$, but in the more general context of equation \eqref{probextra} with $n\ge2$.
The method of proof also leads naturally to a study of the critical exponent in an exterior domain with the Dirichlet boundary
condition in the case $V\equiv0$.
In the case that $V\equiv0$ and that $a$ satisfies
\begin{equation}\label{2sided}
c_1|x|^m\le a(x)\le c_2|x|^m, \ \text{for sufficiently large} \ |x|\ \text{and some}\ m\in (-\infty,\infty), \ c_1,c_2>0,
\end{equation}
the critical exponent $p^*$ for \eqref{probextra} was calculated in \cite{P97}; it is given by
\begin{equation}\label{97}
p^*=1+\frac{(2+m)^+}n.
\end{equation}
In \eqref{root} we defined $\alpha(\omega,n)$ for $\omega>0$.
We now extend the definition of $\alpha(\omega,n)$ in \eqref{root} to $\omega\ge-\frac14(n-2)^2$. Note that $\alpha(\omega,n)<0$
for $-\frac14(n-2)^2\le\omega<0$. Now define
\begin{equation}\label{08}
p^*(\omega, m)=1+\frac{(2+m)^+}{n+\alpha(\omega,n)}.
\end{equation}
We will prove the following theorem.
\begin{theorem}\label{negative}
Let $n\ge3$ and let $-\frac14(n-2)^2\le\omega<0$.
Consider \eqref{probextra} with $a(x)$ satisfying \eqref{2sided}.
Assume that $V\in C^\alpha(R^n-\{0\})$ and that \newline $\liminf_{x\to0}V(x)>-\infty$.
Let $p^*(\omega,m)$ be as in \eqref{08}.
\noindent i. If $V(x)\ge\frac\omega{|x|^2}$, then
there exist global solutions to \eqref{probextra} for $p>p^*(\omega,m)$;
\noindent ii. If $V(x)\le\frac\omega{|x|^2}$, for sufficiently
large $|x|$,
then there are no global solutions
to \eqref{probextra} for $1<p\le p^*(\omega, m)$.
\end{theorem}
\it\noindent Remark.\rm\
Note that in the case of the existence of global solutions, we allow $V$ to be negative up to a precise globally specified
size. The reason for this will become clear in Theorem \ref{spectral}.
We now consider what happens when $\omega<-\frac14(n-2)^2$, $n\ge2$.
We will show that $p^*=\infty$ under a certain general condition on the operator $-\Delta+V$, and that this condition holds
if $V(x)\le \frac\omega{|x|^2}$, for $|x|>\epsilon$, with sufficiently small $\epsilon>0$.
Let $D\subseteqq R^n$ be a domain. Then $-\Delta +V$ on $D$ with the Dirichlet boundary condition
on $\partial D$ can be realized as a self-adjoint operator on $L^2(D)$. Denoting its spectrum by $\sigma(-\Delta +V;D)$, let
\begin{equation*}
\lambda_{0;D}(-\Delta+V)\equiv\inf\sigma(-\Delta +V;D).
\end{equation*}
\begin{theorem}\label{spectral}
If there exists a domain $D\subseteqq R^n$ for which $\inf_{x\in D}a(x)>0$ and $\lambda_{0;D}(-\Delta+V)<0$, then
there are no global solutions to \eqref{probextra} for any $p>1$; that is, $p^*=\infty$.
\end{theorem}
We can use Theorem \ref{spectral} to prove the following corollary.
\begin{corollary}\label{corspectral}
Consider \eqref{probextra} with $a>0$ on $R^n$, $n\ge2$. Let
$\omega<-\frac14(n-2)^2$.
There exists an $\epsilon>0$ such that
if $V(x)\le\frac\omega{|x|^2}$, for $|x|>\epsilon$, then
there are no global solutions to \eqref{probextra} for any $p>1$; that is, $p^*=\infty$.
\end{corollary}
\begin{Remark 1}
Note that there is a discontinuity in the critical exponent at $\omega=-\frac14(n-2)^2$. By Theorem \ref{negative}, if
$V(x)=-\frac{(n-2)^2}{4|x|^2}$, for sufficiently large $|x|$, and $V(x)\ge-\frac{(n-2)^2}{4|x|^2}$, for all $x$, then
the critical exponent is equal to \linebreak $p^*(-\frac14(n-2)^2,m)=1+\frac{2(2+m)^+}{n+2}$.
However, if $V(x)=\frac\omega{|x|^2}$, for some $\omega<-\frac14(n-2)^2$ and $|x|>\epsilon$, for sufficiently small $\epsilon>0$,
then the critical exponent
is $\infty$.
\end{Remark 1}
\begin{Remark 2}
Theorem \ref{spectral} makes it clear why in the theorems of Zhang and of Ishige and in Theorem \ref{negative},
one needed to be careful with regard to stating the existence of global solutions and allowing $V$ to take negative values.
For example, part (iii) of the theorem of Zhang states that
if $\frac\omega{1+|x|^b}\le V(x)\le 0$ for some $b>2$ and $\omega<0$, with $|\omega|$ sufficiently small, then the critical
exponent for \eqref{prob} is $1+\frac2n$. The requirement that $|\omega|$ be sufficiently small is mandatory in light of
Theorem \ref{spectral}. Indeed, for any $D\subseteqq R^n$, if $\omega<0$ and $|\omega|$ is sufficiently large, then $\lambda_{0;D}(-\Delta+
\frac\omega{1+|x|^b})<0$
and thus, by Theorem \ref{spectral}, one has $p^*=\infty$.
\end{Remark 2}
The method of proof in Theorem \ref{negative} also yields the following result for the case $\omega>0$.
\begin{theorem}\label{positive}
Let $n\ge2$ and $\omega>0$.
Consider \eqref{probextra} with $a(x)$ satisfying \eqref{2sided}.
Assume that $V\in C^\alpha(R^n-\{0\})$.
Let $p^*(\omega,m)$ be as in \eqref{08}.
\noindent i. If $V(x)\ge\frac\omega{|x|^2}$, then there exist global solutions to \eqref{probextra}
for $p>p^*(\omega,m)$.
\noindent ii. If $V(x)\le \frac\omega{|x|^2}$, for sufficiently large $|x|$, then there are no global solutions to \eqref{probextra} for
$1\le p\le p^*(\omega,m)$.
\end{theorem}
\noindent \it Remark.\rm\ Note that part (i) requires that $V$ approach $\infty$ as $|x|\to0$. In fact, as Ishige has proven
in the case that $a\equiv1$ and $n\ge3$, the result should hold as long as $V(x)\ge\frac\omega{|x|^2}$, for sufficiently large $|x|$, and
$V\ge 0$ for all $x$. However, our method of proof does not seem to be extendable to this situation.
As will be seen below, the method of proof we employ for the blow-up case in Theorems \ref{negative} and \ref{positive} will lead naturally
to a consideration of the critical exponent for the semilinear heat equation in an exterior domain with the Dirichlet boundary condition and with $V\equiv0$. Let $B_r=\{x\in R^n: |x|<r\}$.
Consider the following problem:
\begin{equation}\label{exterior}
\begin{aligned}
&u_t=\Delta u +au^p \ \text{in}\ (R^n-\bar B_{r_0})\times (0,T);\\
&u(x,t)=0,\ \text{for}\ |x|=r_0,\ t\ge0;\\
&u(x,0)=\phi(x)\gneq0\ \text{in}\ R^n-\bar B_{r_0},
\end{aligned}
\end{equation}
where
\begin{equation}\label{a-ext}
c_1|x|^m\le a(x)\le c_2|x|^m,\ \text{for sufficiently large }\ |x| \ \text{and some}\ m\in(-\infty,\infty), \ c_1,c_2>0.
\end{equation}
We prove that restricting to an exterior domain does not affect the blow-up/global solution dichotomy.
\begin{theorem}\label{extresult}
Let $n\ge2$. Consider \eqref{exterior} with $a(x)$ satisfying \eqref{a-ext}. Let
$$
p^*=1+\frac{(2+m)^+}n
$$
as in \eqref{97}.
\noindent i. If $1\le p\le p^*$, then there exist global solutions to \eqref{exterior};
\noindent ii. If $p>p^*$, then there are no global solutions to \eqref{exterior}.
\end{theorem}
\noindent \it Remark.\rm\ In the case $a\equiv1$, $n\ge3$ and $p\neq p^*$, the result in Theorem \ref{extresult} was proven in
\cite{BL}. For some other works that treat the critical exponent in exterior domains, see
\cite{LZ} and \cite{Z01a}. Most of the results in these papers do not cover the case in which $p$ is equal to the critical exponent.
We end this section with an outline of the methods used to prove Theorems \ref{negative} and \ref{positive}, concentrating
on the case of nonexistence of global solutions, which is where our method is novel, and leads to a consideration of the critical
exponent in the case of a semilinear heat equation in an exterior domain with the Dirichlet boundary condition.
By standard comparison techniques, it suffices to treat the radially symmetric case.
Thus, instead of considering solutions $u(x,t)$ of \eqref{probextra} with $a$ satisfying \eqref{2sided},
we may consider solutions $u(r,t)$ of the equation
\begin{equation}\label{probextrarad}
\begin{aligned}
&u_t=u_{rr}+\frac{n-1}ru_r-V(r)u+a(r)u^p\ \text{in}\ (0,\infty)\times(0,T);\\
&u(r,0)=\phi(r)\gneq0 \ \text{in}\ [0,\infty),
\end{aligned}
\end{equation}
where $p>1$, $T\in(0,\infty]$, $\phi$ is bounded and continuous,
$V\in C^\alpha((0,\infty))$ and $\liminf_{r\to0}V(r)>-\infty$, $0\lneq a\in C^\alpha([0,\infty))$, $\alpha\in(0,1]$, with $a$ satisfying
\begin{equation}\label{r2sided}
c_1r^m\le a(r)\le c_2 r^m,\ \text{for sufficiently large}\ r \ \text{and some}\ m\in(-\infty,\infty),\ c_1,c_2>0.
\end{equation}
For the existence of global solutions when $p>p^*(\omega,m)$ in part (i) of Theorems \ref{negative} and \ref{positive},
we construct a global super-solution to \eqref{probextrarad}.
Note that in general it is much more difficult to use the method of super/sub-solutions to prove blow-up, since
the construction of an appropriate sub-solution would probably require a reasonable knowledge of the blow-up profile.
We now turn to the
nonexistence of global solutions when $1<p\le p^*(\omega,m)$ in part (ii) of Theorems \ref{negative} and \ref{positive},
We may assume without loss of generality that the initial data $\phi$ in \eqref{probextrarad}
satisfy $\phi(r)>0$ for all $r>0$. Indeed, if this is not the case, then for $\delta>0$ sufficiently small, we
can consider $\bar u(r,t)\equiv u(r,t+\delta)$, which also satisfies \eqref{probextrarad} and is strictly positive at $t=0$.
We apply a transformation as follows. Let $u$ be a solution to
\eqref{probextrarad} and define $v(r,t)=r^{-\alpha}u(r,t)$. Let $\psi(r)=r^{-\alpha}\phi(r)$.
Then one calculates that
\begin{equation}\label{transformed}
\begin{aligned}
&v_t=v_{rr}+\frac{n-1+2\alpha}rv_r+\left(\frac{\alpha(\alpha+n-2)}{r^2}-V(r)\right)v+r^{\alpha(p-1)}a(r)v^p\\
& \text{in}\ (0,\infty)\times(0,T);\\
&v(r,0)=\psi(r)>0\ \text{in}\ (0,\infty).
\end{aligned}
\end{equation}
There will be global solutions of $v$ if and only if there are global solutions of $u$; thus it suffices to study
\eqref{transformed}.
In part (ii) of Theorems \ref{negative} and \ref{positive}, we are assuming that $V(r)\le\frac\omega{r^2}$, for sufficiently large $r$,
say for $r\ge r_0$, where $\omega\ge-\frac14(n-2)^2$.
If one now chooses $\alpha=\alpha(\omega,n)$ as in \eqref{root}, then the coefficient of $v$ in \eqref{transformed}
is nonnegative for $r\ge r_0$. By the comparison principle, the solution to
that equation dominates the solution to the equation
\begin{equation}\label{transformedexact}
\begin{aligned}
&w_t=w_{rr}+\frac{N-1}rw_r+\hat a(r)w^p\ \text{in}\ (r_0,\infty)\times(0,T);\\
&w(r,0)=\psi(r)>0\ \text{in}\ [r_0,\infty);\\
&w(r_0,t)=0, \ t>0,
\end{aligned}
\end{equation}
where
\begin{equation}\label{N}
N\equiv n+2\alpha(\omega,n)
\end{equation}
and $\hat a(r)=r^{\alpha(p-1)}a(r)$. In terms of $\hat a$, the assumption \eqref{r2sided} on $a$ is
\begin{equation}\label{hatr2sided}
c_1r^M\le \hat a(r)\le c_2 r^M,\ \text{for sufficiently large}\ r, \ c_1,c_2>0,
\end{equation}
where
\begin{equation}\label{M}
M\equiv\alpha(\omega,n)(p-1)+m, \ m\in(-\infty, \infty).
\end{equation}
(The reason we insisted on $\phi(r)>0$ for all $r>0$, and thus also $\psi(r)>0$ for all $r>0$, is that otherwise we could have ended up with $\psi\equiv0$ in \eqref{transformedexact}.)
Thus, it suffices to show that there are no global solutions to \eqref{transformedexact}-\eqref{M}.
Now \eqref{transformedexact}-\eqref{M} is the radial version of \eqref{probextra}-\eqref{2sided} in the case $V\equiv0$, except that we have placed the Dirichlet boundary condition at $r=r_0$ instead of considering the problem
for all $r>0$, and except that
$m$ in \eqref{2sided} is replaced by $M$ and the dimension
$n$ is replaced by the ``dimension'' $N$. (Note from the definition of $\alpha(\omega,n)$ that
one always has $N\ge2$.)
The critical exponent $p^*$ for \eqref{probextra} with $V\equiv0$ and with $a$ satisfying \eqref{2sided} was given in \eqref{97}.
Substituting $N$ and $M$ for $n$ and $m$ in
\eqref{97}, it is not unreasonable to suspect that no global solutions will exist if
\begin{equation}\label{inequality}
1<p\le1+\frac{(2+M)^+}N=1+\frac{\left(2+\alpha(\omega,n)(p-1)+m\right)^+}{n+2\alpha(\omega,n)}.
\end{equation}
We now solve \eqref{inequality} for $p$.
Consider first the case $\omega<0$, in which case $\alpha(\omega,n)<0$.
Since we are assuming that $p>1$, \eqref{inequality} will never hold if
$2+\alpha(\omega,n)(p-1)+m\le0$; that is,
if
\begin{equation}\label{calc1}
p\ge1-\frac{2+m}{\alpha(\omega,n)}.
\end{equation}
On the other hand, if
$2+\alpha(\omega,n)(p-1)+m>0$, then solving \eqref{inequality} for $p$ gives
\begin{equation}\label{calc2}
1<p\le1+\frac{2+m}{n+\alpha(\omega,n)}.
\end{equation}
One can check that for $m>-2$, the right hand side of \eqref{calc2} is strictly less than the right hand side
of \eqref{calc1}. From this fact along with \eqref{calc1} and \eqref{calc2}, we conclude that
\eqref{inequality} holds if and only
if $1<p\le p^*(\omega,m)$, where
$p^*(\omega,m)$ is as in \eqref{08}.
Now consider the case $\omega>0$, in which case $\alpha(\omega,n)>0$. \linebreak If
$2+\alpha(\omega,n)(p-1)+m>0$, then solving \eqref{inequality} as we did above
gives \eqref{calc2}. On the other hand, if $2+\alpha(\omega,n)(p-1)+m\le0$ (which implies that $m<-2$), then
\eqref{inequality} does not hold. Putting these facts together leads again to
\eqref{inequality} holding if and only if $1<p\le p^*(\omega,m)$.
To turn the above argument into a rigorous proof, we need to show that
indeed no global solutions exist for \eqref{transformedexact}-\eqref{M} when
$1<p\le 1+\frac{(2+M)^+}N$. That is we need to show that the proof in \cite{P97},
which treated the operator $\Delta$ in $R^n$ (whose radial part is $\frac{d^2}{dr^2}+\frac{n-1}r\frac d{dr}$),
can accommodate two changes: (1) operators of
the form $\frac{d^2}{dr^2}+\frac{N-1}r\frac d{dr}$ with fractional $N$ and (2) the Dirichlet boundary condition at $r=r_0$, which serves
to make solutions smaller. The proof in \cite{P97} made rather
heavy use of the explicit form of the heat kernel $p(t,x,y)=(4\pi t)^{-\frac n2}
\exp(-\frac{|y-x|^2}{4t})$ for the corresponding linear operator $\Delta-\frac \partial{\partial t}$ in $R^n$.
In the present case, the corresponding linear operator is
$\frac{\partial^2}{\partial r^2}+\frac{N-1}r\frac \partial {\partial r}-\frac \partial {\partial t}$
with the Dirichlet boundary condition at $r=r_0$. It turns out that if $N>2$ (equivalently, $\omega>-\frac14(n-2)^2$), then
the heat kernel for this operator is comparable in an appropriate sense to the heat kernel for
$\frac{\partial^2}{\partial r^2}+\frac{N-1}r\frac \partial {\partial r}-\frac \partial {\partial t}$ on the entire space $r>0$; thus, we will
be able to use this latter heat kernel, which we can exhibit explicitly.
However, this latter heat kernel
is a much less convenient object than the Gaussian heat kernel. In fact, this obstacle prevented us
from using the method of proof in \cite{P97} to prove the existence of global solutions above the critical exponent; hence the use of super-solutions. However,
we were able to use this heat kernel and amend the nonexistence proof in \cite{P97} at or below the critical value.
When $N=2$ (equivalently, $\omega=-\frac14(n-2)^2$), the heat kernel with the Dirichlet boundary condition is not comparable to the heat kernel on the whole space,
however an appropriate lower bound is known and sufficient for our needs.
In section 2 we prove the existence of global solutions in part (i) of Theorems \ref{negative}
and \ref{positive}. In section 3 we prove the nonexistence of global solutions in part (ii) of
Theorems \ref{negative} and \ref{positive}.
In section 4 we prove Theorem \ref{extresult}.
In section 5 we prove Theorem \ref{spectral} and Corollary \ref{corspectral}.
\section{Proofs of Part (i) of Theorems \ref{negative} and \ref{positive}}
We assume that $p>p^*(\omega,m)$, where $p^*(\omega,m)$ is as in \eqref{08}.
As noted in the first section of the paper, instead of studying \eqref{probextra} with $a$ satisfying \eqref{2sided},
it suffices to study the radial problem \eqref{probextrarad} with $a$ satisfying \eqref{r2sided}.
By the standard theory, it suffices to exhibit a global super-solution.
We look for such a super-solution in the form
\begin{equation*}
v(r,t)=\delta \frac{r^\alpha}{(t+1)^\gamma}\exp(-\frac{cr^2}{t+1}),
\end{equation*}
for some $\delta, c>0$ and some $\alpha,\gamma\in(-\infty,\infty)$.
We have
\begin{equation}\label{vr}
v_r=(\frac\alpha r-\frac{2cr}{t+1})v;
\end{equation}
\begin{equation}\label{vrr}
v_{rr}=(\frac{\alpha^2}{r^2}+\frac{4c^2r^2}{(t+1)^2}-\frac{4c\alpha}{t+1}-\frac\alpha{r^2}-\frac{2c}{t+1})v;
\end{equation}
\begin{equation}\label{vt}
v_t=(-\frac\gamma{t+1}+\frac{cr^2}{(t+1)^2})v.
\end{equation}
The condition on $V$ in part (i) of Theorems \ref{negative} and \ref{positive} is that
$V(r)\ge\frac\omega{r^2}$, with $-\frac{(n-2)^2}4\le\omega<0$ in Theorem \ref{negative} and $\omega>0$ in
Theorem \ref{positive}.
Using this along with \eqref{vr}, \eqref{vrr} and \eqref{vt}, we have
\begin{equation}\label{supersolu}
\begin{aligned}
&v^{-1}(v_{rr}+\frac{n-1}rv_r-V(r)v-v_t+a(r)v^p)\le\\
& (4c^2-c)\frac{r^2}{(t+1)^2}+\frac{\alpha^2+(n-2)\alpha-\omega}{r^2}
+\frac{\gamma-4c\alpha-2cn}{t+1}\\
&+\delta^{p-1}a(r)\frac{r^{\alpha(p-1)}}{(t+1)^{\gamma(p-1)}}\exp(-\frac{c(p-1)r^2}{t+1}).
\end{aligned}
\end{equation}
In order to make the first term on the right hand side of \eqref{supersolu} vanish, we choose
$c=\frac14$, and in order to make the second term on the right hand side of \eqref{supersolu} vanish,
we choose $\alpha=\alpha(\omega,n)$ as in \eqref{root}.
If $m\le0$, the assumption on $a$ in \eqref{r2sided} guarantees that for some $C>0$, $a(r)\le Cr^m$, for all $r>0$.
If $m>0$, the assumption on $a$ in \eqref{r2sided} guarantees that for some $C>0$, $a(r)\le C(r\vee1)^m$, for all $r>0$.
This forces us to break up the next part of the proof into two cases. We will continue the proof under the assumption
that $m\le0$. After the completion of this case, it will be easy to point out how to handle the case
$m>0$.
Since $a(r)\le Cr^m$,
the final term on the right hand side of \eqref{supersolu} (with $c=\frac14$ and $\alpha=\alpha(\omega,n)$) is bounded from above by
$C\delta^{p-1}\frac{r^{\alpha(\omega,n)(p-1)+m}}{(t+1)^{\gamma(p-1)}}\exp(-\frac{(p-1)r^2}{4(t+1)})$.
Letting $z=\frac{r^2}{t+1}$, this upper bound can be written as
$$\frac{C\delta^{p-1}z^{\frac12\alpha(\omega,n)(p-1)+\frac12m}\exp(-\frac14(p-1)z)}{(t+1)^{(\gamma-\frac12\alpha(\omega,n))(p-1)-\frac12m}},
$$
which is itself bounded from above by $\frac{C_1C\delta ^{p-1}}{(t+1)^{(\gamma-\frac12\alpha(\omega,n))(p-1)-\frac12m}}$, where \linebreak
$C_1=\sup_{z>0}z^{\frac12\alpha(\omega,n)(p-1)+\frac12 m}\exp(-\frac14(p-1)z)$.
In light of the above analysis, it follows from \eqref{supersolu} that
\begin{equation}\label{v}
v(r,t)=\delta \frac{r^{\alpha(\omega,n)}}{(t+1)^\gamma}\exp(-\frac{r^2}{4(t+1)})
\end{equation}
satisfies
\begin{equation}\label{supersolu2}
\begin{aligned}
&v^{-1}(v_{rr}+\frac{n-1}rv_r-V(r)v-v_t+a(r)v^p)\le\\
&\frac{\gamma-\alpha(\omega,n)-\frac12n}{t+1}+\frac{C_1C\delta^{p-1}}{(t+1)^{(\gamma-\frac12\alpha(\omega,n))(p-1)-\frac12m}}.
\end{aligned}
\end{equation}
If
\begin{equation}\label{gamma1}
\gamma-\alpha(\omega,n)-\frac12n<0
\end{equation}
and
\begin{equation}\label{gamma2}
(\gamma-\frac12\alpha(\omega,n))(p-1)-\frac12m\ge1,
\end{equation}
then after choosing $\delta>0$ sufficiently small, the right hand side of \eqref{supersolu2} will be non-positive.
The two inequalities \eqref{gamma1} and \eqref{gamma2} together are equivalent to
\begin{equation*}
\frac12\alpha(\omega,n)+\frac{1+\frac12 m}{p-1}\le \gamma<\alpha(\omega,n)+\frac12n,
\end{equation*}
and this latter pair of inequalities can be solved for $\gamma$ if and only if
$\alpha(\omega,n)+\frac{2+m}{p-1}<2\alpha(\omega,n)+n$, or equivalently,
if and only if
$p>1+\frac{2+m}{n+\alpha(\omega,n)}$. Since we have assumed from the outset that $p>1$, we conclude that
if $p>1+\frac{(2+m)^+}{n+\alpha(\omega,n)}=p^*(\omega,m)$, then
it is possible
to choose $\gamma$ so that \eqref{gamma1}
and \eqref{gamma2} hold.
In the case $m>0$, we have $a(r)\le Cr^m$, if $r\ge1$, and $a(r)\le Cr^0$, if $0<r<1$.
Thus, in order for the above analysis to go through in this case, we need to have
\eqref{gamma2} hold as it is written and also with $m$ replaced by 0. However, since $m>0$,
if \eqref{gamma2} holds as it is written, then it holds a fortiori with $m$ replaced by 0.
In the case $\omega>0$,
the function $v$ given by \eqref{v} with $\delta>0$ sufficiently small and $\gamma$ chosen to
satisfy \eqref{gamma1} and \eqref{gamma2} serves as an appropriate global super-solution.
In the case $\omega<0$, there is one technical problem; namely,
that $\alpha(\omega,n)<0$ and thus $v$ is not finite at $r=0$.
This artificial singularity arises from the use of polar
coordinates. Unfortunately, if one replaces $r$ by $r+c$ for some
$c>0$, then $v$ will no longer be a super-solution. Thus, we argue
as follows. Consider $\omega$ and $p>p^*(\omega,n)$ as fixed. Our
work so far allows us to conclude that for sufficiently small initial data
$\phi$, the solution $u(x,t)$ of \eqref{probextra} satisfies
$u(x,t)\le v(|x|,t)$ up until some possibly finite blow-up time.
Choose $\epsilon>0$ sufficiently small so that
$p>p^*(\omega-\epsilon,n)$. The function $v$ in \eqref{v} was
shown to be a super-solution for \eqref{probextra} under the
assumption that the potential $V$ satisfies $V(x)\ge\frac\omega{|x|^2}$.
Recall that in \eqref{probextra} we are also assuming that $V$ is locally bounded from below.
Therefore, there exists an $r_0>0$ such that $V(x)\ge\frac\omega{r_0^2}$ for $|x|\le r_0$.
One can check that it is then possible to
choose an $x_0\neq0$ such that
$V(x)\ge\frac{\omega-\epsilon}{|x-x_0|^2}$. Now consider the
radial version \eqref{probextrarad} of \eqref{probextra} but with
the origin shifted to the point $x_0$. Call the new radial variable
$\rho=|x-x_0|$. Since we have $V(\rho)\ge\frac{\omega-\epsilon}{\rho^2}$,
the construction above shows that there exists a function $\hat
v(\rho,t)=\hat\delta \frac{\rho^{\alpha(\omega-\epsilon,n)}}{(t+1)^{\hat
\gamma}}\exp(-\frac{\rho^2}{4(t+1)})$ such that for sufficiently small
initial data $\phi$, the solution $u(x,t)$ of \eqref{probextra}
satisfies $u(x,t)\le \hat v(|x-x_0|,t)$ up until some possibly finite blow-up
time. We conclude that for sufficiently small initial data $\phi$, the solution
$u(x,t)$ of \eqref{probextra} satisfies
$u(x,t)\le \hat v(|x-x_0|,t)\wedge v(|x|,t)$ up until its blow-up time. But the right hand side
is finite for all $x$ and $t$. Thus $u$ is in fact a global solution.
\section{Proofs of Part (ii) of Theorems \ref{negative} and \ref{positive}}
As was shown at the end of section 1, in order to prove that when $1<p\le p^*(\omega,m)$ there are no global solutions to \eqref{probextra}
with $a$ satisfying \eqref{2sided}, it suffices to show that there are no global solutions for \eqref{transformedexact}-\eqref{M}
when $p$ satisfies \eqref{inequality}.
We will always assume that $M>-2$ since otherwise there is nothing to prove.
We wish to employ the method of proof used in \cite{P97}. This method requires a fairly explicit knowledge
of the heat kernel for the corresponding linear equation.
In the present case, the linear equation is $W_t=W_{rr}+\frac{N-1}rW_r$ with $(r,t)\in (r_0,\infty)\times(0,\infty)$, for some possibly fractional $N$ with
$N\ge2$,
and with the Dirichlet boundary condition at $r=r_0$.
Denote the heat kernel for this equation by $\bar q_{(N, r_0)}(t,r,\rho)$.
Denote by $q_{(N)}(t,r,\rho)$
the heat kernel for the equation
$W_t=W_{rr}+\frac{N-1}rW_r$ with $(r,t)\in (0,\infty)\times(0,\infty)$.
The kernel $q_{(N)}(t,r,\rho)$ is the transition probability density for the Bessel process of order $N$, and is given by \cite{IW}
\begin{equation}\label{qN}
q_{(N)}(t,r,\rho)=\exp(-\frac{r^2+\rho^2}{4t})\frac {\rho^{N-1}}{2t(r\rho)^{\frac N2-1}}I_{\frac N2-1}(\frac{r\rho}{2t}),
\end{equation}
where $I_\nu$ is the modified Bessel function of order $\nu$, given by
\begin{equation}\label{modbess}
I_\nu(x)=(\frac x2)^\nu\sum_{n=0}^\infty\frac{(\frac x2)^{2n}}{n!\Gamma(\nu+n+1)}.
\end{equation}
By the maximum principle, $\bar q_{(N,r_0)}(t,r,\rho)\le q_{(N)}(t,r,\rho)$.
What we need, however, is an appropriate inequality in the reverse direction.
If $N>2$ (equivalently, $\omega>-\frac14(n-2)^2$), then the Bessel process corresponding to the operator $\frac {d^2}{dr^2}+\frac{N-1}r\frac d{dr}$ is transient \cite{P95}. Furthermore,
as will be explained momentarily,
the uniform
parabolic Harnack inequality holds for the heat equation $W_t=W_{rr}+\frac{N-1}rW_r$ on $r>0$.
Thus, it follows from \cite{GS} that there exist constants $K_0,c>0$ such that
\begin{equation}\label{qqbar}
\bar q_{(N, r_0)}(t,r,\rho)\ge cq_{(N)}(K_0t,r,\rho), \ \text{for}\ r>r_0+1, \ \rho>r_0+1, \ t>0\ \text{and}\ N>2.
\end{equation}
(The uniform parabolic Harnack inequality concerns nonnegative solutions $W$ of $W_t=W_{rr}+\frac{N-1}rW_r$ on $r>0$ on a time interval
$[\tau,\tau+T]$ . See \cite[Definition 2.2]{GS}
for the precise definition. Any such solution can be represented as
$W(r,\tau+t)=\int_0^\infty q_{(N)}(t,r,\rho)W(\rho,\tau)d\rho$, $0\le t\le T$.
Using the explicit
formula for $q_{(N)}$ in \eqref{qN}, one can verify the uniform parabolic Harnack inequality. Indeed, in the case that $N$ is an integer,
the above heat equation is just the radial form of the standard heat equation on $R^N$, and it is well-known that
the uniform Harnack inequality holds in this case \cite{LY}.)
The following key a priori lower bound on solutions to \eqref{transformedexact}-\eqref{M}
in the case that $1<p\le 1+\frac{(2+M)^+}N$ will be used to prove the theorem. Then we will come back to prove the lemma.
\begin{lemma}\label{key}
Let $w$ be a solution to \eqref{transformedexact}-\eqref{M} on a time interval $0<t<T$, with $1<p\le 1+\frac{(2+M)^+}N$ and $N>2$.
Then for some $K,C>0$,
\begin{equation}\label{oldresult2}
w(r,t)\ge Ct^{-\frac N2}\log(1+t)\exp(-\frac{Kr^2}t),\ \text{for}\ 2<t<T,\ r>r_0+1.
\end{equation}
\end{lemma}
\noindent \it Remark.\rm\ The proof of Lemma \ref{key} makes use of \eqref{qqbar}. If $N=2$, a weaker lower bound holds
for $\bar q_{(N, r_0)}$ in terms of $q_{(N)}$. This weaker bound is enough to prove \eqref{oldresult2} when $N=2$
with the restriction that $r\ge t^\frac12$.
See Lemma \ref{n=2}
and \eqref{GS2}. As the proof of Theorem \ref{negative} below shows, it is enough to have the estimate \eqref{oldresult2} for
$r\ge t^\frac12$.
In light of the above remark, \eqref{oldresult2} holds for all $N\ge2$ and $r\ge t^\frac12$. We now use this to prove the theorem.
\begin{proof}[Proof of Theorem \ref{negative}]
Assume that $w(r,t)$ is a global solution to \eqref{transformedexact}-\eqref{M}.
For $n>r_0+1$, define
\begin{equation*}
F_n(t)=\int_n^{2n}w(r,t)\phi^{(n)}(r)r^{N-1}dr,
\end{equation*}
where $\phi^{(n)}>0$, normalized by $\int_n^{2n}\phi^{(n)}(r)r^{N-1}dr=1$, is the eigenfunction corresponding to the principal eigenvalue $\lambda_n>0$
for the operator $-(\frac{d^2}{dr^2}+\frac{N-1}r\frac d{dr})=-r^{1-N}\frac d{dr} r^{N-1}\frac d{dr}$ on $(n,2n)$ with the Dirichlet boundary condition at the endpoints.
For an appropriate value of $n$, we will show that $F_n$ blows up in finite time, thereby contradicting the assumption that $w$ is
a global solution.
From the outset, we assume that $n$ is sufficiently large so that \eqref{hatr2sided} holds for $r\ge n$.
Simple scaling shows that $\lambda_n$ is on the order $\frac1{n^2}$ as $n\to\infty$. In particular then, there exists a constant $c>0$ such
that
$\lambda_n\le \frac c{n^2}$.
Since $\phi^{(n)}(n)=\phi^{(n)}(2n)=0$, one has $(\phi^{(n)})'(n)\ge0$ and $(\phi^{(n)})'(2n)\le0$.
Using the facts in this paragraph, integrating by parts and using Jensen's inequality, we have
\begin{equation}\label{intbyparts}
\begin{aligned}
&F_n'(t)=\int_n^{2n}w_t(r,t)\phi^{(n)}(r)r^{N-1}dr\\
&=\int_n^{2n}\left(w_{rr}(r,t)+\frac{N-1}rw_r(r,t)+\hat a(r)w^p(r,t)\right)\phi^{(n)}(r)r^{N-1}dr\\
&=\int_n^{2n}(r^{N-1}w_r(r,t))_r\phi^{(n)}(r)dr+\int_n^{2n}\hat a(r)w^p(r,t)\phi^{(n)}(r)r^{N-1}dr\\
&\ge\int_n^{2n}(r^{N-1}\phi^{(n)}_r(r))_rw(r,t)dr+c_1n^M\int_n^{2n}w^p(r,t)\phi^{(n)}(r)r^{N-1}dr\\
&=-\lambda_n F_n(t)+c_1n^M\int_n^{2n}w^p(r,t)\phi^{(n)}(r)r^{N-1}dr\\
&\ge-\frac c{n^2}F_n(t)+c_1n^MF_n^p(t).
\end{aligned}
\end{equation}
The function $-\frac c{n^2} x+c_1n^Mx^p$ is both positive and increasing for $x>(\frac c{c_1})^{\frac1{p-1}}n^{-\frac{M+2}{p-1}}$. Therefore,
if there exists an $n$ and
a $T_n$ for which $F_n(T_n)>(\frac c{c_1})^{\frac1{p-1}}n^{-\frac{M+2}{p-1}}$, then it follows from \eqref{intbyparts}
and the fact that $p>1$ that $F_n(t)$ will blow up at some finite
value of $t$. From Lemma \ref{key} and the remark following it, we obtain $w(r,n^2)\ge C_1n^{-N}\log n$, for $n\le r\le 2n$ and some $C_1>0$.
Thus, $F_n(n^2)\ge C_1n^{-N}\log n$. Since $1<p\le 1+\frac{(2+M)^+}N$, one can choose $n$ sufficiently large so that
$F_n(n^2)\ge C_1n^{-N}\log n>(\frac c{c_1})^{\frac1{p-1}}n^{-\frac{M+2}{p-1}}$.
\end{proof}
\begin{proof}[Proof of Lemma \ref{key}]
The solution $W$ to the corresponding linear problem $W_t=W_{rr}+\frac{N-1}rW_r$ with the Dirichlet boundary condition at $r=r_0$ and
with initial data $\psi$ is given by
\begin{equation}\label{linear}
W(r,t)=\int_{r_0}^\infty \bar q_{(N, r_0)}(t,r,\rho)\psi(\rho)d\rho.
\end{equation}
By comparison, the solution $w$ to \eqref{transformedexact}-\eqref{M} satisfies
\begin{equation}\label{est-w}
w\ge W.
\end{equation}
On the other hand, the solution $w$ to \eqref{transformedexact}-\eqref{M} satisfies the inequality
\begin{equation}\label{intequ}
w(r,t)\ge\int_{r_0}^\infty \bar q_{(N,r_0)}(t,r,\rho)\psi(\rho)d\rho+\int_0^tds\int_{r_0}^\infty d\rho\
\bar q_{(N,r_0)}(t-s,r,\rho)\hat a(\rho)w^p(\rho,s).
\end{equation}
(See \cite{P97} and \cite{Z99}, where it is also shown that under appropriate conditions, \eqref{intequ} holds with an equality.)
Without loss of generality, we assume that $r_0+2$ is contained in the support of $\psi$ appearing in \eqref{linear}.
From
\eqref{qN}-\eqref{qqbar} and \eqref{linear}-\eqref{intequ} it then follows that
\begin{equation}\label{keyest}
w(r,t)\ge c_1\int_0^tds\int_{r_0+1}^\infty d\rho\ q_{(N)}(K_1(t-s),r,\rho)\hat a(\rho)q^p_{(N)}(K_1s,\rho,r_0+2),\ r>r_0+1,
\end{equation}
for some $K_1,c_1>0$.
In the case that $N$ is an integer, which we denote by $N_0$, $q_{(N_0)}$ is just the standard $N_0$-dimensional Gaussian heat kernel in radial
coordinates, and \eqref{keyest} can be converted back to $N_0$-dimensional Euclidean coordinates. In \cite{P97}, the right
hand side of \eqref{keyest} (converted to Euclidean coordinates and with some other inessential differences) was shown to satisfy the inequality
\begin{equation}\label{oldresult1}
\begin{aligned}
&\int_1^{\frac t2}ds\int_{r_0+1}^\infty d\rho\ q_{(N_0)}(K_1(t-s),r,\rho)\hat a(\rho)q^p_{(N_0)}(K_1s,\rho,r_0+2)\ge\\
&\begin{cases}&
Ct^{1-\frac {N_0}2p+\frac M2}\exp(-\frac{Kr^2}t),\ \text{if}\ p<1+\frac{2+M}{N_0},\\
& Ct^{-\frac {N_0}2}\log(1+t)\exp(-\frac{Kr^2}t),\ \text{if}\ p=1+\frac{2+M}{N_0},
\end{cases}\\
& \text{for}\ t>2,\ r>r_0+1,
\end{aligned}
\end{equation}
where $K,C>0$.
Recall that we are assuming that $M>-2$.
Note that $1-\frac {N_0}2 p+\frac M2>-\frac {N_0}2$, if $p<1+\frac{2+M}{N_0}$, and
$1-\frac {N_0}2p+\frac M2=-\frac {N_0}2$, if $p=1+\frac{2+M}{N_0}$.
Thus,
from \eqref{keyest} and \eqref{oldresult1} it follows immediately that
\eqref{oldresult2} holds for $N=N_0$.
(For \eqref{oldresult1} and \eqref{oldresult2} with $N=N_0$, see the statements and proofs of \cite[Lemma 2, Proposition 1 and Lemma 3]{P97}.
The spatial integral in \cite{P97} is over all of $R^{N_0}$, which would correspond here to $\rho>0$. But one could have worked just as well
with $|x|>r_0+1$ in \cite{P97}, so the restriction here to $\rho>r_0+1$ in the spatial integral causes no problem.)
We now proceed to demonstrate that \eqref{oldresult1}, and consequently also \eqref{oldresult2}, continue to hold
in the case that $N_0$ is replaced by any non-integral $N>2$. We write $N=N_0-\beta$, where
$N_0\ge3$ is an integer and $\beta\in(0,1)$.
Let $K_\nu(x)\equiv(\frac x2)^{-\nu}I_\nu(x)$, and note from the definition of $I_\nu$ in \eqref{modbess} that $K_\nu(x)$ is decreasing
in $\nu$. Thus, we have from \eqref{qN},
\begin{equation}\label{NN0}
\begin{aligned}
&q_{(N)}(t,r,\rho)=\exp(-\frac{r^2+\rho^2}{4t})\frac{\rho^{N-1}}{2t(r\rho)^{\frac N2-1}}(\frac{r\rho}{2t})^{\frac N2-1}K_{\frac N2-1}(\frac{r\rho}{2t})\\
&=\exp(-\frac{r^2+\rho^2}{4t})\frac{\rho^{N_0-1}}{2t(r\rho)^{\frac {N_0}2-1}}(\frac{r\rho}{2t})^{\frac {N_0}2-1}
K_{\frac N2-1}(\frac{r\rho}{2t})\left(\frac{\rho^{-\beta}}{(r\rho)^{-\frac\beta2}}(\frac{r\rho}{2t})^{-\frac\beta2}\right)\\
&\ge\frac{(2t)^{\frac\beta2}}{\rho^\beta}q_{(N_0)}(t,r,\rho).
\end{aligned}
\end{equation}
From \eqref{NN0} we have
\begin{equation}\label{final}
\begin{aligned}
&q_{(N)}(K_1(t-s),r,\rho)q^p_{(N)}(K_1s,\rho,r_0+2)\\
&\ge C_1\frac{t^\frac\beta2}{\rho^\beta}s^{\frac\beta2p}q_{(N_0)}(K_1(t-s),r,\rho)q^p_{(N_0)}(K_1s,\rho,r_0+2), \\
&\text{for}\ 1\le s\le \frac t2,\ 0\le\rho<\infty,
\end{aligned}
\end{equation}
for some $C_1>0$.
From \eqref{final} we have
\begin{equation}\label{connectNN0}
\begin{aligned}
&\int_1^{\frac t2}ds\int_{r_0+1}^\infty d\rho\ q_{(N)}(K_1(t-s),r,\rho)\hat a(\rho)q^p_{(N)}(K_1s,\rho,r_0+2)\ge\\
&C_1t^{\frac\beta2}\int_1^{\frac t2}ds\int_{r_0+1}^\infty d\rho\ \rho^{-\beta}s^{\frac\beta2p}q_{(N_0)}(K_1(t-s),r,\rho)\hat a(\rho)q^p_{(N_0)}(K_1s,\rho,r_0+2).
\end{aligned}
\end{equation}
Note that the only difference between the terms appearing inside the double integral on the right hand side of \eqref{connectNN0} and the
terms appearing inside the double integral on the left hand side of \eqref{oldresult1}
is the addition of the factors $\rho^{-\beta}$ and $s^\frac\beta2$.
Translating the setup and notation in the proof of \eqref{oldresult1} in \cite{P97} to the present situation, we note that the integration over $\rho$
introduced a term of the form $((t-s)r(s,t))^{\frac M2}$, where $r(s,t)=\frac s{s+pK_2(t-s)}$, for some $K_2>0$, and the exponent $\frac M2$
was a consequence of $\hat a$ being on the order $\rho^M$. Since $\hat a(\rho)$ is replaced
by $\rho^{-\beta}\hat a(\rho)$ in \eqref{connectNN0}, in the present situation we obtain a term of the form
$((t-s)r(s,t))^{\frac M2-\frac\beta2}$; see \cite[(2.34)-(2.37)]{P97}.
Thus, whereas in the penultimate step in the proof of \eqref{oldresult1} in \cite{P97} we obtained
\begin{equation*}
\begin{aligned}
&\int_1^{\frac t2}ds\int_{r_0+1}^\infty d\rho\ q_{(N_0)}(K_1(t-s),r,\rho)\hat a(\rho)q^p_{(N_0)}(K_1s,\rho,r_0+2)\ge\\
&C_2\exp(-\frac {Kr^2}t)\int_1^{\frac t2}s^{-\frac {N_0}2p}(r(s,t))^{\frac {N_0}2+\frac M2}(t-s)^\frac M2ds,
\end{aligned}
\end{equation*}
for some $K>0$ (see \cite[(2.37)]{P97}),
we obtain here
\begin{equation}\label{new237}
\begin{aligned}
&t^{\frac\beta2}\int_1^{\frac t2}ds\int_{r_0+1}^\infty d\rho\ \rho^{-\beta}s^{\frac\beta2p}q_{(N_0)}(K_1(t-s),r,\rho)\hat a(\rho)q^p_{(N_0)}(K_1s,\rho,r_0+2)\\
&\ge C_2t^{\frac\beta2}\exp(-\frac {Kr^2}t)\int_1^{\frac t2}s^{-\frac {N_0}2p+\frac\beta2p}(r(s,t))^{\frac {N_0}2+\frac M2-\frac\beta2}(t-s)^{\frac M2-\frac\beta2}ds.
\end{aligned}
\end{equation}
Making the change of variables $u=\frac st$ and recalling that $N_0-\beta=N$, we have
\begin{equation}\label{last}
\begin{aligned}
&t^{\frac\beta2}\int_1^{\frac t2}s^{-\frac {N_0}2p+\frac\beta2p}(r(s,t))^{\frac {N_0}2+\frac M2-\frac\beta2}(t-s)^{\frac M2-\frac\beta2}ds=\\
&t^{1+\frac M2-\frac N2p}\int_{\frac1t}^{\frac12}u^{\frac N2+\frac M2-\frac N2p}(u+pK_2(1-u))^{-\frac N2-\frac M2}(1-u)^{\frac M2-\frac\beta2}du.
\end{aligned}
\end{equation}
If $p<1+\frac{2+M}N$, then $\frac N2+\frac M2-\frac N2p>-1$ and the integral on the right hand side of \eqref{last} is bounded in $t$. However
if $p=1+\frac{2+M}N$, then $\frac N2+\frac M2-\frac N2p=-1$ and that integral is on the order of $\log t$.
Using this fact along with \eqref{connectNN0}-\eqref{last}, we conclude that \eqref{oldresult1} holds with the integer $N_0$ replaced by non-integral $N$.
From this and \eqref{keyest} we then also obtain \eqref{oldresult2} with the integer $N_0$ replaced by non-integral $N$.
This completes the proof of Lemma \ref{key}.
\end{proof}
\section{Proof of Theorem \ref{extresult}}
Note
that \eqref{transformedexact}-\eqref{M} with $N$ equal to an integer is the radial version of \eqref{exterior}-\eqref{a-ext} (with $N$ and $M$ identified
with $n$ and $m$). Thus, in fact,
Lemma \ref{key} and the proof of Theorem \ref{negative} given in section 3 give a proof of Theorem \ref{extresult} in the case $n\ge3$. If we prove
the equivalent of Lemma \ref{key} for $n=2$, then we will also have a proof of Theorem \ref{extresult} for $n=2$.
In fact, as the proof of Theorem \ref{negative} showed, it suffices to have the estimate on $w(r,t)$ in Lemma \ref{key}
for $r\ge t^\frac12$.
Thus, it suffices to prove the following result.
\begin{lemma}\label{n=2}
Let $w$ be a solution to \eqref{exterior} with $n=2$ on a time interval $0<t<T$, with $1<p\le 1+\frac{(2+m)^+}2$.
Then for some $K,C>0$,
\begin{equation}\label{oldresult22}
w(x,t)\ge Ct^{-1}\log(1+t)\exp(-\frac{K|x|^2}t),\ \text{for}\ |x|>t^\frac12\ \text{and}\ 5<t<T.
\end{equation}
\end{lemma}
\begin{proof}
We assume that $m>-2$ since otherwise there is nothing to prove.
Let $p(t,x,y)=(4\pi t)^{-1}\exp(-\frac{|y-x|^2}{4t})$ denote the heat kernel for the Laplacian on $R^2$, and
let $\bar p_{r_0}(t,x,y)$ denote the corresponding heat kernel for the Laplacian on $R^2-\bar B_{r_0}$ with the Dirichlet boundary condition
at $|x|=r_0$.
It was shown in \cite{GS} that for appropriate constants $c_0,K_0>0$,
one has
\begin{equation}\label{GS2}
\begin{aligned}
&\bar p_{r_0}(t,x,y)\ge c_0\frac{\log(1+|x|)\log(1+|y|)}{\left(\log(1+\sqrt t)+\log(1+ |x|)\right)\left(\log(1+\sqrt t)+\log (1+|y|\right)}p(K_0t,x,y),\\
& \text{for}\ |x|>r_0+1,\ |y|> r_0+1,\ t>0.
\end{aligned}
\end{equation}
We now follow to a significant degree the proof of blow-up in \cite{P97}. Similar to \cite[Lemma 1]{P97}, we have
\begin{equation}\label{integralequ}
w(x,t)\ge\int_{R^2-\bar B_{r_0}}\bar p_{r_0}(t,x,y)\phi(y)dy+\int_0^t\int_{R^2-\bar B_{r_0}}\bar p_{r_0}(t-s,x,y)a(y)w^p(y,s)dyds.
\end{equation}
The first term on the right hand side of \eqref{integralequ},
which is the solution of the corresponding linear problem,
constitutes a lower bound for $w$. Thus, using \eqref{GS2}, we have similar to
\cite[Lemma 2]{P97},
\begin{equation}\label{linearbound}
w(x,t)\ge ct^{-1}\exp(-\frac{|x|^2}{2K_0t})
\frac{\log(1+|x|)}{\left(\log(1+\sqrt
t)+\log(1+|x|)\right)\left(\log(1+\sqrt t)\right)},
\end{equation}
for some $c>0$.
Note that for $|x|\ge t^\frac12$, $|y|\ge t^\frac14$ and $t\ge1$, the expression
$\frac{\log(1+|x|)\log(1+|y|)}{\left(\log(1+\sqrt t)+\log(1+ |x|)\right)\left(\log(1+\sqrt t)+\log (1+|y|\right)}$
is bounded and bounded away from 0. Thus,
substituting the estimate \eqref{linearbound} into the second term on the right hand side of \eqref{integralequ}, and using \eqref{GS2} and \eqref{a-ext},
it follows that
for some $C>0$,
\begin{equation}\label{goodbound}
\begin{aligned}
&w(x,t)\ge \frac Ct\int_{t^\frac12}^{\frac12t}\int_{|y|>t^\frac14}s^{-p}|y|^m\exp(-\frac{|y-x|^2}{Ct})\exp(-\frac{|y|^2p}{2K_0s})dyds,\\
&\text{for}\ |x|\ge t^\frac12\ \text{and large}\ t.
\end{aligned}
\end{equation}
Performing some algebraic manipulations similar to those in \cite[p.166]{P97},
one has for $t,s\ge1$ and some $c>0$,
\begin{equation}\label{manipulations}
\exp(-\frac{|y-x|^2}{Ct})\exp(-\frac{|y|^2p}{2K_0s})\ge\exp(-\frac{|x|^2}{ct})\exp(-\frac{|y|^2}{cs}).
\end{equation}
Recalling that $m>-2$ and that $n=2$, it is not hard to show, similar to \cite[Lemma 4]{P97}, that for some $k>0$,
\begin{equation}\label{m-int}
\int_{|y|>t^\frac14}|y|^m\exp(-\frac{|y|^2}{cs})dy\ge ks^{1+\frac m2}, \ \text{for}\ s\ge t^\frac12.
\end{equation}
From \eqref{goodbound}-\eqref{m-int}, we obtain for some $k_1>0$,
\begin{equation}\label{final}
w(x,t)\ge\frac{k_1}t\exp(-\frac{|x|^2}{ct})\int_{t^\frac12}^{\frac12t}s^{1+\frac m2-p}ds,\ \text{for}\ |x|\ge t^\frac12\ \text{and large}\ t.
\end{equation}
By assumption, $1<p\le1+\frac{2+m}2=2+\frac m2$; thus, $1+\frac m2-p\ge-1$. Consequently, for some $k_2>0$ and $t\ge5$, we have
\begin{equation}\label{int-s}
\int_{t^\frac12}^{\frac12t}s^{1+\frac m2-p}ds\ge k_2\log t.
\end{equation}
Now \eqref{oldresult22} follows from \eqref{final} and \eqref{int-s}.
\end{proof}
\section{Proofs of Theorem \ref{spectral} and Corollary \ref{corspectral}}
\noindent \it Proof of Theorem \ref{spectral}.\rm\
It is known that $\lambda_{0;D}(-\Delta +V)$ is non-increasing in $D$ and that $\lambda_{0;D}(-\Delta +V)=\lim_{k\to\infty}
\lambda_{0;D_k}(-\Delta +V)$, if $D_k\uparrow D$ \cite[chapter 4]{P95}.
These properties of $\lambda_{0;D}(-\Delta+V)$ allow us to assume without loss of generality
that the domain $D$ in the statement of the theorem is bounded and has a smooth boundary.
As such, $\lambda_{0;D}(-\Delta+V)<0$ is in fact the principal eigenvalue for $-\Delta+V$ in $D$ with the Dirichlet
boundary condition. Let $\psi_0>0$,
normalized by $\int_D\psi_0(x)dx=1$, denote the corresponding eigenfunction.
Assume now that $u(r,t)$ is a global solution to \eqref{probextra} for some $p>1$.
Define
\begin{equation}
F(t)=\int_Du(x,t)\psi_0(x)dx.
\end{equation}
We will show that $F$ blows up at some finite time, thereby contradicting the assumption that $u$ is a global solution.
Note that $\psi_0$ vanishes on $\partial D$ and that $\nabla\psi_0\cdot \nu\le0$ on $\partial D$, where
$\nu$ is the unit outward normal to $D$ at $\partial D$. Also, by assumption $\inf_{x\in D}a(x)\ge\delta$, for some $\delta>0$.
Integrating by parts, and using Jensen's inequality and the facts above, we have
\begin{equation}\label{Fprime}
\begin{aligned}
&F'(t)=\int_Du_t(x,t)\psi_0(x)dx=\int_D(\Delta u-Vv+au^p)(x)\psi_0(x)dx\\
&\ge-\lambda_{0;D}(-\Delta+V)F(t)+\delta F^p(t)\ge\delta F^p(t).
\end{aligned}
\end{equation}
Although the initial data $\phi$ of $u$ may vanish identically on $D$, one certainly has $F(t)>0$ for $t>0$. Thus, it
follows from \eqref{Fprime} and the fact that $p>1$ that $F$ blows up at some finite time.
\hfill $\square$
\medskip
\noindent \it Proof of Corollary \ref{corspectral}.\rm\
It is well-known that $\lambda_{0;R^n-\{0\}}(-\Delta+\frac \gamma{|x|^2})<0$ if $\gamma>\frac{(n-2)^2}4$ \cite[pp. 153-154]{P95}.
Let $B_k=\{x\in R^n:|x|<k\}$.
Recalling the facts noted in the first line of the proof of Theorem \ref{spectral},
it follows that $\lambda_{0;B_k-\bar B_\epsilon}(-\Delta+\frac\gamma{|x|^2})<0$, for sufficiently large $k$ and sufficiently small $\epsilon>0$.
Since $a$ is continuous and positive by assumption, it follows that $a$ is bounded away from 0 on $B_k-\bar B_\epsilon
$. Thus, the corollary follows from
Theorem \ref{spectral}.
\hfill $\square$
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 80 |
Les BMI Film and TV Awards sont des récompenses décernées annuellement par la société de gestion des droits d'auteur américaine Broadcast Music Incorporated (BMI) dans deux catégories : musique de film (BMI Film Music Award) et musique pour la télévision (BMI TV Music Awards).
Historique
Catégories de récompense
Prix BMI de la meilleure musique de film ()
Meilleure musique de film ()
Chanson la plus interprétée d'un film ()
BMI Film Music Awards
Années 1980
1985
Charles Fox - Bonjour les vacances 2
1987
Miles Goodman pour À propos d'hier soir...
Danny Elfman pour À fond la fac
Peter Best pour Crocodile Dundee
Andy Summers pour Le Clochard de Beverly Hills
Thomas Newman pour Gung Ho, du saké dans le moteur
Lennie Niehaus pour Le Maître de guerre
John Barry pour Out of Africa
John Barry pour Peggy Sue s'est mariée
Jerry Goldsmith pour Poltergeist 2
Michael Gore pour Rose bonbon
David Shire pour Short Circuit
1988
Miles Goodman et Carlos Santana pour La Bamba
Eric Clapton et Michael Kamen pour L'Arme fatale
John Barry pour Tuer n'est pas jouer
Alan Silvestri pour Une chance pas croyable
Alan Silvestri pour Predator
Basil Poledouris pour RoboCop
David Foster pour Le Secret de mon succès
Arthur B. Rubinstein pour Étroite Surveillance
David Newman pour Balance maman hors du train
John Williams pour Les Sorcières d'Eastwick
1989
Peter Best pour Crocodile Dundee 2
Danny Elfman pour Beetlejuice
Michael Convertino pour Duo à trois
Herbie Hancock pour Colors
Nile Rodgers pour Un prince à New York
Michael Kamen pour Piège de cristal
Hans Zimmer pour Rain Man
Jerry Goldsmith pour Rambo 3
Danny Elfman pour Fantômes en fête
Randy Edelman pour Jumeaux
Alan Silvestri pour Qui veut la peau de Roger Rabbit
Années 1990
1990
Alan Silvestri pour Retour vers le futur 2
Danny Elfman pour Batman
John Williams pour Né un 4 juillet
Hans Zimmer pour Miss Daisy et son chauffeur
Randy Edelman, Antonio Reid, Kenneth Edmonds et Daryl Simmons pour « On Our Own » dans SOS Fantômes 2
John Williams pour Indiana Jones et la Dernière Croisade
Michael Kamen, Eric Clapton et David Sanborn pour L'Arme fatale 2
Alan Menken pour La Petite Sirène
David Kitay pour Allô maman, ici bébé
David Newman pour La Guerre des Rose
1991
Alan Silvestri pour Retour vers le futur 3
John Barry pour Danse avec les loups
Hans Zimmer pour Jours de tonnerre
Danny Elfman pour Dick Tracy
Michael Kamen pour 58 minutes pour vivre
John Williams pour Maman, j'ai raté l'avion !
Basil Poledouris pour À la poursuite d'Octobre rouge
John Williams pour Présumé Innocent
James Newton Howard, Per Gessle pour « It Must Have Been Love » dans Pretty Woman
John Du Prez pour Les Tortues Ninja
Jerry Goldsmith pour Total Recall
1992
Hans Zimmer pour Backdraft
Alan Menken pour La Belle et la Bête
Stanley Clarke pour Boyz N the Hood
Bernard Herrmann pour Les Nerfs à vif
John Williams pour Hook ou la Revanche du capitaine Crochet
Randy Edelman pour Un flic à la maternelle
Michael Kamen pour Robin des Bois, prince des voleurs
Jerry Goldsmith pour Les Nuits avec mon ennemi
John Du Prez pour Les Tortues Ninja 2 : Les héros sont de retour
Miles Goodman pour Quoi de neuf, Bob ?
1993
Alan Menken pour Aladdin
Jerry Goldsmith pour Basic Instinct
Danny Elfman pour Batman : Le Défi
Alan Silvestri pour Le Père de la mariée
Thomas Newman pour Beignets de tomates vertes
John Williams pour Maman, j'ai encore raté l'avion !
Hans Zimmer pour Une équipe hors du commun
Michael Kamen, Eric Clapton et David Sanborn pour L'Arme fatale 3
Gary Chang pour Piège en haute mer
Lennie Niehaus pour Impitoyable
1994
Alan Silvestri pour The Bodyguard
Hans Zimmer pour Cool Runnings
Dave Grusin pour The Firm
Basil Poledouris pour Free Willy
George Fenton pour Groundhog Day
Alan Silvestri pour Grumpy Old Men
John Barry pour Indecent Proposal
John Williams pour Jurassic Park
Randy Edelman pour The Last of the Mohicans
Thomas Newman pour Scent of a Woman
John Williams pour Schindler's List
1995
Mark Mancina pour Bad Boys
Graeme Revell pour The Crow
Todd Rundgren pour Dumb and Dumber
David Newman pour The Flintstones
Alan Silvestri pour Forrest Gump
Hans Zimmer, Elton John, Tim Rice pour « Can You Feel The Love Tonight » dans Le Roi lion
William Ross pour The Little Rascals
Thomas Newman pour Little Women
Randy Edelman pour The Mask
Michael Convertino pour The Santa Clause
John Barry pour The Specialist
Mark Mancina pour Speed
David Arnold pour Stargate
1996
Lennie Niehaus pour The Bridges of Madison County
Hans Zimmer pour Broken Arrow
Jerry Goldsmith pour Congo
Hans Zimmer pour Crimson Tide
Michael Kamen pour Die Hard: With a Vengeance
Alan Silvestri pour Father of the Bride Part 2
Éric Serra pour GoldenEye
Alan Silvestri pour Grumpier Old Men
George S. Clinton pour Mortal Kombat
Michael Kamen pour Mr. Holland's Opus
Alan Menken pour Pocahontas
Kenneth Edmonds pour Waiting to Exhale
Randy Edelman pour While You Were Sleeping
1997
Michael Kamen pour 101 Dalmatians
Alan Silvestri pour Eraser
Alan Menken pour The Hunchback of Notre Dame
David Arnold pour Independence Day
Danny Elfman pour Mission: Impossible
David Newman pour The Nutty Professor
Thomas Newman pour Phenomenon (Wayne Kirkpatrick pour « Change the World »)
Hans Zimmer pour The Rock
Jerry Goldsmith pour Star Trek: First Contact
Mark Mancina pour Twister
1998
Air Force One – Jerry Goldsmith
''Anaconda, le prédateur () – Randy Edelman Beavis et Butt-Head se font l'Amérique () – John Frizzell Demain ne meurt jamais () – David Arnold Wedding Singer : Demain, on se marie ! () – Teddy Castellucci Flubber – Danny Elfman L.A. Confidential – Jerry Goldsmith Le Saint () – Graeme Revell Les Ailes de l'enfer () – Mark Mancina Men in Black – Danny Elfman Pour le pire et pour le meilleur () – Hans Zimmer Good Will Hunting – Danny Elfman 1999
Harry Gregson-Williams pour Antz
Trevor Rabin pour Armageddon
Richard Gibbs pour Doctor Dolittle
Harry Gregson-Williams et Trevor Rabin pour Enemy of the State
David Arnold pour Godzilla
Thomas Newman pour The Horse Whisperer
Michael Kamen pour Lethal Weapon 4
Don Davis pour The Matrix
Jerry Goldsmith pour Mulan
Chris Boardman pour Payback
Mark Mothersbaugh pour Les Razmoket
Lalo Schifrin pour Rush Hour
John Williams pour Saving Private Ryan
Stephen Warbeck pour Shakespeare in Love
Randy Edelman pour Six Days Seven Nights
John Williams pour Stepmom
Alan Pasqua pour The Waterboy
George Fenton pour You've Got Mail
Années 2000
2000
Thomas Newman pour American Beauty
Richard Horowitz pour Any Given Sunday
George S. Clinton pour Austin Powers: The Spy Who Shagged Me
Teddy Castellucci pour Big Daddy
Trevor Rabin pour Deep Blue Sea
Christopher Young pour Entrapment
Thomas Newman pour Erin Brockovich
Thomas Newman pour The Green Mile
Jerry Goldsmith pour The Haunting
Jerry Goldsmith pour The Mummy
Danny Elfman pour Sleepy Hollow
John Williams pour Star Wars, Episode I: The Phantom Menace
Mark Mancina pour Tarzan
David Arnold pour The World Is Not Enough
2001
Richard Gibbs pour Big Momma's House
Ed Shearmur pour Charlie's Angels
Harry Gregson-Williams pour Chicken Run
Danny Elfman pour The Family Man
Trevor Rabin pour Gone in Sixty Seconds
Ed Shearmur pour Miss Congeniality
Lalo Schifrin pour Mission: Impossible 2
David Newman, Janet Jackson -« Doesn't Really Matter » dans Nutty Professor 2: The Klumps
John Williams pour The Patriot
Trevor Rabin pour Remember the Titans
Mark Mothersbaugh pour Rugrats in Paris
David Kitay pour Scary Movie
Lennie Niehaus pour Space Cowboys
Cliff Martinez pour Traffic
Richard Marvin pour U-571
John Ottman pour X-Men
2002
Jerry Goldsmith pour Along Came a Spider
John Williams pour Artificial Intelligence: AI
David Newman pour Dr. Dolittle 2
Brian Transeau pour The Fast and the Furious
John Williams pour Harry Potter and the Sorcerer's Stone
David Newman pour Ice Age
Aaron Zigman pour John Q
John Williams pour Jurassic Park 3
Graeme Revell pour Lara Croft: Tomb Raider
Rolfe Kent pour Legally Blonde
David Holmes pour Ocean's Eleven
Danny Elfman pour Planet of the Apes
Lalo Schifrin pour Rush Hour 2
Harry Gregson-Williams pour Shrek
Paul Oakenfold et Christopher Young Swordfish
Mark Mancina pour Training Day
2003
Eminem et Jeff Bass pour « Lose Yourself » dans 8 Mile
George S. Clinton pour Austin Powers in Goldmember
Lalo Schifrin pour Bringing Down the House
John Williams pour Catch Me If You Can
Danny Elfman pour Chicago
Graeme Revell pour Daredevil
David Arnold pour Die Another Day
John Williams pour Harry Potter and the Chamber of Secrets
David Newman pour How to Lose a Guy in 10 Days
Danny Elfman pour Men in Black 2
John Williams pour Minority Report
Teddy Castellucci pour Mr. Deeds
Alexander Janko et Chris Wilson pour My Big Fat Greek Wedding
Thomas Newman pour Road to Perdition
George S. Clinton pour The Santa Clause 2
David Newman pour Scooby-Doo
Danny Elfman pour Spider-Man
John Williams pour Star Wars, Episode II: Attack of the Clones
Jerry Goldsmith pour The Sum of All Fears
George Fenton pour Sweet Home Alabama
Randy Edelman pour xXx
2004
David Arnold pour 2 Fast 2 Furious
Teddy Castellucci pour 50 First Dates
Theodore Shapiro pour Along Came Polly
Teddy Castellucci pour Anger Management
Trevor Rabin pour Bad Boys II
Mark Mancina pour Brother Bear
David Newman pour The Cat in the Hat
Ed Shearmur pour Charlie's Angels: Full Throttle
David Newman pour Daddy Day Care
Thomas Newman pour Finding Nemo
Rolfe Kent pour Freaky Friday
Graeme Revell pour Freddy vs. Jason
Danny Elfman pour Hulk
Rolfe Kent pour Legally Blonde 2: Red, White and Blonde
Don Davis pour The Matrix Reloaded
Don Davis pour The Matrix Revolutions
James L. Venable pour Scary Movie 3
Craig Wedren pour The School of Rock
Theodore Shapiro pour Starsky and Hutch
Steve Jablonsky pour The Texas Chainsaw Massacre
John Ottman pour X-Men 2
2005
Alex Wurman pour Anchorman: The Legend of Ron Burgundy
David Newman pour Are We There Yet?
Harald Kloser pour AVP: Alien vs. Predator
Harald Kloser pour The Day After Tomorrow
Theodore Shapiro pour Dodgeball: A True Underdog Story
Christopher Young pour The Grudge
John Williams pour Harry Potter and the Prisoner of Azkaban
George Fenton pour Hitch
Michael Giacchino pour The Incredibles
William Ross pour Ladder 49
Thomas Newman pour Lemony Snicket's A Series of Unfortunate Events
Harry Gregson-Williams pour Man on Fire
Rolfe Kent pour Mean Girls
Trevor Rabin pour National Treasure
Aaron Zigman pour The Notebook
David Holmes pour Ocean's Twelve
Harry Gregson-Williams pour Shrek 2
Rolfe Kent pour Sideways
Graeme Revell pour Sin City
Danny Elfman pour Spider-Man 2
John Williams pour The Terminal
2006
Gustavo Santaolalla pour Brokeback Mountain
Alex Wurman pour La Marche de l'empereur
Clint Mansell pour Sahara
John Ottman pour Les Quatre Fantastiques
John Williams pour War of the Worlds
2007
Tyler Bates pour 300
Theodore Shapiro pour Blades of Glory
David Arnold pour Casino Royale
Theodore Shapiro pour The Devil Wears Prada
Mychael Danna pour Little Miss Sunshine
Alexandre Desplat pour The Queen
George S. Clinton pour Santa Clause 3: The Escape Clause
Theodore Shapiro pour You, Me and Dupree
2009
Watchmen : Les Gardiens () – Tyler Bates
Années 2010
2013
Men in Black 3 - Danny Elfman 2018
Justice League – Danny Elfman
Chanson la plus interprétée d'un film
1996 : Batman Forever'' – Seal - Kiss from a Rose
BMI TV Music Awards
Liens externes
Site officiel
sur Imdb
Récompense de cinéma aux États-Unis
Récompense de télévision aux États-Unis
Récompense musicale aux États-Unis | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 2,260 |
{"url":"https:\/\/socratic.org\/questions\/how-do-you-write-670-in-scientific-notation","text":"# How do you write 670 in scientific notation?\n\n$6.7 \\cdot {10}^{2}$\nCount how many numbers are after the first number we have $2$ numbers $7$ and $0$.So,we put ${10}^{2}$.And we put $6.70 \\cdot {10}^{2} = 6.7 \\cdot {10}^{2}$","date":"2020-01-23 01:37:56","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 6, \"mathjax_inline_tex\": 1, \"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\": 0.8352459073066711, \"perplexity\": 598.995730843948}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"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-2020-05\/segments\/1579250608062.57\/warc\/CC-MAIN-20200123011418-20200123040418-00106.warc.gz\"}"} | null | null |
\section{Introduction}
The quest for the identification of the missing mass of the universe has been with us since many decades now~\cite{sum}. While explanations in terms of modifications of Newtonian gravity or General Relativity become more and more contrived,
evidence for the particle nature of such Dark Matter (DM) now comes from many astrophysical and cosmological observations.
Non-baryonic new particles that may fulfill the r\^ole of DM have emerged in the latest decades within many
Beyond the Standard Model (SM) theories, most notably supersymmetry.
These constructions try to naturally explain the hierarchy between the ElectroWeak (EW) scale and the Planck scale and, in doing so, introduce a host of new particles with EW masses and interactions.
Some of these particles can be good DM candidates (e.g.\ the lightest neutralino).
DM stability is the result of extra features introduced by hand (e.g.\ R-parity),
usually necessary also to recover many good properties of the SM that are lost in these extensions
(automatic conservation of baryon number, lepton number, etc).
Finally, the richness of these theories implies the introduction of many unknown new parameters (e.g.\ all sparticle masses), so that the phenomenology of the DM candidate remains unclear.
The Minimal Dark Matter (MDM) proposal~\cite{MDM} originates from different motivations:
focussing on the Dark Matter problem only, we add to the SM the minimal amount of new physics (just one extra EW multiplet $\chi$) and search for the minimal assignments of its quantum numbers
(spin, isospin and hypercharge) that make it a Dark Matter candidate without ad hoc extra features, and without ruining the good features of the SM.
As detailed in the following section, we do find one optimal candidate, and we here focus on it.
Its only free parameter (the DM mass) is fixed from the cosmological DM abundance, so that
any DM observable can be univocally predicted.
Indirect searches are one of the most promising ways to detect Dark Matter. DM particles in the galactic halo are expected to annihilate and produce fluxes of cosmic rays that propagate through the galaxy and reach the earth.
Their energy spectra carry important information on the nature of the DM particle (mass and primary annihilation channels). Many experiments searched for signatures of DM annihilations in the fluxes of $\gamma$ rays, positrons and antiprotons.
At the idm08 conference, the PAMELA experiment~\cite{PAMELA} reported preliminary results
that seem to be the first strong hint for a DM indirect signal.
We here assume that PAMELA data will be confirmed and that
on-going re-evaluations of the astrophysical backgrounds will confirm previous studies, such that
the PAMELA excess implies WIMP DM (non-WIMP DM candidates such as the gravitino may remain viable if unstable~\cite{Ibarra}; DM candidates with a relic density due to a baryon-like asymmetry are disfavored).
In view of its univocal predictions, MDM could have been immediately excluded, rendering this talk unnecessary.
After introducing the MDM model we compare its predictions, as previously computed in~\cite{MDMindirect},
with the PAMELA results.
\section{Minimal Dark Matter}
The MDM model is constructed by adding on top of the SM a single multiplet $\chi \oplus\bar\chi$ with weak interactions, fully determined by its hypercharge $Y$ and by the number of its SU$(2)_L$ components,
$n=\{2,3,4,5,\ldots\}$. The Lagrangian is therefore `minimal':
$$
\mathscr{L} = \mathscr{L}_{\rm SM} + \frac{1}{2}
\left\{\begin{array}{ll}
\bar{\chi} (i D\hspace{-1.4ex}/\hspace{0.5ex}+M) \chi & \hbox{for fermionic $\chi$}\\
|D_\mu \chi|^2 - M^2 |\chi|^2& \hbox{for scalar $\chi$}
\end{array}\right.
$$
where the gauge-covariant derivative $D_\mu$ contains the usual electroweak gauge couplings and vectors, $M$ is a tree level mass term (the only free parameter).
Any additional term (such as Yukawa couplings with SM fields) will be forbidden by gauge and Lorentz invariance, as detailed below.
For a given assignment of $n$ there are few assignments of the hypercharge $Y$ such that one
component of the $\chi$ multiplet has electric charge $Q=T_3+Y=0$, as needed for a DM candidate.
For instance, for $n=2$, since $T_3 = \pm 1/2$, the only possibility is $Y=\mp 1/2$.
For $n=5$ one can have $Y = \{ 0, \pm 1, \pm 2\}$, and so on.
\smallskip
But MDM candidates with $Y \neq 0$ interact with the nuclei of direct detection experiments via exchange of a $Z$ boson, giving rise to an effect not seen by the Xenon and CDMS~\cite{dir} experiments.
Thus we restrict to candidates with $Y=0$, and therefore to odd $n$ multiplets.
Also, the list of possible MDM candidates has to stop at $n \le 5~ (8)$ for fermions (scalars) because larger multiplets would cause the running of $g_2$ to hit a Landau pole below the Planck scale.
Next we inspect which remaining candidates are stable against decay into SM particles. For instance, the fermionic 3-plet with hypercharge $Y=0$ would couple with a Yukawa operator $\chi L H$ with a SM lepton doublet $L$ and a Higgs field $H$ and decay. This is not a viable DM candidate, unless the operator is eliminated by some ad hoc symmetry.
For another instance, the scalar 5-plet with $Y=0$ would couple to four Higgs fields with a dimension 5 operator $\chi HHH^*H^*/M_{\rm Pl}$, suppressed by one power of the Planck scale. Despite the suppression, the resulting life-time is shorter than the age of the universe, so that this is not a viable DM candidate.
Now, the crucial observation is that, given the known SM particle content, there are multiplets that cannot couple to SM fields and are therefore automatically stable DM candidates. Only two possibilities emerge:
a $n=5$ fermion, or a $n=7$ scalar.
But since the latter may have non-minimal quartic couplings with the Higgs field, we will set it aside and focus here on the former for minimality.
Quantum corrections due to a loop of gauge bosons generate a small mass splitting between the components of $\chi$. The lightest component turns out to be the neutral one (as required by DM phenomenology), and the $Q=\pm1$ partners are $166\,{\rm MeV}$ heavier~\cite{MDM}.
We can now compute the DM cosmological abundance as a function of the only free parameter, the mass $M$.
The abundance measured by cosmology, $\Omega_{\rm DM} h^2 =0.110 \pm 0.005$~\cite{cosmoDM},
is matched for $M=(9.6\pm0.2)$ TeV~\cite{MDMastro}.
This result is obtained solving the relevant Boltzmann equation
taking into account all co-annihilations and, importantly, electroweak Sommerfeld corrections~\cite{Hisano}.
This non-perturbative phenomenon significantly enhances
non-relativistic annihilations of particles with mass $M\circa{>}M_W/\alpha_2$.
As a result the (co)-annihilation cross section
$\sigma v$ grows as $v\to0$, so that astrophysical signals ($v\sim 10^{-3}$ in our galaxy),
being much more enhanced than DM annihilations in cosmology ($v\sim 0.2$ at freeze-out),
are detectably large despite the large multi-TeV DM mass $M$.
Elastic scattering of $\chi$ on nuclei occurs at 1-loop via the exchange of $W$'s and Higgs~\cite{MDM, MDMastro},
giving rise to a negligible spin-dependent cross section and to a
spin-independent cross section $\sigma_{\rm SI}({\rm DM} \ {\rm N}) \approx 10^{-44} {\rm cm}^2$
(up to reducible uncertainties due to QCD and to the unknown Higgs mass), within the reach of the next generation of direct detection experiments~\cite{dir}.
In summary, the MDM construction singles out a
$$\hbox{fermionic SU(2)$_L$ 5-plet with zero hypercharge}$$
as providing a fully viable, automatically stable DM candidate. It is called `Minimal Dark Matter' since it is described by the minimal gauge-covariant Lagrangian. Its mass is fixed at $(9.6\pm 0.2)$ TeV and its phenomenology is fully computable with no free particle-physics parameters.
\section{Indirect signatures and the PAMELA positron excess}
The MDM fermionic 5-plet annihilates at tree level into $W^+W^-$, and into $\gamma \gamma$, $\gamma Z$ and $ZZ$ at one loop. We neglected 3-body primary final states.
The annihilation cross sections at $v\sim 10^{-3}$ are large thanks to the Sommerfeld enhancement:
for $M=9.6$ TeV one has
$$
\langle \sigma v \rangle_{WW} = 1.1\cdot 10^{-23}\ \frac{{\rm cm}^3}{{\rm sec}} ,\qquad
\langle \sigma v \rangle_{\gamma\gamma} = \langle \sigma v \rangle_{\gamma Z} \frac{\tan^2\theta_w}{2} = \langle \sigma v \rangle_{ZZ} \tan^4\theta_w = 3 \cdot 10^{-25}\ \frac{{\rm cm}^3}{{\rm sec}}.
$$
The Sommerfeld corrections also introduce a strong dependence on $M$, such that, within its $3\sigma$ range, the cross sections change by one order of magnitude around these central values.
The resulting spectra of $e^+$ and $\bar p$, plotted in fig.~\ref{fig:PAMELA}, are obtained from the primary spectra computed
taking into account spin-correlations and propagated in the galactic halo~\cite{MDMindirect}.
The PAMELA experiment presented preliminary results~\cite{PAMELA} for the fluxes of antiprotons and positrons in the cosmic rays. The latters show an excess at $E_{e^+} = (10 - 60)$ GeV with respect to the expected background, compatibly with hints that previous experiments (e.g. HEAT) had already suggested with a much lower significance. At the same time, the $\bar p$ data show no anomaly.
\smallskip
We tried to perform a preliminary fit of the preliminary PAMELA data to have a feeling of which set of astrophysical assumptions allows to reproduce the data and how well.
We have taken the $e^+$ and $\bar p$ astrophysical backgrounds from~\cite{bck}, and multiplied each one of them
times a free normalization factor and times a spectral correction $E^p$ with $p=0\pm0.1$. This conservatively mimics the estimated uncertainties.
Concerning the DM signal, we smoothly vary between the possible halo models and between the propagation configurations considered in~\cite{MDMindirect}, assuming that they are the same for $e^+$ and $\bar p$:
this should reasonably approximate a precise fit where galactic parameters are extracted from CR data.
Uncertainties on $\bar p$ propagation mainly affect the overall $\bar p$ flux, and we anyway
assume different energy-independent boost factors $B_e$ and $B_p$ for $\bar p$ and $e^+$.
Since the overall normalization of the signal is anyhow uncertain,
we presume that it is safe to neglect possible statistical correlations among the PAMELA data points.
Under these assumptions, the best MDM fit is at $B_e \cdot \sigma v = 4~10^{-22}\,{\rm cm}^3/{\rm sec}$
(i.e.\ $3\circa{<}B_e \circa{<} 100$) and for a propagation model intermediate between `MED' and `MAX';
the halo model is not significantly constrained.
Fig.~\ref{fig:PAMELA} shows the MDM fit superimposed to the preliminary PAMELA data; we here used $B_p = 3$, and this fit does not significantly deteriorate until much larger values.
For the moment uncertainties can only be estimated, so that the fact that this fit has $\chi^2/{\rm dof} \sim 1$ is encouraging but cannot be taken as an overall quality indicator.
Alternative tools can be employed.
We varied $M$ in order to see if the MDM value $M\sim 10\,{\rm TeV}$ is preferred by data. We find that increasing the DM mass above $10\,{\rm TeV}$ starts to give a poorer fit of the $e^+$ spectrum.
Lowering the DM mass, one needs to increasingly reduce free parameters such as $B_p/B_e$ in order
to generate the $e^+$ excess without giving at the same time an unseen $\bar p$ excess.
The $e^+$ and $\bar p$ spectra will be measured by
PAMELA (possibly up to 270 GeV for $e^+$ and 150 GeV for $\bar p$) and later by AMS-08 (up to about 1 TeV).
MDM predicts that the positron fraction should continue to grow, and that
an anomaly should appear in the $\bar p$ spectrum, unless
$\bar{p}$ have an unfavorable boost factor or propagation in our galaxy.
\begin{figure}[t]
\vspace{-0.64cm}
\begin{center}
\includegraphics[width=\textwidth]{PAMELA5fit.pdf}
\vspace{-0.62cm}
\caption{\em\label{fig:PAMELA} The PAMELA preliminary data~\cite{PAMELA} compared with the fermion 5-plet MDM prediction,
at the best-fit point for the astrophysical parameters.}
\end{center}
\vspace{-0.89cm}
\end{figure}
Collateral constraints must be considered. The $e^\pm$ from DM annihilations lead to a synchrotron radiation~\cite{MDMindirect} at the level of `WMAP haze' anomaly~\cite{WMAPhaze}.
Ref.~\cite{Ullio} claims that very strong bounds on the DM annihilation cross section can be inferred
from infrared and X-ray observations of the galactic center region, modeled assuming
a certain magnetic field and DM density, that gets extremely high close to the central black hole
leading to a high rate of DM annihilations.
In this region DM becomes relativistic, and in the MDM case this means that the
Sommerfeld enhancement disappears, leaving a small annihilation cross section,
$\sigma \sim \alpha_2^2/M^2\sim 10^{-28}\,{\rm cm}^3/{\rm sec}$ that would not contradict the strong bounds of~\cite{Ullio}. A dedicated computation of the MDM prediction together with a precise description of the galactic center
is necessary to quantitatively clarify this issue.
\smallskip
To conclude: we presented Minimal Dark Matter. Like string theory, MDM has no free parameters, and thereby makes univocal predictions, falsifiable by any single experimental result.
The preliminary data from PAMELA, presented during idm08, show an excess in the flux of cosmic ray positrons at 10-60 GeV which matches the MDM prediction.
Let us compare with supersymmetry, the theoretically favored scenario:
slepton masses can be fine-tuned to be quasi-degenerate with the lightest neutralino in order to enhance 3-body annihilations obtaining the correct relic abundance and a $e^+$ spectrum that, with a boost factor of $\circa{>}10^4$, can be compatible with the PAMELA excess~\cite{BBE}: in such a case the $e^+$ fraction should decrease at higher energy. MDM predicts the continuing rise of fig.~1a.
The PAMELA results recently published on the arXiv~\cite{PAMELA} have one extra data-point at 80 GeV, still consistent with MDM predictions~\cite{MDMindirect}.
The nearby pulsars Geminga or B0656+14 could also produce a rising $e^+$ fraction, together with an angular anisotropy~\cite{Geminga}.
\newpage
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,921 |
Q: Servlet HttpSession cookies disabled In a web app, when user logs in, a HttpSession is created using HttpSession s = request.getSession(true);
This creates a cookie with jsessionid on the browser.
But if cookies are disabled on browser, How can i proceed with login?
A: If Cookies are disabled. You should be using URL Rewriting mechanism for Session tracking.
Code Example:
http://www.javadocexamples.com/javax/servlet/http/HttpServletResponse/encodeURL%28String%20url%29.html
A: The main purpose of logging in is to identify the user. The basic information of the user is stored in the cookie which is basically a text file containing jsessionid. It is the jsessionid we want and not the cookie itself. So, we can get hold of jsessionid and concat it with the url, we will still be able to access contents in the HttpSession object.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,149 |
Q: Convert APK to manifest in a loop I have many APK (Android package) files in a folder and I want to extract the manifest files from each of them. I am using Android apktool to convert them and since there are many APK files I want to convert them in a loop, not one by one.
apktool d hello.apk ./hello is the command for extracting manifest files from hello.apk and produces the output folder named hello.
I tried the command in the command prompt using for loop in the current directory in which all APK files are stored:
for \r %v in (*.apk) do apktool d "%v" "./%v".
I want the output folder of same name for each APK file, i.e. if APK is hello.apk the output folder should be hello. The above command is producing an error: cannot generate the output folder. How can I extract manifest files from all such APK files at once from a loop?
A: Maybe you forgot -o parameter?
That command works fine for me:
for /r %v in (*.apk) do apktool.jar d "%v" -o "./%~Nv"
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,160 |
\section{Introduction}
Higher-order corrections to the Einstein gravity \cite{kim,dm95}
can be derived from the quantum gravity and the string theory
\cite{green}. Application to the study of the inflationary
universe \cite{acc,acc1} have been a focus of research interest.
In particular, higher derivative terms also arise as an effective
theory for the quantum corrections of matter fields in a curved
space\cite{green}.
In addition, Kaluza-Klein theory \cite{kk,visser} is also
important in the study of the evolution of the early universe.
Indeed, the dimensional-reduction process could affect the
evolution of inflation universe significantly. Recently, brane
universe scenario has also become a focus of interest \cite{ib}.
Induced gravity models have been a focus of study for many
reasons. Weyl is the first to propose that the scale invariant
theory is a candidate for the unified theory of gauge field and
gravitational field. In addition, Dirac's large number theory also
asserts that all dimensionful parameters in physical theory are in
fact dynamical functions of time. As a result, various interesting
models have attracted researchers' interest for a long time.
Therefore, we intent to study an $N=4+D$ dimensional Kaluza-Klein
higher derivative induced gravity model with all dimensionful
coupling constants replaced by appropriate scale-dependent fields.
We will show that a constant internal-space solution will lead to
a nontrivial constraint to the field equations. In addition, there
is also another constraint derived from the assumption of constant
internal scale-dependent scalar field $\psi$.
In fact, we will show in this paper that there are three
constraints to be imposed on the choice of three different
coupling constants coupled to the higher curvature terms. Note
that, in four-dimensional space, $ E =
R_{\lambda\mu\nu\rho}\,R^{\lambda\mu\nu\rho} -
4\,R_{\mu\nu}\,R^{\mu\nu}+ R^2 $ is the integrand of the
Gauss-Bonnet term \cite{weinberg1}. In addition, Weyl tensor
\cite{weinberg1} connects these fourth-order curvature terms in
four-dimensional space. Hence we only need to deal with $R^2$ term
in four-dimensional de Sitter space. These constraints does not
hold in higher dimensional spaces. Therefore, we must deal with
all three different fourth-order terms in $N$-dimension. Hence
equations of motion for the higher-derivative Kaluza-Klein induced
gravity theory\cite{zee,ni,kao00,smolin} are much more complicated
than the four-dimensional higher-derivative gravity. We will show,
however, that the mentioned abundant constraints are not only
consistent with the already abundant stability constraints of the
system but also lead to an interesting result: i.e. only the $R^2$
coupling term is consistent with the inflationary solution.
Possible implications will also be discussed in this paper.
In order to reduce the complication of the derivation of field
equations, we will also derive a simple expression for the
Friedmann equation \cite{kao99} in a ($4+D$)-dimensional space in
this paper. The redundancy of the associated field equations due
to the Bianchi Identity will also be analyzed. We will show that
quadratic terms do not affect the Friedmann equation in a constant
flat internal space scale factor $d(t)$ and flat de Sitter four
space.
This paper will be organized as follows: (i) In section II, we
will introduce the Kaluza-Klein higher derivative induced gravity
model with all dimensionful parameters replaced by appropriate
dynamical fields. The constraint derived from the constant $\psi$
field will be obtained in this section. (ii) We will derive a
model-independent expression for the $N$-dimensional generalized
Friedmann equation in the higher-dimensional higher-derivative
theory in section III. These formulae are derived from a reduced
one-dimensional theory. (iii) We will discuss the stability
conditions for an inflationary solution in the induced-gravity
theory in section IV. (iv) Finally, conclusions are presented in
section V.
\section{Kaluza-Klein Higher Derivative Induced Gravity}
The $4+D$-dimensional Kaluza-Klein higher derivative induced
gravity theory can be described by the following Lagrangian:
\begin{equation} \label{Lind}
L_N =\left ( L- {1 \over 2} \partial_A \psi \partial^A \psi \right
) \psi^D.
\end{equation}
with the $4$-dimensional relevant higher derivative induced
gravity Lagrangian $L$ given by:
\begin{equation}
L=L_1+ L_2+L_\phi=- {\epsilon \over 2} \phi^2 {\bf R} -c_1
({\bf R}^{AB}_{\;\;\;\;\;\;CE})^2 - c_2 ({\bf R}^{A}_{\;\;\;B})^2
- c_3 {\bf R}^2- {1 \over 2} \partial_A \phi \partial^A \phi
-V(\phi) \label{pdg}
\end{equation}
Here $L_1 \equiv - \epsilon \phi^2 {\bf R} /2$, $L_2 \equiv -c_1
({\bf R}^{AB}_{\;\;\;\;\;\;CE})^2 - c_2 ({\bf R}^{A}_{\;\;\;B})^2
- c_3 {\bf R}^2$, and $L_\phi \equiv - (\partial \phi)^2/2
-V(\phi)$ denote the induced Einstein-Hilbert Lagrangian, higher
derivative terms, and the scalar field Lagrangian.
Note that, throughout this paper, the curvature tensor ${\bf
R}^E_{ABC} ({\bf g}_{AB})$ will be defined by the following
equation
\begin{equation}
[D_A,\,\, D_B]V_C = {\bf R}^{E}\,\,_{CBA} V_E . \label{eqn:curv}
\end{equation}
Accordingly, ${\bf R}^{E}_{ABC} = - \partial_C {\bf \Gamma}
^E_{AB} - {\bf \Gamma} ^F_{AB} {\bf \Gamma} ^E_{CF} - ( B
\leftrightarrow C)$. Here ${\bf \Gamma} ^C_{AB}$ denotes the
Christoffel symbol (or spin connection of the covariant
derivative, i.e. $D_A V_B \equiv \partial_A V_B - {\bf \Gamma}
^C_{AB}V_C$). To be more specific, ${\bf \Gamma}^C_{AB} = {1 \over
2} {\bf g}^{CE} (\partial_A {\bf g}_{EB} + \partial_B {\bf g}_{EA}
- \partial_E {\bf g}_{AB} )$. Moreover, the Ricci tensor ${\bf
R}_{AB}$ is defined as
\begin{equation}
{\bf R}_{AB} = {\bf R}^{C}\,\,_{ABC}. \label{ricci}
\end{equation}
And the scalar curvature ${\bf R}$ is defined as the trace of the
Ricci tensor ${\bf R} \equiv {\bf g}^{AB} {\bf R}_{AB}$. Also, the
Einstein tensor is defined as ${\bf G}_{AB} \equiv {1 \over 2}
{\bf g}_{AB} {\bf R} - {\bf R}_{AB}$.
Note that we will use bold-faced notation (e.g. ${\bf R}$) to
denote field variables in $N(=4+D)$-dimensional space. In
addition, normal notations will denote field variables evaluated
in the $4$ or $D$-dimensional spaces as the dimensional reduction
process $M^N \to M^4 \times M^D$ takes places. Here $M^4$ is the
four dimensional Friedmann-Robertson-Walker (FRW) space and $M^D$
is the internal space. We will assume that $M^D$ is the $D$
dimensional FRW space for simplicity. Note that the metric of the
$4$+$D$-dimensional FRW anisotropic space $M^N$ is given by
\begin{eqnarray}
ds^2 &\equiv &{\bf g}_{AB} dZ^A dZ^B \equiv g_{\mu \nu} dx^\mu
dx^\nu +
f_{mn}dz^mdz^n \\
& =& -dt^2
+ {a^2}(t) \Bigl( {dr^2 \over 1 - k_1 r^2} + r^2 d^3\Omega \Bigr
) + {d^2}(t) \Bigl( {dz^2 \over 1 - k_2 z^2} + z^2 d^D\Omega
\Bigr ) . \label{eqn:frw} \label{FRW}
\end{eqnarray}
Here $ d^p \Omega $ is the solid angle $d^p \Omega \, = \,
d{\theta_1}^2 + {\sin}^2 \theta_1 \, d{\theta_2}^2 + \cdots
+\sin^2 \theta_1 \sin^2 \theta_2 \cdots \sin^2 \theta_{p-3}
d\theta_{p-2}^2$ and $k_1,\,\, k_2 \, = \, 0, \pm 1$ stand for a
flat, closed or open universe respectively. Note that we will also
write $g_{ij}=a^2 h_{ij}$ and $g_{mn} = d^2 h_{mn}$ for
convenience. Note that $\theta_i$ is the phase angle of the
$D$-dimensional spherical coordinate. For example, we have
\begin{equation}
z_1=z \sin \theta_1 \sin \theta_2 \cdots \sin \theta_{D-2}.
\end{equation}
Note that we will write $N$-dimensional space-time coordinate as
$Z^{A} \to (x^\mu, \,\, z^m)$ with $A (= 0, 1, \cdots , N-1)$,
$\mu (= 0,1,2,3)$, and $m(=1,2, \cdots, D)$ denoting the $N$, $4$,
and $D$-dimensional space-time indices respectively. Specifically,
capital Roman letters $A,B,C, \cdots$ will denote $N$ dimensional
indices. In addition, Greek letters will denote $4$-indices while
the second half of the Roman letters will denote $D$-dimensional
space-time indices. Here we have assumed that the internal space
($z$) is independent of the external space ($x$). The only
$t$-dependence of the internal space is through the scale factor
$d(t)$.
Induced gravity proposes that all dimensionful parameters are
dynamical variables. Therefore all coupling constants in this
models, $\epsilon$ and $c_i$, are dimensionless. Indeed, the
action
\begin{equation}
\int d^4x d^Dz \sqrt{g} L_N
\end{equation}
is invariant under the global scale transformation:
$g_{AB}'=\Lambda^{-2} g_{AB}$, $\phi'= \Lambda \phi$ ,$\psi'=
\Lambda \psi$ in the absence of the potential $V$ unless $V(\phi)
\sim \phi^4$. Here $\Lambda=$ constant denotes the global scale
transformation parameter. For a practical application, one needs
to introduce a symmetry breaking potential so that a physical
scale can be picked up dynamically. As a result a physical
inflationary solution can be managed. In addition, it is easy to
observe from the scale transformation that $\psi$ is introduced to
compensate the transformation properties of the internal
$D$-space. In deed, $\psi^D d^Dz$ is made dimensionless by
construction.
The variational equation of the $\psi$ field gives
\begin{equation} \label{psieq}
D\psi^{D-1} \left ( L- {1 \over 2} \partial_A \psi
\partial^A \psi \right )+ D_A ( \psi^D \partial^A \psi) =0.
\end{equation}
After the dimensional reduction process takes place, the $\psi$
field is expected to be a function of internal space coordinate
$z$ only. Consequently, this internal space scalar field will not
affect the $4$-dimensional physical universe thereafter. For
simplicity, one will assume that a constant solution
$\psi=\psi_0=$ constant is adopted so that the constant $\psi$
field can be absorbed into the internal coordinate $z$ by a proper
re-scaling. In effect, the $\psi=$ constant solution introduces a
physical scale of the internal space. Note that the $\psi=$
constant is not only a solution to Eq. (\ref{psieq}), it is also a
solution consistent with the static internal space solution.
Indeed, the scalar field $\psi$ is responsible for the internal
space dimension such that $dz^D \psi^D$ remain dimensionless. As a
comparison, the scalar field $\phi$ is introduced to take care of
the dynamical dimension of all $4$-space coupling constants. As a
result, the $\psi$ field will decouple from the $4$-space
completely after the
dimensional reduction process is completed. The remaining impact of
this solution is an additional constraint $L=0$ to be made
compatible with the dimensionally-reduced $4$-space of interest.
Therefore, we will focus on the $4+D$-dimensional model given by
the effective Lagrangian density $L$ described by Eq. (\ref{pdg}).
Consequently, we will study the model (\ref{pdg}) in the presence
of the constraint $L=0$ to be imposed later. In fact, we will show
that the constraint $L=0$ is consistent with the inflationary de
Sitter solution binding by abundant and interesting constraints to
be imposed on the coupling constants $c_i$. We will also study the
stability of this inflationary solution and discuss interesting
implications of this Kaluza-Klein induced gravity model.
The Euler-Lagrange equation of the system can be obtained from the
variational equation of the $4+D$-dimensional metric ${\bf
g}_{AB}$. We will write it as
\begin{equation}
{\bf J}_{AB}={\bf G}_{AB}-{\bf T}_{AB}=0.
\end{equation}
The derivation is very complicate and delicate. Fortunately, if we
are only interested in the $4$+$D$-dimensional FRW space, the
dynamical variables reduce to a set of one-dimensional variables
$a(t)$ and $d(t)$ and $\phi(t)$.
Effectively, we can write the Lagrangian $L(\;{\bf g}_{AB}(a(t),
d(t)), \phi(t)\;) \to L_r(\; a(t), d(t), \phi(t)\;)$. Hopefully,
the final expression of the Euler-Lagrange equations can be
reproduced from the variation of $L_r$ with respect to the
dynamical variables $a(t)$ and $d(t)$ and $\phi(t)$.
If this is indeed applicable, the field equations can be derived
more easily without involving complicate tensor algebra. In
particular, this will be more easy to access when complicate
interactions are introduced. We will show that there is a little
problem with this approach for the non-redundant Friedmann
equation. Fortunately, the non-redundant Friedmann equation can be
reconstructed by restoring the ${\bf g}_{tt}$ variable. In a
moment, we will derive a set of modified formulae for this reduced
Lagrangian $L_r$. For simplicity, we will drop the subscript $_r$
in $L_r$ for simplicity and economics of notations.
Note also that the Bianchi identity $D_MG^{MN}=0$ and the
energy-momentum conservation law $D_MT^{MN}=0$ implies that
$D_MJ^{MN}=0$. In addition, the $tt$ component of this Bianchi
identity can be brought to the following form:
\begin{equation}
(\partial_t + 3 H +DI) J_{tt} + 3 a^2H J_{3} +D d^2 I J_D=0,
\label{h3}
\end{equation}
with $J_{ij} = J_3 h_{ij}$. Since we only need two field equations
for the one-D system of $a(t)$ and $d(t)$. Therefore, one of the
three field equations $J_{tt}=0$, $J_3=0$ and $J_D=0$ is
presumably redundant. They are, however, not equally redundant.
Let us first assume that $H \ne 0$ $I \equiv \dot{d}/d \ne 0$ for
simplicity. Indeed, the Bianchi identity implies that the first
equation $J_{tt}=0$ is truly non-redundant: (i) $J_{tt}=0$ implies
that $3 a^2H J_{3} +D d^2 I J_D=0$ for all times. Hence the
constraint $J_3=0$ (or $ J_D=0$) implies the vanishing of the
other equation $J_D=0$ (or $J_3=0$). (ii) $J_3=J_D=0$ implies that
$ (d/dt +3H +DI) J_{tt} =0$. Hence we have $J_{tt}=$ constant
$\exp[-a^3 d^D]$ which does not go to zero unless $a^3d^D \to
\infty$. Cases (i) and (ii) mean that the Friedmann equation
$J_{tt}=0$ is truly non-redundant while $J_3=0$ and $J_D=0$ are
equally redundant. Therefore, we can ignore either one of the
equations without losing any information. This is, however, not
true under the condition where $d=$constant, or $I \equiv
\dot{d}/d=0$. As indicated by Eq. (\ref{h3}), we have instead
\begin{equation}
(d/dt +3H) \bar{J}_{tt} = 3 a^2H \bar{J}_3 \label{bi3}
\end{equation}
under this condition. Here we have written $\bar{J}_{tt} \equiv
J_{tt}|_{I=0}$ and similarly ${\bar J}_3\equiv
J_{3}|_{I=0}$. Therefore, the reduced Bianchi identity
(\ref{bi3}) only tells us that $\bar{J}_3=0$ is redundant as
compared to the non-redundant Friedman equation $\bar{J}_{tt}=0$
under the constraint $I=0$. In fact, the $d$-equation or the
$a$-equation has to be retained for a consistent check in order to
make sure whether the system does accommodate a constant $d$
solution. This point is often overlooked and should be checked
carefully in the analysis of the Kaluza-Klein theory under a
constant internal-space solution.
Bianchi identity implies that the $N(N+1)/2$ Einstein equations
$G_{AB}=T_{AB}$ are not all independent, but related by $N$
constraint equations $D_AG^{AB}=0$. By looking at the conservation
law of energy momentum tensor $D_AT^{AB}=0$, one may interpret
that conservation of energy momentum tensor implies the vanishing
of $D_AG^{AB}$. The Bianchi identity has, however, a more
intrinsic geometric meaning. It is in fact a geometric
conservation law. Note that the Bianchi identity $D_AG^{AB}=0$ has
a simple geometric interpretation, namely, the boundary of a
boundary is zero \cite{misner}. It implies that the energy
momentum is automatically conserved for a system coupled
consistently to the geometry of space-time. In practice, the
Bianchi identity is helpful in providing an easier approach to
study the Einstein equation. For example, we can focus on, with
the help of the Bianchi identity, independent components of the
field equations. Indeed, as shown above that the Bianchi identity
in the FRW space-time implies that : the Friedmann equation, the
$a$-equation and the $d$-equation are related by the differential
Eq. (\ref{h3}). This implies that the Friedmann equation
$G_{tt}=T_{tt}$ has a less differential order than the other
components of the Einstein equation. As a result, Friedmann
equation may serve as an useful tool in solving the differential
equations.
\section{Generalized Friedmann Equation in one-dimensional formulation}
In order to derive the non-redundant Friedmann equation from the
reduced Lagrangian, we must restore the ${\bf g}_{tt}$ dependence
of the reduced Lagrangian $L$. Indeed, the ${\bf J}^{tt}$ comes
from the variation of $L$ with respect to ${\bf g}_{tt}$, $\delta
L /\delta {\bf g}_{tt} \sim \epsilon \phi^2 J^{tt}/2$. Hence the
most convenient way to restore the ${\bf g}_{tt}$ dependence of
the reduced Lagrangian $L$ is to introduce lapse function $b(t)$
connecting the ${\bf g}_{tt}$ metric component:
\begin{eqnarray}
ds^2 &\equiv &{\bf g}_{AB} dZ^A dZ^B \equiv g_{\mu \nu} dx^\mu dx^\nu +
f_{mn}dz^mdz^n \\
& =& -b(t)^2dt^2
+ {a^2}(t) \Bigl( {dr^2 \over 1 - k_1 r^2} + r^2 d^3\Omega \Bigr
) + {d^2}(t) \Bigl( {dz^2 \over 1 - k_2 z^2} + z^2 d^D\Omega
\Bigr ) . \label{eqn:frw1} \label{GFRW}
\end{eqnarray}
This metric will be called as generalized FRW (GFRW) metric for
the $4$+$D$ anisotropic space. Once the non-redundant Friedmann
equation is derived from the variation of $L$ with respect to $b$,
one can set $b=1$ and reconstruct the $b$-independent Friedmann
equation.
The non-vanishing spin connections can be listed as follows:
\begin{eqnarray}
{\bf \Gamma}^\gamma_{\mu \nu} &=& \Gamma^\gamma_{\mu \nu} ,\\
{\bf \Gamma}^p_{mn} &=& \Gamma^p_{mn} , \\
{\bf \Gamma}^\gamma_{mn} &=& - \partial^\gamma \beta g_{mn} ,\\
{\bf \Gamma}^p_{\mu m} &=& \partial_\mu \beta \delta^p_m .
\end{eqnarray}
Here $\partial_\mu \beta \equiv {\partial_\mu d / d}$ comes with a
non-vanishing $t$-component. In addition, we will write $I =
\partial_t \beta$ for convenience from now on. Consequently, all
non-vanishing Riemannian curvature components can be listed as
follows:
\begin{eqnarray} {\bf R}^{ti}_{\,\,\,\,tj}&=&{1\over 2}
[H\dot{B}+2B(\dot{H}+H^2)]\delta^i_j ,
\label{Rti} \\
{\bf R}^{ij}_{\,\,\,\,kl}&=& (H^2B+{k_1 \over a^2} ) (\delta^i_k \delta^j_l
-\delta^i_l
\delta^j_k) \label{Rkl} , \\
{\bf R}^{tm}_{\,\,\,\,\,\,\,\,tn}&=&{1\over 2}
[I\dot{B}+2B(\dot{I}+I^2)]\delta^m_n ,
\label{Rtm}\\
{\bf R}^{im}_{\,\,\,\,\,\,\,\,jn}&=&HI\delta^m_n \delta^i_j ,
\label{Rim}\\
{\bf R}^{mn}_{\,\,\,\,\,\,\,\,pq}&=& (I^2B+{k_2 \over d^2} )
(\delta^m_p \delta^n_q -\delta^m_q \delta^n_p )\label{Rmn} .
\end{eqnarray}
As a result, deriving all Ricci tensors ${\bf R}^{A}_{\,\,B}$ and
scalar curvature tensors ${\bf R}$ is straightforward.
Note that there is also a $t$-dependent factor $b(t)$ in the
square-root of the metric determinant $\sqrt{{\bf g}} \sim
ba^3d^D$. Hence the variational equation of $b$ can be shown to be
\cite{kao99}
\begin{equation}
L - H {\delta L \over \delta H} - I {\delta L
\over \delta I} + [ H {d \over dt}+ H( 3H +DI) -\dot{H} ]
{\delta L \over \delta \dot{H}} + [ I {d \over dt}+ I( 3H +DI)
-\dot{I} ] {\delta L \over \delta \dot{I}}
=\dot{\phi}^2 \label{key} .
\end{equation}
Note that the last term $\dot{\phi}^2$ comes from the kinetic term
of the scalar Lagrangian. Indeed, there is a kinetic coupling term
for $\phi$ via $-g^{tt} (\dot{\phi})^2/2 = b^{-2}
(\dot{\phi})^2/2$. This will bring us an additional $\dot{\phi}^2$
to the left hand side of Eq. (\ref{key}). In fact, Eq. (\ref{key})
can generalized to all fields coupled to the Einstein-Hilbert
action.
In addition, variational equations of $a$ and $d$ also give
\begin{eqnarray} \label{aeq}
&& 3L- H {\delta L \over \delta H} + (H^2- \dot{H}) {\delta L
\over \delta \dot{H}} -(2H +DI + {d \over dt}) [ -(4H +DI + {d
\over dt}) {\delta L \over \delta \dot{H}} +{\delta L \over
\delta {H}} ] -2k_1 {\delta L \over \delta k_1} =0 ,
\\ \label{deq}
&& DL- I {\delta L \over \delta I} + (I^2-
\dot{I}) {\delta L \over \delta \dot{I}} - (3H +(D-1)I + {d \over
dt}) [ -(3H +(D+1)I + {d \over dt}) {\delta L \over \delta
\dot{I}} +{\delta L \over \delta {I}} ] -2k_2 {\delta L \over
\delta k_2} =0 .
\end{eqnarray}
Note that above equations also hold in the presence of the scalar
coupling once we assume $\phi(Z)=\phi(t)$.
We will first study a simple model with a constant $d$ solution.
This is a physical solution since the internal space seems to be
small from any physical observation up to date. As shown above,
the Bianchi identity indicates that the second $a$-equation
(\ref{aeq}) is derived implicitly by the first Friedmann equation
(\ref{key}) for the constant internal space model. Therefore, we
will try to solve Eq.s (\ref{key}) and (\ref{deq}) for a complete
analysis. As a result, the Friedmann equation (\ref{key}) and the
$d(t)$ equation (\ref{deq}) become
\begin{eqnarray}
& & \bar{L} - H {\delta \bar{L} \over \delta H} +[ H {d \over
dt}+ 3H^2 -\dot{H} ] {\delta \bar{L} \over \delta \dot{H}}
= \dot{\phi}^2 \label{key4} , \\
\label{deq4} && D\bar{L} = (3H + {d \over dt}) [ -(3H + {d
\over dt}) {\delta \bar{L} \over \delta \dot{I}} +{\delta \bar{L}
\over \delta {I}} ] +2k_2 {\delta \bar{L} \over \delta k_2}
\end{eqnarray}
under the $d(t)=$ constant background solution. Here a bar
notation of a variable $L$ denotes a variable evaluated at $I=0$,.
Explicitly, $\bar{L} \equiv L|_{I=0}$. In addition, we must also
check whether the solution is consistent with the constraint
$\bar{L}=0$. Our results agree with the equations shown in Ref.
\cite{3}. Details will be provided in the Appendix.
\section{Stability of an Inflationary External Space}
We need to find out whether the inflationary background de Sitter
solution $H=H_0$ and $I=0$ is a possible solution to the
Kaluza-Klein induced gravity model. As a result, a stability
analysis is also needed to find our whether this background
solution is stable or not. Furthermore, following the conventional
approach, the constant internal space solution is assumed and
should be served as a reasonable ansatz. This is because that the
internal space information appears to be minor as compared to the
$4$-space counterpart. Otherwise, we would be able to measure the
impact of the internal space physics once the internal space scale
factor $d(t)$ grows to some appreciable size. In addition, we will
also focus on the $k_1=0$ flat 4-space condition which appears to
agree with latest observations \cite{k=0}.
Therefore, we will study the existence and stability problem of
the inflationary universe for the induced Kaluza-Klein model
described above. The effective Lagrangian $\bar{L}$ for the model
$L$ under the $I=0$ condition can be shown to be
\begin{equation} \bar{L} = 3 \epsilon \phi^2 [ \dot{H} +2H^2 ]
-12 (c_1+c_2+3 c_3) [ (\dot{H} +H^2)^2 + H^4] -12 (c_2+6 c_3) [
(\dot{H} +H^2)H^2 ]+{1 \over 2} \dot{\phi}^2 -V(\phi).
\label{barLi}
\end{equation}
In addition, the variations of the $I$-equation are
\begin{eqnarray}
{\delta \over \delta I} \bar{L} &=& 6DH \left \{ {\epsilon \over
2} \phi_0^2 -c_2 \left [ \dot{H} +3H^2 \right ] -12c_3 \left [
\dot{H} +2H^2 \right ]
\right \} \label{frd3i} , \\
{\delta \over \delta \dot{I}} \bar{L} &=& 2D \left \{ {\epsilon
\over 2} \phi_0^2-c_2 \left [ 3\dot{H} +3H^2 \right ] -12c_3
\left [ \dot{H} +2H^2 \right ] \right \} \label{deqdi}.
\end{eqnarray}
To summarize, there are two metric equations and one $\psi$
equation for the system:
\begin{eqnarray}
\dot{\phi}^2+ H {\delta \bar{L} \over \delta H}&= & [ H {d \over
dt}+ 3H^2 -\dot{H} ] {\delta \bar{L} \over \delta \dot{H}}
\label{key41} , \\
\label{deq410} (3H + {d \over dt}) {\delta \bar{L} \over \delta
{I}} &=& (3H + {d \over dt})^2 {\delta \bar{L} \over \delta
\dot{I}},
\\
&&\bar{L}=0
\end{eqnarray}
under the flat space condition and the constant internal space
solution $I=0$. The equation $\bar{L}=0$ denotes the constraint
from the constant $\psi$ equation. Here $\bar{L} \equiv L|_{I=0}$.
The Friedmann equation reads:
\begin{equation}
{1 \over 2} \dot{\phi}^2 +V = 3 \epsilon \phi^2H^2 +6 \epsilon H
\phi \dot{\phi} +12(c_1+c_2+3c_3)(\dot{H}^2 - 2H \ddot{H} - 6H^2
\dot{H}). \label{f-eqid0}
\end{equation}
At the end of this section, we will show that the perturbation
equation of the constraint $\bar{L}=0$ is consistent with the
inflationary de Sitter solution we are interested in. More
specifically, the linear perturbation equations $\delta \bar{L}$
can be shown to vanish automatically without generating any
further constraint on the system. Therefore, there is no need to
worry about the perturbation effect of this constraint. Hence we
can add or remove the effect of this constraint anytime. This
result also indicates that the constant $\psi$ solution, the
origin of this constraint, is a very reasonable ansatz.
Furthermore, the $\phi$-equation can be shown to be
\begin{equation} \label{eqphi}
6 \epsilon \phi (\dot{H} + 2H^2) = \ddot{\phi} +3 H \dot{\phi} +V' .
\end{equation}
Let $\phi=\phi_0+ \delta \phi$ and $H=H_0+\delta H$ with $\phi_0$
and $H_0$ some constant initial states for the inflationary de
Sitter background solution. Here $\delta \phi$ and $\delta H$
denote small perturbations against the background solutions. We
will try to extract the linear solutions to the perturbation
effect. As a result, the leading-order Friedmann equation
(\ref{f-eqid0}) gives
\begin{equation} \label{eqfriedmann}
V_0=3 \epsilon \phi_0^2 H_0^2.
\end{equation}
Similarly, the leading-order scalar equation ({\ref{eqphi}) gives
\begin{equation}
12\epsilon \phi_0H_0^2=V_0'.
\end{equation}
Here $V'_0 \equiv V'(\phi_0)$. Therefore, we have the constraints
combined together as:
\begin{equation} \label{constraint}
\phi_0 V'_0 =4V_0=12\epsilon \phi_0^2H_0^2 .
\end{equation}
Note that $\phi V'$ counts the effective scale-dimension of the
effective potential $V(\phi)$. For example, $\phi V'=n V$ if $V=
\phi^n$ with effective dimension $n$. Therefore, this condition
implies that the inflationary phase exists only when the effective
dimension of the effective potential is $4$ at the inflationary
phase $\phi=\phi_0$ and $H=H_0$. Since $V =\lambda \phi^4$
represents the scale invariant potential in $4$-dimensional space,
i.e. dim ($\lambda $) $=0$ in $4$-space, this condition will be
denoted as the scaling condition \cite{kao00}. As an example, the
spontaneously symmetry breaking potential of the form:
\begin{equation} \label{V0} V(\phi)= { \lambda \over 4}
(\phi^2-\phi^2_0)^2 +6\epsilon H_0^2 (\phi^2-\phi_0^2) + 3
\epsilon H_0^2 \phi_0^2
\end{equation}
with arbitrary coupling constant $\lambda$ can be shown to be a
good candidate satisfying the scaling condition
(\ref{constraint}).
In addition, the first order perturbation equation of $H$-equation
(\ref{f-eqid0}) and $\phi$-equation (\ref{eqphi}) can be shown to
be:
\begin{eqnarray}
&& \epsilon \phi_0 \left ( \delta \dot{\phi} -H_0 \delta \phi
\right )=4(c_1+c_2+3c_3) \left ( \delta \ddot{H} + 3H_0 \delta
\dot{H} \right )- \epsilon \phi_0^2 \delta H, \\
&& \delta \ddot{\phi} +3H_0 \delta \dot{\phi} + \left (
V''(\phi_0)- 12 \epsilon H_0^2 \right ) \delta \phi =6 \epsilon
\phi_0 \left ( \delta \dot{H} +4 H_0 \delta{H} \right ).
\end{eqnarray}
Writing $\delta H=\exp [hH_0t] \delta H_0$ and $\delta \phi=\exp
[pH_0t] \delta \phi_0$, the above perturbation equations can be
written as:
\begin{eqnarray} \label{ph}
&& \epsilon \phi_0 \left ( p -1 \right )\delta
\phi=4(c_1+c_2+3c_3)H_0 \left ( h^2 + 3h - {\epsilon \phi_0^2
\over 4(c_1+c_2+3c_3)H_0^2} \right )\delta H, \\
&& H_0 \left ( p^2 +3p + {V''(\phi_0)- 12 \epsilon H_0^2 \over
H_0^2} \right ) \delta \phi =6 \epsilon \phi_0 \left ( h +4
\right ) \delta{H} . \label{pp}
\end{eqnarray}
In addition to the trivial solution $\delta H=0$ and $\delta
\phi=0$, consistent solutions also exist when $h=-4$ and $p=1$. If
$h=-4$, we will have the following constraint from the right hand
side of Eq. (\ref{ph})
\begin{equation}
H_0^2 = {\epsilon \phi_0^2 \over 16(c_1+c_2 +3c_3)}. \label{h31}
\end{equation}
In addition, the existence of nontrivial solution $p=1$ implies
that
\begin{equation} \label{phic}
V''(\phi_0)= 12 \epsilon H_0^2 -4 H_0^2
\end{equation}
from the left hand side equation of Eq. (\ref{pp}). As a result,
\begin{equation}
\delta H = \exp [-4H_0t]~ \delta H_0 . \label{dh}
\end{equation}
Equivalently, the linear perturbation gives
\begin{equation}
H=H_0+ \delta H_0 ~\exp [-4H_0t]
\end{equation}
as the solution to the Hubble parameter with a small deviation
from the de Sitter background.
We will show in addition that the $I$-equation (\ref{deq410}) and
the constraint equation $\bar{L}=0$ are both consistent with above
constraints in the presence of static internal space and de Sitter
external space. Indeed, writing $D_t \equiv \partial_t +3H$,
$\delta \bar{L} / \delta {I}\equiv \bar{L}_I$ and $\delta \bar{L}
/ \delta \dot{I} \equiv \bar{L}_{\dot{I}}$, the $I$-equation
$$
(3H + {d \over dt}) {\delta \bar{L} \over \delta {I}} = (3H + {d
\over dt})^2 {\delta \bar{L} \over \delta \dot{I}},$$ under the
condition of flat and static internal space can be integrated to
give
\begin{equation}
Y(H) \equiv \bar{L}_{{I}}-D_t\bar{L}_{\dot{I}}=6 D(c_2+4c_3)
[\ddot{H} +4H \dot{H} ] + { K_1 \over a^3}=0
\end{equation}
with a constant of integration $K_1$. During the inflationary
phase, we can ignore the effect of $K_1$ term. Therefore, the
$I$-equation does not have a leading order contribution. In
addition, the first order perturbation of this equation gives
$\delta Y=6D(c_2+4c_3) [\delta \ddot{H} +4H_0 \delta \dot{H} ]$
which vanishes identically in compatible with the perturbation
$\delta H$ given in Eq. (\ref{dh}). In fact, we can also compute
the complete $I$-equation and find that
\begin{equation}
D_t Y =6D (c_2+4c_3) [\dot{\ddot{H}}+ 4 {\dot H}^2+ 7H \ddot{H}
+12H^2 \dot{H} ]=0.
\end{equation}
There is no leading contribution either. In addition, the
perturbative equation takes the form
\begin{equation}
\delta D_t Y=D_t \delta Y= 6D(c_2+4c_3) D_t[\delta \ddot{H} +4H_0
\delta \dot{H} ]=6D (c_2+4c_3) [\delta \dot{\ddot{H}}+ 7H \delta
\ddot{H} +12H^2 \delta \dot{H} ]=0,
\end{equation}
that vanishes identically with $\delta H$ given in Eq. (\ref{dh}).
As mentioned above, we still have to compute all possible
constraints from the internal space scalar field $\psi$-equation
$\bar{L}=0$. It is interesting to find that the leading order
perturbation equation for $\bar{L}=0$ gives
\begin{eqnarray}
6 \epsilon \phi_0^2 H_0^2 - V_0 =3 \epsilon \phi_0^2 H_0^4= 12
(2c_1+3c_2+12c_3) H_0^4 \label{barL1}
\end{eqnarray}
incorporating the scaling constraint $V_0= 3 \epsilon
\phi_0^2H_0^2$. Therefore, the leading order equation of
$\bar{L}=0$ gives another constraint
\begin{equation}
H_0^2 = {\epsilon \phi_0^2 \over 4(2c_1+3c_2+12c_3)}. \label{hL}
\end{equation}
In addition, the first order perturbation of equation this $\psi$
constraint can be shown to be
\begin{equation}
\left [ 3 \epsilon \phi_0^2 -12 (2c_1+3c_2+12 c_3) H_0^2 \right
] \left [ \delta \dot{H} +4H_0 \delta H \right ] + (12\epsilon
\phi_0H_0^2 -V_0') \delta \phi=0 . \label{barLh}
\end{equation}
Therefore, this equation is completely consistent with the whole
system by observing that all coefficients in above equation
vanishes identically. Indeed, $3 \epsilon \phi_0^2 -12
(2c_1+3c_2+12 c_3) H_0^2 =0$ following Eq. (\ref{hL}). In
addition, $\delta \dot{H} +4H_0 \delta H =0$ and $12\epsilon
\phi_0H_0^2 -V_0'$ are automatically satisfied.
In summary, the constraints (\ref{h31}) and (\ref{hL}) indicate
that the coupling constants should obey the following constrain in
order to admit an inflationary phase in the presence of a static
internal space:
\begin{equation}
2c_1+c_2=0.
\end{equation}
As a result, the Hubble constant and the field parameters are
related by:
\begin{equation}
H_0^2 = {\epsilon \phi_0^2 \over 8(c_2+6c_3)}. \label{hall}
\end{equation}
Note that above results indicate that: (1) static internal flat
space solution is completely compatible with the conditions of
inflationary solution; (2) the perturbation equation of
$\bar{L}=0$ is a perfect identity consistent with all other
constraints derived elsewhere. This indicates that the constant
$\psi$ solution is a very reasonable choice for the stationary
state of the system. In addition, (3) the static internal space
assumptions is also a consistent choice for the existence and
stability of the inflationary phase.
In addition, we can also consider the perturbation of $\psi$ by
setting $\psi=\psi_0+\delta \psi$ and perturb the field equation
(\ref{psieq}). The result is $ D_A \partial^A \delta \psi =0.$
Here we have also used the identity $\delta L=0$ under the linear
perturbation shown above. Assuming $\delta \psi(Z)=\delta\psi (z)$
such that the internal space $z$ is completely decoupled from the
$4$-D space time. As a result the perturbation equation $ D_A
\partial^A \delta \psi =0$ is consistent if $\delta \psi(z)$ is
a harmonic function obeying $\partial^m\partial_m \delta \psi=0$.
Hence $\delta \psi(z) =$ constant for a consistent perturbation.
Therefore, the constant $\psi$ is also a consistent choice of
background solution.
Note also that the effect of the $\psi=$constant implies that
$L=0$. Together with the constraint $2c_1+c_2=0$ for the existence
of an inflationary phase, one has effectively a scalar equation of
the form
\begin{equation}
{1 \over 2}
\partial_A \phi \partial^A \phi + V(\phi) +{\epsilon \over 2}
\phi^2 {\bf R} = {c_2 \over 2} ({\bf R}^{AB}_{\;\;\;\;\;\;CE})^2
- c_2 ({\bf R}^{A}_{\;\;\;B})^2 - c_3 {\bf R}^2 \label{pdg1}
\end{equation}
with a purely geometric source. Although the equation $L=0$ is not
exactly a Klein-Gordon equation of the form $(\partial^2 +m^2 +
R/5) \phi =\alpha R^2$ studied in Ref. \cite{k1}, both theories
appear to have similar physical origin. It was shown that an
effective re-normalized Lagrangian of the form $\alpha \phi R^2$
is a result of dimensional consideration. Indeed, the coupling
constant $\alpha$ can only be made dimensionless, rendering a
system free from introducing any additional arbitrary length
scale, if the space-time dimension $N=6$ \cite{k1}.
Note that the scalar fields $\psi$ and $\phi$, both with dimension
one, considered in this paper are designed to replace all
dimensionful coupling constants with appropriate scalar fields. As
a result, all coupling constants are assumed to be dimensionless
in this approach. The only exception is some parameters associated
with the SSB potential $V(\phi)$ designed to pick up a symmetry
breaking scale. The constraint equation $L=0$ indicates that the
scalar field $\psi$ introduced here may have close relation with
the re-normalizability of the energy-momentum tensor for $\phi$.
In addition, similar model has been studied in Ref. \cite{k2} with
Gauss-Bonnet (GB) Lagrangian coupled to a perfect fluid. The
constraint $2c_1+c_2=0$ in this paper follow first from the
stability of the Friedmann equation (\ref{f-eqid0}) with a
coefficient of the combination $(c_1+c_2+3c_3)$ coupled to the
quadratic interactions $\dot{H}^2 - 2H \ddot{H} - 6H^2 \dot{H}$.
This coefficient vanishes for GB term with $c_1:c_2:c_3=1:-4:1$.
This is the main difference between the model considered in Ref.
\cite{k2} and current models. In addition, we have also shown in
the Appendix that the Friedmann equation agrees with Ref. \cite{3}
up to a difference in the definition of sign of the coupling
constants $c_i$. Our inflationary phase solution also agrees with
Ref. \cite{3} up to a scale due to the effect of the scalar field
in this induced gravity model. Indeed, the Friedmann equation and
the $I$-equation implies that $H_0^2=\Lambda/6$ and
$(c_2+4c_3)\Lambda=1$ respectively after setting $V=\Lambda$ for a
system without a dynamical scalar field $\phi$. As a result,
$H_0^2=1/[6((c_2+4c_3)]$.
\section{Conclusion}
It is shown that replacing the internal space dimensionful
coupling constant with a dimension one scalar field $\psi=$
constant works harmonically with the Kaluza-Klein inflationary
universe under the constraint $2c_1+c_2=0$. In addition, from the
effective Lagrangian shown in Eq. (\ref{barLi}), it is easy to
find that any quadratic Lagrangian must present itself as
combinations of the form: $\bar{L}_2= l_1\dot{H}^2+
l_2(\dot{H}H^2+H^4) \equiv -12 (c_1+c_2+3 c_3) [ (\dot{H} +H^2)^2
+ H^4] -12 (c_2+6 c_3) [ (\dot{H} +H^2)H^2 ]$ with dimensionless
$l_i$ corresponding linear combinations of $c_i$ defined
accordingly. Here $\bar{L}_2$ denotes the quadratic part of the
effective Lagrangian $\bar{L}$. As a result, it can be shown that
any quadratic Lagrangian of the combinations ${\bar L}_2 \sim
l_1\dot{H}^2+ l_2(\dot{H}H^2+H^4)$ will not contribute to the
Friedmann equation.
Indeed, the quadratic terms contribute to the Friedmann equation
(\ref{key41}) according to
\begin{eqnarray} \label{Lg}
E_2=\bar{L}_2 +H ( {d \over dt} +3H )\bar{L}_{\dot{H}} -
H\bar{L}_{H} - \dot{H} \bar{L}_{\dot{H}} \to \bar{L}_2 +3H^2
\bar{L}_{\dot{H}} - H\bar{L}_H
\end{eqnarray}
in the de Sitter background with $L_H \equiv \delta
\bar{L}_2/\delta H$ and $L_{\dot{H}} \equiv \delta
\bar{L}_2/\delta \dot{H}$ shown in above equation. It is clear
that the $l_1$ term does not contribute to above equation $E_2$ in
the de Sitter space with $\dot{H}_0=0$. Therefore, we have
effectively the quadratic Lagrangian $\bar{L}_2 =
l_2(\dot{H}H^2+H^4)$ needed to be considered for its effect on the
leading order Friedmann equation. As a result, we can show that
$\bar{L}_2 \to l_2H_0^4$, $H^2 \bar{L}_{\dot{H}} \to l_2 H_0^4$
and $H\bar{L}_H \to 4l_2H_0^4$. Hence the total contribution of
the quadratic Lagrangian to $E_2$ cancels each other. Therefore,
this proves that the quadratic Lagrangian does not contribute to
the de Sitter solution in four dimension.
The perturbation equation for $\delta \phi$ indicates a constraint
(\ref{phic}) $ V''(\phi_0)= 12 \epsilon H_0^2 -4 H_0^2$ which
turns out to be inconsistent with the SSB scalar potential
(\ref{V0}). Indeed, $V''_0=2 \lambda \phi_0^2+12 \epsilon H_0^2$
for this potential. Hence the constraint (\ref{phic}) implies that
$\lambda \phi_0^2=-2H_0^2$. A negative $\lambda$ indicates that
the SSB potential is an unstable potential without a global
minimum. In fact, we can show that the local minimum is at
$\phi_m^2=0$ and the local maximum is at $\phi^2_M=(1+6
\epsilon)\phi_0^2$. Hence the consistent initial state $\phi_0$ of
the scalar field will be expected to locate at the left hand side
of the maximum point $\phi_M$. The scalar field will hence roll
down to the local minimum which is located at $\phi=0$. This will
lead to an un-physical state with infinite Newtonian constant $G$.
In addition, this local minimum is also not a stable vacuum state.
$\phi$ will eventually tunnel to its global minimum at $\phi \to
\infty$. Therefore, the constraint (\ref{phic}) is not a physical
constraint for the SSB potential and this is also true for the
Coleman-Weinberg effective potential \cite{coleman}. Hence the
only consistent perturbation of $\phi$ is $\delta \phi=0$. This
indicates that the de Sitter background is highly stable and
compatible with the stable mode $\delta H \to 0$. Therefore, the
system will remain stable as long as the scalar field does change
very slowly. Note that the negative coupling constant appears to
be a universal features of any coupled effective potential
including the Eric-Weinberg dynamical symmetry breaking potential
\cite{weinberg}.
Indeed, the $\phi$ equation under the slow rollover assumptions,
$|\dot{\phi}/\phi|\ll H_0$ and $|\ddot{\phi}/\phi| \ll H_0^2$,
states that
$$\ddot{\phi} +3 H_0 \dot{\phi} \sim 0 $$
during the period where $H \sim H_0$. This gives
\begin{equation}
\phi \sim \phi_0 + {\dot{\phi}_0 \over 3 H_0}[1 - \exp (- 3 H_0 t)
]. \label{phit}
\end{equation}
Therefore, the slow rollover-approximation is indeed consistent
with the dynamics of the scalar field equation that has been a
focus of research interests in the literature. Therefore, $\phi$
does change very slowly during this inflationary phase.
In summary, we have derived abundant constraints from the
assumptions: (i) $\psi(z)=$ constant, (ii) $d(t)=$ constant. These
assumptions are adopted partly from the fact that they are both
not appreciable in the four dimensional physical universe observed
today. Hence it is reasonable to freeze their dynamics at certain
stage of the evolutionary process. The abundant consistency shown
in this paper compatible with the abundant constraints from these
assumptions implies that these assumptions are in fact rather
reliable. Although we are unable to provide a dynamical reason for
these assumptions from the first principle, compatibility of these
assumptions with the inflationary four space deserves more
attention for its possible physical implications.
Our result indicates, however, that both assumptions, static
$\psi$ and static $d$, appear to be a consistent set of choice for
the higher derivative Kaluza-Klein models. As a result, the
Kaluza-Klein higher derivative induced gravity theory behaves
similar to the conventional four dimensional induced higher
derivative gravity in the lower-energy limit namely, only $R^2$
and $R_{ab}^2$ couplings remain effective during the inflationary
de Sitter phase. This is in consistent with the $4$-D theories
that $R_{abcd}^2$ terms can be replaced by $R^2$ and $R_{ab}^2$
couplings following the GB theorem. Therefore, related research
deserves more attention.
\section*{Acknowledgments}
This work is supported in part by the National Science Council of
Taiwan.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,647 |
Martin Hollis es un diseñador de videojuegos y fundador y director ejecutivo de la empresa desarrolladora de videojuegos Zoonami. Ha trabajado en la industria de los videojuegos durante más de 20 años y fue el líder de software en la empresa Rare. También fue el director y productor del exitoso videojuego de disparos en primera persona GoldenEye 007 y Perfect Dark.
Hollis abandonó Rare en 1998, cuando Perfect Dark contaba con 14 meses de desarrollo, para trabajar como asesor en el desarrollo de la videoconsola Nintendo GameCube. En 2000, Hollis fundó la empresa Zoonami, en Cambridge.
Referencias
Enlaces externos
Cuenta de Hollis en Twitter.
Perfil de Hollis en el sitio web de Zoonami mediante Wayback Machine.
Diseñadores de videojuegos
Nacidos en Leicester | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,421 |
Q: Play Framework - IntelliJ Issues - IDE suggestions? I'm using IntelliJ IDE to set up a Play project and do my development. I cannot create a new project nor can I get an existing project (e.g.: websocket-chat) compile in IntelliJ.
I posted this on IntelliJ forums http://devnet.jetbrains.com/thread/450345?tstart=0 but no response yet.
Has anyone been able to get Play project set up in IntelliJ? What IDE do you use? I'm using Play 2.2.
A: Likely the fix to your issue is to run "play idea" in the console to generate all the files IntelliJ needs to properly index the project.
I use the EAP version of IntelliJ, believe that I run into fewer problems because while it might incur a breaking change they also release fixes quite fast.
IntelliJ has written its own Scala parser for type highlighting, I find that it doesn't always keep up with the latest Scala features and even some that have been around for a while (there were issues with package objects for a bit). Considering that, I usually turn type highlighting off and keep a console window open to do continuous compilations there. Even when compiling works in IntelliJ its always significantly slower than directly using play or sbt from command line.
A: I managed, but it was a pain to set up. I am going to blog about this, but here is a sneak preview to how I solved it:
*
*Create a new project in IDEA in the directory of your sample. Choose type "Scala module."
*Only after it's done should you navigate to the same directory in the command line and run play.
*When the Play console is up, use the idea command: e.g. [websocket-chat] $ idea
*Go back to IDEA. You should see a prompt that says something along the lines of "Project was modified outside of IDEA. Would you like to reload it?" Do it.
*Once the project is reloaded and indexed, you should be good. At least I was.
Hope that helps. This was unnecessarily difficult. It's bad when I find women easier to understand.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,094 |
@class NSString, WFCasioKeyCommand, WFCasioKeyCommanderService;
@protocol WFCasioKeyCommanderServiceDelegate <NSObject>
- (void)keyCommanderService:(WFCasioKeyCommanderService *)arg1 didReceiveKeyCommand:(WFCasioKeyCommand *)arg2;
- (NSString *)appNameForKeyCommanderService:(WFCasioKeyCommanderService *)arg1;
- (void)keyCommanderServiceDidHandleAppNameReadRequest:(WFCasioKeyCommanderService *)arg1;
@end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,279 |
Müntschemier railway station () is a railway station in the municipality of Müntschemier, in the Swiss canton of Bern. It is an intermediate stop on the standard gauge Bern–Neuchâtel line of BLS AG.
Services
The following services stop at Müntschemier:
Bern S-Bahn:
: hourly service between and .
: evening service between Bern and .
References
External links
Railway stations in the canton of Bern
BLS railway stations | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,647 |
The 279 FC allows technicians to quickly and safely check for hot spots in fuses, wires, insulators, connectors, splices, and switches with the imager and then troubleshoot and analyze issues with the DMM. By combining two powerful test tools into one, electricians and technicians can carry fewer tools and have a higher level of confidence they have the tools handy to solve problems.
The CAT III 1000 V, CAT IV 600 V safety rated thermal multimeter has a rechargeable lithium ion battery that lasts up to a full work day (10+ hours) under normal conditions. | {
"redpajama_set_name": "RedPajamaC4"
} | 9,168 |
\section{Introduction}
The celebrated phenomenological Ginzburg-Landau (GL) theory of
superconductivity was introduced in the seminal paper by Ginzburg and Landau
\cite{GL50} and has been proving ever since to be one of most fruitful and
universal tools in the description basic properties of superconductors. The
examples of its success range from the prediction of the Abrikosov vortex
state \cite{AbrikosovJETP57} to the recent advance in understanding the
complex vortex phase diagram of the high-temperature superconductors
\cite{BGFLV94} and the properties of mesoscopic superconducting systems
\cite{F03}. The Gor'kov's derivation of the GL equations from the BCS theory
\cite{G58} that have put the GL theory on a firm microscopic basis and
related phenomenological constants to material parameters, completed the
construction of the GL theory of superconductors.
The GL theory describes well the properties of almost all superconductors
near transition temperature and is successful even when dealing with the
superconductors with quite complicated band structures. The notorious
exception from the rule is recently discovered multiband superconductor
magnesium diboride (MgB$_{2}$). As it was shown \cite{GK03a,GK03b}, the GL
theory applies to MgB$_2$ only in the very immediate vicinity of the
transition temperature, $T_{c}$, i.e. within the interval which turns out to
be much more narrow than the usual one given by the condition $|T-T_{c}|\ll
T_{c}$. The origin of this narrowing of the interval of validity lies in the
sophisticated band structure of the material and reflects the specific
interplay between its single-electron and superconducting characteristics.
Namely, the Brillouin zone of MgB$_2$ consists of the two families of bands:
the quasi-two-dimensional $\sigma$-bands with the strong superconductivity
and the weakly superconducting three-dimensional $\pi$-bands. Due to the
large difference in anisotropy, the c-axis coherence length of the
$\pi$-bands, $\xi_{2,z}$, is much larger than the c-axis coherence length of
the $\sigma$-bands, $\xi_{1,z}$. Formation of the global coherent
superconductivity with the unique order parameter implies the appearance of
the associated unique effective coherence length $\widetilde{\xi}_{z}\left(
T\right)$, which turns out to be much smaller than $\xi_{2,z}$ at almost any
temperature. As a consequence, the GL applicability interval shrinks to the
parametrically narrow range of temperatures where $\widetilde{\xi}_{z}\left(
T\right) \gg\xi_{2,z}$. Beyond this temperature range the system is
strongly nonlocal along the $z$-axis; to describe such a nonlocality one has
to employ a generalized nonlocal GL model \cite{GK03b}. One of the
spectacular manifestations of the non-GL behavior in MgB$_2$ is the strong
temperature dependence of the $H_{c2}$ anisotropy close to $T_{c}$\
\cite{hc2anisotropy}.
The description of superconducting fluctuations is one of the
major fields for the application of the GL theory. Since the
standard GL approach turns out to be insufficient for MgB$_2$, a
generalization of the GL theory is required in order to describe
its fluctuation properties. The variation of the order parameter
on the scales smaller than the largest intrinsic coherence length
means that the usually assumed local approximation does not hold
anymore and the corresponding short-wavelength fluctuations have
to be taken into account.
In the present paper we develop a nonlocal theory of
superconducting fluctuations that applies to a strongly
anisotropic two-band superconductor \cite{Multi-Two} and show that
the short-wavelength fluctuations are essential in it near the
critical temperature. We start with the derivation of the
microscopic fluctuation propagator for a such two-band model. Then
we use it to nonlocal two-band GL functional and the corresponding
time-dependent GL (TDGL) equations. This, in particular, allows us
to calculate the kinetic and thermodynamic observable quantities
including the fluctuational specific heat and conductivity.
As we have already stated, the main source of the non-GL behavior is the
nonlocality in the $c$ direction, i.e., the strong wave-vector dependence of
c-axis coherence length. The conventional local form of the GL equations
turns out to be valid only within the narrow interval of temperatures,
$|T-T_c|/T_c\ll \xi_{1,z}^2/\xi_{2,z}^2+S_{12}\ll 1$, where $S_{12}\ll 1$ is
the relative interband interaction constant which will be specified below.
Beyond this interval, the superconducting correlations in the $\pi$-band
become nonlocal and their contribution to the effective coherence length
rapidly decreases. Far away from $T_c$ the effective c-axis coherence length
is determined only by the $\sigma$-band. In other words, the effective
c-axis coherence diverges for $T\rightarrow T_c$ faster than it could be
expected from the naive GL extrapolation, $\widetilde{\xi}_z(T)\propto
1/\sqrt{T-T_c}$, started from high temperatures. This also leads to the
decrease of the effective anisotropy factor $\Gamma
(T)=\widetilde{\xi}_x(T)/\widetilde{\xi}_z(T)$. As a consequence, the
temperatures dependencies of all fluctuation corrections exhibit the
characteristic crossovers between the dominating $\sigma$-band regime (far
away from $T_c$) and the ``true'' GL regime (very close to $T_c$). For
example, the $c$-axis component of the paraconductivity diverges faster in
the immediate vicinity of $T_c$ than one could expect from high-temperature
extrapolation using the Aslamazov-Larkin formula \cite{LV02} while the
fluctuation specific heat and $ab$ component of the paraconductivity
diverge slower than the corresponding extrapolations. We will obtain the
temperature dependencies of these fluctuation corrections.
\section{Critical temperature and fluctuation propagator}
\subsection{Cooper pairing in two-band model}
The BCS theory was generalized to the case of the two-band electron spectrum
long time ago \cite{Suhl,Moskal} and has been extended recently to include
the specific features of magnesium diboride in Refs.\ \onlinecite
{Kortus,An,LiuPRL01,Kong,Yildirim,Choi}. We briefly overview this theory
rewriting it in terms of Green's function formalism. The two-band BCS
Hamiltonian is given by
\begin{widetext}
\begin{equation}
\mathcal{H}=\sum_{\mathbf{p},\alpha,\sigma}\zeta_{\alpha}\left(
\mathbf{p}\right) \psi_{\alpha,\mathbf{p},\sigma}^{\dag}\psi_{\alpha
,\mathbf{p},\sigma}-\sum_{\mathbf{p,p}^{\prime},\mathbf{q},\alpha,\beta
,\sigma,\sigma^{\prime}}g_{\alpha\beta}\psi_{\alpha,\mathbf{p+q,}\sigma}%
^{\dag}\psi_{\alpha,-\mathbf{p},-\sigma}^{\dag}\psi_{\beta,-\mathbf{p}^{\prime
},-\sigma^{\prime}}\psi_{\beta,\mathbf{p}^{\prime}+\mathbf{q,}%
\sigma^{\prime}}, \label{BCSham}%
\end{equation}
\end{widetext}
where $\psi_{\alpha,\mathbf{p},\sigma}^{\dag}$ and
$\psi_{\alpha,\mathbf{p},\sigma}$ are the creation and annihilation field
operators in the Heisenberg representation for quasiparticle in band
$\alpha$ with momentum $\mathbf{p}$ and spin $\sigma$,
\begin{equation}
\zeta_{\alpha}\left( \mathbf{p}\right) =\mathbf{v}_{\alpha}\left(
\mathbf{p}-\mathbf{p}_{F\alpha}\right) \label{spectrum}%
\end{equation}
is the quasiparticle spectrum, $\mathbf{v}_{\alpha}$,
$\mathbf{p}_{F\alpha}$ are the Fermi velocity and momentum of the
$\alpha$-band. The matrix nature of the electron-electron interaction
$-g_{\alpha\beta}$ in (\ref{BCSham}) reflects the possibility of the
interband interactions. The free electron Green's functions for each band
have the usual form $G_{\alpha}\left(
r,r^{\prime},\tau,\tau^{\prime}\right) =-i\left\langle
T_{\tau}\psi_{\alpha}\psi_{\alpha}^{\prime\dag}\right\rangle $, where
$T_{\tau}$ is the time-ordering operator. In the Matsubara representation,
\begin{equation}
G_{\alpha}\left( \mathbf{p},\varepsilon_{n}\right) =\left( i\varepsilon
_{n}-\zeta_{\alpha}\left( \mathbf{p}\right) \right) ^{-1} \label{green}%
\end{equation}
with $\varepsilon_{n}=2\pi T(n+1/2)$ being the fermionic Matsubara frequencies.
Now we turn to calculation of the fluctuation propagator
$L_{\alpha\beta}$ which characterizes the properties of fluctuation
Cooper pairs and their effect on observable quantities of
superconductor above $T_{c}$.\cite{LV02} Note first of all, that the
interband electron interactions do not result in the Cooper pairing
of the electrons from different bands but rather lead to the
transfer of the pairing correlations between the bands. Indeed, the
Cooper pairing means the appearance of superconducting-type
correlations between two similar states obeying the condition of the
time reversal symmetry. This means that pairing is possible only for
electrons belonging to the same band, otherwise the electron states
are too diverse (in terms of the plane waves description, their
momenta are not the opposite) and the integral of the product of
their wave functions is zero. Thus the formation of unique
condensate should be understood as the result of the
\textit{intraband} electron correlations and subsequent
\textquotedblleft travel\textquotedblright of the Cooper pair from
one band to another due to off-diagonal interaction components
$g_{12}$ and $g_{21}$. Hence, in terms of diagrams, the entrance and
exit lines of the fluctuation propagator must belong to the same
bands (see Fig.\ \ref{Fig-Dyson}) and it can be presented as the
$2\times2$ matrix $L_{\alpha\beta}\left(
\mathbf{q},\Omega_{k}\right) $ where $\Omega_{k}\!=2\pi Tk$ are the
bosonic Matsubara frequencies. The corresponding Dyson equation for
fluctuation propagator can be written in the ladder approximation as
(see Fig.\ \ref{Fig-Dyson})
\begin{equation}
L_{\alpha\beta}=-g_{\alpha\beta}+g_{\alpha\gamma}\Pi_{\gamma\delta}%
L_{\delta\beta}, \label{Dyson1}%
\end{equation}
where $\Pi_{\alpha\beta}\left( \mathbf{q},\Omega_{k}\right) $ is the
matrix polarization operator which is determined by two Green's functions
loop \cite{LV02}. Without interband electron scattering the only nonzero
components of the operator $L_{\alpha\beta}$ are the diagonal ones.
\begin{figure}[ptb]
\begin{center}
\includegraphics[width=3.4in]{diagram1.eps}
\end{center}
\caption{Graphic representation of Dyson equation (\ref{Dyson1}) for
the fluctuation propagator $L_{\alpha\beta}$ (wavy line). The Greek
letters indicate the band indices. The black dot represents the
coupling-constants matrix $-g_{\alpha\beta}$, the loop represents
the polarization operator $\Pi_{\gamma\delta}$, and the shaded
triangle represents the scattering vertex
$C_{\gamma\gamma}$.}%
\label{Fig-Dyson}%
\end{figure}
Turning to the role of electron scattering, let us note that at the first
sight the short-range impurity potential might lead to the scattering of
electrons all over the whole Fermi surface which would result in the
equalization of all gap values and reduction of $T_{c}$. However, it is
well established now that this does not happen in MgB$_{2}$: even in the
samples with rather strong intraband scattering, interband scattering
remains rather weak. This property gave possibility to fabricate samples
with very high upper critical fields (up to 50 tesla) which have
transition temperatures only slightly smaller than clean
material\cite{highHc2}. Weakness of the interband scattering has been
explained by Mazin \emph{et al.} in Ref.\ \onlinecite{M03} who argued that
different parity symmetry of the $\sigma$- and $\pi$- orbitals leads to
strong reduction of the impurity scattering matrix element between these
bands. For simplicity, we will completely neglect the interband
scattering. In this case the off-diagonal components of the polarization
operator vanish. The averaging over impurities position will result just
in the usual renormalization of the Green's functions:
$\varepsilon_{n}\rightarrow \varepsilon_{n}+1/2\tau_{\alpha}$
($\tau_{\alpha}$\ is the corresponding intraband scattering time) and to
the appearance of the scattering vertex part $C_{\alpha\alpha}$ in the
expression for the polarization operator
\begin{widetext}
\begin{equation}
\Pi_{\alpha\alpha}\left( \mathbf{q},\Omega_{k}\right) =T\sum_{\varepsilon
_{n}}\int\frac{d\mathbf{p}}{\left( 2\pi\right) ^{3}}C_{\alpha\alpha
}(\mathbf{q},\varepsilon_{n+k},-\varepsilon_{n})G_{\alpha}\left(
\mathbf{p+q},\varepsilon_{n}+\Omega_{k}\right) G_{\alpha}\left(
-\mathbf{p},-\varepsilon_{n}\right) . \label{polarizator}%
\end{equation}
\end{widetext}
The scattering vertex part can be calculated in the ladder
approximation\cite{AGD}. In the case of a dirty metal $\left( T\tau
_{\alpha\alpha}\ll1\right) $ this gives\cite{LV02}
\begin{equation}
C_{\alpha\alpha}(\mathbf{q},\varepsilon_{n+k},-\varepsilon_{n}) \!=\!\frac
{1/\tau_{\alpha\alpha}}{|\varepsilon_{n}\!+\!\varepsilon_{n+k}| \!+\!\hat
{D}_{\alpha}q^{2}}\theta\left( \varepsilon_{n+k}\varepsilon_{n}\right) ,
\label{cooperon}%
\end{equation}
leading to the following result for the polarization operator
\begin{equation}
\Pi_{\alpha\alpha}(\mathbf{q},\Omega_{k}) \!=\!\nu_{\alpha}\!\left[ \ln\!
\frac{\omega_{D}}{2\pi T}\!-\!\psi\!\left( \frac{1}{2}\!+\!\frac{|\Omega
_{k}|\!+\!\hat{D}_{\alpha}q^{2}}{4\pi T}\right) \right] , \label{polar_expl}%
\end{equation}
where $\nu_{\alpha}$ is the density of states in the band $\alpha$,
$\omega_{D}$ is the Debye frequency and $\psi\left( x\right) $ is
the digamma-function. We introduced above the notation for the
diffusion-coefficient tensor acting in the momentum and band spaces:
\begin{equation}
\hat{D}_{\alpha}q^{2}\equiv \sum_{a}D_{\alpha,a}q_{a}^2.
\label{diffusion}%
\end{equation}
The diffusivities $D_{\alpha,a}$ determine the band coherence lengths as
$\xi_{\alpha,a}^{2}=\pi D_{\alpha ,a}/8T$. For magnesium diboride the
ratio
\begin{equation}
r=D_{2,z} /D_{1,z}=\xi_{2,z} ^{2}/\xi_{1,z}^{2}, \label{ratio}
\end{equation}
is large, $r\gg 1$, due to the large difference between the band
Fermi velocities in the $c$ direction \cite{Kortus,An}. This
parameter will play an important role in the following
consideration.
The inversion of the Dyson equation (\ref{Dyson1}) gives
\begin{equation}
\widehat{L}^{-1}=-\widehat{\emph{g}}^{-1}+\widehat{\Pi}. \label{propa}%
\end{equation}
We will use now this general expression to reconsider the main properties of
two-band superconductivity and to describe the corresponding fluctuation properties.
\subsection{Critical temperature}
The critical temperature of a two-band superconductor is determined by the
condition $\det\widehat{L}^{-1}=0$ taken at $\Omega_{k}=0$ and $\mathbf{q}%
=0$:
\[
\left( \frac{g_{22}}{\det\widehat{\emph{g}}}\!-\!\nu_{1}\ln\frac{2\gamma_{E}
\omega_{D}}{\pi T_{c}}\right) \!\! \left( \frac{g_{11}}{\det\widehat
{\emph{g}} }\!-\!\nu_{2}\ln\frac{2\gamma_{E}\omega_{D}}{\pi T_{c}}\right)
\!-\!\frac{g_{21}g_{12} }{\det^{2}\widehat{\emph{g}}}\!=\!0.
\]
with $\ln\gamma _{E}\equiv C_{E} \approx0.577$ being the Euler constant.
Introducing the coupling-constants matrix as
\[
\widehat{\lambda}=\left(
\begin{array}
[c]{cc}%
\nu_{1}g_{11} & \nu_{2}g_{12}\\
\nu_{1}g_{21} & \nu_{2}g_{22}%
\end{array}
\right) ,
\]
we can find that the transition temperature is determined by its largest
eigenvalue,
\[
\tilde{\lambda}=\frac{\lambda_{+}}{2}+\sqrt{\frac{\lambda_{-}^{2}}{4}
+\lambda_{12}\lambda_{21}}
\]
with $\lambda_{\pm}\equiv\lambda_{11}\pm\lambda_{22}$, and it is given by the
BCS-type equation:
\[
\ln\frac{2\gamma_{E}\omega_{D}}{\pi T_{c}}=\tilde{\lambda}^{-1}.
\]
Following Ref.\ \onlinecite{GK03b}, we introduce the inverse
coupling-constants matrix%
\begin{widetext}
\[
\widehat{W} =\left(
\begin{array}
[c]{cc}%
W_{11} & -W_{12}\\
-W_{21} & W_{22}%
\end{array}
\right) \equiv\widehat{\lambda}^{-1}-\tilde{\lambda}^{-1}\hat{I}
=\frac{1}{\det\widehat{\lambda}}\left(
\begin{array}
[c]{cc}%
\!\sqrt{ \lambda_{-}^{2}/4\!+\!\lambda
_{12}\lambda_{21}}\!-\!\lambda_{-}/2 & -\lambda_{21}\\
-\lambda_{12} & \!\sqrt{\lambda_{-}^{2}/4
\!+\!\lambda_{12}\lambda_{21}}\!+\!\lambda_{-}/2%
\end{array}
\right) ,
\]
\end{widetext}
where $\hat{I}$ is the unit matrix and $\det\widehat{\lambda}\equiv
\lambda_{11}\lambda_{22}-\lambda_{12}\lambda_{21}$. From the definition of
the matrix $\widehat{W}$ is evident that it is degenerate,
$\det\widehat{W}\equiv W_{11}W_{22}-W_{12}W_{21}=0.$ Having in mind
applications of our theory to MgB$_{2}$, we will use the numerically
computed effective coupling constants for this compound \cite{Golub}:
\begin{equation}
\left(
\begin{array}
[c]{cc}%
W_{11} & W_{12}\\
W_{21} & W_{22}%
\end{array}
\right) =\left(
\begin{array}
[c]{cc}%
0.088 & 0.535\\
0.424 & 2.56
\end{array}
\right) .
\end{equation}
We see now that apart from the already mentioned large ratio $r$
(\ref{ratio}), another characteristic small parameter, the relative
interband coupling,
\begin{equation}
S_{12}=\frac{W_{11}}{W_{22}}\approx0.035\ll1
\end{equation}
appears\cite{GK03a,GK03b}. In what follows we will demonstrate that
it is the interplay between these two parameters that defines the
rich picture of \ fluctuations that occurs beyond the traditional GL
theory.
\subsection{Fluctuation propagator}
In terms of the notations introduced above, the inverse matrix for
the
propagator (\ref{propa}) assumes the form%
\begin{widetext}
\begin{equation}
\widehat{L}^{-1}(\Omega_{k},\mathbf{q})=-\left(
\begin{array}[c]{cc}
W_{11}+\epsilon+\beta_{1}\left( |\Omega_{k}|,q\right)&-W_{12}\\
-W_{21} & W_{22}+\epsilon+\beta_{2}\left( |\Omega_{k}|,q\right)
\end{array}
\right) \left(
\begin{array}[c]{cc}
\nu_{1} & 0\\
0 & \nu_{2}%
\end{array}
\right) , \label{linvers}%
\end{equation}
where $\epsilon=\ln (T/T_{c})$,
\[
\beta_{\alpha}\left( \omega,q\right)\equiv
\beta\left[ \frac{\pi}{8 T} (\omega +\hat{D}_{\alpha}q^{2})\right] ,
\]
and
\begin{equation}
\beta(x) \equiv\psi\left( 1/2+2x/\pi^{2}\right) -\psi\left(
1/2\right)=\left\{
\begin{tabular}
[c]{l}%
$x,\ \ x\ll1$\\
$\ln x+C_{E}+\ln(8/\pi^{2}),\ x\gg1$%
\end{tabular}
\right., \label{beta1}
\end{equation}
Note that due to the identity $W_{12}\nu_{2}=W_{21}\nu_{1}$, the matrix
$\widehat{L}^{-1}(\Omega_{k},\mathbf{q})$ is symmetric.
Calculating $\det\widehat{L}^{-1}$ and inverting the matrix, one can
present $\widehat{L}(\Omega _{k},\mathbf{q})$ as
\begin{equation}
\widehat{L}(\Omega_{k},\mathbf{q})=\frac{\left(
\begin{array}
[c]{cc}%
\widetilde{W}_{22}+\widetilde{\theta}\left[ \epsilon+
\beta_{2}\left(|\Omega_{k}|,q\right) \right] &
\widetilde{W}_{21}\\
\widetilde{W}_{12} & \widetilde{W}_{11}+\widetilde{\theta}\left[
\epsilon+\beta_{1}\left( |\Omega_{k}|,q\right)\right]
\end{array}
\right) \left(
\begin{array}
[c]{cc}%
\nu_{1}^{-1} & 0\\
0 & \nu_{2}^{-1}%
\end{array}
\right) }{\epsilon+\left[ \widetilde{W}_{11}+\widetilde{\theta}%
\epsilon\right] \beta_{2}\left(|\Omega_{k}|,q\right)+\left[ \widetilde{W}_{22}+\widetilde{\theta}%
\beta_{2}\left(|\Omega_{k}|,q\right)\right]
\beta_{1}\left(|\Omega_{k}|,q\right)}, \label{propagator1}
\end{equation}
where we introduced the following notations
\[
\widetilde{W}_{ik}=\frac{W_{ik}}{W_{11}+W_{22}},\widetilde{\theta}=\frac
{1}{W_{11}+W_{22}}.
\]
Since we are interested in the most singular contribution with respect to
$\epsilon$, we omitted the terms $\epsilon^{2}$ and $\epsilon$ as compared
to $W_{22}$.
In order to derive microscopically the TDGL equation and study the effect of
fluctuations on transport phenomena one has to perform the analytical
continuation of the propagator (\ref{propagator1}) from the set of the
imaginary Matsubara frequencies $i\Omega_k=2\pi i T k$, $k=0,1,2\ldots$ to
the upper half-plane of the complex frequencies. Since the function
$\psi(z)$ has poles at points $z_n = 0, -1, -2\ldots$ the analytical
continuation to the real frequencies $\Omega$ can be performed by the simple
substitution $\Omega_k \rightarrow-i\Omega$ in the argument of the function
(\ref{beta1}).\cite{E61,LV02} When this argument is small ($\Omega,
D_{\alpha}q^2 \ll T$) the function $\beta$ is reduced to the Fourier
transform of the diffusion operator:
\[
\beta\left[ \frac{\pi}{8 T} (|\Omega_{k}|+\hat{D}_{\alpha}q^{2})\right]
\rightarrow-i\frac{\pi\Omega}{8T}+\frac{\pi\hat{D}_{\alpha}q^{2}}{8T}.
\]
Performing the analytical continuation, using
$\widetilde{W}_{22}\approx1$, and accounting for the small parameters of
the model ($\widetilde{W}_{11}\approx
S_{12},\widetilde{\theta},\epsilon,\Omega/T, \hat{D}_{1}q^2/T\ll1$), we
obtain the analytically continued propagator
$\widehat{L}^{R}(\mathbf{q,}\Omega)$ in the form
\begin{equation}
\widehat{L}^{R}(\mathbf{q,}\Omega)\approx-\frac{1}{\epsilon+\beta_{1}\left(-i\Omega,q\right)
+\frac{S_{12}\beta_{2}\left(-i\Omega,q\right)}{1+\widetilde{\theta}\beta_{2}\left(-i\Omega,q\right)}}\left(
\begin{array}
[c]{cc}%
1/\nu_{1} & \frac{\widetilde{W}_{21}}{\nu_{2}\left( 1+\widetilde{\theta}%
\beta_{2}\left(-i\Omega,q\right)\right) }\\
\frac{\widetilde{W}_{12}}{\nu_{1}\left(
1+\widetilde{\theta}\beta_{2}\left(-i\Omega,q\right)\right)
} & \frac{S_{12}+\widetilde{\theta}\left[ \epsilon+\beta_{1}\left(-i\Omega,q\right)\right] }%
{\nu_{2}\left( 1+\widetilde{\theta}\beta_{2}\left(-i\Omega,q\right)\right) }%
\end{array}
\right) . \label{progen1}%
\end{equation}
\end{widetext}
Below we will analyze the behavior of this matrix in different temperature
intervals.
\subsubsection{Ginzburg-Landau regime}
Let us take the reduced temperature so small that both $\beta_{1}$ and
$\beta_{2}$ functions can be expanded. At the end of this subsection we will
arrive at the analytical criterion for this condition to be satisfied. In
this case the propagator (\ref{progen1}) significantly simplifies (we use
here the definition $\hat{D}_{\alpha}q^{2}/4\pi T=2/\pi^{2}\xi
_{\alpha,a}^{2}q_{a}^{2}$):
\begin{equation}
\widehat{L}^{R}\left( \mathbf{q},\Omega\right)
\!=\!-\frac{1}{\epsilon\!-\!i\gamma_{GL}
\Omega\!+\!\widetilde{\xi}_{a}^{2}q_{a}^{2}}\left(
\begin{array}
[c]{cc}%
1/\nu_{1} & \widetilde{W}_{21}/\nu_{2}\\
\widetilde{W}_{12}/\nu_{1} & S_{12}/\nu_{2}%
\end{array}
\right) , \label{proGL}%
\end{equation}
where $\gamma_{GL}=\pi/8T$, and the effective coherence length
components $\widetilde{\xi}_{a}$ is given by
\begin{equation}
\widetilde{\xi}_{a}^{2}=\widetilde{W}_{11}\xi_{2,a}^{2}+\widetilde{W}_{22}%
\xi_{1,a}^{2}\approx\xi_{1,a}^{2}\left( 1+S_{12}\frac{\xi_{2,a}^{2}}%
{\xi_{1,a}^{2}}\right) ,\label{xiGL}%
\end{equation}
Typically $\xi_{2,x}\approx\xi_{1,x}$ and, due to the presence of a
small coefficient $S_{12}$, the contribution from the $\pi$-band to
the transversal component of the effective coherence length \
($a=x,y$) turns out to be small and can be ignored. On the other
hand, the c-axis motion in the $\pi$-band, due to the large value of
the ratio $r=\xi_{2,z}^{2}/\xi_{1,z}^{2}$ can play an important role
for the longitudinal component of the effective coherence length
\[
\widetilde{\xi}_{z}^{2}=\xi_{1,z}^{2}\left( 1+S_{12}r\right)
\]
and when $S_{12}\gg 1/r$ it may significantly exceed $\xi_{1,z}^{2}$.
The characteristic momentum $q_{z}$ is determined by the diverging GL
coherence length:
\begin{equation}
q_{z}\sim\sqrt{\epsilon}/\widetilde{\xi}_{z}.\label{char}%
\end{equation}
Therefore the standard GL theory is valid only at temperatures so
close to $T_{c}$ that $\xi_{2,z}^{2}q_{z}^{2}\ll1$ and where both
$\beta$ functions can be expanded. The corresponding condition
acquires the form \cite{GK03a,GK03b}
\begin{equation}
\epsilon\ll\frac{\xi_{1,z}^{2}}{\xi_{2,z}^{2}}+S_{12}=1/r+S_{12}.
\label{GLcondition}
\end{equation}
\subsubsection{Beyond the GL regime}
Let us return to the propagator (\ref{propagator1}) and analyze its
behavior in all the vicinity of the transition, $\epsilon\ll1$, performing
allowed expansions and simplifications. The diffusion in the first band is
slow, therefore we can expand the corresponding $\beta$-functions. On the
other hand, the function $\beta_{2}(-i\Omega,\mathbf{q})\equiv\beta\left[
\frac{\pi}{8 T}(-i\Omega+\hat{D}_{2}q^{2})\right] $ can be expanded only
with respect to $\Omega$ and $q_{\Vert}$ and one has to keep the full
nonlinear dependence on $q_{z}$. As a result, we obtain the expression
similar to (\ref{proGL}) except for the appearance of the explicit $q_{z}%
$-dependence of the GL coefficients $\gamma_{GL}\rightarrow\gamma\left(
q_{z}\right) $ and $\widetilde{\xi}_{a}^{2}\left( q_{z}\right) $
\begin{widetext}
\begin{equation}
\widehat{L}^{R}(\mathbf{q,}\Omega)=-\frac{1}{\epsilon-i\gamma\left(
q_{z}\right) \Omega+\widetilde{\xi}_{a}^{2}\left( q_{z}\right) q_{a}^{2}%
}\left(
\begin{array}
[c]{cc}%
1/\nu_{1} & \frac{\widetilde{W}_{21}}{\nu_{2}\left( 1+\widetilde{\theta}%
\beta_{2}\right) }\\
\frac{\widetilde{W}_{12}}{\nu_{1}\left(
1+\widetilde{\theta}\beta_{2}\right) } &
\frac{S_{12}+\epsilon\widetilde{\theta}+\widetilde{\theta}\xi_{1,a}^{2}%
q_{a}^{2}}{\nu_{2}\left( 1+\widetilde{\theta}\beta_{2}\right) }%
\end{array}
\right) . \label{Lgeneral}%
\end{equation}
\end{widetext}
with
\begin{subequations}
\begin{align}
\gamma\left( q_{z}\right) & \approx\gamma_{GL}\left[ 1+\frac
{S_{12}+\epsilon\widetilde{\theta}}{1+\widetilde{\theta}\beta_{2}(
q_{z})}\beta^{\prime}_2( q_{z})\right],
\label{gammanonGL}\\
\widetilde{\xi}_{x}^{2}\left( q_{z}\right) & =\xi_{1x}^{2}+\frac
{S_{12}+\epsilon\widetilde{\theta}}{1+\widetilde{\theta}\beta_{2}(
q_{z})}\beta^{\prime}_2(
q_{z})%
\xi_{2x}^{2},\label{xinonGL1}\\
\widetilde{\xi}_{z}^{2}\left( q_{z}\right) & =\xi_{1,z}^{2}+\frac{S_{12}%
}{1+\widetilde{\theta}\beta_{2}( q_{z})}\frac{\beta_{2}(
q_{z})}{\xi_{2,z}^{2}q_{z}^{2}}%
\xi_{2,z}^{2}. \label{xinonGL2}%
\end{align}
\end{subequations}
Here
\begin{subequations}
\begin{eqnarray}
&\beta^{\prime}(x)=d\beta(x)/dx, \label{betadef1}\\
&\beta_{2}(q_{z}) \equiv\beta\left( \xi_{2,z}^{2}q_{z}^{2}\right),\label{betadef2} \\
&\beta^{\prime}_{2}(q_{z}) \equiv \beta^{\prime}\left(
\xi_{2,z}^{2}q_{z}^{2}\right).\label{betadef3}
\end{eqnarray}
\end{subequations}
One can see that when the condition (\ref{GLcondition}) is satisfied, the
characteristic $q_{z}$ (see (\ref{char}) ) is small and the expressions
(\ref{gammanonGL}), (\ref{xinonGL1}), and (\ref{xinonGL2})\ reproduce the
TDGL coefficients. In the region
\begin{equation}
1/r+S_{12}\ll\epsilon\ll1
\end{equation}
the argument $\xi_{2,z}^{2}q_{z}^{2}$ of the $\beta$ function
(\ref{betadef2}) for the essential momenta $q_{z}$ becomes large and it
can not be expanded anymore. This means that the gradient expansion needed
for validity of the GL regime fails.
In this region of temperatures the contribution of
the $\pi$-band rapidly decreases and the main role passes to the
$\sigma$-band. Typically, the $\pi$-band strongly contributes to
$\widetilde{\xi}_{z}^{2}\left( q_{z}\right) $ and gives only
small corrections to $\gamma\left( q_{z}\right) $ and
$\widetilde{\xi}_{x} ^{2}\left( q_{z}\right) $.
Now we have in place all the elements required for the microscopic
calculations of fluctuation effects in a two-band superconductor.
However, because of the complex band structure and necessity to
take into account the short wavelength fluctuations the
diagrammatic calculations present itself a bulky calculus. In what
follows we establish another route to address fluctuation
phenomena. Namely, we will re-derive the GL functional and extend
the standard GL scheme to treatment of fluctuations for the
two-band superconductor, and then apply this modified GL approach
to calculations of specific heat and paraconductivity.
\section{Nonlocal two-band GL functional and TDGL equations}
\subsection{GL functional and TDGL equations}
Knowing the explicit form of the fluctuation propagator (\ref{linvers}), one
can write down corresponding GL free-energy functional $\emph{F}_{GL}%
=\emph{F}_{GL}^{\left( 2\right) }+\emph{F}_{GL}^{\left( 4\right) }.$ The
complete procedure of its microscopic derivation is given in Ref.\
\onlinecite{LV02} and here we will present only the specific expressions for
GL\ coefficients corresponding to the model under consideration.
The quadratic in order parameter $\Delta_{\alpha}$ part of the GL functional
$\emph{F}_{GL}^{\left( 2\right) }$\ is expressed in terms of the linearized
GL Hamiltonian density $H_{\alpha\beta}(\mathbf{q})\equiv L_{\alpha\beta}%
^{-1}\left( \mathbf{q},\Omega=0\right) :$
\begin{equation}
\emph{F}_{GL}^{\left( 2\right) }=\int d\mathbf{r}\Delta_{\alpha}^{\ast
}H_{\alpha\beta}(\mathbf{\hat{q}})\Delta_{\beta},\label{F_GL}%
\end{equation}
with
\begin{equation}
H_{\alpha\beta}=a_{\alpha\beta}+\left(
\begin{array}
[c]{cc}%
\nu_{1}\xi_{1,a}^{2}q_{a}^{2} & 0\\
0 & \nu_{2}\left[ \xi_{2,x}
^{2}q_{\parallel}^{2}\beta^{\prime}_2(q_z)+\beta_2(q_z) \right]
\end{array}
\right) , \label{HGL}%
\end{equation}
and $\mathbf{\hat{q}}=-i\nabla-\frac{2\pi}{\Phi_{0}}\mathbf{A}%
$. Here the matrix
\begin{equation}
\widehat{a}=\left(
\begin{array}
[c]{cc}%
\nu_{1}\left( W_{11}+\epsilon\right) & -\nu_{2}W_{12}\\
-\nu_{1}W_{21} & \nu_{2}\left( W_{22}+\epsilon\right)
\end{array}
\right)
\end{equation}
plays the role of the GL coefficient $a$. In general, we have to
keep nonlinear dependence on $q_{z}$ in
$H_{\alpha\beta}(\mathbf{q})$ meaning that
$H_{\alpha\beta}(\mathbf{\hat{q}})$ in Eq.\ (\ref{F_GL}) is not a
simple second-order differential operator. Note that the similar
generalization of the GL functional has been performed by Maki
\cite{MakiHc2} in order to describe a dirty superconductor in the
vicinity of the $H_{c2}(T)$ line.
The coefficients in the fourth order term of the GL\ functional $\emph{F}%
_{GL}^{\left( 4\right) }$ do not change their form with respect to the
noninteracting bands case:%
\begin{equation}
\emph{F}_{GL}^{\left( 4\right) }=b_{\alpha}\int
d\mathbf{r}|\Delta_{\alpha }|^{4}
\end{equation}
with
\[
b_{\alpha}=7\zeta(3)\nu_{\alpha}/(8\pi^{2}T^{2})=\nu_{\alpha}b_{GL}
\]
and $\zeta(3)\approx1.202$.
Now one can write down the linearized TDGL equation in the form
\cite{LV02}
\[
L_{\alpha\beta}^{-1}\left( \mathbf{q},\Omega\right)
\Delta_{\beta}\! \equiv\! \left[ -i\Omega\gamma_{\alpha\beta}\left(
q_z\right) \!+\!H_{\alpha\beta}\left( \mathbf{q}\right) \right]
\Delta_{\beta} \!=\!0
\]
with the matrix of TDGL dynamic coefficients
\begin{equation}
\gamma_{\alpha\beta}(q_z) =\frac{\pi}{8T}\left(
\begin{array}
[c]{cc}%
\nu_{1} & 0\\
0 & \nu_{2}\beta^{\prime}_2(q_z)
\end{array}
\right) \label{gammamat}%
\end{equation}
which directly follows from the dynamic part of the fluctuation
propagator. We see that there are two essential differences from the
standard GL approach: (i) strong nonlocality along $z$-direction
(ii) two-component character of the order parameter. In the case
where the parameter $W_{22}$ is large, one can reduce the functional
with two order parameters to the functional for the single
band-averaged order parameter.\cite{GK03b}
\subsection{Spectral properties of $\hat{L}^{-1}(\mathbf{q},\Omega)$}
The TDGL operator $\widehat{L}^{-1}\left( \mathbf{q},\Omega\right)
=\hat {H}\left( \mathbf{q}\right) -i\Omega\hat{\gamma}\left( q_z
\right) $ is the $2\times2$ matrix defined on the band index space.
It is convenient to diagonalize it. The eigenvalues
$L_{m}^{-1}(\mathbf{q})=\varepsilon_{m}(\mathbf{q})-i\Omega
\gamma_{m}(q_z)$ and the normalized eigenstates $\psi_{m,\beta}$
obey the equation
\begin{equation}
\left[ H_{\alpha\beta}\left( \mathbf{q}\right)
-i\Omega\gamma_{\alpha\beta}\left( q_z\right) \right]
\psi_{m,\beta}=L_{m}^{-1}(\mathbf{q},\Omega)\psi_{m,\alpha},
\label{spectral}%
\end{equation}
where $m=1,2$ is the mode index. Superconducting instability
corresponds to the vanishing of the $m=1$ eigenvalue at
$\epsilon,q,\Omega=0$.
Calculating the determinant of (\ref{spectral}) and equating it to zero one
finds\begin{widetext}
\begin{align*}
L_{1,2}^{-1}\left( \mathbf{q},\Omega\right) & =\frac{\nu_{1}\left(
W_{11}+h_{1}(\mathbf{q},\Omega)\right)
+\nu_{2}\left( W_{22}+\beta_{2}(q_z)+h_{2}(\mathbf{q},\Omega)\right) }{2}\\
& \pm\sqrt{\left( \frac{\nu_{1}\left(
W_{11}+h_{1}(\mathbf{q},\Omega)\right) -\nu_{2}\left(
W_{22}+\beta_{2}(q_z)+h_{2}(\mathbf{q},\Omega)\right) }{2}\right)
^{2}+\nu_{1}\nu_{2}W_{11}W_{22}}
\end{align*}
\end{widetext}
with%
\begin{align*}
h_{1}(\mathbf{q},\Omega) &
\equiv\epsilon+\frac{\pi i\Omega}{8T}+\xi_{1,a}^{2}q_{a}^{2},\\
h_{2}(\mathbf{q},\Omega) &
\equiv\epsilon+\beta^{\prime}_2(q_z)\left[\frac{\pi
i\Omega}{8T}+\xi_{2,x}^{2} q_{\parallel}^{2}\right].
\end{align*}
\paragraph{GL regime --}
In the case of small $\Omega$, $\epsilon$ and $q$, corresponding to the GL
region of temperatures, one can find the simplified expressions for the
eigenvalues of energy:
\begin{align}
L_{1}^{-1}(\mathbf{q}) & \approx\nu_{2}\nu_{1}\frac{\left( W_{22}+W_{11}\right) }%
{\nu_{1}W_{11}+\nu_{2}W_{22}}\nonumber\\
& \times\left[ \epsilon+i\Omega\gamma_{GL}+\widetilde{W}_{22}\xi_{1,a}%
^{2}q_{a}^{2}+\widetilde{W}_{11}\xi_{2,a}^{2}q_{a}^{2}\right]
\label{EigenvalueGL1}\\
L_{2}^{-1} & \approx\nu_{1}W_{11}+\nu_{2}W_{22}. \label{EigenvalueGL2}%
\end{align}
The expression (\ref{EigenvalueGL1}) for $L_{1}^{-1}(\mathbf{q})$ reproduces
the GL relation (\ref{proGL}) while $L_{2}^{-1}$ is not singular.
\paragraph{Beyond GL regime --}
In generally, the value of function $\beta_{2}(q_z)$ may not be small. In
the absence of that the smallness the more general expansions for
eigenvalues have to be used:
\begin{align}
L_{1}^{-1}(\mathbf{q}) & \approx\nu_{1}\nu_{2}\frac{\left(
h_{2}(\mathbf{q})\!+\!\beta_{2}(q_z)\right)\!
W_{11}+\!h_{1}(\mathbf{q})\!\left( W_{22}+\!\beta_{2}(q_z)\right)
}{\nu_{1}W_{11}+\nu_{2}\left(
W_{22}+\beta_{2}(q_z)\right) }\nonumber\\
& \approx\nu_{1}\left( h_{1}(\mathbf{q})+\frac{W_{11}\left(
h_{2}(\mathbf{q})+\beta_{2}(q_z)\right)
}{\left( W_{22}+\beta_{2}(q_z)\right) }\right); \label{Eigenvalue1}\\
L_{2}^{-1}(\mathbf{q}) & \approx\!\frac{\nu_{1}W_{11}(\nu_{2}W_{22}\!+\!\nu_{1}W_{11})}%
{\nu_{2}\left( W_{22}\!+\!\beta_{2}(q_z)\right)
\!+\!\nu_{1}W_{11}}\!+\!\nu_{2}\left(
W_{22}\!+\!\beta_{2}(q_z)\right) \label{Eigenvalue2}.
\end{align}
We will need further the eigenvector for the singular mode, $m=1$, in the
zero order with respect to the small parameters $h_{\alpha}$%
\begin{equation}
\binom{\psi_{1,1}(q_z)}{\psi_{1,2}(q_z)}\approx\binom{\sqrt{1-a^{2}(q_z)}
}{-a(q_z)}
\label{eigenvector}%
\end{equation}
where
\[
a(q_z)=\frac{\sqrt{\nu_{1}\nu_{2}W_{11}W_{22}}}{ \nu_{2}\left( W_{22}+\beta
_{2}(q_z)\right) }.
\]
Now we are prepared to revise the results of the standard
fluctuation theory and to generalize them for the case of a two-band
superconductor.
\section{Fluctuation properties of two-band superconductor}
Before going to detail calculations of different fluctuation properties, it
is instructive to estimate the relative strength of fluctuations in the
available two-band material, MgB$_{2}$. It is characterized by the magnitude
of the Ginzburg-Levanyuk parameter:
\[
Gi=\left( \frac{4\pi^{2}\lambda_{x}^{2}\Gamma (T_{c}) T_{c}}{\Phi_{0}^{2}\widetilde{\xi_{x}}%
}\right) ^{2},
\]
where $\Phi_{0}=2.07\cdot10^{-7}$ G cm$^2$ is the flux quantum,
$\lambda_{x}$ and $\widetilde{\xi_x}$ are the in-plane London penetration
depth and coherence length, and $\Gamma(T_c)$ is the anisotropy parameter
in the limit $T\rightarrow T_{c}$. Making use of the values of parameters
typical for the clean MgB$_{2}$ crystals: penetration depth
$\lambda_{x}=10^{-5}$cm (Ref.\ \onlinecite{CarringtonPhysC03}), coherence
length $\xi_{x}=10^{-6}$cm (Ref.\ \onlinecite{hc2anisotropy}) and the
anisotropy coefficient $\Gamma (T_{c})=2.5$ (Ref.\
\onlinecite{hc2anisotropy}), we obtain $Gi\approx 1.5\cdot10^{-6}$, what
means that fluctuations in this compound are weak. This conclusion is not
so surprising, since MgB$_{2}$ is known to be a good metal with large
concentration of charge carriers. Therefore, identifying experimentally
the contribution of fluctuations in the clean MgB$_{2}$ crystals is a
challenging task. On the other hand, the amplitude of fluctuation is
expected to be much higher in disordered films or in crystals with large
number of substitution impurities. We stress, however, that the effects
discussed in this paper hold only as long as scattering does not mix bands
and this limits an applicability of our theory for strongly disordered
materials. Another complication is that increasing disorder in magnesium
diboride is usually accompanied by doping of the $\sigma$-band leading to
modification of material parameters (e.g., decreasing the $\sigma$-band
anisotropy) \cite{Kurtus04}.
\subsection{Specific heat}
We start with the calculation of the fluctuation contribution to the
free energy of the two-band superconductor above the critical
temperature. It is determined by the partition function $Z$:
$F=-T\ln Z$, which, in its turn, can be expressed in terms of the
determinant of the GL matrix Hamiltonian (\ref{HGL})
\begin{align*}
F & =-T\ln\int\!\!D\Delta\int\!\!D\Delta^{\ast}\exp\left(
-\frac{1}{T}\int \frac{d^{3}q}{\left( 2\pi\right)
^{3}}H_{\alpha\beta}\Delta_{\alpha}^{\ast
}\Delta_{\beta}\right) \\
& =-TV\int\frac{d^{3}q}{\left( 2\pi\right) ^{3}}\ln\frac{A}{\det
H_{\alpha\beta}},
\end{align*}
where $A$ is an insignificant dimensional constant. Separating the
most singular fluctuation contribution (see Eq.\ (\ref{Lgeneral})),
one can find
\[
\frac{F_{sng}}{V}\!\approx\!-T\!\int\!\frac{d^{3}q}{(2\pi)^{3}}\ln\frac{A}{\left(
1\!+\!\tilde{\theta}\beta_{2}(q_z)\right)\! \left(
\epsilon\!+\!\xi_{1,a}^{2}q_{a}
^{2}\!+\!S_{12}\tilde{\beta}_{2}(q_z)\right) }%
\]
with $\tilde{\beta}_{2}(q_z)\equiv\beta_2(q_z) /\left(
1+\tilde{\theta}\beta_2(q_z) \right) $. The corresponding contribution to
the specific heat is given by
\begin{align}
C^{\prime} & =-\frac{T}{V}\frac{d^{2}F_{sng}}{dT^{2}}
\approx\int\frac{d^{3}q}{(2\pi)^{3}}\frac
{1}{\left( \epsilon+\xi_{1,a}^{2}q_{a}^{2}+S_{12}\tilde{\beta}_{2}(q_z)\right) ^{2}} \nonumber\\
& =\frac{1}{8\pi^{2}\xi_{1,x}^{2}}\int\limits_{-\infty}^{\infty}
dq_{z}\frac{1}{\epsilon+\xi_{1,z}
^{2}q_{z}^{2}+S_{12}\tilde{\beta}_{2}(q_{z})},
\label{SpecHeat}%
\end{align}
Note that the denominator of the the logarithm argument coincides
with the denominator of the fluctuation propagator (\ref{Lgeneral}).
Introducing the reduced variable $u=\xi_{1,z}q_{z}/\sqrt{\epsilon}$,
we rewrite this result in the form convenient for numerical
evaluation:
\begin{equation}
C^{\prime}=\frac{\kappa(\epsilon)}{8\pi\xi_{1,x}^{2}\xi_{1,z}\sqrt{\epsilon}}
, \label{SpecHeat1}
\end{equation}
where the dimensionless function $\kappa(\epsilon)\equiv
\kappa(\epsilon, r, S_{12},\tilde{\theta})$ is defined as
\begin{equation}
\kappa(\epsilon)= \int\limits_{0}^{\infty}
\frac{2du}{\pi}\frac{1}{1\!+\!u^{2}\!+\!(S_{12}
/\epsilon)\tilde{\beta}_2\left( r\epsilon u^{2}\right) }.
\label{kappa}
\end{equation}
It weakly depends on temperature and has the following asymptotics
\begin{widetext}
\[
\kappa(\epsilon) \approx \left\{
\begin{array}
[c]{ll}%
\left(1+S_{12}r\right)^{-1/2}=\xi_{1,z}/\widetilde{\xi}_{z},&\text{for }\epsilon\ll 1/r+S_{12}\\
\sqrt{1-(S_{12}/\epsilon)\ln\left[ Cr\left( \epsilon-S_{12}
\right)\right]}, &\text{for } 1/r+S_{12}\ll \epsilon\ll S_{12}\ln
(rS_{12})\\
1-\frac{S_{12}}{2\epsilon}\frac{\ln\left( C_{1}r\epsilon\right) }%
{1+\tilde{\theta}\ln\left( C_{1}r\epsilon\right) },&\text{for }S_{12}\ln
(rS_{12})\ll\epsilon\ll1 \label{interpol}
\end{array}
\right.
\]
with $C_{1}=16\pi^{-2}\gamma_{E}\exp\left( -2\right) \approx 0.391$.
The formulas (\ref{SpecHeat1})-(\ref{kappa}) work in the entire
region $\epsilon\ll1$. The intermediate asymptotic in $\kappa$
appears only in the case $rS_{12}\gg1\ $ which is valid for MgB$_2$.
\cite{Kortus} One can see that the main difference between the GL
and non-GL regions in the temperature dependence of the fluctuation
heat capacity correction is the change in the coefficient of the
$\epsilon^{-1/2}$ dependence in factor
$\widetilde{\xi}_{z}/\xi_{1,z}$.
\subsection{Paraconductivity}
The paraconductivity in the phenomenological GL approach can be expressed
via the eigenvalues of the GL Hamiltonian and the matrix
elements of the ``velocity''\ operator\ $\widehat{v}_{\alpha}%
^{a}=\partial H_{\alpha\alpha}\left( q\right) /\partial q_{a}$.
The approach of Ref.\ \onlinecite{LV02} can be extended it to the
case of two-band model. The general formula for the
paraconductivity tensor then is:
\begin{align}
\sigma^{ab} & =\frac{4Te^{2}}{\hbar}\int\frac{d^{3}\mathbf{q}}{\left(
2\pi\right) ^{3}}\sum_{n,k}\frac{\widehat{v}_{nk}^{a}\widehat{v}_{kn}%
^{b}\gamma_{k}\gamma_{n}}{\varepsilon_{n}\varepsilon_{k}\left( \gamma
_{n}\varepsilon_{k}+\varepsilon_{n}\gamma_{k}\right) }\nonumber\\
& =\frac{4Te^{2}}{\hbar}\int\frac{d^{3}\mathbf{q}}{\left( 2\pi\right
) ^{3}%
}\left[ \frac{\gamma_{1}\widehat{v}_{11}^{a}\widehat{v}_{11}^{b}%
}{2\varepsilon_{1}^{3}}+\frac{\gamma_{2}\widehat{v}_{22}^{a}\widehat{v}%
_{22}^{b}}{2\varepsilon_{2}^{3}}+\frac{2\widehat{v}_{12}^{a}\widehat{v}%
_{21}^{b}}{\varepsilon_{1}\varepsilon_{2}\left( \gamma_{1}^{-1}%
\varepsilon_{1}+\gamma_{2}^{-1}\varepsilon_{2}\right) }\right].
\label{sigma-general}%
\end{align}
\end{widetext}
with $\widehat{v}_{nk}^{a}\equiv
\sum_{\alpha}\psi_{n,\alpha}\widehat{v}_{\alpha
}^{a}\psi_{k,\alpha}$ (we restored dimensional units in this
formula). Let us stress that the summation here is performed over
the mode indices rather than the band indices in other parts of the
paper.
The main contribution to the paraconductivity comes from the projection to
the singular mode (the first term in the square brackets in Eq.\
(\ref{sigma-general})). Keeping only these terms and using results
(\ref{Eigenvalue1}) for the eigenvalue
$L_{1}^{-1}(\mathbf{q})=\varepsilon_{1}(\mathbf{q})
-i\Omega\gamma_{1}(q_z)$ and (\ref{eigenvector}) for eigenvector, we
derive
\begin{equation}
\sigma_{a}^{\prime}\approx\frac{\pi
e^{2}}{\hbar}\int\frac{d^{3}q}{(2\pi)^{3}
}\frac{\xi_{1,a}^{4}q_{a}^{2}\left[ 1+S_{12}r_{a}\tilde{\beta}^{\prime}_{a}\right] ^{2}%
}{\left[ \epsilon+\xi_{1,i}^{2}q_{i}^{2}+S_{12}\tilde{\beta}_{2}\right]
^{3}\,} \label{lastcond}%
\end{equation}
with $\tilde{\beta}^{\prime}_{1}\equiv 1/\left(
1+\tilde{\theta}\beta_{2}\right) ^{2}$,
$\tilde{\beta}^{\prime}_{2}\equiv\beta^{\prime}_2/\left(
1+\tilde{\theta}\beta_{2}\right) ^{2}$ and
$r_{a}=\xi^2_{2,a}/\xi^2_{1,a}$ ($r_z\equiv r$). Below we evaluate the
in-plane and z-axis components of paraconductivity separately.
\subsubsection{In-plane component}
In the case of an in-plane paraconductivity we can neglect the small
renormalization of the in-plane velocity in formula
(\ref{lastcond}), perform the $q_{\Vert}$ integration and get%
\[
\sigma_{x}^{\prime}\approx\frac{e^{2}}{32\hbar\pi}\int\limits^{\infty}_{-\infty}
dq_{z}\frac{1}
{\epsilon+\xi_{1,z}^{2}q_{z}^{2}+S_{12}\tilde{\beta}_{2}(q_{z})\,}.
\]
One can see that the in-plane conductivity has exactly the same
temperature dependence as the fluctuation specific heat and
therefore can be represented in the form analogous Eq.\
(\ref{SpecHeat}):
\begin{equation}
\sigma_{x}^{\prime}=\frac{e^{2}}{32\hbar\xi_{1,z}\sqrt{\epsilon}}\kappa(\epsilon),
\label{sigma-x}
\end{equation}
where the function $\kappa(\epsilon)$ is defined by Eq.\ (\ref{kappa}).
The above results show that $\sigma_{x}^{\prime}$ has a 3D character but
diverges slower than the specific $1/\sqrt{\epsilon}$-law. Numerically
calculated dependence $\sigma_{x}^{\prime}\left( \epsilon\right) $ with
parameters typical for MgB$_{2}$, $S_{12}=0.035$,
$\widetilde{\theta}=0.377$ and $r=300$, is shown in the left panel of
Fig.\ \ref{Fig-sigmas} together with the GL asymptotic for $T\rightarrow
T_c$ and the single $\sigma$-band curve. Taking the estimate for the
coherence length of MgB$_{2}$ crystals as \cite{hc2anisotropy}
$\xi_{1,z}\approx2$nm, we find the typical scale for the fluctuation
correction, $\sigma_{x0}^{\prime}=e^{2}/(32\hbar\xi_{1,z})$, as
$\sigma_{x0}^{\prime}\approx$ 40 [$\Omega$ cm]$^{-1}$. This scale must be
much higher in dirty MgB$_{2}$ films. The in-plane paraconductivity in
MgB$_{2}$ films has been studied recently in Ref.\
\onlinecite{SidorJETPLett02} but in the analysis of the experimental data
the two-band nature of MgB$_{2}$ was not taken into account. Nevertheless,
it was found that the paraconductivity indeed diverges slower than
$1/\sqrt{\epsilon}$, in agreement with our results.
\begin{figure}[ptb]
\begin{center}
\includegraphics[width=3.4in]{sigmas1.eps}
\end{center}
\caption{Temperature dependencies of the paraconductivity components
(solid lines). \emph{Left panel} shows the in-plane component in units of
$e^{2}/(32\hbar \xi_{z,1})$ (function $\kappa(\epsilon)/\sqrt{\epsilon}$,
see Eqs.\ (\ref{sigma-x}) and (\ref{kappa})). This curve also gives the
fluctuation specific heat in units $1/(8\pi\xi_{1,x}^{2}\xi_{1,z})$, see
Eq.\ (\ref{SpecHeat1}). \emph{Right panel} shows the z-axis component in
units of $e^{2}\xi_{z,1}/(32\hbar\xi_{x,1}^{2})$ calculated from Eq.\
(\ref{sigma-z}). Both components were calculated using parameters
$S_{12}=0.035$, $\widetilde{\theta}=0.377$ and $r=300$. For comparison we
also show the Ginzburg-Landau asymptotics (dotted lines) and $\sigma$-band
contribution to paraconductivity (dashed lines). One can see that in-plane
component diverges slower and z-axis component diverges faster than the
paraconductivity in a single-band anisotropic superconductor. In the
$\sigma_z$-plot we indicate three characteristic regions with different
functional dependencies of fluctuation parameters.}
\label{Fig-sigmas}\end{figure}
\subsubsection{z-component}
The longitudinal component of paraconductivity $\sigma_{z}^{\prime}$
is given by the Eq.\ (\ref{lastcond}). Here the velocity
renormalization turns out to be essential and it cannot be omitted.
Performing integration with respect to $q_{\parallel}$ and using the
introduced above reduced variable $u$, the result can be rewritten
as
\begin{equation}
\sigma_{z}^{\prime}\approx\frac{e^{2}\xi_{1,z}}{32\hbar\xi_{1,x}^{2}\sqrt{\epsilon}}\int_{0}^{\infty}\frac{4du}{\pi}\frac{u^{2}\left[
1+S_{12}r\tilde{\beta}^{\prime}_{2}(u)\right] ^{2}}{\left[
1+u^{2}+(S_{12}/\epsilon )\tilde{\beta}_{2}(u)\right] ^{2}\,}.
\label{sigma-z}\end{equation} In the Ginzburg-Landau regime,
$\epsilon\ll1/r+S_{12}$, we obtain\[
\sigma_{z}^{\prime}=\frac{e^{2}\xi_{1,z}\sqrt{1+S_{12}r}}{32\xi_{1,x}^{2}\sqrt{\epsilon}}.
\]
In the regime of nonlocal fluctuations ($\epsilon\gg1/r+S_{12}$),
out of the GL\ region, the behavior $\sigma_{z}^{\prime}$ becomes
quite peculiar. Essential contributions to the integral in Eq.\
(\ref{lastcond}) occur from two regions of $q_{z}$: \ from
$q_{z}\sim1/\xi_{2,z}$ in arguments of functions $\tilde{\beta}_{2}$
and $\tilde{\beta}^{\prime}_{2}$ (mainly $\pi$-band contribution)
and from $q_{z}\sim\sqrt{\epsilon}/\xi_{1,z}$ (mainly $\sigma$-band
contribution). This corresponds to the ranges $u\sim1/r\epsilon\ll1$
and $u\sim1$ in the reduced integral Eq.\ (\ref{sigma-z}). We
evaluate separately contributions from these ranges, or, what is the
same, from $\pi$- and $\sigma$- bands in the most interesting case
$rS_{12}\gg1$ relevant for MgB$_{2}$.
In the range $u\sim1/r\epsilon$ one can drop $\sigma$-band terms
in Eq.\ (\ref{sigma-z}). As we consider the regime $\epsilon\gg
S_{12}$ we can neglect the term with $\tilde{\beta}$ in
denominator. Dimensionalizing the integral, one can obtain the
following result for this term
\begin{align}
\sigma_{z,\pi}^{\prime} & \approx\frac{e^{2}\xi_{1,z}S_{12}^{2}\sqrt{r}}{32\hbar\xi_{1,x}^{2}\epsilon^{2}} C_{2}(\tilde{\theta}),\label{sigma-zpi}\\
C_{2}(\tilde{\theta}) &
=\int_{0}^{\infty}\frac{4dv}{\pi}v^{2}\left[
\tilde{\beta}^{\prime}_2\left( v^{2}\right) \right]
^{2}.\nonumber
\end{align}
Numerical calculation gives $C_{2}(0)\approx1.185$ and
$C_{2}(0.377)\approx0.235$.
In the range $u\sim1$ the main contribution occurs from the $\sigma$-band
and the terms proportional to $S_{12}$ ($\pi$-band terms) can be treated
as small perturbations. Expansion with respect to these terms leads to the
following result for the paraconductivity contribution\begin{equation}
\sigma_{z,\sigma}^{\prime}\approx\frac{e^{2}\xi_{1,z}}{32\hbar\xi_{1,x}^{2}\sqrt{\epsilon}}\left(
1+\frac{S_{12}}{2\epsilon}I_{z}\right) \label{sigma-zsigma}\end{equation}
with\begin{align*} &
I_{z}=\frac{16}{\pi}\int_{0}^{\infty}du\frac{u^{2}}{\left( 1+u^{2}\right)
^{2}}\left[ \epsilon r\ \tilde{\beta}^{\prime}_{2}-\frac{\tilde{\beta}_{2}}{1+u^{2}}\right] \\
& \approx-\frac{\ln\left( C_3r\epsilon\right)
}{1+\tilde{\theta}\ln\left( C_4r\epsilon u^{2}\right) }.
\end{align*}
with $C_3=16\pi^{-2}\gamma_E\exp(-4)\approx 0.053$ and $C_4\approx 2.9$.
Let us note that in this range of temperatures the contribution from
the $\pi$-band comes with the negative sign, as in the cases of the
heat capacity and in-plane paraconductivity. This means that the
$\pi$-band contribution changes sign with increasing temperature.
Comparing contributions (\ref{sigma-zpi}) and (\ref{sigma-zsigma}),
we find that the $\pi$-band term dominates in the interval of
temperatures $\epsilon<S_{12}\left( rS_{12}\right) ^{1/3}$.
Therefore in the case $rS_{12}\gg1\ $ the $z$ axis
paraconductivity $\sigma_{z}^{\prime}$ has three asymptotic
regimes:
\begin{widetext}
\begin{equation}
\sigma_{z}^{\prime}=\frac{e^{2}\xi_{1,z}}{32\hbar\xi_{1,x}^{2}\sqrt{\epsilon
}}\left\{
\begin{array}
[c]{ll}\left(1+S_{12}r\right)^{1/2},&\text{for } \epsilon \ll 1/r+S_{12}\\
\sqrt{r}S_{12}^{2}C_{2}(\tilde{\theta})/\epsilon^{3/2},&\text{for
} 1/r+S_{12}\ll
\epsilon\ll \frac{\left( rS_{12}\right) ^{4/3}}{r}\\
1-\frac{S_{12}}{2\epsilon}\frac{\ln\left( C_{1}r\epsilon\right)
}{1+\tilde{\theta}\ln\left( C_{1}r\epsilon\right) },&\text{for
}\max[1/r+S_{12}, S_{12}\left( rS_{12}\right) ^{1/3}]\ll\epsilon\ll1
\end{array}
\right. .
\end{equation}
\end{widetext}
In the case $rS_{12}<1\ $ the intermediate asymptotic disappears.
The right panel of Fig.\ \ref{Fig-sigmas} shows the numerically
calculated dependence of $\sigma _{z}^{\prime}\left( \epsilon\right)
$ with parameters specified in the captions. For comparison, we also
show the GL asymptotics and the $\sigma$-band contribution.
\section{Final remarks}
In this paper we have presented a microscopic derivation
generalizing the conventional GL description onto two-band
superconductors. We have further applied the developed approach to
the investigation of the fluctuation phenomena in MgB$_{2}$. The
important feature of our approach is that the derived
\textit{nonlocal} GL functional takes into account not only the
long-wavelength fluctuations (as is the case of the conventional
GL theory), but also the short-wavelength fluctuations, which
enables to significantly extend the range of validity of the GL
technique. This approach not only permits the study of the
thermodynamic characteristics of the superconductors, but provides
a convenient technique for calculation of transport coefficients.
It is necessary to underline that we succeeded to solve
analytically the problem of accounting for short-wavelength
fluctuations due to the specific for our model large difference in
the intra-band diffusion coefficients $D_\alpha$. Fortunately,
this assumption corresponds to the practically interesting case of
magnesium diboride.
One can see that the main qualitative effect that determines the
unusual behavior of fluctuations in the anisotropic two-band model
consists in globalization of superconductivity in the immediate
vicinity of transition temperature ($\epsilon \ll 1/r+S_{12}$). It
occurs due to the possibility for electrons of both bands to
participate in fluctuation pairing and to exchange of fluctuation
pairs between them. Formally, this process manifests itself in
the appearance of long range superconducting correlations on the
scale $\widetilde{\xi}_{z}\gg \xi_{1,z}$.
Turning the role of fluctuations in MgB$_{2}$, we refer to the
formulas for paraconductivity in a one-band 3D anisotropic
superconductor \cite{LV02}:
\begin{equation}
\sigma_{x}^{\prime}=\frac{e^{2}}{32\hbar\sqrt{\epsilon}}\frac{\xi_{x}}{\xi_{y}\xi_{z}},\,\,
\sigma_{z}^{\prime}=\frac{e^{2}}{32\hbar\sqrt{\epsilon}}\frac{\xi_{z}}{\xi_{x}\xi_{y}}.
\end{equation}
We see that the growth of the effective $\widetilde{\xi}_{z}$
results in the noticeable increase of the $z$-axis paraconductivity
in the immediate vicinity of critical temperature ($\epsilon \ll
1/r+S_{12}$) with respect to its high temperature ($\epsilon \geq
S_{12}^{4/3}r^{1/3}$) extrapolation based only on the $\sigma$-band
fluctuation pairing. The crossover between these two 3D regimes
occurs in the narrow interval of temperatures $1/r+S_{12}\gg\epsilon
\geq S_{12}^{4/3}r^{1/3}$ where the boson degrees of freedom
corresponding to the pairings in $\pi$-band rapidly freeze out,
leading to the fast decrease ($ \sim \epsilon^{-2}$) of $z$-axis
paraconductivity. We want to stress that this temperature dependence
appears due to the noticeable contribution of short-wavelength
fluctuations in this range of temperatures.
In the case of the in-plane component of paraconductivity and the
fluctuation part of heat capacity, the situation is the opposite. The
coherence length $\xi_{z}$ appears in the denominator of the corresponding
expressions, so $\sigma_{x}^{\prime}$ and $C'$ turn out to be suppressed
in the vicinity of transition with respect to their extrapolation formulas
from the high-temperature behavior. Similar situation occurs in the
temperature dependencies of the in-plane upper critical field and of
anisotropy of the upper critical field \cite{GK03a,GK03b}.
The obtained results coincide with that ones of the diagrammatic approach
but the proposed GL description has an advantage of being more physically
transparent, economic, and universal. The fact that the results derived
via the GL equations coincide with those of our microscopic consideration
is a convincing cross-check of the phenomenological description. The same
approach can be used to derive other fluctuation properties such as the
magnetic susceptibility and the field dependencies of conductivity and
magnetization in the vicinity of transition.
\section{Acknowledgements}
This work was supported by the U.S. DOE, Office of Science, under
contract \# W-31-109-ENG-38. A.A.V. acknowledges the support of the
FIRB project of the Italian Ministry of Science and Education.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,282 |
{"url":"http:\/\/mymathforum.com\/linear-algebra\/33137-linear-transformation-kernel-image-bases.html","text":"My Math Forum Linear Transformation, kernel, image, and bases\n\n Linear Algebra Linear Algebra Math Forum\n\n January 12th, 2013, 05:32 AM #1 Senior Member \u00a0 Joined: Jul 2012 Posts: 225 Thanks: 0 Linear Transformation, kernel, image, and bases Hello everyone, I need help with 1 question, I am fairly new to this so please explain your answers in a way that i can understand T is a linear transformation from R3 to R3 that is defined like this: T(x,y,z) = (2x-y+z,x+3z,x-y-2z) 1) Find the Matrix M of the linear transformation by the base [(1,0,0) , (0,1,0) , (0,0,1)] [I think it means I need to find a matrix M so that M*(x,y,z)=T(x,y,z)] 2) Find the matrix N of the linear transformation by the base of [(1,1,0) , (-1,1,0) , (0,0,-1)] 3) Find bases for Ker(T) and Im(T) Please help!\nJanuary 15th, 2013, 02:57 PM \u00a0 #2\nMath Team\n\nJoined: Sep 2007\n\nPosts: 2,409\nThanks: 6\n\nRe: Linear Transformation, kernel, image, and bases\n\nQuote:\n Originally Posted by OriaG Hello everyone, I need help with 1 question, I am fairly new to this so please explain your answers in a way that i can understand T is a linear transformation from R3 to R3 that is defined like this: T(x,y,z) = (2x-y+z,x+3z,x-y-2z) 1) Find the Matrix M of the linear transformation by the base [(1,0,0) , (0,1,0) , (0,0,1)] [I think it means I need to find a matrix M so that M*(x,y,z)=T(x,y,z)] 2) Find the matrix N of the linear transformation by the base of [(1,1,0) , (-1,1,0) , (0,0,-1)] 3) Find bases for Ker(T) and Im(T) Please help!\nSince you are given a problem like this, I assume you are taking a Linear Algebra class! So you should at least know the definitions of all these things.\n\nThink about exactly what you are asked. What you want in both 1) and 2) is 3 by 3 matrix so a matrix of the form\n$\\begin{bmatrix}a & b & c \\\\ d & e & f \\\\ g & h & i\\end{bmatrix}$\nNow look at what you get if you multiply that matrix by the vectors given:\n$\\begin{bmatrix}a=&b=&c \\\\ d=&e=&f \\\\ g=&h=&i\\end{bmatrix}\\begin{bmatrix}1 \\\\ 0 \\\\ 0 \\end{bmatrix}= \\begin{bmatrix}a \\\\ d \\\\ g\\end{bmatrix}$\nSo what does T map (1, 0, 0) to? What must a, d, and g be?\n\nDo the same with (0, 1, 0) and (0, 0, 1)\n\nFor 2) do the same kind of thing what is\n$\\begin{bmatrix}a & b & c \\\\ d & e & f \\\\ g & h & i\\end{bmatrix}\\begin{bmatrix}1 \\\\ 1\\\\ 0\\end{bmatrix}$?\nWhat does T map (1, 1, 0) to? That gives you three equations to solve.\n\nFor 3) can we presume that you know what \"Ker(t)\" means? The Kernel of a linear transformation, T, (also called the \"null space\") is the set of all vectors, v, such that Tv= 0. Here, Tv= T(x,y,z) = (2x-y+z,x+3z,x-y-2z) so v= (x, y, z) is in the kernel if and only if 2x- y+ z= 0, x+ 3z= 0, and x- y- 2z= 0. Solve those three equation. Generally, three equations in three unknown values will have a single solution. Obviously, one solution is x= y= z= 0. If that is not the only solution then these equations are not independent. If two equations are independent and the third dependent on one of those two, you can solve for two of the unknowns in terms of the other two. That is, you might have z= x+ 3y (that is NOT the equation you get here- I just made that up) Then we could write (x, y, z)= (x, y, x+ 3y)= (x, 0, x)+ (0, y, 3y)= x(1, 0, 1)+ y(0, 1, 3) showing that the space is spanned by (1, 0, 1) and (0, 1, 3). Or, if all three equations are dependent- they are all multiples of each other, we can solve for two, say x and y, in terms of the third, say, z. That is, we might get x= 3z, y= -2z (again, those are NOT from this problem- I just made them up) so (x, y, z)= (3z, -2z, z)= z(3, -2, 1) and the space is spanned by the single vector (3, -2, 1).\n\nFor 4) the \"image of T\" (also called the \"range\") is the set of all vectors v such that Tu= v for some u. Here we would be looking for, say, (u, v, w) such that u= 2x- y+ z, v= x+ 3z, w= x- y- 2z and we want to find relationships between u, v, and w not involving x, y, and z. For example, if we Subtract twice the second equation from the first we eliminate x: u- 2v= -y- 5z. If we subtract the third equation from the second we also eliminate x: y+ 5z= u- w. Finally, add those two equations to eliminate y: 2u- 2v- w= 0. Oh, wow, we have eliminated both y and z and have exactly a single equation relating u, v, and w: 2u- 2v- w= 0. From that equation, w= 2u- 2v so that any such vector is of the form <u, v, w>= <u, w, 2u- 2v>= <u, 0, 2u>+ <0, v, -2v>= u<1, 0, 2>+ v<0, 1, -2>.\n\n Tags bases, image, kernel, linear, transformation\n\n,\n\n,\n\n,\n\n,\n\n,\n\n,\n\n,\n\n,\n\n,\n\n,\n\n,\n\n,\n\n,\n\n,\n\n# linear transformation, bases, range and kernel quiz\n\nClick on a term to search for related topics.\n Thread Tools Display Modes Linear Mode\n\n Similar Threads Thread Thread Starter Forum Replies Last Post ricsi046 Linear Algebra 4 December 22nd, 2013 07:20 AM Vasily Linear Algebra 2 September 19th, 2012 12:48 PM tinynerdi Linear Algebra 0 January 31st, 2010 12:48 PM tinynerdi Linear Algebra 1 January 31st, 2010 12:29 PM sansar Linear Algebra 1 April 7th, 2009 10:07 PM\n\n Contact - Home - Forums - Cryptocurrency Forum - Top","date":"2019-08-22 15:19:58","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\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 3, \"\/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\": 0.7752507328987122, \"perplexity\": 952.7032591228599}, \"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\/1566027317274.5\/warc\/CC-MAIN-20190822151657-20190822173657-00438.warc.gz\"}"} | null | null |
Q: Gsuite integration in Laravel PHP Our Client has the gsuite account. They need to do syn the gsuite employees to our application. how we will do it in php laravel ?
A: Package :
"google/apiclient": "^2.0",
"laravel/socialite": "^4.3",
Redirection
$redirectUrl = Config::get('services.google.redirect');
return Socialite::driver('google')->with(["access_type" => "offline", "prompt" => "consent", "redirectUrl" => $redirectUrl])->scopes([Google_Service_Directory::ADMIN_DIRECTORY_USER_READONLY])->redirect();
CallBack Get Employee:
$client = new Google_Client();
$client->setClientId(config('services.google.client_id'));
$client->setClientSecret(config('services.google.client_secret'));
$client->setApplicationName(env('APP_NAME'));
$client->setDeveloperKey(env('GOOGLE_SERVER_KEY'));
$client->setApprovalPrompt("consent");
$client->setAccessType("offline");
$client->setAccessToken($accessToken);
$service = new Google_Service_Directory($client);
$optParams = array(
'customer' => 'my_customer',
'maxResults' =>500,
'orderBy' =>'givenName',
'projection' => 'full',
'showDeleted'=>true,
'sortOrder' => 'descending',
//'query' => 'creationTime=2001-02-15'
// 'query' => 'isAdmin%3Dtrue'
);
if(!empty($pageToken)){
$pageData = array("pageToken" => $pageToken);
$optParams = array_merge($optParams, $pageData);
}
$results = $service->users->listUsers($optParams);
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,921 |
Q: Fill in the gaps between rows using the previous row's values I have a road_insp table:
create table road_insp
(
insp_id int,
road_id int,
insp_date date,
condition number(38,2)
) ;
insert into road_insp (insp_id, road_id, insp_date, condition) values (1,100,to_date('01-APR-04','DD-MON-YY'),.9);
insert into road_insp (insp_id, road_id, insp_date, condition) values (2,100,to_date('01-APR-11','DD-MON-YY'),.7);
insert into road_insp (insp_id, road_id, insp_date, condition) values (3,100,to_date('01-MAR-12','DD-MON-YY'),.7);
insert into road_insp (insp_id, road_id, insp_date, condition) values (4,100,to_date('01-MAR-17','DD-MON-YY'),.6);
insert into road_insp (insp_id, road_id, insp_date, condition) values (5,100,to_date('01-MAR-18','DD-MON-YY'),.6);
insert into road_insp (insp_id, road_id, insp_date, condition) values (6,200,to_date('01-JUN-10','DD-MON-YY'),.4);
insert into road_insp (insp_id, road_id, insp_date, condition) values (7,200,to_date('01-JUN-12','DD-MON-YY'),.3);
commit;
select
insp_id,
road_id,
extract(year from insp_date) as insp_year,
condition as condition
from
road_insp
order by
road_id,
insp_date
;
INSP_ID ROAD_ID INSP_YEAR CONDITION
---------- ---------- ---------- ----------
1 100 2004 .9
2 100 2011 <-gap .7
3 100 2012 .7
4 100 2017 <-gap .6
5 100 2018 .6
6 200 2010 .4
7 200 2012 <-gap .3
I can visualize road condition over time like this (road #100):
However, as noted in red, there are time gaps between the inspections.
Inspections for road #100 are missing for these years:
*
*2005
*2006
*2007
*2008
*2009
*2010
*2013
*2014
*2015
*2016
The gaps exist because not all of the roads in the City are inspected every year. While I wouldn't consider the gaps to be errors in the data, I am concerned that when I visualize the data, the gaps paint a misleading picture. I say this, because, the time intervals between inspections are certainly not constant,
yet when I look at the graph, I'm lead to believe that the time intervals are constant (which is not true).
To compensate for this quirk, I would like to fill in the gaps between inspections using a select query in a view. Using such a view, the data could be visualized like this:
+---------+---------+------------+-----------+
| INSP_ID | ROAD_ID | INSP_DATE | CONDITION |
+---------+---------+------------+-----------+
| 1 | 100 | 2004-04-01 | .9 |
| | 100 | 2005-01-01 | .9 |
| | 100 | 2006-01-01 | .9 |
| | 100 | 2007-01-01 | .9 |
| | 100 | 2008-01-01 | .9 |
| | 100 | 2009-01-01 | .9 |
| | 100 | 2010-01-01 | .9 |
| 2 | 100 | 2011-04-01 | .7 |
| 3 | 100 | 2012-03-01 | .7 |
| | 100 | 2013-01-01 | .7 |
| | 100 | 2014-01-01 | .7 |
| | 100 | 2015-01-01 | .7 |
| | 100 | 2016-01-01 | .7 |
| 4 | 100 | 2017-03-01 | .6 |
| 5 | 100 | 2018-03-01 | .6 |
+---------+---------+------------+-----------+
| 6 | 200 | 2010-06-01 | .4 |
| | 200 | 2011-01-01 | .4 |
| 7 | 200 | 2012-06-01 | .35 |
+---------+---------+------------+-----------+
As you can see, the time intervals are now constant and more intuitive to interpret.
The filler records would be populated like this:
*
*insp_id would be null
*road_id would be the id of the last completed inspection
*insp_date would be January 1st of the applicable year
*condition would be the condition of the last completed inspection
A: with
date_range as (select min(insp_date) mind, max(insp_date) maxd from road_insp),
insp_dates as (select add_months(trunc(mind, 'YYYY'), (level - 1)*12) as insp_date
from date_range connect by level <= extract(year from maxd) - extract(year from mind))
select
ri.insp_id, ri.road_id,
nvl(case when extract(year from ri.insp_date) = extract(year from id.insp_date)
then ri.insp_date else id.insp_date end, ri.insp_date) as insp_date,
ri.condition
from
insp_dates id right join
(select insp_id, road_id, insp_date, condition as condition,
lead(insp_date) over (partition by road_id order by insp_date) as next_insp_date
from road_insp) ri
on id.insp_date >= trunc(ri.insp_date, 'YYYY')
and id.insp_date < trunc(ri.next_insp_date, 'YYYY')
order by insp_id, road_id, insp_date
;
Generate dates between min and max insp_date.
Find the next insp_date for each inspection to have them in 1 row.
Join the generated dates to the original dataset on date ranges based on year, excluding the upper bound, because that is the next inspection with existing data. Outer join, so the last inspection for a road (where next inspection is null) is included as well.
If there is generated insp_date is in the same year as the original data, use the original data, otherwise use the generated insp_date.
INSP_ID ROAD_ID INSP_DATE CONDITION
---------- ---------- ---------- ----------
1 100 2004-04-01 .9
1 100 2005-01-01 .9
1 100 2006-01-01 .9
1 100 2007-01-01 .9
1 100 2008-01-01 .9
1 100 2009-01-01 .9
1 100 2010-01-01 .9
2 100 2011-04-01 .7
3 100 2012-03-01 .7
3 100 2013-01-01 .7
3 100 2014-01-01 .7
3 100 2015-01-01 .7
3 100 2016-01-01 .7
4 100 2017-03-01 .6
5 100 2018-03-01 .6
6 200 2010-06-01 .4
6 200 2011-01-01 .4
7 200 2012-06-01 .3
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,492 |
Q: How to create a process from a coredump? TLDR
I have a coredump which was manually generated rather than as the result of some signal. I would like to execute some function from the executable on a portion of the memory from the original process.
How can I create a process with the same state as the original at the point at which the coredump was taken?
What I've Tried
I tried to dump the particular segment of memory to a file, run the executable again in GDB, and then restore the segment to its original address in the new process, but GDB gives me an error when trying to restore the memory.
$ gdb <program> <core>
> dump binary memory data.bin <start-addr> <end-addr>
> q
$ gdb <program>
> b <addr-at-which-coredump-was-taken>
> r
> restore data.bin binary <start-addr>
Restoring binary file data.bin into memory (<start-addr> to <end-addr>)
warning: restore: memory write failed ((undocumented errno -1)).
I understand that this might be a bug in GDB, and I've googled around to try and find a fix, but I just want this to work, and so I'm reaching out to see if there is an easier way to accomplish what I want to do.
Assume my program has a function like follows, that performs some complex operation on the memory pointed to by its argument...
int do_something(void* data)
{
// Transform the memory pointed to by 'data' in some complex way...
}
...and assuming I was able to successfully restore memory as I tried, above, I would have then tried to execute do_something(<start-addr>) and retrieve the result like so...
$ gdb <program>
...
> b <addr-at-which-coredump-was-taken>
> r
> restore data.bin binary <start-addr>
Restoring binary file data.bin into memory (<start-addr> to <end-addr>)
Success! <-- I wish...
> set $rip = do_something
> set $rdi = <start-addr>
> set $rsp = $rsp - 8
> set {void*}$rsp = <addr-at-which-coredump-was-taken>
> r
> dump binary memory data-transformed.bin <start-addr> <end-addr>
> q
At this point, I would have the transformed data like I wanted.
The reason why I can't just copy the memory to a buffer and write a program that will just call do_something(...) on that buffer, like shown below, is because, in reality, the data argument is a complex structure that contains pointers to separately allocated data, and so the entire structure isn't contained in contiguous memory. Therefore, if I were to take this approach, I would need to iterate through the entire structure, updating the value of pointers as I go, which would be a pain...
extern int do_something(void* data);
unsigned char data[] = { /* contents of data.bin */ };
int main(void)
{
do_something(data);
// Save transformed data somewhere...
return 0;
}
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,419 |
Let Me in Your Life är ett musikalbum av Aretha Franklin lanserat 1974 på Atlantic Records. Albumet innehöll den stora amerikanska och brittiska singelhiten "Until You Come Back to Me (That's What I'm Gonna Do)" och blev ett av hennes bäst säljande 1970-talsalbum. Även hennes insjungningar av "Ain't Nothing Like the Real Thing" och "I'm in Love" nådde placering på amerikanska singellistan. För insjungningen av "Ain't Nothing Like the Real Thing" tilldelades Franklin senare en Grammy i kategorin "Best Female R&B Vocal Performance".
Låtlista
(kompositör inom parentes)
"Let Me in Your Life" (Bill Withers)
"Every Natural Thing" (Eddie Hinton)
"Ain't Nothing Like the Real Thing" (Nickolas Ashford, Valerie Simpson)
"I'm in Love" (Bobby Womack)
"Until You Come Back to Me (That's What I'm Gonna Do)" (Clarence Paul, Stevie Wonder, Morris Broadnax)
"The Masquerade is Over" (Herbert Magidson, Allie Wrubel)
"With Pen in Hand" (Bobby Goldsboro)
"Oh Baby" (Aretha Franklin)
"Eight Days On the Road" (Michael Gayle, Jerry Ragovoy)
"If You Don't Think" (Aretha Franklin)
"A Song for You" (Leon Russell)
Listplaceringar
Billboard 200, USA: #14
RPM, Kanada: #15
Källor
Musikalbum 1974
Album av Aretha Franklin | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,132 |
Books by Fern Michaels:
The Blossom Sisters
Balancing Act
Tuesday's Child
Betrayal
Southern Comfort
To Taste the Wine
Sins of the Flesh
Sins of Omission
Return to Sender
Mr. and Miss Anonymous
Up Close and Personal
Fool Me Once
Picture Perfect
About Face
The Future Scrolls
Kentucky Sunrise
Kentucky Heat
Kentucky Rich
Plain Jane
Charming Lily
What You Wish For
The Guest List
Listen to Your Heart
Celebration
Yesterday
Finders Keepers
Annie's Rainbow
Sara's Song
Vegas Sunrise
Vegas Heat
Vegas Rich
Whitefire
Wish List
Dear Emily
Christmas at Timberwoods
E-Book Exclusives:
Texas Heat
Texas Rich
Texas Fury
Texas Sunrise
Fancy Dancer
The Godmothers Series:
Breaking News
Deadline
Late Edition
Exclusive
The Scoop
The Sisterhood Novels:
Gotcha!
Home Free
Déjà Vu
Cross Roads
Game Over
Deadly Deals
Vanishing Act
Razor Sharp
Under the Radar
Final Justice
Collateral Damage
Fast Track
Hokus Pokus
Hide and Seek
Free Fall
Lethal Justice
Sweet Revenge
The Jury
Vendetta
Payback
Weekend Warriors
Anthologies:
A Winter Wonderland
I'll Be Home for Christmas
Coming Home for Christmas
Making Spirits Bright
Holiday Magic
Snow Angels
Silver Bells
Comfort and Joy
Sugar and Spice
Let It Snow
A Gift of Joy
Five Golden Rings
Deck the Halls
Jingle All the Way
FERN
MICHAELS
The Blossom
Sisters
KENSINGTON PUBLISHING CORP.
http://www.kensingtonbooks.com
All copyrighted material within is Attributor Protected.
Table of Contents
Books by Fern Michaels:
Title Page
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Chapter 17
Chapter 18
Chapter 19
Chapter 20
Chapter 21
Chapter 22
Chapter 23
Epilogue
Teaser chapter
Copyright Page
Chapter 1
GUS HOLLISTER COULDN'T REMEMBER WHEN HE'D BEEN SO tired as he closed and locked the doors of his CPA firm. Well, yes, actually he could remember. It was last year at exactly the same time, April 16, the last day of that year's tax season. Not that it was totally over; he still had tons of stuff to do, extensions to file, but he'd made his deadline, all clients had their records, and he was going home. If only it were to a home-cooked meal and several glasses of good wine. Like that was really going to happen. But he was simply too tired to care whether he ate or not.
Instead of taking the elevator, Gus trudged down the three flights of stairs and out to the small parking lot. Exercise these days was wherever he could find it. He winced at the lemon yellow Volkswagen Beetle that was his transportation for the day. His wife had taken his Porsche, and he was stuck with this tin can. If only he were a contortionist, which he wasn't. Gus clicked the remote and opened the door. After tossing his heavy briefcase on the passenger-side seat, he struggled to get his six-foot-four-inch frame into the small car. He hated this car. Really hated it. He inserted the key in the ignition, then lowered the windows and stared out at the dark night, an anxiousness, which had nothing to do with taxes and the long days and nights he'd been putting in, settling between his shoulders.
For some reason, he didn't think it would be so dark, but then he remembered that they had turned the clocks ahead a few weeks back. Regardless, it wasn't supposed to be dark at eight-thirty at night, was it? But he couldn't bring himself to care about that, either.
He was almost too tired to turn the key in the ignition, so he just sat for a moment, looking out across the small parking lot to the building his grandmother had helped him buy. A really good investment, she'd said, and she was right. He rented out the two top floors to other businessmen, and the rent money he received covered the mortgage and gave him a few hundred dollars toward his cash flow every month. He owed everything he had in life to his feisty grandmother Rose. Everything. And they were estranged at this point in time because of his wife, Elaine. He wanted to cry at the turn his life had taken in the last year. He banged the steering wheel just to vent before he started the Beetle, put it in gear, and roared out of the parking lot at forty miles an hour.
Thirty-five minutes later, Gus untangled himself from the Beetle, a feat requiring extraordinary concentration and agility. Then he danced around, trying to work the kinks out of his body. The Beetle belonged to his wife. She looked good in it. He looked stupid and out of place sitting behind the wheel.
Today, Elaine had been out job hunting, and she wanted to make an impression, so she'd asked him if she could borrow his Porsche. Every bone and nerve in his body had screamed out no, no, no, but in the end, he had handed her the keys. It was just too hard to say no to Elaine, because he loved her so much. Especially when she kissed him so hard he was sure she'd suck the tonsils right out of his throat. When that happened, he could deny her nothing, not even his beloved Porsche.
Elaine had passed the bar exam six months earlier and was looking for gainful employment. Or so she said. For six months now, she'd been looking for a job. Citing the economy, she'd told him that all the law firms wanted were slaves, not a qualified lawyer who had graduated at the top of her class. That was the reason she hadn't been hired. Or so she said. She hadn't even been called back for a second interview by any of the firms. Or so she said.
Sometimes he doubted her and instantly hated himself for his uncharitable thoughts, thoughts that had been coming more and more frequently of late. His gut was telling him that something was wrong; he just couldn't put his finger on what that something was.
Gus reached across the seat for his briefcase, then closed and locked the Beetle. God, I'm tired. No one in the whole world could or would be happier than he when today, April 16, turned into tomorrow, April 17. He was a CPA, a damned good one if he did say so himself, and he had been working round the clock since January 1 to meet his clients' needs. He'd made a lot of them happy and a few of them sad when he pointed to the bottom line that said, REFUND or PAY THIS AMOUNT!
Gus walked across the driveway, wondering where Elaine was. It was nine fifty-five, and she wasn't home. The jittery feeling between his shoulder blades kicked in again when he saw no sign of his car. He frowned as he walked toward the back entrance of his house, the house his grandmother had bought for him. It was a beautiful four-thousand-square-foot Tudor. He shivered when he thought about what she would say when she found out he'd added Elaine's name to the deed in one of those tonsil-kissing moments. For months, he'd been trying to find the courage—no, the guts—to tell his grandmother what he'd done. He knew she'd go ballistic, as would his two aunts. None of them liked Elaine. No, that wasn't right, either. They hated Elaine; they could not stand her. And Elaine hated them right back.
Elaine said his grandmother and the aunts were jealous of her because she was young and beautiful and had stolen his love away from them. He'd never quite been able to wrap his mind around that, but back then, if Elaine said it, he tended to believe it. With very few reservations. His grandmother and the aunts had been a little more blunt and succinct, saying straight out that Elaine was a gold digger. End of discussion.
The strain between him and his beloved zany grandmother and dippy aunts bothered him. He had hated having to meet them on the sly, then keeping the meeting secret so he wouldn't have to fight with Elaine and suffer through weeks of tortured silence with no tonsil kissing and absolutely no sex. Elaine held a grudge like no one he knew.
He owed everything to his grandmother. She'd raised him, sent him to college, financed his own CPA firm, then helped him again by buying him the beautiful house that he now lived in. With Elaine. And no prenup.
His grandmother had never once asked him even to consider paying her back, even when he'd tried.
He loved her, he really did, and he hated the situation he was in. Tomorrow or the day after, regardless of how it turned out, he was going to have a come-to-Jesus meeting with his wife and lay down some new rules. Family was family, and it was time that Elaine realized that.
Gus opened the gate to the yard, and Wilson came running to him. Wilson was the one thing he'd put his foot down on. Elaine said dogs made her itch and sneeze. Well, too bad; Wilson was his dog, and that was that.
"What are you doing out here, boy?" Gus tussled with the German shepherd a moment before walking up the steps to the deck, which was located off the kitchen. The low-wattage back light was on. He didn't need Wilson's shrill barking to alert him to the pile of suitcases and duffel bags sitting outside the kitchen door. His suitcases. Six of them. And two duffel bags. All lined up like soldiers. Next to the suitcases was a pink laundry basket with Wilson's blanket and toys. He knew even before he put the key in the lock that the door wouldn't open.
"Son of a bitch!" He looked at the hundred-pound dog, who was barking his head off and dancing around the pink laundry basket. The jittery feeling between his shoulder blades had grown into a full-blown, mind-bending pain.
The words gold digger flitted through Gus's mind as he tried to peer in through the kitchen window. The only thing he could see was the faint greenish light coming from the digital clock on the microwave oven. So much for that glass of wine, never mind a home-cooked meal.
"You shoulda called me, Wilson," Gus snarled at the dog. As though what he said was even possible. The big dog barked angrily, as if to say, What do you think I'm doing out here?
"Let's check the front door." Wilson nudged Gus's leg, then slammed himself against the door. The envelope stuck between the door and the jamb fell to the floor of the deck. The dog backed up and sat on his haunches. "Aha!" Gus said dramatically as he ripped at the envelope. He held up a single sheet of computer paper toward the light.
Gus,
I'm sorry, but this just isn't working for me. I don't want to be married anymore. I'm going to file for divorce. I packed all your things, and they're on the deck, along with your dog. As you can see, I had the locks changed. I don't want to see you anymore, so don't come here, or I will file a restraining order against you. I'm keeping the Porsche to show you I mean business.
The signature was a scrawled large E.
"Son of a bitch!" Wilson howled at the tone of his master's voice. "And she's keeping my car! My pride and joy! Next to you, that is, Wilson," he added hastily. "How the hell am I supposed to take all my stuff in that tin can she calls a car? I damned well do not believe this!"
Wilson's shrill barking told Gus that he had damned well better believe it.
Gus sat down on the top step and put his arm around the big dog. His wife didn't want to be married to him anymore. But she wanted his house and his car. Gold digger! So, his grandmother and the aunts had been right all along. His thoughts were all over the map as he tried to figure out exactly how and when it had all gone wrong. There must have been signs. Signs that he'd ignored. How far back? The start of tax season? Before? October, maybe?
Elaine had been looking for a job for over six months, so that would take it back to October. What happened at that time? He racked his brain. Elaine had wanted to go on a cruise, but he'd been too busy to go. She'd pouted for two whole weeks and only gave up when he bought her a diamond bracelet. November was a disaster, and they'd eaten out at Thanksgiving because all Elaine knew how to cook was eggs and pasta. He'd wanted to go to his grandmother's, but she had refused, so he hadn't gone, either. A real man would have gone.
Then came Christmas. Elaine said Christmas trees made her sneeze and itch the way Wilson did. So, no Christmas tree. He'd had a hard time with that as he remembered how his grandmother and the aunts went all out for the holidays. Elaine had gladly accepted presents, however. Lots and lots of presents, was what she'd said. And jerk that he was, he had complied.
He had mentally kicked himself and lost weeks of sleep because he'd kowtowed to his wife and not gone to see his grandmother and the aunts for Christmas. Now, right this moment, he felt lower than a snake's belly. If possible, he'd felt worse on Christmas Day. Here he was, nearly four months later, and he still hadn't so much as spoken to his grandmother or his aunts. He really did have a lock on stupidity. His shoulders heaved. Wilson was on top of him in a heartbeat. Man's best friend. Damned straight. Right now, his only best friend.
"I'm thinking I need a lawyer, Wilson," Gus said, getting up from the steps. He swiped at his eyes. "Real men don't cry. Bullshit!" he said, swiping at his eyes a second time. Wilson howled his misery as he waited to see what Gus would do.
"Okay, my tail is between my legs, so the only game plan I can see at this point is to pack you up in that tin can, take you to my grandmother's, and beg her to let us stay there until I can get my head on straight. If I'm lucky, maybe she'll lend me that farm van of hers so I can come back to get our stuff. Let's go, boy!"
Wilson ran down the steps and over to the yellow Beetle. He scratched at the door, leaving long gashes in the glossy paint. "Chew the damned tires while you're at it, Wilson!" Gus said as he opened the door. Wilson leaped in and tried to settle himself on the passenger seat, but his legs hung off the seat and actually touched the floor. He barked and howled in outrage.
"It's just for five miles, so relax. We'll be there before you know it."
Wilson threw his head back and let loose with an unholy bark that made the fine hairs on the back of Gus's neck stand on end.
Gus clenched his teeth. "Yeah, you're right, Wilson. We're going to be damned lucky if my grandmother doesn't kick our asses to the curb, and I wouldn't blame her one bit. I've been a real shit. She really pulled the wool over my eyes, Wilson. Meaning Elaine, of course, not my grandmother. I'm even worse than a shit!"
Wilson whimpered.
Ten minutes later, they were at the turnoff to Blossom Farm, which his grandmother had renamed after his grandfather, Brad Hollister, had died, and her sisters, Iris and Violet, had come to live with her. For the sake of simplicity, his grandmother had also taken back her maiden name, Blossom.
"Okay, get ready, Wilson, we're coming to the driveway. Look, this is serious, so pay attention. If it looks like Granny is going to kick my ass off her property, you have to step in and whine. However she feels about me, she loves you. You know what to do, so just do it!"
Wilson whined to show he understood his master's words as he tried to untangle himself from the seat. The moment the car stopped, he was pawing the door to get out.
Inside the old farmhouse, the three residents were gaping out the window. "Rose! It's either that gold digger or Gus! What are they doing here at this time of night? Oh, my God, lock the doors! Is the door locked? Of course it's locked, we always keep the door locked," Violet, Rose's sister, squealed.
"We need to hide," Iris, the third sister, said. "Rose, you can't let him in, even if he is your grandson! We can't let him find out what we're doing."
Rose Blossom peered out into the darkness. It was indeed her grandson and his dog coming up to the front porch. In full panic mode, she crouched next to her two sisters under the front bay window. "He knows we're in here. Something must be wrong," she hissed.
"Who cares?" Violet hissed in return. "If you let him in, we go up in smoke. Is that what you want?"
"Good God, no! We could go out on the porch. I'll just tell him . . . something will come to me," Rose dithered.
"No, something will not come to you, Rose. I say we just hunker down and wait him out. Unless, in one of your stupid moments, you gave Gus a key. Did you, Rose?" Violet snarled.
"He's always had a key, you know that. I don't see him using it. We are, after all, estranged," Rose reminded her sisters. "Anyway, the key won't work because we have a deadbolt inside. All he can do is bang on the door. Let's just stay put and see what he does."
"Why is he driving her car?" Iris hissed.
"Maybe she's dead," Violet whispered.
"You wish. Highly unlikely, or we would have seen the obituary," Rose said.
Violet clapped her hands over her ears when she heard the first bang on the front door. Her sisters did the same. Outside, Wilson howled and barked, the sound loud and shrill enough to set the sisters' teeth on edge.
"My legs are cramping," Iris grumbled.
"Mine, too," Violet added.
"I know you're in there, Granny, so open the door. Wilson needs a drink. I'm sorry! I really am. Please, open the door!"
Winifred, the sisters' basset hound, took that moment to waddle up to the door. She barked, a charming ladylike sound that pretty much said, Welcome.
"Damned dog! Now for sure he knows we're in here," Violet hissed. "I really have to get up now, or I'm going to faint."
"If you're going to faint, do it quietly," Rose shot back.
More banging and more apologies ensued. The sisters turned a deaf ear.
Winifred turned and started to waddle toward the kitchen. "Oh, my God, he's going to the back door. All he has to do is smash the glass, and he can open the door," Iris said, momentarily forgetting all about the cramps in her legs.
"Gus wouldn't do that," Rose said. But her tone of voice indicated that she wasn't sure if what she had said was true or not.
"He's not going to give up," Violet said. "That has to mean the reason he's here at this hour is important, at least to him. Maybe you should just open the door and talk to him through the screen. Tell him you were just getting ready for bed or something. You and he are estranged, Rose. I don't think Gus is here just to make nice. Just open the door and tell him to make an appointment to see you. That way we can, you know, just let him see what we want him to see."
"That sounds like a plan. For God's sake, do it, Rose," Iris said.
"Do I have a choice?"
"No, not really," her sisters said in unison.
Rose heaved a mighty sigh as she made her way through the dark house to the kitchen, her sisters following behind. She didn't even bother to turn on the light when she opened the door. She tried to make her voice as cold and unfriendly as she could when she said, "Please stop banging on my door, Augustus Hollister. Why are you here? What do you want?"
"I need to talk to you, Granny. It's important."
"Well then, young man, I suggest you make an appointment," Violet, the bossiest of the sisters, said coolly. "In case you hadn't noticed, we've retired for the evening."
"It's not that late. You guys are night owls. Look, I need to talk to you; it's important. If it weren't, I wouldn't be here, especially in that yellow sardine can that masquerades as a car." The desperation in Gus's voice was getting to the sisters, but they held their ground.
"Tomorrow afternoon around five-fifteen will work for us. I hesitate to remind you, but you do have a wife. Shouldn't you be discussing your important business with her?" Rose asked defiantly.
"That's why I'm here. She kicked me out, stole my car, and is threatening to get a restraining order against me. I need to borrow your van to bring my luggage here. Elaine packed it up and left it on the deck. She changed the locks on all the doors and said she'd call the police if I went back. Elaine does not want to be married to me any longer. So I need to stay with you until I can find a place of my own."
"You have a place of your own! I know because I bought it for you and put your name on the deed. So now we're good enough for you! What's wrong with this picture, Augustus? You cannot stay here with us; stay at your office if you have to." Rose reached behind her for the keys to the van, which were hanging on a hook. She opened the screen door a crack and dropped the keys on the stoop. "Be sure to bring it back in one piece." Her tone was troubled but not unkind.
"Will you at least let Wilson stay here with you?" Gus pleaded, his voice cracking with emotion.
The sisters looked at one another. Iris and Violet shrugged, which meant, okay, open the door and let Wilson in. Rose opened the door, and Wilson bounded into the kitchen. Rose closed and locked the door, then turned to face her sisters.
"Girls, that was so cruel, what I just did. Gus is my grand-son."
"Need I remind you that he is the grandson who turned on you after all you did for him and chose that gold digger over you?" Iris said.
"He's young, and he was in love. We all make mistakes at some point in our lives. Gus just made his mistake earlier than most people," Rose insisted as she tried to defend her grandson.
"Give it up, Rosie," Violet said, wrapping her distraught sister in her arms. "Let's get Wilson settled and have some cheesecake. We need to talk this over and come up with a plan where Gus is concerned."
"We can't let him in the house, that's the bottom line," Iris said. "Not tonight, not tomorrow, not anytime soon. If we do, it's all over."
"We know all that, so will you please stop reminding us?" Violet grumbled.
Chapter 2
GUS HOLLISTER LITERALLY TOOK THE TURN INTO THE DRIVEWAY of the house he had shared with his wife on two wheels. Wife? Ha! His grandmother and the two aunts were absolutely right, and he was totally wrong. Gold digger was Elaine's new name. It had probably been her name all along, and he had just been too stupid to see it. God, how had this happened? When he'd gotten up this morning to leave for work, Elaine had kissed him with such passion. What a sap he was.
"Well, baby, my eyes are open now, you . . . gold digger!" he snarled as he ran around to the back deck and started to haul his six suitcases down the steps, across the yard, and over to the van. Damn, who knew he had so much stuff? Four trips later, carrying the last duffel bag and dragging Wilson's pink laundry basket, Gus stopped to catch his breath. Sweat dripped from every pore in his body. Talk about being out of shape. He took a moment to wonder if he was going to have a heart attack. If that happened, the gold digger would get all his insurance money. Screw that! First thing tomorrow, he was going to change his will and the beneficiaries on his insurance. He'd leave everything to Wilson. "Bitch!" he seethed.
How did undying love go to deep hatred in sixteen hours? He needed to read up on the rules of gold digging.
Gus settled himself behind the wheel of the rickety van. Rickety my ass, Gus thought when he turned the key in the ignition. The engine purred like a kitten. He frowned when he realized it sounded better than the engine on his beloved Porsche.
Gus sat for a moment, the soft purr of the engine almost lulling him to sleep. He reached across the seat, but Wilson wasn't there. He wanted to cry at what was happening to him. All in the name of love.
The roads are quiet tonight, Gus thought as he steered the cumbersome van down the highway. As if by rote, he finally took the turnoff that led to his office. The thought of lugging his suitcases and the duffel bags up the steps to his office almost made him turn around and leave. Damn, I am tired.
An hour later, all his belongings were stacked up in his office. Wilson's laundry basket remained in the van, to be dropped off at his grandmother's house. It would have to wait until morning. That's when it hit him like a bolt of thunder. He hadn't done his own taxes!
Shit! Shit! Shit!
Gus fired up his computer, tapped furiously, and hit the PRINT button. He filed for an extension. And his gold-digging wife could just file her own damned taxes. No more joint anything where she was concerned.
Gus turned off the computer, ripped off his suit jacket, wadded it into a ball, and lay down on the floor. He was asleep in a nanosecond.
It was dark out when Gus rolled over and groaned. He was disoriented, and then he remembered where he was. He groaned again as he struggled to get up. He peered down at his watch: five-ten. His only option under the circumstances was to head for the Hampton Inn and rent a room. Every muscle in his body screamed as he opened his suitcases and pulled out casual clothes, clothes that were wrinkled and messy. He jammed the clothes and his toiletries into a duffel and left the building. He'd given all his employees the rest of the week off in appreciation of all their hard work during tax season, so he had no worries about his staff seeing the disarray in his office.
As he was making his way down the stairs, Gus made a mental note to call a locksmith to change all the locks on the office building. It was going to be a pain in the butt, but there was no way he wanted his gold-digging wife to have access to the building.
Since it was just the beginning of the early morning rush-hour traffic, Gus made good time to the Hampton Inn. The drive over, registering, and trekking to his room took all of twenty minutes before he was headed for the shower in his new home away from home. He used up another twenty minutes showering, shaving, and dressing before he headed downstairs to order breakfast. He was starving, which surprised him. How can I eat like this with a broken heart? He amazed himself at how he wolfed down three eggs, two rashers of bacon, six pancakes, and a dish of fresh fruit. By the time he ordered his second cup of coffee, he felt almost normal.
Gus's thoughts were all over the map as he sipped at his coffee. He had shifted mental gears so many times, he was forced to pull a pen out of his jacket pocket along with the little notebook he always carried. More often than not, he never scribbled anything in the little spiral book. But, for some reason, it was comforting to carry it. Within minutes, he had a long list of things he had to do. He scribbled the word immediate in capital letters. First, though, he had to go out to the farm and drop off Wilson's gear. Then he had to sit down and have a talk with his grandmother and the two aunts. He felt a lump the size of a lemon lodge itself in his throat. He had to make things right with the three of them, no matter what.
Gus called himself every name in the book as he contemplated his list. He loved those old gals more than life itself. Then he turned on himself, and he was back to square one. If they refused to listen to him, to forgive him, he didn't know what he would do. Dig a hole, crawl in, and wait for his gold-digging wife to toss in the dirt? "Well, that's not going to happen," he muttered to himself as he signed the bill the waitress set in front of him.
It was seven minutes past seven when Gus exited the Hampton Inn and crossed the parking lot to where he had parked his grandmother's van. He climbed in and headed out to the farm.
The Blossom sisters, Rose and the twins—Violet and Iris—stood in the kitchen eating cooked oatmeal with raisins and brown sugar and real cream. The dogs sat at their feet as the women ate, mumbling and muttering among themselves.
Rose, the oldest—Gus's grandmother—waved her spoon in the air. "Augustus will be here shortly, I guarantee it." She reached for a strip of crisp bacon and broke it into two pieces. She handed one piece to each of the dogs.
Violet, two minutes older than her twin, Iris, said, "We agreed that we weren't going to let him in. Please tell me you aren't having second thoughts, Rose."
"You aren't, are you, Rose?" Iris hissed.
"No, I am not having second thoughts, but I don't see why he can't at least come into the kitchen. We do need to talk to him; at least, I do. If we don't talk to him, he's going to keep coming around until we do. Do you all want to live in fear of that happening? We won't get anything done. Who knows what he'll see."
"Rose has a point," Violet said. Violet liked to think that she was the voice of reason among the three of them. "I say we allow him into the kitchen, tell it like it is, and send him on his way."
The pessimistic one of the threesome, Iris, looked at her twin and said, "And you think Augustus is going to settle for that? He needs us now. No, that's not right, he wants us, now that his gold-digger wife put the screws to him. Just remember how we all felt at Thanksgiving and Christmas last year. You play, you pay," she said heartlessly.
"Well, that's not very Christian, Iris," Rose said.
"Do I have to remind you that you were inconsolable during those two holidays?" Iris asked in the same heartless tone.
Rose sighed. Her plump body started to tremble as she remembered how distraught she'd been without even a phone call or a card from her grandson during the holidays. "All right, all right! I am hearing you loud and clear. Let's just finish our breakfast and get on with the day."
Violet wasn't about to let up on her sister, knowing sooner or later she'd waffle one way or the other. "Easy for you to say. Do I need to remind you that your grandson has our van? We need the van, Rose. Read my lips. We-need-the-van! Henry will be here at eight-thirty to take the first load to the post office. He does not like to wait, as we all know."
Iris slammed her fist on the table. Both dogs reared up at the sound. "The girls will be coming to work at nine o'clock. Lulu took the golf cart with her when they left yesterday. What are we going to say if Augustus is here when they arrive?"
"Just say we're having an old-lady bingo day," Rose huffed as she dumped the rest of her oatmeal down the garbage disposal.
Wilson raced to the kitchen door, Winnie hot on his heels. Both dogs barked.
"I think your grandson has arrived." Violet sniffed as she, too, disposed of her uneaten cereal at the sink. Unlike her sisters, Iris finished her cereal before proceeding to load the dishwasher. "Shall I make another pot of coffee?"
"Don't bother, Iris. Augustus won't be here long enough to drink it," Violet said. "Right, big sister?"
Rose wanted to cry, but she bit down on her lower lip. "Let's just hear him out. Then we'll send him on his way. We don't want to have any regrets later on, do we?"
Gus knocked on the kitchen door. Rose opened it. She had to fight with herself not to reach out to hug her grandson. "Come in, Augustus. We have fifteen minutes to talk, then we're expecting some friends. Please be quick."
Gus stepped into the old familiar kitchen. He noticed that it had been upgraded at some point. He should have known that, but he didn't. Everything was bright and cheery, with spanking-new, state-of-the-art appliances. He marveled at the built-in coffee machine.
"Coffee?"
"No, we don't drink coffee; we drink herbal tea. It's supposed to be good for old people's digestion. With lemon," Violet said, frost dripping off her words.
"Okay, I'll take that," Gus said, sitting down at the table.
"We're fresh out. Today is grocery-shopping day," Iris said.
Gus shrugged. He could see the three of them weren't going to give an inch. "I brought the van back. Here are the keys. Thanks for the loan," Gus said, sliding the keys across the table to where his grandmother was sitting. "The van sure runs nice."
"We had it tuned up recently," Rose said flatly.
Gus stared at the unfriendly faces of the three sisters glaring at him. Once, those same faces had been full of love. For him. Once. He cleared his throat and folded his hands. "I . . . I want to tell you that I love you all. My love has never wavered. I got derailed and . . . and I'm sorry. I don't expect you to believe me, but I had this plan that I was going to make our situation better this week, regardless of what Elaine said. I just needed to get through yesterday. I know I hurt you, but that was never my intention. I was so . . . so blinded, I just couldn't see straight. Elaine became my world, twenty-four/seven. She was my siren, and, unlike Odysseus, I didn't have any protection against hearing her song.
"I can't unring the bell. I would if I could, you know that. If you want me to get down on my knees, I will. All I can say is I'm sorry. And, I have a confession to make as well, and when I do, I know full well that you are going to boot my ass out of here. But I'm going to tell you anyway."
"Then maybe you shouldn't tell us. Maybe you should just leave before we do boot your ass out of here," Violet snapped.
Before anyone could say anything else, Gus blurted out that he'd put Elaine's name on the deed to his house.
The three women rose from the table as one and leaned across until their faces were inches from Gus's.
"You did WHAT?" the sisters said in unison.
"She . . . she had this . . . this way of kissing me that . . . it was like I had no will of my own. I just did it."
"This is just too pitiful to listen to," Iris said. "I cannot believe you turned into such a wuss. I can't deal with stupid; I'm leaving."
"I don't expect you to understand; you're old," Gus said.
The Blossom sisters were on him then like fleas on a dog, pummeling Gus as they attempted to yank him from his chair and push him to the door. All three of them were screeching at the top of their lungs about being old, working their fingers to the bone so he could have a good life, and how they knew what sex was all about because they'd had some of the best sex in the universe during their earlier years. It was Rose's voice that drowned out everyone else's. "And you gave it away to that . . . that person! Shame on you, Augustus Hollister! Now leave my house!"
"I will not leave this house until . . . until . . . Okay, I'm going." Tears burning his eyes, Gus got up from the table and headed for the kitchen door. He turned around and said, "Will you at least keep Wilson until I can find a place that will accept dogs?" His eyes were wet and burning so badly, he could barely see.
"Yes," Rose said. "Did you bring his things?"
"I did. I put them by the back door. I'll get them. Granny, I'm sorry, really sorry. I don't know what else to say. If you need me for anything, you can reach me at the office or call me on my cell phone. If you still have the number."
"Don't you have that all a little backward, nephew?" Iris said. "Why would we need you? You're here. That means, as usual, you need us. Does it look to you like we need you? Not from where I'm standing, it doesn't. Do we need him, girls? Tell us, what's wrong with this picture?"
Gus struggled to find his voice. Why in the damned hell had he thought his family would welcome him with open arms and make his world right side up again? Why? Because they had always done it before. They were his cushion, his buffer, his safety net. In a million years, he never thought they would turn their backs on him. The realization that they had just kicked him to the curb hit home like a freight train running over him at a hundred miles an hour.
Gus opened the door and picked up the pink laundry basket. He set it inside on the floor near the door. He waited a moment to see if Wilson would attack the basket. He didn't. The shepherd stayed where he was, with Winnie, on the little rag carpet by the sink. That hurt almost as much as his aunts' and grandmother's unbending attitude. "See ya," he said in a strangled voice as he closed the door.
Rose sat down at the table and buried her face in her arms. The twins rushed to console her. Their voices were soothing as they tried to ease their sister's anguish. "We have options, Rose, if we want to pursue them," Iris whispered.
"No, we don't have options, Iris. It would take us months to relocate. It simply is not feasible. Actually, it's impossible. We have a system that works. Remember the last time we deviated, and what happened," Violet said. "It took us almost a year to recover. I, for one, don't want to go through that again, and I'm sure Rose doesn't, either. I suppose it's possible to make some adjustments, but, at this time, I don't see how we can even do that. There are too many people who count on us and are involved now. Rose, look alive here. We need to talk seriously now."
Rose lifted her tear-stained face to stare at her sisters. "Did you see his face? It just about broke my heart. He's just a boy."
"He's not a boy, Rose. Augustus is thirty-two years old. He's a married man. He has to take responsibility for his actions. My conscience is certainly clear. We gave that young man a good life, we raised him properly, we sent him to the best schools, we were there for him every step of the way. We helped him start his own business. You bought and paid for that fancy house he is now going to lose to that gold digger. We did not do anything wrong, so get over whatever guilt you're feeling," Violet continued to rant.
"Maybe we could help him without his knowing we're doing it," Rose said.
"Get that idea right out of your head this very minute, Rose. We are going to go on with our lives, more alert than we've been, and we'll let this play out however it's meant to play out," Iris said softly.
"I don't want to rain on anyone's parade here, but have either one of you given a thought to the wife? What if she files for divorce, which I'm sure is her intent, and her lawyer starts asking questions on her behalf? She'll hire a real sleazebag, we all know that. I'm thinking ahead here. We might need to hire some security or shore up this place. Maybe build a security fence, hire someone with guard dogs to patrol at night, things like that. Before you know it, some smart-ass lawyer will be wanting to take our depositions, then they'll want to see our tax returns. Try explaining those to anyone, Rose," Violet said.
"Oh, for God's sake, Violet, will you give it up already? That's not going to happen."
"It could happen," Iris said. "I saw that same scenario on television last week. We need to move our money offshore. Liechtenstein is where they sent their money on the TV show."
"Stop it right now!" Rose shouted so loud, Wilson barked to show his displeasure. "We are not moving our money to Liechtenstein or anyplace else. Because, we do not know how to do that. We can, however, take it all out of the bank and the brokerage house and bury it in the root cellar if you want."
"That's stupid!" Violet said.
"So is Liechtenstein!" Rose snapped back.
"I hear Henry," Iris said, and ran to the door. Everyone knew that Iris was sweet on Henry. Everyone except Henry, that is.
Chapter 3
GUS HOLLISTER ACCEPTED THE BOX OF NEW KEYS FOR HIS office building from the locksmith. He promised to call if anything went awry. With the rest of his mental to-do list taken care of, he was about to head out of the office. He had no idea where he was going to go or what he was going to do. He slapped at his forehead. He needed to change the code to the security system on the off chance he might have mentioned it to Elaine at some point. No sense in taking chances at this stage of the game. When he was leaving the building, he would turn over the new keys and the new code to his two tenants. Thank God the doors were self-locking.
His last chore taken care of, Gus turned off the lights, took one last look around, and was about to close the door when the office phone rang. He walked back to the reception area and looked at the caller ID. His fist shot high in the air. Barney! His best friend in the whole wide world. Best friend since the age of four, when they had met in a sandbox at the park. Good old Barney. He blasted out a loud hello and waited.
"Hey! How's it going, buddy?"
Instead of answering the question, Gus let loose with a volley of his own. "Where are you? When did you get back? How long are you staying? Can you meet me someplace, Barney? I'm just leaving the office now. I really need to talk to you. The long and short of things . . . never mind, I'll tell you when I see you. Can you make Gilligan's in, say, fifteen minutes? I'll wait for you, all day if necessary."
"That bad, huh?"
"Yeah, that bad, Barney."
"Make it forty-five minutes, and I'm all yours."
Gus stood for a few minutes, staring at the phone console after he disconnected the call. His world was suddenly looking a tad brighter, with Barney back in the picture. Barney, he was sure, would have some words of wisdom for him.
Best friends since the sandbox days, they'd gone through school together. Barney was the nerd, and Gus was the jock. He'd lost count of the jerks he'd popped for tormenting his best friend. They'd gone to the same college, graduated, and gone on to get their master's degrees together, after which Barney took off in the financial world and set it on fire. At age thirty-two, Barney was the youngest hedge-fund manager on Wall Street, and he was worth billions. Not to mention, he had a sterling reputation. No shortcuts for him.
Outside, in the April morning sunshine, Gus looked around. To the east, he saw a bank of dark clouds heading his way. What was it his granny always said? April showers bring May flowers. Yeah, that was it.
His shoulders slumped at the mere thought of his grandmother. Barney was going to have a fit when he found out that Granny Rose wanted nothing to do with Gus. Barney loved Gus's grandmother and dippy aunts as much as Gus did.
Gus went through his contortionist routine as he struggled to get into the Beetle. Barney was going to laugh his ass off when he saw the Bug. Gus winced in pain. Then again, Barney could be diplomatic at times. He might not say a word. Yeah, right.
Gus peeled out of the parking lot—as much as a Beetle could peel—and headed for the main drag of Sycamore Springs, Virginia. Population: eighty thousand. He loved this town. He'd grown up here. Knew every store, every nook and cranny of the town. He knew all the shortcuts, as did Barney, because they'd ridden their bikes all over when they were kids. He was partial, as was Barney, to the old section of town, where the drugstore still had a soda fountain, where the hardware store still set out its wares on nice days, where you could still get penny candy at the Emporium, only it was a nickel now.
Then there was Eva's Café, with her homemade everything. The candy shop, the hat shop, and, of course, the filling station that served lunch to anyone in a hurry. All the shops, he still patronized, as did his grandmother and the aunts.
The new part of town was high tech, with Internet cafés, a Starbucks, it seemed, on every corner, and boutiques. There were trendy eateries and a few high-end bistros for the younger crowd like himself, but he rarely patronized them. Barney didn't frequent them when he was back, either, preferring the comfort of old town. And yet, Barney was as high-tech as they come. Well, that was business. And he was never in town long enough to do much of anything but kick back until it was time to catch a plane to somewhere else. Usually no more than forty-eight hours, barely time to pound a few beers, visit with Granny and the aunts, catch some sleep, and be off again.
Gilligan's was a ramshackle building by design, at least a hundred years old, a family business with the grandkids waiting tables—and doing their homework at the back tables—while aunts and uncles cooked and saw to the customers. Everything was homemade from scratch, all baked goods the envy of every housewife in Sycamore Springs.
Many a husband had been duped over the years, thinking it was his wife who had baked the delectable pastries she served him while, in truth, they came boxed from Gilligan's, the boxes ground into bits in the trash compactor so as not to give away the housewife's little secret.
Gus sighed as he played gymnast again and crawled out of the Beetle. He checked the skies once again. He made a bet with himself that it would be raining in less than an hour. Then the day was going to get even more depressing. He missed Wilson and wondered how the big dog was doing. Probably very well and being spoiled rotten in the bargain. What if his best friend didn't want to come back to him when he finally found a place that would accept an animal? What would he do then? God alone knew the answer. His thoughts turned to his wife, to Elaine, the gold digger. Where in the hell did I go wrong?
Gus realized he wasn't going to find answers standing here in Gilligan's parking lot. Better to go inside and wait for Barney.
When Gus opened the door, he was greeted like a favorite customer and called by name. Even the grandkids doing homework called him Mr. Gus. He often took the time to help the kids with their math. He smiled and waved and was ushered to his favorite table in the back.
Gilligan's wasn't a nautical restaurant by any means. It didn't have any kind of theme or specialty other than home-cooked food and a place that generation after generation took pride in running. There were no celebrity pictures on the walls, but there were plaques from Little League baseball and Pop Warner football, along with pictures of the various teams that Gilligan's sponsored. Hanging from the rafters were green plants that the grandkids watered from stepladders when business slowed down. The tables were rough plank but sanded and polished, the scars of years of use evident. The captain's chairs were oversized, with green-and-white cushions. Gus was thirty-two, and as far as he remembered, the cushions had always been green and white.
There was a counter with stools, where people who popped in for a homemade cinnamon bun and coffee or a slice of pie sat. The tables were for parties of three or more, or two if the restaurant wasn't busy.
Gus loved the smell of Gilligan's because it reminded him of his grandmother's kitchen when he was growing up. It smelled of cinnamon, vanilla, celery, and a touch of garlic. Today there was spaghetti and meatballs, according to the chalkboard, so that accounted for the scent of garlic. The soft garlic twists were every bit as famous as the spaghetti and meatballs. There were never more than two specials on any given day, and today the second special was chicken potpie. He was going to get the spaghetti and meatballs, and he knew that Barney would opt for the potpie. They'd top it off with a big slice of blackberry pie with homemade vanilla ice cream.
One of the grandkids he'd helped with homework carried a large glass of frosty ice tea and set it down in front of him. Gus ordered a second glass for Barney, who came in just as the tea arrived. Gus got up. Manly hugs were followed by ear-to-ear grins, and they were back to the good old days, at least for a few minutes.
"You look like crap, Gus," Barney said as he settled himself in the chair, which just fit his girth. It was then that Gus realized it had been almost a year, and fifteen pounds, since he had last seen Barney. Make that twenty pounds.
"You look a little heavier, Barney," Gus retaliated.
"You're right about that. I have to go on a diet, and I will. Too much rich food. What's your excuse?"
Gus told him.
Barney blinked, then blinked again. "Now, you see, that's why I never got married and will never get married."
"Get off that bullshit, Barney. The reason you won't get married is you don't like to share, you're selfish and materialistic, and no woman will agree to your prenup."
"That, too," Barney said cheerfully. "You should have listened to me about the prenup. Oh, no. You said you were in love, and it was forever and ever and into eternity. What's it been, a little less than a year?" Barney laughed at his own wit. Gus scowled.
"That's got to hurt that she took your Porsche. I know you loved that car. At least she let you keep the dog; that says a lot." Barney laughed again.
"The only reason she let me keep the dog is that Wilson makes her sneeze and itch. Granny has him. She's going to spoil him rotten, and he won't want to come with me when I finally find a place to light that will take animals. I'm staying at the Hampton Inn right now. Granny won't even talk to me. Well, that's not quite true. At first she talked to me through the screen door; then I was allowed into the kitchen. But she won't let me move in. She has all that room at the farm, but I'm definitely persona non grata right now to my family."
"You don't think that extends to me, do you?" Barney asked anxiously. "I was planning on going out to the farm. I brought Granny and the aunts some presents from Paris and wanted to give them to them."
"Nah, they'll let you in. They love you. It's me they hate," Gus said morosely. "Maybe you can plead my case when you go out there. Give Wilson a hug for me. I'm going to spend the afternoon looking for an apartment I can afford. I have to get a lawyer on board pretty quick. Stop looking at me like that, Barney. I know I screwed up, and I take full responsibility. I sure hope she can't come after my business. I busted my ass to build it up, and I don't want her to have any part of it. Damn, I was stupid. Why didn't you warn me or say something?"
Their food arrived. Gus stared down at his plate and couldn't remember ordering. He shrugged as he shook out his napkin.
"I did try to warn you, and you told me to mind my own business. If you recall, I tripped you as I handed you the ring, and told you not to do it. Did you listen to me? No, you did not. I rest my case; my conscience is clear. Having said that, now is the time for you to be in the bosom of your family, but since that isn't going to happen, what are your plans?"
"I'm just glad tax season is over. My head is above water." As he chewed on the delicious meatballs, Gus explained what he'd done about changing the locks, his will, and the insurance policies.
"None of this is computing for me, Gus. Weren't there signs? Did you see them and just ignore them? Something must have triggered this. Was it the last three and a half months of tax season? Did you ignore her? Women don't like to be ignored."
"I was working eighteen hours a day, so, yeah, I guess I ignored her. She was sleeping when I got home, and when I left at five in the morning, she was still sleeping. One does not ever, as in ever, disturb Elaine when she is sleeping.
"But, come to think of it, yesterday, before I left for the office, she kissed me good-bye. I suppose she only got up because I let her have the Porsche for her so-called job hunting. As for the kiss . . . ?"
"So there was no sex in three and a half months?"
"You got that right."
"And you didn't think that was a clue?" Barney gasped.
"I was hoping and dreaming for a spectacular April 17. It was spectacular all right; she booted my ass and my dog out of my house. On top of that, she stole my car!"
Barney wanted to laugh, but he somehow managed not to. "Let's get serious here. Tell me what you know about Elaine. Not the marriage part, but before. Who is she? Where did she come from? What's her background? You're going to need a private detective to get the goods on her in order to have a fighting chance. I know a guy, and when I tell you he is good, he is good. We use him all the time. He can find stuff you would never believe could come to light. I can call him for you and bill it to the firm. No sweat there. And you can use one of our lawyers. I know just the one, too. She is hell on wheels. You need a female lawyer, because she'll know how your wife thinks. She's tops. She's on my payroll, just like the detective, so don't worry about that, either. You can stay at my place as long as you want. I'm leaving for Hong Kong tomorrow and will be gone six months. And you can bring Wilson with you. Built-in maid service, gardener, and you can drive one of my cars. I'm serious, Gus. I can't go off and leave you in the mess you're in. We're friends, remember? You'd do it for me, so just say yes, and let's shake on it."
"Barney . . . I . . . Yeah, okay, thanks. I'll pay you back, you know that."
"Hey, who's the guy who loaned me his last three thousand dollars to start up my own business? I never even paid you back because, jerk that you are, you wouldn't take it. Just so you know, Mr. Smart-Ass, I started a fund for you with some of that three grand, and someday I'm going to tell you what you are really worth financially. And there's no way that person you were married to can ever get near it. Whatever happens with that person, your future is secure, my friend."
Gus's eyes started to burn. All he could do was nod.
The blackberry pie and ice cream arrived, again, without being ordered. Gus ate while Barney sent text messages that went through at the speed of light. He smacked his hands together before he dug his fork into the pie. "They're on it, and you are now officially represented, my friend. Let's finish up here, get all your stuff, and take it out to my house. Then I'm going to go and plead your case with Granny. You okay with that?"
Gus nodded again, not trusting himself to speak. He knew he was in good hands with Barney's people. It still didn't make him feel better.
The bill paid, the two friends left the restaurant. It was starting to drizzle, and the day had turned as gray and gloomy as Gus felt. He looked at the yellow Beetle and groaned.
"I have an idea, Gus. Get in that hunk of junk and drive it to the first fireplug you see and park it. Let the cops tow it and have Miss Elaine fight with the town over it. I think—and this is just a suggestion—but I think you should park it as close to the police station as you can. And, when you get out, wipe off all your fingerprints, just to be on the safe side. It is registered in her name, right?" Gus nodded.
"You won't need it anymore, so that's one less thing on your list to worry about. My detectives will find where your car is, and they'll heist it for you. Since the car is in your name, there is nothing she can do about it. Unless you were dumb enough to put that in her name, too. Were you?"
"No, I didn't put her name on it. But I have to be honest with you, I did think about it; the business, too. She was harping on me about that, last fall, but I just didn't get around to it."
Barney laughed as he climbed behind the wheel of a snappy Mercedes-Benz. "I'll follow you, and, Gus, you're in good hands now."
Two hours later, Barney's car was loaded with all of Gus's belongings. After a forty-minute drive, they set about unloading the car at Barney's place. Gus was never sure what to call Barney's digs. Was it an estate? A minicastle? A palace fit for a king named Barney? Barney said it was just a house to sleep in that happened to have a six-car garage, with a high-end car in each bay. A house that sat on five pristine, manicured acres, which held a tennis court, an Olympic-size swimming pool, a four-bedroom guesthouse, and another building where his live-in housekeeper and gardener resided.
The inside of the palatial house was just as spectacular as the outside, but in a different way. Inside, it was all home and hearth, with comfortable furniture, fireplaces that worked, and a kitchen that would have been any chef's idea of perfection. It was homey, and it smelled like Granny's house. Barney had told Gus once that one of his rules was he always wanted his house to smell like something was cooking or baking, and he had succeeded.
Gus looked over at his pudgy friend—at his owlish glasses, his thinning hair, his kind eyes—and got all choked up. "I don't know what to say, Barney."
"Then don't say anything, okay? You know I hate it when you go all mushy on me. I have an idea. Let's pitch a tent and sleep out tonight. We can make a campfire and roast some weenies and marshmallows. We can tell ghost stories, or you can tell me horror stories of your marriage, whatever pleases you. It will be like old times, but now we're legal to drink beer. What do you say?"
"I say let's do it. Barney, did you ever have anyone kiss you until you thought your tonsils were going to pop out?"
"Yep."
"And you didn't marry her?"
"Nope."
"But why?"
"Well, for one thing, I wanted to keep my tonsils. So I won't get sore throats. You get sore throats once your tonsils are removed. For another thing, when a woman kisses me, I want it to be because she loves me and wants me to be the father of her children."
"Ah."
Chapter 4
GUS ROLLED OVER, UNCERTAIN FOR A MOMENT AS TO WHERE he was, something that it seemed was becoming a habit. He reached out, thinking he was in bed with Elaine, until he felt the stubble on Barney's face. He whooped and sat up, waking Barney.
"What the hell!"
"Bad dream, Barney. Sorry. Damn, it's raining."
"Granny always said April showers bring May flowers," Barney said, sitting up. "I feel like crap. Been awhile since I downed six beers, a bag of marshmallows, and four weenies. Do ya think we're too old for this crap, Gus?"
"Nah! You're never too old for your memories. They just come out different in real life. We never did get around to the ghost stories. That's probably why we feel like shit this morning. We didn't complete the ritual."
"Yeah, well, we aren't ten years old anymore, either," Barney groaned. "Let's pack up the sleeping bags and head on into the house to get cleaned up. Then we can sit down and have a good breakfast. After that, I'm heading out to the farm to see Granny and the aunts. What are you going to do?"
Gus thought about it. What was he going to do? "Guess I'll sit around here and wait for you to get back. Bring Wilson with you, okay?"
"Yeah, sure. You should hang out in my office in case the detective or lawyer fax something over. You need to be on top of everything from here on in. Phil Ross is the detective, and Jillian Jackson is the lawyer. Everyone calls her Jill. You're going to like them both. They're both animal lovers, so that's a plus. Unlike Elaine, who does not like animals. Does she like anyone except herself, do you know?" Barney asked as he rolled up his sleeping bag and stuffed it into a sack, then pulled the drawstring. "We don't have to worry about the tent. Tim will take it down, dry it out, and pack it away."
Gus finished with his sleeping bag and waited until Barney pulled down the zipper of the canvas door. The rain was coming down in sheets. They made a run for the house but got drenched in the process.
"We're wet to the skin. You want to stomp in some puddles before we go in? Fling some mud the way we used to?"
Gus grinned as he kicked off his shoes, which were already soaked, and ran like a crazy man around the yard, Barney whooping and hollering right behind him. Twenty minutes later, they rolled in a huge pile of mud beside a flower bed that one day soon would be sprouting with blooms. They were ten years old again, yelling at each other and pelting mud pies in every direction. Finally, exhausted, they lay down on the grass and let the cool rain clean off the mud.
"I needed to do that, Gus. I really did. I think you did, too. Now we have to go back to being the responsible adults everyone thinks we are."
Gus was the first one up on his feet. He reached down for Barney's hand. "I don't know what I would do without you, Barney. I'm sorry if I don't say it often enough, but I love you. I couldn't love and respect you more if you were a blood brother."
"I feel the same way. The only difference is I have a brother who isn't worth a good spit. Hell, I don't even want anyone to know he's related to me. C'mon, I'll race you to the house!" Barney bellowed.
Gus grinned as he wondered what Barney's millionaire clients would think of him if they could see him now. They'd probably run for the hills or pull out their hair. The visual was so funny to Gus, he burst out laughing. And Barney wouldn't give a good rat's ass. Anyone worried about their tonsils simply wouldn't care. Gus was still laughing when he stripped off the soaking-wet clothes and stepped into a shower with twenty-one jets to pummel his sore body. For sure, he wasn't ten years old anymore.
Wilson leaped up, hopped over Winnie, and raced to the front door. Company!
"Oh, Lord, who is it this time? Don't tell me Augustus has returned," Rose said as she ran after Wilson and Winnie, who had finally woken up long enough to wonder what the commotion was all about. She let loose with two sharp barks to show she was still in the game.
They came from all corners of the house: Iris and Violet from the packing room, Myrt and Gert, Shady Pines star ambulatory residents bounding down the steps, their aprons flapping in the breeze they created. Henry, another resident of Shady Pines—and their driver—stuck his head out of the doorway to the dining room to see what was going on. Six other residents of Shady Pines hung over the upstairs balcony, peering down into the foyer.
"This can't be good," Violet hissed.
"Augustus is sending in his big gun to plead his case," Iris hissed in return.
"We have to let him in," Rose said. "We don't have any other choice. We'll give him fifteen minutes, that's it." Rose then waved her arm to indicate that all the other spectators should disappear.
Rose waited till the house turned silent before she opened the door. She smiled, but it was more like a grimace. The three sisters greeted Barney warmly and headed for the kitchen. That's when Rose remembered the ledger she had been working on. Well, she'd just close it and hope for the best. Wilson and Winnie continued to bark now that a friend had come to visit, a friend who always had treats and was good for a few belly scratches.
Right off the bat, Barney knew he had interrupted something of major importance. The Blossom sisters were nervous and jittery, and it took them a full five minutes before they offered him coffee. Their expressions clearly showed they hoped he wouldn't take them up on the offer. He didn't.
I should have shoved the ledger in the oven to hide it, but Violet is baking two peach pies, Rose thought. Talk about cooking the books, had she done that. She sucked in her breath and said, "It's so nice to see you, Barney. How long are you staying this time?"
"Actually, I'm leaving early this evening for Hong Kong. I'll be there for six months. I just wanted to drop off these presents. French perfume!" Barney said, holding out the shiny black bag he'd brought with him as though it were the Holy Grail.
"Well, that is just so sweet of you, isn't it, girls? We'll be sure to wear it on Sunday when we go to church. Right, girls?" Iris said as she sniffed the expensive perfume. Rose and Violet nodded.
"My pleasure. It looks like I interrupted something," Barney said, eyeing the ledger on the kitchen table. "I won't keep you if you're busy. I just wanted to pop in and say hello." The relief he saw on the women's faces was almost comical.
Rose shrugged. "Household expenses, that kind of thing. I hate to let things go because then I can't remember to make the entries."
"Gus is a CPA, Granny. Why don't you have him take care of that for you?"
"Because . . . well, we started out with an old friend who does our taxes. We can't just take that away from him because of Augustus. It wouldn't be right."
"And Augustus doesn't need to know our business," Violet snapped. "That young man has loyalty issues," she snapped again.
"Whoa! Whoa! Are we talking about my friend Gus, your grandson, Rose, and your nephew, Violet and Iris?" Barney spread his hands wide to show he wasn't buying whatever it was the Blossom sisters were trying to sell him.
"One and the same," Rose said smartly. "We do thank you for bringing us the perfume. I know how busy you must be, since you said you're leaving this evening. You did say that, didn't you?"
Barney knew he was being dismissed, and he didn't like it at all. What the hell is going on here? Suddenly, he felt like he were ten years old again and had just failed his social skills test given by three stern taskmasters. In spite of himself, he shivered, and he didn't like the feeling. Not one little bit.
"We know Gus sent you!" Violet blurted.
"He did not send me. I came here on my own. I come to visit each time I'm in town, and the three of you know it darned well. Whatever your issue is with Gus, it shouldn't have anything to do with me." Barney waited to see if he'd get a slap upside the head. He was so relieved when it didn't happen, he felt weak. "He does know I'm here and asked me to bring Wilson back with me."
Three sets of eyes stared at Barney. "Ask Wilson if he wants to go with you. If he does, he'll drag his basket to the door. If he doesn't, he's staying here," Rose said coldly.
Barney felt like a fool, but he leaned down and said, "Wilson, Gus wants me to take you to him. Get your basket and let's go."
Wilson showed Barney his teeth before he trotted over to the handmade rag carpet by the stove, where Winnie was watching what was going on. He plopped down, showed his teeth again, then barked.
"Guess that's your answer, Barney. Wilson is smart. He knows he was dumped here by Augustus just the way Augustus dumped us."
Barney threw his hands in the air. "You all need to have a meeting to clear the air. Gus loves you three more than anything in life. Can't you cut him a break? He's miserable."
"Young man, tell that to someone who cares. We-do-not-care! You probably should leave now before the three of us pitch a hissy fit. Thank you for the perfume," Violet said.
Iris reached for Barney's arm and escorted him to the front door.
Barney looked around over his shoulder, and was certain eyes were watching his every move. Many eyes. Too many eyes. Unfriendly eyes. Shit!
At the door, Iris opened it and literally shoved him outside. "Thanks for stopping by, Barney. It might be wise to call for an appointment the next time you feel the need to visit."
Bang! The door slammed shut. Barney heard the deadbolt snap into place. He could hear Wilson and Winnie barking their heads off. What the hell is going on inside that house?
If I were a cat, my tail would be between my legs, Barney thought as he pulled up to one of the bays of the garage attached to his house. He pressed the remote, and the door slid upward. Gus was going to be devastated when he saw that Barney didn't have Wilson with him. He'd personally known Wilson since the day Gus got him at the age of six weeks. He considered himself the dog's godfather and had bought him his first collar and leash. Never once had Wilson showed him his teeth. How am I going to explain this to Gus?
Gus practically flew out the door as Barney pulled his car into the garage. He whistled for Wilson, who always came at the sound. When nothing happened, Gus felt his shoulders slump. Even his dog had abandoned him.
Barney lowered the garage door. He stood with his hands on his hips, the rain pelting him for the second time that day. "He showed me his teeth, Gus. He didn't want to come with me. I wasn't about to force him, and those old ladies were in no mood for me today, French perfume or not. I gotta tell you, something is going on out at that farm. And, yeah, you are part of it, but that's not what I'm talking about. Those ladies are up to something. I felt like I was being watched the whole time I was there, and they could not, I repeat, could not, wait for me to leave. They have a hate on for you right now. They said you had no loyalty. I tried to defend you, but they didn't want to hear it. I wouldn't go out there for a while if I were you. Maybe never!" Barney said dramatically as he stomped in a puddle and ruined a second pair of shoes. "C'mon, let's go in and get some fresh coffee. They were baking pies at the farm. Among other things," Barney said through clenched teeth.
"What should I do?" Gus asked as he held the door open for Barney.
"Hope for a miracle, would be my advice. I told you not to marry that gold digger."
"That's what Granny called Elaine. Well, they all did," Gus said as he followed Barney through the house and up the stairs. He, too, had to change his clothes and shoes again.
At the top of the steps, Barney bellowed to Maggie, his housekeeper, to make fresh coffee. Gus hoped she heard from wherever she was, because he was chilled to the bone.
Gus was the first one down to the kitchen. He marveled at the place setting Maggie had laid out. He knew he could get used to being waited on like this in no time. And he liked the roly-poly little housekeeper with the laughing eyes. He wondered if, in the days to come, he'd ever be able to afford a housekeeper. By the time Elaine got through with him, he'd be lucky to eat at Burger King five days a week and starve the other two days. His eyes burned then when he remembered his grandmother telling him that God never gives you more than you can handle. That was easy to tell a little kid who didn't understand that his parents didn't want him because he was a burden. They'd just dumped him at his grandparents' when he was four years old and took off. He'd never heard from them again. God must have been out to lunch that day, because it was more than he could handle, just like now.
Gus was finishing his first cup of coffee when Barney appeared in the kitchen doorway with a pile of papers in hand. "The first report from Phil Ross. It is not pretty, Gus, so be prepared. There's a fax from Jill, too. She's coming out here later this afternoon. I invited her to dinner on your behalf. More casual that way, and you two can get to know one another.
"I'm going to gulp this coffee and head out. I have meetings right up until it's time to head to the airport, so this has to be good-bye for now. Man, I hate leaving you like this, Gus. I really do. But, the good thing is, I'm leaving you in good hands. That much I do know. I'm just a phone call away, and if you really need me, I can be on the first plane home. I mean it, Gus."
Gus nodded, his eyes on the papers lying on the table. He wondered exactly what was not pretty and what he needed to be prepared for. What could be worse than his wife claiming his house and stealing his car? And being mean to Wilson—that was the biggie for him. He looked up at Barney, waiting to see if his friend had more to say. He did.
"Phil said he is going to drop your Porsche off in the parking lot behind Gilligan's, and you can pick it up later, or he can have someone bring it out here. He had to hot-wire it, but he did get your car back. If I were you, I'd drive one of the cars in my garage and park yours in there, at least for now. Elaine still has a key to it, so if you take it into town, and she spots it, then it's gone again. By the way, Phil also said that her Beetle was taken to the impound lot, and she hasn't picked it up yet."
"Damn! He actually got my Porsche back! That's great. Good idea, too, about me not driving it, as long as you don't mind me driving one of yours."
"What's mine is yours, you know that, Gus. So we're good here, right? At least for now. I can go off knowing you're in good hands and not worry too much."
"I don't know what to say, Barney. I just wish there was something I could do for you to repay you. You have everything. What's a guy like me supposed to do?"
"I'll tell you what you're supposed to do. You need to find away to make peace with those old ladies. I don't care if you have to slither on your belly to make it happen, just do it. This whole thing is killing them, Gus. So work on that, and we're square."
The two old friends hugged, both their eyes burning. "See ya when I see ya," Barney said, popping open his umbrella, which was as big as one of those monstrosities one sees at the beach. Gus watched from the kitchen as his best buddy in the whole world approached a large puddle. A very large puddle. He knew before Barney knew that he'd stomp in it. Once a kid, always a kid. He would have done the same thing.
Gus closed the door, poured a third cup of coffee, then sat down at the table to read Phil Ross's report on his wife—soon-to-be ex-wife—Elaine Ramsey Hollister.
The only thing missing was Wilson. God, how he missed the big dog. He felt like crying. He shook his head to clear his thoughts. He knew he had to be alert and in the right frame of mind to read what was written in Phil Ross's report. Knowing it wasn't going to be pretty, according to Barney, before getting started, Gus steeled himself for a very tough read.
Chapter 5
ELAINE RAMSEY HOLLISTER CURLED UP IN THE WINDOW SEAT under the bay window and watched the storm rage outside. She hated storms, but she knew she was safe from the elements. She leaned back and hugged her knees to her chest. Next to her was a notebook and pen. It was one of those black-and-white-marble-covered ones, the kind she'd used back in grade school. She'd found it at one of the dollar stores years ago when she first decided to keep a diary to chronicle her journey to becoming rich. She clearly remembered buying a dozen because they were two for a dollar, and she'd thought that was a real bargain. She was on her last notebook. If she'd written her words smaller, condensed them more, she probably would have several virgin books left, but her childish scrawl was big, and she had felt the need over the years to write everything down.
Elaine flinched when a limb snapped off one of the old sycamore trees. It hit the ground with a loud thump. She peered through the driving rain to see how big the branch was. It looked huge, meaning she'd have to call someone to come and take it away. If she tried to do it herself, she'd ruin her French manicure and possibly pull a muscle in her back. She shrugged. Worst-case scenario, her attorney would require Gus to pay for the removal. She moved on in her thoughts.
Elaine picked up the black-and-white notebook and flipped to the back. She only had four blank pages—eight actually, if you counted the fronts and backs. Not nearly enough pages to continue with the intriguing details of her life saga. She panicked then as she bolted upright and swung her legs off the window seat. Where in this day and age am I going to find these old-fashioned notebooks? They have to be the same as the rest of them. She really hated to admit how superstitious she was, but, despite her cool and calculating personality, she was easily spooked. And she was really spooked now.
Later, she would go on the hunt for the black-and-white notebooks. Maybe eBay or that Web site she'd found a year ago for a company called Initial B Enterprises would have them. She'd really lucked out that day, and she'd been a loyal customer ever since. She'd purchased the company's voodoo kit, purchased an assortment of spells and black candles. She'd utilized their adult sex course, and she'd had more astrology readings than she could remember. She knew she was the company's best customer because they constantly sent her freebies to make sure she came back to order, which she did.
And Gus never knew a thing about it. She kept all her secret doings in a huge suitcase in the attic, someplace Gus never ventured. He had balked, though, when she insisted he install a pull-down ladder, but when she'd kissed him, he capitulated the way he always did. It made it so much easier to be able to cast her spells in the attic, where she was alone with all the paraphernalia she needed. Rituals were time-consuming, spells even more so, but she had become a pro at them. She could probably teach a course on witchcraft if she wanted to.
The only problem was making a payment to Initial B Enterprises. She didn't want to use a credit card or check, so, because she was such a good customer, the kind folks at Initial B Enterprises had agreed to money orders and the use of a post office box number. She used the household money Gus gave her for food and whatever she needed, to buy the money orders. And, from time to time, she helped herself to the bills in Gus's wallet, always careful not to take too much. For a CPA, Gus was pretty stupid when it came to money. But then, she had him wrapped. She corrected her thought: All men were stupid about all things. If they weren't, she wouldn't be where she was now. In the catbird seat, sitting in a half-million-dollar house that was paid for and would be all hers shortly. Not to mention a high-six-figure bank account in the Caymans. As would half of Gus's business, and half if not all of everything in the Hollister coffers. Even his inheritance down the line, when the old battle-axes finally kicked the bucket.
An evil smile on her face, Elaine made her way to the second floor and pulled down the ladder that would take her to the attic, where she would perform one of the daily rituals guaranteed to make her rich beyond her wildest dreams, all thanks to Initial B Enterprises.
Gus Hollister woke with a raging headache. He knew instantly why his head was pounding like a bongo drum. Phil Ross's report on his wife. And his meeting with Jill Jackson and her less-than-encouraging assessment of his current predicament. Then there were the two bottles of wine he'd consumed.
Gus swung his legs over the side of the bed, appalled that he was still wearing the same clothes and shoes he'd worn yesterday. Damn, he must have really been out of it. He hadn't fallen asleep in his clothes since his college days. He wondered if he was on his way to becoming an alcoholic.
That's when he squinted to look out the bedroom window. Shit! It was raining, thundering, and lightning like it was the Fourth of July. He squeezed his eyes shut as he tottered toward the bathroom. Maybe a shower would help, followed by aspirin and coffee. Lots and lots of black coffee. Maybe.
His head pounding like the thunder outside, Gus turned on the water and waited for all the showerheads to bombard his body. He felt like he was participating in a paintball exercise. He hopped and danced around the massive shower as his head continued to pound. He had to get out of here before he exploded. Now!
He obeyed his own instructions and barreled out of the shower. He yanked at a thick, thirsty robe hanging on the shower door and put it on. He toweled his wet head, the hair standing straight up. He tried to smooth it down as he made his way gingerly down the hall to the staircase that would take him to the kitchen, where, hopefully, coffee waited for him.
The first thing he noticed was a place setting at the kitchen table. Obviously, Maggie planned to cook breakfast for him.
Gus looked at the neatly stacked papers that made up the background check on his wife and felt sick to his stomach. If Phil Ross had been standing next to him yesterday when he'd read the report for the first time, he knew without a doubt that he would have pummeled the man into the ground. By the time he'd read it six or seven times and had it committed to memory, he knew he would have pummeled himself into the ground for having been so damned stupid. His head continued to pound.
Maggie entered the kitchen and opened the refrigerator. He shook his head and said, "No breakfast, thank you. Just coffee." Gus looked around the kitchen, but it was neat and tidy, the two wine bottles gone. If ever there was a time for a cigarette, this was it. He'd given up the disgusting habit when he married Elaine, because she said she wasn't sleeping with a chimney stack. But Barney smoked on occasion, usually when he was under the gun on something or other.
Gus rummaged through the kitchen cabinets until he found a pack of Marlboros. He could hardly wait to light the cigarette in his hands. It felt unfamiliar. But at that moment, he didn't give a good rat's ass about the Surgeon General's report or all the horror stories he had read about smoking. This was now, and he needed something to get him through the mess he was wallowing in. And if it was a cigarette or multiple cigarettes, then so be it.
Maggie had disappeared somewhere in the house, leaving him alone in the kitchen. A good thing, Gus decided as he fired up still another cigarette. He was on his third cup of coffee, surprised that it had stayed in his stomach, and on his fourth or fifth cigarette as he tried to come to terms with the stack of papers on the table.
What really got to him, aside from the in-depth report, was the detective's personal note to Barney saying he'd done a background check on the same individual for someone else and, at Barney's insistence, had included it in the report, which he followed up with a current update. The previous client's name was Rose Blossom. His grandmother had hired Phil Ross to check out Elaine before the wedding. Granny had known all along, had tried to tell him, to warn him without actually telling him about the report, and he had pretty much told her to mind her own business. No, not pretty much told her, he had told her to keep her nose out of his love life. Talk about being a total screwup. If they gave an award for biggest chump in the Commonwealth of Virginia, I'd take that prize hands down, he thought. Hell, I'd probably win if the territory expanded to cover everything east of the Mississippi.
How disappointed his grandmother must be in him, deservedly so. I am never going to be able to make this right. Never. Gus massaged his temples, hoping to ease the pounding headache. Why hasn't the aspirin kicked in?
Gus reached over to the counter for his reading glasses. Like he really needed to read this crap again. He'd memorized it, every single word, last night. What he couldn't remember was if it was before the two bottles of wine or after he'd emptied them.
Gus eyed the ugly, hateful dossier on his wife. His stomach crunched itself into a hard knot. Maybe it was better to think about the powerhouse lawyer Barney had presented him with, Jill Jackson. He hadn't been impressed at first. Nor had he been impressed midway through dinner. It wasn't until the end of dinner, when he'd started to really listen to her and look at her. He'd always gone for the flash when it came to women, much to his own detriment. He liked eye candy, he really did. He liked it when other guys looked at him with envy, which didn't say a whole heck of a lot for him. Hell, it didn't say anything about him other than that he was nuts. What good was a pretty package if the contents were downright ugly?
Right up front, the minute he'd shaken hands with Jill Jackson, Gus knew she despised him and the situation he was in. He'd cringed at the look in her eyes, which said he was worse than gum on the bottom of her shoe. To his credit, he'd done nothing to change her opinion of him. Probably because, if he was honest with himself, it was that Jill Jackson was not a looker, not even close to eye candy.
Gus drank more coffee, fired up another cigarette, and blew a perfect smoke ring as he let his mind wander back to the meeting with his brand-new attorney. His headache was now a drumlike throb. He tried to ignore it.
Jill Jackson. Short had been his initial assessment. Good things come in small packages. Sometimes. Not this time, though. Then the word squat came to mind. Then another word, fireplug. A short fireplug. Based, of course, on the clothing she wore. Cargo pants with stuff in the pockets, a Harvard sweatshirt that had seen years of wash and wear. Hair skinned back into a tight ponytail. No makeup. Granny glasses.
His spirits had plummeted during dinner, when he realized she wasn't all that great at small talk or conversation in general. He cursed Barney then for hooking him up with such a dud. He remembered her healthy appetite. He'd struggled to keep the conversation going, but he knew that he had failed. Jackson had cleaned her plate and had two helpings of baked Alaska. He'd only picked at his food, preferring the vintage wine, which she had only sipped. And to think she'd been given the task of getting him out of the mess he was in.
What bothered him more than anything was that this plain Jane fireplug hated his guts on sight. You didn't need to be a rocket scientist to see the lack of respect she tried, though not all that hard, to hide. She had spent a lot of time extolling Barney's wonderful qualities, saying how admirable, how smart, how kind and generous he was, and how he would never get himself into a mess like the one you find yourself in, Mr. Hollister. He'd bristled over that zinger, but he'd bitten his tongue, because it was true.
After that, it had been one zinger after another, her mantra being, you need to get over yourself, Mr. Hollister. Twice she'd said, you reap what you sow. And then she really went at it about his grandmother and aunts. She'd told him in no uncertain terms she could never respect anyone who was unkind to old people or animals. She called him pond scum. He had almost leaped across the table to strangle her, but that statement was true, too. Except for Wilson. The only time he'd been unkind to his dog was when Wilson wanted two Pop-Tarts or when he gave him blueberry when he wanted strawberry. Surely that didn't count. Bullshit; she'd send him to the gas chamber, if she could, for the Pop-Tarts.
When they'd finally called it a night, at nine-thirty, his new attorney hadn't bothered to shake his hand. Instead, she'd looked him in the eye and said, "I detest you and people of your ilk. I'm only representing you as a favor to Barney Beezer, whom I happen to adore. You will get the best representation I can possibly give you because of Barney. Just so you know, Mr. Hollister. One last thing. I am in control, not you. If I tell you to jump, you WILL jump. Are we clear on that, Mr. Hollister? And do not ever be presumptuous enough to call me Jill, because if you do, I will cut off your balls and shove them where the sun doesn't shine. Thank you so much for dinner. You also need to stop drinking. I refuse to defend a drunk. If I ever again smell alcohol on your breath, I will tell Barney to get you a new lawyer. Not to mention the word free representation. That alone should tie you in a knot. Now, Mr. Hollister, tell me you understand everything I just said, and we can say good night."
Gus had offered up a sloppy salute. People of your ilk. Now, that really hurt and was a shot below the belt. "Yes, ma'am, I understand everything you just said. And, for the record, I already hate your guts, and I just met you. I think that levels the playing field."
Jill Jackson had laughed. Gus thought it was the most evil sound he'd ever heard in his whole life.
Dammit, why am I thinking about that crazy-ass drill sergeant posing as a lawyer? Because he didn't want to go back to the papers on the table, that's why.
Gus worked at his temples, trying to lessen the drumroll in his head, which was doing its best to match the thunder outside. He couldn't help but wonder if the storm meant impending doom.
How in the hell is that four-eyed, squirrelly fireplug going to get me out of this mess? Maybe I need to call Barney and voice my disappointment in his legal appointee. Yeah, yeah, I really need to call Barney.
Gus pressed in the digits that would connect him with Barney. His BFF answered on the third ring. "Talk to me. Time is money. Bet you're calling to tell me you love Jill. Don't bother. I knew she would be the perfect choice. She hates your guts, right? You hate her even more, right? She told you to stop drinking and also told you that when she says jump, you will jump and not even presume to ask how high, right? Don't even bother trying to thank me, buddy. What are friends for? Just a word of advice, don't take her to the brink, where she will cut off your balls and shove them you know where. It won't be pretty, and it's damned painful in the bargain. Nice talking to you, buddy. Gotta go and make some money."
Gus looked at the phone he was holding and cursed in a whole new language. His head continued to pound. A bolt of lightning ripped across the sky. He shivered. Elaine hated storms and always hid out in the bathroom. Bitch!
Gus took a moment to wonder if he was the most hated man in Sycamore Springs. He wished Wilson were with him. On a whim, knowing full well his grandmother would probably hang up on him, he called. When she answered, he asked how she was, then said he was calling to see how Wilson was and did she have enough Pop-Tarts on hand and reminded her to give him only one and just the strawberry.
"Augustus, I have more than enough Pop-Tarts, and I give him two strawberry just the way you do, or he pouts, then Winnie gets upset. Is there anything else?"
"Just that I love you and the aunts and want to tell you again how sorry I am for what happened."
"You need to tell that to someone who cares," Gus heard Violet shout in the background. Gus ended the call, reached for a cigarette, and lit up again. If he kept this up, he'd use up all of Barney's stash. He made a mental note to replace the cigarettes and quit smoking after today.
Elaine's dossier beckoned him. He really had to deal with it. Or did he? Now that the fireplug was on the case, let her deal with it all. It was making him crazy, however, that it was another woman who was going to get him out of the mess he was in. His grandmother and the aunts had a saying when he or Barney had gotten into trouble when they were kids: Don't think I'm pulling your chestnuts out of the fire.
Gus swallowed hard. When did he turn into such a loser, such a misfit? He answered himself before he bolted for the bathroom off the kitchen.
When he returned to the table and Elaine's dossier, he felt drained and empty. Maybe now, when he read through the papers, he'd absorb it all again, even though he already had it committed to memory. This time he was going to read it out loud to the empty kitchen so he could hear the words and really, really see what a fool he'd been.
Gus squared his shoulders and tossed the remaining cigarettes into the trash. He didn't need a crutch for this. This called for cold-turkey awareness. He took a deep breath, held it as long as he could, then let it out with a loud swoosh as he picked up the first typed piece of paper. This is your life, Gus Hollister.
Chapter 6
A wicked streak of lightning zipping across the sky followed by a loud roll of thunder startled Gus to the point where he dropped the papers he was holding. He shivered, knowing that the loud sound was an omen of some kind. He just knew it. He thought his head was going to spiral right off his neck when he bent down to pick up the papers and put them in order. Just another diversion, so he could postpone reading again about his perfidious wife.
Gus settled his reading glasses more firmly on his nose.
Elaine Sara Ramsey was born in Newark, Delaware, to parents Helen and John Ramsey, twenty-seven years ago on January 3, 1985. Subject resided with parents until the day she turned sixteen, when she left and hitchhiked out of town, according to parents. Parents say they have had no contact with subject since that day.
Subject was a poor student because of lack of home supervision and barely made it from one grade to the next. There are no records to indicate any type of further education. Parents appear to be honest, hardworking people. They said subject was promiscuous starting at the age of thirteen. Father said subject was a bad seed. Mother just cried at interview. Father said subject was a beautiful girl and used her beauty to get what she wanted. Said subject could pass for eighteen at the age of fourteen. He also said she was a liar and a thief, that there was no controlling her, and that they eventually gave up because they had three other children who were good and decent and needed to be cared for, too.
Tracking subject by Social Security number and work history, subject worked many jobs, mostly in the food industry—waitressing, hostessing, or tending bar. Mostly in upscale establishments where she could meet well-to-do men. At the age of nineteen, she married her first husband, Ian Larsen, a young dentist just starting his practice in Richmond and loaded with debt. Before divorcing him, she hung around long enough to use him to meet other white-collar professionals who did have money. Divorce record states that Dr. Larsen took out a loan and paid her $25,000 to get out of his life. When interviewing Dr. Larsen, who is now happily married and has a thriving practice, he said subject was a living nightmare, and refused to discuss details. The only thing he would say was that she pretended to be going to college and had stacks and stacks of books. Once she married him, she refused to work. They were married for fifteen months.
Husband number two was a man named Clayton Mitchell, a stockbroker to whom she had been introduced by one of Dr. Larsen's colleagues. Subject married him fifty-five days after her divorce from Dr. Larsen was final. According to personal interview with Mr. Mitchell, it was anything but a marriage made in heaven. Same MO with this guy—said she was about to graduate, lied to him about her age, lied about everything. Nothing domestic about her. Wanted to dine out every night and meet his wealthy clients. She flirted with them all and hit on some of them. She drove him to the brink of bankruptcy with her outrageous spending.
Things went from subject's being verbally abusive to becoming physically abusive. Mr. Mitchell moved out of their town house to get away from her. She came to his office, threatened him, and made wild scenes. He paid to get rid of her. She got the town house and the mortgage that went with it. She promptly sold it and netted $146,000. He still doesn't know how that happened, because he said the town house wasn't worth anywhere near that much. He, too, is happily married now, lives in New York, and is quite successful on Wall Street. He also said subject pretended to be studying and she said that she would graduate from the University of Virginia the following year. It was, of course, a lie on top of an elaborate charade. They were married for seventeen months.
Subject then married Hugo Hintermyer—a real-estate broker who had aspirations of becoming a real-estate tycoon—three months later, although she had moved in with him two weeks after he sold the Mitchell town house for her. When they married, HH bought her a Mercedes convertible. They lived in what he told her were properties that he owned. Actually, the properties were investment properties belonging to people who were out of the country and never bothered to check on them. HH was conning her in much the same way that she was conning him. This marriage only lasted nine months. Subject kept the Mercedes convertible and HH gave her $78,000, so she wouldn't turn him in to the licensing board. He had to raise the money from friends and by helping himself to several escrow accounts.
Despite what had happened, he said he was sorry to see the last of her because she was so good in bed, even if she was a bitch on wheels. He also said she pretended to be a student and, from time to time, when she wasn't out charging up a storm on his credit cards, she actually looked like she was studying. HH hopes never to see her again.
There are no records to indicate subject has ever personally filed state or federal income taxes, even though she worked and drew a paycheck. (Check last page of this report for the establishments where subject worked.)
Subject did not remarry for three years. She worked, and pretended to go to school; law school, to be precise. Had tons of law books, carried them with her. Sold her Mercedes convertible the second year after the divorce from HH, as she was short of funds. Hooked up at this point with the manager of an Avis rental. She moved in with him and drove the cars on the lot while she went on the prowl to find someone better than the manager, who showered her with gifts and allowed her to use his credit cards. His name was Leroy Denvile. She cleaned out his bank account, took off with one of his rental cars, and left him holding the bag. He said he wanted to marry her, but she told him he had no potential. He was devastated.
This relationship lasted four and a half months.
Two weeks after leaving Mr. Denvile, subject hit on a circuit court judge old enough to be her grandfather. Name was Nathan Perry. People thought subject was his granddaughter. He was a widower. His children became estranged when he married subject. Within three weeks, she had a brand-new Mercedes, candy-apple red; new credit cards; and plenty of cash. They lived in a fancy Tudor home complete with swimming pool and tennis court. They went out every night to dinner. The judge suffered a stroke; he was eighty-two. He died a week later. His children swooped in and swooped her out. One of them just happened to be an FBI agent. They paid her off with a three-hundred-thousand-dollar check, and she signed a ream of paperwork promising never to darken their doorstep again. The judge had been in the process of changing his will but had the stroke before he could sign off. If he had, she would have been set for life. They were married for nine weeks.
Gus rubbed at his eyes. It was all so unbelievable. And he hadn't had a clue. He knew that if his grandmother had handed him this report back then, he would have refused to read it. He felt sick to his stomach. He shuffled the papers in front of him. There was no need to read the rest of them, since they picked up with his meeting Elaine at his health club, where he worked out after work.
For weeks, he had watched her on the equipment. He liked the look of her toned body, her classy workout clothes. He liked that she was serious about her workouts and didn't mess with any of the male members. He liked seeing her leave the gym with her arms full of books and her gym bag. He'd slipped one of the attendants fifty bucks to let him see her application. All he got out of it was that she was single, was going to law school, worked nights as a bartender in a trendy joint in New Town, and drove a bright yellow Beetle. His kind of girl. He'd made it his business to visit the trendy joint two or three times a week, have one beer, then go home. He'd thought at the time that he was being clever, but she told him later that she had his moves down pat. Then she'd laughed at him when he approached her at the health club, saying, "Don't I know you?" The most tired pickup line of all time.
A month later, in June of last year, they were married. But before that happy event, at her insistence, he'd given her a tour of his business, the building he owned—along with the bank—and his paid-off house. They had gone to the farm where his grandmother lived with the two aunts. She didn't like Wilson from the get-go, but she'd given in on the dog when he'd told her he would never ever part with Wilson even if he did make her itch and sneeze. Wilson hated her and stayed out of her way.
Elaine Sara Ramsey Larsen Mitchell Hintermyer Perry Hollister. He wondered how she fit all those names on her driver's license.
Yessireee, he was one damned lovesick puppy back in those days.
Gus shoved the papers back into the manila folder. Now what am I supposed to do? It was still raining, but it wasn't as dark as it had been. The thunder and lightning seemed to have abated, along with his headache. Maybe he should go into the office instead of just sitting around sucking his thumb. If he did that, he could get a jump-start on next week's work. Yeah, yeah, he'd go to the office. The only question was, which one of Barney's cars should he take? Maybe the vintage Jeep Commander.
Leaving from Barney's house meant that the usual ten-minute drive to his office now took forty minutes, then another ten to wade across the parking lot to the back entrance of his building. He let himself in, climbed the back steps to his office, and opened the door with his brand-new office key. After he locked the door behind him, he turned on the lights and headed to the mini-kitchen, where he started a pot of coffee. While he waited for it to drip, he checked his e-mails and the voice mail. Two voice mails from his tenant on the top floor asking him to call. He did, and was told a client had come by earlier and said he would be back around noon. No, he didn't leave a name, and the tenant hadn't asked, saying just that the man had said he was a new client. Gus shrugged. He really didn't need any new clients; it was all he could do to provide the ones he had with first-class service. Still, tax season was over, so it wouldn't hurt to see what kind of help the guy needed. Plus, it would be someone to talk to.
Gus scrolled through his e-mails. A few from friends, some forwarded jokes, some political cartoons some nitwit thought he would enjoy, an invitation to speak at next week's chamber of commerce luncheon. He typed OKAY and sent the e-mail off after he marked it in his day planner and copied his secretary/receptionist.
Gus walked back to the kitchen, poured his coffee, and returned to his office, where he decided to read the morning news online. Normally, he read the real newspaper while he had his coffee because he didn't like reading online, just the same way he didn't like reading a book with a Nook or a Kindle. When he realized he had forgotten his reading glasses, he turned off his computer, propped his feet on the desk, and drank his coffee. His headache was totally gone by now, thank God.
He should have stayed home. He tried to shift his mental gears to pleasant thoughts, happier times, but it didn't work. He thought about Wilson and how he missed him. Did he dare risk his grandmother's wrath again by going to get the dog and forcefully taking him from her? He wondered if he had the guts to threaten his granny with the cops if she didn't hand over his dog. That was a no-brainer if ever there was one.
Before he could change his mind, he pulled the desk phone closer and pressed in the digits that would connect him with Blossom Farm. His grandmother answered. He identified himself politely and said he would be there within the hour to pick up Wilson, and to have him ready.
"In that case, Augustus, you will have to take Winnie, also. Wilson won't leave without her, and Winnie will cry, and I cannot stand an unhappy animal."
Gus loved Winnie almost as much as he loved Wilson. "Are you sure about the little lard bucket? She never objected before when you kept Wilson, and we left."
"I'm sure," Rose said curtly. "And stop calling my dog a lard bucket."
"Okay, I don't have a problem taking Winnie. But, Granny, she is fat, and she waddles."
"I'll have them both ready in an hour. Good-bye, Augustus."
Maybe Granny was relenting a tad. She loved Winnie, and for her to let him take her dog had to mean something. Gus felt almost happy as he looked around to see where he'd left his umbrella. He was checking his computer one last time and turning off the lights when the buzzer outside his office sounded. The new client, he supposed. Well, since he didn't have an appointment, he would just have to come back later on or next week. Right now it was more important for him to pick up the dogs. He opened the door, the dripping umbrella in his hand.
The man was a nice-looking guy, a little damp, but he smiled. "Are you Augustus Hollister?"
"I am. Are you the new client? Look, I'm just leaving, and I can't stay right now. Can you come back next week, and we can talk then?"
"I don't think I need to come back as long as you're Augustus Hollister. Here! You have been served, Mr. Hollister."
Son of a bitch! "That's a lousy way to earn a living!" Gus shouted to the process server's retreating back. He winced at the man's laughter. He'd earned his sixty-five bucks first crack of the bat. "New client, my ass!" Once a fool, always a fool. There should be a law about those guys lying just to make $65. He had to hand it to his wife; she worked at the speed of light. Then again, maybe not, if, as he suspected, she'd been planning this for some period of time. Everything could have been drawn up and just waiting for her to kick him out. Out of his own goddamned house. Bitch!
Gus folded the summons and shoved it in his hip pocket. He'd read it when he got back to Barney's house.
Chapter 7
GUS WAS SOAKING WET BY THE TIME HE CLIMBED BEHIND THE wheel of the Jeep Commander. And he'd just ruined another pair of shoes. It was black outside, and lights were on everywhere as far as he could see. What the hell kind of April shower was this, anyway? Like none he'd ever seen. A worm of fear crawled around his belly as he goosed the Jeep through the water in the parking lot and out to the main road. Maybe it was the end of the world. Well, if so, he wanted to be with his granny and have his dog at his side when he went to meet his Maker.
Gus crawled along behind the cautious driver in front of him, the taillights a faint, pinkish color. Since Gus was driving one of Barney's prize cars, he tried to stay a good car length behind the other car in case the driver braked suddenly. Barney did like his toys.
As Gus drove, his eyes straining to see ahead of him, his headache came back. He was too tense; he needed to relax, to take deep breaths—inhale, exhale. He prayed then, something he didn't do on a regular basis even though his granny had taught him to pray. She had taught Barney, too.
Gus did pray sometimes, but more often than not when he wanted something to go his way. I really am a shit of the first order, no doubt about it.
Forty minutes later, Gus turned off the road onto a service road that would take him to Blossom Farm. He was driving through water that was midway up his tires. At the first sign of the post lamps—which were like beacons—that started at the entrance to the farmhouse, Gus knew he was less than a mile from the front door and safety. He crawled along, saying all the prayers he could remember, one after the other. When he finally stopped in front of the house, he had a bad moment wondering if the Jeep Commander would start up when he was ready to leave. Would his granny let him stay until the storm eased off, or would she kick his butt out the door? More than likely, she would let him stay since he would be taking Winnie and Wilson with him. He needed to calm down. He sat quietly, the spring storm raging all about him as he struggled with his breathing. It was hard because he was chilled to the bone.
That's all I need now, to get sick. His wild thoughts took him to a wicked place in his mind, his own funeral, with no one in attendance but Barney and his dog. Maybe Elaine, dancing on his grave while his grandmother and aunts hid behind a tree watching the proceedings. Old people got off on funerals, didn't they? Happy to attend one as long as it wasn't their own. Maybe Barney wouldn't make it home from Hong Kong in time, and they'd keep his body in a freezer until he arrived. Maybe someone would give the order to fry him. Elaine! They were still married, so she could do whatever she wanted with his cold, dead body.
"Enough!" The single word exploded from Gus's mouth like a gunshot. He opened the car door and stepped down into water that was almost up to his knees. He slogged through the water to the steps and raced up like a runner, lightning crackling and thunder booming overhead. He couldn't believe that the power was still on. Maybe that was a miracle. But, if it went out, Granny had a kick-ass generator that would take care of all her needs. He and Barney were the ones who had insisted on the generator, and she hadn't balked at the cost or the installation. He mentally patted himself on the back for that one.
Gus rang the doorbell. Iris opened the door and handed him a towel. He kicked off his shoes and did his best not to drip on the floor. Wilson bounded into the foyer, took one look at him, barked, then rushed him. Gus dropped to his knees and hugged the big dog as he whispered in Wilson's ear. Winnie waddled over to them and managed to wiggle next to Wilson. His happy little family. Gus wanted to bawl at what he was feeling. That little ditty that you never knew what you had until you lost it rang in his ears. Just more confirmation that he was a real shit.
"Come along, Augustus, you need to change your clothes before you catch cold. Violet brought down some of the clothes that you left behind in your old room. You can change in the laundry room. Your grandmother is making you some hot tea."
All Gus could do was say thanks. He was shivering so badly, he could barely make it to the laundry room. He closed the door and looked at the contents of the dryer, which were tumbling around. He could see a pair of his old boxer shorts. He stripped down in record time, goose bumps all over his body. He stopped the dryer and couldn't get into his old clothes quick enough. Then he put the clothes he had been wearing in the dryer and turned it on. Nothing ever felt as good as warm clothes next to his body. Who but his grandmother would think to put his clothes in the dryer for him? His eyes burned. He swiped at them as he made his way out to the kitchen and the hot cup of tea that waited for him. His eyes continued to burn.
As Gus took his seat at the table and saw the huge mug of tea, he knew that if some fairy godmother came along and offered him one wish, his wish would be that he could unring the bell and go back to the day he'd first seen Elaine Ramsey. But that was wishful thinking, and it wasn't going to happen. He cupped his hands around the heavy mug and sipped at the blackberry currant tea that his grandmother loved. He loved it, too. Wilson lay down by his feet, Winnie next to him.
They all made small talk, mostly about the crazy storm raging outside, the flooding that was taking place, and, of course, worry that the power was eventually going to go out. There was no real concern for him on their faces. They were just doing what they perceived to be their duty. He missed their open smiles. He was definitely not out of the woods where they were concerned. Maybe he'd blown it all for good. The thought was so awful, Gus had trouble swallowing the tea. He wanted to say something, something meaningful, but he couldn't find the words. Finally, he blurted out, "I love you all so much, I don't have the words to tell you. I know you're disappointed in me. Hell, I'm disappointed in myself. I know those are just words, and, like you guys have always said from the time I was little, actions count more than words. Can't you see it in your hearts to give me a second chance? Please."
Violet was the first to chirp up. "Well, that is not going to happen anytime soon, young man."
"You can't just trample on a person's feelings, flip them the bird, then expect to waltz back into their lives when you get a boo-boo. We are no longer in the lifesaving business," Iris said so coldly, Gus shivered. He thought that was the most he'd ever heard Iris say at one time.
Two down and one to go. Gus looked at his grandmother. "Drink your tea before it gets cold, Augustus, so you can take the dogs and leave us. We have things to do today that we only do on bad-weather days."
They weren't going to give him an inch. Not even half an inch. His eyes still burning, Gus gulped at the tea as instructed. Time to get out of their lives. He finished his tea, stood up, and realized he wasn't wearing shoes or slippers. He did have on socks, a pair knitted at some time in his youth by his grandmother. He looked toward the laundry room, where Violet stood holding his old Bass moccasins. He'd had them since he was a senior in high school. He'd bought them with his own money from his job clerking at the supermarket. They were old, soft, and broken in. He couldn't remember why he hadn't taken them with him when he'd moved out eons ago. Out with the old, in with the new, or something like that, most likely.
Gus shook his head at Violet. "I don't want to ruin them. I'll just take my clothes and shoes. Maybe I can still save the shoes." Violet shrugged as she yanked clothes out of the dryer and stuffed them in a white drawstring trash bag. Trash. Well, he felt like trash. Who in the hell ever thought that these three women, the loves of his life, could turn on him like this? (Probably the same way they wondered how he could cut them out of his life for Elaine.) Certainly not I, he thought to himself. He had a bad moment then, where he just wanted to curl into himself and bawl like a baby, so they would rush to him and hug him, smother him with kisses as they assured him in their gentle, loving voices that they would make it all right for him. He wanted that so bad he could taste it, could feel their warm arms around him, hear the soft words being whispered.
Instead, he heard a noise that shook the house and rattled the windows. He saw the alarm on the older people's faces, heard shrieks and howls coming from all parts of the house. The kitchen door leading into the dining room burst open. He saw a sea of white hair as senior citizens came on the run, their voices fearful. What the hell was going on?
His grandmother sighed mightily, looked around, and said, "I think lightning hit the old sycamore out by the front porch, and it hit the ground or the verandah."
Gus looked around in a daze. "Who are all these people?" he finally managed to ask.
Violet ran to the front of the house and was back in a minute. "You were right, Rose, it was the old sycamore. It's gone. The good news is we'll have firewood for the next ten years once we get Mr. Younger to come and split it for us. Oh, the left side of the verandah is gone. We'll need to use the back door until we can get it repaired."
"Who are these people?" Gus asked again, pointing to the group of chattering seniors with white hair who had barreled into the kitchen from all directions in the house.
"Not that it's any of your business, young fella, but we work here," Oscar said, his dentures clicking as he tried not to lose them in his excitement.
"Doing what?" Gus demanded.
"Don't concern yourself with our friends, Augustus. Just take the dogs and go, so we can do what we have to do," Rose Blossom said. "By that, I mean putting in calls to people to get the best price on repairs, and, of course, the insurance company. We need to be first because I'm sure other people will have damages, too, and we don't like to wait. As you know, I like keeping the house in tip-top shape."
"And that would be what, exactly?" Gus demanded again. He threw his hands in the air. "You know what?" He sat down and planted his feet firmly on the floor. "I'm not going anywhere until someone tells me what the hell is going on here. Like, NOW!" he bellowed at the top of his lungs.
Suddenly it was bedlam, a Chinese fire drill gone bad as the little group that wasn't so little anymore started to chatter and grumble. Gus watched in fear as one old man shook his fist in his direction and called him a young whippersnapper. It took all of Rose's persuasive powers to calm down her little group once she clearly interpreted the look on her grandson's face. Augustus meant exactly what he said. He wasn't going anywhere until he got some answers. She felt defeated, as did her twin sisters, as they all glared at Gus.
"You need to wait right here, Augustus. Wilson, do not let him move. We're going to have a wee meeting in the dining room. If you so much as move a muscle, Augustus, I will personally take the broom to you. Do you understand me?"
"Yes, do you understand your grandmother?" the dude with the loose dentures asked, his voice filled with menace.
"I won't move a muscle," Gus promised. He looked down at his dog, who was taking his orders seriously. Wilson sat up on his haunches, his ears straight up, the fur on the nape of his neck as straight up as his ears. Winnie growled so loud, Gus itched at the sound.
Gus watched as the seniors literally pushed against each other in their haste to get to the dining room. He could hear voices, loud and angry, but he couldn't make out the words, and if someone had offered him his weight in gold to go to the door and listen, he would have turned them down. Instead, he looked at Wilson and hissed, "Traitor!" Wilson showed him his teeth. So did Winnie.
"Yeah, well, guess what, Wilson? From now on it's Milk-Bones, and no more Pop-Tarts for you. See how you like that! What the hell kind of guard dog are you? You let those old ladies brainwash you. You did, Wilson! I'm going to have to take you for therapy, and I have too damned much on my plate right now as it is." Wilson showed him his teeth again. Winnie backed him up, but her heart wasn't in it; her tail wagged.
Wilson noticed. He lifted one paw and smacked her on the side of the head. Winnie's tail stopped wagging in midswing.
The moment the dining-room door opened, Gus sucked in his breath. He watched as the seniors filed into the kitchen. They formed a circle around the table and chair where Gus was sitting. He had never in his life felt so intimidated.
Gus let his breath out slowly as his grandmother advanced, looked him in the eye, and said, "Come along, Augustus. It's time to take a walk on the wild side."
Suddenly, Gus didn't want to get up off the chair. He would have stayed glued to it, but Wilson nudged his knee and showed him his teeth for the third time.
Gus didn't know what made him say the words or where they came from, but they shot out of his mouth at the speed of light: "I'm not going to like this, am I?"
"No, nephew, probably not," Violet snapped.
Gus wasn't sure, but he thought the dude with the clicking dentures said, "We should have just killed him. It's not too late, you know. Or we could shackle him to the tractor in the barn if you're all too squeamish. We vote on everything else. Why didn't we vote on that?"
Gus felt his blood run cold when no one responded.
Chapter 8
THE BLACKNESS OUTSIDE THE OLD FARMHOUSE TURNED BLINDING white. And then the earsplitting sound of the lightning striking something close by brought everyone to a standstill. The old house rumbled again as Gus ran to the front door, his grandmother and aunts right behind him. "It hit the old sycamore again!" He could feel the anxiety of the three women as he opened the front door to stare at the destruction in the front yard.
Gus loved that old tree. Once, a long time ago, there had been a fort nestled among its branches, with a sturdy ladder some handyman had built on his grandmother's orders. He and Barney had practically lived in the fort during good weather. His grandmother would bring out food, and they'd hoist it up in a bucket from a pulley that same handyman had installed. He'd fallen out of the tree when he was nine and had his first broken bone, his arm. Five days later, Barney had fallen out and broken his ankle. Both of them wore casts, and they'd played tic-tac-toe on both casts for the six weeks they'd had to wear them. They'd staked claim to the old sycamore that same year and carved their names in it along with the date. Now it was gone. Gus could feel his eyes start to burn. Gone. The way his old life was gone. And the new life he had, just plain old sucked. Big-time.
"There's nothing left to it. Nothing at all," he said sadly. "Do you think when they come to chop it up, you can ask them if they can save the bark where Barney and I carved our names? I'd like to . . . what I mean is . . . never mind. I know you three aren't in the business of doing me any favors. I can't believe it's gone." The lump in Gus's throat was the size of a golf ball, making it hard to swallow.
"We'll ask," his grandmother said curtly. "Close the door, Augustus, the rain is coming in." Gus slammed the door shut and shot the deadbolt.
"We should get on with this," Violet said. "We're losing valuable work hours with this tour."
"Violet is right; let's just do it and get it over with." Rose nodded as she opened the door to what had once been her beloved husband's library. It was a handsome room, with wall-to-wall bookshelves, a massive fieldstone fireplace, and a stunning oriental rug, which seemed to grow more beautiful with the years. Gus remembered sitting in that room and listening to his grandfather read to him. His grandfather had died when Gus was twelve, and he remembered that his mother and father had not even come home for the funeral. It was after that that his aunts had come to live with him and Granny Rose.
The drapes were gone, replaced with shutters, which seemed to throw the room off kilter even though they matched the bookshelves. The books were gone now, packed away in boxes in the attic. The shelves held manila folders, mailing envelopes, files of every color and description. There were boxes with lids on and initials scrawled on the sides for easy identification.
Gus looked around as he tried to understand what he was seeing. His grandfather's antique desk was gone. He and Barney used to hide under it. In its place were long folding tables that held six computers. Another table held four fax machines. A third table held four copiers. A fourth held nine telephones, the old-fashioned landline kind. Gus blinked. His first thought was wild and crazy: Were these ditzy oldsters running a bookie joint? He didn't mean to blurt the words out, but he did. His grandmother looked at him like he'd sprouted a second head. "That's too silly to dignify with a response."
"What is all this?" Gus insisted, waving his arms about.
"Hit it, Iris!" Rose said.
Iris smiled and sat down at one of the computers and clicked away for several seconds. She got up and motioned for Gus to take her seat. "Check it out! Just scroll down, and everything is there." She moved off to stand to the side with her sisters. "I almost wish we smoked, because we could light up now. We don't even have any gum," she whispered as she eyed her nephew, who looked like he'd gotten caught in a horror movie.
"He isn't going to take this very well," Rose whispered to her sisters.
"And do we care about that?" Violet said out the corner of her mouth. Her sisters ignored the comment.
Ten minutes went by, then three more, before Gus swiveled his chair around to stare at his grandmother and the aunts. "It's an impressive Web site. Whoever did it knew what they were doing. What is Initial B Enterprises?"
The three sisters' chests puffed out. "We are Initial B Enterprises—us, and all the people you saw earlier. It's our business," Rose said. "Iris, show Augustus our financial records."
Iris moved to another computer and clicked the keys. "Even you, nephew, should be able to understand this, you being a certified public accountant and all." She got up and waved her arm with a flourish to indicate Gus should take her seat.
The fine hairs on the back of Gus's neck stood on end as he eyed the screen in front of him. The sisters huddled, not taking their eyes off Gus as they waited for his reaction.
When it came, it wasn't what they expected. "Who handles the accounting? Do you have a lawyer? What am I, chopped liver? You didn't trust me to help you? For God's sake, is this even real? Most important, is what you're doing legal?"
Rose sucked in her breath and tried to straighten her round shoulders and stand tall. "You are in no position to ask us any questions, because what we do is none of your business. But because my sisters and I do not want you storming around here trying to ruin our lives, I will respond. Yes, of course it's legal. We have one of the best lawyers in the state working for us. And our accounting firm is top-notch, one you used to lust after but where you couldn't get hired. I don't know if you're chopped liver or not, Augustus. None of us know what you are anymore. We did not want to involve you. You young people are so irresponsible, and you proved us right. And, yes, it's real."
Gus threw his hands in the air. "What is it you do? I mean . . . how did you generate so much money? What exactly are you selling? It was hard . . . this does not make one bit of sense to me. No offense, but you're old ladies. This is . . . who invests your money?"
"Goldman Sachs! And a fine job they've done for us, as you can readily see!" Violet said smartly. "We're all millionaires. You certainly can't quibble with the numbers, now, can you?"
Gus rubbed at his temples. His headache was back.
"And you never told me. Even back before . . . well, before."
"You wouldn't have understood. You were young, full of spit and vinegar. You thought then the way you think now. That because we're old, we should be put out to pasture. We were going to tell you at one point, but then you got yourself involved with that gold digger, and we couldn't take the chance. Can you even imagine what she would do if she knew about all of this? That's why we took you out of our wills," Rose said.
"You took me out of your wills!" Gus yelped in horror.
"Oh, this is just too much. I can't deal with stupid," Violet said as she made her way to the door.
"Wait! Hold on here! I wasn't talking about money. I don't care about that. I thought we were family. You're all I have. If you take me out of your wills, that means I'm practically an orphan. I don't want to be an orphan!" Gus realized how ridiculous he sounded, but he didn't care. "I don't have any parents. You three were my parents. So, are you saying you disowned me and didn't even tell me?" There was such hurt, such outrage in Gus's eyes, the sisters backed up a step.
"Well, maybe you aren't so stupid after all," Violet said, her faded blue eyes sparkling. "We thought of it as a temporary thing that could be corrected at some point in time. We're leaving our money to no-kill animal shelters across the nation, to shelters for battered women, and, of course, to children's agencies."
"That's great. It's your money, you can do whatever you want with it. But couldn't you at least leave me a dollar so I'm in the will?"
"We did leave you ten dollars," Iris said. Gus deflated like a pricked balloon.
"I know this sounds stupid, but does Barney know about all of this?" Gus asked.
"No, not really, but he is the one who got us the people who made up the Web page. He got us the best of the best. Barney never asked why, he just said okay, and his people contacted us. He had the good sense not to ask questions," Rose said.
"We're wasting time," Violet said. "Are we going to give him the tour, or is this it?"
"I want the damned tour," Gus blustered. "I want to know everything about Initial B Enterprises. In case you get arrested and go to jail. I cannot believe what you are doing is legal."
The sisters rolled their eyes, and they all trooped out the door and down the hall. "Well, here we go. This is Door Number One. Enter please, but stand still," Violet said.
Gus thought his eyes were going to pop out of his head. He saw four sewing machines and boxes stacked almost to the ceiling. There was only a small space that could technically be called a path. The lights were on not only because it was dark outside but because cartons had been stacked up against the windows. "What . . . what do you sew in here?" he asked.
"Underwear. We monogram it," Rose said.
"Thongs to be precise," Violet tittered.
Gus turned pink. His thoughts turned to all he'd seen on the Initial B Enterprises Web site. He struggled to work his tongue around the question he needed to ask. "Whose underwear, excuse me, thongs, and what initials are you monogramming? OMG! OMG! You're selling Anna Nicole Smith underwear? And you're monogramming it?"
The sisters crossed their arms over their chests and stared at Gus. "We can see how you would think that, but it isn't true. We are selling Alice Nolan Sanders underwear. She was a resident of Shady Pines until she expired. We're selling it in her memory. A percentage of sales goes to her family. It's not our fault if people assume, and the key word here is assume, that we are selling Anna Nicole Smith underwear. She's dead now, you know, God rest her soul!" Rose said virtuously.
"And you're telling me some dumb-ass lawyer signed off on this?"
"What's not to sign off on? We told him we were selling Alice Nolan Sanders underwear. There's nothing wrong with that."
Gus slapped at his forehead. "Just how the hell old was Alice Nolan Sanders when she . . . expired?"
"I think she was ninety-two," Violet said, "but she died almost twenty years ago. We didn't start the business until shortly after you and Barney entered high school. And even then it was difficult keeping you and Barney from finding out about it."
"And she wore thong underwear?"
"No, actually, she wore Depends. She wanted to wear a thong, but it wasn't practical," Rose said. "This is one of our biggest sellers. We can't fill the orders fast enough. In fact, it was the first product we ever sold, well before Web sites and the like. Although, when we first started selling them, orders were soft. Then we decided to monogram them, and we couldn't fill the orders fast enough, as you can see by our inventory reports. We had to buy extra machines, but we have a staffing problem. We're looking to expand by recruiting from other assisted-living facilities."
"Expand?" Gus was in a daze as he followed the sisters out of the room.
"Yes, expand." Rose stopped in her tracks and turned around to glare at her grandson. "Where do you think the money came from to raise you, send you to college, buy and pay for the house that is no longer yours, and set you up in business? We don't farm the farm. Your grandfather left just enough insurance to get us through the first few years. And this farm has to be maintained. Well?"
"I don't know, I'm ashamed to say. You never discussed money with me. Never, Granny. Even when I asked, you wouldn't discuss it. I sure as hell never thought you put me through school selling Anna Nicole Smith thong underwear. I'm never going to be able to get that out of my mind."
Violet was heartless. "Easy for you to say after the fact. You'll get over it! Can we just get this show on the road? We're losing valuable work hours."
"Door Number Two. Fortune cookies. We get the fortunes. We bake the cookies, too. But, again, it's a problem keeping up with the demand. We supply all the Chinese restaurants within a twenty-mile radius."
"Well, at least that looks legitimate." The sisters shot Gus a glare that could have melted candle wax.
"Door Number Three. This is our voodoo and spell room. Or witchcraft, if you prefer that word. I think it's self-explanatory. This is very profitable, and we have tons of repeat customers, though we only started this service about five years ago. We craft spells designed to a person's wish. A lot goes into this part of the business. We have a newsletter that goes out once a month. We sell candles, incense, and anointing oils to go with the spells. It's quite lucrative. The referrals are astounding, and we have thousands of repeat customers. Again, a staffing problem. We could be making three times as much money if we had more people to help us," Iris said.
"Door Number Four. This is our astrology room. Big dollars in astrology. We have a newsletter for this, too. Personal horoscopes at a hundred thirty dollars a pop. We have two-hundred-dollar-a-year memberships, and we had to cut it off because we simply can't keep up with the demand. That's another way of saying we know what we're doing," Rose said.
Gus followed the sisters in a daze. He pinched himself to see if he was dreaming. It hurt, so, no, he wasn't dreaming.
"This is Door Number Five, or the parlor. We needed the biggest room in the house for this portion of Initial B Enterprises. We closed off all the pocket doors to keep the room airtight. We have to keep all the vents closed. All we can do for you right now is to open the door a crack so you can see inside. If we open the door all the way, the feathers will start flying, and it is impossible to catch feathers," Violet said.
Gus let his mind go back to the Initial B Enterprises Web page. At the top and at the bottom, there was a duck quacking across the screen. He hadn't thought much about it until this very minute. "You're selling the Aflac Duck's feathers?" he asked in horror. "You could go to jail for that! I'm sure that duck is protected. Oh, my God!"
"Will you stop being so damned dramatic, Augustus. No one said we are selling the Aflac Duck's feathers. You are assuming again. We're selling Audrey's feathers. As you know, we have ducks down in the pond. And we get tons of feathers shipped from Taiwan. Ethel made a dress out of the feathers and put it on our blog, and, yes, we have a blog. Well, that little number sold to a starlet in Hollywood for five thousand dollars. Before you could say feather, we had so many orders we were going crazy. Again, supply and demand, and we don't have enough staff.
"Then, the day we saw on the news that Prince William was going to get married, one of our ladies from Shady Pines said we should start making fascinators. Those are the little feather things ladies in England wear in place of a hat. We got right on it, and we were the Web site from which to order for the nuptials. We cleaned up handsomely on that, and the overseas shipping was almost nil because feathers weigh next to nothing. It almost killed us filling the orders because the feathers from Taiwan are white, as are Audrey's feathers, and we had to spray them different colors. But not only did we persevere, we prevailed. We made a killing on those fascinators."
"Because of the Aflac Duck?"
"The duck just runs across our Web page. We never claimed to be selling his feathers. The insurance company the duck represents has no quarrel with us; we're giving them free Web press, or whatever you call it. We cannot be held accountable for what people presume or assume."
"I think I've seen enough," Gus said.
"Really! We were just getting started. We wanted you to see why you can't stay here," Violet drawled.
"How much more is there?"
"Well, there is the entire upstairs. We have an over-sixty sex hotline, an over-seventy hotline, a newsletter, and an advice column that is beyond active. Then there is the foot room. Old people for some reason get purple feet as they age. We have lotions and creams, all kinds of stuff. Right now, though, we're having a bit of a problem with one of the lotions. Never mind, you wouldn't understand."
"I think I've heard enough. Okay, okay. If your intention was to blow my socks off, you have certainly succeeded. I don't know if I should congratulate you or cry for you. I just don't want you all to get in trouble. Tell me again that this is all legal, and I'll be okay with it."
"Our people tell us we are doing nothing wrong, Augustus. We stand behind all of our products and services. Customers have access to us twenty-four/seven. If a problem crops up, we take care of it immediately. We're giving people what they want, and, at the same time, we're not just sitting around waiting to die. We're busy, and we're active, and we all love what we're doing. Even during the hectic times. Now that you know what we do, are you okay with it?" Rose asked anxiously.
"Well, yes and no, Granny. I'm glad that you're all happy. I'm going to worry, no matter what you say, about the legalities of what you're doing. I won't be able to turn that off. Look, all I want is for us to go back to the way it was. I want you to love me again the way I love you. I screwed up. I'm sorry, but I can't unring that bell. I'm going to try like hell, though. I'd lay down my life for the three of you. I just want you to know that."
And then he started to bawl the way he had when he was six years old. The sisters looked at his miserable face and rushed to wrap him in their arms, tears streaming down their faces.
A good cry was had by all. As if on cue, the sun peaked through the window of the front room.
"I think it's an omen of some kind," Iris sniffled. Violet and Rose agreed. Gus just hung on tight, not wanting to leave the comfort of the warm arms that were wrapped around him.
Finally, Gus was able to say, "What can I do?"
"Are you serious? Do you really want to help?" the sisters asked in unison.
"Damned straight I do. And, no, I do not want your accounting business, but I really need to know one thing for sure. Did you really put me through college selling monogrammed underwear belonging to God only knows who?"
"We did," the sisters said solemnly.
"Well, then, hot damn. I was never first at anything, so I think I can now claim a title of some sort. Not that anyone will ever know, right?"
"Right," the sisters said.
"So, what do you need me to do? I have all kinds of free time now that tax season is over, and I have a lawyer handling my legal affairs. Just spit it out!"
"Recruit for us. Find us people our age who are withering away, old people who have given up and want their lives back, the forgotten ones. Can you do that for us, Augustus? We have a list out in the kitchen, friends of our staff, and, of course, some friends of our own who for one reason or another are living at other living facilities. We hesitated to out-and-out recruit, but if you're serious, we'll give you the list, and you can see what you can do. Next to each person's name is the name of the friend who works here, and you can use that as a recommendation. Are you okay doing that, Augustus?"
Gus couldn't remember the last time the sisters had smiled at him the way they were smiling now. At that precise moment, he would have agreed to anything to keep those smiles on their faces. "I'll give it my best shot or die trying. How many?"
"At least twenty. I think we have only eleven names, but I'm sure that each one of those has a friend whom they themselves can recruit. I guess what I'm saying is, get as many as you can get. And if you want to sweeten the pot, tell them they can relocate to Shady Pines. We run a shuttle service between the Pines and here. Meals are free. Nice clean rooms, a bonus every year. Paid vacation."
"All of that plus a shuttle service! Now, why doesn't that surprise me? Okay, I'm in."
"We thought you'd see it our way, Augustus," Rose said happily.
And he did.
Chapter 9
JILL JACKSON, GUS'S ATTORNEY, LEANED BACK IN HER ERGONOMIC chair and surveyed her domain. It was a beautiful corner office, with two huge bay windows. Barney Beezer had given her carte blanche on the decorating, telling her to order whatever she wanted because he wanted her to be happy and to stay with his company forever. Being an orphan, she'd always been on the frugal side, so she hadn't gone overboard. She'd shopped and bargain-hunted until she found exactly what she wanted, though it had taken her months to get the office to where she was as comfortable in it as she was in her own home.
Barney had been so impressed with her choices, he spent hours in her office when he was in town. He professed to love the buttery-soft camel chairs, the matching sofa nestled in a corner for clients. He said he loved the fish tank, found it so soothing he nodded off a time or two. He'd complimented her endlessly on her green thumb with the two ficus trees, which were full and glossy, and the luxurious ferns she had on matching pedestals. He always kicked off his Brooks Brothers loafers and walked barefoot on the sand-colored carpet. She'd chosen eyeball overhead lighting that bathed the entire room in a soft glow so that clients didn't feel the need to wear sunglasses. Almost against her will, she'd added a small entertainment center along with a minibar and a built-in coffee machine.
She'd brought blankets and pillows from home for the times when she was too tired to make the trek home late at night. All in all, with her own personal bathroom complete with shower and linen closet, she had been more than happy to sign on with Barney Beezer, and she hadn't regretted it even for a second.
Jill turned her chair around to stare out at the magnificent landscaping Barney insisted on. Nestled in the intimate gardens were colorful tables and chairs, where employees took their coffee and lunch breaks or snatched a few minutes to read an actual paper newspaper. She loved it here. Absolutely loved it. What she didn't love at the moment was her new client, Barney's oldest and dearest friend, Gus Hollister. Jill knew in her gut, in her heart, and in her mind that if she screwed up on this case, she would be out the door in a nanosecond. While she didn't like it, she understood the politics of such a friendship.
Everything looked so cleaned and scrubbed now in the bright sunshine. The storm of the century, as the newscasters were calling it, was finally over. It would take at least a week of dry weather before the ground would be dried out enough for her and the other employees to enjoy the garden again. More than likely, she wouldn't really miss the time, because she had a full plate, and that meant eating on the run or at her desk while she saw to business.
Jill swiveled her chair back to the desk. She looked down at her little notepad and interpreted her own squiggles. Appointment in thirty minutes with Lynus Litton, her favorite private investigator. It wasn't that she didn't like Phil Ross; she did like him. As a person. What she didn't like was inheriting other people's staff, and, anyway, Phil had retired and done the report on Hollister's wife as a final favor to Barney. She preferred to work with people she was comfortable with and had trained to her liking. Lynus Litton was such a person.
She'd met Lynus in college, and they had become fast friends because she didn't object to what Lynus called his "gayness." Lynus came from a blue-blooded Ivy League family who couldn't accept his gayness and paid him huge sums of money to stay out of their lives, which he did happily, with his partner of many years, Lewis Lippman.
After college and law school, Lynus further angered his blue-blooded Ivy League family by opening a private security firm. He gave quality service at cheap rates, further annoying his upper-crust family; and then he added insult to injury by having Lewis Lippman, the top pastry chef at a five-star hotel, provide pastries for his clients, which arrived fresh three times a day. Lewis Lippman also came from a blue-blooded Ivy League political family that could not accept his gayness, either. His family, however, chose not to pay him to stay away; they insisted on it and disowned him. Jill adored Lewis as much as she adored Lynus. Lewis had even signed a note saying he would make her wedding cake if she ever decided to get married. "Don't go there," she'd said of the offer, "because that isn't going to happen," to which Lewis had responded, "Never say never."
Lynus had a swanky suite of offices in New Town, where he knew everyone and everyone knew him. He never lacked for clients. When Jill called, he immediately put her and whatever she needed at the top of his list and made sure she had his best investigators, which wasn't hard because everyone he worked with was the best.
Jill gathered up her jacket, her backpack, and her Wellington boots and left the office. She needed the yellow Wellingtons to get across the parking lot—unless she was willing to go barefoot, which she did not want to do. If she showed up either barefoot or wearing the Wellingtons, Lynus's sense of fashion would be offended.
Jill was surprised to see how warm it was. Just three hours ago, when she'd practically canoed into the parking lot, certain the engine of her truck would stall out, it had been around forty-five degrees. Now it felt like it was approaching seventy. The sun was exceptionally bright after the monster storm. She loved days like this, when everything looked like someone had scrubbed the world with a brush and soap and water. The day smelled as wonderful as it looked.
Jill made it out of the parking lot and onto the main road that would take her to New Town and Lynus's swanky offices. The trip, which under normal circumstances could have been made in fifteen minutes, took forty-five minutes, what with the flooded roads, downed trees, and drivers unsure where the detours would take them. When she finally arrived at Lynus's building, she was glad she had worn the yellow Wellingtons. She slogged across the parking lot to the front door, where Lynus was waiting for her.
Jill smiled. Lynus could have posed for GQ or Town & Country in his elegant attire, and the truth was, he had been on the cover of each of these magazines twice, to the absolute mortification of his family. Today, he was wearing a charcoal gray Armani suit with a pristine white shirt and red-striped power tie. Lynus never wore anything but Armani because he said the suits draped his slender body to perfection, something Armani himself attested to. Lynus had even modeled for his buddy Giorgio Armani on more than one occasion.
They hugged. "You smell good," Jill giggled.
"It wouldn't hurt you to spritz yourself with something. Don't you get tired of smelling like grass and fresh air? Those boots have to go!" They bantered back and forth as they walked arm in arm back to Lynus's suite of offices, which had, of course, been professionally decorated, no expense spared.
It was a black-and-white experience. Stark white, pitch-black, yet soft and comfortable at the same time. She didn't know how that could be, with all the chrome and glass, but it was. The carpet was ankle deep and coal black, with not a speck of lint anywhere. The plants were glossy and green, healthy and luxurious. The glass-top modern-looking desk was virtually bare, except for a phone console and a laptop. Jill knew there was a state-of-the-art recording system, somewhere in one of the drawers, which Lynus used instead of taking notes. Lynus was a one-man shop indoors. He did have a reception area, where he had a blowup Betty Boop doll sitting behind the desk. Just for fun. He preferred to greet his clients at the door himself and did not accept walk-in appointments. The foyer door was kept locked at all times, but he did have a remote control in one of his desk drawers that he could activate in case law enforcement showed up regarding clients.
The two old friends made small talk on the leather sofa. In between bites of the delectable pastries and exceptional coffee—made from some exotic beans Lynus had shipped to him from someplace far away that she couldn't pronounce—Jill outlined what she needed from Lynus. Lynus listened, committing it all to memory, knowing that his recording system was his backup.
"Let me make sure I understand all of this. You want Elaine Hollister followed twenty-four/seven. You also want your client, Gus Hollister, followed twenty-four/seven. Because . . . you want to know if he lies to you, because all clients lie to their lawyers. You want to know if Gus meets up with his wife for whatever reason."
"Precisely," Jill said, reaching for another pastry.
"In addition, you want to know everything there is to know about your client's family, meaning, of course, the Blossom sisters, Rose, Violet, and Iris. You want all the paperwork on the farm, their holdings if there are any, the whole ball of wax. I'm assuming you want to know about any inheritance down the line that the soon-to-be-ex might think she's entitled to."
"Precisely," Jill said.
"You faxed me Phil Ross's report. I read it; I was not impressed." Lynus sniffed.
"Neither was I. I want all her financials; my client's as well. I want you to pretend that you never saw Phil Ross's report and do your own. You'll bill the firm the way you always do. Standard expense account. Check with me for anything outgoing over a thousand bucks. I want video as well as stills. Check in with me every forty-eight hours. Did I miss anything?"
"I don't think so. If you did, I'll let you know as we go forward. Tell me something, just between you and me. You don't like your client, do you?"
"Does it show that much?"
"Oh, yeah," Lynus drawled. "Why?"
"Because he chose a gold digger over his family, a family that raised him, gave him the best they could. And, when push came to shove, he chose the gold digger over them. They're old ladies and he broke their hearts after all they did for him."
"People do silly things when they're in love, Jill. Even you know that," Lynus said softly.
"Silly, yes. Silly, I can understand. I don't understand blatant stupidity. What he did to those old ladies and the way he treated them is unforgivable in my eyes."
"That's because you've never been in love, Jill. I'm not saying I'm on Hollister's side. I'm just saying Hollister might turn out to be an okay kind of guy who stepped off the rails and didn't know how to get back on, and this is the outcome. You really shouldn't judge people until you know all the facts. You know what else? If you'd fix yourself up, you'd be a knockout."
Jill was on her feet in a second, her face dark pink, her eyes blazing. "Don't you dare go there, Lynus Litton, or I'm out of here, along with my business."
Lynus smiled. "Testy, aren't we? Must mean I hit a nerve. Okay, peace, my friend. I mean it, though. I know this guy who could turn you into a bombshell in four hours."
"Four hours!" Jill screeched at the top of her lungs. "Did you say four hours? I need four whole hours to bring me to the bombshell level or whatever you call it?!"
Lynus grinned. "Okay, maybe I was a bit hasty. Three and a half. Not a second less."
Jill burst out laughing. "Well, that's not going to happen, but if it does, I'm going to hold you to the three and a half hours. Give up on the fixer-upper business and do what you do best, spying."
Jill looked up at Lynus, who towered over her. She thought he was one of the most handsome men she'd ever seen, with his wavy dark hair and soft brown eyes. He had a killer smile that she knew had bought beachfront property for some orthodontist. Lynus was also the kindest, the gentlest, the most caring person she'd ever met in her life. She also knew he was one of those rare people who would always be in her life because he knew, as she did, how important friendships were.
"Okay, big guy, I'm outta here. Keep me posted and give Lewis a hug for me. Tell him those pastries were awesome."
"Those boots have to go, Jill! Lose the backpack, too. Tell Barney you need a raise, and I'll take you shopping for shoes and handbags. I can get them for you wholesale."
Jill laughed all the way to her car. She called over her shoulder, "You know that is never going to happen, Lynus, so give it up already."
Lynus laughed along with her. "Someday you are going to beg me for those three and a half hours. Mark my words."
He locked the door, then made his way back to the office, stopping only long enough to salute the blowup doll at the reception desk.
Gus Hollister clicked the remote on the visor and waited for the garage door to open. He sailed in, parked, cut the engine, and hopped out. Wilson was next, but he waited, like the gentleman he must have been in his former life, for his master to first lift out Winnie, who was protesting at being groped.
Gus walked the dogs around to the door that led to the kitchen and waited till both dogs were inside before he carried in Wilson's pink basket and Winnie's treasures. He set the baskets down in the kitchen, then whistled for the dogs, who ignored him completely because they were too busy sniffing out their new digs.
Gus eyed the pile of dog things and decided Maggie might not appreciate having all their treasures in her kitchen, so he lugged their beds and the baskets into the family room and placed everything by the hearth. Maybe tonight he'd make a fire. The last thing he'd heard on the car radio before he turned off the engine was the weatherman announcing the evening temperature, a chilly forty-four degrees once the sun went down. Wilson loved a good blazing fire. Gus kind of liked it himself. He wasn't sure about fat little Winnie. She might have to waddle off to the side if the heat was too much for her.
Gus made his way back out to the kitchen, where he saw that the coffeepot was full, and there was a plate of sandwiches along with a bowl of cut-up fruit in the refrigerator just waiting for him. He helped himself.
He tidied up the kitchen before he headed to Barney's home office, where he sent off text messages, an e-mail, and a fax to Barney, apprising him of what he had learned at Blossom Farm and asking for advice. He was certain Barney would respond to either the text or the e-mail, but he wasn't sure about the fax. The main question, however, was, "Were you aware of any of this?" Right now, though, he needed to think, to come up with a game plan to help his granny and aunts.
Gus trudged back to the kitchen for a second cup of coffee, which he carried into the family room. He was not surprised to see both dogs sacked out in their beds. Wilson offered up a feeble wag of his tail and went back to sleep. Winnie was already snoring, her paws wrapped around a ragged doll that might have been a Raggedy Andy at some point in time. He smiled.
He settled down in Barney's favorite recliner to wait for his friend to get in touch. He closed his eyes and drifted off to sleep.
Chapter 10
GUS BOLTED OFF THE RECLINER WHEN HE HEARD THE THREENOTE cell-phone ring. He shook his head to clear away the muzziness from his interrupted sleep. He answered and mumbled a sleepy greeting.
"Well, hi there, sleepyhead," Barney said. "What the hell are you doing sleeping at this time of day? Now, me, I should be pounding out some z's considering the time difference, just so you know."
"I'm stressed, okay? Cut the bullshit, Barney, I'm not in the mood. All I want to know is did you know what my family was doing?"
"No! You spell that, n-o! They came to me and asked my advice about finding someone to construct a Web site for them and I recommended someone. When I asked if they needed any other business services, like a good CPA, they said that they already had an accounting firm. I tried to talk them into switching their business to your firm, but they were adamantly opposed. Said you didn't need to know their business. I had to respect that, and there was no way in hell I was going to go up against the three of them. And, obviously, I could not say anything to you about whatever was going on.
"That is the sum total of my involvement in their activities. I have to say I didn't think anything in this life could surprise me, but you did one hell of a job. Did they really make all that money doing . . . ah . . . what they've been doing?"
"Oh, yeah, and they have the capacity to make twice that much if I can manage to recruit more help for them. I didn't tell you this, but some dude named Oscar, who works with them, wanted to take me out to the barn and kill me. To keep me silent. Did you hear what I just said, Barney? They were actually considering it."
Barney laughed. "Well, they didn't, that's the important thing. What are you going to do? Do you have a game plan?"
"Not exactly, but I will do what they want me to do if that's the only way they're going to let me back in their lives. I have a list of . . . potential employees. I just have to go visit them and give them my spiel. That means I have to snatch them away from their current digs and get them to Blossom Farm."
"I'm thinking that might be kidnapping, Gus." Barney laughed again.
Gus fumed. "You have a better idea? And it's not kidnapping if they come willingly. Oscar, the dude who wanted to kill me, said they have minds of their own and can do whatever they want to do. Wait. Maybe that was Fred. They all look alike to me. And I was worried about my well-being. So that's your advice. You know what, Barney, that wasn't even advice. You just made a comment."
"I can't believe they didn't want me to invest their money. Goldman Sachs, my ass! That really hurt!" Barney said, all trace of his earlier laughter gone. He sounded wounded to his very core.
"Ha-ha! Guess they didn't trust you, either. Now you know how I feel. Felt."
"Well, if that's all your news, I'm going to shut down and go to bed. I have a full day ahead of me."
"There is one other thing. Elaine had me served today. She's charging me with everything under the sun."
"They always do. Just turn it all over to Jill and let her deal with it. You have more pressing things to deal with right now."
"She hates me. Don't you know any other lawyers? Like a man, for instance."
"I do, but they won't work for your situation. Trust me, she will give you superior representation. She doesn't have to like you, and you don't have to like her. The end result is all that counts. And she knows everybody and uses all her contacts. Suck it up, buddy. Keep me posted on how you're doing. I can't believe they didn't want me to invest their money. I seriously doubt I'll ever be able to sleep again knowing that."
"Guess they didn't want you knowing their business, either," Gus jabbed. Instead of a reply or remark, Gus realized he had nothing but dead air on the line. He ended the connection and flopped back into the recliner. Neither dog so much as cracked an eyelid.
Gus sniffed the air as he looked at his watch. He'd slept away the better part of the afternoon. He was smelling the tantalizing aroma of garlic and . . . spaghetti sauce. Maggie was cooking dinner. He could hardly wait to chow down.
Four o'clock! If he hustled, he could make a trip to the Sea Crest facility, where he might be able to recruit someone named Elroy Hitchens. Sea Crest was, at the most, seven or eight miles as the crow flies, from where he was standing. But first he had to fax the papers the process server had handed him to the fireplug.
Gus trudged to Barney's office, ripping papers away from the staple, not caring if the paper ripped at the corner. He caught snatches of the legalese and still couldn't believe what he was reading. The words brutality and physical violence locked on his eyeballs. No way was he going to read this piece of crap again.
Gus scribbled a note on the cover sheet before he shoved the papers into the fax machine and punched in the numbers that would send them flying to Jill Jackson. He dusted his hands dramatically and left the room. His work here was done.
The Sea Crest Adult Living facility was nestled behind a colorful hedge of glossy greenery. Gus parked Barney's Jeep Commander and got out to walk up a flagstone path that would take him to the reception area. A pleasant-looking woman greeted him cheerfully when he said he wanted to visit with Elroy Hitchens.
"Elroy is on the deck. He likes to sit out there and read before dinner. Go down the hall, and the second set of doors on the right will lead you to the deck."
Gus thanked her, followed the instructions, and found Elroy Hitchens without any problem because he was the only one on the deck. He was reading a copy of Moby Dick. Gus introduced himself and sat down. "Fred sent me."
Elroy Hitchens peered at Gus over the top of his glasses. "Why?" He marked the page he was reading by turning down its corner.
Gus told him.
"How do I know you aren't some kind of slick con artist who preys on old people in assisted-living facilities? All that you just said, it sounds too good to be true. When something sounds too good to be true, most likely it isn't true. You following me here, young fella? How'd that all happen?"
Gus told him everything, even his part in what had been going on. He didn't hold anything back.
"You should never turn your back on your family, young fella. In the end, that's all that's left to us. I should know. So now you think you can step up to the plate and make all that sadness and sorrow go away. Is that what you're telling me?"
"I guess I am." Gus had the good grace to look ashamed.
"Well, women are more forgiving than men, so I can see that maybe happening in your case. Before I give you my answer, I need to call Fred. Why don't you go into the dayroom and fetch us some coffee while I make my call."
"Okay. How do you like your coffee?"
"Black, how else?"
That wasn't so hard, Gus thought as he made his way to a huge coffee urn sitting on a table in the corner of the dayroom. It was a cozy room, with wraparound windows on two sides. A giant seventy-six-inch television was mounted on the wall. The chairs and sofas were colorful and looked comfortable. The carpet was a neutral color and flat, for easy wheelchair mobility, he assumed. He looked around. Two men were playing checkers. Two ladies were watching Oprah reruns, and a fat, lazy-looking cat was sitting on the lap of a woman who sat in a wheelchair. She was stroking the cat, her eyes blank. Gus looked away.
Back on the deck, Gus handed over the coffee. He waited.
"Okay, young fella, Fred backed up everything you said and added a bit more. I made a call to another old friend, who is over in Sunrise, who said he knew a few others. It's in the pipeline as we speak. By the time I finish this coffee, I think you'll have enough commitments to make everyone happy. Now, how are you going to get us all out to Blossom Farm? You're going to need a bus, young fella. And we'll be ready to go by ten tomorrow morning, I guarantee it. Give me your phone number, and I'll be calling you sometime this evening. We have things we need to get in order. There is one hitch. We all want a contract; otherwise, we ain't buying no pig in a poke."
Contracts. He hadn't thought of that. "I don't see a problem with that. I'll bring them with me tomorrow if it's a go. What about your families, your bills here?"
"I'm no problem. I don't have any family. I signed myself in here so I can sign myself out. I can do my banking online here. I'll take care of that this evening. As for the others, when it comes to family, while they might be lurking out there, they won't even notice our friends have moved. That's a pretty blanket statement, but ninety-nine percent accurate. All the others have to do is notify their Social Security office and the state that they are no longer responsible for payment to their facility. I can almost guarantee there won't be a problem, but if there is, you can deal with it, young fella. Does that work for you?"
"It does," Gus said happily. He could hardly wait to get home to call his grandmother to report in on his progress. He'd come through for her, and he really hadn't had to sweat it out. A piece of cake.
"Well, it was nice meeting you, Mr. Hitchens. I guess we'll be seeing each other tomorrow. If anything changes, tell me when you call tonight. I'll see about renting a . . . bus or some kind of vehicle to get you all to Blossom Farm. If I can't get a bus, I'll just make several trips. Before I leave, is there anything else you need to know? Any questions?" Gus stood up and offered his hand for a handshake.
"Call me Elroy, everyone else does. There is one thing. What are you going to do about the gold digger? I'm just being nosy here, so that means you don't have to answer me."
Gus sat back down. "I don't know. I have a lawyer. Nothing my wife said in the complaint was true. This is all about money. I don't think she ever loved me. That's pretty hard for me to swallow and accept. I feel like a fool. I must have been blind, is all I can say in my own defense."
"What do you feel about her now?"
"What? You planning on writing a book, Mr. Hitchens?"
"I told you I was just being nosy. See! You still have feelings, and you need to let them go. You need to deal with what's going on in your life, and you can't let her drag you down. Put it behind you and move on. Really move on. In the end, actions speak louder than words, and your family will be watching to see how you handle it. Guess you know that, don't cha, young fella?"
"Yes, I do know that, Mr. Hitchens." Gus was on his feet again, his hand extended for a second time. Elroy offered up a bone-crushing shake. "I'll see you tomorrow. Have a nice evening, Mr. Hitchens."
"I plan to, young fella. See ya."
Gus was back in Barney's house by six o'clock. Just in time, according to Maggie, to sit down and enjoy his dinner. "Do you want me to stay and clean up or to come back later?" she asked.
"I can do the cleanup. It smells wonderful. Did you make some extra meatballs without the sauce for the dogs?"
"I did, and they're in the covered bowl on the counter. The garlic bread is in the warming oven. Just cover the leftovers, and I can either freeze them or you can have them for lunch tomorrow."
"Thanks, Maggie. Have a nice night. Oh, were there any calls?"
"Just one. Well, actually four, but it was the same person. Miss Jackson. She sounded . . . perturbed."
"I bet she did. Is she going to call back, or did she want me to call her back?"
"She didn't say. Each time she called, all she said was, 'Is he back yet?'"
"I'll call her after dinner."
Gus knew he wouldn't be able to enjoy his dinner until he fed the dogs theirs. Winnie was looking at him with adoring wet eyes. Wilson glared at him. "Okay, okay, I'm getting it, Wilson. I forgot to give you guys a Pop-Tart, so you'll get two after you eat your dinner. Cut me some slack here, okay?" Wilson's tail gave a half wag as he sat back on his haunches to wait for his dinner.
Gus mashed up the meatballs, added some wet and dry dog food, and set the bowls down on the floor. The dogs practically inhaled their food and then trotted over to the door to go out. They scratched on the door to be let back in just as Gus sat down to eat. He handed out the two Pop-Tarts, and the dogs scurried back to their beds in the family room.
The phone rang six times as Gus ate his dinner. Knowing it was the fireplug, Gus refused to answer it. Just the sound of the ringing phone was already giving him indigestion. He had a wonderful, tasty dinner in front of him that he should have been enjoying. He knew he wasn't going to be able to enjoy the peach cobbler, either. So he'd save that for later.
The phone continued to ring as Gus finished his dinner, packed up the leftovers, and tidied the kitchen. He turned on the dishwasher and sat back down to enjoy his after-dinner cup of coffee. Just as he brought the cup to his lips, the phone shrilled for the umpteenth time.
"That's it!" He picked up the phone and barked a single one-word greeting. "What?!"
"When I call you, Mr. Hollister, you WILL answer the phone. I can't represent you if we don't communicate. Is that clear?"
Gus grimaced as he pictured the fireplug venting her venom at him. "Tell me how to answer the phone when I'm not here. If you don't want to represent me, then quit. This world is flooded with lawyers. I can take my pick. I faxed you the papers I was served. I included a message saying it was all lies. Do you want me to repeat the message? It is all lies. Now it's your turn to do whatever the hell it is Barney pays you to do. Now, here's another message for you. You only need to ring this number once and leave a message, the way normal people do. Now here's my third message. Sit on a pointy stick and twirl around until it comes out that mouth of yours. Good-bye, Miss Jackson, have a nice evening."
Gus sipped at his coffee as he waited for Barney to call him. He knew in his gut that the fireplug would have called Barney as soon as she hung up, to tell him she was quitting, then Barney would call him and ream his ass. He waited as the minutes crawled by.
When the only phone call that evening was the one from Elroy Hitchens, Gus was almost disappointed.
With nothing else on his agenda, Gus went upstairs, showered, and changed into warm sweats. He returned to the family room, made a fire, and sat down to watch reruns of NCIS, his favorite television show. The dogs were snoring contentedly by the hearth.
Tomorrow is another day.
Chapter 11
GUS BOLTED UPRIGHT IN THE RECLINER. HE WASN'T SURE WHAT had woken him. A bad dream? The pain in his neck from sleeping in the recliner? He looked over at the hearth, where Wilson and Winnie were snoring. Maybe the last log that fell over, shooting sparks up the chimney? He was inclined to go with the bad dream. What the hell was it? Nothing came to mind. He looked at his watch: three a.m.! He must have dozed off around eight, which meant he'd slept seven or so hours, his regular sleep pattern. It also meant he was done sleeping for the night, so he might as well get up, shower, shave, make some coffee, and get a head start on the day and whatever it was going to bring his way.
Gus leaned his head back and closed his eyes, not to sleep but to think. His last conscious thought before falling asleep had been that he had to call the fireplug and apologize for his rudeness. They needed to start over from square one and stop with the one-upmanship. Like Barney said, he didn't have to like her. All he had to do was let her do what she does best, represent him. Well, he could do that. Or die trying.
He made a mental list of things he wanted and needed to do for the day. First, he had to arrange contracts to bring with him when he picked up the seniors. Next, he had to get a bus from somewhere to pick them up and take them to Blossom Farm. Then he had to come up with a work plan for everyone on his grandmother's staff. A daunting job to be sure, but he was good at organizing, or at least he thought so. And he needed to call Barney again at some point today. And he had to get in touch with a Realtor to find him a place of his own. Otherwise, he was going to have a neurotic dog on his hands. Wilson liked routine—his own place, his own things—and for sure he did not like to be shuffled from one place to another. He understood that because it was exactly how he himself felt.
Gus heaved himself out of the recliner and looked at the dogs. Wilson cracked one eyelid as if to say, it's not time yet to get up, and promptly went right back to sleep. Winnie simply continued to snore.
Gus was back downstairs and in the kitchen making coffee. The clock on the Wolf range said it was four-thirty. His grandmother and the aunts would be up at five. He could call then and ask about contracts and if they had any ideas as to how and where he could get a bus.
While the coffee dripped, Gus toasted a bagel he didn't really want. He spread apple butter on it and wolfed it down as he waited for the coffee to finish dripping. He looked around to see where he'd dropped his briefcase yesterday. He saw it sitting by the laundry-room door. He opened it and withdrew a legal pad and pen. He needed to make a list. Phone calls first. Then physical things he needed to do. When he was done, he had the page almost filled, and not because he wrote big. Awesome, he thought.
The coffee, when he poured it, was dark and strong, just the way he liked it. So strong it almost curled the hair on his chest. He grimaced. What man in his right mind would want curly chest hair?
Gus went back to rummaging in his briefcase until he found the fireplug's office number. If he called before office hours, he could take the coward's way out and leave a message, and he wouldn't have to talk to the irritating lawyer. Yeah, yeah, that's what he'd do. But he'd wait till six o'clock. Six o'clock was a decent hour to call and leave a message. Okay, done. He crossed that chore off his list.
Gus yanked his laptop out of his briefcase and booted up. He scrolled down in his address book until he found the name of a Realtor with whom he'd done business before. Marsha Dewey. He fired off an e-mail stating his requirements and said expediency was paramount. He added a P.S. that he needed a fenced-in yard for Wilson.
The next thing he did was to check his business account. He didn't like tapping into it for his personal use, but the way he saw it, at the moment he had no other choice. There was enough money in the account for a deposit on a small house of some kind and some new furniture if he only furnished a bedroom and bought a few chairs and a television. Later on, he could finish furnishing it. If there was a later on. Worst-case scenario, he could always borrow money from Barney. Marsha would do her best for him, that much he knew. He scratched Marsha off his list.
Gus spent the next hour tapping out e-mails in response to clients concerning their filing extensions. He liked to stay in touch and give what he called his own personal touch to his clients. It worked well for him, and he rarely lost a client; when he did, it was because the client had either passed on or moved out of state. That taken care of, he e-mailed his insurance agent and a few other people to bring them up-to-date about his present circumstances.
The last e-mail that he sent off was to his office manager, apprising her of his current status, which was, "You will see me when you see me," and "I'm only a phone call away."
Bus. He needed a bus. As far as he knew, car-rental agencies did not rent out buses. Schools had buses. Churches had buses. But then there was the question of insurance and liability. He groaned. Well, hopefully his granny would have some ideas, or else it was going to be trip after trip in the Blossom Farm van.
Wilson appeared at his side and nosed his leg, his dark eyes asking for forgiveness. At least, that's what Gus wanted to think. Winnie offered up a soft woof of an early morning greeting. Gus opened the door, and, gentleman that he was, Wilson waited until Winnie waddled through. He followed her out to the gray of early dawn. While the dogs sniffed the new territory, marked it, and sniffed some more, Gus got their food bowls ready. He always fed Wilson twice a day, breakfast and dinner. Winnie he rather thought got fed three or four times a day, a rule he was about to break. He fished out a Pop-Tart and broke it in half. First step in cutting back on the dog's food intake. He wasn't worried about Wilson, because Wilson ran off the calories, while tubby little Winnie preferred to laze about. He hoped her bad habits didn't rub off on his dog.
Ten minutes later, Maggie came in with the dogs, looked around, and asked if Gus wanted breakfast. He said no, and she disappeared, probably to make his bed, which hadn't been slept in. God only knew what the little housekeeper thought about her newest guest.
At six-forty, Gus had both dogs loaded into the Jeep and was on his way to Blossom Farm. Winnie moaned and groaned the whole way, while Wilson poked his head out the half-open window to enjoy the early morning air.
Before he got out of the Jeep, Gus checked his cell phone to see if the fireplug had sent a text. She had not. His fist shot in the air. "Okay, guys, let's hit it!" Wilson hit the ground, ran to the kitchen door, and barked. Gus was left to carry Winnie into the house, where all the seniors made a fuss over her. He watched in horror as they all fed the dogs bits of bacon, waffles, and scraps of sausages and toast.
"Keep this up, and that dog is going to have a heart attack. And don't for one minute think dogs can't have heart attacks. She's too fat, Granny. You need to stop giving her extra food. I already fed her kibble and her regular food plus half a Pop-Tart, which I am going to cut back to a quarter, then just a pinch," Gus said half under his breath. He waited to see what the seniors' reaction would be.
"He's right; my old springer spaniel had a heart attack," Fred said. "What are you doing here so early?" he groused.
"Getting ready to get this show on the road. I need to get a bus. Do any of you know where I can get one?"
"As a matter of fact, I do. I'll call Pastor Evans at Sycamore Baptist Church. How long do you think you'll need it, Augustus?" his grandmother said.
"At least till noon. Depends if your new recruits are ready, and how long I have to wait for them at each stop. Noon, and I'm being conservative. Ah, what time do you all start to . . . ah, work?"
"We like to be at our workstations by seven a.m. We get up at five. We were busy last evening trying to set up accommodations at Shady Pines for the newcomers. A few of us got up late this morning as we had only a few hours of sleep last night. We were just trying to figure out how to do kitchen duty. We're going to have a lot of mouths to feed. And a lot of food to order," Rose said softly. To Gus's ears, it sounded like he was back in the fold with his granny.
"You should have called me. I would have helped."
"We thought about it, but decided against it," Violet said in her most unforgiving tone of voice.
"Well, I'm here now, so is there anything you want me to do? I don't have to pick up Elroy Hitchens until ten. He's at Sea Crest."
"No, not right now. Besides, you're on probation," Iris said.
"Probation! You put me on probation? When did that happen? No one said anything about probation!" Gus exploded. Wilson was at his feet, not liking the tone of his master's voice. Winnie whined from the rag carpet by the sink.
"We told you that yesterday morning. You were so busy grumbling and complaining about the old sycamore, you probably didn't hear us," Violet said. "Or else you simply tuned us out. Now, which is it?"
"I didn't tune you out. I didn't hear you. Yes, I was grumbling and complaining about that old tree because I loved it. It was part of my growing-up years. Barney's, too. How long is the probation?"
The Blossom sisters looked at one another. "Ninety days! You have to prove yourself. Then we'll vote on whether to make you a permanent employee," Rose said. "In the meantime, you will receive a stipend of sorts. We still have to vote on that."
"Ninety days! That's three months! And then you're going to vote on me? I don't believe this! I'm your grandson." Gus looked at his aunts and bellowed, "I'm your nephew!" The Blossom sisters shrugged.
"While we're talking about making people employees, Elroy Hitchens said that the seniors would not be coming to, as he put it, buy a pig in a poke, unless they had contracts. I told him I would bring them with me this morning. I assume that you have contracts for your new hires," Gus said.
"Certainly," Rose said. "I'll just get them before you leave."
Having paid no attention to the discussion of contracts, Oscar of the clicking dentures said loud and clear, "Well, you better believe that you're on probation, young fella, because that's the way it is. How do we know that you can measure up? This is not some Mickey Mouse operation we're running here, just so you know. We have to take that into consideration." Clickety-clack went the dentures.
"Okay, okay, I get it! I accept your terms. I will prove myself. Granny, if you call the pastor, I'll be on my way to pick up your new . . . staff . . . as soon as you get me those contracts. Is there anything else I can do for you wonderful people before I leave?"
"Well, you got one thing right. We are wonderful," Fred said. Gus eyed him to see if he was being sarcastic. He wasn't.
Gus felt like a ten-year-old, waiting to hear about the bus. All the old people were staring at him. He didn't know if he should smile, grin, or stare down at the floor as he waited for his granny to say yeah or nay on the bus.
"Okay, it's a go. It's bus number two, and it's parked to the left of the front door that leads into the school. The keys will be on the visor. You are to fill the gas tank before you return it. We have a company gas card," Rose said, rummaging in the cookie jar for the credit card.
"Thank you. I'm on my way. Do you want me to report in on the way, or should I just, you know . . . show up? Should I bring them here first or take your new staff and their belongings to Shady Pines?"
Violet drew herself up to her full height, which was awesome in itself. "This is what we meant about you proving yourself: taking the initiative. We'll be grading you on your performance."
Gus didn't know where it came from or why he said it out loud, but the words were out of his mouth before he could stop them. "I get it, like a sexual encounter when you have to perform, then you get a grade from your partner."
Clickety-clack. "Right on, young fella."
Gus decided to quit while he could still walk. He was out the door in a flash. Wilson howled. Gus stuck his head back in the door and yelled, "You can go next time. There'll be no room in the bus."
Gus slid into the Jeep and drove up the hill and out to the main road. He stopped, took a deep breath, and yanked out his cell phone and called Barney. The moment he heard Barney's What now? he started to babble.
"They fucking put me on probation. I have to prove myself in ninety days, then they're going to vote on me. Did you hear what I just said, Barney? Will you say something, for Christ's sake?"
"They didn't mention my name, did they? Just you, right?"
"What? You're concerned for yourself and not me! I called you for . . . Jesus, I don't know why I called you."
"Well, the way I see it, this isn't about me, for which I am very thankful. This is about your making things right. I'm glad it's you and not me. Probation for ninety days. Damn, that's three whole months. That really sucks. That's going to take you right into the middle of July. And then there's all that worry about how they're going to vote on you. Man, I am so glad I am not you. Oh, and you need to stop calling me unless it's an emergency."
Gus ended the call. He was tempted to pitch his cell phone out the window, but he knew in his gut that would show up some way, somehow, on his performance record. He did his best to shift his thoughts into neutral and concentrate on his driving.
Fifteen minutes later, Gus pulled into the Sycamore Baptist Church parking lot and saw the bus right where his grandmother said it would be. He parked the car, got out, and jogged over to a big yellow bus with a bright-colored rainbow painted on the side. He opened the door, got in, and saw the keys on the visor. That's when he realized he didn't know how to drive a bus. Gears! More gears than the ones in the Porsche. And the bus was BIG! He had to back up this baby. Maybe he could pull it off if he didn't have to park anywhere. Or I could call someone and ask how to drive a bus. The thought was so stupid, he cringed. It all came down to two words: performance and vote.
Gus called Barney a second time. "Do you know how to drive a bus?"
Barney's laugh was so evil that Gus clenched his teeth as he turned the key in the ignition and waited for something to happen. Maybe there was a manual in the bus. Or . . . maybe Elroy Hitchens knew how to drive a bus. It might be worth a call, he decided, when he couldn't find a manual. Performance, performance, performance.
Somebody should have asked him if he could drive a bus. Aha, it was a test. They were testing him for his performance record. Well, by God, he'd just figure this out on his own and drive this damned bus or bust wide open. He was going to perform if it was the last thing he did.
Chapter 12
ELAINE HOLLISTER LOOKED AT HERSELF IN THE ORNATE MIRROR hanging on the back of the closet door. She'd chosen a jonquil-colored suit and a silk blouse with a small bow tie at the throat. She thought it looked demure and at the same time showed off her voluptuous figure. Her heels were high, accentuating her long, shapely legs. Small diamond studs sparkled in her ears. She still wore her engagement and wedding rings, and a gold Rolex watch.
As Elaine twirled this way and that way, a strand of hair slipped out from behind her ear. She loved her hair. It was thick and lustrous and naturally blond. Men loved to run their hands through it. Gus used to love to bury his face in her hair and tell her she smelled like a spring meadow in bloom. Today she wore it artfully piled on her head so that it appeared she was taller than she was. The last thing she did was to spritz a flowery designer perfume into a haze, then stepped under it and twirled around. She sniffed appreciatively.
She was good to go. Such a shame that she had to drive that yellow tin can out in the driveway. She'd be wrinkled and mussed when she arrived at her attorney's office, but it couldn't be helped. Soon, she'd get a new car, one she looked good in. If her attorney was half as good as he said he was, and she was counting on him to be, she just might end up with Gus's Porsche.
In the kitchen, Elaine looked at the clock over the stove—nine forty-five. Fifteen minutes to drive to the lawyer's office, an hour meeting, a ten-minute good-bye, fifteen minutes to get back home, then get her things ready, strip down to a flowing white robe, and head for the attic, where she would set up her altar and cast a new spell precisely at the stroke of noon. It was paramount that she start her spell on time. She shivered at what she needed to do, because it was crucial to her plan to walk away with Gus Hollister's holdings.
Elaine set the new code for the alarm system, scooted out, crossed the deck, and went down the steps to the yellow Beetle. Five minutes later, she was on her way. She didn't look back. If she had, she would have seen a tall man walking a small dog wearing a sparkly colored collar with a matching leash. A man who didn't live in the gated community.
The building that housed the prestigious law firm of Diamond, Diamond, and Diamond in New Town was constructed of old Virginia brick and covered with ivy. The firm itself was as old as the building. The elder Diamond had had it constructed during his last year of law school. It had been completed the day his shingle was handed to him by his father, Sycamore Springs's only doctor at the time. The plaque was brass, and it was polished and buffed every day. The Diamond Building, as it was often called, was more often than not referred to as the oldest building in New Town. Residents were quick to point out, however, that it was not a historic building.
The Diamond family occupied all three floors of the updated, state-of-the-art building, with each attorney, complete with receptionist and two paralegals, having a floor to himself.
Elaine chose the Diamond law firm because of her love of diamonds and the tarot card reading she'd commissioned.
One of the cards, she couldn't remember which one, said that precious gems were all around her. Then, when she'd just been in the planning stage of her divorce, she'd cast a spell, which reinforced her decision.
Elaine took a moment to stare at her reflection in the plate-glass door before she opened it. She looked perfect, stunning actually. She settled the Chanel handbag with its gold-braided chain, the bag Gus had surprised her with on New Year's Eve, on her shoulder. She'd been so surprised, because the holidays had been especially grim. She'd shown her gratitude in the only way she knew how. Sex.
Elaine shrugged away the memory as she made her way to the elevator that would take her to the third floor. Like she would even consider the first two floors and the attorneys they housed, regardless of their being named Diamond, too. Only the founder of the firm was good enough for her, so she had held out for Isaac Diamond. Because, Isaac Diamond was old but still sharp as a razor. Not to mention he was a lascivious old man who couldn't disguise the lust in his eyes when he looked at her. Then there was the Diamond money. Piles and piles of money and all controlled by Isaac, who was a widower.
Elaine followed Isaac's secretary to his sumptuous office, which looked to be professionally decorated. It also looked like there wasn't much foot traffic; nor were there any indentations in the comfortable furniture. It was an office that Isaac still inhabited from long years of habit and routine. A place to come to, to prove he still had control of Diamond, Diamond, and Diamond. Which he did. No decisions were made and no new clients were accepted until Isaac voiced his approval. A tightly run ship with billable hours at an all-time high.
Elaine remembered how she had cringed when she was told the firm charged $550 an hour. Paralegals billed at $300. Isaac had assured her she would get it back in spades from Gus when all was said and done. She hated dipping into her local reserve funds, but she had had little choice, so with a shaking hand, she'd written out a check for $25,000 as a retainer. She told herself she had a money spell that she could cast when she returned home that was all but guaranteed to work in four days. Or was it nine? Right now, she couldn't remember. Everything in witchcraft was geared to the numbers four and nine. She loved those numbers and considered them her lucky numbers.
Isaac stood up and came around the desk to greet his newest client, his only client. He put his arm around her shoulders and led her to a chair across from his desk.
Isaac Diamond was a handsome, imposing figure topping the height charts at six foot three inches. According to his doctors, he was still in excellent physical shape at the age of seventy-eight. He played golf three days a week and worked out with a personal trainer twice a week. Today, he wore a custom-made Hugo Boss suit and Bally shoes that were so shiny, he could see his reflection in them. He was tanned and wore blue contact lenses. His hair was white, and there was plenty of it, thanks to hair plugs. Isaac Diamond was vain. Very vain.
"You look like a breath of spring, my dear. How did you weather that horrible storm?"
Elaine smiled. "Thank you. I had a few limbs come down, and my yard looks like a lake right now, but that was the worst of it. Thank you for asking, Isaac."
"The reason I asked you to come in—other than to ask you to lunch—was to tell you that I've heard from your husband's attorney."
Elaine looked across the desk at her attorney. Her eyes were moist and glistening. "Isaac, please, don't refer to Gus as my husband. Just call him Gus."
"Noted, my dear. It won't happen again. Yesterday, late, I think it was around six, and I had left for the day, but I got her voice mail when I got in this morning. Jill Jackson is Gus's lawyer. I'm sorry to say I knew nothing of her; nor did either of my sons. So, I googled her, and I must say, she is going to be a worthy adversary. She's a powerhouse in her own right. She works for Barnaby Beezer. She is his principal attorney. I'm told that in financial circles, the mere mention of her name sends shivers up the spines of opposing counsel."
Elaine leaned back in the comfortable chair and crossed her legs, the skirt she was wearing hiking up an inch too far. She didn't care. What she cared about right now was the prickle of alarm that was making itself known. Gus's friend's—Barney's—top gun. She should have known Gus would get the best. Well, Isaac Diamond wasn't exactly chopped liver.
For the first time in her life, Elaine was unsure what her next move should be. Should she respond? Should she weep and wail? Should she be blasé and say something witty to Isaac?
Elaine tilted her head to the side and made a little moue with her lips. "You aren't telling me some female attorney can out-lawyer the great Isaac Diamond, are you?"
"What I'm telling you, my dear, is this. Gus Hollister has the best of the best going to bat for him by way of Barnaby Beezer. There's not a judge in this town who isn't invested with Beezer. I am myself, just so you know. I sent out queries to some of my peers, and Jackson is going to be a formidable foe. She doesn't like to lose. Actually, she never does lose. She takes no prisoners. And she's going to go after you like a dog in heat. I would be remiss if I didn't tell you this. Full disclosure is my motto, it always has been. Now, my dear, I want to ask you two questions.
"One: Is everything you told me in our first meeting true and accurate? I do not like to be blindsided. Now is the time to tell me if you exaggerated about anything or if, out of a desire for vengeance, you might have told a few fibs. People tend to do that in the beginning of divorce proceedings."
Elaine dabbed at her eyes. She shook her head. She didn't trust herself to speak because she thought her heart was going to pound right out of her chest.
"Two: Is there anything in your background that you've neglected to tell me? The reason I ask you this is because Jill Jackson utilizes the Lynus Litton security firm. If there is anything you're hiding, Litton and his people will ferret it out. They don't get any better than Litton. And before you can ask, yes, we have a team of private investigators that we use, but even I know that Litton's people are superior. I have my people running checks on Gus, his family, and his friend, Barnaby Beezer. Beezer is going to come up clean, I know that. But we're doing it anyway."
Elaine continued to dab at her eyes and shake her head at the same time. Maybe she'd gone too far this time. Going up against a small-town CPA is one thing. But going against a CPA with a billionaire hedge-fund manager for a best friend was perhaps a bridge too far. Just my luck to get involved with someone who turned out to have Barney Beezer as his best friend. Maybe this time I should cut my losses and move on. Look for a new mark.
But the thought of Gus's five-hundred-thousand-dollar mortgage-free house, his Porsche, a percentage of his business, and a possible inheritance down the road won out. She squared her shoulders and gave one last dab at her eyes before she said, "I trust you to handle my affairs, Isaac. I would like to say one thing, however. When I agreed to marry Gus, we both spoke of our pasts. We both agreed whatever came before we met no longer mattered. Gus insisted we sign a paper, just between the two of us, in case things ever got . . . ah . . . sticky. I have that note somewhere, in my jewelry box, I think. I'll look for it and send it on to you or make a copy and fax it to you."
There was no need to tell Isaac that she was the one who had initiated the episode of the little note. Gus had fallen over himself to sign it. In her opinion, at the time, she'd thought it was as good as a prenup, the difference being that this one gave her carte blanche to do as she wished, since he could not use her past against her. Now, she could only hope that it wasn't going to come back and bite her on the rear.
"Isaac, if there's nothing else, I have to return home as I have a real-estate appraiser due at two o'clock, and I want to tidy up to make a good impression. I have to get out of that house as soon as possible—too many bad memories. If you're successful in getting the house for me, I want to sell it and, of course, invest the money."
"I had plans to take you to lunch," Isaac said, his tone reflecting his surprise at being turned down.
"I'm sorry, Isaac, I can't do lunch, but if you're free this evening, so am I. I would love to go to dinner with you." And ply you with liquor and take you to bed. In one hour, I can make all your sexual fantasies come true, you old coot.
"That's an offer I can't refuse. Shall we meet somewhere, or would you like me to send a car for you?"
"I think I can find my own way if you tell me where you'd like to have dinner."
"I was thinking of La Petite. Shall we say seven-thirty?"
"My absolute favorite restaurant. I'll be there, Isaac. Have a nice afternoon."
Isaac got up, walked around the desk, and escorted Elaine to the elevator. He smiled at her and said, "Don't worry about anything. You're in good hands."
"It's not you I'm worrying about, Isaac. I'm worried about Gus and the way he lies and manipulates situations to suit himself and make himself look good in the process. I didn't find out these traits until after we were married. I put up with it as long as I could. Gus is a control freak. I'm sorry. I said this all before. I'm in no mood to beat a dead horse. I look forward to having dinner with you this evening. Thank you again, Isaac, for taking my case."
Isaac heard the words, but he really wasn't paying attention to them. He was more concerned with the fine-looking woman standing next to him and what he was hoping might follow dinner.
Elaine wiggled her fingers at Isaac as the door to the elevator slid shut. With no one watching her, Elaine leaned against the wall of the elevator and let her shoulders slump. She hadn't pulled it off completely. She was smart enough to know that, and now she had to get to work.
The tall man carrying a black backpack and walking the little dog, a Jack Russell terrier, sauntered up and down the beautiful neighborhood. He seemed not to have a care in the world, being concerned only with his midday stroll on a beautiful April morning. His name was Mickey Yee, Lynus Litton's top investigator. He had an American mother and a Chinese father whom he loved dearly. He didn't speak Chinese, but he more or less understood it. He wasn't married and loved his exciting life as a single man with a dog he adored. Someday he would get married, but not anytime soon.
Lynus Litton had snatched him away from the FBI five years ago with the promise that his offer could top anything the FBI ever had or could pay. The tripled salary and bonuses Lynus paid him, the thirty-day vacations, the company car, and the unlimited expense account made signing on a no-brainer, and he hadn't looked back. Well, sometimes he looked back, when he needed a favor from one of his FBI buddies.
The best part to Mickey was that he was able to take his dog to work with him, something the FBI frowned upon. The dog's name was Booker. Mickey had named him Booker because he'd been working a case, and the scumbag he was chasing owned the dog and had mistreated him—the dog was booking ninety miles an hour to get away from the scumbag. Mickey caught him, cuddled him, and made promises to the dog he'd never broken. Nor would he ever break them.
Mickey did a second lap around the cul-de-sac before he walked to the back of Gus Hollister's house, which was totally screened off from its neighbors by lush foliage. The yellow Beetle was gone. He quickly removed the dog's leash and fished around inside his backpack. Within seconds, he had the back door open and was holding a gizmo in his hand, which he'd paid for through the nose and shouldn't even have to begin with. He watched as the digital display counted down before the gizmo succeeded in turning off the alarm.
"Okay, Booker, we're in. You know the drill. As soon as you hear or see anything, bark twice. You got it?" The dog tilted his head and took a stance beside the back door. "I think I might have an hour at the most."
Mickey prowled the house, looking for anything that might be useful to Lynus and his client. He loved this part of the job—finding things people tried to hide. He corrected the thought—not just people, the bad guys, be they women or men. Women, he knew, were devious, more prone to be secretive, where men just blundered through life. At least, that's what he had been taught by his American mother. He'd never disputed her wisdom.
Mickey took the time to appreciate the layout of Gus Hollister's four-thousand-square-foot house and its manly, comfortable furniture. There wasn't a lot of junk or doodads cluttering up the place. He hated the artificial trees, plants, and flowers people tended to decorate with. Nothing but dust collectors. He found it a little strange that there was no rogues' gallery of family pictures. He shrugged—to each his own.
Thirty minutes later, Mickey was finished with the downstairs. Without pulling up the pine floors or knocking out walls, he'd been unable to find anything. He checked the refrigerator, because people were known to hide things in freezers and in bowls of leftover soups and stews. People's refrigerators as a rule were strange yet informative. This one, however, blew his mind.
Mickey poked his head around inside the refrigerator. Four jugs of apple-cider vinegar. Four gallons! Bags of every herb known to man, all neatly labeled, filled the entire second shelf. The vegetable bin held one withered apple and a rock-hard orange. There were no leftovers in containers, no takeout, no eggs, no milk, no juice. Just four gallons of apple-cider vinegar. What does this woman eat?
What really blew his mind, though, were the six pure white roses nestled in cellophane, each stem encased in a plastic sleeve that held water. Earlier, he'd checked the cabinets, which held only canned and boxed soup, crackers, and some cereal that had never been opened. The cabinets were essentially bare. He looked over at the counter and saw three overripe bananas. The freezer had an icemaker and a freezer pack for injuries.
"You're doing a good job, Booker. I'm going upstairs. I still have about thirty minutes."
Mickey again marveled at the big house. Five bedrooms for two people. He wondered if the couple had planned on having children, before they'd decided to split up. That's usually the way it worked, before a marriage went south for whatever reason. He was surprised that all five bedrooms were fully furnished. Four guest rooms. He shrugged. People were weird. He went through each room carefully and thoroughly, but there was nothing to be found. The chests were empty, the closets bare. No one lived in or even visited these rooms. The adjoining bathrooms held one towel each, one bar of soap, and that was it. Everything smelled fresh and unused. New. He didn't like the smell.
The last room in the long hallway had to be the master bedroom, judging by the king-size bed. More like a California king. It was frilly, flowery, and feminine. A room designed for and by Elaine Hollister's taste. Not really for Mr. and Mrs. Hollister.
The walk-in closet, which was almost as big as each of the guest bedrooms, held so many clothes, Mickey found himself overwhelmed. A lot of the outfits still had price tags dangling from the sleeves. Racks and racks of shoes, purses, scarves, and all the things women thought they needed to make a stellar appearance. There wasn't a single thing to indicate that a man had ever been in residence. Either she had completely obliterated any evidence of Gus Hollister's presence or he was like a ghost, leaving no physical traces of his existence. Mickey rather suspected the former and found it very sad, since he knew the story of the house and how it had once belonged solely to Gus Hollister.
Mickey checked every item—the pockets, the insides of the shoes, the handbags—but found nothing to interest him. He kept his eye on his watch as he sifted through the bureau drawers. It was no surprise to him that Elaine Hollister had a passion for lacy, gossamer-thin underwear. Tons of it, everything matching.
His mother always hid things in her sock drawer. But Elaine Hollister did not have a sock drawer, and he could find nothing to alert him to what she was hiding. Unless you considered six white roses and four gallons of apple-cider vinegar as hidden things. Lynus was going to be upset if he didn't find anything. Hell, he was going to be upset. Everyone had secrets and things they hid. Why would this woman be an exception to the rule? Secrets and lies. He thought of the television show House, where the lead character said that everyone lies. It was so true. Right now, though, he wasn't interested in lies; he was interested in finding out this woman's secrets. His gut and his long years of snooping told him they were somewhere in the house; he just had to find out where.
The chest at the bottom of the huge bed yielded nothing but extra blankets and pillows. Hands on hips, Mickey looked around. What was he missing? He looked behind the artwork on the walls. Nothing. No safe. Nothing taped to the back of the pictures. He looked behind the plasma TV hanging on the wall. Nothing.
Mickey looked at his watch again. He had fifteen minutes, and he would need every single one of them to put the listening devices into the landline phones. He hustled then and was finished with two minutes to spare. At the last second, his gut instinct kicked in and he decided to put one of the little bugs on top of the doorframe leading into Elaine's bedroom. It was almost directly underneath the trapdoor leading to the attic. From here on in, any phone calls or conversations in or out of the bedroom or in the hallway would be picked up by Lynus and his eavesdropping equipment. The part Mickey didn't like was that he was going to have to sneak back into the house in the middle of the night, find Elaine Hollister's cell phone—which would likely be charging overnight—and bug it, too. He'd done it before, and though it was not his favorite thing to do, you had to take the good with the bad on any job.
Mickey looked at his watch. He'd used up his entire hour, and he still hadn't covered the basement, the garage, or the attic. That meant two more visits. Booker was silent, which meant he was going to be able to get out clean if he left immediately.
Standing in the hallway, he looked up at the ceiling and saw the unpainted wood frame around the attic opening. He knew that if he opened it, there would be a pull-down ladder. The wood looked new. Why hasn't it been painted? What's up there? And where is the rope that would pull down the ladder? He was tall enough that he had a good view of the square opening. No pull cord, no handle, no latch. He looked around and saw the switch plate on the wall. He was about to press it when Booker barked twice.
Mickey ran down the steps and whistled for the dog, who came on the run. This time they would exit through the front door. He quickly reset the alarm and walked smartly to the front door, Booker right alongside of him. Outside, they both squatted behind a thick box hedge just as the yellow Beetle roared down the drive to the back of the house.
Man and dog walked rapidly away from the Hollister house as if they had been visitors leaving a meeting. Between the two of them, the only one breathing hard was Booker.
Chapter 13
GUS CHECKED THE HUGE SIDE MIRRORS, SUCKED IN HIS BREATH, shoved his foot down on the clutch, and shifted gears. He cringed at the grinding gears, but, somehow, he was able to get the big yellow bus backed up. He shifted again, the sound as mind-bending as the first time, but the bus was in first gear, then second, and, finally, the behemoth was moving out of the parking lot onto the road. His in-drawn breath was an explosion of sound when he finally released it. The word performance was ringing in his ears the entire time.
Somehow or other, he made it to the first assisted-living facility on his list, and there, right in front, was Elroy Hitchens with three other people, bags and boxes at their feet. Gus pulled to the curb and had a bad moment when he couldn't open the hydraulic door. Cursing under his breath, he finally got it open. His passengers looked at him for permission to board. "Welcome aboard!" he said. His four passengers trooped aboard, introducing themselves as they climbed the steps into the big bus. All of them smiled at him, the men offering their gnarled old hands to be shaken. The little cherub of a lady hugged him and said he must be a blessing to his mama. Her name, she said, was Dolly Madison. Not the real Dolley Madison, she clarified, saying, "I'm not that old!"
His passengers safely aboard and buckled in, Gus took his seat behind the wheel. "Where to, Elroy?"
"You got the contracts, Gus? Gotta have contracts."
"They're right here, Elroy. You look them over while we're going to the next place. Okay?"
"Sure. We trust you. Go out to the main road, follow it for half a mile, make a right, then two lefts, and that will be your stop. You will be picking up six passengers."
"This is what I call a real adventure," Dolly bellowed, the excitement in her voice ringing throughout the bus. Gus grinned, listening to the chatter wafting his way as he concentrated on keeping the bus on the road. He had to perform. That was his bottom line.
Gus's second stop made his jaw drop. Huddled on the apron of concrete that led to the double doors of the assisted-living facility were eight people—not six—their fists shooting in the air at the sight of the big yellow bus sliding smoothly to the curb. Then they all clapped their hands in glee, even the four passengers already inside the bus. Introductions were in order. Gus shook hands, always careful not to squeeze too hard. He smiled, he grinned, and he laughed out loud at the seniors' exuberance.
Suddenly, Gus had a surge of feeling as he steered the big yellow bus down the road. Maybe he should initiate a sing-along. Then again, maybe not; his passengers probably weren't up on the latest music. His feeling of power was short-lived when he heard one of the seniors shout out, asking him why a young fella like him had a bus driver's license.
Ooops!
Honesty, his grandmother had taught him and Barney early on, was always the best policy. "I don't have a license, sir. I'm just filling in to help you guys take it on the lam. This is the first time I ever drove a bus! I'll get you where you need to go, that's a promise. And I promise never to drive a bus again until I get a bus driver's license."
More hand clapping, hooting, and hollering followed Gus's declaration.
A robust voice from the middle of the bus shouted out that if they were pulled over by the fuzz, they'd all step up to the plate and tell the officer that they'd forced Gus to take them on the lam. Then the voice said, "The police never do anything to old people, so your secret is safe with us, sonny."
Gus believed them implicitly. He thanked them profusely as he struggled not to laugh out loud.
"Your next stop is the mother lode, Gus," Elroy Hitchens bellowed. "You'll be picking up eleven passengers from Pine Crest. That's a satellite facility of Sea Crest. It's a dump. We got everyone who is ambulatory. We all agreed last night to use our first paychecks and sign-on bonuses to relocate those who couldn't come with us from Pine Crest." More hooting and hollering.
"Wheee!" Gus said, his fist shooting in the air as he sailed down the road in the big yellow bus.
Fifteen minutes later, Gus pulled to the curb at Pine Crest. The seniors were huddled, huge smiles on their faces, waiting for him. They piled in and greeted the other seniors as they high-fived one another. While all this was going on, Gus stared at the building where the eleven people had lived for God only knew how long. Elroy was right; Pine Crest was a dump. There was no lawn to speak of and the hedges and straggly bushes were sorely in need of pruning. The windows were unwashed and grimy-looking; the window frames' paint was cracked and peeling. The glass door leading to what he assumed was a lobby had a huge crack running across it. The sign on the building was missing two of its screws and hanging lopsided. He knew in his gut that the inside was probably worse than what he was seeing. A dumping ground for elderly people whose families were too busy to care for them.
Gus knew then that he was doing the right thing, and if he had to do it all over again, he would. He had a new mission in life now, to do whatever he could to give these people a better life, and he now had no doubt that his grandmother and his aunts were on the right track in doing what they were doing.
It was at that moment that Gus Hollister committed himself to doing whatever he could to help his grandmother, his aunts, and all these wonderful people he was transferring to Blossom Farm. Maybe he should initiate a sing-along.
The thought flew out of his mind when he realized he was less than a quarter of a mile from the turnoff to Blossom Farm. Should he drop his passengers at the farm, or should he take them to Shady Pines first? No one had said what he was to do. If he dropped them at Shady Pines, how would they get to Blossom Farm, given the flooded grounds? They wouldn't be able to use the golf carts. He seriously doubted the seniors could make the two-mile trek on foot. And yet, his grandmother had said they were up most of the night at Shady Pines, getting it ready for the new residents. How did they get to Shady Pines to do all that? Probably in the van by road instead of across the field. Performance. Gus looked at his watch—eleven-thirty. He had to get the bus back to Pastor Evans by noon. The decision was taken out of his hands when he approached the gravel road that would take him to Blossom Farm. He turned right at the sign, which was flapping in the light breeze. A cheer went up from his passengers.
When Gus brought the bus to a full stop, he left the motor running. There was no way in hell he was going to let any of the seniors see him grinding the gears and trying to back up the big yellow bus. It was all about performance.
Gus waited outside the bus until all his passengers were safely on the ground before he turned to his granny. "I have to get the bus back by noon. I'll be back to help as soon as I can." His grandmother smiled at him, a warm smile that made him feel better than he'd felt in days. Even Violet gave him a thumbs-up. Iris wiggled her fingers in his direction, which meant, well done.
The babble of voices with shouted questions jarred Gus. He heard: What time is orientation? Who is doing it? When is lunch? When do we find out more about salary and bonuses?
Gus held up his hand. "Ladies and gentlemen, that will all be taken care of when I get back. I have to return the bus to the church by noon. Just be patient, okay?"
"Okay, sonny. We have nothing but time," someone in the group shouted.
Gus mentally patted himself on the back as he made his way up the steps to his seat behind the wheel of the big yellow bus. He took a deep breath and wanted to shout his happiness when he shifted gears cleanly and smoothly. He waved as a cheer went up from the group he was leaving behind.
Damn, I feel good!
Gus drove to the closest gas station, topped off the bus's tank, then drove to the church and parked the big yellow bus exactly where he'd found it. He cut the engine, replaced the keys over the visor, then did what all good bus drivers do: he checked the bus to make sure none of his passengers had left anything behind. He found nothing. He left the bus with a light heart and made his way to his vehicle.
Once inside, he pulled out his cell phone to see if anyone had called or sent him a text while he was seeing to the seniors. He had one text and one voice message. The text was from Marsha, his real-estate broker, saying she had found the perfect house for him and had made an appointment to show it to him at four o'clock. Please don't be late was the last line of the text. The voice-mail message was from the fireplug, saying she wanted to see him in her office at four-thirty. She cautioned him not to be late, because she had other late-afternoon appointments scheduled. Gus groaned out loud. He had to make a decision. Before he could think twice, he fired off a text to his broker and said he would meet with her, and he would be on time. He tensed when he called the fireplug and prayed he would get her voice mail. What was it about the lawyer that made him so nuts? He almost let out a whoop when he heard the metallic-sounding voice asking him to leave a message. He quickly left a courteous, polite response, which said he had a prior commitment and couldn't break it, and she needed to give him more notice when she wanted to set up a meeting.
Gus justified the response by telling himself that his divorce case wasn't going anywhere in the next few days, and he might lose the opportunity to view what his broker considered the perfect house to fit his needs. As far as he was concerned, it was a no-brainer. When it came to the fireplug, everything seemed to be a no-brainer.
Not wanting to think about it anymore, Gus turned the key in the ignition and left the parking lot. Why was life always so complicated? Finding no answer to this question, he turned on the radio and listened to Kenny G, who kept him company all the way back to Blossom Farm.
Gus let himself in the kitchen door. A little lady who was one of the original staff was loading the dishwasher. She looked at him, smiled, and asked if she could fix him some lunch. Gus realized he was hungry. "That would be nice, ma'am. I am hungry. Something smells good."
"I'm Aggie," the little lady said, holding out her hand for him to shake. "I work with the feathers." Gus nodded. "We have the U.S. Senate bean soup for lunch with ham-and-cheese sandwiches. Our new guests loved it."
"Well, if it tastes as good as it smells, I can understand why."
Gus sat down and felt guilty when Aggie served him. He said so.
Aggie shook her head. "I love to cook. I grew up on a farm, and my mama taught my sisters and me to cook when we were young. We had to feed the farmhands three times a day. Food is all about the herbs and spices you use. You can take the cheapest, the toughest piece of meat, season or marinate it properly, and you have a gourmet meal. It also helps to serve something sweet afterward." She giggled. "You best hurry, son, the others are chomping at the bit to get going. We seniors say we don't mind waiting, but we really do. We fixate on things. I don't know why that is," she said fretfully.
"You aren't in the minority, Miz Aggie," Gus said as he wolfed down the delicious soup. He gobbled down the sandwich and wished he had a second one. He swigged the last of his sweet tea, wiped his mouth, then carried his dishes to the sink. He thanked Aggie and gave her a hug.
Aggie looked up at him and beamed her pleasure. "That's exactly what a cook wants to hear. Skedaddle now and do what you have to do."
Gus squared his shoulders. Performance time.
The talkative seniors were all crowded into the massive dining room. The twelve seats at the table were full. Folding chairs were set up against the wall. Some of the seniors, mostly men, were standing, their backs to the wall. One seat was waiting for him. He swallowed hard. It was his granny's chair at the head of the table. She was turning it over to him. He felt so light-headed at this show of forgiveness, he had to grab hold of the chair. A laptop stood open on the table, along with a yellow legal pad and two pens.
"Okay, everyone, my name is Gus Hollister. I'm a certified public accountant. Rose is my grandmother, and Violet and Iris are my aunts. This," he said, waving his arms about, "is a family affair." He risked a glance at his grandmother and aunts. They were smiling. He was performing.
"We just met your first need: lunch. I hope you all enjoyed it and thanked Miss Aggie, as she is the one who cooked it. Having said that, now that our numbers have increased by twenty-three, Miss Aggie is going to need kitchen help. That means shopping, preparation, and the actual cooking and cleaning up. Three meals a day. I think two volunteers will do it. Now I'm going to go around the room, give you a pen and a sheet of paper. I want you to write your name, and, if you have a cell phone, include the number. I'll input all this into the computer. Next, on the same paper, I want you to tell me about your strengths and what you perceive to be your weaknesses. After we go through all that, with the help of my grandmother and aunts, we'll be assigning you each a job. We are going to work shifts. Four to five hours each, unless you feel you can put more time into your particular task." Gus looked to his grandmother and aunts to see if they approved of his performance so far. They nodded.
A voice from the back shouted out, "I think we all would like you to address our pay, the bonus we were promised, and what we're going to do about the others left behind at that dump, Pine Crest."
"I'm going to let my grandmother address those matters." Gus got up and turned his chair over to his grandmother. He took that time to watch the faces of the people in the room. He didn't think he'd ever seen a happier group. He let his mind drift to his late-afternoon appointment with Marsha to look at the house that might be his and Wilson's new home. He didn't spend too much time thinking about the house, because he trusted Marsha and knew it would work out.
His thoughts took him to the fireplug and how that was going to play out. Well, the ball was in her court now. He checked his phone to see if he had any texts or messages, since he'd turned the ringer off so as not to interfere with his presentation to his grandmother's new staff. He shoved the phone back in his pocket when he saw his grandmother get up and point to the chair. He was suddenly aware that the seniors were clapping. Obviously, they were happy with whatever his grandmother had said about their contracts.
Gus sat down and looked around. "Do any of you have any questions?"
There was only one question, and Elroy Hitchens was the one who voiced it. "When do we start to work?"
Gus looked at his grandmother, who said, "Tomorrow morning. Breakfast is at seven o'clock. As I explained when you first arrived, we do a shuttle service between here and Shady Pines. So it will be rise and shine early. Sometimes, if business is brisk, we work at least a few hours on the weekends. We'll be posting a schedule, and you'll sign on for weekend duty. Give me a show of hands if you all approve."
Every hand in the room shot upward.
"This is when you show me your papers with your names and phone numbers and what your strengths and weaknesses are, so that I can draw up a schedule for your assignments and your working hours. On your way out of the room, hand me your papers. My grandmother and aunts will now give you a tour and answer any questions you might have," Gus said.
Gus worked industriously for the next several hours. He spread all the papers over the massive dining-room table. He hopped from one end to the other, then from side to side as he made notes on each page and input everything into the laptop. Even in the short period he'd been in the new seniors' company, he felt like he had a handle on their respective personalities. He looked at his watch. Time to leave for his appointment with Marsha. He pulled out his cell phone to check for messages or a possible text. Nothing.
In the kitchen, Aggie was paring vegetables. He explained that he had to leave for two hours and would be back in time—he sniffed—for dinner. "And, will you tell my grandmother not to touch anything in the dining room?" he added. Aggie agreed and continued to peel carrots.
"What's for dessert?" Gus asked.
Aggie wiped her hands on her apron and opened the huge double oven doors. He saw four chocolate cakes, the aroma tantalizing. He nodded and looked around for Wilson and Winnie but didn't see them.
"They're with the parade. Actually, Wilson was leading the way." Aggie laughed.
Gus shrugged and made his way out to his car. He didn't think he'd ever had a day like this one in his entire life. And yet he felt good, really good. So good in fact that he was going to call Barney to brag and to bust his best friend's chops. He grinned at the thought. But no point in making two calls. He'd wait to see how the real-estate deal went down. That way he could tell Barney he was moving out, thank him for his hospitality, and bring him up to speed at the same time.
Life is looking good.
Chapter 14
GUS TYPED THE ADDRESS OF THE PROPERTY WHERE MARSHA WAS waiting for him into the GPS. If there was no traffic, he should make the meeting right on time. He felt anxious for some reason. Buying a house could certainly account for the feeling. Then he thought about his day with his family and all the seniors he'd been helping. No sense lying to himself—he couldn't wait to get back to Blossom Farm to finish his scheduling. He was sure it was all going to work out. So sure, he started to whistle softly, something he always did when he felt happy.
After the storm, today had been a perfect spring day. Bright sunshine, and a warm seventy-one degrees. The air was filled with the sound of chain saws, which would have the town back to normal within a few days. Several more days of weather like today, and the ground would dry out. Just a little while ago, he'd heard the weatherman say there was no rain in the forecast for the next few days. Who could ask for anything more?
The monotone voice on the GPS informed Gus that he was less than an eighth of a mile from his destination.
Gus's first thought was that it was a pretty neighborhood, with full-grown trees lining the streets. He noticed that there were sidewalks on which kids could skateboard and roller-skate. He closed his eyes for a second and envisioned himself and Barney when they were ten years old, skating down the sidewalk or riding their bikes. He hoped it was a neighborhood with kids. The houses were all pink brick, with fireplace chimneys jutting upward. Cozy for the cold Virginia winters.
The generic voice on the GPS said he had arrived at his destination. And he had. He pulled his car alongside Marsha's in the two-car driveway. She was waiting for him, leaning against her car, reading a folder in her hands. They hugged each other. "Where's Wilson? Doesn't he get a vote?"
"He's at my grandmother's. Long story. I like this," Gus said, looking around. "The neighborhood is established, and it looks like everyone takes care of their property. No wooden or chain-link fences, no cracks and weeds in the driveway. Looks freshly painted."
"Trust me, Gus, this is the house for you. The owner is abroad; he's a freelance journalist. He lived here for almost fifteen years, then he got reassigned and rented it out. Renters do not take care of property even when they leave a security deposit. We put it on the market to sell. No takers. The economy hit, and now he just wants to unload it. He had the agency contract the work out, so the house is in pristine condition—new carpeting, new appliances, freshly painted, inside and out. If I had the money, I'd buy it myself, but I have two kids in college and an ex who is fighting me in court so he doesn't have to help pay for college. Oh, you said you needed a fence in the back. Well, you got two of them. When the owner first moved in, he put up a chain-link in the back because he had two springer spaniels. Then he decided he didn't like the way the fence looked, so he planted a boxwood hedge in front and back so now, over the years, the chain-link monstrosity can't even be seen. Wilson will be perfectly safe in the backyard."
"Sounds good; let's take a look."
Fifteen minutes later, Gus said, "I love it. I'll take it."
"I knew you would. Listen, Gus, with what you told me about your impending divorce, I've been thinking about something. Maybe we need to do a little creative, for want of a better word, accounting here. I spoke to the owner earlier this afternoon, and he's okay with it as long as you are. When your wife's attorney runs your financials, this house is going to show up as an asset, and she'll want her share. Instead, you rent for now, the monthly rent going toward your mortgage payment when the divorce is final. The owner is willing to wait on the closing, he just wants the mortgage payment and the utility payments off his back. What you pay in rent will alleviate that. You following me here?"
"I am, and I like it. So, I pay out first, current, and last month's rent on the books and this is mine, right?"
"Yes."
"When can I move in?"
"If you had your toothbrush with you and a sleeping bag, you could move in right now. Give me a check for the rent, and I'll give you the keys, and the place is yours the minute you sign all these papers. We'll hold your check for the down payment at the agency until you tell us it's okay to cash it. You don't want that showing up in your financials, either."
"This is working out just perfectly, Marsha. I don't know how to thank you. I have to get some furniture. Any ideas?"
"Gus, you saved me a boatload of money on my taxes over the past few years. It's I who should be thanking you. Stonehill's can deliver tomorrow. The store is open till six-thirty today. In this economy, store owners are bending over backwards for customers. By tomorrow night, you and Wilson can be snug as two bugs in your own digs."
Gus felt embarrassed for some reason. "That was business. It's what I do."
Marsha laughed. "Well, this is what I do, so we're even. Sign your name, then we can shake hands. I'd like to take you out to dinner the way I always do when I finish up a deal, but I have another appointment, and I don't want to be late."
Gus handed over two checks and signed his name to the real-estate documents. Instead of a handshake, he hugged the Realtor. And then they went their separate ways.
It was almost six-thirty when Gus walked out of the furniture store in New Town, clutching his bill of sale. Delivery tomorrow would be between eight and nine a.m., the first delivery of the day. He'd spent more than he intended but consoled himself with the fact that he planned to stay in the pink brick house for the long haul. If he was lucky enough to get back his old house after the divorce, he'd sell it and give his grandmother the money. He would have a yard sale and get rid of all the furniture and all the memories of Elaine.
On the drive back to Blossom Farm, Gus thought about what he'd bought. Two deep chocolate–colored chairs, a big, deep wheat-colored sofa, a seventy-six-inch plasma TV on which to watch ball games with Wilson, a complete bedroom set, and a set of stools for the kitchen so he could eat at the counter. He'd furnish the dining room and living room at some point when he had more money. For now, he had the basics. All he needed was a trip to Target for towels, bedding, dishes, pots and pans, and stuff for everyday living. One grocery-shopping trip, and he would indeed be a resident at 11 Bombadile Court. He wondered if his neighbors would bake him a welcome cake or bring over a covered dish. He hoped the neighbors were nice. Maybe they'd invite him to backyard barbecues. Or maybe he could barbecue and invite them. Whatever, he'd make it work.
Gus stopped at the last traffic light before he had to turn down the service road that would take him to Blossom Farm.
The car stopped on the opposite side of the road was a bright yellow Volkswagen Beetle. Not many of those in Sycamore Springs. In fact, he didn't think there was another one, which meant Elaine was sitting at the light. The urge to step on the gas pedal and cross traffic to smash head-on into the little car was so strong, Gus had to clutch the wheel to make sure he didn't do it. If he'd been driving his own car, he thought he might, just might, have done it, but he was driving Barney's Jeep Commander. He sat still—even though the car behind him honked its horn—as Elaine whizzed past him without so much as a glance. In the quick glance he got of her, he saw that his wife was what he called dressed to the nines. She used to do that for him when she wanted something. He moved forward when a second, then a third angry honk of a horn forced him to go.
Now he felt depressed. He pressed buttons on the stereo system and stopped when he heard music that felt soothing to his tortured soul. To further torment himself, Gus drove past the turnoff for his grandmother's house, and instead drove all the way to his old house, where he used to live with Elaine. He stopped at the guardhouse and said hello to Eddie, the guard who had worked there from the day he'd moved in.
"Evening, sir. You just missed your wife. New car?"
"Evening, Eddie. Just a loaner for now. I know, I passed Elaine on the way. I'll be coming right back out. Good to see you. Have a nice evening."
The cell phone in his pocket vibrated, but he ignored it. When you were doing something stupid, you needed to concentrate on the stupid part to make sure you got it right. Sitting in the driveway of the house his grandmother had bought him caused him to choke up. His eyes burned. Once upon a time, he had loved this house. Now he hated it with a passion. Sitting here was worse than stupid. He lost track of time as his memories attacked him, one after the other. Finally, as dusk was settling, Gus backed up the car, turned, and headed back the way he came.
When he came to the guardhouse, he waited until Eddie got around to opening the gate for him to leave. He didn't pay one bit of attention to the Asian man walking a Jack Russell terrier on the other side of the guardhouse.
When Gus cut the engine and crawled out of the car, he knew his grandmother and the aunts were going to look at him as undependable, as he had said he'd be back in two hours. It was now about four hours later. Performance be damned. He squared his shoulders and entered the house. For the most part, it was silent, his grandmother sitting alone in the kitchen working at one of her ledgers. She looked tired.
Gus poured himself a glass of sweet tea, perched on the end of a chair, and rattled off what he'd done since he left the house to keep his appointment with Marsha. "I had to take care of things, Granny. I'm all set to go. Did anything happen? Is there anything I need to know before I get started?"
Rose smiled. Her grandson looked more tired than she felt. "Life sometimes has a way of interfering with one's plans. We did okay today. Tomorrow will be better than today, that's for sure. Everyone is tired, the excitement and all. Old people"—she laughed—"can take just so much excitement in one day. Go along and do what you have to do. Did you have dinner?"
"No, but that's okay. I kind of lost my appetite somewhere along the way." It was a lie, he was starved, but he wanted to get to work; the seniors were depending on him. He could always eat. "Where are Wilson and Winnie?"
"With Vi and Iris in the storage room. They're fine, Augustus. Run along now so I can finish this. There's a plate warming in the oven for you if you get hungry later."
Gus worked through the evening, stopping just once for a bathroom break and to refill his glass of ice tea. He barely noticed that at some point Wilson had come into the dining room and settled himself at his feet. He felt comforted.
It was five minutes past midnight when Gus carried the work schedule out to the kitchen and laid it on the kitchen table for his grandmother to see first thing in the morning. Every person was accounted for; every shift of work for whatever endeavor they would work on was accounted for. He'd even made suggestions for increasing inventory, and mapped out a more efficient means of storing supplies and product. He knew he'd whittled down hours, possibly days, of futile work for the seniors if they followed his advice. Tomorrow, after his furniture arrived, and he made his trip to Target and the grocery store, he'd come back and pitch in again.
The house was so silent, Gus felt like an intruder. Wilson waited at the door, but there was no sign of Winnie. "Just me and you, huh? Well, let's head for home. I have a lot to tell you. I think we found our niche. Finally."
Wilson beelined toward the stove and nosed the oven door. "Oh, yeah, dinner. You know what? I'm too tired to eat, Wilson. Let's just go home." Wilson was having none of it. He growled softly until Gus opened the oven door. When he saw the dinner plate loaded with sliced chicken, stuffing, cranberries, mashed potatoes and gravy, string beans, and a dinner roll, he changed his mind. He sat down on the floor and started to eat, sharing with Wilson. "Kind of like old times, huh, big guy?" Wilson woofed softly.
It was eleven o'clock the next morning when Gus unlocked the side door of his new house. The furniture people had delivered on time and even hooked up the new TV for him.
He'd tipped them accordingly. He'd made his run to Target and gotten everything he needed. He'd washed the sheets, and the towels were just waiting to go in the dryer. His new dishes, glasses, silverware, and pots and pans had gone through the dishwasher. The supermarket trip took a little longer than expected, as he picked up just about one of everything, careful to stock up on Pop-Tarts for Wilson.
He was exhausted, but it was still a good feeling. That's when it hit him that he hadn't called Barney. Just as he was about to hit his speed dial, a neighbor about his age walked over and held out his hand. "Jeff Lucas. I live next door. Welcome to the neighborhood. Your Realtor left a short bio of you and your dog in everyone's mailbox yesterday by way of introduction. I'd stay and talk more, but I just came home to check on my sprinkler system; it's out of whack. Don't want my yard to flood. Guess the storm fouled things up. My wife, Sara, said she's going to bake you a cake to welcome you to the neighborhood. See ya," he said as he headed toward his own house.
Gus grinned. "Hop in, Wilson. Seems like a nice guy. I think this is going to turn out just fine." Barney would just have to wait till he got to Blossom Farm, because Gus didn't like driving and talking on his cell phone at the same time.
The minute he parked the car at Blossom Farm, Gus pulled out his cell phone and noticed for the first time that there were four messages from the fireplug. He groaned. Instead of listening to them, he hit the speed dial for Barney, who sounded like he was asleep when he answered. "What now?"
"What now, indeed! I have news to share and thought you would want to know. I can hang up and call you back later if you like."
"I'm awake now. Let's hear it." Gus relayed yesterday's events and what had transpired so far today.
"So what you're saying is you're back in the fold and working your ass off to show everyone that you know how to perform. You bought a house but actually you're renting it and are doing some creative accounting for the time being. You sat outside your old house and had an attack of déjà vu because it was a stupid thing to do. How am I doing so far?"
"You're doing good. Wilson loves me again. Granny and the aunts are feeding me. I'm a happy camper."
"That's good to hear. I was worried about that guilt by association thing where you and your granny were concerned. I don't understand why you were in such a hurry to buy a house. Isn't mine good enough for you?"
"Aren't you listening, Barney? It's not about the money or your big house. It's about me and Wilson picking up the pieces and starting over in our own place. Yeah, it's going to be tough, and I'm going to have to watch my pennies, but I can do it. If I have to, I can moonlight on the weekends for extra money. I appreciate everything you've done for me, you know that. I'm not a taker, Barney. You of all people should know that. Just tell me you're okay with all of it, and you'll make my day."
"Of course I'm okay with it. I'm just jealous that you're having all the fun, and I'm stuck here in Hong Kong. I'm thinking of retiring, Gus. What do you think of that?"
Gus started to laugh and couldn't stop. "I think I know someone who might hire you. Part time. No pay, no benefits, just oodles and oodles of goodwill, smiles—and you'll go to sleep at night with a smile on your face." Barney laughed because he knew Gus expected him to laugh.
"Well, I gotta go. Any news from Phil Ross?" asked Gus.
"Damn, didn't I tell you? Phil retired last year. He just gathered all that information as a personal favor. Jill Jackson hired someone else. Don't worry about it. By the way, how is all that working out for you?"
"Gotta go now, Barney. Granny's at the door, and they need me," Gus said, and let Wilson out of the car.
"How'd you like that, Wilson? I got out of answering him. Pretty slick if I do say so myself. Come on, let's see what the seniors have in store for us today."
Woof.
Chapter 15
MICKEY YEE AND HIS DOG BOOKER STROLLED ALONG THE BIKE and walking path in the gated community where Elaine Hollister lived. He spotted a bench that would allow him to sit as dusk settled. This was the time of evening when dog walkers were out and about. He didn't think anyone would pay attention to him if he sat for a while without drawing attention to himself and his dog. He leaned back on the wooden bench, threw his arm over the back, then handed Booker a rawhide chew to keep him busy. Just a man and his dog out for an evening stroll.
In the pocket of his tee shirt, Mickey had a mini-recorder. He turned it on and listened to Lynus Litton's voice relaying the information from the report that the detective assigned to follow Elaine Hollister had submitted. He'd listened to the tape at least six times since arriving at the gated community. He had already committed it to memory. He understood all that he heard, but something puzzled him. Something Lynus Litton didn't have the answer to.
The investigator, Don Parker, said Elaine Hollister had had no visitors once she arrived home, until the time she left to go to her dinner engagement with her attorney, Isaac Diamond, which was verified by the audio tape from the bug Mickey himself had planted on Hollister's landline. The conversation confirmed the dinner date and renewed the offer of a car to pick her up, an offer Hollister again declined. What Mickey didn't understand was the two hours of muffled conversation or dialogue that Lynus said could be heard on the audio. He had orders to check his bugs to see that they were in working order. Always thorough, Mickey had, as usual, checked the bugs several times before he'd installed them. So, did Elaine Hollister talk to herself? Did she read aloud just to hear her own voice?
Lynus had left instructions for Mickey to stay in touch with Don Parker over open cell phone connections. Don was to call him the minute Elaine left the restaurant in case he was still in the house and needed time to get out clean. His last conversation with Don led him to believe that after dinner, the couple would head for someplace a little more intimate. Probably to discuss Elaine's case, Don had said, tongue in cheek.
Mickey looked at his watch, and saw that it was already seven thirty. By the time he and Booker got to the Hollister house, night would have descended, making his job easier. He got up, settled his backpack more firmly on his shoulders, and picked up Booker's leash. "Time to go, Booker."
Twenty minutes later, Mickey Yee was standing inside the Hollister kitchen. A night-light low on the floor gave the state-of-the-art kitchen a dim, pale glow but gave off just enough light for him to make his way through the dining room, also lit by a low night-light on the baseboard. "You know what to do, Booker. I'll be on the second floor."
He sniffed, wondering what it was he was smelling. Perfume? A room air freshener? Women like those things for some reason. Some kind of aerosol spray like Lysol? No, that isn't it. It was something he'd smelled before, but he couldn't put a name to what it was. Whatever it was, he didn't like it.
Mickey galloped up the steps and ran down the hallway to Elaine Hollister's bedroom. He blinked. It looked like a tornado had swept through the room. Clothes and shoes of every description littered the bed and floor. Obviously, the lady couldn't make up her mind what she should wear to the dinner engagement with her attorney. The bathroom looked worse. Makeup was everywhere, and wet towels littered the floor. What really interested him, though, was the cell phone charging on the vanity. Quicker than lightning, he had the phone bugged. He plugged it back in, careful to place it exactly where it had been. Talk about luck. Now he didn't have to worry about breaking into the house in the dead of night, with Elaine Hollister sleeping upstairs.
Mickey moved to the landline on the night table. He checked it, tested it, and was satisfied there was nothing wrong with the bug. He moved out to the hall, pressed the button that would lower the ladder that led to the attic. The ladder dropped, then unfolded. It looked like a dark pit overhead. The strange scent seemed to sweep through the opening and engulf him. He didn't see a light switch anywhere, so that meant he'd need a flashlight. He rummaged in his backpack and withdrew a small Maglite that, when turned on, would illuminate an entire room.
Mickey stuck the end of the powerful light between his teeth, grabbed the arms of the flimsy ladder, and climbed, the Maglite lighting the way. The fine hairs on the back of Mickey's neck moved. He crawled across the floor as soon as his feet left the ladder. He squatted and looked around, the Maglite showing him something he had never expected to see.
Mickey gaped at the makeshift altar, complete with a crisp white altar cloth. The altar was filled with vases of white flowers, colored beads, black candles, and incense holders. A vial sat in the middle of the altar, clearly labeled, in fine script, Holy Water. Next to the holy water was a dish of salt.
That's what the smell was; Elaine Hollister had been burning incense since his last visit. Here in the attic, the smell was overpowering. Mickey was absolutely, positively certain that by the time he left this place, he'd have a really bad headache.
Still squatting on his haunches, Mickey didn't like what he was seeing at all. He felt creeped out at the strange altar. Then he spotted the Bible, with a pair of reading glasses sitting on top of it. The hair on the back of his neck moved once more. He moved the light to see what was beyond the makeshift altar. He saw cardboard cartons and empty mailers. A furrow built itself between his brows as he tried to comprehend what he was seeing.
Witchcraft? Voodoo? Mickey shivered. He moved the Maglite and saw a sheaf of what looked like heavy yellow parchment with all kinds of symbols and signs that he wasn't familiar with. He could clearly see the words, SPELLS and RITUALS, in heavy black-and-gold lettering. Then he thought about the four jugs of vinegar and the full shelf of herbs in the refrigerator in the kitchen downstairs.
Mickey fumbled with the cell phone in his pocket, on which he had an open line to Don Parker. He whistled softly and told him what he was seeing.
"Sounds to me like you got a high-priestess thing going on. I'd say from what you're telling me that Hollister practices either witchcraft or voodoo. I'm not an authority on the subject. I'm just saying. I think you need to talk with Lynus, but I think that explains the conversation that was on the tapes. She was probably casting spells or chanting. I saw a movie once, and something like that was in it. I gotta say, Mick, looking at that woman, I never would have thought she'd be into something like that."
Mickey cleared his throat. "Me, either. This is creeping me out. What's going on there?"
"Looks like they're having brandy and coffee. They look like any other couple out to dinner. No kitschy-coo, no handholding, nothing like that. They each had two glasses of wine. They'll be leaving in about twenty minutes is my best guess. Keep the line open and get ready to leave in case she heads home. Call Lynus and tell him what you're seeing. You bring a camera with you?"
"Yeah."
"Take pictures of everything. Even if you think it doesn't apply."
"Okay. I'll get back to you." Mickey shoved the cell phone back into his pocket. He pulled out a second one and called his boss. He rattled off his findings. When he heard Lynus whistle, he knew he was really onto something.
"Take pictures, and I want to see you and them in my office first thing in the morning. Don't forget to take a picture of the inside of the refrigerator."
"Okay, no problem." Mickey broke the connection, then dug out his digital camera. He positioned the Maglite to give him the best light. He snapped the altar from all angles. He took a picture of the Bible and the reading glasses. Then he took a shot of the cardboard cartons and the empty mailers. He could see the words INITIAL B ENTERPRISES on one of the mailing labels. When he stretched his arm across the altar to get the boxes and mailers into better position, he knocked over one of the vases holding the white roses. "Oh, crap!" he groaned as he watched the water spread across the altar.
There was no way he could cover that up. Always confident, he decided that the best-case scenario would be Elaine Hollister would think that a rat or a mouse had toppled the vase. He snapped the pictures he wanted, then backed his way to the opening and the ladder that would take him down to the second floor. He looked around to make sure he wasn't leaving any signs that would indicate there had been an intruder. Once he'd reset the alarm and locked the door, Mrs. Hollister wouldn't know the difference.
Mickey put the Maglite back in his backpack and made his way down to the kitchen, where he took pictures of the vinegar jugs and the shelf of herbs. The lighting was perfect for the shot. He closed the refrigerator door and returned the camera to his backpack. He set the alarm, whistled for Booker, and they left the house. Outside, he drew a deep breath. He'd screwed up. He needed to call Lynus.
Mickey and Booker jogged all the way to the security gate and left the area as quickly as they could. The minute he was settled in his car, he called Lynus to report his screwup. He listened as his boss reamed him out about sloppy work, then he listened to his apology, saying mistakes happen. He didn't feel one bit better. The kind of mistake he'd just made could mean the success or failure of the investigation.
"Okay, Booker, let's call it a night. I know you're hungry, and so am I. Tomorrow is another day." That's when he remembered the stack of black-and-white notebooks, the kind they sold in drugstores a long time ago. He wasn't sure, but he thought he'd had one for one of his English classes. Crap. Did I take a picture of the notebooks? Not specifically, he decided, but maybe they'll show up on one of the other shots. You're getting sloppy, Mickey, he warned himself.
Gus woke with Wilson's nose nudging his chin. Time to get up. "Okay, okay! I'm up. Hey, buddy, how'd you do the first night in our new digs?" Wilson let loose with a loud bark. "That good, huh?"
Gus staggered out to the kitchen and opened the door for the shepherd. He stood there watching his dog search out the perfect bush, scratched his head, felt the bristles on his cheeks, and decided coffee was what he needed. His big decision was whether to make breakfast or wait to eat at the farm. Or, he could pick up a breakfast burrito on his way to the fireplug's office. Coffee and juice, he decided, and he'd grab something later. Wilson wouldn't see it that way, he knew, so he filled a bowl with canned dog food and kibble, then set down a fresh bowl of water. The time was six-ten.
As Gus waited for the coffee to drip into the pot, he looked around his new kitchen. He liked that the sun would come in the kitchen window in the morning, and he could look out into the yard while he sipped his morning coffee. He made a mental note to find out if there was a morning newspaper delivery in the neighborhood. There was nothing like a morning cup of coffee and the day's news, in his opinion. He knew there were millions of people who would rather read the news online. He was definitely not one of those people.
Gus poured his coffee and let his mind wander. He'd slept well, felt rested. He felt like he was ahead of the game, because he'd slept in a brand-new bed. Then again, he'd been exhausted when his head hit the pillow.
His thoughts next took him to the day he'd planned out for himself. First and foremost, he was going to see the fireplug to see what she wanted to do where he was concerned. From there, he'd stop by the office to check on things. After that, it was out to the farm and the seniors. He wondered what his grandmother had thought of the schedule he'd left behind and what she'd made of the suggestions he'd like to implement.
Gus finished his coffee, checked Wilson's bowl, then rinsed it and put it into the dishwasher. He refilled his cup and carried it upstairs. He showered and shaved, then dressed in a pair of crisp khakis that Maggie had ironed for him while he was staying at Barney's house. He checked his polo shirts but ended up wearing a pale blue button-down oxford shirt. He rolled it up to his elbows, slipped his feet into Docksiders, and was ready to go.
"Okay, Wilson, time to put a move on. Get whatever you want to bring with you because it's going to be late when we get back. Just ONE thing, Wilson, not an armful. You can play with Winnie's things when we get to the farm." Gus watched, amused at Wilson's attempt to pick one thing to bring to the farm. He picked up a tattered-looking stuffed rabbit with only one ear and half a tail. It was his favorite toy, the one he slept with at night. He picked it up twice, and twice put it back on his bed. He finally chose a ball with a hole in the middle and a ring through it. He looked up at Gus, his signal that he'd made his decision.
"I suppose someone will want to play tug of war with you. Time to get our show on the road."
Gus's plan was to arrive at Barney's offices as close to seven-thirty as he could. He'd had a key to the building ever since Barney opened his offices. He would wait in the lobby to greet the fireplug on her arrival. Whatever was going to happen would then happen.
He had the building to himself when he arrived, and took a seat in one of the buttery-soft chairs scattered throughout the medium-size lobby. Wilson lay at his feet. Gus sat quietly, his thoughts of the farm and what lay ahead of him.
He knew that the fireplug was approaching when Wilson rose to his feet and walked over to the door. If the attorney was surprised to see a dog greet her, she didn't show it. Nor did she show any surprise when she saw Gus getting up off the chair he'd been sitting in. She'd make a good poker player, Gus thought. He watched as she scratched Wilson behind the ears for a few moments.
"Good morning, Mr. Hollister. How nice to see you so early in the morning."
Gus knew that she was thinking, how nice of you to ruin my day so early. "I know we didn't have an appointment, and that we've been playing telephone tag. I'm sorry about that. So, can we discuss whatever it is you want to talk to me about? I also wanted to give you my new address and the phone number at my new house in case you can't reach me on my cell phone."
"Follow me, Mr. Hollister. I can give you exactly thirty minutes, then I have to leave for court on another matter."
Gus looked around the fireplug's office. It surprised him, and he wasn't sure why. He liked it, though. He took a seat across from the polished desk and waited for her to take her seat of power. That's how he thought of it, a seat of power. If he compared his office to this one, his would fall into the pigsty category. Not that it was dirty, just messy.
Jill folded her hands and leaned forward. She adjusted her granny glasses more firmly and stared across at him with unblinking intensity. "Do you have anything you want to ask me before we discuss your wife's petition for divorce, Mr. Hollister?"
"No. My wife is divorcing me. I am not contesting it. If this were a perfect world, I'd tell you to fight till hell freezes over not to give her anything, but I know this is not a perfect world, so I'm probably going to have to make some kind of settlement. You already know the deal on the house. I was a fool, I admit that. So I guess what I'm saying here is do the best you can on my behalf."
Jill's cell phone took that moment to chime to life. Gus watched as she fished it out of the pocket of her jacket. She identified herself, then listened. All Gus could hear were the words, "I'll ask him. He's here right now. Yes, that is strange. Thanks for the heads-up.
"Now, where were we, Mr. Hollister?"
"I was telling you to do the best you can do on my behalf. I'm not naive enough to think I'm going to skate on this. Is there anything you need me to do on my own behalf?"
"I wanted to discuss what you're willing to part with. I'll be calling Isaac Diamond, your wife's attorney, for a face-to-face. I've engaged the services of a private detective agency. We have ongoing surveillance on your wife. Right now, that's all I'm comfortable telling you. And I want to caution you about talking to your wife. I don't want you to be surprised if she calls you. If you're like most people, I'm sure you have caller ID on your new landline at home and, of course, it will show up on your cell phone. If she calls, let it go to voice mail and call me right away."
"Okay, I don't have a problem with that. She's the last person I want to talk to. What is it you hope to find out with surveillance?"
"After I find out, I'll ask you what is normal and not normal where your wife is concerned. Then I'll make a call on it. We do have time before I'm going to schedule a meeting with Mr. Diamond. Again, I'll let you know when that is going to happen. You and your wife might or might not be at that meeting."
"I understand. I hope you got my message where I apologized to you."
Yessireee, this lady would make a great poker player.
"I did. I accept your apology." The expression on the lawyer's face was that of someone who had bitten into a lemon. Jill reached into a drawer and withdrew a yellow legal pad. "Now, give me that new address and phone number. You moved out of Barney's house?! Living in a mansion with live-in maid service, cooked meals, someone to do your laundry, six cars at your disposal, everything free. What's not to like? Why did you move?"
Gus wanted to reach across the desk and grab Jill Jackson's lovely throat. Lovely throat. The words left him confused for a moment. He might have dropped it right there, but Jill started to tap her fingers on the desk as she waited for his reply. "Because I'm not a person who needs a fancy house with maid service and six cars. I can cook and do laundry and take care of myself. My grandmother taught me early on how to be self-sufficient. The only reason I moved into Barney's house was because of Wilson, and because I had to get my head on straight. I'm renting a house with an option to buy if it's a good fit for Wilson and me."
"Is that the same grandmother you turned your back on in favor of Elaine Hollister?"
"You damned well know it is. When are you going to stop jamming that down my throat, Miss Fireplug?" Oh, shit, did I just say that? Obviously, from the look on the lawyer's face, he did just say that, and he'd struck a nerve.
"What did you just call me?"
Gus knew his face was flaming red as he tried to weasel his way out of his comment. "Sorry, I was thinking of something else. I didn't mean . . . I wouldn't . . . I meant to say Miss Jackson."
"Now, why don't I believe you? You know what, Mr. Hollister, I think we've had enough for one day. I'll call you when I need to talk to you again." Gus noticed that her face was as pink as his felt, and her lovely throat was also pink.
"I do need to ask you one question, however. What do you and your wife do with all the vinegar in your refrigerator? Four gallons to be exact. And what do you use all those herbs for?"
Gus thought those were the stupidest questions he'd ever heard in his life. "Vinegar! What herbs? When were you in my house? I don't know what you're talking about."
"Need to know, Mr. Hollister. Okay, so the vinegar wasn't there when you left a few days ago, is that what you're saying?"
"That's what I'm saying, Miss Jackson. I guess Elaine uses it for something."
"And the attic?"
Gus threw his hands in the air. "What about the attic?" There's nothing much up there but my skis and an old toboggan. In the spring, I pack up my winter clothes and put them up there and bring down the spring and summer clothes. I suppose Elaine put some of her stuff up there. She pitched a fit a few months back and wanted a ladder put in so she could go up and down. It's electric. I personally never used it. Why?"
"I'm not sure, Mr. Hollister. I really have to go now. I'll call you when I need you or to apprise you of new developments."
Gus knew when he was being dismissed. He got up just as Wilson did. He almost tripped over his dog, who was hell bent on going around the desk to check out the fireplug. Gus was stunned to see how the lawyer's face softened as she bent over to scratch Wilson behind the ears and rub the sweet spot between his eyes. Wilson was a goner the moment she did that. He licked her hand and whimpered softly as Jill continued to stroke the big dog's head.
"One last thing, Mr. Hollister. I don't want to hear that you're feeling remorseful and need comfort by sitting in the driveway at your old house. Yes, I know about that. Your wife took out a restraining order on you. She could have had you arrested. Do not do that again. Do you hear me?"
"How the hell—? Never mind. Yes, I hear you, and it won't happen again. I knew that Elaine wasn't home; I had passed her on the road going the other way, so I felt safe doing it."
"Like I said, don't do it again."
Gus hung his head. Caught again like a schoolboy. "Let's go, Wilson. Thanks for seeing me without an appointment. I appreciate it." He didn't mean to stare, but he couldn't help but gaze at that lovely throat. He'd hurt her feelings, and she was having a hard time with what he'd called her. He wanted to apologize again but knew he'd just make matters worse.
Outside, he mentally kicked himself as he opened the door of Barney's Jeep. If they were giving out awards for stupidity today, he'd take one hands down.
Gus drove to his office and spent ten minutes hearing that everything was running smoothly. He trooped back outside and headed for Blossom Farm, all the while thinking about the young lawyer. He realized he knew virtually nothing about her other than that she was a capable attorney. What was her personal life like? Obviously, she liked animals in general and dogs in particular. He recalled the fish tank and how restful it was watching the fish swimming in lazy circles. The clean lines of the office and the lack of clutter and the comfortable furniture should have given him some clues. He wondered if Barney had any insights on her personal life. And if he did, would he share what he knew? Doubtful, knowing Barney.
On a whim, Gus made a left turn, then a right turn, and stopped at The Flower Shop. The perfect name for a florist. He parked in the tiny lot and told Wilson to wait and guard the car. He ran into the store and ordered a dozen white roses to be sent to Jill Jackson. "Put lots of green stuff in the arrangement," he added. He scribbled his and Wilson's names on the card. Corny for sure, but he did it anyway. He paid cash and asked for the delivery to be made that day.
Gus felt a little better when he climbed back in the car. "I sent roses, Wilson, and I did that because I have a big mouth and don't stop to think before I talk. I hurt her feelings. Granny taught me better than that. She liked you, though. That's a good thing, Wilson. You might have to run interference for me from here on in where she's concerned.
"Now, we have to get to work, and I have a feeling it's going to be a really long day."
Wilson pawed Gus's arm, his signal that things were okay, before he settled down for the ride to Blossom Farm.
Chapter 16
AFTER COURT, JILL JACKSON ENTERED THE BEEZER BUILDING, A scowl on her face. She swept past the security guard with a flash of her ID pass without even looking at him. Normally, she had a smile for the guard, oftentimes inquiring about his grandchildren and his dog, Molly. Not today, though. Today, the young lawyer sprinted forward like she had a life-or-death destination in mind.
When the elevator stopped at her floor, she sailed past the receptionist and walked down the hall to her suite of offices. Her secretary, an early fiftyish woman, held up her hand and said, "Whoa! Whoa there, Jill. Slow down. What? Did someone rain on your parade? Step on your toes? I know you didn't lose in court, so what's with the attitude I'm seeing here?" Louise Atkins had been with Jill since her first day at Beezer. Familiarity was an okay thing where the two women were concerned. Not only were they boss and employee, they were personal friends. Had anyone else been within hearing distance, Louise would never have allowed personalities to show, because she was too professional to permit that to happen. She waited to see what Jill would say.
"Court was a waste of time; the judge granted a continuance. I knew that would happen going in. Like I said, a waste of time. No one rained on my parade, and no one stepped on my toes. Were there any calls?"
"Mr. Beezer and Lynus Litton called. Mr. Beezer wants you to call him back. Nothing urgent, he said. Mr. Litton said he needs you to return his call ASAP. So, what happened? Why do you look like a thundercloud? Don't tell me there is nothing wrong, Jill. I know you too well. Let me help; that's why I'm here."
Jill took a moment to stare up at her friend and secretary and only saw concern for her. She struggled with herself as she tried to decide if she wanted to respond. "If I ask you a question and tell you all I want is a yes-or-no response, can you do that?"
"Absolutely. What is it, Jill? I've never seen you look like this. Plus, you're agitated, and you're always cool as a cucumber, even when you're losing. Mr. Beezer told me once he'd hate to play poker with you." Louise had said this before to Jill, and it always garnered a smile of sorts. Not this time.
"Okay." Jill took a deep breath. "Do I look like a fireplug to you?"
"Yes!" Louise said smartly without missing a beat.
"I do? Are you just trying to rile me up?"
"Why would I do that? You asked me a question, and I answered it. Don't you tell me time and again that a lawyer should never ask a question he or she doesn't already know the answer to?"
"I do say that. It's true, and it's the first thing you learn in law school."
"Then why did you ask me if you knew what my answer would be?" Louise drew herself up to her full height, adjusted the trim jacket she was wearing, then went back to her desk. She sat down with a hard thump, but her gaze stayed on Jill, who seemed to be having a hard time with her answer. "I assume someone hurt your feelings at some point this morning, and you're having a hard time dealing with it."
Jill crossed her arms against her chest. She nodded, her face miserable.
"Jill, you don't have to look like a fireplug. All you have to do is change your mode of dress. You wear so many layers, it's hard to tell there's even a body under them."
"What's wrong with what I'm wearing? Tell me one thing that's wrong."
"Are you sure you want to ask me that? Do you even look in the mirror before you leave the house in the morning?"
"I wouldn't ask if I didn't want to hear your answer, and of course I look in the mirror before I leave the house. Well?"
"No one wears brindle or drindle skirts or whatever they're called anymore. There must be ten yards of material in that skirt. Minis are in, and so is spandex. A blouse, a vest, and a jacket are way too much apparel for a small person like yourself. Put all that on top of ten yards of material, and you look like a walking tent. And let's not forget those combat boots you wear. And your color choice is drab. All you wear is beige, brown, or gray. It makes you looked washed-out. You don't even wear makeup. You need color."
"Well, thank you for your opinion. I think. My shoes are not combat boots, Louise. They are Ferragamo ankle boots."
"Yeah, well try telling that to the fashionistas. The characters on that old TV show Little House on the Prairie used to wear the kind of shoes you wear."
Jill lifted up the hem of her long skirt and looked at her shoes. She liked them; they were comfortable, and she'd paid a lot of money for them. She liked comfortable shoes because she liked to walk back and forth to the courthouse. Taking care of her feet was important.
"So what are you going to do about your mode of dress?"
Jill whirled around. "What makes you think I'm going to do anything about my mode of dress?" Jill looked so shocked at her secretary's question, Louise had to hide her smile.
"That's a trick question, right?" Louise sniffed. "There's also the pickup truck you drive back and forth to work. Ladies, like some lawyers I know, do not drive pickup trucks. At least not the ones I know."
"Yep. I have a Jaguar. I drive it to church on Sunday. How about some fresh coffee?"
"Coming right up. Be sure to return Barney's call. Lynus Litton said he really needed to talk to you, so you might want to call him first. Is that the same six-year-old car that has four thousand miles on it?"
"GO!" Jill roared.
Settled in her office, Jill removed her jacket and hung it on the coat tree. She looked at the sleeves of her striped cotton shirt. What was wrong with the beige-and-white-striped shirt? She'd washed it, starched it, then ironed it. She was meticulous when she ironed her shirts. The camel-colored leather vest with the three toggle buttons was a favorite of hers. It was worn, soft, and comfortable. Maybe she didn't need to wear a vest. She thought about rolling up the sleeves of her blouse, and removing the vest, but if she did that, Louise would be right. Well, maybe she could open the buttons on the vest and roll the sleeves of the blouse to her elbow. She didn't do either one.
Fireplug. She would never imply to anyone that they looked like a fireplug. Never. Whether or not Jill wanted to admit it, Gus Hollister had hurt her feelings. She thought about her client then and how embarrassed he had been after he'd called her Miss Fireplug. She hated thinking about him and his case. If there were a way to pass him off to someone else, she'd do it in a heartbeat, but Barney would never allow that to happen. Maybe if Gus wasn't so handsome, she wouldn't feel like this. She'd been hard on him, and she wasn't sure why. Maybe because of his beautiful wife. A female thing. She argued with herself then. Gus Hollister was human. His case wasn't unique. Men did stupid things when they were married and the marriage ended. But, in most cases, at least the ones she'd handled, there hadn't been a grandmother and elderly aunts involved.
Gus had further confused her when he said he had moved out of Barney's luxurious house. Most people would love being waited on hand and foot and living in the lap of luxury, and all for free. She had to give him points for that. Maybe there was something there, but she wasn't seeing it. Barney said Gus Hollister was the salt of the earth. He said Gus was kind, generous, caring, a good friend, and that he loved him more than if he were a flesh-and-blood brother. So, yes, there was something there. Maybe she had preconceived ideas about Gus, and he hadn't measured up to those preconceived ideas, and she didn't want to admit that she was wrong about the kind of person he was. Everyone made mistakes. People deserved second chances when they screwed up, providing they admitted the mistakes and corrected them.
Jill was so deep in thought, she didn't see Louise come in until she set a mug of coffee on the desk. "Thanks," Jill said.
Jill waited until Louise closed the door behind her before she picked up the phone and dialed Lynus Litton's personal number. The greetings over, Jill said, "What do you have for me?"
"I just wanted to give you a heads-up. When I hang up, I'm going to upload a bunch of pictures one of my investigators sent me. I think they're going to surprise you. It appears that Elaine Hollister is into voodoo, witchcraft, casting spells, and performing rituals. I have to admit this is something I am not familiar with. I did an Internet search and found it all very interesting. I have to say, I got a little spooked. And there's one other thing. Mickey Yee, the investigator who got the pictures, had a bit of an accident while he was in the attic where Hollister does her . . . whatever it is she does. Trying to position some empty boxes and mailers for a photo, he knocked over a vase of flowers on the altar. That means Elaine Hollister is going to know someone was in her attic. Mickey wore gloves, but he was there. He reset the alarm, but if Mrs. Hollister is as smart and crafty as I think she is, she might call the alarm company and they'll be able to tell her the times the alarm was turned off and on, and she'll know for certain. But, there is also a possibility she might think a rat or a mouse, possibly even a squirrel, got into the attic and knocked over the vase. I just don't know, Jill. But you need to know everything I know. If she goes the route of the alarm company, someone might have seen Gus Hollister sitting in the driveway last night. She'll accuse him in a nanosecond. And he'll have no comeback."
Jill felt like pulling her hair out. "Okay, got it. Anything else?"
"I'll be sending you the report on Gus Hollister. He's clean, Jill. He's who he says he is. He did what hundreds of guys do, got mixed up with the wrong woman, compounded that mistake, and ended up marrying the mistake. Other than that, there's nothing there where he's concerned to throw up any red flags. We're still working on the grandmother and the two aunts."
"Okay, Lynus. Thanks. I'll be in touch." She was just about ready to turn on her computer when Louise opened the door and whistled sharply. "Ta da! Look at this, Jill," she said, thrusting a vase of white roses forward so Jill could get a better look. "Someone actually sent you flowers! And they smell wonderful. Bet these cost a small fortune." She carefully set the vase on the corner of Jill's desk and stepped back. "Well! Aren't you going to look at the card? It's not every day a woman gets flowers sent to her workplace. C'mon, Jill, open the card. When was the last time you got flowers, here or at home?"
"Never! No one ever sends me flowers. I got a corsage for my senior prom, but that's it. Okay, okay, I'm opening it." Jill's eyes popped wide. "They're from Gus Hollister. He signed it with his name and his dog's name."
Louise thought her boss looked shocked. "Now, that's sweet. You need to have more of an open mind where your client is concerned, Jill. They're just beautiful. Enjoy them," Louise said, turning to leave.
Jill waited until the door was closed before she leaned over to smell the huge arrangement of roses. Was Hollister sucking up or was he genuinely sorry for his crass remark, and this was his apology? She sniffed the flowers again, and propped the little card up next to the vase. The flowers were almost in her line of vision, and she'd be able to see them all day long as she worked. Her first flowers. How amazing was that? She felt almost giddy at the thought. A man, a client actually, had taken the time to send her flowers. Later, when she wasn't so busy, she was going to give some serious thought to the white roses. She was glad they weren't red roses. She hated red roses.
Jill clicked on her computer, brought up Lynus's e-mail, and looked at the attached pictures. She studied them for close to an hour before she printed them out. Then she reached for a magnifying glass and studied the printouts. Lynus was right. It looked like Elaine Hollister was into voodoo and witchcraft. She cringed when she saw the toppled vase on the altar. But the mailers and boxes were clearly visible. Initial B Enterprises. She frowned as she tried to recall if she'd ever heard of the company. Nothing came to mind. "Hmmmnn." Jill pressed a button on the console. "Can you come in here, Louise?"
"Yeah, boss. What's up?" Louise asked from the doorway.
"I want you to go to the main library and get me some books on voodoo and witchcraft. Try to get older books. I want everything you can get on rituals and spells. I could order them from Amazon, but that will take about a week. I'm going to search the Net, but I still want to have some books on hand."
Louise raised her eyebrows.
"Take a look at these pictures," Jill said.
Louise picked up the pictures and looked at them one at a time. "Oooh, this is not good. Okay, I'm on my way. Do you want me to bring back some lunch?"
"Sure, a ham and cheese on rye, and don't forget the pickles."
Jill was already clicking away even before Louise was out of the room.
While Jill Jackson was surfing the Internet, Gus Hollister was sitting down to a very late breakfast at Blossom Farm. His grandmother sat across from him, watching him eat. She smiled. Augustus had always had such a healthy appetite. She was complimenting him now on how hard he'd worked on creating a schedule for the seniors.
Gus carried his dishes to the sink, topped off his coffee cup, then sat down across from his grandmother. "Listen, Granny, you need to stop with the trips to the post office; it takes too much time and costs too much. Let's open an account with UPS, and they'll give us the shipping supplies, they pick up, and you save labor. You guys have been chasing back and forth to three different post offices. That's a lot of hours that are being wasted. Now, having said that, do you all understand that you need to tell me which . . . I don't know how you define it . . . but which thing right now is earning you the most money? I'm not talking about the steady bread-and-butter money that keeps you going, like your newsletters."
"That's easy. The fascinators. We have so many orders we can't fill because the feathers are so hard to work with. I'm thinking this is a bit of a fad, so we want to cash in now while they're so popular. I forgot to tell you yesterday that one of our new staff had a great idea. A freebie. A good-luck charm, a talisman, if you will. A faux-jade four-leaf clover. Sonia even knew where we could order them in bulk. Violet placed the order last night for overnight delivery today. We plan to mail them to all past and current customers. A goodwill gesture you can call it. Personally, I jumped at the idea."
"There you go again, massive mailing. All the more reason to use UPS, as they will pick up the packages. You also need a postage meter."
"Okay, I'll put that on my list," Rose said. "I'm glad you're on board, Augustus."
"Me, too, Granny. Me, too."
"Okay, then, let's get down to the nitty-gritty and concentrate our efforts on what we have to do to bring things up to date, where you can make the most money in the shortest period of time. We figure out how to capitalize on our people resources and make it happen. How long does it take to make one of those fascinators—those feather things? One other thing, Granny. Once the members of your staff become familiar with their jobs, I want you to rotate them. Each member of your staff needs to know every other job in case of any kind of setback—and there will be setbacks of one kind or another, you can count on it. If everyone knows everyone else's job, you won't lose momentum. Do you agree or not?"
"I totally agree. We can't keep operating by the seat of our pants. We all know we need structure and discipline of a sort. But to answer your question on the fascinators, it takes a half-hour to make them. Depends on who is working on them. Our fingers are not as nimble as they used to be. It's not an easy task, to attach the thin wires to the feathers. The wires have to be cut just right, so the feathers aren't bouncing all over the place. But we precut them, so we conquered that problem. The main problem, Augustus, is the coloring for the feathers. We've only had a few orders for white ones. Without a doubt, we could make a lot of money but . . ."
"How is your feather supply?"
"We have enough to fill our current orders. We have a long wait list simply because we didn't know if we could fill the demand. Like I said, Augustus, it's coloring the feathers that's our problem. It's dye versus spray and where to do it. We need ideal conditions because feathers are virtually weightless. If you so much as breathe on them, they move. Do you have any suggestions?"
"Actually, I do. Pastor Evans still has bingo nights, doesn't he?" At his grandmother's nod, Gus continued, "You know that big drum they use to turn the numbers before they call them? Do you think he'd let us use it if we made a donation to the church? I remember when Barney and I were kids, you used to take us with you at night when it was your turn to work bingo. We could use the drum to contain the feathers after we dip them in whatever coloring you decide to use. If the feather hats are a lasting sale item, you might think about ordering a new drum for Pastor Evans because the color is going to come off on the wire mesh of the drum. Fans will blow at slow speed to dry the feathers as they tumble. What do you think, Granny?"
"I think you're onto something, Augustus. You go over to the church, and I'll have everyone ready to go to work as soon as you get back. Do you want me to call UPS or will you do that and set up an account for us?"
"I'll make the call when I get to the church. Huddle together and figure out which will work best—dye in tubs or sprays."
Rose rummaged in one of the kitchen drawers for a whistle. She gave it three sharp blasts, which meant, meeting in the kitchen ASAP.
Chapter 17
GUS DUSTED HIS HANDS DRAMATICALLY BEFORE SHAKING HANDS with Pastor Evans. "Appreciate your help, Pastor." He eyed the oversize drum that was resting in the back of the Blossom Farm van. He wasn't sure he could count on help getting it back out of the van when he got to the farm. Out of the corner of his eye, he noticed a man with a backpack walking away from his car, toward the entrance to the day-care and preschool center. He'd seen him somewhere recently but couldn't remember where. Probably the guy's kid forgot his lunch or his gear, and he was dropping it off on his way to work. Gus shrugged. In the scheme of things, it hardly seemed important. He put it out of his mind as he climbed behind the wheel of the van. He had made it as far as the parking-lot exit when his cell phone rang. He looked down at the number and grinned. Barney! He backed up away from the exit and parked while he took the call.
"How are things in Hong Kong, Barney?"
"Nothing much ever changes here. What's going on? Fill me in, Gus."
"Are you calling me because my attorney called you to complain about me?"
"No. Why? C'mon, Gus, what did you do now to ruffle her feathers?"
"I fouled up, okay? I apologized, and I even sent flowers. I guess I hurt her feelings, and there's no excuse for that. I'm trying to screw up the courage to invite her out to dinner. A truce of sorts. What—she didn't call you?"
"She did not. You might as well tell me what it was you did. Guilt is a terrible thing. You know that. And . . . pal, that's another reason why you're in the position you're in now. Tell me, you'll feel better. It's called clearing your conscience."
"I addressed her as Miss Fireplug. Jesus, Barney, it just slipped out. I didn't mean to say it out loud. It's how I think of her. I know I hurt her feelings, and I'm going to do my best to correct my comment. It's all those clothes, and, for crying out loud, she has layers of them. She drives a pickup truck. I try not to be judgmental, but it's what I see, okay?" The silence on the other end of the line bothered Gus. "I know you're pissed, Barney, and you're disappointed in me. I'm sorry."
"Gus, she's a top-notch attorney. If she weren't, I would never have hired her. Did you ever stop to think there might be a reason she dresses like she does and a reason why she drives a pickup truck? And what does her mode of transportation have to do with anything, anyway?"
"You're right, Barney, I'm not arguing with you. I'm not even defending myself. She's my lawyer. I think I'd like to know she's . . . that she has a personality. She's like a goddamned robot. And she hates me. It's hard to be nice to someone you know hates your guts."
"I'm coming home. I should be there sometime tomorrow night. No, I'm not coming back because of you and your problems."
"Then why are you coming back? When you left, you said you were going to be gone six months."
"I'm tired of making money. You seem to be having all the fun. I want to be part of it. All work and no play makes for a dull boy. I believe that. I want to be there to see you take your bus driving test. Tell Granny and the aunts I'll be bringing home some jade and some beautiful silk for them."
"Come off it, Barney. You love money. You worship money. You eat, sleep, and dream about money. You'd rather cut off your left foot than give up money."
"I didn't say I was giving up on money. I still love money, but everyone gets to take a hiatus at some point in their life. I want to take my hiatus now."
Suddenly, alarm crept into Gus's voice. "You aren't sick, are you, Barney?"
"No, I'm not sick, Gus. I'm fine."
Gus wasn't sure he believed his friend, but he let it go. "What are you bringing home for the fire . . . Miss Jackson?"
"None of your business."
"What are you bringing me?"
"A whole new attitude, pal."
Gus felt his blood pressure rising. He tried to shake off what he was feeling. "If you're saying in a roundabout way that you're coming back because you think I'm screwing up, just say it, Barney."
"I told you. I'm coming back because I'm tired of just making money. I want to stop and smell the roses for a little while. And I want to help with Granny and the aunts, if you all want me. Listen, I gotta go. See you tomorrow night."
Gus didn't bother saying good-bye. He just clicked off and took a deep breath. He shifted gears and drove to the EXIT sign. Out the corner of his eye, he saw the man with the backpack coming out the door of the preschool, when he looked in his side-view mirror to see if anyone was behind him.
As Gus drove along, his thoughts went to Barney and his return stateside. Without thinking, he made a left turn and followed a service road that would take him to the DMV so he could pick up a bus driver's manual. And then, when he got back to the farm, he was going to talk to Granny and ask her opinion as to what he should do next where Jill Jackson was concerned. Barney's words rang in his ears. Did you ever stop to think there might be a reason she dresses like she does? Well, hell, yes, he'd thought about it, and the only answer he could come up with was his lawyer liked dressing like a bag lady. End of story. And it wasn't any of his business to begin with. As to her mode of transportation, that wasn't his business, either. As long as a vehicle got you where you had to go, that was all that mattered. So why was it bothering him?
Gus shrugged off his thoughts as he parked, ran into the DMV, and asked for a bus driver's manual. He looked at it and shoved it into his back pocket. He'd read it tonight while he and Wilson watched TV. He wondered then if he was putting the cart before the horse. Where was he going to get a bus to practice on? Pastor Evans? Maybe he could practice in the parking lot. He'd ask Granny to intercede. There was no way he wanted to break a promise to Elroy Hitchens and the other seniors.
Gus pulled to a stop at a traffic light. Tapping on the steering wheel, impatient to get moving, he looked into the rearview mirror and frowned. Two cars back was a silver car. The guy with the backpack had been driving a silvery-colored car. His heart fluttered in his chest. Am I being followed? If I am, is it because of Elaine?
The light changed and Gus moved forward. He didn't have time just then to try to lose his tail, assuming that it was a tail. Watching too much Law & Order, or am I getting paranoid?
Jittery with his thoughts, Gus drove carefully, his gaze going to his rearview mirror when he felt it was safe to take his eyes off the road. If he was being followed, he hated leading his tail to Blossom Farm, but it couldn't be helped.
An hour later, Gus, with the help of several of the seniors, managed to get the huge drum up on the back porch. Seniors swarmed through the doors. They looked like they knew what they were doing, so he entered the house and sought out his grandmother. "I need to talk to you, Granny. I need some advice, and if you can spare Violet and Iris, I'd like to include them, too."
"This sounds serious, Augustus. Are you okay?"
"If you mean am I sick, no, I'm not. I just need some advice. Female advice. I think we should go outside to talk."
Wilson came on the run and waited for Gus to give him a good scratch behind the ears. Gus obliged. Wilson was the first one out the door when Rose, Violet, and Iris appeared.
Outside, Gus let loose with his problem. "Obviously, I know nothing about women, so I'm asking for your help. I don't know what to do. By the way, Barney is coming home. He said he's tired of making money. I don't believe that for one minute. He's bringing jade and silk for you ladies. And I think someone is following me. Probably someone Elaine has hired to keep tabs on me. You need to know that. If you want me to stay away, I can do that. I don't want to cause any problems for any of you. Private detectives dig and dig and dig. That's why they get paid the big bucks. This could mean trouble."
Violet squared her shoulders. "I think we can handle interference, Augustus. I also agree with you about Barney. Now, as to the young attorney who is handling your divorce . . . you said she accepted your apology. You sent her flowers. You are thinking of asking her to dinner. I say, do it." Iris and Rose agreed.
Gus felt dizzy as he tried to absorb all the advice they were throwing at him. What he walked away with was that he needed to be humble, complimentary. "And, Augustus, you need to listen and pay attention to what the young lady says. If you get stuck, go to the men's room and call us; we'll talk you through it."
Gus felt like he was sixteen and going out on his first date. He'd been married, had relationships in the past, for crying out loud. If Barney were here, he'd laugh his head off.
"Where are you going now, Augustus?" Rose asked.
"To the post office to pick up your mail. I can do that every morning to save you guys time. Traveling to three different post offices takes time. I'm sort of surprised that you get orders by way of the postal service as opposed to the Internet."
"There are people who do not have computers, Augustus, or even access to computers. People still write letters and put stamps on the envelopes. I know in your eyes those people are Neanderthals, but it is what it is. When you get to the post office, just say you're there to pick up Initial B Enterprises' mail, and they'll give it to you in a sack. Those sacks have to be brought back here. What is on your agenda for the rest of the day?"
"If you don't need me, I thought I would try to get myself settled in my new digs. I need to pick up a few more things and some additional groceries. I also need to pick up my own mail at the office and pay some bills. I'm just a phone call away if you need me to do anything."
Violet sniffed. Of the three sisters, Violet was the most unforgiving. "I think we can manage, nephew. But, we do appreciate all you've done for us."
"Thanks for your advice. I'll be back with the mail." Gus waved as he exited with Wilson on his heels.
On his way to the Jeep, Gus noticed movement in the front yard; Mr. Younger and his sons working on the old sycamore. Gus walked over and looked down at the monster logs, which were being split into firewood. He asked about the part of the tree where he and Barney had carved their names. "It's right there on the steps, Mr. Gus. Your grandmother told us to save it for you. You can take it now if you want. Shame this old tree had to go like that, but Mother Nature is a strange lady."
Gus was surprised at how heavy the slab of bark was. He felt his eyes start to burn. His index finger traced the deep carvings he and Barney had done what seemed like a lifetime ago. He nodded, picked it up, and carried it out to the driveway. He opened the back of the Jeep and settled it in the corner on top of an old blanket. He walked back to where Alex Younger was standing and shook his hand. He whistled for Wilson, who was sniffing the fresh-cut wood.
Ninety minutes later, Gus had returned to the farm and was unloading the sacks of mail on the back porch. As if by magic, three seniors appeared, scooped up the sacks, and disappeared. Talk about a well-oiled working machine.
Gus was back on the road and headed toward his office. He constantly checked his rearview mirror to see if the silver car was following him. He thought it was there, three cars back. He was certain of it when he pulled into the Target parking lot. "Well, have at it," he mumbled under his breath as he bolted into the store and was back out in thirty minutes. "What'd you see, Wilson?"
Woof!
"Yeah, that's what I thought. Okay, let's take this guy for a ride. Buckle up, Wilson."
Elaine Hollister finished her coffee and headed back upstairs to shower and get ready for the day. She felt irritable and out of sorts. She'd spent a miserable night once she got home from Isaac Diamond's house in the wee hours of the morning. The intimate evening had not gone according to her plan. Isaac Diamond, even in his seventies, was no pushover, and he hadn't bought into her act. In her opinion, he was nothing more than a dirty old man who chewed up the little blue pills like they were M&Ms. She'd never worked so hard for nothing in her entire life, and only to lose.
She needed to get cleansed. Even though she'd scrubbed herself raw when she'd returned home hours earlier, it was imperative that her body be purified before she climbed the ladder to her altar so that she could perform her daily ritual.
The white linen gown felt good when she dropped it over her aching body. She shook her shoulders so that the gown settled more comfortably on her body before she pressed the switch that would lower the ladder to the attic. As the hydraulics kicked in, Elaine did her best to clear her mind so that it was as pure as her cleansed body. She took several deep breaths before making her way up to where her altar waited for her. At the last rung, her arm stretched out and hit the switch in the floor that turned on the lights in the attic.
She saw everything all at once, the boxes and empty mailers behind her altar, the overturned vase of white flowers, the roses wilted and already starting to turn brown. Panic rippled through her as she let her gaze rake all the tools that she used to perform her spells and rituals. Her hands trembled as she set the vase upright. She picked up the wilted roses, turned around, and threw them down the ladder. The petals scattered all over the floor, which meant that when she descended, she'd be stepping all over them. The thought bothered her.
Elaine turned and eyed her altar, her heart beating like a trip-hammer. The cloth is soaking wet. Defiled. And I don't have a backup cloth. She cursed under her breath. She'd had plans to perform two rituals today. Three, now, since she'd spent the better part of the night with Isaac Diamond. Bastard. How could she have been so wrong?
But all that was the least of her problems. Did someone break into the house last night while I was out? How else could the vase have toppled over? A rat? A mouse? Possibly a squirrel. No. Gus had an exterminator come by once a month. If a rodent had taken up residence in the attic, I would have seen droppings when I originally set up the altar. No, someone was in the house, someone who obviously knew how to pick a lock and bypass the alarm system. Gus? No, not Gus. Then who?
Elaine tried to calm her racing heart, her nerves twanging all over the place as she backed up and descended the ladder. She raced into the bedroom and dialed the alarm company and blurted out her questions. When she hung up the phone, she had to sit down on the side of the bed, she felt so light-headed. Someone who was smart enough to know their way around an alarm system had broken into her house not once, but twice. The first time whoever it was had broken in, they spent an hour in the house before turning the alarm back on. The second time, they stayed in the house exactly forty-eight minutes before reconnecting the alarm.
The house looked the same as far as she could tell. Nothing looked out of place. She knew that her jewelry, what there was of it, was still in her jewelry box, because she'd put her earrings in it when she got home, along with her watch with the diamond bezel and the special medallion she'd worn around her neck last night. So, then, why would someone break into her house? Obviously a professional of some sort, looking for . . . what, she didn't know. It had to concern the divorce proceedings. Maybe it even concerned Isaac Diamond, with plans to blackmail her. Although she thought that the latter might be a stretch.
Her head swimming with all manner of possibilities, Elaine raced back up the ladder to carry her materials down to the dining room, where she was going to set up an emergency altar. It took eight trips before she had everything ready. Then she looked around in a panic.
Dammit. I don't have a spare altar cloth. Wait. Maybe I do. She ran over to the buffet and yanked at a drawer. There was a brand-new, white linen tablecloth, complete with a sticky label that said the dimensions were 108 by 96 inches. Just big enough to cover the dining-room table, which had three additional leaves. She peeled off the sticky label, shook the tablecloth out, and spread it across the table. She quickly replaced everything the way she'd had it in the attic, minus one vase of flowers.
Elaine ran into the living room, where there was an elaborate silk flower arrangement. She yanked at several white silk orchids and carried them back to the dining room, where she placed them in the empty vase. She looked at everything with a careful eye.
I'm good to go. She was about to sit down when she looked down at the smudges on her priestess gown and felt like crying. She wasn't pure. She had to take another shower and change into a fresh gown.
Elaine mumbled and muttered all the while she soaped and showered and dried herself off. She ran to the closet, ripped a clean white linen gown off the hanger, pulled it on, and ran back down the stairs.
Like the high priestess she perceived herself to be, Elaine took a seat in front of her altar. She sat quietly, her hands on her knees, as she took deep breaths, holding her breath to the count of seven, then expelling it in a soft swoosh of sound. When she felt sufficiently calm, she reached for a long match, struck it on the side of the special box, and lit the black candle and the two slender incense spears. She waited till the aroma from the incense permeated the room. In her hand, she held a small black bag of herbs to ward off evil. She sprinkled salt over it, then picked up the small bottle of holy water and dripped some on the bag. Then she waved the bag through the vapors of the incense sticks. Back and forth, back and forth.
Finally, Elaine closed her eyes and started to chant words she knew by heart from long months of repeating them daily. The words flowed evenly and with passion. She ended her chant with, "All my enemies to leave my life. I cite the number nine and the number four. Four enemies, Augustus Hollister, Rose Blossom, Violet Blossom, and Iris Blossom. Remove these enemies from my life. I offer up everything on my altar. I want no harm to come to the four because I know if I wish such a thing, that wish will come back to me fourfold. I cite the number nine for this to take place. Nine minutes, nine hours, nine days, nine weeks."
Elaine stared into the flame of the black candle as she envisioned Gus Hollister and the Blossom sisters walking away, their pockets inside out as they left all their worldly possessions behind. For her. Only her.
With spots in front of her eyes from staring into the flame of the candle, Elaine blinked as she reached behind her to the sideboard, where she had placed her Bible and her glasses. She opened the Bible and started to read the psalms that pertained to her ritual. She read aloud, passion ringing in her voice. When she was finished, she closed the Bible, set it back on the sideboard, and removed her glasses from the tip of her nose, where they rested. She stood up, opened her arms wide, and intoned, "The portals to the universe are now closed. Thank you for hearing my pleas."
Elaine sat back down and repeated the earlier procedure. She placed her hands on her knees and did her deep breathing exercises. After she leaned over and blew out the black candle, she carried the container with the incense to the kitchen and set it in the sink.
Elaine felt buoyant as she practically flew back to the dining room, where she prepared her altar for a second ritual. To be sure, she had everything ready for what she called a twofer. She ripped through her ritual manual until she found the page she wanted. Her index finger raced across the words as she committed them to memory.
This second ritual was a money ritual, one she performed weekly, but today was the first time she would add a second part to it. Isaac Diamond was the second part of the ritual.
Elaine placed new sticks of frankincense in a crystal cylinder. She set up four green candles, not the squat black kind she'd used earlier. These candles were more like short, thin tapers, which would burn out by the time the ritual was finished. Green symbolized money. Next to the candles were a small green change purse and a small box covered in green felt. She reached for a green velvet drawstring bag, which, according to the ritual instructions, was called a prosperity bag. From the sideboard she picked up a handful of loose change—four pennies, four nickels, four dimes, four quarters—and placed them in the coin purse. She deposited four one-dollar bills in the green felt money box.
Elaine reached for the special gold medallion. It was old, something she'd found in a pawnshop years before. She'd had it modified several days after purchasing it, into a miniature recording device capable of recording for two full hours before the tiny tape had to be replaced, which in the end had cost more than to purchase it. The medallion had proved to be invaluable over the years.
Elaine walked over to the sideboard and picked up a large green crystal and a small container of cinnamon oil. She would use the oil to anoint her candle, the felt-covered box, and the change purse. The last thing she had to do was place jasmine flowers in the middle of the altar. She rummaged in one of the drawers in the sideboard for the pressed jasmine that she'd preserved last summer when they bloomed at the side of the house. The salt to be used this time was sea salt, as opposed to the table salt she'd used in the first ritual.
Elaine looked at her altar, staring at each article to make sure she had it placed properly. Satisfied, she sat down and did her deep breathing preparations.
Calm now, Elaine stared into the flames of the flickering tapers as the vapors from the incense wafted about the dining room. Her hand stretched out to pick up the medallion. She clutched it in her hand as she started to chant, the number four taking precedence in everything she asked for.
Four minutes, four hours, four days, four weeks. Her voice was as passionate as before, her arms waving upward as she pled for help. When she was finished with her chanting, she reached for the green crystal and rubbed it over her forehead, her cheeks, her chin, then up and down her arms. Then she rolled the crystal in the sea salt. The crystal went into the green velvet drawstring bag. The rest of the sea salt was sprinkled over her head. Then she counted the coins and placed each one into the same bag as the crystal. The four one-dollar bills followed. Once again, Elaine anointed the bag, the change purse, and the green money box with the cinnamon oil. Using the same oil, she dabbed her forehead, her neck at her pulse points, and her wrists.
Elaine sat down, took deep breaths, closed her eyes, and chanted her money ritual. "In hours of four, my money worries will be no more. In days of four, my money worries will be no more. In weeks of four, my money worries will be no more. In months of four, my money worries will be no more." She repeated the chant four times before she let out a long sigh of completion.
Elaine squared her shoulders. She picked up the medallion again and pressed a little button on the back. Isaac Diamond's mellifluous courtroom voice filled the dining room. Elaine grimaced as she stared into the flickering flames of the tapers sitting on the dining-room table. She repeated Isaac Diamond's name four times as she wrote his name four times on a piece of paper. She folded the paper into a little square and reached behind her for a small glass jar. She slipped the folded square into the jar and turned the lid.
"Four, four, four, four." Now she had to wait four minutes before she could fill the jar with the special boiled vinegar mix in the refrigerator, along with the herbs that she'd poured into the vinegar when she returned home in the early hours of the morning.
Elaine watched the minute hand on her watch. When the big hand reached eleven, Elaine ran to the kitchen and opened the door of the refrigerator. When the big hand reached the twelve, she poured the vinegar mixture into the glass jar in her hand. All the while, she chanted, "Four, four, four, four!"
In a flash, she was back at her altar, the small jar still in her hands. She passed it over the flames of the four candles. Then she waved the jar over and through the vapor from the incense sticks. Finally, she anointed the jar with the cinnamon oil.
Done.
But there was one thing she still had to do. She had four hours to take the little jar with the vinegar mixture to a body of water and throw it in.
Elaine leaned her head back against the chair and closed her eyes. Her ritual was complete. She felt drained, but cleansed.
As Elaine set about cleaning up her altar, she kept chanting, "Four, four, four, four."
Chapter 18
GUS FELT JITTERY FOR SOME REASON AS HE PUT HIS GROCERIES away. He looked at Wilson, who was watching him like a hawk; he smelled meat. "I'm going to make it all up to you, Wilson. You and I are going to barbecue two nice, big, thick tenderloins. We'll eat out on the deck and spend the night together. We're home, big guy; this is it for us. We are home." Wilson tilted his head to the side and stared up at his master. At some point, the dog must have made up his mind that things were indeed okay, because he let loose with a soft growling sound that made Gus laugh out loud.
Gus spent the next half-hour marinating the steak, preparing a salad, and scrubbing a potato that he would bake and then top with sour cream and chives. He was as much at home in the kitchen as he was in the laundry room, thanks to his granny, who had taught him to cook and clean and do his own laundry at an early age. He considered himself truly self-sufficient.
Satisfied with his preparations, he reached for a chew bone for Wilson and a beer for himself and went out to his deck. He looked around and decided he needed some flowers or some kind of greenery to take away the starkness from the deck. He liked that the Realtor had chosen bright-colored cushions for the deck furniture, and he really liked the bright, lemon-colored table umbrella. At some point, he might think about ordering a retractable awning, since the deck got sun for the better part of the day. He thought about all those ads he kept seeing on TV each year when winter came to an end.
Gus leaned on the railing as he gulped at his frosty beer. He liked the pruned bushes and shrubs. He thought he could keep up with everything once he got the right equipment. Saturdays would be lawn days and cleaning days—unless one of the trees in the yard turned out to be a money tree that showered him with coins and bills so he could afford to hire a gardener and a part-time housekeeper. The vision of a money tree with the coins and bills raining down was so funny, Gus burst out laughing. Wilson raised his head long enough to look around to see what was so funny. He went back to his chew bone.
Gus let his thoughts wander then. He skimmed over thoughts of Elaine. How weird was that? How was it possible he could skim over someone he'd loved with all his being a little more than a week ago? His thoughts took him to Granny and the aunts and their newly recovered relationship. He smiled with feeling. He so loved those old gals. Barney invaded his thoughts at that point. He loved his best friend as much as he loved his granny and his two zany aunts. It bothered him that Barney was suddenly coming back to the States when he had said he was going to be gone for months. He didn't believe for one minute that Barney was tired of making money. Barney, the protector. Barney wanted to make sure nothing happened to him, since he was going it alone with too many things on his plate. Gus smiled at that thought.
His beer finished, Gus walked over to a bright yellow trash receptacle with a large white daisy painted on the side. Women. He could actually see Marsha painting the daisy on the can. She'd think the colored trash can would perk up the deck. And it did. He made a mental note to send Marsha a gift or, at the very least, some flowers for all her help.
Back in the house, Gus looked at the old-fashioned phone hanging on the wall. He didn't know why, but he felt compelled to call his grandmother. He didn't stop to think, just punched in the numbers. Violet answered the phone. To Gus's ear, his aunt sounded frazzled. "What's wrong, Aunt Vi?"
"Technically, nothing is wrong. We just can't cope with the fortune cookies. We're trying, but we aren't meeting the demand. We have roughly twelve restaurants we supply cookies for—fifteen hundred each a week. That's eighteen thousand cookies each and every week. We have to bake the cookies, insert the fortunes, wrap the cookies, then deliver them. We just don't have enough ovens. We might have to cancel this service, and that would be a shame, because we make some serious money with fortune cookies. We've tried to streamline our operation, but it's hard. If you have any ideas, we'd like to hear them, Augustus. We have to make a delivery in two days and are seriously behind."
Gus didn't think he'd ever heard Violet talk so much at one time. And she had actually asked him for help. His chest puffed out. "I can be there in fifteen minutes, Aunt Vi. I need to see the operation with my own eyes."
"Thank you, Augustus. We'll be expecting you."
Gus set the marinating steak back into the refrigerator and whistled for Wilson. "Wanna go for a ride, big guy?"
Wilson ran to the door as Gus slid the sliding doors shut and locked them. He checked everything the way he always did: lights off, stove off, doors locked. He was good to go.
Seven minutes into his drive to Blossom Farm, Gus knew he was being followed by the silver-colored car. He bit down on his lip, looked over at Wilson who was riding shotgun, and said, "Hold on, bud, we're going to catch this guy." Wilson's ears went straight up as he anticipated action. "When I catch him, you bite him on the ass. You hear me, Wilson?"
Woof.
Gus careened around a corner, downshifted, and pulled to the curb just as the silver car barreled behind him and screeched to a stop. In one swift motion, Gus had his Louisville Slugger bat, which he had transferred from his Porsche to Barney's Jeep, in his hands and was in the middle of the road. He raised the bat and got ready to swing. Straight at the silver car's windshield. A black Mustang swung around Gus as its driver leaned on his horn. Gus ignored it when the silver car's window slid down.
"Get out of the damned car, or your windshield is confetti. Wilson! He makes one wrong move, you bite him on the ass. You hear me, Wilson?"
Unmindful of moving traffic, which was light, Gus approached the man getting out of the car, his hands up in the air.
"I'm not a cop, so put your arms down. Who the hell are you, and why the hell are you following me? And don't lie. You've been following me for days now."
Mickey Yee eyed the menacing shepherd, who was showing him his teeth. He saw the fur on the back of the dog's neck moving in the light afternoon breeze. He put his arms down but froze in position as he wondered what it would be like to get bitten on the ass by the monster dog standing in front of him. The visual was not one that appealed to him. He remained statue still, one eye on the man swinging the bat, his other eye on the ferocious-looking dog.
Gus swung the bat back and forth. "Talk to me and make it good, mister."
"My name is Mickey Yee. I'm a private investigator. I work for Lynus Litton, who is working for your attorney, Jill Jackson. Yeah, I have been following you. Someone else is following your wife. I'm not the one you should be worried about. That black Mustang that went around you when you cut in front of me is who you should be worried about. He's been following you also. It's been like a damned parade for days now. I even know the skank's name: Bill Donovan. He'll do any job, break the law for a buck. I'm thinking he's working for your wife or her attorney, but that's just my guess."
Gus lowered the Louisville Slugger and called Wilson to his side as he digested what the man standing in front of him had just said. "Are you telling me I have a tail on me?"
"For several days now, yes, that's what I'm telling you. The guy's a sleazeball, so when and if you ever see his report, most of it will be lies."
"Why are you following me?"
"Orders. By the way, you're boring as hell. I thought I'd go out of my mind when you were shopping at Target. What, you can't make up your mind when it comes to towels and sheets?"
"Thread count is important. Towel thickness is just as important, for absorbency. Didn't your mother teach you that? Boring! I'm a hell of an interesting guy."
"I guess I missed that lesson. Okay, so you made me, now what?"
"Stop following me."
"You sure you want me to stop? If I keep following you, then I can keep tabs on Bill Donovan. Would that dog really have bitten my ass?" Yee asked anxiously.
"Yeah, and loved every minute of it. Stop following me. I'll deal with Donovan on my own. Go on, get out of here."
"Hollister, hold on a minute. Listen, it's not just Donovan. I saw someone else out at your grandmother's farm yesterday. No clue who he was, but he was snooping around. Mud on his license plate, so I couldn't run the number. I have a soft spot for old people, and I wouldn't want to see anything happen to your grandmother and the people who come and go. I have to admit, they have me wondering what's going on there, and don't try to tell me they're playing bingo or some such shit."
"What did the guy you saw look like? And, they are bingo addicts. They live for bingo. They eat, sleep, and drink bingo."
Mickey Yee looked disgusted. "Hey, the guy's probably a dick, okay? What he looked like yesterday doesn't mean he's going to look the same today. And while he was driving a beat-to-shit Honda yesterday, today he might look like a movie star and be driving a high-end car. Old people are prey. I just gave you a heads-up. So, you want me off this or on it? Or are you still going to go this alone? Makes me no never mind."
Gus realized everything the detective said was true. "No, okay, stay on it. But . . . I don't want you to tell anyone I made you. Will you agree to that?"
"Hell yes, man."
Gus swung the Louisville Slugger. "You go back on your word, you're going to find out what a bite on the ass will feel like."
"You got it. Can I go now?"
"Yeah. I'm going to the farm. If you see anyone at the farm watching my grandmother, call me, okay?" Gus rattled off his cell-phone number, and Yee punched the numbers into his own cell phone.
Wilson whined all the way to the farm. "Get over it, big guy. One of these days you're going to get the chance to bite some bad guy's ass, trust me on that."
Wilson dropped his head onto his paws as if to say, promises, promises, promises. Gus reached over to scratch the dog behind the ears. He grinned. God, how he loved this dog.
The kitchen at the farmhouse smelled wonderful. Chili, if his nose was on the money. He also smelled the sweet scent of vanilla, and something baking. While the kitchen was huge, with two double ovens and two stove tops, every burner seemed to have something cooking and bubbling on it. He could see the trays of something baking in the double ovens.
Iris appeared out of nowhere and said, "Chili and rice pudding for dessert. We can send you home with some of each. We're baking the fortune cookies. With all our new staff's meals to prepare, this kitchen is getting a workout, and we're stumbling over each other. The summer kitchen looks the same as this one does. We simply do not have enough room, Augustus. Something has to give."
"I see that. Tell me how the cookie operation works," Gus said as he headed for the steps that would take him down one level to the old summer kitchen. It didn't look old now—everything was new and modern. In the old days, before air conditioning, the summer kitchen was used for all the cooking so the rest of the house didn't get too hot.
The contents of pots were simmering, and the same vanilla-sugar-cinnamon scent was present. On the long counter, he saw trays and trays of baked fortune cookies ready to be packaged.
"We can bake two trays of cookies every twenty-five minutes. Each tray holds thirty-six cookies. We have two double ovens, so that means we're baking one hundred and forty-four cookies in these two ovens every twenty-five minutes. We need an extra five minutes to slide the cookies off the trays and get the next batch ready, so actually it's thirty to thirty-five minutes. The same goes for the two double ovens upstairs, for a total of two hundred and eighty-eight cookies. We bake from seven in the morning until eight at night. We are not meeting our goal of eighteen thousand cookies for the Chinese restaurants we service, although we did meet it last month. Prep time includes mixing and inserting the fortune into each cookie. Two hours to do all this as we try to mix enough dough to carry us through the whole day. Out of every nine hours the ovens are going, we're only utilizing six of those hours for actual baking. That's a total of 3,456 cookies a day. Having said that, it's not actually 3,456 sellable cookies. Some break, some burn, and we have a lot of throwaways, making the count more like thirty-two hundred on a good day. Sometimes even less than that. Last week, our actual count of cookies that were delivered was fifteen thousand. Having said that, there are seven days in a week and with each restaurant giving out an average of two hundred fifteen cookies a day for lunch and dinner, we're short. We've had to cut back on the number of restaurants we service."
"Just Chinese restaurants?" Gus asked.
"In the beginning, it was just Chinese, then some of the Japanese takeout places wanted to place orders. We also have four Vietnamese locations who want our cookies. Most of the restaurants have takeout orders, so you have to factor that in the numbering, too. People sometimes ask for two cookies; children want them. We don't have a good bead on that end of things. I remember Rose saying that last month when she was doing the final tally for the month."
"How much do you make on, say, fifteen hundred cookies?"
"Rose has all those numbers. We are making a profit, but according to Rose, not enough to justify the work that's entailed. We pay two Asian students at the university to come up with the fortunes. They send them via a download from the Internet. We print them out, cut them to fit the cookie; then there's the cost of the ingredients, the cost of the wrappers, the labor to wrap them, and, of course, to mix the dough and do the actually baking. Then there's the cleanup and getting them ready for delivery on each restaurant's delivery day. Even though our staff does not take a salary per se, our expenses are quite high."
Gus could feel his head start to spin at what he was hearing. "Correct me if I'm wrong here, Aunt Iris. Right now, you can meet demand, but it's taking too much time for the amount of money you're making. Is that what you're saying? You need to ask yourself, is the money worth all the aggravation of trying to make more? Don't take this the wrong way, but you guys are not youngsters anymore, and stress and pressure is not good for anyone, especially the elderly. I give all of you kudos for going at it full bore, but there have to be limits to what you all can do. That's why I made up a work schedule and insisted that each of you and your staff learn each other's jobs, so it doesn't come down to a few pulling the whole wagon. Are you following me here, Aunt Iris?"
Gus watched as Iris's shoulders drooped. "I am, Augustus, and I think you need to speak with your grandmother. We all love the fortune cookie operation, especially the fortune part. We stress to our two Asian students who make them up that they be upbeat and positive fortunes."
"Can you blow that whistle for Granny and Aunt Vi?"
"I can do better than that. They're up in the voodoo and witchcraft room. Seems we have a client who lives in the vicinity and is one of our best customers. Her testimonials will blow off your socks. It's all about cleansing the mind and believing. Vi told me about an hour ago that an e-mail came in from that client relaying a more than positive outcome to a special ritual that was performed today. When we get those, we post them. And then we get a real spike in orders."
All Gus could do was shake his head. Voodoo and witchcraft! Who knew?
Even though he was a CPA, Gus couldn't compute the numbers in his head.
Chapter 19
ELAINE HOLLISTER REMOVED THE SMALL JAR OF VINEGAR FROM her bag and looked around to see if anyone was watching her. As far as she could tell, the few people lakeside were packing up their blankets and picnic baskets to go home. She palmed the little jar, drew her arm back, and pitched it with such force that she would have been the envy of an all-star baseball pitcher had one been watching. She chanted under her breath, then took a long, deep breath, holding it for a count of ten before she expelled it. She felt so light-headed, she thought for a moment that she was going to black out, but she squeezed her eyes shut and waited for the wave of dizziness to pass.
Elaine smiled as she turned and walked back to the picnic area where she'd parked her car. She looked at her watch. Three minutes to four. She'd made her offering to the depths of the lake right on time. Now all she had to do was wait to see what happened to Isaac Diamond. There was no doubt in her mind that something would happen to the lawyer. She just wasn't sure what it would be.
Elaine slid into the little yellow car, settled herself, turned over the engine, flipped in a CD, and drove out of a lot that was now almost deserted.
Overhead, dark clouds were gathering. It would rain shortly, she thought. Just another late afternoon April shower. She hoped it wasn't as ferocious as the one a day or so ago: she'd cowered in the bathroom while Mother Nature had wreaked havoc on the state of Virginia. She hated storms. She didn't like rain, either, when it came right down to it. Who cared if the grass needed watering? Who cared if the leaves on the trees and bushes were wilted? She had more important things to worry about. Gus used to fret about the water bill and about Wilson when it thundered. She had been thinking too much about Gus over the past several days, and that was not a good thing. Gus was out of her life, and she was moving forward. She did think it a tad strange, though, that he hadn't come whining and crying about how much he loved her and he hadn't come to ask her to give him another chance. Why hadn't he done that? Even though she'd put a restraining order in place, he could have called or sent her a text, but he hadn't done either of those things.
Maybe she was slipping, and she'd miscalculated his feelings for her. No, she'd had him, as the saying goes, wrapped around her little finger. His lawyer probably told him the same thing hers had told her—no communication.
Elaine rolled down the window to look upward. The clouds were moving faster, and they looked darker than they had just minutes ago. She stopped for a red light and let her eyes wander to the side of the highway. The Jade Pagoda. She could get takeout. And right next to the Jade Pagoda was the Fine Wine and Spirits Shop. She could pick up a few bottles of wine and have a party all by herself to celebrate what she hoped would be the demise of Isaac Diamond. Ooops, she had to stop thinking like that. She didn't want Isaac Diamond's demise; she just wanted him out of her life and her retainer paid back and maybe something for that obscene performance she'd had the night before. Blackmail was such a sweet thing when you held all the cards. Maybe the right word should be restitution. Blackmail was an ugly word, but sweet at the same time.
The light changed. Elaine turned on her blinker and made a left turn. She parked in the Jade Pagoda's parking lot and was not surprised to see it nearly empty. Too late for lunch, too early for the dinner crowd. That had to mean she'd be in and out in record time. She could go next door, pick up the wine she wanted while they prepared her food, and, if she was lucky, she'd be home before the rain came.
The wind was brisk—the temperature had been falling steadily since she'd started out around three-thirty. Fireplace weather. No sense in turning on the heat for just a few hours.
Elaine loved it when things worked in her favor. She did indeed make it home just as the first raindrops fell on the back deck. The drops were big and splattered in all directions, which told her it would be a brief shower at best, but it was more than chilly.
Safely inside with the door locked and bolted, and the alarm set, Elaine first made a fire, then carried a small folding table into the den. She liked to eat watching television and with a fire at the same time. The truth was, she loved her own company and her own thoughts. She only had one rule in her life—not to get attached to anything but money. Money could buy whatever she needed. Attachments were baggage, and, more often than not, she moved on in the middle of the night. It was so much easier to leave with just a bankbook and an overnight bag, which she kept in the trunk of her car, than to carry cumbersome items she wouldn't need in her new life. A new life meant new things. Always new things, new people, new surroundings, new everything.
Elaine devoured the food until there wasn't a crumb left. She was on her third glass of wine when she pulled out the four fortune cookies she'd insisted the manager at the restaurant give her. Today, four was her magic number. All compliments of Initial B Enterprises.
She read the first one. You are almost there.
Fortune cookie number two: Success is right around the corner.
Fortune cookie number three: Your lucky number is four.
Elaine danced with excitement when she read the third fortune. She bounced up and off her chair as she twirled and whirled, her fists shooting in the air. She was trembling so much she could barely open the last one.
Fortune cookie number four: A windfall is about to drop in your lap.
Elaine slumped back in her chair, her thoughts all over the map as she stared blankly at the television screen. This was when she had to be patient. Sit and wait for whatever was going to happen. She stared into the flickering flames as they danced in the fireplace until her eyes closed, and she fell asleep.
The landline on the table next to the sofa rang at seven-thirty, waking her from a sound sleep. She managed a garbled "Yes" to the person on the other end of the line.
"Mrs. Hollister, this is Wendy Manning, from Isaac Diamond's office. I'm sorry to be calling you at this hour of the day, but the partners asked me to call all of Isaac's clients to inform them that he suffered a serious accident late this afternoon. I saw in his appointment book that he had a meeting scheduled for tomorrow with you. Nick or Lee can see you, or you can wait till we have more news on Isaac's condition."
It wasn't often that Elaine was at a loss for words, but this time she was, as she tried to figure out what to say. The best she could come up with was, "How terrible. Can you tell me what happened and the time it happened?"
"The time?"
"Well, yes, the time, because, you see, I was speaking with him earlier," Elaine lied.
"All I know is that Nick said they, and by they I mean EMS, transported him to the hospital at four-thirty this afternoon. They did say it wasn't life-threatening, but that it was serious. Isaac isn't a youngster, as you know. I'm sorry, but I'm not at liberty to say any more. What do you want me to tell Nick and Lee?"
Elaine had her wits about her now. She hoped her elation wasn't showing. "Just tell them I'll get back to them, and, of course, cancel my appointment for tomorrow. I'd like to send flowers if that's okay."
"Let me get back to you on that," Wendy said.
"That's fine. Thank you for giving me the courtesy of a call." Elaine replaced the phone in its cradle and let out a sigh so loud she startled herself. Talk about instant gratification.
Elaine was so giddy with the news she'd just heard, she picked up the wine bottle and brought it to her lips. She gulped until the bottle was empty. In a wild, crazy moment, she threw the bottle at the fireplace and watched it shatter. She fell back into the chair and closed her eyes. Overcome by the wine, she once again fell into a deep sleep.
As Elaine was drifting off to sleep, Gus Hollister was firing up his new grill on the deck. The rain, what there was of it, had come and gone, but it was too cool to eat outdoors. Wilson was panting at the scent of the marinating meat sitting on the counter.
"You're doing the dishes, Wilson. I'm cooking, so that means you do the cleanup. We really should talk about the division of chores." Gus had always talked to Wilson like this and hadn't the slightest reason why. Wilson listened, then ignored him. Maybe it had something to do with living alone, or maybe it had something to do with Wilson's being his best friend and a stand-in for Barney. He tried to remember if he'd talked to the dog like this when he lived with Elaine. Scratch that thought. He didn't want to think about Elaine now or ever again.
Gus let his thoughts go to his grandmother and the aunts and the massive project they were involved in. He had to do something, come up with a working plan, before things collapsed on top of them. He was convinced in his own mind that it was just a matter of time before that happened. What was going on now was temporary and could not be sustained for any length of time. His thoughts were coming lightning fast as idea after idea popped into his head, only to be rejected. He wished Barney were here, with his analytical mind.
Gus checked his baking potatoes. Not done yet. Wilson wouldn't care, but Gus cared; he liked his potatoes mushy and soft. Wilson just scarfed his down, along with the imitation bacon bits Gus sprinkled on his. He set the table and got Wilson's plate ready. Man and dog. For now, he loved it.
The scent of the sizzling steak on the grill had Wilson dancing in circles. Steak night, his favorite night of the week.
Gus talked to the shepherd nonstop as he poured himself a beer, mixed his salad dressing, and checked the potatoes again. He was always chatty with his dog, but today he rather thought he was going overboard. Wilson must have thought so, too, because he kept looking up at him, wondering what was going on.
Gus knew what was bothering him even if he wouldn't give voice to his thoughts—and it wasn't his grandmother, his aunts, or Initial B Enterprises. He had to call Jill Jackson and invite her out to dinner. He had to make amends, and he had to do it as soon as possible, preferably before Barney returned tomorrow night. "It is what it is. You know that, Wilson." Wilson barked to show he was in the game even though he didn't understand what game, as he waited for his dinner.
An hour later, the kitchen tidy, Wilson out romping in the wet grass, Gus pulled out all his schedules and got to work at the kitchen table. He was going to get this right or die trying. He pushed all thoughts of Jill Jackson, Mickey Yee, and some scummy bastard spying on the seniors out of his mind as he set to work.
At eleven o'clock, his eyes heavy with grit, Gus called it a night. He let Wilson out one last time before trudging upstairs to his new bed. He was about to slip under the sheets when he looked down at Wilson's bed. "You better find it now, Wilson, before I get in bed, because I'm not looking for your baby. Go get it! I'll wait to turn off the light."
He was, of course, referring to Wilson's one-eared rabbit, which he'd had since puppyhood and which was the security blanket that he slept with curled under his chin. Wilson was back in a flash, the bedraggled one-eared rabbit clutched in his teeth.
"'Night, Wilson."
Woof.
Gus grinned as he squirmed and wiggled until he found just the right spot in his brand-new bed. He was asleep within seconds. Not Wilson, who lay quietly in the dark, his ears tuned to any new or strange sound in the house. Ninety minutes later, satisfied that his and his master's world was safe, he lowered his big head on his beloved rabbit and fell asleep.
Gus woke late the following morning and could hardly believe it was eight o'clock. He didn't exactly have a fire burning in his belly, but it was close. He stomped his way downstairs, let Wilson out, then made coffee. He removed his cell phone from the charger and, before he could change his mind, dialed Jill Jackson's personal cell number as opposed to going through the main number to the Beezer building. He sucked in his breath, wishing he'd rehearsed a speech of some sort. She answered in the same flat business tone she always seemed to use when it came to him.
Be witty, be charming, Violet had said. Be yourself, Iris had said. His grandmother had just looked at him with pitying eyes and said, Do your best, Augustus.
"Jill, this is Gus Hollister. I'm calling to invite you to dinner this evening." He rather thought he'd give up his left hand to see the expression on her face at that moment.
Almost at a loss for words, Jill ran her fingers through her hair at this unexpected turn of events. "You don't have to invite me to dinner, Gus. If you want to stop by the office later to discuss the case, we can do that."
"No, no, I don't want to discuss the case. I just want to take you to dinner. You can pick the restaurant if you like. It can be fancy or it could be that hot dog joint in New Town that everyone raves about. I'm thinking, seven o'clock."
Jill tried to suck on her tongue to work up some saliva. "You mean, like a date?"
"Well, yeah. I drive up to where you live, once you tell me where that is, I ring your bell, hand you some flowers, you put them in water, then we get in my car. And I hold the door for you, the way my granny taught me, and off we go. Yeah, yeah, a date."
Jill Jackson laughed. Gus was so startled at the musical sound of her laughter, he felt his face turning beet red. He'd never heard such a pleasing, beautiful laugh. He felt tongue-tied.
"Okay, I accept. I live around the corner from you, on Morningstar Court. I'm the only brick house on the court, you can't miss it. Seven, you said?"
"I did say seven. Yes, ma'am, seven o'clock. Seven is a good time for dinner. I usually eat at seven." Jesus, what the hell is wrong with me? He was babbling like some lovesick teenager. And she lived around the corner from him. How weird was that?
Jill laughed again, and this time Gus felt goose bumps running up and down his arms. "Where would you like to go?"
"How about Bandoliers in New Town? They serve all kinds of food."
"Bandoliers it is. Do you really live around the corner from me?"
"I really do." Jill didn't laugh this time, but there was laughter in her voice.
"Well, that's . . . great. I guess. I'm just renting. I could move if you think I shouldn't live there." Well, damn, did I just say that?
"New neighbors are nice. I don't even know mine. We could probably holler to each other across the fence. My backyard backs up to yours."
Now, how did she know that? Stupid. Stupid. Stupid. He'd told her the other day that he had moved. She'd probably checked it out or was familiar with his address. "Well, let me know when you're going to holler, so I'll know to answer."
Shit, shit, shit. That didn't even make sense. Quit while you're ahead and get the hell off the phone before she thinks you're certifiable. "I'll see you at seven, then."
"Okay."
Done. I have a date. Well, hot damn!
Jill was all thumbs as she tried to press in the number to Lynus Litton's office. Jill said when he answered, "I want those four hours you talked to me about. Three and a half would be better, but I'll take the whole four, and I need them today. Did you hear me, Lynus? Today."
"Whoa! What's got your panties in a knot?"
"You said I need four hours. Okay, I'm calling you on it. It has to be today; I have a date tonight. Seven o'clock."
"You mean a date, where the guy knocks on your door and brings flowers and candy, that kind of date?"
"Yes, dammit. What? You think no one would ever ask me out on a date? Well, someone did, and I need those four hours. Well?"
Lynus turned cagey. "Sounds important. You smitten? You realize when you sign up for those four hours, you turn yourself over to Sam and Mandy, and you have to let them have free rein. You can't back out. You go with it all the way. The works. If you give them any trouble, I'll hear about it. I have a reputation to uphold. I never send them clients unless I think both parties can handle it. You still game?"
Jill thought about it. "Yes," she said curtly.
"Okay, give me ten minutes, and I'll get back to you. This is going to be pricey. You need to know that going in."
"Okay, okay. Will I be happy with the results?"
"Knowing you, probably not, but you'll blow the guy's socks off. You still game?"
Jill didn't even think about her response. "Yes, I'm game."
"Okay, I'll get back to you."
"Louise!"
"My God, what?" Jill's secretary bellowed on the run. "What's wrong?"
"I have a date tonight! Lynus is . . . well, I have a four-hour—I guess you'd call it overhaul of my person. He's calling me back."
"A real date, a knock-on-the-door kind of date?"
"Yeah, yeah. Why does everyone keep saying a knock-on-the-door date? We're going to Bandoliers. It's with Gus Hollister."
"Your client? He's a stud! I thought you hated him! He actually asked you out on a date when you've been so hateful to him? Are lawyers allowed to date their clients?"
Jill squirmed in her chair. "I don't know if they are or not, and I don't care. I think it's up to the individuals. I never dated a client before. I don't hate Gus Hollister. I hate what he did to his grandmother and his aunts by choosing that person he married over them—and look what that got him. There are different kinds of hate, you know. Besides, you know as well as I do that a lawyer cannot pick and choose clients by the way they look and act. And, yes, it's a real date. You sound like Lynus. And, no, he's not a stud. Studs are farm animals. He's just a good-looking guy who looks buffed. Puffed? Whatever the word is these days."
Hands on her hips, Louise looked at her boss over the top of her reading glasses. "So, you are finally going to get rid of that gypsy attire you've been wearing since the big flood a hundred years ago."
"Looks that way. Don't get carried away. It's just a dinner date. Gus Hollister is trying to make amends to me for hurting my feelings. I accepted his apology, but he is obviously still feeling guilty, so I am just trying to . . . help things along. Anger gets you nowhere, as you point out to me time and again. Now, are you happy?"
Louise leaned up against the doorframe and crossed her arms over her chest. "Well," she drawled, "if that was all true, why are you going for that four-hour makeover or whatever it's called? You could go in that same outfit you're sporting right now. Sounds to me like this is more than a thank-you date. I rest my case."
"And you find this all so very amusing? I should fire you."
"Ha-ha!" Louise said as she backed out of the door to return to her desk.
Jill drummed her fingers on her desk as she waited for the phone to ring. She looked at her blunt-cut nails and winced. Everyone wore acrylic nails these days, even Louise. Maintenance. She hated anything she had to keep up with. Although she had thought more than once about getting a French manicure. Thought about it. She thought about a lot of things. Well, now it was time to put up or shut up.
The phone rang. Jill let it ring four times before she picked it up, because she didn't want Lynus to suspect how anxious she was. Her greeting was casual and bored sounding. At least that's how she hoped she came across to Lynus.
"How does eleven o'clock sound?"
"Doable, Lynus, doable. Let's be clear, four hours or three and a half?"
"Might run to five. It's out of my hands. I'm not the expert. Just go with the flow, Jill, and try to enjoy it all."
"Five hours! You could clone someone in five hours! Are you putting me on?"
"No, I'm not. When I explained your . . . situation, they said possibly five hours. Don't shoot the messenger. Let's face it, Jill, you need a lot of work."
Jill was near to tears. "My God, do I really look that bad?"
"Honey, we all let ourselves go at some point, and I'm sure you had your reasons. And I do not want to know what those reasons are. It's going to take some time to . . . to repair all the . . . imperfections you let get out of hand. Just for the record, women kill to get any kind of appointment with Sam and Mandy. That's how good they are. You have a pen handy?" When Jill said she did, Lynus rattled off the address of the salon where Jill was to go for her makeover.
"I can't believe I'm doing this. I can't believe I'm doing this. I can't believe I'm doing this," Jill muttered over and over as she packed up her briefcase. Even though she had hours until her appointment time and what she'd agreed to do, she wanted to go somewhere quiet to think. Her intention was to buy a bagel and some coffee and go to the park and find a quiet bench.
Jill waved to her secretary as she sailed through the office and out the door. She couldn't help but wonder what she'd look like when she walked back through that door the next time.
Chapter 20
JILL JACKSON STOPPED AT THE HUGE YELLOW ARROW AT THE SIGNPOST for the turnoff to the Sunset Spa. As she made her way down a winding road lined by old sycamore trees that were just starting to green up, she thought it a beautiful, serene setting. In her opinion, it was the perfect location for a spa. The building surprised her because she had had no idea it even existed, nestled as it was behind the lush shrubbery. How many times had she driven this road with no thought that this magnificent building was hiding behind the luxurious plantings? She winced when she recalled Lynus's words, Bring your checkbook, as this place is pricey.
Jill parked in the minuscule lot, slid out of her truck, and looked in awe at the building. Mediterranean style, perhaps. Or something out of Babylon. Whatever it was, it was gorgeous. The word pricey ricocheted around and around inside her head. Up close, the building and the landscaping were even more awesome. The shrubbery looked like it had been pruned with manicure scissors. Not a leaf was out of place, every stem in perfect alignment. A rainbow of flowers bordered the colored flagstone walkway. At the door, a discreet sign said to ring the bell for admittance. Jill rang the bell. A pleasant-looking woman in what she thought was like a pale yellow doctor's coat opened the door to her with a wide smile. She introduced herself as Mona and said she would be her guide for her stay at Sunset Spa.
"Let's get you settled, then I'll introduce you to Mandy and Sam."
Five minutes later, Jill was in a small, luxurious, restful-looking room. She struggled to define the scent permeating the room but had to give up when she couldn't identify it. From somewhere, the sounds of water trickling over stones could be heard, along with a tinkling sound from a wind chime somewhere in the building. Jill could feel her eyelids start to droop. Mona smiled.
"Hang your things in the closet and put on the robe and slippers. They're new, and you'll take them with you when you leave. Do you have any questions?" Jill shook her head. "I'll be back in a few minutes to take you to Sam and Mandy."
Jill bit down on her lower lip as she stared at the yawning interior of the closet in which she was to hang her clothing. She looked around as a feeling of panic overwhelmed her. She moved then to the door; her hand was on the knob to open it so she could bolt. She wasn't a prisoner, she could leave anytime she wanted. All she had to do was say that she had changed her mind, that she wasn't in the mood for a makeover, and that she'd come back some other time. But that would mean she was a coward. Lynus would look at her in a different light. She'd be forced to look at herself in a different light.
Her cell phone took that moment to ring. She debated if she should answer it, but the debate didn't last long. She was one of those people who could not ignore a ringing phone. She clicked on to hear her secretary tell her that Isaac Diamond's office had just called to say that Isaac was in the hospital as a result of an accident. She went on to say the other two Diamond partners didn't know if their office would continue to represent Elaine Hollister or if she would engage another law firm. Jill made a face, muttered something that sounded like she'd get back to Louise later. She turned her phone off when she remembered a sign at the entrance that said that all cell phones must be turned off, and they were to be left in the client's locker. Jill always obeyed the rules.
Jill looked around for a mirror. She almost blacked out in relief when she didn't see one. She wondered exactly what a few minutes meant. Five?—ten?—before Mona came back to take her to Sam and Mandy. She licked at her lips and started to remove her clothing. She kicked off her ankle-high boots, placing them neatly on the floor of the closet. Off came the jacket, the vest, the long-sleeved blouse, the skirt, the half-slip. She squeezed her eyes shut as she removed her bra and panties.
She could feel the raised scars that covered the right side of her body. She thought then about the eleven skin grafts she'd undergone to repair the burns before she had called a halt and had said no more. "Suck it up, Jill, and get on with it," she muttered under her breath. She slipped her arms into the fluffy white robe, tied the belt, then slid her feet into the matching slippers, just as a knock sounded at the door. "Are you ready, Miss Jackson?"
"I am." Jill opened the door and stepped into the hallway.
Mona chatted as she pointed out different statues nestled into little nests of greenery along with small fountains with trickling water that lined the hallway. She knocked softly on a door, opening it at the same time.
Jill didn't know what she was expecting, but Sam and Mandy Dressler's appearance surprised her. She had formed a mental picture in her mind of two movie star look-alikes, impeccably dressed and coiffed and made up to look like the beautiful people they catered to. Mandy Dressler was small and round with gray hair, pink cheeks, and granny glasses. She wore pale green scrubs, the kind technicians wore in hospitals. She had a beautiful smile. Sam Dressler was just as small and round. He, too, was pink cheeked and he had snow-white hair and a matching Vandyke beard. He also wore wire-rimmed glasses. His smile was just as beautiful and warm as his wife's. It was hard for Jill not to bask in their warm, welcoming greeting.
"Welcome to Sunset Spa," the Dresslers said in unison. Mandy motioned to a soft, buttery-looking beige chair. "We need to ask a few questions. First, do you have any medical issues, and are you on any medication we should know about?" Jill shook her head as she was handed a clipboard to check off the questions she was being asked verbally. She did it all in record time and signed her name, along with the date. She handed the paper over.
Mandy scanned the printed form, satisfied that it matched Jill's verbal answers. "Question and answer time. You don't seem . . . excited or relaxed to me, Miss Jackson. Why do I have the feeling you'd rather be somewhere else right now instead of preparing to be pampered for a few hours? Am I wrong?" she asked gently.
Jill chewed on her lower lip, something she always did when she was nervous. "The answer is yes and no. Lately . . . lately people have been . . . commenting on the way I dress and saying . . . things that are far from flattering. Lynus . . . Lynus suggested I come here. At first, I said no. And then . . . well, I changed my mind earlier this morning, and I do appreciate your fitting me in on such short notice."
"Is there a reason, in your opinion, why suddenly you've decided to come here? I ask only because we want you to have an enjoyable experience at Sunset Spa," Sam said, his blue eyes twinkling.
Her moment of truth. "Yes, I guess so. I'm tired of evading and explaining, and I was asked out on a date for this evening. The person . . . the man who asked me for . . . for the date . . . is someone who . . . who called me a fireplug. I guess I do look like that sometimes."
"And . . . ," Mandy prompted gently.
Jill felt like she was on the witness stand. She squared her shoulders. "When I was eight years old, I was in a house fire. A new gas hot-water heater had just been installed at our house. It exploded somehow, and my parents and brother died in the fire. I was the only survivor. I was in the hospital off and on for several years. The right side of my body was burned pretty badly. I had many, many skin grafts until I just couldn't do it anymore. I tried to hide it, and I'm still hiding it. I thought . . . the more layers I put on myself, the less noticeable it would be. I've been to shrinks—the aunt who took me in after the fire insisted on it—but it was something I just couldn't overcome. I withdrew from treatment but managed to go to college and law school, and still work. Money was never an issue—my parents had excellent insurance. The people who installed the hot-water heater paid handsomely, and my aunt invested the money for me. Then I turned it all over to my boss, who invested it again with still higher returns. I never have to work another day in my life unless I want to. And, I want to. I never used the money because . . . to me it was . . . death money. Now you have my whole life story."
The Dresslers smiled. "Then let's get you started. We'd like to see a smile, though. How about this, when you leave here, you're going to look and feel like a million dollars. Can you accept that?"
Could she accept that? She was here, wasn't she? She'd just confessed her life story to two strangers. All because some guy called her a fireplug. Was it the word fire that pushed her to come here, or was it guilt and shame? Vanity was probably the answer. She shrugged. "Yes, of course," she responded.
Mandy pressed a button on the desk. Mona appeared as if by magic to lead Jill out of the room. Jill turned in the doorway, and said "Woohoo!" Then she laughed.
Sam and Mandy looked at each other and joined in the laughter. "I think that little confession opened a door that's been locked for a long time. I'll see you later, Sam. I have some shopping to do," Mandy said.
"Have fun, my dear. I know how you love to shop. Just remember our promise to Miss Jackson that she's going to look and feel like a million dollars when she leaves here."
"I'll remember, dear. I so hope that young man is worth all this. I'm thinking, Sam, even if for some reason tonight doesn't end with a promise for the future, Miss Jackson will be able to walk through that door she opened with more confidence than when she walked in here."
"I hope we find out the answer at some point in time," Sam said.
"I'll see you when I see you, my dear," Mandy said as she reached for her purse. This was the part that she liked best, the transformation of the client. She smiled.
The hours passed in a blur. Twice, Jill dozed off because she was so relaxed. She had a deep hour-long body massage and a wonderful facial, which allowed her to fall asleep. She loved the whirlpool, with the jets pummeling her entire body. She dozed off again during her pedicure, while a technician applied acrylic nails to her fingers and finished it off with a French manicure. She slept for thirty minutes before she was transferred to a bare room, where she got spray-tanned.
"It will look just like the sun kissed your entire body. The plus to spray-tanning is it will downplay the pinkness of your scars."
While she stood with her arms and legs spread to dry, Jill decided this was a day she'd never forget, and she wasn't even finished yet.
When the technician announced that the spray-on tan was dry, Jill was taken to still another room, with no mirrors but wonderful lighting. The beautician twirled the chair Jill was sitting on, as she ran her fingers through Jill's long, curly hair. "Do you have something in mind, or are you willing to leave it up to me? First things first, your hair is way too long. Long hair is not in fashion, and is best worn by young girls. Are you ready for a new look to go with the new you?"
Jill drew in a deep breath. "I am. I'm not a fancy kind of person, so can you give me an easy-to-care-for, casual kind of look?"
The stylist, who said his name was Brandon, said, "I think it's time to get rid of the Shirley Temple curls. How will you feel if I straighten your hair and give it some highlights? I'd also like to thin it out a little."
Giddy with what she was going through, Jill could hardly believe her own words when she said, "Go for it, Brandon."
Another ninety minutes passed before Brandon turned down the lighting and pressed a button to reveal a mirror behind a wooden panel. Jill gasped as she leaned forward to view her new hairdo. Who was this person? In her wildest dreams, she never thought she could look as good as she did at that moment.
"You like?" Brandon asked.
"I love it, Brandon. I really do."
Brandon grinned. "Okay, now it's time for your makeup session. Ready?"
"Oh, yeah." Jill grinned in return. Suddenly, she was loving this whole new experience.
While Jill was being pummeled, scrubbed, rubbed, caressed, sprayed, and painted, Gus Hollister was banging his head on the wall for the fourth time. He had gone to Barney's to exchange the Jeep for his Porsche, having decided that he was not going to pick up his date in a Jeep. Now, he was exhausted with the effort he was expending to get through to the Blossom sisters.
Gus threw his hands in the air. "Let's go through this one more time. I know you're tired, and so am I. We've been at this for hours, and I really have to leave, because I have a dinner engagement, which you all endorsed, by the way."
They were on the back porch, with the door to the kitchen closed for privacy. The coffeepot had been filled, then refilled. Everyone's nerves were twanging from too much caffeine.
Violet, more hostile toward Gus than her sisters, looked at her nephew. "Nephew, we made a commitment to our staff. What you're suggesting to the three of us can't possibly work. If we do what you say, there won't be enough work for everyone. We just can't go back on our word. We cannot break a promise; surely you can understand that."
"Yes, Aunt Vi. But there will be work for everyone, just less work. I do understand. Will you just stop, close your eyes, and envision the inside of this farmhouse? It's total chaos, it's overcrowded, you're all meeting yourselves coming and going, plus the kitchen as well as the summer kitchen is being used twenty-four/seven, with all the cooking for so many people three times a day. And don't get me started again on your storage arrangements for supplies. There is not one inch of space available. You need to relocate. Granny, there is all of Shady Pines. Why aren't you all working out of there? There is an industrial kitchen at Shady Pines, and that's what you need. Read my lips, a fully equipped industrial kitchen."
"Because we live here, that's why. We started here, and it just naturally followed that we would continue working here," Rose said defensively.
"What that says to me is you three took the easy way out. Everyone else has to shuttle back and forth while you three call the shots. I'm not trying to demean you, it just doesn't make sense from a productivity standpoint. Shady Pines has to be around fifty thousand square feet and is virtually empty except for the one wing that's occupied. At one time it was a thriving operation, now with just caretakers watching over the property. I know, I know, all the rules and licenses are in effect. Will you all just think about the space, about having everything in one place? It makes more sense for the three of you to take the golf cart over in the morning and back again at the end of the day. You need to scale back and just do an eight-hour shift instead of this round-the-clock nonsense.
"As much as you all don't want to admit it, you aren't getting any younger. Believe it or not, you're actually getting older. Just like everyone else on God's green earth. Why in the name of everything that is holy do you want to work everyone to an early death? You're a family, all of you, so that means you need to enjoy each other's company, make all the things you haven't been able to do—either for health reasons, lack of money, or whatever else—work for you. This is the time when you should be enjoying your lives and still be productive, but not to the point of obsession."
Iris looked up at her nephew. "But you said you wanted us to do away with some of our projects. We need all those projects to keep earning the money we've been earning. More so now that we've added to our staff."
"I looked at your books, ladies. They are robust. You paid out outrageous bonuses none of you need or even want for that matter. I can see a salary of some sort, absolutely. I can see vacations twice a year for as many days as you all decide on. You can take bus trips. Hell, I'll even drive the bus for you, and I'm sure Barney will agree to do it, too. I'm going to get my bus driver's license. You're obsessed with making tons of money and forgetting to live your lives. I'm tired, and I'm sorry if I'm not coming across to your satisfaction."
"I understand everything you're saying, Augustus. You are making some valid points. Perhaps we could arrange a meeting with everyone, and you could give a PowerPoint presentation. Would that work?"
"It would, but I want you to close up shop for a week or ten days. We can hire people to help us move Initial B Enterprises to Shady Pines. What we're doing now, what I set up for you all, was just supposed to be temporary. I told you that at the time, and you agreed. You said you all wanted the new staff to feel like they belonged right off the bat. We assigned jobs, but it's around the clock, with no real routine. People, especially elderly people, and I mean no offense, need to sleep at night; they don't need to work shifts. It's unsettling. They don't need pressure and deadlines. The bottom line is that you have too many irons in the fire. We need to whittle back and go with just your moneymakers. As an example, the fortune cookies. You could corner the entire market here in Sycamore Springs and even the outlying towns. You can hire delivery boys from the college. Think about how much easier it will make your lives."
The sisters looked at one another as Gus droned on and on. Finally, Rose said, "You need to go home now; it's getting late, Augustus. You certainly don't want to keep the young lady waiting. We will talk about all of this tonight, and, by tomorrow, we'll have an answer for you, one way or the other. We appreciate your concern for our well-being, and we know your heart is in the right place. Will that work for you?"
Gus sighed. "It will work if you talk and discuss it all with an open mind. I just want you to remember one thing: Money can't buy happiness. You all found happiness and fulfillment. And made a lot of money in the bargain. You don't need more sacks full of money to continue. Being more than comfortable financially, being happy, and having the companionship of each other should be your top priorities from here on in."
"You're forgetting our overhead, nephew," Violet snapped.
"No, Aunt Vi, I am not forgetting it. If you operate out of Shady Pines, you can take many tax deductions. It has to be a legitimate operation from the get-go. That's what I'm trying to drive home to you all. You can do this. You really can. But you're going to have to make concessions for the well-being of all of you, not just you three.
"Okay, I'm leaving now; you have a lot to think about. I'm here for you and will do whatever I can to get you all on the right road, because I love you and care about you."
Rose stretched out her arms to her grandson. She hugged Gus, and he hugged her back. He turned to see if Violet and Iris would do the same. He was thrilled when both his aunts smiled and held out their arms.
Gus whistled for Wilson, who came on the run.
"Call us," Rose said. "Go to the men's room and call so we know how it's going. Good luck tonight."
Gus laughed. "Didn't you say the exact same thing to me when I went off to my first prom?" The sisters laughed.
It was five-thirty when Gus climbed into his reclaimed Porsche for the trip home. An hour and a half to stop for flowers, get home, feed Wilson, shower, shave, dress, then drive around the corner to pick up his date for the evening. He couldn't decide if he was dreading or anticipating the evening. He started to whistle. Whistling is a good sign, he thought. Maybe the dinner would go well, and he and Jill Jackson would actually become friends of a sort.
Hope springs eternal. That's what his grandmother always used to say. She probably still said it, for all he knew.
Gus felt so good, he continued to whistle. He had a feeling that he had finally gotten through to his grandmother and aunts with the last round of discussions. But he was no fool. He knew things could change on the turn of a dime.
Chapter 21
GUS TOOK SO LONG TO SHOWER, SHAVE, AND DRESS THAT Wilson started prancing around thinking he was going for a ride again, his favorite thing to do. "What do you think, Wilson? Too much gel in my hair? My aftershave too strong?"
Wilson pawed the tiled floor and let loose with a short bark that meant, let's move already.
Gus stretched his lips in front of the mirror to make sure nothing was stuck in his teeth. What the hell is wrong with me? He was acting like he had just marched into puberty. Teeth okay, not too much gel, aftershave minty but faint. His khakis held a sharp crease, his loafers had a nice shine, and his pale yellow shirt was perfectly ironed. By himself. His tie matched the shirt perfectly. His khaki jacket was fairly new and finished off his attire. He was good to go.
Gus checked his back pocket to make sure his wallet was where it belonged. His keys were on the kitchen counter, as were his cell phone and the flowers he'd bought on the way home. Gus hung up his wet towel, exited the bathroom, and headed downstairs, Wilson bounding ahead of him. The time was six-fifty. It would only take him two minutes to drive around the corner, park, walk up to Jill Jackson's door, and ring the bell.
After picking up his keys and cell phone from the kitchen counter, Gus checked the front door to make sure it was locked; it was. He turned the two lamps on in the living room. He made sure there were two night-lights in the kitchen that would start to glow as soon as dusk fell so that Wilson could find his water bowl and the bowl of dry dog food he always left when he went out and left Wilson home.
"Okay, big guy, I'm outta here. Answer the phone, fold the laundry, and, if you have time, make my bed. Get your rabbit and settle in. I won't be more than a few hours. I'll leave Wheel of Fortune on for you. Here's a Pop-Tart—make it last—and a chew bone. You got all that, Wilson?"
Woof.
Gus couldn't believe the butterflies jumping around in his stomach when he got into his car and turned on the engine. He looked over at the bunch of spring flowers wrapped in layers of green tissue paper. He shrugged. He remembered the horror of his first date, when he was a teenager and he'd taken his date to a fast-food joint. He'd been so nervous he couldn't eat, even though he was starved. His grandmother had warned him to check his teeth to make sure nothing was stuck in them. To this day, nothing had ever been stuck in his teeth. She'd told him to chew slowly and not wolf his food the way he always did at home. The horror was he'd obeyed all his granny's advice, and the girl whose name he couldn't even remember had gobbled her food, then ate his.
He hadn't been this nervous with other dates, or with Elaine. What was there about Jill Jackson that had him in such a tizzy? Guilt. That's what his Aunt Vi would say.
Gus pulled into Jill Jackson's driveway. It was a pretty little house, with flower beds and a flower-lined walkway. In the center of the front yard, there was a huge sycamore tree that he knew would shade the entire front of the house when it was in full leaf. He looked down but couldn't see even one weed. The bushes were pruned, the lawn mowed. He didn't know how he knew, but he suspected that the backyard held flowers and shade trees. She probably had a terrace or a deck with nice outdoor furniture, where she would sit going over her legal stuff.
Gus sucked in his breath and rang the doorbell. He stepped back and waited, the flowers moving back and forth in the early evening breeze.
The door opened and Gus said, "I'm here to see Jill Jackson."
He heard the musical laugh, then his face turned beet red. He blinked, then blinked again. He couldn't think of a thing to say, so he thrust the flowers forward. Who is this person standing in front of me? Fireplug, my ass. He could feel the heat on his face and neck. He thought he was going to strangle himself.
"I guess this is where I'm supposed to say, I clean up good. Come in, Gus, and I'll put these flowers in water. They're so pretty. Thank you. I love flowers."
"Yeah, me, too. I mean, I like flowers outside. I don't pick them, I just like to look at them. You look different!" Gus blurted.
Jill laughed again. "Listen, I need to tell you something. Isaac Diamond's office called this morning. It seems he had some kind of accident and is in the hospital. The firm doesn't know if your wife is going to stay with them, or if she'll go with another firm. That means things are at a standstill. Do you have any questions? Because, if you do, I'd like to get them out of the way now and not discuss business over dinner."
Gus shook his head as he listened to the words, but they really didn't signify anything to him. He didn't want to think about Elaine or her lawyer. He was concentrating on this beautiful creature standing in front of him. And to think, he'd called her a fireplug. His face and neck started to heat up again.
"You look great!" Gus blurted.
"Yeah, I know." Jill laughed. She twirled around in her high heels and the bright yellow dress that flirted with her knees. "I'm vain." She giggled again. "You look nice yourself."
Gus Hollister fell in love at that moment. He risked a glance at his watch. At 7:04, he, Gus Hollister, fell in love with Jill Jackson. The date and the time were now engraved in his mind forever and ever. He could hardly wait to tell his grandmother and the aunts. He watched as Jill positioned the vase of flowers on the kitchen counter. He wasn't sure, but he thought she probably sat on the stool on the other side of the counter to eat or have coffee. The flowers would be directly in her line of vision. The thought pleased him.
"You ready?" he asked, his voice husky at what he was feeling.
"I am. All I have to do is lock the door and walk out."
"Turn on a night-light and the outside light. It will be dark when we get home."
"Good point," Jill said lightly as she fit the key in the lock.
Gus held the car door for her, watching how gracefully she got into the bucket seat. He also admired a generous slice of leg when her dress hiked up. He saw the puckered skin on her upper thigh, but it wasn't registering. She showed no embarrassment, but the moment she was settled, she tugged at the dress.
Gus couldn't believe it when he ground the gears. He'd been driving a stick shift for years and years and never let the gears grind. What the hell is wrong with me? He had never felt so inadequate. He had never been good at small talk about trivia, but he struggled to appear manly and nonchalant. He risked a glance at her and saw that she looked amused. Crap. She probably thought he was being sophomoric.
"Do you like Bandoliers?"
"I do. I've only been there a few times, though. I like the tablecloths and cloth napkins. The lighting is good, too. And the tables are generously spaced so you don't hear other people's conversations." She laughed then, and Gus almost melted into the seat. "How's that for casual conversation?"
Gus grinned. "Better than I could have come up with. Dates are . . ."
"Stressful?"
"Yeah."
"But we know each other," Jill said. "Unfortunately for both of us, we got off on the wrong foot. I allowed you to see only the business side of me. And you reacted to that and let me see your unflattering side. Let's just start over and just be Jill and Gus who are going out to dinner at a nice restaurant."
"Whew! That works for me."
"Well, there you go. What would you like to talk about, Gus?"
"I used to be a Boy Scout. Barney was, too. We actually made Eagle Scout. If there was a catastrophe, I could probably save you in some fashion, by building a fire without matches and finding roots and berries for you that are safe to eat."
Jill laughed so hard tears rolled down her cheeks. "That sure does make me feel good, Gus."
In spite of himself, Gus laughed along with her. "Your turn."
"After you save me, I could give you a recital. I took ballet lessons when I was little. I can still stand on my toes. I don't have a tutu, though."
"I have a vivid imagination. What color?"
"Pink and white."
"I have the vision in my mind now. We're here," Gus said, swerving into the first parking place he saw.
Gus bustled out of the sports car, rushed around to the passenger side, and opened the door for Jill. He got another glimpse of her thigh and the long scar, and felt light-headed. He reached for her arm and pulled her forward. She smelled so good, he wanted to bury his face in her hair.
The next thirty minutes passed in a pleasant blur after they were seated in a dim, candlelit corner. They ordered white wine and smiled at each other across the table as they each contemplated the menu.
Gus ordered prawns stuffed with crab meat and Jill ordered pecan potato–crusted salmon. They both chose the house dressing for their salads, then ordered a second glass of wine. They made small talk, mostly about Barney and his anticipated return later that evening.
Gus was now relaxed and enjoying the conversation he was having with his dinner companion, the woman he'd just fallen in love with.
The waiter served dinner, and suddenly Gus fell back into teenage mode. He couldn't eat the delectable food sitting in front of him. He made a pretense of cutting and moving the food around on his plate. It took him forever to chew a piece of the shrimp.
Jill stopped chewing long enough to ask, "Is something wrong? You're not eating. Aren't you hungry?"
Gus was tempted to make up a story about his grandmother making him eat something earlier, but in the end decided to go with full disclosure. He confessed to the teenage episode with his first dining-out date at a fast-food joint.
Jill smiled. "I promise not to watch you eat, and I can guarantee that shrimp or crab won't stick in your teeth."
"I like your sense of humor. I just told you a secret. Your turn," Gus said, popping half a shrimp into his mouth.
"I got burned in a house fire when I was eight years old, and the right side of my body is scarred pretty badly, that's why I dress the way I do. This salmon is really good. Do you think they'd give me the recipe if I asked for it?"
Whoa.
"Secrets aren't good. I'm all for full disclosure. I'm sure they'll give you the recipe minus one of the ingredients. At least, that's what my grandmother told me. 'Recipes,' she said, 'especially family recipes, are meant to stay in the family. ' I'm not sure, but I would think chefs probably feel the same way."
Jill stopped eating and stared at Gus across the table in the candlelight. "Aren't you going to ask me any questions?"
"No. I won't share your secret with anyone. I'm not a kiss-and-tell kind of guy. Not that I kissed you. Oh, hell, you know what I mean. Please don't tell anyone about my secret."
"Deal," Jill said, holding her hand out across the table. Gus reached for it. He thought it felt like soft silk. He held her hand an extra few seconds. Jill drew away first.
Gus finally felt comfortable enough to relax when he realized he was enjoying the give and take with his dinner companion. Being honest with himself, he thought he had never had such an enjoyable dinner. He liked this new Jill Jackson. It appeared she liked him, too. Just after the waiter arrived to remove their dinner plates and take their dessert order, Gus excused himself to go to the men's room, where he called his grandmother. His conversation was bullet fast and ended with his confession of telling Jill about his teenage dinner date. Obviously, his grandmother had him on speakerphone, because he could hear his aunts laugh. He ended with, "She was burned in a fire, and she said she's scarred. It happened when she was a kid."
There was no embarrassment when Gus returned to his seat and said, "I had to check in with my grandmother and aunts."
"That's nice. You're lucky, Gus, that someone cares enough about you to want you to check in. I don't have anyone; the aunt who took care of me after the fire passed away a few years ago."
Jill leaned across the table. Gus thought she looked beautiful in the soft candlelight. "I need to apologize, Gus, for my . . . attitude when we first met. I thought you were throwing away a lifetime of love and caring, for someone who treated you like dirt. I'm sorry, I really am."
"I wasn't exactly a peach myself. But that's behind us. In the end, it will all work out the way it's supposed to. I'm just glad you stuck with me."
The waiter was back with two plates of red velvet cake and coffee.
"I love sweets," Gus confessed.
"Me, too. When I have time, I bake raisin-filled cookies."
"I'm addicted to Pop-Tarts, and so is my dog. That's our sweet and treat every day."
Jill laughed.
God, how I love the sound.
And then dinner was over, and it was time to leave. Gus paid the bill and acted like the gentleman he was and got up to hold the back of her chair.
It was a beautiful April evening. The dark sky sparkled like diamonds. Gus didn't want the evening to end. He wished he knew how Jill felt.
"I really enjoyed dinner, Gus. It's been a long time since I had a night out like this. Thank you." Gus felt his chest puff out. She, too, had enjoyed dinner.
There was very little traffic, and Gus made every green light. He was parking in Jill's driveway in less than fifteen minutes.
"Don't get out, Gus. I can make it to the doorway on my own." She leaned over, gave him a quick kiss on the cheek. The next thing Gus knew, she was sprinting up the walkway. It all happened so quick, he didn't know what to do. He lowered the window and shouted, "Can I call you again?"
Gus heard her laughter. "If you don't, I'll call you!"
The grin stayed on Gus's face on the drive around the corner to his house. He let himself in. Wilson raced to him and barked. Gus gave him a good scratch behind the ears. "Did you fold the laundry?"
Woof.
"Any calls?"
Woof, woof, woof.
"Three calls. Wow! Did you make the bed? I hope you tucked the corners in. I hate it when my bed is wrinkled."
Woof, woof, woof, woof.
Gus laughed. He loved this game he played with Wilson. He listened to the three messages on his phone. Nothing he had to deal with now. He ran upstairs and checked the bed for Wilson's benefit. He laughed. "You're getting better, buddy. You need to work on the other side a little."
Back downstairs, he made a pretense of checking the dryer, then said, "Okay, you couldn't get the door open. Wanna go for a walk?" Wilson ran for his leash and off they went. Down to the corner and around the block, not once but twice, so Wilson could mark his territory. Their evening walk took forty-five minutes, until Wilson tugged on the leash, meaning it was time to head for home and the treat that was always forthcoming after a long evening walk.
"Okay, buddy, let's go home, so I can tell you about my evening before I bust. We can sit on the deck and enjoy each other's company." As they rounded the corner to their street, Wilson jerked free and raced for home, the leash dragging behind him. Gus gaped at the figure sitting on his front steps, a huge duffel bag at his feet.
"Barney!"
"Yeah, it's me." He was tussling with Wilson but stopped to hug Gus. "So, how's it going? How did dinner go?"
"Come on in, we'll have a beer on the deck. I was going to sit out there and tell Wilson how it went. This way, I'll only have to tell it once. You just get in?" Gus said, looking at the huge duffel bag.
"Yeah, came straight here from the airport. I'm moving in with you."
"Huh?"
"Yeah, I'm moving in with you. I like this house. I walked around and peeped in the windows while I waited. I think I can be comfortable here."
"What's wrong with that mausoleum you live in? I only have one bed."
"You just said it, it's a mausoleum. I can sleep on the floor. I'll buy a bed tomorrow unless you don't want me moving in."
Gus shrugged. "Me casa, you casa." He uncapped two bottles of beer, reached for a Pop-Tart, and headed out to the deck.
"Talk to me, buddy," Barney said.
Gus talked and talked until his beer was finished. He walked into the house for two more and returned. "So, what do you think? I want to know more about your return and the decision you made to give up making money."
The two old friends talked into the wee hours of the morning. A parade of beer bottles lined the table, yet neither man was drunk. "Why didn't you tell me about the fire and her scars? It doesn't make a difference, but I wish you had told me. Maybe if you had, I wouldn't feel like such an ass."
"It wasn't my place to tell you. Just so you know, Jill never even told me. It was in her background check. You need to give some thought, now, to perhaps hiring a new lawyer if you plan on seeing her on a social basis. I'm sure she's already working on that herself, but it won't look good, especially if Elaine gets wind of it." Gus nodded.
Gus told Barney about Jill's phone call from the Diamond law firm. "I guess that puts things on hold, at least for the moment. What do you think, Barney?"
"Big white-shoe firm. Big retainers, all about billing. I think they charge something like five hundred dollars an hour. At least that's what I heard, but it was awhile back. I guess my question is, where did Elaine get that kind of money to sign on with them?"
"I don't know, Barney. Elaine always kept her finances separate from mine. We shared my income, though. Don't say it. That's the way marriage is supposed to be, it's all about sharing. You're one, so to speak."
Barney snorted. "Too bad Elaine didn't think the same way you did."
"Yeah. Come on, let's go to bed. We need to be at the farm early in the morning."
Upstairs in the bedroom, Barney looked at the bed and the covers.
"Wilson's job is to make the bed. He's getting better at it. He thinks he just has to do my side. If you sweet-talk him, he might let you sleep with him in his bed."
Barney started to laugh and couldn't stop. "See, this is why I didn't want to go back to my house; it's no fun there."
Gus snapped his fingers. Wilson was on the bed in a heartbeat.
Barney eyed the dog bed. Dog hairs by the boatload. What the hell. "Does Wilson have fleas?"
Wilson reared up and let loose with a yowl of outrage.
"Guess that answers your question," Gus said as he punched his pillow to fluff it up, then turned off the light.
Gus's last conscious thought before he fell asleep was that he would dream about Jill Jackson.
Chapter 22
THE SUN WAS JUST STARTING TO CREEP FROM THE HORIZON when the black candle on Elaine Hollister's altar flickered for the final time. The green candle was just a pool of melted wax in the little dish. She'd been sitting at her altar in her high-priestess robe for twelve hours, chanting, slipping in and out of what she thought of as a trance. She folded her hands into a steeple, bowed her head, and rose to her feet. She uttered one last chant before she ended her night-long vigil. She didn't move as she waited to see if any thoughts or visions would come to her. She wasn't sure in her own mind if she should pack up her altar or leave it as it was until she returned from her visit to the hospital to see Isaac Diamond. She needed a sign. She'd come too far and didn't want to make a rash mistake for lack of patience.
Elaine stood statue still until the sun's early morning rays crept through the slats of the plantation shutters covering the dining-room windows, straight across to her altar in thin stripes. Seeing the stripes of sun on the altar was all Elaine needed. She had her answer.
Slowly and methodically, Elaine packed up everything on her altar. She removed the linen tablecloth, carried it to the washer, and turned the machine on. Later, when the cloth was in the dryer, she would wash her linen gown. She returned to the dining room and replaced the silk flower arrangement that was the centerpiece. Next, she opened all the shutters. The room was instantly flooded with early morning sunshine.
It was after eight when Elaine entered the kitchen to make coffee. While she waited for it to drip into the pot, she smoked two cigarettes. She wasn't a smoker by any stretch of the imagination, but she'd found that smoking after an intense ritual calmed her to the point where she thought she was almost having an out-of-body experience. She loved the feeling.
Two cups of coffee later, Elaine made her way upstairs to get ready for the day.
Showered, powdered, and perfumed, Elaine took exceptional pains with her makeup, hair, and her outfit. She decided that her makeup was flawless, and she looked dewy and healthy. Her luxurious, honey-colored hair was swirled with stray tendrils curling by her ears. She reached for a can of sparkle and sprayed her hair. Just one quick press of the pressurized button and her hair glistened. The outfit she had chosen was a designer suit that was so severe, one knew it had cost a fortune. And it had. It was the color of oyster shells. The blouse that she chose to go under the suit had a demure string bow at the throat. It was the color of a morning dove. She looked at herself from every angle in the mirror. She was satisfied that there was nothing more to do. In her mind, she looked perfect. Simply because she was perfect . And how could one improve on perfection? One could not, that was her bottom line.
Elaine slipped her feet into sling-back spike heels that showed off her legs and gave her a regal look. She was a head turner, and she knew it full well. A smile played around the corners of her mouth as she made her way downstairs. It was a shame that she had to drive that shitty little yellow Volkswagen. She belonged in a Mercedes convertible. Soon, she'd be driving one, she was certain of it.
Elaine had a bad moment when she reached the door. She was about to set the alarm when a thought occurred to her. She quickly rummaged in one of the kitchen drawers for a roll of duct tape. She picked up a pair of shears and a ballpoint pen. Outside, she set the alarm and closed the door behind her. She made a mark on the doorframe and cut off a strip of duct tape and stretched it across the door. She smoothed out the tape so there were no creases or wrinkles. If anyone broke into her house, she'd know it when she returned because the mark she'd made on the doorframe would come off on the sticky side of the duct tape. Plus, no matter how hard you tried to reuse duct tape, you could tell once it had been pulled free of whatever it was sticking to. Gus had told her that, but she couldn't remember why. On a whim, she scribbled a note on the duct tape: the police are watching this house. She ran around to the front door and did the same thing. There wasn't anything else she could do, so she left the house and drove to the hospital where Isaac Diamond was a patient.
Elaine had called precisely at six o'clock last evening when the new shift came on duty, to ask if Isaac could have visitors and was told he could and that no real visiting hours were in effect. The news fit in perfectly with the rituals she had performed all night long. As far as she was concerned, Isaac Diamond was toast. He just didn't know it yet.
Gus stopped the car with a wide sweep in front of Barney's garage. Barney hopped out and opened the garage door. "I'm going inside to fetch some more knock-around clothes, and I'll meet you at Shady Pines in thirty minutes. Listen, pal. You sure it's okay for me to bunk in with you? You sure you don't mind?"
"If I did, you'd know it. Get your stuff and make it snappy. I told Granny we'd be ready by eleven for our sit-down orientation. The seniors get antsy when things don't go off on time."
"No problem," Barney said, sprinting through the garage.
Gus backed up and swung his car around. Ten minutes later, he parked in what was once the Shady Pines assisted-living facility. He reached for his briefcase, which contained all his notes and schedules.
Inside, Gus headed straight for the industrial kitchen. The kitchen was huge, as was a room that was probably a pantry of sorts, with extra refrigerators and cabinets for staples. Gus eyed the industrial ovens and the two stoves with sixteen burners in total. The two industrial ovens had six shelves each for baking trays. The microwave ovens lining a side wall were huge as well. He closed his eyes as he tried to imagine how many people could be served meals from this kitchen. What he didn't know was whether the food had been prepared from scratch, or had come from a food-service company and simply been reheated. He made notes on the yellow legal pad in his hand.
He looked at the page in his notes with the heading, FORTUNE COOKIES. He opened the oven doors, bent over to look inside. He scribbled more notes. He moved on to the stoves. His gut told him his grandmother would never okay prepared and heated food. Sixteen burners going three times a day. It would work for now, since occupancy was a little over thirty, more if you counted Granny and the aunts. Food service versus local vendors. Granny would want local, that much he knew. Which then opened another can of worms. Who was going to do the shopping? Maybe they could cut deals with the locals for delivery if they bought everything in bulk. Gus made more scribbles in his notepad.
Gus eyed the industrial dishwashers and the huge sinks. Hospitals used throwaways. He made more notes on his pad. Labor hours in the kitchen versus throwaway plastic. Maybe they could get rid of one of the sinks and put in another oven if they could justify the use of plastic plates and plastic utensils. More notes. He was so engrossed in his scribbling and his thoughts, he didn't see Barney until his buddy clapped him on the back.
Gus explained what he was doing. Barney absorbed it all as he walked around, then peered at Gus's notes. "I agree, we take out one sink and put in another oven. Right now, there are going to be thirty-some people, not counting Granny and the aunts. When and how will you decide if you're going to take in more people?"
"I don't know, Barney. Let's check out the rest of this place. The good news is it's sound and in excellent condition. Four wings. Right now, only the east wing is being used, with rooms to spare. The seniors are gung ho, and we're going to have to rein them in. I believe they think that they can fill this place and just keep doing what they're doing. They can't do it financially. I need to tell you something, Barney. They do not take kindly to the word no!"
"What you're saying is, they're stubborn?"
"Try fixated. And they want it all done yesterday. We have to convince them that whatever we come up with is beneficial to all of them."
Barney groaned. "Are they more or less stubborn than Granny, Vi, and Iris?"
Gus grinned. "They're running neck and neck. Granny will listen, but that doesn't mean she'll agree. See, they were doing fine, according to Granny, before I came along."
"What about the legal end of things? Do any of these people receive Social Security? Where does that money go? Who controls all of that?" Barney asked.
"Granny has a lawyer and an accountant, but from what I can tell, the lawyer, at least, isn't top-notch. They need hands-on twenty-four/seven help, at least for now."
"Are you thinking what I'm thinking?" Barney asked.
"If you're thinking about asking Jill to take over the legal end, then yeah, and if you mean me and my firm doing the accounting, then yeah again. I'll do it for free, but I guess Jill will need to be paid."
Barney laughed out loud and slapped his knees. "That just goes to show how much you know about that young woman. First things first, she does not need the money. This is something she'd love to do simply because she'd have a whole passel of grandmothers and grandfathers. She is so good with elderly people, you have no idea. I'll hate to lose her, but she's a perfect fit for this operation. Do you want to ask her, or shall I?"
"You sure about that, Barney?"
"Oh, I'm sure," Barney drawled.
"Then, I'll do it. Or we can do it together. We can walk over to her house this evening and broach the subject."
"That'll work. What's next on the agenda?"
"Let's walk this place. I was thinking we could use the entire west wing to store all the supplies. We won't need all the rooms for storage and can use the other rooms for the computers for their newsletters—that voodoo and magic stuff they do. I wish they'd get out of that, but they're digging in on that. They say it's entertainment, not for real. Jesus, Barney, they have Web sites, blogs, they tweet, they have it going on. They just need to be organized. Then there's the sex hotlines, the sex newsletters. Don't go getting excited here. I've seen them, and about all they say is just because there's snow on the roof doesn't mean there isn't a fire in the chimney, that kind of thing. Nothing outlandish. Oh, and they advertise in AARP. Barney, they have thousands and thousands of members. What the hell they're members of, I still don't know."
Barney leaned against the wall so he wouldn't fall over laughing. "Hey, don't get me wrong here. I am not laughing at the seniors; I am laughing with them. I think this whole thing is great. Damn, I'm glad I came home. I can't wait to get started."
Gus looked at his watch. "We should head to the community room, so we can get this show on the road. I have to tell you, none of the seniors are keen on the idea of shutting down for ten days till we get this ball rolling smoothly. They like being productive and contributing. They're going to fight us tooth and nail. We're going to have to be our most persuasive. I gotta warn you about Oscar; he's pretty vocal. He's the one who wanted to take me out to the barn to kill me."
"What?" The word exploded out of Barney's mouth faster than a bullet.
"I think he was joshing me. But he looked serious."
"I got your back, big guy."
"Thanks, Barney."
Gus led the way down one hall, around the corner, down another hall, and finally they came to what Shady Pines back in the day called the community room. The seniors had set up chairs in neat rows. It looked like everyone was present, including his grandmother and the aunts.
Elroy Hitchens shouted out so that everyone could hear, "The bus driving test is next week, young fella." All the seniors clapped.
"I'm on it, Elroy," Gus shouted back. The seniors clapped again. Barney clapped the loudest.
And then the meeting got under way. It went from curiosity to anger to belligerence, then back to anger, with shouted comments that hurt Gus's ears. Barney marched up front to take his place next to Gus. He put his fingers to his lips and whistled. As one, the seniors clamped their lips shut. They sat quietly like chastised children, which had not been Gus's intent.
"Okay, ladies and gentlemen, I'm here to suggest a solution to Initial B Enterprises' problems. I repeat, it's just a suggestion, and I'd like all of you to consider it, then vote on it. So, here we go."
Gus talked for a full hour, outlining a plan that he thought would work for all concerned. When he wound down, the thirty-or-so seniors stared at him like inquisitive squirrels waiting to see if there would be anything else for them to consider.
Albert Givens stood up and posed the first question. "What are we going to do for the ten days you say we are not operational?"
Barney stepped forward and introduced himself. "You'll be working with me. We need to do a lot of paperwork where you are all concerned. We need to square away your Social Security payments. That money was going toward your room and board where you lived prior to moving here. Staying here is free. So we need to make your money work for you, and that's where I come in. You'll be paid a salary, but it won't be a lot of money at the end of the week. But by the same token, you will only be working a few hours a day. Weekends will be free for socializing. We're going to run this operation like the business it is.
"We want each of you to write down everything you think we need to know. What you like to do, if you excel in anything in particular, your food preferences, your current health status, and anything else you want us to know so we can provide the best of the best for you."
A little lady named Anna Bristow stood up and asked about the gardens that she and several of the others had planted that would provide fresh produce for the whole summer.
"I don't see this as a problem, Anna. We have the golf carts, and there's enough room on the back of each cart to transport the produce in baskets. Put that down on your sheet when you write what you're good at or want to do."
Rose took the floor. "How do you want me to discharge the legal firm and the accounting firm when we've been doing business with them since we started?"
"Barney and I can do that. You have both firms on a retainer, and you really haven't utilized all the money you paid out. I'm working for free. The lawyer we plan to bring on board will probably donate her services. It's win-win. People change firms all the time, and no one takes offense; that's just part of doing business. I feel confident when I tell you I think we can have all the legalities and accounting up to snuff inside of a month. You won't have to do the ledgers anymore, Granny. Everything will be computerized and will serve as valid records should you ever have to produce them to any agency making inquiries into your business."
"When do the ten days start?" Violet asked.
"Today. We're going to start carting all your inventories over here and use the west wing to store them. You will also work in designated rooms in the west wing for each project. It will be a day or two of chaos, but we'll get it all worked out. We're up for volunteers to help us cart all your supplies and inventory. We can call Pastor Evans to see if he has any high school kids who want to work a few hours after school.
"Barney and I are going to leave you for a bit. Talk about this among yourselves, and if you're all in agreement, fill out the sheets about your likes, dislikes, and goals. We'll be back in an hour for your decision."
A short round man in the back stood up, introduced himself, and asked for confirmation as to the two weeks' vacation and how it would be arranged.
"With a travel agent," Barney said, heading for the door.
"What about holidays?" Elroy Hitchens called out.
"All holidays are paid and you have Christmas week off, too," Barney shot back.
"Well, I want to go to Las Vegas. They give seniors a free lunch and twenty-five dollars to gamble. Can we do that?"
Gus thought Barney was going to pull his hair out. "You can go wherever you want on your vacation."
"It has to be a senior trip, or you don't get the free lunch and the twenty-five dollars. A bus trip. B-U-S!" Elroy bellowed, his eyes on Gus. "A special trip, not a vacation."
"I'll work on it, Elroy," Gus said, shoving Barney ahead of him.
"Damn! I'd rather go up against a bunch of Wall Street sharks than those people. You sure we can make this work, Gus?"
"Yeah. I'm sure."
"You gonna drive a bus all the way to Vegas, Gus?" Barney laughed so hard, tears rolled down his cheeks.
"Only if you're my copilot." It was Gus's turn to laugh. "I think you need to buy these guys a bus, Barney. I mean, you're rich, it won't make a dent in your bottom line, and I'm sure you can write it off."
"A big yellow bus?"
"Well, yeah. You'll need to call Detroit and order it. Get all the bells and whistles and make sure there are seat belts. Elroy is going to want TV for the long trip."
Barney gaped at his friend.
"Isn't this fun, Barney?" Gus asked.
"I gave up making bushels of money to do this and to buy a bus. Already I'm losing money. And yeah, I'm having a hell of a good time."
"Sure you are. Wait, it's going to get better. I'm feeling the love, I really am. Listen, Barney," Gus said, turning serious, "you're getting this, aren't you? It's not about money with the seniors. It's about being a family, belonging, your peers watching over you, helping you. They just want to be productive, to count for something at their age. Before they came here, according to Granny, they were the forgotten ones. Barney, if I live to be a hundred, I will never forget the looks on the seniors' faces when I rolled up in that yellow bus. They couldn't wait to get on that bus, to get as far away from the facilities where they'd been living. I was the guy who made that happen. At least, the getaway part. We both know that feeling from when we were kids."
"What? You think I'm not getting it? Of course I'm getting it. What the hell do you think I'm here for? Sometimes you're a jerk, Augustus Hollister."
"Takes one to know one." Gus grinned. They were back to being kids again. He loved every minute of it, and he knew Barney did, too.
Chapter 23
ELAINE HOLLISTER SASHAYED INTO SYCAMORE MEMORIAL HOSPITAL and walked straight to the information counter, where she asked for Isaac Diamond's room number. "I'm his granddaughter," she explained. She waited, looking around to see who, if anyone, was watching her. Visitors, nurses in white uniforms and rubber-soled shoes, and technicians moved from area to area. She didn't see anyone who might be paying attention to her. She'd never been here before, so she asked where the gift shop was, then she asked, "By any chance, do you know if Grandpa has any visitors? I don't want to intrude if other members of the family are visiting. I can wait my turn."
The sweet young candy striper offered to call the nurses' station to ask. A moment later, she said, "The head nurse told me that Mr. Diamond has no visitors, and you can go straight up. His room number is E444. The gift shop is around the corner."
Elaine almost fainted when she heard the room number—444. How perfect was that? She forced herself to take several deep breaths before she was ready to walk on jittery legs to the gift shop, where she bought a single white rose with some mixed greenery nestled in a slender glass vase. She hoped she would remember to wipe her fingerprints off it before she left. The gift shop attendant wrapped several napkins around the sweating vase she'd taken out of the cooler. "So it doesn't slip out of your hands," the volunteer said. Problem solved.
Elaine's thoughts were all over the place as she walked to the elevator and pressed the button for the fourth floor. A good-looking young intern stepped into the elevator and stood next to Elaine. Any other time, she would have gone into full flirt mode, but she barely noticed the young man.
Elaine got off the elevator on the fourth floor, and checked the painted arrows on the wall with the room numbers. She didn't bother going to the nurses' station but went directly down the hall to Room E444. The door was closed but not completely. Elaine knocked softly and opened the door at the same time. She made sure she closed it all the way behind her. She didn't step forward until she heard the clack of the heavy-duty door snap shut. "Good morning, Isaac!" She loved it that the old man looked pasty and gray, as well as shocked to see her standing in his hospital room. "How are you? Your office called me the other day to tell me about your accident."
Isaac did his best to cover his surprise at seeing her standing there. His eyes were wary. "Everyone is trying to make my accident more than it is. I'm being discharged tomorrow and will have some physical therapy at home for a few weeks. I told them I was driving myself home tomorrow. I'm so sure of it, I had my son drop off my car last evening. This is just a blip on my hip. Get it—blip hip?"
"I guess what you're trying to say is you're the same seventy-eight-year-old superstud you were the night you manhandled me. With the aid of four little blue pills." Elaine made a sound of disgust in her throat before she said, "I just came here to tell you that I want a refund of my retainer."
"Elaine, as much as I appreciate your coming here, I really am not up to doing business of any kind. I'm sure my partners offered their services. Make an appointment to talk with them. I can tell you this, though. We did quite a bit of work on your case. We hired private detectives, I had meetings about your case, there were e-mails and phone calls and, of course, our hourly rate all gets deducted from that retainer."
"Isaac, Isaac, you aren't listening to me. I didn't ask you to return it. I told you to return my retainer. I won't take no for an answer." Before Isaac could respond, Elaine moved to the bed and reached for the call button, which was twined around the bars of the bed. "Don't even think about calling out, because if you do, I'll give you a chop to your throat that will crush your larynx. Tell me you understand what I just said."
Isaac nodded.
"Okay, now, this is what we're going to do. Ooops, I meant to say what you're going to do. I'm just going to listen. Oh, Isaac, you look . . . scared. What's wrong? Are you not feeling well? Not that I care. Try and get comfortable because I'm going to make your day, you son of a bitch!"
"What's wrong with you, Elaine? Why are you threatening me like this? And you are threatening me."
"Why? You have the nerve to lie there and ask me why? All those disgusting, degrading things you made me do the other night, that's why. You're a pervert. You're a dirty old man."
"You could have left anytime you wanted. You went along with it because you wanted me to lie and cheat for you. I'm a lawyer, and I don't do things like that. I take my profession seriously."
"You took advantage of my greed. I admit it. You said you would make it come out right in the end if I had sex with you. Sex is sex, and, yes, I agreed to a simple bump and grind. What you did to me was not acceptable. And, Isaac, I have it all on tape. So, listen up, you bastard." Elaine pressed the tiny button on the medallion hanging around her neck. Isaac's courtroom voice, filled with lust and passion, reverberated through the hospital room. "Tell me when you've had enough. Make sure you pay attention to my voice when I'm telling you to stop, when I'm fighting you, and you're telling me to shut up and take it like a whore. Once this goes public, if you force me to go that route, I am sure there will be many women, probably clients, who will come forward. Your call, sweetie."
"Turn it off. What do you want, Elaine?"
"Money. Lots and lots of money."
Elaine's mind raced. How much was too much? What if she lowballed it? She thought about her half of Gus's house, which, if she was lucky, would be $250,000 sometime in the future, possibly years, before the house could be sold. She straightened her shoulders and said, "I think three hundred seventy-five thousand dollars plus my retainer back will do nicely. What I want you to do is call your bank, your broker, or whomever you have to call, and tell them to wire the money into an account whose number I will give you when you're ready."
"That's blackmail!" Isaac blustered.
"Yes it is."
"You're insane! I'm not paying you four hundred thousand dollars for a roll in the sack."
"Sure you are. Because if you don't, I'll send copies of your performance to your partners, to the Bar Association, and to every judge in Sycamore Springs and in this part of Virginia. And I'll send it to the newspapers. I'm going to count to five, and if you don't already have the phone in your hand by the time I get to one, I'm walking out of here. And there are no second chances."
"Bitch!"
"Bastard. I'm going to start counting now."
"Wait just a damned minute. If I do what you want, how do I know you won't come back again and again? That's what blackmailers do. They try to suck you dry."
"Guess that's a chance you have to take. What's it going to be, Isaac?"
"Give me that thing," Isaac gestured toward the recorder.
"After you make the call, and I'm sure the money is in my account. Not one second before."
"How many copies have you made?"
"Enough to carry me through till the day you die, you son of a bitch. Do I start counting, or do you want to man up and pay for what you did to me?"
"Give me the damned phone."
An orderly opened the door and said, "Time for rehab, Mr. Diamond."
"Ooooh, can you wait just a few minutes? Grandpa needs to make a phone call first. It will take just a minute."
The orderly ogled Elaine and backed out of the room. "Five minutes, Mr. Diamond. Your time is reserved with the therapist."
"Guess you better make it snappy, Isaac." Elaine handed the phone to the lawyer. She stood close enough so she could hear every word on both ends of the line. She held up her account number and the routing numbers.
Elaine could barely breathe as she listened to Isaac transfer $400,000 into her account. When he broke the connection, Elaine took one long, deep breath. She turned around just as the orderly came back into the room.
"Time to go, Mr. Diamond."
Elaine always prided herself on being able to think on her feet. She knew instantly what she had to do. "I'll just sit here and wait for you, Grandpa. I brought a book with me. Now, you do what they tell you to do so you can get out of here and back home to all of us. I'll just sit here and wait for you," she said playfully as she wagged a finger in Isaac's direction. Just for good measure, she winked at the orderly, who got so flustered he pushed Isaac's wheelchair into the door. She laughed when she heard Isaac curse.
Isaac Diamond glared at Elaine, but said nothing as the orderly helped him out of bed and into the waiting wheelchair.
Elaine waited until she heard the ping of the elevator before she got up to close the door. She moved lightning fast, checking the closet and the drawers of the night chest. She almost laughed out loud when she saw Isaac's car keys and wallet. What a fool he was to leave things like this in a hospital room. She helped herself to the $400 in the wallet, and to the Visa card. Four hundred dollars, another sign. She removed the car key. Time to go.
"Four, four, four," Elaine kept mumbling as she made her way out of the hospital. She headed straight for the parking garage, where she pressed the key to give her some idea of where Isaac's pride and joy, his favorite toy, a Mercedes Maybach worth $450,000, had been parked. She listened, heard the chirp coming from the upper level. She looked around to where she'd parked her VW to get her bearings. She walked over to her car and took a screwdriver out of her trunk, removed the license plate, and stuck it in her purse. She was glad she'd backed the little car into the parking slot. She then made her way up the ramp to the next level as she searched out the Maybach. She looked around for security cameras, but didn't see any. Nor did she see any people looking for their cars. She quickly removed the license plate and screwed the VW's plate onto the Maybach.
Elaine raced back down to the lower level and fixed the plate from the Maybach onto the VW, then back up to the next level, where she opened the car door with the remote, got in, and drove out of the parking garage. She was now $850,000 richer.
Time to get the hell out of Dodge.
Elaine drove the silver Maybach like she was born to do it. As she ate up the miles, a smile stayed on her face all the way home. She swerved into her driveway, bolted out of the car, and ran up to the deck. She checked the duct tape and saw that everything was the way she had left it.
Inside, she went to the front door, checked it, too, then backed into the house. All was well. She ran upstairs and changed into jeans and a tee shirt. Her heels were replaced with Gucci sneakers. She moved then, faster than she'd ever moved in her life. She carried boxes and boxes out to the cavernous trunk in the Maybach. Back inside, she packed all her designer clothes into her designer luggage and carried it all out to the car and jammed it to the ceiling in the car, being careful to leave the driver's side of the rear window free. She stacked the last of her things in the passenger seat and on the floor.
Back in the house, Elaine sat down at the table and typed out a text to Gus's cell phone. It was short and sweet.
Gus,
I'm leaving town. You can have your house back. When I get to where I'm going, I'll sign a Quit Claim deed for my half of the house and send it on to the courthouse. It's all yours, Gus. Check in with the courts to be sure it gets filed. With Mr. Diamond being incapacitated, it will be up to you to file for divorce. I'll be in touch at some point so you can send me the papers to sign. I will lock all the doors and leave the new key above the doorframe on the deck, since I had the locks changed.
Sorry things didn't work out. For whatever it's worth, you're an okay guy.
Elaine
Elaine hit the SEND button and powered down. She slipped the phone into her already loaded shoulder bag. First chance she got, she would ditch the phone and get a new one.
Elaine walked through the house to make sure she hadn't forgotten anything and wasn't leaving something behind. Satisfied, she walked out of Gus's house for the last time. She kept her word and placed the key above the doorframe.
Where to go? Maybe south, the Carolinas. Time to take a few years off to recharge her batteries before going out to find a good old boy with a southern drawl who knew how to treat a lady.
Yeah, time to head south.
Little did Elaine know, as she tooled down the interstate, that the next mark she chose, one Beauregard Levi Mac-Namara, would turn out to be a Bernie Madoff wannabe, and that for years after getting involved with him, she would be back to driving a lemon yellow Beetle.
While Elaine was tooling down the interstate in Isaac Diamond's $450,000 Maybach, Gus and Barney were listening to the seniors' vote of confidence. The vote to go with Gus and Barney's plan was a hundred percent unanimous. Even Oscar, who had wanted to kill Gus, was in total agreement.
Gus and Barney walked among the group to shake each man's hand and to receive a motherly hug from the ladies, including the Blossom sisters.
Fresh fortune cookies and lemonade were served.
At the end of what Violet called the social hour to cement their new plan, the seniors dispersed, and Gus and Barney were left with each senior's résumé.
"Listen, Barney, we have to really read these so we get a clear idea of each person here. When we call them by name, that means we know them and their stories. And each of them has a story. I don't want either of us to think they're just a bunch of old people. I want each one of them to be my friend, and I want us to do what's best for our friends. Do you agree with me?"
"Hell, yes, and I couldn't have said it better. So let's get started. I'm glad it all worked out, Gus."
"Yeah, me, too. Hold on, I'm getting a text. It might be Jill or it might be my office." Barney stared off into space while Gus checked his text. His friend's joyful-sounding whoop almost toppled him off his chair. "Well, damn, take a look at this, Barney."
Barney's eyes popped wide. "Wow! Do you think this is another scam of hers? Or maybe she's trying to set you up for something or other?"
"Damned if I know. Want to take a break and ride out to the house to see if it's true? If she left the key, then I guess she's on the level. Give me five minutes to tell Granny, and I'll meet you out front."
Rose, Violet, and Iris behind her viewed the message. All three asked the same question at the same time. "Do you believe this?"
"It follows her pattern according to all the detective reports I've seen. But she's leaving without a payout. She's never done that before, so, yes, maybe it is a setup of some sort. Guess I won't know till I check out the house. Barney and I are going there now to do just that. We won't be gone long, if it's okay with you ladies."
"Go!" the sisters said in unison.
Gus felt detached when he walked up the steps to the deck that led to the back door. He was surprised when the key was precisely where Elaine had said it would be. He opened the door, expecting the alarm to go off. It didn't. He looked at Barney and shrugged. In the kitchen, he looked around. All was neat and tidy. There was nothing in the refrigerator.
The two old friends walked from room to room and couldn't find anything out of the ordinary. It just looked like a house that no one was living in. They walked upstairs and checked out the master bedroom. The bed was unmade, but that was the only thing to offset the impression of an unoccupied house. The closets were bare, the dresser drawers empty. The tons of makeup that used to dot the vanity in the bathroom were gone. Wet towels were hung over the shower stall.
"She's gone! Everything is gone. She had tons of stuff. I only had one small closet, and she had stuff in all the others. Tons of stuff, Barney."
"What do you make of this?"
Gus shrugged. "I honest to God don't know, Barney. If all her stuff is gone, I guess that means she has no plans to come back. She told me to go ahead with the divorce. I have to assume she'll be in touch. I'm going to put the house up for sale and give the money back to Granny. I don't need a house like this. I'm selling my car, too. I have my eye on a Mustang convertible. If I sell the Porsche, pay off what's owed on it—which isn't much—I can pay cash for the Mustang and have no car payment. The high taxes on this house were killing me, not to mention the homeowner's insurance. That will be a big load off my shoulders. And, no, Barney, you are not going to lend or give me any money, so get that stupid look off your face."
"But you love that Porsche."
"Well, guess what? I love my grandmother and aunts more than I could ever love some damned car. I'll learn to love the Mustang."
Barney wrapped his arms around his old friend. "You're one hell of a guy, Gus Hollister. You put me to shame."
"Nah. Hey, you're the guy who is going to buy a big yellow bus to help a bunch of new friends. I envy you being able to do that without blinking. So, Barney Beezer, you're a hell of a guy yourself."
The old friends left the house, their arms around each other's shoulders.
"You think we're making a difference, Barney?"
"Yeah, I do, Gus."
"Then let's head back to Blossom Farm and make all those dreams of those new friends of ours come true."
"How about heading for the DMV first, so I can pick up the application and manual for bus driving?"
"Okay."
Fifteen minutes later, Barney climbed back into the car and waved the manual under Gus's nose. "Guess what? I have a date tomorrow night!"
"Huh?"
"Yeah, they were out of manuals, so the young lady had to send someone to fetch one. We got to talking, and I asked her out. She said yes."
"Did you tell her who you were?" Gus laughed.
"I think she thinks I'm going to be driving a bus. I told her my name is Barney, and she didn't ask any questions."
"Well, you better hurry up and get that bus."
They were ten years old again as they laughed all the way back to Blossom Farm to work on making dreams come true for some wonderful people.
Epilogue
Two years later
THE SUN WASN'T UP YET, THE SKY JUST STARTING TO PINK UP when Gus and Barney, followed by Wilson, walked through the sliding doors and out to the deck for their first cup of coffee of the day.
Wilson wandered off to water the bushes as the two old friends sat down at the table.
"Today's the day, Gus. You ready for it?"
Gus took so long to answer the question, Barney had to prod him.
"As hard as I try to stop them, Barney, my thoughts keep going back to the day I married Elaine. I was so excited, I actually threw up. I don't feel like that today. I feel . . . anxious. I think I'm afraid to unleash my feelings. I don't want to make another mistake. And yet I can't wait to marry Jill. I feel like she's my life partner. We don't have secrets. We talk out everything. I see us growing old together, like the seniors, and loving every minute of it. I guess I'm ready, but I am scared; I won't lie to you."
"I think that's normal, Gus, not that I'm any kind of authority."
"Well, that's for sure. You're still dating Priscilla from the DMV. Two years is a long time not to make a commitment. What's your game plan, Barney?"
"I don't have a game plan, Gus. Priscilla loves me, I love her, but she can't come to terms with who I am. My money scares her. She'd marry me in a heartbeat if I drove a bus. She said she would never fit in with the kind of people I hang out with. With the exception of you and the seniors. When I showed her my house, which is sitting empty, she started to cry and ran out to the car. She's been on her own for a very long time. She deals with a mortgage payment, a car payment, and one credit card she pays off every month. She shops at discount stores and doesn't recognize designer labels. She's honest, she's frugal, and she allocates a portion of her yearly salary to donate to various causes, what she can comfortably afford. In my eyes, she's as perfect as you can get. I am not perfect in her eyes. Oh, and one other thing. She wants a man who comes home for a supper that she cooks. And a paycheck that goes into a joint bank account. I've asked her to marry me a hundred times and, each time, she says no. Let's not talk about me; this is your day. For whatever it's worth, Gus, you did it all the right way. You found your path, and you stayed on it. I'll find mine, but it may take a little longer."
"Jill really likes Priscilla; they turned out to be great friends. The seniors love her, too. She's what Granny calls good people. We both know what that means."
"I'm happy for you, Gus."
"I know you are, and I have you to thank for it all."
"Nah, you should thank Elaine in a crazy kind of way. If she hadn't demanded a divorce, you never would have met Jill. By the way, have you heard from Elaine?"
"The last time I heard from her was more than a year ago, when I sent the divorce papers to a box number in Alabama. They came back in overnight mail. No note, no nothing. She must be moving around, because when she sent the Quit Claim deed to the house, it was mailed from North Carolina. That was almost two years ago. Elaine is nothing more than a bad memory these days."
"Did the nibble you had on the house come to anything?"
"It was a lowball offer. I'm holding out because I want to return the money to Granny. The market is still bad, but I would at least like to get back the price Granny paid for it, so I'm going to wait as long as I can."
Barney shrugged. "I'm glad you and Jill agreed to get married at Shady Pines. You guys made the seniors so happy. They've been working like beavers to make sure the garden is shipshape. And asking Albert to perform the ceremony put them all over the moon."
"Well, Al is a notary, and he casually said he could marry us if we wanted him to. I talked it over with Jill, and it seemed perfect to us. I hope he remembers the words."
"He's been rehearsing by pretending to marry Iris and Oscar six times a day. I think he has it down pat." Barney laughed.
Wilson trotted up to the deck, looked at Gus and Barney, and let loose with a bark that meant, Where's my breakfast?
"Did you make the bed, Wilson? Did you take the trash out? You need to work in this house, or you don't eat. Hop to it, buddy."
Wilson dropped to the deck and put his head between his paws. Gus shrugged.
Barney grabbed his own coffee cup and reached across the table for Gus's. He carried them into the house for refills. When he returned, he also had a Pop-Tart for Wilson.
"I closed on the house across the street yesterday, Gus. We're going to be neighbors. I bought a John Deere tractor, and they're going to deliver it later today."
"On my wedding day!"
"Yeah. I told them to put it in the garage. No big deal. Next week, Priscilla and I are going to shop for furniture, and, no, she is not moving in. She just offered to help me, so I don't get ripped off."
"Barney, what are you going to do about your business?"
"I'm not giving it up. It's what I do. I am cutting back on my travel, but I can't give it up entirely. I'm good at what I do, and people depend on me. If I can't get Priscilla to see my side, then she and I are not meant to be. I have to be true to myself. Granny taught us that, Gus."
Barney looked at his watch. "Five more hours, pal."
"Hold on, Barney. I have something for you. Groom has to give his best man a present. I got one for you."
"No kidding? You didn't give me one when you married Elaine."
"That's because I didn't know I was supposed to give you a gift. Elaine handled all the details. Granny and the seniors are doing this one, so they explained it to me." Gus got up and went into the house. He returned with a huge box and another Pop-Tart for Wilson.
Barney got up and stood over the box. He pried back the ends of the box and pulled out the slab of bark from the old sycamore tree. Gus watched as his fingers traced their names, then caressed the old bark. Tears rolled down his cheeks.
"Jesus, Gus, how the hell . . . ? I don't know what . . . you couldn't have given . . . this is . . . this is from our kid days. A memory I'll never forget. I don't know what to say," he said, throwing his arms around Gus. Then they both blubbered like little boys as their memories took them both back in time.
"I don't know what you're going to do with it—a doorstop maybe," Gus said, trying to lighten the intensely emotional moment. Barney just hugged him harder.
"I can't believe you gave me this. I guess my question would be, why didn't you keep it for yourself? And how did you get it, anyway?"
"Barney, I don't have a whole hell of a lot to give to show you how much I value our friendship and all you've done for me over the years. I thought . . . I hoped this would say it for me. I told Granny about how I wanted it, and she asked Mr. Younger when he was cutting the tree down. He had to do some serious cutting, but I think he understood how important it was to me to save it. The lightning strike ran down the side, right next to where we gouged out our names. You can see a little dark streak of it there on the side. You know, Barney, you have to stop squeezing me, or you're going to break my ribs on my wedding day."
"Oh, sorry, Gus. I'm just so overwhelmed. Listen, I'm going to take this over to my new house so it's the first thing I bring to my new life here in the neighborhood."
"Go ahead. Do you want me to make some breakfast?"
"No. I'm too excited to eat. Well, okay, maybe some toast and juice."
"Well, if that's all you want, you can make it yourself. I'm going up to take my shower. Now, if you want to cook something, that's okay with me." Like that's going to happen.
Gus made his way upstairs on wobbly legs, Wilson at his heels. He was getting married today, in less than five hours. He pinched himself to prove he wasn't still asleep, dreaming. In the bathroom, he gripped the edge of the vanity to steady himself. He closed his eyes and thought about the past two years and about how a warm friendship had turned into a deep and abiding love for the young woman he'd once called a fireplug. He had to be the luckiest man alive. He bowed his head and thanked Elaine. Because, in the end, Barney was right; if she hadn't kicked him out and filed for divorce, he wouldn't be standing here right now and looking forward to marrying the love of his life. "Wherever you are, Elaine, I hope you're as happy as I am right this moment," he whispered.
Barney drove to Shady Pines because Gus was too nervous. Both were attired in dove gray tuxedos as per Granny's suggestion. They told each other in jittery voices that they looked dashing.
As they drove down the long driveway to the main building, they took time to appreciate the seniors' hard work at sprucing up the grounds for this important day. The lawn had been mowed, and the scent of the newly mown grass permeated the air. It was not an unpleasant scent. Flowers of all kinds bloomed in profusion. There wasn't a weed to be seen. Lush, thick ferns moved gently from the rafters of the wide front porch, where the seniors congregated at night to talk or to play checkers or chess. The building itself looked clean and well kept. The shutters and trim sported a pristine white fresh coat of paint.
The wedding was being held at the back of the property, on the wide expanse of lawn, under a lattice arch. White roses and blooming Confederate jasmine climbed the trellis. Gus thought it looked beautiful.
Barney parked as close as he could to the south entrance to Shady Pines, the door Granny had told them to come to, where they could wait until it was time to see the bride.
"Did Granny tell you what's on the buffet for the luncheon?" Barney asked.
"Everything under the sun. Each senior's favorite, each of our favorites, and, of course, the wedding cake that Lewis Lippman made for the occasion, which Granny said was, as per the instructions, decorated with fortune cookies. One for each guest. Jill thought that the fortune cookie cake was the best idea she'd ever heard of and said she would have liked to have seen the look on Lewis's face when the request for the fortune cookies had arrived."
"They all love Jill. I told you that would happen, Gus. Jill loves having so many grandmothers and grandfathers. She adores each and every one of them. It turned out just the way we thought it would."
Gus laughed. "With a little help from Barney Beezer, who keeps feeding the coffers. I appreciate the help, Barney. The seniors would, too, if they knew. The twenty extra seniors we added the last two years ate into our reserve, but with your help and my creative accounting and Jill's expertise, it's working perfectly. We might have to cut back on the bonus each one gets next year. I don't think anyone will mind. I was also thinking of cutting back vacations from two weeks to one week. Again, I don't think anyone will mind. If we do that, we can take in ten more seniors. You prepared to commit to that?"
"It's done."
"You're a hell of a guy, Barney Beezer. I just wish you'd let me tell all of them how much you've done for them that they don't even know about."
"No. We agreed, Gus. I don't even want Granny or the aunts to know."
"It doesn't seem fair somehow."
"To me, it's fair. So, you ready to get out of the car? Do you think you can stand up? You're gonna be okay, aren't you, Gus?"
"God, Barney, I don't know. I feel like that night when we picked up our dates for our first prom. Remember that?"
"Jesus, is that how you feel?"
"Yeah."
"Well, get over it right now. You are going to marry the most wonderful young woman in this world. You have a huge family here to cheer you on and to wish you well. You have to stand up to that. So, let's put one foot in front of the other and head to the room that was assigned to just you, me, and Albert."
Gus climbed out of the car and stood upright. He started to laugh then and couldn't stop. "I'm getting married!" he bellowed.
"'Bout time you got here, young fella. Thought you might be late for your own wedding there for a minute," Albert said, chuckling.
Gus gaped at the man standing in front of him. He knew it was Albert, yet it wasn't the Albert he knew. The beard was gone, his hair was trimmed, and he wore a stunning blue-and-white seersucker suit that had to be sixty years old. A white sash was draped over his shoulder. Not only was Albert marrying him, he was also going to do all the photography. They all shook hands as Albert paced and recited the words he would say once the wedding was under way.
Granny poked her head in the door. "Ten minutes, Augustus. Violet will escort you and Barney to the waiting area. May I be the first to tell you how beautiful your bride-to-be looks?"
Gus gulped. He felt as nervous as a cat on a hot griddle, a favorite saying of his grandmother's. Now he knew what that particular saying meant.
Violet swooped into the room, checked out Albert from head to toe, then she gave his tie a jerk to straighten it. "Okay, Albert, Iris is going to escort you to the trellis. You go first." Albert smiled as he left the room just as soon as Iris knocked on the door.
"Now, it's your turn, nephew." Violet leaned forward, her gaze soft and gentle. "I want to tell you how proud of you I am, Augustus. You truly redeemed yourself in our eyes. I want to thank you for that. Having said that, neither I nor my two sisters will ever apologize for our actions prior to your first wife's kicking you out of the house. We love you, dear, you're our family, and we care about you, and perhaps, back then, we cared too much. Whatever, that's all water under the bridge. This is now. I hope you will always be as happy as you are today." Then Violet pulled Gus close and whispered in his ear. Gus blinked, then blinked again, as Violet moved forward to lead the two men out of the room, down the hall, and out to the velvety lawn, where they would wait for Jill to make her appearance.
Gus was shaking so bad, Barney had to grip his arm in a viselike hold. "What'd she say, Gus?" he hissed in his ear.
Gus struggled to speak. "She said if I screwed up again, she'd personally help Oscar drag me out to the barn to do me in."
Barney let out a whoop of laughter. "That's Aunt Vi for you. She means it, you know."
"I do know that," Gus mumbled. "God, do I know that."
And then they were standing next to the trellis that smelled so sweet. Gus thought he was going to faint from the heady scent of the flowering jasmine.
"Three minutes and counting," Albert said.
"Two minutes and counting."
"One minute, and here comes the bride!"
The seniors burst into song as every male senior at Shady Pines escorted Jill to the trellis to give her away. They sang loudly, they sang off-key, they forgot some of the words, but their hearts were in the rendition. Jill smiled from ear to ear as Gus stared at his beloved. The gorgeous creature coming toward him loved him. Just him. (And the seniors, he added as an afterthought.) She was willing to spend the rest of her life with him. Just the two of them. Forever and ever.
Barney's arm snaked up to hold Gus erect. He looked at Albert and said, "Hit it, Albert, you're up!"
The ceremony was flawless, everything going off without a hitch. Albert had the words down pat and didn't miss a beat. The only time he screwed up was when he kissed the bride before the groom got to do it.
The seniors broke into another rendition of "Here Comes the Bride." They sang at the top of their lungs. They sang off-key again, but no one cared. They threw popcorn instead of rice because one of the seniors had read somewhere that when wild birds ate rice, it swelled in their stomachs and they got sick. Balloons of all colors sailed high in the air.
Everyone clapped hands as they all made their way back inside to the community room, where the buffet and the champagne toast awaited.
There were only two gifts, one large, one small. The seniors clamored for Jill to open the gift that was from all of them. Tears in her eyes, Jill sat down and undid the wrapping. "Look, Gus, it's an album of our two years with all the seniors. Look, you're splitting wood in this one. Oh, my gosh, I'm cutting Annie's hair in this one. This is a group shot of all of us!" And on and on she went as she flipped the pages. Gus could feel his eyes start to burn. Jill was openly crying.
"Oh, my gosh, I don't know how to thank you. Look at Gus—he's speechless. You guys are the most wonderful family I could ever hope to have. I know Gus agrees." Gus was bobbing his head up and down.
"One more gift. Your turn, Augustus," his grandmother said.
Gus reached for the small package, unwrapped it, and opened the box. A key rested on black velvet. Gus's head jerked up as he looked at Barney. "This better not be a key to a new Porsche or even my old Porsche."
"Not even close, Gus," Barney replied, laughing.
The seniors were giggling and laughing and jostling each other, barely able to contain themselves.
Elroy Hitchens walked over to where Gus was, took his arm, and led him to one of the side windows of the community room. "Look!"
A big yellow bus stood right outside the window, with a big silver bow strapped to the top. "It's from Barney," the seniors shouted as one.
"My own bus!" Gus turned to Barney, who was laughing so hard he could hardly stand. "You son of a gun! How'd you know I wanted my own bus?"
"You talk in your sleep!"
It was chaos, then, as everyone started to talk, to kiss and hug the bride, and to offer congratulations. Gus received handshakes, accepted claps on the back, and listened to well-meaning advice.
Two hours later, Iris announced it was time for the bride to throw her bouquet. All the senior ladies and Jill's friend and former secretary, Louise, lined up and waited for Jill to toss the bouquet over her shoulder. A senior named Sadie caught the bouquet, immediately marched over to Elroy Hitchens, and said, "What do you think about this, Elroy?"
"They smell nice," Elroy said. It wasn't the answer Sadie wanted, but she took it with good grace and moved on so the other ladies could ooh and aah over the flowers.
Rose, Violet, and Iris appeared out of nowhere. "It's time!" they said in unison, the way they always spoke when they were together.
From somewhere, a whistle sounded. It was Albert, who then shouted as loud as he could, "Time to get ready, everyone! The bride and groom will be departing shortly."
The room cleared, as if by magic. Lynus and Lewis walked over to where Jill was talking quietly with Barney and said their good-byes. Before he left, Lewis handed her a small, flat package. Inside, as she and Gus discovered later, were two framed pictures of their wedding cake, decorated all over with sixty fortune cookies.
Forty-five minutes later, everyone was dressed in casual, comfortable clothes. Barney led the parade out to the parking area. He put his arm around Rose and whispered, "This honeymoon is probably going to go down in history. The bride and groom are driving a big yellow bus to Las Vegas and taking along fifty-three seniors plus the best man and the maid of honor!"
"Are you sure, Barney, that the people you hired to clean up and put everything back in place are reliable? The seniors were a little worried about their personal belongings."
"Not to worry, Granny; they're bonded and licensed. There won't be any problems. You guys ready?"
"We are. None of us have ever been to Las Vegas before. Can you imagine Jill and Augustus giving each of us a fifty-dollar bill to gamble? And the casino will give us another twenty-five. Jill said it's customary to do that. I might be old, but I don't think I ever saw that in any of the etiquette books."
"You're slipping, Granny. Even I knew that," Barney said with a straight face.
"I guess I am getting old, but I'm glad I can learn something new each day. Thank you for enlightening us, Barney."
Outside, Albert's whistle blasted through the air. The seniors lined up, not sure which bus to get on. They waited for the bride and groom to make the decision. Gus looked at Barney and grinned. "We're going in my new bus. All aboard!"
Gus, Jill, Priscilla, and Barney were the last to board. The workers Barney had hired to clean up after the wedding waved from the front porch of Shady Pines.
"Isn't this great, Priscilla?" Barney asked the woman he hoped to marry. "Getting married, then taking your family along on your honeymoon. In a big yellow bus. I don't think it gets any better than that, do you?"
"You can't wait to drive this bus, right?" Priscilla asked.
"I take over for the second half of the trip. Got my license right here with me."
"Well, in that case, I'll marry you."
Unaware of what had just happened, Gus settled himself behind the wheel and turned the key in the ignition. The seniors clapped and whooped when the engine of the new yellow bus growled to life.
Before Gus shifted gears, he took a moment to look around at his big family, two of whom had their arms wrapped around each other and were oblivious to the rest of the world. Then he looked at his new bride, who was grinning from ear to ear. In that moment, he knew that if he lived to be a hundred, he would never ever be as happy as he was then. His fist shot in the air. The seniors clapped once again.
"Next stop, Las Vegas!" Gus shouted.
FERN MICHAELS is the USA Today and New York Times
bestselling author of the Sisterhood and Godmother
series, Tuesday's Child, Southern Comfort, Betrayal, Return
to Sender, and dozens of other novels and novellas. There
are over seventy million copies of her books in print. Fern
Michaels has built and funded several large day-care
centers in her hometown, and is a passionate animal lover
who has out-fitted police dogs across the country with
special bulletproof vests. She shares her home in
South Carolina with her four dogs and a resident
ghost named Mary Margaret.
Visit her website at fernmichaels.com.
GOTCHA!
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REVENGE IS NEVER OUTDATED
Sometimes, justice is a long time coming. That's the case
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her greedy daughter-in-law Darlene had something to do
with the mysterious circumstances surrounding her son
Larry's death. She desperately wants to get a confession out
of Darlene—and to ensure the safety of Larry's daughter,
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A Zebra mass-market paperback on sale July 2013!
BALANCING ACT
One of the most acclaimed storytellers of her time, #1 New York
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of love, family, friendship, and self-discovery. Together in one vol-
ume for the first time, here are two classic stories about following
your heart—wherever it leads . . .
ALL SHE CAN BE
Rita Bellamy has had enviable success as an author, but it
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over in a small lakeside cottage, slowly rebuilding the confi-
dence that was shattered. But is the younger man next door
a fun, frivolous diversion or something much more?
FREE SPIRIT
Moving to Washington, D.C. to be with Griff should be the
beginning of an exciting new chapter in Dory's life. Yet
there are adjustments too, and sacrifices she never
expected. And soon Dory must weigh the price of love
against everything she hoped to gain . . .
FANCY DANCER
On his thirty-fifth birthday, Jake St. Cloud inherits a
fortune—and learns the whereabouts of his mysterious
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At least, that's the plan. When their initial meeting goes
badly, a distraught Jake crashes his car and is sentenced to
community work—with Alex as his parole officer. Jake must
spend a year helping Angelica Dancer and her daughter,
Fancy, at the Dancer Foundation for neglected children.
Fancy, scarred within and without by the accident that
ended her ballet career, is even less happy with the arrangement than Jake. Yet as they're thrown together, Jake, Alex,
Angelica, and Fancy make unexpected connections. And as
he unravels the painful truths of his past, Jake realizes that
his mother's greatest gift to him lies not in his inheritance,
but in the future, and the family, he's slowly piecing
together . . .
RETURN TO SENDER
At seventeen, Rosalind "Lin" Townsend found herself pregnant
and alone. Her deeply religious father threw her out of the house,
and Nick Pemberton, her baby's father, refused to marry her. Yet
even at the lowest point in her life, Lin vowed to succeed on her
own terms, and to give her son, Will, all the love and happiness
she'd been denied.
Nineteen years later, Lin has made good on her promises, and
Will is about to start his freshman year at NYU. But when Lin visits
New York with Will, she crosses paths with the one man she
thought she'd never see again—Nick Pemberton, now a million-
aire CEO, and the man who sent back all her letters unopened.
Seeing him fills Lin with anger, and she resolves to right the
wrong he did to Will. If she succeeds, like she has with everything
else, the cost of revenge may be the loss of a bright new future . . .
KENSINGTON BOOKS are published by
Kensington Publishing Corp.
119 West 40th Street
New York, NY 10018
Copyright © 2013 by MRK Productions
Fern Michaels is a Registered Trademark of First Draft, Inc.
All rights reserved. No part of this book may be reproduced in any form or by any means without the prior written consent of the Publisher, excepting brief quotes used in reviews.
This book is a work of fiction. Names, characters, places, and incidents either are products of the author's imagination or are used fictitiously. Any resemblance to actual events or locales or persons living or dead is entirely coincidental.
Kensington and the K logo Reg. U.S. Pat. & TM Off.
Library of Congress Control Number: 2013930667
ISBN: 978-0-7582-8671-0
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package querqy;
import static org.junit.Assert.*;
import org.junit.Test;
public class CharSequenceUtilTest {
@Test
public void testNullDoesNotCauseExceptionInEquals() {
assertTrue(CharSequenceUtil.equals(null, null));
assertFalse(CharSequenceUtil.equals("", null));
assertFalse(CharSequenceUtil.equals(null, ""));
}
@Test
public void testEqualSubstring() throws Exception {
assertFalse(CharSequenceUtil.equals("", "a"));
assertFalse(CharSequenceUtil.equals("a", ""));
assertFalse(CharSequenceUtil.equals("ab", "abc"));
assertFalse(CharSequenceUtil.equals("abc", "ab"));
}
@Test
public void testEqualStrings() throws Exception {
assertTrue(CharSequenceUtil.equals("abc", "abc"));
assertTrue(CharSequenceUtil.equals("", ""));
}
@Test
public void testEqualIsCaseSensitive() throws Exception {
assertFalse(CharSequenceUtil.equals("ABC", "abc"));
assertFalse(CharSequenceUtil.equals("abc", "ABC"));
}
@Test
public void testClassHandling() throws Exception {
assertTrue(CharSequenceUtil.equals("abc", new LowerCaseCharSequence("ABC")));
assertTrue(CharSequenceUtil.equals(new LowerCaseCharSequence("ABC"), "abc"));
assertFalse(CharSequenceUtil.equals("abc", new Object() {@Override
public String toString() {
return "abc";
}}));
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,384 |
CONTENTS
Cover Image
Title Page
Preface
Introduction
Chapter 1: The Origins and Theory of Chinese Medical Knowledge
THE TAOIST THEORY OF YIN AND YANG
THE FIVE ELEMENTS
QI, "VITAL ENERGY"
Chapter 2: The Causes of Illness in Chinese Medical Theory
WAI YIN, "EXOGENOUS PATHOGENS"
NEI YIN, "ENDOGENOUS PATHOGENS"
BU NEI BU WAI YIN, "NEITHER ENDOGENOUS NOR EXOGENOUS PATHOGENIC FACTORS"
CHINESE THEORY AND THE WESTERN PARADIGM
Chapter 3: Eating for Health
HOW TO EAT
WHEN TO EAT VARIOUS FOODS
PERSONAL CONSTITUTION
PERSONAL CHARACTERISTICS QUESTIONNAIRE
Chapter 4: Foods and Their Healing Properties
FRUITS
VEGETABLES
NUTS AND SEEDS
GRAINS AND BEANS
MEAT AND POULTRY
FISH
EGG
HERBS AND SPICES
SWEETENERS
BEVERAGES
CONDIMENTS
Chapter 5: Chinese Home Remedies for Common Health Conditions
COOKWARE
METHODS OF PREPARATION
SPECIAL INGREDIENTS
ABDOMINAL PAINS
ACNE
ALCOHOLISM
ANEMIA
ARTHRITIS
ASTHMA
ATHLETE'S FOOT (TINEA PEDIS)
BLOODY STOOLS
BURNS AND SCALDS
COMMON COLD
COUGHS
CONSTIPATION
CORNS
DIARRHEA
DYSENTERY
FOOD POISONING
GASTRITIS
HAIR LOSS AND PREMATURE GRAYING
HEADACHE
HEMORRHOIDS
HEPATITIS
HYPERACIDITY
HYPERTENSION (HIGH BLOOD PRESSURE)
HYPOTENSION (LOW BLOOD PRESSURE)
INDIGESTION
INSOMNIA
MENOPAUSE
MENSTRUAL CRAMPS (DYSMENORRHEA)
NAUSEA AND VOMITING
OBESITY
PREGNANCY
SEXUAL PROBLEMS
SMOKING DEPENDENCY
STOMACHACHE
WHOOPING COUGH (PERTUSSIS)
Chapter 6: Longevity Banquets
SNACKS AND APPETIZERS
SOUPS
VEGETABLE DISHES
BEEF DISHES
LAMB AND MUTTON DISHES
PORK DISHES
CHICKEN DISHES
DUCK DISHES
EGG DISHES
SEAFOOD DISHES
TEAS
WINES
Chapter 7: Exercising for Health
NEI DAN QI GONG
Appendix 1: Daily Requirements of Protein, Minerals, and Vitamins for the Healthy Adult
Appendix 2: Mail-order Resources
SOURCES OF HERBAL SUPPLIES
Footnotes
Endnotes
About the Authors
About Inner Traditions • Bear & Company
Copyright & Permissions
PREFACE
In China we take many facts about food, eating, and health habits for granted. When I first traveled to the United States in 1988, I was intrigued by many of the differences between Chinese and Western culture. Above all I was surprised by the differences in eating habits.
People in America seem to be obsessed with the concept of a healthy diet. Nutrition facts are printed on every jar, can, and package; everything is "fat free" or "low in cholesterol." People seem to know so much about food. They talk about organically grown foods, about fiber and vitamins and health. All this set me thinking about my own Chinese traditions.
When I lived in China I paid very little attention to tradition. Like most young people of my generation, I believed that everything Western was superior and that our Chinese culture was too old-fashioned to take seriously. Nevertheless, without realizing it I was absorbing many of my cultural traditions. In America, therefore, when I heard people rhapsodizing about low-fat vegetarian and "New Age" diets, I was perplexed. The precious organically grown tomatoes or cucumbers and the cooking methods that people so enthused about appeared to me to be perfectly ordinary. I soon realized that what was considered a normal diet in America must be something quite different from what I was used to.
Indeed, even "Chinese food" in America turned out to be different from what I expected. While there are thousands of Chinese restaurants in the United States, few of them serve the sort of food we expect to eat in China. In China we combine colors and flavors in ways that please the eyes and the palate. We balance our diet to consume a little of everything in the right combination and sequence: too much meat increases internal fire; too many raw vegetables give you a stomachache.
In China we always consider the health merits of what we eat. We don't like to deep-fry because frying is poison. We eat garlic because garlic cleanses the intestines, destroying harmful microorganisms. We select our foods according to the climate and time of year: when it is very hot, we eat cooling foods; in winter we eat warming foods.
We consume our drinks warm—even water is drunk hot. Hot water dissolves fats, assists digestion, and cures colds. As everybody in China knows, iced water blocks digestion. We drink soup at the end of our meals in order to clean the esophagus. Soup for us is a nutritious preparation in clear broth, nothing heavy or creamy. (Cream, milk, and cheeses have no place in Chinese cuisine.)
We know that you get a stomachache if you eat outdoors facing the wind, that green tea is important for burning fats, and that ginger kills germs.
Confucius said, "Ordinary people regard food as heaven." Eating is something that we do every day. The way we eat affects the way we live. Good, healthy cuisine not only improves the quality of our eating; it leads to a healthy body and mind, to harmony, and to a long life. When I stayed several months in America in 1993 I found myself thinking about food and the eating habits of our two cultures more than I had ever before. I decided then that I should write something about health and cuisine.
In my experience writing projects begin with a seed of an idea that makes its way onto a sheet of paper. From there it can either fizzle into oblivion or develop into a research project that engages most of one's waking life. The latter is what happened in this venture; the desire to write about Chinese ideas of health and cuisine led to two years of travel and research in China.
During the course of my research I realized that we Chinese have perhaps the vastest pharmacopoeia of food remedies of any country in the world. Other cultures hand down a few practical remedies from generation to generation. In China we have made a veritable science out of our traditional knowledge. In fact, we cannot separate traditional food remedies from traditional medicine in any meaningful way, beyond stating that the latter sometimes uses herbs and minerals that are harder to come by than raw foods.
I began my research by focusing on the Taoist theories underlying Chinese traditional medicine. At the same time I started collecting remedies and recipes. Some I tried on myself; some I tried on others. Most have proved amazingly efficient. I suffered from premenstrual cramps until I discovered the old Chinese remedy of ginger and brown sugar. Now I drink this broth regularly before my period and have, as a consequence, never needed to concern myself with the problem since. Whenever I suffer from a cough I drink daikon, ginger, and scallion soup to give relief. To anyone suffering from constipation I recommend honey, or, in more stubborn cases, fig tea. They work. When traveling rough in Tibet my husband and I protected ourselves by eating a clove of raw garlic with every meal. It may not be a coincidence that while everyone with us fell victim to the "runs," neither of us had the slightest problem.
Convinced by the evidence, we set about systematically recording and categorizing our facts. This led to a winter spent with a portable computer on a beach in India and then, with the help of my husband, George Ellis, to a manuscript. This book is the end result.
**Zhuo Zhao
Arcata, California**
INTRODUCTION
To the Chinese, longevity is the greatest blessing of a good life. Consequently, it is a Chinese belief that the central duty of every man and woman is to cultivate health and fitness throughout one's entire lifetime. Out of that belief has developed a vast system of preventive methods for maintaining health, consisting of exercise, diet, rest, healthy living habits, and preemptive diagnoses.
When, despite efforts at prevention, disease does arise, the cause is sought in some underlying imbalance between the individual and his environment, and is corrected by proper eating. Only when all else fails does one resort to doctors and medicines.
This book is about the role of Chinese cuisine in the prevention and cure of disease. It also examines traditional Chinese methods of prevention through exercise and healthy living. It describes simple recipes, or "prescriptions" if you like, that anyone can prepare at home, with little expense, in order to cure many common and chronic ailments. Most of the ingredients we mention can be found in the nearest supermarket; a few may have to be obtained from a store specializing in Oriental foods. None of the remedies in this book require particular attention to dosages or mode of preparation: all the ingredients but one are categorized by the Chinese as "high-grade" drugs. Basically, this classification means that they are food items: wholesome beyond their purely medicinal function, they can therefore be taken continuously over a period of time with no ill effects. Examples of such ingredients are garlic, ginger, celery, and coriander, or, when we get more complicated, jujube (Chinese dates) or cardamom seeds.
Traditionally the line separating "food" from "medicine" has never been clear. In the same way there has never been a precise division between popular home remedies and official Chinese medicine. People in China take whatever is available locally to cure their ailments. Even today, more than 80 percent of the population in China live off the land. They eat what they grow in their own fields and when they fall ill they take the traditional remedies of the land. The people have been there for millennia; experience has taught them or their forefathers, or their forefathers' forefathers. Sometimes by pure chance, or on the basis of an intuitive hunch, someone might stumble across a new and unexpected therapeutic effect of a common spice, fruit, or herb. They tell their friends and family. Others try it. Word spreads until the new remedy comes to the notice of one of China's traditional wandering doctors. He tries it himself, uses it on his patients, and records it for posterity. In this way a home remedy becomes an official remedy. This process of testing and transition is called the _empirical method._ Over a single lifetime the empirical method does not go far. Over nearly five thousand years of recorded history, the trials and errors of a people bent on staying physically fit must surely yield results.
These results form the basis of the rules, prescriptions, and remedies in this book, which we have collected from original Chinese sources, ancient and modern, published and unpublished. We hope that by publishing them in English we may both further the understanding of Chinese medical theory and practice in the English-speaking world and, above all, provide access to centuries of clinical experience that may improve the quality of life for anybody willing to try the ancient Chinese way to health through food.
There are several circumstances in which this book might prove useful. You may wish simply to prepare good, wholesome Chinese cuisine with a view to keeping you and your family healthy. Or you may wish to follow a Chinese dietary and fitness regimen for generic disease prevention or for weight control. The suggested recipes and prescriptions will provide relief from many minor and chronic health problems—a headache, a blocked nose, an allergy—that often do not merit the time and expense of a visit to the doctor. Other conditions might require surgery (a hemorrhoid problem, for instance) but your preference would be to try alternatives first. There are occasions when you might be dealing with a common illness—influenza or a cold—when you may not wish to poison your body with chemical medicines, the ill effects of which might take at least two weeks to wear off. Or you might be suffering from one of those ailments, terminal or insignificant, most of them chronic, that Western allopathic medicine simply cannot cure. Chinese medicine cannot guarantee results either, but some of these conditions have been known to regress, if not to disappear, under the influence of Chinese natural remedies. Hypertension, asthma, obesity, anorexia, psoriasis, multiple sclerosis, and some forms of cancer are but a few of these.
At a time when dissatisfaction in the United States with mainstream allopathic medicine seems to be on the rise and when leading research institutes, as well as many of the "alternative" therapies, seem to do little more than contradict everything we knew last year—Is cholesterol bad or isn't it? Are eggs good for the liver? Does alcohol damage the heart or guard against coronary disease?—it seems only reasonable to pay attention to what one-fifth of humanity has been preaching, and practicing, for millennia.
This is not to say that one should go completely in the other direction and put wide-eyed trust exclusively in Chinese medicine. It has its limits. First and foremost, Chinese natural medicine takes time to act, often taxing the patience of all but its most resolute adherents. Secondly, it fails to deliver on some occasions when a mere two-week course of antibiotics could provide a quick and permanent cure. Finally, there is the problem of understanding the theoretical basis of traditional Chinese medicine. When discussing the effects of foods and recipes we refer to imbalances of Yin and Yang or the Five Elements, to "hot" and "cold" syndromes, to the "evil wind," and to "upward," "downward," "outward," and "inward" movements of foods and drugs. Furthermore, Chinese medicine seems to ignore some of the basics that Westerners take for granted. It makes no mention of familiar terms like _bacteria, viruses, vitamins,_ or _enzymes._ This can be confusing.
In order to render the concepts of traditional Chinese medicine meaningful we have attempted, in chapter 1, to illustrate as synthetically as possible the underlying theories behind traditional Chinese beliefs regarding health and illness.
Chapter 2 examines the exogenous and endogenous pathogenic causes of disease, and also discusses some of the doubts and misconceptions that might arise from attempting to fit Chinese theory into the Western paradigm. Both the successes and failures of Chinese medicine are considered.
The rest of the book is about Chinese food remedies themselves. Chapter 3 describes the methods of preparing and eating traditional Chinese cuisine for health. It also provides the reader with a questionnaire for recognizing his or her physical characteristics, with a view to selecting the most suitable balanced diet for perfect health.
Chapter 4 looks at the ingredients used in the recipes and prescriptions. Chapter 5 provides the reader with recipes and prescriptions for curing common ailments. Chapter 6 takes the form of a cookbook as it instructs the reader in the ancient art of preparing easy but complete meals for health and longevity.
Finally, chapter 7 describes traditional Chinese _qi gong_ exercises as a means of keeping healthy.
It is with the traditional Chinese augury of a long and healthy life that we leave you to the exploration of the joys and proven health benefits of Chinese therapeutic cuisine. _Chang ming bai sui_ —A long life of one hundred years!
_Chapter 1_
THE ORIGINS AND THEORY OF CHINESE MEDICAL KNOWLEDGE
According to legend, sometime between 2697 and 2597 B.C. the renowned first Yellow Emperor, Huangdi, otherwise known as Shen-nong or "King of farming," tasted one hundred wild herbs and grasses. He was trying to ascertain their values as cures to various ailments from which he was presumably suffering. As a consequence, the Yellow Emperor is credited as being the first person in China to institute the art of healing.
For the following two thousand years people continued to test herbs, fruits, fungi, and barks on themselves, as well as on some unfortunate patients, and to record the results. Gradually this hit-ormiss approach—tempered, we would hope, by the observation of animals' eating habits and by some sort of primitive ideas about physiology and illness—led to the development of a comprehensive theory of health, disease, and treatment. Inevitably, medical theory was made to fit into contemporary beliefs about the nature of the world. These beliefs have come down to us under the name Taoism—pronounced **dow** -izm—meaning "the Way."
By the so-called Warring States period (475–221 B.C.), Taoist medical theory was sufficiently developed to warrant the systematic compilation of all the then-known facts about human anatomy and physiology, and disease pathology, prevention, diagnosis, and treatment. The compilers of the first such record appear to have been various medics working as a group. Either because they were following the fashion of the times (attributing everything to ancient origins), playing modest, or seeking some sort of legitimacy for wild new theories, the authors called their book Huangdi's (the Yellow Emperor's) Internal Classic _(Huangdi Nei Jing)._ They wrote it as if it were a dialogue between the Yellow Emperor and his chief counselor, Qi Bo. Whatever the origin and true antiquity of the ideas presented by them, the authors of Huangdi's Internal Classic laid the foundation for Chinese medical theory and practice a foundation that is valid to this day.
The _Huangdi Nei Jing_ is divided into two parts. The first part, Su Wen (Plain Questions), considers human anatomy, physiology, and pathology within the Taoist theory of _yin_ and _yang_ and the Five Elements. The remedies it espouses are principally herbal. It is on the basis of the Plain Questions that all subsequent medical theory was founded.
The second part is called Ling Shu, or Miraculous Pivot. It discusses the anatomical theory of vital energy _(qi)_ channels within the body and regulation of the circulating qi and the Five Elements by means of acupuncture.
THE TAOIST THEORY OF YIN AND YANG
Figure 1: Energy of the moon and energy of the sun, signifying Yin and Yang
Taoism is a theory of the equilibrium of all nature. Based on early animism and formalized in approximately 500 B.C. by the writings of Lao Tzu (Old Sage), and subsequently by those of Zhuang Zi (Chuang-Tzu), Taoism envisages a world in which the ideal condition is harmony—a perfect balance between human beings and the environment, and among human beings themselves. Taoism emphasizes relationships between opposites, aiming toward the perfection of equilibrium. The equilibrium itself is never permanent. Life is an ongoing process of give and take, of energy absorption and energy loss. As a consequence, every living process in nature is characterized by conflict, accommodation, and complementarity. Today we call this _homeostasis_.
The fundamental forces of the Taoist world are named Yin and Yang. Yin means "in the shade;" Yang translates as "in the sunlight." Extrapolating from this basic concept Yin and Yang came to mean, repectively, darkness and light, moon and sun, passivity and activity, female and male, cold and heat, inside and outside, down and up, left and right, negative and positive, substance and function, emptiness and fullness, hidden and exposed.
Just as the natural world is characterized by the antagonism and flow of Yin and Yang, so is the human body. Indeed, Taoism would find no reason to differentiate between the natural world and that of human experience. To the Taoist, dualism was the greatest error. Instead, Taoist philosophy suggests that we are an integral part of the whole, a flux and flow of vital energy within a larger energy. Today we would call this _holism_.
Thus, when the authors of Huangdi's Internal Classic set out to study human physiology, they based their concept of health on the equilibrium of Yin and Yang. In chapter 5 of the Su Wen (Plain Questions) they wrote: "Yin and Yang are the law of Heaven and Earth, the outline of everything, the parents of change, the origin of birth and destruction."
The active and dynamic processes of the human body—such as eating, digesting, and metabolizing—they called Yang. The passive functions—such as breathing and blood circulation—are seen as Yin. Diseases were also differentiated between Yin and Yang. Diseases that affect the bodily functions, are virulent in nature, and progress rapidly within the body or ascend from the viscera to the head are considered to be Yang. Those that are organic, lie dormant, are degenerative, are characterized by low activity, or descend from the upper part of the body are Yin. The herbs taken to cure these diseases are, in their turn, also differentiated between Yin and Yang.
Yin and Yang in human health, as in all of nature, are both interdependent and mutually restricting. They rely on each other for their own being. Each contains within it the seed of the other. Where one increases the other decreases; when one reaches its peak the other emerges. These concepts are expressed in pictorial form by the well-known symbol of Yin and Yang's circular complementarity.
Figure 2: The symbol of Yang and Yin. The upper function, Yang, is in the light and is therefore white. The lower function, Yin, represents the shade and darkness. Yet, as symbolized by the dots within each form, Yang and Yin each contains within itself the seed of its opposite; each is born from the other. When one increases the other decreases.
The Yin and Yang aspects within a living body are in constant interaction, and one always increases at the expense of the other. Activity is Yang; nutrient substances are, in general, Yin. Thus any activity—running, walking, talking—that consumes energy from digested nutrients lessens Yin and, as a result, increases Yang. On the other hand, the metabolism of those same nutrient substances (Yin) depletes the functional energy (Yang) and consequently increases Yin at the expense of Yang. In ordinary circumstances the mutual depletion and increase of Yin and Yang balances itself out. Unusual circumstances—too much activity, too much food, impaired metabolism, or too little activity or food—create an imbalance. In the long term, the imbalance can lead to disease.
Yet Yin and Yang do not exert their influence purely as vital functions. They are, according to Chinese medical theory, attributes of parts of the body as well. Yang is above and Yin is below, therefore the top half of the human body is considered to be Yang and everything below the waist is Yin. Yang is outward and Yin inward. The inside of our body is Yin and the outside Yang. Similarly, the back is Yang and the front Yin, the sides are Yang and the central portion is Yin.
What is true of the body as a whole is also considered valid for the vital organs. In Chinese traditional theory the vital organs are divided, according to their functions, into _zang_ (generating and storing organs) and _fu_ (transforming, transporting, and distributing organs). Generating and storing is considered a Yin activity, therefore the five zang organs _(wu zang)—_ the heart, the liver, the spleen, the lungs, and the kidneys—are all considered Yin. Transforming, transporting, and distributing are said to be Yang activities. It follows, therefore, that the six fu organs _(liu fu)_ —the gall bladder, the stomach, the small intestine, the large intestine, the urinary bladder, and the three main body cavities _(san jiao)_ —are considered Yang.
Because Yin and Yang are everywhere complementary and interdependent, the parts of the human body that are Yang also contain aspects of Yin within themselves, and vice versa. What this means is that within the heart there exists a Yang function too: pumping blood through the body. Yet even within that Yang function of pumping lies a passive Yin function: blood circulation. Within that Yin of circulation can be found the Yang of nutrition to the vital organs. The organs themselves are Yin, which takes us back to where we started from: the heart.
The point is that Yang and Yin are interdependent and complementary to one another. They cannot exist in isolation. Each contains the seed and essence of the other. Within Yang there is Yin, within that Yin another Yang, and so on and so on to infinity.
As the Plain Questions of Huangdi's Internal Classic puts it: "In any one function, Yin and Yang could amount to ten in number, be extended to one hundred, to one thousand, to ten thousand and even to the infinite."
All healthy activities of the human body arise from the maintenance of this dynamic equilibrium between Yin and Yang. For example, when the lungs expand and contract they are performing a Yang function, as _all_ activity is Yang. The activity of breathing is based on the substance of the lungs—substance is Yin. Therefore the Yang and the Yin of breathing are interdependent. When one is healthy, the other flourishes; when either one diminishes—through inactivity (improper breathing), malnutrition, or some external factor such as injury or viral disease—the other aspect withers.
The Plain Questions section of Huangdi's Internal Classic states: "When Yin keeps balance with Yang and both maintain a normal condition of qi (vital energy), then health will be high-spirited. A separation of Yin and Yang will lead to the exhaustion of essential qi."
The causes of imbalance between Yin and Yang are many and varied. Traditional Chinese medical theory regards external pathogens ( _xie qi_ , literally, "incorrect" or "evil energy") and the state of the body's resistance to these external pathogens as the major causes of imbalance. Xie qi (pathogens) are seen as external factors. They can arise from climatic aberrations, lack of adaptation to a changed environment, or from the "six excesses." These excesses are wind (frequently referred to as "evil wind"), cold, heat, firelike heat, dampness, and dryness. Pathogens can also be either Yin or Yang in nature. A Yang pathogen—too much dry heat for example—will decrease the body's Yang functions. Because of their interdependence, impairment of a Yang function weakens the generation and development of Yin as well. A so-called heat syndrome results. A Yin pathogen on the other hand will diminish Yin, leading to damage of bodily Yang with a resulting cold syndrome. (As a general rule, Yin excess causes a cold syndrome and Yang excess gives rise to a heat syndrome.)
Therapy will be based on correcting the Yin/Yang imbalance. If excess Yang is the cause of a heat syndrome, it is necessary to nourish the weakened Yin by ingesting cooling Yin foods and herbs. Conversely, when a cold syndrome damages the body's Yang, Yin becomes preponderant and recourse must be made to hot, Yang foods and medicines. The general principle is thus: Treat Yang diseases with Yin foods and treat Yin disorders with Yang foods.
In order to appreciate the complexities of traditional Chinese food therapy, however, more understanding is called for. In addition to grasping the concept of Yin and Yang imbalances, we need to know something about the Five Elements of nature and their relationships to the five zang and the six fu organs, the concept of qi, and the three causes of disease before delving into the principles of using food and herbal medicines.
THE FIVE ELEMENTS
As we have said, according to Taoism everything in nature is either Yin or Yang. Everything in nature is also seen as being constituted by a combination of the five basic elements. This is similar to medieval European and Indian concepts of the five humors (earth, air, water, fire, and ether), though the elements themselves are different. The five Chinese elements, the _wu xing_ , are Metal (Jin), Wood (Mu), Water (Shui), Fire (Huo), and Earth (Tu).
Just as the mutual restriction and enhancement of Yin and Yang is important to understanding Chinese concepts of health, disease, and corrective therapy, appreciating the complex interdependence between the Five Elements is necessary in order to interpret the relationship between human physiology and pathology and the natural environment. For, despite the name, the concepts behind the Five Elements are more complex than the purely material ones of medieval alchemy.
The elements may be referred to simply as metal, wood, water, fire, and earth, but, in actual fact, they are not seen as mere objects. They are more appropriately regarded as attributes and functions. The Chinese term for them, _wu xing,_ does not mean "elements" at all. _Wu_ means "five" and _xing_ can be translated as "movement" or "that which causes action." "Metal" therefore represents the properties of strength and firmness, of cleansing and destroying. "Wood" is a shorthand way of expressing the functions of germination, extension, softness, and harmony. "Water" represents cold, dampness, and flowing downward. "Fire" signifies heat and flaring. "Earth" refers to the processes of growing, nourishing, and changing.
These processes are continuously enhancing, restricting, and subjugating one another in much the same way as Yin and Yang complement and limit one another in all natural phenomena. The relationship between the Elements is a precise one; it exists wherever the Elements themselves induce activity. It exists, therefore, in the changing seasons, in the ebb and flow of climate, in life itself. It also exists within the functions of the human body.
Our internal organs, our organs of sense, our tissues, even our emotional life, all are characterized by specific Elements/ functions. The functions of the heart, for example, are regarded as belonging to the element Fire. Fire is heat and energy, and the heart is regarded as the organ that imparts energy to all the others. Without the Fire-heart, the human body cannot survive. Fire is nourished by Wood; the heart, therefore, is nourished by the principal organ of the Wood element, the liver. As a consequence, the health of the liver is regarded as indispensable to the well-being of the heart. On the other hand, Fire is extinguished by Water. It follows that if the kidneys, whose element is Water, fail to function properly, the heart is affected.
These basic relationships between the Five Elements are described as "generating" and "subjugating." The order of generation between the Five Elements is this: Wood generates Fire, Fire generates Earth, Earth generates Metal, Metal generates Water, and Water generates Wood. This is frequently referred to as the _mother-child relationship._ In the control cycle, Water subjugates Fire, Fire subjugates Metal, Metal subjugates Wood, Wood subjugates Earth, and Earth subjugates Water. These basic generating and subjugating relationships are illustrated in figure 3.
Figure 3: Healthy balance between the Elements and their corresponding organs
Through these mutually enhancing and restrictive relationships, a second level of equilibrium is achieved beyond that of Yin and Yang. According to the _Lei Jing_ , a Ming dynasty commentary on _Huangdi Nei Jing,_ "If there is no generation, there is no growth and development. If there is no restriction, then endless growth and development will become harmful." This concept is central to the Chinese theory of good health.
At the level of the Five Elements, illness is characterized by a breakdown of the equilibrium between generation and subjugation. When one of the Elements becomes overactive it tends to break out of its normal generating/subjugating relationships. Strong Fire, for example, will violate Water, consuming it and turning it into steam instead of being quenched by it. At the same time it will subjugate Metal beyond its ordinary capacity, encroaching on it and threatening to destroy it. These pathological relationships are expressed as "violating" and "encroaching" or "subjugating" to the extreme. In disequilibrium situations, including human illness, Fire violates Water and destroys Metal; Water violates Earth and extinguishes Fire; Earth violates Wood and dries up Water; Wood violates Metal and consumes Earth; Metal violates Fire and utterly destroys Wood. These relationships are illustrated in figure 4.
Figure 4: Pathological relationships between the Elements and their corresponding organs
When consulting with a new patient a Chinese physician will observe, ask about symptoms, and test the pulse in order to base his or her diagnosis on the relative forces of Yin and Yang as well as on these primary relationships of generation, subjugation, violation, and extreme subjugation between the Elements and the internal organs. The doctor will, however, also inquire into the patient's diet and consider the climate, locality, and time of year. No one exists in isolation from the environment; everything about us is charged with the properties of the Five Elements. Therefore the food we eat, the air we breathe, the cli-mate—our entire surroundings—affect us in one way or another. Each of the seasons belongs to a different Element, as does each direction. (In Chinese philosophy there are five of both: spring, summer, late summer, autumn, and winter; north, south, east, west, and center.) It follows, therefore, that the careful doctor must consider all these factors when deciding on the severity of the symptoms and on the appropriate treatment.
What this boils down to, in effect, is that if you are unwell you must first try to understand the relationship between the diseased part of you, your emotions, the time of year, the part of the world you happen to be in, the climate, and what you've been eating. If, to take a light-hearted example, your lips erupt with cold sores in New Orleans in the summer where you've been singing at Preservation Hall and indulging your sweet tooth, you may be suffering from nothing more complicated than an excess of the Earth element. The Earth—or transforming—Element is abundant in the late summer, in damp climates, in song, and in sweet food. Its excess affects the stomach and the mouth. The remedy would be counteracting Earth with its subjugating element, Wood. In order to achieve that you might move to Boston. More practically, you might eat a diet of greens and cool, sour food, and your troubles would likely disappear. The east, a windy climate, the color green, and sour food are all attributes of the Wood element.
This is, of course, a far-fetched example, but it serves to illustrate the point. The elements in the environment, those within you, and those in your food interact continuously to create situations that can lead either to better health or to debility and disease.
Tables 1 and 2 list characteristics of the various Elements within the human body and in nature. This information can help in diagnosing basic imbalances. The effects of imbalances between the Five Elements within the human body can give rise to many and varied symptoms. For example, a lack of qi (vital energy) in any one organ/function may set off a chain reaction whereby the organ/function normally generated by the weakened organ is depleted of energy and the organ it is supposed to subjugate increases its qi to the point that it stagnates. The outcome is usually malaise and then disease.
Let us look at each of the Five Elements and their five corresponding zang (generating and storing organs) to understand how this happens. (Throughout this discussion you may want to refer back to figure 3 illustrating the generation and subjugation cycles.)
** Mu**
**"A single tree," (i.e., Wood)—to germinate**
**Corresponding zang organ: liver**
**Organ, tissues, and sense organ affected by Wood: The gall bladder, the tendons, the eyes**
In China, to explain the function of Wood it is said that "Trees like to spread their branches freely." The liver therefore "germinates" vital energy (qi) and spreads it throughout the body. When Wood flourishes it generates Fire by transforming food into qi. The liver Fire feeds the heart, which is itself of the Fire element. The heart Fire then generates the Earth element, which corresponds to the spleen. The Earth element is subjugated by Wood; the liver, therefore, directly inhibits the function of the spleen, as well as contributing to it through heart Fire.
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**TABLE 1: HUMAN PHYSIOLOGY RELATIVE TO THE FIVE ELEMENTS**
Element:| Wood| Fire| Earth| Metal| Water
Attribute:| Germination| Growth| Transformation| Reaping| Storage
Bodily organs:| Liver| Heart| Spleen| Lung| Kidney
| Gall bladder| Small intestine| Stomach | Large intestine| Urinary system
Sense organ:| Eye| Tongue| Mouth| Nose| Ear
Tissue:| Tendons| Vessels| Muscles| Skin and hair| Bone
Emotion:| Anger| Joy| Worry| Melancholy/grief| Fear
Sound:| Shouts| Laughter| Singing| Crying| Mourning
Flavor:| Sour| Bitter| Sweet| Pungent| Salty
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**TABLE 2: NATURAL PHENOMENA RELATIVE TO THE FIVE ELEMENTS**
Element:| Wood| Fire| Earth| Metal| Water
Color:| Green| Red| Yellow| White| Black
Climate:| Wind| Humid heat| Dampness| Dryness| Cold
Direction:| East| South| Center| West| North
Voice tones:*1| Jiao| Zheng| Gong| Shang| Yu
Season:| Spring| Summer| Late summer| Autumn| Winter
A weak Wood element leads to a feeble Fire element, resulting in headaches, dizziness, flushed features and, occasionally, mental imbalance. As a consequence, the spleen can become dysfunctional as well.
When the Wood element in the liver is too strong, it results in Fire of the liver. The Metal element is consequently subjugated to the extreme (see figure 3). Metal element resides in the lungs. The lungs are therefore impaired by Fire in the liver, leading to a dry cough and chest pains.
Foods that correct these imbalances would do so by acting directly on the underlying weakness. A dysfunctional liver would be treated by nourishing the weak Wood element. Some Wood-nourishing foods are trout, cheese, and many fruits and berries, such as grapes, lychee, mango, olives, pears, plums, raspberries, strawberries, tangerines, and tomatoes. Sour flavors help Wood to germinate and grow; vinegar, therefore, is ideal for exerting a strengthening influence on Wood. Because of the correspondence between human and animal organs, fresh and healthy animal liver is also considered to be a good remedy for weakness in the liver. Celery, egg yolk, chicken, plums, and peppermint are also valid.
When the Wood element is excessively strong it leads to Fire in the liver and to a consequent stagnation of qi in this organ. The main treatment is to circulate the stagnant qi and to allow the liver to rest; alcohol and heavy and oily foods should therefore be avoided. Because Metal is subjugated to the extreme by Fire in the liver, Metal must be built up in order reestablish equilibrium. The foods that are most suitable for this are the herbs and spices: basil, bay leaf, black and white pepper, capers, cayenne, coriander, dill seed, garlic, ginger, marjoram, mustard greens, nutmeg, rosemary, and peppermint.
**Huo**
**"A flame generated by the contact of two flint-stones," (i.e., Fire)—to grow**
**Corresponding zang organ: heart**
**Organ, tissues, and sense organ affected by Fire: The small intestine, the blood vessels, the tongue**
In traditional Chinese medicine the heart is the governing organ of the body. It is thought to be the seat of the self, of spirit and vitality. As such, the health of the entire mind-body system depends on the health of the heart.
The heart belongs to the Fire element. It is generated by Wood (the liver) and, in turn generates Earth (the spleen and the stomach). On the other hand it is suppressed by Water (the kidneys). When the heart Fire is depleted, through lack of qi from the liver for example, the result is poor digestion and diarrhea (the spleen and stomach depend on heart Fire for health) and low energy in the whole body. When the kidneys fail to function normally the heart is directly affected, resulting in insomnia and emotional problems.
When, on the other hand, the heart Fire burns with excessive heat, the "flames" are said to flare upward, resulting in flushed features, headache, sore throat, bleeding gums, abscesses in the mouth, and bloodshot eyes. Excessive fire also melts Metal (the lung), thus injuring this organ.
Foods that nourish Fire are tangerine, lettuce, papaya, pumpkin, scallion, and rye. Being the flavor associated with Fire, bitter foods also strengthen Fire. The organs that correspond to Fire are the heart and the small intestine; any food that strengthens these will, as a consequence, affect Fire. Some heart-nourishing foods are mung bean, egg yolk, ginseng, licorice, longans, persimmon, and red and cayenne pepper.
Excessive Fire (or inflammation) leads to indigestion, constipation, and the stagnation of blood. This condition may be tempered by strengthening Water, the element that subjugates Fire. Suitable foods to this end are water chestnut, banana, and tangerine peel. Drinking plenty of water is also useful.
** Tu**
**"Two layers of soil from which a plant grows," (i.e., Earth)—to transform**
**Corresponding zang organ: spleen**
**Organ, tissues, and sense organ affected by Earth: The stomach, the muscles, the mouth**
Earth (the spleen) is generated by Fire and regulated by Wood (the liver). The function of the Earth element is to transform; the spleen is therefore involved in the digestion and assimilation of food and in the subsequent storing and distribution of nutrients. It generates Metal (the lungs) and subjugates Water (the kidneys).
The Earth element thrives in warm, dry environments and suffers in cold and damp ones. When the spleen is weak it fails to control normal water metabolism, resulting in urinary problems and, frequently, in diarrhea.
Sweet foods correspond to the Earth and therefore nourish this element. Since sweet is the most common flavor, Earth and spleen-nourishing foods are plentiful. They include most ripe fruits, nuts, and vegetables, as well as seafood, meats, tofu, beans, potatoes, rice, and, of course, honey and sugar. Sour foods are detrimental to a weakened Earth because they nourish Wood and can thus subjugate Earth. In terms of the corresponding organs, a dysfunction of the liver (Wood) will give rise to a pathological condition in the spleen and stomach (Earth).
If you suffer from urinary problems caused by weak Earth, you should eat plenty of sweet foods. All ripe fruits exert a positive effect, but watermelon is perhaps the ideal; besides nourishing Earth with its sweetness, its high water content serves to flush out toxins and clear the urinary passage.
** Jin**
**"Two gold nuggets hidden in the earth," (i.e., Metal)—to reap**
**Corresponding zang organ: lungs**
**Organ, tissues, and sense organ affected by Metal: The large intestine, the skin and hair, the nose**
The lungs and the large intestine both correspond to the Metal element. The main function of the lungs is in respiration—absorbing qi, the vital energy of air, and circulating it throughout the body.
From the Five Elements point of view, Metal generates Water and subjugates Wood. The lungs, therefore, contribute to normal water metabolism and regulate the functions of the kidneys. When the lungs are diseased, the kidneys (Water) are directly affected. In China it is said that "a muffled gong does not sound," a reference to the fact that when Metal is attacked by external pathogens, the lungs suffer and hoarseness or low voice ensues.
Because of the correspondence between Metal, the lungs and large intestine, and the pungent flavor, any disease that weakens the lungs or intestines may be treated with pungent—Metal element—foods. These include pumpkin, leek, rosemary, fennel, and red and black pepper. However, since Metal is generated by Earth, eating sweet Earth foods will also nourish the lungs and large intestine: white mushrooms, grapes, and persimmon, for example, are sweet in flavor and generate fluids that lubricate the lungs. Other favored foods for treating the lungs are carrot and radish, basil, licorice, cinnamon twig, garlic, ginger, peppermint, scallion, mustard leaf, olive, peanut, walnut, water chestnut, and tangerine.
The large intestine is also favorably affected by consuming tofu and other soybean products, figs, spinach, lettuce, Chinese cabbage, freshwater fish, maize, cucumber, eggplant, nutmeg, and black and white pepper.
**Shui**
**"Liquid flowing downward," (i.e., Water)—to store**
**Corresponding zang organ: kidneys**
**Organs, tissues, and sense organ affected by Water: The urinary system, the bones, the ear**
The kidneys correspond to Water. Water tends to flow downward, thus exerting influence on the lower (Yin) half of the body. It is therefore believed that sexual debility in both sexes is directly attributable to weakness of the kidneys.
Water generates Wood and subjugates Fire. When Water fails to provide Wood with sufficient nourishment, the liver suffers. As we have seen the liver generates Fire, which maintains a healthy heart. Weak Water energy therefore affects both the distribution of vital energy throughout the body and the proper functioning of the heart. The resulting symptoms are pain in the lumbar region, digestive problems, wind, diarrhea, swelling of the feet and legs, irritability, and insomnia.
Drinking large quantities of water is not the solution, nor is the intake of a lot of salt, despite the fact that salty flavor corresponds to Water. To nourish the kidneys, seeds and nuts such as sesame, caraway, dill seed, fennel, star anise, soybean, walnut, chestnut, and lotus seed may be eaten. Other nourishing foods for the kidneys are freshwater fish, cuttlefish, eel, egg yolk, mutton, pork, and wheat products.
Because of its flowing nature, Water is particularly sensitive to imbalances in all the Elements and organs. If a weak Earth fails to control Water, normal Water metabolism is impaired, resulting in diarrhea and edema. Metal, too, must be strengthened so as to properly nourish Water. Bitter foods such as grapefruit, orange, and tangerine peel; bitter gourd; radish leaf; asparagus; and celery exert a positive effect.
For our purposes, the point of this discussion is not to memorize or even pay too studious attention to the precise interactions between the various organs and Elements. It is to remember that whenever we resort to Chinese food or medical therapies, whether for maintaining health or for curing disease, we should consider the mutually regulating interrelationships that exist between all of the Five Elements and their corresponding organs. While this may seem daunting to those readers unschooled in traditional Chinese medicine, it will suffice to bear in mind the simple fact that often, in order to treat a symptom connected with one part of the body, we may have to act on an underlying weakness somewhere else. Or, to put it the way we do in China: You must treat the mother to cure the child.
QI, "VITAL ENERGY"
Yin and Yang and the Five Elements are not material things. They are processes. As such they involve energy in all their functions and interactions. This energy the Taoists call qi, commonly translated as "vital energy" or "essential energy." Qi involves both function and substance.
Qi is the energy that supports life. It comes into being with life itself and is replenished through food and the inspiration of air. Congenital qi, _yuan qi_ , arouses and promotes the activity of the Five Elements and the organs of the body. Qi from air and food descends through the energy channels of the body to be stored in the center of the body, the _dan tian_ , about four inches below the navel. From the dan tian qi circulates both in the blood and in the conduit channels and collaterals (the meridians of acupuncture theory). Wherever qi goes it nourishes the organs of the body with its life-giving force.
Strong, unobstructed flow of qi ensures life and health; weak qi is generally the precursor of illness. Any organ or part of the body to which the flow of qi is obstructed will weaken, leading to the organ's withering. As a result, qi stagnates elsewhere in the body and Yin and Yang and the Five Elements become imbalanced. Disease is the inevitable outcome.
Too little or stagnant qi manifests in various ways according to the part of the body being affected. Shallow breathing, for example, indicates lack of qi in the lungs; poor appetite and impaired digestion mean that stomach qi is weak. Hence the importance of maintaining healthy, flowing qi _._ This is accomplished through diet and through qi gong, or qi control exercises, which we discuss later in the book.
Although unrecognized by allopathy, qi is fundamental to Chinese medical theory. It is the vital force that sustains life and guarantees good health by oxygenating the blood and nourishing the organs and the lymphatic and nervous systems. Without the concept of qi Chinese medicine would be at a loss to explain the workings of acupuncture, the positive effects of the qi gong system of exercises, the benefits of massage and acupressure, even the fundamental questions relating to the nature of health and of life itself.
Qi, therefore, is referred to continuously both in Chinese medical treatises and in popular discussions about life, health, and disease; we too shall consider the qinourishing properties of food throughout this book.
Whether you wish to accept the Chinese belief that qi is something substantial, or instead prefer to interpret it in terms of oxygen and the processes of oxygenation or as another way of talking about energy, it is important to understand that, from the Chinese point of view, nourishing qi, the health of qi, and qi circulation are as important—and perhaps more important—than the nourishment and health of the blood and its circulatory system.
Weakened or stagnant qi is the precursor of disease. Disease itself, however, requires other factors, both internal and external, to take hold of the body. We shall consider these in the following chapter.
_Chapter 2_
THE CAUSES OF ILLNESS IN CHINESE MEDICAL THEORY
Chinese medical theory traditionally discerns three categories of causes of illness. These are:
1. External factors, or _wai yin._ This classification encompasses climatic and environmental factors: wind, heat, fire, damp, dryness, and cold, as well as pestilence and epidemics.
2. Internal factors, or _nei yin_. This category includes both emotional disturbances that weaken the body's resistance to disease, and unhealthy behaviors such as prolonged malnutrition, overindulgence, inactivity, overstrain, and fatigue.
3. Neither external nor internal factors, or _bu nei bu wai yin_. Included in this category are injuries; wounds; parasites; insect, snake, and animal bites; and bacterial and viral infections.
WAI YIN, "EXOGENOUS PATHOGENS"
The exogenous pathogens of traditional Chinese medical theory are sudden changes in the environment and climate due either to unseasonal aberrations in the weather or as a result of traveling from one region to another too quickly for the body to adapt. If the latter pathogenic factor was even considered in a time when the fastest means of transport was the horse (the Chinese were never much of a seafaring people), it must be reaching fairly epidemic proportions today as we hop around the planet, jumping several time zones and seasons in a matter of hours.
We are, without doubt, the most adaptable species living on this planet. Our ubiquitousness attests to that. Nevertheless, acclimatization takes time. Too sudden a change in the environment leads to imbalances. In Taoist terms, the Earth and the Water of places differ. The Five Elements within the body and the proportions of Yin and Yang change. _Zheng qi_ ("proper" or "correct" qi, referring to the body's resistance to disease) is depleted in the effort to restore equilibrium. When qi is weak, illness is the likely outcome.
The climatic changes that are regarded as directly responsible for illness are collectively called the _xie qi,_ or "evil qi." They are evil wind _(feng),_ cold _(han),_ damp heat _(shu),_ humidity _(shi)_ , intense dryness _(zao),_ and firelike heat _(huo)_. Although the xie qi are principally environmental, or external, factors affecting the body, the symptoms they produce frequently become manifest only when they enter to the very core of the body, affecting the zang and fu organs. When this happens they are considered xie qi syndromes of an internal nature.
**Feng, "evil wind"**
Evil wind is a Yang pathogenic factor. As such, it tends to attack the upper body (Yang) first. It is characterized by swift movement affecting various parts of the body in rapid succession, and by outward dispersion. It often operates in conjunction with another of the evil qi, giving rise to wind cold, wind heat, wind dampness, and, especially, wind fire. The latter is the most virulent combination, as wind is said to fan the Fire. The result is acute and persistent fever.
**Common effects of a feng syndrome:** The common cold, fevers, sweating, joint pains, itchy skin, spasms, and uncontrolled movements of the limbs. Wind tends to attack the liver. When it does, apoplexy, infantile convulsions, paralysis, and Parkinson's disease can result.
**Early clinical manifestations:** Headache, sore throat, blocked or runny nose, fever, perspiration, cough.
** Han, "cold"**
Han, or cold, is a Yin pathogen. It depletes the Yang of the body, particularly that of blood and qi circulation. It is thus characterized by stagnation and by contracting of the blood vessels and muscles.
**Common effects of a han syndrome:** Aching muscles and joints, headache, cough, asthma, nasal blockage, pharyngitis. Sometimes a cold syndrome is brought about by the consumption of cold and uncooked food, or by exposure of the abdomen to cold. When this occurs cold tends to attack the spleen and stomach, thus affecting digestion. The effects are vomiting, diarrhea, and abdominal cramps.
**Early clinical manifestations:** Vomiting, stomachache, general feeling of cold in the extremities and in the abdomen.
** Shu, "summer heat"**
Shu, or damp (summer) heat, is a Yang syndrome. It is said to consume Yin and qi _._ As with all Yang syndromes it affects the upper body, especially the head, giving rise to headaches, dizziness, and excessive sweating.
**Common effects of a shu syndrome:** Fever, heat sensation on the skin, irritability, rapid pulse, thirst, heavy head, stuffy chest, nausea and vomiting, abdominal distention, diarrhea.
Early clinical manifestations: Thirst, general weakness, yellow and scanty urine, constipation.
** Shi, "damp"**
Shi is a Yin pathogen. Its principal action is to obstruct the circulation of zheng qi _,_ the body's disease-resistant force, resulting in sensations of heaviness, stagnation, and sluggishness. Shi usually attacks the lower half of the body (Yin), causing soreness in the muscles and joints of the lower limbs. It is also said to attack the spleen which, being of the Earth element, is particularly susceptible to humidity. The results are distention and soreness of the trunk and abdomen.
**Common effects of a shi syndrome:** Rheumatism, indigestion and constipation, skin rashes and fungi.
**Early clinical manifestations:** Lethargy in the head and body; aching in the limbs; fever; white, viscous-coated tongue; slow pulse.
** Zao, "dryness"**
Zao, or dryness, is considered a Yang pathogen. It consumes Yin substance, especially body fluids. It tends to affect the chest, particularly the lungs, which need humidity to function adequately. Dryness may be either cold or hot, external or internal.
**Common effects of a zao syndrome:** Cold dryness results in symptoms similar to that of han, or cold, syndrome: aching muscles, joints, and head; cough; asthma; nasal blockage; pharyngitis further complicated by insufficient body fluid. Hot dryness causes headaches; a dry, rasping cough; thirst; irritability; red and dry mucous in the mouth and nose. Internal dryness is more serious than external; it can lead to mental instability and emotional distress.
**Early clinical manifestations:** Dry, rough skin and chapped lips.
** Huo, "fire"**
Huo, fire, is both one of the wu xing (Five Elements), and one of the six evil qi _._ It is a Yang pathogen that tends to flare upward. As a consequence, it consumes Yin fluids in the upper half of the body.
**Common effects of a huo syndrome:** Fever, thirst, heavy perspiration, ulcers of the tongue and mouth, nosebleed, irritability, anxiety, and insomnia. In extreme cases a fire syndrome can lead to delerium and loss of consciousness.
**Early clinical manifestations:** Thirst, dry mouth and throat, headache, red and swollen eyes, yellowish urine, dry stool, rapid heartbeat.
NEI YIN, "ENDOGENOUS PATHOGENS"
According to traditional Chinese medical theory the internal factors held responsible for the weakening of zheng qi, and hence the development of disease, are behavioral or emotional in nature. They are:
1. wrong eating habits
2. a stressful lifestyle
3. overindulgence in sex
4. the seven pathogenic emotions
**Wrong Eating Habits**
The pillar of good health is moderation in all things—exactly what parents always tell their children. Moderation—what amounts to common sense—in China became a working medical hypothesis. This hypothesis eventually became theory, and that theory led to a regimen adopted by every health-conscious individual in the country. In China we believe in the value of a long and healthy life. We therefore stick to moderation in whatever we do.
For most Chinese people, moderation means remembering, first of all, the "five forbiddens" _(wu jin)_ of eating. They are:
1. Refrain from monotony. Do not eat only what appeals to your palate, but vary your diet at every meal.
2. Avoid excesses: eat spicy, sour, fried, salty, and sweet food sparingly.
3. Never eat large amounts at a single sitting. You should rise from the dinner table feeling only two-thirds full.
4. Beware of chemical additives and exotic foods. The latter refers to some Chinese delicacies, so infamous in the West, that we actually eat only as a special culinary adventure. These include snake meat, scorpion, insects, dog, badger, mouse, bear paws, snail, and turtle.
5. Do not overindulge in beverages in place of eating solid food.
In addition to these five forbiddens, Chinese medical tradition points out that overeating leads to stress on the digestive system, inefficient absorption of nutrients, weak qi, and disease. Malnutrition, on the other hand, deprives qi and blood of the nutrients necessary to life. Malnutrition includes eating too little for one's body weight; consuming a monotonous, poorly balanced diet; eating contaminated, poisonous, or stale food; and consuming cold food and drinks. Finally, overindulgence in intoxicating liquor is seen as a cause of serious imbalances and maladies, with the liver being particularly affected.
**Stressful Lifestyle**
In China we regard both overstrain and too little physical exertion as factors leading to imbalances and illness.
Overexertion over a long period weakens the body as a whole. It leads to exhaustion, dizziness, sleepiness, fluttering heart, asthma, and low resistance to disease.
Lack of physical exertion causes stagnation in the circulation of qi and blood to the various parts of the body. This results in unhealthy zang and fu organs, weakness, anorexia, dizziness, palpitations, insomnia, and a decreased resistance to the six evil qi exogenous pathogenic factors.
**Overindulgence**
Excessive sexual activity is considered to be a specific form of strain that consumes the kidney (water) essence and leads to lumbar pains, dizziness, ringing in the ears, listlessness, spermatorrhea, leukorrhea, and, in the long run, impotence in men and frigidity in women. What would be considered excessive sex is, perhaps, a matter of opinion; in China, engaging in sex more than twice a week is considered excessive.
**The Seven Pathogenic Emotions**
If a stressful lifestyle is considered deleterious to health, stressful emotions are seen as the pathogens that, one after another, get into your body, affect your qi and your internal organs, and, in the long run, lead to disease. So dangerous are they considered that Chinese medical tradition refers to them specifically as the seven pathogenic emotions. These are anger, melancholy, worry, grief, fear, fright, and joy.
The latter emotion may appear out of place—the experience of joy does not seem likely to lead to stress, distress, and a consequent lowering of resistance to disease. Nevertheless, we in China believe that when any of these emotions are too strong or constant, or when the subject is too sensitive to them, they cause imbalances within the body's zheng qi, and hence lead to disease. Anger is said to make the qi rush upward; joy makes it circulate slowly; grief consumes qi; fear causes it to flow downward; fright makes it flow unevenly; melancholy depletes qi; and worry leads to its stagnation.
A specific relationship is said to exist between each of the principal organ/Elements and the emotions (see table 1). It is recognized, therefore, that anger (Wood) injures the liver (also Wood). Melancholy and grief injure the lungs (Metal), fear injures the kidneys (Water), and joy injures the heart (Fire). It follows also that worry injures the spleen (Earth).
BU NEI BU WAI YIN, "NEITHER ENDOGENOUS NOR EXOGENOUS PATHOGENIC FACTORS"
This category includes wounds; injuries; insect, snake, and animal bites; parasites; fungi; and in our modern day, viruses and germs.
To deal with these factors, including germs and viruses, Chinese medicine resorts to foods and herbs that build qi and strengthen the body's resistance to disease. Nothing in ancient China was known about bacterial and viral infections. According to classical theory, however, no illness of any kind can enter or perpetuate itself within the body as long as qi is strong and circulates freely. As a result all therapies are aimed exclusively at helping the body defend itself, not at eliminating the external microscopic cause.
In practice this holistic approach works well with all ailments except the most virulent. This is the reason traditional Chinese medicine cannot deal with infections as successfully as modern allopathic (Western) medicine. Nevertheless, even today, when most city dwellers in China turn to allopathy for cures to maladies of a bacterial or viral nature, we invariably follow the dictates of traditional medicine at the same time. We may take antibiotics to cure the flu, but, with the antibiotics, we will take garlic and ginger broth with sugar for its warming effect, consume _yin qiao_ pills to dispel fever, and crawl under a heavy quilt fully dressed for a good diaphoretic sweat.
CHINESE THEORY AND THE WESTERN PARADIGM
The fact that Taoist theories of Yin and Yang, the Five Elements, and exogenous climatic pathogens do not fit current Western views of the world may be a matter of concern to many people. In the West, certain facts about nature and disease have been discovered that have opened avenues of therapy undreamed of just fifty years ago, and it would seem that any system of medicine that ignores these facts is bound to be deficient in one way or another. However, the two medical systems of allopathy and Chinese tradition are so different that any attempt to relate one to the other on theoretical grounds is futile. It would be rather like trying to compare the styles and techniques of traditional Peking opera with those of Western classical music, _wushu_ boxing with a world heavyweight title bout, or qi gong with athletic training. The two systems simply arise from different traditions that view the world differently and have attributed different labels to reality as they see it.
It is possible, therefore, that traditional Chinese medical theory does not "ignore the facts" known to allopathy—it just looks at them from a different point of view. That point of view may have its own shortcomings, and we shall examine those in a moment. It may, however, also contain insights into humankind's relationship with nature that people who look at the world through Western eyes are still in the process of discovering.
The Western worldview is confident that disease is caused by exogenous pathogens with strange and exotic Greek and Latin names that can be isolated in laboratories and examined under microscopes. It is ascertained that if any of these exogenous pathogens enter the human body they will cause disease or, at the very least, cause an antipathogenic reaction as the body swings its defense mechanisms into urgent action. The outcome depends as much on the efficiency of the immune system as on the virulence of the external pathogen.
Chinese medicine asserts, on the other hand, that disease is caused by exogenous pathogens (with strange and exotic Chinese names) that twenty-five centuries ago were isolated as functions of nature and have been examined, ever since, in the field of human pathological experience. It is ascertained that if any of these exogenous pathogens enter the body they will cause disease or bring about an antipathogenic reaction. The outcome depends as much on the state of internal health, or balance of all the elements of nature, as on the virulence of the external pathogen.
We do not wish to argue that the traditional Chinese doctors know as much about microbiology and biochemistry as any scientist in the West. They don't. Some of their ideas are worryingly old-fashioned and apparently impervious to change. What is more, a closed system used in a single country cannot hope to compete with the research going on worldwide, including in China, in all fields of allopathic medicine, microbiology, and genetics. Nonetheless, Chinese medicine does appear to consider aspects of biological nature that are still ignored in the West: our interconnectedness with the environment, for example; the importance of eating and living habits, which allopathic physicians often fail to notice; and the healthy management of the qi or vital energy, which we in China recognize as a universal force that circulates both within us and outside our bodies.
Fundamentally, allopathy tends to distinguish the human being from the causes of his or her disease, separate him or her from the environment, isolate the pathogen, and destroy it. Chinese medicine on the other hand considers causes of illness to arise from the interplay between the forces within the living human body and those in the environment. It does not isolate and destroy; instead, it purifies and strengthens.
The fact, therefore, that the West has been and continues to be in the midst of a dynamic process of discovery does not mean that we must throw out all that came before. As universal human beings we can maintain our skepticism, and our faith in the discoveries of Western medical science, while still benefiting from the ancient wisdom of traditional Chinese remedies.
Theories and strange names aside, traditional Chinese remedies can be seen to work. Ample evidence exists that they do. During the Tang dynasty (A.D. 618–907) an itinerant Chinese doctor named Sun Si Miao recommended the consumption of animal livers to cure night blindness. His assumption, tested by clinical practice, was that because the eyes and the liver are both of the Mu (Wood) Element function, a disease of the eyes could be corrected by strengthening the liver. He also believed, in common with Chinese tradition, that by consuming animal liver the patient's own liver would be nourished and strengthened.
It may be only a coincidence that Sun Si Miao's remedy worked, but work it did. We know today that night blindness is caused by a lack of vitamin A, and liver is a rich source of this vitamin. The consumption of liver will thus cure night blindness for reasons totally unknown during Sun Si Miao's lifetime, or indeed for many centuries after that.
Coincidence may have lain behind Sun Si Miao's remedies for goiter—caused by lack of iodine—which consisted of kelp, seaweed, and the thyroid glands of both lamb and pork, all of which are extremely rich in iodine. Similarly, his cure for beriberi—vitamin B1 deficiency—consisting of taking vitamin B1-rich rice bran and apricot seeds with milk, may have been quite fortuitous. On the other hand, the belief that food and drinks that induce perspiration can cure a cold, or that the consumption of energy-rich sugar and honey promote the reconstruction of the liver after a bout of infectious hepatitis, are both clinically and theoretically sound.
Consider, too, some of the discoveries of Chinese medicine:
• In the last century or two the people of the West have learned about the importance of hygiene and the value of disinfectants. In China we have known about them for two thousand years. The disinfectant properties of garlic, for example, have been recognized since the Han dynasty (206 B.C.–A.D. 220). Furthermore, Chinese people have throughout their entire history been aware of the dangers inherent in dirt, and have always been fastidious about cleanliness.
• In 1928 Alexander Fleming made what has been heralded as the greatest discovery of twentieth-century medical science: a mold, which he called penicillin, is an effective antibiotic, able to destroy many bacterial diseases. In China we have used molds and fungi against infections for at least 1340 years.
• In nineteenth-century Europe it was discovered that a live virus low in virulence, when injected into a healthy person, will produce immunity in that person against the disease; the first vaccine to come into general use was that against smallpox. Chinese people have been vaccinating against smallpox since the Northern Song dynasty (960–1127), and perhaps even earlier. The earliest technique was to grind some dried scabs taken from a smallpox patient and blow the powder into the nostril of the healthy person to be inoculated. Later, the technique was perfected; the juice of infected pus was transferred instead.
• The first recorded case of the use of an amalgam of mercury for stopping and filling dental cavities was by Regnart, in Europe, in 1818. In China, silver paste was listed as a treatment for filling cavities in a materia medica of A.D. 659. A Ming dynasty materia medica from approximately A.D. 1500 actually specifies the ingredients used in Europe more than three hundred years later: One hundred parts of mercury to forty parts of silver and nine hundred parts of tin to form a paste that solidifies in the cavity.
There may be other examples that are still awaiting discovery by Western medical science.
Whether coincidental or not, forty-five hundred years of systematically recorded clinical practice have given the Chinese people one of the richest traditions of valid health directives and remedies of any country in the world. It is common sense to pay attention to it.
_Chapter 3_
EATING FOR HEALTH
The Chinese concept of a balanced diet is different from Western concepts. It makes no mention of proteins, calories, vitamins, enzymes, and minerals. Instead, in China we refer to the flavors of foods, as well as to their qualities—the Yin/Yang and Five Element characteristics, and the food's nature as hot, warm, cool, or cold. Although the foundational tenets are different, in the end a balanced diet in both cultures amounts to the same thing: a varied regimen that ensures the consumption of moderate quantities of all available nutrients. The major difference in the two approaches is that the Chinese balanced diet takes into account not only the qualities of food but also those of the person eating it. The climate and the time of year are considered as well.
As a consequence of this wider approach one cannot make a straightforward assertion about whether any one food—mutton or coffee or spinach, for example—is good or bad for you. The value of any particular food is relative to your individual characteristics and the climatic conditions. If it is winter and you have a cold, Yin constitution, mutton and coffee are good for you. They have Yang and warming effects that counteract your personal nature and the climatic conditions. Spinach, on the other hand, is cool and may not be the ideal food for you in winter.
Before getting involved in more specifics regarding individual conditions and needs, let us look at some of the general do's and don'ts of Chinese preventive diet in regard to what and how, as well as when to eat.
It is probably worth recalling the "five forbiddens" listed in chapter 2. These are:
1. Refrain from monotony. Do not eat only what appeals to your palate. Vary your diet at every meal.
2. Avoid excesses. Eat spicy, sour, fried, salty, and sweet food sparingly.
3. Never eat large amounts at a single sitting. You should rise from the dinner table feeling only two-thirds full. Overeating leads to stress on the digestive system, inefficient absorption of nutrients, weak qi, and disease. Three light meals a day is the ideal. However, if you are very physically active and require more calories, several snacks through the day is better than one or two large meals.
4. Beware of exotic foods such as snake meat, scorpion, insects, bear paws, snails, and the like. These foods have their functions for some specific ailments but should not be eaten just for the sake of taste.
5. Do not overindulge in beverages instead of solid food. If you can do so comfortably, you should not drink at all during meals. The intake of liquids dilutes gastric juices and impairs digestion. Take your liquids before or after mealtimes.
Other rules are not even mentioned because they are simply common sense daily practices. These might be called the five obvious forbiddens. They are:
1. Do not eat too little for your body weight and energy expenditure.
2. Do not take toxic, contaminated, stale, rotting, or cold food or drinks.
3. Do not fry your food. If you must use oil, stir-fry briefly in a wok, or add a little raw oil to steamed or boiled food or to your salads.
4. Do not overcook your food. Overcooking destroys its heat-sensitive nutrients (enzymes and some vitamins).
5. Do not overindulge in alcoholic drinks. One beer, one glass of wine, or a single shot of spirits a day appears to have a positive effect on health. Anything more than this is poison.
Following the guidelines regarding what (and how) not to eat will in and of itself lead to better overall health. The customary Chinese way of eating is to serve small portions of many different foods. A traditional Western meal consisting of soup, steak, fried potatoes, and a dessert would be considered by the Chinese to be not only unhealthy but uncouth as well. First of all, there is not enough variety in the menu. Second, we believe that soup should come at the end of the meal (instead of a sweet dessert) in order to wash away strong flavors. Third, most Chinese don't relish the idea of eating a slab of meat. We feel it cannot be cooked properly: either the outside is burned in order to cook the center, or else the inside is eaten raw—which for most Chinese people is too horrific even to contemplate. The only way we cook meat in China is to cut it into pieces. The origin of this practice was to save cooking fuel; however, it also ensures uniformity of cooking, as well as the possibility of sharing with others. Which brings us to our final point: eating individual portions is considered downright antisocial. And eating alone is abhorrent to most Chinese people: it is something that you do in a hurry, consuming perhaps your leftovers from a "real meal." In China, people like to eat together; they like the hot and noisy atmosphere. And the more people there are, the more dishes and the more variety. The point, therefore, is to eat a little of a dozen or so food items at each sitting. A Chinese meal usually starts with a variety of cold dishes: boiled peanuts, ginger, raw tomato, cured jellyfish, bamboo tofu, germinated soybean shoots, and various cuts of cold meat. This is followed by alternating flavors and properties (warm, hot, cool, and cold) in the main dishes. Thus a dish of chicken (sweet [Earth] and warm) cooked with walnuts may be followed by spicy tofu (sweet [Earth] and cool) with hot and pungent [Metal] red pepper, by lettuce leaf in oyster sauce (cool and bittersweet [Fire and Earth]), and by shrimp with garlic (warm and sweet [Earth], balanced by the pungent (Metal) garlic—which, incidentally, also counteracts the cholesterol intake from the shrimp). The meal might proceed with green stringbeans, celery, and black mushrooms (all of which are sweet [Earth] and thermally neutral, with a dash of bitter [Fire] from the celery). If you had crab (cold and salty [Water]), you would eat it cooked with dry ginger (hot and pungent [Metal]) and vinegar (sour and bitter [Wood and Fire]) for balance. Finally, you would have either a bowl of rice or some steamed bread and a clear broth to wash it all down with.
In China, everything is eaten: vegetables, fruits, seeds, roots, berries, fish, fowl, and all manner of four-legged creatures. A few purists argue that eating meat is harmful because it contaminates your vital energy with the grosser (that is, lesser refined) qi of animals; they, and Buddhist monks, are probably the only people in China who do not eat moderate quantities of meat fairly frequently. Yet meat is not the kind of health hazard in China that it is in the West. It is still seen as too much of a luxury to be overindulged in, and even those people who can afford it are aware of the dangers.
Food should be consumed as soon after harvesting as possible, as some vitamins are dissipated in time. People in China make a point of shopping every day. Many families do not have refrigerators or freezers, and those who do possess a refrigerator do not keep food in it for more than a day. Indeed, the purpose of a refrigerator often has more to do with showing off one's new status symbol—or, for the more practically minded, for cooling drinks in summer—than with food preservation. Freezing destroys vitamin C, and canned food often consists of pure bulk, with no enzymes or vitamins. Canned food can also be contaminated by megadoses of preservatives and other toxins. For these reasons it is best to eat all foods as fresh as possible.
HOW TO EAT
Moderation is the key not only to what you eat but to how you eat. The following guidelines should help you stay conservative in your intake.
* Eat only when you are hungry.
* Three meals a day are supposed to be most conducive to good health. Start with a large breakfast, follow it with a medium-sized lunch, and end the day with a light dinner at least three hours before bedtime. In China the evening meal is rarely taken much later than 7 P.M.
* Never eat when you are angry, upset, or in a state of emotional turmoil. Extreme emotions, considered to be one of the causes of disease, interfere with digestion.
* Eat slowly. Chopsticks elegantly used ensure that your food cannot be eaten too rapidly—by "elegantly used" we mean picking up each morsel and carrying it from your bowl to your lips.
* Chew your food properly and relish your drinks. Or, as the Chinese saying goes, "Drink your food and chew your drinks."
* Eat your food at room temperature if raw, or warm if cooked. Never eat food directly out of a refrigerator or piping hot. Extremes in heat and cold are a shock to the body.
* Do not talk when you eat. While people in China like to eat in large groups, they generally save their conversations for the time between courses.
* Eat in a warm and comfortable environment. Do not eat outdoors with your face into the wind; cold air is said to enter your body every time you open your mouth, causing stomachache.
* Avoid being sedentary immediately following a meal. A popular Chinese saying claims that "one hundred steps after meals assures ninety-nine years of life."
WHEN TO EAT VARIOUS FOODS
Other than the actual foodstuffs, climate and time of year are perhaps the most important considerations for someone intent upon maintaining good health through conscientious eating habits.
According to traditional Taoist medical theory, one of the main causes of disease are the exogenous pathogens: the climatic aberrations of evil wind, excessive cold, heat, dampness, dryness, and firelike heat. These pathogens are believed to enter the body and cause havoc with one's equilibrium. The flow of zheng qi is affected, the internal organs are weakened, the individual's personal constitution is thrown out of skew, and illness is the likely outcome.
Because of the interdependence of all nature, the cold and heat that can attack a person from the outside also exist within each one of us as part of our individual constitution—we may be hot, cold, dry, damp, excessive, or deficient physical types. They also exert their influence as warming, heating, cooling, and cold characteristics of everything we eat.
It follows therefore that, when in the depth of a cruel northern Chinese winter a person curls up on a warm _kang_ and considers what to have for dinner, he does not think of salads, seafood, and watermelon, all of which are cold foods. Hot ginger soup, warm chicken, chestnuts, and a dried peach are more likely choices. While this may sound like common sense, because anything and everything is available year-round in Western supermarkets people often make what, in Chinese eyes, would be considered very poor food choices given personal temperament and time of year.
It is important for one's health to eat according to season. Foods that are either slightly warming or cooling and those that are thermally neutral can be consumed without ill consequence during any season. Foods that exert powerful heating or cooling effects should not be consumed in the "wrong" season lest they exacerbate the influence of the pervading climate. However, taking cold food in summer will ensure greater resistance to summer heat. Hot foods in winter, on the other hand, protect against the cold.
Often, distinguishing between hot and cold foods is a matter of intuition or common sense. Nobody would consider black or white pepper cooling, nor would most people regard watermelon as warming. Often, however, we might be in doubt as to the thermal effects of bananas, crabs, or clams (all cold foods), or soybean oil (a hot food). We have therefore drawn up a list of cooling, cold, warming, and hot foods to help guide you in developing your awareness and making proper food choices. It is useful to remember that hot and warm thermal characteristics always correspond to Yang, and that cold and cool foods are always Yin.
**Yin Foods**
**Cooling:** apples, barley, tofu, mushrooms, cucumber, eggplant, zucchini, lettuce, lamb's liver, loquat, mandarin orange, mango, marjoram, mung bean, oyster shell, pear, peppermint, radish, sesame oil, spinach, strawberries, tangerine, wheat (and bran), fresh nonmatured coconut, yogurt, tea, jujube, rosehips.
**Cold:** bananas, grapefruit, melon, watermelon, persimmon, sugar cane, tomato, water chestnut, bamboo shoots, bitter gourd, lotus seed, egg white, clam, crab, kelp, seaweed, salt.
**Yang Foods**
**Warming:** apricot seed, asparagus, brown sugar, butter, caraway, fish, cherry, chestnut, chicken, chive, cinnamon twig, clove, mature coconut, coffee, coriander, cuttlefish, dates, orange, tangerine, grapefruit or mandarin peel, eel, fennel, garlic, fresh ginger, ginseng, green onion (scallion), guava, ham, kidney, liver, kumquat, mustard, leek, longan, lychee, malt, meat, milk, mussels, nutmeg, peaches, raspberries, rosemary, shrimp, spearmint, pumpkin, anise seed, sunflower seed, basil, rice, broad beans, vinegar, walnuts, wine, alcohol.
**Hot:** cinnamon bark, dried ginger, black or white pepper, red or green pepper, soybean oil, pork and greasy meats, cream, cocoa, chocolate, butter.
PERSONAL CONSTITUTION
Every individual has his or her personal characteristics in terms of body build, Yin and Yang, hot and cold, damp and dry, and excessive or deficient constitution. The relations and imbalances between these factors are wholly individual in nature. It therefore becomes important, when balancing your diet, to be aware of your personal characteristics so that abundant qualities are balanced and deficient qualities are enhanced.
A thin person of reddish complexion who prefers cold drinks and food to hot is generally considered to be a preponderantly hot (Yang) physical type. A plump person who is seldom thirsty and prefers hot drinks to cold is said to be of the cold, Yin type. Heavily built, lethargic people are damp (Yin) in character. Wiry individuals who are forever thirsty and suffer from dry skin, hair, nose, and mouth are considered dry (Yang).
The descriptives used to classify a person as hot or cold, damp or dry, deficient or excessive are similar to the classifications of the wai yin (external pathogenic) disease syndromes discussed in chapter 2. The same words are also used to describe the nature of various foods. Good health is seen as the balanced interplay between these properties in the environment, in the human body, and in food and drink. For example, the tall, thin person of ruddy complexion—the Yang, hot and dry characteristics mentioned above—will achieve optimum health by balancing his or her natural tendencies with Yin cold and lubricating foods, such as banana, grapefruit, orange, mango, pear, persimmon, strawberry, watermelon, lettuce, celery, tomato, seaweed, milk, honey, egg, and seafood (except shrimp). If, on the other hand, this person should eat large quantities of meat, scaly fish, or strong Yang foods that are spicy, hot, or salty, he would begin to suffer from lack of energy, indigestion, and eventually from imbalances that lead to illness.
The damp, heavily built person would do well to consume plenty of warm Yang foods: apricot, cherry, lemon, lychee, longan, papaya, raspberry, peach, chestnut, garlic, ginger, fennel, green onion (scallion), radish, peanut, potato, grains (brown rice and bread), beans, shrimp, and a little wine. Large quantities of dairy products, fats, and meat would increase the lethargy and convert into body fats.
Finding your personal body type is a multifaceted exploration. There are several factors to consider beyond build. These include your body heat, your moods and dispositions, your sex drive, and others. No person is exclusively one physical type. Furthermore, energy levels, moods, and the climate change all the time, affecting your physical condition. It would be ideal to consult a Chinese physician for a professional opinion regarding your overall Yin or Yang nature and whether your bodily constitution is essentially hot, cold, dry, humid, excessive, or deficient. However, self-observation aided by the following questionnaire should allow you to make a fairly precise assessment of your underlying physical characteristics.
PERSONAL CHARACTERISTICS QUESTIONNAIRE
Give yourself one point for each question you answer in the affirmative, two points if you feel that the question suits you particularly well.
YIN
If you are a woman, give yourself two Yin points.
Do you consider yourself feminine?
Are you timorous?
Are you the indoor type?
Do you tire easily?
Do you consider yourself lazy?
Do you fall asleep easily when traveling by plane, train, or bus?
Are your hands often cold?
Are your feet often cold?
Do you prefer the cold of winter to the heat of summer?
Are you overweight? (If you answer yes, score one point for every ten pounds over the normal weight for your sex and build.)
Is food better than or just as interesting as sex?
Do you consider your sex drive to be weaker than normal? (Give yourself two points if you answer in the affirmative.)
**Cold constitution**
Do you rarely feel thirsty?
Do you generally prefer hot drinks to cold ones?
Is your complexion usually pale?
Is your urine normally plentiful and clear?
Are your stools normally soft?
Is your tongue usually pink with no coating?
Do you suffer from muscular or joint pains in cold weather?
**Damp constitution**
Do you often feel tired?
Are you overweight?
Is your complexion usually dull?
Are you often sad or depressed?
Do your palms sweat?
Is your tongue usually glossy or greasy?
Do your joints ache when it's raining?
**Deficient constitution**
Are you often low-spirited?
Are you often tired?
Are you skinny or underweight?
Do you sweat a lot?
Do you sometimes suffer from heart palpitations?
Are you of pale or pallid complexion?
Is your tongue white or light pink without coating?
YANG
If you are a man, give yourself two Yang points.
Do you consider yourself masculine?
Are you generally self-confident?
Are you the outdoor type?
Can you work for long stints without tiring?
Do you consider yourself energetic?
Do you find it difficult to sleep when traveling by plane, train, or bus?
Are your hands often hot?
Do your feet sweat?
Do you prefer the heat of summer to the cold of winter?
Are you underweight? (If your answer is yes, score one point for every ten pounds below the normal weight for your sex and build.)
Is sex better than food?
Do you consider your sex drive to be higher than normal? (Give yourself two points if you answer in the affirmative.)
**Hot constitution**
Do you normally prefer cold drinks to warm or hot ones?
Is your complexion generally reddish?
Is your urine usually scanty and of a reddish or yellow hue?
Are you often constipated?
Are your stools usually dry?
Is your tongue normally red with a yellowish coating or no coating?
Do you suffer from frequent skin eruptions?
**Dry constitution**
Are you often thirsty?
Are your nose, throat, and skin usually dry?
When you catch cold, is your cough usually dry without mucus?
Do your eyes and nose often itch?
Is your tongue frequently parched and dry?
Is it difficult for you to gain weight?
Are you often constipated?
**Excessive constitution**
Are you usually full of energy?
Do you consider yourself to be normally high-spirited?
Is the tone of your voice high-pitched?
Is your complexion usually flushed?
Is your blood pressure higher than normal?
Are you restless and impatient?
Do you suffer from constipation?
When you have completed the questionnaire, first add only your scores under the two main headings Yin and Yang; do not include your cold, damp, deficient, hot, dry, and excessive constitution scores in your first tally. The first total will tell you your predominant Yin/Yang characteristic. Few people are ever wholly Yin or Yang, so even if you are an energetic, self-confident male who enjoys sex and the outdoor life, it does not mean that you will have a score of 0 in the Yin section.
Now add up your bodily constitution scores. Once you have these tallied, add the cold, damp, and deficient numbers to your Yin scores; then add the hot, dry, and excessive numbers to your Yang scores. In the end, most people will find themselves scoring more or less equally on both Yin and Yang.
The point of this exercise is simply to be aware of your general tendencies. You will then be in a position to correct any imbalances in your constitution before they begin to affect your health. However, before you go about making drastic changes to your eating habits, you must first bring the Yin or Yang effects of climate into your calculations. If you have a 24 Yin score and a 17 Yang, for example, you might be tempted to include ginger, garlic, or onion in your diet for their warming effects. If it's the middle of summer, however, eating warming foods such as these would be a mistake—summer heat on its own counteracts any Yin or cold tendencies in your body. To further increase the heat with ginger and garlic would overbalance you in the opposite, Yang, direction.
In order to bring climatic effects into your personal Yin and Yang scores, add points according to the season, as shown in the following table.
If, in the final analysis, you find that your Yin and Yang or your body constitution scores are significantly different, all it means is that you should try to include a little more balancing food in your diet in proportion to the differences. Increase your intake of Yin or Yang, warm or cool foods by 10 percent for every five-point spread on the overall Yin/Yang scores. Try also to include more hot and warming foods in your diet if the questionnaire indicates you are of cold, damp, or deficient constitution, or if it is winter; conversely, eat a little more cold or cooling food if you are the hot, dry, or excessive physical type, or if it is summer.
It should be clear by now that Chinese theories of health offer few simple do's and don'ts regarding diet. Health-giving food choices depend on personal constitution, the time of year, and the nature of disease a person might be suffering from. Only when you have a clear picture of your personal health needs can you choose your diet with confidence, noting the warming or cooling properties of foods, their taste and Element, and whether they lubricate or constrict. To help you in growing more discerning, the following chapter, Foods and Their Healing Properties, details the properties (in Chinese terms), vitamin and mineral contents, and usage of many foods commonly employed in Chinese therapeutic cuisine.
_Chapter 4_
FOODS AND THEIR HEALING PROPERTIES
Traditionally, no clear-cut distinction is made between medicinal drugs, folk and home remedies, and many of the ingredients of classic Chinese cuisine. Garlic, cloves, and ginger, for example, are used in medicine, in folk remedies, and for cooking. Nevertheless, since antiquity medicinal drugs and ingredients have been classified into one of three possible categories of toxicity.
The first of the three categories is that of so-called high-grade drugs. These are wholesome beyond their purely medicinal function and can therefore be taken continuously over a period of time with no ill effects. Food therapies fit into this category. The second class is that of medium-grade drugs. These are slightly toxic but serve to relieve some deficiency syndromes. The third category is that of toxic, or low-grade, drugs. These may be taken in small doses for short periods of time, and only to relieve a specific disorder. Toxic herbs and mushrooms and some minerals fall into this class. Modern allopathic drugs, if used by a traditional Chinese medic combining modern and ancient therapies, would also fit into this third category.
Foods and drugs may be further defined for therapeutic purposes according to their Yin and Yang preponderances; their flavors, and thus their Five Element affinities; and their warm, hot, cool, and cold characteristics.
Yin and Yang are, in the Taoist view of the world, the most obvious attributes of nature. As such they are the first aspects of a patient's condition to attract a doctor's attention. The restoration of their equilibrium is the goal to which all therapy aims. As a consequence, foods and drugs that are considered to be of a Yin nature will be prescribed in disorders involving Yin deficiencies or Yang pathogens. Yang therapies serve to treat Yang deficiencies or Yin disorders.
Yin foods and remedies are those with moist, cool, or cold properties, for these are Yin characteristics. Yang foods, on the other hand, have a warming or heating effect on the body. Yang remedies tend to exert most influence on the skin, tissues, and external parts of the body, while Yin remedies work on the internal organs. Yang foods and drugs ascend and disperse; those that are Yin in nature descend with an astringent effect. Yang foods and drugs are pungent, sweet, or tasteless. Yin remedies are sour, bitter, and salty.
Table 1 on page 11 shows the correspondence between the Five Elements in nature and various attributes of human physiology. One of those attributes is flavor. Each of the Elements/functions of nature is said to reside in one of the five flavors. Thus sour food, being of the Wood (germinating) element, influences the health of the liver, which is also Wood. Bitterness corresponds to Fire and affects the heart; sweetness to Earth and spleen. Pungent foods, those of the Metal element, affect the lungs; salty foods correspond to Water and influence the health of the kidneys. It is believed that by taking foods with a specific flavor/Element, the corresponding organ of the body is strengthened. Furthermore, each of the five flavors is said to exert its own therapeutic effect on the body as a whole. We shall therefore refer to the flavor, the Element, and the effect of the foods examined later in this chapter.
As a matter of interest, the effects of sour foods and drugs are said to be astringent; they counteract digestive problems and diarrhea. Bitter ingredients are febrifuges; in other words, they dispel fevers. Sweet foods act as a tonic to the body. Pungent, or tangy, ingredients act as diaphoretics; they induce sweat, reduce intestinal and stomach gas, and are said to promote the movement of qi within the body. Salty ingredients are palliatives, which means they reduce excesses and imbalances of the Five Elements as well as the effects of pathogens. Tasteless foods are considered to be diuretics.
Finally, a word about the so-called warming and cooling characteristics of foods and drugs. Illness, according to Chinese theory, is frequently brought about by the effects of the six evil climatic factors, the xie qi: evil wind, cold, damp heat, humidity, intense dryness, and firelike heat. If, as according to this theory, cold enters the body and causes disease, it is simply common sense to counteract it with warm or hot ingredients. Similarly, cool or cold foods and drugs are used to disperse hot climatic pathogens. The terms _warm, hot, cool, cold,_ and _neutral_ may, however, be confusing. They do not refer to the actual physical temperature of the remedy being taken, but instead denote a fundamental property of the food or ingredient after it has been swallowed and digested. A steaming cup of tea, for example, may exert an immediate warming effect on the body, but tea is fundamentally a "cold" herb, useful for cooling the body (and, incidentally, for burning fats and promoting digestion).
Having mentioned these classifications, it should be noted that few foods or ingredients ever fit a single and precise category—Yin always contains some Yang and vice versa. Herbs, fruits, and vegetables usually combine several distinct flavors. Tea _(Camellia sinensis),_ in both its black and green varieties, is sweet, bitter, and pungent at the same time. Peaches are both sweet and sour. Asparagus is bitter and slightly pungent. A single food item, therefore, may potentially have several therapeutic effects.
A final word about how ingredients can and cannot be used is perhaps called for before continuing on to examine the foods and components of Chinese remedies themselves.
Sometimes a single product, such as ginseng, can be used alone to treat an illness. On other occasions ingredients are combined in order to exert a fuller curative effect on the patient—food recipes are a case in point. These combinations are not always straightforward, however. Sometimes two ingredients mutually reinforce each other; on other occasions a subsidiary ingredient will assist the function of the other, principal component. There are situations also when one Element is necessary to restrain the toxic effect of another. Finally, some ingredients are so incompatible as to give rise to severe side effects if used together.
As an illustration of this last point of incompatibility, ingredients with warm properties acting on the lungs should never be taken with raw and cold (temperaturewise) food. Cooling ingredients should not be taken with greasy foods. Meat should be eaten sparingly when taking black plum for therapeutic reasons. Turnips, radishes, and rape should not be eaten when one takes tonics; neither should black or green tea. Both are said to weaken the strengthening power of the tonic.
Apart from refraining from drinking tea with tonics, there is no need for you to concern yourself about any of the above combinations and contraindications. All the remedies described in this book have been chosen for their simplicity and straightforward wholesomeness. Unless one happens to be allergic to any of the ingredients, none of the recipes will exert the least adverse effect. As to the means and methods of preparation of various prescriptions used in popular Chinese remedies, we refer you to chapters 5 and 6.
Let us now look at the characteristics of the individual foods and herbs used in the Chinese home remedies described in this book. For the purpose of self-diagnosis and gentle experimentation with individual foods, we have given the characteristics of each ingredient in Chinese terms—sweet/sour and corresponding Element, hot/cold, Yin/Yang—as well as in Western terms—protein, fat, carbohydrate, mineral, and vitamin contents per 100 grams (3½ ounces) of edible portion. A mineral or vitamin that is completely absent will be denoted by a zero; a minus sign denotes that the information for that particular nutrient is unavailable. (See appendix 1 for information on daily requirements of those vitamins and minerals for the healthy adult.) In addition to this information, we discuss the predominant healing effects of that food. Most of the foods discussed in this chapter are commonly available in the market; a few will be found in specialty food stores or by mail order. Sources for mail order are given in appendix 2.
FRUITS
Fruits are some of the most nutritious foods available to us. They are rich in vitamins, minerals, enzymes, and fiber.
According to Chinese theory, fruit lubricates, cools, and strengthens the body. It is easily digested and cleanses the intestines. Most fruit is sweet, and therefore tonifies the Earth element.
It is preferable to consume fruit directly from the producer before various intermediaries have sprayed, artificially ripened, waxed, or otherwise adulterated it. Indeed, in China this is the norm. Most of the fruit that is consumed in China is produced locally, ripened on the tree or vine and eaten only in season.
Many fruits have a cooling, or even a cold, effect on the body. Banana, grapefruit, muskmelon, persimmon, and watermelon are all cold fruits. As such they are extremely refreshing during summer, but their consumption in winter could lead to cold-syndrome diseases. The traditional Chinese calendar even specifies a day in the second week of August, for eating one's last watermelon of the year.
It is best to eat organically grown fruit whenever possible. Most people are aware of the harmful effects of insecticides, and make a point of peeling fruit. However, peeling apricots, plums, strawberries, or grapes is not easy; furthermore, although chemicals are only sprayed on the outside of the fruit, they eventually seep through the entire plant. Organically grown produce of all kinds is becoming widely available. Look for it in natural foods markets.
Apple
_Sweet and sour (Earth and Wood)_ _,_ _cool, medium Yi_ _n_
Apple aids digestion, lubricates the lungs, and generally detoxifies. It cures indigestion, morning sickness, and chronic enteritis, and combats diabetes by helping to lower blood-sugar levels. Its plentiful fiber helps to lower cholesterol, and its potassium content has a diuretic effect that reduces sodium and stabilizes blood pressure. Many of the nutrients reside in the skin of the apple; it is thus advisable to eat apples unpeeled—given, of course, that they have not been treated chemically.
Protein, 0.2 g; Fat, 0.3 g; Fiber, 1.4 g; Carbohydrate, 10.5 g; Vitamin A, 37 IU; Vitamin B1, 0.01 mg; Vitamin B2, 0.01 mg; Niacin, 0.05 mg; Vitamin C, 4 mg; Calcium, 5 mg; Phosphorus, 5 mg; Iron, 0.12 mg
Apricot
_Sour and sweet (Wood and Earth), warm, neutral Yin/Yang_
Apricot lubricates and strengthens the lungs; it alleviates asthma and dryness of the mouth. Apricot seeds are used in a variety of remedies. They are, however, considered a medium-grade drug in China. This means that they are slightly toxic, and should therefore only be taken in small quantities and for short periods of time. Bitter apricot seeds can suppress coughing, and are a valid relief for asthma.
Protein, 1 g; Fat, 0.1 g; Fiber, 0.6 g; Carbohydrate, 12.9 g; Vitamin A, 2790 IU; Vitamin B1, 0.03 mg; Vitamin B2, 0.05 mg; Niacin, 0.8 mg; Vitamin C, 7 mg; Calcium, 16 mg; Phosphorus, 23 mg; Iron, 0.5 mg
Banana
_Sweet (Earth), cold, medium Yin_
Banana has a lubricating effect on the intestines. It detoxifies the body by providing plenty of soluble fiber that absorbs cholesterol and cleanses the intestines. It cures constipation, hemorrhoids, and high blood pressure, and counteracts indigestion and alcoholism. Eat two soft bananas every morning to relieve constipation. Two ripe (but not soft) bananas stop diarrhea. The banana's high fiber content helps to lower blood cholesterol. A banana a day cures chronic indigestion. Eat cooked green bananas if you suffer from diabetes—the starch has not yet been converted into sugar.
Protein, 1.2 g; Fat, 0.6 g; Fiber, 1.6 g; Carbohydrate, 26.7 g; Vitamin A, 92 IU; Vitamin B1, 0.05 mg; Vitamin B2, 0.11 mg; Niacin, 0.6 mg; Vitamin C, 10 mg; Calcium, 7 mg; Phosphorus, 22 mg; Iron, 0.35 mg
Cherry
_Sweet (Earth), warm, Yang_
Cherries tone the qi and the blood, and counteract rheumatic pains and stiffness. They also expel wind and damp.
Protein, 1.1 g; Fat, 0.5 g; Fiber, 0.7 g; Carbohydrate, 14.8 g; Vitamin A, 620 IU; Vitamin B1, 0.05 mg; Vitamin B2, 0.06 mg; Niacin, 0.3 mg; Vitamin C, 8 mg; Calcium, 18 mg; Phosphorus, 20 mg; Iron, 0.4 mg
Fig
_Sweet (Earth), neutral, Yang_
Figs tonify the qi and blood. Because they clear the intestines, figs are a useful remedy for constipation and hemorrhoids. Chinese doctors also prescribe figs for sore throat and stomach and intestinal problems, including dysentery and diarrhea: eat two figs a day, either in the morning or in the evening. For a sore throat, steam them and take with honey.
Protein, 0.8 g; Fat, 0.4 g; Fiber, –; Carbohydrate, 19.2 g; Vitamin A, 140 IU; Vitamin B1, 0.06 mg; Vitamin B2, 0.06 mg; Niacin, 0.4 mg; Vitamin C, 2 mg; Calcium, 32 mg; Phosphorus, 14 mg; Iron, 0.32 mg
Grapes
_Sweet and sour (Earth and Wood), neutral, balance of Yin and Yang_
Grapes are a great builder of red blood cells. They have been used since antiquity to tonify the blood and qi. They are eaten as a general tonic as well as to treat coughs, promote urination, and relieve dryness and thirst.
American Concord grapes: Protein, 1.4 g; Fat, 1.4 g; Fiber, 0.5 g; Carbohydrate, 14.9 g; Vitamin A, 80 IU; Vitamin B1, 0.06 mg; Vitamin B2, 0.04 mg; Niacin, –; Vitamin C, 4 mg; Calcium, 17 mg; Phosphorus, 21 mg; Iron, 0.6 mg
European adherent skin grapes: Protein, 0.8 g; Fat, 0.4 g; Fiber, 0.5 g; Carbohydrate, 16.7 g; Vitamin A, 80 IU; Vitamin B1, 0.06 mg; Vitamin B2, 0.04 mg; Niacin, –; Vitamin C, 4 mg; Calcium, 17 mg; Phosphorus, 21 mg; Iron, 0.6 mg
Grapefruit
_Sweet and sour (Earth and Wood), cool, medium Yin_
Grapefruit aids digestion and stimulates the appetite. By virtue of its cooling characteristics, grapefruit can reduce fevers and eliminate toxins. It is especially useful for overcoming intoxication from alcohol.
Protein, 0.5 g; Fat, 0.2 g; Fiber, 0.3 g; Carbohydrate, 10.1 g; Vitamin A, 12 IU; Vitamin B1, 0.04 mg; Vitamin B2, 0.02 mg; Niacin, –; Vitamin C, 40 mg; Calcium, 22 mg; Phosphorus, 18 mg; Iron, 0.7 mg
Guava
_Sweet and sour (Earth and Wood), warm, Yang_
Guava is regarded as having obstructive and constrictive effects on the metabolic processes. As a consequence, when taken raw or as a decoction it is a valid remedy for diarrhea and dysentery. Make a decoction to soothe a sore throat.
Protein, 0.6 g; Fat, 0.6 g; Fiber, 5.5 g; Carbohydrate, 17.1 g; Vitamin A, 250 IU; Vitamin B1, 0.07 mg; Vitamin B2, 0.04 mg; Niacin, 1.1 mg; Vitamin C, 302 mg; Calcium, 18 mg; Phosphorus, 29 mg; Iron, 0.7 mg
Jujube (Chinese date)
_Sweet (Earth), warm, Yang_
Jujube are one of our five most prized remedies in China; they have been grown as a medicinal fruit tree for at least four thousand years. The principal effect of jujube is to nourish the qi and blood, and strengthen the stomach and the body as a whole. Jujube are considered to maintain youthfulness. One traditional story tells of a woman who lived two thousand years ago who ate nothing but jujube. It is said that when she married, at the age of fifty, her appearance was that of a twenty-year-old virgin. To this day many women in China make a point of eating ten to twenty jujube every morning for the complexion.
As a tonic, jujube are usually prepared in decoctions or stews. One remedy for convalescents is to decoct 10 jujube with 10 grams of ginseng every morning. Another, for pregnancy and for a rapid recovery after childbirth, consists of 20 jujube, 2 tablespoons of brown sugar, and 1 egg stewed and eaten once a day.
Recent research in China has demonstrated that jujube has an antibiotic effect that increases the body's resistance to infection and disease.
Fresh: Protein, 1.2 g; Fat, 0.2 g; Fiber, –; Carbohydrate, 20.2 g; Vitamin A, 40 IU; Vitamin B1, 0.02 mg; Vitamin B2, 0.04 mg; Niacin, 0.9 mg; Vitamin C, 69 mg; Calcium, 21 mg; Phosphorus, 23 mg; Iron, 0.48 mg
Dried: Protein, 3.7 g; Fat,1.1 g; Fiber, –; Carbohydrate, 73.6 g; Vitamin A, 95 IU; Vitamin B1, 0.21 mg; Vitamin B2, 0.36 mg; Niacin, 0.5 mg; Vitamin C, 13 mg; Calcium, 79 mg; Phosphorus, 100 mg; Iron, 1.8 mg
Lemon
_Sour (Wood), neutral, Yang_
Lemon is not common in China and is therefore not used extensively as a treatment. It is known to relieve nausea and dryness. Steamed lemon with sugar relieves coughing and catarrh. As a mouthwash, lemon juice helps guard against gum disease and will alleviate a sore throat. Lemon should _not_ be taken by people suffering from acidity and ulcers.
Protein, 0.9 g; Fat, 0.2 g; Fiber, 0.9 g; Carbohydrate, 8.7 g; Vitamin A, 0 IU; Vitamin B1, 0.04 mg; Vitamin B2, 0.01 mg; Niacin, 0.6 mg; Vitamin C, 27 mg; Calcium, 40 mg; Phosphorus, 22 mg; Iron, 0.6 mg
Longan
_Sweet (Earth), warm, Yang_
Longan is a fruit that grows only in tropical climates. It is delicious fresh but may also be taken dried for medicinal purposes. It energizes qi; nourishes the blood, heart, and spleen; and expels cold. It is often prescribed for general debility, insomnia, and nervous disorders.
Protein, 1.0 g; Fat, 0.6 g; Fiber, 1.4 g; Carbohydrate, 15 g; Vitamin A, 200 IU; Vitamin B1, 0.03 mg; Vitamin B2, 0.07 mg; Niacin, –; Vitamin C, 24 mg; Calcium, 35 mg; Phosphorus, 19 mg; Iron, 1.2 mg
Lychee
_Sweet (Earth), warm, balance o_ _f_ _Yin and Yan_ _g_
Lychee nourishes the qi and the blood and expels cold. It is sometimes used as an analgesic for toothache, and is often taken to halt a stubborn hiccup. Lychee alleviates stomachache and thirst. Steamed lychees are recommended as a cure for asthma.
Protein, 0.8 g; Fat, 0.4 g; Fiber, –; Carbohydrate, 16.5 g; Vitamin A, 0 IU; Vitamin B1, 0.01 mg; Vitamin B2, 0.07 mg; Niacin, 0.6 mg; Vitamin C, 72 mg; Calcium, 5 mg; Phosphorus, 31 mg; Iron, 0.31 mg
Mango
_Sweet and sour (Earth and Wood), cool, balance of Yin and Yang_
Mango nourishes qi, the blood, and the functions of the stomach. Its cooling effect dissipates hot-syndrome diseases. Mango is used to relieve nausea and vomiting, coughing, and weakness in the lungs and bronchi.
Protein, 0.55 g; Fat, 0.3 g; Fiber, 1.1 g; Carbohydrate, 17.6 g; Vitamin A, 4030 IU; Vitamin B1, 0.06 mg; Vitamin B2, 0.06 mg; Niacin, 0.6 mg; Vitamin C, 28 mg; Calcium, 11 mg; Phosphorus, 11 mg; Iron, 0.15 mg
Melon
_Sweet (Earth), cold, Yin_
Melon tones the qi and the blood. Its cold characteristic relieves the heat of summer. It is used as a diuretic.
Protein, 0.5 g; Fat, 0 g; Fiber, 0.4 g; Carbohydrate, 8.5 g; Vitamin A, 40 IU; Vitamin B1, 0.05 mg; Vitamin B2, 0.03 mg; Niacin, –; Vitamin C, 23 mg; Calcium, 17 mg; Phosphorus, 16 mg; Iron, 0.4 mg
Orange peel
_Pungent and slightly bitter (Metal and Fire), warm, Yin_
Orange peel affects the stomach and the internal organs of digestion. A decoction of orange peel and ginger will relieve gastritis. Orange peel brewed in water is a valid remedy for inebriation and a preventive against hangover. Dispersed in water, orange peel will also relieve coughs and chest catarrh.
Protein, 0.6 g; Fat, 0 g; Fiber, –; Carbohydrate, 10 g; Vitamin A, 165 IU; Vitamin B1, 0.06 mg; Vitamin B2, 0.06 mg; Niacin, 0.7 mg; Vitamin C, 53 mg; Calcium, 65 mg; Phosphorus, 7 mg; Iron, 0.33 mg
Papaya
_Sweet (Earth), neutral, mild Yang_
Papaya promotes digestion. It cures stomachache, dysentery, and difficult bowel movements. Because papaya dissipates dampness, it is a useful remedy for diseases of a damp nature, such as rheumatism and arthritis. A teaspoon of papaya seeds helps to detoxify the liver.
Fresh raw papaya is a good supplement to meals, in order to counteract indigestion.
Protein, 0.95 g; Fat, 0.2 g; Fiber, 1.4 g; Carbohydrate, 18.9 g; Vitamin A, 3061 IU; Vitamin B1, 0.04 mg; Vitamin B2, 0.05 mg; Niacin, 0.5 mg; Vitamin C, 94 mg; Calcium, 36 mg; Phosphorus, 8 mg; Iron, 0.15 mg
Peach
_Sweet and sour (Earth and Wood), warm, mild Yang_
Peaches are native to China. In Chinese mythology peaches represent immortality. According to legend, a peach tree that stands in the Kunlun mountains blossoms and bears fruit every nine thousand years. Whoever eats these peaches obtains immortal life.
Ordinary peaches, on the other hand, merely nourish the blood and qi, dissipate cold, and lubricate the intestines. Steamed peaches with a tablespoon of sugar or honey alleviates asthma and a bad cough. Fresh peaches are frequently taken as a remedy against high blood pressure.
Protein, 0.5 g; Fat, 0.1 g; Fiber, 0.6 g; Carbohydrate, 12 g; Vitamin A, 880 IU; Vitamin B1, 0.02 mg; Vitamin B2, 0.05 mg; Niacin, –; Vitamin C, 8 mg; Calcium, 8 mg; Phosphorus, 22 mg; Iron, 0.6 mg
Pear
_Sweet and sour (Earth and Wood), cool, medium Yin_
Pear affects the stomach and lungs. It lubricates, counteracting dryness, and is said to eliminate mucus. Fresh pear juice is drunk in China to relieve stubborn coughs and fever. Chinese pears are generally harder, juicier, and more sour than the American variety.
A curious superstition exists in China concerning pears. The word for pear, _li,_ is pronounced exactly like another word meaning "separation." Many people therefore refuse to share a pear with a loved one for fear of bringing bad luck to their union.
Protein, 0.6 g; Fat, 0.5 g; Fiber, 4 g; Carbohydrate, 11.9 g; Vitamin A, 28 IU; Vitamin B1, 0.06 mg; Vitamin B2, 0.03 mg; Niacin, 0.02 mg; Vitamin C, 7 mg; Calcium, 8 mg; Phosphorus, 15 mg; Iron, 0.5 mg
Persimmon
_Sweet (Earth), cold, medium Yin_
The high tannic acid content of unripe persimmon has an "obstructive" or astringent consequence, making unripe persimmon effective in treating diarrhea, dysentery, and chest mucus.
When persimmon ripens, the tannic acid is converted into fructose. Ripe persimmon lubricates the lungs and nourishes the heart, spleen, and intestines. It relieves stomachache, hemorrhoids, and constipation. Persimmon is also used for regulating high blood pressure, treating canker sores in the mouth, and calming a stubborn cough.
Protein, 0.2 g; Fat, 0.1 g; Fiber, –; Carbohydrate, 8.4 g; Vitamin A, –; Vitamin B1, –; Vitamin B2, –; Niacin, –; Vitamin C, 17 mg; Calcium, 7 mg; Phosphorus, 7 mg; Iron, 0.63 mg
Pineapple
_Sweet and sour (Earth and Wood), neutral, Yang_
Pineapple should always be consumed ripe—underripe pineapple is acidic to the extreme and can cause stomach cramps and damage to the teeth and bones.
Soft, sweet pineapple, on the other hand, promotes digestion. It also promotes urination, quenches thirst, and heals swelling. Sweet pineapple stimulates the appetite and is therefore used to treat anorexia.
Protein, 0.6 g; Fat, 0.7 g; Fiber, 2.4 g; Carbohydrate, 19.2 g; Vitamin A, 35 IU; Vitamin B1, 0.14 mg; Vitamin B2, 0.06 mg; Niacin, 0.07 mg; Vitamin C, 24 mg; Calcium, 11 mg; Phosphorus, 11 mg; Iron, 0.57 mg
Plum
_Sweet and sour (Earth and Wood), neutral, balance of Yin and Yang_
Plum nourishes the blood and qi; it also combats dryness. In China plum is eaten to promote digestion and urination and to nourish weak kidneys or liver. A specific remedy for kidney or liver problems is a tea prepared from two crushed whole plums (including the seed) mixed with hot water and drunk twice a day.
Two plums soaked in vinegar and then boiled in water help cure canker sores, sore throat, and chronic tonsillitis. Use the cooled water for washing the mouth and for gargling.
Protein, 0.7 g; Fat, 0.2 g; Fiber, 0.5 g; Carbohydrate, 12.9 g; Vitamin A, 350 IU; Vitamin B1, 0.06 mg; Vitamin B2, 0.04 mg; Niacin, –; Vitamin C, 5 mg; Calcium, 17 mg; Phosphorus, 20 mg; Iron, 0.5 mg
Strawberry
_Sweet and sour (Earth and Wood), cool, mild Yin_
Strawberries nourish qi and lubricate the lungs. Because they are rich in vitamin C, silicon, and water, they alleviate thirst, generate body fluids, and have an antioxidizing effect on cells, blood vessels, and tissues. They also, as a consequence, flush out toxins and regulate urination and kidney function.
Eaten regularly with sugar, strawberries will cure a stubborn dry cough. As an appetizer, strawberries will stimulate the appetite and ensure good digestion. Strawberries are not native to China and have only been cultivated there recently. For this reason they do not figure prominently in Chinese medicine.
Protein, 0.8 g; Fat, 0.5 g; Fiber, 1.4 g; Carbohydrate, 8.3 g; Vitamin A, 60 IU; Vitamin B1, 0.03 mg; Vitamin B2, 0.07 mg; Niacin, –; Vitamin C, 60 mg; Calcium, 28 mg; Phosphorus, 27 mg; Iron, 0.8 mg
Tangerine
_Sweet and sour (Earth and Wood), cool, mild Yin_
Tangerine dissipates heat and dryness. It is often used for treating nausea, vomiting, hiccups, and catarrh in the chest. It is also useful in the treatment of diabetes.
Protein, 0.8 g; Fat, 0.3 g; Fiber, 1 g; Carbohydrate, 10.9 g; Vitamin A, 420 IU; Vitamin B1, 0.07 mg; Vitamin B2, 0.03 mg; Niacin, –; Vitamin C, 31 mg; Calcium, 33 mg; Phosphorus, 23 mg; Iron, 0.4 mg
Watermelon
_Sweet (Earth), cold, mild Yin_
The watermelon is native to Africa but has been cultivated in Asia for at least four thousand years. Because of its thirst-quenching and refreshing properties, watermelon is one of the most popular fruits in China during the hot summer.
Watermelon is a strong diuretic. It dissipates hot- and dry-syndrome problems, such as headaches, dry mouth and throat, red and dry mucus in the mouth and nose, red and swollen eyes, dry stool, rapid heartbeat, and irritability. It heals canker sores in the mouth and sore throat. Watermelon is useful for treating hangover. The rind and seeds are used to treat hypertension. A decoction using the seeds will also relieve constipation.
Protein, 0.5 g; Fat, 0.2 g; Fiber, 0.6 g; Carbohydrate, 6.9 g; Vitamin A, 590 IU; Vitamin B1, 0.05 mg; Vitamin B2, 0.05 mg; Niacin, –; Vitamin C, 6 mg; Calcium, 7 mg; Phosphorus, 12 mg; Iron, 0.2 mg
VEGETABLES
Vegetables constitute the second tier of the human food pyramid. As such, they are the second most important food source, following grains.
Vegetables contain vitamins, minerals, enzymes, and fiber. Enzymes both nourish and cleanse, while fiber absorbs toxins and cholesterol. Because of these properties, vegetables are particularly effective in detoxifyng the body. Ideally, four or five different vegetables should be eaten each day. Most vegetables should be eaten raw so as not to harm their enzyme and heat-sensitive vitamin contents. However, many vegetables are not easy to digest, and others, like carrots, require some cooking before the body is able to absorb their rich nutrient content. Frozen, canned, dried, or otherwise preserved vegetables lack the nutrient properties of fresh produce. Just as with fruit, vegetables are best consumed in season, and obtained from local organic sources.
Asparagus
_Sweet and bitter (Earth and Fire), cold, mild Yin_
Asparagus tones qi and dissipates heat and damp from the body. Its cold properties counteract fire-syndrome diseases, but render asparagus unsuitable in cold weather and when suffering from cold stomachache, diarrhea, or coughing. In China asparagus is prescribed as a diuretic. It is also useful in the treatment of diabetes and chronic bronchitis.
Protein, 2.2 g; Fat, 0.2 g; Fiber, 0.7 g; Carbohydrate, 3.9 g; Vitamin A, 1000 IU; Vitamin B1, 0.16 mg; Vitamin B2, 0.19 mg; Niacin, –; Vitamin C, 33 mg; Calcium, 21 mg; Phosphorus, 62 mg; Iron, 0.9 mg
Bamboo shoot
_Sweet (Earth), cool, mild Yin_
Bamboo shoot nourishes the blood and qi. Its cooling effect dissipates internal heat.
Bamboo shoot is used extensively in Chinese cuisine. The cooling effects of bamboo shoot balance the warming effects of meat. Its high fiber content is effective in treating constipation and in lowering cholesterol levels in the blood.
Protein, 2.0 g; Fat, 0.2 g; Fiber, 2.0 g; Carbohydrate, 4.0 g; Vitamin A, 15 IU; Vitamin B1, 0.11 mg; Vitamin B2, 0.05 mg; Niacin, 0.5 mg; Vitamin C, 3 mg; Calcium, 10 mg; Phosphorus, 45 mg; Iron, 0.38 mg
Carrot
_Sweet (Earth), neutral, Yang_
Carrot exerts a stimulating effect on digestion and nourishes the spleen. It is famed for improving night vision because of its vitamin A content.
Carrots are used in China for treating whooping cough. They are believed to play an important role in maintaining youthful skin and hair. Carrot juice is a valid remedy for anemia, and crushed raw carrot alleviates burns. However, carrots' nutrients are difficult to absorb when eaten raw. It is often preferable, therefore, to render them more easily digestible through cooking.
Protein, 0.7 g; Fat, 0.1 g; Fiber, 1.1 g; Carbohydrate, 7.3 g; Vitamin A, 20,253 IU; Vitamin B1, 0.07 mg; Vitamin B2, 0.04 mg; Niacin, 0.7 mg; Vitamin C, 7 mg; Calcium, 19 mg; Phosphorus, 32 mg; Iron, 0.36 mg
Celery
_Sweet, pungent, and bitter (Earth_ _,_ _Metal, and Fire), cool, slightly Yi_ _n_
Celery, a cooling food, eliminates dampness and nourishes and soothes the liver. Celery is one of the best food remedies for lowering high blood pressure. It also improves the texture of the hair and skin. Celery is traditionally used to treat whooping cough.
Protein, 0.3 g; Fat, 0.1 g; Fiber, 0.4 g; Carbohydrate, 1.5 g; Vitamin A, 51 IU; Vitamin B1, 0.01 mg; Vitamin B2, 0.01 mg; Niacin, 0.1 mg; Vitamin C, 3 mg; Calcium, 14 mg; Phosphorus, 10 mg; Iron, 0.19 mg
Chinese cabbage
_Sweet (Earth), slightly cold, Yang_
Chinese cabbage is a diuretic. It facilitates digestion and exerts a stimulating effect on the stomach and intestines. Chinese cabbage combats inflamation due to heat and Fire, such as rashes, redness and irritation of the eyes, sore throat, and constipation.
Protein, 0.5 g; Fat, 0.1 g; Fiber, –; Carbohydrate, 0.8 g; Vitamin A, 1050 IU; Vitamin B1, 0.01 mg; Vitamin B2, 0.03 mg; Niacin, 0.2 mg; Vitamin C, 16 mg; Calcium, 37 mg; Phosphorus, 13 mg; Iron, 0.28 mg
Cucumber
_Sweet (Earth), cold, balance o_ _f_ _Yin and Yan_ _g_
Cucumber cleans the blood and detoxifies by promoting urination. It affects the spleen, stomach, and large intestine. The juice of fresh cucumber leaves can be used to heal burns, as can slices of cucumber placed gently against the affected part. Cucumber cools body heat. It is therefore useful for counteracting ailments due to heat in the lungs and stomach, such as acne, skin rashes, and dry, hot coughs.
Protein, 0.3 g; Fat, 0.1 g; Fiber, 0.3 g; Carbohydrate, 1.5 g; Vitamin A, 23 IU; Vitamin B1, 0.02 mg; Vitamin B2, 0.01 mg; Niacin, 0.2 mg; Vitamin C, 2 mg; Calcium, 7 mg; Phosphorus, 9 mg; Iron, 0.11 mg
Daikon (white radish)
_Pungent and sweet (Metal an_ _d_ _Earth), cool, weak Yan_ _g_
Daikon affects the lungs and the stomach. It eliminates hot irritation of the throat and bronchi, and is therefore a useful remedy for coughs and laryngitis. It detoxifies and helps digestion, thus curing indigestion and diarrhea. Its juice also helps asthma patients.
Protein, 0.7 g; Fat, 0.1 g; Fiber, 0.8 g; Carbohydrate, 3.4 g; Vitamin A, 3 IU; Vitamin B1, 0.06 mg; Vitamin B2, 0.02 mg; Niacin, 0.5 mg; Vitamin C, 15 mg; Calcium, 35 mg; Phosphorus, 22 mg; Iron, 0.4 mg
Eggplant (aubergine)
_Sweet (Earth), cool, balance o_ _f_ _Yin and Yan_ _g_
Eggplant nourishes the blood and qi and relieves pain, swelling, and heat. The raw juice is used as an application for softening and removing corns. In China eggplant is recommended for treating hemorrhages, ulcerations of the skin and gums, dysentery with blood, and anal bleeding.
Protein, 0.5 g; Fat, 0 g; Fiber, 0.6 g; Carbohydrate, 2.6 g; Vitamin A, 29 IU; Vitamin B1, 0.04 mg; Vitamin B2, 0.01 mg; Niacin, 0.2 mg; Vitamin C, 1 mg; Calcium, 15 mg; Phosphorus, 13 mg; Iron, 0.22 mg
Lettuce
_Bitter and sweet (Fire and Earth), cool, Yin_
Lettuce tones the blood and qi and dissipates heat. Because lettuce promotes the formation of body fluids, it is considered an effective diuretic and a remedy for poor lactation.
Protein, 0.2 g; Fat, 0 g; Fiber, 0.1 g; Carbohydrate, 0.4 g; Vitamin A, 146 IU; Vitamin B1, 0.01 mg; Vitamin B2, 0.01 mg; Niacin, 0 mg; Vitamin C, 1 mg; Calcium, –; Phosphorus, –; Iron, 0.04 mg
Onion, green (scallion)
_Pungent and sweet (Metal and Earth), warm, strong Yang_
Onion, a diaphoretic, affects the lungs and stomach. The white head of the scallion is used in many recipes for colds and nasal congestion. Although not as potent as garlic, onions are of the same famly and exert the same therapeutic effects. In other words, they are antibiotics and blood thinners. Note that the younger and fresher the onion, the stronger its therapeutic properties.
Protein, 1.8 g; Fat, 0.1 g; Fiber, 0.6 g; Carbohydrate, 12.6 g; Vitamin A, 15 IU; Vitamin B1, 0.08 mg; Vitamin B2, 0.02 mg; Niacin, 0.5 mg; Vitamin C, 5 mg; Calcium, 40 mg; Phosphorus, 60 mg; Iron, 1.2 mg
Potato
_Sweet (Earth), neutral, Yang_
Potato nourishes the spleen, pancreas, blood, and qi. It soothes inflammation. Potato juice can be applied to burns both to cool and diminsh pain and facilitate healing.
Protein, 2.3 g; Fat, 0.1 g; Fiber, –; Carbohydrate, 20.1 g; Vitamin A, 0 IU; Vitamin B1, 0.1 mg; Vitamin B2, 0.04 mg; Niacin, 1.7 mg; Vitamin C, 22 mg; Calcium, 8 mg; Phosphorus, 52 mg; Iron, 0.85 mg
Pumpkin
_Sweet (Earth), neutral, balance of Yin and Yang_
Pumpkin is a mild diaphoretic. Because it is able to clear damp conditions, it is a good and often-used remedy for bronchial asthma. It is also taken to relieve abdominal pains during pregnancy.
Protein, 1.3 g; Fat, 0.3 g; Fiber, –; Carbohydrate, 9.9 g; Vitamin A, 26,908 IU; Vitamin B1, 0.03 mg; Vitamin B2, 0.07 mg; Niacin, 0.4 mg; Vitamin C, 5 mg; Calcium, 32 mg; Phosphorus, 42 mg; Iron, 1.7 mg
Shiitake mushroom
_Sweet (Earth), neutral, weak Yang_
Mushrooms have been an integral part of Chinese medicine for centuries. The earliest materia medica from over two thousand years ago describe the medicinal properties of more than twenty species. Hundreds more are treated in modern publications. Among these, shiitake mushrooms, China's most common fungi, are mentioned as useful in treating vomiting, coughs, and urinary deficiencies. Regular consumption is also thought to prevent the development of cancer.
Because shiitake mushrooms are easily cultivated, they are used in everyday cooking as a tasty ingredient to enhance both meat and vegetarian dishes. Shiitake mushrooms are used in popular treatments for coughs, to prevent hardening of the arteries, as a diuretic, and to soothe irritation from food toxins.
Protein, 1.4 g; Fat, 0.2 g; Fiber, –; Carbohydrate, 11.3 g; Vitamin A, 0 IU; Vitamin B1, 0.05 mg; Vitamin B2, 0.19 mg; Niacin, 2.1 mg; Vitamin C, 1 mg; Calcium, 2 mg; Phosphorus, 44 mg; Iron, 0.26 mg
Spinach
_Sweet (Earth), cool, balance o_ _f_ _Yin and Yan_ _g_
Spinach nourishes qi and the blood; its high iron content makes it a useful remedy for anemia. Spinach has a cool, glossy texture, which exerts a lubricating effect on ailments of a hot, dry nature, such as a dry and rasping cough, thirst, and red and dry mucus in the mouth and nose. Spinach also nourishes the intestines; this, coupled with its smooth texture, make it a good laxative.
Spinach broth is a remedy for intoxication. Spinach is often eaten to stop hair loss. Another of its recognized characteristics is that spinach arrests bleeding. It is therefore consumed as a remedy against nosebleed, as well as for anal bleeding.
Protein, 0.4 g; Fat, 0.1 g; Fiber, –; Carbohydrate, 0.7 g; Vitamin A, 1232 IU; Vitamin B1, 0.01 mg; Vitamin B2, 0.04 mg; Niacin, 0.1 mg; Vitamin C, 8 mg; Calcium, 16 mg; Phosphorus, 8 mg; Iron, 0.22 mg
Sweet potato
_Sweet (Earth), neutral, Yang_
Sweet potato nourishes the spleen, liver, blood, and qi. It is a valid remedy for constipation and for indigestion. Sweet potato soup will help to clear the head after drinking alcohol. Its diaphoretic effects render it effective against the common cold.
Protein, 2.7 g; Fat, 0.5 g; Fiber, –; Carbohydrate, 39.8 g; Vitamin A, 27,968 IU; Vitamin B1, 0.09 mg; Vitamin B2, 0.23 mg; Niacin, 1.1 mg; Vitamin C, 28 mg; Calcium, 35 mg; Phosphorus, 44 mg; Iron, 0.92 mg
Tomato
_Sweet and sour (Earth and Wood), slightly cold, Yin_
Tomato dissipates heat and stimulates the appetite and digestion. In China, raw tomato is served as an appetizer to promote digestion. It is prescribed to treat anemia, high blood pressure, constipation, and indigestion. A decoction made from the tomato plant is used to treat amoebic dysentery.
Protein, 1.1 g; Fat, 0.3 g; Fiber, 1.0 g; Carbohydrate, 5.3 g; Vitamin A, 1394 IU; Vitamin B1, 0.07 mg; Vitamin B2, 0.06 mg; Niacin, 0.7; Vitamin C, 22 mg; Calcium, 8 mg; Phosphorus, 29 mg; Iron, 0.59 mg
Water chestnut
_Sweet (Earth), cold, Yin_
Water chestnuts, a popular remedy for indigestion and hepatitis, also relieve fever. They are a useful source of nutrients for diabetics. Cut open and applied to the face, water chestnuts are used to cure acne. Eaten raw or drunk as juice, water chestnuts relieve sore throat and gums and canker sores.
Protein, 0.9 g; Fat, 0.1 g; Fiber, –; Carbohydrate, 14.8 g; Vitamin A, 0 IU; Vitamin B1, 0.09 mg; Vitamin B2, 0.12 mg; Niacin, 0.6 mg; Vitamin C, 3 mg; Calcium, 7 mg; Phosphorus, 39 mg; Iron, 0.37 mg
NUTS AND SEEDS
Nuts and seeds are storehouses of energy. They contain essential fatty acids and carbohydrates, and are rich in minerals and in vitamin E. Vitamin E is a powerful antioxidant that protects cells and nerves from aging and degeneration.
As with all foods, nuts and seeds are best eaten fresh. When freshly picked nuts are unavailable, it is best to select those that are still in their shells. Hulled and shelled nuts and seeds easily become rancid, thereby losing all nutrients and becoming difficult to digest. Nuts left in their shells can be consumed up to one year after harvesting.
Most nuts and seeds have warming properties. They are therefore particularly useful for treating cold-syndrome diseases and for fortifying the body in winter.
As with fruits and vegetables, it is best to eat organically grown nuts and seeds. Sprayed insecticides and poisons accumulate in seeds more readily than in the stem or fruit of plants.
Almonds
_Bitter and sweet (Fire and Earth), warm, Yang_
Almonds, common in northern China, are one of the foods richest in calcium and phosphorus. They nourish the blood and qi, and lubricate the lungs and bronchi. Almonds and almond milk are commonly used to relieve coughs. According to tradition, almonds should be consumed to counteract the development of athlete's foot. Almond and chrysanthemum tea alleviates headaches.
Protein, 20.6 g; Fat, 52.10 g; Fiber, 4.58 g; Carbohydrate, 20.42 g; Vitamin A, 0 IU; Vitamin B1, 0.21 mg; Vitamin B2, 0.77 mg; Niacin, 3.52 mg; Vitamin C, traces; Calcium, 264 mg; Phosphorus, 520.96 mg; Iron, 3.66 mg
Caraway seeds
_Slightly pungent (Metal), warm, Yang_
Caraway seed stimulates the circulation of blood and qi. It affects the internal organs of digestion, in particular the stomach and kidneys.
Protein, 8 g; Fat, 6 g; Fiber, –; Carbohydrate, 22 g; Vitamin A, 160 IU; Vitamin B1, 0.2 mg; Vitamin B2, 0.2 mg; Niacin, 2 mg; Vitamin C, 0 mg; Calcium, 280 mg; Phosphorus, 240 mg; Iron, 6.8 mg
Chestnuts
_Sweet (Earth), warm, Yang_
Chestnuts fortify Yang and nourish qi and blood. Being warm, chestnuts dissipate cold-syndrome diseases. They are used as a remedy for diarrhea, especially when due to cold. They are also often used to treat nausea.
Protein, 4.22 g; Fat, 1.06 g; Fiber, 6 g; Carbohydrate, 48.93 g; Vitamin A, 200 IU; Vitamin B1, 0.18 mg; Vitamin B2, 0.18 mg; Niacin, 0.7 mg; Vitamin C, 35.2 mg; Calcium, 17.6 mg; Phosphorus, 95.04 mg; Iron, 1.41 mg
Peanuts
_Sweet (Earth), neutral, Yang_
Peanuts nourish qi and the blood. They strengthen and lubricate the lungs, and are often used to treat dry coughs. In China, peanuts are not normally served salted. Roasted or boiled peanuts stimulate the appetite, and for this reason are often served at the beginning of Chinese banquets as appetizers. Boiled peanuts with milk and honey is a common remedy both for stomachache and for gastritis. Peanut husks are used as a remedy for anemia.
Eaten fresh, peanuts alleviate coughs with catarrh. Peanuts are also recognized as a remedy for beriberi, and are often prescribed as part of a diet aimed at lowering blood pressure. Peanuts boiled with soymilk or eaten with pork are said to promote the secretion of milk after childbirth.
Protein, 25.7 g; Fat, 44.2 g; Fiber, 2.4 g; Carbohydrate, 23.6 g; Vitamin A, 0 IU; Vitamin B1, 0.66 mg; Vitamin B2, 0.14 mg; Niacin, 14.08 mg; Vitamin C, 0 mg; Calcium, 59.84 mg; Phosphorus, 383.68 mg; Iron, 3.24 mg
Sesame seeds
_Sweet (Earth), neutral, balance o_ _f_ _Yin and Yan_ _g_
The sesame plant has been cultivated in China for five thousand years. The seeds are pressed to make sesame oil, prized all over China as the best oil for condiments and stir-frying. The seeds themselves are used extensively in traditional Chinese medicine. There are two varieties of sesame seeds: black and white. Although their functions are more or less the same, the black variety is usually preferred for medicinal purposes.
Sesame nourishes the blood and improves eyesight. It dispels evil wind, and dryness in the intestines. Sesame aids the production of body fluids and stimulates the secretion of maternal milk after childbirth. It reinforces the functions of the liver and helps to mainain black, shiny hair. Sesame is also used in remedies for general weakness, anemia, constipation, dizziness, ringing in the ears, hypertension, and chronic cough.
Protein, 16.8 g; Fat, 47.6 g; Fiber, –; Carbohydrate, 25.9 g; Vitamin A, 5 IU; Vitamin B1, 1.19 mg; Vitamin B2, 0.45 mg; Niacin, 5.25 mg; Vitamin C, 0 mg; Calcium, 129.5 mg; Phosphorus, 770 mg; Iron, 7.73 mg
Sunflower seeds
_Sweet (Earth), neutral, mild Yang_
Sunflower seeds regulate the action of the large intestine. They are useful in treating severe diarrhea and dysentery with blood in the stools. Sunflower seeds contain plenty of essential minerals, particularly zinc. One teapoon of crushed sunflower seeds dissolved in hot water and drunk as a tea will allow the skin pustules that erupt in measles and chicken pox to mature more rapidly. Two tablespoons of crushed sunflower seeds brewed in the same way is an effective laxative.
Protein, 22.88 g; Fat, 49.63 g; Fiber, –; Carbohydrate, 18.66 g; Vitamin A, 49.28 IU; Vitamin B1, 2.29 mg; Vitamin B2, 0.25 mg; Niacin, 4.58 mg; Vitamin C, –; Calcium, 116.16 mg; Phosphorus, 704 mg; Iron, 6.76 mg
Walnuts
_Sweet (Earth), warm, Yang_
Walnuts are a tonic for the blood and the kidneys. They lubricate the intestines and are thus a good remedy for constipation. Walnuts also alleviate asthma. They are often prescribed in China for male sexual problems such as seminal emission and impotence.
If chewed slowly, raw walnuts give some relief to a sore throat. Mixed with sesame seeds, ginger, and honey, they relieve stomach pains. A decoction of walnuts and fresh ginger is known to relieve fever and headache associated with the common cold.
Protein, 15 g; Fat, 56.67 g; Fiber, 2.1 g; Carbohydrate, 15.6 g; Vitamin A, 30 IU; Vitamin B1, 0.48 mg; Vitamin B2, 0.11 mg; Niacin, 0.7 mg; Vitamin C, 3 mg; Calcium, 83 mg; Phosphorus, 380 mg; Iron, 3.06 mg
GRAINS AND BEANS
Grains are at the base of the human food pyramid. Whole grains provide all our nutritional needs: proteins, carbohydrates, vitamins, enzymes, and minerals.
Being a major source of calories, every agriculture-based culture in the world has selected one of the grains as its preferred staple. In Europe the staple grain is wheat; in pre-Columbian America it was maize and amaranth; in India it is rice; in China it is rice in the south and wheat in the north.
Because whole, unhusked grains contain greater quantities of nutrients than polished or processed grains, it is preferable to consume all grains and cereals as close to their natural state as possible. One problem that may arise from eating whole grains is difficulty in digesting them. This may be partly overcome by thoroughly chewing grains. The process of digesting carbohydrates starts with the action of saliva in the mouth, which converts starch to more easily digestible maltose. The more time grains remain in the mouth, the greater the predigestive efficacy of saliva
Like nuts and seeds, beans are rich in carbohydrates, proteins, minerals, and enzymes. As with whole grains, beans are also difficult to digest and, once digested, are notorious for causing flatulence. Fortunately, several remedies exist. Thorough chewing is one of them. Another is to soak beans overnight before cooking, or until they sprout. Sprouting changes the beans' chemical composition. Although less energetic and cooler than unsprouted beans, they are easier to digest. A common antidote in China to their flatulence-causing properties is to eat beans with ginger; this prevents bloating. Another technique is not to add salt until cooking is almost complete—salt interferes with the proper cooking of the skin of most legumes, thereby rendering them tough and indigestible. One can also cook beans with fennel or cumin seed, which stimulate digestion and the metabolism.
Adzuki bean
_Sour and sweet (Wood and Earth), neutral, balance of Yin and Yang_
Adzuki beans are a classic remedy for beriberi. They are also used as a remedy for bloody stools, diarrhea, balancing hormones during menopause, aiding the secretion of milk after childbirth, and for athlete's foot.
Protein, 8.7 g; Fat, 0.1 g; Fiber, 0.5 g; Carbohydrate, 26 g; Vitamin A, 6 IU; Vitamin B1, 0.13 mg; Vitamin B2, 0.07 mg; Niacin, 0.8 mg; Vitamin C, 0 mg; Calcium, 182 mg; Phosphorus, 22 mg; Iron, 2.36 mg
Mung bean
_Sweet (Earth), cool, balance o_ _f_ _Yin and Yan_ _g_
Mung beans dissipate heat, detoxify, and nourish the heart and stomach. They are a remedy for high blood pressure, hemorrhoids, headaches, and intoxication from alcohol, lead, or mild poisons. The recipe for detoxifying is to boil one-half to one pound of mung beans in water and take as a soup, with seasoning, or grind the same amount into a powder and mix with warm water.
Protein, 6.8 g; Fat, 0.5 g; Fiber, –; Carbohydrate, 10 g; Vitamin A, 28 IU; Vitamin B1, 0.13 mg; Vitamin B2, 0.07 mg; Niacin, 1.3 mg; Vitamin C, 1 mg; Calcium, 46 mg; Phosphorus, 140 mg; Iron, 1.62 mg
Rice
_Sweet (Earth), neutral, weak Yang_
Because rice is the staple dish in southern China, it would be quite surprising were it not recognized as having some therapeutic function within Chinese home remedies. Surprisingly, however, the therapeutic properties of rice turn out to be few. Polished rice is used as a base for various food remedies, usually as a sort of gruel or _congee._ On its own, rice can be eaten as a source of nourishing energy for the spleen and stomach, particularly when suffering from diarrhea and nausea. Two or three tablespoons of rice with a slice of fresh ginger, chewed slowly first thing in the morning on an empty stomach, can help allay morning sickness.
Unfortunately, the relatively recent use of chemical weed killers in the rice-growing industry suggests that commercially grown rice may be harmful to one's health. Rice is grown in rich, fertile soil in a few inches of water, ideal conditions for weeds and other parasites. Until a few years ago these weeds were removed by hand by cohorts of women workers who systematically damaged their bodies by wading, bent double, through the rice paddies, pulling at the weeds—necessary work that no one wanted to do. Chemical weed killers eliminated the need for any further human intervention. Yet the use of these weed killers translates as health risks to the consumer. In order to work, weed killers must be added to the rice crop in such concentrations that the amount of poison present in every grain of unhusked rice is twenty times the danger level for human consumption.
Most of the weed-killing poison settles in the husk. If you eat polished rice, you eliminate the poisons as well as the vitamins.
Polished rice: Protein, 6.8 g; Fat, 0.5 g; Fiber, 0.2 g; Carbohydrate, 78.2 g; Vitamin A, 0 IU; Vitamin B1, 0.06 mg; Vitamin B2, 0.06 mg; Niacin, 1.9 mg; Vitamin C, 0 mg; Calcium, 10 mg; Phosphorus, 160 mg; Iron, 3.1 mg
Unpolished rice: Protein, 7.5 g; Fat, 1.0 g; Fiber, 0.6 g; Carbohydrate, 76.7 g; Vitamin A, 2 IU; Vitamin B1, 0.21 mg; Vitamin B2, 0.16 mg; Niacin, 1.9 mg; Vitamin C, 0 mg; Calcium, 10 mg; Phosphorus, 190 mg; Iron, 3.2 mg
Rice bran
_Pungent (Metal), warm, strong Yang_
Rice bran, a diaphoretic, dissipates cold and affects the stomach and intestines. An ancient remedy for beriberi, rice bran is commonly used in China for treating constipation. When mixed with honey, it provides relief from coughs.
Protein, 11.9 g; Fat, 21.7 g; Fiber, –; Carbohydrate, 45.6 g; Vitamin A, 0 IU; Vitamin B1, 2.21 mg; Vitamin B2, 0.26 mg; Niacin, 31.2 mg; Vitamin C, 0 mg; Calcium, 355 mg; Phosphorus, –; Iron, 7.88 mg
Soybean
_Sweet (Earth), neutral, weak Yang_
Soybeans have been used medicinally in China for five thousand years. Because of their high protein content and ease of digestion, they are one of the most valuable ingredients in Chinese cuisine. Soybeans energize the entire body, nourishing the spleen and lubricating the intestines. They build muscles and regulate body fat, and are therefore valuable for low-fat and weight-reducing diets.
Soybeans are commonly used as a remedy for malnutrition, poor digestion, diarrhea, and high cholesterol. A product of soybeans used extensively in Chinese cuisine and medicine is tofu.
Protein, 11 g; Fat, 5.8 g; Fiber, –; Carbohydrate, 10 g; Vitamin A, 140 IU; Vitamin B1, 0.23 mg; Vitamin B2, 0.14 mg; Niacin, 1.1 mg; Vitamin C, 15 mg; Calcium, 131 mg; Phosphorus, 142 mg; Iron, 2.25 mg
Tofu
_Sweet (Earth), cool, balance o_ _f_ _Yin and Yan_ _g_
Tofu (pronounced **doe** -fu in China) is made from dried, crushed soybeans that are boiled and then coagulated to form solid tofu and soymilk. Tofu is soft and pudding-like; the rubbery skin that forms on the surface during coagulation, called bamboo _tofu,_ is an important ingredient of Chinese vegetarian cuisine.
Tofu dissipates heat and dryness. It tones the entire body and is particularly nourishing to the blood and qi. Tofu is used to treat chronic amoebic dysentery; anemia; stubborn, dry cough; nausea; vomiting; intoxication; high blood pressure; insufficient lactation; and arthritis and rheumatism. According to recent Western research, soy protein's ability to clear cholesterol from the blood is unsurpassed by any other foodstuff.
Protein, 11 g; Fat, 2.3 g; Fiber, –; Carbohydrate, 11 g; Vitamin A, 209 IU; Vitamin B1, 0.2 mg; Vitamin B2, 0.13 mg; Niacin, 0.5 mg; Vitamin C, 0 mg; Calcium, 258 mg; Phosphorus, 239 mg; Iron, 13.9 mg
MEAT AND POULTRY
Chinese people consume little meat, although tourists to China often come away with a very different impression. Tourist meals are about 50 percent meat. The reason for this is simple: Chinese hospitality.
Chinese people are aware of Westerners' partiality to meat and will thus provide plenty of it to "foreign friends." We ourselves eat meat perhaps once a week; when we do it is with therapeutic or nutritional intent. The life of animals is respected both by Buddhists and Taoists. Furthermore, animal qi is considered by some to be bad for humans, and for that reason rituals exist for the slaying of animals. Because misfortune is said to come to one who kills an animal, only old people whose life force is ebbing anyway are supposed to practice butchery. Young people should not even be present when an animal is killed. If a young person must kill an animal, he must bite hard on the blade of the killing knife before using it on the beast. A disculpatory jingle is recited to the animal before it is killed: _"Bu yuan ni, bu yuan wo, guan yuan ni zhu jia mai gei wo."_ No blame on you, no blame on me, just blame your master for selling you to me." Afterward the blood is collected, steamed, and eaten by the butcher as an act of penitence.
Another taboo is that one should never eat an animal that has not been killed after the first attempt. If the first cut missed or only injured the animal, it is said to mean that the gods are protecting it, and it should, if still possible, be allowed to live. If the injury is too great, it should be killed with a second stroke but not eaten.
Beef
_Sweet (Earth), neutral, Yang_
Considered to be of the Earth element, beef builds the qi and blood, tones yin, and strengthens muscles. Beef is prescribed as a general tonic for weakness and convalescence. It is a specific treatment for lumbago, chronic diarrhea, anorexia, and low blood pressure.
Until recently, beef was rarely eaten in China. Indeed, few people know that the taboos that exist in India about the consumption of cow flesh also applied in China before the thirteenth century; beef became more popular only after the Mongolian conquest of China in A.D. 1215. The Mongolian grasslands were ideal for cattle and sheep grazing; the Mongolians have therefore always been meat eaters. They brought their meat-eating habits with them to China, thus influencing local cuisine and doing away with the old taboos forever. Today beef is consumed without any qualms in China, with the exception of those relating to expense.
Protein, 25 g; Fat, 27 g; Fiber, 0 g; Carbohydrate, 0 g; Vitamin A, 0 IU; Vitamin B1, 0.05 mg; Vitamin B2, 0.2 mg; Niacin, 4.1 mg; Vitamin C, 0 mg; Calcium, 11 mg; Phosphorus, 170 mg; Iron, 3.1 mg
Chicken
_Sweet (Earth), warm, Yang_
Chicken assists circulation of blood and qi. It is used in cures for diarrhea and dysentery. Chicken is also prescribed for problems as varied as anorexia; diabetes; leukorrhea; slow lactation; weakness; and liver, kidney, and urinary deficiencies.
Protein, 20 g; Fat, 2.7 g; Fiber, 0 g; Carbohydrate, 0 g; Vitamin A, 0 IU; Vitamin B1, 0.1 mg; Vitamin B2, 0.24 mg; Niacin, 5.6 mg; Vitamin C, 0 mg; Calcium, 15 mg; Phosphorus, 188 mg; Iron, 1.8 mg
Pork
_Sweet and salty (Earth an_ _d_ _Water), neutral, mild Yan_ _g_
So common is the pig to rural family life that the Chinese character for family depicts a pig under a roof. Pork is the most common meat consumed in China. Consequently, it figures prominently in popular food remedies as well.
Pork is used for constipation, debility, malnutrition and emaciation, dry cough, and diabetes. It is also prescribed for combating hyperacidity and gastritis, male sexual problems, and overly dry skin.
Protein, 22.3 g; Fat, 26.1 g; Fiber, 0 g; Carbohydrate, 0 g; Vitamin A, 8 IU; Vitamin B1, 0.52 mg; Vitamin B2, 0.3 mg; Niacin, 3.9 mg; Vitamin C, 0 mg; Calcium, 8 mg; Phosphorus, 206 mg; Iron, 1.19 mg
Mutton
_Sweet (Earth), warm, Yang_
Mutton nourishes qi and the blood. It is considered a good tonic for conditions of general weakness and fatigue. Mutton is the preferred meat for curing male sexual weaknesses such as frequent nocturnal emission and premature ejaculation. It is also prescribed for indigestion, pains in the abdomen, and all cold-syndrome ailments.
Protein, 21.5 g; Fat, 16.1 g; Fiber, 0 g; Carbohydrate, 0 g; Vitamin A, –; Vitamin B1, 0.13 mg; Vitamin B2, 2.3 mg; Niacin, 4.7 mg; Vitamin C, 0 mg; Calcium, 9 mg; Phosphorus, 177 mg; Iron, 1.4 mg
FISH
In China, fish is considered to be one of the most wholesome foods. Fish is also considered to be a symbol of wealth and abundance; the word for fish _(yu)_ is pronounced just like the word meaning "abundance." The golden carp, or goldfish _(yu jing),_ is particularly auspicious because the word sounds similar to the words meaning "abundant gold"—hence the great number of goldfish images one sees on the walls of many Chinese restaurants around the world. Fish are also a positive symbol in Buddhist iconography. For Buddhists they represent freedom from the chains of the material world.
The most commonly eaten fish in China is carp; they are plentiful, as they breed with ease in ponds and rice paddies. Shrimp are among the most prized fish, however, so accorded for their strong Yang energy. Other popular fish are eel, clams, crab, and abalone. The last, however, is not commonly found outside China. Abalone is difficult to digest and does not feature in any of our remedies. We shall not, therefore, describe it here.
Carp
_Sweet (Earth), cold, Yang_
Carp meat nourishes the blood and qi and affects the stomach, kidneys, and spleen. It is a diuretic. Carp also promotes lactation after childbirth.
Protein, 17.75 g; Fat, 5.6 g; Fiber, –; Carbohydrate, 0 g; Vitamin A, 8 IU; Vitamin B1, –; Vitamin B2, –; Niacin, –; Vitamin C, 1 mg; Calcium, 41 mg; Phosphorus, 410 mg; Iron, 1.23 mg
Clam
_Salty (Water), cold, Yin_
Clam meat dissipates toxic heat and dryness. A light, cooling meat, it promotes the flow and distribution of body fluids, thus acting as a detoxifier. Clam meat exerts a beneficial effect on the stomach, lowers high blood pressure, and is known to resolve vaginal bleeding and discharge (leukorrhea). It is sometimes prescribed for treating hemorrhoids.
Protein, 12.8 g; Fat, 1.4 g; Fiber, 0 g; Carbohydrate, 3.4 g; Vitamin A, 110 IU; Vitamin B1, 0.1 mg; Vitamin B2, 0.18 mg; Niacin, 1.6 mg; Vitamin C, 0 mg; Calcium, 96 mg; Phosphorus, 139 mg; Iron, 7 mg
Crab
_Salty (Water), cold, Yin_
Crab is a cold meat and is therefore nearly always cooked with ginger, which is warming, for balance. However, if you are suffering from a toxic heat syndrome, crab has the effect of dissipating the heat. It relieves heat rashes and pustules on the skin.
Protein, 16.9 g; Fat, 2.9 g; Fiber, 0 g; Carbohydrate, 1.3 g; Vitamin A, 0 IU; Vitamin B1, 0.05 mg; Vitamin B2, 0.06 mg; Niacin, 2.5 mg; Vitamin C, 0 mg; Calcium, 45 mg; Phosphorus, 182 mg; Iron, 0.9 mg
Eel
_Sweet (Earth), warm, Yang_
Eel is considered to be a good tonic for the body and qi, and is thus often taken for fatigue or debilitation. It is also prescribed for rheumatic disorders.
Protein, 18.3 g; Fat, 11.5 g; Fiber, –; Carbohydrate, 0 g; Vitamin A, 1034 IU; Vitamin B1, 0.15 mg; Vitamin B2, 0.04 mg; Niacin, 3.5 mg; Vitamin C, 6 mg; Calcium, 19.8 mg; Phosphorus, 213 mg; Iron, 0.5 mg
Shrimp
_Sweet (Earth), warm, Yang_
Shrimp meat dissipates cold, tones Yang, and removes stagnation in the flow of qi. In China, shrimp is valued first and foremost for enhancing male sexual energy, and thus correcting impotence. Because of its strong Yang energy however, it will make seminal emission and premature ejaculation worse. The strong energy of shrimp is an aid during convalescence.
Protein, 20.2 g; Fat, 1.75 g; Fiber, –; Carbohydrate, 0.9 g; Vitamin A, –; Vitamin B1, 0.02 mg; Vitamin B2, 0.03 mg; Niacin, 2.6 mg; Vitamin C, –; Calcium, 51 mg; Phosphorus, 204 mg; Iron, 2.39 mg
EGG
Eggs are birds in the making. As such, they are extremely high-protein foods with powerful nutritional and therapeutic effects.
Eggs are made of three different constituents: the yolk, the white, and the shell. The latter is usually discarded by cooks in the West. In China, however, eggshell has a variety of uses. Eggshell ground into a fine powder and taken with meals decreases gastric acid, and is thus a remedy for gastric and duodenal ulcers. Ground eggshell dissolved in _jiu_ (Chinese rice wine, or Japanese _sake_ ) cures stomach problems. Sterilized ground eggshell applied to a wound will arrest bleeding.
Because milk is not commonly drunk in China, eggshell is often used as a remedy for rickets—insufficient vitamin D leading to defective bone growth—and calcium deficiency in children.
Whole egg
_Sweet (Earth), neutral, Yin_
Considered to be a highly nutritious and energetic food, egg dissipates dryness and nourishes the blood and qi. It is used in a wide variety of remedies, from asthma to coughs and the common cold. It is also included in remedies for dysentery, diarrhea, constipation, hepatitis, anemia, nausea and vomiting, and insomnia.
Protein, 6.1 g; Fat, 5.5 g; Fiber, 0 g; Carbohydrate, 0.6 g; Vitamin A, 260 IU; Vitamin B1, 0.04 mg; Vitamin B2, 0.14 mg; Niacin, 0 mg; Vitamin C, 0 mg; Calcium, 28 mg; Phosphorus, 90 mg; Iron, 1.04 mg
Egg white
_Sweet (Earth), cool, weak Yin_
Egg white has a cooling effect; it also moistens and soothes excessive dryness of the eyes, throat, and lungs. By cooling and moisturizing, egg white effectively detoxifies the entire body. It is also considered to be a good remedy for anemia.
One egg white drunk raw every morning keeps constipation at bay. Mix it with fruit juice if you find the white distasteful on its own. In China, raw egg white mixed with rice wine is an application for scalds and burns.
Protein, 3.4 g; Fat, 0 g; Fiber, 0 g; Carbohydrate, 0.4 g; Vitamin A, 0 IU; Vitamin B1, 0 mg; Vitamin B2, 0.09 mg; Niacin, 0 mg; Vitamin C, 0 mg; Calcium, 4 mg; Phosphorus, 4 mg; Iron, 0.01 mg
Egg yolk
_Sweet (Earth), neutral, medium Yang_
Egg yolks are considered nourishing for the liver, heart, and kidneys. They are more effective than a whole egg for curing vomiting and diarrhea—one remedy for continual vomiting is to swallow half a dozen raw or underboiled egg yolks in a single sitting.
Protein, 2.8 g; Fat, 5.6 g; Fiber, 0 g; Carbohydrate, 0 g; Vitamin A, 313 IU; Vitamin B1, 0.4 mg; Vitamin B2, 0.07 mg; Niacin, 0 mg; Vitamin C, 0 mg; Calcium, 26 mg; Phosphorus, 86 mg; Iron, 0.9 mg
HERBS AND SPICES
All cultures use herbs and spices in their cuisine. China is no exception. Some, such as ginger, cilantro, and garlic, have been used since antiquity. Others, like red or cayenne pepper, made their way to China after their discovery on the American continent, and have been used with great success ever since.
Herbs and spices serve two main purposes. They add or enhance flavor and they exert specific therapeutic effects. These effects are different for every herb and spice. Cinnamon and pepper, for example, are Yang and hot, peppermint and marjoram are Yin and cool.
Basil
_Pungent (Metal), warm, ascending Yang_
Basil promotes circulation of qi and blood, helps digestion, and reinforces the lungs, spleen, and stomach. Basil is not common in China. It is, however, known to traditional medicine, and is sometimes used as a treatment for abdominal pains, bloating, and diarrhea.
Protein, 0 g; Fat, 4 g; Fiber, 0 g; Carbohydrate, 2 g; Vitamin A, 80 IU; Vitamin B1, 0 mg; Vitamin B2, 0.2 mg; Niacin, 0 mg; Vitamin C, 20 mg; Calcium, 140 mg; Phosphorus, 10 mg; Iron, 11.8 mg
Cilantro (coriander or Chinese parsley)
_Pungent (Metal), warm, Yang_
Cilantro is used as a seasoning in many dishes, and particularly with seafood. Besides enhancing the flavor, cilantro serves to balance the cold effect of clams and crab. Cilantro's strong smell and flavor makes it a valuable breath freshener. It is also used in China to quicken the rash in measles: you can either wash the patient with a warm cilantro brew or use it liberally when preparing the patient's food.
Protein, 0.16 g; Fat, 0 g; Fiber, –; Carbohydrate, 0.16 g; Vitamin A, 185 IU; Vitamin B1, 0 mg; Vitamin B2, 0.02 mg; Niacin, 0 mg; Vitamin C, 0 mg; Calcium, 6.7 mg; Phosphorus, 1.6 mg; Iron, 0.13 mg
Cinnamon
_Sweet and pungent (Earth an_ _d_ _Metal), hot, Yan_ _g_
Cinnamon nourishes the spleen, kidneys, and bladder.
Protein, 2 g; Fat, 2 g; Fiber, –; Carbohydrate, 36 g; Vitamin A, 120 IU; Vitamin B1, 0 mg; Vitamin B2, 0 mg; Niacin, 0 mg; Vitamin C, 20 mg; Calcium, 560 mg; Phosphorus, 20 mg; Iron, 17.6 mg
Clove
_Pungent (Metal), warm, Yang that pushes downward_
Clove affects the internal organs of digestion, the stomach and kidneys in particular. It is a warming spice that relieves hiccups, nausea, and stomach problems.
Protein, 2 g; Fat, 8 g; Fiber, –; Carbohydrate, 26 g; Vitamin A, 220 IU; Vitamin B1, 0 mg; Vitamin B2, 0.2 mg; Niacin, 0 mg; Vitamin C, 40 mg; Calcium, 280 mg; Phosphorus, 40 mg; Iron, 3.6 mg
Dill seed
_Pungent (Metal), warm, Yang_
Dill seed tones and regulates qi. A diaphoretic, it is particularly useful for warming the spleen and kidneys. Dill seed is used to treat vomiting, hiccups, and anorexia. Its warming effect counteracts abdominal and stomach pains due to cold.
Protein, 6 g; Fat, 6 g; Fiber, 0 g; Carbohydrate, 24 g; Vitamin A, 20 IU; Vitamin B1, 0.2 mg; Vitamin B2, 0.2 mg; Niacin, 0.2 mg; Vitamin C, 0 mg; Calcium, 640 mg; Phosphorus, 120 mg; Iron, 100 mg
Garlic
_Pungent (Metal), warm, strong Yang_
Garlic, a diaphoretic, warms the lungs, stomach, and spleen and promotes circulation of qi. The antibiotic effects of garlic have been recognized worldwide since antiquity. Northern Chinese chew several cloves of raw garlic with their meals whenever they suspect poor sanitary conditions. If obliged to drink contaminated water, they chew a clove or two of garlic first, swallowing the juice and spitting out the fiber.
Because it destroys worms and bacteria, garlic is used as a remedy for diarrhea and chronic amoebic dysentery. Garlic is also an anticoagulant; taken daily, a clove or two of garlic can guard against blood clots, and thus can prevent heart attack or thrombosis. Garlic lowers cholesterol. As a sweat inducer (diaphoretic), garlic is frequently included in recipes for the common cold and influenza. Recent evidence suggests that garlic may also boost the immune system and slow the growth of tumors.
For best effects, eat garlic raw. Many (though not all) of its benefits are lost through cooking. To counteract the unpleasant odor of garlic on the breath, most Chinese people will recommend chewing green tea leaves. Fresh dates or persimmon are said to banish the smell. You may also rinse the mouth with vinegar or drink a glass of milk to counteract the strong odor.
Protein, 6.3 g; Fat, 0.1 g; Fiber, 0.8 g; Carbohydrate, 29.8 g; Vitamin A, 0 IU; Vitamin B1, 0.06 mg; Vitamin B2, 0.23 mg; Niacin, 0.4 mg; Vitamin C, 13 mg; Calcium, 30 mg; Phosphorus, 310 mg; Iron, 1.3 mg
Ginger
_Pungent (Metal), warm (dry ginger: hot), strong outward-moving Yang_
Ginger acts on the lungs, stomach, and spleen. It disperses cold and relieves nausea; a slice of ginger or some ginger juice taken before a boat, car, or plane trip suppresses motion sickness. Ginger aids digestion; a slice or two chewed after a heavy meal combats indigestion and flatulence. Ginger is a powerful diaphoretic and a strong anticoagulant; a few slices of ginger taken daily can guard against blood clots, thus preventing heart attack or thrombosis. As a sweat inducer (diaphoretic), ginger is a useful remedy for the common cold and influenza.
Note that fresh ginger contains volatile oils not present in the dried variety.
Protein, 2.3 g; Fat, 0.9 g; Fiber, 2.4 g; Carbohydrate, 12.3 g; Vitamin A, 40 IU; Vitamin B1, 0.06 mg; Vitamin B2, 0.03 mg; Niacin, 0.6 mg; Vitamin C, 0 mg; Calcium, 20 mg; Phosphorus, 60 mg; Iron, 2.6 mg
Ginseng
_Sweet and slightly bitter (Earth and Fire), warm, weak Yang_
The word _ginseng_ is an anglicized pronunciation of the Chinese words _ren sheng,_ meaning "root (or spirit) of man." Indeed, since ancient times in China ginseng has been used for building up the human spirit. Ginseng stimulates the nervous system, improving mental concentration, stamina, and memory. It builds resistance to disease and treats a variety of conditions ranging from colds to heart disease.
There exist two varieties of ginseng. _Panax ginseng,_ a native of Asia, has been used in China for centuries. The other, _Panax quinquefolius,_ is native to North America, where it has been cultivated since 1870. Although Asian ginseng is recognized as the stronger of the two, in China American ginseng is frequently favored over the Asian variety. This is not because of some common human trait to regard things that come from overseas as better than that which is homegrown. Unless you are seriously ill or completely depleted of energy, Asian ginseng is too powerful. The American variety gives a steadier and less overpowering energy boost.
Ginseng may be taken in soups or with vegetable dishes. It can be brewed as a tea or macerated in a bottle of rice wine and sipped as a tonic. Dry ginseng is taken to treat morning sickness. Ginseng tea excites the heart and brain and stimulates the appetite. Eating ginseng improves sexual functions in both men and women—indeed, there are only a few conditions for which ginseng is not useful. Ginseng is a stimulant and an antidiuretic. It should therefore **not** be taken for kidney problems, insomnia, high blood pressure, and fever.
Protein, 6.5 g; Fat, 0.3 g; Fiber, –; Carbohydrate, 6 g; Vitamin A, 0 IU; Vitamin B1, 0.02 mg; Vitamin B2, 0.02 mg; Niacin, 0.3 mg; Vitamin C, 1.7 mg; Calcium, 7 mg; Phosphorus, 11.6 mg; Iron, 0.2 mg
Licorice
_Sweet (Earth), neutral, Yang_
Licorice, one of the most important ingredients in traditional Chinese herbal medicine, acts as a catalyst and regulates the effects of other herbal remedies. Its soothing characteristics are known to counteract toxins, and to have a calming effect on a body wracked by acute symptoms of a disease. Licorice invigorates the functions of the heart and lungs; it lubricates the lungs, soothing chronic and irritable coughs, and aids digestion by protecting the spleen and the lining of the stomach.
Licorice is frequently used as an antiphlogisitic (anti-inflammatory) for sore throat, boils, and irritation of the skin. It can also be useful as an antidote to poisoning by too many medicines or herbal drugs.
Licorice is not a common ingredient in American cuisine. Nutrient values for licorice are therefore not available.
Peppermint
_Pungent (Metal), cool, Yang_
Peppermint rises and affects the upper body, particularly the lungs. It also exerts a purifying effect on the organs of digestion and on the liver. It is an aid to digestion and an efficient painkiller. Drink peppermint tea to cool you down in summer; the leaves may be chewed both to freshen the breath and to relieve toothache and mouth sores. Rub a little peppermint oil or fresh juice on your forehead and temples to relieve headache; drop a few drops in your ear for earache; rub some on mosquito bites to relieve itching.
Peppermint is not a common enough ingredient in American culinary practice to find nutrient value statistics.
SWEETENERS
Nearly everybody in America believes that sugar is bad for you. In China, however, sugar is frequently used as a lubricant or as a key ingredient in many food cures. The reason for this difference is that, in the United States, sugar is found in bread, soft drinks, and canned foods, and is often added indiscriminately to savory food preparations. It is thus consumed in vast quantities. Large quantities of sugar are deleterious to health.
Small quantities of sugar, on the other hand, exert a beneficial effect. Sugar soothes the stomach and spleen. It strengthens the qi and blood, and provides energy to the body.
Brown sugar
_Sweet (Earth), warm, medium Yang_
Useful as an energizing tonic, brown sugar nourishes qi and promotes circulation of both qi and blood. It nourishes the liver, spleen, and stomach. Mixed with rice wine, brown sugar raises low blood pressure.
Genuine brown sugar is less damaging than white sugar (sucrose) because some of the minerals from the original sugar cane are intact. The less refined the sugar you consume, the better. Undoubtedly the best sugar source is blackstrap molasses, the syrup left over after the sucrose (white sugar) has been extracted. Molasses contains all the nutrients and minerals of sugar cane in a more concentrated form. Sugar products are rare in China, however, and molasses is virtually unknown. It does not therefore appear in any Chinese home remedy.
It should also be noted that what is often sold commercially as brown sugar is merely the white refined variety, with some molasses added for coloring.
Protein, 0.1 g; Fat, 0.2 g; Fiber, 0 g; Carbohydrate, 9.1 g; Vitamin A, 6 IU; Vitamin B1, 0 mg; Vitamin B2, 0.002 mg; Niacin, 0 mg; Vitamin C, 0 mg; Calcium, 10 mg; Phosphorus, 10 mg; Iron, 1.1 mg. Note that these figures vary according to the degree of refinement.
White sugar
_Sweet (Earth), neutral, medium Yang_
Sugar's dual function in Chinese remedies is to sweeten otherwise unpalatable dishes and to give a quick rush of energy. It is said to lubricate the lungs, produce fluids, and nourish the spleen and liver. Sugar syrup (ordinary sugar boiled in water) is used in China to treat stomachache.
It should be noted that, in the Chinese diet, sugar is consumed in much smaller quantities than in the average American diet. Even though it appears as a main ingredient in several home remedies, it is best to refrain from taking any additional white sugar. We consume so much of it in the form of soft drinks, sweets, and industrially prepared foods that we still take far more than is good for us.
These are some of the drawbacks of eating white sugar. White sugar needs vitamins of the B complex in order to metabolize, so its consumption depletes your B vitamins. As well, the proper digestion of sugar is dependent upon calcium. White sugar can therefore deplete your bone calcium, including the calcium of your teeth. Sugar also causes dental damage because it forms a plaque on the teeth, which produces an acid that corrodes the teeth. Sugar raises cholesterol and triglycerides, which can be dangerous for the heart. Sugar increases uric acid in the bloodstream, a precursor to gout. Sugar combined with a salty diet raises blood pressure. Too much refined sugar overworks the pancreas, leading to its exhaustion and the possibility of diabetes.
Because sugar contains no vitamins in and of itself, and in fact depletes the body's nutrients in the process of metabolizing, it is best not to indulge in white sugar too often.
BEVERAGES
The most common beverage in China is tea, green tea being the most popular. Water is drunk, of course, but not icy cold. Indeed, it is usually sipped steaming hot, or at least warm. In China it is believed that cold water blocks digestion, whereas hot water aids circulation and dissolves fats.
Alcoholic beverages are consumed without qualms, often for social reasons but frequently for purely therapeutic purposes. The most common form of alcohol is distilled rice wine. Beer is also very popular. Grape wine is produced in China in small quantities, but has not yet made its way onto the Chinese dinner table.
Milk
_Sweet (Earth), neutral, mild Yang_
Chinese people do not drink much milk. This fact may account for the low levels of calcium among Chinese children, and the subsequent problem of weak bones. During our research we came across a number of remedies for this deficiency, from bone gruel to mashed eggshells. We have not included these simply because we do not believe that weak bones due to lack of calcium is a problem in the United States, where milk and milk products are consumed in abundance. Also, in only two of the counties surveyed were dairy products consumed in significant quantities, those being Tuoli in the predominantly Muslim and Ugyur region of northwest China and Xianghuang Qi in inner Mongolia. Neither is within the historical boundaries of China. Residents of Tuoli obtain 52.6 percent of their calories and 72.5 percent of their protein from milk and dairy products.
As a matter of interest, unless one is allergic to milk products or is lactose-intolerant, large consumption of dairy products appears to have no detrimental effects on health. The positive effects, on the other hand, are many.
Milk acts as a tonic for the stomach and lungs. It lubricates the intestines and thus counteracts constipation. It is easy to digest and facilitates digestion in general. It has a mild, sedative effect and is thus a remedy for insomnia.
Protein, 3.5 g; Fat, 3.9 g (whole), 0.1 g (nonfat); Fiber, 0 g; Carbohydrate, 4.9 g; Vitamin A, 160 IU; Vitamin B1, 0.04 mg; Vitamin B2, 0.17 mg; Niacin, 0.1 mg; Vitamin C, 1 mg; Calcium, 118 mg; Phosphorus, 93 mg; Iron, 0.1 mg
Tea, green and black
_Bitter and sweet (Fire and Earth), cold, Yin_
Tea originated in China in ancient times—its botanical name, _Camellia sinensis_ (Chinese camellia) tells us as much. Tea was probably first used as a flavoring for the unpleasant tasting water of the Yelow River basin. It was soon discovered that, as well as rendering water drinkable, tea was a nervous system stimulant and an aid to digestion. It has been much prized both as a drink and as a health aid ever since.
All tea, green and black, comes from the same plant; the differences between varieties depends on two main factors. The first of these is habitat conditions, including the soil and climate. The second factor is the degree of processing that the tea leaves undergo between plucking and packaging. Green teas are the least processed: the leaves are "withered" (naturally dried) and then packaged. Oolong teas are withered and then slightly fermented. Lapsang souchong tea is withered, fermented, and smoked. Black teas are withered, fermented, and dried.
Tea is recognized as a diuretic and a mild stimulant. In 1991, studies in cancer research carried out by Dr. Alan Conney demonstrated that tea may also help in combating cancer. Three groups of mice were administered high doses of cancer-inducing drugs with their food. One group of mice was given nothing but water to drink. Another drank black, fermented tea, and a third group drank only green tea. At the end of the sixteen-week experiment all the mice were dissected and examined for cancerous tumors. While the water-drinking and black-tea-drinking mice each had, on average, eighty-five tumors in their bodies, the green-tea-drinking group had developed only fifteen tumorous growths, 80 percent less than the others.
In a second experiment Dr. Conney exposed the mice to strong ultraviolet rays. Ninety percent of the water-drinking mice developed skin cancer, while less than 30 percent of the tea drinkers were affected by the disease. Studies conducted in Israel, Norway, and Japan have indicated that tea might also be beneficial in bringing down cholesterol levels.
Tea is used in China to cure headaches, colds, indigestion, dysentery, and acute gastroenteritis. Ground into a powder and applied externally to the skin two or three times a day, tea leaves are said to eliminate herpes zoster. On the downside, tea can cause constipation. Note that green tea, untreated and unfermented, is said to be better than black, smoked, or flavored teas.
The following nutritional values are for black tea only. Green tea is just now making a wider presence in the American market. As a consequence, nutritional values for green tea are not shown in any of the reference books currently available. Although no precise figures are given here, green tea is known to contain thiamine, riboflavin, niacin, folic acid and biotin, potassium, manganese, magnesium, copper, zinc, and sodium.
Protein, 0 g; Fat, 0 g; Fiber, 0 g; Carbohydrate, 0 g; Vitamin A, 0 IU; Vitamin B1, 0 mg; Vitamin B2, 0.03 mg; Niacin, 0 mg; Vitamin C, 6 mg; Calcium, 0 mg; Phosphorus, 1 mg; Iron, 0.04 mg
Wine
_Sweet, bitter, and pungent (Earth_ _,_ _Fire, and Metal), warm, Yan_ _g_
The term _wine_ here refers not to grape wine but to spirit—generally rice spirit or that of sorghum or other grain.
Wine may be taken alone in order to stimulate blood circulation, relieve cold-syndrome diarrhea, or alleviate arthritic problems. It influences the heart and the liver, and, to a lesser extent, the stomach and the lungs. However, since ancient times medicinal herbs, roots, and other ingredients have been macerated in wine in order to treat specific ailments. In China it is believed that any ingredient that you can prepare with a rice congee or gruel can also be macerated in wine. The congee will affect qi, while the wine will affect blood circulation.
Wine used for medical purposes should be between 50°f and 60°f. It is normally white, however, on occasion yellow wine is used. Wine has no nutritive value.
CONDIMENTS
Condiments are used the world over for the sole purpose of enhancing the flavors of foods. A flavor enhancer frequently associated with Chinese cuisine is monosodium glutamate (MSG)—the allergic reaction associated with an overconsumption of MSG is often referred to as "Chinese restaurant syndrome." In actual fact, in China only poor cooks add MSG to food in order to improve their otherwise uninteresting preparations. MSG has no flavor of its own, but exerts its effect directly on human taste buds so that we experience meats, fish, and vegetable dishes as more savory.
In spite of extensive negative press in recent years, MSG has no adverse effects unless you happen to be allergic to it, suffer from arteriosclerosis or high blood pressure, or consume it in massive quantities.*2 However, although MSG may not be as bad for us as many people believe, it serves no useful health purpose either. It therefore has no place in any of the recipes described in this volume except one: Chinese chicken salad (see page 193). This hot mustard-based dish is assured an extra kick with the addition of a few grains of MSG.
Many other condiments serve important therapeutic purposes.
Olive
_Sweet and sour (Earth and Wood), neutral, balance of Yin and Yang_
Olives nourish qi and blood. They relieve sore throat and dryness in the bronchi and lungs—keep an olive under your tongue when suffering from a sore throat. Olive counteracts alcoholism. An olive and ginger decoction will relieve dysentery and diarrhea.
Green: Protein, 1.5 g; Fat, 13.5 g; Fiber, 1.2 g; Carbohydrate, 4 g; Vitamin A, 300 IU; Vitamin B1, traces; Vitamin B2, traces; Niacin, traces; Vitamin C, traces; Calcium, 87 mg; Phosphorus, 17 mg; Iron, 1.6 mg
Black: Protein, 1.8 g; Fat, 21 g; Fiber, 1.5 g; Carbohydrate, 2.6 g; Vitamin A, 60 IU; Vitamin B1, traces; Vitamin B2, traces; Niacin, traces; Vitamin C, traces; Calcium, 87 mg; Phosphorus, 17 mg; Iron, 1.6 mg
Pepper (black and white)
_Pungent (Metal), hot, Yang_
Pepper has a strong warming effect on the stomach and intestines; it is therefore useful in clearing digestive and abdominal problems due to cold syndromes. Five or six corns of black pepper, ground and mixed with honey or brewed in a tea, are an aid to good digestion. Pepper should, however, be steered away from in summer or when suffering from hot- and dry-syndrome diseases.
White pepper is just black pepper without the skin. It has the same warming effects as black but is slightly more irritating to the taste buds. For medicinal purposes, white pepper is used more frequently than black.
Black: Protein, 4 g; Fat, 2 g; Fiber, –; Carbohydrate, 28 g; Vitamin A, 80 IU; Vitamin B1, 0 mg; Vitamin B2, 0.2 mg; Niacin, 0 mg; Vitamin C, –; Calcium, 180 mg; Phosphorus, 80 mg; Iron, 12.2 mg
White: Protein, 6 g; Fat, 2 g; Fiber, –; Carbohydrate, 34 g; Vitamin A, –; Vitamin B1, 0 mg; Vitamin B2, 0 mg; Niacin, 0 mg; Vitamin C, –; Calcium, 120 mg; Phosphorus, 80 mg; Iron, 6.8 mg
Pepper (red or cayenne)
_Pungent (Metal), hot, Yang_
Red pepper exerts a strong heating effect on the body, thus stimulating the heart, the spleen, the stomach, and all the digestive processes. It is believed in many countries, including China, that the consumption of cayenne pepper lowers cholesterol in the blood and therefore protects against heart disease. The consumption of red pepper is also said to soften the blood vessels, thereby alleviating arteriosclerosis and hypertension. Red pepper is useful as a disinfectant in hot climates, where bacteria thrive and can spoil fresh food in a matter of hours.
Protein, 4 g; Fat, 6 g; Fiber, –; Carbohydrate, 20 g; Vitamin A, 14,000 IU; Vitamin B1, 0.2 mg; Vitamin B2, 0.4 mg; Niacin, 4 mg; Vitamin C, 20 mg; Calcium, 60 mg; Phosphorus, 100 mg; Iron, 2.8 mg
Salt
_Salty (Water), cold, Yin_
Salt, like sugar, has received a lot of bad press in the West: salt leads to edema; it also hardens the arteries and increases blood pressure. Its consumption has been linked to heart disease and thrombosis. Salt, however, can also serve useful therapeutic purposes. Taken in small doses, it stimulates the kidneys and facilitates the functions of the abdominal organs. It softens hardened glands and muscles. It has a cooling effect on the blood, and serves to maintain cellular health.
In China, salt is commonly used as a remedy against abdominal pains. It can either be added to an equal quantity of rice wine and swallowed in one gulp, or it can be heated and pressed against the abdomen in a towel. Salt is also used as a cure for athlete's foot and, when drunk with water, as a remedy for constipation. Drinking large quantities of salt water is a quick way to induce vomiting in cases of food poisoning. Finally, salt is used in China as a mouthwash and oral cavity disinfectant. When no toothpaste is at hand, it is common to brush one's teeth with salt instead.
As is the case with sugar, refined salt (virtually pure sodium chloride) is less advisable than rock or sea salt. The latter contains useful "impurities" such as iodine that are beneficial to health. Refined salt contains no nutrients.
Seaweed
_Salty (Water), cold, Yin_
All varieties of seaweed are a good remedy for goiter because of their high iodine contents. Seaweed is also used in Chinese medicine for curing hypertension and as an expectorant for chronic bronchitis. Seaweed is rich in minerals that it absorbs from the sea bottom and is therefore a general tonic for all physical and mental functions. It is important to point out, however, that the seaweed must come from a nonpolluted seabed. Seaweed is an important part of people's diet in the coastal Zhejiang province of China. Being a highly industrialized area, many pollutants are discarded directly into the sea. It may not be a coincidence, therefore, that there is an extremely high correlation (82%) in Zhejiang province between rectal cancer and the consumption of sea vegetables.
Fresh: Protein, 1.7 g; Fat, 0.6 g; Fiber, 0 g; Carbohydrate, 9.6 g; Vitamin A, 116 IU; Vitamin B1, 0.05 mg; Vitamin B2, 0.15 mg; Niacin, 0.5 mg; Vitamin C, 20 mg; Calcium, 168 mg; Phosphorus, 42 mg; Iron, 2.85 mg
Dried: Protein, 8.5 g; Fat, 3.0 g; Fiber, 0 g; Carbohydrate, 48 g; Vitamin A, 580 IU; Vitamin B1, 0.25 mg; Vitamin B2, 0.75 mg; Niacin, 2.5 mg; Vitamin C, 100 mg; Calcium, 840 mg; Phosphorus, 210 mg; Iron, 14.25 mg
Soy sauce
_Sweet and salty (Earth an_ _d_ _Water), thermally neutral, Yan_ _g_
Soy sauce is used principally as a flavor enhancer. Because of its high sodium content, the excessive use of soy sauce can be deleterious to health. Sodium is known to harden the arteries and to increase blood pressure, however it is also added to food as an aid to digestion.
Soy sauce is commonly used as an application to alleviate the pain from bee or wasp stings; in the Chinese countryside it is sprinkled or lightly daubed on burns.
Protein, 2 g; Fat, 0 g; Fiber, 0 g; Carbohydrate, 4 g; Vitamin A, 15 IU; Vitamin B1, 0.11 mg; Vitamin B2, 0.05 mg; Niacin, 0.5 mg; Vitamin C, 3 mg; Calcium,10 mg; Phosphorus, 45 mg; Iron, 0.38 mg
Vinegar
_Sour and bitter (Wood and Fire), warm, weak Yin_
Chinese vinegar is usually made from rice, wheat, or sorghum. Vinegar stimulates the circulation of the blood, aids digestion, increases appetite, and detoxifies.
Studies conducted at the Research Institute of Epidemic Diseases at the Chinese Academy of Science in Beijing indicate that vinegar acts as a disinfectant. Using vinegar in this way, many people boil vinegar in the home during winter to guard against catching colds or the flu; many rural northern Chinese homes smell quite strongly of vinegar. This same method of boiling vinegar is used in higher dosage to arouse somebody who has fainted. Vinegar is frequently prescribed to treat hepatitis.
Vinegar has no nutritive value.
_Chapter 5_
CHINESE HOME REMEDIES FOR COMMON HEALTH CONDITIONS
Chinese medicine does not generally make clear distinctions between home remedies and official pharmacopoeia. Drugs and food merge in many preparations; however, drugs on their own can never take the place of food.
Most of the remedies in this chapter are food cures. They can be taken over long periods of time for daily nutrition as well as for curing ailments. Many can be taken regularly, even every day, for the rest of your life. If you tend to suffer from constipation, for example, there is no harm in eating two soft, very ripe bananas every morning and evening from now to eternity. However, although none of the remedies will produce ill side effects, a few are nonetheless best taken for short periods only. It would be rash, for example, to eat twenty egg yolks every day (a remedy for dysentery) or to consume bitter apricot kernels (a medium-grade drug in Chinese terms; see page 38) for more than two weeks at a time. Some remedies by nature are not to be taken for too long. This fact will be pointed out both in the written text and by means of the symbol .
At all times, simply use common sense and maintain a generally balanced diet for your body type and the time of year. Don't stick to a hot ginger cure for asthma, for example, if it's the middle of summer and you have a heat rash. The ginger will only make matters worse. Cure the acute problem first and return to your long-term therapy afterward.
When curing problems, one danger that you must always beware of is that of "treating the head when the head aches, treating the foot when the foot hurts," that is, treating the symptoms but not the disease. As you diagnose your condition, don't be superficial. Take a little time to wonder why you are suffering from something as seemingly innocuous as indigestion: was it the cold, too much to eat, or something specific in your food? What brought on your latest asthma attack? See a doctor first and listen to his or her diagnosis, then decide upon an appropriate Chinese food cure.
Occasionally you may come across recipes containing some particularly unpleasant ingredient—nothing toxic or dangerous, but not particularly palatable either. These recipes are described more for their authenticity than for practical purposes, although there is no harm in trying them if you wish to. As well, while traditional Chinese medicine tends toward ingestion of food or herbs as the primary remedy, sometimes massage, skin applications, or insertion of medicaments into orifices (such as garlic drops in the nostrils to cure a runny nose) are suggested. Where feasible, we have included these under the appropriate health problem.
Don't expect miracles. A natural cure always involves a slow process of fine adjustments. It takes time for the body to get out of balance, and time to get back in balance again. Patience is of the essence.
Most of the remedies described in the following pages are straightforward and simple to prepare. No special expertise is necessary. Nevertheless, a few traditional aspects of preparation may be helpful to define.
COOKWARE
In China we traditionally steam rice and vegetables in earthenware, and stir-fry in an iron _guo_ (in English, a "wok"). While these are still considered to be the best utensils, today enameled and stainless steel vessels are used as well. As far as we know there are no health hazards in using any of this cookware. Aluminum, however, may be less safe. Medical evidence links aluminum to Alzheimer's disease (senile dementia); heavy deposits of this metal are found on the brain synapses of Alzheimer's patients. It is not yet known whether aluminum causes Alzheimer's disease or whether the disease encourages the mineral to deposit. Until we know more conclusively, it may be preferable to stay away from aluminum foil and cooking utensils altogether, especially for preparations using acid foods, such as lemon, onion, tomato, or vinegar. The acid tends to corrode, and thus carries more aluminum molecules into the body.
METHODS OF PREPARATION
**Chopping**
Chop your ingredients manually. Traditionalists claim that if you use a blender, the cutting speed and the heat generated will destroy many of the food's essential characteristics. The point is arguable, but there is, we believe, a psychological advantage to manually preparing your ingredients, as it involves time and attention and active care for the process of healing. If it is true that half our battles with illness are won or lost on psychosomatic grounds, spending time to wash, prepare, and concoct our medications by hand will put us in a more receptive frame of mind for taking them than if we simply swallow what an appliance machinates.
**Grinding**
Grind manually using a stone pestle. An alternative would be to grate the raw food, if appropriate.
**Crushing**
You can crush garlic, ginger, and onion by pressing down firmly on the food with the blade of a wide knife. Crushing makes the juice of the food more available.
**Shredding**
Shredding meat makes it more tender when cooked. To shred, first cut the meat into wide slices against the grain of the long muscle fibers. Then stack the slices and cut in the opposite direction. The pieces should end up being about 2 inches (5 centimeters) long and ¼ inch (6 millimeters) wide.
**Squeezing Juice**
While using a juicer is obviously the easiest way to obtain a food's liquid, it has the same drawbacks as using a blender for chopping. The traditional way to squeeze juice out of fruits, roots, and vegetables is to first either grate or chop the raw food into small pieces, then put it in a thin, clean cotton cloth. Squeeze by forming a bundle and tightening the cloth, twisting it in a viselike manner to extract the liquid.
**Steaming**
In China we have been steaming food for at least eight thousand years: the oldest cooking pots found in Neolithic villages in the Yellow River basin are terracotta steamers. Steaming is one of the healthiest ways of cooking food. Frying alters a food's chemical composition, and boiling it causes many of the minerals and vitamins to be lost in the water. Steaming, on the other hand, best retains the food's color and nutritional value.
In order to steam you will need a large pot and a bamboo (or metal) steamer. Traditional Chinese steamers are round bamboo baskets that fit one on top of the other, thus enabling you to steam several dishes at the same time. If one or more of your ingredients are liquid, you will also need a ceramic bowl that fits into the steamer.
Place the food that you want to steam inside the steaming dish. Pour enough water into the bottom of the pot to produce steam for as long as your food cooks, then place the steamer containing your ingredients inside the pot. The steamer must fit comfortably, as there needs to be enough room for steam to circulate freely around the food; make sure, however, that the steamer is seated high enough that the boiling water will not come in contact with the food. Cover the pot with a tight-fitting lid.
In order to steam successfully, the water in the pot must actively boil. The steam from anything less than rapidly boiling water will not be sufficient to cook your food. You generally know the food is ready when you can smell it in the steam escaping from the lid.
**Stir-frying**
Although not generally a mode of preparation for food remedies, stir-frying is a common means of Chinese food preparation. Use a guo, referred to in English as a wok, or an ordinary frying pan. The guo or frying pan should be large enough to make stirring easy.
Use very little oil when stir-frying. In China we use peanut, corn, rape, or sunflower oil. Olive oil has recently become popular as well. Traditionally, sesame oil is considered high-quality oil, and black sesame oil is considered to be the best of all. Sesame oil is precious however, and these days is expensive. It was traditionally used only as a condiment in any but the imperial kitchens of old.
For vegetable dishes you may dispense with oil altogether. Use a nonstick guo, or use a little water instead of oil.
Cut your ingredients into pieces small enough to be cooked in 1 to 3 minutes. Use high heat and stir constantly.
**Roasting**
Roasting is a process of heating foods in a frying pan or wok without using either oil or water. Heat until the ingredient is dry and begins to brown on the outside. This procedure is frequently required for ingredients that need to be ground into a powder.
**Decocting**
To this day, medicinal decoctions are prepared exclusively in earthenware pots. These are specially designed crocks with a handle and spout. No household in China is complete without one.
To prepare a decoction, wash and chop the ingredients. Add water and boil over a low to medium flame for 10 to 15 minutes. (Specific measurements and times will be given in the recipes.) Unless otherwise instructed, always cover the pan to keep the essential oils and other active ingredients from escaping into the air. Allow to cool, then drink the decoction warm or at room temperature. If you wish to, you may eat the boiled ingredients.
**Storing**
Unless specified in the recipes that follow, no preparation should be kept for more than a few days. Freshness assures that all the food's healing properties are intact. You may extend the life of your food remedy by putting it in the refrigerator (but not the freezer). Make sure, though, that you do not consume it refrigerator-cold; always allow it to reach room temperature before ingesting. Reheat gently if the remedy is to be taken hot.
SPECIAL INGREDIENTS
**Vinegar**
The traditional vinegar of Chinese medicine and cuisine is derived from rice. (Rice vinegar can be found these days in most health food stores.) Any vinegar made from fruits or cereals will do, however apple cider vinegar or red grape wine vinegar are among the best.
**Wine**
In China, _wine_ usually refers to "rice spirit," or _sake_ as it is generally known in America. Sorghum or bamboo spirit is also used. What is important in Chinese recipes is not so much the flavor or origin of the wine but its light warming and rising effects. Many liquor stores stock sake and Chinese rice wine, though if you cannot find it, any wine or spirit will do.
**Ginger**
Ginger is one of the most important ingredients in Chinese healing cuisine. Although ginger has been exported to the West since the first century A.D., this pungent rhizome is native to southeast Asia and China, where it has been used as a flavoring, a spice, a food, a mouth cleanser, and a medicine since ancient times. The medicinal uses of ginger are many. Ginger stimulates the lungs, the stomach, and the spleen. Ginger has sweat-inducing (diaphoretic) qualities that render it a useful remedy for the common cold and influenza. It relieves nausea. A slice of ginger or some ginger juice will suppress motion sickness. Ginger combats indigestion and flatulence. It is also a strong anticoagulant; a few slices of this rhizome can guard against blood clots, and thus help prevent heart attack or thrombosis.
Ginger may be taken either fresh or dry.*3 Most of the recipes in this book that include ginger state that it should be fresh. Raw, fresh ginger exerts a milder effect than the dry rhizome; it is also easier to come by in supermarkets. Except when the remedy calls for squeezing the ginger for its juice, you may, if you wish, use dry ginger instead. Where fresh ginger only warms, dried ginger is stronger, more pungent, and has a heating and diaphoretic effect on the body. You may therefore want to take dry ginger for the extra punch, and in winter.
**Rice**
Rice grows all over China; each area has its own favorite variety. The most commonly used Chinese rices are similar to basmati or Thai jasmine rice. You can use either of those rices for all the recipes in this book. Both basmati and Thai jasmine rice can be found at natural foods stores.
**Rice congee** is simply overboiled white rice. To prepare a congee, put 1 cup of rice and 5 cups of water in a saucepan, over a medium-high flame. No salt, stock, or spice of any kind is added. When the water boils, turn the heat to medium; cover the pan and simmer for 20 minutes, stirring occasionally lest the rice stick to the bottom of the pan. The rice is boiled until it is soft and mushy. If necessary, add water every now and then so that you end up with a watery gruel.
**Dried Flowers and Leaves**
Several medicinal remedies in this chapter use dried chrysanthemum flowers, rose petals, and other plant parts. What you can't collect in the outdoors close to your home you can likely pick up at a Chinese grocer. Such plant preparations will sometimes be packaged as tea.
**Bitter Apricot Kernel**
As discussed on page 38, bitter apricot kernel is somewhat toxic and is thus considered a medium-grade drug in Chinese pharmacology. Bitter apricot kernel is used to relieve cough, and as a treatment for asthma and acute or chronic bronchitis. It should not be eaten raw, or consumed for more than ten consecutive days. You can find bitter apricot kernel in Chinese pharmacies.
**Bitter Melon**
Bitter melon looks like a cucumber, but the color of the skin is much lighter. You can find bitter melon in Chinese groceries and in some supermarkets. Before cooking, split the melon lengthwise and discard the white part in the middle of the fruit.
**Rock Sugar**
Rock sugar, sometimes called rock candy, is sold in Chinese groceries. It is light brown in color and is less refined than the white rock sugar sold in candy stores.
Having discussed the special ingredients and basic methods of preparation, we are now ready to look at many common ailments and health conditions that can be successfully treated with Chinese food and home remedies. We have listed these health conditions alphabetically. After a brief discussion of the problem from the point of view of both Chinese and Western medicine, we describe the remedies—the remedies are loosely grouped according to their main ingredients. The ingredient lists use standard measures, with approximate metric equivalents following in parentheses. We show the relative ease of preparation of the remedy, and the availability of the ingredients, by means of the following symbols.
**Key to Symbols**
| | Easy recipe; can be prepared in a matter of minutes.
---|---|---
| | Medium difficulty; takes a little time to prepare.
| | A complex recipe that takes time and a little effort to prepare.
| | All ingredients can be purchased with ease.
| | Some of the ingredients may be difficult to find. You may have to go to a Chinese merchant in your area, or mail order the ingredients. An address list of select Chinese grocers willing to fill mail orders is given in appendix 2.
| | Not recommended over long periods. Some ingredients are either bad for the health if taken for too long, or are slightly toxic (a second- or third-grade drug according to the Chinese classification of toxicity; see page 35).
ABDOMINAL PAINS
Abdominal pains are the physician's nightmare. They can have as many causes as there are diseases, ranging from cold to cancer. They may arise from the muscles of the abdomen, or from the diaphragm, the stomach, the spleen, the gallbladder, the large or small intestines, the appendix, the kidneys, the liver, or the nervous system. Consequently we cannot offer any remedies for abdominal pains without the risk of treating one problem for another, and thus bypassing the real cause altogether.
What we can do, and what the Chinese do before resorting to professional medical help, is to attribute the pains to the simplest possible causes and to take appropriate remedial action. If the pain persists, then you go to the doctor.
The simplest causes for abdominal pain are pathogenic cold (in Chinese terms), blocked digestion of food, and psychological distress.
Pathogenic cold can take hold of the body by two means: by simply catching cold, or by overeating raw or cold food ("cold" in both senses of the word: either direct from the refrigerator, or cold by nature). The symptoms of pathogenic cold are strong, cramplike pains; scanty and runny stools; cold feet and hands; and feeling repulsed by anything cold. A condition arising from pathogenic cold is relieved when the abdomen is covered and warmed.
Abdominal pains from blocked digestion are accompanied by heartburn, indigestion, and lack of appetite; you may also have diarrhea. Going to the toilet relieves the abdominal pain. Poor digestion may also be due to a weak stomach and/or spleen. If this is the case, it manifests as abdominal cramps that grow worse when you are overtired or hungry.
Psychological distresses—such as anger, worry, and frustration—block the free flow of zheng qi through the body. This is said to weaken the liver, spleen, and stomach, with consequent bloating and tummy pains.
Remedies for cold-syndrome abdominal pains require the ingestion of hot or warming foods. It also pays to cover the affected area with woolens.
Salty Wine
3 tablespoons (45 mililiters) rice wine, or sake
5 teaspoons (25 grams) salt
In a small saucepan, heat the wine with the salt until the salt melts.
Drink hot—a single shot is generally sufficient.
Garlic and Ginger Broth
2 garlic cloves, peeled and crushed
2 teaspoons (10 grams) minced fresh or dry ginger
4 teaspoons (20 grams) brown sugar
2 cups (500 milliliters) water
Combine all ingredients in a small saucepan. Boil for 15 minutes over a low flame.
Drink the broth hot to warm, as often as you'd like. Eat the garlic and ginger pieces.
Garlic Tea
5 whole garlic cloves, peeled
2 cups (500 milliliters) water
1 tablespoon (15 grams) brown sugar or molasses (15 mililiters)
Combine the ingredients in a small saucepan. Boil for 15 minutes over a low flame. Remove from heat.
Drink 1 cup three times a day, following a meal. Prepare fresh on each occasion.
Ginger Vinegar
_In many Chinese homes, a bottle of ginger vinegar is always at hand for emergency treatment of abdominal pains._
½ cup (100 grams) fresh ginger, thinly sliced
1 cup (250 milliliters) rice wine vinegar
Place the ginger and vinegar together in a bottle. Cap the bottle and store. (The longer the vinegar is stored the better. Ideally you should leave it for a month, but a few hours will do in an emergency.)
Take 2 teaspoons every morning on an empty stomach.
Sometimes garlic is added for a richer brew: the proportions are ½ cup (100 grams) of ginger, ½ cup (100 grams) of garlic, and 2 cups (500 milliliters) of vinegar. The garlic cloves should be whole when added to the vinegar. Besides curing abdominal ailments caused by cold, ginger and garlic vinegar counteracts abdominal pains resulting from eating too much fruit.
Garlic Vinegar
12 whole garlic cloves, peeled
1 cup (250 milliliters) rice vinegar
Place the garlic cloves and vinegar together in a bottle. Cap tightly and store. Take 2 teaspoons every morning on an empty stomach, or as needed.
In the Chinese countryside some people store vinegar for two or three years before consuming. For a "fast food" version, however, one month is adequate. Garlic vinegar remedies cold pains as well as those due to psychological distress and an irregular lifestyle. (One wonders whether it is the garlic vinegar that cures the pains or just waiting for it that cures the lifestyle.)
Peach Kernel and White Pepper Pills
5 peach seeds
5 jujube (Chinese date)
8 white peppercorns
Break open the peach seeds and remove the kernels. Using a stone grinder or a pestle, manually crush the kernels together with jujube and peppercorns. Compress into swallowable pills.
Ingest with warm rice wine or warm red wine.
Cinnamon Water
1 teaspoon (5 grams) ground cinnamon
1 glass warm water
Dissolve the cinnamon in the water. Drink slowly.
To be effective, this remedy should be taken three times a day.
Cinnamon exerts a warming effect that is also useful in alleviating abdominal pains after childbirth. Again, drink 1 teaspoon of ground cinnamon dissolved in warm water three times a day.
**For cramps and muscular pains in the abdominal region, whatever the cause, the following remedies are recommended.**
Sesame, Walnut, and Ginger Paste
3/4 cup (150 grams) sesame seeds
3/4 cup (150 grams) walnut meats
3/4 cup (150 grams) dried ginger, chopped
3/4 cup (185 milliliters) honey
Grind the sesame seeds, walnuts, and ginger into a medium-grained powder. It is preferable to use either a stone grinder or a pestle. Roast the powder in a dry frying pan or wok for 2 minutes, or until it begins to brown. Transfer the powder to a small bowl. Mix with the honey while still hot.
Take ½ cup (100 grams) of paste on an empty stomach whenever you suffer from abdominal cramps and pains.
Hot Salt Compress
_When suffering from abdominal pains due to cold syndrome it is best to warm the affected area—the Chinese recommend wearing woolen clothes or wraps. You can also press a hot towel or muslin bag containing heated salt over your abdomen. You might want to try this when it is very cold, or if your pains are particularly bad._
1 cup (250 grams) rock salt
Dry cloth towel or muslin bag
Heat the salt in a dry frying pan or wok. When the salt starts to crack, transfer it to a dry towel or cloth bag. (If you are using a towel, fold it to create a pouch for containing the salt.)
Apply to your abdomen for five to ten minutes while lying down. Repeat three times a day. (You can use the same salt.) See also the salt and onion application recommended for diarrhea, page 132.
ACNE
Acne, an inflammation of the skin, affects 80 percent of people during adolescence and early adulthood. Acne occurs when oil from the sebaceous glands gets trapped under the skin, causing bacteria to multiply. The result is inflammation and pustules. Contributory factors to acne are oily skin (which may be hereditary), excessive male hormones, allergies, oral contraceptives, stress, alcohol, sugar, and junk food.
According to Chinese traditional medicine, acne is usually due to one of two possible causes: excessive heat in the lungs and stomach, or external cold interacting with too many alcoholic beverages. (Many Chinese are sturdy drinkers.) In the latter case the blood is said to "silt up"; the nose and the cheeks redden. Finally, the face erupts with acne. The complaint is worsened by psychological tension.
To treat acne, Western and Chinese doctors alike recommend that you avoid fat foods, sweets, and alcohol, and that you wash your face morning and evening with a mild, alkaline-free soap. Do not overwash—this will stimulate an overproduction of sebum as the body tries to replenish its lost oils. Lemon or lime juice can also be used for cleansing. In China, where lemons are not common, other ingredients are used for washing. These include:
* Mix celery and apple juice together in equal quantities. Apply to the face morning and evening.
* Cut a water chestnut in half. Rub the inside cross-section over your face two or three times a day.
* As soon as you wake up, apply your own saliva to the area affected by acne. When the saliva dries, apply again. Repeat throughout the morning.
Two simple food remedies for acne include eating plenty of raw cucumber, which exerts a cooling effect on the stomach and lungs, and drinking large quantities of hot green tea.
To finish, a simple recipe follows.
Walnuts and Orange Pips
2 walnuts, shelled
1 tablespoon (15 grams) dried orange seeds (you might wish to roast the orange seeds slightly in order to hasten the drying process)
Using a stone grinder or pestle, grind the walnuts and orange seeds into a fine powder. Roast in a dry wok for 2 or 3 minutes over low flame, or until the powder begins to brown. Remove the wok from the heat and allow the powder to cool.
Take all the powder with a small amount of rice wine twice a day.
ALCOHOLISM
Although it has been demonstrated that small doses of alcohol have dilative and cholesterol-cleansing effects on the arteries and veins, large quantities of alcohol are poisonous.
Short-term alcohol poisoning—otherwise known as inebriation—may cloud the intellect with temporary euphoria. Other effects such as slower reaction times, speaking incoherently, unsteadiness, and the morning-after hangover may be less welcome.
Long-term alcohol poisoning causes metabolic damage to every cell in the body. It brings about rapid aging, increases susceptibility to disease, and generally shortens one's life span by several years. Alcohol is broken down in the liver, where it is converted into fat; ironically, at the same time as it is being broken down by the liver it is destroying the cells of the liver. A damaged liver impairs metabolism and the processes of digestion and absorption of proteins and vitamins. In short, dependency on alcohol, be it physical or psychological, kills.
Although short-term alcohol abuse in China is fairly common, chronic alcoholism is not. People drink in short, hard bursts rather than out of habit. Liquor—usually rice wine—is quaffed at banquets and during celebrations. People drink when reciting poetry, or as a competitive game to see who gets drunk first. As a consequence, Chinese culture has many popular remedies for drunkenness, but none, besides sheer willpower, for chronic alcoholism.
There are several food cures in China for recovering a modicum of lucidity when drunk.
* The most common remedy for inebriation is to drink a cup of strong black tea; strong jasmine tea also works. Brew the tea as usual; just put more leaves in the pot. Strong tea tastes quite bitter. The sobering effect is enhanced if you do not add sugar.
* Radish juice and vinegar is another common remedy for inebriation. Squeeze ½ cup (125 milliliters) of fresh radish juice, then add 1 teaspoon (5 milliliters) of vinegar. Swallow the mixture in one gulp.
* An easy remedy is to crush 1 raw sweet potato and add sugar. Mix with hot water and drink.
* A quick remedy, if you happen to live in the tropics, is to drink a glass of green sugarcane juice.
* As a preventive measure, it is alleged that eating a persimmon before going on a drinking binge will prevent the ill effects of alcohol.
Some recipes requiring a little more preparation follow.
Mung Bean Soup
¼ cup (50 grams) green mung beans
1 cup (250 milliliters) cold water
Grind the mung beans into a fine powder using a stone grinder or a pestle. Transfer the powder to a glass.
Add water and mix. Drink immediately.
Tea and Mung Beans
¼ cup (50 grams) mung beans
1 teaspoon (5 grams) green tea leaves
2 cups (500 milliliters) water
Roast the mung beans in a dry frying pan or wok until they begin to brown. Allow the beans to cool, then grind them into a powder using a stone grinder or a pestle.
Bring the water to a boil. Put the mung bean powder into a teapot or large cup. Add tea leaves and hot water. Cover the teapot or cup, and steep for 10 minutes.
Drink hot, without sugar.
Black Bean Soup
4 cups (800 grams) black beans
8 cups (2 liters) water
In a soup kettle or large saucepan, boil black beans and water for 45 minutes. Keep the pan uncovered. The mixture will become quite thick as it boils. Check occasionally to make sure that it is not so thick that it begins to dry and burn; add a little water if necessary.
When the beans are done, take the pot off the stove and allow the mixture to cool. Drain, reserving the beans for another use.
Drink the soup, continuing until you throw up.
Orange Peel Soup
The peel of 1 organic orange
2 cups (500 milliliters) water
1/3 teaspoon (1.5 grams) salt
In a dry frying pan, roast the orange peel over medium heat until it turns light brown. Cool and grind to a powder.
In a small saucepan, combine orange peel powder, water, and salt. Boil for thirty minutes, covered.
Drink hot to warm.
Ginger Soymilk
2 teaspoons (10 grams) fresh or dry ginger, minced
1 cup (250 milliliters) soymilk
2 tablespoons (30 grams) rock sugar
Put all the ingredients into a small saucepan. Bring to a boil; continue to boil for 10 minutes.
Remove from heat and allow to cool slightly. Drink warm.
ANEMIA
Anemia results from a reduction of red blood corpuscles and, as a consequence, of the amount of oxygen that the blood is able to carry. Its early symptoms are poor appetite, dizziness, constipation, irritability, ringing in the ears, and headaches. Anemia is characterized by general fatigue and debility, and by pallid nails and inner eyelids.
Anemia is not a common ailment in China. Indeed, one quite surprising fact to emerge from a 1991 survey of Chinese diet, lifestyle, and mortality was that iron intake is much higher in China than in the United States. The reason for the difference puzzled the researchers, as the intake of iron-rich foods seems no higher in China than in America. Leaching of iron from food containers was not considered likely because such containers are not generally used in food storage. A tentative suggestion put forward by the researchers was that iron may simply be absorbed through dust; another possibility is the use of the traditional iron guo (wok) in food preparation. Nothing has been steadfastly agreed upon.
Despite its rarity, anemia is divided by traditional Chinese medicine into three categories:
1. Anemia resulting from a lack of iron in the diet.
2. Anemia brought on by loss of blood from wounds, heavy menstruation, an ulcer, or hemorrhoids.
3. Anemia caused by bone marrow disease, a damaged liver, a thyroid disorder, or rheumatoid arthritis.
Given these variations, whenever anemia is suspected a professional consultation to discover the underlying cause is mandatory.
Temporary, nonpathological anemia can be easily cured by increasing the intake of iron. Iron makes hemoglobin, which carries oxygen in the blood. Good natural sources of iron are apricots, jujube (Chinese dates), beets, grapes, lettuce, cashews, honey, blackstrap molasses, soybeans, and spinach. Liver and raw liver extract contain the elements essential for reconstituting the red blood cells. Iron tablets, an effective cure for temporary anemia, tend to cause constipation. Tannic acid, present in tea and coffee, and dairy products inhibit the absorption of iron. Vitamin C assists its absorption.
Some food remedies for anemia are quite simple.
* You can take 2 or 3 tablespoons (30 to 45 milliliters) of honey a day in any form: in warm water, with your breakfast cereal, on toast, or on its own.
* Another remedy is to tear 1 small fig leaf into strips, then decoct in 1 cup (250 milliliters) of boiling water. Drink the tea.
* You can also grind peanut husks into a powder; take 1 heaping teaspoon twice a day with warm water.
* Mix 2 or 3 tablespoons (30 or 45 milliliters) of raw carrot juice with the same amount of molasses. Take twice a day.
* It is also widely believed that boiled eggs with tomatoes taken as a salad two or three times a day, and 1 apple, 1 tomato, and 3 teaspoons of sesame seeds taken as a salad once or twice a day, will both cure anemia.
**Recipes involving a bit more preparation include the following.**
Soybeans and Jujube
1 tablespoon (15 grams) soybeans
Water for soaking
3 cups (750 milliliters) water
1 tablespoon (15 grams) jujube (Chinese dates)
1 tablespoon (15 grams) brown sugar
Soak the soybeans overnight in 1 cup (250 milliliters) of water. Drain.
In a medium saucepan, bring 1½ cups (325 milliliters) of water to boil. Add the drained beans and boil them for approximately 20 minutes. In a separate saucepan, bring the remaining 1½ cups (325 milliliters) of water to boil. Add the jujube and brown sugar. Boil for 10 minutes.
Add the jujube and their water to the black beans. Stir to mix.
Consume the entire soup warm, in one sitting. Take once a day; a full course of treatment lasts two weeks.
Tofu and Egg White
1 pound (500 grams) tofu, frozen
5 cups (1.25 liters) warm water
2 egg whites
Water for steaming
Place the frozen tofu in warm water. (Freezing tofu changes its texture, rendering it spongelike and thus capable of absorbing the egg white.) When the tofu has become soft, remove it from the water and transfer to a bowl holding the egg whites.
Soak the tofu in the egg whites for 5 minutes, then transfer to a large ceramic bowl. Put the bowl in a steaming dish (see page 66). Using a pot deep enough to fit your steamer, bring water to a boil. Put the steamer in the pot and cover. Steam the tofu for 15 minutes.
Remove from the steamer. Eat warm.
Liver and Spinach Stew
2 cups (500 milliliters) water
4 ounces (125 grams) calf's liver, cubed
½ pound (250 grams) fresh packed spinach
In a medium saucepan, bring the water to a boil. When the water boils, add the liver and spinach. Reduce heat to low and cover the pan.
Stew the mixture for 45 minutes. Check occasionally to ensure that the stew is not too dry; if necessary, add a little water.
Consume hot; eat the stew all at once. Take this remedy as often as you want.
Wood-ear Mushrooms and Jujube Dessert
¼ cup (50 grams) wood-ear mushrooms (also known as tree ears)
Water for soaking
3 cups (750 milliliters) water
30 jujube (Chinese dates)
Brown sugar to taste
Soak the mushrooms in 1 cup (250 milliliters) of hot water for 1 hour, or until soft. Drain.
In a small saucepan, bring the water to a boil. Boil the mushrooms and jujube until the jujube are soft, approximately 20 minutes. Stir in the brown sugar.
Consume in a single sitting, either warm or at room temperature.
ARTHRITIS
Arthritis, one of the most common diseases in China, is characterized by an inflammation of the joints. Rheumatoid arthritis attacks the synovial membranes of the joints, while osteoarthritis affects the bones. Both diseases are degenerative and deforming, and eventually affect the mobility of the limbs and joints. Their causes are hereditary, although cold, humidity, a faulty diet, stress, and emotional repression contribute to worsening the effects of these problems.
According to traditional Chinese medicine, arthritis is caused by the exogenous pathogens, specifically those of feng (wind), han (cold), and shi (dampness). These enter the main and collateral channels of qi circulation, thereby disturbing normal functions. The results are pain or numbness, and swelling in the joints and limbs.
Chinese remedial therapies for arthritis are based on correcting the effects of cold and dampness in one's food intake and in the environment. A person with arthritis should thus stay away from cold and damp foods and environments, and refrain from consuming too much red meat, sugar and sugar products, milk, fats, acid fruits (oranges and lemons), salt, and tobacco. Direct therapies on the affected areas of the body consist of heat and drug application. Movement exercises focused on the affected area are also beneficial. In fact, the most common treatment in China for arthritic disease is qi gong combined with massage and, if possible, acupuncture. See chapter 7 for detailed instruction in qi gong. You should prepare for your exercises by breathing deeply in the qi gong standing position, arms outstretched, for ten to fifteen minutes. Qi gong exercises that specifically loosen the joints are the Eight Brocade _ba duan jin_ series and _tai ji quan_. Hot baths and massage are also useful.
Theory alleges that you can cure a disease in your own body by eating the same body parts from a healthy animal. The classic Chinese remedies for arthritis consist of animals and animal parts, the consumption of which is not only abhorrent to most people in the Western world but is also cruel to the animals concerned. Some of the animals whose bones are so prized by many of China's arthritis patients are endangered; first and foremost of these endangered animals is the tiger.
Tiger and leopard bone and sinew have always been considered the prime remedy for arthritic diseases. Lip service is paid to protecting the animals, yet many Chinese texts still extol the virtues of tiger bone as a cure for arthritis. Tigers continue to be poached, their body parts openly sold in crowded markets.
Because of the difficulty and expense involved in obtaining the prized tiger, it has now become common to use dog bones as an arthritis remedy instead. Sometimes the dog bones are sold fraudulently as tiger; however, most often there is no deception involved. People eat dog meat and consume dog-bone preparations in the belief that these products warm the body and rid it of the external pathogens responsible for arthritis. (Lest some of our readers start getting ideas about their neighbor's bothersome dog, we shall not go into details of how these particular remedies are prepared.)
Deer antlers and tendons are other prized alternatives to tiger parts, as are pig, sheep, and monkey bones.
One recipe that, although unusual, we have few qualms about describing is snake soup. Although frequently seen in small countryside restaurants, particularly in the south of China, snake is not a common dish. It is considered something of an expensive delicacy, to be resorted to only for purposes of restoring good health. Snake meat has a delicate flavor, somewhere between that of chicken and fish. It is highly prized in China. Fresh snake blood and snake bile are drunk with rice spirit; they are said to augment qi and to reinforce the internal organs of digestion. Snake meat is normally eaten in a soup, with the bones included as part of the broth.
Dragon and Phoenix Soup
5 ounces (150 grams) snake meat, cut into 2-inch-long pieces
3½ ounces (100 grams) chicken breast, cut into narrow, 2-inch-long pieces
3/4 ounce (20 grams) ham, cut into narrow, 2-inch-long pieces
3½ ounces (100 grams) bamboo shoots, optional
4 cups (1 liter) water
5 slices fresh ginger
2 teaspoons (10 milliliters) cooking wine, optional
2 teaspoons (10 milliliters) sesame oil
Pepper and salt to taste
Place the meat and bamboo shoots in soup pot. Add water, ginger, and cooking wine (if desired). Cook over a low flame, covered, for 1 hour, or until the snake meat turns white. Add sesame oil, pepper, and salt.
Serve warm.
Snake and Black Bean Soup
1 adult snake, the more venomous the better
1/3 cup (65 grams) black beans
5 slices fresh ginger
10 jujube (Chinese dates)
Water to cover
Salt to taste
In order not to risk snakebite, it is probably preferable to have a professional catch, kill, and skin the snake for you. If you must do it on your own, hold the snake firmly behind the head and away from your body. Cut its head off, being careful not to touch the severed head—the venom is still present and the snake can still bite through muscular contraction. Most people in China collect the snake's blood in a glass, add rice spirit, and drink it in a single gulp.
Skin the snake and clean out the innards. Chop the snake meat into 2-inch-long segments.
Place all the ingredients into a soup pot. Add enough water to cover. Put the lid on the pot. Cook on a medium flame for 1 hour, or until the beans are soft, stirring occasionally. Add salt according to taste.
Serve as part of a several course meal.
Silkworm Excrement Wine
_Perhaps the main problem with this recipe is obtaining silkworm excrement. If you do not live close to a silk-producing area, it is unlikely that you will come by any very easily. However the recipe is interesting, and if you ever happen to go to China, or to where silkworms are abundant, you might wish to try it. Silkworm excrement is said to rid the body of evil wind and dampness._
3 to 4 tablespoons (45–60 grams) silkworm excrement
2 cups (500 milliliters) water
1 shot rice wine, or sake
Place the silkworm excrement in a cloth bag.
In a small saucepan, bring the water to a boil. Add the cloth bag. Cover the pan and continue to boil for 10 minutes.
Add the rice wine, cover the pan, and allow to boil for another minute. Remove from heat.
Divide the wine into three cups. Drink one cup in the morning, one in the afternoon, and one in the evening for as long as the pain persists.
**A few more practical recipes for our less adventurous readers follow.**
White Bean and Jujube Congee
4 tablespoons (60 grams) white black-eyed peas
10–15 jujube (Chinese dates)
2 tablespoons (30 grams) minced fresh ginger
Scant ½ cup (100 grams) rice
4 cups (1 liter ) water
Salt or honey to taste
Put all the ingredients in a medium saucepan and bring to boil over a high flame. Turn the heat to low, cover the pot, and simmer for 30 minutes, or until the rice is soft and mushy. Stir occasionally.
Remove from heat. You may, if you wish to, add either salt or honey for flavor.
Eat whenever your joints are swollen or numb, either for breakfast or before bed.
Fresh Cherry Wine
2 cups (400 grams) fresh cherries
4 cups (1 liter) rice wine, or sake
Wash the cherries. When they are dry, place cherries in a bottle with rice wine. Seal the bottle.
Let stand to macerate for at least 15 days. When aged, take 2 teaspoons twice a day.
Tofu and Scallion
3½ ounces (100 grams) tofu
3 cups (750 milliliters) water
1 tablespoon (20 grams) minced scallions
1 teaspoon (5 milliliters) sesame oil
Soy sauce to taste
In a medium saucepan, bring the water to a boil. Drop the block of tofu into the water and cover the pan. Boil for 10 minutes, then drain.
Cut the boiled tofu into cubes. Season with scallions, sesame oil, and soy sauce. Consume warm.
This remedy should be eaten as part of a meal. Take as often as you want.
Stir-fried Bean Sprouts
1 tablespoon (15 milliliters) peanut oil
1 cup (200 grams) bean sprouts
1 tablespoon (15 milliliters) cooking wine
Salt to taste
Heat the oil in a wok or frying pan. When the oil is hot, add the bean sprouts. Stir-fry for 20 seconds, then add the wine and a little salt according to taste. Continue to stir-fry for 30 seconds. Remove from heat and serve.
This dish is generally served as part of a several course meal, and is eaten with rice.
Bean-thread Noodles and Cucumber
1 cup (200 grams) bean-thread noodles
Water for soaking
2 cups (400 grams) cucumber, sliced
1 teaspoon (5 grams) salt
3 cups (750 milliliters) water
1 tablespoon (15 grams) minced scallions
3 tablespoons (45 milliliters) soy sauce
1 tablespoon (15 milliliters) vinegar
1–2 pinches white pepper
Salt to taste
Soak the bean-thread noodles in 2 cups (500 milliliters) of hot water for 10 minutes, or until soft. Drain.
In a small bowl, toss the cucumber slices with 1 teaspoon (5 grams) of salt. Let stand for 10 minutes to extract the cucumber juice. Drain.
In a medium saucepan, bring the water to a boil. Drop the bean thread in the boiling water. Boil for 5 minutes. Drain.
Mix the bean thread and cucumber with the scallions, soy sauce, vinegar, white pepper, and salt.
This dish may be eaten whenever your joints are swollen or feel hot.
**The following are recipes for compresses to be used on inflamed joints.**
Ginger and Vinegar Compress
4 tablespoons (60 grams) sliced fresh ginger
1 cup (250 milliliters) rice vinegar
2 cups (500 milliliters) water
In a medium saucepan, bring all ingredients to boil over a high flame. Turn the flame to low. Simmer for 5 minutes.
Soak flannel cloths in the hot liquid. Remove the cloths; keeping the liquid simmering in the pot, let the cloths cool to the point that they can be handled. Apply the cloths to the affected body areas.
After the flannel cools, soak and apply again. After 5 or 10 minutes of compress application, massage those same areas of the body to which the cloths have been applied.
Apply twice daily—once in the morning and once in the evening.
Scallion and Vinegar Compress
4 tablespoons (60 grams) chopped scallions, white heads only
4 cups (1 liter) rice vinegar
In a medium saucepan boil the vinegar over a medium flame, uncovered, until half of it has evaporated. Add the chopped scallions to the vinegar and boil for another five minutes.
Turn the flame to low. Soak flannel cloths in the hot liquid. Let the cloths cool to the point that they are possible to touch, all the while keeping the liquid simmering in the pot. Apply the cloths to the affected body areas.
After the flannel cools, soak and apply again. After 5 or 10 minutes of applications, massage those same areas of the body.
Apply twice daily—once in the morning and once in the evening.
Ginger and Honey Compress
2 tablespoons (30 grams) minced fresh ginger
1/3 cup (65 grams) taro root, peeled and sliced
1/3 cup (65 grams) white flour
2–3 tablespoons (30–45 milliliters) honey
Using a pestle, mash the ginger and the taro root into a fairly smooth paste. Transfer to a small bowl. Add the flour and 1 tablespoon (15 milliliters) of honey, mixing the ingredients by hand. Continue adding honey until you have a smooth paste.
Use a clean, dry cloth to collect the paste. Press to the painful joint or limb, and wrap.
Keep the wrap in place all day and night. Use for ten days to one month, changing the compress every 24 hours.
Chili Pepper and Ginger Compress
2 tablespoons (30 grams) chopped dried chili peppers
2 tablespoons (30 grams) chopped fresh or dried ginger
2 tablespoons (30 grams) white flour
2–3 tablespoons (30–45 milliliters) rice wine, or sake
In a small bowl, mix the chili peppers, ginger, and flour. Slowly pour the rice wine, or sake, over the dry ingredients, mixing to form a paste.
Apply the paste to the distressed joint or limb by means of a clean cotton cloth. Wrap or hold in place for half an hour, then wash with warm water and dry.
This compress may be applied twice a day, morning and evening, for as long as the discomfort persists.
ASTHMA
Asthma is generally hereditary in nature. It is characterized by attacks of coughing, wheezing, and gasping for breath. It is usually brought on by an allergic reaction to pollen, animal dander, mold spores, or foodstuffs. The only immediate remedy at the moment of an asthma attack is the administration of antihistamines such as epinephrine, and, in the most acute cases, of oxygen.
Chinese medicine tends to regard asthma as a weakness of the lungs brought about by climatic factors and worsened by poor eating habits and a stressful lifestyle. The first remedy, therefore, is to correct your errors.
The next obvious thing to do is stay away from the source of your allergy. If you are allergic to pollen or house dust, however, there is not a great deal you can do about it. In this case you should simply adopt the Chinese line of defense: get plenty of exercise; practice qi gong; stop smoking; do not fatigue yourself, either at work or in bed; and eat properly.
The latter advice includes eliminating unnecessary toxins from your diet by cutting down on (or dispensing altogether with) coffee, alcohol, strong tea, and fried and greasy food. Eat plenty of greens, fruits, beans, and cereals; eat less meat and few fats. Avoid hot, spicy, sour, salty, and very sweet foods. You should eat regular meals, never overindulging—get up from the dinner table knowing that you could eat a little more without stuffing yourself. Have dinner at least three hours before bedtime; eat slowly and chew properly. Drink plenty of water and fruit juices.
There are eight traditional Chinese remedies for asthma. Five are straightforward food remedies. One contains bitter apricot kernels (see page 69), which are slightly toxic; it must therefore be classified as a medicine rather than a food, and be taken for not more than ten days at a stretch. Another of the remedies for asthma involves the application of garlic to the sole of the foot. The last, involving fourteen eggs, has been practiced in China for centuries. We do not expect many people to try it, but have included it here because of its authenticity.
Many of the remedies for asthma use ginger as a main ingredient. Ginger is a warm and pungent tuber of the Jin (Metal) element. It is an outward- and upward-moving Yang ingredient that directly affects the lungs.
Fresh Ginger Juice
_This remedy is particularly effective for older people with asthma._
16–20 ounces (500+ grams) fresh ginger, peeled and grated
8 tablespoons brown sugar
Place the grated ginger in a thin cotton towel. Squeeze to extract ½ cup of juice.
In a small saucepan, heat the ginger juice. Add the sugar, stirring until it dissolves. Bring the mixture just to the boiling point, then remove from heat and transfer to a cup.
Take this preparation while it is still hot, sipping slowly. Take it as long as the asthma persists.
Daikon Juice with Ginger and Honey
1 4-ounce piece (125 grams) fresh ginger, peeled and grated
1 large fresh daikon, grated
2 tablespoons (30 milliliters) honey
Place the ginger and the daikon in separate thin cotton towels. Squeeze to extract 2 tablespoons of ginger juice and 1 cup of daikon juice.
Mix all ingredients in a small saucepan. Heat but do not boil.
Drink hot once a day.
Ginger and Rice Wine
_Rice wine enhances the warming properties of ginger by making them rise toward the Yang (higher) regions of the body._
2 cups (400 grams) fresh ginger, sliced thin
2 cups (500 milliliters) rice wine, or sake
3 cups (600 grams) rock sugar
Place the ginger in a medium saucepan with the rice wine. Bring to boil over a low flame. Add the sugar. Stir continuously as you simmer for another 20 to 30 minutes, until the mixture is a creamy paste.
Remove from heat and allow to cool.
Younger people can take 1 tablespoon with warm water every morning before breakfast during asthma season. Older adults and chronic asthma sufferers should increase the dosage to 1 tablespoon twice a day, before meals.
Ginger, Walnut, and Bitter Apricot Kernel Pills
_This recipe uses bitter apricot kernels (see page 69), which are toxic when raw. It is therefore defined as a medium-grade drug in the Chinese classification of toxicity (see page 35). We have included it because of its efficacy in treating asthma. Be sure not to take it for more than ten days, and to wait at least three weeks before resuming the cure. The prescription should be taken during periods in which you normally suffer from asthma._
¼ cup (50 grams) walnut meats
¼ cup (50 grams) bitter apricot kernels
Water for soaking
¼ cup (50 grams) fresh ginger
¼ cup (60 milliliters) honey
Soak the walnuts and bitter apricot kernels in water overnight, so as to be able to peel them with ease. Drain.
Peel the skin from the walnuts and the apricot kernels. Chop into fine pieces, together with the ginger. Transfer to a dry bowl. Mix with the honey to make a thick paste.
Roll the paste into 100 round pills. Take 10 pills a day for ten days, before going to bed.
Mud Orange
1 pound (500 grams) powdered clay (use soil if clay is not available)
1 cup (250 milliliters) water
1 orange
In a bowl, mix the clay or soil with water to form a thick paste. Pack the orange in the paste. Bake at 350°F for 10 minutes. Remove from the oven and allow to cool.
Wash the paste off the orange by holding it under running water. Split the orange open and eat the fruit while it is still warm.
To be taken once a day for seven days.
Garlic and Sugar
1 garlic clove, finely minced
2 tablespoons (30 grams) white sugar
1 small glass warm water
Mix the garlic with the sugar in the glass of warm water. Leave to brew for five minutes.
While the asthma is activated, take every evening before bed.
Garlic Foot Application
_In this remedy, a clove of partially squeezed garlic is placed in the center of the sole of the foot, where the toe bones begin. This is an important point associated with the kidney channel. The lungs correspond to the Metal element, which generates Water (kidney) and subjugates Wood (liver). When the lungs are out of balance, as with asthma, the kidneys are directly affected._
2 garlic cloves
2 Band-Aids
Peel the garlic. Crush each clove slightly in order to crack it. Bind a clove to the middle of each sole, in the soft spot where the toe bones begin. Use a fresh clove of garlic every twenty-four hours.
Cured Eggs
14 raw eggs, whole
Your own urine
Soak the raw eggs in the urine for seven days, changing the urine every twenty-four hours. Eat 2 eggs every morning, either raw or soft-boiled for 3 minutes. Continue the treatment for three months.
ATHLETE'S FOOT (TINEA PEDIS)
Athlete's foot is a fungus that thrives in warm, damp folds of skin between the toes. People who wear open sandals or no footwear at all rarely suffer from athlete's foot. However, if one lives in a warm, damp area and wears shoes, the perfect environment is created for this bothersome fungus to develop.
The most obvious preventive measures are to keep the feet aired and dry, and to change your socks and shoes every day. You can wear your shoes again five days later—the passage of time allows the shoes to air out. Get into the habit of rapidly passing the toes of your socks through the area when you put your socks on and when you remove them. Make sure that you dry the area with a towel after bathing or showering.
If, in spite of the preventive methods, you do catch the fungus, you can dab or spray perfume between the toes. Over-the-counter medications consist of zinc salt and undecylenic acid; compounds of this acid are present in perfumes.
Alcohol-based perfumes are not, however, common in China. Other methods have therefore been developed for dealing with athlete's foot.
* Salt renders an environment inhospitable to fungi. Take 6 pounds (2.7 kilos) of common salt. Place the salt in a dry saucepan and roast it for 10 minutes or until hot. Remove from the saucepan and place on a clean, dry towel. Fold the towel over the salt and place on the ground. Stand on the towel until the salt becomes cold. This should be done every day before bed, until you are rid of the problem.
* Apply a small amount of toothpaste between the toes three times a day.
* Take 4 cups (1 liter) of rice vinegar and mix with 2 cups (500 milliliters) of water. Soak your feet in this mixture for one hour twice every day.
* Boil 1 cup (200 grams) of soybeans in 4 cups (1 liter) of water for 30 minutes. Allow the water to cool and use it wash your feet once a day for two weeks. Prepare fresh every two or three days.
According to Chinese medical theory, athlete's foot is not dependent solely on the damp, humid environment of the foot, but also on a person's physical health and resistance. During the Tang dynasty athlete's foot was observed to be a precursor of beriberi, a disease brought on by a vitamin B1 deficiency. Therefore, food that is rich in vitamin B1 is prescribed to combat both athlete's foot and beriberi. Almonds, soybeans, betel nuts, and plantain seed are some of the oldest remedies suggested by the famous long-lived physician Sun Si Miao (A.D. 581–682). Others remedies follow.
Peanuts, Adzuki Beans, and Jujube Decoction
½ cup (100 grams) adzuki beans
Water for soaking
4 cups (1 liter) water
½ cup (100 grams) jujube
½ head (approximately 50 grams) garlic, peeled and lightly crushed
2/3 cup (130 grams) raw peanuts, shelled
Soak the adzuki beans in water for at least 2 hours, then drain.
Bring 4 cups of water to boil in a medium saucepan. Place all the ingredients in the boiling water. When the water returns to a boil, reduce the flame to low. Cover. Decoct for 20 minutes over a low flame.
Allow to cool slightly. Drink warm, as part of a meal. The quantity is sufficient for two servings.
Liver and Beans Congee
5 cups (1.25 liters) water
1½ tablespoons (20 grams) mung beans
½ cup (100 grams) pork liver, cut into
1-inch cubes 1 cup (200 grams) rice
In a medium saucepan, bring the water to a boil. Place the beans and the liver in the water, cover the pan, and boil over a low flame for 20 minutes.
Add the rice. Cover the pan again. Cook for 15 minutes, stirring occasionally, to make a congee.
Divide the congee into four portions. Eat one portion, warm, two times a day as part of a meal.
BLOODY STOOLS
Blood in the stools can result from several causes. If the blood is red and fresh, it usually denotes either hemorrhoids or a lesion of the anus or rectum caused by difficult defecation. If the blood is black and dry, the cause of the lesion is usually found further up the alimentary canal. In the latter circumstance, it is best to consult a physician.
The rupture of fragile blood vessels in the anus can be prevented by eating plenty of food rich in soluble fiber. This ensures that the stools are soft and sufficiently bulky.
All of the following remedies ensure the intake of plenty of fiber and are quite straightforward.
* Eat 3 or 4 figs twice a day on an empty stomach. If fresh figs are not in season, dried figs will do.
* Eat 2 bananas every day on an empty stomach.
* Consume 6 to 12 raw pine nuts three times a day.
* Cut 1 cup (200 grams) of radish or daikon into ½-inch cubes. Boil in 2 cups (500 milliliters) of water for 15 minutes over a medium flame. Allow to cool, and add honey to taste. Take as a frequent snack.
* Take sunflower seeds frequently as a snack. Sunflower seeds can also be prepared and drunk as a tea.
Sunflower Seed Tea
2 tablespoons (30 grams) raw sunflower seeds
2 tablespoons (30 grams) rock sugar
4 cups (1 liter) water
Using a grinding stone or mortar and pestle, grind the sunflower seeds into a powder. Transfer to a cup or bowl, and mix the powder with rock sugar.
In a medium saucepan, combine the powder with the water. Bring to a boil, cover, then reduce heat and simmer over a low flame for 1 hour.
Drink one cup of the tea three times a day, warm.
The following remedies for bloody stools are not based on the intake of a lot of soluble fiber.
Poplar Leaf Tea
12 fresh poplar leaves
Water for steaming
1 cup water
Wash the poplar leaves and place them in a steaming dish (see page 66). Using a pot deep enough to fit your steamer, bring water to a boil. Put the steamer in the pot, cover, and steam for 10 minutes.
Remove the leaves from the steamer and place them on a flat surface to dry. When they are dry, crumble the leaves.
Boil 1 cup of water. Place 1 teaspoon (5 grams) of the dried poplar leaves in a cup and add boiling water. Cover and steep for at least 5 minutes before drinking.
Drink 1 cup a day.
Adzuki Beans and Vinegar
6 cups (1.5 liters) rice vinegar
3 cups (600 grams) adzuki beans
In a medium saucepan, bring the vinegar to a boil. Add the adzuki beans. Simmer over a low flame for 45 minutes, until the vinegar has almost evaporated. Stir frequently.
Transfer the beans to a flat surface and allow them to dry. When dry, grind the beans to a powder with a stone grinder or a mortar and pestle.
Take 1 teaspoon of the powder every morning before breakfast.
BURNS AND SCALDS
Immediate first aid treatment for dry burns should always be to apply cool water to the burn. Cooling is necessary because burned tissues continue to retain heat after the immediate cause of the injury has been removed. This heat can damage deeper layers of skin even several hours after the event.
It is best to plunge the burned area into a basin of cool—not cold—water. (Cold water causes the skin to blister, and the cold-water plunge is painful.) Thrusting the burned area under a running faucet is sufficient if a basin is not available, although strong pressure from the tap might rupture the burned skin. (Or you might, in your panic, turn on the hot tap by mistake!) If the burn is on a part of the body less accessible to a basin plunge, try pouring the water slowly from a pitcher onto the area.
Keep the burn under water for at least ten minutes. After that, what you should do depends on the degree and size of the burn. First-degree burns, and second-degree burns that cover an area one inch in diameter or less, can be treated at home.*4 Anything more serious must be attended to at a first aid clinic or a hospital. In either case, keep the burn free of clothing or bandages—one school of thought claims that first- and second-degree burns should be treated only with air, oxygen being necessary to the process of tissue regeneration. Chinese medicine holds that, while permitting a burn to "breathe" is necessary, healing will take place more easily by applying various natural products.
If you have developed blisters from a burn, do not burst them. To do so would leave scar tissue and open the underlying raw flesh to possible infections.
The following are common Chinese household remedies for burns.
* Soak the burn in a bowl of cool milk, or soak a cotton cloth in milk and apply to the burn.
* Crush a carrot and apply to the injured part.
* Apply natural honey to the burn. Honey has a cleansing and antibacterial effect.
* Fresh ginger juice applied to a burn by means of cotton wool is reported to stop pain instantly, and to reduce inflammation and swelling.
* Place slices of fresh cucumber on the skin. This remedy is commonly used for sunburn.
* Apply cucumber juice to scalds. Scalds are the most common type of burn sustained in the home, especially those caused by hot tap water.
* Place cool slices of raw potato gently against the burn.
* Although yogurt is new to China, it was quickly realized by Chinese people that yogurt applied to first-degree burns, including sunburn, helps to alleviate the discomfort and hasten tissue recovery.
* Aloe vera was introduced to China from central America, and is not, therefore, a traditional remedy. Aloe vera is used in China, as throughout the rest of the world, as a cooling balm for burns. Use either the moist flesh of a cut leaf, or the juice. Apply immediately to first-degree burns, or after the blisters have formed to second- and third-degree burns.
Other remedies are used in China to help the skin heal after emergency treatments have had time to work. Some of these are:
* Place slices of a mature pumpkin inside a jar and bury it in the ground. Leave it for several days, giving the flesh time to rot and liquefy. Then apply the juice to the burn. The application of rotting pumpkin serves to hasten tissue healing several days after the event.
* Mash 2 cakes of tofu, mix with sugar, and apply to the burn.
* Dry some watermelon rind and grind it into a powder. Mix 2 tablespoons (30 grams) of this powder with 1 tablespoon (15 milliliters) of sesame oil, and apply to the burned skin area.
* Blend the white of 1 egg and 1 tablespoon (15 milliliters) of sesame oil. Apply twice a day to the burn.
A diet rich in vitamin C, protein, and liquids is important for recovering from second- and third-degree burns. Raw fruit, especially that which is rich in vitamin C—oranges, kiwi, strawberries—should be eaten in abundance. One should increase one's intake of calories, and especially of protein. Eat tofu, meat, dairy products, and fish. Plenty of liquids should be consumed.
COMMON COLD
According to Chinese theory, there exist two kinds of cold: _feng-han_ (wind and cold) and _feng-re_ (wind and heat).
Feng-han colds are common in winter and spring. Symptoms are a runny nose, sneezing, liquid catarrh, and no sweating. A feng-re cold, on the other hand, causes a blocked nose that does not run, sore throat, thick and yellow catarrh, thirst, and sweating.
The remedies for feng-han colds are warm diaphoretics (sweat inducers). Those for feng-re colds are diaphoretics with cooling or cold characteristics.
What one eats is particularly important to the progress of the cold. Plenty of hot water should be drunk throughout the day. Eat only food that is light and easily digestible. Liquid foods such as milk, congee, soups, and broths should form the basis of your diet. Refrain from fish, meat, and fats—do not eat lamb, beef, pork, or chicken after taking a diaphoretic to induce sweat. Eat plenty of fruit, especially oranges, kiwis, tomatoes, apples, and pears. Consume green vegetables and salads. Spicy ingredients should not be taken until after the symptoms of the cold have disappeared.
Garlic Nose Drops
_During the initial stages of a cold, when one starts sneezing and the nose begins to run, the first remedy that most Chinese people resort to is garlic drops._
2 fresh garlic cloves, peeled
¼ cup (60 milliliters) water at room temperature
Press the garlic cloves to extract the juice. Mix the garlic juice with water—the proportion should be 1 part garlic juice to 10 parts water.
Apply the juice as nose drops.
Daikon Nose Drops
_Instead of garlic, which some people find too powerful, you can instead use daikon juice._
1 tablespoon (15 grams) fresh daikon, grated
¼ cup (60 milliliters) water at room temperature
Squeeze the daikon to extract the juice. Mix the juice with water—the proportion should be 1 part daikon juice to 10 parts water.
Apply the juice as nose drops.
Garlic Pacifier
_As well as combating a runny nose, garlic can also be taken orally to prevent a cough and sore throat._
3 garlic cloves
Peel the garlic. Put 1 clove, whole, into your mouth. Leave it there until you can no longer taste it—this can be as long as one hour. Swallow your saliva as it forms. Do not suck with force or chew.
Spit the clove out when it has lost all flavor. When you are ready, start again with a second clove. Later, take the third.
Do this once a day until you feel better.
Ginger and Scallion Soup
_A good sweat-inducing recipe for when you feel a cold developing is a hot soup._
2 cups (500 milliliters) water
2 tablespoons (30 grams) fresh ginger, sliced
2 tablespoons (30 grams) white head of scallion, sliced
In a medium saucepan, bring the water to a boil. Add the ginger and scallion and simmer over a low flame for 15 minutes, or until the ginger is soft and its smell has spread through your kitchen.
Drink hot before betime. Stay away from the cold, and especially from cold drafts (the "evil air").
Garlic and Scallion Congee
_The following warming remedy for curing a cold in its early stages is especially effective when the cold is accompanied by a headache._
3 cups (750 milliliters) water
½ cup (100 grams) white rice
3 garlic cloves, finely minced
2 teaspoons (10 grams) minced scallion, white heads only
In a medium saucepan, bring the water to a boil. Add the rice, return to a boil, then lower the flame and simmer for 20 minutes, covered, stirring occasionally.
When the rice has been cooked down to a gruel, add the garlic and scallion. Cook for 5 more minutes over a low flame.
Consume hot once a day, as part of a meal. Wear heavy clothing or get into bed so as to maintain the heat of the congee within your body.
Dandelion and Chrysanthemum Tea
1 tablespoon (15 grams) dry dandelion leaves
2 teaspoons (10 grams) dried chrysanthemum flower
2 teaspoons (10 grams) green tea leaves
1 cup (250 milliliters) water
Mix the dandelion leaves, chrysanthemum flower, and tea leaves. Store in a glass jar.
Bring water to a boil. Put 1 heaped teaspoon (5+ grams) of mixed leaves and flowers in a cup. Pour hot water in the cup. Cover and steep for 5 minutes.
Drink hot two times a day.
**The following remedies are diaphoretics for feng-han colds (colds characterized by liquid catarrh and a runny nose). These remedies should be taken just before going to bed either at night or, if the cold is bad enough, during the day. Most of these sweat-inducing dishes are based on ginger and the white head of spring onion, or scallion, two of the best diaphoretics available.**
Ginger Broth
_In this remedy, the ginger induces sweating and brown sugar promotes circulation._
2 cups (500 milliliters) water
2 tablespoons (30 grams) sliced fresh ginger
Brown sugar to taste
In a small saucepan, bring the water to a boil. Add the ginger. When half the water has evaporated, add the sugar. Continue boiling for 3 minutes.
Take the decoction hot. When you have finished, get under a quilt or blanket for a sweat.
Ginger and Pear Soup
2 cups (500 milliliters) water
1 pear
1 tablespoon (15 grams) sliced fresh ginger
1 tablespoon (15 grams) sliced scallion, white heads only
2 eggs, beaten
Bring the water to a boil in a small saucepan. Cut the pear in half; do not peel it. Add the pear, ginger, and scallion to the water. Return to a boil, cover the pan, and reduce the flame to low. Simmer for 20 minutes.
In the meantime, thoroughly beat the eggs in a glass or ceramic bowl. When the broth is ready—you will know it is when the aroma of ginger spreads through your kitchen—pour the decoction into the bowl containing the two beaten eggs. Mix and drink the decoction while it is still hot, then get under a heavy quilt or thick blanket for a good sweat.
Take this remedy once a day for three or four days, or until the cold goes away.
Ginger and Onion Rice
1 teaspoon (5 grams) sliced fresh ginger
1 scallion, including roots and green tops
1 cup (200 grams) rice
6 cups (1.5 liters) water
2 teaspoons (10 milliliters) rice vinegar
Put the ginger, scallion, rice, and water in a medium saucepan. Bring to a boil, then reduce the flame. Simmer on a low flame with the lid half-covering the saucepan, stirring occasionally. Cook for 25 minutes, or until the rice has becomes a gruel.
Stir in the vinegar. Cook for another minute or two.
Divide into four portions. Take one portion, hot, then get into bed or cover up under a warm blanket. Take this remedy two times a day, while the cold persists.
Egg and Sugar
1 fresh egg
2 tablespoons (30 grams) sugar
1 cup (250 milliliters) water
Beat the egg and sugar together in a bowl.
Bring the water to a boil in a small saucepan. Pour the boiling water over the egg and sugar.
Take hot just before retiring to bed for a good, toxin-flushing sweat.
**The following remedies contain cooling ingredients, such as green tea leaves, that balance the sweat-inducing effects of the diaphoretics. These recipes work best for feng-re colds—those with blocked nose, thick catarrh, and cough—which are often accompanied by a headache.**
Ginger and Scallion Tea
_This remedy is particularly useful for clearing headaches caused by colds._
1½ cups (375 milliliters) water
1 tablespoon (15 grams) sliced fresh ginger
1 tablespoon (15 grams) chopped scallion, white heads only
2 teaspoons (10 grams) green tea leaves
Bring the water to a boil in a small saucepan. Add all the ingredients and boil over a medium flame for 10 minutes.
Drink hot, and stay away from "evil air" (cold and drafts).
(If you are suffering from a fever in addition to a cold, you should add 1 tablespoon (15 grams) of walnut meats to this recipe. Boil for 15 minutes instead of 10.)
Ginger Tea
_This effective, fast-acting remedy is good for combating colds that are accompanied by a strong headache._
1 cup (250 milliliters) water
¼ cup (50 grams) fresh ginger, thinly sliced
¼ cup (50 grams) brown sugar
1 teaspoon (5 grams) green tea leaves
Bring the water to a boil in a small saucepan. Add the ginger and sugar. Turn the burner off and wait for 1 minute, then add the tea leaves. (Green tea contains vitamin C; the 1-minute wait after boiling ensures that the vitamin is not destroyed by the heat.) Steep for 5 minutes before drinking.
A frequent addition to this tea is ½ teaspoon (2.5 milliliters) of vinegar. Vinegar exerts a warming and detoxifying effect.
It is recommended that you eat some rice congee immediately after taking this tea.
Sweetened Ginger and Scallion Broth
_This remedy is useful when one is soaked to the skin by a sudden rain shower or by falling into water. It is also effective for curing abdominal pains due to catching cold. This broth should be taken just before going to bed._
1 cup (250 milliliters) water
¼ cup (50 grams) fresh ginger, thinly sliced
5 white heads of scallion, thinly sliced
2 teaspoons (20 grams) brown sugar, or more to taste
In a small saucepan, bring the water to a boil. Place the ginger, scallion, and sugar in a cup or bowl. Pour the boiled water over the ingredients. Steep for 5 minutes, then drink.
Retire to a warm bed. The sweat thus induced should leave you feeling better by morning.
Peppermint and Scallion Broth
_Peppermint rises to the head (Yang) and has a cooling, pungent effect. It is therefore a good relief for colds accompanied by headaches._
20–30 fresh peppermint leaves, or 2 heaped teaspoons (10+ grams) dried peppermint
2 or 3 crushed white heads of scallion
2 cups (500 milliliters) water
Place all ingredients in a small saucepan. Bring to a boil, then reduce the flame. Simmer for 15 minutes, or until half the water has evaporated.
Drink hot or warm.
Scallion Inhalers
_This remedy effectively relieves a blocked nose; it may be used as a natural alternative to vaporubs. In China, this remedy is usually preferred to any over-the-counter medications._
1 white head of scallion, sliced lengthwise
Place the scallion slices directly under your nostrils. Inhale deeply. Continue breathing deeply until your nasal passages are freed.
Watermelon and Tomato Juice
_One recipe commonly employed in summer for a hot and dry cold uses watermelon and tomato. Besides curing hot, dry colds, watermelon and tomato combat dehydration, quench thirst, and relieve indigestion and lack of appetite._
2 pounds (1 kilogram) fresh watermelon
2 pounds (1 kilogram) fresh tomatoes
Chop the watermelon and tomatoes into small pieces, keeping them separate. Put them separately into thin cotton towels. Twist each to extract the liquid.
Mix the juices in equal portions. Drink at room temperature, slightly cooled but not cold, as often as you like.
COUGHS
To provide relief for coughs, ginger and onion combinations are prepared with daikon, which has cool, pungent, and sweet characteristics and eliminates hot irritation of the throat and bronchi.
Daikon, Ginger, and Scallion Soup
_This popular remedy for coughs and colds also clears catarrh and counteracts body pains, weakness, and lethargy due to colds._
3 cups (750 milliliters) water
1 medium daikon, cut it into ½-inch slices
1 tablespoon (15 grams) sliced fresh ginger
6 white heads of scallion, sliced
Bring the water to a boil in a medium saucepan. Add the daikon to the water. Continue to boil over a medium flame for 20 minutes, or until the daikon is soft. ("Soft" is defined in China as yielding enough to push the point of a chopstick through the daikon slice with ease).
Add the sliced scallion and ginger to the pot. Reduce the flame to low. Simmer for another 10 minutes, or until two-thirds of the water has evaporated.
Remove from heat. Consume hot.
Daikon and Tangerine Peel Soup
_This is a classic remedy for a thick-mucous cough._
1 cup (250 milliliters) water
1 small daikon, cut it into ½-inch slices
1 organic tangerine peel, cut it into ½-inch slices
3 slices ginger
1 teaspoon (5 grams) white pepper
In a small saucepan, bring the water to a boil. Add the daikon, tangerine peel, ginger, and pepper to the boiling water. Continue to boil over a medium flame for 10 minutes.
Pour into a bowl and allow to cool. Take the soup twice a day, after lunch and dinner.
**Daikon juice on its own is a good remedy for a cold with headache and cough, as well as for chronic bronchitis. If the cough is particularly persistent, daikon juice can be mixed with ginger and pear juice and the white of an egg.**
Daikon Juice
4 cups (800 grams) fresh daikon, grated
1 tablespoon (15 grams) brown sugar
Place the daikon in a thin cotton towel and squeeze in order to obtain the juice. Mix the juice and brown sugar in a small saucepan. Bring to a boil over medium heat.
Remove from the flame and allow to cool. Drink the juice two times a day, warm to hot, to relieve coughing.
Daikon, Ginger, and Pear Juice
½ cup (100 grams) fresh daikon, grated
½ cup (100 grams) fresh ginger, grated
2 tablespoons (30 milliliters) fresh pear juice
1 egg white
Place the daikon in a thin cotton towel and squeeze to extract 2 tablespoons of juice. Repeat with the ginger.
Mix the ginger and daikon juice with the pear juice and egg white. Drink it cool once a day.
Daikon Juice Drops
½ cup (100 grams) fresh daikon, grated
Place the daikon in a thin cotton towel and squeeze in order to obtain the juice. Use the juice directly as nose drops.
**Garlic is another popular remedy for persistent coughs.**
Garlic Juice
1–2 cups (200–400 grams) fresh garlic cloves
1 cup (250 milliliters) water
1 teaspoon (5 grams) white sugar
Peel and squeeze the garlic in order to extract the juice. Transfer to a clean bottle or jar and refrigerate.
When you need to use a cough remedy, boil 1 cup of water. Mix 1 tablespoon (15 milliliters) of garlic juice and the sugar into the hot water.
To be taken twice a day, morning and evening, until the cough has cleared. Drink the mixture hot.
Garlic Cough Powder
1 tablespoon (15 grams) garlic powder
1 teaspoon (5 grams) sugar, white or brown
Mix the garlic powder with the sugar. Take the mixed powder twice daily, with lunch and dinner.
Jujube Tea
_A favorite remedy for coughs is the jujube (Chinese date)._
5 jujube (Chinese dates)
1 tablespoon (15 grams) minced fresh ginger
1 tablespoon (15 grams) brown sugar
2 cups (500 milliliters) water
In a small saucepan, add all the dry ingredients to the water. Boil over a low flame for 15 minutes.
Consume warm.
Azalea Wine
½ cup (100 grams) azalea flowers
4 cups (1 liter) rice wine, or sake
Wash the azalea flowers. Allow them to dry in the shade.
When the flowers are dry, finely chop them. Place the rice wine and the flowers inside a bottle. Seal the bottle. Allow the mixture to macerate for at least 5 days.
Take 2 or 3 teaspoons (10 or 15 milliliters) two times a day.
**Other ingredients for cough mixtures include celery, tofu, and lard. Drink one glass of fresh celery juice twice a day, morning and evening, for as long as the cough persists. Tofu and ginger are an effective remedy for chronic coughs, especially those due to chronic bronchitis. And while the final recipe for treating coughs may seem unusual, honey and lard have been used in China for centuries to relieve dry coughs without catarrh.**
Tofu and Ginger
3 cups (750 milliliters) water
8 ounces (200 grams) tofu, cut into 1-inch cubes
6 tablespoons (90 grams) brown sugar
2 teaspoons (10 grams) crushed ginger
In a medium saucepan, bring the water to a boil. Add all ingredients to the water. Boil over a medium flame for 15 minutes.
Remove the pan from the heat. Consume warm as a gruel once a day, before bed.
Honey and Lard
_This recipe serves an additional purpose: that of ensuring regular bowel movements._
8 tablespoons (120 grams) lard
8 tablespoons (120 grams) honey
In a small saucepan, heat the ingredients over a low flame, bringing them to a boil. Remove from heat and allow to cool.
Consume when the mixture cools sufficiently to become creamy and opaque.
CONSTIPATION
For optimum health the bowels should be cleared daily. Fecal matter that stays in the intestines for longer than twenty-four hours causes harmful bacteria to spread through the system. Furthermore, chronic constipation can lead to abdominal pain, diverticulitis, hemorrhoids, headaches, insomnia, digestive problems, obesity, circulatory problems, hernia, and cancer of the bowel.
A diet of fresh, raw, leafy green vegetables, fresh fruits, and plenty of fiber helps to produce easy bowel movements. Plenty of water (drunk hot in China) or pure fruit juice is needed to dissolve the added intake of fiber. One may resort to natural laxatives; a few are mentioned below. These have been used for centuries in China. Chemical products should not be used—they are too thorough in cleaning out the intestines, killing all bacteria and giving rise to chronic constipation.
To prevent constipation it is important to exercise. Any exercise will do because all physical activity helps move waste matter through the intestines. Qi gong breathing exercises are especially beneficial in that they exert a salutary, massaging effect on the abdominal and intestinal areas, thus facilitating the elimination of fecal matter.
In a variation of the qi gong standing position that has been designed specifically to relieve constipation, stand with your back straight and knees slightly bent (see page 245). Place your hands on your hips and rotate your pelvis to the left, then to the front, then right, and then back for five to ten minutes each the morning.
Before proceeding with the remedies here, a few words may be in order about Chinese toilet habits. It is believed that people defecate best if they concentrate. Do not therefore take a book or other distraction to the toilet with you—concentrate solely on the matter at hand. Push and, as Chinese parents tell their children, clench your teeth.
In the course of our research, we discovered numerous easy home remedies for the common ailment of constipation. We leave the choice of remedy to the reader.
* Simply add salt to warm water and drink. The more salt you add, the more powerful the effect. Take care: you may find yourself throwing up as well.
* Add 1 tablespoon (15 milliliters) of vinegar to a large glass of warm or hot water. Drink in the morning on an empty stomach. Follow this by another glass of warm or hot water without the vinegar. Go out for a thirty- to sixty-minute walk. On your return, repair to the bathroom.
Some foods taken regularly as part of one's diet are known to facilitate easy and daily bowel movements.
* One of the gentlest and yet most efficient ways of ensuring regular bowel movements is to eat leafy green vegetables.
* Nearly as effective as eating the vegetables is drinking their juice—all leafy green vegetables will work. Extract the juice of the green leaf vegetable of your choice, or boil in water and drink the broth.
* Take 2 soft, very ripe bananas every morning and evening.
* Roast 2 tablespoons (30 grams) of black sesame seeds in a dry frying pan for 3 minutes. Eat the sesame with 1 or 2 ripe bananas. This remedy counteracts both constipation and high blood pressure.
* Take 2 teaspoons (10 milliliters) of honey twice a day, morning and evening. Continue for two weeks. You may mix the honey with warm water and drink.
* Stir 1 teaspoon (5 milliliters) of honey and ½ teaspoon (2.5 milliliters) of sesame oil in a glass of hot water. Take before going to bed.
* Steam 2 cups (400 grams) of honey and 2 cups (400 grams) of lard together in a large ceramic bowl for 15 minutes (see page 66). Store in a jar. Take 1 tablespoon every morning and evening on an empty stomach. This recipe is also used for treating dry coughs with little catarrh.
* Wash 1 cup (200 grams) of figs. Boil the figs in 4 cups (1 liter) of water over a low flame for 20 minutes. Drink the juice as a tea, with a little sugar added according to taste.
* Drink the white of 1 raw egg every morning with your breakfast. You may mix with fruit juice or any other cool drink. Grapefruit is said to be the best fruit juice remedy for constipation.
* Drink a glass of fresh grapefruit every day before breakfast, on an empty stomach.
Honey and Potato Juice
2 pounds (1 kilogram) potatoes, washed but not peeled
1 tablespoon (15 milliliters) honey
Cut the potatoes into ½-inch cubes. Using a thin cotton towel, squeeze the potatoes over a small saucepan to extract the juice.
Heat the juice on a high flame; lower the flame as the juice begins to boil. Add honey and simmer for 5 to 10 minutes until creamy.
Remove from flame. Let cool, then store in a jar or bottle and refrigerate.
Take 1 tablespoon (15 milliliters) once a day, in the morning before breakfast. If you forget you can take it anytime, but always do so on an empty stomach. (In another version of this recipe, the honey and potato juice are mixed cold and drunk raw.)
Sesame, Walnut, and Pine Kernel Muesli
2 tablespoons (30 grams) sesame seeds, black or white
2 tablespoons (30 grams) walnut meats
2 tablespoons (30 grams) pine nuts
2 tablespoons (30 grams) honey
Chop and then grind the sesame, walnuts, and pine nuts, using a stone grinder or a mortar and pestle. Work the ingredients into granules, then add the honey and mix into a paste.
Consume every morning with your breakfast.
Milk, Honey, and Onion
½ cup (100 grams) white onion, chopped fine
1 cup (250 milliliters) milk
8 tablespoons (90 grams) honey
Using a thin cotton towel, squeeze the onion for its juice.
In a small saucepan, bring the milk to a boil. Add the onion juice and allow to simmer for 1 minute. Remove from the flame.
Allow to cool for 5 minutes. Stir in the honey.
Drink warm every morning on an empty stomach.
Onion Compress
_This onion remedy is especially effective for women suffering from constipation after childbirth. It serves to stimulate bowel movement by exerting a warming and relaxing effect on the outside of the abdomen._
Hot water
½ cup (100 grams) onion, finely chopped
Place a towel in hot water. When it is soaked through, remove the towel from the wash basin and squeeze out the excess moisture. Lie down on your back and apply the onion to your navel. Place the hot towel over the onion. Hold the towel in place for 5 minutes.
Reheat the towel and repeat for another 5 minutes. You can, if you prefer, use a hot water bottle instead of a towel. In the latter case, hold in place for 10 minutes.
Onion, Ginger, and Radish Juice Compress
½ cup (100 grams) daikon, grated
1 tablespoon (15 grams) onion, chopped
1 teaspoon (5 grams) ginger, chopped
4 teaspoons (20 grams) salt
Squeeze the daikon to extract 1 tablespoon of juice into a glass.
In a wok or frying pan, stir-fry the onion, ginger, salt, and daikon juice together for 3 minutes.
Remove from the heat and allow to cool. Wrap the mixture in a thin cloth and apply to your navel once a day until you feel well again. Keep the compress in place for 20 minutes.
Sweet Potatoes with Ginger
4 cups (1 liter) water
1 sweet potato, cut in ½-inch slices
1 4-ounce (100-gram) piece of ginger, cut in ½-inch slices
2 tablespoons (30 grams) sugar, white or brown
In a medium saucepan, bring the water to a boil. Add the sweet potato, ginger, and sugar. Boil over a medium flame for 15–20 minutes, until the sweet potato is edible.
Remove from the flame. Mash and consume as part of a meal. This dish may be eaten as frequently as you like.
Steamed Eggplant
1 eggplant (aubergine), peeled and cut in ¼-inch slices
Water for steaming
Salt or oil to taste
Place the eggplant in a ceramic bowl or steaming dish (see page 66). Using a pot deep enough to fit your steamer, bring water to a boil. Put the steamer in the pot, cover, and steam for 10 minutes.
Eat warm once a day, as often as you like. Add salt or oil if you wish.
Cooked Spinach
1 cup (200 grams) fresh packed spinach
2 tablespoons (30 milliliters) water
1 teaspoon (5 milliliters) sesame oil
Place the spinach in a wok or medium saucepan with the water. Setting the flame on high, stir the spinach for 2 minutes.
Remove from the flame and allow to cool. Add sesame oil. Eat warm.
Sesame Eggs
_In China, black sesame seed is considered to be an effective laxative. Sesame can be eaten with eggs, or with rice as a congee._
½ cup (100 grams) black sesame seeds
1 teaspoon (5 grams) salt
1 egg
1 cup (250 milliliters) water
Roast the sesame seeds in a dry frying pan or wok over a low flame for 3 minutes, or until you can smell the distinct odor of sesame. Add salt, and roast for another 30 seconds.
Place the egg in a small saucepan with the water. Bring to a boil, then boil for 10 minutes.
Allow the egg to cool, then cut into segments. Mix the egg with the sesame. Consume warm, two times a day.
Black Sesame Congee
½ cup (100 grams) white rice
3 cups (750 milliliters) water
2 tablespoons (30 grams) black sesame seeds
In a medium saucepan, bring the water to a boil. Add the rice and boil over a low flame for 20 minutes.
Crush the sesame seeds with mortar and pestle or stone grinder. Add the sesame to the congee. Simmer for 10 additional minutes.
Take with meals.
Pine nuts or watermelon seeds may be used in this dish as an alternative to sesame:
* Prepare a rice congee (see page 69). Roast 2 tablespoons (30 grams) of pine nuts in a dry wok or frying pan for 3 minutes. Crush the pine nuts and add to the congee.
* Prepare a congee (see page 69). Roast 2 tablespoons (30 grams) watermelon seeds in a dry wok or frying pan for 4 minutes. Crush the watermelon seeds and add to the congee.
Sometimes even the best laxatives cannot dislodge stubborn constipation. Before resorting to an enema, you might wish to try something of immediate efficacy. This remedy is as straightforward as it is effective.
Take the white head of one scallion; wash and remove the roots. Cover the scallion it with 1 teaspoon of honey. Squat or lie down and slide the scallion up your anus. Keep it in place for 3 minutes.
CORNS
Remedies for corns—the hardening of the skin on the toes—were offered by many people. The following are some of the least complicated to apply.
* Squeeze the juice from an eggplant and apply to the corn two or three times a day.
* Crush an unripe fig and apply to the corn. Hold in place with a bandage. Change the application twice a day. Seven to ten days of treatment should eliminate the corn.
* Apply the white sap of a freshly picked fig directly onto the corn.
* Peel the soft transparent skin from a scallion. Before going to bed, wash your foot in hot water and dry. Apply the scallion skin to the corn. Rub gently. Hold in place overnight with either a cloth bandage or Band-Aid. Repeat every evening until the corn becomes soft and white and eventually falls away of its own accord.
Some Chinese chiropodists (foot doctors) assert that the corn should be filed or cut down before making the application. Others argue that no manual intervention is necessary—indeed, that filing or cutting the corn can irritate the surrounding area and can therefore be harmful.
**The last remedy for corns is a little more elaborate and will thus need a few minutes of preparation.**
Garlic and Onion
1 head of garlic, minced
1 purple onion, diced
1 teaspoon (5 milliliters) vinegar
8 cups (2 liters) water
1 teaspoon (5 grams) salt
In a small bowl, mix the garlic and onion with the vinegar.
Warm the water in a large saucepan. Add the salt to the water. Cut away the thick skin from the corn. Soak the foot in the warm salty water for about 20 minutes, until the skin is soft. Dry the area around the corn.
Apply 1 tablespoon of the chopped onion and garlic to the corn and rub in well. Cover with a bandage. Apply every four hours, if possible. Store the unused garlic and onion mixture in the refrigerator.
Repeat each day for 5 to 7 days. The fresher the onion and garlic, the more effective the remedy.
DIARRHEA
Diarrhea is a symptom with many possible causes. According to Chinese medicine, the causes can range from a weak spleen and stomach to indigestion, overeating, or cold. The patient usually suffers from abdominal pains, has no appetite, feels lethargic, and needs to run to the toilet many times a day. When things get worse, it is probably not diarrhea but dysentery—see pages 135–138 for more powerful remedies.
In China, garlic is considered to be nature's most effective stomach and intestinal disinfectant. Many people won't travel without it, chewing a clove or two whenever in doubt about local conditions of cleanliness. Garlic's proven antibiotic effects render it a valid remedy for diarrhea.
Garlic and Sugar
3 garlic cloves, peeled
2 teaspoons (20 grams) brown sugar
Water for steaming
Put the garlic cloves in a small ceramic bowl, then put the bowl inside a steaming dish (see page 66). Using a pan deep enough to hold your steamer, bring the water to a boil. Place the steamer in the pan, cover, and steam for 10 minutes.
When the garlic is done, crush it, mix with the sugar, and eat.
Alternatively, you can crush the raw garlic, then boil it in 1 cup (250 milliliters) of water with sugar.
Taken two or three times a day, these are both effective remedies for chronic diarrhea and intestinal gases.
Garlic Broth
2 or 3 garlic cloves, unpeeled
1 cup (250 milliliters) water
Roast the garlic in a small, dry saucepan until the skin begins to darken. Add the water. Bring to a boil over a medium flame; continue to boil for 5 minutes.
Remove from heat. Drink warm.
Garlic and Eggs
_Garlic taken with eggs is doubly efficacious in that it counteracts diarrhea accompanied by general weakness._
3 garlic cloves, peeled
2 eggs
1 teaspoon (5 milliliters) sesame oil
Squeeze the juice from the garlic. In a small bowl, beat the garlic juice with the raw eggs.
Heat the sesame oil in a wok or frying pan. When the oil is hot, pour in the eggs and garlic and stir-fry for 1 to 2 minutes.
To be taken twice a day.
Garlic Vinegar
_The following remedy is recommended primarily for diarrhea; it is, however, also effective for treating gastroenteritis. It can be taken as a preventive measure, as well as for curing both diarrhea and gastroenteritis._
4 garlic cloves, minced
3 tablespoons (45 milliliters) vinegar
Squeeze the garlic into a glass to extract the juice. Add vinegar. Sip slowly.
Garlic vinegar may also be prepared by maturing 18 cloves of garlic in 3 cups (750 milliliters) of vinegar for 24 hours. Take 6 cloves for breakfast, 6 for lunch, and 6 for dinner. Repeat each day until cured.
Ginger Tea
2 teaspoons (10 grams) green tea leaves
2 teaspoons (10 grams) minced ginger
2 cups (500 milliliters) water
Prepare a decoction by boiling the tea leaves, ginger, and water over a low flame, covered, for 20 minutes.
Drink the decoction hot.
Ginger and Scallion Omelet
3 eggs
1 tablespoon (15 grams) finely chopped ginger
1 scallion, finely chopped
1 tablespoon (15 milliliters) rice vinegar
Salt to taste
In a small bowl, beat the eggs with the chopped ginger and scallion.
Pour the rice vinegar into a medium frying pan. Heat, then add the eggs, ginger, and scallion mixture.
Cook over a high flame for 3 minutes. Using a spatula, turn the omelette and cook the front side for 1 minute.
Remove from heat and slide the omelette from the pan. Eat once a day until you feel better.
Boiled Apples
10 green apples
16 cups (4 liters) water
In a large pot, bring the water to a boil. Add the apples and boil them whole over a low flame for 40 minutes, until soft.
Eat as many as you can on an empty stomach.
Chestnut Cakes
_Chestnut strengthens zheng qi, the intestines, and the stomach. It also exerts a strong warming and curative effect on cold-syndrome diarrhea._
¼ cup (50 grams) chestnut flour
Sugar to taste
2 tablespoons (30 milliliters) water
Water for steaming
In a small bowl, blend the flour and sugar with water. Divide the dough and roll into four round cakes.
Put the cakes in a steaming dish (see page 66). Using a pan deep enough to fit your steamer, bring water to a boil. Place your steamer inside the pan, cover, and steam for 20 minutes. (If you wish, you may instead bake the cakes at 350°F for 20 minutes.)
Eat the cakes warm. Remember to apply the maxim "Drink your food and eat your drinks." Make sure that each piece of food is well and properly chewed, and is swallowed with plenty of saliva. Chestnut contains starch, and the digestion of starch begins with saliva.
Pork Gall and Honey
_A traditional remedy that is used in the Chinese countryside to cure liver problems, as well as diarrhea, is one using pork gallbladder._
1 gallbladder of pork
8 tablespoons (120 milliliters) honey
Water for steaming
Chop the gallbladder into cubes. Place it in a thin cotton towel and squeeze to obtain the gall. Transfer the gall to a bowl. Stir in the honey.
Put the mixture in a ceramic bowl on a steaming dish (see page 66). Using a pan deep enough to fit your steamer, bring water to a boil. Place your steamer inside the pan and cover. Steam for 15 minutes.
Take the whole remedy in one sitting. One dose should clear the problem.
**Remedies of the kind that follow, in which ingredients are applied to the skin, may be received with a little superstition. Skin applications are popular in Chinese medicine, and are now becoming increasingly acceptable remedies in mainstream Western medicine. By passing through the pores of the skin directly into the capillaries, it is believed that the ingredients may exert a more immediate, albeit milder, effect than by ingestion.**
Garlic and Pepper Compress
2 garlic cloves
8 peppercorns, black or white
Chop the garlic and pepper together to make fine granules. Compress the granules into two cakes.
Bind the cakes to the underside of the feet against the center of the sole, or apply the whole amount to your navel as you lie on your back. Keep in place overnight.
Onion and Salt Compress
_This compress is said to work best for diarrhea due to cold syndromes; it also provides effective relief from abdominal pains._
½ cup (100 grams) onion, chopped
1 tablespoon (15 grams) rock salt
In a dry frying pan or wok, roast the onion together with the salt. When hot, place the salt and onion inside a cotton sachet. Apply as hot as is comfortable to the abdomen, lower back, and waist.
Apply twice each day for as long as the problem lasts.
Other simple food remedies for diarrhea include the following.
* Eat 1 peeled crab apple first thing in the morning, before breakfast. Eat more during the day.
* Drink 1 cup (250 milliliters) of fresh radish juice on an empty stomach once or twice a day.
* Roast 1 whole tuber of ginger in a dry wok or frying pan for 10 minutes, until the outside is dark and dry. Grind the tuber into a powder. Take 1 teaspoon of the powder with warm water three times a day.
DYSENTERY
Dysentery, like food poisoning, is common whenever the climate and poor sanitary conditions encourage bacteria to proliferate, hence the common travelers' complaints of Delhi belly, curse of the pharaohs, and Montezuma's revenge. Symptoms of acute bacillary dysentery are a continuous urgent need to use the toilet; watery stools, sometimes containing blood and puss; nausea; vomiting; abdominal pain; and fever. Chronic amoebic dysentery is slightly less severe in its initial manifestation—there may be no nausea or vomiting—but symptoms persist longer, sometimes for several months. Chronic amoebic dysentery can leave one weak, dehydrated, and many pounds thinner.
The prime defense against bacilli in China is (once again) garlic, the ubiquitous disinfectant of Chinese remedies.
* Raw garlic is a strong and effective antibiotic; however, it exerts an irritating effect on the colon. Raw garlic should therefore only be used sparingly in acute cases of dysentery. If the dysentery is chronic you may take garlic raw—2 or 3 cloves at a time—three times a day for one week.
* Alternatively, you may crush 1 head of garlic and mix it with 4 teaspoons (20 grams) of sugar. Take three times a day.
* Boiled garlic is less irritating to the mucous membranes than raw garlic, and some of its antibiotic effects remain intact. Boiled garlic may therefore be used both for cases of acute and chronic dysentery. Boil a whole garlic head in 1 cup (250 milliliters) of water for 10 minutes, until it is very soft. Remove the skin and mash the flesh with 4 tablespoons (60 grams) of brown sugar. Take twice a day.
* Peel 4 or 5 cloves of garlic, then boil them in a small saucepan containing 2 cups (500 milliliters) of water. After 2 minutes of boiling, remove the garlic and add ¼ cup (50 grams) of rice. Simmer over a low flame for 20 minutes to make a congee, adding water if necessary. When the rice is soft, add the preboiled garlic to the gruel; stir well, then cook for another 3 minutes. To be eaten twice a day for as long as the dysentery persists.
Other food remedies for dysentery include apples, radish, and ginger.
Radish and Ginger Tea
1 4-ounce (125-gram) piece of ginger, grated
16 ounces (500 grams) radish or daikon
1 heaping teaspoon (5+ grams) green tea leaves
1 cup (250 milliliters) water
2 tablespoons (30 milliliters) honey
Over a small bowl, squeeze the grated ginger to extract 1 tablespoon (15 milliliters) of juice. Squeeze the grated radish or daikon over the same bowl to extract 4 tablespoons (70 milliliters) of juice.
Place the tea leaves in a cup. Heat the water in a small saucepan. When the water is about to boil, pour it over the tea leaves. Leave the tea to brew for 10 minutes.
Stir in the ginger and radish juice and honey. Drink warm two or three times a day.
Ginger, Tangerine, and Apple Peel Decoction
4 teaspoons (20 grams) organic apple peel
2 teaspoons (10 grams) organic tangerine peel
2 cups (500 milliliters) water
1 teaspoon (5 grams) ginger, peeled and sliced
Wash and peel 1 organic apple and 1 organic tangerine.
In a small saucepan, bring the water to a boil. Add the apple, tangerine peel, and ginger slices, and boil over a low flame for 15 minutes.
Drink warm or at room temperature two or three times a day.
Eggs and Ginger
_This recipe affects the large intestines and the lungs. It is most effective in allaying a dysentery problem at its onset. Ginger has warming qualities; it induces perspiration and disperses cold. Eggs are sweet and lubricating._
2 eggs
2 teaspoons (10 grams) ginger, finely minced
Water for steaming
Beat the eggs in a small ceramic bowl. Add the ginger to the eggs, then put the bowl in a steaming dish (see page 66).
Using a pan deep enough to fit your steamer, bring water to a boil. Place the steamer in the pan and cover. Steam for 10 minutes.
Take two times a day on an empty stomach.
Green Tea with Vinegar
_The following concoction is not the best way to enjoy a cup of tea. Quite apart from the vinegar, 100 grams of tea leaves produces a foul, bitter brew. Strong tea, however, is known to detoxify or, in Chinese terms, to relieve internal heat. It is also an efficient diuretic._
1½ cups (375 milliliters) water
6 tablespoons (90 grams) green tea leaves
6 teaspoons (30 milliliters) vinegar
In a small saucepan, bring the water to a boil. Add the tea leaves and boil over a low flame for 1 minute.
Remove the tea from heat and brew for 5 minutes. Pour equal quantities of tea into three separate cups. Add 2 teaspoons (10 milliliters) of vinegar to each cup.
Drink each cup separately: one in the morning, another in the afternoon, and the third in the evening. Reheat the tea each time to drink it hot.
An alternative to this recipe is to mix the tea with wine instead of vinegar. Although rice wine, or sake, is a less effective than vinegar, it does without a doubt make for a more pleasurable drink.
Tomato Plant Decoction
16 cups (4 liters) water
2 or 3 tomato plants, complete with stalks and leaves (no fruits)
Bring the water to a boil in a large soup kettle. Wash the tomato plants and remove the roots. Cut the plant into 5-inch-long segments. Place the tomato plants in the water and simmer for 3 hours over a low flame.
After boiling, pass the liquid through a strainer. Drink a cup of the decoction every two hours, warm or at room temperature.
Steamed Potatoes with Honey
1 cup (250 milliliters) water
2 or 3 potatoes, peeled and cubed
2 tablespoons (30 milliliters) honey
In a medium saucepan, bring water to a boil.
Place the potatoes in a steaming dish. Put the dish in the saucepan, cover, and steam the potatoes for 15 minutes. When the potatoes are finished steaming, transfer them to a bowl and add honey. Take two or three times a day for as long as the problem persists.
Additional food remedies are as follows:
* Munch an apple well, the greener the apple, the better, or, better still, grate it before you eat it. Eat 3 to 6 apples a day.
* Hard boil 10 to 20 eggs. Eat the yolks until your mouth tastes like _ji shi_. This expression literally translates as "chicken shit," and is, in fact, a genuine Chinese instruction. Do not take this remedy for longer than a week.
* Squeeze 2 or 3 tablespoons (15 or 30 milliliters) of onion juice and mix with the same quantity of vinegar. Bring to a boil in a small saucepan. Remove from the flame; sip hot.
FOOD POISONING
Food poisoning is not a common occurrence in the United States. Nevertheless, mistakes are made: food may become contaminated by toxic bacteria, or one may eat poisonous plants, fish, or mushrooms.
In China, people are fairly careful not to contaminate food. We rarely keep fresh food for more than a few hours. We do not use frozen foods that may go bad during an electricity outage. If we are ever suspicious about sanitary conditions when we travel, we eat our food with plenty of raw garlic because garlic is a natural antibiotic that kills off any harmful bacteria.
Mushroom poisoning is, however, another matter. In China, mushrooms have been used both as food and for medicinal purposes since time immemorial. Only a few species of mushrooms are cultivated; most varieties cannot be grown at will. People therefore pick wild mushrooms at the risk of consuming toxic or poisonous species.
Very few wild mushrooms are deadly, and only one of these has no known antidote. This is the _Amanita phalloides,_ or death cap. The reason for this mushroom's extreme toxicity is that it contains three kinds of poison that damage cells throughout the body after being absorbed into the bloodstream. Symptoms of _Amanita phalloides_ poisoning therefore appear after digestion is complete, generally between six and fifteen hours after eating. Symptoms include strong abdominal pains, nausea, vomiting, intense thirst, bloody diarrhea, absence of urine, prostration, and convulsions. If any suspicion of _Amanita phalloides_ poisoning exists, rush the patient to a hospital that can circulate the patient's blood outside the body through a special charcoal filter, which will eliminate the poison. Nothing else can help.
Other types of mushroom poisoning are less dangerous. Symptoms appear during digestion and can range from stomach pains and nausea to hallucinations. For these forms of mushroom poisoning Chinese peasants have come up with several remedies, all of which are useful in treating all forms of food poisoning.
First of all, one must induce vomiting. To induce vomiting you can drink salt water in large enough quantities to make you vomit, or thrust your fingers down your throat until you retch and throw up.
Once the toxins have been eliminated from the digestive tract, one can administer the following traditional remedies for mushroom poisoning with greater ease.
* Grind 1 cup (200 grams) of raw mung beans to a fine powder. Stir 2 table spoons (30 grams) of powder into 1 cup (250 milliliters) of water. Drink as many cups as you can manage.
* Boil ½ cup (100 grams) of soybeans in 4 cups (1 liter) of water over a low flame for 45 minutes. Add water if necessary. Take 1 cup of the soup, warm, twice a day.
* Another common antidote to food poisoning is lotus leaf tea. Although common in China, in the United States lotus leaves are available only in specialized Chinese food stores. However, this remedy is worth knowing about in case you need a cure for mushroom poisoning, and lotus leaves are at hand.
Boil 2 teaspoons (10 grams) of lotus leaves in 2 cups (500 milliliters) of water for 30 minutes, until the brew reduces to 1 cup (250 milliliters). If necessary, add water during the preparation. Drink 1 cup three times a day, until the symptoms of poisoning recede.
* Tofu is sometimes poorly prepared, and its ingestion can result in quite severe abdominal pain and nausea. The prescribed remedy for this condition is to drink radish juice. Grate and squeeze enough fresh radishes to extract 1 glass of juice to drink. Alternatively you can boil 12 radishes in 3 cups (750 milliliters) of water for 30 minutes, then drink the soup.
* One of the most common forms of food poisoning is that which occurs from eating prawns and shellfish. The Chinese remedy for this is to drink a tea prepared from orange peel. Peel 1 organic orange, then cut the peel into ½inch slices. Boil in 1 cup (250 milliliters) of water over a medium flame for 10 to 15 minutes. Drink hot or warm three times a day.
GASTRITIS
Acute gastritis is caused by food poisoning, infection, or excessive eating or drinking. It appears and subsides rapidly. The best cure for gastritis is complete abstinence from food.
Chronic gastritis, on the other hand, usually depends on the habitual heavy use of irritants such as chili and pepper in one's diet, and on psychosomatic causes such as anxiety, stress, and frustration.
The obvious solution is to eliminate the irritants and to relax. You might also wish to try one of the following Chinese remedies.
Potato Juice and Honey
1 potato, peeled and grated
1 teaspoon (5 grams) honey
Using a thin cotton towel, squeeze the potato over a glass to extract the juice. Add honey.
Drink on an empty stomach every morning for twenty days.
Ginger and Orange Peel Decoction
2 cups (500 milliliters) water
1 tablespoon (15 grams) sliced ginger
1 organic orange peel, sliced
In a small saucepan, bring the water to a boil. Add the ginger and orange peel. Simmer on a low flame for 20 minutes.
Allow the decoction to cool slightly. Drink two or three times a day.
Powdered Eggshell
_This classic Chinese remedy checks acidity and gastritis and helps cure duodenal and stomach ulcers._
1 chicken eggshell
In a dry wok or frying pan roast the empty eggshell over a low flame for approximately 4 minutes, or until it is thoroughly dry. Remove and allow the shell to cool, then transfer it to a pestle or stone grinder and grind it into a powder.
Take 1 teaspoon of the powder in warm water before meals.
The same effects are obtained from cuttlefish bone. Bake a cuttlefish and extract the bone, then roast it and grind it into a powder. Take 1 teaspoon (5 grams) of the powder with warm water, again before meals.
Peanuts, Milk, and Honey
¼ cup (50 grams) raw peanuts
Water for soaking
1 cup (250 milliliters) milk
2 tablespoons (30 milliliters) honey
Soak the peanuts in hot water for 1 hour. Drain the water, then grind the peanuts to a pulp.
In a small saucepan, bring the milk to a boil. Add the peanuts as soon as the milk begins to rise. Allow the milk to boil again. As the milk rises a second time, remove the saucepan from the flame.
Let cool for 5 minutes. Stir in the honey.
Drink warm just before going to bed.
Pork Tripe and Soybeans
_This recipe not only alleviates chronic gastritis, but also helps to recover strength if one has been weakened by gastric problems._
½ cup (100 grams) soybeans
Water for soaking
6 cups (1.5 liters) water
8 ounces (250 grams) pork tripe, washed and sliced
Soak the soybeans in 2 cups (500 milliliters) of water overnight. When you are ready to prepare the remedy, drain the soybeans and discard the soaking water.
In a large saucepan, bring 6 cups (1.5 liters) of water to a boil. Add the tripe and boil over a low flame for 1 hour. Add the soybeans to the tripe and continue to boil over a medium flame for another 40 minutes. If necessary, occasionally add small quantities of water.
When done, separate into three equal portions. Consume one portion with each meal: breakfast, lunch, and dinner.
HAIR LOSS AND PREMATURE GRAYING
Hair loss and premature graying may be caused by a wide variety of factors, the most common of which are hereditary. When genes are responsible there is little that one can do about hair problems, except to stay fit and healthy in order to delay as long as possible that which is truly inevitable.
Hair loss and graying that are not hereditary are considered to be due either to weakness in the kidneys and the blood or to poor nourishment of the hair follicles. A poorly balanced diet is said to cause the hair follicles to open and xie qi (evil qi) to enter. The xie qi dries and heats the blood which thus no longer feeds the already undernourished roots, thereby causing the hair to fall out or to lose its color.
Healthy hair depends on good nutrition. Good general health means good healthy hair, and healthy skin for that matter. In China we eat many foods throughout our lives that we consider to be specifically for the health of our hair and skin. Some of these foods are seaweed, sunflower seeds, jujube, apples, plums, scallions, carrots, celery, radish, yogurt, black beans, and peanuts. Walnuts, usually taken first thing in the morning on an empty stomach, are also a popular remedy; some people wash them down with a glass of milk. Roasted black sesame seeds ground to a powder and taken with sugar in hot water for breakfast is also known to support good hair and skin health.
The common remedies for hair problems serve to ensure better nutrition to the kidneys, the blood, and the scalp.
Spinach and Black Sesame Seed
_One of the best food items for maintaining healthy hair, as recognized all over China, is black sesame seed. Many people eat black sesame seed in large quantities in order to maintain their black, shiny hair. People add the seeds to soups, vegetable dishes, and meats. They make candies with it, or simply chew on black sesame seeds whenever the occasion arises.
This recipe serves to combat hair loss._
¼ cup (50 grams) fresh packed spinach
4 teaspoons (20 grams) black sesame seeds
2 tablespoons (30 milliliters) water
Wash and drain the spinach. Place the spinach, sesame seeds, and water in a wok or small saucepan. Steam over a medium flame for 5 minutes, stirring continuously.
Eat twice daily.
Walnuts and Sesame
1 cup (200 grams) walnut meats, broken into small pieces
1 cup (200 grams) black sesame seeds
1 cup (200 grams) brown sugar
Roast the walnuts and sesame seeds together in a dry frying pan or wok over a low flame for 3 minutes. Stir to ensure that the nuts and seeds do not burn.
Transfer the roasted nuts and seeds to a mortar and pestle. Allow them to cool, then grind to a fine powder. Mix the powder with the sugar, then store in a jar.
Take 1 tablespoon every morning with breakfast.
Black Sesame Tea
1 teaspoon (5 grams) black sesame seeds
½ teaspoon (2.5 grams) green tea leaves
1 cup (250 milliliters) water
Roast the sesame seeds for 3 minutes in a dry frying pan over a low flame.
Allow the seeds to cool, then grind them into a powder with a mortar and pestle or a stone grinder. In a cup, mix the powder with the tea leaves.
Bring the water to a boil, then pour into the cup. Brew in hot water for 5 minutes, as you would an ordinary cup of tea.
Spinach Roots, Eggplant, and Black Beans
_In some rural areas in the north of China, many people use black beans instead of black sesame seed. The tonifying and ascending Yang qualities, as well as the color of black beans, are said to maintain the hair, making it shiny, black, and healthy. The following recipe comes from Shaanxi province, not far from the Yellow River._
2 cups (500 milliliters) water
2 tablespoons (30 grams) black beans
2 tablespoons (30 grams) spinach root (or the bottom part of the stalk), cut into
1-inch pieces 1 eggplant skin, cut into 1-inch pieces
In a medium saucepan, bring the water to a boil. Add the beans, spinach root, and eggplant skin, and boil over a low flame for 40 minutes, or until the beans are soft enough to eat. Add a little water, if necessary, to ensure that you make a liquid soup rather than a gruel.
Remove from heat. Eat warm. This remedy can be taken as often as you like.
Walnut, Almond, and Jujube Wine
_This recipe stimulates blood circulation and improves the complexion. It reinforces qi, and arrests the premature graying of the hair. This recipe also acts as a lung and kidney tonic, thereby curing shortness of breath and lower back pain due to deficiencies in these organs._
¼ cup (50 grams) almond meats
½ cup (100 grams) walnut meats
½ cup (100 grams) jujube (Chinese dates)
8 cups (2 liters) rice wine, or sake
Grind the almonds and the walnuts into a powder using a pestle or a stone grinder. Put the powder and the jujube in a one-gallon bottle. Add the rice wine. Seal the bottle and leave to macerate for at least 20 days before drinking.
Take 2 teaspoons (10 milliliters) two times a day.
**The following two remedies help combat hair loss.**
Garlic and Honey Poultice
2 heads of garlic, peeled and crushed
2 tablespoons (30 milliliters) honey
In a cup, thoroughly mix the garlic with the honey.
Apply to the affected part of the scalp before going to bed. Wash the poultice off in the morning.
Ginger Head Massage
1 large fresh ginger tuber, grated
Squeeze the ginger thoroughly to extract the juice.
Rub the juice into the affected area of the scalp. Leave to dry naturally. Reapply when the scalp has dried. Apply three times at each sitting.
Best results are achieved by massaging the scalp with ginger juice twice a day. It is claimed that, after a week, soft fine hair will begin to grow, and that, within a month, hair growth will be back to normal.
**This final remedy is a simple one for strengthening hair and preventing its loss.**
Spinach and Carrot Salad
1 cup (200 grams) packed fresh spinach, chopped
1 medium carrot, grated
Mix the spinach and carrot together and eat as salad.
HEADACHE
Headaches can be brought on by so many different factors that it is difficult to prescribe remedies that go to the source of the discomfort. Headaches may be caused by eyestrain, stress, a poor night's sleep, tobacco smoke, toxic fumes, arthritis, a brain tumor, or the common cold. The simplest remedy therefore is to swallow a painkiller and, only if the ache persists, to go to the doctor in order to seek the underlying cause.
In the Chinese countryside, where neither doctors nor painkillers are as easy to come by as in America, other remedies exist. If the cause of the headache is a head cold, one simply cures the cold. Plenty of remedies exist; we refer you to the section on the common cold (pages 98–106) for these.
Headaches without a cold may be alleviated by rubbing eucalyptus oil over the forehead and temples. This gives a cooling sensation that distracts from the pain. Peppermint has a similar effect. You can rub peppermint oil on the temples, dab it under your nose, or drink a cup of peppermint tea.
Another simple headache remedy is to massage the head. Massage is particularly effective if the headache is caused by tension: gently massage the scalp and nape of the neck. A qi gong massage consists of beating on the scalp with the fingers of both hands. Another alternative is to press all your fingers against the scalp and move the entire scalp vigorously backward and forward. Try massaging the temples as well. If no other massage works, press hard with the pads of your thumbs or your two index fingers into the bone of the upper eye socket, close to the top of your nose. Make sure that your fingers are not wet or oily, lest they slip off the bone into the eye itself.
Some of the most effective Chinese food remedies for headaches come in the form of teas.
Ginger Tea
_Ginger tea is particularly effective for headaches that are due to wind and cold weather._
1½ cups (375 milliliters) water
2 teaspoons (10 grams) fresh ginger, sliced
2 teaspoons (10 grams) brown sugar
In a small saucepan, bring the water to a boil. Add the ginger and sugar and simmer on a low flame for 10 minutes. Transfer the tea to a cup and drink hot.
To be taken three times a day for as long as the headache persists.
Almond and Chrysanthemum Tea
_Almonds and chrysanthemum flowers have a cooling effect. Combined in a tea, they are effective against headaches due to wind and heat._
1½ cups (375 milliliters) water
1 teaspoon (5 grams) almond meats, ground or chopped
1 teaspoon (5 grams) dry chrysanthemum flowers
In a small saucepan, bring the water to a boil. Add the almonds and chrysanthemum flowers, reduce the flame, and let simmer for 15 minutes.
Remove from heat and drink hot.
Green Tea and Orange Peel
_This tea is suitable for treating headache associated with nausea and catarrh._
1 teaspoon (5 grams) green tea leaves
1 organic orange peel, chopped
1½ cups (375 milliliters) water
Place the tea leaves, orange peel, and water in a small saucepan. Simmer over a low flame for 10 minutes.
Drink the tea twice a day.
Chrysanthemum Wine
_Sometimes wines are prepared for headaches instead of teas._
1 cup (200 grams) dry chrysanthemum flowers
8 cups (2 liters) rice wine, or sake
Place the flowers in a bottle with the wine. Seal the bottle. Let stand to macerate for at least 10 days.
Take 2 or 3 teaspoons twice a day.
Scallion and Cinnamon Congee
_When the body and head ache due to cold and windy climatic conditions, many people in China seek relief in this scallion and cinnamon gruel._
2 cups (500 milliliters) water
¼ cup (50 grams) rice
10 scallions, cut into ¼-inch segments
2 teaspoons (10 grams) cinnamon
Place the water, rice, scallions, and cinnamon in a small saucepan. Bring to a boil, cover, then simmer for 20 minutes over a low flame. Add a little water if necessary to form a gruel or congee.
To be taken twice a day with meals.
Mung Bean Congee
_This remedy is recommended for headaches due to summer heat, and overexposure to the sun._
6 cups (1.5 liters) water
¼ cup (50 grams) mung beans
½ cup (100 grams) rice
In a medium saucepan, bring water to a boil. Add the mung beans and rice. Boil over a low flame, covered, for 30 minutes, stirring occasionally, to prepare a gruel or congee. Add more hot water if necessary.
Remove from flame. Consume hot or warm.
HEMORRHOIDS
Also known as piles, hemorrhoids are caused by a genetic weakness of the veins in the rectum, by sedentary habits, or by constipation. They are characterized by discomfort and sometimes pain, and by frequent bleeding from the rectum during defecation. Hemorrhoids may either be internal or protrude from the body.
The most effective means of preventing piles is to exercise. Although all exercise is beneficial, Chinese qi gong includes a technique whereby the muscles of the rectum are tightened (see the _nei dan_ exercises, especially on page 246). This exercise helps to maintain firmness in the rectal muscles with a consequent compression of rectal blood vessels, thus preventing hemorrhoids from developing. A suitable low-fat and low-protein diet of fruits and greens that contain plenty of fiber also works to prevent hemorrhoids.
Wood-ear Mushroom Decoction
_An old remedy for piles is to eat wood-ear mushrooms._
¼ cup (50 grams) wood-ear mushrooms
Water for soaking
2 tablespoons (30 grams) sugar
2 cups (500 milliliters) water
Soak the mushrooms in 1 cup (250 milliliters) of hot water for 1 hour. When you're ready to begin cooking, drain the mushrooms and discard the water.
Put the mushrooms, sugar, and 2 cups (500 milliliters) water into a small saucepan. Bring to a boil. Simmer over a medium flame for 10 minutes to make a decoction.
Divide into three portions. Drink the decoction warm, three times a day.
Escargot
_Another ancient Chinese remedy for hemorrhoids is to eat snails._
1 cup (200 grams) bread, torn into large pieces
½ cup (125 milliliters) vinegar
12 escargot (snails)
4 cups (1 liter) water
To clean the snails, put the bread and vinegar in a container. Add the escargot, cover the container, and refrigerate for 24 hours. The snail will come out of its shell to eat the bread, and the vinegar will disinfect the snail.
When you're ready to cook the snail meat, remove the snails from the container and wash them under running water. Discard the bread. Bring the water to a boil in a medium saucepan. Add the snails in their shells and boil for 10 minutes.
The snails can be eaten in a variety of ways. They may be stir-fried with garlic and herbs, or eaten boiled, dipped in soy sauce and vinegar for flavor. When removing from the shell, be sure to discard the top portion of the snail containing the organs of digestion and excretion.
Mung Bean Soup and Bananas
_This high-fiber combination helps prevent hemorrhoids._
1½ cups (375 milliliters) water
2 tablespoons (30 grams) mung beans
2 ripe bananas
Prepare a decoction by bringing the water to a boil, adding the mung beans, and simmering over a low flame 20 minutes.
Eat twice a day, for breakfast and dinner, together with two bananas.
Hemorrhoids can often be painful. The following two remedies are for pain relief.
* Chop and crush 1 medium onion. Transfer the onion to a bowl. Mix with 1 tablespoon (15 milliliters) honey to make a paste. Apply the paste to the hemorrhoid whenever you feel pain.
* Squeeze the juice from 3 or 4 cloves of garlic. Dilute the juice in five times the amount of water. Wash the affected area with warm to hot water. Immediately after washing, soak a piece of cotton-wool in the diluted garlic juice and apply to the hemorrhoid. Continue the treatment for as long as necessary.
HEPATITIS
Hepatitis is an inflammation of the liver that may be brought on by either bacteria or a virus. The two most common forms are hepatitis A (infectious) and hepatitis B (serum). The first is usually transmitted through food and is due to poor sanitary conditions. The hepatitis A bacteria reside in feces; the bacteria can pass into drinking water through faulty sewage systems, or into shellfish that breed close to sewage outlets. Serum hepatitis, on the other hand, is caused by direct contact through blood or body fluids, the same way as the HIV virus is spread.
The symptoms of hepatitis include lethargy, nausea, and fever. Urine takes on a reddish brown hue, and the feces become light brown. Recovery is usually spontaneous, although it takes time and plenty of rest for the liver to restore itself. Treatment consists of little more than bed rest and a light diet that does not put strain on the liver.
A person healing from hepatitis should eat plenty of light and energetic foods: ripe fruits, soups, and broth. They should stay away from fat, oil, and milk products, although an exception may be made for light cottage cheese or skimmed milk. An egg a day helps the liver. So does plenty of fluid—drink water and fruit and vegetable juices in large quantities.
Animal liver is a light and energetic food that is ideal for nourishing and rebuilding a damaged liver. Furthermore if it is true, as Chinese theory asserts, that eating animal organs restores health to one's own corresponding organ, liver should do it best of all. Steam, broil, or boil liver, but do not fry it. Fried oil is heavy to digest and will harm the liver at it struggles to recuperate.
In China, hepatitis was not recognized as being due to bacterial and viral infections until recently. Traditional and home remedies thus treat this disease as a genetic weakness of the liver. The following five remedies are aimed specifically at helping the liver to rebuild after the damage caused by the hepatitis. Sugar or honey are used because they provide energy for liver reconstruction.
Soybean Garlic Soup
¼ cup (50 grams) soybeans
Water for soaking
3 cups (750 milliliters) water
4 tablespoons (60 grams) sugar, brown or white
1 head of fresh garlic, peeled and crushed
Soak the soybeans overnight in 2 cups (500 milliliters) water. When you are ready to cook, drain the soybeans and discard the water.
In a medium saucepan bring 3 cups water to (750 milliliters) boil. Add the soybeans, cover the pan, and boil over a medium flame for 40 minutes. You want to end up with a watery soup, so add water occasionally if necessary.
Remove from heat and stir in the sugar and crushed garlic.
Divide the soup into two portions. Take hot twice a day. This soup should be taken in combination with one or more of the other therapies described below.
Jujube and Peanuts Sweet
3 cups (750 milliliters) water
¼ cup (50 grams) raw peanuts
10 jujube (Chinese dates)
4 tablespoons (60 grams) brown sugar
In a medium saucepan, bring the water to a boil. Add the peanuts, cover, and simmer over a medium flame for 20 minutes. Add the jujube and sugar. Cover the pan again and simmer for another 15 minutes, until the jujube are cooked. If necessary, occasionally add small quantities of water. The end product should resemble a soup rather than a gruel.
Take 2 tablespoons warm every evening for thirty days, before going to bed.
Celery and Honey
_This recipe is a liver reconstructant for infectious hepatitis._
5 stalks of fresh celery, chopped into small pieces
1–2 tablespoons (15–30 milliliters) honey, according to taste
Water for steaming
Using a thin cotton towel, squeeze the celery to extract the juice. Transfer to a bowl for steaming. Add honey.
Put the bowl in a steaming dish (see page 66). Using a pan deep enough to fit your steamer, bring water to a boil. Put the steamer in the pan, cover, and steam for 10 minutes.
Take once a day, preferably in the morning. (You may, as an alternative, heat the celery juice and honey directly in a saucepan for 5 minutes.)
Water Chestnut and Willow Leaf Tea
_Water chestnut is a cold and sweet ingredient commonly used in China for indigestion and for liver problems._
5 weeping willow leaves (approximately 6 grams) (collect these leaves from a nearby tree)
6 water chestnuts, halved
2 cups (500 milliliters) water
Wash the willow leaves. Place the willow leaves and the water chestnuts in a small saucepan with the water. Bring to a boil, then cover and simmer over a low flame for 10 minutes.
Drink frequently as a tea.
Boiled Eggs Flavored with Orange Peel and Anise Seed
3 cups (750 milliliters) water
4 eggs, raw
2 teaspoons (10 grams) organic orange peel, cut
in ½-inch slices
2 teaspoons (10 grams) ground anise seed
In a medium saucepan, bring the water to a boil. Place the eggs, whole, into the water, along with the orange peel and aniseed. Boil over a medium flame, uncovered, for 10 minutes.
Remove the eggs. Crack the shell, but do not remove the shell. Put the eggs back in the water and simmer over low heat for another 20 minutes.
Remove the eggs from the water and let them cool. Peel the eggs. Eat 2 eggs two times a day.
Pork Gall and Honey
_For those adventurous enough to try something unusual, you might take some pork gall with honey. (Anything is worth trying when you are laid up with hepatitis.) Besides strengthening the liver, this recipe also arrests diarrhea._
1 gallbladder of pork, cubed
8 tablespoons (120 grams) honey
Water for steaming
Using a thin cotton towel, squeeze the gallbladder to obtain the gall. Transfer the gall to a ceramic bowl. Stir in the honey.
Put the bowl in a steaming dish (see page 66). Using a pan big enough to fit the steamer, bring water to a boil. Put the steamer in the pan, cover, and steam for 10 minutes. Remove from heat.
Take warm once a day.
HYPERACIDITY
Hyperacidity is a frequent precursor of gastric problems of a more serious nature. To combat hyperacidity, refrain from eating heavy, greasy, sour, or irritating food—that means cutting down on fried foods, heavy roasts, lemon, vinegar and sour fruits, raw vegetables, and green and red chili pepper.
Garlic Pork
_A common food remedy for hyperacidity in China is to eat lean pork with garlic._
5 to 7 ounces (150 to 200 grams) lean pork, cut into ½-inch cubes
1 head of garlic, peeled and crushed
1 cup (250 milliliters) water for steaming
Place the pork in a bowl. Sprinkle the crushed garlic over the pork. Steam together for 30 minutes. Eat as part of your meals.
HYPERTENSION (HIGH BLOOD PRESSURE)
The blood pressure of a healthy adult should ideally be 120 mm Hg (millimeters of mercury), when the lower chamber of the heart contracts to force the blood through the arteries (diastolic pressure), and 80 mm Hg on the rebound, when the same chamber expands to receive blood (systolic pressure). Blood pressure is considered to be "normal" within the range of 90 and 140 mm Hg diastolic, and 60 and 90 mm Hg systolic. Anything higher or lower than that is considered harmful to general health.
Blood pressure is considered to be high when it reads over 140 mm Hg diastolic and 90 mm Hg systolic. Symptoms of high blood pressure are frequent pounding headaches, tension and insomnia, raised arteries at the temple, flushed features, ringing in the ears, ankle swelling, and heart palpitations.
Hypertension arises as a result of the narrowing of the arteries. This may be hereditary, but it may also be due to stress; high cholesterol levels; obesity; the intake of too much alcohol, fat, sugar, or salt; kidney disease; a disease of the endocrine or nervous systems; or to any blockage of the arteries. In the long run, high blood pressure can lead to cardiovascular disease, heart attacks, and stroke. In most cases the cure for hypertension is effected by treating its underlying cause. When this cause is not apparent, as in "essential" or hereditary high blood pressure, it may be treated by the administration of specific drugs or by a combination of diet and exercise.
The first and indispensable dietary measure must be to reduce the intake of sodium, fats, cholesterol, meat, and sugar. A useful second step is to increase the intake of soluble fiber which, it is believed, cleanses the veins and arteries of dangerous cholesterol. Alcohol in doses of one glass of wine or one small shot of Chinese rice wine (or sake) may also combat cholesterol and fat deposits. Any larger amounts, however, harden the arteries and consequently increase blood pressure.
Specific foods used in China to lower blood pressure are kelp and other seaweeds, clams, bean sprouts, bean curd (tofu), celery, garlic, onions, tomatoes, radish, daikon, sesame seeds, sunflower seeds, peanuts, bananas, oranges, persimmon, watermelon (including the rind), potatoes, whole-grain cereals, green tea, and peppermint.
Western studies confirm the validity of all the above products for combating hypertension. Most of them are rich in fiber. Bananas, sunflower seeds, beans, celery, melons and watermelons, oranges, tomatoes, and potatoes—together, with avocados, fish (especially sardines), squash, apricots, and peaches—all contain potassium. Potassium has been shown in numerous studies to neutralize the artery-hardening effects of sodium, as has calcium. Calcium-rich food sources are chickpeas, tofu, beans, greenleaf vegetables, alfalfa sprouts, sunflower seeds, and dairy products. Garlic and onion contain a hormonelike substance called prostaglandin A1 which lowers blood pressure. It has also been found that vegetarians tend to suffer less frequently from hypertension than do meat eaters.
As well as a high vegetable-fiber intake and a low-fat diet, Chinese treatment of hypertension includes early morning qi gong exercise and brisk walks.
Some specific Chinese food remedies for hypertension are:
* Eat up to 5 ripe bananas a day.
* Eat 1 raw tomato every morning before breakfast. In China, a teaspoon of white sugar is often sprinkled on top.
* Grate 2 cups (400 grams) of fresh radish or daikon. Squeeze out the juice. Drink 1 glass twice a day.
* Eat 2 or 3 raw celery stalks every day, or drink 1 cup (250 milliliters) of raw celery juice.
* Take a glass of celery juice as an afternoon drink, with a handful of sunflower seeds. Take every day for at least one month.
**Celery, a diuretic, calms the nerves, warms the stomach, strengthens the liver, and lowers blood pressure. The juice is also considered to be an effective remedy when cooked.**
Celery and Rice
¼ cup (50 grams) celery
3 cups (750 milliliters) water
¼ cup (50 grams) rice
Wash the celery, removing the leaves (do not discard them). Chop the celery stalks into ½-inch segments.
Put two saucepans of water on to boil, one containing 2 cups (500 milliliters) of water, the other with 1 cup (250 milliliters). Place the celery and rice in the larger saucepan, cover, and boil for 20 minutes, stirring occasionally, until the rice is soft and mushy. In the meantime, place the celery leaves in the smaller saucepan and boil for 5 minutes.
Add the leaf broth to the congee when the congee is ready.
Take once a day as part of a meal.
Celery and Vegetable Soup
4 cups (1 liter) water
½ cup (100 grams) celery, chopped
5 garlic cloves, peeled and lightly crushed
5 slices onion
5 peeled water chestnuts
1 tomato
1 teaspoon (5 grams) seaweed, optional
In a medium saucepan, bring the water to a boil. Add all ingredients and boil, uncovered, for 15 minutes. Do not add any salt, soy sauce, or stock.
Consume warm before bedtime. Take this remedy for as long as the problem persists.
**Note:** If you have difficulty finding water chestnuts, you can either dispense with them altogether or use ¼ cup (50 grams) of soybeans or bean sprouts instead.
Boiled Celery Juice
4 cups (1 liter) water
1 cup (200 grams) celery, cut into 1-inch segments
Bring the water to a boil in a medium saucepan. Put the celery into the saucepan and boil for 3 minutes. When it is done, drain the celery and discard the water. Put the celery in a thin cotton towel. Squeeze the celery over a bowl to extract the juice.
Drink the juice either alone or with honey twice a day, morning and evening.
Sugar and Vinegar
½ cup (125 milliliters) rice vinegar
2 tablespoons (30 grams) rock sugar
Place the vinegar in a small saucepan. Heat over a low flame. When the vinegar is warm, add the sugar. Stir until the sugar melts. Allow to cool.
Sip warm following meals.
Mung Beans and Black Sesame
1 cup (200 grams) mung beans
1 cup (200 grams) black sesame seeds
Roast the mung beans and the sesame seeds in a frying pan or wok until they are thoroughly dry. Remove and allow them to cool.
Using a grinding stone or mortar and pestle, grind the roasted beans and seeds into a powder. Take 3 tablespoons (45 grams) of the powder twice a day on cereal or with rice, congee, warm milk, or water.
**In China people sometimes collect rather more abstruse ingredients in order to keep their high blood pressure in check. We have included three simple prescriptions using ingredients that might seem unusual but are, in fact, fairly easy to come by.**
Watermelon Rind, Corn Threads, and Banana Decoction
2 cups (500 milliliters) water
¼ cup (50 grams) watermelon rind, diced
1 banana, chopped
Threads from the head of 1 ripe corn plant
2 teaspoons (10 grams) brown sugar
In a medium saucepan, bring the water to a boil. Add all the ingredients except the sugar. Simmer over low heat until only 1 cup (250 milliliters) of water is left, approximately 40 minutes.
Remove from heat and add the sugar. Consume warm.
Magnolia Flower Tea
1 cup (250 milliliters) water
1 magnolia (Magnolia grandiflora) flower
In a small saucepan, bring the water to a boil. Place the magnolia in a cup and pour the hot water over it. Cover and leave to brew for half an hour.
Drink as a tea.
Earthworm
_Although we left this appealing remedy until last, it is in fact one of the most common remedies for hypertension in China. Its efficacy is well proven._
1 earthworm
Wash and dry an earthworm. Chop it into ½-inch segments.
Roast the earthworm for 3 minutes in a dry frying pan. Cool slightly, then grind the segments into a powder.
Take 1 teaspoon of the powder three times a day in hot water, or any other way you may fancy.
HYPOTENSION (LOW BLOOD PRESSURE)
Low blood pressure (lower than 90 mm Hg diastolic and 60 mm Hg systolic—see page 145) leads to sleepiness, weakness, headaches, dizziness, insomnia, tiring easily, lack of concentration, chest pains, and feelings of suffocation. People with very low blood pressure faint easily when standing up suddenly; they are usually pale, sweat profusely, and have a slow heartbeat.
According to Chinese medicine, low blood pressure is due to weak Yang and qi. It is usually accompanied by a weak spleen and stomach. It tends to occur in sedentary intellectual workers, and in elderly people with heart ailments.
Remedies are to eat well and to exercise. The following specific cures might also help.
* Eat beef any way you like it. In China it is usually eaten in a stew.
* Chew a piece of raw, fresh ginger as you would a candy. You can also add slices of ginger to your soups, teas, or stews. Take three or four a day.
* Two tablespoons of sugar in a glass of wine taken twice a day guarantees an increase in blood pressure. Any wine will do.
Tangerine Peel, Walnut, and Licorice Decoction
2 cups (500 milliliters) water
1 tablespoon (15 grams) organic tangerine peel, chopped
4 or 5 walnut meats
1 teaspoon (5 grams) pure licorice, or 1 inch of a licorice twig
In a small saucepan, bring the water to a boil . Add all the ingredients and stew over a low flame for 15 minutes.
Drink warm twice a day, morning and evening.
INDIGESTION
Indigestion is due either to a weak stomach and spleen—in Chinese terms, a deficient Earth function—or to grave mistakes in eating habits. You might be eating too fast, talking while you eat, or eating too much or out of season. Please refer to chapter 3 for more information on what you might be doing wrong. Once you have become aware of any errors in your eating habits, the first step is to correct them. If, in spite of your attentiveness, you continue to suffer from indigestion, you might wish to try dissolving 1 teaspoon (5 grams) of ground cinnamon in a glass of warm water. You may drink this three times a day, with meals, as an aid to digestion. Or try one or more of the following traditional remedies.
Tangerine Peel and Ginger Tea
2 teaspoons (10 grams) finely minced organic tangerine peel
2 teaspoons (10 grams) finely minced fresh ginger
1 teaspoon (5 grams) sugar, brown or white
1 cup (250 milliliters) water
In a small saucepan bring the water to a boil. Place the tangerine peel and the ginger in a cup with the sugar, and pour the boiling water over them. Brew for 10 minutes.
Drink warm as a tea. This tea may be taken up to three times a day.
Ginger and Nutmeg Decoction
_This remedy strengthens the spleen and stomach; it is commonly used in China to eliminate intestinal worms._
1 cup (250 milliliters) water
1 teaspoon (5 grams) sliced fresh ginger
1½ teaspoons (8 grams) ground nutmeg
In a small saucepan, bring the water to a boil. Add the ginger and nutmeg. Cover and simmer over a low flame for 15 minutes.
Drink ½ cup (125 milliliters) of the decoction twice a day before meals.
Water Chestnut and Radish Juice
20 water chestnuts, sliced
1 cup (200 grams) radish, sliced
Using a thin cotton towel, squeeze the water chestnuts and the radish to extract their juices. Mix the juices in a small saucepan. Warm the juice, but do not allow it to boil.
Drink warm as a tea, following meals.
Peppered Jujube
1 teaspoon (5 grams) black peppercorns
10 jujube (Chinese dates) sliced in half
1½ cups (375 milliliters) water
5 slices dried ginger
Using a grinding stone or mortar and pestle, grind the pepper into a medium-grain powder.
In a small saucepan, bring the water to a boil. Add the pepper and jujube. Cover and simmer for 15 minutes.
Drink warm or cool. To be taken after meals once or twice a day.
INSOMNIA
Insomnia may result from a genetic predisposition, a stressful lifestyle, or worry. It may depend on dietary deficiencies such as a lack of calcium or magnesium, or it may be caused by the consumption of too much caffeine. Whatever the causes, there are several measures you can take to counteract chronic insomnia.
The first thing you should do is stop taking coffee, tea, colas, and other stimulants in the afternoons and evenings. You can drink a glass of milk before going to bed—don't put chocolate or cocoa in it, though, as they too are mild stimulants. You can, like the majority of Chinese people, wash your feet in hot water and then massage the soles of your feet every night just before going to bed. You can make love before going to sleep—both male and female orgasms stimulate the secretion of a morphinelike substance in the brain.
You can also practice relaxing. Regular exercise and qi gong deep breathing will help you to relax. Try standing in the qi gong position for fifteen to twenty minutes two to three hours before going to bed (see page 245). Once in bed, ten to fifteen minutes of slow, deep breathing while lying on your back should ensure a good night's rest.
If, however, you still cannot sleep, try the following Chinese remedy:
1. Stand in the qi gong breathing position with knees bent and arms outstretched until you begin to sweat. Ten to twenty minutes should suffice.
2. Walk between one and two hundred paces, swinging your arms vigorously with each pace.
3. Wash your feet and hands in hot water.
4. Massage the underside of your feet by pressing one hundred times on the soft point in the center of the foot, where the toe bones meet and the arch begins.
5. Go back to bed and try sleeping again.
The following are a few other traditional Chinese remedies for insomnia.
* Chop an onion and keep it in a jar. When you cannot sleep, open the jar and inhale through your nose. The onion fumes send you to sleep within fifteen minutes.
* Eat 20 to 30 sunflower seeds before bed.
* Brew 1 tablespoon (15 grams) of wheat bran in hot water, as if you were making a tea. Filter and drink before bed.
Scallion and Jujube Decoction
_This bedtime decoction frequently accompanies, and is said to enhance the effects of, the foot-soaking ritual described above._
4 cups (1 liter) water
8 white heads of scallions, thinly sliced
15 jujube (Chinese dates)
1 teaspoon (5 grams) brown sugar
In a medium saucepan, bring the water to a boil. Add the scallion, jujube, and sugar. Cover and simmer over a medium flame for 30 minutes. Drink 1 cup of the decoction warm, before going to bed.
Millet Broth and Egg Patty
1½ cups (375 milliliters) water
4 tablespoons (60 grams) millet
1 egg
In a small saucepan, bring the water to a boil. Add the millet and turn the heat to low. Simmer for 30 minutes, uncovered, until the soup becomes a gruel. Stir so as not to allow the millet to clump or burn. Add a little water occasionally if the liquid is evaporating too quickly. When you have a creamy broth, remove from heat. Strain the liquid part into a bowl.
Beat the egg in a separate bowl. Pour the liquid from the millet broth and the beaten egg into a small frying pan or wok. Heat the mixture for 5 minutes over a medium flame, stirring until it solidifies. Remove pan from heat.
Eat warm as part of dinner.
Walnuts and Sesame Seeds
¼ cup (50 grams) walnut meats
¼ cup (50 grams) black sesame seeds
1 tablespoon (15 grams) sugar, brown or white
Roast the walnuts and sesame seeds in a dry frying pan or wok over a low flame. Allow the nuts and seeds to cool, then transfer to a pestle or stone grinder and grind to a medium-fine powder.
Mix the powder with sugar. Take 1 tablespoon (15 grams) two hours before bedtime.
Steamed Rolls
_Some recipes may be taken during the day, well before bedtime. These steamed rolls, for instance, are usually eaten for breakfast._
½ cup (100 grams) wheat flour
2 tablespoons (30 milliliters) water
3 tablespoons (45 milliliters) sesame oil
Water for steaming
Mix the flour with the water and the sesame oil. Roll the dough into two round buns.
Transfer the buns to a ceramic bowl or steaming dish (see page 66). Using a pan deep enough to fit your steamer, bring water to a boil. Put the steamer in the pan, cover, and steam for 20 minutes.
Remove from heat. Take this remedy once a day for a week.
Goats' Hearts and Roses
_This recipe may be difficult to execute unless you live on a farm or happen to know a butcher who can provide the goat_ _'_ _s heart. If goat heart proves too difficult to come by, you might wish to try the recipe with lamb instead.
This remedy counteracts insomnia by strengthening the heart and blood circulation. It is also recommended for depression._
1 cup (250 milliliters) water
2 teaspoons (10 grams) salt
Fresh petals from 1 rose (approximately ¼ cup or 50 grams)
2 ounces (60 grams) goat's heart, cubed
In a small saucepan, bring the water and salt to a boil. Add the rose petals. Simmer over a low flame for 10 minutes.
Put the meat in the rose water. Leave to marinate for 15 minutes. Skewer the meat and roast it over an open fire, or barbecue for 15 to 20 minutes. While cooking, brush frequently with the rose water.
Eat as part of dinner.
MENOPAUSE
Menopause is the cessation of menstruation. Although it is not accompanied by any physical deterioration, the hormonal changes involved do take their toll on the well-being of many women.
The characteristic symptoms of menopause are brought about by the decline in the body's production of the hormone estrogen. The decrease in estrogen disturbs the function of the hypothalamus, which is responsible for regulating body heat and metabolism—hence the characteristic "hot flashes" and the increase in weight frequently accompanying menopause. The hormonal imbalance also takes its toll emotionally, many women feeling that age has finally caught up with them. Until recently, menopause was regarded as the definitive end of sexual activity—of youth, childbearing, and vigor: the conclusion of the "prime" of life and the beginning of old age. It is small wonder, therefore, that many women go through a period of deep depression with the onset of menopause.
In China, youth is not as prized as in the West. Indeed, our culture looks up to older people, paying heed to what they tell us. One of our most common terms of respect is the prefix _lao,_ which means "old." We use this whenever we speak or refer to someone who we respect and who is older than ourselves.
As a consequence of this respect, the postmenopause years are regarded with equanimity. It is a time of freedom from the burdens and responsibilities of childbearing and child rearing. Women are at last able to enjoy the fruits of their labors and to achieve a measure of respect both from within the family and from society. It is little wonder, therefore, that in China a woman's years of maturity can be the happiest of her life.
Be this as it may, it is undeniable that the physical symptoms of menopause can, at the very least, be unpleasant. In China several remedies exist that aim toward reducing the effects of hormonal imbalance, such as sleeplessness and irritability. The first one is a classic remedy that may also be used as a generic tonic for the nervous system. You may have to visit an herbalist or a Chinese food store to obtain the licorice and jujube, or you may purchase it by mail order. Twig licorice is to be preferred. However, if this is difficult to come by, ordinary black unsweetened licorice may be used. If that, too, is unavailable, you can resort to the candy variety.
Licorice, Jujube, and Wheat
¼ cup (50 grams) wheat berries
Water for soaking
3 cups (750 milliliters) water
1 tablespoon (15 grams) licorice
10 jujube (Chinese dates)
Soak the wheat berries overnight in 2 cups (500 milliliters) of water. When you're ready to cook, drain the berries and discard the water.
In a medium saucepan, bring 3 cups (750 milliliters) of water to a boil. Add the licorice. Cover the pan and simmer on a low flame for 20 minutes.
Discard the solid licorice and keep only the liquid decoction. Now add the wheat and the jujube. Cover the pan and cook over a medium flame in the licorice juice for 40 minutes, until the wheat is edible.
Eat as you would a porridge.
**Two more recipes based on the tonifying effects of jujube follow.**
Adzuki Beans and Jujube Congee
4 cups (1 liter) water
½ cup (100 grams) adzuki beans
10 jujube (Chinese dates)
¼ cup (50 grams) rice
In a medium saucepan, bring the water to a boil. Add the beans, jujube, and rice. Cover and simmer over a low to medium flame for 30 minutes. Stir, adding water if necessary until ingredients are cooked.
Consume warm as a porridge. This remedy can be taken as often as you like, as part of a meal.
Jujube and Pork Rind
10 jujube (Chinese dates), split in half
2 ounces (60 grams) pork rind, finely chopped
Water for steaming
Place the pork and jujube in a ceramic bowl or steaming dish (see page 66). Using a pan deep enough to fit your steamer, bring water to a boil. Place the steamer in the pan and cover. Steam for 30 minutes.
Remove from heat. Divide the dish into three portions. Consume them all in one day, at four-hour intervals.
Boiled Jellyfish
_Cold jellyfish is a classic hors d_ _'_ _oeuvre in China. We generally eat it cured in vinegar. Cured jellyfish can be purchased in most Chinese food stores in America._
5 ounces (155 grams) jellyfish
3 cups (750 milliliters) water
Salt to taste
Soy sauce, as garnish
Vinegar, as garnish
Wash the jellyfish thoroughly.
Bring the water to a boil in an earthenware pot (or medium saucepan—the earthenware pot is not indispensable). Put the jellyfish in the pot and boil over a medium flame, uncovered, for 20 minutes, until over two-thirds of the water has evaporated and you are left with a little under 1 cup of liquid.
Remove from heat. Add salt to the broth to taste. Slice the jellyfish, and garnish with soy sauce and vinegar.
Drink the broth hot once a day for five days. After that, take it once every ten days until the unpleasant symptoms of menopause have disappeared. Eat the jellyfish as part of a meal.
Seaweed Soup
_Seaweed is another Chinese remedy for alleviating the unpleasant symptoms connected with menopause. Unless taken from a polluted sea, seaweed is one of the healthiest sources of minerals available. It nourishes the blood and works wonders for pains in the joints and the back.
You can either buy dried seaweed or pick your own on an unpolluted beach. In the latter case, make sure the seaweed is fresh before consuming it. Roast the fresh seaweed over a charcoal fire; this serves to dry the seaweed. Do not cook or burn it. Once dried, you can add the seaweed to a stew or, indeed, to any dish of your choosing. In China, we usually eat seaweed in soup._
1 cup (250 milliliters) water
2 tablespoons (30 grams) dried seaweed
1 teaspoon (5 milliliters) soy sauce
½ teaspoon (2.5 grams) pepper
In a small saucepan, bring the water to a boil. Place the seaweed, soy sauce, and pepper in a bowl. Pour the hot water into the bowl.
Consume hot or warm, as often as you like.
MENSTRUAL CRAMPS (DYSMENORRHEA)
Painful cramps felt just before or during menstruation are usually caused by an excessive release of the hormonelike substance prostaglandin, which causes the uterus to contract vigorously before a period. Therapy usually consists of the administration of drugs that block the formation of prostaglandin.
If you dislike the idea of interfering with the functions of the body by taking drugs, four Chinese natural remedies may be useful in combating the pain. One is an external application to the abdomen; the other three are decoctions or teas.
Ginger, Onion, and Salt Compress
1 cup (225 grams) fresh ginger, finely chopped
½ onion, crushed
1 pound (500 grams) salt
Mix the ginger and onion with the salt. Roast the mixture in a dry frying pan or wok for 10 minutes.
Pack the heated ingredients inside a thin towel. While hot, apply to the abdominal area. It is best to lie on one's back during the application.
Apply twice a day for three days before the onset of menstruation.
Ginger and Sugar Decoction
1½ cups (375 milliliters) water
5 slices (15 grams) fresh ginger
1 tablespoon (15 grams) brown sugar
In a small saucepan, bring the water to a boil. Add the ginger and sugar, lower the flame, and simmer, covered, for 15 minutes.
Drink the decoction warm to hot twice a day, just before the onset of the period until the end of menstruation.
Ginger, Scallion, and Pepper Tea
1 cup (250 milliliters) water
1 2-ounce piece (60 grams) ginger, sliced thin
5 white heads of scallion, chopped
½ cup (100 grams) brown sugar
1 teaspoon (5 grams) black pepper
In a small saucepan, bring the water to a boil. Mix the ginger and scallion with the sugar. Add to the water, cover, and simmer over a low flame for 10 minutes.
Remove from heat, pour into a cup, add the pepper, and drink hot.
To be taken three times a day prior to and during your menstrual period.
Rose Tea
1 cup (250 milliliters) water
Fresh petals from 1 rose (approximately ¼ cup or 50 grams)
In a small saucepan, bring the water to a boil.
Place the petals in a cup and pour the boiling water over them. Steep for 5 to 10 minutes before drinking.
To be taken five days before the onset of your period, until bleeding stops. This therapy is recommended for three successive months.
NAUSEA AND VOMITING
In the West, a common remedy for nausea and vomiting is to drink warm lemon juice with sugar. Since lemons are not common in China, most Chinese remedies include the use of fresh ginger.
Ginger and Honey Tea
1 6-ounce (180-gram) piece of ginger, grated
2 tablespoons (30 milliliters) honey
Water for steaming
2 cups (500 milliliters) water
Using a thin cotton towel, squeeze the ginger to extract 4 tablespoons (60 milliliters) of juice. Transfer the juice and honey to a ceramic bowl, and put the bowl in a steaming dish (see page 66).
Using a pan deep enough to fit your steamer, bring water to a boil. Place the steamer in the pan and steam for 5 minutes, until warm.
Heat 2 cups (500 milliliters) of water in a separate pan. Pour the ginger juice and honey and the warm water into a cup. Sip slowly.
Ginger and Sugarcane Juice
_This recipe is recommended for both chronic nausea due to stomach problems and nausea due to pregnancy._
3 tablespoons (45 grams) grated fresh ginger
1 cup (250 milliliters) sugarcane juice
Using a thin cotton towel, squeeze the ginger to extract the juice. Add the ginger juice to the sugarcane juice. Stir well.
Sip slowly.
Ginger and Tangerine Decoction
1 organic tangerine peel, cut into ½-inch slices
1 teaspoon (5 grams) sliced fresh ginger
1½ cups (375 milliliters) water
Place the tangerine and ginger in a pot with the water. Bring to a boil, then simmer, covered, over a low flame for 15 minutes.
Drink 1 cup, hot, twice a day.
Ginger and Vinegar
3 slices fresh ginger
¼ cup (60 milliliters) vinegar
1 cup (250 milliliters) water
1 teaspoon (5 grams) brown sugar
Soak the ginger in the vinegar for at least 6 hours. Drain.
In a small saucepan, bring the water to a boil. Place the ginger in a cup. Add the boiling water and sugar.
Allow to steep for 5 minutes before drinking slowly.
Ginger, Potato, and Orange Juice
_This ginger juice preparation should be taken with every meal in order to inhibit the sense of nausea._
2 teaspoons (10 grams) grated fresh ginger
1 potato, peeled and grated
1 orange, peeled and sectioned
Using a thin cotton towel, squeeze the ginger, the potato, and the orange to extract their juices.
Store in a small bottle and refrigerate. Take 1 tablespoon (15 grams) before every meal.
Ginger Wine
½ cup (125 grams) fresh ginger, finely minced
¼ cup (60 grams ) organic orange peel, finely minced
1 cup (250 grams) sugar, brown or white
4 cups (1 liter) rice wine, or sake
Place the ginger, orange peel, and sugar in a bottle with the rice wine. Seal the bottle and leave to macerate for at least 10 days.
Take 2 teaspoons once a day after lunch or dinner.
Some remedies for nausea that utilize ingredients other than fresh ginger follow.
* Mix 2–3 tablespoons (30–45 grams) of fresh daikon juice with 2 teaspoons (10 grams) of brown sugar. Add to a cup of hot water and drink slowly.
* Decoct 2 teaspoons (10 grams) of caraway seed with 1 teaspoon (5 grams) of dried ginger and 1 teaspoon (5 grams) of cinnamon in 1½ cups (375 milliliters) of water. Simmer for 15 to 20 minutes. Drink warm to control hiccuping and vomiting.
* A good remedy for nausea due to changing weather, excessive tiredness, and cold is to boil 4 ounces (125 grams) of tofu in water for 20 minutes. Add a little salt and eat warm.
* Boil 12–20 cloves in a small saucepan with 1 cup (250 milliliters) water for 5 minutes. Remove from heat and add ½ teaspoon (2.5 grams) of black tea leaves. Brew for 5 to 10 minutes and drink as an ordinary tea. Clove tea relieves nausea, excessive gastric secretion, and hiccuping.
* In the south of China, where pineapples are common, a few slices of pineapple or sips of pineapple juice are everyday remedies for nausea and vomiting.
OBESITY
Any definition of obesity is probably more cultural and personal than objective. During the Tang dynasty in China, a round, full face and body were the epitome of beauty. The large-paunched laughing Buddha placed at the entrance of Buddhist temples in China represents health and abundance; that is why he is there. Even today, when international standards of health and beauty dictate a slim waistline, people in China still consider a few extra pounds to be a sign of health and prosperity.
Having said that, there is no doubt that too much extra weight is harmful. Extra pounds put stress on the skeleton as well as on the heart and circulation. They lead to exhaustion, circulation problems, lower resistance to diseases, kidney problems, diabetes, and, all too often, an early death.
Chinese doctors believe that the tendency to put on weight comes primarily from genetics—some people burn up calories more slowly than others. However, no matter what one's genetic propensities may be, putting on weight is, in 95 percent of all instances, due to personal habits.*5 In other words, it is caused by nei yin, or endogenous factors: poor eating and exercise habits, a stressful lifestyle, and the seven pathogenic emotions.
People overeat and do not exercise for a variety of reasons. They may be lazy; they may have low blood pressure, which can engender lethargy. They may be depressed or suffering from stress or anxiety. Which leads our discussion to the other cause of obesity—an excess of the seven pathogenic emotions, which include anger, melancholy, worry, grief, fear, fright, and joy.
The first step in dealing with obesity is, therefore, to put some order in one's life. Diminish stress and distress; eliminate those situations that lead to anger, worry, and fear. Try not to indulge in melancholy. Be cheerful, but don't enjoy yourself too much either, remembering that too much joy is also known to take its toll on the body. Above all, try not to overeat.
Qi gong exercise is known to help against obesity. Besides burning off a few calories, qi gong deep breathing appears to readjust the hunger-regulating mechanisms of the hypothalamus, enabling you to stop craving food simply because your hypothalamus does not know that you have eaten enough. Furthermore, regular qi gong exercise breeds discipline, and discipline allows you to keep up the resolve necessary to cut down on calories. Finally, exercise has a calming effect on the emotions, thus balancing the endogenous factors responsible for obesity.
Certain foods are said to burn fat and calories. Others detoxify the body of excess fat. The following remedies are some of the best:
* Eat 1 whole raw cucumber twice a day. Cucumber cools the body and rids toxins from the blood.
* Eat 1 raw daikon every day. Daikon exerts the same cooling and detoxifying effects as cucumber.
* Wash and shred 4 ounces (125 grams) of fresh lotus leaves. Place the shredded leaves in a pot with 1½ cups of water and boil over a low flame for 15 to 20 minutes. Drink the decoction once a day. (Lotus leaves can be found in many Chinese food stores.)
* Boil ½ ounce (15 grams) of corn silk in a pot with 1½ cups (375 milliliters) of water over a low flame for 15 minutes. Consume as a tea. Corn silk burns fats.
* Frequent tea drinking burns excessive fat in the bloodstream and tissues. Green tea without any additive is to be preferred to red or black teas.
Daikon and Mushroom Decoction
½ cup (100 grams) wood-ear mushrooms
Water for soaking
1 cup (200 grams) daikon, sliced
3 cups (750 milliliters) water
Salt to taste
Soak the wood-ear mushrooms in 2 cups (500 milliliters) hot water for 1 hour, or until they are soft.
Place the mushrooms and daikon in a pot with 3 cups (750 milliliters) water. Boil over a low flame for 15 to 20 minutes.
Remove from heat. Add salt to taste.
Drink hot twice a day, for as long as you like.
Soybeans and Vinegar
2 cups (400 grams) soybeans
2 cups (500 milliliters) vinegar
Roast the soybeans in a dry frying pan or wok over a medium flame for 5 minutes, or until the beans are a golden brown. Let the soybeans cool, then pour back into a 1-liter bottle.
Fill the bottle with vinegar. Leave in the refrigerator for 5 days. Eat 1 teaspoon (5 grams) of beans two times a day, morning and evening.
PREGNANCY
**Nausea and Vomiting**
Most women experience at least some nausea during the first months of pregnancy. In fact, the huge number of recipes that exist in China for this condition attests to how common morning sickness is. We have selected those remedies that are easiest to prepare.
Fresh Lemon
3–4 medium lemons, peeled and seeded
1 cup (200 grams) sugar
Cut the lemons into 1-inch segments. Place in a small saucepan. Stir in the sugar. Let stand for 12 hours.
Heat the lemon-sugar mixture over a low flame for 10 minutes, in order to dry the juice. Take 1–2 teaspoons (5–10 grams) of the dry lemon every time you feel nauseous.
Kiwi and Fresh Ginger Juice
_This recipe is relatively new to the folk remedy medicine chest, as kiwi have only recently arrived in China. Ginger is a traditional nausea suppressant, and kiwi has an acidic tang to it that is known to give physical relief from the urge to vomit._
1 kiwi, peeled and chopped
2 teaspoons (10 grams) ginger, grated
Using a thin cotton towel, squeeze the kiwi and the ginger to extract the juice. Mix the juices.
Take two times a day, morning and evening.
Ginger Juice and Milk
_The following remedy inhibits the urge to vomit and is sufficiently nutritious to replenish any solid food that one may throw up or be unable to swallow due to nausea._
1 cup (250 milliliters) milk
2 teaspoons (10 milliliters) fresh ginger juice
4 teaspoons (20 grams) sugar, white or brown
Mix the ingredients and bring them to a boil in a small saucepan. When the milk rises, remove from the heat.
Drink warm, two times a day.
Other remedies using ginger as a nausea suppressant follow.
* Decoct 2 teaspoons (10 grams) fresh ginger and 1 tablespoon (15 grams) brown sugar in 1½ cups (375 milliliters) water, simmering for 15 minutes. Take this decoction two times a day, morning and evening.
* Add 1 tablespoon (15 milliliters) ginger juice to a glass of sugarcane juice. Fresh sugarcane is preferable but if it is unavailable, canned juice will do. Mix well and sip slowly. This is a good remedy for nausea and vomiting, as well as for a poor appetite.
* Mix 1 tablespoon (15 milliliters) ginger juice with 2 tablespoons (30 milliliters) honey and 3 tablespoons (45 milliliters) water. Warm them by steaming in a ceramic bowl and steamer (see page 66). Take three times a day.
* Remove the peel from 1 organic orange. Cut the peel into fine slices. Put the orange peel and 2 tablespoons (30 grams) of chopped, fresh ginger in a cup. Pour freshly boiled water into the cup and leave to brew for 5 or 10 minutes. Add sugar to taste, and drink as a tea.
**The following are simple remedies that do not depend on ginger for suppressing nausea.**
Chive Tea
4 or 5 chives, chopped
1½ cups (375 milliliters) water
In a small saucepan, bring the water to a boil. Add the chives and simmer over a low flame for 10 minutes.
Drink the decoction hot in the mornings, or whenever you feel nauseous.
Egg Cooked in Vinegar
1 raw egg
4 tablespoons (70 milliliters) vinegar
2 tablespoons (30 grams) white sugar
Beat the egg in a bowl.
In a small saucepan, bring the vinegar to a boil. Turn the heat to low and add the sugar. When the sugar has melted, pour in the beaten egg. _Do not stir._ Cook the egg for 4 minutes.
Remove the egg with a slotted spoon.
Eat one egg per day.
Apple Peel and Rice Decoction
_This is a nutritious, nausea-suppressing remedy that is easy to prepare._
2 tablespoons (30 grams) rice
¼ cup (50 grams) organic apple peel, cut into 2-inch pieces
2 cups (500 milliliters) water
Roast the rice in a dry frying pan or wok over a low flame for 3 minutes, until it is golden brown.
Place the apple peel and rice in a medium pot with the water. Simmer over a low flame for 20 minutes.
Drink hot as a tea whenever you feel nauseous.
**Coughing During Pregnancy**
Some women suffer from frequent coughing during pregnancy. The reason for this is that the growing fetus puts pressure on the lower diaphragm, thus irritating the lungs and giving rise to the urge to cough. According to Chinese doctors, this irritation occurs only in women who are weak in Yin. During pregnancy, qi and blood concentrate around the womb, thus reducing their effectiveness in the upper body. The lungs and bronchial passages are thus undernourished, and so become susceptible to any slight irritation.
In order to correct this problem, one should consume foods that strengthen Yin and qi. A tasty breakfast dish with these Yin- and qi-enhancing effects is pears with sugar.
Pears with Sugar
2 pears, cut into small pieces
2 cups (500 milliliters) water
1 tablespoon (15 grams) brown sugar
Place the pears in a small saucepan with the water and the sugar. Bring to a boil, then simmer for 20 minutes over a low flame.
Drink the decoction and eat the pears. To be taken every morning for breakfast.
**Abdominal Pains During Pregnancy**
Another frequent problem that arises during pregnancy is pain in the abdomen. According to Chinese theory, abdominal pains during pregnancy are due to the stagnation of qi in the womb and its poor circulation around the rest of the abdomen. The cure is to nourish the qi and the blood. Two simple recipes serve this purpose.
* Cut 1 daikon into ¼-inch slices. Eat five slices at a time, sprinkling them with a little sugar according to taste. To be eaten three times a day with meals.
* Prepare a congee by mixing ½ cup (100 grams) of sliced, mature pumpkin with 3 cups (750 milliliters) water, 2 tablespoons (30 grams) rice, and 4 tea spoons (20 grams) sugar. Simmer over a low flame for 20 minutes. This congee should be eaten warm two times a day.
**Insufficient Breast Milk**
The problem of insufficient breast milk after childbirth is a common one in China, if we are to judge by the number of recipes that aim to increase breast milk secretion.
Poor lactation can be caused by stress, ill health, general weakness, or an irregular suckling pattern. According to Chinese theory, poor lactation results from weak qi and blood circulation. Accompanying symptoms are soft breasts (and therefore a lack of swelling and pain in these glands) facial pallor, bouts of dizziness, tinnitus, lack of appetite, sweating at night, and irritability. The remedy is to strengthen the mother by means of nutritious and protein-rich foods. One very simple way of doing this is to eat ½ cup (100 grams) of boiled green peas twice a day, on an empty stomach. Other examples of such nutritious food remedies follow.
Adzuki Bean Congee
½ cup (100 grams) adzuki beans
½ cup (100 grams) rice
4 cups (1 liter) water
Place the adzuki beans, rice, and water in a medium saucepan. Bring to a boil, then cover and simmer for 20 to 30 minutes over a low flame. Stir occasionally so the rice does not stick to the pan.
To be consumed warm once or twice a day.
Lettuce and Licorice Congee
4 large leaves of lettuce, chopped
1 teaspoons (5 grams) licorice
4 cups (1 liter) water
½ cup (100 grams) rice
Place the lettuce, licorice, and water in a medium saucepan. Bring to a boil, then simmer over a low flame for 10 to 15 minutes.
Remove from heat and cool slightly. When it is cool enough to work with, pass the mixture through a sieve to remove some of the solid ingredients.
Transfer the liquid back to the saucepan. Add the rice. Simmer over a low flame for 20 minutes, stirring occasionally, to make a rice congee.
Take the congee three times a day for five days.
Sesame Eggs
1 cup (200 grams) black sesame seeds
2 teaspoons (10 grams) salt
2 eggs
2 cups (500 milliliters) water
Roast the sesame seeds in a dry frying pan or wok over a low flame for 1 minute, until you can smell the distinct odor of sesame. Add salt, and roast for another 30 seconds.
Place the eggs in a small saucepan with water. Bring to a boil, then continue to boil over medium heat for 15 minutes.
Remove from heat. Allow the eggs to cool, then remove the shells and cut the eggs into segments. Mix the eggs with the sesame, and consume warm.
Tofu with Sugar
4 ounces (125 grams) tofu, cut into 1-inch cubes
½ cup (100 grams) brown sugar
3 cups (750 milliliters) water
Place the tofu in a medium saucepan together with the sugar and water. Bring to a boil, then simmer for 20 minutes, uncovered, over low heat.
Remove from the heat. Consume warm.
Papaya Fish
2 tablespoons cooking oil
1 tablespoon (15 grams) sliced fresh ginger
Pinch of salt
1 carp or trout, approximately 1 pound (500 grams), cleaned
5 cups (1.25 liters) water
1 cup (200 grams) papaya, cut into 8 slices
Heat the oil in a wok. Throw in the ginger with a pinch of salt. When the ginger begins to crackle, put the fish in the pan. Fry the fish evenly, 5 minutes on each side, until the skin is crisp.
Bring the water to boil in a large terracotta pot. (If a terracotta pot is unavailable, use an ordinary saucepan.) Place the papaya and the fish in the boiling water, and allow to simmer on a low flame, covered, for 30 minutes.
This dish should be eaten at least once a day, until breast milk flows abundantly. If lactation is particularly scant, eat this dish twice a day, for lunch and for dinner.
Pied du Porc Soup
_Pied du porc, otherwise called_ trotters _or_ pig's foot, _is a Chinese peasant dish that was much loved by Chairman Mao._
1 gallon (4 liters) water
1 pig's foot
5 teaspoons (25 grams) black sesame seeds
In a large soup pot, bring the water to a boil. Put the pig's foot in the pot, turn the heat to low, and simmer, covered, for 1½ to 2 hours, adding water occasionally as necessary.
In the meantime, roast the sesame seeds over a low flame in a dry wok or frying pan for 3 minutes. Grind the seeds to a medium-fine powder.
When the pig's foot is done, transfer the broth to a bowl. Sprinkle the sesame powder over the soup.
Take a bowl of the soup with meals, three times a day.
Peanuts and Soymilk
12 raw peanuts, shelled
Water for soaking
1 cup (250 milliliters) soymilk
Soak the peanuts in hot water for 20 minutes. Remove from the water, and peel away the husk. Crush the peanuts with a pestle or grinder. Transfer the crushed peanuts to a cup.
Heat the soymilk in a saucepan. When hot, pour the soymilk into the cup with the peanuts.
Take one cup twice a day, morning and evening.
Dandelion Wine
12 dandelion leaves (approximately 3 tablespoons or 45 grams), washed and chopped
2 cups (500 milliliters) rice wine, or sake
Place the dandelion leaves in a bottle with the rice wine. Seal the bottle and leave to macerate for at least 15 days.
Take 2 teaspoons two times a day.
**Abdominal Pains Following Childbirth**
In the days and weeks following birth, the uterus slowly contracts to its preconception shape and size. The uterine contractions can cause mild to moderate cramping, and consequent pains in the belly area.
Jujube Tea
5 jujube (Chinese dates)
1 tablespoon (15 grams) minced fresh ginger
1 tablespoon (15 grams) brown sugar
2 cups (500 milliliters) water
In a small saucepan, add all the dry ingredients to the water. Boil over a low flame for 15 minutes.
Consume warm.
SEXUAL PROBLEMS
In the course of our research, we found many and varied remedies for common male sexual problems, such as premature ejaculation, seminal emission, and impotence. However, we found nothing for female problems. When we asked about remedies we were merely met by amused bewilderment. "What female sexual problems? There aren't any, are there?"
We explained that we meant frigidity. This led to even greater bewilderment. "That's a love problem. What remedies can there be for love?"
In China, what matters most is the capacity to bear offspring, not to enjoy the intimacy that leads to conception. As a result, remedies have evolved to cure menstrual problems and those directly related to childbearing. In regard to the male, any weakness in the sperm or in the ability to copulate is considered a threat to successful continuation of the family lineage, and thus merits a cure.
Although a few sexual problems, such as impotence for example, may have an anatomical base, most are entirely psychological in origin. Premature ejaculation and nonphysiological impotence may be due to stress, anxiety, or physical exhaustion. Several methods exist to cure these.
Both impotence and premature ejaculation may be cured by meditation, a positive attitude, qi gong exercise, practical techniques, and a correct diet. Frequent seminal emission, by which Chinese doctors mean a nocturnal emission that spontaneously occurs twice a week or more when you are not having sex, may be corrected through diet. Impotence that is not physiological can also disappear if one overcomes anxiety, has fallen in love, or happens to be in the company of a beautiful member of the opposite sex.
**Meditation**
Meditation serves to relax. One just sits, preferably in a cross-legged position, and breathes slowly with eyes closed. Concentrate on breathing. Ignore thoughts that may pass through the mind. Meditate every day at the same time before going to bed.
Another meditation technique is to concentrate on a suitable object, concept, or theme. The "seed" that you meditate upon depends on the problem you are trying to cure. If it is premature ejaculation, meditate on sex either beforehand or during the act itself. You need to render sex as impersonal as possible. You can meditate on the cosmic principal of Yin (female) and Yang (male), or on the significance of this Yin-Yang union in all things. You may objectify your own lovemaking by meditating upon the union of Tantric deities, as Tibetan and Mongolian Buddhists do in China. To do this, imagine yourself as one of the deities and see your partner as the embodiment of that deity's female aspect. Or, before making love, you may visualize this tantric act of cosmic sexual union.
If on the other hand you suffer from impotence that is due to stress or anxiety, your seed for meditation needs to be erotically stimulating, and at the same time as relaxing as possible. Close your eyes, breathe slowly and deeply, and meditate on the healthy joys of sex. Fantasize during meditation. Allow the mind to hold steady on whatever sexual theme arouses you—under no circumstances, however, must you stimulate yourself physically. This exercise is entirely mental. Any physical involvement during the meditative fantasy would defeat the purpose of the exercise. Stay detached—fantasize and observe with relaxed detachment.
**Qi Gong Exercises**
In order to overcome sexual problems, one must learn to control and come to terms with one's physical energy, including the sexual aspect of it. Qi gong is one of the most effective means of doing this. Qi gong calms the nerves, distracts a worried or wayward mind, and builds strength and energy.
You can circulate energy inside the body by means of nei dan qi gong, or internal circulation (see page 245). You may also learn to observe and to control the emotions through meditation and deep breathing, or work off tension through wai dan (external circulation) exercises (see page 248).
If premature ejaculation is the problem, controlled deep abdominal breathing during lovemaking can help. When the urge to ejaculate becomes overpowering, simply hold your breath. This will distract momentarily from the excitement at hand and will reestablish some measure of control over the emotions.
For preventive therapy, qi gong has the following exercise to offer. Lie down in bed with a thick pillow behind your neck. Concentrate on the dan tian, the center of energy four inches below your navel, and massage your abdominal area. Place your left palm flat against your navel and your right palm over your left hand. Beginning with an upward movement from left to right, make thirty-six circles around your navel with your palms. Now place your right palm against your abdomen with the left hand over the top. Make thirty-six circles in the opposite direction.
The second stage of the exercise is to place your palms flat against your abdomen with your thumbs touching the rib cage, your fingers pointing toward one another about six inches apart. Rub your fingers vertically down your abdomen to your groin. Reverse the motion and bring your hands back up to your ribs. Repeat this movement thirty-six times at a rate of one stroke per second. On the downward stroke, pressure should be on your thumbs; on the upward stroke, pressure is on your little fingers. Daily practice is said to assure a definite cure against premature ejaculation.
Another technique similar to that just described but not a true qi gong exercise consists of lying on your back and pressing the fingertips of both hands into your belly, about four inches below your navel. This technique is said to cure premature ejaculation. The technique should be practiced five minutes before getting up in the morning, and again at night before going to sleep. The exercise also serves to massage the liver and kidneys.
There is one more technique that we feel we should mention. It comes from a rural area in central China. While we do not know if any readers will take it seriously, the nature of human sexual curiosity is such that this might turn out to be the most often tried remedy in the whole book.
Take one piece of dry ginger. Peel and then roast it. Place it warm inside your anus before making love. It is said to raise the Yang most wonderfully.
**Correct Diet**
To prevent or allay sexual problems, one should refrain from smoking, drinking too much caffeine, taking alcohol or drugs, consuming saturated fats, or eating sugars and candies that only provide a rush of energy and no stamina. One should, on the other hand, consume protein and carbohydrates—a common source is walnuts. You can roast walnut meats in a dry frying pan or wok over a low flame for 3 minutes, then grind them into a coarse powder with a pestle or grinder. Eat the walnuts for ten days before going to bed. No quantities have been specified because you can eat as much as you like. You can also eat 10 raw walnuts every day for one month.
One of many Chinese men's favorite source of protein when it comes to treating any form of sexual weakness hearkens back to the dictum that a person can treat a problem in one's own organs by eating the corresponding organ of an animal. We shall refrain, however, from describing the various recipes that involve the sexual apparati of dogs, deer, and bulls. More traditional foods are used in many remedies. It is these, therefore, that we shall limit ourselves to describing.
Kidney and Walnuts
4 cups (1 liter) water
2 pork kidneys, washed and shredded
10 walnut meats, chopped
2 garlic cloves, peeled and minced
3 teaspoons (15 grams) sliced fresh ginger
Salt to taste
In a medium saucepan, bring the water to a boil. Add the kidneys, walnuts, garlic, and ginger to the water. Cover and boil over a medium flame for 30 minutes.
Remove from heat. Drain, and discard the water. Add salt according to taste.
To be eaten twice a week as part of a meal.
Cucumber and Sugar
1 medium cucumber, chopped fine
1 tablespoon (15 grams) white sugar
Mix the cucumber with the sugar. Let the mixture sit for 2 hours.
Strain the cucumbers and discard the juice before eating.
Pork with Lotus Seed
2 tablespoons (30 grams) lotus seeds
Water for soaking
6 cups (1.5 liters) water
½ pound (250 grams) lean pork, cut into 1-inch cubes
2 teaspoons (10 grams) fresh ginger, sliced
2 garlic cloves, peeled and minced
Salt to taste
Soak the lotus seed overnight in 1 cup (250 milliliters) of water. Drain.
In a large soup kettle, bring 6 cups (1.5 liters) of water to a boil. Add the diced pork, lotus seeds, and ginger and garlic. Boil over a medium flame for 1 hour, covered. Add salt to taste. Drain, discarding the water.
Eat two times a week, as part of a meal.
Eggs, Lotus Seed, and Mushroom Soup
1 tablespoon (15 grams) wood-ear mushrooms
Water for soaking
4 cups (1 liter) water
8 lotus seeds
1 tablespoon (15 grams) taro root, cut into ½-inch cubes
2 eggs
2 teaspoons (10 grams) sugar, white or brown
Soak the mushrooms in hot water for 1 hour. Drain.
Bring the remaining 4 cups (1 liter) of water to a boil in a medium saucepan. Add the lotus seeds, taro root, and mushrooms to the boiling water. Boil over a medium flame for 30 minutes.
Break the eggs and allow them to drop gently into the soup. Add the sugar. After 5 minutes, remove from heat.
Take the soup hot or warm, at least once a week.
**In China, the preferred meat for sexual problems is mutton. The following are two common mutton recipes.**
Mutton Stew
2 tablespoons (30 milliliters) cooking oil
½ pound (250 grams) mutton, cut into 1-inch cubes
6 cups (1.5 liters) water
¼ cup (60 milliliters) soy sauce
1 teaspoon (5 milliliters) cooking wine
1 scant teaspoon (4 grams) sugar
2 teaspoons (10 grams) chopped scallion
1 teaspoon (3 grams) sliced fresh ginger
Pinch of anise seed
¼ cup potato (50 grams), cut into 1-inch cubes
¼ cup carrot (50 grams), cut into 1-inch cubes
Heat the oil in a wok or frying pan. Add the mutton and stir-fry for 5 minutes.
Transfer the mutton to a soup kettle. Add the water and all remaining ingredients except the potato and carrot. Bring to a boil, then simmer, covered, on a low flame for 1 hour.
Add the potato and carrot. Simmer for another 20 minutes. Remove from heat.
Eat once a day as part of a meal, at least two times a week.
Stir-fried Mutton
2 tablespoons (30 milliliters) cooking oil
1 pound (500 grams) mutton, thinly sliced
½ cup (100 grams) scallion, sliced
2 teaspoons (10 grams) chopped ginger
5 tablespoons (75 milliliters) soy sauce
2 tablespoons (30 milliliters) cooking wine
2 tablespoons (30 milliliters) sesame oil
Set a wok or frying pan over high heat. Add cooking oil. When the oil is hot, drop in the mutton, scallion, and ginger. Stir-fry for 1 minute. Add the soy sauce and wine. Continue to stir-fry for 5 minutes, until the color of the meat changes.
Add the sesame oil. Stir. Remove from heat and transfer to a plate for serving.
To be eaten at least twice a week.
Centipede and Licorice
_Other dietary suggestions for male sexual deficiencies include seafood (shrimp in particular), dog meat, and centipede. Judging by the quantity of dried centipede for sale in Chinese apothecaries, the latter is quite a popular remedy._
30 dried centipedes (you can purchase centipedes from Chinese pharmacies)
1 teaspoon (5 grams) licorice
½ teaspoon (2.5 grams) anise seed
Place the centipedes, licorice, and anise seed in a mortar. Using a pestle, crush them into a fine powder.
Take ½ teaspoon (2.5 grams) of the powder at a time, twice a day, morning and evening.
Finally, perhaps the most important antidote to a sexual problem is to live one's sexuality with joy and freedom from guilt or anxiety. A positive attitude lets us take life more lightly than many people are wont.
SMOKING DEPENDENCY
Stopping smoking is, first of all, a matter of will. One must really want to stop smoking in order to continue with a full and healthy life. The strategy, once the decision has been made, is to steer away from circumstances that create the urge or that perhaps simply remind one of the old habit—if, for example, you are in the habit of smoking an after-dinner cigarette with coffee, give up the coffee.
Flush out the nicotine that remains in the body. Drink plenty of water and fresh fruit juices. Fast. After the fast, eat fresh fruit and vegetables for at least ten days. Stay active with qi gong breathing exercises.
Control your urge to smoke for two weeks, and try the following Chinese remedy during that period.
Fresh Daikon Juice
1 fresh daikon, grated
1 tablespoon (15 grams) sugar, white or brown
Using a thin towel, squeeze the daikon to extract the juice. Pour the juice into a glass, add the sugar, and stir well. Consume before breakfast.
Daikon juice should be drunk every morning for two weeks. If, at the end of the two weeks, you try to smoke, you supposedly will find cigarettes both tasteless and dissatisfying.
STOMACHACHE
According to traditional Chinese medicine, stomachache is due to careless eating habits, unhappiness, weak Yang, or too much cold. Refer to chapter 3 for information about how to avoid these pitfalls.
When you are suffering from stomachache, avoid taking chili (red pepper), garlic, vinegar, wine or alcohol, strong tea or coffee, bananas, papaya, and cabbage. The following remedies should also come in useful.
Ginger and Sugar Decoction
_Brown sugar dispels cold and benefits the blood. Ginger warms the stomach. For a more powerful warming effect, use dried ginger._
2 teaspoons (10 grams) fresh or dried ginger
6 tablespoons (90 grams) brown sugar
1½ cups (375 milliliters) water
Boil the ingredients in a terra-cotta pot or in a small saucepan for ten minutes. Drink hot or warm once a day, until the stomachache goes away.
Ginger and Licorice Decoction
1 stick licorice
½ tuber of dry ginger
1 cup (250 milliliters) water
Using a pestle or grinder, crush the licorice and ginger.
Place the licorice and ginger in a terra-cotta pot or small saucepan with water. Bring to a boil, then simmer, covered, over low heat for 10 minutes.
Drink warm.
Ginger and Black Pepper Broth
_The warming effect of dried ginger may be increased by adding black pepper._
2 teaspoons (10 grams) dried ginger
10 black peppercorns
1 cup (250 milliliters) water
Using a pestle or grinder, crush the ginger and peppercorns into a fine powder. Place the powder in a cup.
Bring the water to a boil. Pour the water into the cup with the powder.
Stir the broth well. Drink hot once a day.
Ginger and Milk with Honey
2 tablespoons (30 grams) grated fresh ginger
1 cup (250 milliliters) milk
1 teaspoon (5 milliliters) honey
Using a thin cotton towel, squeeze the ginger to extract the juice.
Warm the milk in a small saucepan. When the milk is hot, but before it boils, add the ginger juice. Heat for another minute or so.
Remove from heat, transfer to a cup, and stir in the honey.
Drink warm before bed.
Ginger Tripe
_According to the theory that one strengthens the organs of one_ _'_ _s body by eating the corresponding animal organ, one can treat stomachache by consuming tripe. Besides being a remedy for chronic stomachache, weakness of the stomach, and general debility, tripe also nourishes qi._
3½–7 ounces (100–200 grams) pork or other animal tripe
1 cup (250 milliliters) vinegar
2 tablespoons (30 grams) sliced fresh ginger
10 black peppercorns
Water for steaming
Wash the tripe in vinegar. Cut the tripe into strips and place in a ceramic bowl or steaming dish (see page 66).
Add the ginger and pepper to the tripe. Using a pan deep enough to fit your steamer, bring water to a boil. Place the staemer in the pan, cover, and steam for 45 minutes.
Include this dish as part of your lunch and dinner for as long as your stomachache bothers you. Gradually decrease portion size until you are ready to stop the cure altogether.
Cinnamon Tea
1 cup (250 milliliters) water
1 teaspoon (5 grams) cinnamon powder
In a small saucepan, bring the water to a boil.
Pour the hot water into a cup. Dissolve the cinnamon in the water. Let sit for 10 minutes.
Drink warm as often as you like.
Potato Juice and Honey
1 potato, peeled and grated
1 teaspoon (5 milliliters) honey
Using a thin cotton towel, squeeze the potato to extract the juice. Transfer the juice to a cup. Add honey and stir.
Take every morning on an empty stomach for twenty days.
Peanuts with Milk and Honey
_This nightcap is taken primarily to relieve stomachache; it can also be used as a treatment for gastritis and gastric ulcers._
4 tablespoons (60 grams) raw peanuts
Water for soaking
1 cup (250 milliliters) milk
2 tablespoons (30 milliliters) honey
Soak the peanuts in hot water for 1 hour. Drain, then grind the peanuts into a pulp using a stone grinder or a mortar and pestle.
In a small saucepan, bring the milk to a boil. When the milk begins to rise, add the ground peanuts. Allow the milk to begin rising for a second time, then remove at once from the flame. Allow the milk to cool for 5 minutes before adding honey.
Take this drink as a nightcap, just prior to going to bed.
WHOOPING COUGH (PERTUSSIS)
Whooping cough is a bacterial infection characterized by extremely troublesome symptoms that give the disease its name. In fact, whooping cough manifests as sudden attacks of intensive coughing followed by a labored inspiration or "whoop" and then by the production of catarrh and by vomiting. The symptoms are so persistent that children cannot eat or sleep because of them. Although modern medicine is to be preferred to traditional rural remedies for curing the ailment, you might wish to try the following remedies to soothe the cough and the catarrh and to strengthen a weakened patient.
Garlic and Sugar
_This recipe provides some relief against coughing and the production of catarrh during the first week to ten days of whooping cough. After that, the coughing becomes more intense and requires stronger remedies._
½ head garlic, peeled and crushed
1 tablespoon (15 grams) brown sugar
1 cup (250 milliliters) water
Water for steaming
Mix the garlic and sugar well. Place the mixture in a ceramic bowl and add 1 cup (250 milliliters) of water. Place the bowl in a steaming dish (see page 66). Using a pan deep enough to fit your steamer, bring water to a boil. Place the steamer in the pan, cover, and steam for 20 minutes.
After steaming, siphon off the solid residue and divide the liquid into three parts. Drink each portion at five-hour intervals.
Chicken Gall Bladder with Sugar
_When, after the first ten days of pertussis, coughing becomes more intense and more stubborn, this recipe can help._
1 chicken gall bladder
4 tablespoons (60 grams) sugar, white or brown
½ cup (125 milliliters) water
Water for steaming
Place the gallbladder in a ceramic bowl together with the sugar and water. Place the bowl in a steaming dish (see page 66).
Using a pan deep enough to fit your steamer, bring water to a boil. Place the steamer in the pan, cover, and steam for 20 minutes.
To be eaten twice a day for five days.
Sugarcane and Water Chestnut
_Besides the actual cough, other symptoms of pertussis are vomiting, a high temperature, thirst, and weakness. The following is a remedy for thirst and a high temperature._
1 cup (250 milliliters) water
½ cup (100 grams) sugarcane, peeled and cut into small pieces
½ cup (100 grams) water chestnuts, peeled and cut into small pieces
In a small saucepan, bring the water to a boil. Add the sugarcane and water chestnut. Simmer on a low flame, covered, for 15 minutes.
To be taken as often as desired. All the ingredients should be eaten.
Mint Congee
_This remedy is also for thirst and a high temperature._
¼ cup (50 grams) rice
2 cups (500 milliliters) water
20 to 30 fresh mint leaves
1 tablespoons (15 grams) rock sugar
Prepare the rice congee by gently boiling the rice and water in a small saucepan for 20 minutes. When the congee is nearly ready, add the mint and the sugar. Simmer for 2 or 3 minutes more.
To be taken hot or warm, three times a day.
**The following three remedies are all for coughing. The first remedy is also a general tonic that helps the body regain its strength.**
Carrot and Jujube Decoction
½ cup (100 grams) carrot, sliced
10 jujube (Chinese dates)
3 cups (750 milliliters) water
Place the carrot in a terra-cotta pot or medium saucepan with the jujube and water. Bring to a boil, then simmer over a low flame, uncovered, for 20 to 30 minutes, until two-thirds of the water has evaporated.
Divide the decoction into ten doses. Take one dose every two hours.
Walnut and Pear Decoction
5 walnuts, chopped
1 pear, finely chopped
3 tablespoons (45 grams) rock sugar
2 cups (500 milliliters) water
Place the walnuts, pear, sugar, and water in a small saucepan. Bring to a boil. Simmer for 20 minutes, covered.
Remove from heat and allow to cool.
Take 1 tablespoon warm three times a day.
Steamed Celery
1 celery stalk, chopped
Salt to taste
Water for steaming
Wash and chop the celery. Add a little salt. Place the celery in a ceramic bowl or steaming diah (see page 66).
Using a pan deep enough to fit your steamer, bring water to a boil. Place the steamer in the pan, cover, and steam for 15 minutes.
Take 1 tablespoon immediately upon waking up and another at around 7 P.M. for three days.
Garlic Water
_The final recipe for whooping cough is both a prevention and a cure. As a natural disinfectant and antibiotic, garlic protects when there is a whooping cough epidemic in the area, and soothes coughing and catarrh should your child come down with the illness._
½ head (60 grams) garlic
2 cups (500 milliliters) tepid water
1 tablespoon (15 grams) brown sugar
Crush the garlic and soak in the water for 10 hours. Remove the garlic solids and add sugar to the water.
A child under the age of five should take 1 to 1½ teaspoons of the garlic water every two hours. Children over five should take 2 to 3 teaspoons every two hours.
_Chapter 6_
LONGEVITY BANQUETS
This chapter includes a selection of wholesome Chinese dishes. While most of these recipes have specific curative and preventive functions, all of the dishes can be enjoyed as simply part of a meal.
In China a typical family meal consists of one or two vegetable dishes, a protein dish of tofu, fish, seafood, or meat cooked with vegetables or mushrooms, a bowl of rice, and, perhaps, a soup. The number of dishes depends on the number of people at table. In China all dishes are shared; therefore, the greater the number of people, the greater the variety. When six or eight people eat together, the occasion becomes a veritable banquet. The more people and the more dishes at the banquet, the merrier we feel.
Chinese food is prepared to be enjoyed. Variety is important, as are the food's flavor, its appearance, its smell, and its nutritional value. More important still, however, is the spirit with which we eat it. When we are in the right frame of mind to truly appreciate the food before us, our bodies feel relaxed, our digestive systems are primed, and we benefit tenfold from what we eat.
If, on the other hand, we are tense, worried about weight gain, or feeling guilty about what we are eating, we will not only fail to enjoy, but we shall do more harm to ourselves with this stress than we would by indulging in our "unhealthiest" desires. Such negative emotions impair digestion, waste nutrients, weaken qi, and cause stagnation, creating an environment in which the bodily organs wither and Yin and Yang are thrown out of balance. We then easily fall prey to disease.
It is important, therefore, to relax. Invite some good friends over and enjoy a healthy, well-balanced Chinese banquet. Following are some suggestions.
**Serving Portions**
In China it is believed that eating servings that are too large is unhealthy. Because this book discusses Chinese cuisine for health, the serving portions suggested with the recipes are typical portions in Chinese cuisine. Some books on Chinese cuisine differentiate between Chinese and American servings, suggesting that Americans tend to eat larger amounts of food and that one American serving is roughly equivalent to one and a half Chinese servings. Rather than follow the same kind of format, however, we recommend smaller serving sizes, which we believe are healthier and reflective of Chinese culinary tradition.
**A Note on Cooking Methods**
Many of the following dishes are prepared in a guo (a wok) or frying pan and entail stir-frying, which does not necessarily require using oil.
Because oil heats to a higher temperature than water, cooking with oil is faster than cooking with water. Oil is recommended for cooking fish and meat dishes; the oils most commonly used in China are peanut oil and vegetable oil. Olive, corn, and canola oil can also be used. Sesame oil, made from roasted seeds, is idea for cold dishes.
In China we believe that animal flesh contains certain toxins that can be eliminated only by thorough cooking, which occurs with the higher temperatures reached when oil is used for stir-frying. If you are positive, however, that your meat or fish is extremely fresh and uncontaminated, you may dispense with using the oil if you wish.
Unlike the thorough cooking required for fish and meat, vegetables when cooked, are prepared so as not to damage heat-sensitive enzymes and vitamins. Stir-frying vegetables serves only to tenderize them and render them more easily digestible. Cooking vegetables with oil is, therefore, not necessary, and you will notice in the recipes that follow that only very short stir-frying times are given for the preparation of vegetable dishes.
SNACKS AND APPETIZERS
Between-meal snacks are not as common in China as they are in the United States. If we feel peckish or bored we usually resort to something like sunflower seeds or watermelon, fresh fruit being a common alternative to seeds. Indeed, it is a Chinese habit to sit and chat over a packet of dried seeds. Anybody who has traveled by train in China will doubtless have noticed the consequences of this habit in terms of litter.
Except for home banquets, appetizers are common in restaurants but not in the home, and usually consist of peanuts or cold cuts of meat, slices of ginger, seaweed, and dried jellyfish. The various appetizers served in Chinese restaurants in America and Europe are not normally eaten in China. Even so, bearing in mind the Western habit of starting a meal with something light, we have included a handful of dishes that can function as either appetizers or snacks.
Tofu and Scallions
serves 4
_Prescribed to alleviate hot- and dry-syndrome diseases, this cold dish replenishes qi and dispels toxic heat. It also counteracts dryness of the throat and mouth and relieves nasal blockage due to a cold._
1 pound (500 grams) tofu, cubed
½ cup (100 grams) scallions, chopped
2 tablespoons (30 milliliters) sesame oil
2 teaspoons (10 milliliters) lemon juice
1 tablespoon (15 milliliters) soy sauce
½ teaspoon (2.5 grams) salt
Place the tofu cubes in a bowl, sprinkle with scallions, and season with sesame oil, lemon juice, soy sauce, and salt. Toss lightly.
Bean Sprouts
serves 4
_Often prescribed as a treatment for chronic dryness in the mouth and throat and for scanty urine, this dish dispels toxic heat and damp syndromes. It also alleviates a sore throat._
4 cups (1 liter) water
2 cups (400 grams) bean sprouts
1 teaspoon (5 milliliters) sesame or olive oil
1 teaspoon (5 milliliters) vinegar
1 tablespoon (15 milliliters) soy sauce
¼ cup (50 grams) scallions, chopped
Bring water to a boil in a medium saucepan. Throw in the bean sprouts and boil for 1 minute.
Remove the bean sprouts, strain, and allow them to cool. Season with oil, vinegar, and soy sauce.
Add the scallions, toss lightly, and serve.
Fava Beans (Broad Beans)
serves 4
_Sometimes prescribed as a remedy for indigestion, this dish warms the stomach and the spleen and dispels cold and dampness. Fava beans, also known as broad beans, contain plenty of soluble fiber and are therefore an efficient remedy for constipation. Soluble fiber also lowers cholesterol levels in the blood.
In China, fava beans are usually eaten in summer when people tend to consume large quantities of garlic as a protection against bacteria that develop more easily in the heat. For the Chinese ten or fifteen cloves would be normal. The amount we have suggested for this recipe is 3 tablespoons (45 grams) crushed garlic, less than people would actually use in China. The amount of garlic you use for this dish depends on your fondness for its taste._
2 cups (400 grams) fresh fava beans, or 1 cup (200 grams) dried fava beans
Water for soaking
5 cups (1.25 liters) water
3 tablespoons (45 grams) crushed garlic
2 tablespoons (30 milliliters) sesame or olive oil
1 tablespoon (15 milliliters) vinegar
2 tablespoons (30 milliliters) soy sauce
Salt to taste
If using dried beans, soak them overnight and then peel them. If fresh, remove them from their pods.
Bring the water to boil in a large saucepan and add the fava beans. Boil fresh beans over a medium flame for 15 minutes; boil dried beans for 30 minutes.
Remove the beans from the water and strain. Season with crushed garlic, oil, vinegar, and soy sauce, adding salt, if desired, to taste.
Chinese Chicken Salad
serves 4
_This dish warms the digestive organs, nourishes qi, stimulates the appetite, and dispels cold- and damp-syndrome diseases._
8 cups (2 liters) water
4 chicken drumsticks
½ head iceberg lettuce
1 tablespoon (15 milliliters) sesame oil
1 tablespoon (15 milliliters) hot mustard
½ teaspoon (2.5 grams) salt
½ teaspoon (2.5 grams) MSG (monosodium glutamate), optional
1 tablespoon (30 grams) ground peanuts (use a mortar and pestle or stone grinder)
In a medium saucepan bring the water to a boil. Add the chicken drumsticks and cook for 30 minutes, or until done. In the meantime, wash, dry, and shred the lettuce.
Remove drumsticks from water and allow to cool. Remove the skin, and debone. Shred the meat into bite-sized pieces.
In a small bowl, combine the sesame oil, hot mustard, salt, and MSG if desired, and mix to make a dressing.
In a large bowl combine the chicken, the shredded lettuce, and the dressing and mix together. Sprinkle the ground peanuts over the salad and serve.
SOUPS
In China soups are generally drunk at the end of the meal rather than at the beginning. We use the term "drunk" rather than "eaten" because soups are typically light, clear broths that serve to wash down the rest of the meal while clearing the mouth and esophagus of strong flavors. Because soups are usually eaten at the beginning of the meal in many Western countries, we have placed them at the beginning of our recipe collection.
Shrimp and Mutton Soup
serves 4 to 6
_Mutton is sweet and mild. It nourishes qi and has a warming effect. Shrimp, also sweet and mild, nourish the kidneys and enhance the sexual functions. Garlic is warm and pungent. It dissipates cold and nourishes Yang. This soup is prescribed for kidney deficiencies, aches and pains in the lower body, weakness, cold feet and legs, and urinary problems._
1 teaspoon (5 grams) cornstarch
1 teaspoon (5 milliliters) water
4 ounces (125 grams) fresh shrimp, cleaned,
peeled, and deveined
2 tablespoons (30 milliliters) cooking oil
2 slices ginger
4 ounces (125 grams) mutton, sliced into fine strips
4 cups (1 liter) water
2 tablespoons (30 grams) crushed garlic
1 scallion, chopped
½ teaspoon (2.5 grams) salt
½ teaspoon (2.5 grams) pepper
Mix the cornstarch and the teaspoon of water together in a small bowl and set aside. Finely chop the shrimp.
Heat the cooking oil in a medium saucepan. Drop in the sliced ginger and the mutton, stirring quickly until the mutton changes color (about 3 or 4 minutes), and then add the 4 cups (1liter) of water. Bring to a boil. Add the garlic, reduce the heat, and simmer over a low flame, uncovered, for 30 minutes.
Add the chopped shrimp and simmer for another 2 minutes. Finally, add the chopped scallion, the cornstarch mixture, and the salt and pepper. Stir until the soup thickens, then remove from the heat. Serve hot.
Mutton and Ginger Soup
serves 4 to 6
_This soup strengthens qi and the blood, invigorates the functions of the spleen and stomach, strengthens the body as a whole, and—because of the warming effects of ginger—dissipates internal cold. It also stimulates the appetite. For these many healing properties, this soup is often prescribed to convalescents and to women following childbirth._
12 cups (3 liters) water
1 pound (500 grams) mutton
½ cup (100 grams) sliced ginger
2 teaspoons (10 milliliters) rice wine
1 scallion, cut into 4 pieces
1 teaspoon (5 grams) salt
Place 4 cups (1 liter) of the water in a soup pot and bring to a boil. Throw in the mutton. After 1 minute, take the meat out of the pot and discard the water.
Cut the mutton into 1-inch or 1½-inch cubes. Return the cubed mutton to the soup pot along with the remaining 8 cups (2 liters) of water, and the ginger, rice wine, and scallion. Bring to a boil over high heat, then turn down the heat, cover, and let simmer for 1 hour, stirring occasionally, until cooked.
Season with salt when the soup is cooked. Serve hot.
Shrimp and Bean Curd Soup
serves 4 to 6
_This soup invigorates the kidneys and stomach. As well, because shrimp strengthens Yang and tofu strengthens Yin, this soup balances both functions._
½ cup (100 grams) packed fresh spinach
1 slice ginger
2 ounces (60 grams) fresh shrimp, cleaned, peeled, and deveined
½ teaspoon (2.5 grams) salt
2 cups (500 milliliters) chicken broth plus 2 cups (500 milliliters) water, or 4 cups (1 liter) vegetable stock
8 ounces (250 grams) tofu, diced
3 tablespoons (45 grams) cornstarch
1 egg, beaten, optional
Wash the spinach and place it in a saucepan. Add the slice of ginger, the shrimp, and the salt. Heat and stir until the spinach has wilted. Add the chicken broth and water (or vegetable broth) and bring to a boil. When boiling, add the diced tofu.
In a small bowl, mix the cornstarch and the cold water. Add the cornstarch mixture to the soup and stir. As soon as the soup begins to boil again, add the beaten egg, if desired. Stir, remove from heat, and serve.
Tofu, Chicken, and Seaweed Soup
serves 4
_This low-fat, high-energy dish is suitable for anyone with a weight problem. It also prevents weakness, tendency toward dizziness, and excessive phlegm._
2 ounces (60 grams) chicken breast, cut into ½-inch cubes
Pinch of salt, plus 1 to 2 teaspoons
2 tablespoons (30 milliliters) cooking wine
1 pound (500 grams) tofu, cut into 1-inch cubes
5 cups (1.25 liters) water
2 tablespoons (30 grams) seaweed
2 scallions, chopped
Place the chicken in a medium bowl. Stir in a pinch of salt and the cooking wine.
Place the tofu in a medium saucepan along with the water. Bring to a boil over a high flame. Once the water boils, add the chicken. Return to a boil, then reduce the heat. Cook for 20 minutes over a medium flame.
Stir in the seaweed, chopped scallions, and remaining 1 to 2 teaspoons salt. Turn off the burner. When sufficiently cool, the soup is ready to serve.
Tofu, Pork, and Black Mushroom Soup
serves 4 to 6
_This dish warms the stomach, invigorates the functions of digestion, and fortifies qi and the Yin functions of the body. It also alleviates symptoms of dryness, lowers blood pressure, stimulates the appetite, and increases physical energy. It is prescribed to new mothers after childbirth in order to increase lactation and to counteract weakness and dizziness._
5 black mushrooms
Water for soaking
8 ounces (250 grams) lean pork, cut into 1½-inch cubes
4 slices ginger
4 jujube (Chinese dates)
8 cups (2 liters) water
1 pound (500 grams) tofu, cut into 1½-inch cubes
1 teaspoon (5 grams) salt
Soak the mushrooms in a bowl of hot water for 1 hour, then drain and slice.
Place the pork, mushrooms, ginger, jujube, and water in a soup pot. Bring to a boil, lower heat, and cook for 1 hour. Add hot water as needed to retain desired soup consistency.
After an hour, add the tofu. Cook for another 20 minutes. Season with salt and serve hot.
Tofu and Seafood Soup
serves 6
_Prescribed as part of the dietary regimen for hypertension (high blood pressure) and for impotence, this dish also stimulates the appetite. A soup that cools internal heat and relieves dryness, it invigorates the internal organs of digestion, the spleen, and, in particular, the stomach._
_This soup may also be prepared with sole or snapper (cut into ½-inch cubes before cooking) instead of shrimp._
2 shiitake mushrooms
Water for soaking
¼ cup (50 grams) cornstarch
¼ cup (60 milliliters) water
6 cups (1.5 liters) chicken broth, or water
8 ounces (250 grams) tofu, cut into ½-inch cubes
½ cup (100 grams) button mushrooms, sliced
¼ cup (50 grams) fresh peas, shelled
8 ounces (250 grams) fresh shrimp, cleaned, peeled, and deveined
2 egg whites, beaten
1–2 teaspoons (5–10 grams) salt
1 teaspoon (5 milliliters) sesame oil
Pepper, to taste
Place the shiitake mushrooms in a bowl, cover with hot water, and soak for 1 hour. Drain and slice.
In a separate small bowl, whisk together the cornstarch and the ¼ cup (60 milliliters) water and set aside.
Pour the chicken broth (or water) into a soup pot and bring to a boil. Then add the tofu, button and shiitake mushrooms, and peas. Stir for a minute, then add the shrimp.
Reduce heat and simmer over a low flame for 10 minutes. Then slowly add the cornstarch mixture, stirring all the while. Stir in the beaten egg whites and immediately remove from heat.
Season with salt, sesame oil, and pepper to taste. Serve hot.
Tomato Soup
serves 2 to 4
_This recipe dispels toxic heat and reinforces the functions of the stomach, stimulating appetite and improving digestion._
2 tablespoons (30 grams) cornstarch
2 tablespoons (30 milliliters) cold water
1 egg
3 cups (750 milliliters) chicken or vegetable broth
2 tablespoons (30 milliliters) soy sauce
1 tablespoon (15 milliliters) vinegar
¼ teaspoon (1–2 grams) white pepper
2 medium tomatoes, cut into wedges
4 ounces (125 grams) tofu, cut into 1-inch cubes
1 teaspoon (5 milliliters) sesame oil, as garnish
1 tablespoon (15 grams) scallions, chopped, as garnish
In a small bowl, combine the cornstarch and the cold water and mix together thoroughly. Set aside. In another small bowl, beat the egg and set aside.
Place the vinegar and the white pepper in a large serving bowl to be used for the soup. Whisk lightly and set aside.
Pour the broth and the soy sauce into a medium saucepan, stir together, and bring to a boil. When the broth is boiling add the tomato wedges and tofu and return to a boil. Let boil for 5 minutes, then slowly stir in the cornstarch mixture until the soup thickens. Once the soup thickens add the beaten egg, stirring it in using a circular motion, and immediately turn off the heat.
Pour at once into the prepared serving bowl and stir. Garnish with a drizzle of sesame oil and a sprinkle of chopped scallions, and serve.
Egg and Liver Soup
serves 2 to 4
_This soup is good for the liver and improves eyesight._
2 eggs
1–2 tablespoons (15–30 milliliters) peanut or sesame oil
8 ounces (250 grams) pork liver, thinly sliced
6 green tops of scallions, chopped
1 tablespoon (15 milliliters) cooking wine
2 cups (500 milliliters) water
1 teaspoon (5 grams) salt
Beat the eggs in a small bowl and set aside.
In a medium saucepan, heat the oil. When the oil is hot, add the sliced liver and chopped scallions and stir. Add the tablespoon of cooking wine, stir for 30 seconds more, and add the water. Bring to a boil, lower the heat, and simmer for 15 minutes.
When ready, pour the beaten egg into the soup, stirring it in using a circular motion. Season with salt and serve in a large soup tureen or in individual bowls.
Sweet Corn, Chicken, Mushroom, and Egg Soup
serves 4
_Corn is sweet and mild; it lubricates and nourishes the internal organs of digestion. Shiitake mushrooms are sweet and neutral; they nourish the stomach. This dish as a whole strengthens the functions of the stomach, thus stimulating the appetite. It is often prescribed as treatment for urinary problems as well._
4 shiitake mushrooms
Water for soaking
1 chicken breast
2 egg whites
½ cup (100 grams) sweet corn
4 cups (1 liter) stock
2 teaspoons (10 milliliters) cooking wine
1 teaspoon (5 grams) salt
½ teaspoon (2.5 grams) black pepper
Soak the mushrooms in 1 cup of hot water for 1 hour. Drain. Chop the mushrooms into small pieces and set aside.
Remove the chicken breast from the bone and mince. Set aside.
In a medium bowl, beat the egg whites into a foam. Mix the minced chicken and the cooking wine into the beaten egg whites.
In a medium saucepan add the sweet corn to the stock, bring to a boil, and boil for 10 minutes. Then add the chicken and egg white mixture and the mushrooms to the stock. Lower the heat and let simmer for 5 minutes, stirring occasionally.
Season with salt and pepper and serve.
Vegetable Beef Soup
serves 6
_This soup invigorates the spleen and stomach and harmonizes qi. It nourishes the blood and strengthens the bones, joints, and ligaments. It stimulates the appetite, and its energizing properties render it particularly effective for conditions of fatigue, weakness, and convalescence._
12 cups (3 liters) water
8 ounces (250 grams) beef, cut into 1-inch cubes
½ cup (100 grams) carrot, chopped into 1-inch pieces
3 slices ginger
½ cinnamon stick
2 teaspoons (10 milliliters) cooking wine
¼ cup (50 grams) onion, sliced thin lengthwise
½ cup (100 grams) tomato, chopped into 1-inch pieces
¼ head cabbage, chopped into 1-inch pieces
½ cup (100 grams) potato, chopped into 1-inch pieces
1–2 teaspoons (5–10 grams) salt
1 tablespoon (15 milliliters) soy sauce
Bring 4 cups (1 liter) of the water to a boil in a soup pot. Add the beef, return to a boil, and cook for 1 minute. Strain the broth and discard it.
In the same saucepan, add the remaining 8 cups (2 liters) of fresh water to the beef. Throw in the chopped carrot, ginger slices, cinnamon stick, and cooking wine. Bring to a boil, reduce heat, cover, and cook over a low flame for 1 hour.
After 1 hour of cooking, add the onion, tomato, cabbage, and potato. Continue to simmer for another 20 minutes. Season with salt and soy sauce. Serve hot.
Vegetable Chicken Soup
serves 4 to 6
_This soup dissipates heat, relieves water retention, and nourishes the internal organs, invigorating their qi. It is a good remedy for stomachache due to cold syndromes. It is also a treatment for lack of appetite, weakness, convalescence, stubborn coughs, and urinary disorders, and is a favorite among women recovering from childbirth.
This is a convenient recipe that can be made to last for several meals. Also, by eating only a few strips of chicken meat with each bowl of soup, you can keep the chicken as a base. If you prefer, for each meal you can add other vegetables or additional cabbage, or substitute cauliflower for cabbage and cook for 15 more minutes._
1 whole chicken (about 3 pounds or 1½ kilograms)
3 slices ginger
1 cup (200 grams) carrot, cut into 1-inch pieces
½ cup (100 grams) daikon, cut into 1-inch pieces
20 cups (5 liters) water
1 cup (200 grams) Napa cabbage, cut into strips
2 teaspoons (10 grams) salt
Wash the chicken and pat it dry. Cut away the skin and fat.
Place the chicken in a deep saucepan along with the ginger slices, carrot, and daikon. Cover with water and bring to a boil. Reduce heat, cover, and simmer over a low flame for about 1 hour, or until the chicken is cooked.
Add the cabbage and cook for another 15 minutes. Season with salt and remove from heat. Serve warm.
VEGETABLE DISHES
Although few people in China—aside from Buddhist monks—are vegetarians, the Chinese diet does tend to rely more heavily on grains and vegetables than on meats. In 1989 in China only 9 percent of calories were obtained from animal products. The latest available figures show that by 1996 the general improvement of economic conditions and the consequent change in dietary habits led to a 3.8 percent increase in meat consumption. In contrast, in the United States the corresponding figure for calories from animal protein was 34 percent, and in Great Britain it was 35 percent. In China, an ordinary meal in the home only rarely includes more than a few morsels of fish or meat. We reserve meat eating for special occasions, for when we have guests, or for specific health problems. Chinese cuisine, therefore, includes many more recipes for vegetable dishes than for fish, poultry, or other meat dishes. Following are just a few of these.
Sautéed Celery
serves 4
_Celery cools the blood and eliminates dampness. It also nourishes and soothes the liver. This dish regulates blood pressure and is prescribed for people who wish to lose weight._
2 tablespoons (30 milliliters) oil, or water
5 garlic cloves, peeled and crushed
2 cups (400 grams) celery, stalk only, cut into 1-inch pieces
1 tablespoon (15 milliliters) soy sauce
Salt and pepper to taste
In a wok or frying pan, heat the oil or water. Drop in the crushed garlic, then throw in the celery. Stir well.
Add the soy sauce and a little salt and pepper, as desired. Stir again, and cover the pan. Cook over a medium flame for 20 to 25 seconds.
Remove from heat and serve.
Mustard Celery
serves 4
_Celery cools the blood, eliminates dampness from the body, nourishes and soothes the liver, and lowers high blood pressure. This dish is prescribed for people who wish to lose weight and sometimes_ _—_ _because of the rising effect of the mustard_ _—_ _as a remedy for headache._
1 tablespoon (15 grams) dry mustard
3/4 tablespoon (11 milliliters) warm water
4½ cups (1,125 milliliters) water
¼ teaspoon (1–2 grams) sugar
½ tablespoon (7 grams) cornstarch
Pinch of salt, or to taste
1 cup (200 grams) celery, cut into 1½-inch pieces
Place the dry mustard in a small bowl and add the 3/4 tablespoon (11 milliliters) of warm water. Mix together to form a paste and let stand for 10 minutes.
Pour ½ cup (125 milliliters) water into a small saucepan, along with the sugar, cornstarch, and a pinch of salt. Mix together and bring to a boil, stirring well until the mixture thickens. Stir in the mustard paste, remove from heat, and set aside.
Place the remaining 4 cups (1 liter) water in a medium saucepan and bring to a boil. When boiling, throw in the celery. After 30 seconds, remove from the heat and drain.
Place the celery in a serving dish, cover with the mustard sauce, mix thoroughly to coat, and serve.
Spinach with Celery
serves 4
_This dish prevents high blood pressure, dizziness, palpitations, tinnitus, constipation, and liver problems._ Caution: _Because spinach contains oxalic acid it should not be eaten with tofu, which contains calcium. When oxalic acid and calcium are mixed, they react to form an indigestible compound._
1 cup (200 grams) packed fresh spinach
3½ cups (875 milliliters) water
1 cup (200 grams) celery, chopped
2 teaspoons (10 milliliters) sesame oil
1 tablespoon (15 milliliters) soy sauce
1 teaspoon (5 milliliters) vinegar
Wash the spinach thoroughly. Place it in a small saucepan with ½ cup (125 milliliters) of water and bring to a boil. Reduce the heat and simmer for 5 minutes.
Place the remaining 3 cups of water in a separate medium saucepan, add the celery, and bring to a boil. Reduce heat and simmer for 5 minutes. When cooked, strain the spinach and the celery and place them together in a serving bowl.
In a small bowl whisk together the sesame oil, soy sauce, and vinegar to make a dressing. Pour over the spinach and celery and toss lightly to combine. Serve hot.
Sautéed Asparagus
serves 4
_Asparagus dissipates toxic heat from the body, lubricates dryness, acts as a diuretic, lowers blood pressure, and benefits qi, blood circulation, and the heart._
2 tablespoons (30 milliliters) oil, or water
4 garlic cloves, peeled and crushed
2 cups (400 grams) asparagus, cut into 1½-inch pieces
2 tablespoons (30 milliliters) soy sauce
3 tablespoons (45 milliliters) water
Salt and pepper to taste
Heat a wok or frying pan with the oil (or water). When the oil is hot, drop in the crushed garlic and stir. Lower the flame to medium. Add the asparagus and stir. Add the soy sauce and stir-fry for 30 seconds.
Add the 3 tablespoons of water, cover the pan, and simmer for 30 more seconds.
Salt and pepper to taste and stir well. Remove from heat and serve.
Lohan Jai, "Buddha's Delight"
serves 4
_Lohan, or Arhat to use the Sanskrit name, are the Buddha_ _'_ _s principle disciples. The name of this dish may thus be translated as_ _"_ _vegetarian dish_ (jai) _of Buddha_ _'s disciples._ _"_ _It is considered one of the tastiest and most nutritious dishes for vegetarians.
Lohan jai_ _'_ _s properties strengthen qi, dispel dampness, and warm the stomach. In China this dish is often eaten as part of a therapeutic regimen for lowering high blood pressure. It is a favorite among people who feel weak or tired, and among the elderly._
6 shiitake mushrooms
½ ounce (15 grams) wood-ear mushrooms
½ ounce (15 grams) dry lily flowers
3/4 ounce (20 grams) tofu
Water for soaking
2 tablespoons (30 milliliters) oil, or water
5 garlic cloves, peeled and crushed
½ cup (100 grams) peeled potatoes, thinly sliced
2 teaspoons (10 milliliters) cooking wine
2 tablespoons (30 milliliters) soy sauce
10 ounces (300 grams) gluten, braised
Salt to taste
Place the shiitake mushroons, wood-ear mushrooms, dry lily flowers, and tofu in separate bowls. Cover each ingredient with hot water and soak until they are soft. If you are in a hurry, 45 minutes is the bare minimum for palatability. (In China, most cooks soak these overnight.)
When they are soft, strain the shiitake mushroons and reserve the soaking water, setting it aside. Drain all other soaked ingredients. Slice the shiitake and wood-ear mushrooms. Cut the soaked tofu into 1-inchlong (about 2-centimeter-long) segments.
Heat the oil (or water) in a wok or frying pan. Add the crushed garlic and stir-fry for 5 seconds. Add the sliced potato, the shiitake and wood-ear mushrooms, the lily flowers, and the tofu and stir. Add the cooking wine and the soy sauce and stir thoroughly.
Add about ¼ cup (60 milliliters) of the water in which you soaked the shiitake mushrooms. Cover the wok and allow to simmer for 5 minutes, stirring occasionally and adding a little water if needed.
After 5 minutes, add the braised gluten. Stir well. Cover the pan again and simmer for another 5 minutes.
Add salt to taste, remove from heat, and serve.
Spicy Eggplant
serves 2 to 3
_This dish stimulates the stomach and the spleen as well as the functions of digestion, and thus improves the appetite._
1½ tablespoons (23 grams) cornstarch
2 tablespoons (30 milliliters) water
2 tablespoons (30 milliliters) cooking oil, or water
2 cups (400 grams) eggplant, peeled and cut into 2-inch-long (4-centimeter-long) strips
1 teaspoon (5 milliliters) sesame oil
1 scallion, chopped
2 teaspoons (10 grams) grated ginger
3 garlic cloves, peeled and crushed
3 teaspoons (15 grams) chili paste
2 teaspoons (10 grams) black bean paste
2 teaspoons (10 milliliters) cooking wine
2 tablespoons (30 milliliters) soy sauce
1 teaspoon (5 grams) sugar
1 teaspoon (5 milliliters) vinegar Salt to taste
Blend the cornstarch with 2 tablespoons (30 milliliters) of water in a cup or small bowl and set aside.
Heat the cooking oil, or water if you prefer, in a wok or frying pan. Add the eggplant and stir-fry for 5 minutes until it is soft (10 minutes if you are using water). Transfer to a dish and set aside.
Place the sesame oil in the wok or frying pan and reheat the pan. Add the scallion, ginger, garlic, and chili paste. Stir for a few seconds, until the ingredients give off their aroma, then add the black bean paste, cooking wine, soy sauce, sugar, and vinegar. Stir quickly, then add the eggplant together with the cornstarch, stirring until thoroughly combined. Sprinkle with salt to taste.
Turn off the heat. Transfer to a serving bowl or platter and serve.
Multiflavored Eggplant
serves 4
_This eggplant dish strengthens qi, invigorates circulation of blood, and dispels toxic heat and evil wind syndromes. It is suitable for people with high blood pressure and also provides relief for constipation and hemorrhoids. As well, the generous amount of garlic acts as an antibiotic, curing stomach problems and sore throat._
2 cups (400 grams) eggplant, peeled and cut into strips
Water for steaming
1 head garlic, cloves peeled and crushed
1 scallion, chopped
1 tablespoon chopped cilantro
2 tablespoons (30 milliliters) soy sauce
1 teaspoon (5 grams) sugar, optional
1 tablespoon (15 milliliters) vinegar
1 teaspoon (5 milliliters) sesame oil
Salt and pepper to taste
Place the eggplant in a ceramic bowl, then put the bowl inside a steaming dish (see page 66).
Using a pan deep enough to fit your steamer, bring water to a boil. Place the steamer inside the pan, cover, and steam for 20 minutes.
In a small bowl, mix together the crushed garlic, chopped scallion, and cilantro. Stir in the soy sauce, sugar (if desired), vinegar, sesame oil, and a little salt and pepper to taste.
Remove the eggplant from the steamer. Transfer to a serving dish and pour the garlic sauce over it. Serve hot.
Spinach and Bean Sprouts
serves 2 to 3
_A dish that nourishes qi and the blood and counteracts dryness and toxic heat syndromes, it is prescribed for headaches, dizziness, high blood pressure, and constipation._
½ cup (100 grams) packed fresh spinach
½ cup (100 grams) bean sprouts
3 tablespoons (45 milliliters) water
3 garlic cloves, peeled and crushed
3 tablespoons (45 milliliters) water
Salt to taste
Wash and drain the spinach and the bean sprouts.
Heat the water in a wok or frying pan. When the water begins to boil, add the garlic, followed immediately by the spinach and the bean sprouts, and stir. Add salt to taste.
Simmer over medium heat for 5 minutes, until just cooked. Remove from heat and serve.
Steamed Tofu
serves 4
_This dish removes pathogenic heat from the lungs and dissolves catarrh. It both tones and nourishes the internal organs of digestion, particularly the spleen and the stomach. It also reinforces Yin essence, and relieves dryness.
Steamed tofu is often prescribed for people who are overweight and for those who suffer from indigestion. Because it dissolves catarrh, this dish is frequently taken as a remedy for nasal blockage, coughs, and heavy colds._
1 pound (500 grams) tofu
Water for steaming
2 tablespoons (30 grams) chopped cilantro
2 tablespoons (30 milliliters) lemon juice
3 tablespoons (45 milliliters) soy sauce
1 tablespoon (15 milliliters) sesame oil
Salt to taste
Chili spice, optional
Place the tofu in a steaming dish (see page 66). Using a pan deep enough to fit your steamer, bring water to a boil. Place the steamer inside the pan, cover, and steam for 20 minutes.
When it is finished, remove the tofu from the steamer and cut into 1½-inch cubes.
To make a sauce, mix the cilantro with the lemon juice, soy sauce, sesame oil, a little salt, and chili spice if you like it spicy.
Pour the sauce over the tofu. Mix well and serve.
Tofu with Mushrooms
serves 2
_Because of tofu_ _'_ _s cooling effect, this dish dispels pathogenic heat from the stomach and the lungs. It also nourishes Yin essence. It is often prescribed to people with diabetes._
5 shiitake mushrooms
2 tablespoons (30 grams) wood-ear mushrooms
2 tablespoons (30 grams) dry lily flowers
Water for soaking
2 tablespoons (30 milliliters) oil, or water
4 garlic cloves, peeled and crushed
8 ounces (250 grams) tofu, cut into 1½-inch cubes
2 tablespoons (30 milliliters) soy sauce
Salt and pepper to taste
Put the shiitake mushrooms, the wood-ear mushrooms, and the dry lily flowers in separate bowls, cover each with hot water, and soak for 1 hour. (Soaking them overnight will ensure the perfect consistency, however 1 hour of soaking is sufficient if you are in a hurry.)
When the shiitake mushrooms are soft, strain them, reserving the water in which they were soaked. Set the reserved liquid aside. Drain the wood-ear mushrooms and the lily flowers, discarding their soaking water. Slice all the mushrooms.
Heat the oil (or water, if you prefer) in a wok or frying pan. When hot, add the crushed garlic and the tofu. Stir-fry for 1 minute (4 minutes if you are using water), then add the shiitake and wood-ear mushrooms and the lily flowers.
Stir in the soy sauce, mixing thoroughly. Add ¼ cup (60 milliliters) of the water in which you soaked the shiitake mushrooms. Cover the wok, reduce heat, and let simmer over a low flame for 10 minutes.
Season with salt and pepper to taste. Remove from heat and serve.
BEEF DISHES
Cabbage Beef
serves 4
_This dish nourishes the spleen and stomach, alleviates stomachache, builds physical strength and resistance, and stimulates appetite._
1 tablespoon (15 milliliters) cooking wine
1 tablespoon (15 milliliters) soy sauce
Salt and pepper to taste
1 teaspoon (5 grams) sugar, optional
2 ounces (60 grams) beef, sliced into thin, 3-inch-long (7-centimeter-long) strips
2 tablespoons (30 milliliters) cooking oil
5 garlic cloves, peeled and crushed
3 slices ginger
2 cups (400 grams) cabbage, sliced into thin, 3-inch-long (7-centimeter-long) strips
2 tablespoons (30 milliliters) water
Place the wine, soy sauce, salt and pepper to taste, and sugar (if desired) in a bowl and combine to make a marinade. Add the beef, stir to coat, and let stand for 15 minutes.
When the beef has been marinated, heat 1 tablespoon (15 milliliters) of the oil in a wok or frying pan. Transfer the beef to the wok. Quickly stir-fry until the beef changes color, then remove it from the wok.
Heat the remaining tablespoon of oil in the wok. Add the garlic and the ginger. Stir for a few seconds before adding the cabbage and 2 tablespoons (30 milliliters) of water. Stir-fry for 4 minutes.
Add the beef. Stir briefly, salt to taste, and serve.
Beef with Prickly Pear Cactus
serves 2
_Beef is sweet and mild; it nourishes the spleen and the stomach. Prickly pear cactus is cold and bitter; it removes evil heat and heat inflammation. Together these ingredients balance cold and warm within the body. In China it is believed that if this dish is eaten regularly it will banish all problems of the stomach and the digestive organs._
1 tablespoon (15 milliliters) soy sauce
4 slices ginger
1 tablespoon (15 milliliters) cooking wine, optional
3 ounces (90 grams) beef, sliced into 3-inch-long (7-centimeter-long) strips
1 tablespoon (15 grams) cornstarch
1 tablespoon (15 milliliters) water
2 tablespoons (30 milliliters) oil
2 ounces (60 grams) prickly pear cactus, sliced into 3-inch-long (7-centimeter-long) strips
Salt to taste
Combine the soy sauce, cooking wine (if desired) and ginger in a bowl. Mix the cornstarch and water in a small bowl. Add the beef and marinate for 5 to 10 minutes. Set aside. Heat the oil in a wok or frying pan. Drop in the beef and stir-fry until the meat changes color. Add the cactus and stir-fry for 2 or 3 minutes. Add a little salt. Pour in the cornstarch and stir again. Remove from heat and serve.
Onion Beef
serves 2
_This dish nourishes qi and the blood, strengthens the bones and ligaments, and stimulates the appetite. Onion and beef also reinforce the functions of the spleen and the stomach._
1 tablespoon (15 grams) cornstarch
1 tablespoon (15 milliliters) soy sauce
1 tablespoon (15 milliliters) cooking wine
9 ounces (255 grams) beef, sliced into thin, 3-inch-long (7-centimeter-long) strips
3 tablespoons (45 milliliters) cooking oil
¼ cup (50 grams) onion, shredded or grated
Salt to taste
Place the cornstarch, soy sauce, and cooking wine in a medium bowl and mix well. Add the beef strips and mix to coat.
Heat the oil in a wok or frying pan. When the oil is hot, add the beef and the onion and stir-fry for 5 minutes.
Add salt to taste. Remove from heat and serve.
LAMB AND MUTTON DISHES
Mutton, Taro, and Mushroom
serves 2
_Mutton strengthens Yang energy. It nourishes the blood, stimulating its circulation, and reinforces the kidneys. This dish is a valid tonic for the whole body and is therefore effective in overcoming debility, exhaustion, and convalescence._
2 tablespoons (30 grams) wood-ear mushrooms Water for soaking
1 tablespoon (5 grams) cornstarch
2 tablespoons (30 milliliters) cooking wine
1 tablespoon (15 milliliters) soy sauce
Salt to taste
9 ounces (255 grams) mutton or lamb, cut into 1-inch by 2-inch pieces
3 ounces (90 grams) taro
3 tablespoons (45 milliliters) cooking oil
2 teaspoons (10 grams) chopped onion
3 slices ginger
1 teaspoon (5 milliliters) sesame oil
Place the wood-ear mushrooms in a small bowl, cover with hot water, and soak for 1 hour. When soft, drain the mushrooms and dry them.
Place the cornstarch, cooking wine, soy sauce, and salt in a bowl and mix together. Add the lamb or mutton pieces and stir to coat.
Chop the taro into pieces about the same size as the meat.
Heat 2 tablespoons of the cooking oil in a wok or frying pan. Add the meat and stir-fry for 5 minutes, or until the meat changes color. Remove the meat from the pan and and set aside in a clean dish.
Heat the remaining tablespoon of cooking oil in the wok. Drop in the onion and ginger and stir for a few seconds. Add the taro and wood-ear mushrooms. Stir-fry for 3 minutes, then mix in the meat. Stir well.
Sprinkle the sesame oil over the dish and add a little salt to taste.
Remove from heat and serve.
Garlic Mutton
serves 2
_This dish warms the spleen and the kidneys. It reduces swelling and relieves inflammation due to a preponderant Fire element, and is prescribed as a specific remedy for swelling, pain, cold, and numbness in the knees and joints. It also detoxifies and is sometimes prescribed for impotence and chronic nephritis (inflammation of the kidneys)._
9 ounces (255 grams) mutton, cut into 1-inch cubes
4 cups (1 liter) water
1 large head garlic, peeled
Salt and pepper to taste
In a medium saucepan, bring the water to a boil. Add the mutton and the garlic, cover, turn the flame to low, and stew for 1½ hours, or until cooked. (In China meat is considered fully cooked when the tip of a chopstick pushes through with ease.) Add a little hot water occasionally, to keep the stew from drying out.
Add salt and pepper according to your taste.
Mutton and Shrimp Pudding
serves 2
_This dish warms and reinforces the kidneys. Often prescribed to alleviate cold syndromes in the lower half of the body, it corrects urinary deficiencies, soothes pains in the waist and knees, decreases the frequency of seminal emissions, and calms chronic kidney inflammations._
1 tablespoon (15 grams) cornstarch
1 tablespoon (15 milliliters) water
5 ounces (155 grams) mutton, finely shredded
1 tablespoon (15 milliliters) cooking oil
2 slices ginger
3/4 cup (180 milliliters) water, plus more for thinning
2 tablespoons minced garlic
3 ounces (90 grams) fresh shrimp, cleaned, peeled, and deveined
1 tablespoon (15 milliliters) cooking wine
1 tablespoon (15 milliliters) soy sauce
2 scallions, chopped
Salt and pepper to taste
Mix the cornstarch and the tablespoon of water in a small bowl. Dice the shrimp.
Heat the oil in a wok or frying pan. Drop in the mutton and the ginger. Stir for 10 seconds, then add 3/4 cup (185 milliliters) of water. Allow the water to come to a boil, then add the garlic. Wait another 30 seconds before adding the shrimp, followed by the wine, and finally by the soy sauce.
Cook for 20 minutes. When the water evaporates, add more a little at a time. Be sure not to pour in too much water, though, as the end product should resemble a semicompact pudding more than a soup or a stew.
When the cooking time is almost up, add the chopped scallions and salt and pepper to taste. Finally, add the cornstarch-water mixture and stir. When the dish is compact enough, with a thickness like pudding, remove from heat and serve.
Mutton Stew
serves 4
_Mutton provides strong Yang energy. This dish fortifies the entire body, and the masculine reproductive functions in particular._
2 tablespoons (30 milliliters) cooking oil
1 pound (500 grams) mutton, cut into 1½-inch cubes
½ cup (125 milliliters) soy sauce
1½ teaspoons (7 grams) sugar
2 teaspoons (10 milliliters) cooking wine
6 slices ginger
2 tablespoons (30 grams) chopped onion
8 cups (2 liters) water
1/3 teaspoon (2 grams) anise seed
½ cup (100 grams) potato, diced
2 carrots, cut into small pieces
Heat the cooking oil in a wok or frying pan and drop the mutton in. Add soy sauce, sugar, and cooking wine, and stir-fry the mutton for about 5 minutes, or until brown.
Pour half of the water into a large soup pot or stove-top casserole dish. Place the ginger slices, onion, and anise seed in the pot with water. Simmer over low heat, covered, for 1½ hours.
Add the potato and the carrot to the pot, adding water if necessary. Simmer for 20 minutes longer.
Remove from heat and serve in a large tureen or in individual bowls.
Stir-fried Mutton
serves 2
_Like the previous dish, stir-fried mutton also provides strong Yang energy to the body._
1 tablespoon (15 milliliters) cooking oil
½ pound (250 grams) mutton, thinly sliced
½ cup (100 grams) scallions, chopped
1 teaspoon (5 grams) chopped ginger
¼ cup (60 milliliters) soy sauce
2 tablespoons (30 milliliters) cooking wine
2 tablespoons (30 milliliters) sesame oil
Set a wok or frying pan over high heat and add the cooking oil. When hot, drop in the mutton, chopped scallions, and ginger and stir-fry.
After 1 minute, add the soy sauce and the wine. Stir-fry for 1 more minute, or until the meat is cooked.
Add the sesame oil and stir, then transfer to a serving plate.
PORK DISHES
Pork with Celery
serves 2
_This dish soothes the liver and clears up toxic heat. It also invigorates the functions of the stomach and combats high blood pressure, dehydration, poor appetite, dryness in the mouth, dizziness, and chronic headache._
_An alternative to this dish is to use onion in place of celery. Onion warms the internal organs of digestion while celery cools them._
2 ounces (60 grams) lean pork, cut into long shreds
1 tablespoon (15 milliliters) soy sauce
½ teaspoon (2.5 grams) sugar
2 tablespoons (30 milliliters) cooking oil
3 slices ginger
1 cup (200 grams) celery, cut into 2-inch-long pieces
Pinch of salt
Place the shredded pork in a medium bowl. Add the soy sauce and sugar and mix well. Let marinate for 5 to 10 minutes.
Heat 1 tablespoon of the oil in a wok or frying pan. When heated, drop the ginger into the wok, followed immediately by the marinated pork. Stir for 1 minute, or until pork is cooked to your liking. Transfer temporarily to a separate dish.
Pour the remaining oil into the wok. Reheat and add the celery and a pinch of salt. Stir-fry over high heat for 1 minute, then add the pork. Stir-fry for another 10 seconds. Transfer to a dish and serve hot.
Pork Liver and Bitter Melon
serves 4
_In this dish the pork liver and the bitter melon both nourish the blood. Bitter melon detoxifies the blood and cools internal heat syndromes. Eating liver nourishes and strengthens the human liver and cures anemia. Pork Liver and Bitter Melon is known for its ability to alleviate headache and dizziness._
_If you dislike the taste of bitter melon, you can blanch the melon for 3 to 4 minutes before frying to remove some of the bitter taste._
1 tablespoon (15 milliliters) soy sauce
1 tablespoon (15 milliliters) cooking wine
½ teaspoon (2.5 grams) sugar
10 ounces (280 grams) pork liver, thinly sliced
½ pound (250 grams) bitter melon (see page 70)
3 tablespoons (45 milliliters) cooking oil
8 garlic cloves, peeled and chopped
1 teaspoon (5 milliliters) sesame oil
Salt to taste
Place the soy sauce, cooking wine, and sugar in a medium bowl and mix together. Add the liver and marinate for 10 minutes.
Cut the bitter melon in half lengthwise. Remove the pulp and the seeds and discard them. Cut the melon into ¼-inch-thick slices.
Heat 2 tablespoons (30 milliliters) of the oil in a wok or frying pan. Add the sliced liver and half of the garlic. Stir-fry for 4 minutes, then remove and place on a dish.
Place the remaining tablespoon (15 milliliters) of oil in the pan and heat. When the oil is hot, add the remainder of the garlic along with the bitter melon. Stir-fry for 2 minutes, or until evenly cooked. Add the liver and stir for 30 seconds.
Add the sesame oil and salt to taste. Remove from heat and serve.
Pied du Porc with Peanuts
serves 2
_Because this dish is fairly fatty it is not suitable for everyone. In China it is often taken when one feels weak or fatigued. Pigs_ _'_ _feet provide rich nourishment for qi and the blood. This dish is also prescribed to lactating mothers to stimulate the production of breast milk._
1 pig's foot
½ cup (100 grams) raw peanuts
3 slices ginger
1 tablespoon (15 milliliters) cooking wine
6 cups (1.5 liters) water
Place all the ingredients in a large saucepan. Bring to a boil, cover the pan, reduce heat to low, and simmer for 1½ hours. Add water as needed. When ready, add salt.
Strain the meat and the peanuts—reserving the water, as you can use it at a later date to prepare a nutritious vegetable soup—and place on a serving dish to serve.
Almond Pork
serves 4
_This dish invigorates the functions of the spleen and tones the lungs. It reduces phlegm, relieves coughing, alleviates breathing problems, and is frequently prescribed to people suffering from chronic bronchitis._
1 tablespoon (15 grams) almond meats
Water for soaking
1 tablespoon (15 milliliters) cooking oil
2 tablespoons (30 grams) sugar
1 pound (500 grams) pork, cut into 1-inch pieces
1 teaspoon (5 grams) chopped onion
1 teaspoon (5 grams) chopped ginger
2 tablespoons (30 milliliters) soy sauce
1 tablespoon (15 milliliters) cooking wine
4 cups (1 liter) water for cooking, plus more as needed
Place the almonds in a small bowl, cover with hot water, and soak for 2 hours or until you can remove the skin with ease.
Heat the oil in a wok or frying pan. Add the sugar and stir-fry for 1½ minutes over medium heat, or until the sugar turns dark red.
Add the pork and stir-fry for 1 minute. Add the onion, ginger, almonds, soy sauce, and wine and stir-fry for 1 more minute. Add the 4 cups of water and continue to cook. (Add more water, a little at a time, if it evaporates too rapidly.) Stew over a low flame for about 1 hour, or until ready. (In China meat is considered done when the tip of a chopstick pushes through with ease.)
Add salt according to taste and serve.
Wood-ear Pork
serves 2
_This dish alleviates circulation problems and stops bleeding by dispelling pathogenic heat from the blood. In China it is often prescribed to alleviate menstrual pains as well as heavy menstrual bleeding._
¼ cup (50 grams) wood-ear mushrooms
Water for soaking
1 teaspoon (5 milliliters) cooking wine
1 tablespoon (15 milliliters) soy sauce
1 teaspoon (5 grams) cornstarch
4 ounces (115 grams) lean pork, finely sliced
1 tablespoon (15 milliliters) cooking oil
Salt and pepper to taste
Soak the wood-ear mushrooms in hot water for 1 hour, or until soft. Strain and slice.
Combine the wine, soy sauce, pepper, and cornstarch in a medium bowl. Add the pork, stir to coat, and marinate for 10 minutes.
Heat the oil in a wok or frying pan. Drop the pork and the mushrooms into the pan. Stir-fry over high heat for 3 to 4 minutes, or until done.
Add salt and pepper to taste and serve.
Daikon Pork
serves 4
_Daikon dispels toxic heat and dissolves phlegm. This dish normalizes the stomach, and thus the functions of digestion. It is an efficient remedy for bloated stomach, indigestion, intestinal gas, and constipation._
1 tablespoon (15 milliliters) cooking oil
2 teaspoons (10 grams) sugar
8 ounces (250 grams) pork, cut into ¼-inch cubes
4 tablespoons (60 milliliters) soy sauce
1 tablespoon (15 milliliters) cooking wine
3 slices ginger
1 tablespoon (15 grams) chopped onion
2 cups (500 milliliters) water
2 cups (400 grams) daikon, cut into ¼-inch cubes
Salt to taste
Heat the oil in a wok or frying pan. Add the sugar and the pork. Stir-fry for 3 to 4 minutes, or until the pork has changed color. Add the soy sauce, wine, ginger, and onion.
Pour the water into the wok to cover the ingredients. Bring to a boil, reduce heat, and simmer over a low flame for 45 minutes. Add the daikon. Continue to cook for 20 more minutes.
Add salt to taste and serve.
Pork with Watermelon
serves 2
_This dish dispels heat. It also alleviates thirst, dryness in the throat, headache, and dehydration caused by summer heat or sunstroke._
1 egg white, beaten
1 tablespoon (15 grams) cornstarch
½ teaspoon (2.5 grams) salt, plus a pinch
3½ ounces (100 grams) pork, shredded
½ pound (250 grams) watermelon rind
2 teaspoons (10 milliliters) sesame oil
2 tablespoons (30 milliliters) cooking oil
1 tablespoon (15 milliliters) water
Mix the egg white and the cornstarch in a medium bowl. Add the ½ teaspoon (2.5 grams) of salt.
Place the pork in the bowl with the egg white–cornstarch mixture, stir to coat, and let marinate for 5 minutes.
Wash the watermelon rind thoroughly and remove all but the thick external green shell. Shred the rind. Place the rind in a bowl, sprinkle a pinch of salt over it, then leave to rest for about 5 minutes. After 5 minutes, drain off the water. Add 1 teaspoon (5 milliliters) of sesame oil.
Heat the cooking oil in a wok or frying pan. Add the marinated shredded pork and stir for 3 minutes. Remove, place on a clean plate, and set aside.
Pour the tablespoon (15 milliliters) of water into the pan and place over medium-high heat. Bring the water to a boil, then add the pork and the watermelon rind. Stir for 2 minutes.
Sprinkle the remaining teaspoon (5 milliliters) of sesame oil over the dish, remove from heat, and serve.
CHICKEN DISHES
Jasmine Flower Chicken
serves 2
_This dish relaxes the nerves and the nervous system, thus reducing tension. It tones circulation, enriches the blood, and is a good general tonic for combating lack of energy, anemia, and general weakness._
1 tablespoon (15 milliliters) cooking wine
2 egg whites
1 teaspoon (5 grams) cornstarch
¼ teaspoon (about 1 gram) salt
8 ounces (250 grams) boneless chicken breast, thinly sliced
1 tablespoon (15 milliliters) cooking oil
24 jasmine flowers
Pepper to taste
In a bowl, whisk together the wine, egg whites, cornstarch, and salt. Stir in the chicken and let marinate for 10 minutes.
Heat the oil in a wok or frying pan. Transfer the chicken and the jasmine flowers to the wok. Stir-fry over high heat for 3 minutes, or until cooked. Transfer to a serving dish and sprinkle with a little pepper to taste.
Chestnut with Chicken
serves 4
_The strong Yang ingredients in this dish nourish the kidneys and the liver. Because of its strong Yang functions, this dish strengthens male sexuality, combating seminal emission, premature ejaculation, and impotence due to weakness or stress. It also soothes the nerves and combats body pains._
1 cup (200 grams) chestnuts, fresh or dry
Water for soaking
1 tablespoon (15 milliliters) cooking wine
1 tablespoon (15 grams) scallions, chopped
1 tablespoon (15 grams) sugar
2 tablespoons (30 grams) cornstarch
3 cups (750 milliliters) water
2 tablespoons (30 milliliters) cooking oil
1 pound (500 grams) chicken, cut into 1½-inch cubes
4 teaspoons (20 milliliters) soy sauce
Prepare the chestnuts first. If they are dry, soak them in water overnight or until they are soft. If they are fresh, cut a cross in the shell and boil in water for 2 minutes, then peel them. Set aside.
In a medium bowl, mix together the wine, scallions, sugar, cornstarch, and water to make a sauce. Set aside.
Heat the oil in a wok or frying pan. When the oil is hot, place the chicken in the wok, add the soy sauce, and stir-fry for 3 to 4 minutes, or until chicken is golden brown, then add the sauce and the chestnuts. Stir for 1 minute. Add the sauce.
Simmer over a low flame for 30 minutes, or until chicken is cooked, adding a little water if necessary. Remove from heat and serve.
Walnut Chicken
serves 4
_This dish invigorates the Yang functions; purifies qi and the blood, stimulating their circulation; and nourishes the kidneys. It is a good remedy for sexual weakness, dizziness, constipation, and lethargy, and prevents premature graying of the hair._
1 egg white
2 teaspoons (10 grams) cornstarch
10 ounces (280 grams) boneless chicken breast, sliced
¼ cup (50 grams) walnut meats
1 tablespoon (15 milliliters) cooking oil
3 shiitake mushrooms, sliced
1 teaspoon (5 grams) finely chopped ginger
1 teaspoon (5 grams) finely chopped scallion
1 teaspoon (5 milliliters) soy sauce
1 teaspoon (5 milliliters) cooking wine
Salt to taste
Place the egg white and cornstarch in a medium bowl and mix well. Add the chicken and stir to coat. Set aside.
Roast the walnuts in a dry wok for 3 minutes, or until golden brown.
Heat the oil in a medium saucepan. When the oil is hot, add the mushrooms, ginger, and scallion. Stir for 30 seconds, then add the chicken. Stir-fry for 2 minutes. Add the soy sauce and the wine. Continue to stir-fry for 3 more minutes.
Drop the walnuts in last and stir-fry for another 30 seconds. Add salt to taste and serve.
Basil Chicken
serves 4
_This chicken dish reinforces the functions of the liver and the kidneys and nourishes the skin, rendering it soft and shiny. It also stimulates circulation of the blood and alleviates internal ear problems, including dizziness, tinnitus, and minor hearing problems.
This recipe calls for chicken drumsticks, but chicken breast or other chicken meat may be used if preferred._
1 pound (500 grams) chicken drumsticks
5 garlic cloves, peeled and split lengthwise
¼ cup (60 milliliters) black sesame oil
5 slices ginger
1/3 cup (90 milliliters) cooking wine
¼ cup (60 milliliters) soy sauce
1 tablespoon (15 grams) sugar
½ cup (100 grams) packed fresh basil leaves
Using a meat cleaver chop each drumstick in half, through the bone. Set the drumstick halves aside.
Heat the sesame oil in a medium saucepan. When the oil is hot, drop in the garlic and ginger and stir for 10 seconds. Then add the chicken. Stir-fry for 2 minutes over high heat. Add the wine, soy sauce, and sugar, reduce the heat, and simmer over a low flame for 20 to 30 minutes, stirring occasionally.
Add the basil leaves. Simmer for 1 more minute and serve.
Pomelo Chicken
serves 4
_Grapefruit (pomelo) is sweet, sour, and cold. It eliminates catarrh and strengthens the functions of the stomach, thus aiding digestion. As a whole, this dish invigorates qi. It also reinforces the functions of the spleen, dissolves phlegm, calms coughing, helps digestion, and stimulates the appetite._
1 grapefruit
1 whole chicken (approximately 3 pounds or 1½ kilograms)
1 tablespoon (15 grams) salt
2 white heads of scallion, sliced in half lengthwise
5 slices ginger
1 tablespoon (15 milliliters) cooking wine
4 cups (1 liter) water for steaming
Peel and section the grapefruit and cut each section into three pieces. Clean the chicken inside and out and pat dry.
Place the grapefruit pieces inside the chicken. Rub the salt over the outside of the chicken.
Put the chicken inside a ceramic bowl, together with the scallions, ginger, soy sauce, and wine. Place the bowl with the chicken in a large steaming dish (see page 66).
Bring the water to boil in a large soup pot. When water is boiling, place the steamer in the pot. Cover, turn the heat down to medium, and steam the chicken for 1½ hours. Add hot water to the pot when necessary.
Allow the chicken to cool, then cut it into portions for serving.
Chrysanthemum Chicken
serves 4
_This dish nourishes the spleen and liver and improves eyesight. It is good for insomnia, dizziness, and general weakness._
3 egg whites
1 tablespoon (15 milliliters) cooking wine
2 tablespoons (30 grams) cornstarch
½ teaspoon (2.5 grams) salt
1 pound (500 grams) boneless chicken meat, sliced into 2-inch-long pieces
2 tablespoons (30 milliliters) cooking oil
2 teaspoons (10 grams) chopped scallion
2 teaspoons (10 grams) chopped ginger
2 tablespoons (30 grams) dry chrysanthemum flowers
1 teaspoon (5 grams) sugar
1 teaspoon (5 milliliters) sesame oil
Place the egg whites, cooking wine, cornstarch, and salt in a large bowl and mix together. Add the chicken slices and stir to coat.
Heat the cooking oil in a wok or frying pan. Drop in the chopped scallion and ginger. Stir for a few seconds, then add the chicken. Stir-fry for 2 or 3 minutes. Add the chrysanthemum flowers and sugar. Continue to stir-fry for 1 minute.
Remove from heat, place in serving dish, sprinkle with sesame oil, and serve.
DUCK DISHES
Yin Yang Duck
serves 4
_Duck warms the stomach and spleen, reinforces all the vital functions of the body, and invigorates Yang. This duck dish is, therefore, particularly suited to Yang-deficiency syndromes. It also alleviates stomachache and diarrhea caused by low resistance to cold._
1 whole duck (approximately 5 pounds or 2½ kilograms)
18 cups (4.5 liters) water
5 slices ginger
¼ cup (50 grams) onion, chopped
1 cup (250 milliliters) soy sauce
2 tablespoons (30 milliliters) cooking wine
2 teaspoons (10 grams) salt
2 cinnamon sticks
2 teaspoons (10 grams) anise seed
2 tablespoons (30 grams) sugar
Clean the duck inside and out and pat dry.
Place the duck in a large soup kettle with the water, ginger, and onion. Bring to a boil over high heat. When the water boils, reduce heat to low. Using a spoon, remove the surface foam and discard. Cook for about 20 minutes, until done. The duck is ready when you are able to pass the point of a chopstick through the flesh of the leg.
Turn off the heat. Drain the duck, reserving 2 cups (500 milliliters) of the broth for later use.
Return the duck to the saucepan and add the soy sauce, cooking wine, salt, cinnamon, and anise seed. Add the reserved broth.
Cook over low heat for 15 minutes. Turn the duck over, add the sugar, and cook for another 15 minutes. Near the end of the cooking time, use a spoon to pour the juice over the duck. Transfer the duck to a plate and allow it to cool, then cut and serve individual portions.
Lychee Duck
serves 4
_This duck dish strengthens the functions of the spleen and nourishes the blood. It also cures anemia, improves the appetite, and invigorates the body as a whole.
This recipe calls for a lotus flower, which is not easy to come by in the United States. If unavailable, a rose—grown without exposure to chemicals or pesticides, of course—may be used._
1 whole duck (approximately 5 pounds or 2½ kilograms)
1 fresh lotus flower (or rose)
12 cups (3 liters) water
7 ounces (200 grams) lean pork, chopped
1 tablespoon (15 grams) chopped scallion
3 slices ginger
1 tablespoon (15 milliliters) soy sauce
1 tablespoon (15 milliliters) cooking wine
½ teaspoon (15 grams) salt
Water for steaming
1 cup (200 grams) lychees, fresh or canned
Clean the duck inside and out and pat dry.
Remove the petals from the flower. In a large soup pot, bring the water to boil. Drop the petals into the water and boil for 30 seconds. Remove the petals and set aside, reserving the water for later use.
Mix the pork with the chopped scallion, ginger, soy sauce, wine, and salt in a medium bowl.
Boil the duck in the reserved flower-petal water for 1 minute. Remove the duck and discard the water.
Place the duck in a large steaming dish (see page 66) and spread the pork mixture over it. Using a pot deep enough to fit your steamer, bring the water to a boil. When the water is boiling, place the steamer in the pot. Cover, turn the heat down to medium, and steam the duck for 1 hour, or until cooked. (In China meat is considered fully cooked when the tip of a chopstick can easily pierce the meat.)
Open the steamer, remove the onion and the ginger, and add the lychees and flower petals in their place. Steam for another 15 minutes
Transfer the duck to a plate and allow it to cool, then cut for serving.
EGG DISHES
Scrambled Egg with Tomato
serves 2
_This dish cools internal heat, nourishes Yin, and stimulates gastric juices, thus improving the appetite. The nerve-relaxing properties of this dish make it a suitable remedy for people suffering from nervous tension, stress, and insomnia.
Because we are not used to sour flavors in China, sugar is generally added to this recipe. Tomato without sugar is deemed too sour. If you like a little sourness, the sugar may be dispensed with._
2 tablespoons (30 milliliters) cooking oil
3 eggs, beaten
3 garlic cloves, peeled and crushed
1 cup (200 grams) diced tomato
1 teaspoon (5 grams) sugar, optional
3 tablespoons (45 milliliters) water
Salt to taste
Heat 1 tablespoon (15 milliliters) of the cooking oil in a wok or frying pan. Add the eggs and scramble for 3 minutes. Remove when ready.
Reheat the wok with the remaining tablespoon of cooking oil (you may use water as an alternative to oil). Throw in the crushed garlic and stir for a few seconds. Add the tomato and, if you wish to use it, the sugar. Stir over medium heat for 2 minutes.
Return the scrambled eggs to the pan and stir well. Add 3 tablespoons (45 milliliters) of water. Cover the wok for 1 minute.
Remove cover, stir, add salt to taste, and transfer to a serving dish.
Ginger and Onion Omelette
serves 2
_This omelette dispels pathogenic wind and cold and stimulates the appetite. The ginger and scallion in this dish make it a valid remedy for colds, headaches, coughs, and blocked nasal passages._
3 eggs
1 teaspoon (5 grams) finely minced ginger
4 white heads of scallions, chopped
Pinch of salt, or to taste
1 tablespoon (15 milliliters) cooking oil
Beat the eggs in a medium bowl together with the ginger, scallion, and a pinch of salt.
Heat the oil in a wok or frying pan. When the oil is hot, pour the beaten egg into the pan and cook over a medium flame for 3 minutes. Using a spatula, turn the egg over and cook the top side for 1 minute.
Remove from heat and serve.
SEAFOOD DISHES
Shark
serves 2
_Shark cooked with garlic and ginger nourishes the blood and promotes the normal flow of qi; the garlic and ginger in this dish also has a warming effect that dissipates cold and cold-syndrome diseases. This dish invigorates the functions of the stomach. It stimulates the gastric juices, thereby alleviating stomachache and digestive problems, including gas and a bloated abdomen. It also stimulates the appetite. Recent theory asserts that eating shark meat may be a defense against cancer._
1 tablespoon (15 milliliters) cooking oil
1 head of garlic, cloves separated and peeled
3 slices ginger
10 ounces (280 grams) shark, cut into 1-inch cubes
2 teaspoons (10 milliliters) cooking wine
½ teaspoon (2.5 grams) sugar, optional
4 tablespoons (60 milliliters) water
½ teaspoon (2.5 grams) salt
Heat the oil in a wok or frying pan. When the oil is hot, drop in the garlic cloves and the ginger. Stir for 1 minute, then add the shark meat, cooking wine, and sugar if desired. Stir over medium heat. Add the water, cover the pan, and cook for 2 minutes.
When the fish is cooked, season with salt and serve.
Steamed Trout
serves 2 to 4
_Steamed carp is a classic dish in China. In fact, carp is our most common fish. It thrives in the millions of small ponds and rice paddies of eastern China.
Since carp is not common in the United States_ _—_ _and, as a result, it is not the favorite fish of most people_ _—_ _we have based this recipe on another freshwater fish with similar medicinal properties_ _—_ _the trout. Any fish may be prepared in this traditional manner. Steamed salmon steak is one favorite, although salmon is not as lean as carp or trout and has very different medicinal properties than freshwater fish. The most important requirement for this dish is that the fish be fresh._
1 fresh whole trout
4 slices ginger, finely shredded
Water for steaming
2 stalks cilantro
3 scallions, finely chopped
2 tablespoons (30 milliliters) soy sauce
Salt and pepper to taste
1 tablespoon (15 milliliters) sesame or olive oil, optional
Clean the trout and place on a shallow ceramic dish that will fit inside your steamer (see page 66). (If the trout won't fit, cut it in half.) Sprinkle the ginger over the fish.
Using a pan deep enough to fit your steamer, bring water to a boil. Place the steamer in the pan, cover, turn the heat down to medium-low, and steam for 15 minutes.
Turn off the heat and remove the dish from the steamer. Drain off any liquid. Garnish the fish with the cilantro, scallions, and soy sauce. Sprinkle with salt and pepper to taste.
As a finishing touch, you may heat 1 tablespoon (15 milliliters) of sesame or olive oil and sprinkle it over the fish before serving, if desired.
Snapper
serves 2
_Snapper nourishes the spleen and enhances qi. It also counteracts diarrhea. Although filling, this dish stimulates the appetite._
10 ounces (200 grams) snapper
1 tablespoon (15 milliliters) cooking wine
1 tablespoon (15 milliliters) soy sauce
2 tablespoons (30 milliliters) cooking oil
1 scallion, chopped
2 slices ginger
½ cup (100 grams) taro root, sliced
¼ cup (60 milliliters) water
½ teaspoon (2.5 grams) salt
Cut the snapper into 2-inch-thick slices.
In a medium bowl, mix the cooking wine and soy sauce. Place the snapper in the bowl and toss to coat. Let it sit for 10 minutes to marinate.
Heat the oil in a wok or frying pan. Drop in the chopped scallion and the ginger and stir for a few seconds, then add the snapper and the taro. Stir for a few more seconds, then add the water. Cover the wok and let cook for 3 minutes.
Remove from heat. Arrange the snapper on a serving dish. Add salt and serve.
Ginger Calamari
serves 2 to 4
_Calamari nourishes the brain and the blood. It reinforces the spleen and the stomach and dispels cold.
This dish is often prescribed for women who suffer from amenorrhea, the abnormal absence or cessation of menses._
2 tablespoons (30 milliliters) cooking oil
2 teaspoons (10 grams) minced ginger
1 pound (500 grams) calamari, cleaned and sliced
1 tablespoon (15 milliliters) cooking wine
1 teaspoon (5 grams) salt
Heat the oil in a wok or frying pan. Drop in the ginger. Stir for a few seconds. Drop in the calamari. Add the cooking wine and stir for 2 to 3 minutes until cooked. Sprinkle with salt and serve.
Shrimp with Lettuce
serves 4
_Shrimp invigorates the Yang functions and replenishes the essence of the kidneys. Consequently, shrimp is often prescribed as a cure for low sex drive or even impotence. Eating shrimp with lettuce is said to clear skin problems, rendering the skin smooth and elastic. Asthma sufferers are also advised to eat this dish in abundance._
1 pound (500 grams) fresh shrimp, cleaned, peeled, and deveined
1 egg white, beaten
1 tablespoon (15 grams) cornstarch
½ teaspoon (2.5 grams) salt
1½ teaspoons (8 grams) minced ginger
2 scallions, minced
12 leaves iceberg lettuce
2 tablespoons (30 milliliters) cookingoil
1 tablespoon (15 milliliters) water
1 teaspoon (5 milliliters) sesame oil
Mince the shrimp and place in a medium-to-large bowl with the egg white, cornstarch, and salt. Mix well.
Mix the ginger and scallions together in a small bowl.
Clean the lettuce leaves and trim to round them off. Arrange the lettuce leaves on a serving plate.
Heat the cooking oil in a wok or frying pan. Throw in the shrimp–egg mixture along with the ginger–scallion mixture. Stir-fry over medium heat for 2 to 3 minutes. Add the tablespoon of water and stir. Stir in the sesame oil and remove from heat. Transfer to a serving plate.
Present the two plates, one of lettuce leaves and one of minced shrimp, separately at the table. Have each diner place a mound of shrimp inside a lettuce leaf and roll it up to eat it from the hand.
Shrimp with Tofu
serves 2 to 3
_This dish strengthens Yang, invigorates the functions of the kidneys, and stimulates the appetite. Shrimp is usually prescribed for male sexual problems, such as premature ejaculation and impotence._
4 ounces (125 grams) fresh shrimp, cleaned, peeled, and deveined
1 tablespoon (15 milliliters) cooking wine
Pinch of salt
1 tablespoon (15 grams) cornstarch
2 tablespoons (30 milliliters) plus ¼ cup (60 milliliters) water
1 tablespoon (15 milliliters) cooking oil
8 ounces (250 grams) tofu, cut into 1-inch cubes
1 teaspoon (5 milliliters) sesame oil
In a medium bowl, mix the shrimp with the cooking wine and a pinch of salt. In a small bowl, mix together the cornstarch and the 2 tablespoons (30 milliliters) of water.
Heat the cooking oil in a wok or frying pan. When the oil is hot, add the tofu cubes and stir-fry for 1 minute, then add the ¼ cup (60 milliliters) of water. Lower the heat, cover the wok, and simmer for 5 minutes.
Add the shrimp and stir. Simmer for another 3 minutes. Now add the cornstarch mixture. Stir.
Sprinkle with the sesame oil and stir well. Remove from heat and serve.
Celery Shrimp
serves 2 to 3
_This dish replenishes the essence of the kidneys and subdues hyperactivity of the liver. It also brings down swelling, counteracts dizziness and headaches, regulates blood pressure, and alleviates dehydration.
Shrimp are considered a valid remedy for male sexual weaknesses, such as premature ejaculation, over-frequent nocturnal emission, and low sex drive._
1 tablespoon (15 milliliters) cooking oil, or more as needed
5 garlic cloves, peeled and crushed
4 ounces (125 grams) fresh shrimp, cleaned, peeled, and deveined
½ cup (100 grams) celery, chopped into 1-inch-long pieces
Salt and pepper to taste
Heat the oil in a wok or frying pan. When the oil is hot, add the garlic and stir-fry for 10 seconds, then add the shrimp and stir-fry for 3 minutes. Transfer the shrimp to a bowl and set aside.
Reheat the wok, adding a little more oil or a tablespoon of water if needed. Add the celery segments and stir-fry for 3 minutes.
Return the cooked shrimp to the pan. Stir thoroughly. Add salt and pepper to taste, remove from heat, and serve.
Oysters in Black Bean Sauce
serves 4
_Oysters are renowned throughout the world for their aphrodisiac effects. As is often the case with aphrodisiacs, however, these effects exist more in the mind than in the oysters.
Chinese medicine does not emphasize any specific aphrodisiac function in oysters, but it does regard them as a general tonic that may lead to a stronger sex urge. According to Chinese theory, oysters do, in fact, consolidate the vital energy_ _—_ _the qi_ _—_ _of the kidneys, thereby arresting frequent nocturnal seminal emission.
Oysters also nourish the heart, the blood, and Yin essence. They reduce phlegm and soothe the nerves, thus curing such problems as insomnia and nervous sweating._
1 pound (500 grams) oysters, shelled
1 tablespoon (15 grams) cornstarch
2 tablespoons (30 milliliters) plus 4 cups (1 liter) water
2 tablespoons (30 milliliters) cooking oil
2 or 3 garlic cloves, peeled and crushed
1 tablespoon (15 grams) crushed ginger
1 tablespoon (15 grams) black bean sauce
3 scallions, chopped
2½ tablespoons (38 milliliters) soy sauce or oyster sauce
Salt to taste
Wash the oysters under running water and drain them. Examine the oysters for size. They should be small enough to fit easily in the mouth or to be lifted using chopsticks. If they are too large, cut them in half.
In a small bowl, mix the cornstarch with the 2 tablespoons (30 milliliters) of water and set aside.
Fill a medium saucepan with the 4 cups (1 liter) of water, set over high heat, and bring to a boil. When the water is boiling, throw in the oysters. Remove oysters from the water after 20 seconds.
Heat the cooking oil in a wok or frying pan. When the oil is hot, add the crushed garlic, the crushed ginger, and the black bean sauce. Stir-fry for 10 seconds, then add the oysters, scallions, and soy sauce or oyster sauce. Stir for 1 minute, then add the cornstarch mixture and stir well. Add salt to taste. Remove from heat and serve.
Fish with Spinach
serves 2 to 4
_This dish is good for the liver. It also combats high blood pressure, poor appetite, dizziness, and chronic headache._
8 ounces (250 grams) lean fish (cod, snapper, or sole), cut into 1-inch cubes
4 cups (1 liter) water
1 cup (200 grams) packed fresh spinach, in 2-inch-long pieces
2 tablespoons (30 milliliters) cooking oil
3 garlic cloves, peeled and chopped
1 teaspoon (5 grams) chopped ginger
2 scallions, chopped
1 tablespoon (15 milliliters) cooking wine
½ teaspoon (2.5 grams) salt
In a medium saucepan, bring the water to a boil. Drop the spinach into the boiling water, boil for 30 seconds, then drain and set aside.
Heat the cooking oil in a wok or frying pan over high heat. When the oil is hot, drop in the garlic, ginger, and scallions. Stir for a few seconds and add the fish. Add the cooking wine. Stir for 1 minute and add the spinach. Cover the wok, reduce heat, and simmer for 1 minute.
Add salt and stir well. Remove from heat and serve.
TEAS
Tea, what we call _chia_ in China, usually refers to an infusion made with the leaves of the _Camellia sinensis_ plant, which is drunk without milk, sugar, or other additives. In China this refreshing drink accompanies meals and, indeed, the activities of most people's entire day.
The following infusions are made from other ingredients in addition to tea leaves. They have specific medicinal properties but, if you like their flavor, they may also be enjoyed simply as beverages. The proportions given in most recipes are for one person. Note that you should always cover the cup or pot when steeping or brewing the tea, lest the volatile oils and other active ingredients escape into the air.
Black Sesame Tea
_This tea nourishes the blood, liver, and kidneys and cures bouts of dizziness. It is often prescribed for premature gray hair, pain in the knees, and pain in the lumbar region of the back._
1 teaspoon (5 grams) black sesame seeds
½ teaspoon (2.5 grams) green tea leaves
1 cup (250 milliliters) water
Heat a dry wok or frying pan and roast the sesame seeds in it for 1 minute. Remove the sesame seeds from the wok. Grind them into a powder using a grinder or a mortar and pestle.
Mix the powder and the tea leaves together.
Bring the water to a boil. Pour the boiling water over the sesame–tea mixture, cover, and brew for 5 minutes.
Ginseng Tea
_This tea nourishes the wu zang (the five generating and storing organs of the body_ _—_ _heart, liver, spleen, lungs, and kidneys). Ginseng tea soothes the nerves and stimulates the production of body fluids. It is prescribed specifically for general weakness and exhaustion after childbirth, illness, or surgery, and as a tonic for the elderly.
_Caution: _You should not drink this tea when you eat daikon or radish, as they weaken the ginseng_ _'_ _s effects._
4 fine slices ginseng root
1 cup (250 milliliters) water
Bring the water to a boil. Pour the water over the sliced ginseng, cover, and brew for 10 to 15 minutes.
Drink immediately.
Dry Dandelion and Chrysanthemum Tea
_This infusion dissipates toxic heat and evil wind and treats colds as well as sore throats._
3 teaspoons (15 grams) dry dandelion leaves
2 teaspoons (10 grams) dry chrysanthemum flowers
2 teaspoons (10 grams) tea leaves
1 cup (250 milliliters) water
Mix the dandelion leaves, the chrysanthemum flowers, and the tea leaves together. Put 1 heaped teaspoon (5 grams) in a cup.
Bring the water to a boil. Pour the water over the flower–tea mixture, cover, and brew for 5 minutes.
Drink immediately.
Barley Tea
_A typical summer drink in China, barley tea has a cooling effect. It is given to people who have suffered from sunstroke and heat exhaustion. It also prevents and cures indigestion._
4 teaspoons (20 grams) barley
1½ cup (375 milliliters) water
Heat a dry wok or frying pan and roast the barley for 5 minutes, stirring continuously. When done, put the roasted barley in a cup.
Bring the water to a boil. Pour over the roasted barley, cover, and brew for 10 to 15 minutes.
This tea can be drunk either hot or cold.
Ginger Tea
_Ginger tea dispels cold, strengthens the functions of the stomach and intestines, and blocks diarrhea. It is also a valid remedy for stomachache._
2 teaspoons (10 grams) minced ginger
2 teaspoons (10 grams) green tea leaves
1½ cups (375 milliliters) water
Place the ginger, tea leaves, and water in a small saucepan. Bring to a boil, reduce heat to low, cover, and decoct for 10 minutes.
Drink hot.
Rose Petal Tea
_This tea stimulates qi and blood circulation and soothes the liver. It is a useful remedy for stomachache, breathing difficulties, and menstrual problems._
1 teaspoon (5 grams) dried rose petals, or jasmine petals
1½ cups (375 milliliters) water
Bring the water to a boil. Pour the boiling water over the dried petals, cover, and brew for 10 minutes.
Drink immediately.
Mint and Chrysanthemum Tea
_A good summer drink, this tea dispels heat, soothes the liver, improves eyesight, and aids digestion._
1 teaspoon (5 grams) dry chrysanthemum flowers
2 teaspoons (10 grams) sugar
2 cups (500 milliliters) water
1 teaspoon (5 grams) chopped mint
Place the chrysanthemum and sugar together in a saucepan with the water. Bring to a boil, reduce heat to low, cover, and simmer for 10 minutes.
Add the mint and simmer for another 10 minutes. Drink immediately.
Ginseng and Walnut Tea
_This tea nourishes qi, strengthens the functions of the kidneys, and moistens the lungs. It is prescribed for shortness of breath, nervous sweating, dizziness, and tinnitus (ringing in the ears)._
4 fine slices ginseng root
3 walnuts, shelled and broken into pieces
4 cups (1 liter) water
Place the ginseng and the walnuts in a saucepan with the water. Bring to a boil over high heat. Lower the heat and simmer for 45 minutes, or until liquid reduces to 1 cup.
Drink immediately.
Fig Tea
_Fig tea dissipates heat and moistens the lungs. It also cures sore throat and constipation._
1 cup (200 grams) fresh figs
2 cups (500 milliliters) water
Sugar, to taste
Wash the figs. Place them in a saucepan with water and bring to a boil. Reduce heat to low, cover the pan, and simmer for 20 minutes.
Strain and drink the juice as a tea. Add sugar as you like.
Mung Bean Tea
_A cooling tea that is frequently drunk in China during hot weather, mung bean tea removes heat and dispels thirst and dryness in the throat and mouth. It is used as a remedy in cases of heat exhaustion and sunstroke and is also an effective diuretic. Finally, it lowers blood pressure and is said to improve eyesight._
4 cups (1 liter) water
½ cup (100 grams) green mung beans
Honey or sugar to taste
In a medium saucepan, bring the water to a boil. Add the mung beans, cover, and boil for 20 to 30 minutes.
Mung bean tea is best drunk cold, but not iced, with a little honey or sugar. The beans are usually eaten too.
WINES
The term "wine," _jiu_ in Chinese, refers not to European grape wine but to spirits—generally rice spirits or that of sorghum or other grains.
The wines described below are suitable as after-dinner drinks. Their function is not merely curative; they can be taken for prevention, as a tonic, or simply for the enjoyment of their flavor.
A medicinal dosage for these wines is 2 teaspoons (10 milliliters) two times a day. Wine that is used for medicinal purposes, normally a white wine, should be kept between 50°F and 60°F.
Walnut, Almond, and Jujube Wine
_This wine stimulates blood circulation and improves complexion, reinforces qi, and stops premature graying of the hair. It is good for shortness of breath and lower back pain, and for lack of energy due to deficiency of the lungs and the kidneys._
¼ cup (50 grams) almond meats
Water for soaking
½ cup (100 grams) walnut meats
½ cup (100 grams) jujube (Chinese dates)
4 cups (1 liter) rice wine, or sake
Soak the almonds in hot water for 2 hours and remove the skin.
Use a mortar and pestle or stone grinder to grind the almonds and the walnuts into a powder. Put the powder in a large (at least 4-pint or 2-liter) bottle along with the jujube. Add the rice wine, seal the bottle, and let stand to macerate for at least 20 days before drinking.
American Ginseng Wine
_This ginseng wine strengthens qi, nourishes Yin, and stimulates the production of body fluids. It is prescribed for weakness, dizziness, shortness of breath, dryness in the mouth and throat, and dry coughs._
¼ cup (50 grams) American ginseng, finely sliced
4 cups (1 liter) rice wine, or sake
Place the ginseng in a bottle with the rice wine.
Seal the bottle and let stand to macerate for at least 15 days before drinking.
Fresh Cherry Wine
_Prescribed for weakness, arthritis, and numbness of the legs and arms, this wine strengthens qi, nourishes the blood, dispels wind, and resolves dampness._
2 cups (400 grams) fresh cherries
4 cups (1 liter) rice wine, or sake
Wash the cherries and place them in a bottle with the rice wine.
Seal the bottle and let the wine stand to macerate for at least 15 days before drinking.
Ginger Wine
_Ginger wine strengthens qi, harmonizes the stomach, and arrests nausea and vomiting. It also dispels cold and mitigates wai yin, or external causes of disease. It is beneficial for regulating menstrual periods._
½ cup (100 grams) ginger, finely minced
¼ cup (60 grams) orange peel, finely minced
½ cup (100 grams) sugar
4 cups (1 liter) rice wine, or sake
Place the ginger, orange peel, and sugar in a bottle with the rice wine.
Seal the bottle and let stand to macerate for at least 10 days before drinking.
Rose Petal Wine
_This wine stimulates blood circulation and normalizes the flow of qi in the body. Its specific functions are to heal bruises and swellings due to trauma, to regulate menses when there is either too little or too much blood, to relieve a bloated stomach, and to mitigate shortness of breath._
1 cup (200 grams) fresh rose petals
½ cup (100 grams) sugar
4 cups rice wine, or sake
Place the rose petals in a bottle along with the sugar and rice wine.
Seal the bottle and let stand to macerate for at least 10 days before drinking.
Azalea Wine
_This wine strengthens qi, loosens phlegm, and alleviates catarrh. It also treats coughs._
¼ cup (50 grams) azalea flowers
4 cups rice wine, or sake
Wash the azalea flowers and place them in a shaded area to dry. When dry, chop the flowers. Place the chopped flowers inside a bottle with the rice wine.
Seal the bottle and let the wine stand to macerate for 5 days before drinking.
White Chrysanthemum Wine
_This wine dispels evil wind, helps to improve eyesight, and is a good treatment for headaches and head colds._
½ cup (100 grams) chrysanthemum flowers
4 cups (1 liter) rice wine, or sake
Place the flowers in a bottle with the rice wine.
Seal the bottle and let the wine stand to macerate for at least 10 days before drinking.
Dandelion Wine
_This is a recipe recorded in Li Shi Zhen_ _'_ _s sixteenth century materia medica. This wine dissipates toxic heat and relieves all swellings and skin infections. It stimulates lactation after childbirth. It also cures the intital symptoms of acute mastitis._
¼ cup (50 grams) dandelion leaves
2 cups (500 milliliters) rice wine, or sake
Wash and dry the dandelion leaves. Chop them and place them in a bottle with the rice wine.
Seal the bottle and let the wine stand to macerate for at least 10 days before drinking.
Honeysuckle Vine Wine
_This wine dissipates toxic heat and stimulates blood circulation. If taken early it also blocks suppurative infections of the skin._
½ cup (100 grams) honeysuckle vine
2 tablespoons (30 grams) licorice root
2 cups (500 milliliters) water
1 cup (250 milliliters) rice wine, or sake
Place the honeysuckle vine and licorice in a saucepan with the 2 cups of water. Bring to a boil over medium heat. Continue to boil for about 40 minutes, until only about one-quarter of the water is left. Strain, reserving the liquid, and discard the solid portion.
Pour the reserved liquid from the decoction into a bottle and add the wine.
This wine may be drunk immediately, or at any time after preparation.
_Chapter 7_
EXERCISING FOR HEALTH
Everybody in China exercises. School children exercise collectively once a day. Adolescents and young adults go in for wushu and Shaolin boxing. Parents jog, swim, walk, bicycle, and swing weights. Grandparents perform early morning tai ji quan or take a radio to a park for a spot of geriatric disco dancing. Great-grandparents twirl metal spheres in the palms of their hands to exercise their fingers (and the acupuncture points on the hands) or swing their pet canaries' cages as they stroll in the park. But the exercise everybody recognizes as the best for overall fitness and health is one that the Chinese people have been practicing for at least three thousand years. It is qi gong.
_Qi_ corresponds to the Sanskrit word _prana_ and the Greek _pneuma_ ; it means "breath," or "breath of life." The word also refers to material energy, vital matter, the earth's atmosphere, or the fundamental substance of material beings. The word _gong_ translates as "mental control over the body." _Qi gong_ thus means "mental control over the flow of qi in one's body. "
Various techniques for exercising control of qi have developed over the centuries. Many of these techniques are medical; others branched out into various disciplines of martial arts. There are Buddhist techniques, Taoist techniques, and Confucian techniques. Fundamentally, however, qi gong may be divided into two basic methods of exercising: _nei dan_ and _wai dan,_ which respectively mean "internal elixir" and "external elixir."
Nei dan, or internal qi gong, consists of breathing deeply while concentrating on circulating qi inside the body. Wai dan, or external qi gong, is the practice of stimulating certain areas of the body by means of movement and exercise so that qi builds up and flows outward.
NEI DAN QI GONG
In China it is said that where the mind focuses the qi will follow. Therefore, during nei dan the mind focuses the incoming breath and sends it to the dan tian, the center of all bodily energy, thought to be situated in the lower abdomen. The abdominal muscles are strengthened by the breathing exercises, and more energy is generated. When sufficient qi has accumulated in the dan tian, the mind directs this energy through the two major qi channels, the _ren mei_ and _du mei,_ which are said to be situated at the front and back of the torso respectively. This practice is referred to as the small circulation of qi, or _xiao zhou tian_. When one is proficient at the small circulation technique, one may then generate stronger qi that is made to flow through all twelve energy channels in the body and limbs in what is known as the _da zhou tian,_ or grand circulation. This is said to result in perfect fitness and health.
The first step in the above exercise is to find a good position that allows for correct abdominal breathing. According to some teachers, the best position for practicing internal circulation of qi is sitting with legs crossed. They explain that it is useful to keep the legs crossed because, when you are trying to circulate the qi around the torso (in the small circulation exercise), it can easily go shooting off down your legs unless you obstruct the entrance to the lower channels in the legs by crossing them.
Later, when the grand circulation is attempted, qi is supposed to flow through all the limbs. Therefore, a standing position becomes necessary. This position is the one most frequently used by practitioners of qi gong in China (figure 1).
Figure 1
Stand with your feet shoulder-width apart, toes pointing slightly inward. Bend your knees slightly, as if you were about to sit down; the weight of your body should be on your feet and lower legs, not on your thigh muscles. Hold your back and neck straight and raise your arms, bending them at the elbows, as if to encircle a large balloon. Your fingers should be splayed in this same balloon-encircling position. Do not raise your shoulders. Your body should feel relaxed and comfortable.
This position strengthens the muscles of the back, legs, arms, and abdomen. Take care, however, not to overexert yourself in the beginning. The position may look easy but, because of the unusual angle of the legs, a good deal of strain is put on the thighs as well as on the arms. Ten minutes of this position can leave one feeling quite weak. Gradually increase your time spent in the position.
**Xiao Zhou Tian (Small Circulation Abdominal Breathing)**
There are two techniques for _xiao zhou tian_ abdominal breathing—one is Buddhist and the other Taoist. Both employ a cross-legged seated pose (figure 2), although with experience they may also be done standing.
Figure 2
The Buddhist technique consists of focusing on the abdomen while breathing slowly and uniformly through your nostrils. Expand your abdomen as you breathe in; contract it as you breathe out. Do not hold your breath.
The Taoist technique is the opposite of the Buddhist. You concentrate on your abdomen, as above, but you contract it when you inhale and expand it when you exhale. This Taoist breathing technique also goes by the name of _fan hu xi,_ or reverse breathing.
Abdominal expansion should never be forced, but should be perfected gradually, with gentle daily practice, until you can expand your abdomen from your navel to your pubic bone.
Once this has been achieved you should sit in quiet meditation, concentrating on your breathing. Imagine the breath traveling through your nose and down to the dan tian, as if you were swallowing something and you could feel it descending all the way to your navel. After a few sittings you should begin to feel a tingling sensation and warmth in the abdominal area. This means that your qi has accumulated sufficiently and that you are now ready to attempt the circulation aspect of the exercise. This is done by guiding the qi around your torso with your mind. At first it will only be a question of imagination and little qi. With time, however, the flow of qi will become stronger and thus more perceptible.
Begin by guiding your qi in the following breathing sequence:
1. Close your mouth and eyes. Press your tongue against your palate. Inhale and guide the incoming qi through your nose and down to the dan tian. Tighten your anal sphincter muscles during the inhalation.
2. Exhale and guide the qi from the dan tian through the groin and into the cavity in front of the coccyx, or tailbone. This is called the wei lu cavity. Relax your anal sphincter as you exhale.
3. Inhale and guide the qi to the base of your neck, between your shoulders.
4. During the final exhalation, guide the qi from the back of your neck to your ears, and then down to your nose and mouth. When the qi enters your mouth, relax your tongue from its position against the roof of your mouth.
One full cycle of xiao zhou tian thus includes two respirations.
You should continue the small circulation exercise for ten minutes two or three times a day. After three months of regular practice you should be ready to go on to the grand circulation exercise.
These exercises are beneficial to the lungs, abdominal viscera, heart, and nervous system.
**Da Zhou Tian (Grand Circulation Abdominal Breathing)**
You are ready to go on to the da zhou tian only when you are confident that you are able to circulate qi around your torso, as in the small circulation exercise. Evidence that you are able to do this correctly consists of a feeling of warmth in all the areas of your body through which your qi is being guided by your mind.
Your pose for the first phase of the grand circulation technique should be either sitting in a chair or standing, preferably in the qi gong standing position. Your thumb and little finger should be touching.
1. Breathe in while contracting your abdomen (or expanding it, if you prefer the Buddhist method of respiration). Guide the qi from your nose to the dan tian. Tighten the anal sphincter muscles.
2. Exhale and guide the qi to the wei lu in the coccyx. Relax your sphincter muscles.
3. Inhale while guiding the qi to the back of your neck, between the shoulders.
4. During the final exhalation do not guide the qi over the top of your head to your nose as previously, but direct it from the shoulders to your hands and fingers.
Repeat this cycle through several sittings until you feel a warm flow of qi to the center of your palms.
In order to guide the flow of qi to your lower limbs, the usual procedure is followed except that you should adopt a supine position. By lying down and relaxing your leg muscles, the qi is said to flow with greater ease. A standing position will not obstruct the flow of qi completely, but simply constrains the channels a little more.
1. Breathe in as before, guiding the qi from the nose to the dan tian. Exhale and guide the qi through your groin, down your legs, to the center of the soles of your feet.
2. On your subsequent inhalation and exhalation, take the qi up your back and over your head to your nose.
You know that the da zhou tian has been achieved when you are able to feel the warmth of the flowing qi both in your hands and your feet. Your feet may feel hot and numb for several days after you have successfully directed your qi to them. However, do not expect results too quickly. It will take months, at least, to circulate your qi successfully to your hands and feet. Later you will be able to guide the qi to both your hands and feet simultaneously, and direct the qi to any part of your body at will. You will not only be able to cure your own ailments, but you will be able to expand your qi beyond your own body, transmitting it to others and thereby healing their illnesses.
After completing a session of nei dan qi gong, most people need to release some of the energy they have been controlling. This can be done through massage of the limbs, face, and head, or by means of movement exercises such as stretching, turning the head from side to side, or rotating the shoulders.
WAI DAN QI GONG
Most people prefer to train the qi by means of external elixir techniques, or wai dan. Wai dan qi gong does not have to follow nei dan breathing techniques. It may be practiced before them or entirely independently.
Wai dan qi gong techniques involve many complex movements that are not easy to learn from a book. To try to do so would inevitably lead to mistakes in practice. Without a qualified teacher's guidance, a student cannot know if his posture, his sequences and his speed are correct. Schools of martial arts exist in most towns and cities in America. If you would like to take your study of Oriental breathing techniques further and to practice wai dan qi gong, you should enroll in one of these courses.
However, a short description of one of the earliest forms of wai dan qi gong will do no harm. This practice was taught by the Indian Buddhist monk Bodhidharma, who traveled to China in the sixth century A.D. Bodhidharma was called Da Mo in China, hence the name of this exercise.
When Bodhidharma settled in the Shaolin Buddhist monastery in Henan province in central China in 527 A.D., he is said to have been shocked by the emaciated condition of the local monks. As a consequence, he taught them a series of twelve drills based in Indian yoga that ensure fitness and build muscular power as well. These basic drills were later elaborated upon by future generations of monks until they became the world-renowned wushu (literally, "martial" [wu] "art" [shu]) system of Shaolin boxing, also known in English by the Cantonese term kung fu.
The twelve exercises of Da Mo wai dan should be performed in sequence. Each drill consists of at least twenty breaths—energy is built up by relaxing a muscle during inhalation and tensing it during exhalation. By performing the exercises in sequence, the energy built up in one exercise is carried forward to the next. The full sequence of twelve exercises should take about fifteen minutes. Longer sittings would include as many as fifty breaths per drill.
Throughout the Da Mo wai dan exercise you should stand straight with your feet parallel to one another, about twenty-four inches (45 centimeters) apart.
Exercise 1
Stand with your feet approximately two feet apart. Hold your arms by your sides, your elbows slightly bent and your palms open toward the ground (figure 3). Your fingers should be pointing forward. Inhale slowly and uniformly. Exhale and imagine pressing firmly downward with your hands. In this exercise qi is built up in the wrists.
Exercise 2
Maintain the same position as in exercise 1. Close your hands into fists with your thumbs extended toward your body (figure 4). During exhalation imagine tightening your fists and pushing backward with your thumbs. In actual fact, your wrists should only be slightly tensed.
This exercise builds up energy in your hands and fingers.
**Exercise 3**
Maintain the same position as in exercise 2. Close your thumb over your fingers, making a fist. Turn your fists so the inside of your wrist faces your body (figure 5). Inhale. Then imagine tightening your fists, and exhale.
This exercise builds up energy in the whole of the lower arm.
Figure 3
Figure 4
**Exercise 4**
Keeping your fists clenched, extend your arms in front of you, the insides of your wrists Figure 3 facing inward (figure 6). Imagine firmly clenching your fists during your exhalation.
This exercise builds qi energy in your chest and shoulders.
Figure 5
Figure 6
Figure 7
**Exercise 5**
Now raise your arms further until they are straight above your head. Maintain the fist position of your hands (figure 7). Imagine clenching your fists while breathing out.
This exercise builds qi in the shoulders, the neck, and the flanks.
**Exercise 6**
Bend your elbows and lower your fists to within six inches of your ears. The insides of your wrists should be facing forward (figure 8). Inhale slowly. Exhale and imagine clenching your fists.
This exercise builds qi in the flanks, the upper torso, and the arms.
Figure 8
**Exercise 7**
Keeping your fists clenched, extend your arms sideways, parallel to the ground. The insides of your wrists should be facing forward (figure 9). Inhale. Exhale and imagine tightening your fists.
In this exercise, qi builds in the upper torso.
Figure 9
**Exercise 8**
Bring the extended arms forward. Bend your elbows slightly, giving a circular effect to the position of your arms (figure 10). Imagine clenching your fists during exhalation.
This exercise builds qi in the arms and shoulders.
Figure 10
**Exercise 9**
Pull your clenched fists back from the previous position, toward your face. Bend your elbows and hold your fists, palms forward, just in front of your cheeks (figure 11). Imagine tightening during your exhalations.
In this exercise, qi is further enhanced in the arms and shoulders.
Figure 11
**Exercise 10**
Pull your elbows back and raise your forearms so that your fists are held about one foot from either side of your head (figure 12). Imagine clenching your fists during your exhalations.
This exercise is designed to start circulating the qi accumulated in your shoulders.
Figure 12
**Exercise 11**
Keeping your elbows bent as in exercise 10, lower your fists to a position immediately in front of your dan tian, about four inches (10 centimeters) below your navel (figure 13). Imagine clenching your fists during your exhalations, and mentally guide the qi through your arms.
In this exercise qi is no longer accumulated. Instead, the qi already in your body is gathered, and directed to flow through your arms.
Figure 13
**Exercise 12**
Unclench your fists, straighten your elbows, and raise your arms straight out in front of you. Hold your palms facing skyward (figure 14). When exhaling imagine lifting a heavy weight with your arms.
Figure 14
In this exercise, qi is recovered for redistribution around the body.
When you have completed the whole wai dan sequence, it is good to relax for a few minutes, either seated or lying down, breathing normally.
Da Mo wai dan qi gong strengthens the body as a whole, and the muscles, joints, and inner organs in particular. These exercises also improve circulation. They ensure the equilibrium of the nervous system, and build up resistance to disease.
There are many other popular wai dan exercises that have derived directly from Bodhidharma's original sequence. One well-known sequence of eight drills, called _ba duan jin,_ or Eight Pieces of Brocade, was created by a famous patriotic general, Yue Fei, in the twelfth century, to maintain fitness in the ranks. Yue Fei's ba duan jin was based on an earlier series of exercises by the same name devised by Zhong Li during the Tang dynasty (618–907 A.D.). Other versions of the ba duan jin have been developed over the centuries, some during the last forty years as qi gong started becoming fashionable. Another well-known sequence of qi gong exercises is tai ji quan, an intricate sequence of movements during which the mind guides qi around the body.
Qi gong is becoming ever more popular in the West. Tai ji quan and qi gong lessons are now standard in many health clubs. Together with the increased acceptance of Chinese physical exercise, other aspects of Chinese health systems are also entering Western consciousness. Acupuncture has been used for years in alternative health circles, but is now entering mainstream medical practice. The use of Chinese herbal medicine is becoming increasingly common, to the extent that many allopathic doctors and researchers express interest in discovering the curative properties of these herbs and medicines. Chinese medical theory and practice may still be dismissed by conservatives as mere quackery. Other people extol Chinese traditions beyond all scientific reasonableness, sometimes suggesting curative effects that verge on the miraculous. As is usually the case, the truth lies somewhere between these two extremes.
Chinese traditions spanning millennia cannot be dismissed offhand. Enough empirical and experimental evidence exists to demonstrate that Chinese medical traditions are still valid today. On the other hand, Chinese medicine does not invariably provide a cure whenever Western medicine fails to deliver. What Chinese traditions of healthy living can assure us is that, if we carefully follow their precepts, we can stay healthy and youthful for many years to come.
_Appendix 1_
DAILY REQUIREMENTS OF PROTEINS, MINERALS, AND VITAMINS FOR THE HEALTHY ADULT
Protein
1 gram of protein for every two pounds of body weight. A person weighing 150 pounds should thus consume 75 grams of protein per day. This amounts to approximately six eggs' worth, or 8 ounces of steak.
Carbohydrates
160–240 grams, equivalent to 300–400 grams of bread (10–14 ounces) or 400–500 grams of rice
Fat
Not more than .25 gram a day for every pound of your ideal body weight, thus if your ideal weight is 150 pounds you should not consume more than 35 grams of fat per day. Two fried eggs exceed that amount, as do 100 grams (3.5 ounces) of whole-milk cheese. A single cream puff will probably carry a hefty 100 grams of fat.
**Fiber**
At least 25 grams a day, but the more fiber you eat the better. In the Chinese countryside, 90 grams of fiber a day is considered normal. You would have to eat 1½ pounds of green peas, a high-fiber food, to consume 25 grams of fiber.
**Calcium**
400–500 milligrams per day, equivalent to one pint of milk. The daily requirement increases to 1000–1400 milligrams during pregnancy and lactation.
**Phosphorus**
1 gram per day. One hundred grams (3.5 ounces) of meat or mushrooms, or a mere 30 grams (1 ounce) of fish, meets the daily requirement.
**Iron**
10 milligrams per day. Higher dosages (18 milligrams per day) are necessary for women during their childbearing years (from puberty to menopause), to replenish blood iron lost during menstruation. Iron in the body is used many times over. Intake is necessary only to replenish that which is lost in the feces, during menstruation, or through other blood loss. Women in their childbearing years therefore require more iron than others.
It is dangerous to consume too much iron because excess iron is not easily eliminated. One hundred grams (3½ ounces) of brown bread, meat, spinach, or soybeans contain 2–3 milligrams. One cup of kidney beans contains 5.2 milligrams; 100 grams (3½ ounces) of chives contain 8.5 milligrams; 100 grams of cocoa contains 11.5 milligrams; and 100 grams of pork liver contains18 milligrams of iron.
**Vitamin A**
5000 IU (increase to 8000 IU during pregnancy and lactation). Two oranges, one mango, or 10 ounces of cheese would each provide 5000 IU.
**Vitamin B 1 (Thiamine**)
1.25–1.5 milligrams, equivalent to one bowl of oatmeal or one-half cup of sprouted wheat berries.
**Vitamin B 2 (Riboflavin**)
1.7–2 milligrams, equivalent to 400 grams (14 ounces) of almonds, or 100 grams (3.5 ounces) of liver.
**Niacin**
20 milligrams, equivalent to 100 grams (3.5 ounces) of liver, or of peanuts.
**Vitamin C (Ascorbic Acid** )
60 milligrams, although megadoses (500– 1000 milligrams) function as a valid antioxidant. You can get 60 milligrams of vitamin C from a glass of orange juice or a bowl of fresh strawberries; one would have to go about consuming larger quantities more systematically. Remember that vitamin C is destroyed by heat, and decreases with the passage of time between picking and eating.
The last five essential vitamins and minerals listed in this table are not included in the nutrient properties of foods discussed in chapter 4. They are nonetheless important to health and wellness, and are therefore included here.
**Magnesium**
400 milligrams. Magnesium activates an enzyme that allows the absorption of carbohydrates in the body. It is common in greenleaf vegetables and in beans. One-half cup of raw parsley contains 13 milligrams of magnesium, one cup of raw spinach contains 22 milligrams, and 100 grams (3.5 ounces) of stir-fried soybean sprouts contain 28 milligrams.
**Iodine**
150 micrograms. Iodine is indispensable for the thyroid gland's synthesis of the hormone thyroxine. It is found in soil and most underground water supplies and is absorbed into the body by consuming vegetables grown in an iodine-rich soil. In areas lacking iodine in the soil, goitre, a swelling of the neck due to iodine deficiency, used to be common. Nowadays most brands of table salt have added iodine. Iodine deficiency is therefore extremely rare.
**Copper**
2 milligrams. Copper appears to aid the action of iron in the formation of red blood corpuscles. Bodily requirements are so low that there is rarely any real danger of deficiency. A two-cup portion of boiled soybeans provides 2 milligrams of copper. Small amounts are found in most foods.
**Zinc**
15 milligrams. Zinc is essential to the red blood corpuscles for the metabolism of carbon dioxide. It is also an important factor in regulating enzyme production, protein synthesis, muscular contraction, the formation of insulin, and the acid-alkaline balance in the blood. Zinc is found in meat, brewer's yeast, wheat germ, sunflower seeds, and eggs.
**Vitamin E**
30 IU. Vitamin E is an important antioxidant, indispensable for maintaining cellular efficiency and youthfulness. Wheat germ is the richest source of vitamin E; a single tablespoon provides 20.3 milligrams. Almonds, sweet potatoes, and greenleaf vegetables are also rich in vitamin E.
_Appendix 2_
MAIL-ORDER RESOURCES
SOURCES OF HERBAL SUPPLIES
The following are mail order suppliers of Chinese herbs and other ingredients. Some of them have minimum orders of $10 to $20.
**California**
**East Earth Trade Winds**
P.O. Box 493151
Redding, CA 96049
(800) 258-6878
**Great China Herb Company**
857 Washington Street
San Francisco, CA 94108
(415) 982-2195
FAX (415) 982-5138
**Moonrise Herbs**
826 G Street Arcata, CA 95521
(707) 822-5296
**Superior Trading Company**
837 Washington Street
San Fransico, CA 94108
(415) 982-8722
**Trans Trading Company**
849 Washington Street
San Francisco, CA 94108
(415) 788-0110
**New York**
**Chinese Herbal Center**
28 Bowery
New York, NY 10013-5100
(212) 732-4548
**Lay Hang**
220 Centre Street
New York, NY 10013-3632
(212) 431-5636
**Lee Bok Kyong**
124 W 30th Street
New York, NY 10001-4009
(212) 244-0030
FOOTNOTES
*1 Traditionally the Chinese physician based his diagnosis in part on the timbre and tone of voice of the patient. The names of the tones are untranslatable—they correspond to our _do, re, mi, fa,_ and _so_. _La_ and _si (ti)_ do not exist because the ancient Chinese system envisaged only five tones.
*2 It is the sodium that one needs to avoid in the case of arteriosclerosis and high blood pressure.
*3 Dried ginger as referred to in these recipes is still in root form; it is not powdered. Dried ginger is used a lot in Chinese medicine. It is available at Chinese pharmacies.
*4 First-degree burns are characterized by redness of the skin—sunburn is a typical example. Second-degree burns are characterized by redness and blistering. Third-degree burns destroy all the skin and some of the underlying muscle and appear dry, leathery, and charred.
*5 About 5 percent of all cases of obesity are due to hormonal imbalances or glandular defects.
ENDNOTES
**Introduction**
1. In case there are no Oriental markets in your area, addresses of select shops that accept mail orders are included in appendix 2.
2. The one exception is raw bitter apricot kernel, used in a cure for asthma. It is toxic only when eaten raw, and must not be consumed in large quantities or over a long period of time. For more information on bitter apricot kernel, see pages 38 and 69.
3. Some famous medics went as far as to systematically test the effects of all known medical substances on themselves. One of these, Li Shi Zhen (1518–1593), tested 1,892 ingredients and, on the basis of these, went on to prescribe over ten thousand preparations. The result was China's definitive illustrated pharmacopoeia of medicinal ingredients, Li Shi Zen's Ben Cao Gang Mu (Compendium of Materia Medica), published in 1590.
4. Many hospitals and clinics in China provide a combination of therapies. Western allopathic cures are prescribed where these work best, and traditional medicines are suggested for chronic conditions that need time and patience to remedy.
**Chapter 1**
1. The Yellow Emperor was so called not because of the color of his skin but because he ruled over the earth. In Chinese tradition, yellow is the color associated with the Earth element.
2. Oracles written on bovine hip bones and tortoise shells indicate that it was understood as early as the Shang dynasty (c. 1750–1100 B.C.) that disease could arise independently within various organs of the body, or as a result of external causes, such as in the case of an epidemic.
3. Lao tzu is reputed to be the author of the Taoist classic, the _Tao Te Ching_ (The Way and Its Power). Zhuang Zi (perhaps recognized more readily by Western readers as Chuang-tzu) was the author of a work bearing his own name that had considerable influence on Chinese Buddhism, landscape painting, and poetry.
4. As is common in English-language writings on traditional Chinese medical theory, the names of the individual Elements are capitalized to remind the reader of the more expansive meanings of the words.
5. The Lei Jing, or Systematic Compilation of the Internal Classic, was compiled by Zhang Jie Bin during the late Ming dynasty, in 1624. It is recognized as the most important book of reference in the study of the Huangdi Nei Jing.
**Chapter 2**
1. Although these various causes of illness have been referred to since antiquity, it was not until the Southern Song dynasty (1127–1279) that the three categories of pathology were formally classified. In 1174, Chen Yan (also known as Chen Wu Ze) published an eighteen-volume text, the title of which translates as A Treatise on the Three Categories of Pathogenic Factors of Diseases. He based his classifications on those originally suggested by Zhang Zhong Jing between A.D. 159 and 219 in another of China's most famous medical classics, Synopsis of Prescriptions of the Golden Chamber. Zhang Zhong Jing's three categories of _causa morbi_ were:
1. Endogenous cause of disease, when pathogenic factors invade the channels and collaterals;
2. Exogenous causes, when external pathogenic factors invade the four extremities and the nine body orifices and then circulate through the blood vessels, thus obstructing the flow of qi;
3. Intemperance in sexual life, various traumata, animal and insect bites (from Synopsis of the Golden Chamber, chapter 1, clauses 1–2).
2. Xie qi is often called the _liu yín_ or "six aberrations." This _y_ _í_ _n_ is not the same as the _yin_ for cause (as in _wai_ and _nei yin_ ) nor, indeed, as the _yin_ of Yin and Yang. It is sometimes translated as "devil."
3. Yin qiao pills are febrifugal pills of lonicera (honeysuckle), forsythia, balloonflower root, burdock fruit, _Lophaterum, Schizonepta,_ soybean, peppermint, and licorice.
4. The first official pharmacopoeia, which included reference to fungi, was published during the Tang Dynasty in A.D. 659.
5. The first reliable reference to inoculation is by Chen Zhong Yang, who lived during the tenth century A.D. Some authors affirm that the practice actually began in the sixth century.
6. The method was not, of course, without its dangers. Since Pasteur's ninteenthcentury discoveries that a virus can be weakened for use as an inoculation, modern Western methods of immunization have entirely taken over in China.
**Chapter 3**
1. This is true everywhere but in Guangdong (Canton) province in the south, where soup is eaten first, as in Europe and America.
2. The famous dish Cantonese fried rice originated as a way to use leftovers. When in a hurry, you throw some rice into a pan together with whatever remains from a previous meal.
3. Contrary to popular belief, rice is not the staple dish all over China. It is consumed in larger quantities in the south, where it grows faster. Northern Chinese cuisine tends to prefer wheat (bread or noodles).
4. On average, Chinese people obtain 87 percent of their total calories from plant sources and only 13 percent from animals. In the United States, 39 percent of all calories consumed are obtained from animal sources; in the United Kingdom, foods from animal sources account for 35 percent of all calories consumed. Source: The United Nations Food and Agriculture Organization yearbook. Rome, 1992.
5. A kang is the traditional hollow brick platform found in peasant homes. It is heated from the inside. The entire family eats, works, and sleeps on top of the kang during the cold season.
6. This questionnaire is based on one drawn up by Dr. Henry C. Lu in his excellent book _Chinese System of Food Cures: Prevention and Remedies_ (New York: Sterling, 1986).
**Chapter 4**
1. Combining traditional therapies with modern Western medicine is a practice frowned upon by most traditional doctors. Nevertheless, today few people are in fact patient enough to wait for traditional remedies to take full effect. It is common, therefore, particularly among city dwellers, to resort to a quick antibiotic "fix," combining that with traditional food therapies to counteract resulting toxic imbalances.
2. Tannins and alkaloids react biochemically with protein-based tonics. Although ancient Chinese doctors had no understanding of biochemistry, experience taught them the negative effects of some ingedients when combined with others.
3. Our sources are various nutrition handbooks, including Bowes and Church's _Food Values of Portions Commonly Used,_ 15th ed. (New York: Harper and Row, 1989).
4. Ying Jianghe, et. al., _Icones of Medicinal Fungi from China_ (Beijing: Science Press, 1987). This book describes 272 varieties of medicinal fungi.
5. Private communication with the president of Italy's rice growers' association. Shortly after our conversation in 1985, this man died of cancer of the liver, caused (it is suspected) by eating too much (poisoned) rice.
6. K. Napier in "Taking Soy to Heart," Harvard Health Letter, November 21, 1995, 1–2.
7. In India beef is not eaten for two basic reasons, both of them economic. First there is the question of space. Cattle need space. Five hundred percent more land is needed to provide the same amount of nutrients from beef as from agriculture. Clearly, therfore, in an overcrowded land like India or China, cattle ranches are not the norm. Second, cattle are more useful to the Indian (and Chinese) peasant alive rather than dead. Cattle pull the plow, provide milk to babies, and turn pumps and grinders, and their dried droppings are used both as insulation and as a smokeless fuel for cooking.
8. As far back as B.C. 4000, a daily ration of garlic was handed out to the workers on the Great Pyramid of Cheops in Egypt in order to keep them fit and healthy. Garlic was used extensively by the Romans and the ancient Indians. Hippocrates, from the Greek island of Kos, founder of medical science, recommended garlic against infectious disease and for intestinal disorders. Louis Pasteur confirmed its antibiotic effects in1858.
Finally, a poem written in England in 1607 by Sir John Harrington makes for educational and amusing reading:
_Sith garlicke then hath power to save from death,
Bear with it though it make unsavoury breath.
And scorn not garlicke like some that thinke
It only makes men winke and drinke and stinke._
9. Drinking an extract of garlic in water appears to slow the growth of bladder cancer in laboratory mice. Dale R. Riggs, Jean I. DeHaven, and Donald J. Lamm, "Allium Sativum (Garlic) Treatment for Transitional Cell Carcinoma," _Cancer_ 79, no. 10 (1997): 3.
10. The greatest production of ginseng in the world is in the Kamloops area in southern British Columbia, Canada.
11. The precise date of the first use of tea is not known. We do know, however, that by the first millennium B.C. tea was already an old and well-established drink.
12. According to one story, tea was created by the compassionate Buddha for the benefit of Buddhist monks who fell asleep during meditation. Bodidharma was an Indian monk who went to China in the sixth century A.D. to teach meditation. During an early morning meditation he fell asleep. So angry was he on awakening that he cut off his eyelids. (Bodidharma is always depicted with wide, staring eyes.) The Buddha took pity on him. Where Bodidharma's eyelids had fallen there grew two green plants. The leaves of these plants brewed in hot water would, from that time forward, ensure that Bodidharma and other monks would never again fall asleep during meditation.
13. Chen Junshi, et. al., _Diet, Lifestyle and Mortality in China: A Study of the Characteristics of 5 Chinese Counties,_ Beijing: Oxford University Press, Cornell University Press, and People's Medical Publishing House, 1991.
14. Soybeans are low fat, fiber-filled, and able to clear cholesterol from circulation. According to the Harvard Health Letter, regularly eating five ounces of firm tofu may lower bad cholesterol by up to 25 percent. _Medizin_ November/ December 1996 issue.
15. At the Research Institute of Epidemic Diseases at the Chinese Academy of Science in Beijing.
**Chapter 5**
1. It is worth pointing out that, although aluminum does enter the bloodstream at what might be considered dangerous levels through cooking in aluminum vessels, a far greater quantity of the metal is ingested every time one swallows a buffered medication—approximately one hundred times as much as is introduced through cooking with aluminum pots.
2. Some of these ancient pots are on display at the Banpo Neolithic archaeological site and museum on the outskirts of Xian.
3. If, when you need to make a decoction, you find that your pot is broken or missing, the customary thing to do is to borrow your neighbor's. You use it until you are cured. When you have finished with it you do not return it; if you were to do so, superstition decrees that you would be passing your ailment on to your neighbor. Instead, when he needs it, and only when he needs it, the neighbor will come to your place to ask for the pot.
4. _Sake is the Japanese word for rice wine. The Chinese word is jiu._
5. _Diet, Lifestyle and Mortality in China._ The figures are: 0.073 to 0.247 mg/dl in Chinese males and 0.064 to 0.146 in Chinese females compared to 0.060 to 0.150 mg/dl and 0.050 to 0.130 in American men and women, respectively. The difference between iron counts in men and women is due to women's blood loss during menstruation.
6. In June, 1997, one of the authors photographed a tiger paw for sale in Guangzhou's (Canton) crowded public market. It was not on display in one of the stalls, but was instead placed on the ground at the end of the market by two men who said that they had traveled to Canton from Xinjiang region, in the remote west of the country. Nobody around them seemed to be disturbed by the nature of their wares.
7. In the West it is widely believed that dogs are eaten in China. However, in actual fact the consumption of dog meat in China is not, by any means, a common occurrence; neither of the authors has ever tasted it or seen it cooked. Only two people of our acquaintance in China have ever eaten dog. One of those people ate it once in his sixty-year-long life because he was suffering from a cold-disease syndrome and because, as he told us, he was curious. The other had eaten dog on half a dozen occasions and boasted that he liked it.
8. Yogurt was first introduced in northern China in the late 1980s. The Chinese took to it at once. Today it is sold at street stalls in all large northern cities. In the south of China (south of the Yangtze River) yogurt is still virtually unknown. A recent response there to my request for yogurt (called _suan nai_ [sour milk]) was met with open-mouthed incredulity. "What do you want sour milk for?" I was asked. "It's bad for you!"
9. Milk contains large quantities of the amino acid tryptophan, which is a natural sleep inducer. Other foods containing tryptophan, and which might thus be useful taken before bedtime, are chicken, turkey, tuna fish, beef, cheese, yogurt, and buttermilk.
Traditional Chinese dietary measures for counteracting insomnia do not include milk and dairy products simply because these are not common in China. However, we did hear that a cup of steaming milk is a common nightcap in the central Asian and predominantly Muslim western province of Xin Jiang where milk is an integral part of people's diets.
**Chapter 6**
1. This is true everywhere but in Guangdong (Canton) province in the south where soups are taken at the start of the meal as in Europe and the United States.
2. World Health Organization Yearbook, Rome, 1989 and 1996.
3. The recent improvements in living standards means that "special occasions" for many families are becoming the norm, thus leading to an increase in meat eat-ese is pronounced zen. Bodhidharma ing. This fact is beginning to cause some can thus be considered the founder of health concerns among Chinese dieti-Zen Buddhism. tians and doctors.
**Chapter 7**
1. The earliest known reference to qi gong is from the Warring States Period (476–221 B.C.) However, there exists pictorial evidence from the Shang and Zhou dynasties (1122–770 B.C.) that qi gong breathing exercises were being used then for medical purposes.
2. Bodhidharma is the founder of the Chan school of Chinese Buddhism. The word _chan_ comes from the Sanskrit _dhyan_ , which means meditation. _Chan_ in Japanese is pronounced zen. Bodhidharma can thus be considered the founder of Zen Buddhism.
3. More commonly known in English as tai chi. _Tai ji quan_ literally translates as: "the grand ultimate equilibrium," in reference to the Taoist theory of Yin and Yang. The word _quan_ means "boxing style."
**Appendix 1**
1. It was only in 1963 that it was realized that zinc was important to the human metabolism; it took another ten years for RDA guidelines to be issued. Because of the uncertainty regarding zinc, some authorities suggest that 15 milligrams may be too high.
About the Authors
Zhuo Zhao learned the traditional arts of cooking and healing from her family in Beijing and spent an additional two years of intensive research to create this book. Zhuo Zhao and George Ellis met in Beijing in 1985 and married in 1988.
George Ellis traveled extensively in Asia in the 1970s and 1980s, writing and translating texts on Yoga, Ayurveda, and Naturopathy. He is the author of _The Breath of Life: Mastering the Techniques of Pranayama and Qi Gong_. George Ellis and Zhuo Zhao met in Beijing in 1985 and married in 1988.
About Inner Traditions • Bear & Company
Founded in 1975, Inner Traditions is a leading publisher of books on indigenous cultures, perennial philosophy, visionary art, spiritual traditions of the East and West, sexuality, holistic health and healing, self-development, as well as recordings of ethnic music and accompaniments for meditation.
In July 2000, Bear & Company joined with Inner Traditions and moved from Santa Fe, New Mexico, where it was founded in 1980, to Rochester, Vermont. Together Inner Traditions • Bear & Company have eleven imprints: Inner Traditions, Bear & Company, Healing Arts Press, Destiny Books, Park Street Press, Bindu Books, Bear Cub Books, Destiny Recordings, Destiny Audio Editions, Inner Traditions en Español, and Inner Traditions India.
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Copyright © 1998 by George Ellis and Zhuo Zhao
All rights reserved. No part of this book may be reproduced or utilized 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.
Note to the reader: This book is intended as an informational guide. The remedies, approaches, an _d_ _techniques described herein are meant to supplement, and not to be a substitute for, professiona_ _l_ _medical care or treatment. They should not be used to treat a serious ailmen_ _t_ _without prior consultation with a qualified health care professional_ _._
LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA
Zhao, Zhuo, 1963–
The healing cuisine of China : 300 recipes for vibrant health and longevity / Zhuo Zhao and George Ellis.
p. cm.
Includes index.
print ISBN 978-0-89281-778-8
ebook ISBN 978-1-62055-025-0
1. Diet therapy—Recipes. 2. Cookery, Chinese. 3. Medicine, Chinese. I. Ellis, George, 1949– . II. Title.
RM219.Z 1998
615.8'54'0951—dc21 98-42723
CIP
The questionnaire on pages 29–32 was adapted with permission of Sterling Publishing Co., Inc., 387 Park Ave. South, New York, N.Y. 10016 from _Chinese System of Food Cures_ by Henry C. Lu, © 1986 by Henry C. Lu.
Electronic edition produced by
www.dmiepub.com
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