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Q: Supress/filter exception context when raised within a trigger In a Python application I'm catching exceptions thrown from stored procedures on my database as psycopg2.InternalError. I've noticed that when they are thrown from within triggers, the exception message comes with whatever message I throw plus the current context.
Since I'm forwarding the error message to the user, I would like to remove the context part from it.
I've done this in the past using regular expressions, but I feel there must be a better way.
Apparently there's a low level function called PQsetErrorVerbosity that exists for this specific purpose, but I'm not sure if there's anything available through psycopg2.
A: Don't parse messages with regular expressions unless there's absolutely no alternative. It'll break horribly on version updates if the wording/formatting changes, or if the user is in a different locale. Good on you for recognising this problem.
What you should be doing is using the Diagnostics object in the exception.
Example
Given:
create or replace function do_exception() returns void as $$
begin
raise exception 'eep!';
end;
$$ language plpgsql;
create or replace function call_do_exception() returns void as $$
begin
PERFORM do_exception();
end;
$$ language plpgsql;
and:
import psycopg2
conn = psycopg2.connect('');
curs = conn.cursor();
try:
curs.execute("SELECT call_do_exception()")
except psycopg2.InternalError, ex:
saved_ex = ex
I get a message with context:
>>> print saved_ex
eep!
CONTEXT: SQL statement "SELECT do_exception()"
PL/pgSQL function call_do_exception() line 3 at PERFORM
... but it also has a diag field:
>>> saved_ex.diag
<psycopg2._psycopg.Diagnostics object at 0x7f822e36c150>
... with individual message components:
>>> saved_ex.diag.message_primary
'eep!'
| {
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<parameter id="kc_r" name="Reverse complex formation rate" value="1" constant="true"/>
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<parameter id="kd" name="Degradation rate" value="0.0075" constant="true"/>
<parameter id="kecd" name="Extracellular degradation rate" value="0.005" constant="true"/>
<parameter id="nc" name="Stoichiometry of binding" value="2" constant="true"/>
<parameter id="nr" name="Initial RNAP count" value="30" constant="true"/>
<parameter id="ko" name="Open complex production rate" value="0.05" constant="true"/>
<parameter id="kb" name="Basal production rate" value="0.0001" constant="true"/>
<parameter id="ng" name="Initial promoter count" value="2" constant="true"/>
<parameter id="np" name="Stoichiometry of production" value="10" constant="true"/>
<parameter id="ka" name="Activated production rate" value="0.25" constant="true"/>
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1972: The J Geils Band @ Holy Cross, Worcester, MA
1974: Postcards From The Road (Documentary)
1976: Silent Super 8 Film - The J. Geils Band @ Seattle Center Arena
1979: Chorus TV Show (France)
1979: The Boston Garden
1980: TV Commercial Promoting the 1980 LP Love Stinks (Video)
1980: Saturday Night Live TV Show (USA)
1980: PINK POP FESTIVAL – Geleen, Holland (Video + Info)
1980: 3-SAT TV Show (Germany)
1981: Concert - Candlestick Park, San Francisco, CA
1982: Best Hit USA TV Show (Japan)
1982: The Joe Franklin Show (Video)
1982: Feyenoord Stadion, Rotterdam, The Netherlands (Video)
1984: TV Show - Saturday Night Live
1986: Peter Wolf as Johnny Bannon, Talent Manager @ Kiss 108's Garden Party
1990: The Late Show With David Letterman
1994: J. Geils Band Induction Into The Boston Garden Hall Of Fame (Video)
1999: TV Show - The Today Show
1999: TV Show - The Late Show With David Letterman
1999: Concert - Jones Beach Amphitheatre
2005: Jay Geils Interview on CNN
2006: Danny Kleins Surprise 60th Birthday Party – Scullers Jazz Club, Boston, MA
2012: Magic Dick @ Boston's Red, White & Blues Festival (Videos)
2013: Jay Geils Interview On TV Show Greater Boston
Photos & Set-List: Peter Wolf @ The Center For Art... | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,518 |
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Board index Book Reviews / Critiques The Sword of Fate
The Sword of Fate
Post by Stevie P » Sun 26 Oct, 2008 17:25:05
The Sword of Fate was published in October (1942) and it "Did all I had hoped for it†(DW – Drink and Ink). He doesn't elaborate on what his "hopes†were.
I can't help thinking that with the war on and his having to write novels in amongst all his other wartime activities, they weren't too high.
This was my first reading of the book, which is basically a love story which takes place in Egypt, Libya and Greece during the time of General Wavell's brilliant Libyan campaign from Mersa Matruh to Benghazi and later across the Mediterranean to Athens and Mount Olympus.
The two lovers are Julian Day and Daphnis Diamopholus. She is the stepdaughter of a Greek millionaire.
DW starts this book in an unusual way. It starts at the end, and then tells the story leading up to that point. Not particularly unusual nowadays but it was the first time that DW had used this method in a novel.
After a lengthy search Julian is desperately pleased to find Daphnis sleeping in the cellar of a bombed out Greek house in Ventsa, when the brutal Nazi, Baron Feldmar von Hentzen appears behind the pair of them. He fires 5 shots at Daphnis.
The story begins;
Julian Day feels the natural urge to volunteer for the war effort and so meets up with his old colleague, the English Police chief Essex Pasha who attaches him to the Arab bureau primarily on account of the fact that he speaks several European languages as well as Arabic.
He purchases a motorbike (a la Lawrence of Arabia) and decides to visit Alexandria when his first leave came up. He was passing through the 'Park Lane' of the city when his front wheel twisted on an oily patch and Julian is catapulted through the air heading for the nearest lamp post.
"Daphnis was bending over me. Her lovely face was within 6 inches of mine and, as our eyes met, in that very first glance, I knew that, if only had the courage and resolution to win her, here was the one woman who would prove the crown and glory of my life.â€
Daphnis is part of a rich family and so Julian has to be careful in the way he approaches her and her family he decides to send her a heart shaped aquamarine with a note telling her that she should mark out a triangle in the dust on the ground between three palm tree's. She should enter the triangle and then place a bowl of fresh water on the ground and walk three times around it with the amulet in her hand. She should then halt, facing North and, on the stroke of midnight, she should kneel down, pressing the amulet to her heart. She will then see, reflected on the surface of the water, the face of the man she is to marry.
(Very much an idea borrowed from The Arabian Nights).
Julian plans to hide in an appropriate place to see if she carries out these instructions.
The plan doesn't quite work as he actually planned as he observes her discussing war time secrets with a man whose voice he recognises but can't place.
Major Cozelli, one of Essex Pasha's men tells JD that he believes Daphnis to be a spy passing on details of British shipping to the enemy.
JD questions Daphnis on this and whilst she agrees that she was involved in some espionage she would never do anything to harm Britain's war effort now that she had met Julian.
JD asks Daphnis to marry him - she agrees and has to tell her fiancé, the unfortunate Paolo a secretary at the Italian Legation to get lost!! Paolo recognises JD as the Julian Fernhurst who was accused of selling British secrets to international espionage agents. (See - The Quest of Julian Day).
Before JD has time to explain he is whisked off to his battalion as Italy have just entered the war.
JD and Daphnis are to be married on Wednesday 27th November but The Sword of Fate was still between them. On November 12th JD was taken prisoner by the Italians.
After his release he happened to be sitting in the lounge of his Hotel when he overhears the voice of the man that Daphnis was talking to in the garden of her family's house. Cautiously he turned to look – It was the Portuguese, Count Emilo de Mondragora, one of the seven devils who had brought about poor Caruthers suicide and wrecked his own career. (The Quest of Julian Day).
After following him to his hotel he finds Mondragora in league with the Grand Mufti of Jerusalem and the Nazi Von Hentzen. They were discussing a German airborne invasion of Egypt. A gun battle ensues and the Police are called in.
The Police accuse JD of hiding some important documentation written by Daphnis.
JD is imprisoned but eventually set free as long as he doesn't try to get in contact with her or leave Alexandria.
JD immediately does just that. He manages to get himself on a troop ship heading for Athens. He catches up with Daphnis stepfather who tells him that she had managed to get a job working with von Hentzen .
JD has to get back to the battalion and the war effort predominantly around Mount Olympus. Excellent battle descriptions against the German Planes and tanks are given by DW as usual.
The finale is when JD happens to see Mondragora by accident (again) and follows him to his hide out. Von Hentzen is there also. JD manages to get the info relating to Daphnis whereabouts. We are now back at the beginning/end of the story.
Hutchinson.
Page 31 - JD doesn't want Daphnis 'besmirched' in any way. Not a common expression these days.
Page 107 – JD remembers that he was not too far away from the place where he hunted for the lost treasure of Cambyses in 1938. (The Quest of Julian Day)
Page 110 – JD captured by the eye-ties (Italians - for info to all non cockney's)
Page 161 – For those of you who are not too sure what a Grand Mufti is. See attached
http://en.wikipedia.org/wiki/Grand_Mufti_of_Jerusalem
Page 203, 212 & 228 - The term Total War is used again.
Page 223 & 224 – DW expresses his admiration for the Greeks and the way they live their lives.
Page 282 – JD actually kills one of his enemies without asking lots of endless questions.
It's a shame he didn't do the same a few hours earlier. (you'll have to read the book!!!)
I did enjoy this book but not as much as 'The Quest of Julian Day', which I felt was more of an in depth read. As I said at the beginning I got the impression that DW was writing this fairly quickly to maintain momentum. He had more important War work to do.
However the reviews of the book state;
"Magnificent story of love and high adventureâ€
"A love story with a real kick in itâ€
The book doesn't state where the reviews come from though!!
Post by Alan » Thu 30 Oct, 2008 00:29:18
This is a really great review, and I really enjoyed reading it. I'd suggest anyone new to DW checks out this part of the site and sees if you've dealt with any DW book they are planning to read.
The interesting thing about the Julian Day books is that they were among the few DW wrote that didn't have a happy ending... in all of the JD books, the eponymous lead fails to get the girl and ends up failing in whatever he sets out to do. Add to this the fact that JD seems to have a deeper, more complex character than other DW heroes (apart, perhaps, from Le Duc and Gregory) really sets them aside, I think, as some of the Prince's most "serious" works.
The other thing I remember from this book is Julian's defence of Italian fighting qualities. As a know-it-all 14 year old, when I first read "Sword..." I was of the opinion - absorbed from father, uncles, etc - that the Italian army was a joke. "Sword" contains a kind of disclaimer of this, pointing out (I paraphrase) that we think of Italians as gentle men who are content to roll their eyes at every pretty woman who passes and sing "O Sole Mio" in the moonlight, but that we shouldn't forget that Al Capone's gangsters were of this race! At another point he mentions the British having to "fight like tigers" to beat them. I think DW probably likes Mediterranean people (he also, as you say, says nice things about the Greeks) better than most non-English apeaking folk!
Post by Stevie P » Thu 30 Oct, 2008 17:32:28
Thanks for the kind words Alan. The cheque is in the post .
I very much agree with your comments on the Italians even though I can't get the image of Nicholas Cage as an Italian army captain out of my mind................... I don't want to get the image of Penelope Cruz out of my mind.
Garry Holmes
Joined: Sat 23 Jul, 2005 12:17:18
Post by Garry Holmes » Thu 30 Oct, 2008 20:36:41
Stevie P wrote: I very much agree with your comments on the Italians even though I can't get the image of Nicholas Cage as an Italian army captain out of my mind................... I don't want to get the image of Penelope Cruz out of my mind.
Agree on all counts. Cage's performance proved that the era of racial stereotyping in movies is not dead. As he would probably say---
'Ia don'ta knowa whata you'rea talkinga about...a.'
Return to "The Sword of Fate" | {
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Adult Programming and Outreach Services
The New York Public Library has been an essential provider of free books, information, ideas and education for all New Yorkers for more than 100 years. Founded in 1895, NYPL is the nation's largest public library system, featuring a unique combination of 88 neighborhood branches and four scholarly research centers, bringing together an extraordinary richness of resources and opportunities available to all.
Serving more than 17 million patrons a year, and millions more online, the library holds more than 55 million items, from books, e-books and DVDs to renowned research collections used by scholars from around the world. Housed in the iconic 42nd Street library and three other research centers, NYPL's historical collections hold such treasures as Columbus's 1493 letter announcing his discovery of the New World, George Washington's original Farewell Address and John Coltrane's handwritten score of "Lover Man." NYPL's neighborhood libraries in the Bronx, Manhattan and Staten Island — many of which date to Andrew Carnegie's visionary philanthropy at the turn of the 20th century — are being transformed into true centers of educational innovation and service, vital community hubs that provide far more than just free books and materials.
The library's Adult Programming and Outreach Services department works with staff across the circulating branch system to provide centralized resources that support the diverse needs of patrons from all walks of life.
1 year 1 month
Community Conversations: Lessons Learned at NYPL's Mid-Manhattan Library
Community Conversations: Failing Forward
Community Conversations: Dialogue about Health
A Tale of Two Organizations: Talking about Affordable Housing on the Lower East Side
Community Conversations: Engagement through Local History | {
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Stunning and unique three bedroom maisonette, located in the heart of the North Laine area of Brighton close to the city centres local shops and amenities, Brighton train station and the Brighton Nightlife. Situated minutes from the sea this fantastic property is offered fully furnished throughout.
The accommodation has a patio area leading to the main entrance. Open the door and you will find a modern galley style kitchen with a range of appliances and stairs leading up to the large living area and separate first double bedroom. Stairs lead up to the second floor where there are two large double bedrooms.
Please quote the property reference 6841008 when enquiring. | {
"redpajama_set_name": "RedPajamaC4"
} | 8,444 |
{"url":"https:\/\/www.darey.io\/docs\/33274-2\/","text":"# Step 6 Prepare the etcd database for encryption at rest.\n\n#### Step 6 Prepare the etcd database for encryption at rest.\n\nKubernetes uses etcd (A distributed key value store) to store variety of data which includes the cluster state, application configurations, and secrets. By default, the data that is being persisted to the disk is not encrypted. Any attacker that is able to gain access to this database can exploit the cluster since the data is stored in plain text. Hence, it is a security risk for Kubernetes that needs to be addressed.\n\nTo mitigate this risk, we must prepare to enc...","date":"2021-07-27 22:53:07","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\": 0.2748442590236664, \"perplexity\": 2935.1892515669324}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-31\/segments\/1627046153491.18\/warc\/CC-MAIN-20210727202227-20210727232227-00018.warc.gz\"}"} | null | null |
Utricularia petertaylorii este o specie de plante carnivore din genul Utricularia, familia Lentibulariaceae, ordinul Lamiales, descrisă de Allen Lowrie. Conform Catalogue of Life specia Utricularia petertaylorii nu are subspecii cunoscute.
Referințe
Utricularia | {
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all: *.cpp
g++ -O3 -Wall `pkg-config --cflags --libs opencv` -lrt -o hesaff pyramid.cpp affine.cpp siftdesc.cpp helpers.cpp hesaff.cpp
| {
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NEW YORK, March 20, 2019 (GLOBE NEWSWIRE) -- Pawar Law Group announces that a class action lawsuit has been filed on behalf of shareholders who purchased shares of Bristow Group Inc. (NYSE: BRS) from February 8, 2018 through February 12, 2019, inclusive (the "Class Period"). The lawsuit seeks to recover damages for Bristow investors under the federal securities laws. Pawar Law reminds investors of the April 15, 2019 lead plaintiff deadline.
To join the class action, go to http://pawarlawgroup.com/cases/bristow-group-inc/ or call Vik Pawar, Esq. toll-free at 888-589-9804 or email info@pawarlawgroup.com for information on the class action.
A class action lawsuit has already been filed. If you wish to serve as lead plaintiff, you must move the Court no later than April 15, 2019. A lead plaintiff is a representative party acting on behalf of other class members in directing the litigation. If you wish to join the litigation, go to http://pawarlawgroup.com/cases/bristow-group-inc/ or to discuss your rights or interests regarding this class action, please contact Vik Pawar, Esq. of Pawar Law Group toll free at 888-589-9804 or via e-mail at info@pawarlawgroup.com. | {
"redpajama_set_name": "RedPajamaC4"
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Spotlight on For Always Series by Janae Mitchell w/a rafflecopter giveaway!
"First & foremost, I'm a country girl. I'm no different than most, I just happen to write… a lot. If I'm not writing books, I'm reading them. I live for the HEA. I've been interested in the paranormal most of my life, living in a 'haunted' house growing up. This fascination, mixed with my love of writing, made my first YA paranormal romance series, For Always, inevitable. Of course I'd have to throw a spooky ghost story in there, too.
PAPERBACK COPY of one of the books in the series! Winner's choice!
Previous postBook Blitz for Sugar Baby Beautiful by J.J. McAvoy w/a rafflecopter giveaway! | {
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From sleep apnea which, left untreated, can lead to high blood pressure, heart disease, stroke, depression, diabetes and other ailments, to Alzheimer's disease, researchers continue to discover why we need to sleep. Now investigators from the Intramural Research Program (IRP) of the National Institute on Aging (NIA) are saying feeling excessively sleepy during the day could be a sign of increased risk for the brain pathology of Alzheimer's disease.
According to a new study published in the September 25, 2018 issue of the journal Sleep, older adults who felt sleepy during the day when they wanted to be awake were almost three times more likely to have deposits of beta-amyloid—the protein that clumps in the brain as part of Alzheimer's pathology. The research team was led by Dr. Adam Spira of Johns Hopkins University and included Dr. Murat Bilgel, Dr. Luigi Ferrucci, Dr. Susan Resnick and Dr. Eleanor Simonsick of NIA's Intramural Research Program.
Using Neuroimaging Substudy data from the Baltimore Longitudinal Study of Aging (BLSA), researchers looked at the reported daytime sleepiness levels and napping habits of 124 cognitively healthy men and women and then matched that information with PET and MRI scan results from an average of 16 years later. The BLSA is America's longest-running study of human aging.
Overall, 50% of BLSA participants were women and 21% were non-white. About 24% had EDS and 29% were nappers. Those with EDS were older than those without EDS, and compared with non-nappers, nappers were older, more likely to be male and had slightly more education.
"They found that people who said they often felt sleepy during the day were nearly three times more likely to have deposits of beta-amyloid, the protein that clumps in the brain as part of Alzheimer's disease pathology, than their peers who didn't report daytime sleepiness," researchers reported. "While not a direct correlation, the researchers see the results as further evidence that sleep problems and Alzheimer's pathology may be connected. The exact mechanism that connects disturbed sleep with beta-amyloid buildup is unclear, but multiple studies have shown that people with dementia often experience sleep disturbances, and other studies have shown buildups of beta-amyloid in the brains of animals whose sleep was disturbed." Napping habits were not significantly connected to beta-amyloid deposits, the team reported.
Researchers concluded common causes of excessive daytime sleepiness (EDS) (e.g., sleep-disordered breathing, insufficient sleep) being associated with biomarkers for Alzheimer's disease could help identify those with elevated dementia risk and have important implications for prevention of the disease.
Disturbed sleep has emerged as a candidate risk factor for Alzheimer's disease, multiple studies link poor sleep to cognitive impairment and decline, and more recent studies link sleep disturbance to biomarkers for Alzheimer's disease, study authors wrote. Researchers showed that shorter sleep duration and poorer sleep quality were associated with greater beta-amyloid buildup as shown on positron emission tomography (PET) scans. They noted another study had linked poorer sleep and reports of frequent napping with cerebrospinal fluid (CSF) measures of beta-amyloid deposition. The authors said that numerous studies have linked sleep-disordered breathing (SDB) to poor cognitive outcomes, and more recent studies have tied SDB to Alzheimer's disease.
Excessive daytime sleepiness may have resulted directly from disturbed sleep that itself promotes beta-amyloid deposition.
Authors noted the study's primary limitations as well, including its observational design and the absence of a baseline beta amyloid measure, which they say limited them from drawing firm causal inferences.
According to the NIA, future steps for this research include examining if sleep apnea and similar disorders, medications or other health conditions that often affect sleep quality in older adults may be a factor in beta-amyloid accumulation. | {
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Q: How to blit from the x and y coordinates of an image in Pygame? I'm trying to lessen the number of files I need for my pygame project by instead of having a folder with for example 8 boots files, I can make 1 bigger image that has all of them 8 pictures put next to each other and depending on animation tick, that specific part of the image gets blitted.
Currently, I utilise lists.
right = ["playerdesigns/playerright0.png","playerdesigns/playerright1.png","playerdesigns/playerright2.png","playerdesigns/playerright3.png"]
my code then just depending on animation tick, takes on of those files and blits it
but I wish to make it into one playerright.png image file that 0-100 Xpixels of the picture has playerright1.png, 101-200 Xpixels has playerright2.png etc, and then depending on need, I can blit 100 wide image from any point.
A: You can define a subsurface that is directly linked to the source surface with the method subsurface:
subsurface(Rect) -> Surface
Returns a new Surface that shares its pixels with its new parent. The new Surface is considered a child of the original. Modifications to either Surface pixels will effect each other.
The Rect argument of subsurface specifies the rectangular area for the sub-image. It can either be a pygame.Rect object or a tuple with 4 components (x, y, width, height).
For example, if you have an image that contains 3 100x100 size sub-images:
right_surf = pygame.image.load("playerdesigns/playerright.png")
right_surf_list = [right_surf.subsurface((i*100, 0, 100, 100)) for i in range(3)]
| {
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\section{Introduction}
Multivariate time series~\cite{zheng2014time,gaoreinforcement,hou2022multi} are ubiquitous for many web applications~\cite{yin2016forecasting,sezer2020financial}, which are sequences of events acquired longitudinally and each event is constituted by observations recorded over multiple attributes. For example, the electrocardiogram (ECG) signals~\cite{sarkar2020self} in electronic health records (EHRs) can be formulated as multivariate time series data since they can be obtained over time and multiple sensors. Comprehensive analysis of such data can facilitate decision-making in real applications~\cite{rim2020deep,Liu2022OnePO}, such as human activity recognition, healthcare monitoring, and industry detection. Particularly, multivariate time series classification (MTSC) tasks, as one fundamental problem of time series analysis, received significant attention in both academia and industry.
Accordingly, numerous efforts~\cite{zhang2020tapnet,tan2022multirocket} have been devoted to the MTSC problem over the last decades. In general, most of these current works can be divided into two categories: pattern-based and feature-based models. The former type usually extracts useful bag-of-patterns or shapelet patterns from the whole time series, and then transforms these extracted patterns into features to be used as inputs for the classifier. Since they are generated in raw time series, the corresponding patterns are often interpretable. The main concern is the often-incurred expensive computation cost during the process of pattern extraction. In contrast, feature-based methods can be very efficient and can be scaled to large-scale time series data but their classification capacity greatly depends on the effectiveness of labor-intensive features based on domain experts.
Hence, researchers begin to explore more expressive feature maps for improving classification capacity. Deep learning-based models~\cite{zheng2014time,goel2017r2n2,ismail2019deep,karim2019multivariate,zhang2020tapnet,tran2021radflow,cheng2022towards} have achieved remarkable success and have become ever-increasingly prevalent over past advancements. The main reason is that discriminative features related to time series can be learned in an end-to-end manner, which significantly saves manual feature engineering efforts. Among them, convolutional-based methods nearly have become the dominant approach due to the strong representation capacity of convolution operations~\cite{ruiz2021great,cheng2022towards}. In general, the strengths of convolutional models in performing time series classification can be summarized as follows: (1) convolutional networks can easily learn multi-scale representations by controlling the strides of convolutional kernels ~\cite{wang2021pyramid}, and preserve the capacity of temporal-invariant via the weight-sharing mechanism, which are of great significance for MTSC tasks; (2) Very deep convolutional networks can be stacked by employing residual connections, enabling larger receptive fields for capturing the sequence dependence; (3) Convolution operations can be efficiently computed without suffering from limitations of sequence length or instance number, and thus can be easily scaled to massive datasets. Despite their effectiveness, we argue that the classification performance is still restricted in failing to capture global contexts in convolution operation.
Recently proposed transformer architecture~\cite{vaswani2017attention,Wu2022FlowformerLT} have shown promising capacity in capturing global contexts for language modeling tasks. Motivated by this, we seek to transfer the powerful capacity of transformers from language domain to time series. However, it would easily incur severe issues in applying the transformer to the MTSC problem. First, in language transformers, only fixed-scale representations can be learned since word tokens serve as the basic elements. By contrast, the information density of a single object in time series is too small to reflect helpful patterns related to class labels. Taking an example in ECG classification, informative patterns are typically characterized by a series of continuous points or various sub-series instead of a single point. As such, multi-scale feature maps~\cite{tang2021omni} are necessary and can take a significant influence on the classification capacity. Second, the capacity of temporal-invariant is largely weakened in vanilla transformers since self-attention is permutation-variant, which may also restrict the final performance~\cite{oh2018learning}. Last, the sequence length of time series usually can be much longer than language sentences, which inevitably incurs an expensive computation burden since the time and memory complexity of the self-attention mechanism in the transformer architecture is quadratic to the sequence length input. Though some pioneering efforts~\cite{zerveas2021transformer,liu2021gated, tay2020efficient} based on transformers have been devoted before, the problems discussed above are still under exploration in the MTSC task.
To tackle these severe issues, in this work, we present FormerTime, a hierarchical transformer network for the MTSC task. Specifically, we design a hierarchical structure by dividing the whole network into several different stages, with different levels of scales as input. We also develop a novel transformer encoder to perform hidden transformation with two distinct characteristics: (1) we replace the standard self-attention mechanism with our newly designed temporal reduction version to save computation cost; (2) we design a context-aware positional encoding generator, which is designed to not only preserve the order of sequence input but also enhance the capacity of temporal-invariant of the whole model. In general, our FormerTime exhibits the following merits. First, in contrast to convolutional-based classifiers, FormerTime always yields a global reception field, which is useful for capturing the long-range dependence and interaction of the whole time series. Second, FormerTime can conveniently learn time series representations on various scales via its hierarchical architecture. Third, in the FormerTime, the inductive bias of temporal-invariant is well enhanced by leveraging the contextual positional generators. More importantly, the computation consumption of FormerTime is largely saved, and could be acceptable even for very long sequences.
To evaluate the effectiveness of the FormerTime, we conduct extensive empirical studies on $10$ public datasets from the UEA archive~\cite{bagnall2018uea}. The experimental results clearly show that FormerTime can yield strong classification performance in average. It significantly outperforms compared strong baselines. In summary, we initially demonstrate the potential of transformers in the MTSC problem. To the best of our knowledge, we first the few attempts of transformer-based models in breaking the efficiency bottleneck and achieving great performance improvements. We hope our work can facilitate the study of applying transformers to the MTSC problem.
\vspace{-0.1in}
\section{Related Work}
\subsection{Time Series Classification}
Tremendous efforts have been devoted to time series classification. Generally speaking, previous works can be roughly divided into two types: pattern-based and feature-based methods. Pattern-based methods typically first extract bag-of-patterns~\cite{schafer2017multivariate} or shapelet patterns~\cite{ye2009time}, and then feed them into a classifier. For example, shapelet-based methods usually extract some useful subsequence, which is distinctive for different classes. Then, distance metrics are employed to generate features for classification. DTW has been proved as an effective distance measurement in time series classification. Recently proposed work~\cite{schafer2017multivariate} uses symbolic Fourier approximation to generate discrete units for classification. The strength of these methods is that the generative patterns are usually interpretable~\cite{crabbe2021explaining} while the largest weakness~\cite{bagnall2017great,zhang2020tapnet} is inevitablely incurring expensive computation in producing discriminative patter features. A series of methods have been proposed to overcome this weakness by either speeding up the computation of distance or constructing the dictionary~\cite{ye2009time}. In contrast to pattern-based methods, feature-based methods can be more efficient by depending on hand-crafted static features based on domain experts. However, it is difficult to design good features to capture intrinsic properties embedded in various time series data. Therefore, the accuracy of feature-based methods is usually worse than that of sequence distance-based ones. Recently, extracting time series feature with deep neural networks~\cite{zheng2014time,karim2019multivariate,ismail2019deep} gradually become prevalent in time series classification tasks. As a pioneering attempt, multi-channel convolutional networks~\cite{zheng2014time} have been proposed to deal to capacity of classification for the MTSC problem. Later, a series of convolutional-based methods, like ResNet~\cite{he2016deep}, InceptionTime~\cite{ismail2020inceptiontime} have also proposed to achieve remarkable success due to their powerful representation ability in extracting time series features. ROCKET~\cite{dempster2020rocket} employs random convolution kernels to train linear classifiers and has been recognized as a powerful method in recent empirical studies~\cite{ruiz2021great}. Other than pure convolutional based methods, ~\cite{karim2019multivariate} perform time series classification by designing a hybrid network, in which both the LSTM layer and stacked convolutional layer along with a squeeze-and-excitation block are simultaneously used to extract features. Besides, mining graph structure among time series with graph convolutional networks for comprehensive analysis have also attracted some researchers~\cite{wu2020connecting,duan2022multivariate}.
\subsection{Transformers in Time Series.} Designed for sequence modeling, the transformer network~\cite{vaswani2017attention} recently achieves great success in nature language processing (NLP). Among multiple advantages of transformers, the ability to capture long-range dependencies and interactions is especially attractive for time series modeling. Hence, a large body of transformer-based methods~\cite{zhou2021informer,wen2022transformers} has been proposed by attempting leveraging transformers for time series forecasting or regression. For time series classification, recent advancements still lie in the early stage and mainly focus on multivariate time series classification. \cite{russwurm2020self} studies the transformer for raw optical satellite time series classification and obtains the latest results comparing with convolution-based solutions. GTN~\cite{liu2021gated} explores an extension of the transformer network by modeling both channel-wise and step-wise correlations, simultaneously. Besides, pre-trained transformers are also investigated in time series classification tasks. For example, TST~\cite{zerveas2021transformer} employs the transformer network to learn unsupervised representations of time series so as to alleviate the data sparsity issue. Despite their effectiveness, both the efficiency issues incurred by the self-attention and the properties of time series classification task are largely ignored in these current works. Although some prior works focusing on improving the efficiency of self-attention were developed~\cite{tay2020efficient}, these works mainly use heuristic strategies to perform sparse attention computation without global context modeling. In this work, we aim to tackle the efficiency bottleneck and achieve performance improvements in the proposed FormerTime.
\begin{figure*}[t]
\centering
\includegraphics[width=1.0\textwidth]{figure_formertime/formertime}
\vspace{-0.2in}
\caption{Illustration of the FormerTime, i.e., a efficient hierarchical transformer architecture for the MTSC task.}
\vspace{-0.12in}
\label{fig:formertime}
\end{figure*}
\section{The FormerTime Model}
In this section, we first formally introduce the definition of multivariate time series classification (MTSC) problem. Then, we introduce the overall architecture of our designed FormerTime. After that, we elaborate the FormerTime via respectively introducing two aspects of key designs, i.e., the hierarchical architecture and the designed transformer encoder. Finally, we demonstrate the difference between the FormerTime and other relative methods.
\subsection{Problem Definitions}
We introduce the definitions and notations used in the following. $\mathbb{D} = {(X^1, y^1), (X^2, y^2),..., (X^n,y^n)}$ is a dataset containing a collection of pairs $(X^i, y^i)$, in which $n$ denotes the number of examples and $X^i$ denote a multivariate time series with its corresponding label denoted by $y^i$ . Each multivariate time series $X = [x_1, x_2, ..., x_l]$ contains $l$ ordered elements with $m$ dimensions in each time step. The task of multivariate time series classification is to learn a classifier on $\mathbb{D}$ so as to map from the space of inputs $X$ to a probability distribution over the class $y$.
\subsection{Model Architecture Overview}
An overview of the FormerTime is depicted in Figure~\ref{fig:formertime}. The input of the whole model is a set of multivariate time series, involving multiple dimensions (a.k.a. channels). For each dimension, the time series share the same sequence length. To produce multi-scale representations for time series data, we adopt a hierarchical architecture. Specifically, we divide the whole deep network architecture into multiple different stages so as to generate feature maps on various time scales. For simplicity, all stages share a similar architecture, which is composed of a temporal slice partition processing operation and successive $L_i$ our designed transformer encoder layers. Relying upon such hierarchical architecture, the time series representation on various scales can be effectively extracted. Meanwhile, we use the mean pooling operation over the representation of each temporal point to denote the time series representations. The model's output is the predicted distribution of each possible label class for the given input time series. The FormerTime model can be trained end-to-end by minimizing the cross-entropy loss~\cite{Cheng2021LearningRS}, and the loss is propagated back from the prediction output across the entire network. The following sections would mainly introduce several key designs in the FormerTime.
\subsection{Multi-scale Time Series Representations}
Integrating information on different time scales~\cite{chen2021multi} is essential to the classification capacity in the MTSC task. However, the vanilla transformer model only can produce fixed-scale representations of the sequence input. Thus, we devise a hierarchical architecture for learning time series representations on various time scales. The key idea is that the whole model is divided into several stages so as to hierarchically performing feature maps. Here, we vary the time scale input for different stages by leveraging a temporal slice partition strategy, i.e., aggregating successive neighborhood points with a window slicing operation.
Specifically, suppose that we have sequence input $X=\{x_1, x_2, ...x_l\}$ in stage $j$, and the window slicing size is $s_j$, which denotes the scale size of the processed time series. Every $s_j$ successive points will be grouped into a new temporal slice. Considering the semantic gap issue, we then feed these temporal slices to a trainable linear projection layer to project this raw feature to a new dimension $C_j$. Notably, the weights of this linear projection layer is weight-shared, in which we use $d_j$ to denote the stride of projection operations. To some extent, these temporal slices can be regarded as the ``tokens'' of new time series, analogous to the relationship between word and whole speech input. Assume that the whole model is divided into three stages, and the fine-grained raw time series can be processed into a new granularity version, which contains $\frac{l}{s_1}$ slices and each size is $s_1\times m$. Then, the linear projection layer project it into a new dimension $C_1$, and the output is reshaped to size of $\textbf{F}_1\in \mathbb{R}^ {\frac{l}{s_1}\times C_1} $. After that, the normalized embeddings of each temporal slice along with its positional embeddings are fed into the transformer encoder with $L_1$ layers. In the same manner, by using the feature maps of the previous stage's output as the input of the next stage, different scales of time series representations, denoted by $\textbf{F}_j$, can be effectively learned by stage-wise propagation.
The primary motivation is the information density difference between time series and language domain. Unlike the tokens in language data, which are human-generated signals and highly semantic and information-intensive, the time series are naturally redundant, e.g., a missing point can be easily recovered from its neighbors. The benefits of adopting temporal slice operation are two-fold. First, the time scales of sequence data can be flexibly transformed, naturally forcing the network to generate hierarchical feature maps. Second, with this partitioning strategy, the sequence length of the whole time series can be largely reduced before sent into the encoder, saving an amount of computation consumption.
\subsection{The Transformer Encoder Network}
In this subsection, we will introduce our designed encoder to extract the robust global contexts of the whole sequence input.
\subsubsection{Temporal Reduction Attention.}
To capture the global contexts of the whole time series, we would like to benefit from regarding the transformer network as the encoder to perform non-linear hidden representation transformation. One of the core designs of the vanilla transformer network is to employ a multi-head self-attention mechanism. Each temporal point needs to be computed the attention scores among all other sequence points with the inner product so as to capture the long-range dependence. However, the computation complexity incurred by the attention operation can be very heavy, growing quadratically in the sequence length of the input sequence. Unlike language data, the sequence length of time series data regularly can be very long to uncover the event of classification tasks. Directly leveraging the standard attention computation strategy is memory-expensive, making it hard for transformers to be applicable in time series.
To solve this dilemma, inspired by recent works~\cite{wang2020linformer}, we present a novel attention computation strategy named temporal reduction attention (TRA) mechanism to replace the vanilla self-attention strategy. The core idea of TRA is to compute the attention with a sub-sampled version of all input points. To be more specific, similar to standard self-attention, our TRA receives a query $Q$, a key $K$, and a value $V$ as input, and outputs a refined feature. Details of TRA operation in stage $j$ can be formulated as follows:
\begin{small}
\begin{equation}
\label{equ:tra_qkv}
\rm TRA (\textbf{Q}, \textbf{K}, \textbf{V}) = Concat(head_0, ..., head_{N_j})\textbf{W}^O,
\end{equation}
\end{small}\noindent in which the $\rm Concat$ denotes the concatenation operation, and $N_i$ is the number of heads in the attention layer.
\begin{small}
\begin{equation}
\label{equ:head}
\rm head_j =Attention(\textbf{Q}\textbf{W}_j^Q, TR(\textbf{K}) \textbf{W}_j^K, TR(\textbf{V})\textbf{W}_j^V),
\end{equation}
\end{small}\noindent where $\rm \textbf{W}_j^Q\in \mathbb{R}^{C_j\times d_{head}}, \textbf{W}_j^K\in \mathbb{R}^{\textbf{C}_j\times d_{head}}, \textbf{W}_j^V\in \mathbb{R}^{\textbf{C}_j\times d_{head}}$ are linear projection parameters. In this way, the dimension of each head is equal to $\frac{\textbf{C}_j}{N_j}$. Here, $\rm TR$ indicates the temporal reduction on $K$ and $V$, which can be written as
\begin{small}
\begin{equation}
\label{equ:tr}
\rm TR(x) = Norm(Reshape(x, R_j)\textbf{W}^T),
\end{equation}
\end{small}\noindent where $\textbf{x}\in\mathbb{R}^{l_j \times C_j}$ represents a input sequence, and $R_i$ denotes the reduction ratio of the attention layers in stage $j$. $\rm Reshape(x, R_j)$ is an operation of reshaping the input sequence $x$ to a sequence of size $\frac{L_j}{R_j}$ and $\textbf{W}^T$ is a linear projection that reduces the dimension of the input sequence to $C_j$. Here, we employ layer normalization operation~\cite{vaswani2017attention} to implement $\rm Norm$. Like the original attention computation mechanism, our $\rm Attention(\cdot)$ can be represented as
\begin{small}
\begin{equation}
\label{equ:attention}
\rm Attention(q,k, v) = softmax(\dfrac{qk^\intercal}{\sqrt{d_{head}}})v.
\end{equation}
\end{small}\indent
In this way, the computational cost of our attention operation is $\frac{1}{R_i}$ of standard self-attention, so our TRA can handle longer input feature maps/sequences without requiring too many resources. The main difference between our TRA and the prior version is that our TRA reduces the temporal scale of $\textbf{K}$ and value $\textbf{V}$ before the attention operation, largely reducing the computational/memory overhead. Note that the capacity of global context modeling is still well-remained in our attention layer.
\subsubsection{Contextual Positional Encoding.} As claimed in~\cite{vaswani2017attention,chu2021conditional}, positional information is a key operation in the success of the transformer network. The main reason is that the self-attention operation can be used to preserve the order of the sequence property of input data. Two types of position information in transformers have been widely adopted, including absolute and relative encodings, which respectively denote static and learnable embeddings. For the former type, absolute temporal information provides helpful cues for whenever the object would appear in the whole time series. Despite its effectiveness, it severely weakens the capacity of temporal-invariant since each temporal slice is added with a unique positional encoding. In fact, the temporal invariance plays a significant role in time series classification tasks since we hope the model to release the same response whenever the discriminative pattern appears in the time series. Though relative positional encodings can greatly alleviate the aforementioned issues, the relative encodings lack absolute position information, which is important in classification tasks~\cite{islam2020much,chu2021conditional}. Previous works have uncovered that one of the main merits of such positional information is that absolute information can be added for enhancing classification performance. Besides, we also argue that these two types of positional information actually model each temporal slice individually and only achieve sub-optimal performance because that extracted patterns from time series evolve in time and highly depend on their surrounding points.
Based on the above analysis, we hold that the well-informed positional information should possess two aspects of characteristics. First, making the input sequence permutation-variant but temporal-invariant is a necessity for time series classification. Second, having the ability to provide absolute information also matters. To fulfill the two demands, we find that characterizing the contextual information among neighboring temporal slices can be sufficient. As shown in Figure~\ref{fig:formertime}, we use $1$-D convolutional kernel size $k$ along with $\frac{k}{2}$ zero paddings to extract the localized contextual information as positional encodings. Note that the zero padding is vital to make the model aware of the absolute position information.
\subsubsection{Entire Transformer Encoder Network.}
Based on the designed temporal reduction attention mechanism and context positional encodings, we organize them together to form a novel transformer encoder block for learning the time series representations. We give a sketch of the newly designed encoder at the bottom of Figure~\ref{fig:formertime}. On the basis of the design of standard transformer encoder~\cite{vaswani2017attention}, the entire encoder is composed of successive layers of the TRA layer and followed by a feed-forward neural network (FFN) layer. These two layers are further wrapped with a residual connection to avoid the the vanishing gradient problem. Particularly, we set a trainable parameter $\alpha$, initialized with zero, according to the previous work~\cite{bachlechner2021rezero}. Such a simple trick can further help the FormerTime converge more stable.
\subsection{Summary and Remarks}
In the following, we summarize the characteristics of FormerTime and discuss its relations to transformer-based and convolutional-based approaches in the multivariate time series classification.
\paragraph{\textit{Relation to Transformer-based Models}.}
Transformer architecture has shown its superiority in global sequence modeling tasks. However, the dot-product computation in self-attention easily incurs quadratic computation and memory consumption on sequence input. Hence, the efficiency of the transformer architecture becomes the bottleneck of applying them to time series classification tasks. Besides, the vanilla transformer model lacks some key designs of inductive bias, such as multi-scale representation and temporal invariance, which can greatly benefit the time series classification task. Although some prior works of efficient transformer variants~\cite{tay2020efficient} have been proposed, they fail to solve these two aspects of limitations, simultaneously. In contrast, the proposed FormerTime not only breaks the bottleneck of efficiency but also achieves performance improvements in the MTSC task.
\paragraph{\textit{Relation to Convolutional-based Models}.}
Recently, researchers have demonstrated the extremely expressive capacity of convolutional models in MTSC tasks. In fact, convolutional networks can yield several aspects of strength: 1) their memory and time complexity in feature extraction are not constrained by the sequence length of the sequence input, 2) they can easily learn time series with various scales of feature maps with varying strides and preserve the prior capacity of temporal-invariant with the weight-sharing mechanism for the classification task. However, convolution operation cannot achieve a global receptive field of whole sequence input while the global context information is vital for the classification capacity. Our proposed FormerTime not only absorbs the strength of convolutional models but also meets the demands of long-range dependence modeling.
\begin{table}[t]
\centering
\setlength{\tabcolsep}{1.0pt}
\vspace{-0.12in}
\caption{Statics of datasets in the experiments. }
\vspace{-0.1in}
\begin{tabular}{cccccc}
\hline
Dataset & Train Size & Test Size & Dimensions & Length & Classes \\
\hline
AWR & 275 & 300 & 9 & 144 & 25 \\
AF & 15 & 15 & 2 & 640 & 3 \\
CT & 1,422 & 1,436 & 3 & 182 & 20 \\
CR & 108 & 72 & 6 & 1,197 & 12 \\
FD & 5,890 & 3,524 & 144 & 62 & 2 \\
FM & 316 & 100 & 28 & 50 & 2 \\
MI & 278 & 100 & 64 & 3,000 & 2 \\
SRS1 & 268 & 293 & 6 & 896 & 2 \\
SRS2 & 200 & 180 & 7 & 1,152 & 2 \\
UWG & 120 & 320 & 3 & 315 & 8 \\
\hline
\end{tabular}%
\vspace{-0.2in}
\label{tab:datasets}%
\end{table}%
\vspace{-0.1in}
\section{Experiments}
\subsection{Experimental Setup}
\subsubsection{Datasets}
We perform all experiments by conducting experiments on ten public datasets, which are selected from the well-known UEA multivariate time series classification (MTSC) archive. In reality, the UEA archive has become nearly the most widely used multivariate time series benchmarks. We select a set of 10 multivariate datasets from the UEA archive~\cite{bagnall2018uea} with diverse characteristics in terms of the number, and the length of time series samples, as well as the number of classes. Specifically, we choose: ArticularyWordRecognition (AWR), Atrial Fibrillation (AF), CharacterTrajectories (CT), Cricket, FaceDetection (FD), FingerMovements (FM), MotorImagery(MI), SelfRegulationSCP1 (SRS1), SelfRegulationSCP2 (SRS2), UWaveGestureLibrary (UW). In these original dataset, training and testing set have been well processed. We do not take any processing for these datasets for a fair comparison. We summarize the main characteristics of dataset in Table~\ref{tab:datasets}.
\begin{table*}
\centering
\setlength{\tabcolsep}{3.0pt}
\caption{Detailed Hyper-parameter settings of the proposed FormerTime. }
\vspace{-0.1in}
\begin{tabular}{c|cc|cc|cc}
\hline
\multirow{2}[2]{*}{Datasets} & \multicolumn{2}{c|}{Stage 1} & \multicolumn{2}{c|}{Stage 2} & \multicolumn{2}{c}{Stage 3} \\
& Temporal Slice & Encoder & Temporal Slice & Encoder & Temporal Slice & Encoder \\
\hline
AWR & s\_1=2,C\_1=64,d\_1=2 & \multirow{10}[2]{*}{\makecell{L\_1=6 \\ R\_1=2 \\ N\_1=4 }} & s\_2=2,C\_2=64,d\_2=2 & \multirow{10}[2]{*}{\makecell{L\_2=6 \\ R\_2=2 \\ N\_2=4}} & s\_3=2,C\_3=64,d\_3=2 & \multirow{10}[2]{*}{\makecell{L\_3=6 \\ R\_3=1 \\ N\_3=4} } \\
AF & s\_1=16,C\_1=64,d\_1=8 & & s\_2=2,C\_2=64,d\_2=2 & & s\_3=2,C\_3=64,d\_3=2 & \\
CT & s\_1=16,C\_1=64,d\_1=8 & & s\_2=2,C\_2=64,d\_2=2 & & s\_3=2,C\_3=64,d\_3=2 & \\
CR & s\_1=8,C\_1=64,d\_1=8 & & s\_2=2,C\_2=64,d\_2=2 & & s\_3=2,C\_3=64,d\_3=2 & \\
FD & s\_1=2,C\_1=64,d\_1=2 & & s\_2=2,C\_2=64,d\_2=2 & & s\_3=2,C\_3=64,d\_3=2 & \\
FM & s\_1=4,C\_1=64,d\_1=4 & & s\_2=2,C\_2=64,d\_2=2 & & s\_3=2,C\_3=64,d\_3=2 & \\
MI & s\_1=8,C\_1=64,d\_1=8 & & s\_2=2,C\_2=64,d\_2=2 & & s\_3=2,C\_3=64,d\_3=2 & \\
SRS1 & s\_1=2,C\_1=64,d\_1=2 & & s\_2=2,C\_2=64,d\_2=2 & & s\_3=2,C\_3=64,d\_3=2 & \\
SRS2 & s\_1=16,C\_1=64,d\_1=8 & & s\_2=2,C\_2=64,d\_2=2 & & s\_3=2,C\_3=64,d\_3=2 & \\
UWG & s\_1=8,C\_1=64,d\_1=8 & &s\_2=2,C\_2=64,d\_2=2& & s\_3=2,C\_3=64,d\_3=2 & \\
\hline
\end{tabular}%
\vspace{-0.1in}
\label{tab:formertime}%
\end{table*}%
\begin{table*}[htbp]
\centering
\caption{Classification performance of compared methods in ten datasets. \textbf{Bold} numbers represent the best results.}
\vspace{-0.1in}
\begin{tabular}{ccccccccccccc}
\toprule
Datasets & IT & LS & ST & MCDCNN & TCN & MCNN & ResNet & MR & TST & GTN & Informer & Ours \\
\midrule
AWR & 0.9827 & 0.9127 & 0.8700 & 0.7800 & 0.9467 & 0.8200 & 0.9827 & 0.9720 & 0.9789 & 0.9767 & 0.9820 & \textbf{0.9847 } \\
AF & 0.4400 & 0.2533 & 0.2667 & 0.3733 & 0.4933 & 0.3467 & 0.4000 & 0.3333 & 0.4000 & 0.4000 & 0.4267 & \textbf{0.6000 } \\
CT & \textbf{0.9983 } & 0.9866 & 0.7224 & 0.8826 & 0.9915 & 0.9238 & 0.9965 & 0.9876 & 0.9882 & 0.9783 & 0.9862 & 0.9914 \\
CR & 0.9889 & 0.9639 & 0.9722 & 0.6278 & 0.9083 & 0.9167 & \textbf{0.9972 } & 0.9806 & 0.9583 & 0.7917 & 0.9778 & 0.9806 \\
FD & 0.6820 & 0.5129 & 0.5085 & 0.5000 & 0.6801 & 0.6747 & 0.5760 & 0.6065 & 0.6005 & 0.5542 & 0.5265 & \textbf{0.6872 } \\
FM & 0.6000 & 0.4840 & 0.4940 & 0.5920 & 0.5880 & 0.5920 & 0.6080 & \textbf{0.6380 } & 0.5900 & 0.5350 & 0.6120 & 0.6180 \\
MI & 0.5860 & 0.5180 & 0.6100 & 0.5000 & 0.6040 & 0.5980 & 0.5780 & 0.5640 & N/A & N/A & 0.6240 & \textbf{0.6320 } \\
SRS1 & 0.8942 & 0.7038 & 0.6724 & 0.9079 & 0.9031 & 0.8949 & 0.8730 & \textbf{0.9352 } & 0.8771 & 0.8019 & 0.9188 & 0.8867 \\
SRS2 & 0.5689 & 0.5111 & 0.5300 & 0.5256 & 0.5978 & \textbf{0.5989 } & 0.5622 & 0.5411 & 0.5796 & 0.5611 & 0.5767 & 0.5922 \\
UWG & 0.8869 & 0.8031 & 0.7769 & 0.8438 & 0.7981 & 0.8044 & 0.7994 & \textbf{0.9075 } & 0.8271 & 0.8406 & 0.8363 & 0.8881 \\
\hline
Average & 0.7628 & 0.6649 & 0.6423 & 0.6533 & 0.7511 & 0.7170 & 0.7373 & 0.7466 & 0.7555 & 0.7155 & 0.7467 & \textbf{0.7861 } \\
MACs (M) & 89 & - & - & 263 & 283 & 929 & 132 & - & 408 & 1,565 & 141 & 98 \\
\bottomrule
\end{tabular}%
\vspace{-0.1in}
\label{tab:main_results}%
\end{table*}%
\subsubsection{Compared Baselines.}
For comprehensive evaluation, we choose the following prevalent baseline methods for evaluation: Shapelet Transformation (ST)~\cite{lines2012shapelet}, Learning Shapelet (LS)~\cite{grabocka2014learning}, TST~\cite{zerveas2021transformer}, GTN~\cite{liu2021gated}, Informer~\cite{zhou2021informer}, MCDCNN~\cite{zheng2014time}, MCNN~\cite{cui2016multi}, ResNet~\cite{he2016deep}, TCN~\cite{bai2018empirical}, InceptionTime (IT)~\cite{ismail2020inceptiontime}, MiniROCKET (MR)~\cite{dempster2021minirocket}. Among them, ST and LS are two shapelet-based methods. TST and GTN are two transformer-based models proposed for time series classification. Though Informer is originally proposed for time series forecasting, we also treat it as a competitive baseline to verify the effectiveness of our FormerTime. In addition, the remaining compared baselines are convolutional-based models applied to the MTSC problem. Note that some traditional classifiers~\cite{middlehurst2021hive} are not considered here, since it is difficult to construct hand-crafted features for all time series. Also, we do not choose well-known distance-based methods, like HIVE-COTE~\cite{middlehurst2021hive}, as baseline due to their expensive computation consumption. We adopt accuracy as the metric.
\subsubsection{Implement Details.}
For learning shapelet (LS), we adopt the codes in \footnote{https://tslearn.readthedocs.io/} while adopting the publicly available codes~\footnote{https://pyts.readthedocs.io/} to run shapelet transformation (ST). To implement GTN, we use the source code provided by the corresponding authors \footnote{https://github.com/ZZUFaceBookDL/GTN}. We implement TST by strictly following the network architecture settings of original works using PyTorch. We replace the decoder in Informer\footnote{https://github.com/zhouhaoyi/Informer2020} with a linear classifier layer so as to adapt it for MTSC tasks. The remaining baselines' code consistently leverages the codes in~\footnote{https://timeseriesai.github.io/tsai/}. For full reproducibility of the experiments, we release our codes and make it available ~\footnote{https://anonymous.4open.science/r/FormerTime-A17E/}. The specific hyper-parameters of our FormerTime are listed as follows:
\begin{itemize}
\item $s_j$: the temporal slice size of stage $j$;
\item $C_j$: the hidden size of the output in stage $j$;
\item $d_j$: the stride size of window slicing operation of stage $j$;
\item $L_j$: the number of transformer encoders in stage $j$;
\item $R_j$: the temporal reduction rate in stage $j$;
\item $N_j$: the number of attention heads of temporal reduction attention in stage $j$.
\end{itemize}
More details of hyper-parameter settings in FormerTime for specific datasets can be found in Table~\ref{tab:formertime}. For common hyper-parameters of all models, we set the embedding size as $64$. The initialized learning rate is set to $1\times 10^{-3}$ without additional processing, and we employ Adam optimizer to guide all model training. All other hyper-parameters and initialization strategies either follow the suggestions from the original works' authors or are tuned on testing datasets. We report the results of each baseline under its optimal hyper-parameter settings. For a fair comparison, all models are trained on the training set and report the accuracy score on the testing set. All models are trained until achieving the best results. \textbf{All experiments in our work are repeated for $5$ times with $5$ different seeds, and we reported the mean value score.}
\begin{figure}
\centering
\includegraphics[width=0.46\textwidth]{figure_formertime/cdg}
\vspace{-0.1in}
\caption{Critical difference diagram over the mean ranks of FormerTime, baseline methods. }
\vspace{-0.1in}
\label{fig:cdg}
\end{figure}
\subsection{Experimental Results}
\subsubsection{Classification Performance Evaluation.}
Table~\ref{tab:main_results} summarizes the classification accuracy of all compared methods while Figure~\ref{fig:cdg} reports the critical difference diagram as presented in~\cite{demvsar2006statistical}. The results of ``N/A'' indicates that the corresponding results cannot be run due to the out-of-memory issue. Overall, the accuracy of our proposed FormerTime could outperform previous classifiers on average. Such results demonstrate the success of FormerTime in enhancing the classification capacity in the MTSC problem. For each dataset, the classification performance of FormerTime is either the most accurate one or very close to the best one. These existing proposed models typically cannot always achieve the most distinct results. One may wonder whether the FormerTime can be effective enough. However, the experimental results are largely consistent with previous empirical studies~\cite{bagnall2017great,ruiz2021great}, i.e., one single model cannot always achieve superior performances in all scenarios. In particular, we observe that FormerTime could surpass other baselines to a large margin in datasets of AF and MI, in which the sequence length of these two datasets is very long. We guess that our temporal slice setting can be very robust for these two datasets.
\begin{table}
\centering
\caption{Experimental results w.r.t. studying the hyper-parameter sensitivity with varying stages.}
\vspace{-0.1in}
\begin{tabular}{ccccc}
\hline
Datasets & 1 & 2 & 3 & 4 \\
\hline
AWR & \textbf{0.9811} & \textbf{0.9811} & 0.9720 & 0.9767 \\
AF & 0.4222 & 0.4667 & \textbf{0.6000} & 0.5778 \\
CT & 0.9907 & 0.9909 & \textbf{0.9914} & 0.9902 \\
CR & \textbf{0.9861} & 0.9815 & 0.9806 & 0.9769 \\
FD & 0.6750 & \textbf{0.6793} & 0.6776 & 0.6748 \\
FM & \textbf{0.6200} & 0.6033 & 0.6140 & 0.6067 \\
MI & 0.6200 & 0.6267 & \textbf{0.6280} & 0.6133 \\
SRS1 & 0.8760 & 0.8692 & 0.8771 & \textbf{0.8840} \\
SRS2 & 0.5722 & 0.5815 & \textbf{0.5922} & 0.5889 \\
UWG & \textbf{0.9021} & 0.8948 & 0.8844 & 0.8844 \\
\hline
Averge & 0.7645 & 0.7675 & \textbf{0.7817} & 0.7774 \\
\hline
\end{tabular}%
\vspace{-0.1in}
\label{tab:stage}%
\end{table}%
For these baseline approaches, we observe that convolutional-based methods, like MR, exhibit strong classification performances in some datasets, which is analogous to the experimental results of recent empirical studies~\cite{ruiz2021great}. We hold the characteristics of multi-scale representation and temporal invariance of the convolution operations make a great contribution. Besides, in MR, the feature of PPV, denoting the proportion of positive values of extracted deep representations, also matters. However, for transformer-based classifiers, it seems that the performance cannot always outperform convolutional algorithms. We guess the main reason behind the performance is that: (1) the plain transformer architecture fails to learn hierarchical feature maps from time series data, and (2) the naive positional information might not be suitable for modeling time series since the semantic information of one single temporal point individually modeled. Besides, compared to these deep learning-based methods, shapelet-based methods exhibit the worst classification performance due to a lack of poor representation capacity. However, in shapelet-based approaches, interpretable sub-sequence patterns can be extracted to make the model more understandable, which is vital in some applications.
In time series classification tasks, model efficiency has always been an important concern. Here, we also show the computation cost by recording MACs\footnote{https://github.com/Lyken17/pytorch-OpCounter} of compared methods. Note that only methods trained with end-to-end manner are reported. Though we adopt a self-attention operation, the computation cost of our methods can be very economical. Particularly, compared to the standard transformer network, our proposed FormerTime could significantly save computation costs. The main reason could be attributed to two aspects: 1) we model the raw time series with hierarchical architecture, which significantly shorten the sequence length, and 2) we develop a temporal reduction layer to ensure each input point can attend to all other data points.
\subsubsection{Study of Multi-scale Representations.}
In this part, we decide to study the effectiveness of hierarchical feature maps in FormerTime by setting different types of model variants w.r.t. the different number of stages. Specifically, we report the average classification experimental results of ten datasets in Table~\ref{tab:stage}, varying the number of stages from 1 to 4. Note that the total number of layers is consistent in these model variants to eliminate the other influence factors. From the reported results, we observe that feature maps at various scales can indeed perform much better than the single-scale representation versions. Such results demonstrate the importance of multi-scale representation in time series classification tasks. Furthermore, we also empirically analyze the effectiveness of hierarchical structure by performing hyper-parameter sensitivity analysis on the size of window slicing in temporal slice partition. The average accuracy of ten datasets is recorded in Table~\ref{tab:slice}. An attractive experimental phenomenon is that FormerTime equipped with a large slice size yields more promising results. We guess that the semantic information of a smaller temporal slice is too small to characterize discriminative patterns of distinguishing other examples.
\begin{table}
\centering
\caption{Experimental results w.r.t. studying the hyper-parameter sensitivity w.r.t. temporal slice size.}
\vspace{-0.1in}
\begin{tabular}{ccccc}
\hline
Datasets & [16,32,64] & [8,16,32] & [4,8,16] & [2,4,8] \\
\hline
AWR & 0.9720 & 0.9740 & 0.9820 & \textbf{0.9847} \\
AF & \textbf{0.6000} & 0.5600 & 0.4267 & 0.4400 \\
CT & \textbf{0.9914} & 0.9886 & 0.9868 & 0.9873 \\
CR & \textbf{0.9806} & 0.9806 & 0.9778 & 0.9667 \\
FD & 0.6776 & \textbf{0.6794} & 0.6823 & 0.6872 \\
FM & 0.6140 & 0.6080 & \textbf{0.6180} & 0.6040 \\
MI & \textbf{0.6280} & \textbf{0.6280} & 0.6160 & 0.6180 \\
SRS1 & 0.8771 & 0.8826 & 0.8710 & \textbf{0.8867 } \\
SRS2 & \textbf{0.5922} & 0.5811 & 0.5856 & 0.5600 \\
UWG & 0.8844 & \textbf{0.8881} & 0.8781 & 0.8775 \\
\hline
Averge & \textbf{0.7817} & 0.7770 & 0.7624 & 0.7612 \\
\hline
\end{tabular}%
\label{tab:slice}%
\end{table}%
\begin{table}
\centering
\vspace{-0.12in}
\caption{Experimental results w.r.t. studying the effectiveness of contextual positional embeddings.}
\vspace{-0.12in}
\begin{tabular}{ccccc}
\hline
Datasets & None& Static & Learnable & Ours \\
\hline
AWR & 0.9433 & 0.9822 & 0.9811 & \textbf{0.9720} \\
AF & 0.4667 & 0.5111 & 0.5556 & \textbf{0.6000} \\
CT & 0.9821 & 0.9902 & 0.9863 & \textbf{0.9914} \\
CR & \textbf{0.9815} & 0.9676 & 0.9769 & 0.9806 \\
FD & 0.6740 & \textbf{0.6804} & 0.6774 & 0.6776 \\
FM & 0.5900 & 0.5867 & \textbf{0.6200} & 0.6140 \\
MI & 0.6233 & 0.5833 & 0.6167 & \textbf{0.6280} \\
SRS1 & 0.8635 & \textbf{0.8817} & 0.8749 & 0.8771 \\
SRS2 & 0.5704 & 0.5759 & \textbf{0.6018} & 0.5922 \\
UWG & 0.8479 & 0.8729 & 0.8677 & \textbf{0.8844} \\
\hline
Averge & 0.7543 & 0.7632 & 0.7758 & \textbf{0.7817} \\
\hline
\end{tabular}%
\label{tab:pos}%
\vspace{-0.2in}
\end{table}%
\begin{figure*}[t]
\centering
\includegraphics[width=1.0\textwidth]{figure_formertime/pe_1}
\vspace{-0.2in}
\caption{Normalized attention score from the first encoder block of the first stage in FormerTime: (1) without taking positional information into account, (2) using static embeddings, (3) using learnable vectors, (4) using our contextual embeddings.}
\vspace{-0.1in}
\label{fig:position_attention_score}
\end{figure*}
\begin{figure}[t]
\centering
\includegraphics[width=0.5\textwidth]{figure_formertime/semantic_ts}
\vspace{-0.2in}
\caption{Left plot: Visualization of the t-SNE result of the embedding layer output on the AF dataset. Right plot: visualization of sub-sequences on raw time series data.}
\vspace{-0.2in}
\label{fig:semantic}
\end{figure}
\subsubsection{Study of Positional Information Encoding.} In the following, we would like to empirically verify the effectiveness of contextual positional information. A natural choice is to replace the contextual embedding with static or learnable version~\cite{vaswani2017attention}, respectively. Moreover, we also evaluate the results of FormerTime without leveraging any forms of positional embedding information. The average experimental results conducted on ten datasets are shown in Table~\ref{tab:pos}. From these results, we notice that FormerTime equipped with contextual positional information could surpass all other model variants, verifying the effectiveness of extracting contextual information as positional encodings. Also, FormerTime's performance dramatically degrades while absolutely discarding the positional information. We believe this is reasonable because self-attention computation is permutation-variant, whose performance would dramatically degrade if discarding the positional information. To further deeply understand the scheme of several types of positional encoding, we choose one sample from SRS1 data to visualize the attention weights of corresponding model variants. As shown in Figure~\ref{fig:position_attention_score}, unlike the widely adopted static and learnable positional embeddings, more specific attention map patterns could be well learned by our contextual positional information generating strategies. Also, it seems that most of the temporal slices would produce uniform attention weights if we remove the positional information. We believe these visualized cases further demonstrate the effectiveness of our contextual information-generating strategies.
\subsubsection{Analyzing Semantic of Time Series Slice Representations}
In this part, we aim to analyze the semantic descriptions of constructed temporal slices encoded by the embedding layer. To achieve this goal, we apply t-SNE to reduce the embedding of each temporal slice on an example selected from AF datasets. For better understanding, we further map each temporal slice to the raw time series. As shown in Figure~\ref{fig:semantic}, we find that the similarity of raw time series data is well-maintained in projected vector space. Such results reflect that the semantics of time series can be accurately represented by their corresponding latent representations. We also observe that the temporal slice nearby in the vector space forms some successive sub-sequences (a.k.a. shapelets) in raw time series. This phenomenon indicates that the embedding learned by the FormerTime retains the potential of preserving the strength of shapelet-based methods.
\subsubsection{Visualization of the Extracted Embeddings}
As shown in Figure~\ref{fig:tsne}, we visualize the extracted feature vector from FormerTime by applying t-SNE to reduce the dimension. Here, we randomly choose examples from SRS1 and UWG datasets. In this figure, each point denotes an example and the same color denotes the corresponding original class labels. This figure suggests that the proposed FormerTime is able to project the data into an easily separable space to ensure good classification results.
\begin{figure}
\centering
\includegraphics[width=0.45\textwidth]{figure_formertime/ts_label}
\vspace{-0.1in}
\caption{Visualization of the representation of whole time series on the SRS1 (left plot) and UW (right plot) datasets, extracted by pooling operation from the last hidden layer.}
\vspace{-0.1in}
\label{fig:tsne}
\end{figure}
\section{Conclusion}
In this work, instead of employing the prevalent convolutional architecture as the main backbones, we proposed FormerTime, a hierarchical transformer network for MTSC tasks. In FormerTime, both the strengths of transformers and CNNs were well absorbed in a unified model for further improving the classification capacity. Specifically, two aspects of vital inductive bias, including multi-scale time series representations and temporal-invariant capacity, are incorporated for enhancing the classification capacity in the MTSC task. Moreover, the terrible computation dilemma incurred by the self-attention mechanism was largely overcome in the proposed FormerTime, whose computation costs are acceptable for very long-sequence time series and large-scale data. Extensive experiments conducted on $10$ publicly available datasets from the UEA archive demonstrated that FormerTime could surpass previous strong baseline methods. In the future, we hope to empower the transferability of FormerTime~\cite{cheng2021learning}.
\begin{acks}
This research was partially supported by grants from the National Key Research and Development Program of China (No. 2021YFF0901003)
\end{acks}
\bibliographystyle{ACM-Reference-Format}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 782 |
\subsection{Further Reading}
Details about nanowire growth can be found in \cite{Badawy2019}.
More information about Majorana zero modes and Andreev bound states in nanowires is discussed in \cite{Lutchyn2018,Stern2013,Prada2012}.
More three-terminal geometry measurements in nanowires are reported in \cite{Anselmetti2019,Gramich2017,Cohen2018}.
\subsection{Methods}
Nanowire growth: Metalorganic vapour-phase epitaxy is used to grow the InSb nanowires used in this work. Devices are made from nanowire with 3-5 $\mu$m length and 120-150 nm diameter.
Fabrication: InSb nanowires are manually transferred from the growth chip to the device chip, which has prefabricated bottom gates, using a micromanipulator. Contact patterns are written using electron beam lithography. In the first lithography cycle, superconducting contact (5 nm NbTi and 60 nm NbTiN) is sputtered onto the nanowire with an angle of 60 degree regarding the chip substrate. In the second lithography cycle, 10 nm Ti and 100 nm Pd is evaporated as normal contacts. Sulfur passivation followed by a gentle argon sputter cleaning is used to remove the native oxide on the nanowire before metal deposition.
Measurements are performed in a dilution refrigerator with multiple stages of filter at a base temperature of 40 mK. Standard low-frequency lock-in technique (77.77 Hz, 5 $\mu$V) is used to measure the devices. To remove the contribution from the measurement circuit, we normalized the differential conductance directly measured with the lock-in amplifiers, as described in Ref.\cite{Yu2021}.
\subsection{Volume and Duration of Study}
To study the delocalized states and quantized ZBCP, 15 chips were fabricated and cooled down, on which more than 40 three-terminal devices were measured. Many of the devices had high contact resistance and were not studied in detail. About half of them were studied in detail, among which four devices showed delocalized states. For the device studied in this paper, more than 9000 datasets were obtained within three months.
\subsection{Data Availability}
Data on several three-terminal devices going beyond what is presented within the paper is available on Zenodo (DOI 10.5281/zenodo.3958243).
\subsection{Author Contributions}
G.B. and E.B. provided the nanowires. P.Y. and J.C. fabricated the devices.
P.Y. performed the measurements. B.W. and T.S. performed numerical simulations. P.Y., B.W., T.S. and S.F.
analyzed the results and wrote the manuscript with contributions from all of the authors.
\subsection{Acknowledgements} We thank S. Gazibegovic for assistance in growing nanowires.
S.F. supported by NSF PIRE-1743717, NSF DMR-1906325, ONR and ARO. T.S. supported by NSF grant No. 2014156.
\bibliographystyle{apsrev4-1}
| {
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} | 1,180 |
In every negotiation, you have to plan out what you plan to give away, and what you plan to receive in return. If you're getting taught that negotiations are only all about getting what you want, drop that information source like a hot potato. The real world doesn't work that way.
Concession planning needs to be done in advance of negotiations. The only way it can be done is through investigative strategies to determine what the other party's needs and wants are, what their motivators are, and what their fears are. The biggest mistake you can make in negotiations is to assume you know the answers to those questions. You know what they say happens when you assume.
Now how is it that some negotiators can give away a little in the form of concession and the other party is thrilled, while other negotiators may give away a lot in the form of concessions, and the other party is somehow still not happy?
There are many answers to this, including that the negotiator who gave away a lot may have given away the wrong things. But another thing that could happen, and happens more often than you think, is that the negotiator packaged the concessions incorrectly. There's a lot of research to support this. But let me convey the point with a personal story.
I ran an experiment for 3 years in a row during the holiday season, and nobody knew it but me.
In Christmas 2013, I gave my wife and kids the normal amount and value of gifts, but I packaged them all in one box for each of them respectively (i.e., they each got one big box full of gifts). All the gifts had the same wrapping on the outside.
In Christmas 2014, I once again gave my wife and kids the same amount and value of gifts, but I packaged them in separate boxes – each gift in its own box – but with the same wrapping. This resulted in many small boxes instead of just a few large ones. All of them still had the same wrapping on the outside however.
In Christmas 2015, I did the same thing as in Christmas 2014 (same number and value of gifts, but packaged them individually into many smaller boxes), but this time I gave each gift a unique wrapping. This resulted in each person getting many small gifts, each with unique wrapping.
Irrespective of age or gender or status in the household, everyone got more excited when the gifts were individually packaged into smaller boxes, giving them more small gifts to open, and even more so when they had different and unique wrapping, because it made them feel special. If the same gifts were aggregated into large boxes and had homogenous wrapping – the same as everyone else's – they got much less excited. This was true for every single person I gave gifts to. This is fascinating stuff.
Did they know that I was doing an experiment? Absolutely not. I watched the tape over and over and marveled at what this meant from a human psychology perspective. This was exactly what I had been practicing and teaching in negotiations seminars and consulting for years.
So what's the big takeaway here? When you are making concessions to a supplier, you should break them up into small chunks. Make them feel like you are making LOTS of concessions, not just one big concession. Give them many small gifts, in other words. And package each one individually – let them know why you are making this concession just for them, based on your understanding and appreciation of their unique wants, needs, and motivators. Don't just give it away, tell them the thought you put behind the concession, and how you wanted to help them. Suppliers will love you for it.
When you read off the summary of the outcome of the negotiation to the supplier at the end of negotiations, read out what concessions you've made in as much line item detail as possible – giving them many small gifts again. Negotiations are all about how you make the other party feel. Make them feel like they've gotten a great deal.
Now conversely, when you list off what they've agreed to concede to you – employ the opposite strategy – because you don't want the supplier feeling like they gave away too much. Lump everything they've agreed to do into broader and more all-encompassing concessions, so they don't feel like they've given so much. Make it seem like they only gave away a few gifts. Their receiving list should be much longer. Why? Because they like it that way.
Keep in mind, I'm not telling you to fool your suppliers, far from it. We're just packaging information strategically, and will still be fully transparent in the process. I'm advising you that there are certain fundamental aspects of human behavior that are pivotal for you to understand if you want to achieve success in negotiations. And this is one of them.
Next post: Be Careful What You Negotiate – It Could Come Back to Bite You! | {
"redpajama_set_name": "RedPajamaC4"
} | 169 |
Q: block execute php script if another one execute it I have the following PHP code:
<?php
$host = "localhost";
$username = "root";
$pw = "root";
$db_name = "marketing";
$Connect = mysqli_connect($host, $username, $pw) or die("Couldn't connect to+ MySQL:<0br>" . mysqli_error($Connect) . "<br>" . mysqli_errno($Connect));
$Db = mysqli_select_db($Connect, $db_name)or die("Couldn't select database:<br>" . mysqli_error($Connect). "<br>" . mysqli_errno($Connect));
mysqli_set_charset($Connect, "utf8");
mysqli_autocommit($Connect,TRUE);
$query1 = "select status from cron_statuses where offset = 0";
$res = mysqli_query($Connect, $query1);
$status = mysqli_fetch_assoc($res);
if (!$status['status']){
$query2 = "update cron_statuses set status = 1 where offset = 0";
$res = mysqli_query($Connect, $query2);
//do something
sleep(20);
$query2 = "update cron_statuses set status = 0 where offset = 0";
$res = mysqli_query($Connect, $query2);
}
else{
echo 'cron blocked';
}
?>
Default value for status = 0. if I run the script it will then update status to 1 and then sleep 20 secs and update the status back to 0.
Whiles sleeping, if the script is run in another tab I would expect the status to equal to 1, and should enter the echo cron_block but if its = 0 it should do the same as the first tab.
A: I can reproduce your case IF I create a table using ENGINE=InnoDB and set autocommit to FALSE. This is my testing code, more or less the same as yours except setting autocommit to FALSE forcefully:
$dbconn = mysqli_connect("localhost","root","password");
$db = mysqli_select_db($dbconn,"test");
mysqli_autocommit($dbconn,FALSE);
$res = mysqli_query($dbconn,"SELECT status FROM test WHERE offset = 0;");
$status = mysqli_fetch_assoc($res);
if ( $status['status'] == 0 ) {
$res = mysqli_query($dbconn,"UPDATE test SET status = 1 WHERE offset = 0;");
sleep(10);
$res = mysqli_query($dbconn,"UPDATE test SET status = 0 WHERE offset = 0;");
}
So please double check your table is using storage engine that support transaction or not, and what's the default autocommit setting.
Best Regards,
Ken
A: the issue because I run the same script in same browser (firefox) with 2 tabs.
when I run the first on firefox and the second in chrome the behaviors went as I expected.
also, when run the first with localhost/script.php and the other 192.10.1.5/script.php on same browser with different tabs the behaviors went as I expected.
I do not know why but the issue not in code.
| {
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Please note that we may no longer collect cards on behalf of clients, nor may we deliver cards to clients.
How will you get your card?
The licensing department will give you a progress update via return sms.
When the card is ready for collection, you have to collect it yourself. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,942 |
{"url":"https:\/\/electronics.stackexchange.com\/questions\/150265\/what-is-the-minimum-supply-voltage-for-the-mc34063e-in-step-up-boost-configura","text":"# What is the minimum supply voltage for the MC34063E in step-up (boost) configuration?\n\nI need help determining the minimum supply voltage specification for the MC34063E in step-up (boost) configuration. I can't tell for sure by reading this datasheet.\n\nFirst, on page 1 they say:\n\nFeatures:\n\n\u2022 ...\n\u2022 Operating from 3 V to 40 V\n\nThen, in page 7, table 8, under section \"Electrical Characteristics - Total Device\", which I copy below, they say that the device start-up voltage ($V_{START-UP}$) is 1.5V, which is the \"minimum power supply voltage at which the internal oscillator begins to work.\"\n\nI understand that the start-up voltage is not necessarily the supply voltage at which the device starts regulating properly. It's the voltage at which oscillation starts. But then, what's the relevance of this information? Why would I need to know that the device starts oscillating at 1.5V if it is only guaranteed to regulate voltage properly at inputs above 3V? If I apply the lowest possible input voltage (3V), that's already above the start-up voltage (1.5V) so it will get the oscillation started anyway.\n\nI understand that this parameter (start-up voltage) is relevant for other devices (such as the MCP1640) in which the start-up voltage is higher than the minimum input voltage. That means we must apply the start-up voltage when the device is initially powered on and then its input voltage may be lowered.\n\nThe specs for the MCP1640 are:\n\n\u2022 Low Start-up Voltage: 0.65V\n\u2022 Operating Input Voltage: 0.35V\n\nBut that's not the case for the MC34063E. Its start-up voltage is lower than its stated minimum input voltage:\n\n\u2022 Start-up voltage: 1.5V\n\u2022 Operating from 3V\n\nMy interpretation is that minimum supply voltage for the MC34063E is really 1.5V and not 3V as stated. Is that correct?\n\nMy question is: What is the minimum input voltage for the MC34063E to operate within its specifications in the step-up (boost) configuration?\n\nAnother thing that is annoying me is that the 3V minimum supply voltage doesn't appear in any other part of the datasheet. It only appears on what I consider to be the \"marketing\" section of the sheet. Is that spec stated in any other \"more technical\" part of the datasheet, such as a table under Electrical Characteristics section and I'm not seeing it?\n\n\u2022 such as the MCP1640) in which the start-up voltage is lower than the minimum input voltage. -> higher ? Jan 21 '15 at 16:51\n\u2022 @Russell - Right: higher! Sorry, I'm all confused after posting this. Corrected. Jan 21 '15 at 16:54\n\u2022 @Russell - or I left the error intentionally to make sure you guys are paying attention to what you're reading :D You passed. Jan 21 '15 at 16:56\n\u2022 I think this question should be closed because it's about reading data sheets and not about electronic design. Right ? :-) :-) :-) :-) :-) :-) :-) . +1 anyway :-) Jan 21 '15 at 17:04\n\u2022 FWIW I have 100,000+ of these working at down to a bit under 3V OK. They were probably mainly LRC brand = Leshan Radio Corp = classic Motorola IP due to a joint venture. At 3V they seem fairly happy. Even slightly below that they start to stop. (Or stop to start?) Jan 21 '15 at 20:30\n\nNever trust a 'typical'. My experience tells me that typical values in a datasheet are the most atypical.\n\nSeriously though, these start-up values are cited as typical with no minimum or maximum. As Russell pointed out, many things are spec'd at 5V, and the threshold voltage line regulation parameter agrees with the front-page spec (3 to 40V).\n\nIf you ever get into a spec-lawyer discussion with a supplier, the most restrictive conditions in the datasheet will apply, measurement conditions matter, and typical values are utterly redundant. (Trust me.)\n\nI would read this datasheet as, \"I should probably start at 5V, maybe go as low as 3V for supply voltage: it may start sucking juice below 3V but the outcome may not be nice. Consider external UVLO. Unit-to-unit variation is possible between 3-5V.\"\n\n\u2022 Oh, boy! That 1.5V is listed under the typical column and I didn't see it. Well spotted. Thanks for the answer +1 Jan 21 '15 at 17:17\n\u2022 Talk about the outcome not being nice, as you mentioned. Just got a batch of MC33063E's from ST and they behaved wildly at input voltages below 2.6V in my step-up converter. Although I had it adjusted to output 5V, the voltage spiked up to 25V without a load. I wasn't expecting that at all, as I had a bunch of 063A's from another manufacturer behaving completely differently. Sometimes we think \"how bad could it be if I use this device just a little bit outside its spec\". Now I know that bad, unexpected things can happen. Jan 21 '15 at 22:14\n\u2022 Oh, the 063E from ST behaved nicely above the 2.6V threshold. Only now I realize what you meant by \"consider external UVLO\". So when input voltage drops, I don't get this sort of behavior (voltage spiking up). Just now I realized the significance of that. But that's a dangerous thing for a regulator to do (voltage spiking up) in a low voltage condition... Jan 21 '15 at 22:18\n\nIf you wish to obtain datasheet wisdom by adumbration you could look at other hints as well :-)\n\nNote fig 12 where they could easily have taken Vin under 5V and have chosen not to do so.\n\n5V is used as reference test Vcc in many cases.\n\nNote that at any sort of current the internal darlington saturation eats a significant amount of your lunch at < 3V Vcc.\n\nThat's an ST data sheet but I think it looks like a redraw of the very old Motorola version. What do other manufacturer's data sheets say?\n\nIn practice I have found that MC34063xxx curl up their toes at slightly under 3V Vcc. I've run them from 3V on up with good results.\n\n\u2022 +1 for the answer - it's really helpful - and for adding a new word to my vocabulary :D Jan 21 '15 at 17:11\n\u2022 By the way, I thought that reading a datasheet = obtain datasheet wisdom by adumbration. Sometimes I feel that reading datasheets is more art than science. Jan 21 '15 at 17:11\n\u2022 The reason I posted this question was that I was able to get 100mA @5V output with 2AA NiMH cells (~2.5V input) from the MC34063A and wanted to go lower, but I was afraid I was in the \"make my day\" area of your classic chart. Now I know I'm certainly in that area. Jan 21 '15 at 17:20\n\u2022 +1 for \"a dumb ration\"... it's almost like \"oxy moron\", I'll start calling people that way immediately!\n\u2013\u00a0user20088\nJan 21 '15 at 21:16\n\nMy interpretation is that minimum supply voltage for the MC34063E is really 1.5V and not 3V as stated. Is that correct?\n\nI read it like this - you are stepping up a supply voltage and the manufacturer says that the chip will work as low as 3V. It says 3V on the front page and that is nearly always a typical figure because the front page of the data sheet tries always to say the nicest things about the device without being dishonest.\n\nLater on it says 5V is the test voltage for the main body of the data sheet's written values (page 6 and 7). This then concerns me as to how far the device will be guaranteed to work under 5V.\n\nI then see \"Figure 12. Supply current vs. input voltage\" and it does not show operation below 5V. That's sealed it for me - I can't expect this device to work as expected below 5V 100% of the time and for 100% of every chip I might buy. In other words I can't realistically design it to operate below 5V unless I'm prepared to test it below 5V and expect failures.\n\nBut, then I notice Figure 17. Voltage inverting converter and it shows it operating at 4.5 volts. I then have to make a decision based on how this circuit works as to whether I can transfer it's good news (4.5 volts) to my circuit (step-up). Maybe I can.\n\nLastly, I go back to where it says the oscillator may start at 1.5 volts and this to me is a warning that maybe if I dropped the voltage to that sort of area strange behavior will occur and I worry because at 1.5 volts any old thing may happen. Take the 1.5 volt operation as a warning that things could go stupidly wrong at too low of a supply voltage.","date":"2021-12-09 11:26:05","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\": 0.37351295351982117, \"perplexity\": 1849.9198601163869}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-49\/segments\/1637964363791.16\/warc\/CC-MAIN-20211209091917-20211209121917-00469.warc.gz\"}"} | null | null |
Mobb Deep Baltimore Soundstage, Baltimore MD, May 21
Photo: Natalie Zina Walschots
By Natalie Zina Walschots
One of the most unexpected performances of the festival may stand as one of its best; about a month before the event, Deathfest organizers and promoters of the Mobb Deep show scheduled to take place at one of Deathfest's venues decided to partner up and allow anyone with passes or single-night tickets into the event.
The result was a resounding success, with an enthusiastic and high-energy crowd made up of both metal and hip-hop fans. The Queens, NY hip-hop duo were in excellent form, feeding off of the energy of the crowd and winning over curious metalheads left and right. Metal and hip-hop are sometimes portrayed as opposing genres despite the long history of crossover and mutual respect between them, and it was a delight to see that connection honoured and represented at this performance.
MARYLAND DEATHFEST
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"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,383 |
Website: https://menabebawy1.github.io/Biology-Website/
I created this website for my AP Biology class. It was created for anyone who was interested in the class and wanted to know more about it. They would simply go to the website and see the themes and get a good idea of what they would be studying. I was going for a clean, minimal, and professional look.
The website includes the main themes of the class and points that go into details about those themes.
The following is a little preview:
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,407 |
namespace fpl {
namespace zooshi {
struct World;
// Class that performs various rendering functions on a world state.
class WorldRenderer {
public:
// Initialize the world renderer. Must be called before any other functions.
void Initialize(World* world);
// Refresh global shader defines with current rendering options.
void RefreshGlobalShaderDefines(World* world);
// Call this before you call RenderWorld - it takes care of clearing
// the frame, setting up the shadowmap, etc.
void RenderPrep(const corgi::CameraInterface& camera,
World* world);
// Render the shadowmap from the current camera.
void RenderShadowMap(const corgi::CameraInterface& camera,
fplbase::Renderer& renderer, World* world);
// Render the world, viewed from the current camera.
void RenderWorld(const corgi::CameraInterface& camera,
fplbase::Renderer& renderer,
World* world);
// Render the shadowmap into the world as a billboard, for debugging.
void DebugShowShadowMap(const corgi::CameraInterface& camera,
fplbase::Renderer& renderer);
// Sets the position of the light source in the world. (Where the light is
// located when generating shdaow maps, etc.)
void SetLightPosition(const mathfu::vec3& light_pos) {
light_camera_.set_position(light_pos);
}
private:
fplbase::Shader* depth_shader_;
fplbase::Shader* depth_skinned_shader_;
fplbase::Shader* textured_shader_;
Camera light_camera_;
fplbase::RenderTarget shadow_map_;
// Create the shadowmap for the current worldstate. Needs to be called
// before RenderWorld.
void CreateShadowMap(const corgi::CameraInterface& camera,
fplbase::Renderer& renderer, World* world);
void SetFogUniforms(fplbase::Shader* shader, World* world);
void SetLightingUniforms(fplbase::Shader* shader, World* world);
};
} // zooshi
} // fpl
#endif // ZOOSHI_WORLD_RENDERER_H_
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,264 |
Tag: Hemingway
Review: Across the River and Into the Trees by Ernest Hemingway. Cross-Generational Romance in Fiction
October 17, 2018 February 4, 2019 hopewellslibraryoflife2 Comments
I'm late to liking Hemingway. I finally discovered I could stand him reading A Moveable Feast in college, then The Green Hills of Africa pre-Peace Corps and finally A Farewell to Arms with my son about a decade ago. Today I'm a fan, thanks to the book I'm reviewing today.
Back in post World War II Italy, real-life Hemingway bet a beautiful young Italian aristocrat–Adriana. A short while ago, I reviewed the non-fiction book on this relationship, Autumn In Venice: Ernest Hemingway and His Last Muse. This then is Hemingway's not-very-fictionalized version of the story.
Colonel, formerly Brigadier General, Richard Cantwell is a mid-life, 50, no longer married, no children. He has an injured hand and arm, but the arm still works. He falls for the beautiful Renata–just 18 years old. (In aristocratic circles this has never been a big deal. He was not seen as "grooming" her or as a pervert or anything.) She enjoys his attention and begins to fall in love. He calls her "daughter," which is a tad cringe-worthy, but he only did so in private or with trusted friends. Yes, I know, I know, but times were different.
The real "Colonel" and the real "Renata"
Her head was on his chest now, and the Colonel said, 'Why did you not want me to take off the tunic?'
'I like to feel the buttons. Is it wrong?'
I loved their romance. I loved that Hemingway, the classic man's man, could be tender in his thoughts. I have to believe their conversations in the story were largely those of the real couple–certainly the Colonel's emotions HAD to be Hemingway's own. The sweet, silly things they said–the way she has him tell her about the war as they lie down together. The joy in holding each other. The gondola rides. It was all like being on the best date ever. I wanted to be Renata, I wanted to feel those military tunic buttons, wanted to be engulfed in the scent of this real man–a man who would never wax anything or anywhere but a car!
'Kiss me first.'
She kissed him kind, and hard, and desperately, and the Colonel could not think about any fights or any picturesque or strange incidents. He only thought of her and how she felt and how close life comes to death when there is ecstasy. And what the hell is ecstasy and what's ecstasy's rank and serial number? And how does her black sweater feel? And who made all her smoothness and delight
'Is she really dead?'
'Deader than Phoebus the Phoenician. But she doesn't know it yet.'
'What would you do if we were together in the Piazza and you saw her?'
'I'd look straight through her to show her how dead she was.'
'Thank you very much,' the girl said. 'You know that another woman, or a woman in memory, is a terrible thing for a young girl to deal with when she is still without experience.'
'There isn't any other woman,' the Colonel told her, and his eyes were bad and remembering. 'Nor is there any woman of memory.'
'Thank you, very much,' the girl said. 'When I look at you I believe it truly. But please never look at me nor think of me like that.'
'Should we hunt her down and hang her to a high tree?' the Colonel said with anticipation.
'No. Let us forget her.'
'She is forgotten,' the Colonel said. And, strangely enough, she was. It was strange because she had been present in the room for a moment, and she had very nearly caused a panic; which is one of the strangest things there is, the Colonel thought. He knew about panics. (Hemingway, Across the River and Into the Trees)
I do have one small complaints–you knew I would, right? He used his then wife as the Colonel's ex-wife, right down to her coming to bed with her hair pinned into pin-curls. That was a cheap, mean shot. Otherwise, I loved every word.
Across the River and Into the Woods is available on Project Gutenberg/Canada for free here. Or, for the book on Amazon click the linked title. Remember, I do not make any money off this blog–not even when you click on a link I provide to Amazon for your convenience.
Read the nonfiction account of the romance that sparked the novel–Autumn in Venice: Ernest Hemingway and His Last Muse. My review is here.
My Mind Wandered….
…as is often the case, to my favorite fictional older wounded man (likely a colonel, too) and his younger woman: Sir Anthony Strallan and Lady Edith Crawley of Downton Abbey. I know, I know, but that was Julian Fellowes doing–Sir Anthony would NEVER have been so unchivilrous! And, yes, I also know, that in the end Edith got to outrank Mary by being a Marchioness–and that is all that really matters….
Uncategorized · Valentine
Review: Autumn in Venice: Hemingway & His Last Muse. Literary Cross-Generational Romance
August 13, 2018 hopewellslibraryoflife5 Comments
Ernest Hemingway, the image of American machismo from the 1920s until his death in the early 1960s was not much for monogamy. Even with his fourth wife, in the post-World War II era, he still had a roving eye and well-greased zipper.
In 1948, Hemingway and his fourth wife, Mary Welsh, visited Italy. In Venice they were visiting with the Ivancich family and Ernest's roving eye landed on the family's 18 year old daughter, Adriana. Yes, she was "legal," as we'd say today. And, about to turn 50, Hemingway was ripe for a bright red sports car, a tummy tuck and a much younger Mrs.
Ernest and Adriana
Autumn in Venice tells the story of this odd relationship. Was it physical? Probably to some extent. "Papa" and the young woman he called "Daughter" had a hold on each other to be sure, but while it was fun and slightly intoxicating to have the attention of a great man at only 18, the relationship was more one-sided. For Hemingway, Adriana became an obsession. She was a "muse" in the classical sense of that–she invigorated and mentally (and, true to any mid-life crisis, physically) stimulated him. He got his groove back we'd say today and began writing again.
Ernest and wife Mary
But, wait! Wasn't he married? YES. While Mary Hemingway, (nine years younger than her husband), like all of Hemingway's wives, was devoted to him in ways most women wouldn't be today, she did her best to ignore it all for as long as possible. Until she couldn't any longer. [Sidebar: I was amazed to read Hemingway writing to his wife what brand/color # of hair dye he wanted her to use next and that, in spite of his young friend, he was anticipating the effect this color would have when debuted by her wearing only her new mink coat!]
With Hemingway writing again he naturally chose to write about, wait for it, a 50-something "Colonel" and his young lover who was a dead ringer for, you guessed it! Adriana. The book, Across the River and Into the Trees, owed it's title to Stonewall Jackson, but the rest was pure romantic obsession on loving Papa's part. This is when it all hit the fan. The press got involved–at least in Venice. Adriana, expected to make a great marriage by her aristocratic family, was now in danger of being labeled damaged goods. Hemingway pulled out all the stops to postpone the book's publication in Italy and France to protect his "daughter," Finally, Mary had enough of it all and put her dainty, wifely, foot down–amazingly, she'd even tolerated Adriana and her mother at the Hemingway's Cuban home! She put up with it because Ernest was working steadily. But even near-saints snap on occasion. An ultimatium got her husband's attention at last.
All good things must come to an end and eventually, Adriana married, but divorced, then married again and got it "right enough" to put Hemingway mostly away. As for Ernest, the obsession seemed to finally lessen a little. He wrote The Old Man of the Sea, (for which Adriana again designed the cover), won both Pulitzer and the Nobel Prizes, and wrote Islands in the Stream, which was published a few years after his death. Then he and Mary were in a plane crash and the world thought they were dead. Remarkably, he was in a second plane crash the next day! We all know his tragic ending, but the good news is, that Mary stayed around and got to be the widowed Mrs. Hemingway and control a lot of things after his death. I supposed that's "good news." Poor Adriana took the same exit as Ernest though. Sad.
I thought it sad that all that was really available for depression and axiety was horrific electric shock treatment. I wonder if any of this would have happened if Hemingway had had access to modern anti-depressants. But, would they have robbed him of his creativity? His drinking was so out-of-control at various points in his life that he was clearly "self-medicating."
Mary seems to have been wise enough to understand things he could control and things he could not. He was blessed to have a wife like that. She knew his talent, knew that his stability depended upon his work going well. She was patient, but her feelings were trampled upon time and time again–as were those of each Mrs. Hemingway in turn. But, great men have always gotten away with that and not only back in the day when a women's best career choice was to be the wife of a very successful and talented man.
As for Adriana, she was a spoiled girl whose mother couldn't really control her. And, in 1948, aristocratic young women were still married off to older men–albeit not those with a wife in tow. It is doubtful though that her family would have approved the match had Hemingway dumped Mary. But she married an older man the first time–and older man who took her to Africa even, so I wonder if she didn't have regrets at that point. Sad.
Autumn in Venice: Ernest Hemingway and his Last Muse by Adrea Di Robilant | {
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{"url":"https:\/\/www.studypug.com\/pre-calculus\/square-and-square-roots","text":"# Square and square roots\n\n## What is a square root?\n\nTo explain square roots, let\u2019s take a step back and remember what it means to square a number. To square is to raise the number to the second power. Square roots are the opposite of that, and is actually the inverse operation of squaring. To square root is to find the two identical factors of a number.\n\n## How to find the square root of a number\n\nFor numbers that are perfect squares, you can find whole numbers as answers. However, for numbers that aren\u2019t perfect squares, you\u2019ll have to use a method that involves estimation (or you can use a table of square and square roots).\n\n## Finding square root of perfect square numbers\n\nLet\u2019s first take a look at this question here:\n\nWhat is the square root of 64? If you have a calculator, you can always just punch in it and get the answer. But do you know how to find the square root of a number without a calculator?\n\nNow, if you do remember your perfect squared numbers, the root of 64 is just eight. Eight times eight gives you 64. But let's say you can\u2019t freely recall perfect numbers. How would do we do this from scratch?\n\nFirst, you will have to find all the prime factors of 64. So, let's go ahead and do that:\n\nImagine that the question now becomes 2x2x2x2x2x2\u2014 2 is multiplied 6 times here. So we\u2019ve just determined that 64 is just a square root of six 2s, all multiplied together.\n\nBefore we move on, we must remember that the radical sign actually means \u201cthe square root\u201d. The square root symbol should really be written with a tiny little two here:\n\nSince it\u2019s a square root, you can pick a pair of identical numbers to work with and bring them out from under the radical. In this case, we\u2019ll take out a 2 from the first pair of 2s, another 2 from the second pair, and another 2 from the last pair. It should look something like this:\n\nNow if you multiply the 2s with one another, what do you get? You\u2019ll find that you get 8, which is exactly the same as what you would have remember if you knew your perfect squares. However, this is the correct way to find the square root of a number without memorization.\n\n## Finding square root of numbers that aren\u2019t perfect squares\n\nThe basic method to find the square root of a number that is not a perfect square is as follows:\n\n1. Estimate: Pick a number that if you square comes close to, but is less than, the square root of the number you\u2019re trying to find.\n\n2. Divide: Divide the number that you are finding the squared root for with the number you picked in step 1\n\n3. Average: Take the average of the number you got in step 2 and the square root\n\n4. Repeat: Repeat steps 2 and 3 until the number is accurate enough for you\n\nNow you\u2019ve learned how to find the square root for numbers that both are and are not perfect squares. Continue on with our lessons to learn how to deal with different radical numbers examples.\n\n### Square and square roots\n\nTo square is to raise the number to the second power. In other words, to square is to multiply the number by itself. Square root is the inverse operation of squaring. To square root is to find the two identical factors of a number.\n\n#### Lessons\n\nTo square:\nRaise the number to the second power\nEx: ${5^2}$= $5\\times 5 = 25$\n${8^2}$= $8\\times 8 = 64$\n\nTo square root:\nFinding the two identical factors\nEx: $\\sqrt{16}$ = $\\sqrt{4\\times 4}$ = 4\n$\\sqrt{49}$ = $\\sqrt{7\\times 7}$ = 7\n\nPerfect squares numbers:\n${0^2}$ = 0\n${1^2}$ = 1\n${2^2}$ = 4\n${3^2}$ = 9\n${4^2}$ = 16\n${5^2}$ = 25\n${6^2}$ = 36\n${7^2}$ = 49\n${8^2}$ = 64\n${9^2}$ = 81\n& so on... {100, 121, 144, 169, 196...}\n\n\u2022 1.\nUnderstanding the negative square roots of the following\na)\n$\\sqrt{225}$ \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 $-\\sqrt{225}$ \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 $\\sqrt{-225}$\n\n\u2022 2.\nFind the square roots\na)\n$\\sqrt{64}$\n\nb)\n$-\\sqrt{676}$\n\nc)\n$\\sqrt{-81}$","date":"2018-05-27 05:24:25","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 24, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.746191143989563, \"perplexity\": 262.515289681677}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-22\/segments\/1526794868003.97\/warc\/CC-MAIN-20180527044401-20180527064401-00456.warc.gz\"}"} | null | null |
Spider-Man Returns!
Excelsior! Spider-Man has rejoined the fold at Marvel Studios! Spider-Man, the glaringly absent Avenger, has now been brought into the Marvel Cinematic Universe!
What's that? He wasn't part of it already? Yes! Back in the late 1990's, Marvel Comics was still an independent company and made two deals with Sony Pictures and 20th Century Fox to produce theatrical films based on Spider-Man and X-Men, its biggest franchises. These deals gave the studios the rights to make films as long as they kept doing so. This led to two gigantic franchises that, while they provided cash for Marvel, were less lucrative than they could have been. So Marvel set about creating its own Cinematic Universe using the characters it hadn't sold off.
Wall Street felt that the leftover characters were not going to be successful and largely wrote off the endeavor. After the humongous success of Iron Man, however, they couldn't write off Marvel for much longer. Soon Disney came calling and bought Marvel Comics outright for what Wall Street thought was too much money. Sure a lesser title like Iron Man had been successful, but there couldn't be much more to mine, right?
Wall Street was wrong yet again. Marvel Studios has consistently produced films that have grossed BILLIONS with no end in sight. The success of Guardians of the Galaxy which was a relatively unknown commodity prior to this summer made everyone take notice. At this point, Marvel could probably reboot Howard the Duck into a successful property.
Enter Spider-Man. Sony Pictures made another Spider-Man film this summer because it had to and the product suffered at the box office. After an unknown Guardians beat the established Spider-Man head to head, it was only a matter of time before Sony would rethink things. And they have in a big way- Spider-Man will now be a part of the Marvel Cinematic Universe. Sony will still produce its films, but they will be made in concert with Marvel's films. Spider-Man will also be able to appear in Marvel's Avengers films as well. It's long overdue! Welcome home, Spidey!
Labels: Movies
The Story of DISNEYLAND: What's In A Name?
The Disney Brothers Studio
Quackaroonie!
Walt Disney, Grandfather
The DISNEYLAND Art Corner
Disney Legends #18 & #19: The Sherman Brothers
The Story of DISNEYLAND: "Disneylandia"
Flying Saucers at DISNEYLAND
The Mouse Factory
A Vision of Perfection
The Story of DISNEYLAND: Mickey Mouse Park
Anaheim Vacationland: Stovall's Apollo Inn
The Disney Phone Company
Joss Whedon's Toy Story
Happy Birthday, Disney California Adventure!
The Story of DISNEYLAND: Waiting on the World
The Disney Sunday Movie
Marvel's The X-Men
The Wonders of Fantasound!
Medfield! Medfield! Rah! Rah! Rah! | {
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} | 3,059 |
<?php
namespace Drupal\Tests\wmcontent\Kernel;
use Symfony\Component\Routing\RouterInterface;
/**
* @covers \Drupal\wmcontent\Routing\WmContentRouteSubscriber
*/
class WmContentRoutesTest extends WmContentTestBase
{
/** @var RouterInterface */
protected $router;
protected function setUp()
{
parent::setUp();
$this->router = $this->container->get('router');
// Rebuild routes
$this->container->get('router.builder')->rebuild();
}
public function testAreRoutesAdded(): void
{
$routeNames = [
sprintf('entity.%s.wmcontent_overview', self::ENTITY_TYPE_ID),
sprintf('entity.%s.wmcontent_add', self::ENTITY_TYPE_ID),
sprintf('entity.%s.wmcontent_edit', self::ENTITY_TYPE_ID),
sprintf('entity.%s.wmcontent_delete', self::ENTITY_TYPE_ID),
];
foreach ($routeNames as $routeName) {
self::assertNotNull(
$this->router->getRouteCollection()->get($routeName),
sprintf("Route with name '%s' is not added to host entity type with ID '%s'", $routeName, self::ENTITY_TYPE_ID)
);
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,598 |
Q: PyLint Error: Probably a beginner's mistake I know this might be a over repeated question but I'm having troubles with package import process in python for VSCode.
I don't really understand the logic behind the error that keeps popping out although i pip install the packages i need.
For this specific task, I'm trying to import matlib to plot a chart of some crypto time series i already acquired.
I don't know why, no matter what i do ( even setting autocomplete paths ecc in settings.json) I keep getting this error: {
"message": "Unable to import 'matplotlib'".
I'm not using a virtualenv for the simple reason I don't know how to and this might complicate things for a beginner like me.
The complete error code is this.
{
"resource": "/c:/Users/Main Client/Documents/CRYPTOBOT/api_request/request.py",
"owner": "python",
"code": "import-error",
"severity": 8,
"message": "Unable to import 'matplotlib'",
"source": "pylint",
"startLineNumber": 12,
"startColumn": 1,
"endLineNumber": 12,
"endColumn": 1
}
If anyone could kindly and patiently explain why this happens I might learn how to avoid this in future. Please don't tell me that I have to do everything up from scratch because I think I could cry
A: 1.Check if you've installed matplotlib to current used python environment. Open a new integrated Terminal and run pip show matplotlib to see its location. If it's not under the current_used_python\lib\site-packages, reinstall it.
2.If the location is right, check if the module is complete and not lack of components. Turn to the folder site-packages, delete files related to matplotlib, then reinstall it to see if the error goes away.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,129 |
Q: Writing service in clojure I am writing a simple service to retrieve images from different sources (instagram, flickr, google)
Currently every service served in a separate .clj file with bunch of functions, both common and specific.
I am thinking about introducing protocol ImageService for that and each specific service will implement that protocol. This way we could add documentation at the protocol level and reuse common methods.
What are pros and cons with using protocols for such type of problem? How do we create specific implementation for service: deftype, defrecord or reify? What is idiomatic approach in clojure?
A: We've had a great deal of success at my company using protocols over external services just like you described. Protocols are nice because they allow you to write calling code in a single agnostic fashion, and also do dependency injection for easy testing (with mock implementations of your protocol). The main downside of protocols I've run into is that you can't have (shared) default implementations, otherwise I"m very happy with them.
deftype and defrecord differ in several ways, in practice the most prominent difference is that types generated with defrecord can also behave like maps:
(defrecord Foo [bar])
(->Foo 1) ; or (Foo. 1)
; => #user.Foo{:bar 1}
(assoc (Foo. 1) :norf 2)
; => #user.Foo{:bar 1, :norf 2}
Up to you if you need this behavior or not. reify just creates an 'anonymous' implementation of your protocol, we tend not to use it much and instead use a pattern like
(deftype MyService [args...])
; Our own public constructor
(defn ->my-service [config]
(->MyService (parse-config config)))
; etc ...
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,264 |
\section{Introduction and summary}
The quantum corrections in ${\mathcal N}\!=\!2$ theories have received a great deal of attention. These are of two types: corrections proportional to the inverse tension of the string and corrections proportional to the string coupling constant. The former arise from perturbative and instantonic world-sheet corrections and are encoded in higher derivative terms in the ten-dimensional supergravity action, while the latter come from string loops and brane instantons. Perturbative low energy effective actions are expanded in a double perturbation series in the inverse tension and the coupling constant.
These corrections not only affect the moduli spaces of ${\mathcal N}\!=\!2$ theories, but are manifested in the higher-derivative couplings. A better control of these couplings is hence essential, as is demonstrated by the study of terms involving the Weyl chiral (supegravity) super field $W$. However most of the other (higher-derivative) couplings in ${\mathcal N}\!=\!2$ theories and their relation to string theory remain largely unexplored. We make some steps in this directions. Our study is mostly restricted to string one loop results and Calabi-Yau compactifications, and will not cover gauged ${\mathcal N}\!=\!2$ theories.
\medskip
\noindent
The better-understood structures, involving $W$ holomorphically, are captured by the topological string theory. In particular, the F-term in the low energy effective action in four dimensions is related to the scattering amplitude of 2 selfdual gravitons and $(2g - 2)$ self-dual graviphotons in the zero-momentum limit and is computed by the genus-$g$ contribution $F_g$ to the topological string partition function \cite{Bershadsky:1993cx, Antoniadis:1993ze}. Crucially, the genus-$g$ contribution $F_g$ also determines the partition functions of ${\mathcal N}\!=\!2$ global gauge theories.
There exists, however, a continuous deformation of the gauge theory which uses nontrivially the manifest SU(2) R-symmetry of theory. This is what happens in the so-called Omega background. \cite{Nekrasov:2002qd, Nekrasov:2003rj}.The two-parameter gauge theory partition function in the Omega background has been computed recently and reduces to the standard gauge theory partition function only when the two parameters are set equal. It is an outstanding open problem to find string theory realisation of these backgrounds and understand the extension of the genus-$g$ function $F_g$ which determines the general ${\mathcal N}\!=\!2$ partition function, and which should involve scattering amplitude among 2 gravitons, $(2g - 2)$ graviphotons, and $2n$ gauge fields in vector multiplets. Theses considerations have lead to a recent interest in explicit realisation of couplings $F_{g,n} W^{2g} V^{2n}$ \cite{Morales:1996bp, Antoniadis:2010iq, Nakayama:2011be, Antoniadis:2013bja, Antoniadis:2013mna}.
Let us recall that the genus one partition function $F_1$ is special due to the fact that it is the only perturbative four-dimensional contribution, which survives the five-dimensional decompactification limit. The ten/eleven dimensional origin of these couplings is related to M5 brane anomalies and they lift to certain eight-derivative terms in the effective action \cite{Ferrara:1996hh, Antoniadis:1997eg}. Until very recently only the gravitational part of these couplings was known (and it was checked that their reduction on CY manifolds does correctly reproduce $F_1$). At present, we have a much better control of the more general form of the couplings in general string backgrounds with fluxes turned on, so that an explicit calculation of the one-loop four-, six- and eight-derivative couplings in ${\mathcal N}\!=\!2$ theories, which should lead to the generalisation of $F_1$, is now within the reach.
\medskip
\noindent
In the four dimensional setting, recent developments in going beyond chiral couplings described by integrals over half of superpace \cite{deWit:2010za}, allow us to extend the list of higher derivative terms in several ways. The new couplings are constrained by ${\mathcal N}\!=\!2$ supersymmetry to be governed by real functions of the four dimensional chiral fields. The latter naturally include vector multiplets and two types of chiral backgrounds, one of which is the Weyl background, $W^{2}$, introduced above. The second chiral background we consider is constructed out of the components of a tensor multiplet containing the NS two-form, the so called universal tensor multiplet\footnote{While there is no obstacle in considering a background of an arbitrary number of tensor multiplets in principle, we restrict our considerations to the universal tensor multiplet. We therefore ignore here all the complex deformations of the internal Calabi-Yau; including these in the reduction should yield couplings for generic
hyper-
matter.} and contains four derivative terms on its
components, such as $(\nabla H)^2$, where $H = d B$ and $B$ is the NS two-form. These ingredients then
allow us to describe couplings which are characterised by polynomials of the type $[F^2 + R^2 + (\nabla H)^2]^{n}$, generalising the purely gravitational $R^2$ couplings discussed above. The function of the vector multiplet scalars and Weyl background controlling these couplings directly corresponds to the extended couplings $F_{g,n} W^{2g} V^{2n}$, when the tensor multiplet is ignored. Inclusion of the latter results to more general couplings that have not yet been discussed in the literature.
\medskip
\noindent
From a quantum gravity point of view, higher-derivative corrections serve as a means of probing string theory at a fundamental level. Even though the complete expansion involves all fields of the theory, so far the attention has been mostly concentrated on the gravitational action. In particular, the one-loop eight derivative $R^4$ ($\mathcal{O}(\alpha'^3)$) terms stand out among the stringy quantum corrections. Due to being connected to anomaly cancellation, they are not renormalised at higher loops and survive the eleven-dimensional strong coupling limit. These couplings also play a special role in Calabi-Yau reductions to four-dimensional ${\mathcal N}\!=\!2$ theories. Firstly, they have been instrumental in understanding the perturbative corrections to the metrics on moduli spaces.
In addition, they give rise to the four-derivative $R^2$ couplings, and as mentioned above agree with $F_1 W^2$.
In order to understand the stringy origin of more general higher derivative couplings in ${\mathcal N}\!=\!2$ theories,
one needs to go beyond the purely gravitational couplings in ten dimensions. In the NS-NS sector of string theory, $H^2R^3$ couplings are specified by a five-point function \cite{Peeters:2001ub}. Direct amplitude calculations beyond this order are exceedingly difficult, but recent progress in classification of string backgrounds using the generalised complex geometry and T-duality covariance provide rather powerful constrains on the structure of the quantum corrections in the effective actions. A partial result for the six-point function, obtained recently, together with T-duality constraints and the heterotic/type II duality beyond leading order, allows to recover the ten-dimensional perturbative action almost entirely \cite{Liu:2013dna} (the few yet unfixed terms mostly vanish in CY backgrounds and hence are not relevant for the current project). The eleven-dimensional lift of the modified coupling leads to the inclusion of the M-theory four-form field strength; the subsequent reduction on a non-
trivial KK monopole background allows to incorporate the full set of RR fields in the one-loop eight-derivative couplings. This knowledge will be crucially used for obtaining the relevant four-dimensional ${\mathcal N}\!=\!2$ couplings.
\medskip
\noindent
The goal of this paper is to bring together some of these recent developments. In the process, we shall:
\begin{itemize}
\item[ ] Confirm and specify some of the predictions of general ${\mathcal N}\!=\!2$ considerations and fix the a priori arbitrary quantities constrained solely by supersymmetry in terms of Calabi-Yau data
\item[ ] Discover new terms and couplings that have not been previously considered
\item[ ] Provide some tests and justification for the proposed lift of type IIA $R^4$ terms to eleven dimensions
\end{itemize}
A brief comment on the last point. Since the lift from ten to eleven dimensions involves a strong coupling limit, ones is normally suspicious of simple-minded arguments associated with just replacing the string theory NS three-form $H$ by a four-form $G$. In ${\mathcal N}\!=\!2$ theories however the three- and four-form give rise to fields in the same super multiplet, namely the (real part of the) scalars $u^I$ and the vectors $A^I$ in the vector matter respectively (here the index $I$ spans the vector multiplets). Hence verifying that the respective couplings involving $u^I$ ad $A^I$ are supersymmetric completions of each other provided a test of the lifting procedure.
\medskip
\noindent
We conclude this section by a summary of our results. A variety of four dimensional higher derivative
terms of the type $[F^2 + R^2 + (\nabla H)^2]^{n}$ are characterised by giving the relevant functions of
four dimensional chiral superfields that control them. From the point of view of the CY reduction, the
order of derivatives of all terms in four dimensions is controlled solely by the power of the CY Riemann
tensor appearing in the internal integrals. We therefore find that the eight, six and four derivative
terms are controlled by the possible integrals involving none, one or two powers of the internal Riemann tensor, respectively.
We find, in particular, that only the lowest order K\"ahler potential is relevant for the eight derivative
terms, since this is the natural real function of vector multiplet moduli arising in Calabi-Yau compactifications,
describing the total volume of the internal manifold.
At lower orders in derivatives, the K\"ahler potential still appears as part of the functions describing the various
invariants, combined with the Riemann tensor on the CY manifold $X$, denoted by $R_{mnpq}$. Given that all traces
of the latter vanish, the relevant internal integrals must necessarily contain the harmonic forms on the CY manifold.
In the case at hand, the relevant forms are the $h^{(1,1)}$ two-forms $\omega_I \in H^2(X, \mathbb{Z})$, where
$I,\, J = 1, \dots, h^{(1,1)}$, since we ignore the hypermultiplets arising from the $(2,1)$ cohomology.
We then obtain the following tensorial objects
\begin{gather}
{\mathcal R}_{IJ} = \int_{X} R_{mnpq}\,\omega_{I}{}^{mn}\omega_{J}{}^{pq} \,,
\nonumber\\
X_{IJ} = \int_X \epsilon_{m n m_1 \ldots m_4} \epsilon_{pq n_1 \ldots n_4}
R^{m_1m_2n_1n_2}R^{m_3 m_4 n_3n_4} \,\, \omega_I\,^{mn} \, \omega_J\,^{pq} \label{eq:R-expr}\,,
\end{gather}
which control all the couplings that we were able to describe within ${\mathcal N}\!=\!2$ supergravity at six- and four-derivative order respectively. Similar to the standard derivation of the lowest order K\"ahler potential, one can deduce the existence of corresponding real functions whose derivatives lead to the the couplings \eqref{eq:R-expr}. Finally, the inclusion of the Weyl and tensor superfields
through additional multiplicative factors leads to the functions that characterise the corresponding
couplings involving $R^2$ and $(\nabla H)^2$ respectively. For example, the $R^2 F^4$ and $R^2 F^2$
couplings lead to the functions
\begin{align}
R^2 (\nabla F)^2 \quad \Rightarrow \quad &\, A_{\sf w} \, \mathrm{e}^{2\,{\mathcal K}(Y ,\bar{Y})}\,,
\nonumber\\
R^2 F^2 \quad \Rightarrow \quad &\,
-\mathrm{i}\,\frac{\bar{A}_{\sf w}}{(\bar{Y}^0)^2} \,{\mathcal R}_{IJ}
\left( \frac{Y^I}{Y^0} - \frac{\bar{Y}^I}{\bar{Y}^0}\right)\,\left( \frac{Y^J}{Y^0} + \frac{\bar{Y}^J}{\bar{Y}^0}\right)\,,
\end{align}
where $A_{\sf w}$ is the scalar in the Weyl multiplet and the $Y^I$, $Y^0$ are standard vector multiplet projective coordinates, so that $z^I = Y^I/Y^0$, and
${\mathcal K}(Y ,\bar{Y})$ is the lowest order K\"ahler potential.
There are further invariants arising from the reduction, that cannot be currently described in
components\footnote{Note, however the final comments in section \ref{sec:H2F2}, which may lead to more general couplings.}
within supergravity, and are associated to terms involving $H^{2n}$ with $n$ odd, such as $H^2 F^2$, $H^2 R^2$ etc.
We comment on some of these terms, either giving the leading terms that characterise them, or pointing out their
apparent absence.
An inventory of the four- and six-derivative couplings studied in this paper is given in Table \ref{tbl:sum}.
The first line in this table describes the terms based only on holomorphic functions of vector moduli and the
two chiral backgrounds. These are the only couplings that are controlled by a topological quantity, namely the vector of second Chern classes of the Calabi-Yau four-cycles. The gravitational $R^2$ coupling is the first nontrivial
coupling $F_{g} W^{2g}$ above, related to the topological string partition function
\cite{Bershadsky:1993cx, Antoniadis:1993ze}. The second, third and fourth lines correspond to the
non-holomorphic couplings of \cite{deWit:2010za}, where the tensor multiplet background is included. Note the
diagonal of underlined invariants of the type $R^2 F^{2n}$, which correspond to the first nontrivial couplings
$F_{g,n} W^{2g} V^{2n}$, for $g=1$, recently discussed in
\cite{Antoniadis:2010iq, Antoniadis:2013bja, Antoniadis:2013mna}. The diagonal of the blue boxed invariants gives the one-loop copings of vector multiplets only, controlled by the tensors \eqref{eq:R-expr} and are the ones defining the structure of all other invariants in each line. To the best of our knowledge, the string original of such couplings have not been discussed in the literature. The remaining invariants in the last line
can arise a priori and their description remains unknown within supergravity. We comment on the expected
structure of some of these below\footnote{In fact, we find that some of these couplings involving the tensor
multiplet seem to be missing in the specific compactification we consider, but cannot be excluded if more
tensor/hyper multiplets are considered.}.
\begin{table}[t]
\centering
{\renewcommand{\arraystretch}{1.7}
\begin{tabular}{|c|c|c|c|}
\hline
\backslashbox{invariants}{derivatives} & 4 \, & 6 \,& 8 \\ \hline
$ F(X, A_{\sf w}, A_{\sf t})$ & \underline{$R^2$},\,\,$(\nabla H)^2$ & -- & --
\\ \hline
$\big[ F^2 + R^2 + (\nabla H)^2 \big]^2$ & \colorbox{LightBlue}{$(\nabla F)^2$} &
\underline{$R^2 F^2$},\, $(\nabla H)^2\, F^2$ & $R^4$,\, $R^2 (\nabla H)^2$,\, $(\nabla H)^4$
\\ \hline
$\big[ F^2 + R^2 + (\nabla H)^2 \big]^3$ & -- &\colorbox{LightBlue}{$F^2(\nabla F)^2$} & \underline{$R^2 (\nabla F)^2$},\, $(\nabla H)^2 (\nabla F)^2$
\\ \hline
$\big[ F^2 + R^2 + (\nabla H)^2 \big]^4$ & -- & -- & \colorbox{LightBlue}{$(\nabla F)^4$}
\\ \hline
Unknown & $H^2 F^2$ & $H^2 F^4$ & $R^4$,\, $H^6 F^2$,\, $H^2 F^6$ \\ \hline
\end{tabular}
}
\caption{A summary of higher-derivative couplings discussed here. The first row corresponds to chiral couplings
involving the Weyl and tensor multiplets. The next three rows display the known non-chiral ${\mathcal N}\!=\!2$ invariants
at each order of derivatives, while the last row summarises the currently unknown invariants that can arise.
The double appearance of $R^4$ at the eight-derivative level corresponds to two different invariants
(see \eqref{eq:R4-red} below). }
\label{tbl:sum}
\end{table}
\medskip
\noindent
The structure of the paper is as follows: In the next section we shall review briefly the one-loop $R^4$ couplings as well as some of our conventions and the reduction ansatze. The structure of known higher derivative couplings in four-dimensional ${\mathcal N}\!=\!2$ theories is presented in sec. \ref{sec:n2d4}. We then proceed to consider the various higher derivative terms arising from the Calabi-Yau compactification of the one-loop term, organised by the order of derivatives. Hence, in section \ref{sec:eightder} we consider the eight derivative terms, while in sections \ref{sec:sixder} and \ref{sec:fourder} we discuss the six and four derivative invariants respectively. Some open questions are listed in section \ref{sec:open}. The extended appendices contain further technical details of the structures appearing in the main text. In particular, appendix \ref{sec_A:R4in10d} contains the fully explicit expressions for the quartic one-loop terms in 10D. Appendices \ref{App:4D-chiral-multiplets}
and
\ref{sec:tensor} deal with chiral
couplings of general chiral multiplets and the composite chiral background of the tensor multiplet respectively. Finally, appendix \ref{app:kinetic} reviews the structure of the kinetic chiral multiplet and the various invariants that can be constructed based on it, up to the eight derivative level.
\section{Higher derivative terms in Type II theories}
The starting point for our considerations is the ten-dimensional eight-derivative terms that arise
in Type II string theories. The structure of the gravitational part of these couplings has been
known for a long time, but the coupling to the remaining Type II massless fields was not explicitly
known. Recently, a more concrete understanding of the terms involving the NS three-form field strength,
$H$, has been achieved \cite{Liu:2013dna}. The structure of the corresponding terms involving RR gauge
fields is constrained to a large extend, using arguments based on the eleven dimensional uplift to M-theory.
Upon reduction on a Calabi-Yau manifold without turning on any internal fluxes, the NS three form
leads to two types of objects in the four dimensional effective theory, namely a lower dimensional
three-form field strength and $h^{1,1}$ scalars. The former is naturally part of a tensor
multiplet\footnote{Upon of the two-form gauge field to a scalar, this
leads to the so called universal hypermultiplet, but we will not consider this operation here.},
while the latter are part of vector multiplets in Type IIA and tensor/hyper multiplets in Type IIB.
In this section, we start by giving an overview of the ten-dimensional eight-derivative terms in
section \ref{sec:10-act}, from which all the lower dimensional higher-derivative terms arise. In
section \ref{sec:CY-red} we then turn to a discussion of the reduction procedure on Calabi-Yau
three-folds, which is central to the derivation of four dimensional couplings.
\subsection{The eight-derivative terms in ten dimensions}
\label{sec:10-act}
In summarising the structure of $R^4$ with the NS three-form $H$ included, it is most convenient to start by introducing the connection with torsion which reads in components
\begin{equation}
\Omega_{\pm \,\mu_1}{}^{\nu_1\nu_2}=\Omega_{\mu_1}{}^{\nu_1\nu_2} \pm \ft12H_{\mu_1}{}^{\nu_1\nu_2}.
\end{equation}
The curvature computed out of $\Omega_{\pm}$ is then
\begin{equation}
R(\Omega_{\pm})=R \pm \ft12d\mathcal H+\ft14\mathcal H\wedge\mathcal H,\qquad
\mathcal H^{\nu_1\nu_2}=H_{\mu_1}{}^{\nu_1\nu_2}dx^\mu.
\end{equation}
Denoting the Riemann tensor by $R_{\mu\nu}{}^{\nu_1\nu_2}$ , we may write in components
\begin{equation}
R(\Omega_{\pm})_{\mu_1\mu_2}{}^{\nu_1\nu_2}=R_{\mu_1\mu_2}{}^{\nu_1\nu_2}
\pm \nabla_{[\mu_1}H_{\mu_2]}{}^{\nu_1\nu_2}+\ft12H_{[\mu_1}{}^{\nu_1\nu_3}H_{\mu_2]\nu_3}{}^\beta.
\end{equation}
Note that the first and last term in this expression satisfy the pair exchange property,
while the second term is antisymmetric under pair exchange due to the Bianchi identity on
the three-form.
The Type II eight-derivative terms can be written in terms of two standard "$\mathcal{N}=1$
superinvariants", defined as
\begin{align}
J_0(\Omega) = &\, \left(t_8 t_8 + \ft18\, \epsilon_{10} \epsilon_{10}\right)R^4
\equiv \left(t_8 t_8 + \ft18 \epsilon_{10} \epsilon_{10}\right)^{\nu_1\dots\nu_8}_{\mu_1\dots\mu_8}
R^{\mu_1 \mu_2}{}_{\nu_1\nu_2} \dots R^{\mu_7 \mu_8}{}_{\nu_7\nu_8} \,,
\nonumber\\
J_1(\Omega) = &\, t_8 t_8 R^4 - \frac14\, \epsilon_{10} t_8 B R^4
\equiv
t_8 t_8 R^4 - \frac14 \,t_8{}_{\mu_1\dots\mu_8} B\wedge R^{\mu_1 \mu_2} \wedge \dots \wedge R^{\mu_7 \mu_8}
\,,
\label{eq:R4inv}
\end{align}
which provide a convenient way of encoding the kinematic structure of $R^4$ terms. The tensor $t_8$
and the associated tensorial structures appearing here are spelled out in appendix \ref{sec_A:R4in10d}.
Note that at this stage the terms \eqref{eq:R4inv} are build from Levi-Civita connections only,
and the three-from $H$ is not included.
It has been argued in \cite{Liu:2013dna} that these will be completed with the $B$-field as follows:
\begin{subequations}
\begin{eqnarray}
\label{superinv}
J_0(\Omega) &\longrightarrow&
J_0 (\Omega_+) + \Delta J_0(\Omega_+, H) \\
&& = \left(t_8 t_8 + \frac18 \epsilon_{10} \epsilon_{10}\right)R^4(\Omega_+)
+ \frac 13 \epsilon_{10} \epsilon_{10} H^2 R^3 (\Omega_+) + ... \nonumber \\
J_1(\Omega) &\longrightarrow&
J_1(\Omega_+) =
t_8 t_8 R^4 (\Omega_+) - \frac18 \epsilon_{10} t_8 B \left(R^4 (\Omega_+) + R^4(\Omega_-) \right).
\label{superinv-b}
\end{eqnarray}
\end{subequations}
Note that $J_0 (\Omega_+) + \Delta J_0(\Omega_+, H)$ appears at tree level both in IIA and IIB
and at one loop in IIB, while $J_0 (\Omega_+) - 2 J_1(\Omega_+) + \Delta J_0(\Omega_+, H)$
appears at one loop in IIA. The structure of $\Delta J_0(\Omega_+, H)$ is more elaborate and kinematically different form the standard $\ft18 \epsilon_{10} \epsilon_{10} R^4 (\Omega) $ terms, and in fact it is the only part of the eight-derivative action that is not written purely in terms of $R(\Omega_{\pm})$.\footnote{Incidentally, using the connection with torsion $\Omega_{\pm}$ and $R(\Omega_{\pm})$ is not sufficient for writing the two-derivative effective action. For this one also needs the Dirac operator that appears in supersymmetry variations. Note that the Dirac operator, the covariant derivative with respect to $\Omega_{\pm}$ and the effective action are related via generalisation of the Lichnerowicz formula.} Here we should also use the full six-index un-contracted combination of $H^2$. These structures receive contributions starting form five-point odd-odd amplitudes:
\begin{align}
\label{}
\Delta J_0(\Omega_+, H) = &\,
-\frac13\,\epsilon_{\alpha\mu_0\mu_1\cdots\mu_8}\epsilon^{\alpha\nu_0\nu_1\cdots\nu_8}
\,R^{\mu_7\mu_8}{}_{\nu_7\nu_8}(\Omega_+)
\nonumber\\
&\qquad
\times \big[ H^{\mu_1\mu_2}{}_{\nu_0}H_{\nu_1\nu_2}{}^{\mu_0}\,
R^{\mu_3\mu_4}{}_{\nu_3\nu_4}(\Omega_+) R^{\mu_5\mu_6}{}_{\nu_5\nu_6}(\Omega_+)
\nonumber \\
&\qquad\quad
-\frac3{16}\,
(9\,H^{\mu_1\mu_2}{}_{\nu_0}H_{\nu_1\nu_2}{}^{\mu_0}+\ft19\, H^{\mu_1\mu_2\mu_0}H_{\nu_1\nu_2\nu_0}) \,
\nabla^{\mu_3}H^{\mu_4}{}_{\nu_3\nu_4} \nabla^{\mu_5}H^{\mu_6}{}_{\nu_5\nu_6} \big]
\nonumber \\
&+ \ldots.
\label{eq:ooLaghat}
\end{align}
The order $H^4 R^2$ contribution is known up to some ambiguities, while the terms with higher
powers of $H$ remain a conjecture. Luckily these terms play little role in ${\mathcal N}\!=\!2$ reductions and we comment on the cases where they are relevant below.
The last term in (\ref{superinv-b}), coming form the worldsheet odd-even and even-odd structures corresponds to the gravitational anomaly-canceling term. The relative sign between the two terms is fixed by the IIA GSO projection,
so that the coupling contains only odd powers of $B$-field. The explicit contribution to the effective action is
\begin{gather}
\label{eq:x8}
- (2 \pi)^6 \alpha'^3 B \wedge \overline{X}_{8} = - \frac{ (2\pi)^2}{192} \alpha'^3 B\wedge \left(\tr R^4-\frac14(\tr R^2)^2 + \mbox{exact } \right) \,,
\\
\overline{X}_{8} =\frac12 \, \left[ t_8 R^4 (\Omega_+) + t_8 R^4(\Omega_-) \right]\,. \nonumber
\end{gather}
Since $t_8 R^4 \sim \, \frac14 p_1^2 - p_2$ is made of characteristic classes and $H$ enters in (\ref{eq:x8}) like a torsion in the connection, its contribution amounts to a shift by exact terms. For completeness, we record the complete expression,
\begin{align}
\label{eq:x8shift}
\overline{X}_{8} =&\, \frac1{ 192 (2\pi)^4}\bigg[ \left( \tr R^4 -\frac1{4}(\tr R^2)^2 \right)
\nonumber \\
\hspace{1cm} &\quad
+ d \,\, \bigg( \frac1{2} \tr \left( \mathcal {H} \nabla \mathcal {H} R^2 + \mathcal {H} R \nabla \mathcal {H} R
+ \mathcal {H} R^2 \nabla \mathcal {H} \right)
\nonumber \\
& \qquad\qquad
-\frac1{8} \left( \tr R^2 \, \tr \mathcal {H} \nabla \mathcal {H} + 2\, \tr \mathcal {H} R \, \tr R \nabla \mathcal {H} \right)
\nonumber \\
& \qquad\qquad +\frac1{16}\, \tr \left( 2 \mathcal {H}^3 (\nabla \mathcal {H} R + R \nabla \mathcal {H}) + \mathcal {H} R \mathcal {H}^2 \nabla \mathcal {H}
+ \mathcal {H} \nabla \mathcal {H} \mathcal {H}^2 R \right)\nonumber\\
& \qquad\qquad - \frac1{16}\,\left( \tr \mathcal {H} \nabla \mathcal {H} \, \tr R \mathcal {H}^2 + \tr R \nabla \mathcal {H} \, \tr \mathcal {H}^3
- \tr \nabla \mathcal {H} \mathcal {H}^2 \, \tr \mathcal {H} R \right)
\nonumber \\
& \qquad\qquad +\frac1{32} \tr \nabla \mathcal {H} \mathcal {H}^5 + \frac1{16} \tr \mathcal {H} (\nabla \mathcal {H})^3
\nonumber \\
& \qquad\qquad + \frac1{192} \tr \nabla \mathcal {H} \mathcal {H}^2 \, \tr \mathcal {H}^3
-\frac1{64} \tr \mathcal {H} \nabla \mathcal {H} \, \tr (\nabla \mathcal {H})^2 \bigg) \bigg].
\end{align}
since its reduction will be useful in the following.
The eight-derivative (tree level and one-loop) terms are the origin of the only perturbative corrections to the metrics on the ${\mathcal N}\!=\!2$ moduli spaces. The corrections respect the factorisation of the moduli spaces, and the classical metrics on moduli space of vectors and hypers receive respectively tree-level and one-loop corrections, both of which are proportional of the Euler number of the internal Calabi-Yau manifold \cite{Antoniadis:1997eg, Antoniadis:2003sw}. Needless to say, our discussion is consistent with these corrections, and from now on we shall concentrate only on the higher-derivatives terms. Recent progress in understanding the hyper-multiplet quantum corrections is reviewed in \cite{Alexandrov:2013yva}.
As already mentioned, the reduction of type IIA super invariant $J_0 (\Omega) - 2 J_1(\Omega)$ on Calabi-Yau manifolds yields the one loop $R^2$ terms in ${\mathcal N}\!=\!2$ four-dimensional theory, and this is the only known product of the reduction so far that leads to higher derivative terms in 4D. We shall return to the four-dimensional $R^2$ terms in section \ref{sec:fourder}. Clearly, the inclusion of the $B$ field leads to further couplings to matter upon dimensional reduction, to which we now turn.
\subsection{Reduction on Calabi-Yau manifolds}
\label{sec:CY-red}
We now consider the reduction of the ten-dimensional eight-derivative action on a Calabi-Yau threefold $X$, and its relation to the ${\mathcal N}\!=\!2$ action. The metric can be reduced in the standard way, as\footnote{We use numbered Greek letters for 10D curved indices, while ordinary Greek letters denote 4D curved indices. We use Latin letters from the beginning of the alphabet for 4D flat indices, and Latin letters from the middle to the end of the alphabet, $m, n, \dots$ are reserved for CY indices. We reserve the letters $i,j,k,l$ for $SU(2)$ R-symmetry indices. Capital Latin indices $I,J = 1, ..., h^{1,1}(X)$ span the matter vector multiplets.}
\begin{equation}
g_{\mu_1\mu_2} = \begin{pmatrix} g_{\mu\nu} & 0 \\ 0 & g_{mn} \end{pmatrix}\,,
\end{equation}
where $g_{mn}$ is the metric on the Calabi-Yau manifold, X, which we will not need explicitly. The three-form $H$ reduces as
\begin{eqnarray}
H_3 = H + f^I \wedge \omega_I\,,
\label{eq:H3red}
\end{eqnarray}
where the four-dimensional $H$ is part of the tensor multiplet, and the one-forms $f^I$ can be locally written as $f^I = d u^I$, with $u^I$ being a part of the vector multiplet scalars. The index $I$ spans over $h^{1,1}(X)$, and $\omega_I \in H^2(X, \mathbb{Z})$.
Hence reducing the terms built out of $R(\Omega_{\pm})$ and $H_3$ (where $\Omega_{\pm}=\Omega \pm\ft12\mathcal {H}$), one expects at a given order of derivatives various couplings involving the Riemann tensor, $R$, as well as the tensor multiplet and vector multiplets. For example, at the four-derivative level one recovers the four-dimensional $R^2$ couplings and expects to obtain further couplings quartic in tensor multiplet and vector multiplets, as well as mixed terms. We use the symbolic computer algebra system Cadabra \cite{DBLP:journals/corr/abs-cs-0608005, Peeters:2007wn} to systematically derive the structure of these terms.
The vector moduli shall be denoted $z^I = u^I + i t^I$, where $t^I$ are the K\"ahler moduli, defined through the decomposition of the Calabi-Yau K\"ahler form, $J$, as $J = t^I \omega_I$. The total volume, ${\mathcal V}$, of the CY manifold is given by the standard volume form, cubic in $J$ as
\begin{equation}
{\mathcal V}= \frac{1}{3!}\,\int_X J\wedge J\wedge J = \log[-{\mathcal K}]\,,
\end{equation}
where we defined the 4D K\"ahler potential. We shall not need the vector fields themselves, but only their field strengths, denoted as $F^A$, where the index $A={0,I}$ runs over the $h^{1,1}(X)+1$ vector fields (in places where the shorthand notation is used, $F$ will stand for the entire multiplet).
Reducing the NS eight-derivative couplings we obtain couplings that contain $u^I$ and $t^I$. The couplings to $F^I$ can be recovered by thinking of the (one-loop) couplings as being reduced from five (or eleven) dimensions. In practical terms, one has to add an extra index on $f^I_{\mu} \, \mapsto F^I_{\mu \nu}$. Since (the affected parts of) the expressions are even in powers of $F^I$, the extra index will always be contracted with a similar counterpart. Moreover most of the expressions are only quadratic in $F$, hence the lifting is unique. A little combinatorial imagination is needed for $F^4$ terms. This procedure follows the lifting of one-loop NS couplings to eleven dimensions, outlined in \cite{Liu:2013dna} and is analogous to the way one can recover graviphoton couplings from the $R^2$ term - one just has to think of the lifting of the couplings to five dimensions and their consequent reduction.
As already mentioned, here we can benefit from the explicit ${\mathcal N}\!=\!2$ formalism in verifying that the couplings involving $t^I$ and $F^I$ complete each other sypersymmetrically and hence provide a verification of the lifting of the complete one-loop eight-derivative terms from type IIA strings to M-theory.
Since we are focusing on Calabi-Yau compactifications without flux, different pieces in the reduction will involve integrating over $X$ expressions containing some power of the internal curvature and $\omega_I \in H^2(X, \mathbb{Z})$.\footnote{Since the four-dimensional three-form $H$ in \eqref{eq:H3red} is in the hyper matter, some of the couplings involving hyper multiplets will be discussed here. However we mostly concentrate on the vector multiplets here, and do not consider any internal expressions involving forms in $H^{2,1}(X)$.} We shall start with the familiar integrals.
At the four derivative level, one needs to consider terms with exactly two powers of the Riemann tensor
in the internal Calabi-Yau manifold. In the purely gravitational sector, one then finds an $R^2$ term
in four dimensions, originating from the $R^4$ couplings in ten dimensions. In this case, one obtains
\begin{equation}
t_8 t_8 R^4 = -\frac18\epsilon_{10} \epsilon_{10} R^4 =
12\, F_1\, R^{\mu\nu\rho\lambda}R_{\mu\nu\rho\lambda} \,,
\end{equation}
where we note that only terms completely factorised in internal and external objects contribute.
The function $F_1$ is an integral over the internal directions that takes the form
\begin{equation}\label{eq:zero-id}
F_1 = \int_{X} R^{mn pq}R_{mn pq}
= \frac{1}{8}\,\int_{X} \epsilon_{mn m_1 \ldots m_4} \epsilon^{mn n_1 \ldots n_4}
R^{m_1 m_2}{}_{n_1n_2} R^{m_3 m_4}{}_{n_3n_4}
= \alpha_I t^I\,,
\end{equation}
where the first equality holds up to Ricci terms and in the second equality we evaluated the integral.
The fine balance between the two a priori different terms in \eqref{eq:zero-id} can be extended
to more complicated integrals, that are relevant in the reduction of the non-purely gravitational
terms. In this case, we have checked explicitly the identity
\begin{align}\label{eq:two-id}
&\,t_8{}_{\mu m \nu n m_1 \ldots m_4} t_8{}^{\rho p \sigma q n_1 \ldots n_4}
\omega_I{}^m{}_p \omega_J{}^n{}_q \, R^{m_1m_2}{}_{n_1n_2} R^{m_3 m_4}{}_{n_3n_4}
=
\nonumber\\
&\,\hspace{4.5cm}
-\frac{1}{8}\, \delta_{\mu}{}^{\sigma}\, \delta_{\nu}{}^{\rho}
\epsilon_{mn m_1\ldots m_4} \epsilon^{pq n_1\ldots n_4}
\omega_I{}^m{}_p \omega_J{}^n{}_q \, R^{m_1m_2}{}_{n_1n_2} R^{m_3 m_4}{}_{n_3n_4}\,,
\end{align}
up to Ricci terms. Note that the structure of spacetime indices is different in the two
sides, while the remaining terms are purely internal.
Upon contraction with the K\"ahler moduli, each side of \eqref{eq:two-id} reduces to
the expression in \eqref{eq:zero-id}.
Even further, the identity in \eqref{eq:four-id} can be generalised to an identity
involving eight indices, as follows.
\begin{align}\label{eq:four-id}
&\,t_8{}_{m_1\dots m_4 p_1 \ldots p_4} t_8{}^{n_1\dots n_4 q_1 \ldots q_4}
\omega_I{}^{m_1}{}_{n_1} \omega_J{}^{m_2}{}_{n_2} \, \omega_K{}^{m_3}{}_{n_3} \omega_L{}^{m_4}{}_{n_4} \,
R^{p_1p_2}{}_{q_1q_2} R^{p_3 p_4}{}_{q_3q_4}
=
\nonumber\\
&\,\hspace{1.5cm}
-\frac{1}{8}\,
\epsilon_{p_0 q_0 m_1\dots m_4 p_1\ldots p_4} \epsilon^{p_0 q_0 n_1\dots n_4 q_1\ldots q_4}
\omega_I{}^{m_1}{}_{n_1} \omega_J{}^{m_2}{}_{n_2} \, \omega_K{}^{m_3}{}_{n_3} \omega_L{}^{m_4}{}_{n_4} \,
R^{p_1p_2}{}_{q_1q_2} R^{p_3 p_4}{}_{q_3q_4}\,,
\end{align}
again up to Ricci-like terms. These two expressions are relevant for the terms in $R(\Omega_+)$
that are odd or even under pair exchange, respectively.
The reduction to six- and eight-derivative couplings will require integration over expressions
linear or zeroth order in the Riemann tensor of the internal Calabi-Yau manifold. In view of
the vanishing of the Calabi-Yau Ricci tensor, these are essentially unique, and given by
\begin{align}
G_{IJ} =&\, \tfrac12\, \int_X\!\omega_I^{mn} \omega_J{}_{mn}\,,
\nonumber\\
{\mathcal R}_{IJ} =&\, \int_{X} R_{mnpq}\,\omega_{I}{}^{mn}\omega_{J}{}^{pq}\,,
\end{align}
where $G_{IJ}$ ultimately leads to the vector multiplet K\"ahler metric and ${\mathcal R}_{IJ}$ is
a new coupling to be discussed in due time.
\section{The four dimensional action}
\label{sec:n2d4}
We now describe the structure of the effective ${\mathcal N}\!=\!2$ supergravity action in four dimensions,
that arises from the reduction of the one-loop Type IIA Lagrangian. Given that the original
ten dimensional action contains eight derivatives, one obtains a variety of
higher derivative couplings, next to the lowest order two derivative action.
In order to describe these in a systematic way, we will consider the off-shell formulation
of the theory, which allows to construct infinite classes of higher derivative invariants
without modifying the supersymmetry transformation rules. However, since the higher
dimensional one-loop action and the reduction scheme are on-shell, one has to deduce the
off-shell invariants from the desired terms that result upon gauge fixing to the on-shell
theory. In the following, we take the pragmatic approach of matching the leading,
characteristic terms in each invariant and promoting to off-shell variables by standard
formulae for special coordinates for the vector multiplet scalars. In practice, these
choices are essentially unique, and below we comment on this issue in the examples where
this is relevant.
The defining multiplet of off-shell ${\mathcal N}\!=\!2$ supergravity is the Weyl multiplet, which
contains the graviton, $e^a_\mu$, the gravitini, gauge fields for local scale and R-symmetries
and various auxiliary fields. Of the latter, only the auxiliary tensor $T_{ab}{}^{ij}$ is
directly relevant, since it is identified with the graviphoton in the on-shell formulation
of the theory, at the two-derivative level. The reader can find a short account of the Weyl
multiplet in Appendix \ref{App:N2sugra}.
In what follows, we will mostly deal with the covariant fields of the Weyl multiplet,
which can be arranged in a so-called chiral multiplet (see Appendix \ref{App:4D-chiral-multiplets}
for more details), which contains the auxiliary tensor $T_{ab}{}^{ij}$
and the curvature $R(M)_{\mu \nu}{}^{ab}$. The latter is identified with the Weyl tensor,
up to additional modifications. These observations will be very useful in the identification
of the various higher derivative couplings.
There are various matter multiplets that can be defined on a general
supergravity background. Here, the fundamental matter multiplets we consider are
vector multiplets and a single tensor multiplet, corresponding to the universal
tensor multiplet of Type II theories. Both these multiplets comprise $8 + 8$
degrees of freedom and are defined in appendices \ref{App:4D-chiral-multiplets}
and \ref{sec:tensor} respectively, to which we refer for further details.
Moreover, they can be naturally viewed as two mutually non-compatible projections of
a chiral multiplet, which is central to our considerations.
All Lagrangians considered in this paper are based on couplings of chiral multiplets, which
contain $16 + 16$ degrees of freedom and can be defined on an arbitrary
${\mathcal N}\!=\!2$ superconformal background. We refer to appendix \ref{App:4D-chiral-multiplets} for
more details on chiral multiplets. Here, we simply state that these multiplets are labeled
by the scaling weight, $w$, of their lowest component, $A$, and that products of chiral
multiplets are chiral multiplets themselves, obtained by simply considering functions
$F(A)$, which must be homogeneous, so that a weight can be assigned to them. As mentioned
above, the matter multiplets we consider are also chiral multiplets of $w=1$, on which a
constraint projecting out half of the degrees of freedom is imposed and the same property
holds for the covariant components of the Weyl multiplet. This implies that
actions for all the above multiplets can be generated by considering expressions
constructed out of chiral multiplets, which are invariant under supersymmetry.
\subsection{Two derivatives}
The prime example is given by the invariant based on a $w=2$ chiral multiplet, implying
that its highest component, $C$, has Weyl weight 4, and chiral weight 0, as is appropriate
for a conformally invariant Lagrangian in four dimensions. It can be shown that the expression
\begin{align}
\label{eq:chiral-density}
e^{-1}\mathcal{L} =&\, C -\tfrac1{16}A( T_{ab\,ij} \varepsilon^{ij})^2
+ \text{fermions}\,,
\end{align}
is the bosonic part of the invariant, including a conformal supergravity background described by
the auxiliary tensor $T_{ab\,ij}$ of the gravity multiplet.
The two derivative action for vector multiplets is now easily constructed, by setting the chiral
multiplet in this formula to be composite, expressed in terms of vector multiplets labeled by
indices $I,J,\dots= 0,1,\ldots,n_\mathrm{v}$. It is possible to show (cf.~\eqref{eq:chiral-mult-exp})
that the relevant terms of such a composite multiplet are given by\footnote{The function $G$
in \eqref{eq:chiral-mult-exp} is conventionally chosen as $G(X^I)= -\tfrac {\mathrm{i}} 2 F(X)$
in this context.}
\begin{align}
\label{eq:chiral-mult-comp}
A =&\, -\tfrac {\mathrm{i}} 2 F(X) \,,\nonumber\\
C =&\, \mathrm{i}\,F(X)_I\, \Box_\mathrm{c} \bar X^I
+\tfrac{\mathrm{i}}8\, F(X)_{IJ}\big[ B_{ij}{}^I B_{kl}{}^J\,
\varepsilon^{ik} \varepsilon^{jl} + X^I\,G^{+}_{ab}{}^J T^{ab}{}_{ij} \varepsilon^{ij}
-2\, G^{-}_{ab}{}^I G^{-abJ}\big] \,,
\end{align}
where $F_{I}$ and $F_{IJ}$ are the first and second derivative of the function $F$, known
as the prepotential and $B_{ij}{}^I$, $G^{-}_{ab}{}^I$ are the remaining bosonic components
of the chiral multiplets (which in this case are constrained by \eqref{eq:vect-mult} for
vector multiplets). As the bottom composite component, $A$, has $w=2$, the function $F(X)$
must be homogeneous of degree two in the vector multiplet scalars $X^I$. Taking into account
the constraints in \eqref{eq:vect-mult}, the bosonic terms of the Lagrangian following from
\eqref{eq:chiral-density} read
\begin{eqnarray}\label{eq:4d-lagr-v}
8\pi\,e^{-1}\, {\cal L}_{v} &=&
\mathrm{i} {\cal D}^{\mu} F_I \, {\cal D}_{\mu} \bar X^I - \mathrm{i} F_I\,\bar X^I
(\ft16 R - D)
-\ft18\mathrm{i} F_{IJ}\, Y^I_{ij} Y^{Jij} \nonumber\\
&&+\ft14 \mathrm{i} F_{IJ} (F^{-I}_{ab} -\ft 14 \bar X^I
T_{ab}^{ij}\varepsilon_{ij})(F^{-Jab} -\ft14 \bar X^J
T^{ijab}\varepsilon_{ij}) \nonumber\\
&&-\ft18 \mathrm{i} F_I(F^{+I}_{ab} -\ft14 X^I
T_{abij}\varepsilon^{ij}) T^{ab}_{ij}\varepsilon^{ij}
-\ft1{32} \mathrm{i} F (T_{abij}\varepsilon^{ij})^2 + {\rm h.c.}\;,
\end{eqnarray}
where in the last line we added the hermitian conjugate to obtain a real Lagrangian.
Here, $F^{I}_{ab}$ are the vector multiplet gauge field strengths, $R$ is the Ricci
scalar and $D$ is the auxiliary real scalar in the gravity multiplet.
This Lagrangian is invariant under scale transformations and can be related to an
on-shell Poincar\'e Lagrangian by using a scale transformation to set the coefficient
of the Einstein-Hilbert term, $\mbox{Im} (F_I\,\bar X^I)$, to a constant. For standard Calabi-Yau
compactifications of Type II theories, one obtains a cubic prepotential, as
\begin{equation}\label{eq:CY-prep}
F = -\frac16\,\frac{C_{IJK}Y^I Y^J Y^K }{Y^0}\,,
\end{equation}
where the constant tensor $C_{IJK}$ stands for the intersection numbers of the manifold.
As it turns out, the Lagrangian \eqref{eq:4d-lagr-v} is inconsistent as it stands, so
that one needs to add at least one auxiliary hypermultiplet, which is to be gauged away
by superconformal symmetries, similar to the scalar $\mbox{Im} (F_I\,\bar X^I)$ above.
In addition, in this paper we consider a single tensor multiplet, corresponding to
the universal hypermultiplet upon dualisation of the tensor field. We refer to
appendix \ref{sec:tensor} for more details on this multiplet. For later reference, we
display the bosonic action for the auxiliary hypermultiplet and the physical tensor multiplet
that needs to be added to \eqref{eq:4d-lagr-v} to obtain a consistent on-shell
theory with a physical tensor multiplet, as
\begin{align}\label{eq:4d-lagr-t}
8\pi\,e^{-1}\, {\cal L}_{t} =&
- \ft12 \varepsilon^{ij}\,\Omega_{\alpha\beta} \,\big[
{\cal D}_\mu A_i{}^\alpha \,{\cal D}^\mu A_j{}^\beta
- A_i{}^\alpha A_j{}^\beta \big(\tfrac{1}{6} R + \tfrac12\, D) \big]
\nonumber\\
&\,
- \, \tfrac{1}{2} \, F^{(2)} \,\mathcal{D}_\mu L_{ij} \, \mathcal{D}^\mu L^{ij}
+ F^{(2)} \, L_{ij} \, L^{ij} \, \Big(\tfrac{1}{3} R + D \Big)
+ F^{(2)} \, \Big[ E_{\mu} \, E^{\mu} + G \bar{G} \Big]
\nonumber\\
&\, + \tfrac12 \mathrm{i} e^{-1}
\varepsilon^{\mu \nu \rho \sigma} \, \frac{\partial F^{(2)}}{\partial L_{ij}}\,E_{\mu\nu} \,
\, \partial_\rho L_{ik} \, \partial_\sigma L_{jl} \,\varepsilon^{kl} \, .
\end{align}
Here, $A_i{}^\alpha$ is the hypermultiplet scalar, described as a local section of
$\mathrm{SU}(2)\times\mathrm{SU}(2)$, and $\Omega_{\alpha\beta}$ is the invariant
antisymmetric tensor in the second $\mathrm{SU}(2)$.
The on-shell fields of the tensor multiplet are the triplet of scalars $L_{ij}$ and the
two-form gauge field, $B_{\mu\nu}$, while
\begin{equation}
E^\mu = \tfrac{1}{2}\mathrm{i}\, e^{-1} \, \varepsilon^{\mu \nu
\rho \sigma} \partial_\nu B_{\rho \sigma}\,,
\end{equation}
is the dual of its field strength and $G$ is a complex auxiliary scalar. The
functions $F^{(2)}$ and $F^{(3)}$ can be viewed as the second and third
derivative of a function of the $L_{ij}$, that can easily be generalised to
an arbitrary number of tensor multiplets \cite{deWit:2006gn}
(see \eqref{eq:chiral-constraints}-\eqref{eq:sc-tensor}). For a single tensor
multiplet, there is a unique choice, as
\begin{align}\label{eq:two-der-ten}
F^{(2)} = \frac{1}{\sqrt{L_{ij} L^{ij} } }\,,
\end{align}
which we will assume throughout. However, as we ignore all tensor multiplet scalars in
our reduction scheme, all scalars and $F^{(2)}$ are kept constant and only appear as overall
factors.
\subsection{Higher derivatives}
In this paper we construct higher derivative actions based on the properties of chiral
multiplets, as discussed above. One way of doing this is to consider the function
$F$ in \eqref{eq:chiral-mult-comp} to depend not only on vector multiplets, but also on
other chiral multiplets, which are treated as background fields. Alternatively, one
may consider invariants more general than \eqref{eq:chiral-density}, containing explicit
derivatives on the chiral multiplet fields. Here we use both structures, which we
discuss in turn, emphasising the methods and the structure of invariants rather than
details, which can be found in \cite{de Wit:1996ix, deWit:2006gn, deWit:2010za}.
We consider two chiral background multiplets, one constructed out of the Weyl multiplet and one
constructed out of the tensor multiplet, whose lowest components we denote as
$A_{\sf w}$ and $A_{\sf t}$ respectively. These are proportional to the auxiliary fields
$(T_{ab}{}^{ij}\varepsilon_{ij})^2$ of the Weyl and and $G$ of the tensor multiplet and we
refer to appendices \ref{App:4D-chiral-multiplets} and \ref{sec:tensor} for more
details on their precise definition. Considering a function $F(X^I, A_{\sf w}, A_{\sf t})$
leads to a Lagrangian of the form \eqref{eq:4d-lagr-v}, where the set of
vector field strengths is extended to include the Weyl tensor $R(M)_{ab}{}^{cd}$
in \eqref{eq:curvatures-4} and the combination $\nabla_{[a} E_{b]}$, so that four
derivative interactions of the type
\begin{equation}\label{eq:chiral-coup}
\mathcal{L} = \int F(X^I, A_{\sf w}, A_{\sf t}) \propto
\int \left( \frac{\partial F}{\partial A_{\sf w}}\, R(M)^{-\,2}
+ \frac{\partial F}{\partial A_{\sf t}}\,(\nabla_{[a} E_{b]_{-}})^2 + \dots \right)\,,
\end{equation}
are generated.
The explicit expressions for the relevant chiral multiplets can be found in
\eqref{eq:W-squared} and \eqref{eq:CT} respectively.
These couplings are distinguished, in the sense that they are described by
a holomorphic function and correspond to integrals over half of superspace.
The $R^2$ term has been studied in detail, especially in connection to BPS black holes,
see e.g. \cite{Antoniadis:1997eg, Maldacena:1997de, Mohaupt:2000mj, LopesCardoso:2000qm, Banerjee:2011ts}.
The full function $F(X^I, A_{\sf w})$ is in this case related to the topological string
partition function \cite{Bershadsky:1993cx, Antoniadis:1993ze}. We will only be concerned
with the linear part of this function, originating in the one-loop term in section \ref{sec:10-act},
which is controlling the $R^2$ coupling through \eqref{eq:chiral-coup}.
The $(\nabla E)^2$ term has appeared more recently \cite{deWit:2006gn},
without any coupling to vector multiplets.
More general higher derivative couplings can be constructed by looking for invariants
of chiral multiplets that contain explicit derivatives, unlike \eqref{eq:chiral-density}.
Indeed, such invariants can be derived by considering a chiral multiplet whose components
are propagating fields, i.e. described by a Lagrangian containing derivatives. This can
be done in the standard way, by writing a K\"ahler sigma model, which in the simple case
of two multiplets reads
\begin{equation}
\int \!\mathrm{d}^4\theta\;\mathrm{d}^4\bar\theta \;\Phi\,\bar\Phi^\prime
\approx
\int \!\mathrm{d}^4\theta \,\Phi\,\mathbb{T}(\bar\Phi^\prime) \,,
\end{equation}
where both $\Phi$ and $\Phi^\prime$ must have $w=0$ for the integral to be well defined.
In the second form of the integral we defined a new chiral multiplet, $\mathbb{T}(\bar\Phi^\prime)$,
the so called kinetic multiplet, since it contains the kinetic terms for the various
fields. This multiplet was constructed explicitly in \cite{deWit:2010za} and is
summarized in appendix \ref{app:kinetic} below (see also \cite{Butter:2013lta} for a
recent generalisation). In practice, one can think of the operator $\mathbb{T}$ as an
operator similar to the Laplacian, acting on the components of the multiplet, as we find
\begin{align}
\label{eq:quad-chir}
\int \!\mathrm{d}^4\theta \,\Phi\,\mathbb{T}(\bar\Phi^\prime) =&\,
C\,\bar C^\prime + 8\, \mathcal{D}_a F^{-ab}\, \mathcal{D}^c F^{\prime +}{}_{cb}
+4\,\mathcal{D}^2 A\,\mathcal{D}^2\bar A^\prime
+ \cdots \,,
\end{align}
where we only display the leading terms.
One can now simply declare the chiral multiplets $\Phi$, $\Phi^\prime$ to be composite
by imposing \eqref{eq:chiral-mult-comp}, where the corresponding functions $F$, $F^\prime$
can depend on vector multiplet scalars, as well as the Weyl and tensor multiplet
backgrounds, exactly as described above. As described in section \ref{app:kinetic} and
in \cite{deWit:2010za}, this leads to a real function ${\mathcal H}=F \bar F^\prime + \text{c.c.}$,
homogeneous of degree zero, which naturally describes a variety of higher derivative couplings,
corresponding to the combinations generated by
\begin{equation}
\big[ F^{-\,2} + R^{-\,2} + (\nabla E)^{-\,2} \big] \otimes \big[ F^{+\,2} + R^{+\,2} + (\nabla E)^{+\,2} \big]\,,
\end{equation}
where the $\pm$ stand for selfdual and anti-selfdual parts.
Each of these is controlled by a function of the vector multiplet moduli as
\begin{align}
\label{eq:quad-expand}
{\mathcal H}(X^I, A_{\sf w}, A_{\sf t}, \bar{X}^I, \bar{A}_{\sf w}, \bar{A}_{\sf t})= &\,
\sum_{i+j \leq 2} {\mathcal H}^{(i,j)}(X^I, \bar{X}^I) (A_{\sf w})^i\, (\bar{A}_{\sf t})^j + \text{c.c.}
\Rightarrow
\nonumber\\
\qquad \qquad
{\mathcal H}^{(0,0)}(X^I, \bar{X}^I) &\,\qquad \Rightarrow \qquad (\nabla F)^2, F^4
\nonumber\\
\qquad \qquad
\big[{\mathcal H}^{(1,0)} A_{\sf w} + \text{c.c.}\big] &\,\qquad \Rightarrow \qquad R^2 F^2
\nonumber\\
\big[{\mathcal H}^{(0,1)}\, A_{\sf t} + \text{c.c.}\big] &\,\qquad \Rightarrow \qquad (\nabla E)^2 F^2
\nonumber\\
\qquad \qquad
{\mathcal H}^{(2,0)} A_{\sf w}\, \bar{A}_{\sf w} &\,\qquad \Rightarrow \qquad R^4
\nonumber\\
{\mathcal H}^{(0,2)}\, A_{\sf t}\, \bar{A}_{\sf t} &\,\qquad \Rightarrow \qquad (\nabla E)^4
\nonumber\\
\big[{\mathcal H}^{(1,1)}\, A_{\sf w}\, \bar{A}_{\sf t} + \text{c.c.}\big] &\,\qquad \Rightarrow \qquad R^2 (\nabla E)^2\,,
\end{align}
where we display the characteristic terms at each order.
Note that we consider a function at most quadratic in $A_{\sf w}$, $A_{\sf t}$, since
a higher polynomial would lead to the same terms, multiplied by additional powers of these
auxiliary scalars. These are analogous to the non-linear parts of the chiral coupling
in \eqref{eq:chiral-coup} and go beyond one-loop terms, so we do not consider them in
the following. Finally, note that due to the expansion \eqref{eq:quad-expand}, the functions ${\mathcal H}^{(i,j)}$
are not homogeneous of degree zero for $i,j\neq 0$, but we we will always refer to the
corresponding degree zero monomial in \eqref{eq:quad-expand}, for clarity.
The invariants based on \eqref{eq:quad-chir} are the simplest ones containing
the kinetic multiplet. It is straightforward to construct more general integrals, for
example
\begin{equation}
\int \!\mathrm{d}^4\theta \,\Phi\,\mathbb{T}(\bar\Phi)\,\mathbb{T}(\bar\Phi) \,,
\quad
\int \!\mathrm{d}^4\theta \,\Phi\,\mathbb{T}(\bar\Phi)\,\mathbb{T}(\bar\Phi)\,\mathbb{T}(\bar\Phi) \,,
\quad
\int \!\mathrm{d}^4\theta \,\Phi_0\mathbb{T}(\bar\Phi)\,\mathbb{T}(\bar\Phi_0\mathbb{T}(\Phi)) \,,
\end{equation}
which are the cubic and quartic invariants discussed in section \ref{app:kinetic}. In exactly the
same way as above, the first of these integrals leads to a homogeneous function of degree
$-2$, describing couplings cubic in $F^2$, $R^2$ and $(\nabla E)^2$. Only some of these
are relevant in the following, in particular the $(R^2 +(\nabla E)^2)F^4$ and $F^6$, since
the rest contain more than eight derivatives. Finally, the last two integrals describe
couplings with at least eight derivatives and lead to homogeneous functions of degree $-4$.
Only the last integral is relevant for us, namely for the $F^8$ term.
\section{Eight derivative couplings}
\label{sec:eightder}
We start by considering terms containing the maximum number of derivatives appearing in
the one-loop correction, i.e. we consider the possible eight derivative invariants in
four dimensions. This may seem counterintuitive at first and in fact some of these
invariants have not been described explicitly. However, the terms that
are known in four dimensions are the simplest to describe, setting the stage for the more
complicated structures to follow.
Applying the rules and assumptions spelled out in section \ref{sec:CY-red}, one can characterise
the various terms appearing in the reduction by the order of Riemann tensors, tensor multiplet
fields strengths and vector multiplet fields strengths arising in four dimensions.
Schematically, we then find a decomposition of the type
\begin{align}\label{eq:8-dec}
\mathcal{L}^{1-\text{loop}} \Rightarrow &\,
\textcolor{blue}{R^4} + \textcolor{blue}{R^2 (\nabla H)^2} + \textcolor{blue}{(\nabla H)^4}
+ \textcolor{red}{ \underline{R^4}} + \textcolor{red}{\underline{H^6 F^2}}
+ \textcolor{blue}{H^4 F^4} \nonumber\\
&\,
+ \textcolor{red}{\underline{H^2 F^6}}
+ \textcolor{blue}{R^2\,(\nabla F)^2} + \textcolor{blue}{(\nabla F)^4}\,,
\end{align}
where we write in blue the terms which correspond to the known four-dimensional invariants. The supersymmetric invariants for the underlined (red) terms are not known.
\subsection*{Gravity and tensor couplings}
The most obvious and simplest term is the $R^4$ term, which arises by trivial reduction of the
corresponding ten dimensional term. Note that only the even-even contribution survives the
reduction and leads to a four dimensional $R^4$ term as
\begin{align}\label{eq:R4-red}
t_8t_8 R^4 \rightarrow &\,
192\,(R_{\mu\nu \rho\lambda} R^{\mu\nu \rho \lambda})^2
+ 144\,\tr[R_{\mu\nu} R_{\rho\lambda}] \tr[R^{\mu\rho} R^{\nu\lambda}] + \dots
\nonumber\\
=&\,
768\,(R^+)^2 (R^-)^2
+48\,\left( (R^+)^2 - (R^-)^2\right)^2 + \dots\,.
\end{align}
The second line corresponds to two different invariants in four dimensions, each
with its own supersymmetric completion, corresponding to the double appearance of $R^4$
in \eqref{eq:8-dec}. The supersymmetrisation of the second
term is not known in ${\mathcal N}\!=\!2$ supergravity (see however \cite{Moura:2007ks} for a
discussion in the ${\mathcal N}\!=\!1$ setting).
The supersymmetric completion of the first term was found in \cite{deWit:2010za},
where it was shown that it is governed by a homogeneous degree zero real function of
the vector multiplet moduli and the Weyl multiplet scalar $A_{\sf w}$. In the present
case however, \eqref{eq:R4-red} does not depend on moduli other than the total volume of
the CY manifold, so that we can immediately identify the relevant function as depending
only on the K\"ahler potential as
\begin{equation}\label{eq:R4-fun}
{\mathcal H}_{R^4}= \frac{3}{16}\,\mathrm{e}^{2\,{\mathcal K}(Y ,\bar{Y})}\, A_{\sf w} \bar{A}_{\sf w} \,.
\end{equation}
Here, the function of the off-shell scalars ${\mathcal K}(Y ,\bar{Y})$ is very closely related to
the lowest order K\"ahler potential, as
\begin{equation}
\mathrm{e}^{-{\mathcal K}} = 2\,\mbox{Im} F_{AB} Y^A\bar{Y}^B\,,
\end{equation}
with the prepotential \eqref{eq:CY-prep}, and is equal to it once special coordinates
are chosen (for $Y^0=1$). Note however, that
this is only the most natural choice that results in the first coupling in \eqref{eq:R4-red}
upon taking the on-shell limit and one might consider more elaborate off-shell functions
leading to the same result.
Upon taking derivatives of this function with respect to the vector multiplet moduli,
various couplings involving vector multiplet field strengths and auxiliary fields
arise at the off-shell level, resulting to further eight derivative terms in the on-shell
theory.
The corresponding purely tensor coupling is the eight derivative term of the tensor
multiplet, which takes the form
\begin{equation}
\label{eq:H8-red}
t_8t_8 R^4 \rightarrow
96\,\left( (\nabla_{[\mu} E_{\nu]} \nabla^{[\mu} E^{\nu]})^2
- 4\,\nabla_{[\mu} E_{\nu]} \nabla^{[\nu} E^{\rho]} \nabla_{[\rho} E_{\sigma]} \nabla^{[\sigma} E^{\mu]} \right)
\,.
\end{equation}
These couplings can be described in a way completely analogous to the $R^4$ term, through a
homogeneous real function corresponding to \eqref{eq:R4-fun}, as
\begin{equation}\label{eq:H8-fun}
{\mathcal H}_{H^{4}}= \frac{3}{16}\,\mathrm{e}^{2\,{\mathcal K}(Y ,\bar{Y})}\, A_{\sf t} \bar{A}_{\sf t} \,.
\end{equation}
The final possible combination at the eight derivative level for NS fields is the $R^2 H^4$
coupling, which in 4D is characterised by the term
\begin{equation}
\label{eq:R2H4-red}
t_8t_8 R^4 \rightarrow
-96\,(\nabla_{[\mu} E_{\nu]_-} \nabla^{[\mu} E^{\nu]})^2
R^-_{\kappa\lambda}{}^{\rho\sigma} R^-{}^{\kappa\lambda}{}_{\rho\sigma}
\,.
\end{equation}
These couplings can be described by the obvious mixed combination of the two
functions \eqref{eq:R4-fun} and \eqref{eq:H8-fun} above, as
\begin{equation}\label{eq:R2H4-fun}
{\mathcal H}_{R^2H^4} = \frac{3}{16}\,\mathrm{e}^{2\,{\mathcal K}(Y ,\bar{Y})}\, A_{\sf w} \bar{A}_{\sf t} + \text{c.c.}\,.
\end{equation}
The last function can be straightforwardly added to the functions above, to define a total
function of the vector multiplet moduli and Weyl and tensor multiplet backgrounds, defined as
\begin{equation}\label{eq:NS8-fun}
{\mathcal H}_{NS}^{8}= \frac{3}{16}\,\mathrm{e}^{2\,{\mathcal K}(Y ,\bar{Y})}\, |A_{\sf w} + A_{\sf t}|^2\,,
\end{equation}
describing the eight derivative couplings of NS sector fields.
At this point it is worth pausing, to note that the form of these equations exhibits
a correspondence between the graviton and the B-field, since the complete eight
derivative action for the gravity and tensor multiplet is controlled by the
combination $A_{\sf w} + A_{\sf t}$. This will appear in several instances below, at
all orders of derivatives, and reflects the structure of the 10D Lagrangian, which
is controlled by the combination $R(\Omega_+)$.
\subsection*{Couplings involving vector multiplets}
We now turn to some of the eight derivative terms involving derivatives on vector
multiplet fields. We start with mixed terms between NS and RR fields, namely the ones
where the order of derivatives is balanced between the two sectors. Indeed, it is
straightforward to obtain the function characterising the $R^2 F^4$ coupling, which
in 4D is described by the cubic invariant in appendix \ref{app:kinetic}, where one
considers one of the chiral multiplets to be the Weyl multiplet. The $R^2 F^4$
coupling is then characterised by the terms
\begin{align}\label{eq:R2F4-4dterms}
&\,{\mathcal H}^{(8)}_{A_{\sf w} A\, \bar B}
R^{-}_{\mu\nu\rho\lambda} R^{-}{}^{\mu\nu\rho\lambda} \,\left(
\nabla F^{-\, A} \nabla F^{+\,\bar{B}} + \Box X^{A} \Box X^{\bar{B}}
\right)
\nonumber\\
&\,+{\mathcal H}^{(8)}_{A_{\sf w} A B\, \bar C \bar D}
R^{-}_{\mu\nu\rho\lambda} R^{-}{}^{\mu\nu\rho\lambda} \,
F^{-\,A} F^{-\,B} F^{+\,\bar{C}} F^{+\,\bar{D}}
+ \dots\,.
\end{align}
In this case, only the Ricci-like terms
contribute to the reduction altogether, so that we obtain for the relevant coupling
\begin{equation}
{\mathcal H}^{(8)}_{A_{\sf w} I\, J} = -576\,\int_X \omega_I{}^{m n} \omega_J{}_{m n} \equiv -576\, G_{IJ}\,,
\end{equation}
i.e. proportional to the lowest order K\"ahler metric $G_{IJ}$.
This result determines the coupling of the vector multiplet scalars and the corresponding vector fields, but
we still need to fix the couplings to the Type IIA RR gauge field, labeled by $0$ in four dimensions. These
can be derived by the observation that all field strengths can be introduced by lifting the three-form
$H_{\mu_1\mu_2\mu_3}$ to the eleven dimensional four-form field strength $G_{\mu_1\mu_2\mu_3\mu_4}$ and
reducing back on a circle, keeping all components. The result of the reduction of the four-form to 4D
gauge fields, $F^I_{\mu\nu}$, naturally leads to the combination $F^I_{\mu\nu} + u^I\, F^0_{\mu\nu}$, which
should replace the field strengths in the couplings shown above, so that the full coupling becomes
\begin{equation}\label{eq:gr-ph-exten}
{\mathcal H}^{(8)}_{A_{\sf w} I\, J} \rightarrow {\mathcal H}^{(8)}_{A_{\sf w} A\, \bar B}
=-576\,
\begin{pmatrix}
G_{IJ} & G_{IJ} u^J\\
u^I G_{IJ} & G_{IJ} u^I u^J
\end{pmatrix}
\,.
\end{equation}
Combined with the fact that the relevant function depends on the Weyl multiplet background only
linearly, as implied by \eqref{eq:R2F4-4dterms}, one can now integrate to obtain
\begin{equation}\label{eq:R2F4-fun}
{\mathcal H}_{R^2 F^4}= 9\,A_{\sf w} \, \mathrm{e}^{2\,{\mathcal K}(Y ,\bar{Y})} \,.
\end{equation}
This form is in line with the observation that the $R^2 F^4$ coupling can
be roughly seen as the product of the chiral $R^2$ term with the real $F^4$
term. Note that, unlike for the lowest order K\"ahler potential, the
$0I$ and $00$-components of the second derivative ${\mathcal H}^{(8)}_{A_{\sf w} A\, \bar B}$
in \eqref{eq:R2F4-4dterms} are physical in this case, since they describe the
couplings of the RR one-form gauge field. In fact, the coupling
${\mathcal H}^{(8)}_{A_{\sf w} A\, \bar B}$ is proportional to the real part of the
period matrix, which describes the the theta angles in the two derivative theory.
The natural extension of \eqref{eq:R2F4-fun} to a function where $A_{\sf w}$ is
replaced by $A_{\sf t}$ and thus describes couplings of the type
$(\nabla E)^2 (\nabla F)^2$ is straightforward. However, in the compactification we
consider all such terms cancel identically, in a nontrivial way. Similarly, there
are no parity odd terms of this type either, so that this particular coupling
seems to be absent in four dimensions.
The same conclusion seems to hold for terms of the type $(\nabla H)^2 H^2 F^2$,
which would in principle be characteristic of the $H^6 F^2$ term in \eqref{eq:R4-red},
even though this coupling is not known in four dimensions. Terms of this order
in fields do not appear in the odd sector as well.
Finally, we consider the purely vector multiplet eight derivative couplings, corresponding to an $F^8$ term.
This can be obtained by a trivial dimensional reduction, leading to the four
dimensional coupling
\begin{equation}\label{eq:f8-coup}
t_8t_8 R(\Omega_+)^4 \rightarrow
72\, \big(\int_X \omega_{I}{}^{m n} \omega_J{}_{m n} \omega_K{}^{pq} \omega_{L}{}_{pq} \big)\,
\partial^{\mu\nu}u^{(I} \partial_{\mu\nu}u^J \partial^{\rho\sigma}u^K \partial_{\rho\sigma}u^{L)}\,,
\end{equation}
which can be described by the second quartic invariant in \eqref{eq:chiral-n4}.
Since the coupling above is given purely in terms of the product of the $(1,1)$ forms, $\omega_{I} \cdot\omega_J$,
the relevant real function is related to the K\"ahler potential and is given by
\begin{equation}\label{eq:F8-fun}
{\mathcal H}_{F^8}= 6\,\mathrm{e}^{4\,{\mathcal K}(Y ,\bar{Y})} \,.
\end{equation}
This function is consistent with \eqref{eq:f8-coup} for the $I$, $J$, indices and naturally
extends to the $0$-th gauge field in four dimensions as seen above, but we have not checked
those couplings explicitly.
\section{Six derivative couplings}
\label{sec:sixder}
At the six derivative level, we need to saturate two of the derivatives in the
internal directions, so that exactly one Riemann tensor will appear in the
relevant integrals on the Calabi-Yau manifold. This requirement turns out to
be quite restrictive, since all traces of the Calabi-Yau curvature vanish. It
follows that the internal integrals must also involve harmonic forms on which
the indices of the Riemann tensor are contracted. Given that we do not consider
any complex structure deformations, this observation directly
implies that no invariants involving only NS-NS fields, such as $R^2 H^2$ or
$H^6$, can arise in four dimensions\footnote{Note that these will become
nontrivial if more hyper/tensor multiplets are included in the reduction.}.
However, mixed couplings involving fields from both the NS-NS and the R-R sector
are nontrivial and a priori include three types of couplings, namely $R^2 F^2$,
$(\nabla E)^2 F^2$ and $H^2 F^4$. The latter has not been described in the context
of ${\mathcal N}\!=\!2$ supergravity, while the former two can be constructed using the techniques
in \cite{deWit:2010za}. In addition, a purely vector multiplet coupling including six
derivatives on the component fields, i.e. an $F^6$ invariant arises.
In particular, the $R^2 F^2$ term was already constructed explicitly in \cite{deWit:2010za},
and is governed by a function, ${\mathcal H}(X, A_{\sf w}; \bar{X})$, that is linear in the Weyl
multiplet, while the vector multiplet scalars appear through a holomorphic function of
degree $-2$ and an anti-holomorphic function of degree $0$. The relevant $R^2 F^2$ coupling is
\begin{equation}
{\mathcal H}_{A_{\sf w}\, \bar A \bar B}
R^{-}_{\mu\nu\rho\lambda} R^{-}{}^{\mu\nu\rho\lambda} \,
F^{+\,\bar{A}}{}_{\kappa \sigma} F^{+\,\bar{B}}{}^{\kappa \sigma} + \dots\,,
\end{equation}
where the part of the coupling coming from the R-R fields, as derived
from the reduction is
\begin{equation}\label{eq:RIJ-def}
{\mathcal H}_{A_{\sf w}\, \bar I \bar J}=\,
-48\,\int_{X} R_{mnpq}\,\omega_{I}{}^{mn}\omega_{J}{}^{pq}
\equiv -48\, {\mathcal R}_{IJ}\,,
\end{equation}
where in the second equality we defined the tensor ${\mathcal R}_{IJ}$ for later convenience.
This tensor clearly describes a non-topological coupling, since it depends on the curvature of
the Calabi-Yau manifold explicitly. In fact, the definition \eqref{eq:RIJ-def} is invertible,
as one can reconstruct the Riemann tensor $R_{mnpq}$ from ${\mathcal R}_{IJ}$ by contracting with
the harmonic two-forms. We record the following properties of ${\mathcal R}_{IJ}$, which will be useful
in the discussion below,
\begin{equation}
{\mathcal R}_{IJ}={\mathcal R}_{JI}\,, \qquad t^I{\mathcal R}_{IJ}=0\,, \qquad G^{IJ}{\mathcal R}_{IJ}=0\,,
\end{equation}
where $t^I$ and $G^{IJ}$ are the K\"ahler moduli and $G^{IJ}$ is the inverse of the K\"ahler
metric.
In order to extend \eqref{eq:RIJ-def} to include the $0$-th gauge field, we follow the same
procedure as in \eqref{eq:gr-ph-exten}, to obtain the additional couplings
\begin{equation}
{\mathcal H}^{(6)}_{\bar{A}_{\sf w}\, A B} =
\begin{pmatrix}
{\mathcal R}_{IJ} & {\mathcal R}_{IJ} u^J\\
u^I {\mathcal R}_{IJ} & {\mathcal R}_{IJ} u^I u^J
\end{pmatrix}
\rightarrow
\begin{pmatrix}
{\mathcal R}_{IJ} & {\mathcal R}_{IJ} \mbox{Re}( z^J)\\
\mbox{Re}(z^I) {\mathcal R}_{IJ} & {\mathcal R}_{IJ} \mbox{Re}(z^I) \mbox{Re}(z^J)
\end{pmatrix}
\,.
\end{equation}
We then obtain for the function describing the $R^2 F^2$ invariant
\begin{equation}\label{eq:R2F2-fun}
{\mathcal H}_{R^2F^2} =\,
-\frac{3\mathrm{i}}{8}\,\frac{\bar{A}_{\sf w}}{(\bar{Y}^0)^2} \hat{{\mathcal R}}_{IJ}
\left( \frac{Y^I}{Y^0} - \frac{\bar{Y}^I}{\bar{Y}^0}\right)\,\left( \frac{Y^J}{Y^0} + \frac{\bar{Y}^J}{\bar{Y}^0}\right)\,,
\end{equation}
where $\hat{{\mathcal R}}_{IJ}(Y, \bar{Y})={\mathcal R}_{IJ}(t)$ is viewed as a function of the $t^I=\mbox{Im}(\tfrac{Y^I}{Y^0})$,
as obtained in the standard special coordinates. Note that \eqref{eq:R2F2-fun} is manifestly homogeneous
in the holomorphic scalars $Y^A$, but non-homogeneous in the anti-holomorphic scalars $\bar{Y}^A$, as expected.
It is straightforward to obtain a term of the type $(\nabla E)^2 F^2$ by simply replacing
$A_{\sf w} \rightarrow A_{\sf t}$ in \eqref{eq:R2F2-fun}, in line with previous observations.
It turns out that this invariant is also generated by the reduction, as
\begin{equation}
{\mathcal H}_{A_{\sf t}\, \bar A \bar B}
\nabla^{[a} E^{b]^{-}} \nabla_{[a} E_{b]^{-}} \,
F^{+\,\bar{A}}{}_{\kappa \sigma} F^{+\,\bar{B}}{}^{\kappa \sigma} + \dots\,,
\end{equation}
where the two couplings ${\mathcal H}^{(6)}_{A_{\sf t}\, \bar I \bar J} = {\mathcal H}^{(6)}_{A_{\sf w}\, \bar I \bar J}$,
are equal. By the same argument as above, the function \eqref{eq:R2F2-fun} can be extended
to include the tensor multiplet coupling as
\begin{equation}\label{eq:RP2F2-fun}
{\mathcal H}^{(6)}(\bar{A}_{\sf w}, \bar{A}_{\sf t}, Y, \bar{Y} ) =\,
-\mathrm{i}\,\frac{\bar{A}_{\sf w} + \bar{A}_{\sf t}}{(\bar{Y}^0)^2} \hat{{\mathcal R}}_{IJ}
\left( \frac{Y^I}{Y^0} - \frac{\bar{Y}^I}{\bar{Y}^0}\right)\,\left( \frac{Y^J}{Y^0} + \frac{\bar{Y}^J}{\bar{Y}^0}\right)\,,
\end{equation}
which describes the first row in the six-derivative part of table \ref{tbl:sum}.
We now turn to the $F^6$ term, which is computationally more challenging than the
couplings described above. This is due to the fact that there are no terms cubic in the
two-form field strength $H$ in ten dimensions, so that $(\nabla F)^3$ terms do not arise
in four dimensions. This is consistent with the fact that similar terms cancel in the
$F^6$ coupling that follows from the cubic invariant described in appendix \ref{app:kinetic}.
One therefore is forced to consider terms of the type $(\nabla F)^2 F^2$, which are
quartic in the $(1,1)$ forms $\omega_I$, from the point of view of the Calabi-Yau reduction.
The result is a coupling containing all possible combinations of an internal Riemann tensor
and four $\omega_I$, as in
\begin{equation}
\omega_I{}^{mn} \omega_J{}_{mn} R^{pqrs}\omega_K{}_{pq}\omega_L{}_{rs}\,,
\quad
\omega_I{}^{mn} \omega_J{}_{np} R^{pqrs}\omega_K{}_{qm}\omega_L{}_{rs}\,,
\quad
\dots\,,
\end{equation}
which in principle determine the function controlling the $F^6$ coupling. However, we also
find nontrivial odd terms for the scalars resulting from \eqref{eq:x8}, in contrast to the
known coupling in section \ref{app:kinetic}. These terms include
\begin{eqnarray}\label{eq:F6-odd}
\mathcal{L}_{\text{odd}} &\sim& Y_{IJKMN}\,d u^I \wedge d u^J \wedge d u^K \wedge (\partial^\mu u^M d\, \partial_\mu u^N )\,,
\nonumber\\
Y_{IJKMN}\,&=& \int \omega_I\wedge\omega^m{}_M\wedge\omega^n{}_N \wedge
\left( 2\,R_{np} \omega^{pq}{}_J \omega_{qm}{}_K + \omega_{np}{}_J R^{pq} \omega_{qm}{}_K \right) + \dots \,,
\end{eqnarray}
where the dots stand for terms containing the same objects in double traces rather than s single one.
We observe that a term completely antisymmetric in three indices $I\,, J\,, K$ arises and conclude
that the known coupling is not sufficient to describe these terms. We leave it to future
work to determine the possible new coupling(s) that can complete the structure.
Finally, it is worth discussing in brief the invariant of the type $H^2 F^4$, which
is not known explicitly in supergravity. Such terms do appear and seem to be controlled
by the same tensor ${\mathcal R}_{IJ}$ in \eqref{eq:RIJ-def} above, since we find the characteristic
couplings ${\mathcal R}_{IJ} E^2 \nabla F^I \nabla F^I$ for all possible contractions of indices
between the vector and tensor multiplet field strengths. Similarly, we find the parity odd
terms
\begin{gather}
W_{IJKL}\,H\wedge (\partial^\mu u^I d \partial_\mu u^J ) (\partial^\nu u^K \partial_\nu u^L )\,,
\nonumber\\
W_{IJKL} = \int_X \! \omega^m{}_I\wedge\omega^n{}_J \wedge
\omega_m{}_K\wedge\omega^p{}_L \wedge R_{np} + \dots\,,
\label{eq:H2F4-odd}
\end{gather}
where in the last integral we used similar conventions as in \eqref{eq:F6-odd} above.
Indeed, the two integrals appear to be closely related, so that the two couplings may
have a similar origin in terms of superspace invariants.
\section{Four derivative couplings}
\label{sec:fourder}
In order to obtain four derivative couplings in four dimensions from the 10D
$R^4$ invariant, one needs to consider terms that include exactly two Riemann
tensors in the internal directions. It follows that the integrals controlling
the 4D couplings are quadratic in the Calabi-Yau curvature, in the same way as
the six derivative couplings of the previous section are controlled by the
Calabi-Yau Riemann tensor through \eqref{eq:RIJ-def} above.
At this level in derivatives, four structures can appear, namely $R^2$, $F^4$,
$H^2 F^2$, and $H^4$. Given our assumption of no hyper/tensor multiplets other than
the universal tensor multiplet, all of these structures will be described by
functions involving vector multiplet scalars, but only the latter two involve the
tensor multiplet explicitly. All couplings except the $H^2 F^2$ terms can be
described straightforwardly in ${\mathcal N}\!=\!2$ supergravity, and we now discuss each in turn.
\subsubsection*{The $R^2$ term}
The $R^2$ term has been known for quite some time \cite{Bergshoeff:1980is, Antoniadis:1997eg}, and arises from
terms that can be completely factorised in internal and external indices, as
\begin{align}
\label{eq:gr-te}
(t_8t_8 -\tfrac18\epsilon_{10}\epsilon_{10})R(\Omega_+)^4 \rightarrow
\,& \alpha_I t^I\, \left( R_{\mu \nu \rho \lambda} (\Omega_+) R^{\mu \nu \rho \lambda} (\Omega_+) + \epsilon_{abcd} R^{ab}_2(\Omega_+) \wedge R^{cd}_2(\Omega_+) \right)
\nonumber\\
B \wedge t_8 \left[ R^4 (\Omega_+) + R^4(\Omega_-) \right] \rightarrow
\,&\alpha_I u^I \,\big( \tr R(\Omega_+)\wedge R(\Omega_+) + \tr R(\Omega_-)\wedge R(\Omega_-) \big)
\end{align}
where we used \eqref{eq:zero-id} and
\begin{equation}
\alpha_I = \int_X \omega_I \wedge \tr R^2\,,
\end{equation}
are the the second Chern classes of the Calabi-Yau four-cycles. Note that this is a topological
quantity, unlike the objects controlling higher derivative couplings described above, as e.g. in \eqref{eq:RIJ-def}.
The supergravity description requires to allow the lowest order prepotential to
depend on the Weyl multiplet through $A_{\sf w}$ \cite{deWit:1996ix}, so that the
explicit prepotential arising from \eqref{eq:gr-te} is given by
\begin{equation}\label{eq:pert-prepot}
F = -\frac16\, \frac{C_{IJK} Y^I Y^J Y^K}{Y^0} + \frac{1}{24\cdot 64}\,\frac{\alpha_I Y^I}{Y^0}\, A_{\sf w}\,,
\end{equation}
where we remind the reader that the physical moduli are given by $z^I=\frac{Y^I}{Y^0}$ in terms of the
scalars $Y^A$ above.
\subsubsection*{The $H^4$ term}
Turning to the tensor multiplet sector, an explicit computation using \eqref{eq:two-id} leads to
the following terms in four dimensions
\begin{align}
(t_8 t_8 - \frac18\,\varepsilon_{10}\varepsilon_{10})R^4 =&\,
48\, R^{m n p q} R_{m n p q}\,\big(
2\, {\partial}^{[\mu} E^{\nu]}\, {\partial}_{[\mu} E_{\nu]}
+\frac34\, (E^{\mu}E_{\mu})^2
\big)
\,,
\end{align}
where, in complete analogy with the $R^2$ terms, only factorised traces contribute.
It follows that the four dimensional Lagrangian contains the four derivative tensor
multiplet invariant arising from \eqref{eq:CT}, controlled by exactly the same prepotential
in \eqref{eq:pert-prepot}, upon extending the term containing the Weyl background to include
the tensor background, as
\begin{equation}\label{eq:pert-prepot-H}
F = -\frac16\, \frac{C_{IJK} Y^I Y^J Y^K}{Y^0} + \frac{1}{24\cdot 64}\,\frac{\alpha_I Y^I}{Y^0}\, (A_{\sf w} + 8\,A_{\sf t})\,,
\end{equation}
with $A_{\sf t}$ as in \eqref{eq:A-tens-sq}. This function describes the couplings in the
first line of Table \ref{tbl:sum}.
Once again we observe the close relation between the $R^2$ and tensor multiplet couplings,
which are characterised by exactly the same functional form in terms of the corresponding
chiral backgrounds. This structure arises despite the fact that in ${\mathcal N}\!=\!2$ supergravity
in four dimensions the tensor $H$ and gravity are not in the same multiplet anymore, so that,
a priori, more flexibility, parametrized by two functions is allowed. However, we find that
the Calabi-Yau reduction leads to a single function of vector multiplet scalars for both couplings.
\subsubsection*{The $F^4$ term}
In the purely RR sector, an invariant quartic in derivatives on the vector multiplet components
exists in 4D, which is characterised by an $(\nabla F)^2$ coupling. As above, we analyse the
terms arising from the odd term under pair exchange in $R(\Omega_+)$ in order to obtain these
explicitly. Using \eqref{eq:two-id}, the terms coming from non-Ricci combinations cancel, and
the remaining ones are Laplacians of four dimensional fields. Explicitly, we obtain that the
total $(\nabla F)^2$ term reads
\begin{align}\label{eq:two-index}
(t_8 t_8 - \frac18\,\epsilon_{10}\epsilon_{10})R^4
\rightarrow&\,
3\,X_{IJ} \nabla^2 u^I \nabla^2 u^J\,,
\end{align}
where $X_{IJ}$ is the tensor
\begin{eqnarray}\label{eq:X-def}
X_{IJ} &=& \int_X \epsilon_{m n m_1 \ldots m_4} \epsilon_{pq n_1 \ldots n_4}
R^{m_1m_2n_1n_2}R^{m_3 m_4 n_3n_4} \,\, \omega_I\,^{mn} \, \omega_J\,^{pq}\,,
\end{eqnarray}
and is explicitly given by
\begin{align}
X_{IJ} =\, 8\,
\, \big[ & ({R}_{m n p q})^2 \omega_I{}^{rs} \omega_J{}_{rs}\,
- 8\, {R}^{m n p q} {R}_{m n p}\,^{r} \omega_I{}_{q}\,^{s} \omega_J{}_{rs}
+ 4\, {R}^{m n p q} {R}_{m n}\,^{r s} \omega_I{}_{p r}\, \omega_J{}_{q s}\,
\nonumber\\
&\,
+ 2\, {R}^{m n p q} {R}_{m n}\,^{r s} \omega_I{}_{p q}\, \omega_J{}_{r s}\,
- 8\, {R}^{m n p q} {R}_{m}\,^{r}\,_{p}\,^{s} \omega_I{}_{n r}\, \omega_J{}_{q s}
\big]
\end{align}
The gauge field partner of these scalar couplings is obtained by lifting to eleven
dimensions the original expression and reducing back on a circle times a Calabi-Yau.
It then follows that the result for gauge fields takes the
form
\begin{align}\label{eq:two-index-vec}
(t_8 t_8 - \frac18\,\epsilon_{10}\epsilon_{10})R^4
\rightarrow&\,
3\,X_{IJ} \nabla^a F_{ac}^I \nabla^b F_b{}^c{}^J\,.
\end{align}
Comparing \eqref{eq:two-index} and \eqref{eq:two-index-vec} to the known $F^4$
term in supergravity, given in \eqref{eq:real-susp-action}, we find that the
interactions of the vector multiplets arising from expansion along the second
cohomology are governed by the tensor $X_{IJ}$ above.
We now turn to the three-index structure, and compute the parity odd term quadratic in 4D field
strengths. Following the same lifting and reducing procedure, we
find that the only even-odd term quadratic in 3-from field strengths is
\begin{equation}
t_8{}_{\mu_1\dots \mu_8} B \wedge \nabla G^{\mu_1 \mu_2 \mu_9} \wedge \nabla G^{\mu_3 \mu_4}{}_{\mu_9} \wedge R^{\mu_5 \mu_6} \wedge R^{\mu_7 \mu_8} \,,
\end{equation}
which upon reduction to 4D gives rise to a term of the type
\begin{equation}
6\,u^K\,H_{IJ,K}\,\epsilon^{\mu\nu\rho\lambda} \nabla_{\mu} F^I{}_{\nu}{}^{\kappa} \nabla_{\rho} F^I{}_{\lambda \kappa}
\simeq
-3\,H_{IJ,K}\,\epsilon^{\mu\nu\rho\lambda} \nabla_{\mu}u^K\, F^I{}_{\nu\rho} \nabla_{\kappa} F^I{}_{\lambda \kappa}
+\dots\,,
\end{equation}
where in the second step we partially integrated and the dots denote terms involving the derivative
of the coupling $H_{IJ,K}$. The explicit expression for this three index coupling follows from the
relation
\begin{align}
u^K\,H_{IJ,K}= -16\,
\, \int_{X} B\wedge & \big[ {R}^{m n}\wedge {R}_{m n} \omega_I{}^{rs} \omega_J{}_{rs}\,
- 8\, {R}^{p q}\wedge {R}_{p}\,^{r} \omega_I{}_{q}\,^{s} \omega_J{}_{rs}
\nonumber\\
&\,
- 4\, {R}^{p q} \wedge {R}^{r s} \omega_I{}_{p r}\, \omega_J{}_{q s}\,
+ 2\, {R}^{p q} \wedge {R}\,^{r s} \omega_I{}_{p q}\, \omega_J{}_{r s}\, \big]\,,
\end{align}
where we note the important identities
\begin{align}
t^K\,H_{IJ,K}
= - X_{IJ}\,,
\qquad
t^I X_{IJ} = 32\,\alpha_I\,.
\end{align}
The remaining interactions with the ten dimensional RR gauge field, $F^0$, described
by ${\mathcal H}_{0I}$ and ${\mathcal H}_{00}$, are obtained by viewing $F^0$ as a Kaluza-Klein gauge
field, coming from the reduction from 11D. As these must necessarily be quadratic
in the Kaluza-Klein gauge fields, only the factorised term in the 10D invariant
contributes. It then follows that, as far as terms quadratic in Riemann tensors are
concerned, the lifting and reducing procedure is identical to the 4D/5D connection
studied in \cite{Banerjee:2011ts}. Therefore, we can simply add the couplings ${\mathcal H}_{0I}$
and ${\mathcal H}_{00}$ found in that work, given by
\begin{align}
\label{eq:4D-5D-res}
\mathcal{H}_{0\bar{I}}\big|_{\text{\tiny KK}}
=&\, -12\, \mathrm{i} \alpha_I = -\frac38\,\mathrm{i}\, X_{IJ}t^J \,,
\nonumber\\
\mathcal{H}_{0\bar{0}}\big|_{\text{\tiny KK}}
=&\,24\, \alpha_I t^I = \frac34\, X_{IJ} t^I t^J \,,
\end{align}
to the ones in \eqref{eq:two-index} and \eqref{eq:two-index-vec} above.
After adding the extra contribution in \eqref{eq:4D-5D-res} to \eqref{eq:two-index}, and
performing the by now standard shift in \eqref{eq:gr-ph-exten} to account for the
axionic coupling to the $0$-th gauge field strength, we obtain the final form of the
coupling ${\mathcal H}_{AB}$, as
\begin{equation}\label{eq:F4-metric}
{\mathcal H}_{A\bar{B}} =
\begin{pmatrix}
X_{IJ} & - X_{IJ} z^J\\
-\bar{z}^I X_{IJ} & X_{IJ} z^I \bar{z}^J
\end{pmatrix}
\rightarrow
|Y^0|^{-4}
\begin{pmatrix}
|Y^0|^2\, X_{IJ} & - \bar{Y}^0\, X_{IJ} Y^J\\
- Y^0\,\bar{Y}^I X_{IJ} & X_{IJ} Y^I \bar{Y}^J
\end{pmatrix}\,,
\end{equation}
where in the second step we passed from the special coordinates $z^I$ to the
projective coordinates $Y^A$. Note that the coupling $X_{IJ}$ is real and
depends only on the K\"ahler moduli $t^I$, similar to the lowest order K\"ahler
potential.
The couplings \eqref{eq:F4-metric} satisfy the condition $Y^A {\mathcal H}_{A\bar{B}}=0$,
so that they belong to the class of \cite{deWit:2010za}. Recently, a more general class
of $F^4$ invariants appeared in \cite{Butter:2013lta}, which allows for $Y^A {\mathcal H}_{A\bar{B}}\neq 0$
and contains additional terms quadratic in the Ricci tensor. However, we find that no such extra
terms appear in the reduction of the 10D action, beyond the one in the familiar (Weyl)$^2$ term,
consistent with the properties of ${\mathcal H}_{A\bar{B}}$ above.
\subsubsection*{On $H^2F^2$ terms}
\label{sec:H2F2}
Finally, we comment on the possible four derivative terms which mix tensor and vector
multiplets. Such terms have not been explicitly constructed in the literature and it
is a interesting open problem to tackle, even for rigidly supersymmetric theories. Indeed,
a construction of such an invariant is likely to lead to insight into more general mixed
terms of the type $H^{2n} F^{2m}$, where $n$ is odd, examples of which have been mentioned
above (e.g. the $H^{2} F^{4}$ term).
An explicit computation of the terms arising from reduction of the parity even terms at this
order reveals that terms involving derivatives of $H$ and $F$ do not arise. However, we do find
nontrivial terms involving field strengths only, e.g.
\begin{equation} \label{eq:H2F2-even}
\mathcal{L} \propto X_{IJ} E^\mu E^\nu \partial_\mu u^I \partial_\nu u^J\,,
\end{equation}
and terms related to this by introducing the gauge field strengths, i.e.
$X_{IJ} E^\mu E^\nu F^I{}_{\mu}{}^{\rho} F^J{}_{\nu \rho}$, where $X_{IJ}$ is the integral
defined in \eqref{eq:X-def} above. In order to obtain this result, we used \eqref{eq:two-id}
and we note that the additional terms $\Delta J_0(\Omega_+, H)$ in \eqref{eq:ooLaghat} are
nontrivial in this case.
In addition, the parity odd terms are also nontrivial for these couplings,
since one can easily verify that the parity odd term \eqref{eq:x8} leads to couplings of
the type
\begin{equation}\label{eq:H2F2-odd}
Y_{IJ}\, H \wedge \partial^\mu u^{[I} d \partial_\mu u^{J]}
\,,
\end{equation}
where $Y_{IJ}$ is the integral
\begin{equation}
Y_{IJ}= \int \left(
R^{mn}\wedge R_{np}\wedge \omega_I{}^p \wedge \omega_J{}_m
-\frac1{8} \, R^{mn}\wedge R_{mn}\wedge \omega_I{}^p \wedge \omega_J{}_p \right) \,.
\end{equation}
In the last relation, the two-forms $\omega_I$ are viewed as vector valued one-forms, for
convenience. Note that the term \eqref{eq:H2F2-odd} is linear in the tensor field strength,
unlike the parity even coupling \eqref{eq:H2F2-even}. This may seem counterintuitive, but
we stress that our simplifying choice of ignoring the scalars in the tensor
multiplet may obscure the connection between tensor multiplet couplings that are expected
to be controlled by appropriate functions of these scalars. Finally, we point out that
$Y_{IJ}$ is by definition antisymmetric in its indices, which is similar to the corresponding
six derivative terms in \eqref{eq:F6-odd}-\eqref{eq:H2F4-odd} above. This type of odd terms
is somewhat unconventional in the ${\mathcal N}\!=\!2$ setting and may point to a common origin of
all these unknown invariants.
One possible way to construct couplings of this type is to make use of the results of
\cite{Butter:2010jm}, on arbitrary couplings of vector and tensor multiplet superfields.
In terms of the superfields $G^2$ and $W^A$ describing the tensor and vector multiplets
respectively, one may consider an integral of the type\footnote{We thank Daniel Butter
for pointing out this possibility.}
\begin{equation}\label{eq:vec-ten}
\int\! d^4\theta d^4\bar\theta \, {\mathcal H}({ W,\bar W})\, G^2 \,,
\end{equation}
in order to describe couplings such as above, where the function ${\mathcal H}$ must be such that
the couplings \eqref{eq:H2F2-even}-\eqref{eq:H2F2-odd} are reproduced. It is worth
mentioning that including kinetic multiplets in \eqref{eq:vec-ten} may lead to even
higher derivative couplings that can account for some of the unknown couplings pointed
out above, i.e. of the type $H^{2n} F^{2m}$, where $n$ is odd. The explicit realisation
of the possible Lagrangians following from the integral \eqref{eq:vec-ten} in components
would require the construction of a density formula for a general real multiplet of
${\mathcal N}\!=\!2$ supergravity and falls outside the scope of the present work.
\section{Some open questions}
\label{sec:open}
We shall conclude with a list of some open questions.
\medskip
\noindent
One immediate consequence of this work is the prediction of new four-dimensional higher-derivative ${\mathcal N}\!=\!2$ invariants. It would be nice to be able to verify this prediction by explicitly constructing some of these terms, either using the structure in \eqref{eq:vec-ten}, or new techniques. It is interesting to point out that the new invariants involve terms, descending from the eleven-dimensional anomalous terms $C_3 \wedge X_8$, which are top-form Chern-Simons-like couplings. Examples of these at the six-and four-derivative are discussed in sections \ref{sec:sixder} and \ref{sec:fourder} respectively. It would also be very interesting to verify whether the terms that we find to be vanishing but could in principle be nontrivial, such as the $H^6 F^2$ and $(\nabla H)^2 (\nabla F)^2$ terms, do exist or not.
Moreover, we stress that we have been focusing on the leading terms, matching to the invariants constructed
in \cite{deWit:2010za} and disregarding the possibility of more detailed structures that might appear. While we have
not found any inconsistencies, we cannot exclude the existence of subleading terms that are not captured here. For example,
the types of invariants recently constructed in \cite{Butter:2013lta} allow for additional couplings proportional to
the square of the Ricci tensor, rather than the Weyl tensor alone.
\medskip
\noindent
There is a number of important omissions here. We have worked exclusively with one-loop terms, and avoided the discussion of the dilaton. Our excuse can be that the tree-level terms neither survive the eleven-dimensional limit, nor contribute to the well studied $R^2$ terms in four dimensions. Yet they are important for understanding the corrections to the moduli spaces. In addition the dilaton is subtle and important enough to merit a discussion.
As already mentioned, we have largely ignored the complex deformations of the internal CY. It might be of some interest to extend our results to generic hyper-matter, since that would most likely turn on the couplings that we find to be vanishing.
We have concentrated only on CY compactification and hence ungauged ${\mathcal N}\!=\!2$ theories. Quantum corrections to the super potential have been much studied and are of obvious interest. It would be very interesting to extend the discussion of (at least some of ) the higher derivative couplings to the gauged theories. The fact that the couplings described here have an off-shell formulation is helpful in that respect.
\medskip
\noindent
The relation of our calculation to the topological string calculations needs further elucidation. Most of our CY integrals are not topological and one may ask if there is an extension or refinement of topological strings that may capture the physical string theory couplings described here. Our calculations are exclusively one-loop, but one might hope that the structure of the terms discussed here, and the relations between different supersymmetric invariants are sufficiently restricted by supersymmetry to extend to all genus calculations.
\medskip
\noindent
The structure of the various functions describing the coupling of the gravity and tensor multiplets seem to treat the two backgrounds on the same footing, somehow reflecting the structure of the ten dimensional action built out of the torsionfull curvature tensor $R(\Omega_+)$. Given that this structure was instrumental in checking T-duality in \cite{Liu:2013dna}, it would be interesting to consider the properties of our couplings under the $c$-map, which is the lower dimensional analogous operation. Note that this would explicitly relate the vector and tensor multiplets, especially in view of the fact that the various couplings mix the two kinds of multiplets.
\medskip
\noindent
The new terms discussed here are not relevant for BPS black hole physics, at least at the attractor \cite{deWit:2010za,Dabholkar:2010uh,Gomes:2013cca}, as they
vanish by construction on fully BPS backgrounds and do not affect the entropy and charges. However, our results are relevant for non-BPS black holes
and may be related to the one-loop modifications to the entropy of such objects, as in \cite{Sahoo:2006rp}.
\section*{Acknowledgement}
We thank G. Bossard, D. Butter, B. de Wit, I. Florakis, Y. Nakayama, H. Ooguri, R. Savelli, S. Shatashvili,
A. Tomasiello and E. Witten for stimulating discussions.
The work of S.K. is supported by the European Research Council under the European Union's Seventh Framework Program (FP/2007-2013)-ERC Grant Agreement n. 307286 (XD-STRING). The work of RM is supported in part by ANR grant 12-BS05-003-01.
\begin{appendix}
\section{Tensor structures in ten dimensions}
\label{sec_A:R4in10d}
We define the tensor, $t_8$, as having four antisymmetric pairs of indices and given
in terms of its contraction with an antisymmetric tensor $F^{\mu\nu}$ by
\begin{align}
t_8 F^4 = &\, 24\, \tr F^4 - 6\, (\tr F^2)^2\,.
\end{align}
Taking derivatives of this identity with respect to $F$ one can obtain the explicit
tensor $t_8$.
The Type IIA one-loop correction in ten dimensions contains terms quadratic in $t_8$ and
quartic in the modified curvature $R(\Omega_+)_{\mu_1\mu_2}{}^{\mu_3\mu_4}$. The latter
is antisymmetric in each pair of indices, but does not satisfy the Bianchi and pair
exchange identities. Considering a general tensor, ${\mathcal R}$, with these symmetries, the
relevant expression reads
\begin{equation}
t_8 t_8 {\mathcal R}^4 = 192\, {\mathcal R}_{1} + 384\, {\mathcal R}_{2}
+ 24\, {\mathcal R}_{3} + 12\, {\mathcal R}_{4} - 96\,( {\mathcal R}_{5 a} + {\mathcal R}_{5 b}) - 48\, ({\mathcal R}_{6 a} + {\mathcal R}_{6 b}) \,,
\end{equation}
where the ${\mathcal R}_i$ are defined in \eqref{eq:R-struct} below. Similarly, we display for completeness
the full expression for the odd-odd term quartic in ${\mathcal R}$ as
\begin{align}
-\frac18\,\varepsilon_{10} \varepsilon_{10} {\mathcal R}^4 = &\,
192\,\tilde{\mathcal R}_{1} + 24\,\tilde{\mathcal R}_{3} + 12\, \tilde{\mathcal R}_{4} - 192\, \tilde{\mathcal R}_{5} - 384\, \tilde{\mathcal R}_{6} - 384\, \tilde A_{7}
\nonumber\\
&\,
+ 4\, {\mathcal R}\, {\mathcal R}\,\left( {\mathcal R}\, {\mathcal R}\,
+ 6\,{{\mathcal R}}^{\mu_1 \mu_2 \mu_3 \mu_4} {{\mathcal R}}_{\mu_3 \mu_4 \mu_1 \mu_2}
- 24\, {\mathcal R}\, {\mathcal R}\, {{\mathcal R}}^{\mu_1 \mu_2} {{\mathcal R}}_{\mu_2 \mu_1}
\right)
\nonumber\\
&\,
+ 384\, {\mathcal R}\,{{\mathcal R}}^{\mu_1 \mu_2}\, \left(
{{\mathcal R}}_{\mu_2}\,^{\mu_3}\,_{\mu_1}\,^{\mu_4} {{\mathcal R}}_{\mu_4 \mu_3}
-{{\mathcal R}}_{\mu_2}\,^{\mu_3 \mu_4 \mu_5} {{\mathcal R}}_{\mu_4 \mu_5 \mu_1 \mu_3}
+\frac23\, {{\mathcal R}}_{\mu_2}\,^{\mu_3} {{\mathcal R}}_{\mu_3 \mu_1}
\right)
\nonumber\\
&\,
+ 32\, {\mathcal R}\,{{\mathcal R}}^{\mu_1 \mu_2 \mu_3 \mu_4} \, \left(
{{\mathcal R}}_{\mu_3 \mu_4}\,^{\mu_5 \mu_6} {{\mathcal R}}_{\mu_5 \mu_6 \mu_1 \mu_2}
-4\,{{\mathcal R}}_{\mu_3}\,^{\mu_5}\,_{\mu_1}\,^{\mu_6} {{\mathcal R}}_{\mu_4 \mu_6 \mu_2 \mu_5}
\right)
\nonumber\\
&\,
+ 96\, {{\mathcal R}}^{\mu_1 \mu_2} {{\mathcal R}}_{\mu_2 \mu_1} \, \left(
2\, {{\mathcal R}}^{\mu_3 \mu_4} {{\mathcal R}}_{\mu_4 \mu_3}
- {{\mathcal R}}^{\mu_3 \mu_4 \mu_5 \mu_6} {{\mathcal R}}_{\mu_5 \mu_6 \mu_3 \mu_4} \right)
\nonumber\\
&\,
+ 768\, {{\mathcal R}}^{\mu_1 \mu_2} {{\mathcal R}}_{\mu_2}\,^{\mu_3}\,_{\mu_1}\,^{\mu_4}
\big(
{{\mathcal R}}_{\mu_4}\,^{\mu_5 \mu_6 \mu_7} {{\mathcal R}}_{\mu_6 \mu_7 \mu_3 \mu_5}
\nonumber
\\
&\,\hspace{4.3cm}
- {{\mathcal R}}_{\mu_4}\,^{\mu_5}\,_{\mu_3}\,^{\mu_6} {{\mathcal R}}_{\mu_6 \mu_5}
- 2\,{{\mathcal R}}_{\mu_4}\,^{\mu_5} {{\mathcal R}}_{\mu_5 \mu_3}
\big)
\nonumber\\
&\,
+384\, {{\mathcal R}}^{\mu_1 \mu_2} {{\mathcal R}}_{\mu_2}\,^{\mu_3}\,\left(
2\, {{\mathcal R}}_{\mu_3}\,^{\mu_4 \mu_5 \mu_6} {{\mathcal R}}_{\mu_5 \mu_6 \mu_1 \mu_4}
-{{\mathcal R}}_{\mu_3}\,^{\mu_4} {{\mathcal R}}_{\mu_4 \mu_1}
\right)
\nonumber\\
&\,
+ 384\, {{\mathcal R}}^{\mu_1 \mu_2} {{\mathcal R}}_{\mu_2}\,^{\mu_3 \mu_4 \mu_5} \big(
{{\mathcal R}}_{\mu_4 \mu_5 \mu_1}\,^{\mu_6} {{\mathcal R}}_{\mu_6 \mu_3}
- {{\mathcal R}}_{\mu_4 \mu_5}\,^{\mu_6 \mu_7} {{\mathcal R}}_{\mu_6 \mu_7 \mu_1 \mu_3}
\nonumber\\
&\,\hspace{4.2cm}
+ 2\, {{\mathcal R}}_{\mu_4}\,^{\mu_6}\,_{\mu_1 \mu_3} {{\mathcal R}}_{\mu_5 \mu_6}
+ 4\, {{\mathcal R}}_{\mu_4}\,^{\mu_6}\,_{\mu_1}\,^{\mu_7} {{\mathcal R}}_{\mu_5 \mu_7 \mu_3 \mu_6} \big)
\end{align}
where ${\mathcal R}_{\mu_1\mu_2}={\mathcal R}_{\mu_1\mu_3\mu_2}{}^{\mu_3}$ is a non-symmetric tensor corresponding to
the Ricci tensor and the scalar ${\mathcal R}$ is its trace.
The various non-Ricci combinations appearing in both the even-even and odd-odd structures are defined as
\begin{align}\label{eq:R-struct}
{\mathcal R}_{1} =&\, \tr {\mathcal R}^{\mu_1 \mu_2} {\mathcal R}_{\mu_2 \mu_3} {\mathcal R}^{\mu_3 \mu_4} {\mathcal R}_{\mu_4 \mu_1} \,,
\qquad
\tilde{\mathcal R}_{1} = \tr {{\mathcal R}}_{\mu_1 \mu_2} \tilde{\mathcal R}^{\mu_2 \mu_3} {{\mathcal R}}_{\mu_3 \mu_4} \tilde{\mathcal R}^{\mu_4 \mu_1} ,
\nonumber\\
{\mathcal R}_{2} = &\, \tr {\mathcal R}^{\mu_1 \mu_2} {\mathcal R}_{\mu_2 \mu_3} {\mathcal R}_{\mu_1 \mu_4} {\mathcal R}^{\mu_4 \mu_3} ,
\nonumber\\
{\mathcal R}_{3}= &\, \tr {\mathcal R}_{\mu_1 \mu_2} {\mathcal R}^{\mu_3 \mu_4} \tr {\mathcal R}^{\mu_1 \mu_2} {\mathcal R}_{\mu_3 \mu_4} ,
\qquad
\tilde{\mathcal R}_{3}= \tr {\mathcal R}^{\mu_1 \mu_2} \tilde{{\mathcal R}}^{\mu_3 \mu_4} \tr {\mathcal R}_{\mu_3 \mu_4} \tilde{{\mathcal R}}_{\mu_1 \mu_2},
\nonumber\\
{\mathcal R}_{4}= &\, \tr {\mathcal R}^{\mu_1 \mu_2} {\mathcal R}_{\mu_1 \mu_2} \tr {\mathcal R}^{\mu_5 \mu_6} {\mathcal R}_{\mu_5 \mu_6} ,
\qquad
\tilde{\mathcal R}_{4}= \tr {\mathcal R}^{\mu_1 \mu_2} \tilde{{\mathcal R}}_{\mu_1 \mu_2} {\mathcal R}^{\mu_5 \mu_6} \tilde{{\mathcal R}}_{\mu_5 \mu_6} ,
\nonumber\\
{\mathcal R}_{5a} = &\, \tr {\mathcal R}_{\mu_1 \mu_2} {\mathcal R}^{\mu_2 \mu_5} \tr {\mathcal R}_{\mu_5 \mu_6} {\mathcal R}^{\mu_6 \mu_1} ,
\qquad
{\mathcal R}_{5b} = \tr \tilde{{\mathcal R}}^{\mu_3 \mu_4} \tilde{{\mathcal R}}_{\mu_3 \mu_5} \tr \tilde{{\mathcal R}}^{\mu_5 \mu_8} \tilde{{\mathcal R}}_{\mu_4 \mu_8} ,
\nonumber\\
\tilde{\mathcal R}_{5} = &\, \tr {\mathcal R}^{\mu_1 \mu_2} \tilde{{\mathcal R}}_{\mu_1 \mu_5} \tr {\mathcal R}^{\mu_5 \mu_6} \tilde{{\mathcal R}}_{\mu_2 \mu_6} ,
\nonumber\\
{\mathcal R}_{6a} = &\, \tr {\mathcal R}^{\mu_1 \mu_2} {\mathcal R}^{\mu_5 \mu_6} \tr {\mathcal R}_{\mu_1 \mu_5} {\mathcal R}_{\mu_2 \mu_6} ,
\qquad
{\mathcal R}_{6b}= \tr \tilde{{\mathcal R}}^{\mu_3 \mu_4} \tilde{{\mathcal R}}_{\mu_5 \mu_6} \tr \tilde{{\mathcal R}}_{\mu_3 \mu_5} \tilde{{\mathcal R}}_{\mu_4 \mu_6} ,
\nonumber\\
\tilde{\mathcal R}_{6} = &\, \tr {\mathcal R}_{\mu_1 \mu_2} \tilde{\mathcal R}^{\mu_5 \mu_6} {\mathcal R}_{\mu_8 \mu_5}{}^{\mu_7 \mu_1} {\mathcal R}_{\mu_7 \mu_6}{}^{\mu_8 \mu_2},
\nonumber\\
\tilde A_{7} = &\, {\mathcal R}_{\mu_1 \mu_2}{}^{\mu_3 \mu_4} {\mathcal R}_{\mu_3 \mu_5}{}^{\mu_1 \mu_6}
{\mathcal R}_{\mu_4 \mu_7}{}^{\mu_5 \mu_8} {\mathcal R}_{\mu_6 \mu_8}{}^{\mu_2 \mu_7} \,,
\end{align}
for any tensor ${\mathcal R}_{\mu_1 \mu_2}{}^{\mu_3 \mu_4}$ that is antisymmetric in each pair of indices, but does not satisfy the Bianchi identity and we use the shorthand notation $\tilde{\mathcal R}_{\mu_1 \mu_2}{}^{\mu_3 \mu_4} = {\mathcal R}^{\mu_3 \mu_4}{}_{\mu_1 \mu_2}$ in order to keep expressions compact. Note that if ${\mathcal R}$ is identified
with a Riemann tensor, all tilded quantities become equal to their untilded counterparts.
\section[Off-shell N=2 supergravity and chiral multiplets]{Off-shell ${\mathcal N}\!=\!2$ supergravity and chiral multiplets}
In this appendix we summarise some general formulae on the ${\mathcal N}\!=\!2$ Weyl multiplet in
four dimensions and the chiral multiplets in a general superconformal background.
Our conventions are as in \cite{deWit:2010za}, where the reader can find a more detailed account.
\subsection*{${\mathcal N}\!=\!2$ superconformal gravity}
\label{App:N2sugra}
The off-shell formulation of four-dimensional ${\mathcal N}\!=\!2$ supergravity is based on the
Weyl multiplet of conformal supergravity, whose components are given in Table
\ref{table:weyl}. This consists of the vierbein $e_\mu{}^a$, the
gravitino fields $\psi_\mu{}^i$, the dilatational gauge field $b_\mu$, the
R-symmetry gauge fields $\mathcal{V}_{\mu i}{}^j$ (which is an
anti-hermitian, traceless matrix in the $\mathrm{SU}(2)$ indices
$i,j$) and $A_\mu$, an anti-selfdual tensor field $T_{ab}{}^{ij}$, a
scalar field $D$ and a spinor field $\chi^i$. All spinor fields are
Majorana spinors which have been decomposed into chiral
components. The three gauge fields $\omega_\mu{}^{ab}$, $f_\mu{}^a$ and $\phi_\mu{}^i$, associated
with local Lorentz transformations, conformal boosts and
S-supersymmetry, respectively, are not independent as will be
discussed later.
\begin{table}[t]
\renewcommand{\arraystretch}{1.5}
\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}}
|c||cccccccc|ccc||cc| }
\hline
& &\multicolumn{9}{c}{Weyl multiplet} & &
\multicolumn{2}{c|}{parameter} \\[1mm] \hline \hline
field & $e_M{}^{A}$ & $\psi_M{}^i$ & $b_M$ & $A_M$ &
$\mathcal{V}_M{}^i{}_j$ & $T_{AB}{}^{ij} $ &
$ \chi^i $ & $D$ & $\omega_M^{AB}$ & $f_M{}^A$ & $\phi_M{}^i$ &
$\epsilon^i$ & $\eta^i$
\\ [.5mm] \hline
$w$ & $-1$ & $-\tfrac12 $ & 0 & 0 & 0 & 1 & $\tfrac{3}{2}$ & 2 & 0 &
1 & $\tfrac12 $ & $ -\tfrac12 $ & $ \tfrac12 $ \\[.5mm] \hline
$c$ & $0$ & $-\tfrac12 $ & 0 & 0 & 0 & $-1$ & $-\tfrac{1}{2}$ & 0 &
0 & 0 & $-\tfrac12 $ & $ -\tfrac12 $ & $ -\tfrac12 $ \\[.5mm] \hline
$\gamma_5$ & & + & & & & & + & & & & $-$ & $ + $ & $
- $ \\ \hline
\end{tabular*}
\vskip 2mm
\renewcommand{\baselinestretch}{1}
\parbox[c]{\textwidth}{\caption{\label{table:weyl}{\footnotesize
Weyl and chiral weights ($w$ and $c$) and fermion
chirality $(\gamma_5)$ of the Weyl multiplet component fields and the
supersymmetry transformation parameters.}}}
\end{table}
The infinitesimal Q, S and K transformations of the
independent fields, parametrized by spinors $\epsilon^i$ and $\eta^i$
and a vector $\Lambda_\mathrm{K}{}^A$, respectively, are as
follows,
\begin{align}
\label{eq:weyl-multiplet}
\delta e_\mu{}^a =&\, \bar{\epsilon}^i \, \gamma^a \psi_{ \mu i} +
\bar{\epsilon}_i \, \gamma^a \psi_{ \mu}{}^i \, , \nonumber\\[1mm]
%
\delta \psi_{\mu}{}^{i} =&\, 2 \,\mathcal{D}_\mu \epsilon^i - \tfrac{1}{8}
T_{ab}{}^{ij} \gamma^{ab}\gamma_\mu \epsilon_j - \gamma_\mu \eta^i
\, \nonumber \\[1mm]
\delta b_\mu =&\, \tfrac{1}{2} \bar{\epsilon}^i \phi_{\mu i} -
\tfrac{3}{4} \bar{\epsilon}^i \gamma_\mu \chi_i - \tfrac{1}{2}
\bar{\eta}^i \psi_{\mu i} + \mbox{h.c.} + \Lambda^a_K e_{\mu a} \, ,
\nonumber \\[1mm]
\delta A_{\mu} =&\, \tfrac{1}{2} \mathrm{i} \bar{\epsilon}^i \phi_{\mu i} +
\tfrac{3}{4} \mathrm{i} \bar{\epsilon}^i \gamma_\mu \, \chi_i +
\tfrac{1}{2} \mathrm{i}
\bar{\eta}^i \psi_{\mu i} + \mbox{h.c.} \, , \nonumber\\[1mm]
\delta \mathcal{V}_\mu{}^{i}{}_j =&\, 2\, \bar{\epsilon}_j
\phi_\mu{}^i - 3
\bar{\epsilon}_j \gamma_\mu \, \chi^i + 2 \bar{\eta}_j \, \psi_{\mu}{}^i
- (\mbox{h.c. ; traceless}) \, , \nonumber \\[1mm]
\delta T_{ab}{}^{ij} =&\, 8 \,\bar{\epsilon}^{[i} R(Q)_{ab}{}^{j]} \,
, \nonumber \\[1mm]
%
\delta \chi^i =&\, - \tfrac{1}{12} \gamma^{ab} \, \Slash{D} T_{ab}{}^{ij}
\, \epsilon_j + \tfrac{1}{6} R(\mathcal{V})_{\mu\nu}{}^i{}_j
\gamma^{\mu\nu} \epsilon^j -
\tfrac{1}{3} \mathrm{i} R_{\mu\nu}(A) \gamma^{\mu\nu} \epsilon^i\nonumber\\
&\, + D \, \epsilon^i +
\tfrac{1}{12} \gamma_{ab} T^{ab ij} \eta_j \, , \nonumber \\[1mm]
%
\delta D =&\, \bar{\epsilon}^i \, \Slash{D} \chi_i +
\bar{\epsilon}_i \,\Slash{D}\chi^i \, .
\end{align}
Here, $D_\mu$ denotes the full superconformally covariant derivative,
while $\mathcal{D}_\mu$ denotes a covariant derivative with respect to
Lorentz, dilatation, and chiral $\mathrm{SU}(2)\times \mathrm{U}(1)$
transformations, e.g.
\begin{equation}
\label{eq:D-epslon}
\mathcal{D}_{\mu} \epsilon^i = \big(\partial_\mu - \tfrac{1}{4}
\omega_\mu{}^{cd} \, \gamma_{cd} + \tfrac1{2} \, b_\mu +
\tfrac{1}{2}\mathrm{i} \, A_\mu \big) \epsilon^i + \tfrac1{2} \,
\mathcal{V}_{\mu}{}^i{}_j \, \epsilon^j \,.
\end{equation}
Under local scale and $\mathrm{U}(1)$ transformations the various
fields and transformation parameters transform as indicated in table
\ref{table:weyl}.
The various quantities denoted by $R(\mathcal{Q})$, and appearing in
the supersymmetry variations above denote the supercovariant curvature
tensors corresponding to each generator, $\mathcal{Q}$, whose detailed definition can be
found in \cite{deWit:2010za}. Here, we only give the following
\begin{align}
\label{eq:curvatures-4}
R(P)_{\mu \nu}{}^a = & \, 2 \, \partial_{[\mu} \, e_{\nu]}{}^a + 2 \,
b_{[\mu} \, e_{\nu]}{}^a -2 \, \omega_{[\mu}{}^{ab} \, e_{\nu]b} -
\tfrac1{2} ( \bar\psi_{[\mu}{}^i \gamma^a \psi_{\nu]i} +
\mbox{h.c.} ) \, , \nonumber\\[.2ex]
R(Q)_{\mu \nu}{}^i = & \, 2 \, \mathcal{D}_{[\mu} \psi_{\nu]}{}^i -
\gamma_{[\mu} \phi_{\nu]}{}^i - \tfrac{1}{8} \, T^{abij} \,
\gamma_{ab} \, \gamma_{[\mu} \psi_{\nu]j} \, , \nonumber\\[.2ex]
R(M)_{\mu \nu}{}^{ab} = & \,
\, 2 \,\partial_{[\mu} \omega_{\nu]}{}^{ab} - 2\, \omega_{[\mu}{}^{ac}
\omega_{\nu]c}{}^b
- 4 f_{[\mu}{}^{[a} e_{\nu]}{}^{b]}
+ \tfrac12 (\bar{\psi}_{[\mu}{}^i \, \gamma^{ab} \,
\phi_{\nu]i} + \mbox{h.c.} ) \nonumber\\
& \, + ( \tfrac14 \bar{\psi}_{\mu}{}^i \,
\psi_{\nu}{}^j \, T^{ab}{}_{ij}
- \tfrac{3}{4} \bar{\psi}_{[\mu}{}^i \, \gamma_{\nu]} \, \gamma^{ab}
\chi_i
- \bar{\psi}_{[\mu}{}^i \, \gamma_{\nu]} \,R(Q)^{ab}{}_i
+ \mbox{h.c.} ) \,,
\end{align}
which are necessary to introduce the conventional constraints
\begin{align}
\label{eq:conv-constraints}
&R(P)_{\mu \nu}{}^a = 0 \, , \nonumber \\[1mm]
&\gamma^\mu R(Q)_{\mu \nu}{}^i + \tfrac32 \gamma_{\nu}
\chi^i = 0 \, , \nonumber\\[1mm]
&
e^{\nu}{}_b \,R(M)_{\mu \nu a}{}^b - \mathrm{i} \tilde{R}(A)_{\mu a} +
\tfrac1{8} T_{abij} T_\mu{}^{bij} -\tfrac{3}{2} D \,e_{\mu a} = 0
\,,
\end{align}
defining the composite gauge fields associated with local Lorentz transformations,
S-su\-per\-sym\-me\-try and special conformal boosts, $\omega_{M}{}^{AB}$,
$\phi_M{}^i$ and $f_{M}{}^A$, respectively.
\subsection*{Chiral multiplets}
\label{App:4D-chiral-multiplets}
Chiral multiplets are the basic building blocks of all supersymmetric invariants in
this paper. We therefore give a concise overview of their most basic properties, to
be used in the various constructions.
Chiral multiplets are complex, carrying a Weyl weight $w$ and a chiral
$\mathrm{U}(1)$ weight $c$, which is opposite to the Weyl weight,
i.e. $c=-w$, while anti-chiral multiplets can be obtained from chiral
ones by complex conjugation, so that anti-chiral multiplets will have
$w=c$. The components of a generic scalar chiral multiplet are a complex
scalar $A$, a Majorana doublet spinor $\Psi_i$, a complex symmetric
scalar $B_{ij}$, an anti-selfdual tensor $G_{ab}^-$, a Majorana
doublet spinor $\Lambda_i$, and a complex scalar $C$. The assignment
of their Weyl and chiral weights is shown in
table~\ref{table:chiral}.
The Q- and S-supersymmetry transformations
for a scalar chiral multiplet of weight $w$, are as
follows
\begin{align}
\label{eq:conformal-chiral}
\delta A =&\,\bar\epsilon^i\Psi_i\,, \nonumber\\[.2ex]
%
\delta \Psi_i =&\,2\,\Slash{D} A\epsilon_i + B_{ij}\,\epsilon^j +
\tfrac12 \gamma^{ab} G_{ab}^- \,\varepsilon_{ij} \epsilon^j + 2\,w
A\,\eta_i\,, \nonumber\\[.2ex]
%
\delta B_{ij} =&\,2\,\bar\epsilon_{(i} \Slash{D} \Psi_{j)} -2\,
\bar\epsilon^k \Lambda_{(i} \,\varepsilon_{j)k} + 2(1-w)\,\bar\eta_{(i}
\Psi_{j)} \,, \nonumber\\[.2ex]
%
\delta G_{ab}^- =&\,\tfrac12
\varepsilon^{ij}\,\bar\epsilon_i\Slash{D}\gamma_{ab} \Psi_j+
\tfrac12 \bar\epsilon^i\gamma_{ab}\Lambda_i
-\tfrac12(1+w)\,\varepsilon^{ij} \bar\eta_i\gamma_{ab} \Psi_j \,,
\nonumber\\[.2ex]
%
\delta \Lambda_i =&\,-\tfrac12\gamma^{ab}\Slash{D}G_{ab}^-
\epsilon_i -\Slash{D}B_{ij}\varepsilon^{jk} \epsilon_k +
C\varepsilon_{ij}\,\epsilon^j
+\tfrac14\big(\Slash{D}A\,\gamma^{ab}T_{abij}
+w\,A\,\Slash{D}\gamma^{ab} T_{abij}\big)\varepsilon^{jk}\epsilon_k
\nonumber\\
&\, -3\, \gamma_a\varepsilon^{jk}
\epsilon_k\, \bar \chi_{[i} \gamma^a\Psi_{j]} -(1+w)\,B_{ij}
\varepsilon^{jk}\,\eta_k + \tfrac12 (1-w)\,\gamma^{ab}\, G_{ab}^-
\eta_i \,, \nonumber\\[.2ex]
%
\delta C =&\,-2\,\varepsilon^{ij} \bar\epsilon_i\Slash{D}\Lambda_j
-6\, \bar\epsilon_i\chi_j\;\varepsilon^{ik}
\varepsilon^{jl} B_{kl} \nonumber\\
&\, -\tfrac14\varepsilon^{ij}\varepsilon^{kl} \big((w-1)
\,\bar\epsilon_i \gamma^{ab} {\Slash{D}} T_{abjk}
\Psi_l + \bar\epsilon_i\gamma^{ab}
T_{abjk} \Slash{D} \Psi_l \big) + 2\,w \varepsilon^{ij}
\bar\eta_i\Lambda_j \,.
\end{align}
\begin{table}[t]
\begin{center}
{\renewcommand{\arraystretch}{1.5}
\renewcommand{\tabcolsep}{0.2cm}\begin{tabular}{|c||cccccc| }
\hline
& & \multicolumn{4}{c}{Chiral multiplet} & \\ \hline \hline
field & $A$ & $\Psi_i$ & $B_{ij}$ & $G_{ab}^-$& $\Lambda_i$ & $C$ \\[.5mm] \hline
$w$ & $w$ & $w+\tfrac12$ & $w+1$ & $w+1$ & $w+\tfrac32$ &$w+2$
\\[.5mm] \hline
$c$ & $-w$ & $-w+\tfrac12$ & $-w+1$ & $-w+1$ & $-w+\tfrac32$ &$-w+2$
\\[.5mm] \hline
$\gamma_5$ & & $+$ & & & $+$ & \\ \hline
\end{tabular}}
\vskip 2mm
\renewcommand{\baselinestretch}{1}
\parbox[c]{10.8cm}{\caption{\label{table:chiral}{\footnotesize
Weyl and chiral weights ($w$ and $c$) and fermion
chirality $(\gamma_5)$ of the chiral multiplet component fields.}}}
\end{center}
\end{table}
Any homogeneous function of chiral superfields constitutes a chiral superfield,
whose Weyl weight is determined by the degree of homogeneity of the function at
hand. Indeed, one can show that a function $G(\Phi)$ of chiral
superfields $\Phi^I$ defines a chiral superfield, whose component fields
take the following form,
\begin{align}
\label{eq:chiral-mult-exp}
A\vert_G =&\, G \,, \nonumber\\
\{ \, \Psi_i\,, B_{ij}\,, G_{ab}^- \, \}\vert_G
= &\, G_I \,\{ \, \Psi_i{}^I\,, B_{ij}{}^I\,, G_{ab}^-{}^I \, \}
\,,\nonumber\\
\Lambda_{i}\vert_G =&\, G_I \,\Lambda_{i}{}^I
-\tfrac12
G_{IJ}\big[B_{ij}{}^I \varepsilon^{jk} +\tfrac12\, G^{-}_{ab}{}^I\gamma^{ab}\delta_i^k \big]\,\Psi_{k}{}^J
\,,\nonumber\\
C\vert_G =&\, G_I\, C^I -\tfrac14
G_{IJ}\big[ B_{ij}{}^I B_{kl}{}^J\,
\varepsilon^{ik} \varepsilon^{jl}
-2\, G^{-}_{ab}{}^I G^{-abJ} \big] \,,
\end{align}
where $G_{I}$, $G_{IJ}$ etc. are the derivatives of the function $G$ with
respect to the scalars $A^I$ and we omitted all terms nonlinear in fermions
for brevity.
\begin{table}[t]
\begin{center}
\renewcommand{\arraystretch}{1.5}
\begin{tabular*}{13.5cm}{@{\extracolsep{\fill}}|c||cccc||cccc| }
\hline
& \multicolumn{4}{c||}{vector multiplet} &
\multicolumn{4}{c|}{tensor multiplet}\\
\hline \hline
field & $X$ & $W_\mu$ & $\Omega_i$ & $Y^{ij}$& $L^{ij}$ &
$B_{\mu\nu}$ & $\varphi_i$ & $G$ \\[.5mm] \hline
$w$ & $1$ & $0$ & $\tfrac32$ & $2$ & $2$& $0$ &$\tfrac52$& $3$
\\[.5mm] \hline
$c$ & $-1$ & $0$ & $-\tfrac12$ & $0$ &$0$&$0$&$-\tfrac12$ &$1$
\\[.5mm] \hline
$\gamma_5$ & && $+$ & &&&$-$& \\ \hline
\end{tabular*}
\vskip 2mm
\renewcommand{\baselinestretch}{1}
\parbox[c]{13.5cm}{\caption{\label{table:vector}\footnotesize Weyl and chiral weights ($w$
and $c$) and fermion chirality $(\gamma_5)$ of the vector
multiplet and the tensor multiplet. }}
\end{center}
\end{table}
Chiral multiplets of $w=1$ are special, because they are reducible upon imposing a reality constraint.
The two cases that are relevant are the vector multiplet, which
arises upon reduction from a scalar chiral multiplet, and the Weyl multiplet, which is a reduced
anti-selfdual chiral tensor multiplet.
The constraint for a scalar chiral superfield implies that $C\vert_{\text{vector}}$ and
$\Lambda_i\vert_{\text{vector}}$ are expressed in terms of the lower components of the multiplet,
and imposes a reality constraint on $B\vert_{\text{vector}}$ and a Bianchi identity on $G^-\vert_{\text{vector}}$ \cite{Firth:1974st,deRoo:1980mm,deWit:1980tn}, as
\begin{align}
\label{eq:vect-mult}
A\vert_{\text{vector}}=&\,X\,,\nonumber\\
\Psi_i\vert_{\text{vector}}=&\, \Omega_i\,,\nonumber\\
B_{ij}\vert_{\text{vector}}=&\, Y_{ij}
=\varepsilon_{ik}\varepsilon_{jl}Y^{kl}\,,\nonumber\\
G_{ab}^-\vert_{\text{vector}}=& F_{ab}^-
-\tfrac14\,
\bar{X}\, T_{ab}{}^{ij}\,\varepsilon_{ij} \,,\nonumber\\
\Lambda_i\vert_{\text{vector}}
=&\,-\varepsilon_{ij}\Slash{D}\Omega^j\nonumber\\
C\vert_{\text{vector}}= &\,-2\, \Box_\mathrm{c} \bar X -\tfrac14 G_{ab}^+\,
T^{ab}{}_{ij} \varepsilon^{ij}
\,,
\end{align}
where $F_{\mu\nu}= 2 \partial_{[\mu} A_{\nu]}$ is the field strength of a gauge
field, $A_{\mu}$. The corresponding Bianchi identity on $G_{ab}$ can be written as,
\begin{align}
\label{eq:Bianchi-vector} D^b\left(G_{ab}^+-G_{ab}^- +\ft14 X
T_{abij}\varepsilon^{ij}-\ft14 \bar{X}
T_{ab}{}^{ij}\varepsilon_{ij}\right)
=0 \,,
\end{align}
where in both \eqref{eq:vect-mult} and \eqref{eq:Bianchi-vector} we again omitted
terms nonlinear in fermions.
The reduced scalar chiral multiplet thus describes the
covariant fields and field strength of a {\it vector multiplet}, which
encompasses $8+8$ bosonic and fermionic
components. Table~\ref{table:vector} summarizes the Weyl and chiral
weights of the various fields belonging to the vector multiplet: a
complex scalar $X$, a Majorana doublet spinor $\Omega_i$, a vector
gauge field $A_\mu$, and a triplet of auxiliary fields $Y_{ij}$.
The Q- and S-supersymmetry transformations for the vector multiplet
take the form,
\begin{align}
\label{eq:variations-vect-mult}
\delta X =&\, \bar{\epsilon}^i\Omega_i \,,\nonumber\\
%
\delta\Omega_i =&\, 2 \Slash{D} X\epsilon_i
+\ft12 \varepsilon_{ij} G_{\mu\nu}
\gamma^{\mu\nu}\epsilon^j +Y_{ij} \epsilon^j
+2X\eta_i\,,\nonumber\\
%
\delta A_{\mu} = &\, \varepsilon^{ij} \bar{\epsilon}_i
(\gamma_{\mu} \Omega_j+2\,\psi_{\mu j} X)
+ \varepsilon_{ij}
\bar{\epsilon}^i (\gamma_{\mu} \Omega^{j} +2\,\psi_\mu{}^j
\bar X)\,,\nonumber\\
%
\delta Y_{ij} = &\, 2\, \bar{\epsilon}_{(i}
\Slash{D}\Omega_{j)} + 2\, \varepsilon_{ik}
\varepsilon_{jl}\, \bar{\epsilon}^{(k} \Slash{D}\Omega^{l)
} \,,
\end{align}
and, for $w=1$, are in clear correspondence with the supersymmetry
transformations of generic scalar chiral multiplets given in
\eqref{eq:conformal-chiral}.
We now turn to the covariant fields of the Weyl multiplet, which can be arranged in an
anti-selfdual tensor chiral multiplet, whose chiral superfield components take the following form,
\begin{align}
\label{eq:W-mult}
A_{ab}\vert_{W} =&\,T_{ab}{}^{ij}\varepsilon_{ij}\,,\nonumber \\
%
\Psi_{abi}\vert_{W} =&\, 8\, \varepsilon_{ij}R(Q)^j_{ab} \,,\nonumber\\
%
B_{abij}\vert_{W} =&\, -8 \,\varepsilon_{k(i}R({\cal V})_{ab}^-{}^k{}_{j)} \,,\nonumber\\
%
\left(G^{-}_{ab}\right){}^{cd}\vert_{W} =&\, -8
\,\hat{R}(M)_{ab}^-{}^{\!cd} \,,\nonumber\\
%
\Lambda_{abi}\vert_{W} =&\, 8\left(\mathcal{R}(S)_{abi}^- + \ft34 \gamma_{ab}\Slash{D}\chi_i\right)
\,,\nonumber\\
%
C_{ab}\vert_{W} =&\, 4 D_{[a} \,D^cT_{b]c\,ij}
\varepsilon^{ij}-\text{dual} \,.
\end{align}
Note that all quantities involved in the components above are either manifestly supercovariant
curvatures or (covariant) auxiliary fields of the Weyl multiplet. In particular,
$\mathcal{R}(S)_{abi}$ is the curvature of the S-supersymmetry gauge field, which is solved in
terms of the derivative of the gravitino curvature, $\mathcal{R}(Q)_{abi}$, due to the conventional
constraints.
All higher derivative terms involving powers of the Weyl tensor in this paper are constructed
by couplings of the scalar chiral multiplet with $w=2$ is obtained by squaring the Weyl
multiplet above. The various scalar chiral multiplet components of this multiplet are given by,
\begin{align}
\label{eq:W-squared}
A_{\sf w} =&\,(T_{ab}{}^{ij}\varepsilon_{ij})^2\,,\nonumber \\[.2ex]
%
\Psi_{\sf w}{}_i =&\, 16\, \varepsilon_{ij}R(Q)^j_{ab} \,T^{klab}
\, \varepsilon_{kl} \,,\nonumber\\[.2ex]
%
B_{ij}{}_{\sf w} =&\, -16 \,\varepsilon_{k(i}R({\cal
V})^k{}_{j)ab} \, T^{lmab}\,\varepsilon_{lm} -64
\,\varepsilon_{ik}\varepsilon_{jl}\,\bar R(Q)_{ab}{}^k\, R(Q)^{l\,ab}
\,,\nonumber\\[.2ex]
%
G^{-ab}_{\sf w} =&\, -16 \,\hat{R}(M)_{cd}{}^{\!ab} \,
T^{klcd}\,\varepsilon_{kl} -16 \,\varepsilon_{ij}\, \bar
R(Q)^i_{cd} \gamma^{ab} R(Q)^{cd\,j} \,,\nonumber\\[.2ex]
%
\Lambda_i{}_{\sf w} =&\, 32\, \varepsilon_{ij} \,\gamma^{ab} R(Q)_{cd}^j\,
\hat{R}(M)^{cd}{}_{\!ab}
+16\,({\cal R}(S)_{ab\,i} +3 \gamma_{[a} D_{b]} \chi_i) \,
T^{klab}\, \varepsilon_{kl} \nonumber\\
&\, -64\, R({\cal V})_{ab}{}^{\!k}{}_i \,\varepsilon_{kl}\,R(Q)^{ab\,l}
\,,\nonumber\\[.2ex]
%
C_{\sf w} =&\, 64\, \hat{R}(M)^{-cd}{}_{\!ab}\,
\hat{R}(M)^-_{cd}{}^{\!ab} + 32\, R({\cal V})^{-ab\,k}{}_l^{~} \,
R({\cal V})^-_{ab}{}^{\!l}{}_k \nonumber \\
&\, - 32\, T^{ab\,ij} \, D_a \,D^cT_{cb\,ij} +
128\,\bar{\mathcal{R}}(S)^{ab}{}_i \,R(Q)_{ab}{}^i +384 \,\bar
R(Q)^{ab\,i} \gamma_aD_b\chi_i \,.
\end{align}
In practice, we will only use the lowest component, $A_{\sf w}$, to construct
functions that define composite chiral multiplets, as in \eqref{eq:chiral-mult-exp},
which determines completely all instances of the higher components in the
relevant couplings. The components \eqref{eq:W-squared} can then
be substituted straightforwardly in the final expressions to obtain the
explicit couplings to the fields of the Weyl background.
\section{Tensor multiplet as a chiral background}
\label{sec:tensor}
We now turn to the tensor multiplet, which is also defined as an off-shell
multiplet in an arbitrary superconformal background. The field content of
this multiplet includes a pseudoreal triplet of scalars, $L_{ij}$, a
two-form gauge potential, $B_{\mu\nu},$ a Majorana fermion doublet,
$\varphi^i$, and an auxiliary complex scalar, $G$, with the Weyl and chiral
assignments given in \ref{table:vector}. The corresponding
supersymmetry transformation rules are as follows
\begin{equation}
\label{eq:tensor-tr}
\begin{split}
\delta L_{ij} =& \,2\,\bar\epsilon_{(i}\varphi_{j)} +2
\,\varepsilon_{ik}\varepsilon_{jl}\,
\bar\epsilon^{(k}\varphi^{l)} \,,\\
\delta\varphi^{i} =& \,\Slash{D} L^{ij} \,\epsilon_j +
\varepsilon^{ij}\,\Slash{\hat E}^I \,\epsilon_j - G \,\epsilon^i
+ 2 L^{ij}\, \eta_j \,,\\
\delta G =& \,-2 \, \bar\epsilon_i \Slash{D} \, \varphi^{i} \,
- \bar\epsilon_i ( 6 \, L^{ij} \, \chi_j + \tfrac1{4} \,
\gamma^{ab} T_{ab jk} \, \varphi^l \,
\varepsilon^{ij} \varepsilon^{kl}) + 2 \, \bar{\eta}_i\varphi^{i}
\, ,\\
\delta B_{\mu\nu} =& \, \mathrm{i}\bar\epsilon^i\gamma_{\mu\nu}
\varphi^{j} \,\varepsilon_{ij} - \mathrm{i}\bar\epsilon_i\gamma_{\mu\nu}
\varphi_{j} \,\varepsilon^{ij} \, + \,2 \mathrm{i} \, L_{ij} \,
\varepsilon^{jk} \, \bar{\epsilon}^i \gamma_{[\mu} \psi_{\nu ]k}
- 2 \mathrm{i}\, L^{ij} \, \varepsilon_{jk} \, \bar{\epsilon}_i
\gamma_{[\mu} \psi_{\nu ]}{}^k \, ,
\end{split}
\end{equation}
and we refer to \cite{deWit:2006gn} for the precise definitions of the
superconformally covariant derivatives on the various fields. The vector
$\hat E^\mu$ is the superconformal completion of the dual of the three-form
field strength, $\hat E^\mu = \tfrac{1}{2}\mathrm{i}\, e^{-1} \, \varepsilon^{\mu \nu
\rho \sigma} \partial_\nu B_{\rho \sigma}$.
The couplings of the tensor multiplets are given in terms of composite
vector multiplets \cite{deWit:2006gn}, described by functions of a set
of tensor multiplets, labeled by $I$.
To this end, we define the first component, the scalar $X_I$ as
\begin{equation} \label{eq:X-tens}
X_I = {\cal F}_{I,J} \, \bar G^J +
{\cal F}_{I,JK}{}^{ij}\,\bar\varphi_i{}^J\varphi_j{}^K \,,
\end{equation}
which, by \eqref{eq:tensor-tr}, transforms according to the first
of \eqref{eq:conformal-chiral} into the remaining bosonic components of the
vector multiplet, as
\begin{eqnarray}
\label{eq:Omega-tens}
Y_{ij \,I} &=& -2\,{\cal F}_{I,J}\, \Big[\Box^{\rm c} L_{ij}{}^J +
3\,D L_{ij}{}^J \Big]
-2\,{\cal F}_{I,JKij} \,( \bar G^J\,G^K + \hat E_{\mu}{}^J\,\hat
E^{\mu K}) \,,
\nonumber\\
&&{}
-2\, {\cal F}_{I,JK}{}^{kl}\,( D_\mu L_{ik}{}^J\,D^\mu
L_{jl}{}^K + 2\,\varepsilon_{k(i}\, D_\mu L_{j)l}{}^J\,
\hat E^{\mu K} )
\nonumber\\
\label{eq:sc-eqF}
F_{\mu\nu\,I} &=& - 2\,{\cal F}_{I,JK}{}^{mn} \,\partial_{[\mu}
L_{mk}{}^J \, \partial_{\nu]} L_{nl}{}^K \,\varepsilon^{kl} \nonumber\\
&&{}
-4\, \partial_{[\mu} \left( {\cal F}_{I,J} \,\hat E_{\nu]}{}^J
-\tfrac12\,{\cal F}_{I,J} \, \mathcal{V}_{\nu]}{}^i{}_j \,
L_{ik}{}^J \, \varepsilon^{jk}
\right)
\, ,
\nonumber \\
C_I & = &\,-2\, \Box_\mathrm{c} ( {\cal F}_{I,J} \,G^J )
-\tfrac14 \, ( F_{ab\, I}^+ -\tfrac14\,{\cal F}_{I,J} \,\bar G^J T_{ab\,ij} \varepsilon^{ij})\,
T^{ab}{}_{ij} \varepsilon^{ij} \,,
\end{eqnarray}
where we suppressed all fermions and the component $C_I$ is consistent with \eqref{eq:vect-mult}.
In order for this multiplet to be well defined, the first
derivative of ${\cal F}_{I,J}(L)$ with respect to
$L^{K\,ij}$, denoted by ${\cal F}_{I,J,Kij}$, must satisfy
the constraints
\begin{equation}
\label{eq:chiral-constraints}
{\cal F}_{I,J,Kij}= {\cal F}_{I,K,Jij}\,,\qquad
\varepsilon^{jk}\, {\cal F}_{I,J,Kij,Lkl}(L)=0\,,
\end{equation}
while Weyl covariance requires the condition
\begin{equation}
\label{eq:sc-tensor}
{\cal F}_{I,JKik}\,L^{kjK} = -\tfrac1{2} \delta_i{}^j \,{\cal
F}_{I,J}\,,
\end{equation}
which implies that the function ${\cal F}_{I,J}$ is
${\rm SU}(2)$ invariant and homogeneous of degree $-1$, so
that it has scaling weight $-2$.
The expressions for the composite chiral supermultiplet above can be
used to construct actions with higher derivative couplings.
In general, one can use \eqref{eq:X-tens}-\eqref{eq:sc-eqF} on the same
footing as any vector multiplet to obtain actions containing vector-tensor
couplings. This is beyond the scope of this paper, where we only consider
a background chiral multiplet containing four derivatives on the components
of a single tensor multiplet, similar to \cite{deWit:2006gn} but allowing
for couplings depending on vector multiplet scalars as well.
For a single tensor multiplet, the functions $\mathcal{F}_{I,J}$
in \eqref{eq:X-tens} reduce to a single function $\mathcal{F}(L)$,
while the constraints \eqref{eq:chiral-constraints}-\eqref{eq:sc-tensor}
imply the constraint,
\begin{equation}
\label{eq:laplace-F}
\frac{ \partial^2\mathcal{F}(L)}{\partial L^{ij}\,\partial L_{ij}} = 0
\,.
\end{equation}
We then consider the chiral multiplet of $w=2$ defined by its first
component as the square of \eqref{eq:X-tens}, through
\begin{equation}\label{eq:A-tens-sq}
\hat A^{\sf t} = \mathcal{F}^2 \bar G^2
+ 2\,\mathcal{F}\,\mathcal{F}^{ij}\, G \,\bar\varphi_i{}\varphi_j
= {\mathcal H}\,G^2 + {\mathcal H}^{ij}\, \bar G \,\bar\varphi_i{}\varphi_j
\,,
\end{equation}
where we defined the function $\mathcal{H}(L) = [\mathcal{F}(L)]^2$, and
its derivatives, as
\begin{equation}
\label{eq:H-der}
\mathcal{H}^{ij} = \frac{\partial\mathcal{H}}{\partial
L_{ij}}\;,\qquad \mathcal{H}^{ij,kl} =
\frac{\partial^2\mathcal{H}}{\partial L_{ij}\,\partial L_{kl}}\;.
\end{equation}
As noted in \eqref{eq:two-der-ten}, for a single tensor multiplet the
function $\mathcal{F}$ is essentially unique, so that $\mathcal{H}$ is simply
given by its square, as
\begin{align}\label{eq:F-sing-ten}
\mathcal{H} = \frac{1}{ L_{ij} L^{ij} }\,,
\end{align}
where in the reduction we consider in the main text, the scalars $L_{ij}$ contain
the dilaton and are kept constant throughout.
The remaining components of this composite background multiplet are given by
\eqref{eq:chiral-mult-exp} for $G(A)=A^2$, as follows from \eqref{eq:A-tens-sq}.
For completeness, we display their form for a general function ${\mathcal H}$, as follows
\begin{align}
B^{\sf t}{}_{ij} =&\,
2 \,\bar G \,
\left( 2\,{\mathcal H}\, \Big[\Box^{\rm c} L_{ij} + 3\,D L_{ij} \Big]
-{\mathcal H}_{ij} \,( |G|^2 + \hat E_{\mu}\,\hat E^{\mu})
\right. \nonumber\\
&
\left.-{\mathcal H}^{kl}\,( D_\mu L_{ik} \,D^\mu L_{jl}
+ 2\,\varepsilon_{k(i}\, D_\mu L_{j)l} \, \hat E^{\mu} ) \right)
\,,\nonumber\\
G^{\sf t}{}_{ab}^-{} =&\,
- 2\,{\mathcal H}^{mn} \,\bar G \, \mathcal{D}_{[a}
L_{mk} \, \mathcal{D}_{b]} L_{nl} \,\varepsilon^{kl}
-8\,{\mathcal H}\,\bar G \, \left( \mathcal{D}_{[a}\hat E_{b]}
-\tfrac14\, R_{ab}{}^i{}_j(\mathcal{V}) \,
L_{ik} \, \varepsilon^{jk} \right) \nonumber\\
&\,
-4\,\bar G {\mathcal H}_{mn} \, \mathcal{D}_{[a} L^{mn} \hat E_{b]}
-\tfrac12\, {\mathcal H} \, |G|^2 T_{ab}{}^{ij} \varepsilon_{ij}
\,,\nonumber\\
\end{align}
for the lower components and
\begin{align}
\label{eq:CT}
C^{\sf t} = & \, \mathcal{H}(L) \Big\{
-4 \bar G \Box_\mathrm{c} G
- 2 \left( \Box_\mathrm{c} L_{ij} + 3\,D\,L_{ij} \right)^2
+ 16\, \mathcal{D}_{[a} E_{b]^-} \, \mathcal{D}^{[a} E^{b]^-} \nonumber\\
& \qquad\quad
- 8\,\mathcal{D}_a E_b \big( {R}^{ab}{}^{i}{}_j^-(\mathcal{V}) L_{ik}
\varepsilon^{jk}
- \tfrac14 [ T^{ab}{}^{ij} \varepsilon_{ij} \,G + \mbox{h.c.}]\big)
\nonumber\\[1ex]
&\qquad\quad
+\tfrac1{16} \left((T_{ab}{}^{ij} \varepsilon_{ij})^2 G^2
+ 2\,(T_{ab}{}_{ij} \varepsilon^{ij})^2 \bar G^2 \right)
+ 12\, (\vert G \vert^2 + E^2)\,D
\nonumber\\[1ex]
&\qquad\quad
+ {R}^{ab}{}^{m}{}_n(\mathcal{V}) L_{ml} \varepsilon^{nl}
\big( {R}_{ab}{}^{i}{}_j^-(\mathcal{V}) L_{ik} \varepsilon^{jk}
- \tfrac12 [T_{ab}{}^{ij} \varepsilon_{ij} \,G + \mbox{h.c.}] \big)
\Big\}
\nonumber\\[1ex]
&\, + \mathcal{H}^{ij}(L) \Big\{
\left( \Box_\mathrm{c} L^{kl} + 3\,D\,L^{kl} \right)
\left(\mathcal{D}_\mu L_{ik} \mathcal{D}^{\mu} L_{jl}
-4\, \varepsilon_{ik} E^\mu \mathcal{D}_\mu L_{jl} \right)
\nonumber\\[1ex]
& \qquad \qquad
-2\,\Box_\mathrm{c} L_{ij} (2\,\vert G \vert^2 + E^2 )
-4\,\bar G\, \mathcal{D}^\mu G\, \mathcal{D}_\mu L_{ij}
\nonumber\\[1ex]
& \qquad\qquad
-4\, \big(E_b \mathcal{D}_a L_{ij} +\tfrac12 \mathcal{D}_a L_{ik}
\mathcal{D}_b L_{jl} \varepsilon^{kl} \big)
\big( {R}^{ab}{}^{m}{}_n^-(\mathcal{V}) L_{mo} \varepsilon^{no}
- \tfrac14 \,T^{ab}{}^{mn} \varepsilon_{mn} G
\big)\nonumber\\[1ex]
&\qquad\qquad
+8 (\mathcal{D}_a L_{ik} \mathcal{D}_b L_{jl} \varepsilon^{kl}
-2\, E_a \mathcal{D}_b L_{ij}) \mathcal{D}^{[a} E^{b]^-}
\Big\}
\nonumber\\[1ex]
& + \mathcal{H}^{ij,kl}(L) \Big\{
- \varepsilon_{ik} \varepsilon^{pq}
\mathcal{D}^\mu L_{mp} \mathcal{D}^\nu L^{mn}
\mathcal{D}_\mu L_{jn} \mathcal{D}_\nu L_{ql}
\nonumber\\[1ex]
& \qquad \qquad
- 8\, \varepsilon_{ik}
E^b \mathcal{D}^a L_{jm}
(\mathcal{D}_a L^{mn} \mathcal{D}_b L_{nl}
+ \tfrac16 \epsilon_{abcd}\mathcal{D}^c L_{mn} \mathcal{D}^d L_{nl} )
\nonumber\\[1ex]
& \qquad\qquad
+ 2\,\mathcal{D}_\mu L_{ik} \mathcal{D}^{\mu} L_{jl} \vert G \vert^2
- (\vert G \vert^2 + E^2 )\,
\left( \varepsilon_{ik} \varepsilon_{jl}(\vert G \vert^2 + E^2 )
+ 4 \varepsilon_{ik} E^\mu \mathcal{D}_\mu L_{jl} \right)
\nonumber\\[1ex]
& \qquad\qquad
+ 2 \varepsilon_{ik}\varepsilon^{mn}\mathcal{D}_\mu L_{jm} \mathcal{D}^{\mu} L_{nl}\,E^2
+ 4 \varepsilon_{ik}( \mathcal{D}_\mu L_{jm} \mathcal{D}_\nu L_{ln} \varepsilon^{mn}
) E^\mu E^\nu
\Big\} \, ,
\end{align}
for the top component.
\section{The kinetic multiplet and supersymmetric invariants}
\label{app:kinetic}
The central object in constructing the various higher derivative invariants
of the type $R^{2n} F^{2m}$ in this paper is the so called
kinetic chiral multiplet. The term `kinetic' multiplet was first used in
the context of the $N=1$ tensor calculus \cite{Ferrara:1978jt}, because
this is the chiral multiplet that enables the construction of the
kinetic terms, conventionally described by a real superspace integral,
in terms of a chiral superspace integral. In \cite{deWit:1980tn, deWit:2010za}
a corresponding kinetic multiplet, $\mathbb{T}(\bar\Phi)$, for a chiral
$w=0$ multiplet, $\Phi$, was identified for $N=2$ supersymmetry,
which now involves four rather than two covariant $\bar\theta$-derivatives.
It follows that $\mathbb{T}(\bar\Phi)$ contains up to four space-time
derivatives, so that the expression
\begin{equation}
\label{eq:real-chiral-n2}
\int \!\mathrm{d}^4\theta\;\mathrm{d}^4\bar\theta \;\Phi\,\bar\Phi^\prime
\approx
\int \!\mathrm{d}^4\theta \,\Phi\,\mathbb{T}(\bar\Phi^\prime) \,,
\end{equation}
corresponds to a four derivative coupling. Expressing the chiral
multiplets in terms of (functions of) reduced chiral multiplets,
\eqref{eq:real-chiral-n2} leads to higher-derivative couplings
of vector multiplets and/or the Weyl multiplet.
Denote the components of a $w=0$ chiral multiplet by
$(A,\Psi,B,G^-,\Lambda,C)$, out of which we construct the components of
$\mathbb{T}(\bar \Phi_{w=0})$, denoted by
$(A,\Psi,B,G^-,\Lambda,C)\vert_{\mathbb{T}(\bar\Phi)}$.
In \cite{deWit:2010za} the following relation was established,
\begin{align}
\label{eq:T-components}
A\vert_{\mathbb{T}(\bar\Phi)} =&\, \bar C \,, \nonumber\\[.3ex]
\Psi_i\vert_{\mathbb{T}(\bar\Phi)}=&\,-2\,\varepsilon_{ij}
\Slash{D}\Lambda^j
-6\, \;\varepsilon_{ik} \varepsilon_{jl} \chi^j B^{kl}
-\tfrac14\varepsilon_{ij}\varepsilon_{kl} \, \gamma^{ab} T_{ab}{}^{jk}
\stackrel{\leftrightarrow}{\Slash{D}}\Psi^l \,, \nonumber\\[.6ex]
%
B_{ij}\vert_{\mathbb{T}(\bar\Phi)} =&\, - 2\,\varepsilon_{ik}\varepsilon_{jl}
\big(\Box_\mathrm{c} + 3\,D\big) B^{kl} -2\, G^+_{ab}\,
R(\mathcal{V})^{ab\,k}{}_{i}\, \varepsilon_{jk}
\,, \nonumber \displaybreak[0]\\[.6ex]
%
G_{ab}^-\vert_{\mathbb{T}(\bar\Phi)} =&\, - \big(\delta_a{}^{[c} \delta_b{}^{d]}
-\tfrac12\varepsilon_{ab}{}^{cd}\big)
\big[4\, D_cD^e G^+_{ed} + (D^e\bar A
\,D_cT_{de}{}^{ij}+D_c\bar A
\,D^eT_{ed}{}^{ij})\varepsilon _{ij} \big] \nonumber\\
&\, +\Box_\mathrm{c} \bar A \,T_{ab}{}^{ij}\varepsilon_{ij}
-R(\mathcal{V})^-{}_{\!\!ab}{}^i{}_k \,B^{jk} \,\varepsilon_{ij}
+\tfrac1{8} T_{ab}{}^{ij} \,T_{cdij} G^{+cd}
\,, \nonumber \displaybreak[0]\\[.6ex]
%
\Lambda_i\vert_{\mathbb{T}(\bar\Phi)} =&\, 2\,\Box_\mathrm{c}\Slash{D}
\Psi^{j}\varepsilon_{ij}
+ \tfrac1{4} \gamma^c\gamma_{ab} (2\, D_c
T^{ab}{}_{ij}\,\Lambda^{j} + T^{ab}{}_{ij} \,D_c \Lambda^{j})
\nonumber\\
&\,
- \tfrac1{2}\varepsilon_{ij} \big(R(\mathcal{V})_{ab}{}^j{}_k +
2\mathrm{i} \, R(A)_{ab}\delta^j{}_k\big)\,\gamma^c\gamma^{ab} D_c\Psi^k
\nonumber\\
&\,
+\tfrac12\,\varepsilon_{ij} \big( 3\, D_b D
- 4\mathrm{i} D^a R(A)_{ab}
+\tfrac{1}{4}
T_{bc}{}^{ij}\stackrel{\leftrightarrow}{D_a} T^{ac}{}_{ij}
\big)\,\gamma^b \Psi^{j} \nonumber\\
&\,
-2\,G^{+ab}\, \Slash{D}R(Q)_{ab}{}_{i}
+6\,\varepsilon_{ij} D\, \Slash{D} \Psi^{j} \nonumber\\
&\, + 3 \,\varepsilon_{ij}\,\big(\Slash{D}\chi_k\,B^{kj}
+\Slash{D} \bar A\,\Slash{D}\chi^{j} \big) \nonumber\\
&\,
+ \tfrac32\big( 2\,\Slash{D}B^{kj} \varepsilon_{ij}
+\, \Slash{D} G_{ab}^+ \gamma^{ab} \, \delta^k_{i}
+\tfrac14 \varepsilon_{mn} T_{ab}{}^{mn}\,\gamma^{ab}
\,\Slash{D}\bar A\, \delta_i{}^k\big) \chi_k
\,, \nonumber \displaybreak[0]\\[.6ex]
%
C\vert_{\mathbb{T}(\bar\Phi)}=&\,
4(\Box_\mathrm{c} + 3\, D) \Box_\mathrm{c} \bar A -\tfrac12
D_a\big(T^{ab}{}_{ij} \,T_{cb}{}^{ij}\big) \,D^c\bar A
+\tfrac1{16} (T_{abij}\varepsilon^{ij})^2 \bar C
\nonumber\\
&\,
+ D_a\big(\varepsilon^{ij} D^a T_{bc ij}\,G^{+bc} +4
\,\varepsilon^{ij} T^{ab}{}_{ij} \,D^cG^{+}_{cb} -
T_{bc}{}^{ij}\, T^{ac}{}_{ij} \,D^b\bar A \big) \nonumber\\
&\,
+ \big( 6\,D_b D - 8\mathrm{i}D^a R(A)_{ab} \big) \,D^b \bar A
+ \,,
\end{align}
where we suppressed terms nonlinear in the
covariant fermion fields. Observe that the right-hand side of
these expressions is always linear in the conjugate components of the
$w=0$ chiral multiplet, i.e. in $(\bar A,\Psi^i,B^{ij}, G^+_{ab},
\Lambda^i, \bar C)$.
Using the result \eqref{eq:T-components} one can construct a large
variety of superconformal invariants with higher-derivative couplings
involving vector multiplets, as well as the tensor and Weyl chiral
backgrounds. The construction of
the higher-order Lagrangians therefore proceeds in two steps. First one
constructs the Lagrangian in terms of unrestricted chiral multiplets of
appropriate Weyl weights, in the form
\begin{equation}
\label{eq:general-kin}
\int \;\mathrm{d}^4\theta \,\Phi_0 \,\mathbb{T}^{(n_1)}\,\mathbb{T}^{(n_2)}
\cdots \,\mathbb{T}^{(n_k)} \,.
\end{equation}
Here, the $n$-th power of the kinetic multiplet is defined recursively as
$\mathbb{T}^{(n)}= \mathbb{T}(\bar\Phi_n \,\mathbb{T}^{(n-1)})$ for
$\Phi_n$ of appropriate weight. Subsequently, one expresses the
unrestricted supermultiplets in terms of the reduced supermultiplets in
section \ref{App:4D-chiral-multiplets}. In these expressions it is natural to
introduce a variety of arbitrary homogeneous functions, so that resulting
final Lagrangian is controlled by a function of given homogeneity and
holomorphicity in the various fields, corresponding to the original structure
in \eqref{eq:general-kin}.
In this work, we will make use of invariants of the type \eqref{eq:general-kin},
where one, two or three kinetic multiplets appear, and are naturally quadratic,
cubic and quartic in chiral multiplet components, respectively. While the first
of these was described in detail in \cite{deWit:2010za}, the other two have not
appeared in the literature. These are straightforward to write, using the formulae
above and in \cite{deWit:2010za} but are rather unilluminating,
so that we prefer to emphasise the structure of the corresponding Lagrangians,
restricting ourselves to the leading terms.
\subsection*{The quadratic invariant}
The simplest case of a Lagrangian involving a kinetic multiplet is the one
in \eqref{eq:real-chiral-n2}, where a $w=0$ chiral multiplet is multiplied
with the kinetic of an antichiral one. In components, the leading bosonic
terms in the resulting Lagrangian read
\begin{align}
\label{eq:quadratic-chiral-Lagr}
e^{-1}\mathcal{L} =&\,
C\,\bar C + 8\, \mathcal{D}_a F^{-ab}\, \mathcal{D}^c F^+{}_{cb}
+ 4\, F^{-ac}\, F^+{}_{bc}\, R(\omega,e)_a{}^b
\nonumber \\[.1ex]
&\,
+4\,\mathcal{D}^2 A\,\mathcal{D}^2\bar A
+ 8\,\mathcal{D}^\mu A\, \big[R_\mu{}^a(\omega,e) -\tfrac13
R(\omega,e)\,e_\mu{}^a \big]\mathcal{D}_a\bar A
\nonumber \\[.1ex]
&\,
- \mathcal{D}^\mu B_{ij} \,\mathcal{D}_\mu B^{ij} + (\tfrac16
R(\omega,e) +2\,D) \,
B_{ij} B^{ij}
+ \cdots
\,,
\end{align}
where we suppressed the prime on the second chiral multiplet
indicated in \eqref{eq:real-chiral-n2} for brevity.
The next step is to consider the components of the chiral and anti-chiral
multiplet in \eqref{eq:quadratic-chiral-Lagr} to be composite, given as
holomorphic and anti-holomorphic functions, $F$, $\bar F$ of the fundamental
vector, tensor and Weyl multiplet respectively. The result is a Lagrangian that
is controlled by a homogeneous function of degree zero,
\begin{equation}\label{eq:patch-functions}
F(X^A, A_{\sf w}, A_{\sf t})\, \bar{F}(\bar{X}^A, \bar{A}_{\sf w}, \bar{A}_{\sf t})
\sim {\mathcal H}( X^A, A_{\sf w}, A_{\sf t}, \bar{X}^A, \bar{A}_{\sf w}, \bar{A}_{\sf t} )\,,
\end{equation}
which depends on the vector multiplets scalars, $X^A$, and the
Weyl and tensor multiplet composites, $A_{\sf w}$ and $A_{\sf t}$.
This invariant corresponds to higher derivative couplings that are
quadratic in the leading terms, $F^2$, $R^2$ and $(\nabla E)^2$ respectively.
The arbitrariness of the function in $A_{\sf w}$ is analogous to the similar
dependence of the chiral couplings, $F(X^A, A_{\sf w})$ which describes the
full topological string partition function.
Note that the various combinations have different order of derivatives,
as e.g. $F^4$ comprises only four derivatives, while $R^2 F^2$,
$(\nabla E)^2 F^2$ contain six derivatives and $R^4$, $R^2 (\nabla E)^2$,
$(\nabla E)^4$ contain eight derivatives. However, all these invariants
have a common structure, found by substituting the definitions of the
chiral multiplets in terms of $F$, $\bar F$ and ${\mathcal H}$ in
\eqref{eq:quadratic-chiral-Lagr}.
This was done in \cite{deWit:2010za}, where the $F^4$ coupling was
constructed, based on a real function ${\mathcal H}(X,\bar X)$, which plays the
role of a K\"ahler potential, as it is defined up to a real function, as
\begin{equation}
\label{eq:kahler}
\mathcal{H}(X,\bar X)\to \mathcal{H}(X,\bar X) +
\Lambda(X)+\bar\Lambda(\bar X)\,.
\end{equation}
The explicit form of the Lagrangian is
\begin{align}
\label{eq:real-susp-action}
e^{-1}\mathcal{L} =&\, \mathcal{H}_{IJ\bar K \bar L}\Big[\tfrac14
\big( G_{ab}^-{}^I\, G^{-ab\,J}
-\tfrac12 Y_{ij}{}^I\, Y^{ijJ} \big)
\big( G_{ab}^+{}^K \, G^{+ab\,L} -\tfrac12 Y^{ijK}\,
Y_{ij}{}^L \big)
\nonumber\\
& \qquad\quad +4\,\mathcal{D}_a X^I\, \mathcal{D}_b \bar X^K
\big(\mathcal{D}^a X^J \,\mathcal{D}^b \bar X^L
+ 2\, G^{-\,ac\,J}\,G^{+\,b}{}_c{}^L -
\tfrac14 \eta^{ab}\, Y^J_{ij}\,Y^{L\,ij}\big)
\Big]\nonumber\\[.5ex]
+&\,\Big\{ \mathcal{H}_{IJ\bar K}\Big[4\,\mathcal{D}_a X^I\,
\mathcal{D}^a X^J\, \mathcal{D}^2\bar X^K
- \mathcal{D}_a
X^I\, Y^J_{ij}\,\mathcal{D}^aY^{K\,ij} \nonumber\\
& \qquad\quad - \big(G^{-ab\,I}\, G_{ab}^{-\,J} -\tfrac12 Y^I_{ij}\,
Y^{Jij})
\big( \Box_\mathrm{c} X^K + \tfrac18 G^{-\,K}_{ab}\, T^{ab ij}
\varepsilon_{ij}\big) \nonumber\\[.5ex]
& \qquad\quad +8 \,\mathcal{D}^a X^I G^{-\,J}_{ab}
\big( \mathcal{D}_cG^{+\,cb\,K}- \tfrac12 \mathcal{D}_c\bar X^K
T^{ij\,cb} \varepsilon_{ij}\big) \Big]
+\mathrm{h.c.}\Big\} \displaybreak[0] \nonumber\\[.5ex]
+&\mathcal{H}_{I\bar J}\Big[ 4\big( \Box_\mathrm{c} \bar X^I + \tfrac18
G_{ab}^{+\,I}\, T^{ab}{}_{ij} \varepsilon^{ij}\big)
\big( \Box_\mathrm{c} X^J + \tfrac18 G_{ab}^{-\,J}\, T^{abij}
\varepsilon_{ij}\big) + 4\,\mathcal{D}^2 X^I \,\mathcal{D}^2
\bar X^J \nonumber\\
& \quad\quad +8\,\mathcal{D}_{a}G^{-\,abI\,}\,
\mathcal{D}_cG^{+c}{}_{b}{}^J - \mathcal{D}_a Y_{ij}{}^I\,
\mathcal{D}^a Y^{ij\,J}
+\tfrac1{4} T_{ab}{}^{ij} \,T_{cdij}
\,G^{-ab\,I}G^{+cd\,J}
\nonumber\\
&\quad\quad
+\big(\tfrac16 \mathcal{R} +2\,D\big) Y_{ij}{}^I\, Y^{ij\,J} + 4\,
G^{-ac\,I}\, G^{+}{}_{bc}{}^J \, \mathcal{R}_a{}^b \nonumber\\
&\quad\quad + 8\big(\mathcal{R}^{\mu\nu}-\tfrac13 g^{\mu\nu}
\mathcal{R} +\tfrac1{4} T^\mu{}_{b}{}^{ij}\, T^{\nu b}{}_{ij}
+\mathrm{i} R(A)^{\mu\nu} - g^{\mu\nu} D\big) \mathcal{D}_\mu X^I
\,\mathcal{D}_\nu \bar X^J \nonumber\\
&\quad\quad
- \big[\mathcal{D}_c \bar X^J \big(\mathcal{D}^c
T_{ab}{}^{ij}\,G^{-\,I\,ab} +4
\,T^{ij\,cb} \,\mathcal{D}^aG^{-\,I}_{ab} \big)\varepsilon_{ij}
+[\mathrm{h.c.}; I\leftrightarrow J] \big]\nonumber\\
&\quad\quad -\big[\varepsilon^{ik}\, Y_{ij}{}^I\, G^{+ab\,J}\,
R(\mathcal{V})_{ab}{}^j{}_k +[\mathrm{h.c.}; I\leftrightarrow J]
\big] \Big] \,,
\end{align}
where (we suppress fermionic contributions),
\begin{align}
\label{eq:def}
G_{ab}^-{}^I =&\, F^-_{ab}{}^I
-\tfrac14\, \bar{X}^I\, T_{ab}{}^{ij}\varepsilon_{ij} \,,
\nonumber\\
\Box_\mathrm{c} X^I=&\, \mathcal{D}^2 X^I + \big(\tfrac16
\mathcal{R} +D\big) \,X^I \,.
\end{align}
One can obtain the more general couplings as discussed above, resulting in similar
expressions. For example, the $R^2F^2$- and $R^4$-type couplings feature terms
found by substituting $F^2\rightarrow R^2$ and similarly for the other components
in \eqref{eq:real-susp-action} and are discussed in \cite{deWit:2010za}.
\subsection*{The cubic invariant}
The next more complicated example of Lagrangians containing kinetic multiplets
is to consider an integral quadratic in kinetic multiplets, as
\begin{equation}
\label{eq:chiral-n3}
\int \;\mathrm{d}^4\bar\theta \,\bar\Phi_0\mathbb{T}(\Phi_1)\,
\mathbb{T}( \Phi_2) \,,
\end{equation}
where $\Phi_0$ is a $w=-2$ chiral, while $\Phi_1$ and $\Phi_2$ are $w=0$
anti-chirals, as above. It is straightforward to apply the multiplication rule
for chiral multiplets, to obtain the analogous master formula of the type
\eqref{eq:quadratic-chiral-Lagr}, in this case. The result takes the form
\begin{align}
\label{eq:cubic-chiral-Lagr}
e^{-1}\mathcal{L} =&\,
C^2\,\bar C - \tfrac1{16}\,\bar A\,C^2 (T^+)^2
\nonumber \\[.1ex]
&\,
+ 2\,\bar{A}\, C\,\big[
4\,(\Box + 3\,D)\Box A + \tfrac1{16}\,C\, (T^-)^2
+4\, D_a\big( T^{+\,ab} \,D^cG^{+}_{cb}\big)
+ \dots \big]
\nonumber \\[.1ex]
&\,
- \bar{A}\, C\,\big[
2\,\varepsilon^{ik}\varepsilon^{jl}(\Box + 3\,D)B_{ij}\,(\Box + 3\,D)B_{kl}
- D_{[a}\big(D^c G^{-}_{c b]_+} \big) D^{[a}\big(D_c G^{-}{}^{c b]_+} \big)
+ \dots \big]
\nonumber \\[.1ex]
&\,
+ 2\,C\,\big[ B^{ij}\,(\Box + 3\,D)B_{ij}
- G^{+\,ab} \left( D_{[a}\big(D^c G^{-}_{c b]_+} \big) - \Box A\,T^+_{ab} \right)
+ \cdots \big]
\,,
\end{align}
which is manifestly quadratic in holomorphic and linear in anti-holomorphic components.
Note that we again use a simplified notation that naively identifies the three a priori
independent multiplets, despite the fact that the anti-chiral multiplet is of weight
$-2$, while the chiral ones are of $w=0$. The most general invariant follows by completing
the combinations given above with the components of the kinetic multiplet given in
\eqref{eq:T-components} and viewing the holomorphic components as quadratic forms in
the components of the two chiral multiplets in \eqref{eq:chiral-n3}, as done in
\eqref{eq:quadratic-chiral-Lagr}.
It is now straightforward, if cumbersome, to consider the three multiplets in
\eqref{eq:chiral-n3} as functions of the vector multiplets, the tensor multiplet
and the Weyl multiplet, as done in \eqref{eq:patch-functions}, leading to a Lagrangian
described by a function, ${\mathcal H}( X^A, A_{\sf w}, A_{\sf t}, \bar{X}^A, \bar{A}_{\sf w}, \bar{A}_{\sf t} )$,
which is homogeneous of degree zero in the holomorphic components and homogeneous of
degree $-2$ in the anti-holomorphic components. We refrain from giving the corresponding
expression \eqref{eq:real-susp-action} in this case, since we will only be dealing with
the leading terms and the properties of the corresponding function ${\mathcal H}$.
Once again, the generic function of all available multiplets leads to various
invariants, which contain different orders of derivatives but share the same structure,
as in \eqref{eq:cubic-chiral-Lagr}. The prototype of these terms is the $F^6$ invariant
arising by taking ${\mathcal H}( X^A, \bar{X}^A)$, i.e. a function of vector multiplet scalars
only. Allowing for holomorphic/anti-holomorphic dependence on the scalars $A_{\sf w}$
and $A_{\sf t}$ leads to terms of the type $R^2 F^4$, $R^4 F^2$, $(\nabla E)^2 F^4$ and
so on for all possible combinations. Note that many of these contain more than eight
derivatives and therefore fall outside the scope of this work.
\subsection*{The quartic invariants}
We finally consider integrals of the type \eqref{eq:general-kin} which are cubic in
the kinetic multiplet operator, $ \mathbb{T}$, in which case we find two possibilities.
Indeed, this is the first case where one needs to consider nested kinetic multiplets,
since the two possible integrals,
\begin{equation}
\label{eq:chiral-n4}
\int \;\mathrm{d}^4\bar\theta \,\bar\Phi_0\mathbb{T}(\Phi_1)\,
\mathbb{T}(\Phi_2)\, \mathbb{T}(\Phi_3) \,,
\qquad
\int \;\mathrm{d}^4\bar\theta \,\bar\Phi_0\mathbb{T}(\Phi_1)\,
\mathbb{T}( \Phi^\prime_0 \mathbb{T}(\bar \Phi_2) )\,,
\end{equation}
are not equivalent upon partial integration. Here, the first integral is the
straightforward extension of \eqref{eq:real-chiral-n2} and \eqref{eq:chiral-n3}, while in the
second integral $\Phi_0$ and $\Phi^\prime_0$ are $w=-2$ chirals, while $\Phi_1$ and
$\Phi_2$ are $w=0$ chirals, as above.
Once again, one can apply the multiplication rule for chiral multiplets, to obtain
the analogous master formula of the type \eqref{eq:quadratic-chiral-Lagr}, in these
cases. The expression for the first integral is similar to \eqref{eq:cubic-chiral-Lagr},
where three chiral multiplets appear and is not used in this paper.
The second integral is more cumbersome, but can be easily computed by an iterative
procedure, by noting that $\bar\Phi_0\mathbb{T}(\Phi_1)$ and
$\Phi^\prime_0 \mathbb{T}(\bar \Phi_2)$ are $w=0$ multiplets, so that
\eqref{eq:quadratic-chiral-Lagr} applies for their components. One can then
obtain the result to the integral by making the following substitutions
\begin{align}
A \rightarrow &\, A_0\, A\vert_{\mathbb{T}(\bar\Phi)}\,,
\nonumber\\
B_{ij} \rightarrow &\, B_{0\,ij}\, A\vert_{\mathbb{T}(\bar\Phi)} + A_0\,B_{ij}\vert_{\mathbb{T}(\bar\Phi)}\,,
\nonumber\\
G^{-\,ab} \rightarrow &\, G^{-\,ab}_{0}\, A\vert_{\mathbb{T}(\bar\Phi)} + A_0\,G^{-\,ab}\vert_{\mathbb{T}(\bar\Phi)}\,,
\nonumber\\
C \rightarrow &\, C_{0}\, A\vert_{\mathbb{T}(\bar\Phi)} + A_0\,C\vert_{\mathbb{T}(\bar\Phi)}
- \tfrac14\,\big( \varepsilon^{ik}\varepsilon^{jl}B_{0\,ij} \,B_{kl}\vert_{\mathbb{T}(\bar\Phi)}
- 2\, G^-_{0\,ab} \,G^{-\,ab}\vert_{\mathbb{T}(\bar\Phi)} \big)\,,
\end{align}
in \eqref{eq:quadratic-chiral-Lagr}, where the components labeled with $\vert_{\mathbb{T}(\bar\Phi)}$
are as in \eqref{eq:T-components}.
As above, allowing for the four chiral multiplets involved
to depend on the vector, tensor and/or the Weyl multiplet, exactly as in \eqref{eq:patch-functions},
one obtains various higher derivative invariants, sharing the same structure. However, all but one of
the invariants described by each of the two integrals in \eqref{eq:chiral-n4} necessarily contain more than eight
spacetime derivatives if the Weyl and tensor multiplet backgrounds are allowed, so that they are not relevant
for our consideration. The exception is the case where all the composite chiral multiplets only depend on the vector multiplets, in which case we obtain two $F^8$ invariants from \eqref{eq:chiral-n4}.
\end{appendix}
\bibliographystyle{utphys}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,128 |
Gyalopion canum är en ormart som beskrevs av Cope 1861. Gyalopion canum ingår i släktet Gyalopion, och familjen snokar. IUCN kategoriserar arten globalt som livskraftig. Inga underarter finns listade.
Utbredning
Gyalopion canum förekommer i södra USA och norra Mexiko i Nordamerika.
Källor
Externa länkar
Kräldjur i nearktiska regionen
Snokar
canum | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,536 |
Q: JMeter "Parameters" variable not convertable to Integer I can't get my ${invoiceTotalCsv} parameter to respond to math equations. I am taking it from from a CSV file in which it is a number, usually with a decimal place.
The below code works, but if ${invoiceTotalCsv} = 10, then the log writes 101, not 11. This leads me to believe the variable is passed as a string. BUT, I've tried Parameters.toInteger() which throws a NumberFormatException.
No other clues are given by JMeter.
A: You need to convert String to number/int, in groovy script:
def total = Parameters as double
A: You can use JSR223 Sampler element and then convert your Jmeter variable in int, float or double as required.
For better understanding see this page
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} | 3,053 |
{"url":"https:\/\/www.albert.io\/ie\/waves-and-sounds\/physics-of-the-didjeridu","text":"Free Version\nDifficult\n\n# Physics of the Didjeridu\n\nWAVES-EIN4EI\n\nA didjeridu is an Australian aboriginal musical instrument that consists of a long cylindrical tube. A musical tone is produced by closing off one of the open ends with the mouth and buzzing the lips to create a resonant harmonic set of standing waves.\n\nA recording of a single long tone from a didjeridu was made. The figure below shows the spectrum of that musical note indicating the frequencies present (horizontal axis) and their relative amplitudes (vertical axis).\n\nDecide what sort of standing waves should exist in a didjeridu. Is this a pipe closed at one end or open at both ends? We can determine various characteristics of the Didjeridu based on which frequencies are present in the graph. Use the data from the figure to calculate the length of the instrument. Assume the speed of sound to be ${v}_{s} = 344 m\/s$ .\n\nA\n\n$0.58 m$\n\nB\n\n$1.72 m$\n\nC\n\n$1.94 m$\n\nD\n\n$1.29 m$\n\nE\n\n$0.65 m$","date":"2017-02-24 06:27:52","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\": 0.3931407034397125, \"perplexity\": 718.1363233737286}, \"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-2017-09\/segments\/1487501171416.74\/warc\/CC-MAIN-20170219104611-00483-ip-10-171-10-108.ec2.internal.warc.gz\"}"} | null | null |
{"url":"https:\/\/learnings.desipenguin.com\/posts\/emacs-for-writers-1\/","text":"# Emacs for Writers : Part 1\n\nYoutube Video of Jay Dixit\u2019s presentation.\n\n# Background\n\nI came across this video (I think) from Sacha Chua\u2019s weekly Emacs news (But I am not certain, may be it was a tweet.) Personally, I prefer to refer to the presentation (PPT\/PDF) that goes with such video, assuming it contains written notes that viewer can refer to later.\n\nBut I could not find the notes\/presentation that go along with this. Since the video contains a lot of gems, I decided to make my own notes (and in process help some other emacs-noobs like myself)\n\nPlease note that there are lot of \u201cvisuals\u201d, so it is useful to watch the video. At least the second half hour is \u201cdemo\u201d mode, so there couldn\u2019t be any notes.\n\nThe way programmers write code comments, which are meant for themselves (or other developers) Similarly, writers also need to comment their articles (Who knew) These are Notes-for-self, but do not show up in the exported format. Trick is simple, start a line with a #, and the line is considered as as comment. Check the source org file of this article and see a comment right below this sentence.\n\nOff course for multi-line comment, one can use well known #+BEGIN_COMMENT and #+END_COMMENT blocks.\n\nIf you want to comment out an entire subtree, use C-c ;. Such subtree is not exported.\n\n# workflowy meets scrivener\n\nJay opens up with how he liked both these products separately, but wanted combination of these\n\nOutline to the left, contents on the right controlled by keyboard as much as possible without using mouse a lot\n\nHe showed two \u201ctricks\u201d (I couldn\u2019t hear them properly, but here is how I was able to get such a functionality)\n\n### Split the window\n\nSplit the window to the right (assuming you started with single window) In spacemacs you can do this by SPC w V\n\nNow you have the same buffer in two windows. You edit in one windows, but the changes are visible in other window immediately.\n\nThat is not exactly what you (or Jay) want. He wanted outline in one (left) window and contents in the right. So we ..\n\n### Separate the buffers\n\nGo the window on your left, and clone-indirect-buffer-other-window Now you can see the outline in the left pane, and edit in the right pane. The left pane can remain \u201cfolded\u201d. It doesn\u2019t update unless you add a node.\n\nContinue to Part 2","date":"2019-01-20 21:11:46","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\": 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\": 0.5133447647094727, \"perplexity\": 2030.4032984147905}, \"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-2019-04\/segments\/1547583739170.35\/warc\/CC-MAIN-20190120204649-20190120230649-00447.warc.gz\"}"} | null | null |
"""Benchmark for merge1.
Trains a small percentage of autonomous vehicles to dissipate shockwaves caused
by merges in an open network. The autonomous penetration rate in this example
is 25%.
- **Action Dimension**: (13, )
- **Observation Dimension**: (65, )
- **Horizon**: 750 steps
"""
from copy import deepcopy
from flow.core.params import SumoParams, EnvParams, InitialConfig, NetParams, \
InFlows, SumoCarFollowingParams
from flow.scenarios.merge import ADDITIONAL_NET_PARAMS
from flow.core.params import VehicleParams
from flow.controllers import SimCarFollowingController, RLController
# time horizon of a single rollout
HORIZON = 750
# inflow rate at the highway
FLOW_RATE = 2000
# percent of autonomous vehicles
RL_PENETRATION = 0.25
# num_rl term (see ADDITIONAL_ENV_PARAMs)
NUM_RL = 13
# We consider a highway network with an upstream merging lane producing
# shockwaves
additional_net_params = deepcopy(ADDITIONAL_NET_PARAMS)
additional_net_params["merge_lanes"] = 1
additional_net_params["highway_lanes"] = 1
additional_net_params["pre_merge_length"] = 500
# RL vehicles constitute 5% of the total number of vehicles
vehicles = VehicleParams()
vehicles.add(
veh_id="human",
acceleration_controller=(SimCarFollowingController, {}),
car_following_params=SumoCarFollowingParams(
speed_mode=9,
),
num_vehicles=5)
vehicles.add(
veh_id="rl",
acceleration_controller=(RLController, {}),
car_following_params=SumoCarFollowingParams(
speed_mode=9,
),
num_vehicles=0)
# Vehicles are introduced from both sides of merge, with RL vehicles entering
# from the highway portion as well
inflow = InFlows()
inflow.add(
veh_type="human",
edge="inflow_highway",
vehs_per_hour=(1 - RL_PENETRATION) * FLOW_RATE,
departLane="free",
departSpeed=10)
inflow.add(
veh_type="rl",
edge="inflow_highway",
vehs_per_hour=RL_PENETRATION * FLOW_RATE,
departLane="free",
departSpeed=10)
inflow.add(
veh_type="human",
edge="inflow_merge",
vehs_per_hour=100,
departLane="free",
departSpeed=7.5)
flow_params = dict(
# name of the experiment
exp_tag="merge_1",
# name of the flow environment the experiment is running on
env_name="WaveAttenuationMergePOEnv",
# name of the scenario class the experiment is running on
scenario="MergeScenario",
# simulator that is used by the experiment
simulator='traci',
# sumo-related parameters (see flow.core.params.SumoParams)
sim=SumoParams(
restart_instance=True,
sim_step=0.5,
render=False,
),
# environment related parameters (see flow.core.params.EnvParams)
env=EnvParams(
horizon=HORIZON,
sims_per_step=2,
warmup_steps=0,
additional_params={
"max_accel": 1.5,
"max_decel": 1.5,
"target_velocity": 20,
"num_rl": NUM_RL,
},
),
# network-related parameters (see flow.core.params.NetParams and the
# scenario's documentation or ADDITIONAL_NET_PARAMS component)
net=NetParams(
inflows=inflow,
additional_params=additional_net_params,
),
# vehicles to be placed in the network at the start of a rollout (see
# flow.core.params.VehicleParams)
veh=vehicles,
# parameters specifying the positioning of vehicles upon initialization/
# reset (see flow.core.params.InitialConfig)
initial=InitialConfig(),
)
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,337 |
{"url":"https:\/\/kalevala.pl\/breyers-delight-uyd\/aeedc1-aluminum-electron-configuration","text":"The next six electrons will go in the 2p orbital. Electronic configuration of Aluminium. Alum is potassium aluminum sulfate. [11] When an electron is added to a neutral atom, energy is released. Electron Configuration Lab You will explore how electron configurations vary around the periodic table. It was used in tanning, dyeing, and as an aid to stop minor bleeding and even as an ingredient in baking powder. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. There are 118 elements in the periodic table. The aluminum ion \u2026 The Environmental chemistry of Aluminum. For that, we have electron shell diagrams.. In the welding of large objects, the thermite reaction is used: $2Al_{(s)} + Fe_2O_{3(s)} \\rightarrow Al_2O_{3(s)} + Fe_{(s)}$. 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Retention in the case of aluminum the abbreviated electron configuration for aluminum ( Al ) than... Expert in welding and passionate about materials a step-by-step description of how to write electron! Andreas Marggraf found he could use an alkali solution to precipitate a new substance from alum named! 3S^2 3p^1 determine their magnetism ; +1 ; +2 ; +3 meaning that they readily accept a pair of..","date":"2021-04-15 11:11:18","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\": 0.32765987515449524, \"perplexity\": 5755.44718152008}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-17\/segments\/1618038084765.46\/warc\/CC-MAIN-20210415095505-20210415125505-00114.warc.gz\"}"} | null | null |
Q: How to express must be in past tense in an inference How do I express something like below in correct grammar:
If he is 21 this year, he must be 20 last year.
The problem is that I want to express that his being 20 is in the past tense. It doesn't feel right to say he must have been 20.
Searching around in ESL, I found related questions (but the answers don't apply): Past tense of "must" when meaning logical probability , whose answer suggest to use must have been; Is "must" ever grammatical as a past tense verb? , whose answer suggests to use had to. But he had to be 20 doesn't sound right either.
A: It really has to be
If he is 21 this year, he must have been 20 last year.
because the past tense applies logically to "he be 20 last year". Using an adverb to express the "must" part, we'd have
Necessarily, if he is 21 this year, he was 20 last year.
where the past tense of the clause "he be 20 last year" is expressed by using the past tense form of "be", which is normal in English.
When instead of "necessarily", we use "must", you might expect the second clause to be expressed
*He must was 20 last year.
But here we run into some idiosyncrasies of English grammar. You can't have a tensed verb like "was" following a modal verb; English permits only tenseless, i.e. non-finite, verb forms after a modal. And in a position where a tense inflection is not allowed, a present tense is just lost, but a past tense is converted to perfect "have". That's why we get "He must have been 20 last year". This is not logically a perfect; it's a substitute for a past tense which otherwise could not be expressed.
You can also see this conversion of a past tense to a perfect in some infinitive verb complements. "Believe" takes either a "that"-clause complement or an infinitive complement:
I believe that Mars is red.
I believe Mars to be red.
Notice that the present tense of "is" is simply not expressed in the infinitive form. But in a past tense complement,
I believe that Mars was watery at one time.
I believe Mars to have been watery at one time.
the logical past tense turns up as a perfect, because a tense is not permitted in a "to"-infinitive in English.
A: If he is 21 this year, he had to have been 20 last year.
There are other ways to express hypothetical or logical proposition as well, such as:
If he is 21 this year, he surely was 20 last year.
... or
Being 21 this year, he would have been 20 last year.
In this latter example, "would have" is used in the sense of "by reason of logic".
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,662 |
Welcome to my (late!) Spring newsletter! This is the first of my seasonal newsletters I would like to sent to you. It will highlight special offers, news which may be of interest, and relevant health tips for the season. I will not be bombarding you with any more than 6 of these a year but if you do not wish to receive it let me know and I will take you off the mailing list immediately!
Throughout the month of May I am offering £10 of the usual cost of initial consultations. This includes both acupuncture and Facial Enhancement Acupuncture. If you are already a patient, and you refer a new patient for treatment you get £10 off your next treatment too!!
Thanks for reading, and look forward to seeing you soon! | {
"redpajama_set_name": "RedPajamaC4"
} | 3,094 |
Coronavirus Roundup: State Legislature to Scrutinize Nursing Home Policy
All the news and announcements from New York State, the Hudson Valley, and the Catskills for Friday, June 26.
7:20 PM EDT on Jun 26, 2020
State legislators are asking questions about a policy from Governor Cuomo dictating how nursing homes handled COVID-19 patients.
Matt H. Wade
This is a roundup of coronavirus news and announcements from New York State and Hudson Valley and Catskills counties published on Friday, June 26.
Did a controversial order by the Cuomo administration cause needless deaths among nursing home residents? That question is going to get a public hearing in the New York State legislature, CNHI's Joe Mahoney reports. Manhattan Democrat Richard Gottfried, who chairs the Assembly Health Committee, said that there will be an announcement soon on the date of the hearing. Cuomo has repeatedly dismissed criticism of a now-reversed state Department of Health directive that ordered nursing homes to take in COVID-19-positive residents as partisan politics, but Democrats as well as Republicans in state government are asking sharp questions.
A federal judge blocked Cuomo's restriction of religious services to 25 percent capacity, holding in a Friday ruling that religious ceremonies should not be treated differently than other kinds of gatherings, and must be allowed to be held at up to 50 percent capacity. On June 6, Cuomo announced that religious services could now be held at 25 percent capacity in Phase Two regions, expanding on a previous order that permitted religious services with a maximum of 10 people. That order was also challenged in court; the NYCLU sued the state for permitting religious services and Memorial Day ceremonies but not other kinds of small gatherings, and Cuomo quickly moved to allow all gatherings of up to 10 people for any lawful purpose.
As of Wednesday night, travelers to New York, New Jersey, and Connecticut from highly infected states have been ordered to quarantine for 14 days or face steep fines: $2,000 for the first violation, and up to $10,000 if someone is harmed or killed as a result of a quarantine breach. Washington State was dropped from the list of states after erroneously being included, Governor Jay Inslee said in a press conference Wednesday. The states affected, which are on the list either because their rate of positive tests exceeds 10 percent or their positive tests exceed 10 people per 100,000 on a seven-day rolling average, are Alabama, Arkansas, Arizona, Florida, North Carolina, South Carolina, Utah, and Texas. Politico notes that California, where cases have been spiking, recently released case data that push its seven-day average above 10 positive tests per 100,000 residents; so far, New York has not announced that travelers from California are subject to quarantine.
On Friday, Cuomo announced that contact tracing has led to the discovery of outbreaks in Montgomery and Oswego counties, both linked to workplace infections: an Oswego County apple packaging plant and a Montgomery County aluminum manufacturing plant. Almost half of the workers at Champlain Valley Specialties—82 out of 179—have tested positive for COVID-19, Syracuse.com reports. Contact tracers from the state and the Oswego County Health Department found that the outbreak spread from the apple processing facility to the aluminum plant as well as an onion farm in Central New York. None of the workplaces were named in the state announcement.
Hospitalizations from COVID-19 have dropped below 1,000 in New York State this week for the first time since March, Cuomo announced on Thursday.
New York's statewide ban on single-use plastic bags, which was supposed to go into effect in March, has been repeatedly delayed because of fears that reusable bags and containers would be a vector for spreading the coronavirus, a concern peddled by plastics industry lobbyists, who've encouraged consumers nationwide to use disposable plastics as a safety measure. "As the COVID-19 virus spreads across the country, single-use plastics will only become more vital," wrote Plastics Industry Association president and CEO Tony Radoszewski in March. But the latest research indicates that reusables are perfectly fine—as long as you wash them, according to a statement released this week signed by more than 125 virologists, epidemiologists, and health experts from 18 different countries. Grist has more on the latest science concerning the safety of reusables during the pandemic.
"How The Virus Won": On Thursday, The New York Times published an interactive digital article that uses simple visuals—red dots on a gray map—to tell the story of the novel coronavirus's relentless march across the US, aided every step of the way by official blunders. It's clear, easy to read, and more than a little depressing.
A Friday feature in The Atlantic by Robinson Meyer and Alexis Madrigal digs into recent case numbers in the US, which surpassed all previous records in the past week, fueled by outbreaks in the South and West that have been ballooning as Northeastern case numbers shrink. Despite optimistic talk from federal officials and some state governors, the recent news is bad, they write: "Ignore any attempt to explain away what is happening: The American coronavirus pandemic is once again at risk of spinning out of control. A new and brutal stage now menaces the Sun Belt states, whose residents face a nearly unbroken chain of outbreaks stretching from South Carolina to California. Across the South and large parts of the West, cases are soaring, hospitalizations are spiking, and a greater portion of tests is coming back positive."
New York State will offer assistance to highly infected states, Cuomo announced on Friday, returning to a promise made early on in the pandemic to extend aid to other states once New York's crisis had passed.
The overall average rate of positive tests in the past week statewide is 1.1 percent, according to a Friday statement that broke down the past few days' worth of test results by region.
The first five upstate regions to enter the phased reopening process reached Phase Four on Friday: the Southern Tier, Mohawk Valley, Finger Lakes, Central New York, and the North Country. While the advent of Phase Four brings some lower-risk recreational activities back to upstate New York, Cuomo and the state Department of Health are not yet allowing gyms, theaters, or malls to reopen. In Friday's briefing, Cuomo cited research that has shown that COVID-19 can be spread via air conditioning systems, and said that the state is studying ways to filter out viruses in air conditioning systems. "Our Department of Health is trying to determine if there is any filtration system for an air conditioning system that can successfully remove the virus from air circulation. Is there a filter that can be added to an air conditioning system that we know will filter out the virus?"
New Rochelle on Thursday launched Rebound New Rochelle, a program that provides grants and business assistance to local businesses and residents impacted by the pandemic. The program is a partnership between the New Rochelle Chamber of Commerce, New Rochelle Business Improvement District, the Business Council of Westchester, and the private sector, and has $1.8 million to disperse in financial aid, according to a press release.
Saxon Woods Pool, in White Plains, and Sprain Ridge Pool, in Yonkers, opened as scheduled on Friday in Westchester. Tibbetts Brook Pool and Wilson Woods Pool will open next Friday, July 3.
Pace University, a private NYC university with secondary campuses in Westchester County, announced this week that it will begin the 2020-21 academic year on August 24 with a combination of in-person, online, and hybrid learning and finish classes in time for the Thanksgiving break.
Ulster County Executive Pat Ryan announced a substantial change to testing in the county: Nuvance/Health Quest will transition their mobile testing locations to on-site testing at facilities around the county, and will close the testing site at TechCity on June 30. Nuvance has added testing for existing patients at multiple Health Quest Medical Practice locations in Ulster County, including: 9W in Ulster, Kingston Plaza, Route 299 in Lloyd, Route 32 in Modena, Zena Road in Woodstock, and Route 28 in Boiceville. Non-HQMP patients can get tested at Vassar Diagnostic Lab at the Hudson Valley Mall in Kingston.
Illicit swimmers still haven't gotten the message that Big Deep and Little Deep swimming holes are closed, it appears. So town police are expected to patrol more often in the area, Woodstock Supervisor Bill McKenna said. The Daily Freeman has more on the crackdown.
Ulster County's Fourth of July fireworks display will be an "Independence Weekend Salute" to essential workers that will include a drive-in and socially distanced fireworks. (Editor's note: We recommend maintaining six feet of distance between yourself and all pyrotechnics, pandemic or no pandemic.) The fireworks display will be July 4 at TechCity.
The New York Department of Environmental Conservation announced additional campgrounds in the Catskills and Adirondacks that will open July 1 to existing reservations. In Catskill Park, the sites being opened are the Devils Tombstone Campground and Day-Use Area in Hunter, the Kenneth L. Wilson Campground and Day-Use Area in Mount Tremper, and the Mongaup Pond Campground and Day-Use area in Livingston Manor.
Delaware County officials announced another death from COVID-19 on Thursday, bringing the pandemic death toll in the rural county to 6. So far, 82 county residents have tested positive for COVID-19. The county currently has only one known active infection, a resident who is isolating in their home.
The indoor pool at the Catskill Recreation Center in Arkville reopened on Thursday, June 25 with new restrictions: Swimmers must reserve a limited number of time slots in advance and arrive in their bathing suits. Note: In their announcement about the pool reopening, the CRC writes incorrectly that gyms will be allowed to reopen in Phase Four. The reopening of gyms in Phase Four was widely anticipated among gym operators, some of whom brought back furloughed workers in preparation for reopening, but state officials announced Wednesday that they were still studying potential safety issues and would issue a separate recommendation for gyms.
The town of Fallsburg has opted not to hold its day camp this year, the Sullivan County Democrat reports. Municipally-run day camps in Thompson and Liberty are also canceled for the season; nearby camps in Bethel and Mamakating are proceeding with reduced numbers of campers. New York State has officially allowed children's day camps to operate, but some camp managers are opting to cancel anyway, feeling that they are not able to operate safely.
Two upcoming Sullivan County town halls are planned for next week. The first, at 1pm on Monday, June 29, will feature Phil Vallone, president of Rolling V Bus Company, along with county government and public health officials. The second, at 1pm on Thursday, July 2, will feature the town supervisors of Bethel and Tusten as guest speakers. Residents can submit questions by email to sctownhall@co.sullivan.ny.us or by Facebook private message to facebook.com/sullivancountygov; questions must be received by 7am on the date of the town hall.
To read more coronavirus coverage from The River, visit our coronavirus page. | {
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} | 8,710 |
THE HOLY LAND
CONTEMPORARY VISIONS
AND SCRIPTURES
**THE HOLY LAND**
CONTEMPORARY VISIONS
AND SCRIPTURES
EDITED BY
ITHAMAR HANDELMAN-SMITH
CONTENTS
INTRODUCTION
_by Ithamar Handelman-Smith_
**PART ONE: YAMA**
_(In ancient Hebrew: "the sea", meaning "west". Gharb in Arabic.)_
HOUSE OF THE WISE AT HEART
_by Shlomzion Kenan_
METZIZIM
_by Dana Kessler_
[FRIDAY AFTERNOON
AT THE MERSAND CAFÉ](08_9781910924600_Ch03.html)
_by Rana Werbin_
THROUGH THE STORY OF THE GRID
_by Ronen Shamir_
THE UNDERSHIRT
_by Sahar Shalev_
A TRAIN RIDE TO THE PAST
_by Ronen Shamir_
SABICH
_by Ron Levy-Arie_
INSOMNIA
_by Ithamar Handelman-Smith (as Ithamar Ben Canaan)_
**PART TWO: KEDMA**
_(Translates both as "east" and as "progress" or "forward-facing", as the ancient Israelites looked at the east instead of today's north. Alshrq in Arabic.)_
BEULAH LAND
_by Eran Sebbag_
IN MY HEART
_by Reuven Miran_
TECHNICOLOUR IN JERUSALEM
_by Tom Shoval_
FEAR AND LOATHING IN THE DEAD SEA
_by Dan Shadur_
ONCE IN ROYAL DAVID CITY
_by Julia Handelman-Smith_
THE JERUSALEM SYNDROME
_by Julia Handelman-Smith_
MY LIFE AS A DOG IN EAST JERUSALEM, OR SMELLY WALKS
_by Karin Gatt-Rutter_
**PART THREE: TZAFONA**
_(In ancient Hebrew the north was called Tzafona or Semola, meaning "left", which is like the Arabic Shamal, as in "north".)_
IN THE NAME OF THE FATHER
_by Shay Fogelman_
GALILEE MYTH
_by Nili Landesman_
[WE ALL GOT LOST IN THE SAME
ANCIENT ALLEYS (VISITING KFAR KAMA) ](25_9781910924600_Ch18.html)
_by Nadia T Boshnak_
BETWEEN THREE NORTHERN CITIES
_by Ron Levy-Arie_
HIPPIES
_by Ithamar Handelman-Smith_
[THE RELUCTANT HOTELIERS:
THE SCOTTISH HOTEL IN TIBERIAS ](27_9781910924600_Ch20.html)
_by Julia Handelman-Smith_
**PART FOUR: NEGEB**
_(Negeb or Timna is the southern desert, meaning "south" in ancient Hebrew. Janub in Arabic.)_
[A PATCHWORK CITY
– THE STORY OF BEERSHEBA ](30_9781910924600_Ch22.html)
_by Dr David Sorotzkin_
[ISRAELI TEXTILE
– A JOURNALISTIC POEM ](31_9781910924600_Ch23.html)
_by Roy "Chicky" Arad_
THE SPICE ROUTE
_by Ithamar Handelman-Smith_
DREAMERS UNDER THE SUN
_by Sagi Benita_
THE RED CANYON
_by Sagi Benita_
ICE CREAM VAN
_by Ithamar Handelman-Smith_
**INTRODUCTION**
_by Ithamar Handelman-Smith_
_Israel is not a country; it is not even, as someone has suggested, a state of mind. It is simply a disorderly systematic collection of paradoxes that somehow seem to make sense - don't ask me to explain how. Whatever you may say about Israel or Israelis, the opposite is equally true: every man, woman or child seems to be mobilised for war, yet every time they want to say hello, goodbye, how's your grandmother, or what's up, they say shalom, which means peace; and in a crazy way they make you believe they mean it. Here is no aristocracy of rank or wealth, not even a sense of rank in their army, not because they are so democratic but because everyone here thinks he's a general. And the greatest paradox of them all is that I, Roy Hemmings, have got myself stuck here, to report on a war that will not take place..._
With this monologue, director-turned-rabbi (read Dana Kessler's beautiful essay " _Metzizim_ ") Uri Zohar, one of Israel's best known artists of all time, decided to open his 1968 film, _Every Bastard a King_.
The film is an exceptional and unique description of the Israeli-Arabic conflict; told from the point of view of Roy Hemmings, a Hemingway-esque American journalist reporting from Israel and the Palestinian (then Jordanian) territories. It is the eve of the Six-Day War, a pivotal point in the modern history of this land. Through these foreign eyes, Zohar examines the complexity of this story, the story of Israel and Palestine, even before the actual occupation. The story of the Holy Land.
Throughout history, this little piece of land in the southern Levant, stretching between the sea and the Jordan River, has had many different names: there was the biblical pagan land of Canaan, then it was the Promised Land (or simply Eretz Israel) that God promised Abraham, and there were the ancient Jewish kingdoms of Israel (Samaria) and Judah. In the Babylonian and Persian period, the land was referred to as the province of Yehud Medinata, and under Hellenistic occupation it was Coele-Syria. The Romans called it the Province of Judea, and under the Byzantine Empire it was known as Palaestina Prima. The many different Arab and Muslim conquerors gave it many different names (Al-Urdunn, Filastin etc.) and the crusaders named it the Latin Kingdom of Jerusalem. Under the Ottoman Empire it was known mainly as part of Greater Syria. Then it was the British Mandatory Palestine, and eventually the state of Israel. But all along, it was the Holy Land: for Jews, Christians and Muslims alike.
As Zohar wrote, it "is not a country, it is not even, as someone has suggested, a state of mind", but a "collection of paradoxes" that "somehow seem to make sense". In this anthology of short fiction, poetry, essays and artworks, we try to make a bit more sense out of it all. While offering no specific political solution to the ongoing conflict over this, we try to put together diverse reflections and personal and subjective perspectives in order to shed some more light on the different places and landscapes of the Holy Land. We try to give voice to the many different communities living here, in this land today, from secular to orthodox Jewish Israelis through to Muslim and Christian Palestinians, the Circassians of the north and the Bedouin of the south. This is a kaleidoscope through which the reader might be able to see the Holy Land in new light and colour.
## PART ONE: YAMA
_(In ancient Hebrew: "the sea", meaning "west". Gharb in Arabic)_
HOUSE OF THE WISE AT HEART
_by Shlomzion Kenan_
_The heart of the wise is in the house of mourning;
But the heart of fools is in the house of mirth._
(Ecclesiastes 7:4)
One afternoon in the autumn of 1832, a young Arab horseman was hunting for gazelle in the swamplands that stretched beyond the citrus groves of Jaffa when he chanced upon a traveller. Recognising him immediately, the young horseman rode up to greet him, introducing himself (as Alphonse de Lamartine will later recount in his _Voyage en Orient_ ), in Italian, as an Arab; Italian by origin; French at heart. His father, he said, the French Consul to Jaffa, a certain Monsieur Damiani, has heard about the imminent arrival of the famous Frenchman and would like to warmly welcome him as a guest at his home.
Around that time, the reign of the "modern father of Jaffa" – the Turkish Sultan's governor, Muhammad Abu-Nabbut – was drawing to a close. During his fifteen years as governor, Abu-Nabbut rebuilt Jaffa for the hundredth time, after a hundred devastations, this time around as an imposing, prosperous, commercial, multicultural port town. A year prior to Lamartine's visit, as the Egyptian Mohammad Ali moved in, he fled to Mecca. Ten years earlier, a North African Jewish community began to prosper in the Old City. One traveller concluded in 1823 that the fruit of the city were each larger than a man's fist and that no man could carry its red, sweet watermelons. So Lamartine was invited to Damiani's beautiful home, where the breeze, thick and salty, entered through the paneless windows, rattling the chandeliers. Lamartine has a street named after him in Jaffa to this day. Damiani, the hospitable consul, doesn't.
Two years ago, crowded out of Tel Aviv by booming real estate prices, I moved to Jaffa, to the top two floors of what was once a one-family home and is now a quietly dilapidating six-family home. It was still grand, though. With the fivepoint star, symbol of the Ottoman Empire, sculpted in crumbling clay above the front door. Tile roofed, perched on a hill, its cedar wood shutters and portholes were fixed upon the Mediterranean that was surely and quickly being eclipsed by construction and gentrification. The two chickens I saw in the alleyway on the first day belonged to a fisherman whose Bedouin family had fished in the waters of Jaffa for seven generations. From their rickety fishing boat they saw the battleships of Napoleon sailing in. After the Nakba (the Palestinian term for the exodus during the 1948 war) – with the original landlords turned refugees – the father moved into this house and added a few rooms to it, down where the stables must have once been. The other five residents of the house did more or less the same throughout the 1950s. Like ground squirrels that move into dens meerkats have vacated, one by one they moved in – some by orders from the state, others by orders of the gut or heart. They erected new walls between them, dividing the place up, de-gentrifying it, keeping what they lost private and letting the gossip pour out into the alleyway publicly. Three Muslims, one Christian-Armenian and two Jews. Up until some of them sold and moved on or died, all were refugees or sons and daughters of refugees whose story had been written and archived by a state of refugees that had made refugees of others.
There were some bright tracksuits drying, bellowing in the wind, up the front, on that first day I moved in, and through a creaky, battered double blue door, I entered the high limestone-walled courtyard, with its stooped, dusty birds of paradise, its dried out pond, and the lemon tree that arched over from the churchyard across the wall. The windows were dreamily draped with ancient bougainvillea in pink, white and purple, but the trademark Jaffa floor tiles had been pulled out decades earlier by previous tenants who wanted to ease themselves into the erasure of the past.
When I went to City Hall to fetch the blueprints of the house, I found a crumpled 1947 scroll with a beautiful sketch of the house and the name of its owner scribbled in handwritten Arabic on top: Hanna Damiani – prosperous landowner and proprietor of the olive oil soap factory at the old Turkish Serail building.
It was this Hanna Damiani's great-grandfather who welcomed Alphonse de Lamartine in 1832, dressed in a sky-blue double-buttoned kaftan and a crimson silk belt which Lamartine found to be "grotesque" and "oriental". Could they have been chatting away in French and Italian amidst silver trays and Chinese porcelain right here, where I am now sitting and writing this, looking out towards Andromeda's Rock? Probably not. My home, at the Maronite section of Ajami, south of the Old City gates, was most likely built no sooner than the late nineteenth century.
It stands to reason, then, that it could not have been the same home in which an older ancestor of Monsieur Damiani hosted Napoleon Bonaparte in the spring of 1799, just between the latter killing a few thousand people who bled into the sea, asking his doctor to poison with opium those who had to be left behind, and failing to conquer Acre and become emperor of the east.
But the young lad who rode his horse in the swamps that day and ushered the travel-weary Frenchman through the groves, towards the 130-foot lush green hill from which the Old City of Jaffa once cascaded into the sea, was certainly one of Hanna Damiani's ancestors, an illustrious family of diplomats and consuls for France, England and Italy, whose coat of arms once adorned the ceiling of my next-door neighbour's carved wooden ceiling until it was painted over.
Like all things beautiful and exquisite, Jaffa has been ravaged, ransacked, taken, loved, destroyed and rebuilt dozens of times over four millennia. Pirates and pilgrims dubbed it a Belvedere of Joy. Palestinian refugees cherish it as their Bride of the Sea. As old as the Bronze Age, Jaffa is one of the oldest and most important ports on the Via Mare. Its name, some say, is a tribute to Noah's son Yeffet. Others say it predates the flood. In Hellenistic tradition, it was Joppa or Iopeia, after Andromeda's mother, Cassiopeia. In the language of the Sidonians it was Yaffa, the beautiful. According to Lamartine there were roughly five thousand people living in Jaffa in the 1830s: Turks, Armenians, Greeks, Maronites and Catholics. Of a population of seventy thousand Palestinians living in Jaffa in 1948 (not counting surrounding villages), it is assumed that three thousand remain. For the most part, they were gathered up from the Old City and the Casba and locked up in Ajami, where martial law was instated until the 1960s.
A race of particularly short people once hunted for rhinos in its oak woods, centuries before the sky was lost to housing developments flanked by drug stops and asbestos huts, embittered by wars of class, nation and religion. The multicultural Terra Irredenta, Palestine's lost Shambala, the colonial idea of paradise, had turned into purgatory. Still very much the Provence of the Middle East to the large international community living here, but scratch the surface and there's that beautiful, harsh, crazy, old, trendy, peaceful, warful, chaotic, regal, rundown, conflicted hill on the water some call home. Indeed, the Jaffa of 2013 I moved into is a far and bitter cry from the city the romantic one Lamartine visited in 1832. He describes coming upon a hill that looms over the turquoise waves, covered in oak, citrus, fir, and pomegranate trees, streaked with freshwater streams that flowed through a row of jutting capes into the sea. Rows of firs protected the fruit trees from the harsh sea winds and church bells carried on the magic air. Jaffa, he wrote, offers "the perfect haven of repose for the life-weary man who wants nothing but to enjoy a benevolent sun".
In the spring of 1948, Hanna Damiani left his Jaffa home – perhaps my home – perhaps by boat, perhaps by land, never to return. Did he leave the stove on? Did he take a key? Did he keep it all these years? I know that some Irgun soldiers, some who were recently liberated from the camps, were seen looting enormous crystal chandeliers from the palatial villas of the Maronite neighbourhood, holding them in their arms and running. Small, frightened men with the bright blue sea and the yellow sun reflected a million times in their arms.
The Assyrians conquered Jaffa from the Philistines, who conquered it from the Egyptians. In the eleventh century, the Muslims destroyed it to prevent the crusaders from seizing it. Two centuries later, it was destroyed again by the Mamluks. Canaanites, Ethiopians, Philistines, Egyptians, Assyrians, Greeks, Jews, Romans, Muslims, Mamluks, English, French, Turks, Israelis. Flavius Josephus had seen Andromeda's shackles still attached to the rock. He had seen the wind of the black north tear ships in half, serendipitously for the Romans, who were able to take Jaffa over from the Jews without a struggle and "turn it into a wasteland".
During the second century bc Jaffa was annexed to the Hasmonean kingdom, a synagogue was built in the eighteenth century, and long before that, a thousand devastations ago, King Solomon brought cedar trees from Lebanon to Jaffa to build his temple in Jerusalem. The Jewish traveller, Rabbi Itzhak Chelo, wrote in 1334 that Jaffa's main trades are olive oil, cotton wool, scented soaps, glass bowls, dried fruit. The Jews of this town, he wrote, have a splendid synagogue with precious old books, but few can read.
In the late nineteenth century, when my house, along with other Christian-Maronite homes to the south of the Old City were built, Jaffa was an international, bustling, cultured, commercial port town, with oranges, ships, cinemas, theatres, hospitals, schools and hotels. Today, there are no ships, no oranges, no hotels, no cinemas, no theatres – just secure housing, slums, drug-stops, the trendy bars of the flea market and orientalist tourist attractions. Yaffa, the beautiful, is losing its good looks. It's hard to tell how the Pizzeans or the Franks, the Turks or the Egyptians, rebuilt Jaffa after its numerous devastations, but I'm pretty sure that the Israelis, after having levelled the Casbah and other parts of Jaffa in 1948, did one of the worse jobs. While the Old City and some Ottoman-era buildings are being beautifully restored and preserved, some new tenement buildings erected along the Ajami coast look like they could use a hint from history's penchant for demolition. If Abu-Nabbut, the Turk, rebuilt modern Jaffa and made it flourish, Ron Huldai, the residing mayor of Tel Aviv-Yafo, is responsible for gentrifying it. Indeed, Jaffa appears to be the only case of gentrification in the world that has kept the criminal classes – bred and nurtured by decades of calculated neglect – intact and abloom. This, after Huldai's predecessor, Shlomo Lahat, had turned Jaffa into a permanent demolition site. During the Seventies and Eighties, the palatial mansions of Ajami were systematically demolished to prevent absentees from returning. The debris was then piled high along the beach to deny the denizens their view of the sea. Finally, with the idea – either, as some say, inspired by a planned conspiracy, or by natural market forces – to bring more Jews to Jaffa and boost up the prices, the debris was covered up in earth and grass and turned into a park. Nowadays, the sea view is slowly hidden – not by garbage, but by the rich. And the skies of Jaffa, once lacerated by steeples and minarets, are also lost. Darkened.
It was the Armenian lady, who lives downstairs with her dog, who first told me about the gold. According to her, it was her late husband, or maybe a relation of her late husband, who, shortly after the Nakba, met a refugee from Jaffa in Lebanon. This refugee, perhaps a member of the Damiani family, perhaps not, described the house and explained precisely where the wall was in which he had buried the gold. It is the porous limestone wall that now surrounds my limestone patio, with an old lemon tree stooping forth, as sweet and as sour as the longings for what Jaffa was. I don't know if the Armenian family came to Jaffa in pursuit of the gold, or perhaps they came to work with Abu George, the French company's lighthouse attendant up until 1966 – or was he already living in Jaffa? At any rate, one night he started hitting the wall with a sledgehammer. He looked for a weak spot and sure enough, after a while he heard a metallic sound and hit a hard place. The jackpot came pouring out, glittering in the moonlight. Hearing all the racket, the upstairs neighbours, the Jewish immigrants from Iraq who sold the place after fifty years to a real estate investor who sold it to me, came down and, seeing what was what, called the police. The Armenian was arrested for three days and then released, with the gold, which he had to split up with the other families living in the house.
Nothing else was split very evenly. Except, perhaps, exile and dislocation. The mother of the Jewish-Iraqi family, who lived for fifty-odd years in the same apartment in which I'm living now, always wore slippers outside. This, the neighbours thought, was a constant reminder of the last time she left her home in Iraq, and like Damiani, had locked the door for the last time, then, after having seen her father dragged through the streets, walked by foot to Israel. Next door to her (and as of recently, to me) lives a German Jew with her all too familiar German Jewish story, and downstairs, for another fifty-odd years, still lives another Palestinian-Arab family, whose village was demolished in 1948. Though they have some family members in jail, some assassinated and some in rehab, the women of the house are always laughing, always watering the herbs outside, trying to make things grow. Once, there was a Muslim cat lady living on her own downstairs. The cats were buried in my patio, next to the wall where the gold was found, and the woman was buried in a cemetery, and the house was auctioned and bought by one of Jaffa mobsters who, like many others, had discovered the newly lucrative avenue of real estate-related crime. One day, he too broke down the wall with a sledgehammer. Not for gold, but for installing a door in the patio and thus bettering his investment. Like the calcareous sandstone Jaffa is made of, these stories, past and present, are filled with holes. Their matter is porous. Weathered. Patinated by time, sedimented by water, legends sieved through them, tall tales, tragedies, like a nebulous fishnet they ebb and flake off through the centuries. Andromeda, Jonah, St Peter: one is now a gentrified, doorman-secure real-estate-swimming-pool-project, one a high-end port restaurant, the third still a church.
British journalist Robert Fisk tracked down David Damiani, Hanna Damiani's son, in Beirut, and interviewed him for a book. David told him about his ancestor Boutros Damiani, who was born in Jerusalem in 1687. His four sons were consuls in Jaffa for Britain, France, Holland and Tuscany. The last consul in the Damiani family was Ferdinand, he writes, who represented Mexico in 1932. In the days of Napoleon, it was Anton Damiani who interceded on behalf of the Muslim community. According to Fisk's interview, David Damiani had only just moved into a new home with his new wife shortly before 1948. One day, on the third week of April, they left their home for the last time and locked the front door behind them just before lunchtime. They carried only one suitcase, a jewellery case and the registry deeds to their lands and got on a boat to Beirut.
After conducting this interview, Fisk travelled to Jaffa and found the house that was once David Damiani's. Living there now was Israeli sculptor Shlomo Green, a Holocaust survivor who had lost a hundred relatives in Auschwitz. After learning about the Damianis and their story, of how David Damiani stood at the stern on the ship leaving the Jaffa port wishing he could turn around, the sculptor "looked up quite suddenly with tears in his eyes and said, 'I am very moved by what you have told me... what can I say? I would like to meet these people, if you can say for me...'" Here,
Fisk writes, he paused, and then said:
'It's a tragedy of both our people. How can I explain in my poor English? I think the Arabs have the same rights as the Jews and I think it is a tragedy of history that a people who are refugees make new refugees. I have nothing against the Arabs... They are the same as us. I don't know that we Jews did this tragedy – but it happened.'
In Beirut, Fisk told Damiani about what Green had said, writing, "I repeated the details of how so many of Green's family had been murdered at Auschwitz. Damiani showed no bitterness. 'I wish him happiness,' he said."
I don't think, however, that the current descendants of the illustrious family feel the same way. I have tried to make contact with them, first through Fisk, whom I was told does not respond to Israelis, then through a go-betweener from Jaffa, who had sent my letter through London to Beirut, where he was assured that it had reached the three grandchildren of Hanna Damiani. An answer did not come.
Ramses II, Cleopatra, Pompeius, Alexander the Great, Saladin Richard the Lionheart, Napoleon, Abu-Nabbut, Mohammad Ali, Selim the Grim, and now us israeli, loved it, ruined it and rebuilt it, and some day it will be ruined again. When the crusaders went on a new conquest spree in the 1300s, the Ottoman Sultan decided to take no further risk and demolished Jaffa to the ground. He left no stone on stone and blocked down the port. John Polloner, a traveller in 1422, discovered a ruined city, empty of men, without one house standing, except the ruins of St Peter's church. De La Brockierre, a French traveller, wrote in 1432: "I have never seen such destruction anywhere else, and I am puzzled at how they were able to topple such thick walls."
These walls, the thick walls of this house, can crumble even if they are strong. They are made of empty cavities and stories. They can crash to reveal a grave, a treasure, a door. Their stories can become histories in the same way that men and women become communities and nations. But it is up to the people – not the nations and what they have done – to choose which way the souls of this purgatory wish to go. To mend the walls of their homes and tear down the ones in their hearts. Even as the same stories keep repeating themselves throughout the eons, with one in particular that stands out above the rest.
The one about the virgin bride of the sea and her wedding night. Since before the flood she had been beautiful. But time and again, when her orchard beds are strewn white with citrus blossoms, her streets wash red with blood.
BIBLIOGRAPHY
Aldor, Gaby (Hebrew), _The Lane of White Chairs_ , play produced by the Arab-Hebrew Theatre of Jaffa (1989)
Fisk, Robert, _Pity the Nation: The Abduction of Lebanon_ , Nation Books, New York (1990)
De Lamartine, Alphonse, _Voyage en Orient_ , Paris (1835)
Lebore, Adam, _City of Oranges: An Intimate History of Arabs and Jews in Jaffa_ , ww Norton & Company, London/New York (2007)
Shezaf, Tzur (Hebrew), _A Guide to Jaffa_ , shezaf.net
Tolkowsky, Samuel (Hebrew), _A History of Jaffa_ , Dvir, Jerusalem (1926)
Original poster for _Metzizim_ , 1972
METZIZIM
_by Dana Kessler_
Nobody remembers exactly when, but at some point the popular beach located at the northern edge of Tel Aviv's sea shore changed its name from Sheraton Beach to Metzitzim Beach. It probably happened around the time that _Metzitzim_ – a once forgotten cinematic gem from the early Seventies – suddenly started to develop a huge cult following, as well as recognition as one of Israel's best-loved movies of all time.
More than forty years after its initial release, _Metzitzim_ (or _Peeping Toms_ as it is known outside of Israel) is considered by many as the greatest film in the history of Israeli cinema. This is one of the few cases in which film critics and mass audiences agree on a movie, but it is probably just because when they watch _Metzitzim_ they see two very different films.
_Metzitzim_ revolves around a gang of adult men who refuse to grow up. Imagine the Mediterranean version of Richard Linklater's or Kevin Smith's slackers, or maybe Seinfeld's gang years before Gen X reared its ugly head. Gutte (played by Uri Zohar, who also directed the film) and Eli (Arik Einstein, who wrote the script with Zohar) are two thirtysomething beach bums. Being best friends, they do all they can to help each other stay submerged in a constant state of denial about the fact that they really should begin to take responsibility for their lives.
They hang out at the beach, looking to get laid and pulling silly pranks. Eli, a good-looking musician, has a loving and very cute wife and a little girl at home, but prefers to hang out with Gutte at the beach, constantly whining about his life and blatantly disregarding the vows he took, probably not very long ago. As Einstein once described him: "He's a little dreck".
Gutte works as a lifeguard and lives in a shack on the beach, which he lets Eli use for his sexual escapades. Although a big part of his everyday chores is to drive away the voyeurs who come to the beach to catch a glimpse of what goes on inside the ladies' showers, Gutte can't resist a peek through the wall whenever Eli picks up a groupie after playing a club gig.
Today _Metzitzim_ is a part of Israeli history, and a landmark of Tel Aviv culture. It was the first of three Zohar films that are known as the Tel Aviv trilogy, along with _Einayim G'dolot_ ( _Big Eyes_ ), which also paired Zohar with Einstein in the leading roles and might even be superior to _Metzitzim_ in quality (but certainly not in popularity), and _Hatzilu Et HaMatzil_ ( _Save the Lifeguard_ ), Zohar's last film, which seems like a dumbed-down version of _Metzitzim_ , done in terribly poor taste.
These days you'd be hard pressed to find an Israeli who hasn't seen _Metzitzim_ at least once or twice or a hundred times. While the old shack from the movie has been demolished by the local government and the beach has been renovated to cater to families rather than the wayward teenagers who used to frequent it, bored soldiers still amuse themselves by quoting naughty lines from the film (one thing you should know about Israeli soldiers is their undying love of Israeli cult films), while aging bohemians with cracked tans boast about being extras in it in their long-lost youth.
It is hard to believe today, but when _Metzitzim_ was first released, the masses didn't flock to see it. Many excuses have been made over the years for this failure – excuses that blossomed into myth. Since Israeli mythology usually has something to do with one war or another, some people believe _Metzitzim_ failed because it was released immediately before the Yom Kippur War. But since ten months had passed from the film's premiere at the now defunct Orly Movie Theatre in Tel Aviv (on which – true to cliché – a parking lot now stands) until the Arab coalition launched its surprise attack, that excuse doesn't really hold water.
Another explanation – perhaps more plausible than the first – is that _Metzitzim_ is a summer movie (even though it doesn't have the mandatory summer movie happy ending) released in winter. While no one in their right mind would release _Grease_ in December, dragging the audience out in the cold to see Zohar sweat his hairy ass off at the beach probably wasn't the best of ideas. Apart from that, most of Israel's movie-goers probably weren't ready at the time for Zohar's dirty mouth and filthy behaviour. When accused of blatant and unnecessary vulgarity in an interview a few weeks after _Metzitzim_ 's release, Zohar quoted one of his idols, Lenny Bruce, who said, "If God created the Body, and the Body is dirty, then the fault lies with the Manufacturer."
Apart from being well received at the 23rd Berlin International Film Festival, where it entered the competition in June 1973, _Metzitzim_ was pretty much forgotten for many years. It resurfaced in the Eighties at midnight screenings in art-house cinemas in Tel Aviv, and together with the help of the vcr, it started to gain the cult status it enjoys today.
_Metzitzim_ initially bombed even though Zohar and Einstein were key figures in Israel's entertainment industry. Both were all-round entertainers, who did pretty much everything in the biz. Zohar was a popular actor, comedian (sometimes credited as being Israel's first stand-up comic) and entertainer. And while his tv career was often of the embarrassingly mainstream kind (at one point he hosted Israel's first game show – a local version of _I've Got a Secret_ ), he always strived to be a serious film director, and indeed an auteur.
Before making _Metzitzim_ , Zohar already had an impressive filmography under his belt, ranging from satirical comedies to very personal modernistic films influenced by the French New Wave. At first Zohar, like many international directors, adopted the method of "one for the money, one for the soul" (while most of the time the one for the money was made to recuperate the losses from the one for the soul). But it seems that with _Metzitzim_ he actually tried to combine the two, merging two opposing genres that traditionally appealed to two very different types of audiences.
Einstein – a singer, actor and comedian – was no less of a star, and is to this day considered Israel's greatest male singer of all time. In the early Seventies Zohar and Einstein collaborated on the sketch-and-song tv show _Lool_ ( _The Chicken Coop_ ), which also eventually became a cult hit. The show's creators and cast became known as the Lool Gang, and together they produced Einstein's albums at the time and a couple of movies, one of them being _Metzitzim_.
The Lool Gang is remembered not only for its art, but also for its lifestyle. Zohar, Einstein, Shalom Hanoch (Israel's prime rocker, who wrote the music for _Metzitzim_ ) and their friends will forever be credited – or blamed – for bringing the Sixties to the Jewish state. They brought the sound, the look (it's hard to say they were hippies exactly, but they did sport an unkempt style and long hair), the drugs, and above all – the spirit of free love. Together with a handful of albums, movies and other cultural artefacts, _Metzitzim_ became a symbol of late-Sixties and early-Seventies Tel Aviv bohemia. Of course, it didn't hurt that the film's starlet and sex symbol, Mona Zilberstein – who made her mark on celluloid with the sexy scene in which Zohar hoses her sandy body off – later died of a heroin overdose.
For today's audience, _Metzitzim_ is pure nostalgia. A large part of the film's charm lies in its local colour, in the way it authentically captures a certain moment in the history of Tel Aviv. The film's believable characters, the use of non-actors in the cast and Adam Greenberg's superb cinematography (before he emigrated to the us and was later nominated for an Academy Award for his work on _Terminator 2: Judgment Day_ ) make up a large part of _Metzitzim_ 's realistic charm. As _Haaretz_ 's film critic at the time, Yosef Shrick, beautifully put it when it was first released: "Adam Greenberg's camera followed the gang around as if it were a stray dog." Anything Gutte, Eli and their friends did or said – no matter how vulgar or shocking – the camera loved. And that's the magic of cinema: what the camera loves, the viewer can't help but fall in love with too.
_Metzitzim_ was atmospheric and, of course, funny. At first glance it is a hilarious comedy, with enough vulgarity to match _American Pie_ , but _Metzitzim_ is much more than a cult phenomenon or a piece of Israeli nostalgia. As Einstein has pointed out many times, the film was, and still is, very much misunderstood. Since it combined elements of the two opposing genres that dominated Israeli cinema at the time – the popular comic melodramas known as Bourekas films and the personal films that critics loved but the public ignored – it is no surprise that the audience didn't exactly know what to make of it. But watching it today, it is impossible to escape its persistent, and almost depressing, melancholic undercurrent. Under the film's light façade lies Gutte's heartbreaking loneliness, and the feeling that even if the Sixties were a glorious time of freedom and frivolity, the emptiness of this hedonistic lifestyle left quite a few souls deeply wounded.
Looking back at Zohar's well-documented biography and the history of Israeli society, it is clear that what might seem a light-hearted comedy about a gang of useless beach bums is in fact a harsh manifestation of the inevitable identity crisis the Jewish nation faced a quarter of a century after its foundation. At the heart of _Metzitzim_ lies the deep existential crisis that Zohar went through in his personal life, one that characterised his entire generation. Not only were the new Israelis – born in the late Thirties and Forties – devoid of the Zionist passion of their immigrant parents who came to Palestine to build their people a homeland, they also neglected to fulfil their parents' expectations. Instead of the strong collective that Israel was founded upon, _Metzitzim_ shows a group of lost individuals with empty lives who swapped the lofty ideals of their parents for cheap thrills – some booze and a roll in the sand with a banana model, or at least a peek at it through a hole in the wall.
While in America the Sixties ethos of free love was accompanied by anti-war protests, in Israel it reeked of escapism. _Metzitzim_ came out just before the end of the Six-Day War euphoria, and just before the trauma of the Yom Kippur War. In those days (almost) no one in their right mind would protest against Israel's military actions. Zohar and his friends weren't into fighting, and they weren't into the Ashkenazi bourgeois life that was expected of them either. They preferred to hang out at the beach as if they were carefree teenagers. The only problem was that they were much too old for that. Einstein once told an interviewer that a film critic who had written about _Metzitzim_ when it was first released claimed it was ridiculous that he and Zohar played the roles of beach boys at their age, but – as Einstein pointed out – that was the whole point. It was high time for them – and for Israel – to grow up.
Gutte and Eli's disregard for the establishment and bourgeoisie can easily be compared to the disillusionment with the American Dream seen in movies like _Easy Rider_ and _Midnight Cowboy_ just a few years before. But of course, this is the Israeli version, and in real life Zohar found a very Jewish solution to his problem.
Many believe that the aimless existence of _Metzitzim_ 's protagonists – based on some level or other on the Lool Gang's real life – eventually made Zohar a _hozer betshuva_ (literally "one who came back with an answer", meaning turned to Orthodox Judaism). At the peak of his success, Zohar decided to trade in the spotlight for a brighter light, as did quite a few of his friends and peers from Tel Aviv's bohemian scene (Einstein's ex-wife and children also became Orthodox Jews at the same time, and Einstein's two daughters eventually married Zohar's two sons). Abandoning their parents' ideals must have created quite a father complex for Zohar's generation, thus turning to God was only to be expected.
In 1977, Zohar retired from show business and moved to a Yeshiva (a university-like religious school) in Jerusalem and became a rabbi. The only reminders of his former life were the commercials which he directed for Shas – an ultra-orthodox religious political party – as part of its election campaign.
As _Metzitzim_ clearly shows – at least to whomever cares to see more than the film's horny exterior – Zohar was part of a lost generation, one that struggled to find new meaning for life, having lost the one its parents had. Zohar was impatient and turned to God. Had he waited a couple of decades, the mind-numbing capitalistic rat race that finally caught up with Israel might have given him – as it did the rest of Israel's secular population – a new _raison d'être_.
FRIDAY AFTERNOON AT THE MERSAND CAFÉ
_by Rana Werbin_
So Ynet says that Orthodox women are finally fed up with getting married in their late teens and then giving birth every year till their forties.
Like that'll help them much. The chances of them being able to avoid pregnancy subjugation are equal to the chance that all women sitting around us here today will have the nerve to go around braless. We talk about it, bitch about it, send each other Facebook cards saying "Home is where the bra comes off," but we all know we won't dare to actually do it. There was a time in the Seventies... but then everyone was young and perky-breasted. It wouldn't have worked with the older women. No one can be that liberal. Anyway, that time is gone now. It's all rounded cups now, wherever you go.
I still sometimes go braless, Sarah! Or with an unwired, uncapped bra. And I'm no spring chicken, I'm about to turn forty soon! My God.
But you only go without a bra when you wear something so tight that it holds 'em up nicely. Admit it!
I do. But that's just because I'm not even.
I'm not even either, so what! And mine are larger and droopier than yours. It took me over a year before I went braless around Avi. And that's even though he sees me in bed naked almost every night. Still, I just couldn't face him bare-breasted under a loose shirt. I was afraid he'd be disgusted. A year! Let's face it, we wear our bras like our great-grandmothers wore their bodices, like the modern intellectual Arab women wear a hijab, like the national-religious young married women wear a smartly tied scarf showing just a tiny allowed bit of hair in the front. We all conform, and we fool ourselves to think that just having this little something around your head or around your tits is way better than covering yourself up entirely in a burka or shaving your head to wear a wig or squeezing your intestines in a whale-boned corset, and that we've advanced so much. We're lying to ourselves, Rana, not just to the men we fear won't find us attractive anymore if we disobey the rules.
But anyway, we're always lying to ourselves, don't you think, Sarah? I mean, even if we all walked around with our tits shaking about freely, our wombs vacant and carefree, hair wild and loose, and even if men were still somehow attracted to us, maybe because all the perky twenty-year-olds were already taken, and we would never ever be shamed for looking as we naturally do – even then, we would still lie to ourselves and shut our eyes to oppression. Only we'd be lying about other things, that's all. All people lie to themselves, all the time.
Are you gonna talk about politics again? I thought we agreed it's an off subject on weekends!
No! Fine! Even though it's all politics, you know. But, no, OK, don't give me that look, I promise, no Eritrean refugees, Chinese labourers or Palesti—
Hey, speaking of, what happened with Saleh, did he ever answer your text?
No.
No?
No. I don't really want to talk about it.
Fine, we don't have to. But I thought for sure he was going to text you back after—
Hey! I said I don't wanna talk about it. Can we please change the subject!? Let's just talk about work, OK?
FRIDAY EVENING AT MINZAR
God, Rana, I'm just so sick of being poor and having to work for money. I just wish I could do what I like and make a decent living out of it. I don't even need much. I simply want to not hate my life. Why are people even supposed to work eight hours a day at foaming milk? It kills your soul. Your brain dies. It sucks the energy right out of you and when you come back home you can't do anything but watch porn. Or whatever trashy reality show they have on TV. And what's the deal with foamed milk anyway? Why can't people just drink their coffee without having some poor guy stand for hours to foam it and then draw stupid pictures on top of it? What are they, three-year-olds?
I used to love my milk foamed when I still drank coffee or milk at all. But now my Ayurvedic nutritionist says milk makes me phlegmy so I've stopped with dairy altogether. No more cheese, butter, even yogurt. And I gave up bread too. And coffee, because I liked to drink it with a sweetener and that's poison. And no sugar, naturally, it's bad for you, even the brown kind. Lost three kilos in a month though, so that's cool.
How come you're drinking booze then?
I'm allowed to have wine and arak. Just no beer or whiskey or any other grain-based liquor, which is fine with me. I love arak. I also can't have tomatoes or cucumbers or eggplants or hummus...
That's, like, all the food there is! God, what do you eat?
All the rest, I guess. Pumpkin, carrot, green beans, barley, I don't know. Kasha. She says I'm kapha-pitta with too much vata, which is what makes me have my panic attacks. So I need to balance out the vata.
But I thought your panic attacks are related to war situations, no?
Yes. But the thing is that if I want to live here, you know, and not exile myself to some other place entirely, just live here in my homeland by the sea, in perfect weather, surrounded by my family and friends and all the countries around that don't recognise our right to be here – then I must find a way to cope with war-related stress.
And you think the way to do that is by balancing your Ayurvedic vata or whatever that is?
No, the vata is just one type, you see, we're all made of three types – kapha, pitta and—
OK, OK, let's not delve into that right now. With all my love and respect to India, and to you, I'm just not much into talking about New Age mumbo jumbo right now, ok? I say if you can't hold yourself from reading online news, which you know you shouldn't, and you find yourself panicking again because nobody helps the Syrians and you think they won't help us either when the day comes, which they won't, I assure you, or you make the huge mistake of watching tv news and you end up realising that Iran will evaporate us in one atomic split, to the sincere condolences of the West and the joyous rooftop dancing of the rest – just take Clonex. Really, it would do you much better than all that Ayurvedic bull.
Seriously, you don't know what you're talking about, Danny. First of all, it's not New Age at all, it's an ancient—
No, you know what, I just don't want to hear about it. Let's just roll a joint and talk about my hate for customers, alright? Believe me, it's much healthier.
FRIDAY NIGHT AT AFRICA
So he says why don't you just take Clonex? To which I say, you do realise that you're offering me a Western capitalistic solution to stress which is caused by the same Western system in the first place, the system which is now trying to push its expensive trademark pharmaceutical drugs into me, but outlaws the much better drugs that I could have grown myself, but no, those are only to be smuggled illegally by Bedouins in the south, whose homes are now being demolished by the same horrid system, which is just mind-blowing, it's just—
But wait, where is he now, Danny? Why didn't you bring him with you?
Because I'm telling you, Noa, it's not gonna work out with him! All we ever do is smoke pot and fuck, there's never a decent conversation, and he always talks about himself for hours but won't listen to one full sentence of mine, and even if he did, I miss Saleh. I don't know if I can fall in love with someone else now.
Saleh! Didn't hear that name for a while now! I thought it was over months ago.
It was. It is. I just had too much pot to smoke and too much arak to drink. No, Saleh's back to Haifa now. Looking for someone that he can say "habibti" to and she will truly understand. As if I can't understand "habibti". As if I can't mean it when I say "habibi". He just enjoys breaking hearts.
Jewish hearts.
Don't be mean, Dorit.
I'm mean, Noa? I'm mean? Remind me who said she pities Liat for marrying an African refugee? Yes, Noa? Yes? Come on. Who's the racist?
Hey, I'm not a racist! It's not my fault you're all so PC it's like you were programmed at Microsoft. Let's face it – it's a hard life to be married to someone far less educated than you, who comes from a completely different culture, who's all alone here, while you are surrounded by your family and friends. Dorit, come on, remember yourself all alone in ny? Remember being stopped at the airport every single time because of your skin colour? Imagine that, times a hundred, everywhere, and that's Liat's husband's life here. They may have the cutest son ever, but it's terribly not easy.
Hell, I remember myself as a kid in London, when we lived there for a year so my dad could study laparoscopy, it was cutting-edge surgery back then in the early Eighties, but people in the shops would treat my mother like she's retarded. They would sometimes ignore her altogether or patronise her awfully simply because of her accent and foreign looks. I was just barely seven and I hated them. But really, all people everywhere are condescending pricks. That's why it's always better to live in your own homeland and be strong enough to take care of your own people, because nobody else will give a shit.
Hail to that! To the fatherland!
Oh, come on Rana, you know exactly what I mean. Don't turn on me now just because I'm saying the truth. You and Noa, you two privileged Ashkenazi white girls who grew up in the north of Tel Aviv, you're the last ones who should ever talk about liberal shit. You didn't grow up as the daughters of immigrants from Arab countries in an Eastern European version of a working utopia. You had it good in your nice liberal socialistic schools and your clean white secular neighbourhoods. It's all fun and nice and goody to believe in the kindness of strangers until you have to actually live with them or be them. Believe me, the majority of people who leave their homeland, whether as refugees or work immigrants or just because they want to try to live in another place, are lonely and homesick. It's hard to make new friends and succeed in a new language. That's what I think. And if you're gonna say that most people in the modern urban cities are just that anyway – lonely and homesick – then it just doesn't make it any better in my view. It's a fault, not an achievement. It shows we did something wrong.
OK, Dorit, we're with you. We hear you. We love you. We'll never desert you! Even if we are all of us refugees one day, after the bomb, we shall stick by you and give you a homey feeling wherever you go. To the camps of the future! Because no people has suffered enough, least of all the Persian Jews.
Great, Noa. But really.
No, really. Really. I love you.
Hey, me too! I love you Dorit. And you too, Noa. And I hope we can be three happy elderlies in the camps of the future. We'll take care of each other and never wear a bra even if our lives depended on it. The header at our camp's gate should say, in Persian wrought iron – _Love frees you_. In your ancestors' honor, Dorit. And also because we love the Iranians, except the very religious ones, and we wish all sides would dismantle their bombs. To Persian love! To love's labour camps! To the Labour Party!
Oh, God. I'm defeated. I love you all back, OK? My little drunk campy girlfriends. Now who's up for another round of arak?
Me!
Me!
Sababa, ya habibties. Back in a bit. Don't hit on any men, foreign or local, without me.
SATURDAY, VERY EARLY MORNING, OUTSIDE THE BLOCK
God, you're a great kisser.
You're not too bad yourself.
I won't normally ever start kissing a girl dancing next to me unless I'm totally shitfaced, you know.
I know. I can see you're British.
Scottish.
Oh, I'm sorry, I don't really follow the news anymore, I didn't know they...
No, they didn't, that's not what, oh – oh, that was nice.
It was.
Should we get a cab?
We can take a sherut, it goes all the way.
Let's go all the way then.
Funny Scot. Don't make promises you're too shitfaced to keep.
Haha. Don't worry, love. You ain't seen nothing yet.
So show me.
I will.
Oh, that wasn't bad at all.
No, it wasn't.
Can I teach you a word? Habibti.
Habibti, sounds like phlegm.
It does. That's funny. Perhaps we should stop saying that. Here, let's get on this one.
No, but it's a nice word, I like it. Habibti. What does it mean?
Can you pass our money? Twice, please. Thanks. It means, my love.
So where are you taking me, habibti?
Home, ya habibi. I'm taking you home.
**THROUGH THE STORY OF THE GRID1**
_by Ronen Shamir_
_"The sun never sets on the British Empire," says Miss Lumley, tapping the roll-down map with her long wooden pointer. In countries that are not the British Empire, they cut out children's tongues, especially those of boys. Before the British Empire there were no railroads or postal services in India. And Africa was full of tribal warfare, with spears, and had no proper clothing. The Indians in Canada did not have the wheel or telephones, and ate the heart of their enemies in the heathenish belief that it would give them courage. The British Empire changed all that. It brought in electric lights._
—Margaret Atwood, _Cat's Eye_
Among the various physical infrastructures around us, the electric grid is arguably the most critical for urban survival. Wherever we go, we see electric wires, streetlamps, and poles. They crawl under our feet, spring out of the ground, and cut across the sky above our heads. In fact, electric grids have become such a strong feature of life that they tend to disappear from view; we hardly notice them anymore. But here is an invitation: to follow electric wires, to walk the city along some of their routes, to discover some of their original logic and to uncover some hidden and forgotten aspect of the city.
In Mandate-day Palestine, wired electricity began in 1921 with a British concession to a Jewish entrepreneur by the name of Rutenberg who was licensed to produce and distribute electrical energy in the district of Jaffa (and, later, in the whole of Palestine). Herbert Samuel, the first British High Commissioner for Palestine (after whom the Tel Aviv beachfront promenade is still named), enthusiastically supported the concession and Winston Churchill, in charge of the British Colonial Office in London, put his political clout behind it as well.
At the time, Tel Aviv was just a modest middle-class neighbourhood next to bustling Jaffa. Almost all commercial activities took place in Jaffa and many neighbourhoods consisted of Arabs and Jews living side by side; in fact, the municipal borders between Jaffa and Tel Aviv were far from being firmly established and even when they were, they hardly reflected a strict ethnic division. The "business plan" of the Jaffa Electric Company that Rutenberg established had been to contract the Municipality of Jaffa and the local Council of Tel Aviv. Both bodies, each for its own population, were expected to buy electricity for water supply and streetlights. In this way, the company would also be able to branch off from this grid of electric distribution to individual residences and shops.
And so it was that the Jaffa Electric Company decided to build its electric powerhouse (producing electricity by means of diesel engines) in a neutral place between Jaffa and Tel Aviv. The work had begun in 1921. The architectural design of the powerhouse followed the latest hi-tech blueprints of Europe and the impressive building – for many years now deactivated as an electrical station – remains intact today.
Yet what was once a remote area is today one of Tel Aviv's most trendy areas. It is located in Ha'chashmal (literally "Electricity") Street. Right next to it are small coffee-houses and neighbourhood restaurants, as well as an array of small designer shops. Buildings in the neighbourhood are rapidly being gentrified, and just walking around, it is possible to get a good sense of the city's blend of "old" (well, almost one hundred years old!) and new. Right across from the powerhouse, crossing the busy Begin Road, is a completely different type of area: locally known as the "old central [bus] station", today it is home to documented and undocumented migrant workers from all over Africa, South America and south-east Asia, giving the area a very special (if controversial) character. It is highly recommended to walk around the area and experience a part of the city which is regrettably hardly frequented by visitors these days.
And then follow the wires. In tandem with the construction of the powerhouse, electrical works had also begun. The German electrical firm AEG supplied the machinery and the expertise. German engineers came to Jaffa to oversee the works, and the electric company opened a liaison office in Berlin. One of the notable features of the newly built grid was that the high-tension line that started at the powerhouse ran more or less parallel to the old Ottoman railway line connecting Jaffa and Jerusalem (see the essay on Lydda Junction in this book). Moreover, this high-tension line physically and visibly drew a boundary between Jaffa and Tel Aviv (see original map above). Although fed from the same source, the low-tension wires and poles that branched from the central high-tension line in the direction of Jaffa received their own serial numbers and constituted the grid "of Jaffa"; and the low-tension wires and poles that branched from the central high-tension line in the direction of Tel Aviv received their separate serial numbers and constituted the grid "of Tel Aviv".
You can still go down this central line today. Just walk from the powerhouse down Jaffa Road. Facing west, on your right will be Allenby Street (named after the British army general who led the conquest of Palestine in World War I) and Nachlat Binyamin Street. These were the first two streets that were ceremoniously lighted in June 1923. A bit further down on your left is the Levinsky Market area, strewn with some of the city's best delicatessen shops, spice and nut places, cafés and small tapas-like bars. A bit further to the south lies the neighbourhood of Florentin, home to many artists, street art wannabes, hipsters and all sorts of alternative lifestyle types. But you are digressing from the electric line by now. So, head back to Jaffa Road and, walking west, it soon becomes Eilat Street. Now you are approaching Jaffa. The reconstructed old train station will be on your right. You would be better avoid it if you prefer to stay away from tourist traps. Your route, following the wires, will soon bring you to Sderot Yerushalayim (Jerusalem Boulevard). Its original name was Jamal Pasha Boulevard, built by the modernising Ottoman ruler of Jaffa. After the British conquest, it was renamed King George Boulevard. After the 1948 Jewish occupation of Jaffa, it got its present name.
In November 1923, the boulevard also ceremonially got its first dose of wired electric light. The Jaffa Electric Company located a transformer on the boulevard, where electric current from the high-tension line was transformed into low-voltage. This peculiar structure is still there as well, right where you are on the crossing of the Boulevard with Eilat Street. Comparing the photograph below (as well as that of the power station above) to the current landscape allows you a first-hand appreciation of the tremendous changes that has taken place here over the last eighty years.
So by now you can tell, just by having followed the wires, how the grid took an active part in the process of dividing the area into what eventually became two separate and often hostile towns – one Arab, one Jewish; a process that sadly culminated in the elimination of Jaffa as a significant Arab-populated city in 1948.
1© Materials are based on _Current Flow: The Electrification of Palestine_ , Stanford University Press, 2013, by Ronen Shamir.
THE UNDERSHIRT
_by Shahar Shalev_
It's hard to walk around Tel Aviv in the summer and not notice that a lot of men are wearing sleeveless undershirts – and not only to the beach. On central arteries, in the bars and clubs, in the shops and show windows – the masculine undershirt has a prominent place in the local wardrobe, perhaps more than any other fashion item.
The history of this garment is connected to pioneering anti-fashionability, simplicity and masculinity – all of which might serve to explain, in a paradoxical manner, its current appeal. Later, those characteristics worked their way into international trends, and the undershirt became one of the items beloved of local gay men. As they celebrate the liberation of the male body, it has become their ultimate fashion symbol.
What caused the undershirt to come out of the local closet here more than it has anywhere else in the world? Why do gay men see it as a desirable item? And can its story teach us something about the hidden connection between the male body, the Zionist project and local slovenliness, a connection we hadn't known about before?
At the end of the nineteenth century, undershirts and underpants as we know them didn't exist. There were only undergarments resembling overalls with long sleeves, something similar to an infant's onesie. Only at the beginning of the twentieth century did these union suits, as they were known in the United States, divide into pants resembling long underwear bottoms – affectionately known here by the Yiddish word gatkes – and T-shirts with long sleeves.
The T-shirt proper was invented only in 1913 in the British and American navies, as undergarments evolved as part of a re-evaluation of the uniforms worn by sailors serving on ships. The idea was to leave sailors' arms free when they were busy with tasks on deck (previous garments did not allow this). Thus, the white T-shirt was born.
The shirt was adopted immediately, since it was easy to see stains and dirt on it and thus maintain strict military hygiene, but it was still made of wool and other fabrics that are tough to get dry, and not particularly comfortable. Then companies like the British Sunspel (which has recently opened a new store in New York) and the American Fruit of the Loom developed and began manufacturing T-shirts from cotton, a move that made their shirts more popular, but still seen as an undergarment.
An early advertisement exhorted, "You don't need to be in the army to have a T-shirt of your own" – an ad that made the direct connection between the shirt and its military context, but at least until the end of World War II it was not considered legitimate to wear it without a top-shirt.
Or, in fact, at least not until Marlon Brando came along. Then, in the Fifties, the real revolution began and the T-shirt became a symbol of youth rebellion with all the sexy implications dripping from it, thanks to Brando in _A Streetcar Named Desire_ , James Dean and jazz trumpeter Chet Baker, who wore it at every opportunity.
Only in the Seventies, with the flourishing culture of discotheques, drugs and the gay body cult, did the sleeveless undershirt – which eventually became known as the tank top – succeed in coming out of the closet and being displayed to the public in a context not connected to sports. In those years, men began to spend more and more time at gyms developing muscular bodies to show off, and the tank top became the ultimate garment that maximised the physical potential of its wearer.
The packed discotheques, with the energising drugs and sex that flourished in them, required minimal clothing, and the tank top was discovered to be a garment that revealed the male torso, from the arm muscles to the chest muscles. It was then that gay culture began to use the tank top as a sex symbol – a garment that, like jeans and the flannel shirt, had signified anti-fashion and the dripping masculinity that rejects preening and decoration.
Artists like Tom of Finland began to inundate the world with their gay pornographic paintings centred on cowboys, labourers and military men in torn jeans, boots, and tight, nearly bursting T-shirts or undershirts – and the undershirt became the gay popular front.
From there it moved into the male mainstream, thanks to Calvin Klein in the Eighties and Nineties, and fashion photographer Herb Ritts, who shot film actor Richard Gere in jeans and a white undershirt by a car in a garage. And a wealth of other icons in undershirts from the worlds of music and film – from Queen's Freddie Mercury to Brad Pitt in _Fight Club_ – loaded patches of sweat and drool from gals and guys around the globe.
Surprisingly, however, the Israeli plain white undershirt came out of the closet way before all the rest. Maybe this was connected to the absence of proper dress rules, or maybe the perplexing mix of socialism and the pioneering ethos that built the foundations of fashion culture here – but the white undershirt had already been transformed from underwear to a symbol of the working proletariat back in the early days of the state.
During the years of the austerity regime, a decision was made to ration clothing items and shoes. In the annual allocation of ration coupons, relates Ayala Raz in her book _Changing Styles: 100 Years of Fashion in Eretz-Israel_ , men were able to buy a woollen jacket, khaki shorts, a khaki shirt, a pair of cotton socks and two (!) undershirts, one for winter and one for summer – which marked the item out as the bread and butter of the local man.
At that time, the undershirt became fixed as the ultimate garment of the Zionist body: an item of clothing that expressed the muscular body, the grime of the labourer; the absence of decoration and elegance; something that rejected the fashionable bourgeoisie and celebrated Zionist labour and the pioneer beneath it.
Along with the uniform under which it peeked out or on its own, the men of Tel Aviv wore their undershirt and ate watermelon on the balconies of their homes, and the Israeli summer sanctified it on the way to the beach – thus, the undershirt became the unofficial male uniform, a minimal item for the maximal man.
**LYDDA JUNCTION:
A TRAIN RIDE TO THE PAST 1**
_by Ronan Shamir_
"Night Train to Cairo" is a popular and highly recognisable 1980s Hebrew song by the legendary rock band Mashina. Its lyrics are about a fantasy trip, a badly needed getaway, or better still a hideaway. It is also a strong reminder of bygone days. Imagine Tel Aviv, Palestine, back in, say, the Thirties. The weekend is just around the corner and a friend suggests we spend it in Cairo. It should be fun and, moreover, simple to reach. We pack up lightly and walk south along the beachfront, approaching the towering mosques and churches of Jaffa a couple of miles ahead. Soon we have to turn left, walking down the road that leads to the Jaffa railway station. The train is about to leave for Jerusalem, but we only need a ticket for the shorter ride to Lydda Junction down its route. Once there we move from Platform 1 to Platform 3, catching the train to Kantara, via Gaza Strip, and from there to Cairo. On the platform, we come across the women in the photograph on the opposite page.
The women, posing for a farewell photo, are on their way to Cairo too. They are part of a formal delegation to Egypt, and they are proud and excited. Some of them are traditionally dressed, some are showing off the latest European fashion; most are on high heels, while others have their heads properly covered. A British soldier is on guard, tensed; and yet the atmosphere is relaxed, even festive. This is the Middle East as it has been, or better still, as it still can be. A Holy Land that knows no borders.
This is not the Thirties. Yet the town of Lydda, for years downtrodden, forgotten, hardly on its feet, is still there. A fourteen-minute train ride and twelve-and-a-half shekels (roughly £2) are what it takes to reach the once glorious Lydda Junction railway station from the present-day Savidor Central railway station in Tel Aviv. Fourteen minutes, and a half-day excursion, allows one to step onto the platform – still the same one – that sustained late nineteenth-century Christian pilgrims to Jerusalem, Jaffa merchants on their way to the markets of Damascus, Palestinian dignitaries en route to Cairo, British soldiers who were stationed all over the land, or plain fun-seekers heading for a weekend in Cairo or Beirut.
"Hardly anyone remembers Lydda Junction these days," despairs the station master on a late Friday afternoon, and still "this is the heart of the country". Geographically speaking, he is right. When one looks around, with sharper eyes these days, it is possible to appreciate that it is still a major hub: multiple rails, parked locomotives, and quite a few cargo and passenger trains speeding through every few minutes. But, paradoxically, the distances it is possible to travel from Lydda Junction today have shrunk considerably since the Thirties and Forties. Rather than Cairo or Damascus, Beersheba – one hour away – or Nahariya, roughly two hours away – are the most once can hope for these days. Inaccessible borders and derelict lines prevent longer distances.
The original terminal building is still there, almost intact. "We saved it from total destruction," says the station master. Yet it is poorly maintained and latter-day additions hardly respect its old days of glory. The story of Lydda Junction goes back to the later years of the nineteenth century, when the Ottoman rulers of Palestine became eager to modernise the country. They licensed a French company to build and run a railway line from Jaffa to Jerusalem. Jaffa was the main sea port of the country, for hundreds of years the launching pad to the holy city of Jerusalem, roughly sixty kilometres to the east. As it were, the east-west line between the two cities also ran through the middle of the country, marking its northern from its southern hemisphere. And Lydda, a modest Palestinian village next to the bigger and more glorious town of Ramlah, was located roughly midway on the Jaffa-Jerusalem railway line. The British army – occupying Palestine in 1917 – had been quick to realise the strategic importance of the place. Lydda Junction was the point where the Jaffa-Jerusalem Railway line met the railway line that came all the way from Cairo in the south, heading north through Kantara and Rafah (in the Gaza Strip). Soon it also became a junction for a line that headed north to Haifa and to an extension of the famous Hedjaz railway line that was to carry Muslim pilgrim from Damascus, through Trans- Jordan, all the way to Medina in present-day Saudi Arabia. The British were therefore quick to locate the army and air force headquarters nearby (Sarafand) and these very same military barracks are now home to many training centres of the Israeli army (Zrifin). The proximity to Lydda Junction is also the reason the British built the country's major airport nearby, appropriately named Lydda Airport. Today, this is the very same Ben Gurion International Airport.
No wonder that the accidental traveller meets a crisp breeze of history on the Lydda Junction platform! Once there, take a loving look around, sort out the old from the recent, and fly your imagination to the past. When you have had enough, a small digression is highly recommended. Just two miles away, easily reached by foot or bus, lies the town of Ramlah with its old churches, bustling markets and superb restaurants. For Arab food lovers, the Halil restaurant is the princess and its masabacha (a fine version of hummus) is the jewel in the crown. People will send you to Abu Hassan in Jaffa, and you are most welcome to sample and compare, but absolutely nothing compares with the masabacha of Halil. So hop on a train, get a sense of the country's modestly hidden "heart", sense the neglect, imagine a better past and future, and treat yourself to a hearty meal before your return trip to reality. 2
Photograph by Ellen Levy-Arie
1© Materials are based on _Current Flow: The Electrification of Palestine_ , Stanford University Press, 2013, by Ronen Shamir.
2 For historical photographs see:
<http://actsofminortreason.blogspot.co.il/2009/05/pdp-46-day-guard-at-lydda.html>
THE STORY OF THE SABICH (OR THE NEW FALAFEL)
_by Ron Levy-Arie_
What started out originally as a Saturday morning breakfast food of Iraqi Jews has become a sort of a national Israeli street food that has even cast a shadow over the well-known and much-loved falafel. The urban legend of the dish starts in the sleepy suburb of Ramat Gan back in 1961. A newcomer from Iraq opens up a small food stand in a neighbourhood by the name of Nahalat Yitzhak. The young man sells a simple sandwich he knows from back home. The ingredients are basic, yet compose a perfect combination for the mouths of No. 63 bus drivers on their way to their daily route. The clients used to call the owner by his first name, Sabich. They used to call at him, and say: "Make me a dish, Sabich!" (No "please" included, typical Israeli style.) Therefore the name of the dish was born. Others disapprove of this version, and claim that the dish had been familiar amongst Iraqis by that name because the word sounds similar to the Arab word "sabach", meaning "morning", and since it is a breakfast delight, it would make sense for this to be the true reason for the name. In Israel, even street food brings conflict.
The sandwich is made in pitta bread, includes slices of deep-fried aubergine, hard-boiled brown egg, tahini sauce, shredded onions and parsley, some finely chopped salad, homemade hot sauce and the secret ingredient, amba – a word in Arabic that originated from Sanskrit, meaning mango. This unique product made its way to Iraq due to the work of spice traders from India, who brought pickled mangoes to the Iraqis. They then mixed and diluted them with water and oil, and this sauce merged into Iraqi cuisine. It carries a strong fenugreek and allspice aroma that comes from an Iraqi spice blend known as baharat, which is also mixed into that special shining-yellow sauce. Some folks avoid including it in the sandwich due to the fact that the smell lingers with you throughout the day, and you can even smell it when you sweat. Yet it is still worth taking that risk.
Right until the late Nineties and early Noughties, falafel was the undisputed national street food. Usually Israel tends to "borrow" food invented by Arab countries and call it her own. From the Fifties onwards, falafel was the ultimate street food favourite, made by local Palestinians or by Jews coming from Egypt, Yemen or Syria. It was cheap and accessible and is made by the most lovable pea in the Middle East, the chickpea. The other key ingredient is hummus, which by itself stands as the ultimate dish of the Middle East.
Then the sabich started shining. The guy who popularized it the most is called Oved, and comes from the neighbouring town of Ramat Gan, Givatayim. Oved claims to make the best sabich dish in the universe, and even invented a sabichbased slang and a theatrical way of preparing the dish, in which he addresses the customer in the manner of an enthusiastic football announcer and questions them about their desired amount of toppings in a dialect that derives from the football fields. He created the craze, and after Israelis had been through the "Oved experience" – which also includes a diy Hall of Fame of record-breakers in sabicheating – others soon started opening sabich shops, such as the famous Sabich Frishman in Tel Aviv. Even old-time The Story of the Sabich (or The New Falafel) falafel stands added sabich to their falafel-based menus. The sabich of today is even served as a sandwich in posh cafés and restaurants, rising from rags to riches.
The "godfather of the sabich", the originator of the dish, kept selling it at the corner of Negba and Haroe, with his scanned id hanging on the wall showing his first name. Sadly, this culinary genius passed away a couple of years back, but his sons continue their father's tradition and serve the dish with great pride.
INSOMNIA
_by Ithamar Handelman-Smith (published under the pen name Ithamar Ben Canaan, translated by Shlomzion Kenan)_
I walk into the Allenby 58 club with Oren Agmon. We get past the guest list bouncer and go straight down to the lower-deck lounge. Oren Agmon, my boss, runs into three of his college pals and they hit the dancefloor.
"I don't like this music," I yell into his ear. "I hate rap. I'm going upstairs."
"Are you going up?" Ivy, one of those 'pals' of his, is asking.
"I'll come with you," she continues. She's a medium-height girl with short black hair cut just below her ears. She's wearing black pants and there's some sort of black rag wrapped around her chest. "You remind me of Anaïs Nin – well, anyhow, of the actress who played her in that film – what was the name of it... about their life together, about Henry Miller and Anaïs Nin..."
" _Henry and June_ ," she says. "That must be on account of my being French. I have this French look."
We go upstairs to the dancefloor. She locks her arm into mine, and then yells, "Let's go dancing. I'm nuts about this song." I say, "Yes, 'Insomniac', that's a fine song."
"Inso-maniac," she giggles. "Inso-MANIAC."
In the background we hear the line, "I can't get no sleep," then it hits off. The music elevates, higher and higher until everyone's hands are up in the air, glasses are breaking and people are screaming and then...74boom, boom.... The bass kicks in, the beat picks up and I fix my gaze at her dancing.
"Aren't you dancing?"
"What? I can't hear you."
"Aren't you dancing?" she asks again, her slim arms batting in the air and her pelvis twisting and whirling about.
"No, no," I say, "I'm too blasted. I had four hits just before I got here and a couple of drinks." She takes hold of me, her hands grabbing my arms at the elbows, her head draws near, her lips press against mine and we kiss.
"Let's go upstairs," she says.
We go up to the gallery. I pull her to the far-left corner, under the top bar staircase. We go through a black curtain and kiss. She unties the knot off that rag that's wrapped around her, and I undo her bra that opens up front. Her breasts are pretty small, with dark, erect nipples. I lick her and her hand glides down my pants and into my underwear and she jerks me off. With her free hand she pushes my fingers into her cunt, which is, by now, totally wet. I feel her pussy, play with her clitoris, and insert my fingers into her. I start with one finger, then two, three and finally four.
"Wow... wow..." she moans. Then she gives a faint sigh and comes.
"Let's go to your place," I say.
"Yeah," she says. "Let's go."
It's raining outside. We catch a cab and drive up to her place on Weizmann Street. All the way there, in the back seat of the cab, she has her left hand in my pants, jerking me off. The cab pulls over in front of her building and I pay up. The stony path that leads to her front door is covered with overhead shrubbery. When she's halfway across, she stops.
"I have a boyfriend," she says. "This doesn't feel right."
"So you want me to leave?"
"No, no," she says. "That's the problem. I need you to fuck me."
We go into her apartment, on the first floor. We undress and get into bed. She blows me and I give her head and then penetrate her. The first time is over pretty quickly. The second time lasts longer, we do it doggy style.
We smoke a cigarette and I hold her. She strokes my cock.
"I've never had anything like this. You see, I was a virgin 'til twenty. Then, for three-and-a-half years since my first time, I couldn't stop fucking. I just love sex. But with you... you're something else... it's as though... almost like losing my virginity all over again. I'd like you to come and fuck me all the time. Just call me, come over, fuck me and leave. That's all I want. I just... wow... I can't get over this cock of yours." I take another puff off my cigarette and say nothing.
"Pity you have so many tattoos though. I don't care for that at all. Such a nice body, why cover it up with silly cartoons..."
"But you said you loved my cock."
"Oh yes, I'm crazy about your cock, that's one hell of a penis you've got there between your legs, mister, the largest by far I ever had," she says, and proceeds to suck on it again. She's licking my balls and my arsehole. I don't respond.
"Fine, we'll carry on next time," she says. "But you will come, won't you? Listen, I won't freak out on you. I have a boyfriend and I love him, but how can I make love to him now that I've developed a taste for your amazing penis? So just drop by and fuck me. Whenever you feel like it. I will always spread my legs for your exceptional cock."
"So you want me to come and fuck you whenever I feel like it?"
"Yes," Ivy says. "Come over, fuck me, fuck me as much as you like and leave, and now," she says, "I'm going to get some sleep."
I get off the bed and put my suit on. The tie has whiskey stains on it and the knot is loose. Ivy scribbles her phone number on a flyer I was handed at Allenby 58, an invitation to hear dj Brandon Block, who'll be playing the club the following Thursday night.
"I bet you won't call."
"I'll call you," I say.
"Call me," she says. "I'll be waiting right here, legs wide apart. Call, come over, fuck me, then leave."
We kiss and I go. Before leaving the apartment I rinse my hands in the sink. I go out to the street. It's a quarter before six and the sky is luminous. I walk past a green garbage can. I pause, take out the invite to Thursday night's party featuring Brandon Block on the turntables, the flyer with Ivy's number scribbled on it with a blue Parker pen. I hold it out briefly and then toss it into the garbage can. I keep walking towards Judas Maccabi Street. When I hit Judas Maccabi I turn left and walk down the street until it intersects with Ibn Gabirol. I wait for a bus, the 48, which will take me to my folks' house in Herzelia. I smoke my last cigarette, which I drew out of a crushed pack and straightened out a little. I sniff the tips of my fingers; they still give out her scent. At twenty past six I get on the bus and sit next to a Thai construction worker. I stir nervously in my seat. It seems as though everyone in the bus can smell the odour that's emanating from me, the cunt aroma of Ivy or Shmivy or whatever her name was, the smell of her cunt that's oozing from my fingers.
## PART TWO: KEDMA
_(Translates both as "east" and as "progress" or "forward-facing", as the ancient Israelites looked at the east instead of today's north. Alshrq in Arabic)_
BEULAH LAND: THE LINE BETWEEN THE TWO WORLDS (THE BLUES AND THE PROMISED LAND)
_by Eran Sebbag (Translated by Eilam Wolman)_
On Maxwell Street Market in Chicago, Illinois, childhood haunt of brothers Leonard and Phil Chess, who later formed the Chess Records label, a legendary graffiti on a wall reads: "Blacks + Jews = Blues." Maxwell Street is the cradle of Chicago blues. The inscription was there before the eyes of all who passed.
These words referred to the historical link between Blacks and the Jewish children of European immigrants who went into the business of recording, producing and marketing blues music. The following essay isn't concerned with the logistics of this musical collaboration, but with the inherent connections between the Jews and the bluesmen. At first, this relation may seem curious, perhaps even illogical: what do the Jews of Europe have to do with African-American music from the Mississippi Delta? Few Jews settled in the South and the Mississippi Blacks who reached the shtetls of Podolia were quite scarce to say the least. Our concern is the connection that many Jews felt to Black music – music rooted in the chain gang, born in the struggle for freedom. To understand the unlikely yet deep connection between Jewish thought (especially movements such as Hasidism 1 and ancient mysticism) and the gospel of the blues, we must explore the two doctrines' common root.
The blues originated in the Mississippi Delta. We don't know who the first person to sing the blues was, and probably never will, but what cannot be denied is that the woeful chant which arose from slavery and bondage created a canon that transcended the miserable historic and material circumstances of its formation. Its object being simply the human struggle of one's soul, the blues became a universal song of comfort and solidarity. Whether this was the direct intention of the blues or simply how it came to be received is irrelevant. What is important is that the blues was an existential rebellion of the exploited and enslaved, speaking to universal feelings of persecution. As Mississippi Fred McDowell put it in the short lines of his song "You Got to Move", a practical anthem distilling the deep existential gospel of the Blues:
You may be high
You may be low
You may be rich, child
You may be po'
But when the Lord gets ready
You got to move
Mississippi Fred sums it up. The slave, the master, the wealthy and the destitute are one. As Ecclesiastes (the exemplary biblical book of the blues) states:
What profit hath a man of all his labor which he taketh under the sun? One generation passeth away, and another generation cometh: but the earth abideth forever.
The bluesman understands that in the deepest sense – we are all slaves, all insignificant to the ruthless vagaries of the world.
Africans were brought to the New World in the most degrading way imaginable – taken captive, sold into slavery and boarded onto slave ships. Their identity was eradicated and they were rendered as nothing more than property. A hundred years after the abolition of slavery, the social state of African-Americans remained quite unchanged: segregation laws, the Ku Klux Klan, lynching, and blatant racism.
The African-American's static condition as a degraded and excluded individual fomented an unwavering perception of man's fate. Though rooted in this social context, the blues offered relief for any predicament the living soul encounters in the world. It is perhaps because of this that the blues is usually composed in the present tense. Even when there is a reference to the past, it is the immediate past ("Woke up this mornin'"), and the undefined future in the blues mostly goes only as far as a few moments from the present time ("I'm going, don't know where I'm going but I'm going"). This song of the present teaches us that "the thing that hath been, it is that which shall be" and that it is futile to imagine anything "new under the sun".
The Jew in exile and the enslaved African-American share a marginalised status and a common experience of insistent persecution and oppression. They were both concerned with their everyday lives and did not aspire to change the world or envision a different future.
Just as Jewish and Hasidic spiritualism provided a critique of the "old" institutionalised religion, the blues transcended the churches and houses of worship in the South. Religion offers its believers redemption and guarantees that every believer will receive his reward in the next world. Yet the bluesman and the mystic understand that man's business and heavy load are matters of this world, and that we do not live for the future but for today.
The blues did move beyond the church and venture into the expanses of life in the painful present, but it did not forget its religious roots, transposing religion's terms into symbols man can use in everyday life. The blues never separated from the gospel, and the gospel retained a tacit critique of the white Christian establishment.
Taking biblical events and terms from the Old Testament can be seen as a rebellion against the new one. Many blues texts resonate with the Jew, who from time immemorial has struggled to survive in exile, and who uses the same concepts put forth in the blues to describe his own redemption. The slaves undoubtedly saw themselves as the children of Israel enslaved in Egypt and used the narrative of the Old Testament to describe their plight. The white master is seen as Pharaoh and the segregated South is Egypt. The land of Israel – or in the language of the blues, the Promised Land – is the place where one could live fearlessly, where there is no lynching and no subservience. Accordingly, the Jordan River is not only the river itself, but also the line between the two worlds. This one and the next. Good and evil. The chains and unattainable freedom. The historic root is identical in both cases and was used in the folk singing which developed later as well. For the Jew of the diaspora, there was also the material concept of the land of Israel, the Jordan River, Jerusalem, etc., although, as he spent generations in exile, the land of Israel and its regions became internal concepts, a guiding and comforting ideal in a chaotic world. Hence, it emerges that for the Jew hearing the blues for the first time in his life, not only the religious concepts but the geography itself was familiar. The blues can be considered the non-Jewish tradition closest to the essence of Jewish spiritualism and of the Hasidic faith, which also broke through the confines of its religious establishment.
Mississippi bluesman John Hurt sings: "I got a mother in Beulah Land outside the sun / Way beyond the sky."
"Beulah Land", a married land, refers to the land whose sons returns to and unite with, just like the union between man and woman. This hymn derives from the King James version of Isaiah 62:4: "Thou shalt no more be termed Forsaken; neither shall thy land any more be termed Desolate; but thou shalt be called _Hephzibah_ and thy land _Beulah_ ; for the LORD delighteth in thee, and thy land shall be married." The verse is in reference to the return of the Jews from their exile in Babylon, in which the Jews shall no longer be called _Forsaken_ , but _Hephzibah_ (My Delight Is in Her), and Jerusalem shall no longer be called _Desolate_ , but _Beulah_ (Married). This implies that the Jews have turned back to the worship of God.
In this case, it is the English-speaking bluesman who lacks the necessary Hebrew to get to the bottom of the term. Beulah means a land that has been cultivated by its inhabitants – which is to say, be fruitful and multiply, and the land will provide.
There is no shortage of such examples. The Hebrew language, the geography of the land of Israel, the biblical heroes, and above all, an unrevealed shared fate of the Blacks and Jews, exist both in the gospel and later in the blues. Both traditions share the hope for survival and peace of mind in a material world of pain.
1 Hasidism (or Hasidic Judaism), derives from the Hebrew word "hesed", meaning "piety" or "loving kindness", and is a large branch of the Jewish ultra-orthodoxy that was founded in mid-eighteenth-century Ukraine by rabbi Israel (Yisroel) Baal Shem Tov, who placed emphasis on a popular and common version of kabbalah (Jewish mysticism) and the joy and happiness in worshiping Hashem (God) rather than just learning the Talmud and the Torah in the strict and academic manner of the Lithuanian branch of ultra-orthodoxy.
IN MY HEART
_by Reuven Miran (Translated by Eilam Wolman)_
One warm morning in early July, Ella Fitzgerald and I drove from Kfar Saba to Jerusalem. We started driving east, and then we turned south, then east again. The sun was still low and it stung my eyes intermittently. From south of Rosh HaAyin, we entered a dusty boulevard of carob trees. Crushed scraps piled among the dry branches. Washers, baking and cooking ovens, broken and crinkled plastic and aluminium blinds, which once concealed many things. The east wasn't far. Dust rose from the direction of the quarries that suddenly blocked the eastern horizon. Migdal Afek – or Mirabel Fortress, depending on the period and circumstances – seemed abandoned. We drove up there for a moment without leaving the car. A single word was smeared in thick black on one of the thick external walls – Palestine. The once-black soot of bonfires now grayed upon the stones.
We came down and continued, driving by the olive and fig trees haphazardly scattered on the hills, between the rocks whose grey heads alone glanced through the thorns. The thorns were dry. Tall, thin cypresses grew between them. One spark, I thought, one spark is all it would take.
In Bayt Nabala junction we saw burnt eucalyptuses. What was left of their leaves was yellow and grey. Scorched branches were growing from the sooty trunks. Not far, next to a stop sign, stood a boy with a stroller which was once green and now carried a large pile of pretzels. A brown military truck passed him and stopped for two seconds, because of the sign. The road was empty. Bright, thin dust ascended from its double back wheels.
We stopped close to him. Ella stayed in the Subaru. I got off. The shift stick was in the dead zone. The engine kept running. The air was cool and pleasant. A light wind brought it to us from the west.
"Small pretzel for a shekel and a half, a big one for two," said the boy.
He was an Arab boy with yellow hair and big, blue eyes, like the sky enfolding the entire land. The dust on his tall forehead mixed with sweat and their composite was slowly dripping behind his earlobes.
"Two big ones," I said. One for me and one for Ella, I thought. The scent of baked dough and singed sesame hit my salivary glands. The boy inserted two big pretzels into a transparent black nylon bag. Afterwards he threw some za'atar in the bag from a yellow page torn from an old phone book.
As soon as I opened the car door, I heard Ella again. The pretzels were warm. Their tender scent filled the tight space. We ate driving between the fields of cotton, corn and vine. An old Boeing 707 clambered westward slowly and noisily, the sun blazing on its tail. I was silent, so I could hear Ella better.
Before the unsignposted left turn to Kfar Truman, she said: "I always knew / I would live my life through / with a song on my lips for you."
I wasn't sure and I also don't remember if it was "with a song on my lips" or "with a song in my heart", and I didn't care too much, at least not at that moment. The big band accompanying her was fighting with the constant rattle of the engine. Together they overpowered my eardrum, and I didn't exactly hear the words woven in her big, warm voice.
_Photographs by Assaf Shoshan (originally in colour)_
_Photograph by Assaf Shoshan (originally in colour)_
Ella didn't make it all the way to Jerusalem with me. I bade her farewell at Sha'ar HaGai and she might have moved to a different driver on a different station. I continued alone among the pastel pines and cypresses. The armoured vehicles, painted with anti-rust primer, were there as usual, the withered flower bouquets from a previous ceremony laid on them. The sky was blue like the large eyes of the boy whose pretzels' scent still stood in the car. Something suffocated me from inside. I thought after Motza the air would be chillier and easier to breathe. But it was hot and heavier and it sat deep in my chest. I turned on the ac. A brisk gust filled the car and opened up my lungs at once. I drove slowly. In the side mirror, I saw a truck cutting me without hesitation. It had a blue license plate from the territories and it was full of empty Coca-Cola bottles. It disappeared behind the curve and I was alone again.
Suddenly I remembered. "In my heart," she said. I was sure of it now. In my heart.
TECHNICOLOUR IN JERUSALEM
_by Tom Shoval (Translated by Eilam Wolman)_
I'm a cinephile. Cinema is like a religion to me. This means that my life is divided into two spheres: reality, which I find comparatively interesting; and reality's mirror image, cinema, where I would rather live. Aware of the impossibility of living inside movies, I search for archaeological findings, evidence on the ground that cinema was here, next to me. By unearthing the dinosaur tracks of cinema, I prove that reality and magic did in fact intersect. Of course, from the prism of reality, it looks like I'm only collecting memorabilia from past films and nothing more. It's a matter of perspective, but also one of principle.
The trouble with being a cinephile and living in Israel is the dearth of findings. Israeli cinema is indeed maturing, but its past, though solid, lacks in sensational revelations. Cinema flourishes in other continents, in the Hollywood climate, or as a reflection of the subtle European light. Israel is an historical and Archimedean site, but for cinema it is a land not sown. With the basalt stones and the stark light disfiguring every frame, living up to the exciting portrayals of the land in the Hebrew Bible, the Quran and the New Testament is nearly impossible for a film. It's as though Israel were a trap laid for the very pretence to film it. Still, I don't despair, and continue my searches for a pivotal moment where cinema history took place in the country. Indeed, the Lumière brothers were here and they shot a train leaving a station in Jerusalem. But that doesn't really count either; the Lumières were eminent globetrotters who shot trains leaving every station in every country. Doesn't count.
Seeking out every book I could find that might contain a nugget of information about such a cosmic convergence, I eventually came upon acclaimed cinematographer and director Jack Cardiff's book _Magic Hour_ (Faber & Faber, 1996). Cardiff, one of the greatest cinematographers who ever lived, is most famous for the Technicolour nature shots he took in the films of Michael Powell and Emeric Pressburger – _The Red Shoes_ , _The Tales of Hoffmann_ , _A Matter of Life and Death_ , _Black Narcissus_ , and, of course, _The Life and Death of Colonel Blimp_. Cardiff's intricate artistry lent a new form to the fierce colours afforded by Technicolour and almost turned the frames in these films into moving paintings.
Technicolour is a method of developing film which allows for the containment of colour. The technique itself was invented in the first years of the previous century and continued to evolve, unleashing a fierce fabric of colours on celluloid as early as the late Twenties. One of the greatest moments in the history of cinema, the arrival of Dorothy in Oz in _The Wizard of Oz_ , was shot in Technicolour, which was crucial for Oz's magical, glowing atmosphere. Hollywood couldn't resist the magic of Technicolour and it painted its films with its fierce, saturated pigments. Cinema was like a fresh bouquet of flowers in those days. Director Francis Ford Coppola famously said that Technicolour has babied cinema. In 1932, the elders of the Technicolour community developed a special camera that would film in Technicolour so the colour wouldn't have to be injected or processed in a laboratory. The camera they produced was as innovative as it was unwieldy. In addition to the bulky camera, Technicolour film required plenty of light and a special exposure, and getting good results from it wasn't easy for cinematographers.
Around that time, a German count by the name of von Keller and his wife came to the offices of Kay Harrison, managing director of Technicolour in the uk. They wanted to hire a Technicolour camera and a cameraman to shoot travelogues around the world. Harrison tried to explain that the cumbrous camera required constant maintenance. The wealthy von Kellers kept insisting, and eventually they had their way. The Technicolour camera's results impressed von Keller to such a degree that it became his mission to prove to the film world that the device was invulnerable to any production mishap and could deliver excellent results in any condition and under any exposure. He needed a cinematographer who would be willing to embark on such an adventure as would convince everyone that the Technicolour camera was the next big thing.
Jack Cardiff had already shot a few films in Technicolour, and he was a master at producing beautiful frames with speed and little effort. He had a flair for adventure and he took the offer immediately. Von Keller sought to re-accomplish the Lumière brothers' achievement and shoot all over the world with the Technicolour camera. He wanted to create a "second take" of the Lumière Brothers' act of cinematic wonder. As they had made the audience flee the theatre for the fear that the train would burst from the screen and run them over, von Keller believed he could make the audience see the beauty of the world's colours for the first time. Perhaps the name "cinema" would be replaced with the more mysterious "Technicolour". Cardiff found himself loading the awkward camera equipment onto a ship and sailing across the sea with the von Kellers and a limited crew to shoot a series of Technicolour shorts called _World Window_. Their second stop was Jerusalem.
When I read this, my jaw dropped. One of the first attempts at location shooting with the Technicolour camera happened in _Jerusalem_. Cardiff describes shooting in Jerusalem in great detail in his book. To me, his stories read like something out of Verne or Kipling, a British expedition's adventures in an unknown place – a modern excursion to the ancient Holy Land.
The year is 1937 and Palestine is under the rule of the British mandate. There are tensions towards the mandate from both Arabs and Jews. The crew docks in the port of Haifa, shoots around Mount Carmel and continues towards Jerusalem, which captivates Cardiff. He seems to have almost prepared himself in advance to experience the divine presence in the holy city, but amazingly and perhaps predictably for a cinematographer, he finds spirituality in the city's light, of all phenomena. Here is Cardiff from the book:
There is something splendidly defiant about old Jerusalem. Walking through the narrow, dark, traffic-free lanes of the old quarter, one is magically transported to biblical times... the scene is wonderfully unchanged. Only my Technicolour camera was out of harmony, but the light was heavenly: shafts of sunlight, sharpened by the dust which penetrated shadowed air like golden swords.
Was it merely his foreign eye, eager for sanctity, that imagines these swords of light? Is it the colonial gaze of his time and place? Perhaps, but it's impossible to ignore Cardiff's genuine passion for the holy city and the urgency he felt to capture the light that falls over it.
_Jack Cardiff, cameraman_
Cardiff's awe is palpable in the slow pans with which he reveals the area, shooting through cracks in the walls and revealing bits of landscape struck by the fierce light. He shoots a deserted valley with broken basins that look as if they'd just been placed there. Some of the "natives", the narrator will testify in the final edit, still use them to carry water. A gorgeously coloured shot of a group of girls walking with heavy water basins on their heads will cut to a shot of Franciscan priests on their way to prayer.
Cardiff shot non-stop, and he relates how the residents were distracted by and drawn to the film crew, and especially to the massive Technicolour camera. Imagine this modern mammoth at the centre of an ancient quarter in 1937 Jerusalem, absorbing and immortalising the images of everyday life.
The camera performs a religious function, operating as a mythologising filter, manufacturing spirituality, or making a latent one explicit. Armed with his naked eye, Cardiff joyously and sensitively creates a new mythology.
The film reveals a spiritual world full of pathos and grandeur. The camera is in constant circular motion, shooting from low angles, grabbing bits of sky, revealing sacred areas where the past is still alive. The provisional is filtered out. Extras walk in exemplary order and silence with no outside interruptions. The _mise-en-scène_ is standard, archaic yet breathtaking. Ever the professional, Cardiff deftly processes what's before his eyes while sketching outlines of the ghosts that might still wander the Via Dolorosa.
In the evenings, Cardiff presents a different Jerusalem, turbulent and modern. Ragtime at the King George Hotel. Cigars, women in lace dresses and men in frock suits, their hair slicked back with European gel. Dancing continues into the small hours of the morning. Cardiff marvels at the coexistence of the hallowed with the modern. With the muses singing and the night-time rousing his instincts, he doesn't imagine that this harmony might be only in his head.
Cardiff, the hunter of light, wants to shoot the walls of the Old City during the magic hour. The crew rushes to a steep hillock overlooking the city. Afraid to lose the valuable minutes of sunset, Cardiff quickly sets up the camera. Suddenly gunshots ring out. Bandits who, like anyone else in the Old City, couldn't help but notice the technological beast want to take the metal giant captive. The crew members look at each other, wondering whether to fold the camera that could take a bullet at any moment or perhaps save themselves first. Cardiff is concerned only with the completion of the shot he is taking, and as the gunshots escalate, he finishes the exposure process. He sends his crew to the car at once, takes the camera apart by himself and runs away with it. A bullet singes his shirt.
They drive north to Haifa. There, in a hotel room, Cardiff recounts the latest events to Count von Keller. After asking Cardiff to promptly send the rushes for development, von Keller telephones the British High Commissioner of Palestine and tells him about the film crew's run-in with the bandits. The concerned commissioner promises to look after the matter. The next morning, Cardiff is awoken by a phone call from a British officer who tells him the outlaws have been apprehended on the previous night and will be trialled. He asks to meet with Cardiff and pick up his testimony.
Cardiff meets the officer for breakfast on the terrace of the King George Hotel. They have a pleasant and intelligent conversation. The cinematographer is very impressed with the young officer. That same day, he boards a ship to meet his crew, which is already waiting for him in Damascus. Eventually, Cardiff realises that the young officer he'd met was the legendary Orde Charles Wingate, one of the originators of modern guerrilla warfare, whose unconventional ideas about organising guerrilla troops were successfully implemented in British campaigns and adopted by many corps. A devout Christian, Wingate was an ardent champion of Zionism and saw it as a moral and religious virtue to build the Jewish community in Palestine a state. He was crucial in training Haganah fighters, and his ideas provided the foundation for what was to become the Israel Defense Forces (IDF). Cardiff didn't only look to the past but also came across a man whose effect on the future of the place was immense. His Technicolour camera documented the empty alleyways where Jesus walked, and also illumined the conflicts that continue to fissure the land many generations later.
And so, another point of contact between the history of Israel and the history of cinema has been found. Allow me to note another interesting confluence in closing. In 1965, the great director Pier Paolo Pasolini arrived in Israel to scout for locations for a film he intended to make based on the New Testament, _The Gospel According to St Matthew_ (1964). With a 16mm camera, Pasolini passes more or less through the same places in Israel that Cardiff had thirty years before. But Pasolini's impression couldn't be farther from Cardiff's. He finds no holiness in Israel to speak of. The land doesn't contain the open expanses which would allow for such holiness to emerge. He films his visit and makes a short documentary called _A Visit to Palestine_ (1963). Did the years gone by and the founding of the state of Israel terminate the air of sanctity, or is it just the sharper, more critical and disenchanted gaze of a Marxist intellectual such as Pasolini? As always, history too is a matter of perspective.
_Pier Paolo Pasolini and Tonino Delli Colli at work on_ Il Decameron
_Pasolini in Palestine_
FEAR AND LOATHING IN THE DEAD SEA
_by Dan Shadur_
The ac at the Golden Tulip Hotel can barely ward off the furnace outside. Tzachi, the photographer, is staring at a large mosaic in the lobby. It's supposed to be a depiction of some biblical episode, calling to mind archaeological findings from the area. I'm calling Shiri, the pr woman, who isn't picking up. The night before, I got an urgent call from the editor of the paper I work for. He found out that Leonora Souza, one of his favourite South American actresses – he's obsessed with telenovelas, don't ask me – is shooting a campaign for an Israeli cosmetics company with plants in occupied Palestinian territories, and he thought it would be interesting to send his political reporter on her trail. Since it was too late to book an interview, he gave me the pr woman's number and said if I come back without a story he's "hanging me from the balls in the middle of the newsroom". Shimi Goldberg sometimes liked to pretend he was a tough American actor in a political thriller set in a newspaper building. It was almost as equally effective as it was ridiculous.
I picked Tzachi up from his apartment in Tel Aviv. We eventually reached Sodom Arad Road, winding along a variety of rocks in changing shades down to the Dead Sea, possibly the most beautiful drive in Israel. Tzachi wasn't the greatest photographer in the annals of Israeli media, but his fondness for drugs and unusual experiences helped kill the dead hours between tasks and increased the likelihood of something interesting happening. He would also take laborious portraits of the writers he worked with that we could frame and be proud of, which made us all forgive him for the many photo ops he had botched. Now he's extracting his camera, unable to take a single picture. I think he's experiencing artistic castration anxiety in the face of the stunning, lunar-looking scenery; the sun glistening in the black basalt and white chalk and countless shades of brown and red, until the glittering blue of the sea emerges from beyond the road. Without saying anything, I stop the car at one of the lookout points and we leave the ac for the arid furnace. Somebody stuck an ugly pirate memorial here for a loved one who died in a horrifying motorcycle accident. We smoke a joint and gaze into the horizon. In the summer, this is one of the hottest places in the world. In the winter, the weather here is perfect. Behind us, the arresting desert rocks are changing with the light. Before us lie the endless mountains of Jordan and the sea. Where is Leonora Souza right now and what is she doing? Does she know we're coming to look for her?
This convergence of the mountains with the sea is always absorbing and inspiring, but what the Dead Sea evokes is not tranquil harmony. The Dead Sea poses several physical and mental challenges to all who approach it. It's incredible to think that this impossible barrenness was such a fertile ground for human and cultural ferment from the early days of Jericho nine thousand years ago, through biblical Sodom, the Nabatian, Jewish, and Hellenistic settlements of the Second Temple period, to the tourist industrial projects of the last decades. This marvellous area, where everything is glaringly exposed and at the same time veiled and intriguing, instils you with a perplexing feeling, intermittently pleasant but somewhat troubling as well. If you come here enough times throughout the years, you too will accrue memories to weave into the big story.
When Sodom Arad Road ends, on the way to the coastal strip of Ein Bokek, where most of the hotels in the Dead Sea are, we pass the Dead Sea Works plant, which at night looks like a huge spaceship. For years, these immense machines have been evaporating water to produce potash in commercial quantities, and they are part of the reason it's disappearing at a horrifying rate. I'm trying to remember whether Shiri from pr also represents the owner of the plant while phoning her again, unsuccessfully. I quickly scan the lobby overlooking the pool. Herds of vacationers, tiredly sailing their flip-flops, producing the familiar Israeli noise of speech within an inch of yelling. I look at Tzachi – I already recognise the little tics that start to seize him when he goes for too long without smoking or drinking something, and to preempt future disagreeableness, I suggest we visit the bar at the edge of the lobby.
Only inside of it do I realise it's a traditional Irish bar. A heavy oak tree, stout barrels, clovers and green elves hanging from every corner, and plasma screens broadcasting highlights from a match between Bolton and Sunderland which took place under torrential rain very far from here. "Who the fuck builds an Irish pub in the Dead sea?" I ask Tzachi, who is already ordering "a pint of Guinness and a shot of Jameson" from the languid Palestinian bartender. Somehow his Irish accent is flawless. "You need to be more positive," he says dryly. I order a Guinness too, and after a few sips our spirits pick up and we begin to jovially chat up two middle-aged couples who came here as part of a weekend package for their workers' committee, which includes a show by a famous Mizrahi music singer and a lecture on love and kabbalah. The women are flattered by our attention and the men continue to stare at the screen apathetically. The rain in Sunderland is only getting stronger. The ball bounces blindly on the wet grass. After a few moments I'm starting to picture this quartet having sex and to sink into deep despair, when suddenly a young woman in a subtle T-shirt and tight jeans appears in the crowd. She is obviously not on vacation here and also obviously on her way to us.
"Shiri from Bar-de Haan-Yakin. I got your message. We can't give you an interview with Leonora. We promised exclusivity to the competing newspaper, and we don't see why the political reporter needs to interview the most famous actress in Latin America. We're actually a little apprehensive about it."
"I like Leonora – I thought we could give a slightly different angle on the whole story."
"Different how?"
"Maybe she can say a few words about the conflict?"
"We don't discuss our relationships with business associates or competitors, and the whole affair with the previous CEO... Wait, which conflict are you talking about?"
I feign a naïve look. Shiri sighs. "I'm sorry they sent you all the way here. I'm not interested in politics but Yakini says you're a good writer, and I know your crazy boss will insist that you get this story at any cost. But you'll have to leave now. You're not guests at the hotel and it's booked to capacity today. I checked with the manager."
Shiri leaves. Three security guards and a manager had been watching us from a distance. The women at the adjacent table smile, curious to see what we'll do next. The men continue to watch the game. The security guards take a few steps in our direction. Tzachi has somehow ordered another Guinness at some point and is finishing it with a long sip. We go outside.
In the car, Shimi the editor calls and says if we don't bring him at least a photo and one quote from Leonora – doesn't matter what – he's "cutting our guts open and feeding them to the cats at the Carmel Market". I have no idea why we're taking him seriously but we are, presently trying to imagine where they might be shooting with Leonora. We decide to proceed north towards Ein Gedi, where the hotel we'll be staying in is – thanks to a barter agreement made by the paper's marketing CEO, who suffers from psoriasis and tries to spend as much time in the Dead Sea as possible.
A bus of Korean tourists passes by us. They take photos of Mount Masada, which is on our left. Two thousand years ago, hundreds of Jews who were weary of the corruption and materialism in decadent Jerusalem came here to find a purer, more religious life. When the Roman armies besieged them, they preferred suicide to capitulation. This myth is still very much alive, and around the age of thirteen every Jewish Israeli comes here on a special school trip which includes staying the night in the nearby field school, receiving a wakeup call at 4am and climbing up the snake path – the original route used by the Jewish suicide rebels – to the top of the fortress, where a special ceremony is held before the students' parents. I remember something was troubling me that night and I couldn't fall asleep, and by the time we'd climbed up I was feeling so bad my mother had to take me down in the funicular while the other kids held the valour ceremony on the mountain. "Isn't it insane that they put kids through this?" I ask Tzachi, and realise he is asleep, the edge of his hair washing in the rays of sunlight hitting the windshield.
At the entrance to Ein Gedi beach I stop the car with a grinding screech. Tzachi wakes up annoyed. He picks up his camera case with great difficulty. We're greeted by a biting, unpleasant scent of sulphur. The entrance is crowded with tourists, mostly Russian, and with dozens of tables stocked with cosmetic and medicinal products. Tzachi comes to life, photographing the elderly Russian tourists, gradually focusing on one old woman who is eating a drumstick ice cream cone and looking a little ridiculous. When she looks up and notices Tzachi, she starts cursing him in Russian, but he just continues to take photos of her. Her bullish husband walks up to him and a confrontation is only averted thanks to the fortuitous intervention of a security guard. As the husband continues to curse him in Russian, Tzachi disappears into the wardrobes, going over the photos he'd taken as if all the fuss has nothing to do with him.
Since the coastline has moved so much farther away from where it was only a decade ago, a train harnessed to a tractor wagon takes the sweaty vacationers from the main area to the waterline. It's a few minutes' drive to the edge of the world. The rocks and waste scattered at the side of the road moan along with the vacationers under the heavy heat and barrenness. I see the reception on my phone is fading. On the shoreline are a few beds and thatches, young lifeguards and a few girls, probably from the neighbouring kibbutz, drinking vodka Red Bulls and laughing. Tzachi lights another joint and it's quickly digested in the dry hot air. It's hard to move here. We are carefully walking on the hot rocks, which quickly become a beautiful crystalline bed of salt, absorbed into the sea. The water is warm and oily and we cautiously get in. "Aaaahhh," Tzachi screams and I laugh. "This isn't a brothel," I tell him. "It burns," he keeps yelling, and everyone around is looking until he calms down. We lay on the water and start floating, slowly shedding the hardships of the day, the salt tingling the pores without hurting too much and then soothing us. The eyes wander from the skies to the wonderful mountains of Edom before shutting peacefully. Pleasant and abstract thoughts supplant their predecessors. Images from an old 8mm film I might or might not have seen flood my field of vision – three blonde women at the end of the Sixties, clutching an Uzi and laughing, swinging it at the camera. I think there was something I was supposed to do today.
I don't know how much time passes before I open my eyes again. I didn't notice the water carrying me so far from the beach. My eyes drift to a small cove in the northern shoreline. Something's twinkling there. At first I think it's a hallucination brought on by the drugs and the sun, but on a second look I see it's coming from a large piece of styrofoam surrounded by what looks like a camera crew, and in front of it – I'm now seeing – is a female model in a full-body bathing suit. I get myself together and try to stand in the water. I spray some water on my face and it burns my eyes. I start walking toward the beach but the water is heavy and I'm moving very slowly. I skip across the sharp gravel to wash myself in the showers. Around me are dozens of figures smeared in mud. I look for Tzachi but can't find him anywhere. His stuff is gone too. I grab my things and hurry towards the flickering light, moving on a hard space which, up until recently and for millions of years, has been covered in sea, and is now too exposed. I cross a makeshift fence at the end of the beach and then stop. The lack of minerals and water doesn't only bring about a vaporisation of the sea and move the bathing beaches farther and farther away from the shore, but also makes sinkholes – large depressions in the ground that suddenly gape and suck all they can into them – appear with increasing regularity. The sinkholes adumbrate new pathways, make footholds change their locations and roads change their routes. Nature avenges its vandals so parabolically and graphically, like an ecological horror picture written especially for this slab of earth. This hole is also what now denies me access to Leonora – a woman I'd only heard of yesterday, who has by now become the object of infinite desire. I must meet her, must get a picture of her, must get a quote out of her.
I hurry back to the jerry-built train that will take me to the road, and wait another fifteen minutes in the scalding heat for it to arrive. Eventually I'm back at the main vicinity but Tzachi is missing. Only after forty-five minutes of sweaty anticipation does he suddenly appear, peaceful and radiant, enthusiastically telling me about the massage he'd received from a proselyte German who fell in love with an Israeli New Age guru and moved into a cabbalist hippie community in Metzoke Dragot. I snatch the bag with the keys from him and run towards the vehicle, but running isn't really possible in this heat – everything is happening in a continuous slow motion. The Koreans' bus passes us again as we quickly come up on the main road, and I'm honking like an insane person – making a trail of German tourists panic and three camels resting at the side of a young Bedouin nuzz with disdain. We drive down a dirt road that quivers the chassis of the small Japanese vehicle and eventually reach a small anchorage. About two hours have passed from the moment I'd seen them until I got here, and the crew is already wrapping up and loading the rest of the equipment into a commercial vehicle. Leonora is making jokes with the makeup artist. I don't see Shiri or any security guards anywhere. I approach Leonora and introduce myself as a journalist from the competing publication who will be interviewing her.
"I thought we were meeting in the evening," she smiles obligingly. A thin white cloth covers her full bathing suit. Beads of water are still twinkling on her smooth skin. There is nothing in her body that isn't perfect.
"I wanted to see you at work."
"I've been up since 5am, but this landscape is wonderful. It's a great honor for me to shoot at such a beautiful and unique place, for such an original and innovative company."
"Is there a message you would like to send the Israeli public?"
"I want to tell them that their love moves me in a new way every time. That they're always on my mind and that even when I'm far my heart is with them. I have many fans in many places but only a small part of them are here, in the land where Jesus was born, and where so many miracles happened in the past. I look at my relationship with the Israeli fans as a big miracle also, made out of many little miracles, and I feel that God has sent me here."
Her smile is perfect. I look back at the car to make sure Tzachi's getting all this. Now my moment has come.
"How do you think the Palestinian people would respond to your doing advertising for an Israeli company with plants in an occupied territory?"
Leonora becomes silent. The idyllic veil has been rended. She looks around for help. Her face sobers. I've done this to so many interviewees in the past, but something about this woman's face makes my heart crumble.
"I don't think I'm supposed to answer that question." She's helplessly signalling the assistant, who arrives in a panic. She whispers something to her. The assistant looks at me angrily. "What did you say your name was?" She dials the iPhone with one hand and beckons two security guards with the other. I retreat backward, signalling Tzachi to move to the driver seat and start the car. To my surprise he does this with maximal efficiency. We take off without looking back.
Within a few minutes we're at our hotel in Kibbutz Ein Gedi. What started as a humble guesthouse is slowly expanding and becoming a kind of sophisticated and over-expensive boutique hotel. We spend two hours in the nice pool on the edge of a cliff with a view to the sea. At sunset we walk along a new promenade overlooking Nahal Arugot. Two ibexes skip between the rocks in the wadi below. I call Tzachi's attention to them but he ignores me. Something about him will remain inscrutable to me forever. The hotel dining room is packed and, as in the Irish bar, most of the workers are Arabs. The buffet is stocked with diverse courses but I have never had anything good to eat at the Dead Sea and tonight's not going to be any different. Something about this place always thwarts the indulgence of hedonism. The desire for beauty, pleasure, and the money that makes them attainable, always comes up against a more mysterious, primordial element. It's a part of the intensity of the place, for good or ill. I fill my plate with a kiddie schnitzel and French fries and eat too much.
In the evening, pleasant air replaces the sweltering heat. We smoke another joint and walk between the botanical garden and the rooms. The people who built this place toiled and sweated to start a new social utopia. Their grandchildren sell spa packages to tourists from around the world. Tzachi says it's a shame the world has changed so much and I say I don't really miss anything. This kibbutz is an oasis covered in exotic plants. We hear playing from one of the open yards – a group of twenty men and women in their sixties is sitting around a table and singing in Russian. We come near them, they don't speak a word of English, but as it turns out Tzachi can speak basic Russian with them – I have no idea why and how – and it's as if they'd been his friends forever. They all have a genial look in their eyes, like true believers do, and they tell us how much they love Israel and how happy they are that we came to sit with them. They pretend to have not lost the thread when I sentimentally hold forth on the importance of Jesus in the world history of class division. Later they dedicate us a song and begin singing "How good and how pleasant it is for brethren to dwell together in unity" in Russian. We hum along with them, they in Russian and us in Hebrew, without knowing if there's any overlap between the two versions, and I think I haven't sung this song in years. Tzachi is moved, and he gives each one of them a big hug, and then retires – leaving me stranded before their cryptic smiles.
When I come back to the room Tzachi is sleeping. I take his camera to look at Leonora's photos. He took about forty of them during our short talk. They're all too highly exposed, completely washed out. In some of them you can discern an arm or a piece of cloth, but the famous actress is impossible to make out. I put the camera down. There's no story without these pictures. I fall into a heavy slumber and after a few hours wake up with a start.
I go outside. The sun begins to rise from the mountains of Edom. The kibbutz is still sleeping, and the beach under me is starting to clear, rendering into view with the Jordan mountains and the blue-green sea like a freshly taken Polaroid picture. Not far from it, at the northern edge of the sea, is Jericho, the most ancient existing settlement in the world. I remember going there on trips as a kid in the early Eighties, before the first intifada, when Israelis would travel the Palestinian territories practically freely. I remember the abandoned green swimming pools of ancient Arab villas, a Trappist monastery with a rock-cut winery that seized my imagination, and my mother bargaining with a local merchant over a large clay pot that I can't remember if she ended up buying or not. When I went back there at the end of the Nineties to do a story on the casino that for a brief spell was one of the most profitable gambling establishments in the world, thanks to thousands of Israeli addicts who lost their life savings to it, the Austrian security guards wouldn't allow me to get far enough from the casino and hotel area to see whether the places I remembered were real. I wonder what became of those slot machines that were abandoned after Arik Sharon visited the temple mount and ignited the second intifada, which left thousands of casualties and probably irremediable degrees of hatred in its wake. What happened to the poker and blackjack tables. What happened to the Russian prostitutes, the Palestinian dealers, the taxi driver from Jerusalem who sobbed by the roulette at five in the morning when he realised his life had just been ruined.
The mountains and the water continue to clear slowly. Leonora, Shimi, the editor and Tzachi, Shiri, they're all probably still asleep, hovering between the ciphers of yesterday and the oracles of tomorrow, waiting to tackle a new day of desires, successes and failures, as this lake – the vestige of a tectonic collision from twenty-five million years ago – where nothing ever happened, except for a fathomless wrestle of chemicals and minerals, wakes up to a new day.
ONCE IN ROYAL DAVID'S CITY
_by Julia Handelman-Smith_
My first Christmas away from home was in the Holy Land. A lifetime of Christmas Eves had passed in the same rural village in the English Midlands, and with minor tweaks over the years had followed the same traditional patterns: carol singing around the village fuelled by mulled wine, midnight mass, and drinks in the pub with our friends and neighbours.
The decision to do something different was for practical reasons, rather than religious or ideological. I was living in Tel Aviv, and work commitments made it difficult to travel home. Instead, my parents would come to visit me and we would travel with other members of the Church of England community in a specially organised diplomatic convoy to Bethlehem. I did not feel like a pilgrim, but there it was, on my doorstep.
I had visited Bethlehem a few times before. The fast-track section for diplomatic cars made it fairly straightforward to pass through the intimidating checkpoint process, and I had spent afternoons walking around its sleepy streets. Rather too sleepy, for the birthplace of Jesus Christ. I was always quite unnerved by the lack of visitors in this this iconic place: the political graffiti that far outweighed religious symbols, and the temptation to haggle up for the beautifully carved olive wood nativity sets that local craftsmen create far faster than they can sell. This was Bethlehem in 2007, when decades of conflict, continuing Israeli settlement and a twelve-metre Israeli partition had splintered its communities.
Traditionally a Christian town, internal displacement within the Holy Land and the emigration of its conflict-exhausted inhabitants has shifted the demographic to a Muslim majority. Many pilgrims can experience the Christian story with more peace of mind within the Old City of Jerusalem, where they are also able to purchase Bethlehem's Christian souvenirs, albeit at an amazing mark-up. There is a lot of argument about the Christian communities in the Holy Land. Statistics state that the percentage of Christians has remained relatively constant since Mandatory times; however, that belies a lot of emigration overseas, either as a result of the 1947 conflict, or later for economic and quality of life reasons. Both of the major protagonists in the continuing conflict – Israeli and Palestinian – have been accused of unequal treatment of Christians. Both sides accuse the other of racist abuse and harassment of the Christian community.
But on 24 December some fifteen thousand people flock to the city, a pilgrimage that is repeated a few weeks later for the Orthodox celebrations. Political leaders from both Israel and Palestine, as well as senior figures from around the world, take part in a televised midnight mass from the ancient Church of the Nativity led by the Roman Catholic bishop of Jerusalem. Access to this vip event is almost impossible, but we were joining a group of Anglican worshippers for a much smaller celebration led by the Anglican Bishop of Jerusalem earlier in the evening.
The Anglican Community in the Holy Land is a minority amongst minorities. With Christians in the Holy Land already a tiny slice of the overall population, Anglicanism is a pinprick amongst the Catholic, Orthodox and other numerous factions of the Christian faith. Over the years, different branches of the Christian community have developed complex arrangements of sharing the major Christian sites of the Holy Land, but no Anglican chapel exists at either the Church of the Nativity in Bethlehem or in its sister Church of the Holy Sepulchre in Jerusalem. In one of the many, but nevertheless incongruous, streaks of pragmatism that exist within religious communities, the Greek Orthodox community had loaned us their chapel on the site – unneeded for their Christmas celebrations until two weeks later.
As we gathered at the English church on Nablus Road, instructions were given to stick to the car in front. Our convoy sped recklessly along the short road to Bethlehem, slowing to a crawl as we manoeuvred through the narrow and crowded streets. Israeli soldiers, mostly youngsters completing their obligatory military service, waved us through the checkpoints and handed us over to the Palestinian police.
Because Christmas Eve in Bethlehem is not peaceful. A solidarity concert taking place in Manger Square featured performances from all over the world, and an audience of thousands thronged the square. Supporters of Bethlehem, or Palestine, or the Holy Land – or simply local people with a rare opportunity to see live art in their own town crowded the streets. Our attempts to reach the Church of the Nativity touched on the biblical. Every attempt to enter the church involved a heated debate with a policeman. Whilst the dignitaries at the front of our convoy drove to the church door with no difficulty, we found it hard to convince the authorities that we were also invited. Our cars were turned back and we had to try several routes and parking places before returning to the church on foot, and still the local police didn't want us to access the church. They had no idea that the Anglican community had arranged a small celebration ahead of the official Catholic service at midnight.
I grew increasingly uneasy: it had been a mistake to put my parents through an experience that was rapidly turning into an ordeal. Whilst the police officials were very cheerful, they waved their large guns around in a very casual way and spoke animatedly and loudly. I realised how anaesthetised I had become to the military states of the Holy Land: armed checkpoints and teenage soldiers with heavy weaponry on the streets of Tel Aviv. My parents, quietly spoken people from a peaceful English village where regular policemen don't even carry a handgun, were finding the whole process pretty unnerving. Normally, the most confrontational part of Christmas might be the jostle at the pub bar, and by now they had seen more military hardware this evening than they had in their lives. Added to that, none of us spoke Arabic and we started to realise that should we be split up from our group, we would have no idea how to get home.
Eventually, miraculously, we found ourselves stooping through the tiny door of the church, built to deter mounted crusaders from entering on horseback. There were probably only about one hundred of us, but we filled the tiny space, standing or perched on stone steps and the odd chair. We were led through an informal, multilingual service of readings, prayers and carols with no hymn sheets or service books. Often we sang carols to a familiar tune, each person singing the well-worn words of their own language. Coming from a tradition where much of the celebration of Christmas is attached to the choreography of music, candlelight and ceremony, it could not have been further from a traditional Christmas. Yet, perhaps because our journey to Bethlehem had been so fraught, the rather stilted version of "Silent Night" in several different languages had more meaning than it does on a quiet village green. Silence, after all, is much more appreciated if you have also experienced cacophony and chaos.
About halfway through the service there was a sudden rush of cameras as Palestinian Authority chairman Mahmoud Abbas arrived to address the congregation. He spoke for five or ten minutes and left, followed by his retinue of journalists and supporting staff. I remember little of what he said now, but he spoke of peace and the importance of Christmas in bringing communities and people together. But despite this, the moment jarred with the rest of the ceremony. This rare opportunity for people from many different communities to come together and celebrate privately was plunged back into the world of conflict and insecurity just outside the church walls.
Because Christmas in the Holy Land, like everything else, is political. Even an apolitical speech is a political statement. It is impossible to think about the holy city of Bethlehem without drawing attention to its plight and the daily uncertainty of its citizens.
We quickly recovered, and the service ended with a haunting solo of a traditional Palestinian carol. And it was in that moment that I realised that I had finally shaken off the stress and confusion of our short but highly-charged journey to Bethlehem. Although brief, it was a moment of complete serenity, because I could think of nowhere else I would rather be at that moment than here. Afterwards, we filed out of our tiny chapel and visited the grotto of the nativity, and enjoyed a brief but exceptional moment in the larger part of the church, emptied of tourists and worshippers in preparation for the politicians to arrive for the main event later in the evening. I had no envy or curiosity about attending what was obviously the main event in Bethlehem that evening – or even that year. I felt more privileged to have attended our improvised, quieter service.
We spent Christmas Day in Tel Aviv, celebrating quietly at home amongst a community that sees it as another ordinary day in the working calendar. Without our Bethlehem visit, I'm not sure we would have remembered it was Christmas ourselves. Most of my Christian friends in Israel celebrate the Orthodox Christmas (either Greek or Russian) in early January, and from the wall-to-wall sunshine to the traffic and bustle of a normal working day, there was nothing in our surroundings to remind us of Christmas.
Two Christmases later, my mother-in-law, Sari, joined us in Hickling, Nottinghamshire to experience her first ever Christmas. Although thousands of miles from the Holy Land, she enjoys something closer to the traditional Christmas she expects from thousands of western depictions: carol singing with mulled wine, midnight mass and the pub. She excitedly points to "Bethlehem" in all of our traditional carols, and we laugh because it is so close – no more than an hour away – from her home in Israel. But for Sari, Bethlehem is as distant and as iconic as it is to the other carollers, only for different reasons. Bethlehem is both a religious and a political icon in the Holy Land, and whilst for we middle- Englanders it is physically far and raised to mythical status by our religion and culture, for both of us it is made even more inaccessible because of conflict. In ordinary circumstances, there would not be many barriers to visiting Bethlehem these days. But ironically Bethlehem has maintained its mystery, shielded – or overshadowed – by a conflict that that has become almost as iconic as its religious significance.
I haven't spent Christmas in Bethlehem since, choosing to return to my traditional western roots. For my parents, too, once seemed to be enough. However, my experience of Bethlehem has entered the fabric of my Christmas. Although I would borrow the words of the late Johnny Cash and describe myself as a "C-minus" Christian, the Christmas of 2007 reminds me of so many things about the Christmas story and what it is supposed to mean to be a Christian. Albeit in modern times, I have a fragment of empathy for the trauma of a young pregnant woman, seeking refuge in Bethlehem amongst thousands of others. I can also associate this with the thousands of people today who continue to struggle to live in Bethlehem. But beyond that, I also remember a group of people stumbling their way through "O Little Town of Bethlehem" in whatever language they know, and a very rare, and equally brief, moment of private peace in the Holy Land.
THE JERUSALEM SYNDROME
_by Julia Handelman-Smith_
A lot is said, even between the covers of this book, about the invisible walls that divide the Holy Land. Most cities retain a distinct character: Jewish, Arabic Christian, Arabic Muslim, Druze. Yet despite lying at the heart of the Holy Land conflicts, Jerusalem's Old City maintains a brittle but functioning peace where Muslim, Jewish and Christian communities live cheek by jowl. Barely changing over several centuries, not least because the slightest alteration can cause mayhem not only between, but within communities, a walk through the Holy City captures both a sense of times past as well as (on a good day) what a peaceful Holy Land might look like.
If you can, and it is not too hot, start at the Mount of Olives. Here you will get the iconic view of the ancient city and the Golden Gate. This is the first shot taken for every documentary or newsreel, and it doesn't disappoint. Walk down the hill (taking the road) and stop halfway at the Garden of Gethsemane, which remains a peaceful spot often left off the pilgrimage trail for being slightly out of the city centre.
Continue towards the city and enter the Muslim Quarter of the Old City through St Stephen's, or the Lions' Gate. If you haven't already guessed, you are taking the route many believe Christ took on his journey to the crucifixion, the Via Dolorosa. Although this has recently been contested by archaeological findings it is still a route of pilgrimage for Christians, with signs en route to show different stages of Christ's journey. However, you are still in the heart of a modern city, and on this part of the route there will even be groups of young men hanging out on a Saturday afternoon. Some shopkeepers may invite you to see the "real" stages of the cross, often one or two floors below street level because the ancient city of Jerusalem was said to be at least five metres below the present-day city. Single female travellers should beware – this may include an (un)welcome proposition at station five that requires a hasty exit!
At the junction, stop at the Austrian hospice on the right for a touch of old colonial charm. Elegant but worn, the café has a great sachertorte if you've already overdone it on the falafel and baklava. Most important is to get up onto the roof of the building for another fine view of the city, which you can probably enjoy in solitude.
From here, take a left and immediate right and enter the labyrinth of the ancient souk. Directions at this stage are useless – the best part is to get lost. If you're keen, you can continue to follow the stations of the cross, not least because this brings you into the Church of the Holy Sepulchre by the best route, which is through the Ethiopian and Coptic monasteries on the roof of the St Helena Chapel. At some point in the souk, you have passed the seamless divide into the Christian Quarter of the city, but a quick trip down HaNotsrim leads you past the Jaffa Gate entrance to the city and into the much quieter Armenian Quarter. This is where you will find some of the more peaceful monasteries and Christian guesthouses in the city; the Armenian Garden and Cathedral of St James are worth a stop.
Moving back eastwards, you finally enter the Jewish Quarter of the city, and modernity slowly enters back into the Old City. Many Jewish communities have moved back to this part of the city since 1967, and it has become a prime area of real estate. Consequently, there is more renovation and visible affluence here than in other parts of the city. Finally, don't be put off by the security to enter the Western Wall plaza and to visit the Temple Mount.
By this stage you have just about done a full circle, and might be needing a break from religion, full stop. I'd recommend heading south-west to the Jerusalem Cinematheque or north to the American Colony Hotel: both offer tranquil, secular spots for quiet meditation.
MY LIFE AS A DOG IN EAST JERUSALEM, OR SMELLY WALKS
_by Karin Gatt-Rutter_
My name is Ramses and I am a boxer from Haifa. At the early age of six weeks I moved to my home in Sheikh Jarrah. Sheikh Jarrah is located north-east of the famous American Colony Hotel and houses many diplomatic missions, the Office of the Middle East Quartet, and two hospitals, St John's and St Joseph's. The latter I visited once, by mistake, as I managed to get off my leash and run after some kids. Everyone was screaming and I thought it was a lot of fun. But I was just five months old. Today, I would of course know that hospitals are off-limits for dogs.
I am lucky because my house is big and I can also roam around in the garden where I chase cats – but sometimes they scare me, although I am bigger; cats in East Jerusalem are not to be messed with, I have learned.
I go out on dog walks normally in the neighbourhood. I am still very undisciplined and therefore have to be on the leash. It is ok – you get used to it after a while.
Most of my walks are along Route 1, along the so-called Green Line which marks the division between Israel and the territories captured in the Six-Day War. It has nice green lawns on the side of the busy two-lane roads in each direction, and bushes and trees. But before reaching the green and smelly spots I have to pass the open-air sports ground, where even at six in the morning women and men, mostly from east Jerusalem, walk or run in sports gear or traditional clothing, and the Spanish consulate general facing the sports ground. I adore the funny hats that the Guardia Civil guys wear.
I love to sniff around the containers of trash everywhere. It is amazing how much litter there is in this part of town! The scary thing is that there is a lot of broken glass, which can cut my sensitive paws.
I rarely meet any dogs – not too many people own dogs that go out on walks. But I can smell that there are other dogs around. I know there are wild dogs around the area close to the Ambassador Hotel or down in the valley from the Mount of Olives Road to Wadi Joz (the Walnut Valley). When I was a puppy they scared me with their barking and my mistress had to throw stones at them to make them run away. It is tough for dogs in this part of town. So, stone-throwing is good.
Another smelly walk is the area next to Route 1, heading north and passing the police headquarters. There, I hear and smell my canine brothers and sisters who are running around inside the fence. They never come close to the fence as I don't think they have a long leash. Before I head up to the statute I have to pass a dangerous road with many lights. I have to sit pretty and wait until it is green (not that I see the difference between green and red, but that is what my mistress tells me) before I can run up the hill. In the summer people sometimes have picnics there. They are mostly students from the Hebrew University who leave packages of fries or other things I can gobble up. But I know I am not allowed to eat from the ground. But who cares? I am a dog!
My bestest walk, though, is the Tabachnik Park, which is part of the Mount Scopus Campus of the Hebrew University. There, if I am lucky, I get to run off the leash, as there are not too many people or dogs there. It has nice Mediterranean vegetation including trees to climb in, if I could. It has a magnificent view over the Old City of Jerusalem. In fact many people come in buses to stop and look at the view and take photos. But they never come into the park.
When it is too hot my mistress brings a special water bottle, which is a gadget I can drink from the way we dogs drink. Once I could also lick water from the sprinkler system of the Jerusalem municipality. The plastic tubes had dog-convenient holes.
As I said, I love the rubbish containers with everything in them that humans throw away. It would be great to have a treasure hunt one day. I know I would do very well because once I found a black bra.
_Ramses_
## PART THREE: TZAFONA
_(In ancient Hebrew, the north was called Tzafona or Semola, meaning "left", which is like the Arabic Shamal, as in north.)_
IN THE NAME OF THE FATHER
_by Shay Fogelman_
My father was one of the conquerors of the Golan Heights.
On the noon of 9 June 1967, he and the Eighth Armoured Brigade stormed the black basalt mountains with cannon fire. They led the battlefront and encountered fierce Syrian resistance. Most of the tanks of the first battalion were hit in the first hours of fighting. Many soldiers were killed or wounded, but six more Israeli brigades joined the attack later that day. The war ended the next day.
During the six days of the war, my father and the Israel Defense Forces (IDF) fighters defeated the armies of ten Arab countries. The accumulated territory they occupied was three times larger than Israel had been before the war.
Six years later, in October 1973, my father fought in the Golan Heights once again. Like hundreds of thousands of other Israelis, he was called in the middle of Yom Kippur, the most sacred day for the Jewish people, to go defend the land from the Egyptian and Syrian armies, which had launched a surprise attack from their respective fronts. This time, my father was added to the Seventh Armoured Brigade as a reservist. The brigade's confrontation with Syrian forces in the northern Golan is considered one of the most heroic battles of the war to this day. For four days of battle, my father and the brigade soldiers barely succeeded in holding back an armoured Syrian force that outnumbered them six soldiers to one. Half their tanks were hit. Many of them were killed.
I was born between the two wars, between the euphoria of the 1967 victory and the collective mourning that enfolded the country after the Yom Kippur War. In one of his poems, the wonderful Hebrew poet, Shaul Tchernichovsky, wrote, "Man is nothing but the image of his native landscape." My native landscape is a country in conflict, blood pouring from its borders, the names of conquerors and wars outlining its history books. Although I grew up in one of Tel Aviv's grey suburbs in the middle of Israel, the Golan Heights played an important role in shaping my conflicted childhood landscape.
When I was a child, my father would take my little brother and me on trips to the Golan almost every summer. Sometime we would spend a few nights in a tent or under the sky, by the fire. I loved the trips in the Golan Heights; the wonderful landscapes, the wildlife, all the historical sites. My father always brought along topographic maps, history books, and plant and bird guides. He taught me how to navigate the turf by myself, how to identify poisonous summer snakes, and how to purify the stream waters before I drank them. At night he taught me how to light a fire with a single match, how to brew excellent tea from leaves we'd picked up in the area, and how to find the north with the stars in the sky as my only guide. I loved the trips to the Golan Heights, especially spending time with my father, who knows every stream and path in the Golan very well.
The Golan Heights are in northern Israel, next to the border with Lebanon, Jordan and Syria. It is a tall, flat region. In its east rise several volcanoes shaped like trimmed cones. The Golan soil is hard. The rocks are black. The streams are steep and narrow. It is a tough and battle-scarred land. The Israelites fought for it in the Bible. One of the decisive battles of the Great Revolt was waged in the Golan during the Roman period. In the seventh century ad it was the scene of the Battle of Yarmouk, which led to the fall of the Byzantine Empire and the Muslim conquest of the land. The memory of that battle remains one of the preeminent symbols of world jihad.
Human settlement in the Golan was among the most ancient in the world, and there are several spectacular archaeological sites in the area, some dating back to prehistoric times. In the eastern Golan Heights there's the "Wheel of Ghosts" (Rujm el-Hiri), a mysterious monument of stone circles surrounding a fifteen-foot-tall tumulus. The most outlying circle is 520 feet wide and archaeologists estimate that the site was constructed six thousand years ago, long before Stonehenge.
My father and I visited many archaeological sites in our summer trips to the Golan. I mainly remember the visit to the excavations at the city of Gamla, which was destroyed during the Jews' rebellion against the Romans in 67 ad. The city was built as a fortress, surrounded from three directions by a tall and steep cliff. It took the Romans two attempts to subdue the Jewish rebels. Four thousand Jews died in the fights. Another five thousand refused to surrender and jumped to their deaths from the cliff. I read all this as a child, in the book _The Wars of the Jews_ by the historian Flavius Josephus. I received it after visiting the site as a gift from my father.
We also walked in the wild nature a great deal. The wars have left desolation almost everywhere, and you find remnants of bunkers, entrenchments, fences and minefields wherever you turn. In many places, human entry has remained forbidden and the vegetation has grown wild. The small civilian population in the Golan allows Mediterranean nature to grow practically freely in a large part of the territory. The last bears and tigers were hunted a hundred years ago, but foxes, wolves, hyenas, wild boar and a great variety of other animals are still around.
I remember a hike we took in Nahal Yehudia, a trail in the southern Golan that includes a thirty-foot-high waterfall. You can go around it through a narrow path, but you can also jump into the little water pool that was formed under it. It's a very dangerous leap because of the rocks hiding in the water. I won't forget the first time I stood at the head of the waterfall and looked down into the placid water. I repeated my father's instructions to myself. "Jump far. Watch for the rock on the right. Dive with both legs. When you come back up, stay clear of the thorny bushes." I was very afraid. I was more afraid of being a coward. I jumped.
The wars also played a part in our Golan trips. On the drive, my father would show us the Israeli lines of defence, the fortifications and the attack paths of the Syrian tanks. For dozens of years the two sides entrenched themselves and created one of the most complex aggregates of trenches, embankments, minefields and other barriers for storming forces in the world. Sometimes we would stop on an isolated hilltop and look over the border to the ruins of the town of Quneitra, which was ravaged in the battles and has remained empty and deserted. Then my father would tell us about the war. He would describe the battles and point to the places where his friends were killed. Once he told us about a Syrian plane that dropped bombs on an armed convoy of theirs, killing some of his friends. He remembered their names well and described the joy of life that was interrupted. He talked about sleepless nights, shooting and bombing sounds, the smell of gunpowder. He described the sights from the morning after the battle: burnt tanks, bullet-marked jeeps, the corpses of soldiers, Syrian and Israeli.
_Ruins of a Syrian village_
_Syrian military camp_
Ever since its occupation in the '67 war, the Golan has been the main bone of contention between Israel and Syria. The border is usually quiet. Quieter than Israel's other borders. But tension and wariness around it persist. The Syrian claim towards Israel is simple: "You took it, give it back." Israel argues that there was no other choice. In several skirmishes that took place before the war, Syrian cannons fired at agricultural settlements by the border. Throughout the years, a number of Palestinian organisations have sent armed squads through the border to carry out actions against civilian population in Israel. When questions about the future of the Golan come up, many Israelis ask who is to guarantee that such things won't happen again if the Golan is returned. This is what my father fears as well. "The death toll we have paid for this land is too high," he tells me every time I bring up the possibility that a peace agreement leads to the cession of the Golan. I'm concerned about the blood that is yet to be spilled.
Israel has other excuses for retaining the Golan Heights. A considerable number of the water sources of the Kinneret, the largest freshwater lake in the country, are in the Golan. Mount Hermon, the highest mountain in Israel, is also in the Golan, and there are military intelligence facilities of great importance on its summit. The Israeli security establishment defines it as a strategically significant site. Although few would admit it, many Israelis will also have a hard time giving up Mount Hermon because its top is the only place where it snows in the winter, making it the only skiing site in the country.
Another issue that complicates a future peace agreement between the two sides concerns the Jewish settlement in the Golan. Since its occupation, thirty settlements have been founded in the Golan, and today, about twenty thousand Israeli citizens live there, along with twenty thousand Syrian citizens, mostly from the Druze community, who remained in their five ancient villages at the foot of Mount Hermon after the Israeli occupation. There's another Syrian village under Israeli sovereignty between the Golan and Lebanon called Ghajar, whose inhabitants are Alawites.
As a child, I paid many visits to the Druze villages in the Golan Heights. Almost every time my father and I came, we would stop to eat at one of the local restaurants and finish with a cup of coffee. Most of the Druze community lives in the Middle East. The Druze practice a secret religion which was developed from Shia Islam and they believe in reincarnation, among other things. They are known around the Middle East for being valiant fighters. They have managed to survive as a small minority for hundreds of years, mainly thanks to their loyalty to every sovereign and opposition to every conqueror. They are mountaineers, obstinate folk living in a very conservative and traditional society.
My summer trips to the Golan Heights with my father stopped when I reached adolescence. I preferred going to the desert or to other areas of the country with friends my own age. My father was disappointed. He kept going back up to the Golan but said it wasn't the same anymore without my little brother and I. But what pained him most in that period was how, as my political stances began to crystallise, I became firmly opposed to the Israeli occupation of the Golan Heights and to visiting the region.
The change was gradual. For many months I read every book, article and opinion piece I could find about the Arab-Israeli conflict. I audited lectures, met with peace activists, even started learning a little Arabic, and came to acknowledge my people's collective responsibility for the conflict's history and for its future. At first my father regarded these stances as part of my teenage rebellion. Later he even forbade me from going to meetings with Palestinian activists and Israeli leftists who resisted the ongoing occupation of the West Bank and the Golan. Of course, I kept going behind his back.
_Israeli tank positioned on the Syrian border_
My political dispute with my father wasn't resolved over the years. He's still convinced that the state of Israel must keep control of the occupied Golan and even planned to move there a few years ago. Thankfully, my mother was adamantly opposed to the idea. I could easily attribute the source of our differences to his war experiences or to the generational gap between us, but things are more complicated. My father sees the Golan Heights as a homeland where Jewish history has been developing for thousands of years. The ruins of the Jewish city of Gamla, which was destroyed in the Roman period, the vestiges of the Katzrin synagogue which was built in the Byzantine period, and even the Jewish settlement in the Golan at the end of the nineteenth century, which began long before the founding of the state of Israel, all reinforce the connection he feels to the place. I prefer to look at the future, and am positive that we must leave the Golan Heights and reach a peace agreement with Syria, even tomorrow morning if possible.
However, in recent years I've returned to the Golan Heights many times. I had a deep journalistic interest in the tradition of the Druze villagers and in their complex identity as a minority living under an occupation. My meetings with them produced a number of articles I published in _Haaretz_. One article concerned the Druze who served as Syrian soldiers in the war of 1967. I was curious to know what fighting against my father was like and what the Israeli occupation looked like through their gunsights.
Many of the fighters I tracked down wouldn't speak to me. They don't give interviews to Israeli journalists, who they still consider their enemies. Others were very apprehensive and agreed to talk about the events of the war but refrained from describing their parts in it. I was surprised to discover that after so many years, many of them still feel humiliated by the defeat. Naturally, I kept my father's part in that war to myself.
Another article investigated a Druze spy ring that operated before the Yom Kippur War. I found that its members passed crucial information to Syrian intelligence, which brought Syria great success in the first days of the war. None of them has expressed any remorse, even though some have spent decades in Israeli prison. On the contrary, they are proud of what they did for their homeland to this day. I didn't tell them about my father and his friends who died in action either.
One of the investigations that yielded the most discoveries came about unexpectedly, when I heard from a Druze villager that until the war, tens of thousands of Syrians resided in a number of towns and villages in the Golan. This surprised me. In the Israeli history books and in my research on the wars in the region I never read about what became of the Syrian villages, towns and farms. My father didn't mention a civilian population when he described the wars in the Golan, and I never saw any traces of civilian settlements on our trips, only dozens of bunkers and army camps.
For several months, I rummaged through the archives and interviewed Israeli combatants and officers and Druze still living in the Golan, uncovering secret military documents and new testimony. I found that a substantial part of the Syrian civilians living in the Golan had left their homes right after the war broke out. Most of them had left because they feared the battles, and later the idf prevented them from returning to their homes. But I also discovered that there were instances of organised evacuation, in which the few residents who remained in the villages were put on army trucks and transferred over the border with the aid of the International Red Cross. Their homes were either bulldozed or blown up in the months after the war. Israel only left the army camps in their place, serving a widespread myth about the Fearful Golan Heights.
_The cadet school of the Syrian army, now abandoned_
Unlike the other territories Israel occupied in 1967, which either remained under military administration or belong to the Palestinian Authority, the Golan Heights were nationalised in the early Eighties. By means of a controversial law, a way for prime minister Menachem Begin to compensate the parties of the right for his agreeing to return the Sinai peninsula to Egypt in the Camp David accords, the government decided to apply Israeli law to the Golan. No country in the world acknowledges this annexation and the un Security Council has unanimously adopted a resolution calling on Israel to annul it. The Druze residents of the Golan started a popular struggle against it and went on strikes that were quickly repressed by the authorities. The law has allowed them to become Israeli citizens, but few of them have. Most of them still view themselves as Syrian patriots living under an occupation. They have special resident IDs, don't vote in the Israeli elections, and are exempt from military service. They are entitled to education, medical care and other civil services in both countries. No one in Israel but them gets permission to cross the border to visit relatives in a country defined as an enemy state.
The Syrian civil war in recent years has further complicated the issue of the Golan Druze's identity. Some of them support the dictatorial rule of the Assad family, while others identify with the rebel forces. The side they choose could prove to be crucial for some of them. The Druze are a small minority in Syria, and several mass slaughters have already been carried out against them by each of the warring sides.
The Syrian civil war also keeps a political agreement with Israel and a solution to the question of the future of the Golan from being reached. The government in Syria is busy surviving. It has neither the motivation nor the ability to come to a peace agreement with Israel right now. No element in the opposition forces is capable of reaching any such agreement either, and ironically, this perplexing state of affairs allows my father to keep travelling in his beloved Golan, for the time being.
_Grandpa Hillel_
GALILEE MYTH
_by Nili Landesman_
I recently found myself seated on a bus, ready to embark on a four-hour pilgrimage to Tel Chai. Though the two words, "tel" and "chai" mean "mount' and "life" respectively, I have always referred to Tel Chai as the yard of blood – a reconstructed place of worship and myth, for those who see no choice but to live by the sword.
Each year a memorial service is held in Tel Chai to commemorate the eight men and women who died in combat on 1 March 1920 – the story goes that the rest of the defenders withdrew from the battleground, leaving it to be burnt to the ground by the Arab attackers.
Seated at my bedside, my late grandfather, Hillel Landesman, would tell me the story of the immortal hero, Joseph Trumpeldor, commander of the isolated bloc in the upper Galilee Valley. My grandfather was one of the few to survive the battle that fateful day. He passed away in 1973, having never missed the annual memorial service held at the old cemetery, a few kilometres away from the famous courtyard, beneath the giant paws of the Lion of Judah perched atop the grave.
My grandfather was actually in the room when Trumpeldor gave up the ghost. Thirty-five years later, as chairman of the Galilee regional council, he gave a speech in which he stated "a miracle did not happen to us, although it was Purim". He went on to remind those present of the words written by the great Labour leader, Berl Katznelson, in response to an article written by his political opponent, Ze'ev Jabotinski (who had expressed his doubts regarding the necessity of this semi-suicidal act): "The only proof for our right upon our land is in this stubborn and desperate withstanding, without looking back."
That morning was indeed beautiful. Sunshine and raincloud battled overhead, and as I rode the bus I reread the protocol created for the conference held a week before the fall of Tel Chai. In a room full of giant Zionist key figures (such as David Ben-Gurion and Yitzhak Tabenkin), Jabotinski was the only person brave enough to suggest that it would be more responsible to evacuate the defenders. As the politicians argued, the defenders (as they used to call them back then) felt abandoned. Well, you can't argue with the Zionist karma, can you?
That day the guest of honour was the deputy minister of defence, Danny Danon, who had served as head of the Betar movement founded by Jabotinski. The founder had adopted Trumpeldor as the movement's iconic hero. Danon gave the main speech at the cemetery in front of hundreds of kids, members of the youth group, armed with whistles and decorated for Purim. Jabo's name popped up frequently. Did Danon even remember that Jabo's guiding spirit was actually against the whole mess? "We still have so many Trumpeldors," Danon declared loudly, "the settlers of Yehuda and Shomron."
The valley spread out at our feet, and I tried to visualise it under a thick blanket of snow, the way it was back in 1920, quiet, legendary, frightful. A little girl approached the bench where I was seated with my nineteen-year-old son Emanuel. "Is this a cemetery?" she wondered, "Is this a grave?"
When I was her age and lived in the kibbutz that gave shelter to fugitives from Tel Chai, I spent many happy hours in this graveyard. All those mysterious dead relatives made it feel great to be a daughter of the tribe.
Yitzhak, my eighty-four-year-old father, picked us up. The parking lot was packed with rented buses. "Once upon a time," Papa said as we hit the road, "back then in the early Fifties when we were still on top, Ben-Gurion needed to break the resistance for the reparations agreement between Israel and Germany. So he filled twenty-six buses with young, strong _kibbutzniks_ from across the land, armed with clubs. Dad was there with them, enjoying a rare trip to Tel Aviv, the big city, on their way to beat the shit out of the other side – those guys from Betar, asking for trouble, protesting against the agreement in the main square. I was on those buses as a teenager, whenever the peace movement needed mass."
So hard, so sad, that you have to pick a side, especially if you live in a tradition of telling yourself a lie in the name of "truth". The spectacular kibbutz of my youth, Ayelet Hashachar, located a half-hour drive from Tel Chai, is named after the morning star. The story of how fifteen pioneers came up with this poetic name had been told to us many, many times before the lights were turned out. We would be sent to our beds with vivid impressions of that final scene – the hardworking dreamers, after spending the entire night arguing, suggesting and rejecting names, suddenly heard their colleague, the night guard, calling out, "Good morning, friends, the morning star is on the rise, time to get up and work." And they jumped and cried with joy, "We have found a name for ourselves!"
My dad was not one of the favourites when it came to putting us kids to bed. When he was on duty, no one joined us for our evening ceremony. He had no patience for those children's books – they were too long. So he would read one page to us, fast, skipping the next two pages. "They got stuck together," he would say, but I didn't mind. I could read them myself. It was easier to let him go. Yes, he was familiar with that romantic version of the story, but if he were to tell us the true story, how disappointed we would have been. _You want to know the truth? It just happened to be the Arab name of the place – Nijmat el Subach._
It had been so long since I had visited this place, and I took a walk as the sun was setting. Ninety-nine years ago they came here, to the top of this hill, five men and one woman. This hill formed part of the land which – perhaps, perhaps not – once belonged to a small, perhaps large, village, Nijmat el Subach (that's how Dad pronounces it), that was located north-east from here, perhaps an hour's walk or more. Nijmat or "Njmat" (as it called on the Nakba map, which is considered to be a reliable Palestinian source) means "star". "El" means "of the", and so you can easily guess that "Subach" means "morning".
It was getting dark and chilly as I stood staring at the white square houses of the kibbutz. In 1923, they had moved from this original spot to the hill across the way, as the area had become too small. There were no good memories from this place. Life had been unbearable for the six pioneers, and they had had to leave by the end of their first year. Three of them returned, two years later, with more people and supplies. The original structure where I now stood, which exists only in photographs, had served as a house to the settlers and their animals. Now nature had taken over; above me a dark, clouded sky, over a hidden valley and rising mountain. Fields of young wheat stood silently. I could hear the birds in the trees, the frogs in the _vaddi_ (the Arab word for "stream") unloading all their secrets, the wind whispered beneath the sound of my footsteps. When I heard the jackals argue I became a little frightened.
_The Nijmat Settlers_
_Young Papa_
There were no jackals here when I was a part of this broken dream. I had never been afraid to walk alone at night, nor sleep without my parents who were asleep in their own house. You were never alone, whether you were asleep or awake. We ate, played and had showers together, twenty kids well-trained to get along no matter what. When night finally came, you could always wait with anticipation for the moment when all the adults retreated to their lives, leaving us to be wild and crazy.
I couldn't remember the details; my memory was full of darkness. You don't need to remember that, I reminded myself, just focus on the past. There were no trees at all when young grandpa Hillel arrived here, at what is known as the "old Ayelet", on his way to join the defenders under siege in Tel Chai. This was the only resting point in a valley surrounded by Arabs, Bedouins and other tribes. All considered hostile, in our minds nothing more than names – Krad Bagara and Krad Ra'name, Achsaniya.
They had all fled by 1948. We tore these villages apart. Their names, however, were left with us to claim as we liked. Kibbutz Ayelet Hashachar is where the apples, pears and palm groves grow, where the cotton and cornfields can be found. If you spoke the dialect you would know where you were with the help of these Arab names. For us they were no more than waypoints for direction.
The following day, I spotted the morning star just above Krad Ra'name. I arrived at the kibbutz graveyard, so peaceful and beautiful, and as always, so well-kept. A silent place where you could talk as much as you liked. And besides, grandpa Hillel was half deaf. When he fought alongside Trumpeldor and his band of men, grandpa had lost his hearing. Unfortunately, it happened during the crucial fight and this is the story of how he had failed to hold his fire, when the replacing commander had shouted an order to do so.
Grandpa Hillel – every child in the kibbutz called him by this name, but he was most definitely my grandpa – didn't like to fight at all. According to the documents pertaining to the battle, he screwed up. That was his official job whenever things went wrong with the neighbours from differing tribes. Until his last day he held on to his utopia – that we should all learn to live together. If children could handle this, why couldn't the Jews and Arabs? Dad says his father was naïve, no big hero. He never fails to mention that his father didn't live to see the _kibbutzim_ fall from grace. Clearly my dad has had it with this subject. The terrible stories he is rolling around in a glass of whisky – the once upon a time in the kibbutz – are not the kind you wish to tell a child
WE ALL GOT LOST IN THE SAME ANCIENT ALLEYS (VISITING KFAR KAMA)
_by Nadia T Boshnak (Translated by Eilam Wolman)_
If you ask me what makes a thing authentic and unique, I'll tell you – it's the packaging. Uniqueness grows in proportion to how small, humble and personal a thing is.
I'll explain. Picture a corner bookshop, not terribly large, with a plain, unadorned sign. The letter "K" is hardly noticeable anymore – it reads "Boo Store" and no one cares. The humble display window isn't lit at night, but if you pass by it in the day, you'll notice that it changes every few days. On one day, you would find novels there, at some other time autobiographies, on another day it would be children's stories that take you back to your own childhood. It has limited editions and rare books with autographs and personal dedications. If you try to search for it in the last pages of the weekend paper, where all the ads appear, you probably won't find it. It's reserved only for people who know it. The smaller and more personal it is, the more unique it is.
The store you've imagined with me exists somewhere very near you, and the reason you don't know it is because somebody else, probably your neighbour, would like it to remain his "secret bookshop", or his "secret pizzeria", or some other kind of secret.
My village, Kfar Kama, is small and authentic, like the country it's in, like that secret shop in the corner. The country is so complex, the way its troubles come in bundles can be exhausting, but luckily, every evening I return to my village, my home, I understand that as troubled as it is, my country is worth it all. It's a magical place, and many before me have tried to capture that magic in words. But what makes my village special?
It's hard to say exactly. It may be how much all the residents, myself included, share in common, as if we were all raised by the same mother. How unified and pleasant the village is. We're all Circassians – Circassian is our mother tongue, although most of us also learned Hebrew, Arabic and English at a very young age. We're all Muslim; we were all brought up on the same traditional food, the same customs. We all got lost in the same ancient alleys as kids and all swept the street where we grew up at least once, because a great emphasis was always placed on cleanliness in the village. We even all had the same kindergarten teachers, and they are still a part of our lives, and we were all raised on the traditional story of our arrival in the land of Israel:
Our homeland lies near the north Caucasus Mountains, between streams and green fields. After it was conquered by the Russian empire, some of us were exiled to Europe and to the lands of the Mediterranean.
The journey was long and tough, and many didn't survive. At first, we moved to neighbouring Turkey. Although Turkey was Muslim, some of us were transferred to the Balkan countries under its rule designed primarily to defend the borders of the Ottoman Empire. We stayed in the Balkan area for fourteen years until the great uprising began, when some of the Bosnians and Circassians were transferred to Mediterranean countries.
Some of us had come from towns in the Kosovo area, others came from Greece – together we were fifty thousand Circassians who sailed to the Middle East. The sea blustered and a fire started on one of the ships, leaving only seven hundred of the passengers alive. Only when they stood on dry land at the port at Acre in the north of Israel were they willing to believe they had survived. They were Shapsugs, one of the large tribes among the twelve Circassian tribes.
It was the spring of 1878 when we arrived in the land of Israel. A procession of wooden carriages drawn by bulls and horses slowly made its way from the Acre port, quietly crossing the coastal plain and turning east to Jezreel Valley.
The road was scattered with small villages and Bedouin encampments. Everything was new and strange to the immigrants: the inhabitants spoke Arabic, wore kafias and colourful clothes. Further east, overlooking the entire area, stood Mount Tabor, tall and round. The coaches went around the mountain and to the north-east.
Not long afterwards, the man in charge of the procession, who was the Turkish ruler, stopped.
"Ladies and gentleman," he turned to the people in the coaches.
"Here is where you'll be staying for now. Take down your things and sit here, until your permanent residence is determined." The immigrants looked around. The place was barren, desolate, derelict and ruined. Remnants of houses, shrub thickets, miserable-looking cabins.
"How could we settle here?" they asked.
"The place is entirely deserted and ruined; even the animals won't be able to survive here... and in our home country, along the River Afips, there was fresh greenery! It was a beautiful place! A Garden of Eden! How can we move from our paradise to this parched and desolate river?"
After some quiet, desperate moments, they looked at the mountain they had passed. They saw the buds of flowers about to bloom, the emerging green in the fields and the caressing sun above them, portending the oncoming spring.
Without wasting much time, they began to build their home with inspiring mutuality, one house after the other. They put bars in all the windows and erected a tall wall to keep bandits and strangers from penetrating the yards, while retaining the beauty of the black basalt constructions, turning each of the yards, down to the smallest one, into a blooming orchard with a variety of fruit trees and flowers.
Before the streets in Kfar Kama were paved, the denizens would sweep the streets around their houses. Their perception to this day is that a house and the street it is in are inseparable. Organisation and cleanliness are a way of life, and every day you can see many of the village residents taking the time to clean up the streets.
One hundred and forty years have passed since those men, women and children built this little village I live in, along with 3,200 other residents. The children are still being raised on the same values and customs that our forefathers brought from the Caucasus. It seems like nothing has changed since then, apart from the buildings that now have a more modern style. However, the closer you get to the heart of the village, the alleyways get narrower and the architecture slowly changes. Blocks become basalt stones and live wires replace the high, hard walls. A picturesque scene emerges. You don't need to have grown up there to feel the historic atmosphere and to hear the past echoing in the sounds of the children playing, building their own childhood in that old place at that very moment.
In one of the alleys, you will find the fascinating Circassian Museum, run by Zoher Thawcho, where, among other things, you can see a performance of Circassian folk dancing. The village includes many cafés and restaurants where you can taste Circassian delicacies such as pastries, kreplachs, and smoked cheeses.
There is another Circassian village in Israel called Rehaniya, which is in the Upper Galilee (Kfar Kama is located in the Lower Galilee, between the Sea of Galilee and Mount Tabor). The two villages have very close relations. Hundreds of thousands of Circassians are scattered elsewhere around the globe: Turkey, Syria, the United States, Germany, Jordan, and of course, the Caucasus.
HIPPIES
_by Ithamar Handelman-Smith (Translated by Julia Handelman-Smith)_
The hippies are sitting on a bench next to a long, rough-hewn wooden table, the kind you see in Israeli nature reserves. We're sitting in the 1921 pub of Kibbutz Ein Harod Meuhad. The man has a red tilaka between his eyes. His hair is black, long, wavy. Pointy beard. His body long and slender. He is wearing a black knitted top, a short dark leather jacket, a wide black belt, purple gabardine flares, cowboy boots. On his chest, a gigantic silver medallion. The woman, a narrow, brown leather ribbon tied around her broad forehead. Wearing a pinkish sarong. Her hair bright, her eyes bright, her skin transparent – you could see her soul through it. Sahar, my friend, says that all people are transparent and you can see through them.
Sahar is a clever bloke. The way I see it, his wisdom is his obstacle. His abilities of observation and phrasing things, the way he sees and understands the world surrounding him – all of it brings a death wish upon him. One day, I say to him, your wisdom will kill you.
Sahar is fascinated by the medallion on the hippy's chest. The Freemasons, Sahar says, and I don't understand what he's talking about. This is the symbol of the Freemasons. The square and the compasses. I must talk to that hippy, he says, and approaches their table.
We don't speak the same language, but I can understand Sahar. I am urban, lower middle class, the offspring of Holocaust survivors. Something in Sahar's manner of speech testifies to his ancestry, his culture, his roots. He is the son of a kibbutz, an indigenous Israeli. His mum's family stretches back seven generations in the land of Israel. On his father's side, he is the grandson of one of the greatest mythological generals and members of Parliament of the Zionist movement. All the men in his family are high-ranking officers in top combat units. Sahar didn't serve in the army. He never wanted to take part in that story. But his Hebrew gives him away. I was afraid the hippies wouldn't understand him, thinking he was patronising or arrogant, but they said they're going with his flow, man. My brother, said the hippy that introduced himself as Hillel, doesn't have a clue what this medallion stands for. I just love it, man.
The girl, Renana, invited us for a round of Goldstar beer. Fast enough, it became clear that Sahar, Hillel and Renana have a mutual friend, Elifelet, from Beit She'an. Let's go all together to see Elifelet now, Sahar says, he's got something to smoke.
Sahar takes one of the communal kibbutz cars, a white Subaru, and we are driving to Elifelet's. It is the only time in my entire life that I have visited somebody in Beit She'an.
Elifelet looks a lot like Hillel, but he is bigger and broader than him. His hair long, curly, reaching the middle of his back. He is wearing a white Arabic tunic. He's got a didgeridoo in his house, djembe drums, a lute, stuff like that. Indian sitar music is playing in the background. We smoke Lebanese hash at his place, and we listen to different talk of "spirituality".
2.30am, Sahar wants to head back to the kibbutz, and he's offering Hillel and Renana a lift. They need to get to Heftziba. Instead of going on Route 71, we're coming down Route 90, heading south towards Kibbutz Ein HaNetziv, and then we turn right on to Route 669. In the night-time the lorries that pass us look like prehistoric cattle. On our right, the man-made fish pools and on our left, the fig and eucalyptus groves. The car stereo is playing a cd of Creedence Clearwater Revival.
So where do you guys live, anyway, in Heftziba? Sahar is asking Hillel, who sits with Renana in the back seat.
No, only for the time being, until the house we're building will be ready, Hillel says.
And where is that?
Rotem, do you know it? Hillel says.
The road is empty, and Sahar slams the brakes.
What happened? I say. Is everything alright?
Rotem? Sahar repeats, and says, What is that? Where is that? It's in the Jordan Rift Valley, innit? It's beyond the Green Line. It's in the bloody Occupied Territories. It's a settlement, an illegal settlement.
Yes, my brother, but it's an ecological settlement, you know. No ideology or anything. What do I care about politics? I'm all in for peace, man, Hillel says, in a soft, gentle voice, as if there is no subtext, no underlying meaning to the fact that he is building a house in an Israeli settlement.
You are scum, you and your kind, Sahar says. Because of people like you, the worst things in history happened, and you are so stupid and dumb that you can't even understand that, can you? But, _man,_ I am not scum. I will take you home, though I would rather just leave you here, on the side of the road, in the middle of nowhere.
Man, my brother, I'm really sorry that I made you feel blue, Hillel says. But truly, I'm not a right-wing person or anything like that, brother. I just want to live in an ecological, green environment, you know what I mean, man? Isn't that so, Renana?
Renana doesn't say anything.
Two years later, Sahar, aged twenty-six, goes to sleep and never wakes up. The funeral takes place in the kibbutz cemetery. We're heading back to Tel Aviv from the funeral in a friend's car. The Galilee landscape passes the car window through a curtained gaze. We cross the Jezreel Valley. From here, in our current state of matter, Jezreel Valley spreads in front of us and is made out of Lego.
From the car, in the light of the early afternoon, the little houses on the little hills are perceived as toys. The trees are toys. The cars, the clouds, everything made out of Lego. My girlfriend is staring at the clouds above Mount Gilboa and says, look, you could see the world moving.
What Jezreel Valley used to be for us has fallen and smashed to smithereens that gather in the billowing haze. And then, out of nowhere, come the horses; white and big, grazing The horses that are only puppets of horses.
THE RELUCTANT HOTELIERS: THE SCOTTISH HOTEL IN TIBERIAS
_by Julia Handelman-Smith_
When visiting my husband's family in Tiberias for Passover, a colleague urged me to stay at the Scots Hostel. Having lived in Israel for a few years, I had grown used to staying in many of the Holy Land's Christian hostels. Most of them offer simple, tranquil accommodation in some of the most historic locations. In this case, I must have missed the absent "s" and was quite unprepared for the experience.
What awaited us was Israel's 2008 Boutique Hotel of the Year. Situated on the bank of the Sea of Galilee, we were led through idyllic gardens to a large, cool room in the Doctor's House, one of the three original buildings of classic honey-coloured stone of the mid-nineteenth-century Ottoman Empire.
There seems to be little to connect this Middle Eastern paradise to Scotland apart from the Scottish flag flying from the garden tower and the odd bit of tartan in the hotel's Ceilidh Bar. However, the Scots Hotel started out as the Scottish Hospital, founded by Dr David Watt Torrance in 1894, and formed part of the Church of Scotland's extended mission in the Holy Land. The complex served as a fully functioning hospital, treating patients from as far away as Damascus, right up until the fledgling Israeli state opened its first hospital in the region in 1959.
Following that, the complex became a Christian guesthouse, offering accommodation for Christian visitors to the iconic sites of the Galilee, much like its sister institution in Jerusalem. However, come the late Nineties the buildings were crumbling and the meagre hostel fees stood no chance of covering the cost of its upkeep.
And so, after existing gracefully through Ottoman rule, Jewish settlement, Israeli independence and the subsequent Arab-Jewish wars, the Scottish mission in Tiberias entered into its most turbulent times when a £13million investment was approved for a boutique hotel. There are still those both within and outside the Church of Scotland that fervently oppose its ownership of a luxury hotel that primarily serves a wealthy Jewish clientele. Whilst the hotel does much to support local charities by providing reduced rates to local Christian groups and supporting the Church of Scotland's mission in the north of Israel, it seems that it has yet to fulfil its promise of providing revenues for the Church's wider mission overseas. The hotel hit the headlines once again last year as investment was approved for a wellness centre to keep up with the Joneses in the luxury hotel market. Many in the Church of Scotland feel that this business concern in Israel's territory is compromising its decisions in relation to the wider Israel-Palestine debate and missions.
However, any of us who have spent any time in the Holy Land understand that it doesn't take a luxury hotel to force you into the realm of compromise. Religious missions in the Holy Land started to make compromises from the moment they arrive, and I can't help feeling that the real and concrete challenges of running a viable business in Israel could only make the Church stronger in its understanding of the Galilee and its communities. As social enterprise becomes the new buzzword, I sense that the Church will become more comfortable with its luxury hotel.
Easter morning falls during Passover, and we wandered across the road to the small Scottish church for the Easter service. This is very much off-season for the Galilee – serious pilgrims are in Jerusalem – and so there were five of us, including the minister and his wife. This did not deter the enthusiastic and welcoming minister from demanding full participation.
For the guidebook part, the place is paradise. The gardens approach the biblical as you wander through pomegranate and hibiscus groves. The rooms are airy, cool and luxurious. The staff is diverse, and exceptionally welcoming and helpful. The breakfast is non-kosher and divine.
As I dropped a meagre twenty shekels into the offering plate in the Church, I thought about the two hundred quid I'd blown on our accommodation and realised it's the largest single contribution I've ever made to the Church. If you're weary after a series of worthy but basic hostels in the Holy Land, give yourself a treat – you will be supporting one of the few inclusive and politically neutral enterprises in the Galilee, and you'll have a wonderful time.
BETWEEN THREE NORTHERN CITIES
_by Ron Levy-Arie_
HAIFA: CAPITAL OF THE NORTH
Haifa is an interesting place. Well, for me as a person growing up on the dirty pavements of Tel Aviv, Haifa was not really love at first sight. It is unique and sometimes boring, multicultural yet slightly divided, outstandingly beautiful but grim, new mixed with ancient – it is the "Capital of the North", only an hour away from Tel Aviv, yet still it is a place with its own special character. A few months ago, we went to hang my wife's artworks at a gallery of our friends called HaMirpeset, meaning the veranda or the porch. We drove that same evening through one of the most casual residential streets in the middle of town on our way to the Hadar neighbourhood – when suddenly we saw a nine-hundred-pound wild boar crossing the road. We closed the car's windows, pressed the gas pedal hard, and drove away from the spot with great panic mixed with excitement. We turned on the radio to hear if there were any reports of a boar running wild with vengeance in the rural streets of Haifa – but there were none. We made it to the gallery and started telling our friends of our brave encounter with that big, fat beast, expecting to hear them praise us for our courageous experience – but they were as apathetic about it as if you told a New Yorker that you saw a squirrel in Central Park. Giving us the classic: "Oh, we get it all the time" – Haifa folks are special.
On the art front, Haifa does not stop surprising, with more and more artists appearing in several fields, like the crew of street artists that go by the name of Broken Fingaz. This crew pretty much reinvented Haifa in the mid-Noughties. They started out as a crew of graffiti artists who covered the inner streets of Haifa with their own special touch. Their favourite topics and imagery are big fat yellow men, sexual scenes between horny skeletons and seductive pink and purplish women, a touch of occult symbology, American billboards aesthetics and, yeah, wild boars and beasts. The crew widened its activity to being party promoters, fashion designers, musicians and DJs, and nowadays members of the Broken Fingaz extended family have shows, exhibitions and art displays worldwide. There are also bands like 3421, artists like Tant, Unga, Kip & Deso, and the talented Miss Red, who tours with uk producer The Bug. Not forgetting Easy, who are artists, MCs, a soundsystem and more. You can say that this scene today mainly revolves around HaMirpeset
Hadar was a proper downtown kind of place, with junkies and a poor population of shady characters and other _les misérables_. The place bloomed in the Sixties, but somehow it had been forgotten until the people from HaMirpeset came and started doing art exhibitions, parties, live shows and happenings, and rejuvenated the place. Actually, Hadar is right down below a street called Masada, which is known as the "young people" street in Haifa, with hipster cafés and some great early works by Broken Fingaz covering some of the walls.
Now the question many people ask is: Why Haifa? (And there are a lot more artists apart from the shortlist above.) Some claim that the main talent competition is between Jerusalem and Tel Aviv. There is an old saying in Hebrew, "two quarrel, and the third wins" – and Haifa is obviously the third in this equation. People also attribute the special character of Haifa to the chemical refinery chimneys that pollute the air of this beautiful town located on Mount Carmel, overlooking the tranquil Mediterranean Sea. Or maybe it's because Haifa is a natural cosmopolitan place with Muslims, Christians, Jews and members of the Bahá'i religion living side by side in a sort of harmony.
Haifa was originally a "workers' town", with people working at the Haifa Harbour (which is still the main harbour in Israel) and in different factories in the city, and maybe there are still relics here of its old socialist atmosphere that makes people more inclined towards sharing and caring. You genuinely feel it – Haifa is less standoffish than Tel Aviv, maybe because people in Haifa don't try to constantly convince themselves that they live in the centre of the world, a feeling that Tel Avivians tend to have slightly too much. Therefore, Haifa is blessed with a certain humbleness – pretty much the opposite to Tel Aviv's arrogance.
And if I have to sum it up, and if you're already in the northern part of Israel – Haifa is a must. It's easy to get to – about an hour train ride from Tel Aviv. The train station is located at the foot of the mountain on which Haifa is built. There is the lower city (in Hebrew, "Hair HaTachtit"), with all the authentic restaurants you can find – some wonderful Arab restaurants and shawarma places. As you climb up you'll see the Bahá'i Temple, surrounded by the most beautifully attended gardens – you might even say that it is the Israeli version of the Taj Mahal. The Bahá'i are really cool people – the faith originated in Persia and it feels like a harmonious, monotheistic mix of Islam and Hinduism. You can also take a grand tour of the Temple before 4pm. The Haifa Museum of Art, with its changing exhibitions, is also worth checking out. You'll find some more galleries downtown, because they keep opening up. In addition, if you want some live indie shows, the hottest place right now is Syrup, which has a vibrant scene on the rise with many live performances coming from Tel Aviv merged with bands from the local scene – imagine that Tel Aviv is the village-sized version of London and Haifa is like Manchester in her glory years. Moreover, if Haifa's city life is getting too intense and you wish to wash off your hangover at the beach, you can always go to Hof Hakshatot, south of Hof Hacarmel.
AKKO: CITY OF MANY LAYERS
Akko (or in English, Acre), like Jerusalem, is a city of many layers, both historically and culturally speaking.
Historically, the city offers a glimpse of the cave of the crusaders, otherwise known as the Templars' Tunnel. It's always fascinating to think about what is underneath the surface of a place and penetrate this underworld for a better understanding of the city as a whole. Like in Paris, where you have the catacombs, and under Jerusalem, where you can take a tour of the chain of caves that are dug under the Old City, Akko has its own set of caves to be proud of. The tunnels' restoration started in 1994, and they were only opened to the public relatively recently in 2007 – and they are really worth a visit.
The old market is also an enchanting place, where you can see all the herbs and spices from the Galilee Mountains and fish that you can only get up north. The hummus that you find in the heart of the market at Sa'eed is considered to be some of the best in the whole country, and the stall is open only until noon. It is like heaven for hummus fanatics – creamy like Italian mascarpone and hardly spiced with any extras, a real treat for foodies. When you finish licking your fingers and you feel like having a dessert, don't you dare miss the cnaff'e available around the corner – it's an ultra-sweet delight made with the tiniest macaroni and special goat's cheese sweetened with aromatic sugar waters. Have that with some fine Arabic coffee and you're the happiest camper alive.
_Entrance to the Echo Chamber_
_Tsfat cheese_
_The Hebrew calendar on a wall in the Old City_
In English they call the city Acre for some reason; we just call the place Akko, and please do the same when you get to Israel. It has been around for a good four thousand years, so when it comes to history, it's the place to go. If you're into early Christianity, Roman and Greek history, Jewish history from the rabbinical perspective, crusaders, early Islam or Napoleon Bonaparte you should never think about skipping Akko.
One of the city's main attractions is the annual Israel Fringe Festival. Imagine all these twelfth-century buildings with heavy stones and arches filled with the most cutting-edge and obscure yet tasteful live theatre, and hundreds of performers filling the ancient streets of the city, with actors and shows from across the country and worldwide. The festival usually takes place in September, but it is best to check online. Many of the shows are co-productions between the local community and directors and different artists from varying performance fields, which can create fascinating combinations and even helps to build a cultural bridge that binds the many gaps we tend to have in Israeli society. The Festival started in 1980, and you might say that now it's one of the most important cultural attractions in the country. But if the Festival is not on when you visit, then there is the Akko Theatre Centre, established in 1985, which has a fully active year-round artistic programme that intermingles Arab and Israeli artists with off-centre plays and postmodern theatre – things that are even hard to find in Tel Aviv.
There's also a very famous restaurant called Uri Buri that is considered one of the finest fish restaurants in the country – it is best to book a table before, since the place is always jam-packed. They know what they are worth, and it might not be the cheapest experience, but it is certainly worth it. Akko in a way is like being in Jerusalem with a sea, which maybe is the greatest difference that there could be – Jerusalem is a mystical fortress surrounded by mountains, but you can't throw a fisherman's net and catch your dinner. Akko is in the middle of the Mediterranean Sea, and the sea breeze balances it and makes it a more peaceful place – I guess that geography affects people and their political agenda. Let's not forget that throughout the years Akko has been conquered by any conqueror worth his salt. But after years of wars, bloodshed and conquest, Akko can now start moving towards a better future.
TVERYAH: THE GOSPEL ROAD
Let's face it, Tiberias (or as we say in Israel, "Tveryah") is a has-been kind of town – a town with a glorious past and an uncertain future. But the setting is a killer when it comes to beauty. It's a dozy little town on the banks of the Sea of Galilee. But when saying "Sea", let's tell the honest truth, it's not really a sea – it's a medium-sized lake, or a very small one compared to Lake Michigan, that is the source of most of the drinking water in Israel.
Today's Tveryah has a highly orthodox Jewish population living in a place that was once a great tourist attraction. A few decades ago, Tveryah was a popular tourist destination for both local and international holidaymakers that gave them the full "Israeli experience" – holy places, a beach and fried fish. In other words, an awkward combination of Jerusalem and Palm Springs. Tveryah is one of the four holy cities of Judaism. It was the place where the _Mishna_ was written (one of the most significant texts in Jewish studies) and where the Sanhedrin (the Jewish court of law) was formed back in the third century. It is also home to many tombs of the main figures of the Jewish world, like those of the "Rambam", Rabbi Mei'r Baal Ha'nes, and others. People gather from all over the world to pray to the tombs while lighting a candle for their virgin daughter or for better welfare for their family, for health, strength and encouragement. Some call it "Jewish voodoo", and some say it's just part of the tradition.
_Yirmiyahu and me_
_So where does all the magic happen?_
_Rabbi Yosef Karo Synagog_
Tveryah is also the cradle of Christianity, the dwelling place of Jesus Christ and his disciples. Here is where he fed the five thousand with only five loaves of bread and two fish – and don't you dare call JC stingy, because back in the day it was the best meal in town. My wife and I went to the very church where it is written to have taken place, which is called Tabgha, a very modest chapel compared to the spectacular churches you'll find in Jerusalem. It's pretty much a souvenir shop with a designed fountain at the entrance with a few huge Chinese goldfish swimming in it. Funny thing is that the fish were the friendliest fish that we had ever met. They were as friendly as poodles. One particular fish was so friendly, he kept getting his little fish nose out of the water wanting us to pet him as if he was a little dolphin. I imagine that if all the fish had acted this way before the feeding of the five thousand, probably most of the folks would have said, "Let's skip the fish; I'll do just fine with a piece of bread. You know what, skip the bread – I'll give it to the fish, he seems kinda hungry." The beautiful thing about this church specifically is that the interior is quite minimalistic. In the stained-glass artworks in most churches one finds mainly figurative imagery, but in Tabgha it's all abstract, and its illuminated wall decorations can seem like clouds, mist, smoke, judgment day or a Rorschach test. And that raises some questions about the divine deity. These images don't show the story of the feeding of the five thousand – it's as if they're saying: "Everything is open to interpretation."
If you came all the way to Tveryah to grasp some of the living history of JC in order to get some spirituality, you might find it between a gift shop and abstract stained glass windows in a humble church, and I kinda like that concept. I asked the housekeeper at Tabgha if she knows a way to get to the seashore from the church. She said, "Yeah, just walk up the road to the hidden fountain." We took the car, and I guess it was so hidden that we missed it (it's supposed to be a nice place, though). Instead, we found ourselves walking in a beautiful grove leading us to the sea. I said to my wife, "It reminds me of northern Jamaica." Apparently, it was St Peter's church. It is truly a peaceful place with access to the seashore, or lakeshore to be exact. We spent some time there reflecting.
As I looked over my shoulder, still wondering if I was in Jamaica for a moment, I saw a Rastaman walking with a group of pilgrims. I approached him and greeted him. He kindly answered me and a fascinating conversation developed. He was originally from Jamaica and we had many mutual friends and acquaintances, so we both started shooting the breeze in patois. He was a singer-songwriter and wrote a very famous song, and other songs by him are collector's items. I hooked him up with a music producer from Tzfat and felt there was something mystical about how these things came together, and how people from different cultures can find a common language after all on the banks of the Sea of Galilee.
_The Rastaman_
_Hungry fish at Tabgha_
## PART FOUR: NEGEB
_(Negeb, or Timna, is the southern desert, meaning "south" in ancient Hebrew. Janub in Arabic.)_
A PATCHWORK CITY – THE STORY OF BEERSHEBA
_by David Sorotzkin (Translated by Eilam Wolman)_
How might one define Beersheba? A patchwork city. Like a jigsaw puzzle full of negative spaces that were gradually filled by parts of other puzzles, made of dozens of other puzzles. An urban jumble shaped primarily by a disinclination to remember, the desire to obliterate at any cost, with the residents seeming to move through the town's different parts out of a persistent, insatiable flight instinct.
Modern Beersheba was built in the beginning of the twentieth century as an Ottoman county town with a modern grid structure. Wide, crisscrossing streets of Arabian-style houses made of yellow desert sandstone, with arched windows, courtyards, and extensive entrances. The city was meant to assist the Turkish – and later the British – authorities in supervising over the Bedouin population, which stretched over the entire Negev and was uneager to submit to the rule of any central administration.
In the early Fifties, the Zionist leadership of Beersheba adopted an urban plan called the garden city movement, a blueprint for working-class cities conceived at the end of the nineteenth century by philosopher Ebenezer Howard and adopted both throughout various cities around the world and in Israel. This plan divided Beersheba into neighbourhoods with large open spaces between them. Every neighbourhood was meant to provide for its own needs. In each one, an urban centre was set up with shops, kiosks, and in some cases, a movie theatre. The original plan was for green vegetation to grow all over the neighbourhoods.
The consensus is that the garden city plan has failed. The neighbourhood gardens remain barren. The wide stretches between each section became wastelands crossing the geometric neighbourhoods. The neighbourhoods were filled with working-class homes, inhabited mostly by Oriental Jews, and built in line with the visions of socialist construction characteristic of Israel in its first decades. Public housing projects, or "blocks", as we called them, with tiny units for the emerging Israeli proletariat, made up of new immigrants. With these engineered urban spaces, the ruling party controlled the peripheries from its Tel Aviv and Jerusalem offices.
The new neighbourhoods sprung up north of the original Turkish centre, called the Old City for the stark contrast between its housing style and that of the more recent architectural projects. The immense empty spaces between the neighbourhoods were quickly overrun with insects, turtles and porcupines. As a child, I would come down from our apartment building and follow swarms of beetles and worms around for hours on end.
The planning of Beersheba was the old elite's response to a conflict with the local Bedouin population. In a different way, it was also a response to a conflict with the new, mostly north African immigrants. David Tuviyahu, Beersheba's first mayor, gave the city its character, and renowned architect and city planner Arieh Sharon drafted its urban outline. The new neighbourhoods were built as an antithesis to the Old City, which represented the Arabic and Levantine elements that the new Israelis of the Fifties and Sixties wished to distance themselves from.
Until the end of the Eighties, the Old City functioned as Downtown Beersheba, the floundering shopping area where everything was sold from haberdashery and food to clothes and hats. From the early Eighties onwards it was badly neglected, and after an abortive attempt to develop and make it into an artists' quarter – an initiative that resembled such restoration programs as in Jaffa, Acre and other Arabic towns – the Old City sank into decay. The Jewish population, which consisted mostly of Orthodox and other observant groups, was forsaking it for newer neighbourhoods and other cities: Bnei Brak, Ashdod and Jerusalem.
During the Nineties, with the collapse of many of the city's older businesses, the state began settling Palestinian collaborators from the occupied territories in the Old City, and it was soon filled with brothels, gambling houses, junkies and migrant workers. In recent years, there's been a change of direction. The Arabian architectural style became an attraction. The Old City is in great demand. Assets are few and prices are rising. Beersheba is giving students property tax discounts so that they would settle in the area, and various associations devoted to "Jewifying" the Negev and the Galilee are acquiring houses in it.
As early as Jewish Beersheba's first decades, Bedouin presence was distanced from the Old City as part of the subjugation and Jewification of the territory. Many transformations were imposed on the traditional Bedouin markets, which included livestock, clothes and rug markets, in order to distance them from the Jewish areas. At the level of regional geographic and demographic planning, the Bedouins, who dominated the entire Negev up until 1948, were now concentrated in a narrow geographic triangle – like the Pale of Settlement designated for Jews in imperial Russia – between Beit Kama, Arad and Dimona. The Bedouins' land was confiscated by the state, which to this day continues to claim there is no proof that it belonged to them. The Bedouins themselves were forced into semi-desolate permanent settlements and entirely desolate piratic settlements without water or electricity. Being a very non-compliant group with an aversion to authority, some of them have turned to the twilight zone of protection businesses, burglary, drugs and "illegal" – at least in the eyes of the state – settlement.
As a child, my father would take me to Bedouin areas that were still somewhere between nomadic tent encampments and temporary settlements of rickety tin shacks. The head of the family would sit in the central tent and receive his guests. During each visit, I would straddle one of the donkeys and journey the endless, open territory with a wooden rod in my hand. I'll never forget these jaunts, the evening light, the desert soil spreading everywhere in yellow-brown colours. Meanwhile a lamb would be slaughtered, and blood came flowing from its neck in a long, black stream. Two hours later, we would feast on the wonderful Bedouin mansaf in the tent – slices of lamb and rye served on a bed of thin pittas.
During that period, the late Seventies and early Eighties, the remaining migrating Bedouins settled in the outskirts of Beersheba's then-nascent southern industrial area, with the paradoxical name Emek Sara ("The Valley of Sarah") – perhaps the same desert to which Hagar, according to the biblical story, fled from her mistress Sarah. Today, many of them are still living in impoverishment, in what the state calls "illegal settlements", between this area and where most of Israel's chemical waste is handled, south of industrial area Ramat Hovav. Every time rockets from Gaza are fired at Israel, some are intercepted above the skies of the familiar cities, and some are allowed to fall in "open areas". Only recently, two Bedouin men, two girls and a baby were mortally wounded following such falls in "open areas". The state insists that it will continue to refrain from shielding unrecognised settlements.
The new neighbourhoods of Beersheba were given the names of Hebrew letters: Neighbourhood Alef (A), followed by Beit (B), Gimmel (C), Dalet (D) and so on. Shikun Darom (south housing) was erected on the ruins of a transit camp south of the Old City. Shikun Darom, and Beersheba's northernmost neighbourhood, Dalet, became the roughest neighbourhoods in town. In the Seventies and Eighties, Dalet Tsafon (north) Neighbourhood, which we called "North Dallas", was known as one of the roughest neighbourhoods in Israel. Hordes of junkies hung around there, and grenades casually tossed into balconies were a common sight. We would meet the neighbourhood youth around the pubs of the Old City. Some of them kept razorblade halves under their tongues, which they would draw during brawls to carve "lines" in their adversaries: the lifetime memento of a long and ugly gash.
Between these two neighbourhoods, new ones were being built, which later came to be perceived in the local bourgeois jargon as "islands of sanity". The first among them, built in the early Sixties, was Hei Ledugma, modelled on the Carpet Settlement, which consisted of single-floor patios connected to each other by paths. Next to it was the "quarter kilometre block", inspired by Le Corbusier, which became a hotbed of crime and drugs. Contrary to plan, the socialist housing of Hei Ledugma became an attraction for the sated Beersheba bourgeoisie. More bourgeois neighbourhoods were built in the following decades, such as Rasco City near the Old City in the south, and Vilot Metsada ("Masada Villas") up north, not far from the crime scenes of Dalet.
Following the founding of these neighbourhoods, the middle class began leaving in droves for satellite settlements Omer, Lehavim and Meitar, homogeneous villa suburbs that provided their residents with high living standards and, most importantly, distanced them from the rest of the Beersheba population and their derelict houses. By the beginning of the Nineties, Beersheba consisted of neighbourhood islands, each surrounded by the wilderness of the collapsed Garden City: the carcass of a socialist vision that never took shape.
In 1972, after a number of setbacks, the current Beersheba City Hall building was erected near the centre of town, on the main road that crosses the length of the city. A flat cement structure engraved with horizontal lines that veil narrow windows, with a tall tower from its front to its left reminiscent of the torch held aloft by Lady Liberty, City Hall is located next to what was once Cinema Keren – Beersheba's largest auditorium, built in the Fifties and demolished in the Nineties – and not far from Beit Ha'am ("House of the People"). Both were quality modernist structures, singular in the city, inclined with straight, clean lines. Beit Ha'am, similar to the Culture Palace in Tel Aviv but smaller, was home to the Beersheba Theatre, where various films played every afternoon. My father was among the theatre's founders, and as a child I saw many movies there. One of them was _Planet of the Apes_ , and its final scene is etched in my mind forever. Charlton Heston standing on the beach, facing what's left of the head and torch of the Statue of Liberty as it is being submerged by the sand. His hope to flee the doomed planet crashes before his eyes. The place from which he'd hoped to escape is the very place he aspired to reach. The freedom of the future is engulfed in the sands of the past. In various stages of my tangled relationship with Beersheba, my plans to escape it alongside its reappearance at the edge of my life's tunnel, I had similar feelings towards the city; as if my future was leading nowhere but to the past, in ideal cyclic motion which resembles the idea of Chris Marker's featurette _La Jetée_.
During my early childhood, my father was Beersheba's deputy mayor. I spent many hours in the municipal building where his office was. As a small child, I walked around the straight and dark hallways made of bricks and concrete, charmed by the mysterious structure and its insinuated secrets. One day, as I was walking down one of the hallways, a man suddenly appeared and drew a handkerchief out of nowhere. The handkerchief in his hand quickly became a rabbit, and immediately afterwards he laid it on my hand and pulled it again, leaving in its wake many pieces of a spongy substance that miraculously reassembled into one complete sponge. It was Meir Buyom, the legendary magician of Beersheba, who worked in maintenance at the City Hall during the day and concocted his magic tricks by night. Spellbound, I began following him around in all of my many visits to City Hall until I became his shadow.
In my childhood memories, Buyom's magic merged with the municipal offices' dim corridors, leading into each other as in an ideal rectangular prison, going around and around, and with the no-man's-land of Garden City that surrounds the City Hall, barren areas where the desert left its bite marks. Neighbourhoods and desert, round and round. And beyond this, virginal industrial areas divided by mixtures of tin shacks and Bedouin tent encampments. If man is "nothing but the image of his native landscape", such are my landscapes and images: cement mixing with tin and sand, and the primal, suffocating pain.
The stages of maturation and disillusionment from the enchanted realms of childhood resemble the processes of rationalisation circumscribed by Max Weber with the term "the iron cage". Initial enchantment is followed by the "saint's cloak" of strict rules, and then by the "iron cage", which is made lengthwise and crosswise, just like the city, and which encases our lives with a grip of steel. In this journey, we abandon the enchanted days of childhood, in which we've been poured into the world, and become barren structures ourselves. Most of us still remain trapped in an early sphere where the magic cycle that surrounded us is enclosed by square and rectangular cage structures. The faraway dream remains trapped in a shell which itself became a dream. Open spaces between heatwave, stricken tenement islands. The indigested remains of our real, severed lives, surrounded by barbed wire fences.
With the collapse of the Soviet bloc and the wave of Russian immigration to Israel, the face of Beersheba was transformed completely. A "development momentum" was set in motion to settle the tens of thousands of new olim (immigrants to Israel). This was mixed with intersections of capital and power, as well as more than a dash of contractor interests. The empty spaces that remained from the Garden City skeleton were quickly occupied with high-rises. Gardens were wiped out, old buildings were demolished and the residents seemed relieved to finally see the mound of memories from the city that never was sinking into oblivion.
Anyone who enters Beersheba now would hardly recognise the city it used to be. Patches over patches of precariously and incidentally related structures, meant only to fill empty urban spaces, and perhaps a large void felt by the residents. The development momentum which suffocated the city also eliminated its urban centres. From the end of the Eighties, shopping malls were built in their stead, and more recently shopping centres have opened in the eastern outskirts of town as well, near the old road to Hebron. The residents work, sleep and shop, because that's what there is to do in Beersheba, just let life pass; in the Israeli periphery at the turn of the twenty-first century, in the rubble of our childhood, in the ruins of our primordial Garden City.
ISRAELI TEXTILE – THE MORNING KITAN FACTORY IN DIMONA WAS CLOSED
_by Roy "Chicky" Arad (Translated by Ithamar Handelman-Smith)_
Hananiah Ohayon, who worked at the factory for thirty-two years,
The union chairman,
On the other side of the fence, beyond the gate,
Wearing a dark green tracksuit and a black kippah,
He refuses to open
Neither for me nor for anyone else. The rusty lock is wrapped on the gate.
Orange cardboard signs spelling "let us finish with dignity" on its side
And a garden of dying hibiscus.
"It's a disgrace," he tells me,
"The management has sent us a tabulation
I've got nothing to lose,
There will be blood."
Yesterday,
When he realised that everyone is getting fired, he locked himself inside
The factory
And slept there with four co-workers.
They were the last ones to stay and fight.
He slept in the guarding booth where he used to work, The other four slept in inner rooms
Where it's warmer.
When it was freezing in the morning, they burned some charcoal for heat.
He tells me
That they are demanding to be compensated
For 170% of their wage,
Like it was in Kitan Nazareth,
But they are willing to compromise on 150%.
The company is only willing to give them 120%.
We're only talking about fifteen employees on the payroll And the monetary difference of a few hundred thousand shekels
But for that the employees it's a matter of principle,
A matter of pride,
Anything less than 150% and we're like slaves.
It is a pride that sparkled too late,
After years of being put down,
After years of pay cuts,
After years of sacking and sacking and sacking,
After years of silence,
Years of letting them walk all over
You.
"I was once a sportsman
I was a footballer in Hapoel Ofakim. I was a chief mechanical engineer.
I became a cripple because of work,
And I've been guarding the entrance ever since."
Jenya Sulver,
Twenty-two years in the factory. Quality control.
Began working within a month of immigrating to Israel from Ukraine.
"Straight to Dimona,
Straight to Kitan factory
It was hard from the beginning, but I loved the factory.
But I loved the people
I never thought they'd treat me like
That.
A year ago they labelled me "employee of the year" in _Yedioth Ahronoth_ newspaper.
There was a photo of me then in
_Yedioth Ahronoth_.
When there were thirty-six employees left,
They said that we were the best.
What do we want?
We only want to be let go in a respectful manner."
The factory is at 1 Herzel Street, Dimona
It was purchased a few years ago, by Len Blavatnik.
Though the workers aren't at all sure
If Len Blavatnik is still the owner.
"He's in the USA,
He didn't even send us any of his representatives,"
Says Jenya. She's fifty-seven years old. "We've never seen him.
"When we asked the CEO to put us in touch with the representatives,
She said 'I am the representatives'."
Jenya's daughter, Yelena, is a secretary at a law firm.
She is dressed elegantly
And has come to ensure that her mother
Doesn't immolate herself,
Which Jenya has threatened to do here and there.
The fence is barricaded by tires.
Moisture of gasoline has already been cast upon them And it blackens even further the black colour of the tires.
"I'm proud of my mother," says the daughter,
"Some people only talk but are afraid to fight.
My mother knows no other life than working at the Kitan factory,
She's not here only for the sake of it."
"The management that was hired doesn't care about textile, only figures,"
Says Jenya, "From the first day that the new ceo set foot here,
There has been a bad luck in the factory.
They told us that they'll only cut a little bit here
And things would get better.
These days everything is manufactured in China or Turkey.
They ship it in containers
And then brandit Kitan
What do I want?
Well, I'm just looking for a respectful way to close the factory."
I ask her about the general elections next month and she replies:
"Netanyahu and Lieberman are a strong couple.
Everything they say about Lieberman is wrong.
Everything they say about him is because they are afraid of him.
He's trustworthy and takes care of the people.
He'd come to this factory if it weren't for those
Troubles he is having."
And then the mayor arrives.
He's about to leave his office soon,
And become a member of parliament in a party led by a former TV star
And columnist, the son of another former member of parliament,
Columnist and TV star as well.
The mayor also blames the factory's CEO,
He has a soothing and pleasant voice,
"I told you so. I told that this girl always wanted
To close this factory."
The mayor calls the chairman of the Histadrut, Israel's biggest trade union,
Hananiah complains he hasn't shown enough support.
Afterwards the mayor says "I've spoken With the
Chairman of the Histadrut."
Because they let the mayor into the factory
They let me in as well
Accidently, we're both a bit early.
The mayor's advisor is wearing a black suede jacket similar to the
One that I've got at home, though his jacket is cleaner.
And All the buttons are intact.
The factory is full of old posters:
A model partially covered by a blanket tagged with the slogan:
"Kitan – Get in bed with the real thing."
The model's leg has an odd tattoo.
A newspaper article announces the factory's closure.
It is glued to the wall with heaps of scotch tape
That creates a big transparent cross on the wall of Kitan.
"Those greedy pigs don't want to pay you a fair share," the mayor tells the employees.
"Greedy bastards", says Ohayon "and we were naïve,
To allow them to sack so many people."
Hananiah Ohayon stands at the parking lot, A broken textile hero,
A shiny tear runs down his cheek
And curls along the side of his nose,
When Armand Lankari arrives at the scene,
He is the leader of the Dead Sea factories union,
And the chairman of the local branch of the Likud party, He is wearing a fancy watch and a pair of Prada sunglasses.
Arrives the deputy mayor, who is also responsible for the City's welfare, with golden Ralph Lauren embroidery
On her jacket.
As I try and photograph the employees with my cellular phone,
The deputy mayor jumps into the frame with her Ralph
Lauren and hugs
One of them. "I too am Kitan Dimona," she says.
"Unfortunately," the mayor says, "I already told the employees two years
Ago to prepare for bad days.
The workers were too naïve and didn't realise
That they were up against
Cynics."
The mayor's advisor whispers to Hananiah
To start burning the tires now,
As the mayor is here
And then needs to move on.
But Hananiah refuses. They were aiming to start at 10 o'clock.
There's another one hour and a half. The mayor arrived too early.
I start a conversation with Nissim Nagouker, sixty-one years old. He
Became deaf in the factory due to years of noisy machinery.
Nissim, an emigrant from India, worked in the factory forty-three years
But it's hard for us to talk, he can't hear
My questions and replies with irrelevant answers.
His name is written on a sign in the parking lot.
Inside the factory there's also Abraham Avishar, sixty-two years old.
"I'm new here," he says jokingly
"I've only been working here for the last eleven-and-a-half years
So I'm second-class kind of employee.
Paid by the hour on minimum wages.
But I was lucky to get overtime for working on Saturdays."
He says. Apparently, he often protested about being a second Class employee,
But he's not complaining anymore. Anyway everybody is fucked
They're going to sack them all, be it first or second class of Employees.
He used to operate a forklift but injured his back,
So then he was put on a guard duty.
"I can't stand seeing more employees
Leaving the factory with tears in their eyes.
At my age, what are my chances getting out of here
And compete with young kids who just got out of the army?
If I'm not willing to work on holidays
They'll say 'Go, it doesn't suit us.' And I have sons in the army.
"Kitan just opened twenty-two new stores. They've got money.
A father can't buy himself a few villas before feeding his kids," says
Tzipi Hayon who has been sacked six months ago and she's proud
To have discovered the compensation pay at Kitan Nazareth.
She is the one who have brought the one hundred and seventy,
The woman who brought the one hundred and seventy.
Jenya recalls the day the factory had one-thousand-two-hundred employees
"Some came from Dimona, some from Hebron," she says
"We had a good life
We knew how to squeeze the good life out of our small salaries.
Right?
Didn't we have fun? Weren't we always happy?"
And Hananiah recalls the holiday breaks to Eilat.
"We're on the fringe, nobody cares about us,
This is why nobody is coming
Because we're not the doctors
Or employees of the Dead Sea factories," says Hananiah Ohayon.
Armand from the Dead Sea factories is offended
And offers to bus over eighty of his own employees to show support.
But also says that they need to do it right and agree on the time.
"Where is the minister of the periphery?
All they ever did for us is close down the factories," says Hananiah.
We approach the deputy of Human Resources
Who was somehow able to sneak into the building despite the employee's
Siege.
Hananiah says that he must have cut through the fence.
Walking Kitan's yard, a ghost factory.
Useless buildings, a gigantic plastic bag that is carried by the wind.
But the deputy hr's office appears to be tidy
And even a secretary is here somehow.
When the deputy sees the reporters he turns pale and says, "No comment."
Behind him, framed certificates and qualifications bearing his name,
And on his side, a wall covered with a photograph of textile workers.
It's a black-and-white photo but not the black-and-white of the outside
But the black-and-white of a Photoshop.
Armand Lankri, a gentleman with a moustache,
He could have a bit of Hollywood look, if he had a gun on his side,
He takes the deputy aside for a private conversation.
He knows everybody.
Later on, when we're back at the mess,
Lankri tells us that the Dead Sea factories workers bought every year
Kitan's products in order to support the factory's workers, "Every year Kitan always kept cutting their workforce. It's the Chinese that breaks them and also, what's their name,
The Palestinian cheap labour as well."
Armand passes on the hr deputy's offer
To meet later on this afternoon and to close things quietly.
"The deputy hr manager should call us," Jenya says furiously, "You are in no position to negotiate." Armand explains And tells them that this week he had a three-hour long meeting with
The Secretary of Treasury, though they once had a row.
"Dimona is not Nazareth. Most of the employees already agree with him.
And listen man,
Life is all about compromising."
"It's true, life is all about compromising," says Hananiah, nods his
Head approvingly and offers Armand to join them in the meeting.
And then comes a photographer from Channel 10
And asks when will they start burning the tires.
The employees are worried
That Armand's bmw will be damaged once the tires are lit On fire and ask him to move the car.
And then, on Thursday, 9.50am, ten
Minutes before the time they had scheduled to start burning the tires,
Someone's had enough and the tires are lit.
"I'm going to burn myself,"
Cries Jenya Sulver while running towards the
Flames in tears until one of the employees stop her.
I bring her a glass of water as she is crying.
Everybody is silent and nobody knows what to do next.
"I hope that the whole factory burns down," hissed another employee
With a pierced nose.
Maybe she isn't an employee, I don't know.
In the beginning the fire is weak but it grows steadily and it's smoky.
Two fire trucks are storming in
With their sirens on full blast
And stops in front of the workers, rattling.
It's few minutes after 10am when some photographers arrive as well
And they are upset that nobody waited for them
As the workers lightened the fire before the time they've arranged with
The press,
Nonetheless, their ponytails blowing in the wind, they photograph the
Workers crying and shouting and mumbling broken speeches
Down by the great smoke that obscures Kitan factory. The pride of Israel's textile industry,
All the rides Sapir4 took in his car!
All the rides Modai5 took in his car!
All the ministers of trade and industry!
All the ribbon-cutting ceremonies! All the grants!
Fifty-four years of industry!
The smoke of the Kitan factory is rising and darkening everything.
Hananiah Ohayon stands against the wind
Covered in a thick black devilish carcinogenic.
"You may be able to put out this fire,
But the fire in my heart will never die." Says Hananiah
To the firemen who approaches him in their yellow suits, Of gigantic Lego soldiers.
I notice that on all the signs that the workers prepared with marker pens
Somebody added stickers of the
New Histadrut.
Curious locals start to arrive, to get a glimpse of the action.
"Wow, it looks like all Dimona's fire trucks are here," someone says
Excitedly.
He has an earring in both ears.
And then Jenya faints
The glass of water that I gave her falls from her hand.
It shatters on the flo
Or.
The flo
Or
Is all covered with shattered glass
It's becoming dangerous. Someone pours water on Jenya's face
And she regains consciousness after a few minutes.
Everybody is surrounding her, I take a step back.
An ambulance arrives.
They place her on a wheelchair and start to move her towards the
Ambulance but she wakes up and demands to be released, It's a fight for our home,
It's a struggle for 170% of the compensation but
We'll settle for 150%.
The fire is burning along
And one of the workers throws a plastic chair at the burning flames.
Boom!
Jenya leans on the paramedic
And gets up from the wheelchair.
She rejoins the protest.
As the ambulance starts to leave
Jenya faints again in front of the Factory.
The ambulance hasn't left the parking lot yet and it returns Only for Jenya.
Pinchas Sapir, born Pinchas Kozlowski, 15 October 1906-12 August 1975, was Israel's Minister of Finance during the first decades following the country's founding.
Yitzhak Moda'i, 17 January 1926-22 May 1998, was Israel's Minister of Finance from 1984-1986.
THE SPICE ROUTE
_by Ithamar Handelman-Smith (Translated by Eilam Wolman)_
"Whoever kills will get killed," a sandwich maker in Florentine once told me, swinging a cutting knife before my eyes.
A starred agama, thirty centimetres long, head large for its body, scales grey-brown like the desert, crawls on the asphalt. On the edge of Highway 40, a silver Toyota 4x4 Jeep is making its way from Mitzpe Ramon through the Alpaca Farm to the Wise Observatory. A large body of water is hovering on the horizon, a mirage, the sky's reflection in the hot air. You can see the agama on the road reflecting in the waters of the mirage. The Jeep passes the farm and turns right into a dirt road, delimited by two asymmetrical lines of bright, round, medium-sized stones. These serve as an aesthetic, psychical preface to the atmosphere that will soon prevail. At the edge of the long dirt road, the grounds become visible. Eight wooden cabins scattered on the sandy, rocky soil in deliberate disarray. The place is called A Caravan in the Desert, a kind of guesthouse. Mitzpe Ramon isn't far, about seven kilometres from here. The huts are simple cabins, similar to some of the ones you find in the half-island of Sinai. They're made from wood, cloth, nylon, a shading net and palm fronds. They have no cement foundations. The furnishing inside is sparse, the design incoherent; a mishmash of Bedouin elements with features recalling the Rainbow and Burning Man festivals. The Jeep parks next to Abraham's tent. The jazz quartet gets off. The four are now returning from their last concert at Hangar Adama, at the Mitzpe Ramon Poetry and Literature Festival.
The next morning, Uriah leaves his cabin and sits down on a low easy chair, a green canvas sheet stretched on white iron perches. The saxophone rests on his knees like a rifle. Three girls sit on the wooden bench between his hut and the one nearest his. They're also in a band, they're called Habanot Ruchama or something, and they played in the festival too. Uriah hasn't really spoken to them but he and the prettiest one of the three got to exchange a few not-innocent glances.
The prettiest one of the three is wearing plastic flipflops the colours of the Brazilian flag and her toenails are painted deep red. Her pants are tight and very short and her legs are tanned and long. The little pot belly exposed by her sleeveless belly shirt conveys fierce sexuality. With her brown, long hair fluttering in a warm desert wind, she approaches Uriah and assumes an alluring position above him, her muscular legs spread over his easy chair.
"Yes," Uriah says. "Can I help you with anything?"
"I could see you staring at me all the time, at the Orly Castel-Bloom talk, and then the Yoram Kaniuk talk, before you and your friends went up to play. You couldn't take your eyes off me," she says.
"Let's, I..." he falters. "Let's assume that's true. What do we do about it?"
"I don't know. We're leaving today," she says and tosses a glance at her friends, who return her a vague, knowing look.
"So are we," he says, and sits bolt upright on the low chair, his eyes meeting her deep navel.
"You're going back to Tel Aviv?"
"No, we're going up the spice route and then taking the Arabah road to Eilat and then to Sinai. You want to join?"
His eyes climb from her navel to the conical breasts under the thin top and then to her long neck and her round, pretty, intense face.
"I wish I could but I need to go back," she says, brings her legs back together and moves aside.
"Don't just go."
"Do you have another idea?" she says, seemingly uninterestedly.
"Hmm... you want to go for a walk?"
"I'm too hot."
"Let's take a shower then..." he says, lighting himself a rolled cigarette of hydroponic marijuana.
"You're not so shy after all, are you?" She takes a puff from his cigarette, scratches her chin to mime deliberation and then extends her hand to him.
"Let's go," she says, and they head to the communal showers area together.
An hour later, Uriah and his friends are on the road again. They go north towards Sde Boker and enter Avdat, to see the Nabatean antiques. Avdat is a central town on the Nabatean trade axis, which two thousand years ago stretched from Petra to the port of Gaza. The acropolis, the town centre of Avdat, stands at the side of the ancient axis, and spreads across the Negev mountains, reaching 2150ft above sea level. Once, the ancient Nabateans stood on the Avdat acropolis and worshipped Arabian mountain god Dushara or love goddess Al-Uzah. Now Uriah and his friends are standing there and smoking weed.
They're going back towards Mitzpe Ramon. The journey begins at the northern cliff. From the visitor centre on the cliff's edge they survey the entire crater. In the midday light of a tangerine October sun, a little after Sukkot, the crater looks like the view on the moon or on Mars. Afterwards, they proceed to the woodshop and to Wadi Ardon. On their way to the nature reserve, they stop at the side of the road to look at a male mountain goat standing on one of the low cliffs near the road and looking at them.
"Come on, let's move on," says Jack, the pianist, who is also the driver, thanks to his parents, who let him borrow their Toyota Rav Jeep. "I want to get to see some more Nabatean cities."
"What do you want with these Nabatean cities?" says Danny, the drummer, while rolling another spliff, this time with hash which had come all the way from Lebanon.
"People lived here in real cities for two thousand years or one thousand and five hundred years, like this, in the middle of the desert, with no air conditioning... you wouldn't last five minutes here without air conditioning."
"Who cares? Who were they again?" Danny asks, smoking the potent hash and coughing.
"Merchant tribes who journeyed from the half-island and traded all sorts of old goods, I don't know, silk, perfumes, spices..."
"Frankincense and myrrh," says Uriah.
"Where did you get that from?" Danny says, smiling.
"Anyway, what made them special was that they knew to survive in the desert and they could always find water in it. Picture a long procession of hundreds of camels crossing this desert on the way to the Gaza port, where they'd load the goods on ships that sailed to Egypt and Europe too. It's crazy, isn't it? Like, two thousand years ago..." Jack says. They don't stop for the whole way on Highway 40 towards the Arabah until they reach Highway 90, by Faran, and proceed from there to the ruins of Nabatean city Moa, the last one on the spice route before Jordanian Petra. The antiques there don't impress them as much but Jack reads every encyclopaedic entry he can find about them on his Galaxy smartphone. They turn around and drive towards Eilat. In the east, a twilight sun paints the mountains of Edom with a fervent colour, making them truly red.
"I'm hungry," Jack says.
"Me too," says Ronnie. Danny and Uriah are hungry as well. At the side of the road they notice signage to a nearby tavern, simply called The Spice Route. They turn to a side road leading to the place, a removed farm in the no man's land between Israel and Jordan.
A low wooden fence surrounds The Spice Route. The inn is made of wood too. The entrance door is like a swing door from Wild West saloons. Colourful "Spice Route Inn" signage hangs above it. The place is empty save for tall a man in his mid-fifties with broad chest and shoulders. His sunburnt face is ploughed with wrinkles and adorned with a black grey beard, loose, unclean. He's wearing a green cowboy hat and a buttoned plaid shirt, mostly red and green, worn jeans, pointed cowboy shoes. A familiar combination of a retired idf combatant and an Israeli cowboy; a rather obsolete style.
"Hello," he greets them assertively.
"Hello, mister," says Uriah. "What do you have to eat?
The place looks closed."
"We're open and there's plenty of food," says the man.
"Why don't you sit down, have some lemonade and beer and look at the menu?"
"Sure, I'm starving," Jack says, and the quartet sits on brown wooden benches at the foot of a large and long wooden table, in matching colours, in the centre of the restaurant.
"Great place you got here," Uriah tells the man "How did you get here?"
"I ran away from life," says the man. "I served in the military for thirty-five years. I was in Unit 101 and I was in the Paratroopers Brigade. Everybody here knows me and knows that you don't mess with Jeroboam Hanegbi."
"What does that mean?" Danny asks, and immediately adds, "Can I smoke?"
"Smoke as much as you want, it's your lungs. What does it mean that you don't mess with me? It means what it means. Would you all like the pesto ostrich steak?"
"Sounds good," Ronnie says,
"We'll go for it," the rest say unanimously, and Jeroboam Hanegbi begins to prepare the food on the counter before their eyes, swinging his butcher's knife.
"Did you come from Tel Aviv to travel?" he asks.
"Yeah. We performed in some festival in Mitzpe Ramon. Now we're heading to Eilat and Sinai."
"What festival?"
"Poetry and literature," says Danny.
"Nice. Eilat is great. But why Sinai? I don't visit Arab countries," Hanegbi says, slicing slabs of ostrich meat.
"What does that mean?" says Uriah, sipping his beer.
"It means what it means. You're probably leftist Tel Avivians, but I know things you guys don't know."
"Like what? You people always say that. But look at you, making your steaks with pesto and preaching these right-wing opinions... don't you think it's funny?" Jack says, moving his thin-framed optical glasses up and then down the bridge of his long, Jewish nose.
"What's funny about it, kid? What do you know about life anyway? I'll bet none of you even went to the army."
"So what?" says Uriah. "We believe in other things, man. We believe in peace and love, you know... think about Rabin, he was a soldier and a fighter and everything and didn't know anything outside of that life, and even he understood the importance of peace."
"Rabin? Ha..." Hanegbi grunts, now swinging the knife in his hand. "Rabin was a traitor, even back in the Altalena days, and the Bible says 'whoever kills will be killed', it is written."
"Where does it say that, can you show us?" Ronnie laughs.
"Yeah, where?" says Jack. "You just made that up the same way you'd made up your entire funny existence over here, in this hole..." he says and bursts into laughter. The others join him and now the four of them are mooing with bellowing laughter. At first, they don't even see Jeroboam Hanegbi pulling out his old M1 carbine. The thunder of the first shot will petrify them. White-red slivers of Uriah's brain will scatter all over the table, the bench and the exposed floor. The others won't be spared. Hanegbi will shoot everywhere and empty a full magazine of thirty 0.3-inch bullets on them. Horrified and screaming, they will try to escape, hide under the table and behind the benches, but to no avail. Danny will catch five bullets in different areas of his body but the last one will hit the neck, splay copious blood and finally kill him. Ronnie and Jack will crawl on the floor bleeding, leaving a long and dark trail of blood in their wake. Hanegbi will stand above them and shoot them in the back. Blood puddles everywhere. Hanegbi will confirm the kill with a bullet from zero range to the head of each of his young victims.
DREAMERS UNDER THE SUN
_by Sagi Benita (Translated by Eilam Wolman)_
Under a cowboy-hat-shaped monument by the southern sea shore, an engraving reads:
God's Neshama Yeseira belonged to Nelson Raphael. The man who never did a thing he could put off to the next day. The man who saw with one eye what others couldn't see with two. The man who put beer and humor first. The man who put Eilat on the sea as well as on the map.
He had lost an eye in the battle of Malkia in the Galilee, and with his black beard and the cowboy hat he never took off had the appearance of some British admiral called Nelson who lived in the eighteenth century and lost his eye in Corsica. Nelson owned a resort village on the Taba border. The women travellers there were always naked. The strong sun was washed down with beer. Food was foraged from the sea, and the heady herbs were imported from Sinai. People ate with their hands, made love with other organs, danced with ecstasy up the mountain by the golden calf, and sang Ray Charles with all their hearts. The only doctrine preached was the village's slogan: "Every day is a holiday."
Eilat is an autonomous state of mind, separate from other parts of the land – not only because of its geographic isolation and the combination of the gulf and the mountains. It's the only resort town bordering two Arab states, Jordan and Egypt. Nelson passed on in 1988, and a year later, Israel returned Taba to Egypt, and the village went with it.
The generation born in the Seventies would come to embody Rafi Nelson's Neshama Yeseira. Wild beach kids, drinkers and voluptuaries, taking everything the generous little piece of the sea had to offer: tourists, roasted fish, cheap beers.
When we were kids, we would fantasise that one day, oil reserves would be discovered in the Eilat Mountains, or gold would be found in the mines of the Timna Valley, and we could live off the dividends and never work. We believed one day we could swim to the glittering lights in Aqaba, row a small boat from Eilat to Jordan. Our lives were a mess of fact and fiction. Our dreams rotated on a spit of lassitude. "Don't do today what you can do the day after the next," as it were; except the day after the next became the year after the next. Years passed in staring at the Red Sea, nights in watching the mountains of Edom wearing the Aqaba lights like a diamond ring.
Eilat's ancient name was Etzion Gever, which was an ancient city in the land of Edom at the top of the gulf, near the Eilat and Aqaba of modern times. In the Bible, the children of Israel rest there after the exodus from Egypt. They must have known what we had felt in our bones since we were born in Eilat: Rest. There's nowhere to go. We are free. Some people call the Golan Heights up north the "eyes of the country". Eilat, the most southern city, must be Israel's lazy feet. It's so hot and arid you always end up dipping in the sea. If you've made it to Eilat, you know there's nowhere to go to from here. When there's nowhere to proceed towards, you withdraw inward and cross psychical continents, become a desert sage, an official spokesperson for the sea. We always dreamed of an avocational life. Destination is secondary. I'm only now realising what a great distance I'd travelled just to return to the seaside. The beach is freedom. The final destination. What _is_ purpose? Where does it lead? Our lives became one long exemplary sunrise; first, an inwardly incandescent indolence, then, meaning spraying from everything.
THE ROAD TO EILAT: FROM THE DEAD SEA TO THE RED SEA
the ancient Arabah is a narrow valley, about ninety-nine miles long. It separates the mountains of Edom in the east from the Negev mountains in the west. Walking on the vaporous, reddish surfaces of the Edom mountains must be what walking on Mars feels like. You can always ponder weightless issues, disconnect from Earth's atmosphere, search for signs of new, alien lifeforms.
Life on Arabah kibbutzes has in fact taken on new, alien forms with time. Forty-three miles from Eilat, at the kibbutz of Neot Smadar in the southern Negev mountains, a mirage is revealed: next to a lake at the heart of the desert is a magnificent pink palace where people walk in silence. The kibbutz was founded in the late Nineties by academics from Jerusalem who had left the bloody tensions behind to create a community based on the philosophical ideas of Krishnamurti and Carlos Castaneda; the letting go of the past and removal of social conditioning. Wearing brand-name clothing is prohibited in Neot Smadar, as is the use of cellphones in public spaces. The economy is based on organic agriculture. The kibbutz motto is displayed on the dairy wall: "To effectively examine the secret of cooperation between people and create a learning community." I only sneaked in once, through the plum orchard. A gong sounded exactly when I got inside. All members of the kibbutz ceased their work and spent a long minute in awe of the moment. The place looked like heaven on Earth, but their spirit was trapped. Their redemption seemed to have imprisoned them. Like a scene out of _Invasion of the Body Snatchers_ , their sensors had picked up on me and within less than ten minutes I was outflanked and kicked out. They did not learn a single thing about hospitality from either Krishnamurti or Castaneda. They did bring one miracle into being at the kibbutz. The best organic plum juice I'd ever had was at the Neot Smadar Inn, on the main road between Ramon Lookout and Eilat.
The testy intestines of our land have puked up many fanciful minds onto the arid Arabah. In the Fifties it was adventurous young men who were testing their own courage by trying to infiltrate Jordan and reach the red rock in Petra.
_Beyond the mountains and the desert_
_So the legends have it_
_Is a place no one's returned from alive_
_And it is called the red, red, rock_
– Haim Hefer
One of these adventurers was Shimon Rimon, whose nickname was "Kushi". In 1959, along with his friend Victor Friedman, Kushi crossed the border into Jordan with a Jeep and uniforms the two had stolen from the un. Since the Fifties, Kushi had managed to get embroiled in drug deals in Germany and all manner of burglary and larceny due to his uninhibited penchant for adventure. He eventually chilled out and opened the Kushi Rimon Inn on the 101st kilometre. People on their way to Eilat had a tourist attraction waiting for them at the Inn – a zoological garden in the heart of the desert, including a two-headed snake, a two-headed turtle and a goat with six feet. In 2005, a fire consumed the zoological horror show. There are freaks that even nature won't tolerate.
In the Seventies, for the first time in Israel, a film city was built in the style of the Wild West, by Nahal Shlomo in Eilat. It all started when an Italian western, _Don Carlos_ , was shot in Wadi Shahamon. The film crew stayed at the Caravan Hotel. By the end of the shoot, the production didn't have enough money left to pay for the hotel. It was decided that in return for the crew's stay, the farm that was built for the set would remain standing. A few years later, it went up in flames. The community leaders hired the same man who had constructed the set for the film, and the Texas Ranch Farm was built.
As we entered the Ranch, Ennio Morricone's desert harmonica was playing in our heads. A convoy of horses stood by the saloon. At the centre of town were a guillotine and hanging ropes. A thorn bush was rolling in the wind towards the prison by the sheriff's offices. Riding our horses up Nahal Shlomo, all we were missing to make the picture perfect were Indians, or enemies to fight. We never had enemies or wars. We fought the greatest enemy of all – boredom.
The climate and primeval scenery made Eilat and the Arabah an arable ground for film shoots. Breakthrough Israeli films like _Hole in the Moon_ , popular comedies like _Israel Forever_ , and big-budget American and British films were all shot there. At one point, a rumour started running around that the third movie in the _Rambo_ series would be shot in the Timna Valley. The headlines in the local newspaper read: "English-speaking extras needed." We were thrilled and we brushed up on our English so we could get in the picture, but the requirements included a dark skin colour. We dreamed of Hollywood, unaware we would be playing the Afghan kids. Every ten-year-old in 1988 with a dark skin colour was accepted to play in the film. The ones whose skin was browner, like the Yemenites, received a hundred dollars a day. The rest had to settle for fifty and paint their skin with a black, greasy polish. Early in the morning, they drove us along with hundreds of other kids to Timna Valley. Next to Mangan River, an Afghan village was erected from the foundations up. We stood in the sun for twelve hours with the polish running down and stinging our eyes. Blasts kept going off, but Stallone never came to rescue us. We didn't even see him. Lunch included a juicy steak and fries. We gobbled it and drank cold Coke. It really was good. In the evening, they returned us to Eilat and paid us in dollars. It took me two hours to get the paint off my body. That's all I remember from being an Afghan child under Soviet rule.
THE RED CANYON
_by Sagi Benita (Translated by Eilam Wolman)_
Holding the promise of a serenity greater than the sea, the pristine Eilat mountains at the tip of the gulf are the crown of the desert's beauty, offering the widest variety of rocks in the country.
Hiking at the beautiful Red Canyon, only a twenty-minute drive from Eilat, is most suitable for both families and lovers. The canyon stands seven hundred metres above sea level and is therefore great for hiking in the summer, so long as it's done in the early morning and afternoon hours. In the winter, dress warm and be mindful of floods. Two circular trails are available to visitors: one is a kilometre-and-a-half long, the other four kilometres long. The long one is marked with red and begins at the parking lot. We will focus on the shortened trail and take Road 12, which leaves west of Eilat, towards Avdat village and Mitzpe Ramon. Let's go up the road, along the tops of the Eilat Mountains. Stop for a minute and take in the beautiful view of the gulf. Twenty kilometres later, signs appear with directions to the Red Canyon. We'll take a right to the dirt road and zigzag with it until it diverges in two. Proceed on the trail marked in green towards the canyon. The parking lot is four hundred metres from where the trails diverge, so just stay in the vehicle until you get there.
At the parking lot, a trail marked in green leads us into a short creek, at the end of which we are spilled into a larger gully, called Wadi Shani. Another trail is marked in black. It would lead us up a path overlooking the same creek. At the very start of the road, you can see unique geologic phenomena such as sandstone, congealed layer by layer over hundreds of millions of years. Sandstone is a result of quartz grains agglutinating due to long weathering from igneous rocks such as granite. You can see yellowish chalk rocks encrypted with remnants of shell and fish skeleton fossils, formed back when the sea had wrapped the mountains of Eilat with reefs and corals. The floods that have passed through Wadi Shani notched the stone and created a narrow cleft in mesmerising red colour. The wonder begins when we get to the waterfall. The river gets narrower, the atmosphere more bucolic. The wind and the waters have colourfully sculpted the rock. Handles and banisters assist us as we descend into the viscera of the canyon. Take the time and appreciate the surrealistic formations of the slopes. They began forming millions of years ago, when the hard sandstone drifted in giant African rivers. After the area dried, iron oxides and other minerals created the red colour we see in the canyon. Part of the descent is done by sliding inside smooth Nubian sandstone. Be careful, place your hands at the sides of the wall and use your legs for support. Along the way, the observant may notice nimble cape hyraxes peeking from the rock clefts, or a flock of ibexes on a cliff. Ancient rock paintings also appear in the clefts. Some of the passages are very narrow and, in the days of old, the canyon's crevice was used as a tiger trap. Relax. The tigers are long extinct. However, tiger traces and dung are found every once in a while in the Arabah and Negev. At the end of the canyon segment of the trail, a path on the right goes above the canyon and returns to the earlier river. It's narrow, somewhat frightening and not recommended for people with a fear of heights; they are advised to turn around and go back up the canyon. We'll return to the parking lot on the green trail. The hike takes ninety minutes, and is one-and-a-half kilometres in length. Bring water, comfortable walking shoes and a hat. Entrance is free, as it is on every trail in the Eilat Mountains Nature Reserve. Leave your cellular phone in the hotel room; there's no reception in the Red Canyon and on the Eilat mountains.
_Photographs by Assaf Shoshan (originally in colour)_
_Photographs by Assaf Shoshan (originally in colour)_
_Photographs by Assaf Shoshan (originally in colour)_
ICE CREAM VAN
_by Ithamar Handelman-Smith_
There was no ice cream van in Eilat.
But there was the sea.
On Saturday mornings we would go to the sea. My father would take us.
My father never swam. He had a trauma, he said.
When he was a young boy, five years old, his older brothers dislocated
His shoulder,
While he was swimming.
He never swam since.
But when we would go to the sea on Saturday mornings, Father
Would bring along with him tin
Cans
Of
Snails and oysters which the sailors had brought for him.
He worked at the port as a cargo engineer. Once, when we were with him at the sea, me
And my little brother,
We asked him to swim. He stumbled into the water until it reached his knees.
"Look at me," he said and smiled.
He didn't smile much.
There was no ice cream van in Eilat.
And there was no rag-and-bone man.
But there were plenty of tourists sun bathing topless on the beach
Or at the hotels' swimming pools.
On school holidays my baby brother and I would go with Mum
To the hotel where she worked.
Once it was the Red Rock hotel and after that
Club Inn and it was always some
Hotel.
At the Red Rock Hotel I stared at these two topless bright- Haired tourists.
I was staring at them for two whole days. I was maybe seven years old. On the third
Day one of them stepped over me
I was lying on a blue water mattress and she stepped over me. I smiled. She had stopped and
Stepped over me again placing
Her bare foot on my little back.
The next couple of days I would spend between her big boobs, and her friend's boobs.
I would come early in the morning and I would wait for them. I don't know how old they were
But I
Remember
Myself sitting on their lap and playing with their boobies Until my older sister noticed it one day and ran and told Mum.
There was no ice cream van in Eilat.
But at school we played that we were ancient Romans. I would be Julius Caesar
And Dror would be
Drordorakis and Sagi would still be Siegel from that other game when we were
Gangsters.
I would spend the afternoons mainly at home. Or at the public library. And sometimes,
I would go
And play with my little brother. Through all those years in Eilat, my brother and I would
Dream of other countries.
And we had that game with the swing.
We would swing high on the swing seats and we would imagine that they were aeroplanes. I
Would be the pilot explaining
Where we were
Flying to. We would fly to Athens to see the Parthenon, to Rome to see
The Colosseum, Eiffel Tower
In Paris and Buckingham Palace in London. We would fly over to the Americas as well but
We didn't have anything specific to do over there
And when it would get dark Mum would call us to dinner, shouting out of the window
And we would say
"Just a minute Mum,
We need to fly back to Eilat."
We would always dream of
Other countries.
There was no ice cream van in Eilat.
And in the winter nothing was growing.
It was just
That there was nothing green about Eilat.
When I was ten years old we moved to Herzliya.
We arrived there on the break between the fifth and sixth grade. It was summer
And it didn't seem that different from Eilat.
In the winter everything seemed greener, especially the road leading
To Weizmann elementary school.
There were chrysanthemums and lots of grass.
In Herzliya there was a rag-and-bone man. An old cart and an old grey horse. But
It wouldn't make that big a difference
Anyway.
I clearly remember this moment, when I came down that
Leafy hill with the other kids from class,
That hill spreading from the other side of the road
In front of our school gates.
Dark cumulus drifted in the grey skies above us like the old cart of
The rag-and-bone man
And then that tune, and the white van covered with "Strauss ice cream" stickers
And photos of the many different ice creams
And popsicles.
Between the green hill and our school gates it stood
The ice cream van.
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| {
"redpajama_set_name": "RedPajamaBook"
} | 7,601 |
Florida has got the highest number of registered boat owners than any other state in the U.S. As a major attraction to tourists, Florida is surrounded by inland lakes and rivers, as well as the ocean and gulf. There are about 1,000,000 watercraft owners in the water. That is why, it is recommended that before you get wet, extra safety measures should be taken.
Although the use of a life jacket and other reasonable safety practices will obviously go a long way, however, getting a boat insurance is also very needful, as an essential solution to every other unexpected risk at sea.
Typically, this aspect of your Florida boat insurance is designed to take care of your trailer, motor and boat. Ensure to determine the right amount of physical damage coverage for your boat with your agent and choose the amount you will pay on any claim as deductible before kicking in your policy.
If you get hurt when you are on the water, a medical coverage will be essentially required as it will help to cover your eligible medical expenses.
It is often recommended that you take a close look at your new or existing marine policy whether you are just getting started in the water or you are a lifelong water lover. With a Florida boat insurance policy, you can achieve an extensive watercraft coverage that can keep you safe and secure while you are on the water.
There is no other better peace of mind you can ever experience in water than when you are sure that if anything goes wrong, you are covered by Florida Boat insurance. This will help you enjoy a good time on the water without having to worry about anything. All you need to do is get a reliable agent that can tailor the most appropriate insurance policy to your unique need. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,291 |
Odiaone Entertainment is an entertainment digital channel of Odisha. It also does film production of regional language of Odisha. It was founded by Samaresh Routray in 2012.
History
Odiaone Entertainment is the first digital channel in Odisha which was founded in 2012 by Samaresh Routray.
Filmography
Films Under Music Label of Odiaone
Katak
Hey Sakha
Luchakali
Mun
Love Master
Rumku Jhumana
Rudra
Sapanara Naika
Hari Om Hari
Mu Diwana To pain
Omm Sai Tujhe Salam
Alar
Tanka Tate Salam
Kaunri kanya
Gaddabadd
Sandehi Priyatama
Tu Aau Mun
Khas Tumari Pain
Sahitya Didi
Omm
Sangam
Aame Ta Toka Sandha Marka
My First Love
Oolala Oolala
Rockstar
Films under Digital Channel of Odiaone
Suna Chadei
Suna Palinki
Hasila Sansar Bhangila Kia
Kotea Re Gotea
Dhauli Express
Lal Tuk Tuk Sadhaba Bohu
Rasika Nagar
Tumaku Paruni Ta Bhuli
Dhire Dhire Prema Hela
Tu Mo Girl Friend
Hero
Kemiti Ea Bandhan
Kebe Tume Nahan Kebe Mu Nahin
Chanda Na Tume Tara
Dharma
Chowka Chhaka
Aasha
Sunya Swaroop
Bhul Bujibani Mate
References
Companies based in Bhubaneswar
2012 establishments in Odisha | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 647 |
\section{Introduction}
\label{sec:intro}
Direct imaging of exoplanets is expected to play a vital role in characterizing Earth analogs in habitable zones and beyond.
Substantial work has gone into predicting detectable features in disk-integrated spectra of Earth and other planets, as they are observed from an astronomical distance.
Disk-integrated spectra or even multi-band photometry (colors) in principle include the effects of the surface reflectance as well as the atmosphere. (We use the terms spectra and colors interchangeably.)
However, interpreting disk-integrated colors is not trivial.
This is particularly true for Earth-like planets that harbor diverse atmospheric and surface characteristics, including liquid water, partial cloud cover, continents, and possibly vegetation.
A key here is to leverage the time variation of the spectrum/color \citep{Ford2001}: the regions that contribute to the scattered light change due to the planetary rotation and orbital motion, so the time variability can be used to map the heterogeneity of the surface environment \citep[for a recent review, see][]{Cowan2017}.
\citet{Cowan2009, Cowan2011} performed principal component analysis (PCA) on the observed multi-band photometry of Earth. They found that the number of surface types can be inferred from the number of dominant principal components: (\# of surface types) $\ge $ (\# of principal components) $+ 1$.
\citet{Fujii2010, Fujii2011} decomposed multi-band photometric data of Earth assuming the template reflectance spectra of the known major surface types, and they found that the relative abundance and longitudinal variation of these surfaces are approximately recovered.
Moreover, by coupling the rotational variation with orbital (phase) variation, a two-dimensional map of the surface may be retrieved \citep{Kawahara2010, Kawahara2011, Fujii2012}.
\citet{Cowan2013} took another approach to the same inverse problem.
Their strategy was to estimate the reflectance spectra of surfaces and their geographical maps across the globe simultaneously, by making all of them fitting parameters.
They applied their method to the light curves of Earth observed by EPOXI, and appeared successful in that they obtained reflectance spectra roughly matching the average spectra of clouds, oceans, and continents.
However, the longitudinal map of these components did not match the actual geography.
Motivated by this unsatisfactory result, we revisited their analysis.
We start by creating mock light curves to see if we can fully retrieve the known answer.
Taking a close look at the mathematical relation between the colors and geographical maps of the surfaces, we discuss the degeneracy among the parameters to be estimated.
We then demonstrate, using mock data, how our estimates are nevertheless constrained by boundary conditions, including the expectation that albedo is between 0 and 1.
We also apply the same procedure to the EPOXI data.
This paper is organized as follows.
In Section \ref{s:mockdata}, we introduce our toy-model multi-band diurnal light curves of Earth.
We analyze the mock data in Section~\ref{s:frame} and develop a general framework for this problem.
In Section \ref{s:EPOXI}, we apply our procedure to the EPOXI light curves and attempt to estimate the surface colors of Earth.
In Section \ref{s:discussion}, we discuss possible improvements and a few confounding factors, including the degeneracy between the planetary albedo and radius.
We conclude in Section~\ref{s:conclusion}.
\begin{figure}[h]
\begin{center}
\includegraphics[width=\hsize]{mockdata_ver2.pdf}
\end{center}
\caption{Our mock data based on the IGBP classification map of Earth. \emph{Top panel:} distribution of three surface types (ocean: blue; sand: red; vegetation: green). \emph{Next panel:} assumed albedo spectra with matching colors. \emph{Bottom four panels:} rotational light curves in four photometric band with varying phase angles, $\alpha = 135^{\circ }$ (purple, long-dashed), $90^{\circ }$ (olive, solid), and $45^{\circ }$ (gold, short-dashed). }
\label{fig:mockdata}
\end{figure}
\section{Preparing Mock Data Sets}
\label{s:mockdata}
In order to facilitate the discussions in the following sections, in this section we introduce a mock dataset to be used for demonstrations.
We consider diurnal light curves of a toy model of the atmosphere-less Earth, in four photometric bands.
We use a simplified surface map as shown in the top panel of Figure \ref{fig:mockdata}.
This map is based on the land classification scheme of the International Geosphere-Biosphere Programme (IGBP)\footnote{\url{https://climatedataguide.ucar.edu/climate-data/ceres-igbp-land-classification}}.
Although the original classification assumes 16 land surface types plus ocean, in this paper we adopt three surface types for simplicity regarding ``Open Shrublands,'' ``Permanent Wetlands,'' ``Urban,'' ``Snow/Ice,'' and ``Barren/Desert'' as ``sand'' (red in the top panel of Figure \ref{fig:mockdata}) and other land surface types as ``vegetation'' (green), while keeping the ``ocean'' (blue) regions.
The assumed albedo spectra of these surface types in four photometric bands are shown in the middle panel of Figure \ref{fig:mockdata}.
These four photometric bands correspond to 0.4--0.5 $\mu $m, 0.5--0.6 $\mu $m, 0.6--0.7 $\mu $m, and 0.7--0.8 $\mu $m, respectively, but we will simply refer to them by the band indices ($j$) unless otherwise noted.
The albedo spectrum for an ocean is based on \citet{Mclinden1997},
and the data for sand and vegetation are taken from the ASTER spectral library\footnote{\url{https://speclib.jpl.nasa.gov/}. Specifically, we adopt ``Brown to dark brown sand'' for ``sand,'' and ``Grass'' for the ``vegetation.''}.
Scattering from the surface is assumed to obey the Lambert law, i.e., the radiance is (incident flux)$\times $(albedo)/$\pi$, independent of the direction of scattering.
Note that in reality they are not Lambertian scatterers; among others, scattering by the ocean is particularly anisotropic at the crescent phase (see Section \ref{ss:deviate_Lambert}).
The diurnal light curves are synthesized given the relative positions of the star, planet, and observer.
For the sake of simplicity, we consider a planet with zero obliquity in an edge-on orbit, and change the phase angle (the planet-centric angle between the star and the observer) denoted by $\alpha $ to $45^{\circ }$, $90^{\circ }$, and $135^{\circ }$.
We also assume that the spin period is significantly shorter than the orbital period and that the orbital phase does not change in a single spin rotation.
However, the following discussion does not depend on these assumptions.
We consider noise-free data. Clearly, noise in real observations of Earth twins is expected to be substantial, and the effect of such observations will be discussed in a forthcoming study.
The bottom panels of Figure \ref{fig:mockdata} display examples of diurnal light curves in four photometric bands, represented in terms of {\it apparent albedo}.
Apparent albedo is the albedo of the planet weighted by illumination and visibility; it is obtained by normalizing the planetary intensity by that of a lossless Lambert sphere with the same radius and at the same phase \citep{Qiu2003, Seager2010}.
In this paper, we use apparent albedo unless otherwise noted.
The apparent albedo is straightforwardly obtained from the observed planetary intensity, if and only if the orbital phase of the planet, the distance between the star and the planet, and the planetary radius are all known.
We assume these quantities are known, but discuss the effect of unknown planetary radius in Section \ref{sss:uncertain_radius}.
The problem throughout this paper is that, from these kinds of multi-band diurnal light curves, we would like to know how---and how well---we can retrieve the albedo spectra of different surface types and the longitudinal distributions of these surface types.
\section{Inverse problem}
\label{s:frame}
In this section, we discuss the general framework for analyzing the diurnal light curves, and present some demonstrations using mock data created in the previous section.
Sections \ref{ss:model} and \ref{ss:PCplane} are essentially the recapitulation of previous papers, in particular \citet{Cowan2013} \citep[see also][]{Cowan2009,Cowan2011,Fujii2010,Fujii2011}.
We choose to include these discussions, however, as a baseline to establish the later arguments.
\subsection{Algebraic Formulation}
\label{ss:model}
\begin{table}[b]
\caption{Indexes}
\begin{center}
\begin{tabular}{lcc} \hline \hline
Name & Symbol & Maximum \\ \hline
Observation Time & $i$ & $I$ \\
Band & $j$ & J \\
Surface Type & $k$ & $K$ \\
Longitudinal Slice & $l$ & $L$ \\
Principal Components & $n$ & $N$ \\ \hline
\end{tabular}
\end{center}
\label{tab:index}
\end{table}%
Assuming that the planetary surface is everywhere Lambertian scattering, and that it is composed of a certain number $K$ of spectrally distinct surface types, then the disk-integrated scattered light is a weighted summation of the reflectance spectra of different surface types, as shown below.
The apparent albedo of the planet at time $t$ and at wavelength $\lambda $, $d (t, \lambda )$ (``$d$'' for data), is the integral of the local albedo (denoted by $s (\lambda, \bm{\Omega })$, where $\bm{ \Omega }$ indicates a position on the planetary surface), weighted by the cosine of the zenith angle of insolation (denoted by $\theta _0 (t, {\bm \Omega})$) and the cosine of the zenith angle of the observer (denoted by $\theta _1 (t, {\bm \Omega})$), i.e.,:
\begin{eqnarray}
d (t_i, \lambda_j) &=& \displaystyle \frac{ \int_{{\rm IV}_i} s (\lambda _j, {\bm \Omega }) \, W (t_i, {\bm \Omega}) \; d \Omega }{ \int_{{\rm IV}_i} W (t_i, {\bm \Omega}) \; d \Omega } \\
W (t, {\bm \Omega}) &\equiv & \cos \theta_0 (t, {\bm \Omega}) \cos \theta_1 (t, {\bm \Omega})
\end{eqnarray}
where $i$ and $j$ are the indices for time and wavelength, respectively, and ${\rm IV }_i$ represents the illuminated and visible area of the planetary surface.
The weight function, $W (t, {\bm \Omega})$, is also referred to as the convolution kernel \citep{Cowan2017}.
In the following, the maximum values of $i$ and $j$ are denoted by $I$ and $J$, respectively, as summarized in Table \ref{tab:index}, along with other related indices.
By decomposing the local albedo as $s(\lambda _j, {\bm \Omega }) = \sum _k s_{kj} f_k({\bm \Omega })$ where $s_{kj}$ and $f_k({\bm \Omega })$ are the spectrum and the local area fraction of $k$-th surface type, respectively, the above equation becomes
\begin{eqnarray}
d (t_i, \lambda_j) &=& \sum _{k} s_{kj} \; \displaystyle \frac{ \int_{{\rm IV}_{i}} f_k (\bm \Omega ) \, W (t_i, {\bm \Omega}) \; d \Omega }{ \int_{{\rm IV}_i} W (t_i, {\bm \Omega}) \; d \Omega } \notag \\
&=& \sum _{i,k} \tilde f_{ik} \, s_{kj} \label{eq:tilde_d_f_ast_s}
\end{eqnarray}
where $\tilde f_{ik}$ represents the apparent covering fraction of $k$-th surface type at time $t_i$:
\begin{equation}
\tilde f_{ik} \equiv \frac{ \int_{{\rm IV}_{i}} f_k (\bm \Omega ) W (t_i, {\bm \Omega}) \; d \Omega }{ \int_{{\rm IV}_i} W (t_i, {\bm \Omega}) \; d \Omega } \label{eq:def_ftilde}
\end{equation}
Thus, spectral unmixing is equivalent to estimating both the apparent covering fraction ($\tilde f_{ik}$) and colors ($s_{kj}$) from the apparent albedo of the planet ($d (t_i, \lambda_j)\equiv d_{ij}$).
Because $f_k({\bm \Omega })$ should not be negative and should sum up to unity, $\tilde f _{ik}$ should also not be negative and they should sum up to unity at each observation time, $i$. In addition, reflectance spectra, $s_{kj}$, should be between 0 and 1 for any surface type ($k$) at any band ($j$).
Therefore, the constraints on apparent covering fraction ($\tilde f_{ik}$) and colors ($s_{kj}$) of the surfaces are:
\begin{subnumcases}
{}
0 \leq \tilde f_{ik} \;\;\; & \mbox{for any $i$, $k$} \label{eq:tilde_f_range} \\
\sum_k \tilde f_{ik} = 1 & \mbox{for any $i$} \label{eq:tilde_f_sum} \\
0 \leq s_{kj} \leq 1 \;\;\; & \mbox{for any $k$, $j$} \label{eq:tilde_s_range}
\end{subnumcases}
The time variability of the apparent covering fraction, $\tilde f $, due to the planet's rotation, is related to the surface inhomogeneity in the longitudinal direction.
From Equation (\ref{eq:def_ftilde}), $\tilde f _{ik}$ may be approximately written as the weighted sum of the average area fraction of the $k$-th surface type in the $l$-th longitudinal slice, denoted by $f_{lk}$:
\begin{eqnarray}
\tilde f _{ik} &=& \frac{ \int_{{\rm IV}_i} f_k (\bm \Omega ) \; W (t_i, {\bm \Omega}) \; d\Omega }{ \int_{{\rm IV}_i} W (t_i, {\bm \Omega}) \; d\Omega } \\
&\approx & \sum_l W_{il} f_{lk} \label{eq:Wf}, \\
W_{il} &\equiv & \frac{ \int_{{\rm IV}_i \cap \Omega _l} W (t_i, {\bm \Omega}) \; d\Omega }{ \int W (t_i, {\bm \Omega}) \; d\Omega }
\end{eqnarray}
where $\Omega _l$ denotes the $l$-th longitudinal slice.
Strictly speaking, the approximation is valid only when the local area fraction, $f_k(\bm{\Omega })$, does not change or changes little across each longitudinal slice for all $K$ surface types.
One can therefore recast Equation (\ref{eq:tilde_d_f_ast_s}) in terms of the longitudinal map, $f_{lk}$:
\begin{equation}
d_{ij} \approx \sum _{l,k} W_{il} \, f_{lk} \, s_{kj} \label{eq:d_f_s}
\end{equation}
Again, the area fractions in each longitudinal slice, $f_{lk}$, cannot be negative and should sum up to unity. Thus, a set of conditions similar to Equations (\ref{eq:tilde_s_range})-(\ref{eq:tilde_f_sum}) is imposed:
\begin{subnumcases}
{}
0 \leq f_{lk} \;\;\; & \mbox{for any $l$, $k$} \label{eq:f_range} \\
\sum_k f_{lk} = 1 & \mbox{for any $l$} \label{eq:f_sum} \\
0 \leq s_{kj} \leq 1 \;\;\; & \mbox{for any $k$, $j$} \label{eq:s_range}
\end{subnumcases}
Now the relevant problem is to estimate both the geographical map ($f_{lk}$) and colors ($s_{kj}$) given the time series of apparent albedo of the planet ($d_{ij}$), subject to the constraints of Equations (\ref{eq:s_range})-(\ref{eq:f_sum}); this is where \citet{Cowan2013} stood.
In principle, constraints (\ref{eq:f_range}) and (\ref{eq:f_sum}) for the longitudinal geographical map are more stringent than constraints (\ref{eq:tilde_f_range}) and (\ref{eq:tilde_f_sum}) for the apparent covering fraction, due to the low-pass filter nature of the convolution from map to light curve.
\begin{figure}[b!]
\begin{center}
\includegraphics[width=0.9\hsize]{schematics_ver2.pdf}
\end{center}
\caption{Schematic figure to illustrate the relation between observed data ($\{{\bm d}_i\} $; crosses) and surface spectra ($\{{\bm s}_k\} $; filled points). The dashed cube shows the range of physical albedos (between 0 and 1). }
\label{fig:schematic}
\end{figure}
\subsection{Graphical Conception of \\Principal Component Plane}
\label{ss:PCplane}
Equation (\ref{eq:tilde_d_f_ast_s}), coupled with the conditions (\ref{eq:tilde_f_range}) and (\ref{eq:tilde_f_sum}), indicates that the observed planetary albedo ($d_{ij}$) is a convex combination of the colors of representative surface types ($s_{kj}$).
Geometrically, this means that in the $J$-dimensional color space, $\{{\bm d}_i\}$ are located in the convex hull with $K$ vertices, $\{{\bm s}_k\} $.
For example, in the case of $K=3$, this convex hull is simply a triangle, and thus $\{{\bm d}_i\}$ are confined in the triangular region of a plane.
Figure \ref{fig:schematic} graphically shows this relation in the case of $K=3$ and $J=3$.
In general, the data points, $\{{\bm d}_i\}$, are in a $K-1$ dimensional subspace of the $J$-dimensional color space.
This subspace can be identified by performing PCA \citep{Cowan2009,Cowan2011}, as PCA extracts the major, mutually orthogonal axes along which the data are scattered.
Consequently, the number of dominant principal components (PCs) is less than or equal to $K-1$ \citep{Cowan2011}.
Note that non-Lambertian reflectance, partially transparent cloud cover, or observational noise would in practice ensure that the PC space has some additional dimensions (see also Section \ref{ss:deviate_Lambert}).
From the mock light curves prepared in Section \ref{s:mockdata},
we extract two PCs through PCA, with other components having virtually zero contributions, consistent with the three input surface types.
The PCs extracted from the light curves at $\alpha = 90^{\circ }$ (olive lines in Figure \ref{fig:mockdata}) are presented in the upper panel of Figure \ref{fig:trajectory}.
For later use, we denote these PCs by $V_{nj}$, where $n=1$ or $2$, corresponding to the first and second PC.
The PC spaces (plane) of the light curves at different phases are the same, since we use the same three surface spectra as inputs, while the individual PCs may be rotated.
Using the PCs, $V_{nj}$, and the time average of the colors, $\bar d_j$, in the case of $\alpha = 90^{\circ }$, the light curves are projected onto the PC plane by:
\begin{equation}
d_{ij} = \sum_n U_{in} V_{nj} + \bar d_j
\end{equation}
where $U_{in}$ represents the time-dependent trajectory on the plane.
The trajectories of the light curves at different orbital phases are shown by the colored lines in the lower panel of Figure \ref{fig:trajectory}.
The color excursions are greater at a larger phase angle (crescent phase), because less surface area is averaged together.
Likewise, the albedo spectra of representative surface types may be projected onto the PC plane by
\begin{equation}
s_{kj} = \sum_n t_{kn} V_{nj} + \bar d_j ,
\end{equation}
where $t_{kn}$ are the coordinates of the albedo spectra on the plane.
The circle, square, and triangle in the figure indicate the input albedo spectra of ocean, sand, and vegetation, respectively, projected onto this plane.
As described above, the trajectory of the observations is always in the convex hull (triangle in this case) of the surface albedo spectra.
\begin{figure}[t]
\begin{center}
\includegraphics[width=\hsize]{PCplane_mockdata_lc_ver2.pdf}
\end{center}
\caption{\emph{Upper panel:} principal components of the light curves at $\alpha = 90^{\circ }$ shown in olive lines in Figure \ref{fig:mockdata}. \emph{Lower panel:} trajectories of the four-band light curves on the PC plane, defined by two PCs shown in the upper panel, in the cases of $\alpha = 135^{\circ }$ (thick indigo line), $\alpha = 90^{\circ }$ (olive line), and $\alpha = 45^{\circ }$ (thin gold line). The points indicate the input albedo spectra of an ocean (blue circle), sand (red square), and vegetation (green triangle) on the PC plane. Points in the gray region violate the condition (\ref{eq:tilde_s_range}); specifically, the left, right, and bottom boundaries are set by $s_{k,4} > 0$, $s_{k,1} > 0$, and $s_{k,3}> 0$, respectively.
The dotted lines are random triangles that could be solutions (see the text). }
\label{fig:trajectory}
\end{figure}
\subsection{Degenerate Solutions}
\label{ss:degeneracy}
When it comes to the inverse problem of estimating surface spectra given the trajectory/-ies, {\it any} set of $\{ {\bm s}_k \}$ that encloses the data points $\{{\bm d}_i\}$ in the PC plane can be a solution of Equation (\ref{eq:tilde_d_f_ast_s}) subject to the conditions (\ref{eq:tilde_f_range}) and (\ref{eq:tilde_f_sum}).
Two such examples are shown by the dotted lines in Figure \ref{fig:trajectory}.
Note that the associated matrix, $\tilde f _{ik}$, can always be found.
Additional constraints come from the condition (\ref{eq:tilde_s_range}) that the albedo of each surface be between 0 and 1 in each band.
In Figure \ref{fig:trajectory} any points in the shadowed region are rejected based on this condition: specifically, the left, right, and bottom boundaries are set by $s_{k,4}> 0$, $s_{k,1}> 0$, and $s_{k,3}> 0$.
In other words, surfaces lying in the forbidden gray regions have negative albedos in the fourth, first, and third photometric bands.
While in this particular example the permitted region happens to be a triangle, the shape can differ depending on the location of the PC plane relative to the albedo boundaries.
Since each of the four bands has lower and upper bounds on albedo, the physically allowed region of color space is a 4-dimensional hypercube, also known as a tesseract. Depending on the orientation of the PC plane with this tesseract, the allowed region may have a variety of geometries.
In general, the allowed region is an $N$-dimensional slice through a $J$-dimensional hypercube.
The randomly drawn two triangles in Figure \ref{fig:trajectory} also satisfy the condition (\ref{eq:tilde_s_range}) for an albedo, in addition to the conditions (\ref{eq:tilde_f_range}) and (\ref{eq:tilde_f_sum}), as do many others.
Thus, predicting $\tilde f _{ik}$ and ${\bm s}_k$ from ${\bm d}_i$ is clearly degenerate.
For example, with a large triangle one can have spectrally interesting surfaces with boring geography (small longitudinal variation in area fractions), while with a small triangle one can have boring surface spectra (different surfaces have nearly the same color) and interesting geography.
A formally equivalent degeneracy is found in Equation (\ref{eq:d_f_s}) coupled with the conditions (\ref{eq:f_range})-(\ref{eq:s_range}).
Essentially, the term $\sum _k f_{lk} s_{kj}$ represents the average albedo spectra of $l$-th slice.
Suppose that ideally we can retrieve the average spectra of longitudinal slices from the light curves through $W_{il}$; the black trajectory in the bottom panel of Figure \ref{fig:trajectory} represents the color variation as a function of longitude based on the upper panel of Figure \ref{fig:mockdata}.
We again have different sets of end-member colors, $\{ {\bm s}_k \}$, that enclose the averaged albedo spectra of longitudinal slices {\it and} are located in the region of physical albedo presented by condition (\ref{eq:s_range}).
Nevertheless, the excursions of the longitudinal colors are more dramatic than the disk-integrated colors of the light curves, thus the possible solutions are somewhat restricted.
\subsection{``Best Guess'' of the Surface Types}
\label{ss:guess}
\begin{figure*}[tbh!]
\begin{minipage}{0.33\hsize}
\begin{center}
\includegraphics[width=\hsize]{PCplane_mockdata_90deg_3types_t360_hatch.pdf}
\end{center}
\end{minipage}
\begin{minipage}{0.33\hsize}
\begin{center}
\includegraphics[width=\hsize]{PCplane_mockdata_135deg_3types_t360_hatch.pdf}
\end{center}
\end{minipage}
\begin{minipage}{0.33\hsize}
\begin{center}
\includegraphics[width=\hsize]{PCplane_IGBP_lon_hatch.pdf}
\end{center}
\end{minipage}
\caption{Probability of surface albedo spectra estimated from the light curves at orbital phases of $\alpha = 90^{\circ }$ (left), $\alpha = 135^{\circ }$ (middle) as well as from the colors of longitudinal slices. The hatched region is not permitted because of negative albedo. Points indicate the input albedo spectra of ocean (circle), sand (square), and vegetation (triangle) on the PC plane. }
\label{fig:PCplane}
\end{figure*}
Given that any three vertices in the PC plane that enclose the trajectory/-ies can be a solution, the choice of the solution depends on the prior probability distribution.
With no assumptions or information on the geography or spectral albedo of the surface types, it is reasonable to assume that any points in the PC plane except for the forbidden regions are equally likely to correspond to a surface type.
Despite this uninformative prior, the location of the light curve trajectory allows us to constrain the location of the surface spectra in a probabilistic sense.
For example, in Figure \ref{fig:trajectory}, in order to enclose the trajectory with three surface types within the permitted region, we must have at least one point near the bottom left corner of the permitted region; this is consistent with the fact that one of the input albedo spectra (ocean) resides there.
In order to evaluate this more quantitatively, we assume that any combination of three points that enclose the data is equally likely to be a solution for surface end-member colors. We then compute the marginalized probability for the location of one surface type in the PC plane.
Specifically, we make a grid on the PC plane with an interval of 0.2 and only consider grid points in the permitted region. For each point, we compute the number of combinations of two other points with which it can make a triangle that encloses the trajectory. The number of such triangles is proportional to the probability of there being a surface at that location in color space. This number is normalized so that the integral over the permitted region is unity.
The resultant probability distribution is shown in Figure \ref{fig:PCplane}.
As expected, we find a definite peak near the ocean color.
The vegetation in the bottom right corner is moderately constrained.
On the other hand, the very light gray color in the upper part of the triangle indicates that the location of the end-member there (sand) is essentially unconstrained. Note that when one integrates the probability over the upper light gray region, it sums up to about 1/3, implying that one of the end-members should exist ``somewhere'' in the light-gray region.
\subsection{Conditions for Successful Guess\\of Surface Spectra}
\label{ss:guess}
We reiterate that in this framework the success of the surface retrieval critically depends on the relative configuration of the trajectory within the allowed region.
More specifically, the good constraints on the colors of an ocean appear to be due to the combination of the large covering fraction of the ocean and the location of the ocean color close to a corner in the PC plane (due to low albedo at longer wavelengths).
In order to illustrate these two effects and see under what conditions we can faithfully retrieve surface spectra, we create two additional mock light curves, (a) with the geographical maps of sand and vegetation swapped, and (b) with the geographical maps of sand and ocean swapped.
The left and right panels of Figure \ref{fig:swap} correspond to (a) and (b), respectively.
\begin{figure}[htb!]
\begin{center}
\includegraphics[width=\hsize]{swap_map.pdf}
\includegraphics[width=\hsize]{PCplane_mockdata_90deg_3types_t360_swap_hatch.pdf}
\end{center}
\caption{\emph{Left:} trajectory of the light curves with the geographical maps of sand and vegetation swapped, and the resultant color contour of the probability for albedo spectra of surface types. \emph{Right:} same as the left panel but with the geographical maps of sand and ocean swapped.}
\label{fig:swap}
\end{figure}
When we swap sand and vegetation (left panel), the covering fraction of vegetation becomes smaller, and the trajectory of the light curves does not approach the vegetation end-member. As a result, the constraints on the color of vegetation become weaker. Thus, a large covering fraction of the surface type tends to yield a better constraint on the albedo spectra of that type; this agrees with our intuition.
Meanwhile, in (b) we swap sand and ocean.
Although sand is now the dominant component,
our analysis prefers other locations toward the top of the allowed region, because there is more space there.
Therefore, a large covering fraction is not a sufficient condition for obtaining strong constraints on the color of a surface.
Better constraints on a surface spectrum can be obtained if its location on the PC plane is close to more than one boundary of the allowed region.
In other words, a surface spectrum can be well retrieved if it has a favorable geography (ideally an entire hemisphere solely covered with that surface) {\it and} it has a favorable albedo spectrum (albedo close to 0 or 1 at as many wavelengths as possible).
\section{Application to EPOXI data}
\label{s:EPOXI}
\begin{figure}[t!]
\begin{center}
\includegraphics[width=0.9\hsize]{PCs_raddata_2_norm.pdf}
\includegraphics[width=0.9\hsize]{PCplane_raddata_2_norm.pdf}
\includegraphics[width=0.89\hsize]{PCplane_raddata_2_norm_spectra.pdf}
\end{center}
\caption{\emph{Top panel:} the two dominant principal components from EPOXI June data \citep{Livengood2011}. \emph{Middle panel:} color contour similar to Figure \ref{fig:PCplane}, but based on EPOXI June data. The red line shows the light curve trajectory. The hatched region is not permitted because of the physicality constraints for albedos. \emph{Bottom panels:} spectra corresponding to the locations (A-J) shown in the upper panel. The ocean, sand, and clouds appear to be close to A, D, and F, respectively. }
\label{fig:EPOXI}
\end{figure}
In this section, we apply our procedure to the multi-band light curves of Earth obtained by the EPOXI mission.
Specifically, we use the same datasets as \citet{Cowan2013}, i.e., the seven-band diurnal light curves observed in June 2008 \citep{Livengood2011}.
We obtain the two dominant PCs shown in the top panel of Figure~\ref{fig:EPOXI}, which suggests at least three spectrally distinct surface types, consistent with \citet{Cowan2013}.
Using these two PCs, we perform the same analysis described in the previous section.
The middle panel of Figure \ref{fig:EPOXI} shows the trajectory of the light curve on the PC plane, with the hatched region being forbidden by the physicality constraints for albedo.
While the permitted region appears to be close to a square, it is in fact a heptagon, bounded by seven inequalities (2-dimensional slice through a 7-dimensional hypercube).
Overall, the upper boundaries come from the requirement that albedo cannot be negative at any wavelength, i.e., $s_{kj}>0$, while the lower boundaries comes from the requirement that albedo should be less than unity, i.e., $s_{kj}<1$.
In principle, any three or more points that enclose the trajectory can be solutions for the surface albedo spectra. The example albedo spectra corresponding to different locations in the permitted region are shown in the lower panels of Figure \ref{fig:EPOXI}. This library conservatively represents the range of possible surface spectra.
Going one step further, we evaluate the preferred surface spectra following the procedure discussed in Section \ref{ss:guess}. We assume that there are three spectrally distinct surface types. The grayscale in the middle panel of Figure \ref{fig:EPOXI} indicates the probability distribution equivalent to those in Figures \ref{fig:PCplane} and \ref{fig:swap}, which is simply related to the number of possible combinations each location can make to enclose all of the data points.
In this case, the trajectory of planetary color is far from the boundary because the color variations of the real Earth are muted by the cloud cover.
Consequently, we do not see three peaks.
Nevertheless, we are likely to find one surface type in the upper part of the allowed region, near label A, which can be interpreted as ocean.
\section{Discussion}
\label{s:discussion}
\subsection{Confounding Factors}
\label{ss:confonting_factors}
\subsubsection{Uncertain Planetary Radius}
\label{sss:uncertain_radius}
So far, we have assumed that the data can be expressed in terms of apparent albedo.
In reality, the primary observables from direct imaging observations are the intensities of the planet and the star.
In order to convert them to apparent albedo, we need to know the orbital distance from the star, the phase angle, and the planetary radius.
While the former two may be constrained from multi-epoch observations, the radius continues to be severely degenerate with albedo.
How would the unknown planetary radius affect our retrieval?
Not knowing the planetary radius and hence the normalization of the planetary albedo, we cannot put a tight upper limit on the surface albedo spectra, $s_{kj}$.
Thus, the condition (\ref{eq:tilde_s_range}) or (\ref{eq:s_range}) is essentially reduced to $0 \leq s_{kj}$.
How much this limits our estimation depends on the configuration of the PC space in the $J$-dimensional color space.
For example, in the case of our mock data, the three significant constraints actually come from $0 \leq s_{kj}$ (see Figure \ref{fig:trajectory} and its caption), therefore the unknown normalization of planetary albedo does not affect the permitted region.
Thus, the constraints of the spectral shapes of the surfaces can be obtained (but not the absolute scale).
On the other hand, in the case of EPOXI data, roughly half of the boundaries of the permitted region originate from the upper limit for albedo, $s_{kj} \leq 1$.
In this case, not knowing the normalization would change the permitted region itself.
Nevertheless, because the upper boundaries still come from $0 \leq s_{kj}$, the inference that at least one surface type is present near the upper left corner will hold.
\subsubsection{Additional Coplanar Surface Spectra}
The retrieval would become more complicated if the actual number of surface types were larger than the dimension of the PC space plus 1 ($K > N + 1 $).
For example, if there were four important surface types in EPOXI rather than three, all in the PC plane we obtained, then we would have to consider a tetragon to enclose all of the data rather than a triangle, thus affecting our estimates of surface spectra.
The greater $J$ is, the more probable it is for important surface colors in the $J$-dimensional space to be affinely independent (i.e., to make a simplex).
Thus, obtaining light curves in as many bands as possible will help disentangle the surface colors and reduce the uncertainty in the number of surface types.
\subsubsection{Deviation from Lambert's Law}
\label{ss:deviate_Lambert}
We have assumed that the surface scattering obeys Lambert's law, but in reality they are not perfectly Lambertian.
In particular, scattering by surface liquid water is characterized by specular reflection and the reflectivity increases when the incident light is grazing, or equivalently at crescent phase \citep[e.g.,][]{Williams2008,Robinson2010,Robinson2014}.
Scattering by cloud/haze layers exhibits prominent forward scattering, which also becomes evident at crescent phase \citep[e.g.,][]{Robinson2010}.
For surfaces with strongly anisotropic scattering, apparent albedo can even exceed unity.
Furthermore, the albedo spectrum of a surface overlaid by an atmosphere changes with phase angle.
Considering these effects, the trajectories of the light curves at different phases do not have to reside in the same PC space.
These light curves can be analyzed independently, and the components varying with phase would give us insights into the anisotropic scatterers.
\subsection{Enhancing Constraints}
\label{ss:enhancing_constraints}
\subsubsection{Power of Many Bands}
As we discussed in Section \ref{ss:guess}, constraints on surface spectra rely on the relative configuration between the light curve trajectory and the boundaries of the physically permitted region, namely that the albedo of any surface must be between 0 and 1 at all wavelengths.
It depends on geography and the albedo spectra of the surface types, neither of which we can directly change.
However, we can potentially increase the number of boundaries of the permitted region by increasing the number of photometric bands, and some of them may have tighter constraints than others.
Obtaining light curves in as many bands as possible will therefore be beneficial.
In particular, observing at wavelengths where one or more surface types have albedos close to 0 or 1 constrains the possible albedos more tightly.
Albedos close to 0 (i.e., the condition of $0 \le s_{kj}$) are more useful because they do not depend on the uncertain planetary radius.
In reality, the albedo of ocean is close to 0 at longer wavelengths toward the near infrared, that of sand is small at 0.4 $\mu $m and shortward, that of vegetation is close to 0 at 0.7 $\mu$m and shortward, and that of H$_2$O snow is close to 1 in the visible and closer to 0 at the 1.5 $\mu$m and 2 $\mu$m bands.
Observations at different bands covering these characteristic wavelengths would be useful.
\begin{figure*}[hbt!]
\begin{minipage}{0.33\hsize}
\begin{center}
\includegraphics[width=\hsize]{IGBP_PCplane_Nside2_ver2.pdf}
\end{center}
\end{minipage}
\begin{minipage}{0.33\hsize}
\begin{center}
\includegraphics[width=\hsize]{IGBP_PCplane_Nside1_ver2.pdf}
\end{center}
\end{minipage}
\begin{minipage}{0.33\hsize}
\begin{center}
\includegraphics[width=\hsize]{IGBP_PCplane_Nside0_ver2.pdf}
\end{center}
\end{minipage}
\caption{Making the map coarser from the upper panel of Figure \ref{fig:mockdata}. Pixelating the surface into 192 (left), 48 (middle), and 12 (right) equal-area pixels using HealPix, we plot the synthesized pixel colors with crosses on the same PC plane as Figures \ref{fig:trajectory} to \ref{fig:swap}. The triangular shape of the locus of points becomes apparent with as few as 48 pixels. Thus, resolving the surface colors in 2 dimensions eases the challenge to identify surface types. }
\label{fig:lowresolution}
\end{figure*}
\subsubsection{Utilizing Light Curves at Different Phases}
Light curves at different orbital phases are useful for spectral unmixing because they are sensitive to different locations on the planet, exploring the PC space in different directions.
As a result, the volume of color space where the solution can exist will be narrowed.
In particular, the diurnal light curves at thinner phases tend to exhibit larger color variations, giving tighter constraints (but see the caveat in Section \ref{ss:deviate_Lambert}).
In addition, diurnal light curves at different orbital phases in principle allow us to map the color in two dimensions \citep{Kawahara2010,Kawahara2011,Fujii2012}.
We could then use the spectra of various surface patches resolved in two dimensions to identify different surface types, in the same spirit as that of estimating the end-member colors from the colors of the longitudinal slices.
In fact, this ``map first'' approach is likely more appropriate with 2-dimensional maps than with longitudinal maps.
In the diurnal light curves at a single phase, colors of very distant pixels beyond the correlation length of the geography are mixed together, even at crescent phases---for example, the colors of the Arctic, tropics, and Antarctic are mixed in an equatorial observation, no matter how extreme the orbital phase is.
As a result, the colors of longitudinal slices never approach the colors of vegetation or sand regardless the number of slices, as shown in the right panel of Figure \ref{fig:PCplane}.
The situation is different when we gradually lower the resolution of the 2-dimensional maps.
Figure \ref{fig:lowresolution} shows the colors of HEALPix pixels \citep{Gorski2005} with varying resolutions: from left to right, we change the resolution from 192 pixels, to 48 pixels, to 12 pixels, starting from the map in Figure \ref{fig:mockdata}.
The triangular shape of the locus of points becomes apparent with as few as 48 pixels.
Thus, resolving the surface colors in two dimensions will potentially ease the challenge of identifying surface types.
\subsubsection{Invoking Additional Assumptions}
Occasionally, we may want to adopt additional constraints on the behavior of $\tilde f _{ik}$ ($f_{lk}$) or $s_{kj}$ based on prior knowledge.
For example, we may assume that the covering fractions of surface types vary ``smoothly'' as a function of time or longitude.
Such an assumption could be implemented via a Gaussian process \citep[e.g.,][]{Rasmussen2005}, i.e., the area fractions at different times/longitudes have a joint gaussian distribution with the relevant correlation length.
We must exercise caution because the actual covering fractions of surface types are not necessarily Gaussian processes and can exhibit sharp boundaries.
We could also consider a regularization on albedo spectra as a function of wavelength.
This can be regarded as a prior probability distribution on the PC plane.
For example, in Figure \ref{fig:PCplane}, albedo spectra corresponding to the upper part of the permitted region exhibit a dramatic decrease in albedo between 0.65~$\mu $m and 0.75~$\mu $m, which may seem implausible.
However, the albedo spectrum of vegetation in fact has a sharp feature, the red edge; similar, unfamiliar features may exist on other planets.
In addition, with an atmosphere, absorption by atmospheric molecules can also produce sharp changes in albedo spectra.
\section{Conclusion}
\label{s:conclusion}
In this paper, we revisited the problem of estimating the albedo spectra of major surface types and their distributions from disk-integrated colors of exoplanets.
We pointed out the inherit degeneracy that makes it impossible to find unique solutions.
Despite the degeneracy, the following physical conditions narrow down the possible solutions for surface albedos, on the assumption of Lambertian surfaces:
the actual surface albedo spectra in the $J$-dimensional color space are
(1) to be located in the PC subspace,
(2) to enclose all of the data points of the disk-integrated colors, and (3) to be in the $J$-dimensional hypercube, bounded by 0 and 1 for all axes. %
We demonstrated using both a simplified toy model of Earth and the observed data by EPOXI that such constraints point us to the approximate spectrum of ocean.
In general, we find that the success of the estimates critically depends on the degree of excursions of the time-dependent trajectory of the disk-integrated colors, and its orientation in the color space. %
In other words, the estimates will be better if the covering fraction of each surface type becomes close to 1, as intuition suggests.
In addition, observations at wavelengths where surface albedos are close to 0 or 1 could improve the estimates.
As the wavelength coverage/resolution increases, and as the light curves are obtained at more orbital phases, precision for surface estimates will improve.
\acknowledgements
We thank the anonymous referee whose comments helped us greatly improve the clarity of this manuscript.
We acknowledge the Exo-Cartography workshops supported by the International Space Science Institute (ISSI).
We thank D. Foreman-Mackey for a useful discussion of parameter retrieval.
Y.~F. is thankful to Eric Smith and Haru Negami for discussions on the geometrical aspect of the study.
Y.~F. acknowledges the generous support from the Universities Space Research Association through an appointment to the NASA Postdoctoral Program at the NASA Goddard Institute for Space Studies.
Y.~F. is also supported by the NASA Astrobiology Program through the Nexus for Exoplanet System Science.
J.~L.~Y. is supported by the NASA Astrobiology Institute's Virtual Planetary Laboratory under Cooperative Agreement number NNA13AA93A.
N.~B.~C. is supported by the McGill Space Institute and l'Institut de recherche sur les exoplan\`etes.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,263 |
\section{Introduction}
Why do we classify radio galaxies, or any objects for that matter? I see three main benefits to classification, in general:
\begin{itemize}
\item {Communication -- so we have language to describe what objects we are interested in. {\em "I'm investigating one-sided jets."}}
\item{Investigation -- so we can define samples for study, e.g. to look for correlated variables. {\em "I'm studying whether one-sided jets appear more frequently in variable core sources."}}
\item{Interpretation -- so we can develop physical models to explain observed phenomena. {\em "I'm working on how relativistic beaming can determine whether jets would appear one- or two-sided."}} \end{itemize}
The challenges inherent in our classification system are well-known, but difficult to avoid. Different people often mean different things but use the same term - could we get a group of astronomers to decide on what a {\em dying radio galaxy} is? Often, objects don't fit nicely into the boxes we've defined -- ADS lists 230 articles with "hybrid", "radio" and "galaxy" in their abstracts. And in a remote talk for the 2019 3Csky conference in Turin, Bernie Fanaroff (of FR reknown) lamented "{\em [recently] I worked on a sample of sources. I couldn't classify them. They were too ambiguous and irregular.}" In other cases, we group together objects with very different physical origins, (e.g., the broad variety of "X-shaped" radio galaxies) confounding studies that look for correlations, develop physical models, etc.
So where are we today? Table \ref{tab1} summarizes many of the classes of sources in the current literature. Some of these classes are exclusive, i.e., a source can be one or the other, e.g., either ``flat" or ``steep" spectrum, and either ``S-shaped" or ``C-shaped", but not both. Other classes can be combined, e.g., a source can be in both the FRI and narrow-angle tail classes. These multiple uses, and the lack of a clean definition for many of the classes, can lead to confusion, and worse, can lead to scientifically inconsistent results from different studies. Other measured quantities, such as polarization information as a function of wavelength, or X-ray counterparts, add additional layers of complexity.
\begin{specialtable}[H]
\small
\caption{Examples of radio galaxy classifications in current use.\label{tab1}}
\begin{tabular}{ccc}
\toprule
\textbf{Category} & \textbf{Classes} \\
\midrule
Morphology & Double; Classical double; Triple; Narrow-angle tail; Wide-angle tail; \\
& Bent-tail; FRI, FRII, FR0*; Hybrid; X-shaped;\\
& S-shaped; C-shaped; Relaxed; Dying RG; Double-double; \\
& Core-dominant; Core-halo; Core-jet; CSO; 1-sided \\
Size & Compact (pc); Galactic (<10 kpc); extended RG (10-1000 kpc);\\
& Giant RG (>1 Mpc)\\
Host & Radio Galaxy; SFG: Spiral; Seyfert I,II; QSO; Blazar \\
& BLLac; BLRG; NLRG; ULIRG; LERG; \\
& HERG; LINER; BCG \\
Spectra & Flat; Steep; Ultra-steep; GigaHz Peaked; \\
& Inverted; Convex; Concave; Complex \\
\bottomrule
\end{tabular}
\\ *This unfortunate nomenclature is now being more widely adopted and should by dropped; see the critique in \citet{hard20}.
\end{specialtable}
Over the past several years, I have led discussions and surveys on these issues with over 100 members of the radio astronomy community, at meetings and workshops; I acknowledge without mentioning names the many people who contributed fertile ideas. Several lessons became clear:
\begin{itemize}
\item {The current classification schemes are confusing and have started to break down.}
\item{As a community, we want to document a very wide variety of characteristics for large samples of radio sources. Some of the more commonly mentioned (at least today) are listed in Table \ref{priorities}.}
\item{Multi-wavelength information should be included where available.}
\item{Confidence levels should be provided.}
\item{Classifications should evolve as more information becomes available.}
\item{Criteria for classification should be completely transparent.}
\end{itemize}
\begin{specialtable}[H]
\small
\caption{Commonly mentioned priorities for catalog {\em source} descriptions. These assume that {\em components} have been assembled into {\em sources}. Some require information external from the survey.} \label{priorities}
\begin{tabular}{ccc}
\toprule
\textbf{Category} & \textbf{Measurements/Descriptors} \\
\midrule
Direct & Peak and total flux; Brightness temperature;\\
& Angular size and area; Linear Size and area;\\
& Redshift; Spectral index; Fractional polarization; RM;\\
& Number of components/peaks in source\\
Structural & Core/total flux; Number of jets (0,1,2); Jet-flux/total-flux;\\
& Peak-separation/total-extent (FRI,II); Shape (e.g., linear, bent);\\
& Symmetry (S-, C-, X-)\\
Supplemental & Host properties (include SFR); X-ray properties;\\
& pc-scale structure; group or cluster environment\\
\bottomrule
\end{tabular}
\end{specialtable}
In the face of these challenges and aspirations, we are fortunately at a time of great opportunity, since new catalogs with millions of radio components are being or will be produced by LOFAR, EMU and POSSUM at ASKAP, MeerKAT, VLASS at the VLA, Apertif at Westerbork, $\mu$GMRT, GLEAM at the MWA, etc.. If new classification schemes can be incorporated into those catalogs, then their scientific usefulness will blossom.
\section{\#Tags}
To take advantage of these opportunities, I propose that instead of putting a source into a {\em box} so that it belongs in that box and not in other boxes, we use a series of criteria-based \#{\em tags~ }. Each source can have any number of \#{\em tags~ }, as long as the source passes the criteria for each \#{\em tag~ }.
This system forces a subtle, but important distinction in how we think about these classes -- instead of deciding that "Source A {\em IS} a member of Class X," we say, more narrowly, "In Survey G, Source A passes the test to be assigned \#{\em X}." Although this may seem trivial, it provides enormous advantages. For example, no longer will we need to argue about whether a source detected in a high-resolution survey is {\em really} a small one-sided jet; if it passes the criteria, it will be assigned \#{\em one-sided-jet}. Then, if a new low frequency survey shows that it is part of a much larger structure, with two jets and extended lobes visible, then the new survey will assign it a different \#{\em tag~ }, particular to that survey. \#{\em Tags~ } are thus explicitly dependent on the properties of the observations/survey that were used to make the assignment.
Figure \ref{1265} gives a further example of this re-conceptualization. It shows two views of the prototypical narrow-angle-tail source NGC~1265. Such tails, when seen near the AGN at high resolution, will always look like wide-angle-tails (WATs). If we follow the criteria in the defining paper for WATs (\citet{WAT}), the ``source" on the left would be classified a \#{\em WAT}. This is not a mistake -- if we follow the \#{\em tag~ } schema; it simply means that it passed the relevant test. A theorist, e.g., may well want to model the properties of this source as part of studying the gently bent portion of jets, and select it as part of a sample of \#{\em WAT}s from a catalog. On the other hand, an observer studying ICM interactions might want to exlcude this \#{\em WAT} based on other catalog entries, e.g., because its small linear size shows that it is still being influenced by its host's ISM.
\begin{figure}[H]
\begin{center}
\includegraphics[width=10.5 cm]{Figures/ThisIsNotWAT2.png}
\caption{ \textbf{Is this not a WAT?}. Using the VLA data presented in \citet{MLpers}: \textbf{(Left)} Close-up view of the head of NGC~1265; \textbf{(Right)} Larger scale view of the same source.}
\label{1265}
\end{center}
\end{figure}
\subsection{\#{\em Tag} Principles}
The following summarizes the principles, characteristics of \#{\em tag~ } systems that are required to meet the scientific needs expressed in our discussions. These are likely to need refinement once such systems go into use.
\begin{itemize}
\item{\#{\em Tags~ } {as proposed here} apply to {\em sources}, where all the emission is believed to originate in a single host, whether visible or not. \#{\em Tags~ } {currently} do not apply to the source's constituent components, as identified by ``source" finders, {although such schemes could also be developed}.}
\item {Each source can have multiple \#{\em tags~ }. }
\item {A source can pass or fail to meet the criteria of each \#{\em tag~ }, or not have sufficient information to be tested. For example, a barely resolved double source cannot be tested for the number of jets present.}
\item {There can be multiple versions of \#{\em tags~ } for the same purpose, with different underlying criteria. For example, \#{\em Giant$_A$} might include bent sources, where the sum of the length of the two lobes was $>$700~kpc, while \#{\em Giant$_B$} might only include sources that cannot fit in a 700~kpc box.}
\item{\#{\em Tags~ } must be based on well-defined criteria, quantitative wherever possible, with the definitions or algorithms made available.}
\item{\#{\em Tags~ } can change with time as more information or better algorithms become available. (Keeping track of versions will become important.)}
\item{\#{\em Tags~ } should have corresponding confidence values, if possible.}
\item{\#{\em Tags~ } will be specific to a given survey, since they will depend on resolution, sensitivity, dynamic range, availability of auxiliary information, etc.}
\item{\#{\em Tags~ } can be valuable even when they appear trivial. For example, although sizes and errors may be included in a catalog, the distinction between extended and compact sources may need expert judgement, and be embodied in the \#{\em tag~ }. The experts would consider the dependencies on signal:noise, dynamic range, the presence of artifacts, etc. in setting up the \#{\em tag~ } criteria.}
\end{itemize}
\subsection{Tag Example}
The following illustrates the application of \#{\em tags~ } to an anonymous source from the MeerKAT Galaxy Cluster Legacy Survey (\citet{knowles21}). Only a handful of \#{\em tags~ } are shown; each catalog may use as many \#{\em tags~ } as are appropriate or practical. Note that there will be many other catalog entries for this source. These would include positions, fluxes, etc as listed in Table \ref{tab1}, and would be used as criteria for each \#{\em tag~ }. The assumption, for this illustration, is that in-band spectral indices are available, as well as the optical host, but not a redshift.
\begin{figure}[H]
\begin{center}
\includegraphics[width=5 cm]{Figures/TagExamp.png}
\caption{ Anonymous example source from the (fictitious) EMK Survey, for the application of \#{\em tags~ }. Radio map is actually from \citet{knowles21}. Optical inset is from the Dark Energy Survey.}\label{examp}
\end{center}
\end{figure}
\begin{specialtable}[H]
\small
\caption{\#{\em Tag} example for source in Figure \ref{examp}. +1 = satisfied \#{\em tag~ } criteria. -1 = failed \#{\em tag~ } criteria. 0~=~insufficient information to test \#{\em tag~ } criteria. Each \#{\em tag~ } is prepended by EMK, to identify it with the (fictitious) EMK survey.}
\label{tab2}
\begin{tabular}{cc|cc}
\toprule
\textbf{{\em \#Tag}} & \textbf{Value} &\textbf{{\em \#Tag}} & \textbf{Value} \\
\midrule
\ul {Structural} & & \ul {Spectral+}& \\
\#{\em EMK:S-symmetry} & +1 & \#{\em EMK:SteepSpec} & +1\\
\#{\em EMK:C-symmetry} & -1 & \#{\em EMK::ConvexSpec} & 0 \\
\#{\em EMK:FRI} (peaksep/tot$<$0.5) & +1 & \#{\em EMK:Backflow} & -1 \\
\#{\em EMK:FRII} (peaksep/tot$>$0.5) & -1 & \#{\em EMK:Outflow} & +1 \\
\#{\em EMK:Coredom} & -1 & \#{\em EMK:Polarized} & 0\\
\#{\em EMK:Giant} & 0 & \#{\em EMK:BCG} & 0\\
\bottomrule
\end{tabular}
\end{specialtable}
Careful readers will note two unfamiliar \#{\em tags~ }, \#{\em EMK:Backflow} and \#{\em EMK:Outflow}. I introduce them here as an example of how individuals can add \#{\em tags~ } that they think are important, without affecting earlier alternative \#{\em tags~ }. In this case, the new \#{\em tags~ } are alternatives to the FRI,II scheme, and are likely to be much more scientifically informative. \#{\em EMK:Backflow} denotes sources with spectral indices that steepen from their leading edge back to the nucleus; \#{\em EMK:Outflow} sources have spectral indices that steepen with increasing distance from the nucleus. These represent two physically different jet behaviors, and the FRI,II scheme can be understood as a less precise proxy for these behaviors. The disadvantage of these new \#{\em tags~ } is that they can be applied only to sources that are sufficiently large and bright; but since they only add information, nothing is lost. Another technical detail is that spectral changes due to magnetic field variations on a curved electron spectrum would have to be considered in applying this criterion, to isolate the effects of radiative ageing.
\subsection{ Implementation of \#{\em Tags~ }}
Although individual investigators could and should develop their own \#{\em tags~ } to address questions of scientific interest, the most useful use of \#{\em tags~ } will come from observatory or survey teams that incorporate them into catalogs. The EMU Survey has begun such a process in the design of {\em EMUcat}, with many of the details still being worked out. Following are some notes and guidelines that may be useful in implementing such a scheme. As before, these will certainly need to be revisited as the community gets experience with this new classification tool.
\begin{itemize}
\item {{For a source-based \#{\em tag~ } scheme,} components from source-finders will first have to be assembled into sources, with or without a host identification.}
\item {Each \#{\em tag~ } will require measurements or other data about the source, that are already included in the catalog. Early identification of \#{\em tags~ } to be used will ensure that the required information is available.}
\item {Some \#{\em tags~ } will be based on catalog data; other \#{\em tags~ } will require algorithms to be run on images (e.g., symmetries, jet presence or dominance)}
\item{Some \#{\em tags~ } will require information from auxiliary databases not included with the catalog; links or other references to that information are needed.}
\item{All criteria and algorithms should be made publicly available, either as metadata, or in software repositories, etc.}
\item{Different surveys will require different schemes; however, wherever common definitions can be used, those will be highly desirable.}
\item{It is desirable to allow for new \#{\em tags~ } developed by individuals and teams to be added to the catalog, after appropriate vetting by the survey team.}
\item{Versioning of \#{\em tags~ } will have to be built into the catalog design.}
\end{itemize}
{One quite promising opportunity and challenge to a strict algorithmic approach is to} incorporate classifications that are done by visual inspection, such as Radio Galaxy Zoo (\citet{rgz}) or LOFAR Galazy Zoo (\citet{lzoo}) and their planned successors. The use of MaNGA morphologies from Galaxy Zoo for SDSS entries (\citet{manga}), where available, may provide guidance on how to include non-quantitative \#{\em tags~ }. Similarly, classifications from supervised and unsupervised machine learning algorithms will become available over the next several years, and the community will have to determine how to best utilize those. One innovative effort using machine learning to build on a \#{\em tag~ }-like schema has now been used in the classification of supernova spectra (\citet{sn21}).
\section{Conclusions:}
The mammoth new catalogs and increasingly sophisticated scientific questions being asked about radio galaxies demand a new approach to radio galaxy classification. \#{\em Tags~ } provide a promising alternative.\\
\acknowledgments{Although I've been interested in this issue for many years, I credit Ray Norris for ``recruiting" me to take on this task because of the demands imposed by the EMU Survey. The advice of many colleagues over the last several years has been of immeasurable value. The questions surrounding implementation have benefited enormously by the work of Josh Marvil and his EMUcat team.}
\funding{This work was supported, in part, by U.S. National Science Foundation grant AST17-14205 to the University of Minnesota.}
\conflictsofinterest{The author declares no conflict of interest.}
\reftitle{References}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 965 |
Q: Array of pictures leaking This is what I'm doing. I have an ever growing array of pictures pictures for a photo slideshow. I display picture i as follows:
pictures[i]
.fadeIn(500)
.delay(5000)
.fadeOut(500, function () {
$(this).remove();
delete this;
});
Despite my attempts to flush the memory by using .remove() and delete, I am still having a memory leak. Am I doing something wrong?
A: Update
As per the comments below, this was tested in Chrome and the browser seems to hold on to the memory from the images until the page is no longer actively rendered (reloaded, switched tab, etc.). Unfortunately, this holds true in Firefox and IE as well.
IE and Firefox had much better memory de-allocation (continually dropping memory as the page stayed open) but both still grew indefinitely. Upon switching tabs in both (by opening a new tab) the memory was almost immediately freed.
I haven't inspected your code thoroughly so I'm not sure if this problem can somehow be avoided (it doesn't appear so on first pass) though you should keep in mind that you are continually adding indicies to an ever-growing array that will continue to use more and more memory on its own. Perhaps it is the reference in the array that is sticking around which could be avoided if you came up with another way to implement the slideshow.
The reason why I'm guessing it might be this is from this discussion: garbage collection with node.js. The browser garbage collector needs to ensure that they are not reachable (which they always are, since the array is ever-growing). Thus you have to wait for the garbage collector to clean up the <img> values inside the indices to free the memory, and that doesn't necessarily happen right when you set them to null.
You'll need to pass your iterator i to your callback function. Then you'll be able to null the picture after it fades out and free the memory it was using. Just make sure you don't get caught in the common closure-iterator problem -- something like this should work:
pictures[i].fadeIn(500).delay(5000).fadeOut(500, (function(i) {
pictures[i] = null;
})(i);
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,215 |
Q: Mapreduce POJO mapping i have a file in hdfs system which is the output of join of 3 tables related to sales data.
(sales header, item detail,tender detail).
The file will have columns from all the three tables combined.
If there are 3 items and 1 tender , i will have 6 rows for a transaction.
So there will be 6 lines in the file with same transaction number.
I can read this in mapper and create a DTO with all the fields
Now i want to construct the complex DTO structure out of this flattened DTO.
Is there any pojo mapping framework available for this and will it support maping from a plain DTO to a complex structure.
Structure
public class PlainDTO{
String tranId;
String processDate;
String itemNumber;
String itemName;
int tenderId;
.......
......
}
From List, i need to convert to
below structure
public class ComplexDTO{
private SlsHeader slsHeader;
private Collection<SlsItems> items;
private Collection<SlsTender> tenderDetails
}
A: Conversion from flat DTO to complex DTO is plain java stuff. Once you write it, and it stays like that. From complex DTO to json, you can use any JSON-Java parsers like Jackson or Gson.
The challenge could be, once you have this one-many mapping(DTO complex structure) in json, you should see how the Elastic search manages these relationships. I worked with Solr(similar to Elastic Search). They have child documents concept in Solr.
Also, at higher level, if your Elastic search client is java based, you can directly go from Flat structure to ES client, skipping json.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,364 |
Brady: Edelman is too good to just put someone else in
Published: Nov. 16, 2015 at 12:39 p.m.
Updated: Nov. 17, 2015 at 08:27 a.m.
For the second straight week, Tom Brady watched one of his top playmakers lost for a large swath of the season.
Last week, shifty back Dion Lewis went down with an ACL injury. Sunday it was reliable Julian Edelman who left with a broken bone in his foot that will keep him out 6-8 weeks, NFL Media's Albert Breer reported, per a source briefed on the injury.
The dynamic pass-catcher was on pace for the second 1,000-yard season of his career prior to the injury. On Monday morning, Brady went with the Coach Boone response when asked on WEEI-FM how the Pats would replace Edelman.
Every game, all season
"When someone's really integral to part of basically everything you're doing, and then you lose that person, it may take a little bit to kind of figure out how you can move things around and get comfortable with what you're doing, because you want to have a lot of confidence in the things that you're doing," Brady said.
"That's just the way kind of it is. There's nothing that's really seamless when you lose a great player. When it's someone that's been the leading receiver on your team for multiple years and you lose them, it's not like you go, 'OK, well, let just put someone else in.' He's too good of a player for that. You've just got to kind of find your way to make some adjustments. I think we just made some critical plays when we needed to, which was really important down the stretch, certainly defensively, and special teams we did. And on offense I thought we just did enough."
New England's offense wasn't the same after Edelman exited on the last play of the first quarter. The Pats gained 137 yards in the first frame and 269 total in the final three. Brady was 5 of 6 on third down (83 percent) with Edelman on the field and 2 of 8 (25 percent) without him, via the Providence Journal's Mark Daniels.
Brady dismissed that Danny Amendola could just slide over and fill Edelman's role, noting that the two are different types of players. As is the norm with Bill Belichick's teams, they'll plug in different players, adjust their game plan to what fits them best and continue to roll on towards the playoffs.
"We'll need to find different ways to produce with the guys that are on the field," Brady said matter-of-factly. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,202 |
What is magicJack go and how does it work?
The influx of new technical concepts has left the tradition phone calling far behind. Usage of these new technologies proves of great use as you do only not enjoy distortion-free calling with dears and business partners but also save a big amount of money for great savings. Have a look at magicJack Go.
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A timely call to MagicJack Customer Support certainly makes you a great beneficiary while providing a credible tool to enjoy local and international calling. This technology perfectly suits all kinds of the household as it does not eat much space. Due to its compact size, you can easily place at the desired corner to easily match the pace with the latest trends and standards of modern times.
Digital analysts always opine to not delay in taking the right steps for beneficial decision. Lethargic attitude decreases the momentum of smart decision-making senses whereas right call at a congenial time automatically multiplies the delights. Anyway, tiring efforts are not needed to arrange the contact details. Rely on the internet. This online tool will certainly help in an expected manner while ensuring great comfort for each and every user.
What are the common problems with MagicJack Plus? | {
"redpajama_set_name": "RedPajamaC4"
} | 1,208 |
package org.terasology.world;
import org.terasology.entitySystem.Component;
import org.terasology.math.geom.Vector3i;
/**
*/
public class RelevanceRegionComponent implements Component {
public Vector3i distance = Vector3i.one();
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,684 |
- Tensai & Brodus Clay beat Bo Dallas & Sami Zayn in a dark match prior to this week's Smackdown taping.
- Jim Ross Tweeted on Tuesday that he's not looking for work and that he's enjoying football season. Speaking of JR, he has a new blog entry online that you can read at this link.
- Ryback is scheduled to represent WWE in Mumbai this weekend to promote WWE 2K14. He is not scheduled for weekend live events as a result.
- Speaking of Ryback, he talks about failing a drug test while in WWE developmental and his program with CM Punk coming full circle with SunHerald.com. You can read now at this link. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,922 |
Systematic dysphagia screening and dietary modifications to reduce stroke-associated pneumonia rates in a stroke-unit
Yvonne Teuschl,
Roles Conceptualization, Data curation, Methodology, Writing – original draft
Affiliation Department for Clinical Neuroscience and Preventive Medicine, Danube University Krems, Krems, Austria
Michaela Trapl,
Roles Conceptualization, Data curation, Investigation, Methodology, Writing – review & editing
Affiliation Department of Neurology, University Hospital Tulln, Tulln, Austria
Paulina Ratajczak,
Roles Formal analysis
Karl Matz,
Roles Conceptualization, Writing – review & editing
Affiliations Department for Clinical Neuroscience and Preventive Medicine, Danube University Krems, Krems, Austria, Department of Neurology, University Hospital Tulln, Tulln, Austria, Karl Landsteiner University of Health Sciences, Krems, Austria
Alexandra Dachenhausen,
Roles Conceptualization, Funding acquisition, Writing – review & editing
Michael Brainin
Roles Conceptualization, Funding acquisition, Methodology, Supervision, Writing – review & editing
* E-mail: michael.brainin@donau-uni.ac.at
Yvonne Teuschl Michaela Trapl ... Michael Brainin
While formal screening for dysphagia following acute stroke is strongly recommended, there is little evidence on how multi-consistency screening and dietary modifications affect the rate of stroke-associated pneumonia (SAP). This observational study reports which factors affect formal screening on a stroke-unit and how dietary recommendations relate to SAP.
Analyses from a database including 1394 patients admitted with acute stroke at our stroke-unit in Austria between 2012 and 2014. Dietary modifications were performed following the recommendations from the Gugging Swallowing Screen (GUSS). Patients evaluated with GUSS were compared to the unscreened patients.
Overall, 993 (71.2%) patients were screened with GUSS; of these 50 (5.0%) developed SAP. In the 401 unscreened patients, the SAP rate was similar: 22 (5.5%). Multivariable analysis showed that either mild to very mild strokes or very severe strokes were less likely to undergo formal screening. Older age, pre-existing disability, history of hypertension, atrial fibrillation, stroke severity, cardiological and neurological complications, nasogastric tubes, and intubation were significant markers for SAP. Out of 216 patients, 30 (13.9%) developed SAP in spite of receiving nil per mouth (NPO).
The routine use of GUSS is less often applied in either mild strokes or very severe strokes. While most patients with high risk of SAP were identified by GUSS and assigned to NPO, dietary modifications could not prevent SAP in 1 of 7 cases. Other causes of SAP such as silent aspiration, bacteraemia or central breathing disturbances should be considered.
Citation: Teuschl Y, Trapl M, Ratajczak P, Matz K, Dachenhausen A, Brainin M (2018) Systematic dysphagia screening and dietary modifications to reduce stroke-associated pneumonia rates in a stroke-unit. PLoS ONE 13(2): e0192142. https://doi.org/10.1371/journal.pone.0192142
Editor: Stefan Kiechl, Medizinische Universitat Innsbruck, AUSTRIA
Received: October 2, 2017; Accepted: January 17, 2018; Published: February 1, 2018
Copyright: © 2018 Teuschl et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: We provide data as csv file in the supporting information.
Pneumonia is a frequent complication after stroke and increases the risk for mortality and dependency [1–2]. Approximately 14% of patients suffer from pneumonia during the first week after stroke, but there is high variability in the reported numbers depending on the population, the study design and the diagnosis criteria [3]. Dysphagia is a major risk factor for stroke-associated pneumonia (SAP) observed in up to 78% of stroke patients, and has been associated with higher mortality, worse functional outcome and longer hospital stay [4–7].
There is some evidence from observational studies that formal screening for dysphagia following acute stroke can reduce the risk of pneumonia [8–13], and guidelines [14–15] strongly recommend screening of the swallowing abilities for all acute stroke patients as soon as patients are awake and alert.
We developed the Gugging Swallowing Screen (GUSS) in 2007 as a brief bed-side assessment screen for dysphagia and aspiration risk that can be used by speech and language therapists (SLT) as well as nurses [16]. In the meantime, the GUSS has been translated into 11 languages and has been further validated by use of fiberoptic endoscopic evaluation of swallowing (FEES) [17] and by an intervention study for use by trained nurses [13]. The GUSS allows a classification of the severity of dysphagia into 4 severity codes and provides nutritional recommendations accordingly.
In this study, we report the use of GUSS in clinical routine and how its dietary recommendations relate to dysphagia and the rate of SAP. We focus on three questions: 1) We analyse how many acute stroke patients were screened with GUSS at our stroke-unit and which were the factors associated with screening. 2) We analyse the frequency of dysphagia and the factors associated with its severity. 3) We report the frequency of SAP in relation to the use of GUSS and the prescribed diet.
This retrospective database analysis includes all patients (n = 1394) admitted with acute stroke from 2012 to 2014 to the acute stroke-unit at the University Clinic Tulln, Austria. All patients referred to the hospital under suspicion of stroke were directly admitted to the stroke-unit. The diagnosis of stroke was based on clinical presentation and brain imaging (computed tomography [CT] or magnetic resonance imaging [MRI]). A transient ischemic attack (TIA) was diagnosed if clinical symptoms of stroke lasted less than 24 hours and no lesion was detected on the CT or DW-MRI. All patients admitted to the stroke-unit were entered in the Austrian Stroke Unit Registry. The Austrian Stroke Unit Registry collects anonymized, stroke-relevant data on baseline characteristics, management and outcome of all stroke patients admitted to Austrian stroke-units (for more details see [18–19]). All aspects of data entry, data protection, administration and scientific analysis are regulated by law. A formal ethical approval from the local Austrian ethics committee was not needed. Data collection, ratings and data entry were performed by experienced stroke neurologists at the time of admission and discharge to the stroke-unit as well as via follow-up phone call three months thereafter. Stroke severity was assessed on admission and discharge from the stroke-unit using the National Institute of Health Stroke Scale (NIHSS). The modified Rankin Scale (mRS) was used to evaluate functional status before stroke, on admission and discharge from the stroke-unit as well as on follow-up three months later. Vascular risk factors were determined according to medical history, pre-stroke medication or were newly diagnosed during the stay at the stroke-unit. Stroke types were classified on the basis of neuroimaging findings and according to the International Classification of Diseases (ICD)-10 code into ischaemic stroke (I63 or I64) or haemorrhages (I60, I61 or I62). In line with previous evaluations in the acute stroke setting, standard diagnostic criteria were used for assessment of clinical complications [19].
Diagnosis criteria for pneumonia were based on the modified CDC criteria and the recommendations from the pneumonia in stroke consensus group for probable SAP [20]: clinical symptoms (e.g. cough, purulent sputum) in combination with clinical signs such as fever, rales, bronchial breath sounds or elevation of inflammatory markers in laboratory tests confirmed by at least one chest x-ray within 7 days after stroke. Pneumonia diagnosed later than 7 days after admission was defined as hospital associated pneumonia (HAP). Patients' medical records which include all information (reports, examinations) of all medical wards during hospital stay were reviewed by a SLT. In cases with at least one chest x-ray, the reports from the radiologist, the internist and the final medical report from the neurologist were reviewed for a diagnosis of pneumonia during hospitalisation. When the reported diagnoses differed or did not correspond to the chest x-ray or to the reported symptoms and signs, the diagnosis of the internist was used. The occurrence of pneumonia after hospital discharge was not recorded during the 3-month follow-up.
Dysphagia screening was performed in accordance with stroke guidelines and the SOPs for Austrian Stroke Units: In brief, patients with tracheostomy and inflated cannula tubes or with reduced consciousness were restricted to receive nil per mouth (NPO). Patients with suspected impairment in cranial nerves involved in swallowing (V, VII, IX, X, XII), neurological diseases in the medical history, with neuropsychological deficits (e.g. apraxia, neglect) were tested by trained nurses or SLTs within 24h after admission with GUSS. All other patients were examined for swallowing disorders using a simple water swallowing test. Conspicuous patients are transferred to SLTs for further investigation and treatment.
Dietary modifications were performed according to the recommendations from the GUSS Score [16,21] and are described using the levels of the International Dysphagia Diet Standardisation Initiative (IDDSI) framework for texture-modified foods and thickened fluids [22]. As a consequence of the clinical experience gained over the years, an additional diet (NPO-med) was assigned under the supervision of the SLT to patients scoring 8 to 9 points on the GUSS: patients were not fed per mouth except for medications which were crushed and mixed with apple sauce. Data on GUSS (day of screening, GUSS score, recommended diet, profession of person performing the screening) were systematically recorded for all patients and entered in their medical records as part of the clinical therapeutic process either by the SLT or by the nurses performing the screening. As the GUSS is part of the clinical routine and data are analysed anonymously, no ethic approval is needed for the analysis of these data.
Univariate comparisons were made using the t-test for continuous normally distributed variables, the Mann Whitney U-test for continuous non-normally distributed variables and the Chi2 or the Fisher exact test for binary variables.
Patients evaluated with GUSS within 7 days were compared to the unscreened patients in a step-wise backward multivariable binary logistic regression analysis optimizing the AIC criteria including demographic factors, risk factors, stroke type, stroke severity (linear, quadratic), complications, treatment, delay of screening, day of screening, and stroke-unit mortality as explaining variables. The number of cases with pneumonia was low, making the multivariable models unstable. Therefore factors associated with pneumonia were only reported in a descriptive way by using univariate comparisons. The factors associated with dysphagia (<20 points on the GUSS) and with aspiration risk (<15 points) [16] were analysed in binary logistic regression models.
Because of the increasing risk of dysphagia starting at the age of 60 [23] the following categories were chosen for age: <60, 60–69, 70–79, 80–89, ≥90 years.
There were 1394 patients with acute stroke in the stroke registry between 2012 and 2014. Of these, 993 (72.2%) were tested with GUSS within the first 7 days. Of the remaining 401 patients 339 were not tested, 32 were transferred to SLTs for diagnostic reasons other than swallowing disorders (language disorders, facial paralysis) and 30 were tested more than 7 days after admission (Fig 1). Overall 899/1023 (88%) of all patients undergoing a GUSS were tested on the same or the next calendar day, and 939/1023 (92%) within the first three calendar days. The median stroke-unit stay was 2 days (IQR: 1 to 4).
Fig 1. Patient flowchart.
GUSS: Gugging Swallowing Screen, HAP: hospital-acquired pneumonia (>7 days post-stroke); SAP: stroke-associated pneumonia (≤7 days post-stroke); SLT: speech and language therapist, SU: stroke-unit. *According to the discharge diagnosis based on neuroimaging findings.
Factors associated with GUSS testing
Characteristics of the entire population as well as those tested with GUSS are shown in Table 1. The multivariable analysis showed that patients who were screened were older, had more often previous strokes, more often ischemic strokes, were more often admitted during working days, were more often treated with thrombolysis, suffered less from neurological complication and died less often on the stroke-unit (Table 2). Furthermore, the analysis showed a bimodal distribution of the stroke severity with either mild strokes or severe strokes being less likely to get screened (Table 2).
Table 1. Characteristics of patients undergoing (n = 993) and not undergoing (n = 401) the Gugging Swallowing Screen (GUSS) within 7 days.
Table 2. Fal stepwise backward binary logistic regression model optimizing the AIC criterion for the factors associated with undergoing a Gugging Swallowing Screen within 7 days (R2 = 0.237, n = 1388).
For 20 of the 22 patients with SAP that were not tested with GUSS, possible reasons for not using the GUSS were identified: 2 patients died within 2 days, 6 were transferred to intensive care on the same or the next day, 14 were treated with nasogastric tubes, percutaneous endoscopic gastrostomy, intubated or had a tracheostomy, and 4 had an impaired level of consciousness on admission.
Factors associated with dysphagia
The first GUSS was performed in 331/993 (33%) of the cases by nurses and in 662/1051 (67%) by a SLT in median on the day of admission to the stroke-unit (median: 0 days; IQR: 0 to 1). According to the first GUSS evaluation 389 (39.2%) patients had no sign of dysphagia (20 points), whereas 126 (12.7%) showed slight (15–19 points), 232 (23.4%) moderate dysphagia (10–14 points) and 246 (24.8%) severe dysphagia (0–9 points) (Fig 2). The presence of dysphagia (<20 points) was associated with older age, a worse functional status before stroke, diabetes, no stroke in medical history, haemorrhagic stroke, and more severe stroke (Table 3). The risk of aspiration (<15 points) was associated with older age, worse functional status before stroke, haemorrhagic stroke, and more severe stroke (Table 4).
Fig 2. Severity of dysphagia according to the first Gugging Swallowing Screen (GUSS) score after admission at the stroke-unit: no (20 points), slight (15–19 points), moderate (10–14 points), severe (0–9 points) dysphagia.
Table 3. Final stepwise backward binary logistic regression model optimizing the AIC criterion for the factors associated with dysphagia (Gugging Swallowing Screen score <20 points; R2 = 0.41; n = 990).
Table 4. Final stepwise backward binary logistic regression model optimizing the AIC criterion for the factors associated with aspiration (Gugging Swallowing Screen score <15 points; R2 = 0.417; n = 990).
Factors associated with SAP
Overall 102 patients developed pneumonia (Fig 1). Of those 72 (4.8%) were classified as SAP: 22/401 (5.5%) in patients without GUSS and 50/993 (5.0%) in patients with GUSS. Due to the low numbers of SAPs, risk factors for SAP were only described by univariate comparisons (Table 5). Older age, pre-existing disability, history of hypertension, atrial fibrillation, stroke severity on admission, haemorrhagic strokes, cardiological and neurological complications, nasogastric tubes, and intubation were significant markers for the occurrence of SAP.
Table 5. Demographic factors, vascular risk factors, stroke related factors and treatment related factors in relation to incidence of stroke associated pneumonia (SAP).
GUSS, dietary modifications and SAP
SAP was highest in patients with severe dysphagia according to GUSS scores: 3/389 (0.8%) patients with normal swallowing functions, 3/126 (2.4%) with slight, 12/232 (5.2%) with moderate, and 32/246 (13.0%) with severe dysphagia developed SAP.
The diet that was prescribed to the patients was in accordance with the recommendations of the GUSS. Only 6 of the 993 patients with GUSS received a diet that was less strict than the recommended diet (Table 6). None of these patients developed SAP. Another 33 patients with severe dysphagia were assigned to NPO-med, i.e. they were assigned to NPO but received their medication orally, crushed and mixed with apple sauce. Two of these patients developed SAP. Overall, 30 of the 50 (60%) patients who developed SAP were assigned to receive NPO (Table 6). In 41 of the 50 (82%) patients with SAP the GUSS was performed on the same or the next calendar day.
Table 6. Diet that was administered according to the severity of dysphagia, measured with the Gugging Swallow Screen (GUSS).
The number of stroke associated pneumonia (n = 50) are presented in parentheses; grey cells represent diet recommendations according to GUSS, cells above the grey cells indicate a diet less strict, cells below a diet stricter than recommended by GUSS; spotted cell indicate 8–9 points on the GUSS and administered to NPO-med diet.
Overall, 52 (3.7%) patients died on the stroke-unit. Mortality was higher among patients with SAP (8.3%) compared to those without (3.5%) (Table 5). Of those patients alive at discharge from the stroke-unit with a follow-up (n = 918) another 155 (16.9%) died during the next 3 months; 25 (55.6%) of those with SAP compared to 130 (14.2%) without SAP (Table 5).
In this cohort of patients admitted with acute stroke or TIA to a stroke-unit, 72% were tested with the GUSS. The GUSS was less often applied in mild strokes as well as in very severe strokes. The GUSS identified patients with the highest risk of SAP and they were assigned to NPO. However, dietary modifications could not prevent pneumonia in all stroke cases—especially not in patients who had already developed severe dysphagia.
Use of formal dysphagia screening
In clinical centres following recommendations for formal dysphagia screening the percentages of patients screened after acute stroke varied between 69% and 88% which is comparable to the 72% of patients tested with GUSS in our study [8,11,24–26]. Unfortunately, we did not systematically document the reasons for not using a GUSS and thus the number of patients ineligible for testing. In our study, dysphagia screening was not performed when patients were strongly affected, probably making early testing impossible, or in very mild cases where no pneumonia was expected. This is comparable to the results of a German stroke registry where two groups of patients were identified who did not undergo dysphagia screening: younger and less affected patients, as well as patients with highly impaired consciousness [25]. Similarly two other observational studies showed that patients with more severe stroke were more likely to be screened [9,26]. Patients with mild strokes are at lower risk of dysphagia and pneumonia. Nevertheless, 2.3% of our patients with mild strokes (NIHSS score ≤6) developed pneumonia, 130 of 527 (25%) were at risk of aspiration (GUSS score <15), and 203/527 (39%) had dysphagia (GUSS score <20; data not presented). Similarly, 33% of mild strokes failed dysphagia screening in the Ontario stroke registry [26]. These percentages might be overestimated because patients with mild stroke and clinical signs of swallowing disorders may be more likely to be screened. However, given that dysphagia is not included in the NIHSS and because of possible pre-existing swallowing disorders in elderly patients, mild strokes should not be omitted from dysphagia screening.
The GUSS has been validated to be used by SLT as well as by nurses [16]. Indeed our study showed that the first GUSS was performed in 35% of cases by nurses. A recent study conducted on another Austrian Stroke-Unit showed that the systematic training of nurses to perform the GUSS decreased the rate of pneumonia from 11.6% to 3.8% [13]. This underlines the importance of an interdisciplinary bedside screen such as GUSS which can be used on weekends, holidays and outside the regular working hours in the absence of a SLT.
Incidence of dysphagia
Of those patients undergoing a screening 61% were diagnosed with dysphagia according to the first GUSS. The rate is comparable to an incidence rate of 30% to 55% found in a review when only clinical testing is used after acute stroke [4]. The rate of dysphagia found in our study might over- or underestimate the incidence of dysphagia as mild and severe stroke were less likely to be screened. Furthermore, as in other studies, pre-existing swallowing impairment was not assessed. Apart from pre-stroke conditions, anatomical, physiological, psychological, and functional changes as part of "normal aging" contribute to alterations in swallowing in persons older than 60 years [23]. However, swallowing disorders in the apparently healthy elderly population often occur without clinical complaints [27], and it may thus be difficult to evaluate them retrospectively after the stroke event.
Prevalence of SAP
As previously found in other studies, the rate of SAP was higher for patients with dysphagia compared to patients with normal swallowing function [4,6,25,26], and was highest for those with severe dysphagia.
Early interventions such as dietary adaptations, intensive swallowing therapy and oral hygiene can reduce the incidence of chest infections in stroke patients with dysphagia [28,29]. In our study, 5.2% of patients developed SAP. Compared to overall rates of post-stroke pneumonia of 10% and 14% in two recent meta-analyses [3,30] this rate is relatively low and suggests that the dietary modifications recommended by the GUSS may be successful in preventing SAP. However, there is high variability in the reported numbers of pneumonia depending on the population, the study design and the diagnosis criteria. In a multi-centre study formal dysphagia screening was found to lower pneumonia rate as low as 2.4% compared to 5.4% in sites with no formal screening [10]. Similarly, the implementation of a dysphagia screen increased the percentage of patients being screened from 39% to 74% and decreased HAP from 6.5% to 2.8% in a prospective single-centre study [9]. In a Japanese single-center study the implementation of a multidisciplinary swallowing team decreased the rate of SAP from 16% to 7% [12]. Recent analyses of stroke registers of centers following national guidelines recommending dysphagia screening in acute stroke may be more comparable to our study and reported pneumonia rates between 4% and 10% [8,11,24–26].
As in previous studies, more severe strokes, older age and impairment before stroke were associated with dysphagia as well as with SAP [6,26]. Indeed, these three variables are key elements of SAP prediction scores such as the A2DS2, the AIS-APS or the integer-based pneumonia risk score (ISAN) [31]. We did however not find an association between sex and pneumonia.
Dietary modification and SAP
While the GUSS was validated as bed-side screening instrument to identify acute stroke patients at risk of aspiration and dysphagia, the nutritional recommendations were not tested for their ability to prevent SAP [16].
The rate of SAP was not lower in the group of patients screened with GUSS. A similar result was found by Titworth et al 2013 who found that after the implementation of a dysphagia screen the rate of pneumonia decreased but was not different between patients that were screened and those that were not [9]. This may be explained by screening being more likely in more severe strokes and thus masking the positive effects of interventions. In the majority of patients that were not screened with GUSS but developed SAP we identified reasons which might have prevented early testing or which show that patients have been assigned to NPO anyway—independent of a GUSS. It is thus probable that the GUSS and its diet recommendations would not have prevented SAP in those patients.
As recommended by the GUSS, patients with severe dysphagia were assigned to NPO—nevertheless 60% of all SAPs occurred despite of NPO. A retrospective database analysis of Australian hospitals showed a similar result: NPO and nasogastric tubes were found to be predictors for respiratory infections. Respiratory infection developed in 37% of patients with nasogastric tube compared to 5% without [32]. Similarly, in our study 15% of patients with nasogastric tube developed SAP compared to 4% without. It has been suggested that nasogastric tubes might not only decrease the risk of aspiration by lowering the risk of aspiration during eating but may as well increase the risk of respiratory infections due to a higher bacterial load of the saliva [33]. However, studies were not randomized, and the causal relationship remains unclear. Indeed 96% of patients with nasogastric tubes in the study of Brogan et al. [32] and 94% in our study were dysphagic. Furthermore, additional factors that may influence the development of respiratory infections in patients with nasogastric tubes such as oral hygiene, immobility or additional treatment with antibiotics were not documented systematically in the current study. Another important factor which was not recorded was the timing of nasogastric tube insertion. It has been suggested that the risk for respiratory infections is highest in the first 3–4 days post-stroke and that other methods (e.g. intravenous) might be used during this time before starting with enteral feeding [33].
Apart from assigning patients with severe dysphagia to NPO, the multiconsistency screening GUSS is the only screening instrument that recommends special diets for patients with slight or moderate dysphagia. Compared to a water test which would have assigned these patients to NPO because of problems with swallowing liquids, patients with moderate dysphagia (218/993; 22%) were instead assigned to a special diet thereby increasing the quality of life for those patients. Only 9/218 (4%) developed SAP in this group. Furthermore, the data suggest that it may be safe to give medication orally, crushed and mixed with apple sauce to patients with severe dysphagia (8–9 points on the GUSS), as only 2/33 (6%) developed SAP compared to 30/212 (14%) of NPO patients. This allows parenteral nutrition in the first 2–3 days after the event in patients not being at risk for malnutrition—avoiding thereby nasogastric tubes [34].
The main limitation of this study is its single centre retrospective observational design. The stroke-unit registry was established prospectively and data were collected with standardized methods. The occurrence of pneumonia was however analysed retrospectively using diagnoses from medical records and was limited to the time of hospitalization.
Despite that, the majority of screenings were performed on the day of admission, the exact time of dysphagia testing was not recorded. Delay in dysphagia screening during the first 8 hours has however been associated with SAP risk [8]. Further limits were missing variables such as ineligibility for GUSS, speech language therapy, other stroke management factors such as oral hygiene or treatment with antibiotics.
Swallowing functions vary during the first week post-stroke. In practice, SLTs are therefore screening patients several times, include more comprehensive dysphagia assessments such as FEES and adapt constantly the diet recommendations accordingly. Analysing only the first GUSS that was performed after admission and the according diet prescription may therefore not reflect the whole picture.
In clinical routine the GUSS is applied in 72% of patients and, if eligible, the majority of those who later developed pneumonia were screened. Despite of an identification of patients at risk by the GUSS and the use of dietary modifications, 5.2% of patients still developed SAP. Additional to diet other management factors such as timing of nasogastric tubes, oral hygiene or antibiotics may help to further decrease the rate of SAP.
S1 File. Dataset.
(CSV)
1. Katzan IL, Cebul RD, Husak SH, Dawson NV, Baker DW. The effect of pneumonia on mortality among patients hospitalized for acute stroke. Neurology. 2003;60:620–5. pmid:12601102
2. Finlayson O, Kapral M, Hall R, Asllani E, Selchen D, Saposnik G, et al. Risk factors, inpatient care, and outcomes of pneumonia after ischemic stroke. Neurology. 2011;77:1338–45. pmid:21940613
3. Kishore AK, Vail A, Chamorro A, Garau J, Hopkins SJ, Di Napoli M, et al. How is pneumonia diagnosed in clinical stroke research? A systematic review and meta-analysis. Stroke. 2015;46:1202–9. pmid:25858238
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5. Paciaroni M, Mazzotta G, Corea F, Caso V, Venti M, Milia P, et al. Dysphagia following Stroke. Eur. Neurol. 2004;51:162–7. pmid:15073441
6. Arnold M, Liesirova K, Broeg-Morvay A, Meisterernst J, Schlager M, Mono M-L, et al. Dysphagia in Acute Stroke: Incidence, Burden and Impact on Clinical Outcome. PloS One. 2016;11:e0148424. pmid:26863627
7. Smithard DG, Smeeton NC, Wolfe CDA. Long-term outcome after stroke: does dysphagia matter? Age Ageing. 2007;36:90–4. pmid:17172601
8. Bray BD, Smith CJ, Cloud GC, Enderby P, James M, Paley L, et al. The association between delays in screening for and assessing dysphagia after acute stroke, and the risk of stroke-associated pneumonia. J. Neurol. Neurosurg. Psychiatry. 2017;88:25–30. pmid:27298147
9. Titsworth WL, Abram J, Fullerton A, Hester J, Guin P, Waters MF, et al. Prospective quality initiative to maximize dysphagia screening reduces hospital-acquired pneumonia prevalence in patients with stroke. Stroke. 2013;44:3154–60. pmid:23963330
10. Hinchey JA, Shephard T, Furie K, Smith D, Wang D, Tonn S, et al. Formal dysphagia screening protocols prevent pneumonia. Stroke. 2005;36:1972–6. pmid:16109909
11. Lakshminarayan K, Tsai AW, Tong X, Vazquez G, Peacock JM, George MG, et al. Utility of dysphagia screening results in predicting poststroke pneumonia. Stroke. 2010;41:2849–54. pmid:20947835
12. Aoki S, Hosomi N, Hirayama J, Nakamori M, Yoshikawa M, Nezu T, et al. The multidisciplinary swallowing team approach decreases pneumonia onset in acute stroke patients. PloS One. 2016;11:e0154608. pmid:27138162
13. Palli C, Fandler S, Doppelhofer K, Niederkorn K, Enzinger C, Vetta C, et al. Early Dysphagia Screening by trained nurses reduces pneumonia rate in stroke patients: A clinical intervention study. Stroke. 2017;48:2583–5. pmid:28716980
14. European Society for Swallowing Disorders [Internet]. ESSD Position Statements on Screening, diagnosis and treatment in stroke patients [cited 2017 Sep 28]. http://www.myessd.org/docs/position_statements/ESSD_Position_Statements_on_OD_in_stroke_patients_-_4_01_13.pdf
15. European Stroke Organisation (ESO) Executive Committee, ESO Writing Committee. Guidelines for management of ischaemic stroke and transient ischaemic attack 2008. Cerebrovasc. Dis. 2008;25:457–507. pmid:18477843
16. Trapl M, Enderle P, Nowotny M, Teuschl Y, Matz K, Dachenhausen A, et al. Dysphagia bedside screening for acute-stroke patients: the Gugging Swallowing Screen. Stroke. 2007;38:2948–52. pmid:17885261
17. Warnecke T, Im S, Kaiser C, Hamacher C, Oelenberg S, Dziewas R. Aspiration and dysphagia screening in acute stroke—the Gugging Swallowing Screen revisited. Eur. J. Neurol. 2017;24:594–601. pmid:28322006
18. Teuschl Y, Brainin M, Matz K, Dachenhausen A, Ferrari J, Seyfang L, et al. Time trends in patient characteristics treated on acute stroke-units: results from the Austrian Stroke Unit Registry 2003–2011. Stroke. 2013;44:1070–4. pmid:23412371
19. Ferrari J, Knoflach M, Kiechl S, Willeit J, Schnabl S, Seyfang L, et al. Early clinical worsening in patients with TIA or minor stroke: the Austrian Stroke Unit Registry. Neurology. 2010;74:136–41. pmid:20065248
20. Smith CJ, Kishore AK, Vail A, Chamorro A, Garau J, Hopkins SJ, et al. Diagnosis of Stroke-Associated Pneumonia: Recommendations From the Pneumonia in Stroke Consensus Group. Stroke. 2015;46:2335–40. pmid:26111886
21. Gugging Swallowing Screen [Internet]. Sheet English May 2017. [cited 2017 Sep 28]. https://gussgroupinternational.files.wordpress.com/2017/01/guss_english_mai2017.pdf
22. Cichero JAY, Lam P, Steele CM, Hanson B, Chen J, Dantas RO, et al. Development of International Terminology and Definitions for Texture-Modified Foods and Thickened Fluids Used in Dysphagia Management: The IDDSI Framework. Dysphagia. 2017;32:293–314. pmid:27913916
23. Baijens LW, Clavé P, Cras P, Ekberg O, Forster A, Kolb GF, et al. European Society for Swallowing Disorders—European Union Geriatric Medicine Society white paper: oropharyngeal dysphagia as a geriatric syndrome. Clin. Interv. Aging. 2016;11:1403–28. pmid:27785002
24. Masrur S, Smith EE, Saver JL, Reeves MJ, Bhatt DL, Zhao X, et al. Dysphagia screening and hospital-acquired pneumonia in patients with acute ischemic stroke: findings from Get with the Guidelines—Stroke. J. Stroke Cerebrovasc. Dis. 2013;22:e301–9. pmid:23305674
25. Al-Khaled M, Matthis C, Binder A, Mudter J, Schattschneider J, Pulkowski U, et al. Dysphagia in Patients with Acute Ischemic Stroke: Early Dysphagia Screening May Reduce Stroke-Related Pneumonia and Improve Stroke Outcomes. Cerebrovasc. Dis. 2016;42:81–9. pmid:27074007
26. Joundi RA, Martino R, Saposnik G, Giannakeas V, Fang J, Kapral MK. Predictors and Outcomes of Dysphagia Screening After Acute Ischemic Stroke. Stroke. 2017;48:900–6. pmid:28275200
27. de Lima Alvarenga EH, Dall'Oglio GP, Murano EZ, Abrahão M. Continuum theory: presbyphagia to dysphagia? Functional assessment of swallowing in the elderly. Eur Arch Otorhinolaryngol. 2017 Nov 9. pmid:29124360
28. Carnaby G, Hankey GJ, Pizzi J. Behavioural intervention for dysphagia in acute stroke: a randomised controlled trial. Lancet Neurol. 2006;5:31–7. pmid:16361020
29. Sørensen RT, Rasmussen RS, Overgaard K, Lerche A, Johansen AM, Lindhardt T. Dysphagia screening and intensified oral hygiene reduce pneumonia after stroke. J. Neurosci. 2013;45:139–46.
30. Westendorp WF, Nederkoorn PJ, Vermeij J-D, Dijkgraaf MG, van de Beek D. Post-stroke infection: a systematic review and meta-analysis. BMC Neurol. 2011;11:110. pmid:21933425
31. Smith CJ, Bray BD, Hoffman A, Meisel A, Heuschmann PU, Wolfe CDA, et al. Can a novel clinical risk score improve pneumonia prediction in acute stroke care? A UK multicenter cohort study. J. Am. Heart Assoc. 2015;4:e001307. pmid:25587017
32. Brogan E, Langdon C, Brookes K, Budgeon C, Blacker D. Respiratory infections in acute stroke: nasogastric tubes and immobility are stronger predictors than dysphagia. Dysphagia. 2014;29:340–5. pmid:24445382
33. Langdon PC, Lee AH, Binns CW. High incidence of respiratory infections in "nil by mouth" tube-fed acute ischemic stroke patients. Neuroepidemiology. 2009;32:107–13. pmid:19039243
34. Trapl M, Teuschl Y, Matz K, Dachenhausen A, Brainin M. Overestimating the risk of aspiration in acute stroke. Eur J Neurol. 2017;24:e34. pmid:28544406
Is the Subject Area "Dysphagia" applicable to this article?
Is the Subject Area "Pneumonia" applicable to this article?
Is the Subject Area "Hemorrhagic stroke" applicable to this article?
Is the Subject Area "Stroke" applicable to this article?
Is the Subject Area "Ischemic stroke" applicable to this article?
Is the Subject Area "Swallowing" applicable to this article?
Is the Subject Area "Diet" applicable to this article?
Is the Subject Area "Nurses" applicable to this article? | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,459 |
The young people are becoming older, as our grandmothers. And is that in a short time we have seen the growth of a number of names such as Emma Watson, who even starred in editorials dressed cabaret or own Hayden Panettiere, that after the boom with the series Heroes is a reference for many teens.
Even so, while adults are made, not all are improving at the same level. The first class are still Watson and Hudgens y Hayden Panettiere must be limited to be in a second group, with outfits that sometimes convince and others the opposite.
One of their failures seen again in this look: so very nice to be, not convinced. Because you can dress up party and go more fixed you can, which is still missing the something. In part due to its height, it is very low and a dress does not look like.
So seeing her with a short prom dress, with sequins and black heels, does not convey the same than when someone carries it flawlessly. In the images is with a jacket, but it perhaps your partner because it seems man, to avoid so cold.
I also liked your hairstyle, it not favored it to his face. A look that turns to leave indifferent. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,099 |
#include <QDir>
#include <QDebug>
#include <QtDBus/QtDBus>
#include <kcalcoren/ksystemtimezone.h>
#include <unicode/timezone.h>
#include <clockmodel.h>
#include "clocklistmodel.h"
using namespace std;
ClockListModel::ClockListModel(QObject *parent)
: QAbstractListModel(parent), settings("MeeGo", "meego-app-clocks"),
m_type(-1), m_initialized(false)
{
QHash<int, QByteArray> roles;
roles.insert(ClockItem::ID, "itemid");
roles.insert(ClockItem::ItemType, "itemtype");
roles.insert(ClockItem::Title, "title");
roles.insert(ClockItem::Name, "name");
roles.insert(ClockItem::GMTOffset, "gmtoffset");
roles.insert(ClockItem::Index, "index");
roles.insert(ClockItem::Days, "days");
roles.insert(ClockItem::SoundType, "soundtype");
roles.insert(ClockItem::SoundName, "soundname");
roles.insert(ClockItem::SoundFile, "soundfile");
roles.insert(ClockItem::Snooze, "snooze");
roles.insert(ClockItem::Active, "active");
roles.insert(ClockItem::Hour, "hour");
roles.insert(ClockItem::Minute, "minute");
roles.insert(ClockItem::GMTName, "gmtname");
setRoleNames(roles);
m_storage = eKCal::EStorage::localStorage(KCalCore::IncidenceBase::TypeEvent,
"alarmsnotebook",
true);
m_calendar = m_storage->calendar();
m_storage->registerObserver(this);
m_storage->startLoading(); // Asynchronous
}
ClockListModel::~ClockListModel()
{
clearData();
}
void ClockListModel::clearData()
{
if(!itemsList.isEmpty())
{
beginRemoveRows(QModelIndex(), 0, itemsList.count()-1);
for(int i = 0; i < itemsList.count(); i++)
delete itemsList[i];
localzone = NULL;
itemsList.clear();
endRemoveRows();
}
}
QString ClockListModel::cleanTZName(QString title) const
{
QStringList temp = title.split("/", QString::SkipEmptyParts);
if (temp.isEmpty())
return title;
QString res = temp.last();
res.replace("_", " ");
return res;
}
void ClockListModel::setType(const int type)
{
if(type == m_type)
return;
clearData();
m_type = type;
emit typeChanged(m_type);
QList<ClockItem *> newItemsList;
if(m_type == ListofClocks)
{
QString localzonename = "GMT";
int gmt = 0;
QString name = localzonename;
QString title = localzonename;
mClockModel.reset(new ClockModel());
connect(mClockModel.data(), SIGNAL(timezoneChanged()),
this, SLOT(timezoneChanged()));
if (!mClockModel->timezone().isEmpty()) {
title = mClockModel->timezone();
KTimeZone zone = KSystemTimeZones::zone(title);
name = cleanTZName(title);
gmt = zone.currentOffset(Qt::UTC);
}
localzone = new ClockItem(name, title, gmt);
newItemsList << localzone;
if(!settings.contains("firstuse"))
{
QStringList defaultzones;
defaultzones << "Europe/London"
<< "America/Los_Angeles"
<< "Asia/Shanghai";
settings.setValue("firstuse", "false");
settings.beginGroup("clocks");
for (int i = 0; i < defaultzones.size(); i++) {
KTimeZone zone = KSystemTimeZones::zone(defaultzones[i]);
settings.setValue(QString("00%1/name").arg(i+1), cleanTZName(zone.name()));
settings.setValue(QString("00%1/title").arg(i+1), zone.name());
settings.setValue(QString("00%1/gmt").arg(i+1), zone.currentOffset(Qt::UTC));
}
settings.endGroup();
}
settings.beginGroup("clocks");
QStringList ids = settings.childGroups();
for(int i = 0; i < ids.count(); i++)
{
QString name = settings.value(ids[i] + "/name", "undefined").toString();
QString title = settings.value(ids[i] + "/title", "undefined").toString();
int gmt = settings.value(ids[i] + "/gmt", 100).toInt();
newItemsList << new ClockItem(name, title, gmt);
}
settings.endGroup();
}
else if(m_type == ListofAlarms)
{
newItemsList = getAlarmsFromCalendar();
}
else if(m_type == ListofTimers)
{
}
else
{
qDebug() << "Invalid Type";
return;
}
// Set the new clock items
setClockItems(newItemsList);
}
/*!
* Set the new clock items in the model to \a items.
* The caller should make sure clearData() is called before setting the new items.
*/
void ClockListModel::setClockItems(const QList<ClockItem *> &newItemsList)
{
Q_ASSERT(itemsList.isEmpty());
if(!newItemsList.isEmpty())
{
beginInsertRows(QModelIndex(), 0, newItemsList.count()-1);
itemsList = newItemsList;
endInsertRows();
}
emit countChanged(itemsList.count());
}
/*!
* Loads the alarms from the calendar and return them.
*
* \return The list of alarms in the calendar as ClockItems, an empty list if the
* calendar is not ready yet.
*/
QList<ClockItem *> ClockListModel::getAlarmsFromCalendar() const
{
Q_ASSERT (m_type == ListofAlarms);
QList<ClockItem *> newItemsList;
if (!m_initialized) {
// The storage is not done loading, the alarms will be retrieved once it is
return newItemsList;
}
// The calendar is initialized, retrieve the alarms from it
KCalCore::Event::List eventList;
eventList = m_calendar->rawEvents(KCalCore::EventSortStartDate, KCalCore::SortDirectionAscending);
for (int i = 0; i < eventList.count(); i++)
{
KCalCore::Event *event = eventList.at(i).data();
QStringList desc = event->description().split("!");
QString name = event->summary();
int soundtype = (desc.isEmpty())?0:desc.at(0).toInt();
QString soundname = (desc.count() < 2)?"":desc.at(1);
QString uid = event->uid();
KCalCore::Recurrence* theRecurrence = event->recurrence();
QBitArray qb = theRecurrence->days();
int days = 0;
for(int i = 0; i < 7; i++)
if(qb.at(i))
days |= (1<<i);
KCalCore::Alarm::List alarms = event->alarms();
if (alarms.count() < 1)
continue;
KCalCore::Alarm::Ptr alarm = alarms.at(0);
QString soundfile = alarm->audioFile();
int snooze = alarm->snoozeTime().asSeconds()/60;
bool active = alarm->enabled();
QTime thetime = alarm->time().toLocalZone().time();
int hour = thetime.hour() + 1;
int minute = thetime.minute();
newItemsList << new ClockItem(name, days, soundtype, soundname, soundfile, snooze, active, hour, minute, uid);
}
return newItemsList;
}
void ClockListModel::timezoneChanged()
{
Q_ASSERT(itemsList.size() > 0);
ClockItem *item = itemsList[0];
item->m_title = mClockModel->timezone();
item->m_name = cleanTZName(item->m_title);
KTimeZone zone = KSystemTimeZones::zone(item->m_title);
item->m_gmtoffset = zone.currentOffset(Qt::UTC);
emit dataChanged(index(0, 0), index(0, 0));
}
bool ClockListModel::getClock(const QString &id, ClockItem *&item, int &idx)
{
for(idx = 0; idx < itemsList.count(); idx++)
if(itemsList[idx]->m_id == id)
{
item = itemsList[idx];
break;
}
if(idx >= itemsList.count())
return false;
return true;
}
bool ClockListModel::addClock(const QString &name, const QString &title, const int gmt)
{
if(m_type != ListofClocks)
{
qDebug() << "Can only add clocks to ListofClocks type";
return true;
}
// search for duplicate clock
ClockItem *clock;
foreach (clock, itemsList) {
if (clock->m_title == title) {
return false;
}
}
beginInsertRows(QModelIndex(), itemsList.count(), itemsList.count());
itemsList << new ClockItem(name, title, gmt);
endInsertRows();
QString group;
group.sprintf("clocks/%03d", itemsList.count()-1);
settings.beginGroup(group);
settings.setValue("name", name);
settings.setValue("title", title);
settings.setValue("gmt", gmt);
settings.endGroup();
emit countChanged(itemsList.count());
return true;
}
QString ClockListModel::calendarAlarm(const QString &name, const int days,
const int soundtype, const QString &soundname, const QString &soundfile,
const int snooze, const bool active,
const int hour, const int minute, QString uid)
{
Q_ASSERT(m_initialized);
KCalCore::Event::Ptr coreEvent;
if(uid.isEmpty())
{
/* this is an ADD call, create a new item */
coreEvent = KCalCore::Event::Ptr(new KCalCore::Event());
}
else
{
/* this is an EDIT call, load the alarm item */
coreEvent = m_calendar->event(uid);
/* if the database lacks this item, create a new one */
if(coreEvent == NULL)
{
qDebug() << "can't edit this: " << name;
coreEvent = KCalCore::Event::Ptr(new KCalCore::Event());
}
}
/* if somehow we still have nothing, kick over the table and storm off */
if(coreEvent == NULL)
{
qDebug() << "alarm not found in calendar db: " << name;
return uid;
}
coreEvent->setSummary(name);
QString desc = QString("%1!%2").arg(soundtype).arg(soundname);
coreEvent->setDescription(desc);
//coreEvent->setAllDay(true);
coreEvent->clearAlarms();
KCalCore::Alarm::Ptr eventAlarm(coreEvent->newAlarm());
eventAlarm->setAudioAlarm( soundfile );
eventAlarm->setSnoozeTime( KCalCore::Duration( 60*snooze ) );
eventAlarm->setRepeatCount(10);
KDateTime thetime = KDateTime::currentDateTime(KDateTime::Spec(KSystemTimeZones::local()));
thetime.setTime(QTime(hour-1, minute, 0, 0));
eventAlarm->setTime(thetime);
eventAlarm->setEnabled(active);
coreEvent->addAlarm( eventAlarm );
QBitArray qb(10);
for(int i = 0; i < 7; i++)
{
qb.setBit(i,(days>>i)&0x1);
}
KCalCore::Recurrence* newRecurrence = coreEvent->recurrence();
newRecurrence->setWeekly(1, qb, 1);
m_calendar->addEvent(coreEvent);
m_storage->save();
return coreEvent->uid();
}
void ClockListModel::addAlarm(const QString &name, const int days, const int soundtype,
const QString &soundname, const QString &soundfile,
const int snooze, const bool active,
const int hour, const int minute)
{
if(m_type != ListofAlarms)
{
qDebug() << "Can only add clocks to ListofAlarms type";
return;
}
QString uid = calendarAlarm(name, days, soundtype, soundname, soundfile,
snooze, active, hour, minute);
beginInsertRows(QModelIndex(), itemsList.count(), itemsList.count());
itemsList << new ClockItem(name, days, soundtype, soundname, soundfile,
snooze, active, hour, minute, uid);
endInsertRows();
// QString group;
// group.sprintf("alarms/%03d", itemsList.count()-1);
// settings.beginGroup(group);
// settings.setValue("name", name);
// settings.setValue("days", days);
// settings.setValue("soundtype", soundtype);
// settings.setValue("soundname", soundname);
// settings.setValue("soundfile", soundfile);
// settings.setValue("snooze", snooze);
// settings.setValue("active", active);
// settings.setValue("hour", hour);
// settings.setValue("minute", minute);
// settings.setValue("uid", uid);
// settings.endGroup();
emit countChanged(itemsList.count());
}
void ClockListModel::editClock(const QString &id, const QString &name, const QString &title, const int gmt)
{
int idx = 0;
ClockItem *item = NULL;
if(!getClock(id, item, idx))
return;
if(idx == 0)
return;
QString group;
group.sprintf("clocks/%03d", idx);
settings.beginGroup(group);
settings.setValue("name", name);
settings.setValue("title", title);
settings.setValue("gmt", gmt);
settings.endGroup();
item->m_name = name;
item->m_title = title;
item->m_gmtoffset = gmt;
emit dataChanged(index(idx, 0), index(idx, 0));
}
void ClockListModel::editAlarm(const QString &id, const QString &name, const int days,
const int soundtype, const QString &soundname, const QString &soundfile,
const int snooze, const bool active,
const int hour, const int minute)
{
int idx = 0;
ClockItem *item = NULL;
if(!getClock(id, item, idx))
return;
QString uid = calendarAlarm(name, days, soundtype, soundname, soundfile,
snooze, active, hour, minute, item->m_uid);
// QString group;
// group.sprintf("alarms/%03d", idx);
// settings.beginGroup(group);
// settings.setValue("name", name);
// settings.setValue("days", days);
// settings.setValue("soundtype", soundtype);
// settings.setValue("soundname", soundname);
// settings.setValue("soundfile", soundfile);
// settings.setValue("snooze", snooze);
// settings.setValue("active", active);
// settings.setValue("hour", hour);
// settings.setValue("minute", minute);
// settings.setValue("uid", uid);
// settings.endGroup();
item->m_name = name;
item->m_days = days;
item->m_soundtype = soundtype;
item->m_soundname = soundname;
item->m_soundfile = soundfile;
item->m_snooze = snooze;
item->m_active = active;
item->m_hour = hour;
item->m_minute = minute;
item->m_uid = uid;
emit dataChanged(index(idx, 0), index(idx, 0));
}
void ClockListModel::setOrder(const QString &id, const int order)
{
if((m_type == ListofClocks)&&(order < 1))
return;
int idx = 0;
ClockItem *item = NULL;
if(!getClock(id, item, idx))
return;
if((m_type == ListofClocks)&&(idx == 0))
return;
int idxtgt = order;
if(idx == idxtgt)
return;
itemsList.swap(idx, idxtgt);
storeClockData();
emit dataChanged(index(idx, 0), index(idx, 0));
emit dataChanged(index(idxtgt, 0), index(idxtgt, 0));
}
void ClockListModel::storeClockData()
{
if(m_type == ListofClocks)
{
settings.remove("clocks");
for(int i = 1; i < itemsList.count(); i++)
{
QString group;
group.sprintf("clocks/%03d", i);
settings.beginGroup(group);
settings.setValue("name", itemsList[i]->m_name);
settings.setValue("title", itemsList[i]->m_title);
settings.setValue("gmt", itemsList[i]->m_gmtoffset);
settings.endGroup();
}
}
else if(m_type == ListofAlarms)
{
settings.remove("alarms");
for(int i = 0; i < itemsList.count(); i++)
{
QString group;
group.sprintf("alarms/%03d", i);
settings.beginGroup(group);
settings.setValue("name", itemsList[i]->m_name);
settings.setValue("days", itemsList[i]->m_days);
settings.setValue("soundtype", itemsList[i]->m_soundtype);
settings.setValue("soundname", itemsList[i]->m_soundname);
settings.setValue("soundfile", itemsList[i]->m_soundfile);
settings.setValue("snooze", itemsList[i]->m_snooze);
settings.setValue("active", itemsList[i]->m_active);
settings.setValue("hour", itemsList[i]->m_hour);
settings.setValue("minute", itemsList[i]->m_minute);
settings.setValue("uid", itemsList[i]->m_uid);
settings.endGroup();
}
}
}
void ClockListModel::destroyItemByID(const QString &id)
{
int idx = 0;
ClockItem *item = NULL;
if(!getClock(id, item, idx))
return;
if(item->m_type == ClockItem::AlarmItem)
{
KCalCore::Event::Ptr ptr = m_calendar->event(item->m_uid);
if(ptr == NULL)
qDebug() << "alarm not found in calendar db: " << item->m_name;
else
{
m_calendar->deleteEvent( ptr );
m_storage->save();
}
}
beginRemoveRows(QModelIndex(), idx, idx);
itemsList.removeAt(idx);
delete item;
endRemoveRows();
storeClockData();
emit countChanged(itemsList.count());
}
QVariant ClockListModel::data(const QModelIndex &index, int role) const
{
if (!index.isValid() || index.row() > itemsList.count())
return QVariant();
ClockItem *item = itemsList[index.row()];
if (role == ClockItem::ID)
return item->m_id;
if (role == ClockItem::ItemType)
return item->m_type;
if (role == ClockItem::Title)
return item->m_title;
if (role == ClockItem::Name) {
if (m_type == ListofClocks) {
TimeZone *zone = TimeZone::createTimeZone(UnicodeString(static_cast<const UChar*>(item->m_title.utf16())));
UnicodeString result;
zone->getDisplayName(TRUE, TimeZone::GENERIC_LOCATION, result);
delete zone;
return QString(reinterpret_cast<const QChar*>(result.getBuffer()), result.length());
} else {
return item->m_name;
}
}
if (role == ClockItem::GMTName) {
TimeZone *zone = TimeZone::createTimeZone(UnicodeString(static_cast<const UChar*>(item->m_title.utf16())));
UnicodeString result;
zone->getDisplayName(TRUE, TimeZone::LONG_GMT, result);
delete zone;
return QString(reinterpret_cast<const QChar*>(result.getBuffer()), result.length());
}
if (role == ClockItem::GMTOffset)
return item->m_gmtoffset;
if (role == ClockItem::Index)
return index.row();
if (role == ClockItem::Days)
return item->m_days;
if (role == ClockItem::SoundType)
return item->m_soundtype;
if (role == ClockItem::SoundName)
return item->m_soundname;
if (role == ClockItem::SoundFile)
return item->m_soundfile;
if (role == ClockItem::Snooze)
return item->m_snooze;
if (role == ClockItem::Active)
return item->m_active;
if (role == ClockItem::Hour)
return item->m_hour;
if (role == ClockItem::Minute)
return item->m_minute;
return QVariant();
}
QVariant ClockListModel::data(int index) const
{
if(index >= itemsList.size())
index = itemsList.size() - 1;
return QVariant::fromValue(static_cast<void *>(itemsList[index]));
}
int ClockListModel::rowCount(const QModelIndex &parent) const
{
Q_UNUSED(parent);
return itemsList.size();
}
int ClockListModel::columnCount(const QModelIndex &parent) const
{
Q_UNUSED(parent);
return 1;
}
bool ClockListModel::removeRows(int row, int count, const QModelIndex &parent)
{
beginRemoveRows(parent, row, row + count - 1);
for(int i = row; i < row + count; i++)
itemsList.removeAt(i);
endRemoveRows();
return true;
}
void ClockListModel::insertRow(int row, ClockItem *item)
{
beginInsertRows(QModelIndex(), row, row);
itemsList.insert(row, item);
endInsertRows();
}
void ClockListModel::moveRow(int rowsrc, int rowdst)
{
beginMoveRows(QModelIndex(), rowsrc, rowsrc, QModelIndex(), rowdst);
itemsList.move(rowsrc, rowdst);
endMoveRows();
}
/*! \reimp */
void ClockListModel::loadingComplete(bool success, const QString &error)
{
qDebug() << Q_FUNC_INFO << success << error;
m_initialized = success;
if(m_initialized && m_type == ListofAlarms) {
// The calendar is done loading and the model is supposed to contain the alarms
// so we retrieve them from the calendar and populate the model.
setClockItems(getAlarmsFromCalendar());
}
}
/*! \reimp */
void ClockListModel::savingComplete(bool success, const QString &error)
{
qDebug() << Q_FUNC_INFO << success << error;
}
| {
"redpajama_set_name": "RedPajamaGithub"
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{"url":"https:\/\/physics.stackexchange.com\/questions\/473050\/expectation-value-of-x-y-z-for-general-nlm-state-of-hydrogen-atom","text":"# Expectation value of $x,y,z$ for general $nlm$ state of hydrogen atom\n\nHow to calculate expectation value of $$\\langle x\\rangle, \\langle y\\rangle,\\langle z\\rangle$$ for the general $$\\psi_{nlm}$$ state? $$x$$ has $$\\sin(\\theta)\\cos(\\phi)$$ angular part which can be expressed as $$\\frac{1}{\\sqrt{2}}(Y_{1}^{-1}+Y_{1}^{1})$$, now the angular integration becomes $$\\frac{1}{\\sqrt{2}}\\left(\\int (Y_{1}^{-1}Y_{l}^{m*}Y_{l}^{m})\\sin(\\theta)d\\theta d\\phi+\\int (Y_{1}^{1}Y_{l}^{m*}Y_{l}^{m})\\sin(\\theta)d\\theta d\\phi\\right).$$ Here after I can apply Wigner-Eckart theorem and the problem can be solved. However, is there any other way of simplifying this expression to something simple general formula just like the Kramer relations for $$\\langle r^{s} \\rangle$$?\n\nThe probability densities for all of those states are symmetric under rotations around the $$z$$ axis and reflections in the $$x,y$$ plane. This then requires all of those expectation values to vanish.\n\n\u2022 Can you please bit elaborate? Is there any way that I can simplify this expression for $<x>$ and $<y>$ and $<z>$. \u2013\u00a0user135580 Apr 16 '19 at 7:14\n\u2022 Does it vanish for all the states $\\psi_{nlm}$? \u2013\u00a0user135580 Apr 16 '19 at 7:14\n\u2022 Yes, it can be simplified: $$\\langle x\\rangle = \\langle y \\rangle = \\langle z\\rangle = 0,$$ for all $\\psi_{nlm}$, on symmetry grounds. \u2013\u00a0Emilio Pisanty Apr 16 '19 at 7:50\n\u2022 If you absolutely want to do things via methods which are utterly unnecessarily complicated, you can reduce the integrals in your question to the triple products of harmonics in e.g. this question (being careful with the conjugate), and then using the properties of the Wigner 3j symbols (specifically, that they vanish if the bottom row dies not add to zero). But that route is the wrong thing to do - unless you really understand the physical content, you're just obscuring the reason instead of clarifying it. \u2013\u00a0Emilio Pisanty Apr 16 '19 at 8:02\n\n$$\\def\\mxelm#1#2#3{\\langle#1|\\,#2\\,|#3\\rangle}$$ It's much easier to use parity, i.e. symmetry of the wavefunction wrt space inversion $$x \\to -x \\qquad y \\to -y \\qquad z \\to -z.$$ It's known that $$\\psi_{nlm}(-x,-y,-z) = (-1)^l\\,\\psi_{nlm}(x,y,z).$$ Then $$|\\psi_{nlm}|^2$$ is even whereas $$x$$ is odd. You have $$\\mxelm{nlm}x{nlm} = \\int\\!x\\,|\\psi|^2\\>dx\\,dy\\,dz.$$ The integrand is odd under space inversion, so the integral vanishes. The same holds true for $$y$$ and $$z$$.\n\nNote that Wigner-Eckart theorem if applied to rotation SO(3) group can't give the answer. Consider $$L_z=x\\,p_y-y\\,p_x$$. Under rotations it transforms as $$z$$ does, yet $$\\mxelm{nlm}{L_z}{nlm} = m\\,\\hbar$$ and not 0. Of course this result doesn't contradict W-E theorem as it only says that $$\\mxelm{nlm}x{nlm} = k\\,\\mxelm{nlm}{L_x}{nlm}$$ $$\\mxelm{nlm}y{nlm} = k\\,\\mxelm{nlm}{L_y}{nlm}$$ $$\\mxelm{nlm}z{nlm} = k\\,\\mxelm{nlm}{L_z}{nlm}$$ withe same $$k$$, but doesn't rule out $$k=0$$.\n\nSo $$k=0$$ has another cause: which?\n\nIt is easy to prove given the amount of symmetry as mentioned in the comments. Focus on the azimuthal angle, since standard spherical coordinates are taken such that the $$z$$-axis coincides with $$\\theta=0=\\pi$$, we expect the azimuthal integration already to be zero since the atom looks the same from every angle. So recall that the spherical harmonics have the form: $$Y_\\ell^m(\\theta,\\phi) = K(\\ell,m)P_\\ell^m(\\cos\\theta) e^{im\\phi}$$ where $$K$$ is a normalization coefficient and depends on $$\\ell$$ and $$m$$. When one multiplies a spherical harmonic with its conjugate you will eliminate the $$\\phi$$ part, $$Y^{*m}_\\ell Y^m_\\ell \\propto P_\\ell^{-m}P_\\ell^m,$$ this holds for any $$\\ell$$ or $$m$$. So the azimuthal part of the integrals in your question are reduced to $$\\int d\\phi\\, e^{-i\\phi} + \\int d\\phi\\, e^{i\\phi} = 0.$$ So the message is to have the physical intuition to say that it is zero and then prove it rigorously exploiting the physical observations.\n\n\u2022 This works for x and y, but not for z. \u2013\u00a0Emilio Pisanty Apr 16 '19 at 8:58\n\u2022 For $z$ one can rotate the coordinate system so that $z$ lies in the plane $\\theta = \\pi\/2$ and the same argument holds, since the location of your \"northpole\" is completely arbitrary. \u2013\u00a0ohneVal Apr 16 '19 at 9:16\n\u2022 No, that argument doesn't work - your state is already specified, and rotating the system would change the state. The hamiltonian is symmetric, but the eigenstates do not share its full symmetry. \u2013\u00a0Emilio Pisanty Apr 16 '19 at 9:17\n\u2022 I can change coordinates within the integral if it serves you better, then use the property of rotations of the harmonics which will produce just an annoying combination of harmonics with the same $\\ell$ and opposite sign $m$'s which will end up in the same sort of integrals as above. \u2013\u00a0ohneVal Apr 16 '19 at 9:23\n\u2022 For $z$, why not just use the symmetry of $P^m_l(\\cos(\\theta))$.We have the volume element $dV = d\\cos(\\theta)d\\phi dr$. $z = r \\cos(\\theta)$, thus the integrand becomes $$\\propto (P^m_l(\\cos(\\theta)))^2\\cos(\\theta)d\\cos(\\theta)$$ where $\\cos(\\theta) \\in (0,1)$. Since $P^m_l(x) = (-1)^{m+l}P^m_l(-x)$ it quickly follows $\\langle z \\rangle = 0$. \u2013\u00a0denklo Apr 16 '19 at 10:15","date":"2020-04-05 04:20:25","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\": 37, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9336882829666138, \"perplexity\": 232.6592383444084}, \"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-2020-16\/segments\/1585370528224.61\/warc\/CC-MAIN-20200405022138-20200405052138-00214.warc.gz\"}"} | null | null |
{"url":"https:\/\/de.zxc.wiki\/wiki\/Gradient","text":"The course of the change in a numerical physical variable depending on the location is called a gradient or gradient (from Latin gradiens , striding '' ). The gradient of a size indicates for each location how much the size changes and in which direction the change is greatest.\n\nMathematically, the gradient is described by the vector (\u201cdirection arrow\u201d and its length) defined by direction and magnitude , which indicates at the point under consideration in which direction the measured scalar variable increases the most and how strong the increase is; see Gradient (mathematics) .\n\nExample: Several candles are burning in a room, spread out, on candlesticks of different heights. There is exactly one temperature gradient for each point in the room. This describes in which direction the temperature rises the most and how strong the rise is.\n\n2. a proton gradient is the spatial or temporal difference in the concentration of protons ( e.g. acting as a pH gradient)\n3. the increase or decrease in an electrochemical potential is referred to as an electrochemical gradient\n4. a color gradient describes a color gradient or a transition in brightness in art and image processing\n5. In road and rail construction, a gradient describes the height profile of a planned or existing route in relation to the route ( axis ).\n6. The hydraulic gradient describes the groundwater gradient in hydrology (the ratio between the pressure height difference or the water level difference and the flow length).\n7. In photography, the photographic density is the measure of the blackening of a light-sensitive material\n\nThe term is also used outside of physics in other disciplines to describe the course of a change in an influencing variable, for example\n\n\u2022 as a social gradient , for the linear relationship between social status and general living conditions ( morbidity ) or life opportunities ( mortality ).\n\u2022 As an ecological gradient , the gradual change of an environmental factor in an ecosystem , which is determined in a gradient analysis using gradients of factors (e.g. amount of precipitation, temperature profile) in order to document the distribution of animal or plant populations depending on these factors. A kline is a continuous change of a biological characteristic of a species in relation to an ecological gradient (e.g. a degree of latitude ).\n\u2022 The goal gradient effect is the phenomenon in which a person exerts more effort to achieve a goal, the closer that person is to that goal. For this purpose, the approach gradient and avoidance gradient were also defined (see also avoidance behavior ).\n\nThe temperature gradient is a directed physical quantity that describes in the sense of a mathematical gradient at each point of a temperature field in which direction the temperature rises the most and how much . The internationally used unit \u00a0( SI unit ) of its amount is Kelvin per meter \u00a0(K \/ m). The temperature gradient drives heat conduction and can cause currents (see B\u00e9nard experiment , K\u00fcppers-Lortz instability ). It plays an important role in thermophoresis and thermo-osmosis and is one of the causes of weathering . At the interfaces of substances at different temperatures, the temperature gradient - neglecting the thermal boundary layer - is not mathematically defined; vividly it goes there towards infinity .\n\nIn meteorology and geology , the vertical component of the temperature gradient is of particular interest, i.e. the change in temperature with the distance from the earth's surface. This vertical component of the temperature gradient is called the atmospheric temperature gradient in the earth's atmosphere and the geothermal depth level in the earth's crust . ${\\ displaystyle {\\ tfrac {\\ mathrm {d} T} {\\ mathrm {d} z}}}$\n\nIn temperature gradient gel electrophoresis , a process for separating charged biomolecules . For example , a temperature gradient or chemical gradient is used for DNA separation .\n\nmeteorology\n\nIn meteorology , a gradient indicates how much a location-dependent variable changes with the location, i.e. in the horizontal or vertical direction:\n\nThere is a gradient for each point. According to the mathematical definition, a gradient has not only a magnitude , but also a direction, ie it represents a vector. This vector always points in the direction of the greatest increase in the observed variable. For example, the information on the temperature gradient in a point contains the direction of the greatest temperature difference in the vicinity of the point and the size of this difference. The component of this vector with respect to a given direction, e.g. B. the vertical, gives a directional derivative . A horizontal directional derivation of the terrain height is called a slope or a slope . The latter is also used in a figurative sense, e.g. B. Pressure gradient as the driving force of the wind (see gradient wind ).\n\n\u201cHectopascal per 60 nautical miles \u201d (which corresponds to one degree of latitude ) was previously used as a unit for the pressure gradient\u00a0 . The sense and benefit of such gradients was that tables for calculating the wind speed only had to be multiplied by the gradient factor in order to output the calculated wind speed (i.e. only tables for \"Gradient = 1\" were required).\n\nApplications\n\nfor example:\n\n1. A pressure gradient microphone uses the pressure differences between spatial points.\n2. In density gradient centrifugation, particles sediment in a density gradient .\n3. In contrast to the usual nuclear magnetic resonance spectroscopy , inhomogeneous magnetic fields are deliberately used in field gradient NMR .\n4. the deflection of a light beam in a material with a variable refractive index is the subject of gradient optics","date":"2022-01-19 19:07:15","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 1, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 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\": 0.8171333074569702, \"perplexity\": 735.4316721136165}, \"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-2022-05\/segments\/1642320301488.71\/warc\/CC-MAIN-20220119185232-20220119215232-00486.warc.gz\"}"} | null | null |
Q: Return only unique objects from an array in Javascript Having the following array:
const arr = [{ id: 'A', version: 0, name: 'first' },
{ id: 'A', version: 1, name: 'first' },
{ id: 'B', version: 0, name: 'second' },
{ id: 'A', version: 2, name: 'first' },
{ id: 'B', version: 1, name: 'second' }];
I need to use this as input for two drop-downs.
For the first drop-down it should show in the list only two values, A and B.
For doing that:
const firstDropdownOptions = [...new Set(arr.map((el) => el.id))];
Unfortunately, this returns ['A', 'B'] which doesn't contain any information about the other properties.
It would be more useful to be like:
[{ id: 'A', version: '0', name: 'first' }, { id: 'B', version: '0', name: 'second' }]
Any ideas on how to make it return the above array?
A: I have found a short solution to this problem:
const result = arr.filter((value, index, self) => {
return self.findIndex(v => v.id === value.id) === index
});
A: You could group by id and set all options for the second select by the selection of the first.
const
setOptions = id => groups[id].forEach(o => {
const option = document.createElement('option');
option.value = o.version;
option.innerHTML = o.version;
second.appendChild(option);
});
data = [{ id: 'A', version: 0, name: 'first' }, { id: 'A', version: 1, name: 'first' }, { id: 'B', version: 0, name: 'second' }, { id: 'A', version: 2, name: 'first' }, { id: 'B', version: 1, name: 'second' }],
first = document.createElement('select'),
second = document.createElement('select'),
groups = data.reduce((r, o) => ((r[o.id] ??= []).push(o), r), {});
document.body.appendChild(first);
document.body.appendChild(document.createTextNode(' '));
document.body.appendChild(second);
Object.keys(groups).forEach(k => {
const option = document.createElement('option');
option.value = k;
option.innerHTML = k;
first.appendChild(option);
});
setOptions('A');
first.addEventListener('change', function (event) {
let i = second.options.length;
while (i--) second.remove(i);
setOptions(first.value);
});
A: Observation : As you are only returning id in array.map() method. Hence, it is giving you only unique Id's [A, B] in a new array. To get all the other properties you have to fetch via condition to check if version === 0.
Working Demo :
const arr = [{ id: 'A', version: 0, name: 'first' },
{ id: 'A', version: 1, name: 'first' },
{ id: 'B', version: 0, name: 'second' },
{ id: 'A', version: 2, name: 'first' },
{ id: 'B', version: 1, name: 'second' }];
const firstDropdownData = arr.filter((obj) => obj.version === 0);
console.log(firstDropdownData);
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,075 |
\section{Analyses and results}
The observed samples of galaxies are the same as those used
in \citet{Georgiev3}. A plot of $M_{\rm GC}/M_b$ as a function of $M_b$ is shown in Figure \ref{mgcmb}. The $M_{\rm GC}/M_b$ versus $M_b$ data is described as a three-part function of $M_b$. For galaxies with $M_b < 3\times10^{10}\rm M_\odot$, $M_{\rm GC}/M_b$ either decreases as $M_b$ increases, or $M_{\rm GC}/M_b=0$, i.e., in some dwarf galaxies no GC systems are observed. For galaxies with $M_b>3\times 10^{10}\rm M_\odot$, $M_{\rm GC}/M_b$ increases as $M_b$ increases. For the galaxies with GCs, the fit parameter for the relation of $M_{\rm GC}/M_b$ and $M_b$ are given in the figure.
\begin{figure}{}
\begin{center}
\resizebox{9.cm}{!}{\includegraphics{mgcmb_2.eps}}
\makeatletter\def\@captype{figure}\makeatother \caption{The $M_{\rm GC}/M_b$ ratio as a function of $M_b$. The colours of the data points represent different sources of data: \citet[][black, for ellipticals]{Peng08}, \citet[][magenta, for dwarf ellipticals]{ML07}, \citet[][cyan, for ellipticals]{Spitler08}, \citet[][yellow, for sprials]{Spitler08}, \citet[][green, for nearby dwarf galaxies]{Georgiev1,Georgiev2}. The gray triangles at the bottom of the figure show galaxies without any GCs observed, while the dotted line shows galaxies only containing one GC. The blue and red lines show, respectively, the linear fit for the data points corresponding to $M_b \le 3 \times 10^{10}\rm M_\odot$ and $M_b > 3\times 10^{10}\rm M_\odot$, the least square fitting parameters are labelled in the figure.
}\label{mgcmb}
\end{center}
\end{figure}
\subsection{The apparent virial mass and apparent dynamical mass-to-light ratio}\label{secmvir}
Milgrom's original proposal for a new effective gravitational dynamics \citep[][]{Milgrom1983,BM1984} which is sourced purely by baryonic matter, has passed all tests that have been performed until now on galactic scales. It accounts for the
baryonic Tully-Fisher relation, the shapes of rotation curves of
galaxies, the dark matter effect in tidal dwarf galaxies, the
universal scale of baryons, and the projected surface density of
apparent dark matter within the core radius of the apparent dark
matter halos
\citep{TF1977,Milgrom_Sanders2003,Sanders_Noordermeer2007,
Gentile_etal2007,Gentile_etal2009}. In Milgromian dynamics, the
Newtonian gravitational acceleration $g_{\rm N}$ is replaced with
$g=\sqrt{g_{\rm N} a_0}$ when the gravitational acceleration is much
smaller than $a_0 \approx c\Lambda^{1/2}$, while the strong gravity
behaves Newtonian. Here $\Lambda$ is the cosmological constant. The
weak field approach empirically links the gravity in galaxies with
the baryonic distribution without any cold or warm dark matter. The
modified Poisson equation in Milgromian dynamics is
\begin{equation} \nabla
\cdot [\mu(\frac{|{\bf g}|}{a_0}){\bf g}]=-4\pi G \rho_b,
\end{equation}
where $\rho_b$
is the baryonic density and $\mu(\frac{|{\bf g}|}{a_0})$ is an
interpolating function. $\mu \rightarrow |{\bf g}|/a_0$ when $g\ll a_0$
and $\mu \rightarrow 1$ when $g\gg a_0$ \citep{BM1984}.
\citet{Famaey_McGaugh2012} review the observational sucesses and
problems of Milgrom's dynamics. Milgromian dynamics can be related to
space-time scale invariance \citep{Milgrom2012a,Kroupa_etal2012} and quantum-mechanical processes in the vacuum (\citealt{Milgrom1999,Zhao2008}, see also Appendix A in \citealt{Kroupa_etal2010}).
From the weak field approach, the circular
velocity at large radii of a galaxy follows as being
\begin{equation}\label{eq_vc}v_{\rm c}=(Ga_0M_{\rm b})^{1/4}.\end{equation}
This implies flat rotation curves and thus, in terms of Newtonian dynamics, an apparent phantom dark matter
distribution with an isothermal profile at large radii. Here $G$ is
the gravitational constant and $M_{\rm b}$ is the total baryonic mass of a
galaxy.
The apparent virial radius and the mass of the phantom dark matter halo
can be derived from the asymptotic behaviour of the rotation curve.
The apparent phantom dark matter halo (Newtonian)
virial masses, $M_{\rm vir}$, and the apparent (Newtonian) dynamical
mass-to-light ratios of the \citet{Georgiev3} galaxies are here studied in
Milgromian dynamics.
The virial radius is defined as the radius where the average density of
enclosed apparent dynamical matter which leads to the flat rotation curve of a galaxy (baryonic matter and phantom dark matter) is 200 times the critical density, $\rho_{\rm crit}$, of the universe, i.e.,
\begin{equation}
M_{\rm vir}\equiv pr_{\rm vir}^3 =v_{\rm c}^2r_{\rm vir}/G.
\end{equation}
The virial mass of the phantom
dark matter halo can be written as
\begin{equation}\label{eq_mvir}M_{\rm vir}=v_{\rm c}^3p^{-1/2}G^{-3/2},\end{equation}
where $p=\frac{4}{3}\pi \times 200\rho_{\rm crit}$, here $\rho_{\rm crit}=\frac{3H^2}{8\pi G}$ is the critical density of the universe and $H$ is the Hubble
constant, $H=70\, {\rm km \, s}^{-1} \, {\rm Mpc} ^{-1}$. Therefore the
apparent virial mass is proportional to $M_{\rm b}^{3/4}$. The apparent
virial mass is plotted in dependence of the V-band absolute magnitude, $M_V$, of the galaxies used in
\citet{Georgiev3} in the upper left panel of Figure
\ref{mvir}. Clearly, there is a tight anti-correlation between
$M_{\rm vir}$ and $M_V$. Such a correlation can indeed be expected, since the apparent virial mass is determined by the total mass of the baryonic matter in Milgromian dynamics.
The observed $M_V$ and $L_V$ data of the galaxies (here $L_V/L_{\odot V}=10^{-0.4(M_V-M_{\odot V})}$, where $L_{\odot V}$ and $M_{\odot V}$ are the luminosity and absolute magnitude of the Sun in the V band) and of $M_{\rm GC}$ in each galaxy used in this paper are originally taken from various observations \citep{ML07,Peng08,Spitler08,Georgiev_etal2008,Georgiev1,Georgiev2}, and the data for $M_b$ of the galaxies are obtained by performing the same calculation as \citet[][see \S 3.2.1 in their paper]{Georgiev3}: The masses of most of their sample galaxies are computed by using a luminosity-$M/L$ relation derived from \citet{Bell_etal2003}, except for the dwarf galaxies from \citet{ML07}, for which a constant mass to light ratio of $3$ is assumed. Combining Equations \ref{eq_vc} and \ref{eq_mvir}, the virial mass of the phantom dark matter halo is derived as
\begin{equation}\label{eq_mvir2} M_{\rm vir}=(Ga_0M_{\rm b})^{3/4}p^{-1/2}G^{-3/2}.\end{equation} The apparent dynamical mass-to-light (V band) ratios of
the galaxies, $M_{\rm vir}/L_{\rm V}$, are shown in the lower left panel of Figure \ref{mvir}.
$M_{\rm vir}/L_{\rm V}$ correlates with $M_V$, for
brighter galaxies the $M_{\rm vir}/L_{\rm V}$ ratios are small, while for
fainter galaxies the $M_{\rm vir}/L_{\rm V}$ ratios are large.
\subsection{$M_{\rm GC}$, Specific frequency $S_{\rm N}$ and $\eta$ values}\label{secmass}
It has been suggested that $M_{\rm GC} \propto M_{\rm vir}$
in CDM models of galaxies \citep{Blakeslee1997,Blakeslee1999,Spitler_Forbes2009}. $M_{\rm GC}$ and apparent $M_{\rm vir}$ in Milgromian dynamics are compared in the upper
right panel of Figure \ref{mvir} ($\log$ is $\log_{10}$ hereafter). The slopes of $\log M_{\rm vir}$ in Milgromian dynamics and $\log M_{\rm GC}$ are given in this panel by a linear fit function, for $M_{\rm vir}\le 10^{12}\rm M_\odot$ on the top left and for $M_{\rm vir} > 10^{12}\rm M_\odot$ on the bottom right. For galaxies with
apparent $M_{\rm vir} \le 10^{12} \rm M_\odot$, $M_{\rm vir} \propto M_{\rm GC}^{4/3}$, while
for massive galaxies with apparent $M_{\rm vir} > 10^{12}\rm M_\odot$, $M_{\rm vir}
\propto M_{\rm GC}^{0.43}\approx M_{\rm GC}^{3/7}$. However a rather good agreement with the empirical CDM scaling (\citealt{Spitler_Forbes2009}, see the gray line in the upper right panel of Fig. \ref{mvir}) is evident.
For the massive galaxies, in Milgromian dynamics, the ratio
$M_{\rm GC}/M_{\rm vir}$ is larger than for the less massive galaxies, since
$M_{\rm vir}/M_{\rm b}$ is smaller for the massive galaxies.
The above trend comes from the observed non-universality of $M_{\rm GC}/M_{\rm b}$ (see Figure \ref{mgcmb}) and the one-to-one relation between $M_{\rm vir}$ and $M_b$.
The $M_{\rm vir}/L_{\rm V}$ values of the galaxies are plotted in dependence of $M_{\rm GC}$ in the lower right
panel of Figure \ref{mvir}. $M_{\rm vir}/L_{\rm V}$ decreases
faster when $M_{\rm GC}$ is increasing and $M_{\rm GC}$ is smaller than
about $2\times 10^7\rm M_\odot$ (i.e., where $M_{\rm vir}\le 10^{12}\rm M_\odot$),
and the decreasing trend becomes shallower for
systems with larger $M_{\rm GC}$ (i.e., where the $M_{\rm vir}>10^{12}\rm M_\odot$).
This agrees with the trend of $M_{\rm vir}$ as a function of $M_{\rm GC}$.
\begin{figure}{}
\begin{center}
\resizebox{9.cm}{!}{\includegraphics{mvir_magv_mass_2.eps}}
\makeatletter\def\@captype{figure}\makeatother \caption{The
apparent phantom cold or warm dark matter virial masses versus absolute magnitude, $M_V$, of
galaxies (upper left panel), apparent Newtonian dynamical mass-to-light
ratios in Milgromian dynamics versus $M_V$ (lower left). The blue lines on left panels show
the linear fit to the data points, and the least square fitting parameters are labelled
in the left panels.
The upper right panel shows the
apparent virial masses against the total GC masses. The blue and red lines show, respectively, the linear fit for the data points corresponding to $M_{\rm vir} \le 10^{12}\rm M_\odot$ and $M_{\rm vir}>10^{12}\rm M_\odot$, and
the dotted
line shows the linear fit for CDM halos from
\citet{Spitler_Forbes2009}. The lower right panel shows the
apparent Newtonian dynamical mass-to-light ratios in Milgromian dynamics against the total GC
masses. The colours of the data points are the same as in Figure \ref{mgcmb}.}\label{mvir}
\end{center}
\end{figure}
From \S \ref{secmvir}, $M_{\rm vir} \propto M_{\rm b}^{3/4}$ in Milgromian dynamics. It is known that $S_{\rm N} =N_{\rm GC}\times 10^{0.4(M_V+15)} \propto M_{\rm GC} L_{\rm V}^{-1}$. Since the stellar mass to light ratios of galaxies, $M_b/L_V$, are determined by the stellar population and stellar evolution, and also the dark baryonic components like hot gas, the relation of $M_b$ and $L_V$ is not simply $M_b\propto L_V$. A power law relation between $L_V$ and total baryonic mass in a galaxy is fitted in \citet{Georgiev3}, which is $M_b\propto L_V^{1.11} \approx L_V^{10/9}$. So $S_{\rm N} \propto M_{\rm GC} M_{\rm vir}^{-6/5}$.
Therefore $S_{\rm N}$ is a function of apparent $M_{\rm vir}$:
\begin{eqnarray}\label{snmvir}
S_{\rm N} &\propto& M_{\rm vir}^{3/4} \times M_{\rm vir}^{-6/5}=M_{\rm vir}^{-9/20},~~~~M_{\rm vir} \le 10^{12}\rm M_\odot \nonumber\\
S_{\rm N} &\propto&
M_{\rm vir}^{7/3}\timesM_{\rm vir}^{-6/5}=M_{\rm vir}^{17/15},~~~~M_{\rm vir}>10^{12}\rm M_\odot \end{eqnarray} The specific frequency $S_{\rm N}$
is shown in dependence of $M_{\rm vir}$
in the left panel of Figure \ref{sn}. The values of $S_{\rm N}$ are from
\citet{Georgiev3}. It is confirmed that the trend of data points has two
components, as expected in Eq. \ref{snmvir}. The two-component
function for galaxies with GCs implies that for low mass galaxies with
$M_{\rm vir} \le 10^{12}\rm M_\odot$ the number of GCs decreases with the apparent virial
mass; for massive galaxies with $M_{\rm vir}>10^{12}\rm M_\odot$, the
number of GCs increases with the apparent halo mass.
\begin{figure}{}
\begin{center}
\resizebox{9.cm}{!}{\includegraphics{mvir_eta_S_2.eps}}
\makeatletter\def\@captype{figure}\makeatother \caption{Left panel:
the specific frequency of GCs as a function of
apparent virial mass for galaxies from \citet{Georgiev3}. Right
panel: the ratios of $M_{\rm GC}/M_{\rm vir}$ as a function of $M_{\rm vir}$. The symbols are defined as in Figure \ref{mvir}. The dotted gray lines in both panels show the $S_{\rm N}$ and $\eta$ values for galaxies hosting only one GC, and the areas below the gray dotted lines correspond to galaxies hosting fewer than one GC.
}\label{sn}
\end{center}
\end{figure}
Since apparent (phantom) dark matter halos in Milgromian dynamics have
different density profiles compared to the dark halos obtained
from CDM cosmological simulations, it is therefore unnecessary that the $M_{\rm GC}/M_{\rm vir}$ ratio is a universal constant. From the trend of $M_{\rm GC}$ as a function of
$M_{\rm vir}$ in the upper right panel of Figure \ref{mvir},
the trend of the $\eta$ values for galaxies with GCs can be obtained: for galaxies with apparent halo
mass $M_{\rm vir} \le 10^{12}\rm M_\odot$, $\eta \propto M_{\rm vir}^{-1/4}$; for
massive galaxies with $M_{\rm vir} >10^{12}\rm M_\odot$, $\eta \propto M_{\rm vir}^{4/3}$.
Thus the mass fraction of GCs in galaxies decreases with increasing apparent
halo virial mass
when the galaxies are less massive than $10^{12}\rm M_\odot$, and for the
massive galaxies the mass fraction of GCs increases with increasing
apparent virial mass.
The $\eta$ values for Georgiev's galaxies
\citep{Georgiev3} are shown in the right panel of Figure \ref{sn}, and they
argee with what is expected from the above discussion.
The function of $\eta$ in
Milgromian dynamics comes from the $100\%$ conspiracy of apparent dark matter
with baryons, and implies non-constant $M_{\rm GC}/M_{\rm b}$ ratios for the
GC-hosting galaxy systems. This is a natural expectation if the star formation rate (SFR) of a galaxy and thus its production of massive clusters \citep{Weidner_etal2004} depends on the depth of the potential well, although details need to be worked out.
\section{Discussion and summary}
In this work, it has been found that the apparent virial mass of the phantom dark matter halo (observed with Newtonian eyes) predicted in Milgromian dynamics
tightly anti-correlates with the V-band galaxy absolute magnitude
$M_V$, and that the apparent Newtonian dynamical mass-to-light ratios
correlate with $M_V$ in a Milgromian dynamics universe.
The relationship of total GC mass in a galaxy
and the apparent dark matter halo virial mass of the hosting galaxy in Milgromian
dynamics has been studied here. It follows that $M_{\rm GC}$ is a two-part
function of the apparent dark matter halo virial mass $M_{\rm vir}$ for galaxies with GCs.
For dwarf galaxies with $M_{\rm vir} \le 10^{12}\rm M_\odot$,
$M_{\rm GC} \propto M_{\rm vir}^{3/4}$, while for massive galaxies with
$M_{\rm vir}>10^{12}\rm M_\odot$, $M_{\rm GC} \propto M_{\rm vir}^{7/3}$. Therefore, the overall
mass of a GC system increases more slowly with the increase of
apparent virial mass for galaxies with shallower potential wells (i.e., $M_{\rm vir}\le 10^{12}\rm M_\odot$),
whereas the total mass of a GC system increases more rapidly with the
increase of the apparent virial mass for galaxies with deeper
potentials (i.e., $M_{\rm vir} > 10^{12}\rm M_\odot$).
For galaxies with GCs, the specific GC formation
efficiency is $\eta \propto M_{\rm vir}^{-1/4}$ for galaxies with
$M_{\rm vir}\le 10^{12}\rm M_\odot$, while for massive galaxies with $M_{\rm vir}
> 10^{12}\rm M_\odot$, $\eta \propto M_{\rm vir}^{4/3}$, in contrast to a universal constant
$\eta$ obtained assuming CDM halos to be real.
The scaling relations of specific frequency $S_{\rm N}$ and specific GC
formation efficiency $\eta$ as functions of apparent halo mass are different
to what is derived from CDM models. The two-component functions of
$S_{\rm N}(M_{\rm vir})$ and $\eta(M_{\rm vir})$ indicate that GCs form more efficiently in
massive galaxies in Milgromian dynamics and in dE galaxies with small apparent
virial mass.
\section{Acknowledgments}
Xufen Wu gratefully acknowledges support through the Alexander von
Humboldt Foundation. We thank Iskren Georgiev for providing the observed
data from Georgiev et al. (2010) and for the useful comments to the manuscript.
\bibliographystyle{mn2e}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,465 |
\section{Exponential Lower bound}
In this section we will exhibit lower bounds on the size of mimicking
networks using a subtle rank argument. Fix $p =
2^{k-1}-1$ for the remainder of the section.
\begin{definition}
A \textit{minimum terminal cut vector(MTCV)} $m^{G,K}$ for graph $G$ with terminal set $K$ is a $p$-dimensional vector where $i$'th coordinate $m_i^{G,K}=h_K^G(U_i)$ i.e., it corresponds to the value of terminal cut separating $i$'th subsets of terminals from rest of the terminals for $i \in \{1, 2, \cdots p(=2^{k-1}-1)\}$.
\end{definition}
Let $M_k$ be the set of all possible minimum terminal cut vectors with
$k$ terminals. Not all vectors $v
\in \mathbb{R}^{2^{k-1}-1}$ can be minimum terminal cut vectors. The
submodularity of the cut function introduces constraints on the
coordinates of the minimum terminal cut vector.
For example there are 3 possible terminal cuts for graphs with terminal set size 3. However \textbf{[0.1, 0.1, 0.8]} is not a valid MTCV.
First we prove that these minimum terminal cut vectors form a convex set.
\begin{lemma}
\label{lemma:cutcomb}
$M_k$ is a convex cone in $\mathbb{R}^{2^{k-1}-1}$.
\end{lemma}
\begin{proof}
Note that by scaling the edges of a graph $G$, the corresponding
minimum terminal cut vector also scales. Therefore, it is sufficient
to show the convexity of the set $M_k$.
Let $G_1$ and $G_2$ be graphs with terminal set $K$ of size $k$. Let $N_1$ and $N_2$ be their set of non-terminals respectively i.e., $N_i \cup K= V(G_i)$ for $i=1,2$. Note that these graphs might have different edge weights or different number of vertices. So depending on the edge values minimum terminal cuts will have different values.
Let us assume $t_1$ and $t_2 $ be the minimum terminal cut vectors for graphs $G_1$ and $G_2$ with same terminal set $K$ and non negative edge cost functions $\mathcal{C}_1$ and $\mathcal{C}_2$ respectively.
We claim that for any nonnegative $\lambda_1, \lambda_2$ such that $ \lambda_1 + \lambda_2=1 $, there exists a graph $H$ with same terminal set $K$ and edge cost function $\mathcal{C}'$ such that its minimum terminal cut vector $t' = \lambda_1 t_1 + \lambda_2 t_2$.
We create $H$ with nonterminals $N_1 \cup N_2$. We start with all edge costs in $H$ to be 0.
Then for $i=1$ and $2$, for all edges $(u,v) \in G_i$, we increase the cost of edge $(u,v)$ in $H$ by $\lambda_i \mathcal{C}_i(u,v)$. The final graph has a minimum terminal cut vector of value $\sum _{i=1}^2 \lambda_i t_i$.
\end{proof}
Now we show the central lemma regarding the range of the minimum terminal cut vectors.
\begin{lemma}
\label{lemma:cutrange}
The set $M_k$ has nonzero volume.
\end{lemma}
\begin{proof}
The \textbf{0} vector is MTCV for a completely disconnected graph.
For each $i \in \{1,\ldots,2^{k-1}-1\}$, we will show that a line segment
in the $i^{th}$ direction belongs to $M_k$.
By the convexity of the set $M_k$ (lemma \ref{lemma:cutcomb}) this
will imply that the set $M_k$ has nonzero volume, i.e., full
dimensional.
To demonstrate a line segment along direction $i \in \{1,\ldots
2^{k-1}-1\}$, we will show that there
exist two MTCVs which differ only in $i$'th coordinate and same in all
other $p-1$ coordinates. Fix a subset $U_i$ of terminals. To
construct MTCVs that differ only on the $i^{th}$ coordinate, construct a graph $H_i$ for terminal sets $U_i$ as shown in Fig. 1.
\begin{figure}[h!]
\label{figure:graph}
\centering
\includegraphics[width=0.5\textwidth]{graph.png}
\caption{Graph corresponding to terminal cut $[U, K_U]$}
\end{figure}
Add all terminals in $K-U_i$ to a non-terminal $u_0$ with edge costs $1/|K-U_i|$. Add all terminals in $U_i$ to another non-terminal $v_0$ with edge costs $1/|U_i|$. Put an edge between $u_0$ and $v_0$ with edge cost $1 -\epsilon$ where $0<\epsilon< min \{1/|U_i|, 1/|K-U_i \}$. So, value of minimum terminal cut separating $U_i$ from $K-U_i$ is $1 -\epsilon$ and it contains only the edge $(u_0, v_0)$. All other terminal cuts have value $\le 1$ and does not contain the edge $(u_0, v_0)$.
So, we can change value of $\epsilon$ between 0 and $min \{1/|U_i|,
1/|K-U_i \}$ to obtain a line segment contained in $M_k$ along
direction $i$.
\end{proof}
\begin{definition}
For a given graph $G$ with terminal set $K$, the cut matrix $S_G$ is a $p \times |E(G)|$ matrix where $S_{ij}=1$ if edge $e_j \in h_K^G(U_i)$ and 0 otherwise.
\end{definition}
\begin{theorem}
\textit{(Restatement of Theorem \ref{thm:lower})}
There exists graphs $G$ for which every mimicking network has size
at least $2^{(k-1)/2}$.
\end{theorem}
\begin{proof}
Suppose every graph $G$ with $k$ terminals has a mimicking network
with $t$ vertices.
Consider a mimicking network $H$ with $t$ vertices for a graph $G$
with $k$ terminals. There are
$2^{t}-1$ possible cuts in the graph $H$. Therefore, there are at
most $(2^{t}-1)^p$ different cut matrices $S_H$ of $H$. The specific
cut matrix $S_H$ depends on the weights of the edges in $H$.
Let us refer to these matrices as $S_1, S_2,\ldots, S_{(2^{t}-1)^p}$.
Each matrix $S_i$ can be thought of as a linear map $S_i :
\mathbb{R}^{\binom{t}{2}} \to \mathbb{R}^{2^{k-1}-1}$.
For every graph $G$, there exists a choice of weights $w_{ij}$ for the
edges of $H$, and a choice of cut matrix $S_{\ell}$ (determined by the
weights), such that $S_\ell w$ is equal to the minimum terminal cut
vector $h_{K}^G$ of the graph $G$. Therefore, the set $M_k$ of all
MTCVs is in the union of the ranges of the linear maps $\{S_i\}_{i
=1}^{(2^{t}-1)^p}$.
However, since $M_k$ has non-zero volume (is of full dimension), at least one of the linear maps
$S_i$ must have rank $ = 2^{k-1}-1$. Therefore $\binom{t}{2} \geq 2^{k-1}-1$
implies that $t \geq 2^{(k-1)/2}$.
\end{proof}
\begin{corollary}
There exists graphs $G$ for which every cut sparsifier that preserves $C$ minimum terminal cuts exactly has size
at least $|C|^{1/2}$.
\end{corollary}
As the graph constructed in the theorem \ref{thm:lower} has tree-width $(k+1)$, we get the following corollary.
\begin{corollary}
There exists graphs $G$ with treewidth $\ge (k+1)$ for which every
mimicking network has size
at least $2^{(k-1)/2}$.
\end{corollary}
\begin{comment}
\begin{lemma}
A metric $M$ on $N$ points embeddable in $L_{1}^{d}$ can be represented as sum of $Nd$ cuts.
\end{lemma}
The cut metric is given on $k$ vertices(only terminals).
In our case we k points can be embedded in $l_1^{k}$.
we need to show the following lemma:
\begin{lemma}
Any k points cut metric can be expressed as sum of $k^2$ cuts.
\end{lemma}
\begin{lemma}
Given an undirected, capacitated graph $G=(V,E)$ and a set $K \subset V$ of terminals of size $k$, we can create a vertex sparsifier $H=(K',E')$ for which the cut-function exactly approximates the value of {\em{every}} minimum cut separating any subset $U$ of terminals from the remaining terminals $K-U$ where $|K'|=2^{k^2}$.
\end{lemma}
Given $k^2$ cuts we do the same as the previous case and get a hypercube on $2^{k^2}$ vertices that preserves the cuts absolutely.
\begin{theorem}
Given any cut strategy we can get a vertex sparsifier with $2^{k^2}$ nodes that preserves the cut values exactly.(Note we may not get a single vertex sparsifier with that many nodes for every strategy)
\end{theorem}
Q: These cuts are not same?
\textbf{Problem:}
In Ankur Moitras paper for each cut streategy he provides a 0-extension.
Finally he gives a distribution over 0-extensions and final graph is an average over all
these graphs.
However in our case we simple cannot average like this.
First of all non terminal sets can be different in each cases and thus simple averaging will not work.
\subsection{Averaging of graphs}
Given two graphs $G_1(T \cup N_1,E_1)$ and $G_2(T \cup N_2,E_2)$ we can average the
graphs such that if $C_1$ and $C_2$ are mincuts separating the terminals, new graph has mincut averaging them. Basically we add edges $N_1$ and T with 1/2 cost, same for $N_2$ and $T$. On the other hand average out intra edges in $T$.
Clearly this is applicable to a convex combination of graphs.
So, we take all $(2^k)C(K^2)$ cuts and create graph for each of them.
Hence, total number of new vertices $(2^k).(2^k)C(K^2)$.
Total $2^(k^3)$ nodes.
Now use distortion to improve this bound.
Read Makarychevs paper to get their constructive idea.
Use of symmetry in Moitra's paper.
Question: Can we use l1 dimension reduction for metric embedding.
\end{comment}
\section{Improved Upper Bounds on Size of Mimicking Networks}
In this section we construct a mimicking network for a given
undirected, capacitated graph $G=(V,E)$ with a set of terminals $K
(\subset V) := \{ v_1, v_2 \cdots v_k \}$. Without loss of
generality, we may assume $G$ to be connected, otherwise we can consider each component separately.
\begin{theorem}\textit{(Restatement of Theorem \ref{thm:ccut})}
For every graph $G$, there exists a mimicking network with
quality $1$ that has at most $(|K|-1)$'th Dedekind number ($\approx 2^{{(k-1)} \choose {\lfloor {{(k-1)}/2} \rfloor}}$) vertices. Further, the
mimicking network can be constructed in time polynomial in $n$ and $2^k$.
\end{theorem}
\begin{proof}
First we present the algorithm \ref{alg:Exact-Cut-Sparsifier} that
constructs the mimicking network from the graph.
\IncMargin{1em}
\begin{algorithm}
\SetKwInOut{Input}{input}\SetKwInOut{Output}{output}
\SetAlgoLined
\LinesNumbered
\Input{ A capacitated undirected graph $G$, set of terminals $K \subset V$ }
\Output{ A capacitated undirected graph $H$.}
\BlankLine
Find all $2^{k-1} -1$ minimum terminal cuts using max-flow algorithm\;
Partition the graph into $2^{2^{k-1} -1}$ clusters $\mathcal{C}_1, \mathcal{C}_2 \cdots \mathcal{C}_{2^{2^{k-1} -1}}$ such that two vertices $u, v$ belong to same cluster if they appear on same side of all the minimum terminal cuts \;
Contract each non-empty cluster into single node \;
\emph{ Return} the contracted graph $H$ \;
\caption{{ \sc{Algorithm to construct Exact-Cut-Sparsifier}}}\label{alg:Exact-Cut-Sparsifier}
\end{algorithm}\DecMargin{1em}
\begin{comment}
There exist $2^k -2$ nonempty proper subsets of $k$ terminals. The cuts $[C,\overline{C}]$ and $[\overline{C}, C]$ are the same. Thus we need to preserve terminal cuts due to $p=2^{k-1} -1$ subsets of terminals to preserve all cuts separating a subset of terminals from the remaining terminals.
To construct the mimicking network $H$, we find a mapping $\phi : V(G) \rightarrow V(H)$.
Consider a $p$ dimensional hypercube $H$ where $i$'th coordinate corresponds to $h_K^G(U_i)$, i.e., the minimum cut in $G$ separating $U_i$ from $K \setminus U_i$ for $i = 1, 2, \cdots p$.
Assume $h_K^G(U_i)=(A_i, V \setminus A_i)$ i.e., the minimum terminal cut divides $V$ into two subsets $A_i$ and $V \setminus A_i$ where $U_i \subset A_i$.
For each vertex $v$ in $G$, we set $i$'th coordinate $v_i=\textbf{1}_{v_i \in A_i}$ i.e., $v_i=1$ if $v_i$ is in the component containing $U_i$ and else $v_i=0$. Thus for each vertex $v$ in $G$ we get a $p$-dimensional $0/1$ vector that corresponds to a vertex of the hypercube $H$.
So there is a cluster(may be empty) of vertices associated with each
vertex of the hypercube. We contract all vertices in the same cluster
to obtain the mimicking network $H$.
\end{comment}
We claim that $H$ exactly preserves all minimum terminals cuts.
\begin{claim}
$H$ is a mimicking network for $G$.
\end{claim}
\textit{Proof of claim: }
Note that we are just mapping vertices of $G$ to vertices of $H$ and not deleting any edges of $G$ in $H$, thus the minimum cut value can only grow up. Hence, $h_K^G(U) \le h_K^{H}(U)$ for any $U \subset K$. But the minimum cut separating $U$ from $K-U$ in $H$ is the dictator cut parallel to the $i$'th axis. It contains only the edges of the minimum cut separating $U$ and $K-U$ in $G$. Thus $h_K^G(U) \ge h_K^{H}(U)$. Therefore we get $h_K^G(U) = h_K^{H}(U)$. $\qed$\\
We upper bound the number of vertices in $H$ by Dedekind number to complete the proof.
\end{proof}
While the algorithm creates $2^{2^{k-1}}-1$ clusters, we will argue
that by an appropriate choice of cuts many of the clusters will be
empty. Let $N(k)$ be the number of vertices in the mimicking network
constructed by Algorithm \ref{alg:Exact-Cut-Sparsifier}, i.e., it is
the number of non-empty regions created by $2^{k-1}-1$ minimum
terminal cuts. Here we show $N(k)$ is at most $(k-1)$th Dedekind
number. Dedekind numbers are a rapidly-growing integer sequence
defined as follows: Consider the partial order $\subseteq$ induced on the subsets
of an $n$-element set by containment. The $n^{th}$ Dedekind number
$M(n)$ counts the number of antichains in this partial order. Equivalently, it counts monotonic Boolean functions of $n$ variables, the number of elements in a free distributive lattice with $n$ generators, or the number of abstract simplicial complexes with $n$ elements
For a terminal cut $[U,K-U]$ where $v_k\notin U$, let $\{S(U),
V_G-S(U)\}$ denote the partition induced by the minimum cut separating
$[U,K-U]$. If there are multiple minimum terminal cuts we take any
one with smallest cardinality $|S(U)|$.
Now let us prove two structural properties of these minimum terminal cuts.
\begin{lemma}
\label{lemma:subsetCut}
If $X \subseteq Y \subseteq K$ then $S(X) \subseteq S(Y)$.
\end{lemma}
\begin{proof}
From submodularity property of cuts we get,
\begin{eqnarray}
(h_G(S(X)) +h_G(S(Y))) &\ge& (h_G(S(X) \cup S(Y)) + h_G(S(X) \cap S(Y))) \nonumber \\
& \ge &(h_G(S(X\cup Y) + h_G(S(X\cap Y))) = (h_G(S(Y)) +h_G(S(X))) .
\end{eqnarray}
Here the second inequality follows from the fact $h_G(S(X) \cup S(Y)) \ge h_G(S(X \cup Y))$ and $h_G(S(X) \cap S(Y)) \ge h_G(S(X \cap Y))$. Now as all inequalities are tight in (1), we get $h_G(S(X) \cup S(Y)) = h_G(S(X \cup Y))= h_G(S(Y))$ and $ h_G(S(X) \cap S(Y)) = h_G(S(X \cap Y))= h_G(S(X))$.
We have $h_G(S(X) \cap S(Y)) = h_G(S(X))$, but recall that among all
minimum cuts separating $(X, K-X)$, $S(X)$ has the smallest
cardinality. This implies $S(X) \subseteq S(Y)$.
\end{proof}
\begin{lemma}
\label{lemma:disjointCut}
If $X \cap Y = \phi$ then $S(X) \cap S(Y)=\phi$.
\end{lemma}
\begin{proof}
Assume $S(X) \cap S(Y)\neq \phi$. Then $ h_G(S(X) \setminus S(Y)) + h_G(S(Y) \setminus S(X)) \le ( h_G(S(X))+ h_G(S(Y))$. On the other hand as we always take the minimum terminal cut with smallest $|S(X)|$. Hence $ h_G(S(X)) < h_G(S(X) \setminus S(Y))$ and $ h_G(S(Y)) < h_G(S(Y) \setminus S(X))$. This contradicts.
\end{proof}
Note that each region created by algorithm
\ref{alg:Exact-Cut-Sparsifier}, is basically intersection of
partitions containing $S(X)$ for some minimum terminal cuts $(X,K-X)$ and
complement of $S(X)$ for remaining minimum terminal cuts.
Let $X \subseteq \{ U \subset K, v_k \notin U \}$ i.e., $X$ is a
collection of subsets of $K$ that do not contain $v_k$. Let us define
$A(X)= (\cap_{Z \in X} S(Z)) \cap (\cap_{W \notin X}
\overline{S(W)})$. Each $A(X)$ corresponds to a cluster produced by
the algorithm. We will show that $A(X)$ is empty for many choices of
$X$.
\begin{lemma}
\label{lemma:upsetLemma}
If $A(X) \neq \phi$ then $X$ is upward closed set i.e., ($\forall P \in X, P \subseteq Q \Rightarrow Q \in X$).
\end{lemma}
\begin{proof}
Suppose there exists a $Q \notin X$ such that for some $P \in X$ and $Q \supseteq P$.
From lemma \ref{lemma:subsetCut},
\begin{equation}
S(P) \subseteq S(Q).
\end{equation}
Also, note that by definition, $A(X) \subseteq S(P) \cap
\overline{S(Q)}$. Hence, we get $A(X) \subseteq S(P) \cap
\overline{S(Q)} = \phi$ -- a contradiction.
\end{proof}
From lemma \ref{lemma:upsetLemma}, if $A(X) \neq \phi$ then $X$ is upward closed set. Now minimal elements of upper sets form an antichain. So $N(k)$ is upper bounded by the number of antichains of subsets of an $(k-1)$-element set i.e., $M(k-1)$. Kleitman and Markowsky\cite{KM75} had shown that:
\begin{equation}
{n \choose {\lfloor {n/2} \rfloor}} \le \log M(n) \le {n \choose {\lfloor {n/2} \rfloor}}(1+O(\log n/n))
\end{equation}
Moreover from lemma \ref{lemma:disjointCut}, if there are two completely disjoint elements in $X$ that will lead to an empty region. So $N(k)$ is upperbounded by the number of antichains of subsets of $(k-1)$-element sets where all members of the antichain share at least one common element. Let us call this number to be $Z(k-1)$. Clearly $M(k-2) \le Z(k-1) \le M(k-1)$.
Table \ref{table:nonlin} compares different bounds.
\begin{table}[ht]
\caption{Different bounds related to N(k)}
\centering
\begin{tabular}{c c c c c c}
\hline\hline
$k$ & Lower & Best Upper & Upper Bound & $(k-1)$th & $2^{2^{k-1}}-1$\\ [0.5ex]
&bound & bound & from Contraction & Dedekind No. & \\[0.5ex]
& & & $Z(k-1)$ & $M(k-1)$ & \\[0.5ex]
\hline
2 & 2 & 2 & 2 & 2 & 3\\
3 & 3 & 3 & 4 & 5 & 15\\
4 & 5 & 5 & 11 & 19 & 255\\
5 & 6 & 6 & 54 & 167 & $65535$\\
6 & 9 & * &687 & 7580 & $4.29 \times 10^9$\\ [1ex]
\hline
\end{tabular}
\label{table:nonlin}
\end{table}
\begin{comment}
\begin{table}[ht]
\caption{Different bounds related to N(k)}
\centering
\begin{tabular}{c c c c c c}
\hline\hline
$k$ & Lower & Best Upper & Upper Bound & $(k-1)$th & $2^{2^{k-1}}-1$\\ [0.5ex]
&bound & bound & from Contraction & Dedekind No. & \\[0.5ex]
& & & $Z(k-1)$ & $M(k-1)$ & \\[0.5ex]
\hline
$k$ & 2 & 3 & 4 & 5 & 6\\
lower bound & 2 & 3 & 5 & 6 & 9\\
Best upper bound & 2 & 3 & 5 & 6 & *\\
Best upper bound from contractions $Z(k-1)$ & 2 & 4 & 11 & 54 & $687$\\
Dedekind Numbers $M(k-1)$ & 2 & 5 & 19 & 167 & 7580\\
$2^{2^{k-1}}-1$& 3 & 15 & 255 & 65535 & $4.29 \times 10^9$\\ [1ex]
\hline
\end{tabular}
\label{table:nonlin}
\end{table}
\end{comment}
The observations made in this section together with results on bounded treewidth on \cite{ChaudhuriSWZ00} implies improved bound for graphs with bounded treewidth.
\begin{corollary}
Let $G$ be a $n$-vertex network of treewidth $t$. Then we can create
an mimicking network for $G$ that has size at most $k 2^{3(t+1) \choose {\lfloor {3(t+1)/2} \rfloor}}$.
\end{corollary}
\subsection{Contraction-Based Mimicking Networks}
Here we will show that on every graph $G$ that has unique
minimum terminal cuts, Algorithm
\ref{alg:Exact-Cut-Sparsifier} produces a mimicking network that is
optimal among all contraction-based mimicking networks.
\begin{theorem}
\textit{(Restatement of Theorem \ref{thm:loweRestrict})}
Let $G$ be a graph with unique minimum terminal cuts. Then the
mimicking network constructed using Algorithm
\ref{alg:Exact-Cut-Sparsifier} is optimal among contraction-based
mimicking networks for $G$ i.e., it has minimum number of vertices
among all contraction-based mimicking networks.
\end{theorem}
\begin{proof}
Let $H$ be the contraction-based mimicking network for graph $G$ with terminal set $K$ constructed using function $\phi: V(G) \rightarrow V_H$ in Algorithm \ref{alg:Exact-Cut-Sparsifier}.
First, we claim that all edges in $H$ belong to some minimum terminal cut in $G$.
\begin{claim}
\label{claim:edge}
For all edges $(y,z) \in G$, $\phi(y) \neq \phi(z)$ if and only if
$(y,z) \in h_K^G(U)$ for some $U \subset K$.
\end{claim}
\begin{proof}
The claim is clear from the construction presented in Algorithm
\ref{alg:Exact-Cut-Sparsifier}. Two vertices are merged if and only
if the edge between them does not belong to any minimum cut.
\end{proof}
Assume $H'$ is the optimal contraction-based mimicking network with
minimum number of vertices, i.e.,
$|V(H')| \le |V_H|$. Since $H'$ is contraction-based, it is
defined by a function $\phi' : V(G) \rightarrow V_{H'}$.
\begin{claim}
\label{claim:edge1}
For all edges $(y,z) \in G$, if $(y,z) \in h_K^G(U)$ for some $U
\subset K$ then $\phi'(y) \neq \phi'(z)$
\end{claim}
\begin{proof}
Consider an $e = (y,z)$ in the original graph $G$, that
belongs to some minimum terminal cut $(U,K-U)$. We claim that the
clusters containing $y$ and $z$ are distinct in $H'$.
By definition of $H'$, the minimum cut $h_{K}^{H'}(U)$ has
the same value as the minimum terminal cut $h_K^G(U)$. Since all
minimum terminal cuts in $G$ are unique, this implies that the cut
induced by $h_K^{H'}(U)$ in $G$ is exactly the same as $h_K^G(U)$.
Therefore, for every edge $(y,z)$ in the graph $G$ that belongs
to a minimum terminal cut $h_K^G(U)$, the corresponding clusters in
$H'$ are distinct.
\end{proof}
From the previous two claims, $\phi(y) \neq \phi(z) \implies \phi'(y)
\neq \phi'(z)$ for every edge $(y,z) \in G$. This implies that the
number of clusters in $H$ is at most the number of clusters in $H$.
\end{proof}
\section{Introduction}
Suppose there are small number of terminals or clients that are part of a
huge network such as the internet. Often, it is useful to
construct a smaller graph which preserves the
properties of the huge network that are relevant to the terminals.
For example, if the terminals or clients are interested in routing
flows through the large network, one would want to construct a small
graph which preserves the routing properties of the original network.
The notion of {\it mimicking networks} introduced by Hagerup et.\ al.
\cite{HagerupKNR95} is an effort in this direction.
Let $G$ be an undirected graph with edge capacities $c_e$ for
$e \in E$, and a set of $k$ terminals $K \subset V$.
A {\it mimicking network} for $G$ is an undirected
capacitated graph $H=(V_H,E_H)$ such that $K
\subseteq V_H$ and for each subset $U \subset K$ of terminals, the
size of the minimum cut separating $U$ from $K-U$ in $H$ is exactly
equal to the size of the minimum cut separating $U$ and $K-U$ in
the graph $G$. As a corollary, the set of realizable external flows (possible total
flows at terminals) in $G$ are preserved in a mimicking network.
Therefore, the smaller graph $H$ {\it mimics} the graph $G$ in terms
of external flows routable through it. The vertices of the mimicking
network that are not terminals, namely $V_H - K$ will be referred to
as {\it Steiner} vertices.
The work of Hagerup et.\ al.\cite{HagerupKNR95} exhibited a construction a
mimicking network with at most $2^{2^k}$ vertices for every graph with
$k$ terminals. Subsequently, Chaudhuri et.\
al.\cite{ChaudhuriSWZ00} proved that there exists graphs that require
at least $(k+1)$ vertices in its mimicking network. The same work
also obtained improved constructions of mimicking networks for special
classes of graphs namely, bounded treewidth and outer planar graphs.
Specifically, they showed that graphs of treewidth $t$ admit a
mimicking network of size $k 2^{2^{3(t+1)}}$, while outerplanar graphs
admit mimicking networks of size $(10k -6)$.
Mimicking networks constituted the main building block in the development of $O(n)$ time algorithm for computing maximum $s-t$ flow in a bounded treewidth network \cite{HagerupKNR95} and for obtaining an optimal solution for the all-pairs minimum-cut problem in the same class of networks \cite{ArikatiCZ98}.
However, there still remained a doubly exponential gap between the
known upper and lower bounds for the size of mimicking networks for general
graphs.
\subsection{Vertex Sparsifiers}
Closely tied to mimicking networks is the more general notion of
{\it vertex sparsifiers} introduced by Moitra \cite{MoitraFocs09}.
Roughly speaking, a {\it vertex cut sparsifier} is a mimicking network
that only approximately preserves the cut values. Formally, let $G$ be an undirected graph with edge capacities $c_e$ for
$e \in E$, and a set of $k$ terminals $K \subset V$.
A {\it vertex cut sparsifier} with quality $q$ is an undirected
capacitated graph $H=(V_H,E_H)$ such that $K
\subseteq V_H$ and for each subset $U \subset K$ of terminals, the
size of the minimum cut separating $U$ from $K-U$ in $H$ is within a
factor $q$ of the size of the minimum cut separating $U$ and $K-U$ in
the graph $G$.
The original motivation behind the notion of
vertex cut sparsifiers was to obtain improved approximation
algorithms for certain graph partitioning and routing problems.
If the solution to some combinatorial optimization problem only
depends on the values of the minimum cuts separating terminal subsets,
then given any approximation algorithm for the problem, we can first
compute a cut sparsifier $H$ for graph $G$ and run the approximation
algorithm on the graph $H$ instead of $G$. If the approximation
guarantee of the algorithm depended on the number of the vertices of
the input graph, then this would yield an algorithm whose
approximation guarantee only depends on the size of the sparsifier
$H$.
The problem of constructing {\it vertex cut sparsifiers} has received
considerable attention since their introduction in
\cite{MoitraFocs09}. Naturally, the goal would be to obtain as good an approximation as
possible, while keeping the size of the sparsifier $H$ small. In
fact, the notion of vertex sparsifiers as defined in
\cite{MoitraFocs09} require that the graph $H$ have only the terminals
$K$ as the vertices, i.e., $V_H = K$ (no Steiner vertices). Much of the subsequent efforts
have been focused on vertex sparsifiers with this additional
requirement that $V_H = K$. In this setting, Moitra
\cite{MoitraFocs09} showed the existence of vertex sparsifiers with
quality $O(\log^2 k/ \log \log k)$. Subsequent works by Leighton et al.\ \cite{LeightonMStoc10}, Englert et al.\ \cite{EnglertGKRTT10} and Makarychev et al.\ \cite{MM10} gave polynomial-time algorithms for constructing $O(\log k/ \log \log k)$ cut sparsifiers, matching the best known existential upper bound.
On the negative side, Leighton and Moitra \cite{LeightonMStoc10}
showed a lower bound of $\Omega(\log \log k)$ on the quality of cut
sparsifiers without Steiner vertices, which was subsequently improved to
$\Omega(\sqrt{ \log k/\log \log k})$ \cite{MM10}.
In light of these lower bounds, it is natural to wonder if better
approximation guarantees could be obtained by vertex sparsifiers that
include {\it steiner vertices}, i.e., vertices of the sparsifier $H$ are a strict
super-set of the set of terminals $K$.
In fact, for $k \ge 4$, there exist graphs for which no cut sparsifier
without Steiner vertices preserves terminal cuts exactly. But by
Hagerup \cite{HagerupKNR95}, there exists cut sparsifiers (mimicking
networks) with
$2^{2^4}$ nodes that exactly preserves all the cuts.
Initiating the study of vertex sparsifiers with steiner nodes, Chuzhoy
\cite{Chuzhoy12} exhibited efficient algorithms to construct
$3(1+\epsilon)$-quality cut sparsifiers of size $O(C/\epsilon)^3$ for
a constant $\epsilon \in (0,1)$, where $C$ denotes the total capacity of
the edges incident on the terminals, normalized so as to make all the
edge-capacities at least $1$. The same work also gives an
efficient construction of a $(68+\epsilon)$-quality vertex flow sparsifier of size $C^{O(\log \log C)}$ in time $n^{O(\log C)}. 2^C$.
Notice that the size of the sparsifiers depend on the total capacity
$C$ of edges incident at the terminals, which could be arbitrarily
large compared to the number of terminals $k$.
While there has been progress in efficient constructions of vertex
sparsifiers without Steiner nodes, the power of vertex sparsifiers with Steiner nodes is poorly
understood. For instance, the following question originally posed by
Moitra \cite{MoitraFocs09} remains open.
\textit{Do there exists cut sparsifiers with $k^{O(1)}$ additional
steiner nodes that yield a better than $O(\log k /\log\log k)$
approximation?}
In fact, Moitra \cite{MoitraFocs09} points out that there could exist
exact cut sparsifiers (quality $1$) with only $k$ additional Steiner
nodes.
\subsection{Our results:}
In this paper, we show upper and lower bounds for {mimicking
networks} aka vertex cut sparsifiers with quality $1$.
First, we present an improved bound on the size of mimicking networks for
general graphs. Specifically, we exhibit a construction of
mimicking networks with
at most $(|K|-1)$'th Dedekind number ($\approx 2^{{(k-1)} \choose
{\lfloor {{(k-1)}/2} \rfloor}}$) of vertices, as opposed to $2^{2^k}$
vertices.
\begin{theorem}
\label{thm:ccut}
For every graph $G$, there exists a mimicking network with
quality $1$ that has at most $(|K|-1)$'th Dedekind number ($\approx 2^{{(k-1)} \choose {\lfloor {{(k-1)}/2} \rfloor}}$) vertices. Further, the
mimicking can be constructed in time polynomial in $n$ and $2^k$.
\end{theorem}
We also note that the mimicking network constructed above is a
{\it contraction-based} in the sense that the mimicking network $H$ is
constructed as follows: Fix an appropriate partition $\mathcal{C}$ of
the vertices of the graph $G$ and contract every subset of vertices $S
\in \mathcal{C}$ in the partition to form a vertex of $H$.
Contraction-based sparsifiers have also referred to as {\it restricted
sparsifiers} in literature \cite{CharikarFocs09} who show that they
are a strictly stronger notion than vertex cut sparsifiers.
For restricted sparsifiers, we will use the terms -- non-terminal and Steiner vertex interchangeably.
We prove that construction is optimal
for the class of contraction-based mimicking networks.
\begin{theorem}
\label{thm:loweRestrict}
Let $G$ be a graph with unique minimum terminal cuts. Then the
mimicking network constructed using Algorithm
\ref{alg:Exact-Cut-Sparsifier} is an optimal among contraction-based
mimicking networks for $G$ i.e., it has minimum number of vertices
among all contraction-based mimicking networks.
\end{theorem}
Next, we obtain an exponential lower bound on the size of
the mimicking networks. Specifically, we show the following result.
\begin{theorem}
\label{thm:lower}
There exists graphs $G$ for which every mimicking network has size
at least $2^{(k-1)/2}$.
\end{theorem}
We also obtain improved constructions of mimicking networks for
special classes of graphs like trees and graphs of bounded tree width.
For the case of a tree, we show that $\frac{13|K|}{8}-\frac{3}{2}$
suffice, while for a graph with treewidth $t$ there exists mimicking
networks of size $|K|2^{ (3t+2) \choose {\lfloor {{(3t+2)}/2}
\rfloor}}$. We also exhibit mimicking networks that preserve cuts separating terminal set of size $\le 2$ from other terminals using only one extra Steiner vertex.
\paragraph{Related Work} In an independent work, Krauthgamer and Rika
\cite{KrauthgamerR12} obtained upper and lower bounds for the size of
mimicking networks in general graphs, and certain special classes of
graphs. Specifically, they show a lower bound of $2^{\Omega(k)}$ for
the size of mimicking networks even for the case of bipartite graphs.
Furthermore, the lower bound is shown to hold for the size of any data
structure that stores all the minimum terminal cut values of a graph.
The paper also obtains improved upper and lower bounds for the special
case of planar graphs.
It has been brought to our attention that the improved upper bound of
Dedekind number of vertices for mimicking networks was also observed
by Chambers and Eppstein \cite{ChambersE10}.
\section{Preliminaries}
In this section, we set up the notation and present formal definitions
of vertex cut sparsifiers and mimicking networks. Let $G=(V, E)$ be an undirected capacitated graph with
edge capacities $c(e)$ for all edges $e \in E$ and a set $K \subset V$ of terminals of size $k$.
Without loss of generality, we assume that $G$ is connected, otherwise
each component can be handled separately.
Let $c: E \rightarrow \mathbb{R}^+$ be the capacity function of the graph. Let $h_G : 2^V \rightarrow \mathbb{R}^+$ denote the cut function of $G$:
\begin{equation}
h_G(A)=\sum_{e \in \delta(A)} c(e) \nonumber
\end{equation}
where $\delta(A)$ denote the set of edges crossing the cut $(A, V \setminus A)$.
Now we define terminal cut function $h_K^G : 2^K \rightarrow
\mathbb{R}^+$ on $K$ as
\begin{equation}
h_K^G(U)=min_{A\subset V , A \cap K =U}h_G(A)\nonumber
\end{equation}
In words, $h_K^G(U)$ is the cost of the minimum cut separating $U$
from $K \setminus U$ in $G$. Let $S(U)$ be the smallest subset of $V$ such that $h_G(S(U))=h_K^G(U), S(U) \cap K =U$ i.e., $S(U)$ is the partition containing $U$ in the minimum terminal cut separating $U$ from $K-U$ and if there are multiple minimum terminal cuts we take any one with minimum number of vertices in the partition that contains $U$.
For any fixed $U \subset K$, the minimum
cut $h_K^G(U)$ can be computed efficiently. We will sometimes abuse
the notation and use $h_K^G(U)$ to denote both the size of the minimum
cut and the set of edges belonging
to the minimum terminal cut.
If $|U|=1$, we call the minimum terminal cut separating $U$ from $K-U$ to be \textit{mono-terminal cut}.
If $|U|\le 2$, we call the minimum terminal cut separating $U$ from $K-U$ to be \textit{bi-terminal cut}.
\begin{definition}
$H=(V_H,E_H)$ is a cut-sparsifier for the graph $G=(V, E)$ and the
terminal set $K$, if $K \subseteq V_H$ and if the cut function $h_K^H: 2^{V_H} \rightarrow \mathbb{R}^+$ of $H$ satisfies for all $U \subset K$,
\begin{equation}
h_K^G(U) \le h_K^H(U). \nonumber
\end{equation}
\end{definition}
Quality of cut sparsifier is a measure of how well the cut function of $H$ approximates the terminal cut function.
\begin{definition}
The quality of a cut sparsifier $H$: $Q_C(H)$ is defined as
\begin{equation}
max_{U \subset K} h_K^H(U)/h_K^G(U). \nonumber
\end{equation}
\end{definition}
In this paper, we will study mimicking networks that are a special
class of vertex sparsifiers.
\begin{definition}
A vertex sparsifier $H$ for graph $G$ and terminal set $K$ is a
mimicking network if $Q_C(H)=1$.
\end{definition}
Nearly all existing constructions of vertex sparsifiers are based on
edge-contractions. Now we present a simple lemma to show contraction of edges always gives us a vertex sparsifier.
\begin{lemma}
Given a graph $G$ and an edge $e$, contracting the edge $e$ in the
graph $G$ will not decrease the value of any minimum terminal cut.\cite{MoitThes}
\end{lemma}
\begin{proof}
Let $G/e$ be the graph obtained by contracting the edge $e = (u,v)$ in
the graph $G$. For any $U \subset K$, the minimum cut in $G/e$
separating $U$ from $K-U$ is also a cut in G separating $U$ from
$K-U$, with the additional restriction that $u$ and $v$ appear on the same side of the cut.
Thus contracting an edge (whose endpoints are not both terminals) cannot decrease the value of minimum cut separating $U$ from $K \setminus U$ for $ U \subset K$.
\end{proof}
Vertex sparsifiers that can be obtained by contracting edges of the
original graph will be referred to as {\it contraction-based} vertex sparsifiers.
\begin{definition}
A graph $H=(V_H, E_H)$ is a {\it contraction-based} vertex
sparsifier/mimicking network of graph $G=(V, E)$ with terminal set $K$ if there exists a function $f: V \rightarrow V_H$ such that the edge cost function of $H$ is defined as follow: $c_H(y, z)= \sum_{u, v|f(u)=y, f(v)=z} c(u,v)$ where $(y, z) \in E(H)$ and $(u, v) \in E(G)$.
\end{definition}
\begin{comment}
Now we define flow sparsification. Assume $D$ is a demand vector that specifies the demand between every pair of terminals. A flow $F$ is a routing of demands if it satisfies demand constraints for all pairs. Congestion of an edge $e$ due to flow $F$: $Cong(e,F)$ is $F(e)/c_e$ where $F(e)$ is the flow sent along $e$ and $c_e$ is the capacity of the edge. Congestion $Cong(G,D)$ due to routing of demands $D$ is $min_{F \phantom{.} routes \phantom{.} D} max_{e\in E(G)} Cong(e,F)$.
\begin{definition}
$H=(V_H,E_H)$ is a flow-sparsifier of quality $q$ for the graph $G=(V,
E)$ and the terminal set $K$, if $K \subseteq V_H$ and if for any set of demands $D$ over terminals,
\begin{equation}
Cong(H,D) \le Cong(G,D) \le q \cdot Cong(H,D) . \nonumber
\end{equation}
\end{definition}
\end{comment}
\section{Improved Constructions for Special Classes of Graphs}
\subsection{Trees}
\begin{theorem}
\label{thm:uppertree}
Given an undirected, capacitated tree $T=(V,E)$ and a set $K \subset
V$ of terminals of size $k$, we can construct a mimicking network
$T_H=(V_H,E_H)$ for which the cut-function exactly approximates the
value of {\em{every}} minimum cut separating any subset $U$ of
terminals from the remaining terminals $K-U$ where $|V_H| \le 2k-1$
and this is tight for contraction-based mimicking networks. We can
also create an outerplanar mimicking network which has at most $\frac{13k}{8}-\frac{3}{2}$ vertices.
\end{theorem}
\begin{proof}
Let $H'$ be the smallest sized mimicking network. We can assume each non-leaf non-terminal vertex in $H'$ has degree at least 3. Otherwise, if nonterminal vertex $v$ is a degree 2 vertex with neighbor $u$ and $w$, then we can delete $v$ and add an edge $(u,w)$ with cost $min(c(v,u), c(v,w))$ to preserve the minimum terminal cuts. In other words, we can contract the minimum capacity edge among $(v,u)$ and $(v,w)$. Similarly if a nonterminal is a leaf, we can delete that nonterminal as it does not affect any minimum terminal cuts.
Therefore, finally the tree $T'$ contains only terminals as leaves and each non-leaf vertex has degree at least 3. So at most there are $(2k-2)$ vertices.
To show this is tight for contraction-based mimicking network, consider a 3-regular tree with uniform edge costs and leaves as terminals. Each edge $e$ is in at least one unique minimum terminal cut $C_e$. To preserve cut $C_e$, we can not contract $e$. Thus we need at least $(2k-3)$ edges in this case.
Now we add appropriate 0-cost edges(if needed) in $T'$ to make the tree 3-regular and set of terminals as set of leaves. We call this tree $T$.
We can rearrange the tree such that for any node $v$ in tree $T$, height of the subtree rooted at left child of $v$ is greater than the height of the subtree rooted at right child of $v$.
Now we define an operation called $(Y$-$\Delta)$-transformation which
reduces the number of vertices further. However the mimicking network
remains no more contraction-based. Let $x$ be a degree-3 nonterminal with neighbors $u,v,w$, then we can delete $x$ and add edges $(u,v),(v,w),(w,u)$ with edge cost $\frac{c(u,x)+c(v,x)-c(w,x)}{2}, \frac{c(v,x)+c(w,x)-c(u,x)}{2}, \frac{c(u,x)+c(w,x)-c(v,x)}{2}$ respectively. We call this $(Y$-$\Delta)$-transformation. We consider non-terminals one by one in an in-order traversal of $T$.
We apply the transformation if a vertex has degree-3 and modify the graph.
Then we find the next vertex in the in-order traversal of $T$ that has
degree 3 in the modified graph. If there exists such a vertex, we
continue applying the transformation on it. Otherwise we stop to get
the mimicking network $H$. Note that $H$ is a cactus graph i.e., two cycles share at most one vertex in the graph. This is also an outerplanar graph. Assume $V(H)=n$.
Now we claim that there are at most $\lfloor k/2 \rfloor$ leaves in $H$. Consider the leaves(terminals) in the in-order traversal $v_1, v_2, \cdots v_k$. Pair $(v_i, v_i+1)$ for $i=1, 2, \cdots \lfloor k/2 \rfloor$. We claim that at most one of them is a leaf after completion of $(Y$-$\Delta)$-transformation. Take the path from $v_i$ to $v_{i+1}$ in $T$. At least one degree-3 nonterminals $v_t$ is on the path such that $(Y$-$\Delta)$-transformation was applied to $v_t$, making one leaf in $T$ to have degree $\ge2$ in $H$. Also note than $v_1$ and $v_2$ both are leaves due to the arrangement.
So $H$ has at most $k/2$ leaves and at least $(n-k)$ nodes of degree 4 or more.
As $(Y$-$\Delta)$-transformation keeps number of edges same. $H$ still has at most $(2k-3)$ edges.
Thus we get, $4(n-k)+2\frac{k}{2}+\frac{k}{2} \le 2(2k-3)$ i.e., $n \le \frac{13k}{8}-\frac{3}{2}$.
\end{proof}
\begin{comment}
\subsection{Complete Graphs with uniform edge-cost}
\begin{theorem}
\label{thm:complete}
Given an undirected, complete graph $G=(V,E)$ with uniform edge cost($\rho$)and a set $K \subset V$ of terminals of size $k$, we need at least $k+1$ vertices to construct an exact vertex sparsifier and we can efficiently construct such an exact vertex sparsifier $H$ with $k+1$ vertices.
\end{theorem}
\begin{proof}
We will need the following lemma from Charikar et. al.\cite{CharikarFocs09}:
\begin{lemma}
\label{lemma:autom}
If there is a cut-sparsifier $H$ for $G$ which has quality $\alpha$, then there is a cut-sparsifier $H'$ which has quality at most $\alpha$ and is invariant under the automorphisms of the weighted graph $G$ that send $K$ to $K$.
\end{lemma}
First, let us assume that there is an exact cut sparsifier with no Steiner vertices.
So according to lemma \ref{lemma:autom}, we will have an exact cut sparsifier $H'$ with no Steiner vertices and uniform edge cost. As the exact cut sparsifier preserves all mono-terminal cuts all edge costs must be $\rho(|V|-1)/(k-1)$. However then minimum bi-terminal cuts in $H'$ will have value $2\rho(k-2)(|V|-1)/(k-1)$ where as minimum bi-terminal cuts in $G$ have value $2\rho(|V|-2)$. This contradicts.
Now we show the efficient construction of $H$ with $k+1$ vertices. we can create $H$ by defining $c(u,v)=\rho$ for all $u,v \in K$ and $c(z,u)=(|V|-|K|)\rho$ where $z$ is the extra vertex and $u \in K$.
Now, $h_K^H(U)=h_H(U)=(|U|(|K|-|U|)+|U|(|V|-|K|))\rho=|U|(|V|-|U|)\rho$=$h_K^G(U)$ where $U \subset K$ and $|U|\le|K-U|$.
\end{proof}
\subsection{Improved bound for cut sparsifiers that preserve small-sized terminal cuts}
Now we show construction of best cut sparsifier for special cases where we only want to preserve all minimum terminal cuts $(U,K-U)$ where $min\{|U|, |K - U|\} \le c$ for $c=1$ (mono-terminal cut) and $2$ (bi-terminal cut). For brevity we will us use $R(i)$ to denote $h_K^G(\{v_i\})$ i.e., the cost of minimum terminal cut separating $\{v_i\}$ from $\{K \setminus \{v_i\}\}$ and $R(ij)$ to denote $h_K^G(\{v_i, v_j\})$. We will also use $(K-i)$ to denote $K\setminus \{v_i\}$.
\begin{theorem}
\label{thm:smallCuts}
For every graph $G$, there exists a cut sparsifier with $k$ vertices that preserves all single terminal cuts.
\end{theorem}
\begin{proof}
Define $c(ij)=\frac{(R(i)+R(j))}{(n-1)} - \Sigma_{l \in K\setminus \{i,j\}}\frac{R(l)}{(n-1)(n-2)}$ for all $(i,j) \in K\times K$.
\end{proof}
However it is not possible to preserve all bi-terminal cuts($c=2$) without using a Steiner vertex. We will show $k+1$ vertices are sufficient to preserve all bi-terminal cuts. In the proof we will be heavily using the following lemma from \cite{ChaudhuriSWZ00}.
\begin{lemma}
\label{lemma:CSW}
Let $G =(V, E)$ be a network with $k$ terminals $v_1, v_2, \cdots v_k$ . Let $M = \{ m_1, m_2, \cdots m_p\}$ be a multiset of min-cuts in $G$ and let $\delta_{ij}$ be the number of $m_i$'s, that separate $v_i$ and $v_j$ . Let $N$ be a second multiset of min-cuts with $N =\{ n_i^r | i \in \{1,2, \cdots k\}, r \in \{1,2, \cdots u_i\}\}$ where each $n_r^i$, $1 \le r \le u_i$ , separates $v_i$ from all other terminals.
If for all $i, j ; u_i + u_j \le \delta_{i j}$ , then $w(N) \le w(M)$.
\end{lemma}
\begin{theorem}
\label{thm:smallCuts}
For every graph $G$, there exists a cut sparsifier with $k+1$ vertices that preserves all minimum terminal cuts $(U,K-U)$ where $min\{|U|, |K - U|\} \le 2$.
\end{theorem}
\begin{proof}
There are at most $({k \choose 1}+{k \choose 2})$ minimum terminal cuts $(U,K-U)$ where $min\{|U|, |K - U|\} \le 2$
We present the algorithm to find a cut sparsifier that exactly preserves all these cuts in Algorithm \ref{alg:Small-Cut-Sparsifier} .
\IncMargin{1em}
\begin{algorithm}
\SetKwInOut{Input}{input}\SetKwInOut{Output}{output}
\SetAlgoLined
\LinesNumbered
\Input{ A capacitated undirected graph $G$, set of terminals $K \subset V$ }
\Output{ A capacitated undirected graph $H$.}
\BlankLine
Find $({k \choose 1}+{k \choose 2})$ minimum terminal using max-flow algorithm\;
Construct a new graph $H$ with $k$ nodes $v_1, v_2, \cdots v_k$ each one corresponding to one terminal and one extra node $z$\;
Add edge $(v_i,v_j)$ between two terminals $v_i$ and $v_j$ with cost $(R(i)+R(j)-R(ij))/2$\;
Add edge $(z,v_i)$ with cost $(R(i)- (\Sigma_{j \in (K- i)}(R(i)+R(j)-R(ij))/2)$\;
\emph{ Return} the constructed graph $H$ \;
\caption{{ \sc{Algorithm to construct Cut-Sparsifier that preserves all minimum terminal cuts $(U,K-U)$ where $min\{|U|, |K - U|\} \le 2$}}}\label{alg:Small-Cut-Sparsifier}
\end{algorithm}\DecMargin{1em}
Now we show the graph $H$ constructed by algorithm \ref{alg:Small-Cut-Sparsifier} preserves all minimum terminal cuts $(U,K-U)$ where $min\{|U|, |K - U|\} \le 2$ by following two claims.
\begin{claim}
\label{claim:nonneg}
All edge costs in $H$ are non-negative.
\end{claim}
\textit{Proof of claim:}
From submodularity, $R(i)+R(j) \ge R(ij))$.
Thus $c(v_i, v_j) \ge 0$.\\
On the other hand to show $c(z,v_i) \ge 0$, we need to show
\begin{equation}
(R(i)- (\Sigma_{j \in (K- i)}(R(i)+R(j)-R(ij))/2) \ge 0
\end{equation}
\begin{equation}
\label{eqn:5}
i.e., \Sigma_{j \in (K- i)}R(ij) \ge (k-3)R(i)+ \Sigma_{j \in (K- i)} R(j)]
\end{equation}
But from lemma \ref{lemma:CSW}, we get inequality \ref{eqn:5} to be true as here $d_{ij}=k-2, u_i=k-3, u_j=1$.
$\qed$\\
\begin{claim}
$c(U \cup \{z\}) \ge c(U)$ for all $U \subset K, |U| \le min\{2, |K \setminus U|\}$.
\end{claim}
\textit{Proof of claim:}
To prove the claim we need to show, $\Sigma_{i \in U} c(i,z) \le \Sigma_{j \notin U} c(j,z)$\\
i.e., $\Sigma_{i \in U}(R(i)-\Sigma_{l \in (K-i)}\frac{(R(i)+R(l)-R(il))}{2}) \le \Sigma_{j \notin U}(R(j)-\Sigma_{j \in (K-i)}\frac{(R(l)+R(j)-R(lj))}{2})$.
After arranging similar terms together we get,
\begin{equation}
\Sigma_{i \in U}R(i) - \Sigma_{j \notin U}R(j) + \Sigma_{j \notin U}\Sigma_{l \in (K-j)}\frac{(R(l)+R(j))}{2} -\Sigma_{i \in U}\Sigma_{l \in (K-i)}\frac{(R(l)+R(i))}{2} \nonumber \\
\end{equation}
\begin{equation}
\label{eqn:6}
\le \Sigma_{j \notin U}\Sigma_{l \in (K-j)}R(lj)/2+\Sigma_{i \in U}\Sigma_{l \in (K-i)}R(il)/2
\end{equation}
Now from inequality \ref{eqn:6} we get, \\
$$
u_{i} = \left\{
\begin{array}{ll}
2-u & i \in U \\
k-u-2 & i \notin U
\end{array}
\right.
$$
and
$$
\delta_{ij} = \left\{
\begin{array}{ll}
4-2u& \{i,j\} \subseteq U \\
2k -2u -4 & \{i,j\} \subseteq K-U \\
k-2u & |\{i,j\}\cap K|=1
\end{array}
\right.
$$
It is easy to verify for all pairs $(i,j)\in V\times V$, $u_i+u_j \le \delta_{ij}$.
Thus from lemma \ref{lemma:CSW} the above inequality is true.
$\qed$\\
So from above claims we get $h_K^G(U)=h_H(U)$ where $|U| \le min\{2, |K \setminus U|\}$.
\end{proof}
Thus the theorem generalizes results of \cite{ChaudhuriSWZ00}.
\begin{corollary}
For $|K|=3,4,5$, there exist exact cut sparsifiers of size 3, 5, 6 respectively.
\end{corollary}
\end{comment}
\end{document}
| {
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} | 1,078 |
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Home » Southeastern Freight Lines Promotes Kevin Owens to Service Center Manager in Garland, Texas
Southeastern Freight Lines Promotes Kevin Owens to Service Center Manager in Garland, Texas
Southeastern Freight Lines, the leading provider of regional less-than-truckload (LTL) transportation services, today announced Kevin Owens has been promoted to service center manager in Garland, Texas.
With over 13 years of experience at Southeastern, Owens started his career at the Dallas, Texas, service center in a regional process improvement role. Since then, he has served as operations manager and most recently, as service center manager at the Sherman, Texas, service center.
"Throughout his more than 13 years, Kevin continuously emulates the service, dedication and strength we strive to reflect here at Southeastern," said Jim Jones, regional vice president of operations for Southeastern Freight Lines. "We could not be more excited to see Kevin thrive as he continues to demonstrate exemplary leadership throughout this new role as service center manager in Garland."
Owens looks forward to serving the Southeastern team in this capacity.
About Southeastern Freight Lines
Southeastern Freight Lines, a privately-owned regional less-than-truckload transportation services provider founded in 1950, specializes in next-day service in the Southeast and Southwest and operates 89 service centers in 13 states, Canada and Puerto Rico. Southeastern has a network of service partners to ensure transportation services in the remaining 36 states, the U.S. Virgin Islands and Mexico. Southeastern Freight Lines provides more than 99.35% on-time service in next day lanes. A dedication to service quality and a continuous quality improvement process that began in 1985 has been recognized by more than 400 quality awards received from customers and associations. For more information, please visit www.sefl.com and www.facebook.com/SoutheasternFreight.
Hope Torruella
Largemouth Communications (on behalf of Southeastern Freight Lines)
hope@largemouthpr.com
More Info: https://www.sefl.com
Southeastern Freight Lines Promotes Shannon Mangrum to Service Center Manager in Lubbock, Texas
Southeastern Freight Lines Promotes Matt Hughes to Service Center Manager in Dallas, Texas
Southeastern Freight Lines Promotes Justin Proffitt to Service Center Manager in Fort Worth, Texas | {
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} | 487 |
\section{ Introduction}
The existence of fixed lightcone structures is one of the characteristics of classical gravitational theory.
Lightcones are basically hypersurfaces which distinguish timelike separation from spacelike separation and
divide spacetime into causally distinct regions. However, if gravity is to be quantized, it is natural to
expect that the quantum metric fluctuations would smear out the lightcone,
and the concept of a fixed lightcone structure has to be abandoned.
Based upon the observation that the ultraviolet divergences of quantum field theory arise from the
light cone singularities of two-point functions, and that quantum fluctuations of the spacetime metric ought
to smear out the light cone, thus possibly removing these singularities, Pauli\cite{Pauli} conjectured many years
ago that the ultraviolet
divergences of quantum field theory might be removed if gravity is quantized. This idea was further explored
by several other authors \cite{Deser,DW,ISS}. At present time, this conjecture remains unproven.
If lightcones fluctuate, so do horizons, which are, of course, lightcones.
The horizon fluctuations could then presumably lead to information leakage across the black hole in a way
that is not allowed by classical physics.
Bekenstein and Mukhanov \cite{MB} have suggested that horizon fluctuations could result in discreteness of
the spectrum of black holes. Since the existence of black hole horizons is the origin of the so-called black
hole information
paradox, which has been widely discussed in the literature but still remains to be resolved, the
study of lightcone fluctuations might help us better understand the problem.
Recently the problem of light cone fluctuations has been investigated
\cite{Ford95,Ford96}
in a model of quantum linearized theory of gravity, where the fluctuations are produced by gravitons propagating on
a background spacetime. The lightcone is smeared out if the linearized gravitational perturbations are quantized.
It has been demonstrated that
gravitons in a quantum state, such as a squeezed vacuum state, or a thermal state, can produce light cone fluctuations, thus smearing out the light cone. Because of the fluctuating light cone,
the propagation time of a classical light pulse over distance $r$ is no longer
precisely $r$, but undergoes fluctuations around a mean value of $r$. The
fluctuations in the photon arrival time can also be understood as fluctuations
in the velocity of light. This model
has been applied to study the quantum cosmological and black hole horizon fluctuations \cite{Ford97}. It is interesting to note that recently, the quantum gravitational metric fluctuations have also
been discussed within a different context, i.e., a Liouville string formulation of quantum
gravity \cite{AEMN,EMN} .
In this paper
we shall examine light cone fluctuations in flat spacetime with nontrivial topology based upon the model proposed in
Ref\cite{Ford95} . In Sec. II, we review the basic formalism and examine its
gauge invariance, then derive general expressions for the vacuum graviton
two-point functions in the transverse trace-free gauge. In Sec. III we study the light cone fluctuations in
flat spacetimes with a compactified spatial dimension, and with a single plane boundary. Our results are summarized and
discussed in Sec. VI.
\section{ Basic formalism and graviton two-point function in transverse trace-free gauge}
Let us consider a flat background spacetime with a linearized perturbation
$h_{\mu\nu}$ propagating upon it , so the spacetime metric
may be written as
\begin{equation}
ds^2 = g_{\mu\nu}dx^\mu dx^\nu = (\eta_{\mu\nu} +h_{\mu\nu})dx^\mu dx^\nu
= dt^2 -d{\bf x}^2 + h_{\mu\nu}dx^\mu dx^\nu \, . \label{eq:metric}
\end{equation}
Let $\sigma(x,x')$ be one half of the squared geodesic separation
for any pair of spacetime points $x$ and $x'$, and $\sigma_0(x,x')$
be the corresponding quantity in the flat background . We can expand,
in the presence of the perturbation, $\sigma(x,x')$ in powers of
$h_{\mu\nu}$ as
\begin{equation}
\sigma = \sigma_0 + \sigma_1 + \sigma_2 + \cdots \, , \label{eq:sigma}
\end{equation}
where $\sigma_1$ is first order in $h_{\mu\nu}$, etc. We now suppose
that the linearized perturbation $h_{\mu\nu}$ is quantized, and that the
quantum state $|\psi \rangle$ is a ``vacuum'' state in the sense that
we can decompose $h_{\mu\nu}$ into positive and negative frequency parts
$h^{+}_{\mu\nu}$ and $h^{-}_{\mu\nu}$, respectively, such that
\begin{equation}
h^{+}_{\mu\nu} |\psi \rangle =0, \qquad \langle \psi|h^{-}_{\mu\nu} =0 \,.
\end{equation}
It follows immediately that
\begin{equation}
\langle h_{\mu\nu} \rangle =0
\end{equation}
in state $|\psi \rangle$. In general, however,
$\langle (h_{\mu\nu})^2 \rangle_R \not= 0$, where the expectation value is
understood to be suitably renormalized. This reflects the quantum metric
fluctuations.
\subsection{Basic formalism and gauge invariance}
If we average the retarded Green's function, $G_{ret}(x,x') $, for a massless scalar field, over
quantized metric fluctuations, we get \cite{Ford95}
\begin{equation}
\Bigl\langle G_{ret}(x,x') \Bigr\rangle =
{{\theta(t-t')}\over {8\pi^2}} \sqrt{\pi \over {2\langle \sigma_1^2 \rangle}}
\; \exp\biggl(-{{\sigma_0^2}\over {2\langle \sigma_1^2 \rangle}}\biggr)\, .
\label{eq:retav}
\end{equation}
This form is valid for the case in which $\langle \sigma_1^2 \rangle > 0$.
It reveals that the delta-function behavior of the
classical Green's function, $G_{ret}$, has been smeared out into a Gaussian
function peaked around the classical lightcone. This smearing can be understood as due to the fact
that photons may be either slowed down or speeded up by the
light cone fluctuations. Photon propagation now becomes a statistical phenomenon, with some photons traveling slower than
the light on the classical spacetime, and others traveling faster. Note that the Gaussian function
in Eq.~(\ref{eq:retav}) is symmetrical about the classical light cone, $ \sigma_0=0$, and so the quantum
fluctuations are equally likely to produce a time advance as a time delay.
Light cone fluctuations are in principle observable. It has been shown, by considering light pulses
between a source and a detector separated by a distance $r$, that
the mean deviation from the classical propagation time is related to $\langle \sigma_1^2 \rangle$
by \cite{Ford95}
\begin{equation}
\Delta t= {\sqrt{\langle \sigma_1^2 \rangle}\over r}\,.
\label{eq:MDT}
\ee
Note, however, that $\Delta t$ is the ensemble averaged deviation, not necessarily the expected variation in
flight time of two photons emitted close together in time. The latter can be much smaller than $\Delta t$ due
to the fact that the gravitational field may not fluctuate significantly in the interval between the two photons.
This point is discussed in detail in Ref.~\cite{Ford96}.
In order to find $\Delta t$ in a particular situation,
we need to calculate the quantum expectation value $\langle \sigma_1^2 \rangle$ in a chosen
quantum state. For this purpose, we first have to compute $\sigma_1$ for a given classical perturbation
along a certain geodesic, then average $\sigma_1^2$ over the quantized metric perturbation. If
we consider a null geodesic specified by
\begin{equation}
dt^2=d{\bf x}^2-h_{\mu\nu}dx^{\mu}dx^{\nu},
\ee
then by following the same steps as those of Ref.\cite{Ford95}, we can show that in a general gauge
\begin{equation}
\sigma_1 = {1\over 2}\Delta r \int_{r_0}^{r_1}
h_{\mu\nu} n^{\mu} n^{\nu}\,dr\,,
\end{equation}
and
\begin{equation}
\langle \sigma_1^2 \rangle = {1\over 4}(\Delta r)^2
\int_{r_0}^{r_1} dr \int_{r_0}^{r_1} dr'
\:\, n^{\mu} n^{\nu} n^{\rho} n^{\sigma}
\:\, \langle h_{\mu\nu}(x) h_{\rho\sigma}(x') \rangle_R \,.
\end{equation}
Here $ dr=|d{\bf x}|$, $\Delta r=r_1-r_0$ and $ n^{\mu} =dx^{\nu}/dr$.
The graviton two-point function,
$\langle h_{\mu\nu}(x) h_{\rho\sigma}(x') \rangle_R$,
is understood to be renormalized, so that it is finite when $x=x'$ and vanishes
when the quantum state of the gravitons is the Minkowski vacuum state.
A few comments on the derivation of Eq.~(\ref{eq:retav}) are in order here.
It is obtained by averaging the Fourier representation of a $\delta$-function.
It may come as a surprize that although we started with an analytic expansion
of $\sigma$ in powers of $h_{\mu\nu}$, the result is not analytic as
$\langle \sigma_1^2 \rangle \rightarrow 0$. This arises because we use the
first order expansion of $\sigma$ in the argument of an exponential function,
but afterwards retain all powers of $h_{\mu\nu}$. One can reasonably ask
whether this is a valid procedure. A test of the self-consistency is to
retain the $\sigma_2$ term and then follow the same procedure. The result is
Eq.~(\ref{eq:retav}) with $\sigma_0^2$ replaced by $\sigma_0^2 + \sigma_2$.
This has the same physical interpretation as before; the only effect of the
$\sigma_2$ part is to shift the location of the mean lightcone. Thus in
this order we encounter the backreaction of the gravitons in perturbing the
original classical geometry to a new classical geometry. Although this is
less than a complete demonstration of the validity of Eq.~(\ref{eq:retav}),
it does indicate that it arises from a self-consistent calculation. In any
case, the only result that we really need in the remainder of this paper is
Eq.~(\ref{eq:MDT}), which may be derived either from Eq.~(\ref{eq:retav}),
or else more directly by averaging the square of Eq.~(\ref{eq:sigma}).
Let us now turn to the question of the gauge invariance of the formalism.
Under a gauge transformation specified by
\begin{equation}
x^{\prime \mu}=x^{\mu}+\xi^{\mu}(x),
\ee
\begin{equation}
h^{\prime }_{\mu\nu}(x')= h_{\mu\nu}(x)-\xi_{(\mu,\nu)}(x)\,,
\ee
where $\xi^{\mu}(x)$ is of order $h_{\mu\nu}$, the quantities $\sigma_1$ and
$\langle \sigma_1^2 \rangle$ are not in general invariant. However, we can show that this is due to the fact
that $\Delta t$ is a coordinate time interval rather than a proper time interval.
To better understand the gauge invariance, let us examine a situation in which a light
signal travels between two points in space labeled by $P$ and $Q$, with a classical metric perturbation
$h_{\mu\nu}$ in the intervening region, as illustrated in Fig. 1.
\begin{figure}[hbtp]
\begin{center}
\leavevmode\epsfxsize=1.6in\epsfbox{fig1.eps}
\end{center}
\caption{ A light ray ( dashed line ) makes a round trip travel between two points, P and Q, in space.}
\label{fig=fig1}
\end{figure}
For simplicity, let us assume
that the propagation is in the $x$-direction. We shall look at the travel time in two different gauges,
or coordinate systems, primed and unprimed.
For light rays traveling in $x$ direction, we have
\begin{eqnarray}
{dt\over dx }& =& \pm \sqrt{ 1-h_{\mu\nu}(x){dx^{\mu}\over dx}{dx^{\nu}\over dx}}\,\nonumber\\
&&\approx \pm 1 \mp{1\over2}h_{\mu\nu}(x){dx^{\mu}\over dx}{dx^{\nu}\over dx}\,.
\end{eqnarray}
Here the upper sign is used for outgoing light rays and the lower sign for incoming rays.
So, one way travel time $\delta t$ in the unprimed gauge is
\begin{eqnarray}
\delta t_{P\rightarrow Q}&=&\int^{x_Q}_{x_P}\,dx\,-{1\over 2}\int^{x_Q}_{x_P}\,h_{\mu\nu}(x){dx^{\mu}\over dx}
{dx^{\nu}\over dx}\,dx\nonumber\\
&& =\int^{x_Q}_{x_P}\,dx\,-{1\over 2}\int^{x_Q}_{x_P}\,h^{'}_{\mu\nu}(x'){dx^{\mu}\over dx}
{dx^{\nu}\over dx}\,dx -{1\over 2}\int^{x_Q}_{x_P}\,\xi_{(\mu,\nu)}(x){dx^{\mu}\over dx}
{dx^{\nu}\over dx}\,dx\,, \nonumber\\
\end{eqnarray}
which, within the linearized theory, can approximated as
\begin{eqnarray}
\delta t_{P\rightarrow Q}&=&
\int^{x_Q}_{x_P}\,dx\,-{1\over 2}\int^{x^{'}_Q}_{x^{'}_P}\,h^{'}_{\mu\nu}(x'){dx^{'\mu}\over dx'}
{dx^{'\nu}\over dx'}\,dx' -{1\over 2}\int^{x_Q}_{x_P}\,\xi_{(\mu,\nu)}(x){dx^{\mu}\over dx}
{dx^{\nu}\over dx}\,dx, \nonumber\\
&&=\int^{x_Q}_{x_P}\,dx\,-{1\over 2}\int^{x^{'}_Q}_{x^{'}_P}\,h^{'}_{\mu\nu}(x'){dx^{'\mu}\over dx'}
{dx^{'\nu}\over dx'}\,dx' -\int^{x_Q}_{x_P}\,{d\xi_x\over dx}\,dx-\int^{x_Q}_{x_P}\,{d\xi_t\over dx}\,dx
\nonumber\\
&&=x_Q(t')-\xi_x(Q,t')-(\,x_P(t_0)-\xi_x(P,t_0)\,)-\xi_t(Q,t')+\xi_t(P,t_0)\nonumber\\
&&\quad -{1\over 2}\int^{x^{'}_Q}_{x^{'}_P}\,h^{'}_{\mu\nu}(x'){dx^{'\mu}\over dx'}{dx^{'\nu}\over dx'}\,dx'\,,\nonumber\\
\end{eqnarray}
where we have used the fact $ dt/dx=1$ for outgoing light rays within our approximation.
Similarly, we have
\begin{eqnarray}
\delta t_{Q\rightarrow P}&=&-\int^{x_P}_{x_Q}\,dx\,+{1\over 2}\int^{x_P}_{x_Q}\,h_{\mu\nu}(x){dx^{\mu}\over dx}
{dx^{\nu}\over dx}\,dx\nonumber\\
&& =\int^{x_Q}_{x_P}\,dx\,-{1\over 2}\int^{x_Q}_{x_P}\,h^{'}_{\mu\nu}(x'){dx^{\mu}\over dx}
{dx^{\nu}\over dx}\,dx +{1\over 2}\int^{x_P}_{x_Q}\,\xi_{(\mu,\nu)}(x){dx^{\mu}\over dx}
{dx^{\nu}\over dx}\,dx, \nonumber\\
&&=\int^{x_Q}_{x_P}\,dx\,-{1\over 2}\int^{x^{'}_Q}_{x^{'}_P}\,h^{'}_{\mu\nu}(x'){dx^{'\mu}\over dx'}
{dx^{'\nu}\over dx'}\,dx' +\int^{x_P}_{x_Q}\,{d\xi_x\over dx}\,dx-\int^{x_P}_{x_Q}\,{d\xi_t\over dx}\,dx
\nonumber\\
&&=x_Q(t')-\xi_x(Q,t')-(\,x_P(t_0')-\xi_x(P,t_0')\,)+\xi_t(Q,t')-\xi_t(P,t_0')\nonumber\\
&&\quad -{1\over 2}\int^{x^{'}_Q}_{x^{'}_P}\,h^{'}_{\mu\nu}(x'){dx^{'\mu}\over dx'}{dx^{'\nu}\over dx'}\,dx'\,,\nonumber\\
\end{eqnarray}
using the fact that for incoming light rays, $dt/dx=-1$.
Note that
\begin{equation}
x'_Q(t)=x_Q(t)-\xi_x(Q,t)\,,
\ee
\begin{equation}
x'_P(t)=x_P(t)-\xi_x(P,t)\,,
\ee
so
\begin{equation}
\delta t_{P\rightarrow Q} =\delta t'_{P\rightarrow Q}-\xi_t(Q,t')+\xi_t(P,t_0)\,,
\ee
and
\begin{equation}
\delta t_{Q\rightarrow P}=\delta t'_{Q\rightarrow P}+\xi_t(Q,t')-\xi_t(P,t_0')\,.
\ee
It follows that the round trip travel time is
\begin{equation}
\Delta t=\delta t_{P\rightarrow Q}+\delta t_{Q\rightarrow P}=\Delta t' +\xi_t(P,t_0)-\xi_t(P,t_0')\,.
\label{eq:corrditime}
\ee
Therefore, the one way travel times, $\delta t_{P\rightarrow Q}$ and
$\delta t_{Q\rightarrow P} $ are, in general, not invariant unless both the source and the
detector are outside the regions where gravitational perturbations $h_{\mu\nu}$ are non-zero.
In that case, it is physically
reasonable to set $\xi(P,t)$ and $\xi(Q,t)$ to zero. Similarly, the round trip time $\Delta t$
is invariant only if the source ( it also acts as a detector in this case ) is outside of the
gravitational perturbations.
However, it is interesting to note that the round trip proper time interval for the source,
$\Delta \tau$, is gauge invariant. Denote the proper
time intervals in two different gauges by $\Delta \tau$ and $\Delta \tau'$, and keep in mind the fact that on the
world line of the source, generally, ${dx^i\over dt}<<1$. We then have
\begin{eqnarray}
\Delta \tau'&=&\int \sqrt{1+h'_{00}}\,dt'=\int dt'+{1\over 2}\int h'_{00} dt'\nonumber\\
&&=\Delta t'+{1\over 2}\int h_{00}dt-\int {d \xi_t\over dt}\, dt\nonumber\\
&&=\Delta t'+\xi_t(P,t_0)-\xi_t(P,t_0')
+{1\over 2}\int h_{00} dt \nonumber\\
&&=\Delta t+{1\over 2}\int h_{00} dt=\Delta \tau\,, \nonumber\\
\end{eqnarray}
where we have used Eq.~(\ref{eq:corrditime}).
This shows that we should really consider how proper time rather than the coordinate time is
affected by light cone fluctuations.
However, the calculation of the proper time in a
general gauge is a rather difficult task, because the source (and detector) may not be at rest with
respect to the chosen coordinate system, and thus in general the emission and the subsequent reception
may not
happen at the same point in space. To find the proper time, we have to integrate along the
geodesic between two events, the emission and the subsequent reception. In general, there is a
Doppler shift due to fluctuations in the positions of the source and the mirror. However, the analysis
can be greatly simplified if we adopt the transverse-tracefree ( TT ) gauge, which is
specified by the conditions
\begin{equation}
h^j_j = \partial_j h^{ij} = h^{0\nu} = 0\, . \label{eq:the TT}
\end{equation}
To see this, let us examine the geodesic equations for a test particle
\begin{equation}
{d^2x^{\mu}\over d^2\lambda}=\,-\Gamma^{\mu}_{\rho\sigma}\,{dx^{\rho}\over d\lambda}
{dx^{\rho}\over d\lambda}\,,
\ee
which, when written in term of derivatives with respect to coordinate time $t$, becomes
\begin{equation}
{d^2x^{\mu}\over d^2 t}\,+\Gamma^{\mu}_{\rho\sigma}\,{dx^{\rho}\over dt}{dx^{\sigma}\over dt}\,
-\Gamma^{t}_{\rho\sigma}\,{dx^{\mu}\over dt}\,{dx^{\rho}\over dt}{dx^{\sigma}\over dt}=0\,.
\ee
For a non-relativistic test particle, ${dx^i\over dt}<<1$, so, to the leading order,
\begin{equation}
{d^2x^i\over d^2 t}\,\approx \Gamma^{i}_{tt}\,.
\ee
But, in the TT gauge, $\Gamma^{i}_{tt}=0$. Therefore, from the above equation,
we can see that if the test particle is at rest at $t=0$, then it will subsequently always remain at rest
\cite{MTW}. So, if we are considering the
emission and reflection of a light signal between two points (particles) in the TT gauge,
then the proper time $\delta \tau$ between emission and reception (after
reflection) of the signal is related with the coordinate time by
\begin{equation}
\delta \tau=\int \sqrt{g_{tt}}dt=\int \sqrt{(1+h_{00})}dt=\int dt=\delta t\,.
\ee
Here we have appealed to the fact that $h_{00}=0$ in the TT gauge. Therefore, the coordinate time for the round trip in the TT
gauge is the proper time, and $\Delta t $ calculated from Eq.~(\ref{eq:MDT}) in the TT guage is actually a
gauge invariant quantity.
In this gauge, the mean squared fluctuation in the geodesic
interval function reduces to
\begin{eqnarray}
\langle \sigma_1^2 \rangle &&= {1\over 4}(\Delta r)^2
\int_{r_0}^{r_1} dr \int_{r_0}^{r_1} dr'
\:\, n^i n^j n^k n^m
\:\, \langle h_{ij}(x) h_{km}(x') \rangle_R \, \nonumber\\
&&= {1\over 8}(\Delta r)^2
\int_{r_0}^{r_1} dr \int_{r_0}^{r_1} dr'
\:\, n^i n^j n^k n^m
\:\, \langle h_{ij}(x) h_{km}(x')+ h_{ij}(x') h_{km}(x) \rangle_R \,.
\label{eq: interval}
\end{eqnarray}
Here $ n^i =dx^i/dr$ is the unit three-vector defining the spatial
direction of the geodesic.
\subsection{Graviton two-point function in transverse trace-free gauge}
If we work in the TT gauge, the gravitational perturbations have only spatial components $h_{ij}$
and they may be quantized using a plane wave expansion
as
\begin{equation}
h_{ij} = \sum_{{\bf k},\lambda}\, [a_{{\bf k}, \lambda} e_{ij} ({{\bf k}, \lambda})
f_{\bf k} + H.c. ].
\end{equation}
Here H.c. denotes the Hermitian conjugate, $\lambda$ labels the polarization
states, and
\begin{equation}
f_{\bf k} = (2\omega (2\pi)^3)^{-{1\over 2}} e^{i({\bf k \cdot x} -\omega t)}
\ee
is the mode function, where
\begin{equation}
\omega=|{\bf k}|, \qquad |{\bf k}|=(k_x^2+k_y^2+k_z^2)^{{1\over2}},
\ee
and the $e_{\mu\nu} ({{\bf k}, \lambda})$
are polarization tensors. ( Units in which $32\pi G =1$, where $G$ is
Newton's constant and in which $\hbar =c =1$ will be used in this paper.)
Now we shall first calculate the Minkowski spacetime Hadamard function for gravitons in the
transverse tracefree gauge. Let us define
\begin{equation}
G^{(1)}_{ijkl}(x,x')=\langle 0| h_{ij}(x) h_{kl}(x')+ h_{ij}(x') h_{kl}(x)|0 \rangle \,.
\end{equation}
Then we have
\begin{equation}
G^{(1)}_{ijkl}(x,x')=\frac{2 Re}{(2\pi)^3}\int\,d^3{\bf k}\sum_{\lambda}
\, e_{ij} ({{\bf k}, \lambda}) e_{kl} ({{\bf k}, \lambda})
{1\over{2 \omega}}e^{i{\bf k} \cdot({\bf x}-{\bf x'})}e^{-i\omega(t-t')}\,.
\end{equation}
Equation~(\ref{eq:polsum}) in the Appendix for the summation of polarization tensors in the
transverse tracefree gauge gives
\begin{eqnarray}
\sum_{\lambda}\, e_{ij} ({{\bf k}, \lambda}) e_{kl} ({{\bf k}, \lambda})&=&\delta_{ik}\delta_{jl}
+\delta_{il}\delta_{jk}-\delta_{ij}\delta_{kl}
+\hat k_i\hat k_j \hat k_k\hat k_l+\hat k_i \hat k_j \delta_{kl} \nonumber\\
&&+\hat k_k \hat k_l \delta_{ij}-\hat k_i \hat k_l \delta_{jk}
-\hat k_i \hat k_k \delta_{jl}-\hat k_j \hat k_l \delta_{ik}-\hat k_j \hat k_k \delta_{il}\,,
\end{eqnarray}
where
\begin{equation}
\hat k_i=\frac{ k_i}{ k}\,.
\end{equation}
We find that $ G^{(1)}_{ijkl}(x,x')$ can be expressed as \cite{Footnote}
\begin{eqnarray}
G^{(1)}_{ijkl}(x,x')&&=2 Re \,(\delta_{ik}\delta_{jl}+\delta_{il}\delta_{jk}-\delta_{ij}\delta_{kl} + D_{ij} )
\times {1\over{(2\pi)^3}}\int\, d^3{\bf k}{1\over{2 \omega}}
e^{i{\bf k} \cdot({\bf x}-{\bf x'})}e^{-i\omega(t-t')}\nonumber\\
&&=2 Re \,(\delta_{ik}\delta_{jl}+
\delta_{il}\delta_{jk}-\delta_{ij}\delta_{kl} +D_{ij})\times \langle 0|\phi(x)\phi(x') |0 \rangle\,,\
\end{eqnarray}
where we have defined a formal operator
\begin{equation}
D_{ij}=\left( {\partial_i\partial^{\prime}_j\over{\nabla^2}}\delta_{kl}+
{\partial_k\partial^{\prime}_l\over{\nabla^2}}\delta_{ij}
- {\partial_i\partial^{\prime}_k\over{\nabla^2}}\delta_{jl}
- {\partial_i\partial^{\prime}_l\over{\nabla^2}}\delta_{jk}
- {\partial_j\partial^{\prime}_l\over{\nabla^2}}\delta_{ik}
-{\partial_j\partial^{\prime}_k\over{\nabla^2}}\delta_{il}
+{\partial_i\partial_j^{\prime}\partial_k\partial_l^{\prime}\over\nabla^4}
\right),
\end{equation}
and $ \langle 0|\phi(x)\phi(x') |0 \rangle$ is the usual scalar field two-point function. Here the formal
operator $\nabla^{-2}$ should be understood in the sense of a Green's function, but when we do our
calculations in momentum space its effect is to bring in a factor of $k^{-2}$.
The combination of these results with Eq.~(\ref{eq: interval} ) gives
\begin{equation}
\langle \sigma_1^2 \rangle = { 1\over 4}(\Delta r)^2
\int_{r_0}^{r_1} dr \int_{r_0}^{r_1} dr'
\:\,\left( 1-{ 2 ({\bf \nabla }\cdot {\bf n})({\bf \nabla}^{\prime} \cdot {\bf n})\over{\nabla^2} }
+{ ({\bf \nabla }\cdot {\bf n})^2({\bf \nabla}^{\prime} \cdot {\bf n})^2\over{\nabla^4} }
\right) \langle \phi(x)\phi(x') \rangle_R\,.\nonumber\\
\end{equation}
Introduce two functions $F_{ij}(x,x')$ and $H_{ijkl}(x,x')$ by
\begin{eqnarray}
F_{ij}(x,x')&&= Re {\partial_i\partial^{\prime}_j\over{\nabla^2}}
\langle 0|\phi(x)\phi(x') |0 \rangle \nonumber\\
&&= Re {\partial_i\partial^{\prime}_j\over{\nabla^2}}
{1\over{(2\pi)^3}}\int\, d^3{\bf k}{1\over{2 \omega}}e^{i{\bf k} \cdot({\bf x}-{\bf x'})}e^{-i\omega(t-t')}\nonumber\\
&&={Re\over{(2\pi)^3}}\int\, d^3{\bf k}{k_ik_j\over{2 \omega^3}}e^{i{\bf k} \cdot({\bf x}-{\bf x'})}e^{-i\omega(t-t')} \,,
\end{eqnarray}
and
\begin{eqnarray}
H_{ijkl}(x,x')&&= Re {\partial_i\partial^{\prime}_j\partial_k\partial_{l}^{\prime}
\over{\nabla^4}} \langle 0|\phi(x)\phi(x') |0 \rangle \nonumber\\
&&= Re {\partial_i\partial^{\prime}_j\partial_k\partial_l^{\prime}\over{\nabla^4}}
{1\over{(2\pi)^3}}\int\, d^3{\bf k}{1\over{2 \omega}}e^{i{\bf k} \cdot({\bf x}-{\bf x'})}e^{-i\omega(t-t')}\nonumber\\
&&={Re\over{(2\pi)^3}}\int\, d^3{\bf k}{k_i k_j k_k k_l\over{2 \omega^5}}e^{i{\bf k} \cdot({\bf x}-{\bf x'})}e^{-i\omega(t-t')} \,.
\end{eqnarray}
$G^{(1)}_{ijkl}$ can be expressed as
\begin{eqnarray}
G^{(1)}_{ijkl}&=&
2F_{ij}\delta_{kl} +2F_{kl}\delta_{ij}-2F_{ik}\delta_{jl}-2F_{il}\delta_{jk}-2F_{jl}\delta_{ik}
-2F_{jk}\delta_{il}+2H_{ijkl}\nonumber\\
&&\quad +2D^{(1)}(x,x')(\delta_{ik}\delta_{jl}+\delta_{il}\delta_{jk}-\delta_{ij}\delta_{kl}),
\end{eqnarray}
where
\begin{equation}
D^{(1)}(x,x')= -{1\over{8\pi^2\sigma_0^2}}
\ee
is the usual Hadamard function for massless scalar fields with
$2\sigma_0^2=(t-t')^2-({\bf x-x' })^2$, and $F_{ij}(x,x')$ and $H_{ijkl}(x,x')$, which will be
calculated in the Appendix, are given by
\begin{equation}
F_{ij}(x,x')=-{1\over{(2\pi)^2}}\partial_i\partial_j'\,\left[{1\over 2}\ln ( R^2-\Delta t^2 )
+{\Delta t \over 4R}\ln \Bigg( \frac{R+\Delta t}{R-\Delta t}\Bigg)^2 \right]\,,
\label{eq:Ffunc}
\ee
and
\begin{eqnarray}
H_{ijkl}(x,x')&=&{1\over 96\pi^2}\partial_i\partial_j'\partial_k\partial_l'\,
\Bigg[ (R^2+3\Delta t^2)\ln (R^2-\Delta t^2)^2\nonumber\\
\quad && + \left(3R\Delta t+{\Delta t^3\over R}\right)\ln \Bigg( \frac{R+\Delta t}{R-\Delta t}\Bigg)^2\Bigg]\nonumber\,.\\
\label{eq:Hfunc}
\end{eqnarray}
Here $R=|{\bf x}-{\bf x}'|$.
\section{Lightcone fluctuations in flat spacetime with nontrivial topologies or boundaries}
In this section, we study lightcone fluctuations in two cases:
flat spacetime with a compactified spatial section, and with a single plane boundary.
\subsection{ Flat spacetime with a compactified spatial section}
Let us now assume that the spacetime is flat but compactified in the $z$ direction with a
periodicity length
$L$ ( ``circumference of the universe'' ). This means the spatial points $z$ and $z+L$ are identified.
The effect of the space closure is to restrict the field modes to a discrete set
\begin{equation}
f_{\bf k} = (2\omega (2\pi)^2L)^{-{1\over 2}} e^{i({\bf k \cdot x} -\omega t)}
\label{eq:mode1}
\ee
with
\begin{equation}
k_z={2\pi n\over L}, \qquad n=0,\pm 1, \pm 2, \pm 3,...
\ee
We now analyze the lightcone fluctuations, assuming that the gravitons are in the new vacuum state
$|0_L\rangle$ associated the discrete modes of Eq.~(\ref{eq:mode1} ).
First consider a light ray along $z$ direction, i.e. along the direction of compactification
(Fig.2 ),
propagating from point $(0,0,a)$ to point $(0,0,b)$ in space,
then, we have from Eq.~(\ref{eq: interval})
\begin{eqnarray}
\langle \sigma_1^2 \rangle &&= {1\over 8}(b-a)^2
\int_{a}^{b} dz \int_{a}^{b} dz'
\:\, \langle 0_L| h_{zz}(x) h_{zz}(x')+ h_{zz}(x') h_{zz}(x)|0_L \rangle_R \,\nonumber\\
&&= {1\over 8}(b-a)^2
\int_{a}^{b} dz \int_{a}^{b} dz'\, G_{zzzz}^{(1) R}(t,0,0,z,\,t',0,0,z').
\label{eq: interval1}
\end{eqnarray}
Here we have defined
\begin{eqnarray}
&&G^{(1)R}_{zzzz}(x,x')=\langle 0_L| h_{zz}(x) h_{zz}(x')+ h_{zz}(x') h_{zz}(x)|0_L \rangle_R\nonumber\\
&&\qquad=\langle 0_L| h_{zz}(x) h_{zz}(x')+ h_{zz}(x') h_{zz}(x)|0_L \rangle-
\langle 0| h_{zz}(x) h_{zz}(x')+ h_{zz}(x') h_{zz}(x)|0 \rangle\,,
\end{eqnarray}
and the integral is to be carried out along the geodesic.
\vskip.25in
\begin{figure}[hbtp]
\begin{center}
\leavevmode\epsfxsize=1.8in\epsfbox{fig2.eps}
\end{center}
\caption{ A light ray ( dashed line ) propagates in the direction of compactification in a cylindrical ``universe''
from point $(t,0,0,a)$ to point $ (t',0,0,b)$. Here only two spatial dimensions are plotted. }
\label{fig=fig2}
\end{figure}
If we adopt the notation
\begin{equation}
(t,0,0,z,\,t',0,0,z')\equiv(t,z,\,t',z')\,,
\ee
the renormalized two-point function can be found by using the method of images
to be
\begin{eqnarray}
G_{zzzz}^{(1) R}(t,z,\,t',z')&&={\sum_{n=-\infty}^{+\infty}}^{\prime}G_{zzzz}^{(1) }(t,z,\,t',z'+nL)\nonumber\\
&&=2\,{\sum_{n=-\infty}^{+\infty}}^{\prime}\,\Biggl(D^{(1)}(t,z,\, t', z'+nL)-2F_{zz}(t,z,\,t',z'+nL)
\nonumber\\
&&\quad +H_{zzzz}(t,z,\,t',z'+nL)\Biggr)\,,\nonumber\\
\end{eqnarray}
where the prime on the summation indicates that the $n=0$ term is omitted. Substituting $R_t=0$
into Eq.~(\ref{eq:tpFunc}) in the Appendix and replacing $\Delta x$ by $\Delta z$, we have
\begin{eqnarray}
G_{zzzz}^{(1) R}(t,z,\,t',z')&&=-{2\over \pi^2}{\sum_{n=-\infty}^{+\infty}}^{\prime} \Bigg[ \frac{\Delta t^2}{(\Delta z-nL)^4}
+\frac{\Delta t^3}{4(\Delta z-nL)^5}\ln\left( \frac{\Delta z-nL-\Delta t}{\Delta z-nL+\Delta t} \right)^2
\nonumber\\
&& - {2\over 3(\Delta z-nL)^2}-\frac{\Delta t}{4(\Delta z-nL)^3}\ln\left( \frac{\Delta z-nL-\Delta t}{\Delta z-nL+\Delta t} \right)^2
\Bigg].
\label{eq:TPF1}
\end{eqnarray}
For the null geodesic
\begin{equation}
\Delta t=\Delta z,
\ee
we get, after an evaluation of the integral,
\begin{eqnarray}
&&\int_{a}^{b} dz \int_{a}^{b} dz'\, G_{zzzz}^{(1) R}(t,z,\,t',z')|_{\Delta t=\Delta z }\nonumber\\
&&\quad ={1\over12\pi^2 }{\sum_{n=-\infty}^{+\infty}}^{\prime}
\Bigg[{8\epsilon^2 (n^2-2\epsilon^2)\over {(n^2-\epsilon^2)^2}}
+\frac{(n+2\epsilon)^3}{2(n+\epsilon)^3}\ln\left(1+{2\epsilon\over n}\right)^2
+ \frac{(n-2\epsilon)^3}{2(n-\epsilon)^2}\ln\left(1-{2\epsilon\over n}\right)^2 \Bigg]\nonumber\\
&&\quad ={1\over12\pi^2 }{\sum_{n=1}^{+\infty}}
\Bigg[{16\epsilon^2 (n^2-2\epsilon^2)\over {(n^2-\epsilon^2)^2}}
+\frac{(n+2\epsilon)^3}{(n+\epsilon)^3}\ln\left(1+{2\epsilon\over n}\right)^2
+ \frac{(n-2\epsilon)^3}{(n-\epsilon)^3}\ln\left(1-{2\epsilon\over n}\right)^2 \Bigg]\nonumber\\
&&\quad\equiv{1\over12\pi^2 }{\sum_{n=1}^{+\infty}}f(n,\epsilon)\nonumber\,,\\
\label{eq:series1}
\end{eqnarray}
where we have defined
\begin{equation}
\epsilon\equiv{(b-a)\over L}={r\over L}\,,
\ee
and
\begin{equation}
f(n,\epsilon) \equiv {16\epsilon^2 (n^2-2\epsilon^2)\over {(n^2-\epsilon^2)^2}}+
\frac{(n+2\epsilon)^3}{(n+\epsilon)^3}\ln\left(1+{2\epsilon\over n}\right)^2
+ \frac{(n-2\epsilon)^3}{(n-\epsilon)^3}\ln\left(1-{2\epsilon\over n}\right)^2\,.
\ee
It appears that there is a singularity in the summand $f(n,\epsilon)$ whenever $n=\epsilon$, i.e.,
whenever the distance $r$ is an integer multiple of $L$.
However this singularity is illusionary, as it should be from a physical point of view since there is nothing special
when $n=\epsilon$. This can be seen if we expand the summand at the point $\epsilon=n$ to get
\begin{equation}
f(n,\epsilon)\approx {19\over 3}+{27\over 4}\ln(3)+\frac{27\ln(3)+68}{8n}(\epsilon-n)+O((\epsilon-n)^2)\,.
\ee
So, $f(n,\epsilon)$ is finite as $\epsilon$ approaches $n$.
Note also that $2\epsilon=n$ is also not a singularity.
The summation converges, as the asymptotic form of $f(n.\epsilon)$ as $n\rightarrow \infty$ is
\begin{equation}
f(n,\epsilon)\sim {32\epsilon^2\over n^2} + O(n^{-4})\,.
\ee
However, a generic closed form result for the summation is
hard to find. So we now discuss two special cases. The first
is the one in which
the distance traversed by the light ray is much less than the periodicity length, $ b-a \ll L$.
Then we get
\begin{equation}
\int_{a}^{b} dz \int_{a}^{b} dz'\, G_{zzzz}^{(1) R}(x,x')
\approx\sum_{n=1}^{+\infty}{8\epsilon^2\over3 \pi^2}{1\over n^2}
={4\epsilon^2\over9}\,.
\ee
Substitution of this result into Eq.~(\ref{eq: interval1}) yields
\begin{equation}
\langle \sigma_1^2 \rangle \approx {r^4\over 18L^2 }.
\ee
Therefore the mean deviation from the classical propagation time is
\begin{equation}
\Delta t={\sqrt{\langle \sigma_1^2 \rangle }\over r} \approx {1\over 3\sqrt{2} }
\,{r\over L}\,.
\label{eq:t2}
\ee
Since we are working in Natural Units, this result reveals that the mean deviation in travel time
is less than the
Planck time and grows linearly with increasing $r$ when
$r$ is small compared to the periodicity length $L$ of the universe.
If $\epsilon\gg 1$, i.e., $r\gg L$, the light loops around the `` universe '', and summation
Eq~(\ref{eq:series1}) can be approximated by the following integral
\begin{eqnarray}
\int_{a}^{b} dz \int_{a}^{b} dz'\, G_{zzzz}^{(1) R}(t,z,\,t',z')&&\approx
{\epsilon\over 12\pi^2}\int_{1/\epsilon}^{\infty}\,dx
\Bigg[\frac{(x+2)^3}{(x+1)^3}\ln\left(1+{2\over x}\right)^2
+ \frac{(x-2)^3}{(x-1)^3}\ln\left(1-{2\over x}\right)^2 \nonumber\\
&& \qquad \qquad \qquad \quad +{16(x^2-2)\over {(x^2-1)^2}}\Bigg]\,.
\end{eqnarray}
Evaluating the integral with the aid of the computer algebra package Maple,
series expanding the result and keeping the leading terms only, we arrive at
\begin{equation}
\int_{a}^{b} dz \int_{a}^{b} dz'\, G_{zzzz}^{(1) R}(t,z,\,t',z')
\approx \epsilon-{8\ln(2\epsilon)\over 3\pi^2 }\,.
\ee
Therefore the mean deviation from the classical propagation time is
\begin{equation}
\Delta t={\sqrt{\langle \sigma_1^2 \rangle }\over r} \approx {1\over 2\sqrt{2}} \,\sqrt{{r\over L}},
\ee
where $r$ is assumed to be much greater than $L$. So the lightcone fluctuations can, in principle,
get as large as one would like if the light ray travels around and around. This is interesting in the sense that
it suggests that a fluctuation which is much greater than the Planck scale could be achieved.
Now we turn to the case where the light ray moves along the direction perpendicular to that of compactification,
for instance, along $x$ direction.
If the light ray travels from point $(a,0,0)$ to point $(b,0,0)$, as illustrated in Fig. 3, then
\begin{eqnarray}
\langle \sigma_1^2 \rangle &&= {1\over 8}(b-a)^2
\int_{a}^{b} dx \int_{a}^{b} dx'
\:\, \langle 0_L| h_{xx}(x) h_{xx}(x')+ h_{xx}(x') h_{xx}(x)|0_L \rangle_R \,\nonumber\\
&&={1\over 8}(b-a)^2
\int_{a}^{b} dx \int_{a}^{b} dx'\, G_{xxxx}^{(1)R }(t,x,0,0,\,t',x',0,0), \,\nonumber\\
&&= {1\over 8}(b-a)^2
\int_{a}^{b} dx \int_{a}^{b} dx'\,{\sum_{n=-\infty}^{+\infty}}^{\prime} G_{xxxx}^{(1) }(t,x,0,0,\,t',x',0,nL)\,.
\end{eqnarray}
\vskip.15in
\begin{figure}
\begin{center}
\leavevmode\epsfxsize=1.8in\epsfbox{fig3.eps}
\end{center}
\caption{ A light ray ( dashed line ) propagates perpendicular to the direction of compactification
in a cylindrical ``universe''
from point $(t,a,0,0)$ to point $ (t',b,0,0)$. Here only two spatial dimensions are plotted. }
\label{fig=fig3}
\end{figure}
Let us now define
\begin{equation}
\rho=x-x',\quad\quad b-a=r,
\ee
then if we use Eq.~(\ref{eq:tpFunc}) in the Appendix and bear in mind the fact that for the light ray $\Delta t=\Delta x$,
we have
\begin{equation}
G_{xxxx}^{(1)R }(t,x,0,0,\,t',x',0,nL)\equiv g_1(\rho)+g_2(\rho)\,,
\label{eq:G1}
\ee
where
\begin{equation}
g_1 = 2 {\sum_{n=-\infty}^{+\infty}}^{\prime}- {\displaystyle \frac {1}{8\pi^2}} \,{\displaystyle
\frac {\rho^{2}\,(nL)^{4}}{(\rho^{2} + (nL)^{2})^{4}}} - {1\over3\pi^2 } {\displaystyle \frac {\rho^{6}}{(\rho^{2} + (nL)^{2
})^{4}}} + {\displaystyle \frac {47}{12\pi^2}} \,{\displaystyle
\frac {\rho^{4}\,(nL)^{2}}{(\rho^{2} + (nL)^{2})^{4}}} \,,
\ee
and
\begin{eqnarray}
g_2=-2{\sum_{n=-\infty}^{+\infty}}^{\prime} \frac {1}{2\pi^2} \,\ln\left( \frac {\sqrt{\rho^{2} + (nL)^2} + \rho}{\sqrt{\rho^{2} + (nL)^{2}} - \rho}\right )^2
&&\Biggl[ - \frac {1}{16} \, \frac { \rho\,(nL)^6 }{ (\rho^{2} + (nL)^{2})^{(9/2)} } - \frac {3}{4} \,
\frac { \rho^3\,(nL)^4 }{ (\rho^{2} + (nL)^{2})^{(9/2)} } \nonumber\\
&& \quad + \frac {3}{2} \,\frac { \rho^{5}\,(nL)^2 } { (\rho^2 + (nL)^2 )^{(9/2)} }\Biggr]\,.
\nonumber\\
\label{eq:G3}
\end{eqnarray}
We can clearly see that $G_{xxxx}^{(1)R}$ is an even function of $\rho$, so,
\begin{equation}
\int_{a}^{b} dx \int_{a}^{b} dx'\, G_{xxxx}^{(1)R }(t,x,0,0,\,t',x',0,0)=
2\int_0^r d\rho (r-\rho)(g_1+g_2) \,.
\ee
Performing the integration (integrate by parts for those terms involving logarithmic function), we arrive at
\begin{eqnarray}
&&2\int_0^r d\rho (r-\rho)(g_1+g_2)\nonumber\\
&&\quad ={2\over\pi^2 }{\sum_{n=-\infty}^{+\infty}}^{\prime}\Bigg[
-\frac{\epsilon^4}{2(\epsilon^2+n^2)^2}-\frac{\epsilon^2n^2}{4(\epsilon^2+n^2)^2}
\nonumber\\
&&\quad\quad \quad\quad+\frac{8\epsilon^5+
8n^2\epsilon^3+3n^4\epsilon}{24(n^2+\epsilon^2)^{5/2}}
\ln\left({\sqrt{n^2+\epsilon^2}+ \epsilon}\over{\sqrt{n^2+\epsilon^2}- \epsilon} \right)\Bigg]\,,\nonumber\\
\label{eq: series2}
\end{eqnarray}
where $\epsilon=r/L$ as before.
The above series can be shown to be convergent.
Yet a result in closed form is not easy to find. Let us first
examine the case in which $ r\ll L$, where
\begin{equation}
\int_{a}^{b} dx \int_{a}^{b} dx'\, G_{xxxx}^{(1) R}(x,x')\approx
\sum_{n=1}^{+\infty}{64\epsilon^6\over 45\pi^2}{1\over n^6}
={64\pi^4\epsilon^6\over 45^2\times21}\,.
\ee
Here we have used
\begin{equation}
\sum_{n=1}^{+\infty}{1\over n^6}={\pi^6\over 45\times 21}\\.
\ee
Thus the mean deviation from the classical propagation time is
\begin{equation}
\Delta t={\sqrt{\langle \sigma_1^2 \rangle }\over r}\approx \sqrt{{{2\over21 }}} {2\pi^2\over 45}\,
\left({r\over L}\right)^3\,.
\ee
This result holds in the small $\epsilon$ regime.
The time deviation is much smaller than that for light rays propagating along the compactification direction ( compare with Eq.~(\ref{eq:t2}) ).
This reveals that light cone fluctuations due to topology change are more likely to be felt in the direction
of
compactification than in the transverse direction, if we perform local
experiments in which $r$, the distance between the source and the
detector, is very small as compared to $L$, the periodicity length.
We now turn our attention to the case in which $r\gg L$, i.e., $\epsilon\gg 1$.
Here it is easy to see that the summation in Eq.~(\ref{eq: series2}) can be approximated by the
following integral
\begin{eqnarray}
&&\int_{a}^{b} dx \int_{a}^{b} dx'\, G_{xxxx}^{(1) R}(t,x,0,0,\,t',x',0,0)\nonumber\\
&& \quad \quad \approx {4\epsilon\over\pi^2 }\int_{1/\epsilon}^\infty d x
\Bigg[-\frac{1}{2(1+x^2)^2}-\frac{ x^2}{4(1+x^2)^2}\nonumber\\
&&\quad \quad\quad\quad\quad\quad\quad\quad
+\frac{8+
8x^2+3x^4}{24(x^2+1)^{5/2}}
\ln\left({\sqrt{x^2+1}+ 1}\over{\sqrt{x^2+1}- 1} \right)\Bigg]\,.\nonumber\\ \,
\end{eqnarray}
If we perform the integral and series expand the result, we have, to the order of $O(\epsilon)$,
\begin{eqnarray}
&&\int_{a}^{b}dx \int_{a}^b dx'\, G_{xxxx}^{(1) R}(t,x,0,0,\,t',x',0,0)
\nonumber\\
&& \quad \quad \approx c_1^2\epsilon -c_2^2\ln(\epsilon)\,,\nonumber\\
\end{eqnarray}
where $c_1$ and $c_2$ are constants given, respectively, by
\begin{equation}
c_1^2=\int_0^\infty\,dx \frac{\ln(x+\sqrt{x^2+1})}{x\sqrt{x^2+1}}\approx 2.468\,.
\ee
and
\begin{equation}
c_2^2={8\over 3\pi^2}\,.
\ee
Therefore we have for the mean squared geodesic interval fluctuation
\begin{equation}
\langle \sigma_1^2 \rangle \approx {1\over 8}\left({c_1r\over \pi }\right)^2\epsilon\,,
\ee
and the mean deviation from the classical propagation time is
\begin{equation}
\Delta t={\sqrt{\langle \sigma_1^2 \rangle }\over r}\approx {c_1\over \pi}\,{1\over 2\sqrt{2}}
\sqrt{{r\over L }}.
\ee
This result applies in the regime where $r\gg L$. Here we have the same functional dependence on $r$ as in
the case where light rays loop around the compactified dimension many times. The only difference lies in the proportionality constants. In fact, here the mean time deviation is also
smaller than that for light rays traveling in the direction of compactification,
since the numerical constant $ c_1/\pi\approx 0.5$.
\subsection{Single plane boundary}
Let us assume that there is a single plane boundary located at $z=0$ in space such that metric perturbations satisfy
the following Neumann boundary condition (The reason that we use the Neumann boundary condition instead of the
Dirichlet boundary condition here is to get a positive $\langle \sigma_1^2 \rangle$. )
\begin{equation}
\partial_z h_{jk}|_{z=0}=0\,.
\ee
In the presence of the boundary, the field mode no longer has the form of
Eq.~(\ref{eq:mode1} )
but becomes
\begin{equation}
f_{\bf k} = (\omega (2\pi)^2\pi)^{-{1\over 2}} e^{i({\bf k_t \cdot x_t} -\omega t)}\cos(k_zz),
\label{eq: mode2}
\ee
where ${\bf k_t}$ and ${\bf x_t}$ denote the components of ${\bf k} $ and ${\bf x}$, respectively, in
directions parallel to the boundary.
Now if we assume that the gravitons are in the vacuum state $|0'\rangle $ associated with
the modes of Eq.~(\ref{eq: mode2}),
we have, for a light ray propagating perpendicular
to the boundary from point $(0,0,a)$ to $(0,0,b)$,
\begin{eqnarray}
\langle \sigma_1^2 \rangle &&= {1\over 8}(b-a)^2
\int_{a}^{b} dz \int_{a}^{b} dz'
\:\, \langle 0'| h_{zz}(x) h_{zz}(x')+ h_{zz}(x') h_{zz}(x)|0' \rangle_R \,\nonumber\\
&&=\int_{a}^{b} dz \int_{a}^{b} dz'
\:\, G_{zzzz}^{(1)R}(t,0,0,z,\,t',0,0,z') \,.
\label{eq: interval2}
\end{eqnarray}
\vskip.25in
\begin{figure}
\begin{center}
\leavevmode\epsfxsize=1.8in\epsfbox{fig4.eps}
\end{center}
\caption{ A light ray ( dashed line )propagates in the direction perpendicular to the plane boundary,
starting $a$ distance away from the boundary}
\label{fig=fig4}
\end{figure}
Here the renormalized graviton two point function
$ G_{zzzz}^{(1)R}(x,x') $
can be found by the method of images as usual and the only difference is an overall sign change as we go from
the Dirichlet boundary condition to the Neumann boundary condition. The reason for this is that, to satisfy
the Neumann boundary condition, we need to add the image term instead of subtracting it as in the case of the
Dirichlet boundary condition. So, $ G_{zzzz}^{(1)R}(x,x') $ may be obtained by picking out the
$n=0$ term in Eq.~(\ref{eq:TPF1}) and setting $\Delta z=z+z'$ to get
\begin{eqnarray}
G_{zzzz}^{(1)R}(t,0,0,z,\,t',0,0,z')&=&-\frac{2(t-t')^2}{\pi^2(z+z')^4}
-\frac{(t-t')^3}{2\pi^2(z+z')^5}\ln\left( \frac{z+z'-(t-t')}{z+z+(t+t')} \right)^2
\nonumber\\
&& + {4\over3\pi^2 (z+z')^2}+\frac{(t-t')}{2\pi^2(z+z')^3}\ln\left( \frac{z+z'-(t-t')}{z+z'+(t+t')} \right)^2\,.
\end{eqnarray}
Substituting this result into Eq.~(\ref{eq: interval2}) and performing the integration, we finally get
\begin{equation}
\langle \sigma_1^2 \rangle =\frac{(b-a)^3\left[ b^2-a^2+(a^2+4ab+b^2)\ln({b\over a})
\right]}
{24\pi^2(b+a)^3}\,.
\ee
Note that this result is always greater than zero. However, had we chosen the Dirichlet boundary condition, we would have
that $\langle \sigma_1^2 \rangle < 0$. Recall that the
formalism which we are using applies only if $\langle \sigma_1^2\rangle > 0$.
When the light ray starts very close to the boundary such that $a\ll r$,
we have
\begin{equation}
\langle \sigma_1^2 \rangle\approx {r^4\over 24\pi^2}\left(1+\ln(r/a)\right)\,.
\ee
The mean deviation in travel time is
\begin{equation}
\Delta t={\sqrt{\langle \sigma_1^2 \rangle }\over r}=\sqrt{{ 1+\ln(r/a)\over 24\pi^2}}\,,
\label{eq:t1}
\ee
which diverges as $a$ approaches 0. This is not surprising since the energy density of a
quantized field blows up on the boundary. However, it has been shown recently \cite{Ford98} that,
if one treats the boundaries as quantum objects with a nonzero position uncertainty, the
singularity in energy density is removed. The result, Eq.~(\ref{eq:t1}),
applies whenever $r\gg a$.
The other
limit is when $ r\ll a$, where the mean squared fluctuation in the geodesic interval function
is approximated as
\begin{equation}
\langle \sigma_1^2 \rangle\approx {r^4\over 24\pi^2 a^2}\,,
\ee
consequently, the mean deviation in time is given by
\begin{equation}
\Delta t={\sqrt{\langle \sigma_1^2 \rangle }\over r}={1\over 2\sqrt{6}\pi}{r\over a}\,.
\ee
We now consider a null geodesic which is $z$ distance away from and parallel to the plane boundary.
The relevant renormalized Hadamard function is
given by Eq.~(\ref{eq:tpFunc}) with $\Delta z$ being replaced by $z+z'$.
\vskip.25in
\begin{figure}
\begin{center}
\leavevmode\epsfxsize=1.8in\epsfbox{fig5.eps}
\end{center}
\caption{ A light ray ( dashed line )propagates in the direction parallel to the plane boundary,
starting $z$ distance away from it }
\label{fig=fig5}
\end{figure}
Now suppose
the geodesic starts at point $(t,a,0,z)$ and ends at point $(t',b,0,z)$, then the mean squared
fluctuation in the geodesic interval function is
\begin{equation}
\langle \sigma_1^2 \rangle = {1\over 8}(b-a)^2
\int_{a}^{b} dz \int_{a}^{b} dz'
\:\, G_{xxxx}^R(t,x,0,z,\,t',x',0,z). \,
\ee
Here
$ G_{xxxx}^R(t,x,0,z,\,t',x',0,z) $ is also given by Eqs.~(\ref{eq:G1}-\ref{eq:G3}) but with a replacement of $nL$ by $2z$.
Therefore
\begin{eqnarray}
&&\int_{a}^{b} dx \int_{a}^{b} dx'\, G_{xxxx}^{(1)R }(t,x,0,z,\,t',x',0,z)
\nonumber\\
&&\quad ={2\over\pi^2 }\Bigg[
-\frac{\epsilon^4}{2(\epsilon^2+4)^2}-\frac{\epsilon^2}{(\epsilon^2+4)^2}
\nonumber\\
&&\quad\quad \quad\quad+\frac{8\epsilon^5+
32\epsilon^3+48\epsilon}{24(4+\epsilon^2)^{5/2}}
\ln\left({\sqrt{4+\epsilon^2}+ \epsilon}\over{\sqrt{4+\epsilon^2}- \epsilon} \right)\Bigg]\,,\nonumber\\
\end{eqnarray}
where $\epsilon =r/z $.
Since the above expression is very complicated, we shall discuss two interesting special cases.
One is when $r\gg z$, then we have
\begin{equation}
\langle \sigma^2 \rangle\approx {r^2\over 6\pi^2}\ln(r/z)
\ee
and
\begin{equation}
\Delta t={\sqrt{\langle \sigma_1^2 \rangle }\over r}=\sqrt{{\ln(r/ z)\over 6\pi^2} }\,.
\ee
This also blows up as $z$ approaches 0, however the functional dependence upon $z$ is different from that of
Eq.~(\ref{eq:t1}).
The other limit is when $r\ll z$. For this case, we find
\begin{equation}
\langle \sigma^2 \rangle\approx {r^8\over 720z^6\pi^2}
\ee
and
\begin{equation}
\Delta t={\sqrt{\langle \sigma_1^2 \rangle }\over r}={1\over 12\sqrt{5}\pi}\, \left({r\over z}\right)^3 \,.
\ee
\section{Summary and Discussion}
In this paper, we have obtained general expressions, in the transverse tracefree
gauge, for the vacuum graviton
two-point function for various boundary conditions.
These were used to study the lightcone fluctuations in flat spacetimes
with a compactified spatial section and with a plane boundary. The mean squared
fluctuations of the geodesic interval function and therefore the mean
deviations from the classical propagation time have been obtained.
In the case
of a compactified spatial section, when the travel distance is less than the periodicity
length, the fluctuation in the propagation time is less than the Planck time. In this limit,
the effect is much larger for propagation in the periodicity direction than for propagation
in the transverse direction. Thus the local lightcone fluctuations become anisotropic,
reflecting the global structure of the spacetime. When the travel distance is
large compared to the periodicity length, the fluctuation in travel time increases with
the square root of the distance
traveled for propagation in either direction, and the only difference lies in the
proportionality constants. Here we have
a possibility of having fluctuations larger than Planck scale by several orders of magnitude.
In the case of a plane boundary, as light rays start closer and closer to the boundary,
the lightcone fluctuations blow up as the square root of the
logarithm of the starting distance both when light rays propagate perpendicularly and parallelly to the boundary. This
is not as surprising as it might seem because the imposition of a fixed boundary
can lead to singular expectation values of local observables, such as energy
densities. However we expect this singularity to disappear if one treats the
boundary as a quantum mechanical object with a nonzero position uncertainty
\cite{Ford98}. It is also found that if the starting distance from the
boundary is fixed, then the fluctuation in travel time grows as the square root of the
logarithm of the distance traversed when this distance is large compared to the starting
distance.
In summary, we have demonstrated that in the linearized theory of quantum gravity,
changes in the topology of flat spacetime produce lightcone fluctuations. These fluctuations
are in general larger in
the directions in which topology changes occur and are typically of the order of Planck scale,
but they can get larger for path lengths large compared to the compactification scale. It is
interesting to note that this effect could become significant in theories which postulate
extra dimensions compactified on a very small scale.
\begin{acknowledgments}
We would like to thank Tom Roman for interesting discussions and X. Y. Zhong
for help with graphics. This work was supported in part by the
National Science Foundation under Grant PHY-9800965.
\end{acknowledgments}
\newpage
\section*{Appendix}
\setcounter{equation}{0}
\renewcommand{\theequation}{A\arabic{equation}}
\subsection{ Summation of graviton polarization tensors in the TT gauge}
Let us introduce a triad of orthonormal vectors $({\bf e }_1({\bf k}) ,
{\bf e }_2({\bf k}) , {\bf e}_3({\bf k}) )$
with
\begin{equation}
{\bf e}_3({\bf k}) ={{\bf k}\over|{\bf k}|}=\hat{\bf k},
\ee
the unit vector in the direction of propagation. The triad
satisfies the orthonormality relation
\begin{equation}
{\bf e}_a({\bf k})\cdot{\bf e}_b({\bf k}) =\delta_{ab}, \quad \quad a,b =1,2,3.
\ee
This relation can be written, in terms of the components in the coordinate system
characterizing the metric, as
\begin{equation}
e_a^i({\bf k}) e_b^i({\bf k}) =\delta_{ab}, \qquad a,b=1,2,3.
\ee
Here the Einstein summation convention is employed. We also have
\begin{equation}
e_a^i({\bf k}) e_a^j({\bf k}) =e^i_1e^j_1+e^i_2e^j_2+\hat k^i\hat k^j
=\delta_{ij}, \qquad i,j= x,y.z.
\ee
Therefore, the two independent graviton polarization tensors in the TT gauge
are given, in
terms of the triad, by
\begin{eqnarray}
&&e^{ij}({\bf k},+)=e^i_1({\bf k}) \otimes e^j_1({\bf k})
-e^i_2({\bf k})\otimes e^j_2({\bf k})\,,\\
&&e^{ij}({\bf k},\times)=e^i_1({\bf k})\otimes e^j_2({\bf k})
+e^i_2({\bf k})\otimes e^j_1({\bf k})\,,\\
\end{eqnarray}
where we have adopted the notation of Ref \cite{MTW}.
Hence,
\begin{eqnarray}
\sum_{\lambda}\, e_{ij} ({{\bf k}, \lambda}) e_{kl} ({{\bf k}, \lambda})&&=
e_{ij} ({{\bf k}, +}) e_{kl} ({{\bf k}, +})+
e_{ij} ({{\bf k}, \times}) e_{kl} ({{\bf k}, \times}) \qquad \qquad\nonumber\\
&&=e^i_1e^j_1e^k_1e^l_1-e^i_1e^j_1e^k_2e^l_2-e^i_2e^j_2e^k_1e^l_1+
e^i_2e^j_2e^k_2e^l_2\nonumber\\
&&\quad e^i_1e^j_2e^k_1e^l_2+e^i_1e^j_2e^k_2e^l_1+e^i_2e^j_1e^k_1e^l_2+
e^i_2e^j_1e^k_2e^l_1\nonumber\\
&&=(e^i_1e^k_1+e^i_2e^k_2)(e^j_1e^l_1+e^j_2e^l_2)
+(e^i_1e^l_1+e^i_2e^l_2)(e^j_1e^k_1+e^j_2e^k_2)\nonumber\\
&&\quad -(e^i_1e^j_1+e^i_2e^j_2)(e^k_1e^l_1+e^k_2e^k_2)\nonumber\\
&&=(\delta^{ik}-\hat k^i\hat k^k)(\delta^{jl}-\hat k^j\hat k^l)
+(\delta^{il}-\hat k^i\hat k^l)(\delta^{jk}-\hat k^j\hat k^k)\nonumber\\
&&\quad -(\delta^{ij}-\hat k^i\hat k^j)(\delta^{kl}-\hat k^k\hat k^l)\nonumber\\
&&=\delta_{ik}\delta_{jl}
+\delta_{il}\delta_{jk}-\delta_{ij}\delta_{kl}+\hat k_i\hat k_j \hat k_k\hat k_l +\hat k_i \hat k_j \delta_{kl}+\nonumber\\
&& \quad \hat k_k \hat k_l \delta_{ij}-\hat k_i \hat k_l \delta_{jk}
-\hat k_i \hat k_k \delta_{jl}-\hat k_j \hat k_l \delta_{ik}-\hat k_j \hat k_k \delta_{il}\,.
\label{eq:polsum}
\end{eqnarray}
This result can also be obtained as follows.
Let us introduce a 4th-rank tensor
\begin{equation}
T^{ijkl}({\bf k})=\sum_{\lambda}\, e^{ij} ({{\bf k}, \lambda}) e^{kl} ({{\bf k}, \lambda})\,,
\ee
which has the following symmetry properties
\begin{equation}
T^{ijkl}=T^{jikl}=T^{ijlk}=T^{klij}.
\ee
However, the objects, which are at our disposal to construct $T^{ijkl}$,
are only $k^i$ and $\delta^{ij}$, thus in general, we have
\begin{eqnarray}
T^{ijkl} &=& A\delta^{ij}\delta^{kl}+B\delta^{ik}\delta^{jl}+B\delta^{il}\delta^{jk}+
C(\hat k^i \hat k^j\delta^{kl}+\hat k^k\hat k^l\delta^{ij})\nonumber\\
&& + D(\hat k^i \hat k^k\delta^{jl}+ \hat k^i \hat k^l\delta^{jk}
+ \hat k^j \hat k^l\delta^{ik}+ \hat k^j \hat k^k\delta^{il})
+E \hat k^i \hat k^j \hat k^k \hat k^l\,,\nonumber\\
\end{eqnarray}
where $A,B,C,D,E$ are constants to be determined.
This tensor is subject to the transversality condition
\begin{equation}
k_iT^{ijkl}=k_jT^{ijkl}=k_kT^{ijkl}=k_lT^{ijkl}=0\,,
\ee
and the trace-free condition
\begin{equation}
T^{iikl}=T^{ijkk}=0\,.
\ee
Applying these constraint conditions to $T^{ijkl}$ and solving the resulting equations
leads to
\begin{equation}
a=d=-e=-c=-b\,.
\ee
Therefore $T^{ijkl}$ is the same as the right-hand side of Eq.~(\ref{eq:polsum}), apart
for a multiplicative normalization constant which can be chosen to be unity.
\subsection{ Vacuum graviton Hadamard function in the TT gauge}
Here we evaluate the function $F_{ij}(x,x')$ and $H_{ijkl}(x,x')$ defined
in Eqs.~(\ref{eq:Ffunc}) and (\ref{eq:Hfunc}), respectively. Once these functions are given, the graviton
two point functions are easy to obtain.
Define
\begin{equation}
R=\sqrt{(x-x')^2+(y-y')^2+(z-z')^2},\quad \Delta t=t-t',\quad k=|{\bf k}|=\omega \,.
\ee
Then,
\begin{eqnarray}
F_{ij}(x,x')&&={Re\over{(2\pi)^3}}\int\, d^3{\bf k}{k_ik_j\over{2 \omega^3}}e^{i{\bf k} \cdot({\bf x}-{\bf x'})}e^{-i\omega(t-t')} \nonumber\\
&&={Re\over{(2\pi)^3}}\partial_i\partial_j'\int_0^{\infty}\,{e^{-ik\Delta t}\over 2 k}\,dk
\int_0^{\pi}\, d \theta\,\sin\theta e^{i k R \cos\theta}\int_0^{2\pi}\,d\phi\, \nonumber\\
&&={1\over{(2\pi)^2}}\partial_i\partial_j'\,{1\over R} \int_0^{\infty}\,{dk\over k^2} \sin kR\, \cos k\Delta t\,.
\nonumber\\
\end{eqnarray}
Because there is an infrared divergence in the above integral, we will introduce a regulator
$\beta$ in the
denominator of the integrand and then let $\beta$ approach 0 after the integration is performed.
\begin{eqnarray}
F_{ij}(x,x')&&={1\over{(2\pi)^2}}\partial_i\partial_j'\,\lim_{\beta\rightarrow 0}\,{1\over R } \int_0^{+\infty}\,
{dk\over k^2+\beta^2} \sin kR\, \cos k\Delta t\, \nonumber\\
&&={1\over{(2\pi)^2}}\partial_i\partial_j'\,\lim_{\beta\rightarrow 0}\, f(\beta, R, \Delta t)\,.
\nonumber\\
\end{eqnarray}
Here we have used a integral in Ref.~ \cite{GR1} and defined
\begin{eqnarray}
f(\beta, R, \Delta t)&& = {1\over 4\beta R}\Bigg\{ e^{\beta(\Delta t-R)}{\rm Ei} [\beta(R-\Delta t)]+ e^{-\beta(\Delta t+R)}{\rm Ei} [\beta(R+\Delta t)]\nonumber\\
\quad &&- e^{\beta(\Delta t+R)}{\rm Ei} [-\beta(R+\Delta t)]-e^{\beta(R-\Delta t)}{\rm Ei} [\beta(\Delta t- R)]\Bigg\}\,.\nonumber\\
\end{eqnarray}
Here ${\rm Ei(x)}$ is the exponential-integral function. Making use of the fact that, when $x$ is small,
\begin{equation}
{\rm Ei(x)}\approx \gamma +\ln|x|+x+{1\over 4}x^2+{1\over 18}x^3+O(x^4)\,,
\ee
where $\gamma$ is the Euler constant, and expanding $f$ around $\beta=0$ to the order of $\beta^2$, we get
\begin{equation}
f(\beta, R, \Delta t)\approx 1-\gamma -\ln \beta -{1\over 2}\ln ( R^2-\Delta t^2 )
-{\Delta t \over 4R}\ln \Bigg( \frac{R+\Delta t}{R-\Delta t}\Bigg)^2 +O(\beta^2)\,.
\ee
Taking the limit and keeping in mind that the constant terms ( with respect to $x$ and $ x'$ ) vanish under
differentiation, we finally obtain
\begin{equation}
F_{ij}(x,x')=-{1\over{(2\pi)^2}}\partial_i\partial_j'\,\left[{1\over 2}\ln ( R^2-\Delta t^2 )
+{\Delta t \over 4R}\ln \Bigg( \frac{R+\Delta t}{R-\Delta t}\Bigg)^2 \right]\,.
\ee
Now let us turn our attention to $H_{ijkl}(x,x')$. We have, proceeding with similar steps as we did
for $F_{ij}(x,x')$,
\begin{eqnarray}
H_{ijkl}(x,x')&&={Re\over{(2\pi)^3}}\int\, d^3{\bf k}{k_i k_j k_k k_l\over{2 \omega^5}}e^{i{\bf k} \cdot({\bf x}-{\bf x'})}e^{-i\omega\Delta t}\nonumber\\
&&=-{1\over{(2\pi)^2}}\partial_i\partial_j'\partial_k\partial_l'\,
\lim_{\beta\rightarrow 0}\,{1\over 2\beta R }{\partial\over \partial\beta} \int_0^{+\infty}\,
{dk\over k^2+\beta^2} \sin kR\, \cos k\Delta t\, \nonumber\\
&&=-{1\over{(2\pi)^2}}\partial_i\partial_j'\partial_k\partial_l'\,\lim_{\beta\rightarrow 0}\, {1\over 2 \beta } {\partial\over \partial\beta} f(\beta, R, \Delta t)\,.
\nonumber\\
\end{eqnarray}
Now expand ${1\over 2 \beta } {\partial\over \partial\beta} f(\beta, R, \Delta t) $ to order
$\beta^2$ to find
\begin{eqnarray}
{1\over 2 \beta } {\partial\over \partial\beta} f(\beta, R, \Delta t)\,&&=-{1\over 2\beta}-{1\over 3}
\left[ (\ln \beta +\gamma-1)R^2+3(\ln \beta +\gamma-1)\Delta t^2\right]\nonumber\\
\quad &&-{1\over 12 R}\left[ (R+\Delta t)^3\ln|R+\Delta t|
+ (R-\Delta t)^3\ln|R-\Delta t|\right]\,.\nonumber\\
\end{eqnarray}
Plugging this result into Eq.~(A22) and noting that only terms higher than quadratic in $R$ contribute after
the differentiation, we obtain
\begin{eqnarray}
H_{ijkl}(x,x')&=&{1\over 48\pi^2}\partial_i\partial_j'\partial_k\partial_l'\,
\Bigg[ (R^2+3\Delta t^2)\ln (R^2-\Delta t^2)^2\nonumber\\
\quad && + \left(3R\Delta t+{\Delta t^3\over R}\right)\ln \Bigg( \frac{R+\Delta t}{R-\Delta t}\Bigg)^2\Bigg]\,.
\nonumber\\
\end{eqnarray}
For convenience, we give the explicit forms for $G_{xxxx}^{(1)}$ and $G_{zzzz}^{(1)}$ here:
\begin{eqnarray}
G_{xxxx}^{(1)}(x,x')\,&&=2\left(D^{(1)}(x,x')-2F_{xx}(x,x')+H_{xxxx}(x,x')\right)\nonumber\\
&&={1\over 12\pi^2R^8\sigma^2}\Bigg\{(\Delta x^2-\Delta t^2)(16\Delta x^6-24\Delta x^4\Delta t^2)
-3\Delta t^2 R_t^6\nonumber\\
&&\quad +(9\Delta t^4+69\Delta x^2\Delta t^2+16\Delta x ^4)R_t^4+(-72\Delta x^2\Delta t^4+32\Delta x^4\Delta t^2+32\Delta x^6)
R_t^2\Bigg\} \nonumber\\
&&\quad-{\Delta t\over{16\pi^2R^9}}\ln\left(\frac{R+\Delta t}{R-\Delta t}\right)^2
\Biggl[-R_t^6-(3\Delta t^2 +9\Delta x^2)R_t^4\nonumber\\
&&\quad +24\Delta t^2\Delta x^2R_t^2-8\Delta x^4\Delta t^2
+8\Delta x^6\Biggr]\,,\nonumber\\
\label{eq:tpFunc}
\end{eqnarray}
where
\begin{eqnarray}
&&R_t^2=\Delta y^2+\Delta z^2\\
&&\Delta x =x-x'\\
&&R^2=R_t^2 +\Delta x ^2=\Delta x ^2 +\Delta y^2+\Delta z^2\\
&&\sigma^2=R^2-\Delta t ^2=\Delta x ^2 +\Delta y^2+\Delta z^2-\Delta t ^2\\
\end{eqnarray}
To get $G_{zzzz}^{(1)}(x,x')$, all we need to do is to replace $R_t^2 $ in Eq~(\ref{eq:tpFunc}) by
$R_t^2=\Delta y^2+\Delta x^2$.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,488 |
{"url":"https:\/\/cs.stackexchange.com\/questions\/56187\/lookup-complexity-in-b-trees-database","text":"# Lookup complexity in B-trees [Database]\n\nGiven that:\n\nB = n\/R blocks in the file\n2d index records per block (blocking factor): 2d > R\nan extra block access from the index to the datafile\n\n\nI am not able to wrap my head around as why the lookup would incur an cost[number of block accesses] of\nless than or equal to\n\n2 + log(base to d) (n\/2)\n\n\u2022 What have you tried? Where did you get stuck? We do not want to just do your (home-)work for you; we want you to gain understanding. However, as it is we do not know what your underlying problem is, so we can not begin to help. See here for a relevant discussion. If you are uncertain how to improve your question, why not ask around in Computer Science Chat? You may also want to check out our reference questions. \u2013\u00a0Raphael Apr 20 '16 at 0:09\n\u2022 Note that you can use LaTeX here to typeset mathematics in a more readable way. See here for a short introduction. \u2013\u00a0Raphael Apr 20 '16 at 0:09","date":"2019-10-16 23:36:02","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\": 0.6455470323562622, \"perplexity\": 846.6020252222165}, \"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-2019-43\/segments\/1570986670928.29\/warc\/CC-MAIN-20191016213112-20191017000612-00377.warc.gz\"}"} | null | null |
Food or Supplements… Or Both?
I just had a consultation with a young man who was, as many young men in the gym are, trying to gain weight and "get big". When the topic got on to nutrition he happily told me about his daily diet intake and supplementation. It basically consisted of a handful of protein shakes per day (various protein blends for different times of the day), a bunch of Gatorade, and an evening meal consisting of a chicken breast and brown rice. His list of pills and powders (most of them with very fierce names) was about half a page long.
Now, I'm certainly not a supplement hater. In fact, I'm a bit of a nutrition and supplementation geek and as such, I really enjoy debating the effects of various substances. However, I think that many people are missing the forest for the trees when it comes to supplementation.
-Convenient to carry around, generally no special care such as cooking or refrigeration is necessary.
-Very easy to mix and match for precise nutrition.
-Meal replacements and protein supplements can be used to keep overall calorie intake down as many people tend to overeat with food in front of them.
-Missing a lot of "micronutrients" that are present in food.
-Some non-natural vitamins and minerals aren't taken up by the body as well.
-Large, isolated amounts of some nutrients aren't taken up by the body as well as smaller, mixed doses.
-Often meal replacements and other supplements aren't particularly satisfying.
-Nobody wants to go out to dinner with the dude who sits there with a protein shaker.
As for the pros and cons of real food, they tend to be the opposite.
In my mind supplements are exactly that: Supplements. They are not substitutes when you look at the diet as a whole. I'm a firm believer in packing my athletes with as much real food as possible. Look, we're omnivores and pretty good ones at that. Our body is pretty well equipped to deal with most anything that rolls across its path and make some use of it. As a matter of fact, our nutritional needs are such that it prefers a varied diet. That's hard to manage if you're taking the majority of your nutrition in from the same few powders.
To sum it up, I do support judicious use of supplements for most athletes and fitness seekers, but only the basics. Until your diet is in line, supplements should take the back seat to real food. As far as the young man I spoke to the first thing I told him is to stop taking most of the crap he was loading up on and switch to the basics of good, quality food. From there he could add back in some basic supplements until he had exhausted the benefits of good training and good eating, which will be a very long time. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,651 |
Los X Juegos Centroamericanos y del Caribe se celebraron en la ciudad de San Juan, Puerto Rico del 11 al 25 de junio de 1966.
Historia
Para esta edición Estados Unidos denegó el visado para los deportistas cubanos para asistir a las justas deportivas en Puerto Rico, pero Cuba defendió su derecho ante el Comité Olímpico Internacional
Equipos participantes
Las Islas Vírgenes estadounidenses debutaron en los juegos.
Medallero
La tabla se encuentra ordenada por la cantidad de medallas de oro, plata y bronce.
Si dos o más países igualan en medallas, aparecen en orden alfabético.
Véase también
Juegos Centroamericanos y del Caribe
Organización Deportiva Centroamericana y del Caribe
Juegos Deportivos Centroamericanos
Juegos Suramericanos
Juegos Bolivarianos
Juegos Panamericanos
Referencias
Enlaces externos
Organización Deportiva Centroamericana y del Caribe (Odecabe)
Historia de los Juegos Deportivos Regionales más antiguos del mundo
X Juegos Centroamericanos y del Caribe
Ediciones de los Juegos Centroamericanos y del Caribe
Deporte en 1966
Puerto Rico en 1966
Puerto Rico en los Juegos Centroamericanos y del Caribe
Deporte en San Juan (Puerto Rico) | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 970 |
James Vincent
Vincent Terrone
Mike Friesenegger
Andrew Grimberg
Len Santalucia
Ji Chen
Ingo Adlung
## Agenda topics
- Introduction of new attendees
- Update on core infrastructure badge effort
- Access to z/VM environment for testing/development
- CI/CD infrastructure to Linux Foundation
- List of features to add
## Meeting Notes
### Introduction of new attendees
- Len is the Vicom Infinity CTO and sits on the OMP board
- Ingo is the IBM Chief Architect and CTO for Z and LinuxONE and is on the OMP technical steering committee
### Update on core infrastructure badge effort
- Nothing to report
- **TODO:** Everyone please review for a discussion next meeting
- https://bestpractices.coreinfrastructure.org/en
### Access to z/VM environment for testing/development
- Discussion about hot to access environments
- Vicom Infiinity
- Send Len an email with request
- Vincent will provide a second level guest
- Vicom has a ZR1
- Velocity Software
- Can submit request on Velocity website
- Barton will ask James to create a second level VM
- zPro is being used to provision the guest
- Guest wll have a short life span but James can work to lengthen this
- **TO DO:** Create a how-to document that explains using Vicom and Velocity resources
- Mike will start the creating a how-to with Vincent and James
### CI/CD infrastructure to Linux Foundation
- LF CI/CD team requires budget authority for this effort
- LF CI/CD team will need to do a discovery
- Andrew will connect John Mertic to confirm this effort
- **TO DO:** Andrew ill send a list of questions to Ji Chen for discovery
- Link to CI/CD LF environment information from previous meeting
- https://docs.releng.linuxfoundation.org
- LF does not have access to a Z
- LF will connect to an external Z infrastructure
- Possibly use marist resources
- Andrew Grimberg <agrimberg@linuxfoundation.org> is available to answer questions about LF CI/CD environment and requirements
## Next meeting agenda topics
- Update on CI/CD infrastructure effort
- Update on how-to access z/VM resource effort
- List of features to add
- Discussion about core infrastructure badge effort
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,384 |
/* global describe, test, it, expect */
import cheerio from 'cheerio'
export default function ({ app }, suiteName, render) {
async function get$ (path, query) {
const html = await render(path, query)
return cheerio.load(html)
}
describe(suiteName, () => {
test('renders a stateless component', async () => {
const html = await render('/stateless')
expect(html.includes('<meta charSet="utf-8" class="next-head"/>')).toBeTruthy()
expect(html.includes('My component!')).toBeTruthy()
})
test('renders a stateful component', async () => {
const $ = await get$('/stateful')
const answer = $('#answer')
expect(answer.text()).toBe('The answer is 42')
})
test('header helper renders header information', async () => {
const html = await (render('/head'))
expect(html.includes('<meta charSet="iso-8859-5" class="next-head"/>')).toBeTruthy()
expect(html.includes('<meta content="my meta" class="next-head"/>')).toBeTruthy()
expect(html.includes('I can haz meta tags')).toBeTruthy()
})
test('renders styled jsx', async () => {
const $ = await get$('/styled-jsx')
const styleId = $('#blue-box').attr('class')
const style = $('style')
expect(style.text().includes(`p.${styleId}{color:blue`)).toBeTruthy()
})
test('renders properties populated asynchronously', async () => {
const html = await render('/async-props')
expect(html.includes('Diego Milito')).toBeTruthy()
})
test('renders a link component', async () => {
const $ = await get$('/link')
const link = $('a[href="/about"]')
expect(link.text()).toBe('About')
})
test('getInitialProps resolves to null', async () => {
const $ = await get$('/empty-get-initial-props')
const expectedErrorMessage = '"EmptyInitialPropsPage.getInitialProps()" should resolve to an object. But found "null" instead.'
expect($('pre').text().includes(expectedErrorMessage)).toBeTruthy()
})
test('allows to import .json files', async () => {
const html = await render('/json')
expect(html.includes('Zeit')).toBeTruthy()
})
test('default export is not a React Component', async () => {
const $ = await get$('/no-default-export')
const pre = $('pre')
expect(pre.text()).toMatch(/The default export is not a React Component/)
})
test('error', async () => {
const $ = await get$('/error')
expect($('pre').text()).toMatch(/This is an expected error/)
})
test('asPath', async () => {
const $ = await get$('/nav/as-path', { aa: 10 })
expect($('.as-path-content').text()).toBe('/nav/as-path?aa=10')
})
test('error 404', async () => {
const $ = await get$('/non-existent')
expect($('h1').text()).toBe('404')
expect($('h2').text()).toBe('This page could not be found.')
})
describe('with the HOC based router', () => {
it('should navigate as expected', async () => {
const $ = await get$('/nav/with-hoc')
expect($('#pathname').text()).toBe('Current path: /nav/with-hoc')
})
it('should include asPath', async () => {
const $ = await get$('/nav/with-hoc')
expect($('#asPath').text()).toBe('Current asPath: /nav/with-hoc')
})
})
})
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,688 |
Cyclists in Rome take part in a 26 November bike rally to protest the staging of the 2018 Giro d'Italia race in Israel, which activists say is part of an effort to whitewash crimes against the Palestinians.
This means that race organizers are parroting Israel's political claim that Jerusalem is a "unified" city, and Israel's capital under its sole and uncontested sovereignty.
Israel's Channel 2 reported Wednesday that the Trump administration may become the first government to do so in coming days, as a preliminary step to moving the US embassy to Jerusalem in line with long-standing demands from hardline Israel lobby groups.
The United Nations and world governments consider East Jerusalem, which Israel invaded in 1967, to be part of the occupied West Bank.
The first stages of the May 2018 bicycle race will be held in Jerusalem and parts of present-day Israel as part of a major international propaganda effort backed by Israel's government around the time of the 70th anniversary of the Nakba, the ethnic cleansing of more than 750,000 Palestinians by Zionist militias.
Giro d'Italia used the term "West Jerusalem" in materials presented at a high-profile launch event in Milan on Wednesday to announce details of the 2018 race route.
That may have been an attempt to mollify the growing protests about the world famous cycle race's complicity in Israel's efforts to whitewash its image, including its ongoing ethnic cleansing of Palestinians in East Jerusalem.
On Wednesday, Israel's ministers of sport and tourism immediately threatened to pull their lucrative sponsorship of the race unless organizers fell into line.
Giro d'Italia organizers wasted no time scrubbing their website and social media from references to "West" Jerusalem. They even deleted a tweet featuring a video that used the term.
A still from a video published and subsequently deleted by Giro d'Italia organizers after use of the term "West Jerusalem" prompted threats from Israel.
Organizers also issued a statement signaling their compliance with Israel's political demands.
"Giro d'Italia, instead, shamefully chose to bow to Israeli pressure and recognize Israel's illegal annexation of occupied East Jerusalem, contravening international law and the Italian government's own position," Adam added.
PACBI also noted that the Israel Cycling Federation frequently sponsors races "in areas under Israeli military occupation in violation of international law" – a reference to West Bank settlements.
Hosting the Giro d'Italia is a major propaganda coup for which Israel has been willing to pay a high price.
It is reportedly paying RCS Sport $12 million and another $2.4 million to reigning Tour de France champion Chris Froome to ride in the race.
Israeli Prime Minister Benjamin Netanyahu has even tried to enlist Pope Francis in the propaganda campaign, inviting the pontiff to attend the start of the race.
A major goal of "Brand Israel" propaganda is to market Israel as a venue for apolitical "cultural" and "sporting" events, distracting from these violations.
In that sense, the Giro d'Italia has already backfired. Six months before its start, the race is already deeply mired in politics. Last week, hundreds of cyclists held bike rallies across Italy demanding that organizers relocate the race.
Even if the Giro d'Italia goes ahead in Jerusalem, the controversy and ongoing protests will send a strong message to other international franchises to steer clear of Israel or face major reputational damage.
I was saddened to see Froome in the French sportspaper "L'équipe" , supporting this venture. 2000km between "Jerusalem" and the real race, and Froome and others accept this horrible public spectacle. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,704 |
@class MISSING_TYPE;
@interface _TtC13DVTFoundation16DVTXCSigningTool : NSObject
{
MISSING_TYPE *toolname;
MISSING_TYPE *logAspect;
MISSING_TYPE *defaultArguments;
}
- (void).cxx_destruct;
- (id)init;
- (BOOL)pkgSignWithPkgPath:(id)arg1 certificate:(id)arg2 error:(id *)arg3;
- (BOOL)codesignWithMode:(long long)arg1 path:(id)arg2 certificate:(id)arg3 entitlementsFile:(id)arg4 signingIdentifier:(id)arg5 error:(id *)arg6;
- (id)initWithLogAspect:(id)arg1;
@end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,840 |
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:tools="http://schemas.android.com/tools"
android:layout_width="match_parent"
android:layout_height="match_parent"
android:orientation="vertical"
android:gravity="center_vertical|center_horizontal"
android:background="@color/steps_blue"
tools:context="com.steps.activities.AddGroup"
android:padding="5dp">
<FrameLayout
android:id="@+id/fragment"
android:layout_width="match_parent"
android:layout_height="wrap_content" />
</LinearLayout>
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,181 |
\section{Introduction}\mlabel{s:intro}
In \cite{confol} Eliashberg and Thurston explore the relationship between foliations and contact structures on oriented $3$-manifolds. Foliations respectively contact structures are locally defined by $1$-forms $\alpha$ such that $\alpha\wedge d\alpha\equiv 0$ respectively $\alpha\wedge d\alpha>0$ (more precisely this defines {\em positive} contact structures).
One of the main results of \cite{confol} is the following remarkable theorem.
\begin{thm}[Theorem 2.4.1 in \cite{confol}]\mlabel{t:El-Th approx}
Suppose that a $C^2$-foliation $\xi$ on a closed oriented $3$-manifold is different from the product foliation of $S^1\times S^2$ by spheres. Then $\xi$ can be $C^0$-approximated by a positive contact structure.
\end{thm}
In the main part of the proof of this theorem a given foliation on $M$ is modified so that the resulting plane field is somewhere integrable while it is a positive contact structure on other parts of $M$. This motivates the following definition.
\begin{defn}
A {\em positive confoliation} on $M$ is a $C^2$-smooth plane field on a $3$-manifold $M$ which is locally defined by a $1$-form $\alpha$ such that $\alpha\wedge d\alpha\ge 0$. We denote the region where $\xi$ is a contact structure by $H(\xi)$.
\end{defn}
\thmref{t:El-Th approx} remains true when foliations are replaced by confoliations. Like foliations and contact structures the definition of confoliations can be generalized to higher dimensions (cf. \cite{AlW, confol}) but in this article we are only concerned with dimension $3$. All plane fields appearing in this article will be oriented, in particular these plane fields have an Euler class.
In the last chapter of \cite{confol} Eliashberg and Thurston discuss several properties of foliations (tautness, absence of Reeb components) and contact structures (symplectic fillability, tightness) and what can be said about a contact structure approximating a taut or Reebless foliation. For example they establish the following theorem.
\begin{thm*}[Eliashberg, Thurston, \cite{confol}]
If a contact structure $\xi$ on a closed $3$-mani\-fold is sufficiently close to a taut foliation in the $C^0$-topology, then $\xi$ is symplectically fillable and therefore tight.
\end{thm*}
Another result in this direction is due to V.~Colin.
\begin{thm*}[Colin, \cite{colin pert}]
A $C^2$-foliation without Reeb components on a closed oriented $3$-manifold can be $C^0$-approximated by tight contact structures.
\end{thm*}
In \cite{cont from fol} J.~Etnyre shows that every contact structure (tight or not) may be obtained by a perturbation of a foliation with Reeb components. This result is implicitly contained in \cite{mori}. Moreover, J.~Etnyre improved \thmref{t:El-Th approx} by showing that $C^k$-smooth foliations can be $C^k$-approximated by contact structures provided that $k\ge 2$ (a written account will hopefully be available in the near future, cf. \cite{etnyreCk}).
In order to understand better the relationship between geometric properties of foliations and properties of the contact structures approximating them, it is interesting to ask about properties of confoliations which appear in the approximation process. For example the notion of symplectic fillability can be extended to confoliations in an obvious fashion.
The question how to generalize the notion of tightness is more complicated. One aim of this article is to clarify this point. The following definition is suggested in \cite{confol}.
\begin{defn} \mlabel{d:tight confol}
A confoliation $\xi$ on $M$ is {\em tight} if for every embedded disc $D\subset M$ such that
\begin{itemize}
\item[(i)] $\partial D$ is tangent to $\xi$,
\item[(ii)] $TD$ and $\xi$ are transverse along $\partial D$
\end{itemize}
there is an embedded disc $D'$ satisfying the following requirements
\begin{itemize}
\item[(1)] $\partial D=\partial D'$,
\item[(2)] $D'$ is everywhere tangent to $\xi$,
\item[(3)] $e(\xi)[D\cup D']=0$.
\end{itemize}
\end{defn}
This definition is motivated by the following facts. If $\xi$ is a contact structure, then there are no surfaces tangent to $\xi$ and \defref{d:tight confol} reduces to a definition of tightness for contact structures. In the case when $\xi$ is a foliation on a closed manifold \defref{d:tight confol} is equivalent to the absence Reeb components by a theorem of Novikov \cite{No}. Thus \defref{d:tight confol} interpolates between tight contact structures and Reebless foliations. The following theorem is also shown in \cite{confol} (we recall the definition of symplectic fillability in \secref{s:tightness of confol}).
\begin{thm}[Theorem 3.5.1. in \cite{confol}] \mlabel{t:fillable confol are tight}
Symplectically fillable confoliations are tight.
\end{thm}
As pointed out in \cite{confol} there are inequalities imposing restrictions on the Euler class $e(\xi)$ of $\xi$ when $\xi$ is a tight contact structure or a Reebless foliation. Before we can state these inequalities we need one more definition.
\begin{defn}
Let $\gamma$ be a nullhomologous knot in a confoliated manifold $(M,\xi)$ which is positively transverse to $\xi$. For each choice $F$ of an oriented Seifert surface of $\gamma$ we define the {\em self linking number} $\mathrm{sl}(\gamma,F)$ of $\gamma$ as follows. Choose a nowhere vanishing section $X$ of $\xi|_F$ and let $\gamma'$ be the knot obtained by pushing $\gamma$ off itself by $X$. Then
$$
\mathrm{sl}(\gamma,F)=\gamma'\cdot F~.
$$
\end{defn}
\noindent Obviously $\mathrm{sl}(\gamma,F)$ depends only on $[F]\in H_2(M,\gamma;\mathbb{Z})$.
In \cite{Be} D.~Bennequin proved an inequality between $\mathrm{sl}(\gamma)$ of a transverse knot in the standard contact structure $\ker(dz+x\,dy)$ on $\mathbb{ R}^3$ and the Euler number of a Seifert surface of $\gamma$. This inequality was extended to all tight contact structures by Eliashberg in \cite{El}. From Thurston's work in \cite{Th} it follows that the same inequalities hold for surfaces in foliated manifolds without Reeb components. We summarize these results as follows.
\begin{thm}[Eliashberg \cite{El}, Thurston \cite{Th}] \mlabel{t:TB Ungl tight}
Let $\xi$ be a tight contact structure or a foliation without Reeb components on a closed manifold $M$ (different from a foliation by spheres) and $F\subset M$ an embedded oriented surface.
\begin{itemize}
\item[a)] If $F\simeq S^2$, then $e(\xi)[F]=0$.
\item[b)] If $\partial F=\emptyset$ and $F\not\simeq S^2$, then $|e(\xi)[F]|\le-\chi(F)$.
\item[c)] If $\partial F\neq\emptyset$ is positively transverse to $\xi$, then $\mathrm{sl}(\gamma,[F])\le -\chi(F)$.
\end{itemize}
\end{thm}
The inequalities stated in this theorem are usually referred to as Thurston-Benne\-quin inequalities. They imply that only finitely many classes in $H^2(M;\mathbb{ Z})$ are Euler classes of tight contact structures or foliations without Reeb components. Foliations by spheres violate a) and we exclude such foliations from our discussion.
It was conjectured (Conjecture 3.4.5 in \cite{confol}) that tight confoliations satisfy the Thurston-Bennequin inequalities. We give a counterexample $(T^3,\xi_T)$ with the property that $e(\xi)[T_0]=-4$ for an embedded torus in $T^3$. Therefore every contact structure which is close to $\xi_t$ must be overtwisted. This yields a negative answer to Question 1 on p.~63 of \cite{confol}. The construction of $(T^3,\xi_T)$ is based on the classification of tight contact structures on $T^2\times[0,1]$ due to E.~Giroux and K.~Honda.
In this article we show that a) is true for tight confoliations and c) holds when $F$ is a disc. On the other hand we give an example of a tight confoliation $\xi_{T}$ on $T^3$ which violates b) and c) for surfaces which are not simply connected.
Our example indicates that tight confoliations are much more flexible objects than tight contact structures or foliations without Reeb components. For example infinitely many elements of $H^2(T^3;\mathbb{ Z})$ are Euler classes of tight confoliations. Nevertheless, tight confoliations have some rigidity properties. In addition to the Thurston-Bennequin inequalities for simply connected surfaces we show the following theorem.
\begin{ballapproxthm*}
Let $M$ be a manifold carrying a tight confoliation $\xi$ and $B\subset M$ a closed embedded ball in $M$. There is a neighbourhood of $\xi$ in the space of plane fields with the $C^0$-topology such that $\xi'\eing{B}$ is tight for every contact structure $\xi'$ in this neighbourhood of $\xi$.
\end{ballapproxthm*}
This theorem leads to restrictions on the homotopy class of plane fields which contain tight confoliations. For example only one homotopy class of plane fields on $S^3$ contains a tight confoliation by Eliashberg's classification of tight contact structures on balls together with \thmref{t:tight on balls}. For the proof of \thmref{t:tight on balls} we study the characteristic foliation $S(\xi)=TS\cap\xi$ on embedded spheres $S\subset M$ (we generalize the notion of taming functions introduced in \cite{El} to confoliations and use results from \cite{giroux2}).
Motivated by the example $(T^3,\xi_T)$ we define the notion of an overtwisted star. Roughly speaking, an overtwisted star on an embedded surface $F$ is a domain in $F$ whose interior is homeomorphic to a disc, the boundary of this domain consists of Legendrian curves and all singularities on the boundary have the same sign. The main difference between overtwisted stars and overtwisted discs is that the set theoretic boundary of an overtwisted star may contain closed leaves or quasi-minimal sets of the characteristic foliation.
An example of an overtwisted star is shown in \figref{b:starfish} on p.~\pageref{b:starfish}. It will be clear from the definition of overtwisted stars that contact structures which admit overtwisted stars are not tight, ie. they are overtwisted in the usual sense. Following Eliashberg's strategy from \cite{El} we prove the following theorem.
\begin{nostarsimplytbthm*}
Let $(M,\xi)$ be an oriented tight confoliation such that no compact embedded oriented surface contains an overtwisted star and $(M,\xi)$ is not a foliation by spheres.
Every embedded surface $F$ whose boundary is either empty or positively transverse to $\xi$ satisfies the following relations.
\begin{itemize}
\item[a)] If $F\simeq S^2$, then $e(\xi)[F]=0$.
\item[b)] If $\partial F=\emptyset$ and $F\not\simeq S^2$, then $|e(\xi)[F]|\le-\chi(F)$.
\item[c)] If $\partial F\neq\emptyset$ is positively transverse to $\xi$, then $\mathrm{sl}(\gamma,[F])\le -\chi(F)$.
\end{itemize}
\end{nostarsimplytbthm*}
Moreover, \thmref{t:fillable confol are tight} can be refined as follows.
\begin{sympfillthm*}
Symplectically fillable confoliations do not admit overtwisted stars.
\end{sympfillthm*}
These results indicate that tightness in the sense of \defref{d:tight confol} together with the absence of overtwisted stars is the right generalization of tightness to confoliations.
This article is organized as follows: In \secref{s:facts} we recall several facts about confoliations and characteristic foliations. \secref{s:manipulation} contains a discussion of several methods for the manipulation of characteristic foliation on embedded surfaces. For example we generalize the elimination lemma to confoliations and we discuss several surgeries of surfaces when integral discs of $\xi$ intersect the surface in a cycle. In \secref{s:example} we describe an example of a tight confoliation on $T^3$ which violates the Thurston-Bennequin inequalities while we prove \thmref{t:tight on balls} in \secref{s:rigid}.
In \secref{s:discussion} we discuss overtwisted stars and establish the Thurston-Bennequin inequalities for tight confoliations without overtwisted stars. Moreover, we prove that symplectically fillable confoliations do not admit overtwisted stars.
Throughout this article $M$ will be a connected oriented $3$-manifold without boundary and $\xi$ will always denote a smooth oriented plane field on $M$. Moreover, we require $M$ to be compact.
{\em Acknowledgements:} The author started working on this project in the fall of 2006 during a stay at Stanford University, the financial support provided by the "Deutsche Forschungsgemeinschaft" is gratefully acknowledged. It is a pleasure for me to thank Y. Eliashberg for his support, hospitality and interest. Moreover, I would like to thank V.~Colin and J.~Etnyre for helpful conversations.
\section{Characteristic foliations, non-integrability and tightness } \mlabel{s:facts}
In this section we recall some definitions, notations and well known facts which will be used throughout this paper. Most notions discussed here are generalizations of definitions which are well-known in the context of contact structures (cf. for example \cite{Aeb}, \cite{intro-etnyre}, \cite{giroux} and the references therein).
\subsection{Characteristic foliations on surfaces}
We consider an embedded oriented surface $F$ in a confoliated $3$-manifold $(M,\xi)$ and we assume that $\xi$ is cooriented. The singular foliation $F(\xi):=\xi\cap TF$ is called the {\em characteristic foliation} of $F$. The leaves of the characteristic foliation are examples of {\em Legendrian curves}, ie. curves tangent to $\xi$.
The following convention is used to orient $F(\xi)$: Consider $p\in F$ such that $F(\xi)_p$ is one-dimensional. For $X\in F(\xi)(p)$ we choose $Y\in\xi(p)$ and $Z\in T_pF$ such that $X,Y$ represents the orientation of $\xi(p)$ and $X,Z$ induces the orientation of the surface. Then $X$ represents the orientation of the characteristic foliation if and only if $X,Y,Z$ is a positive basis of $T_pM$.
With this convention, the characteristic foliation points out $F$ along boundary components of $F$ which are positively transverse to $\xi$. An isolated singularity of $F(\xi)$ is called {\em elliptic} respectively {\em hyperbolic} when its index is $+1$ respectively $-1$. A singularity is {\em positive} if the orientation of $\xi$ coincides with the orientation of $F$ at the singular point and {\em negative} otherwise. Given an embedded surface $F\subset M$ we denote the number of positive/negative elliptic singularities by $e_\pm(F)$ and the number of positive/negative hyperbolic singularities is $h_\pm(F)$.
\subsection{(Non-)Integrability} \mlabel{ss:confolmeaning}
The condition that $\xi$ is a confoliation can be interpreted in geometric terms. The following interpretation can be found in \cite{confol}.
Let $D$ be a closed disc of dimension $2$ and $\xi$ a positive confoliation transverse to the fibers of $\pi : D\times\mathbb{ R}\longrightarrow D$. Then $\xi$ can be viewed as a connection. We assume in the following that this connection is complete, ie. for every differentiable curve $\sigma$ in $D$ there is a horizontal lift of $\sigma$ starting at a given point in the fiber over the starting point of $\sigma$.
We consider the holonomy of the characteristic foliation on $\pi^{-1}(\partial D)$
\begin{equation} \label{e:holonomy}
h_{\partial D} : \pi^{-1}(p)\simeq\mathbb{ R}\longrightarrow\mathbb{ R}\simeq\pi^{-1}(p)
\end{equation}
where $h_{\partial D}(x)$ is defined as the parallel transport of $x\in\mathbb{ R}$ along $\partial D$.
\begin{lem}[Lemma 1.3.4. in \cite{confol}] \mlabel{l:neg-curv}
If the confoliation $\xi$ on $\pi : D\times\mathbb{ R}\longrightarrow D$ defines a complete connection, then $h_{\partial D}(x)\le x$ for all $x\in\pi^{-1}(p)$ and $p\in\partial D$. Equality holds for all $x\in\pi^{-1}(p)$ if and only if $\xi$ is integrable.
If $D=D\times\{0\}$ is tangent to $\xi$, then the germ of the holonomy is well defined without any completeness assumption and $h_{\partial D}(x)\le x$ for all $x$ in the domain of $h$. The germ of $h_{\partial D}$ coincides with the germ of the identity if and only if a neighbourhood of $D$ is foliated by discs.
\end{lem}
Of course, the second part of the lemma applies to the case when on considers only the part lying above or below $D\times\{0\}\subset D\times\mathbb{ R}$. A consequence of \lemref{l:neg-curv} is the following generalization of the Reeb stability theorem to confoliations.
\begin{thm}[Proposition 1.3.9. in \cite{confol}] \mlabel{t:Reeb stability}
Let $M$ be a closed oriented manifold carrying a positive confoliation $\xi$. Suppose that $S$ is an embedded sphere tangent to $\xi$. Then $(M,\xi)$ is diffeomorphic to the product foliation on $S^2\times S^1$ by spheres.
\end{thm}
Foliations by spheres appear as exceptional case in some theorems. They will therefore be excluded from the discussion.
Another useful geometric interpretation of the confoliation condition can be found on p.~4 in \cite{confol} (and many other sources): Let $X$ be a Legendrian vector field and $F$ a surface transverse to $X$. The slope of line field $F_t(\xi)$ on the image of $F$ under the time-$t$-flow of $X$ is monotone in $t$ if and only if $\xi$ is a confoliation. This interpretation is useful when one wants extends confoliations along flow line which are Legendrian where the confoliation is already defined.
We define the {\em fully foliated part} of a confoliation $\xi$ on $M$ as the complement of
$$
\{x\in M | \textrm{ there is a Legendrian curve connecting }x\textrm{ to }H(\xi) \}.
$$
If $\gamma$ is a Legendrian curve in a leaf of $\xi$ and $A\simeq\gamma\times(-\delta,\delta), \delta>0$ an annulus transverse to the leaf such that $\gamma=\gamma\times\{0\}$, then we will consider several types of holonomy $h_A$ of the characteristic foliation on $A$.
\begin{itemize}
\item We say that there is {\em linear holonomy} or {\em non-trivial infinitesimal holonomy} along $\gamma$ if $h'_A(0)\neq 0$.
\item The holonomy is {\em sometimes attractive} if there are sequences $(x_n),(y_n)$ which converge to zero such that $x_n>0>y_n$ and
\begin{align*}
h_A(x_n) <x_n, h_A(y_n) >y_n \textrm{ for all } n\in\mathbb{N}.
\end{align*}
\end{itemize}
\subsection{Tightness of confoliations} \mlabel{s:tightness of confol}
In this section we summarize several facts about tight confoliations. We shall always assume that $\xi$ is a tight confoliation but it is not a foliation by spheres.
If $(M,\xi)$ is tight and $D\subset M$ is an embedded disc such that $\partial D$ is tangent to $\xi$ and $\xi\eing{\partial D}$ is transverse to $TD$, then the disc $D'$ whose existence is guaranteed by \defref{d:tight confol} is uniquely determined. Otherwise there would be a sphere tangent to $\xi$ and by \thmref{t:Reeb stability} $\xi$ would be a foliation by spheres. But we explicitly excluded this case.
The definition of tightness refers to smoothly embedded discs but of course it has implications for discs with piecewise smooth boundary and slightly more generally for unions of discs.
\begin{lem} \mlabel{l:limit cycles on spheres imply integral disc}
Suppose that $(M,\xi)$ is a tight confoliation and $S\subset M$ is an embedded sphere such that the characteristic foliation $S(\xi)=TS\cap\xi$ has only non-degenerate hyperbolic singularities along a connected cycle $\gamma$ of $S(\xi)$. Then there are immersed discs $D_i', i=1,\ldots k$ in $M$ which are tangent to $\xi$ and
$$
\partial\left(\bigcup_{i=1}^k D_i\right)=\partial D.
$$
\end{lem}
This follows by considering $C^\infty$-small perturbations of $S$ such that $\gamma$ is approximated by closed leaves of the characteristic foliation of the perturbed sphere. We will continue to say that a disc bounds the cycle $\gamma$ although the ``disc'' might have corners or be a pinched annulus, for example.
The most important criterion to prove tightness is \thmref{t:fillable confol are tight}. It is based on the following definition.
\begin{defn} \mlabel{d:symp filling}
A positive confoliation $\xi$ on a closed oriented manifold $M$ is {\em symplectically fillable} if there is a compact symplectic manifold $(X,\omega)$ such that
\begin{itemize}
\item[(i)] $\omega\big|_\xi$ is non-degenerate and
\item[(ii)] $\partial X=M$ as oriented manifolds where $X$ is oriented by $\omega\wedge\omega$.
\end{itemize}
\end{defn}
In this definition we use the ``outward normal first'' convention for the orientation of the boundary. There are several different notions of symplectic fillings and the \defref{d:symp filling} is often referred to as weak symplectic filling. It is clear from \thmref{t:fillable confol are tight} (and \thmref{t:no polygons if filled}) that the existence of a symplectic filling is an important property of a confoliation.
Note that if $(M,\xi)$ is symplectically fillable, then the same is true for confoliations $\xi'$ which are sufficiently close to $\xi$ in the $C^0$-topology.
\thmref{t:fillable confol are tight} can sometimes be extended to non-compact manifolds. Then one obtains the following consequence.
\begin{prop}[Proposition 3.5.6. in \cite{confol}] \mlabel{p:complete connection}
If a confoliation $\xi$ is transverse to the fibers of the projection $\mathbb{ R}^3\longrightarrow \mathbb{ R}^2$ and if the induced connection is complete, then $\xi$ is tight.
\end{prop}
In \cite{confol} one can find an example which shows that the completeness condition can not be dropped.
\section{Properties and modifications of characteristic foliations} \mlabel{s:manipulation}
The characteristic foliations on embedded surfaces in manifolds with contact structures has several properties reflecting the positivity of the contact structure. Moreover, there are methods to manipulate the characteristic foliation by isotopies of the surface. Similar remarks apply when $\xi$ is a foliation. In this section we generalize this to the case when $\xi$ is a confoliation. If $\xi$ is tight, then there are more restrictions on characteristic foliation. Some of these additional restrictions shall be discussed in \secref{s:rigid}.
\subsection{Neighbourhoods of elliptic singularities}
With our orientation convention positive elliptic singular points lying in the contact region are sources. The following lemma shows that this statement can be interpreted such that it generalizes to confoliation.
\begin{lem} \mlabel{l:little discs}
Let $(M,\xi)$ be a confoliated manifold and $F$ an immersed surface whose characteristic foliation has a non-degenerate positive elliptic singularity $p$.
There is an open disc $p\in D\subset F$ such that each leaf of the characteristic foliation on $D$ is either a circle or there is a closed transversal of $F(\xi)$ through the leaf. If $p$ is positive respectively negative and $\partial D$ is transverse to $F(\xi)$, then $F(\xi)$ points outwards respectively inwards.
\end{lem}
\begin{proof}
We fix a defining form $\alpha$ for $\xi$ on a neighbourhood of $p$. If $d\alpha(p)\neq 0$, then $p$ lies in the interior of the contact region and the claim follows from \cite{giroux}. When $d\alpha(p)=0$, then $F(\xi)$ is transverse to the gradient vector field $R$ of a Morse function which has a critical point of index $0$ or $2$ at $p$.
In the following we assume that $p$ is positive and $R$ points away from $p$ and coorients $\xi$ away from $p$ (the other cases are similar). The Poincar{\'e} return map characteristic foliation is well defined on a small neighbourhood of $p$ in a fixed radial line starting at the origin (cf. \cite{marsden} for example) and by our orientation convention $F(\xi)$ is oriented clockwise near $p$. We want to show that Poincar{\'e} return map is non-decreasing when the orientation of the radial line points away from $p$. In the following we assume that the Poincar{\'e} return map is not the identity because in that situation our claim is obvious.
Let $D\subset F$ be a small disc containing $p$ such that $\partial D$ is transverse to $F(\xi)$. Fix a vector field $Z$ coorienting both $F$ and $\xi$. We write $D_z$ for the image of $F$ under the time $z$-flow of $Z$. We may assume that the tangencies of $D_z$ and $\xi$ are exactly the points on the flow line $\gamma_p$ of $Z$ through $p$.
We extend $R$ to a vector field on a neighbourhood of $p$ tangent to $D_z$ such that it remains transverse to $\xi$ on $U\setminus\gamma_p$. Then the vector field $T=zZ+R$ is transverse to $\xi$ on $\{z\ge 0\}\setminus\{p\}\subset U$. The flow of $T$ exists for all negative times $t$ and every flow line of $T$ approaches $p$ as $t\to-\infty$. Since $d\alpha(p)=0$ there are local coordinates $x,y$ on $D$ around $p$ such that $p$ corresponds to the origin and
\begin{equation} \label{e:alpha}
\alpha=dz+\left(xdx+ydy\right)+\widetilde{\alpha}
\end{equation}
where $\widetilde{\alpha}$ denotes a $1$-form such that $\widetilde{\alpha}/(x^2+y^2)$ and $\widetilde{\alpha}/z$ remain bounded when one approaches the origin.
We choose a closed embedded disc $D'$ in $\{z\ge 0\}$ which is transverse to $T$ and $D$ such that $\partial D'=\partial D$ and $D\cup D'$ bound a closed half ball $B$. The half ball is identified with a Euclidean half ball of radius $1$ and we fix spherical coordinates $\rho,\vartheta,\phi$ (where $\rho$ denotes the distance of a point from the origin, $\vartheta$ is the angle between $\gamma_p$ and the straight line connecting the point with the origin) such that $T$ corresponds to $\rho\partial_\rho$. In this coordinate system
\begin{equation} \label{e:pullback alpha}
\alpha=\cos(\vartheta) d\rho+\rho\sin(\vartheta)\left(-d\vartheta+\sin(\vartheta)d\rho+\cos(\vartheta)\rho d\vartheta \right)+\widetilde{\alpha}
\end{equation}
and $\widetilde{\alpha}/(\rho^2\sin^2(\vartheta))$ and $\widetilde{\alpha}/(\rho\cos(\vartheta))$ remain bounded when one approaches the origin.
Consider a closed disc $D''$ lying in the interior of $D'$. We identify the union of all flow lines of $T$ which intersect $D''$ with $D''\times(0,1]$ such that the second factor corresponds to flow lines of $T$. On $D''\times(0,1]$ the factor $\cos(\vartheta)$ is bounded away from $0$. By \eqref{e:pullback alpha} the plane field $\ker(\alpha)$ extends to a smooth plane field on $D''\times[0,1]$ such that $D''\times\{0\}$ is tangent to the extended plane field. Therefore $\ker(\alpha)$ extends to a continuous plane field on $(D'\times[0,1])\setminus(\partial D'\times\{0\})$ which is a smooth confoliation on $D'\times(0,1]$.
The holonomy of the characteristic foliation on $\partial D''\times[0,1]$ is non-increasing by \lemref{l:neg-curv} when $\partial D''\times\{0\}$ is oriented as the boundary of $D''$. Our orientation assumptions at the beginning of the proof imply that the characteristic foliation on $\partial D'\times(0,1]$ is oriented in the opposite sense. This implies that the Poincar{\'e}-return map of the characteristic foliation around $p$ is non-decreasing.
\end{proof}
\subsection{Legendrian polygons} \mlabel{ss:legpoly}
In the proof of rigidity theorems for tight confoliations and also in \secref{s:discussion} we well use the notion of basins and Legendrian polygons. In this section we adapt the definitions from \cite{El}.
\begin{defn} \mlabel{d:leg poly}
A {\em Legendrian polygon} $(Q,V,\alpha)$ on a compact embedded surface $F$ is a triple consisting of a connected oriented surface $Q$ with piecewise smooth boundary, a finite set $V\subset \partial Q$ and a differentiable map $\alpha : Q\setminus V \longrightarrow F$ which is an orientation preserving embedding on the interior such that
\begin{itemize}
\item[(i)] corners of $Q$ are mapped to singular points of $F(\xi)$,
\item[(ii)] smooth pieces of $\partial Q$ are mapped onto smooth Legendrian curves on $F$,
\item[(iii)] for points $v\in V$ the image $\alpha(b_\pm)$ of the two segments $b_\pm\subset\partial Q\setminus V$ which end at $v$ have the same $\omega$-limit set $\Gamma_v$ and $\Gamma_v$ is not a singular point.
\end{itemize}
A {\em pseudovertex} is a point $x\in\partial Q$ such that $\alpha(x)$ is a hyperbolic singularity and $\alpha|_{\partial Q}$ is smooth at $\alpha(x)$.
\end{defn}
A hyperbolic singularity $\alpha(x)$ on $\alpha(\partial Q)$ can be a pseudovertex only if both unstable or both unstable leaves are contained in $\alpha(\partial Q)$.
The points in $V$ should be thought of as missing vertices in the boundary of $Q$. \figref{b:legpoly} shows the image $\alpha(Q)$ of a Legendrian polygon $(Q,V,\alpha)$ where $Q$ is a disc, $V=\{v\}\subset\partial Q$ and the corresponding ends of $\partial Q\setminus\{v\}$ are mapped to leaves of the characteristic foliation whose $\omega$-limit set is the closed leaf $\gamma_v$. There are three pseudovertices.
\begin{figure}[htb]
\begin{center}
\includegraphics{legpoly}
\end{center}
\caption{\label{b:legpoly}}
\end{figure}
The following definition generalizes the notion of injectivity of a Legendrian polygon to the context of confoliations.
\begin{defn} \mlabel{d:identify}
A Legendrian polygon $(Q,V,\alpha)$ {\em identifies edges} if there are edges $e_1,\ldots,e_l, l\ge 2$ in $\partial Q$ such that $\alpha(e_1)\cup\ldots\cup\alpha(e_l)$ is a cycle containing the image of the pseudovertices lying $e_1,\ldots,e_l$ and leaves of the characteristic foliation such that
\begin{itemize}
\item[(i)] the preimage of each point of the cycle $\gamma_{e_1\ldots e_l}$ except the image of pseudovertices has exactly one element while
\item[(ii)] the preimage of points on the segments and of the images of the pseudovertices consists of exactly two elements.
\end{itemize}
A Legendrian polygon which does not identify edges is called {\em injective}.
\end{defn}
Notice that $\alpha$ may identify vertices even if $(Q,V,\alpha)$ is injective. An example of a Legendrian polygon which identifies three edges such that $\gamma_{e_1e_2e_3}$ is not trivial is shown \figref{b:identify}.
\begin{figure}[htb]
\begin{center}
\includegraphics{identify}
\end{center}
\caption{\label{b:identify}}
\end{figure}
Because $F$ is compact and the singularities of $F(\xi)$ are isolated the limit sets of individual leaves of the characteristic foliation on $F$ belong to one and only one of the following classes (cf. Theorem 2.6.1. of \cite{flows}
\begin{itemize}
\item fixed points,
\item closed leaves,
\item cycles consisting of singular points and leaves connecting them and
\item quasi-minimal sets, ie. closures of non-periodic recurrent trajectories.
\end{itemize}
At this point we use the smoothness of $\xi$ (smoothness of class $C^2$ would suffice).
\begin{lem} \mlabel{l:leg poly}
Let $F\subset M$ be a surface and $\xi$ a confoliation on $M$ such that $\partial F$ is transverse to $\xi$ and the characteristic foliation points inwards along $\partial F$. Assume that $U\subset F$ is a submanifold of dimension $2$ such that every boundary component is either is tangent to $F(\xi)$ or transverse to $\xi$ and the characteristic foliation points outwards.
Let $B(U)$ be the union of all leaves of $F(\xi)$ which intersect $U$. Then $\overline{B(U)}$ has the structure of a Legendrian polygon.
\end{lem}
\begin{proof}
A preliminary candidate for $(Q,V,\alpha)$ is $Q_0:=U, V_0=\emptyset$ and $\alpha$ the inclusion of $Q_0$. We will define vertices and edges of $Q$ and we will glue $1$-handles to components of $\partial Q_0$. The existence of $\alpha$ will be immediate once the correct polygon with all pseudovertices, corners and elliptic singularities and $V$ are defined.
Each intersection of $\partial U$ with a stable leaf of a hyperbolic singularity of $F(\xi)$ defines a vertex of $Q_0$. We obtain a subset $P_0\subset\partial Q_0$ which will serve as a first approximation for the set of pseudovertices. For $p\in P_0$ we denote the corresponding hyperbolic singularity of $F(\xi)$ by $\alpha(p)$.
First we consider the boundary components $\Gamma$ of $Q_0$ which are transverse to $F(\xi)$ and $\Gamma\cap P_0=\emptyset$. All leaves of $F(\xi)$ passing through $\Gamma$ have the same $\omega$-limit set $\Omega(\Gamma)$ (cf. Proposition 14.1.4 in \cite{katok}).
We claim that $\Omega(\Gamma)$ is an elliptic singularity or a cycle: Assume that $\Omega(\Gamma)$ is quasi-minimal. According to Theorem 2.3.3 in \cite{flows} there is a recurrent leaf $\gamma$ which is dense in $\Omega(\Gamma)$. There is a short transversal $\tau$ of $F(\xi)$ such that $|\gamma\cap\tau|\ge 2$ and there are leaves of $F(\xi)$ passing through $\Gamma$ which intersect $\tau$ between two points $p_1,p_2$ of $\gamma\cap\tau$. Because $\gamma$ is recurrent it cannot intersect $\Gamma$. Let $I\subset\tau$ be the maximal open segment lying between $p_1,p_2$ such that the leaves of $F(\xi)$ induce a map from $I$ to $\Gamma$. It follows (as in Proposition 14.1.4. in \cite{katok}) that the boundary points of $I$ connect to singular points of $F(\xi)$ which have to be hyperbolic by our assumptions. These hyperbolic singularities are part of a path tangent to $F(\xi)$ which connects $\Gamma$ with $\tau$ and this path passes only through hyperbolic singularities. This is a contradiction to our assumption $\Gamma\cap P_0=\emptyset$.
Thus if $P_0\cap\Gamma=\emptyset$, then there are two cases depending on the nature of $\Omega(\Gamma)$.
\begin{itemize}
\item If $\Omega(\Gamma)$ is an elliptic singularity respectively a closed leaf of $F(\xi)$, then we place no vertices on $\Gamma$ and $\alpha$ maps $\Gamma$ to the elliptic point respectively the closed leaf while $\alpha=\alpha_1$ outside a collar of $\Gamma$.
\item If $\Omega(\Gamma)$ is a cycle containing hyperbolic points, then we place a corner on $\Gamma$ for each time the cycle passes through a hyperbolic singularity. The map $\alpha|_{\Gamma}$ is defined accordingly.
\end{itemize}
Next we consider a boundary component $\Gamma$ of $Q_0$ which is transverse to $F(\xi)$ and contains an element $p$ of $P_0\cap\Gamma$. Let $\eta$ be an unstable leaf of the corresponding hyperbolic singularity $\alpha(p)$ of $F(\xi)$ and $\Omega(\eta)$ the $\omega$-limit set of $\eta$. Depending on the type of $\Omega(\eta)$ we distinguish four cases.
\begin{itemize}
\item[(i)] $\Omega(\eta)$ is an elliptic singular point. Then we place an elliptic singularity on $\Gamma$ next to the pseudovertex.
\item[(ii)] $\Omega(\eta)$ is a cycle of $F(\xi)$ or a quasi-minimal set. Then we place a point $v$ on $\Gamma$ and add this vertex to to the set of virtual vertices $V_0$.
\item[(iii)] $\Omega(\eta)$ is a hyperbolic point and $\alpha(p)$ is part of a cycle. Some possible configurations in this case are shown in \figref{b:teardrop} (except the top right part). More precisely, the configurations in \figref{b:teardrop} correspond to the case when there are are at most two different hyperbolic singularities of $F(\xi)$ which are connected. This assumption is satisfied for surfaces in a generic $1$-parameter family of embeddings and it would suffice for our applications.
In the present situation we add a $1$-handle to $Q_0$ along $\Gamma$. This defines a new polygon $Q_1$. We define $\alpha_1: Q_1\longrightarrow F$ such that one of two new boundary components is mapped to the cycle containing $\alpha(p)$ and we place a corner on this connected component of $\partial Q_1$ for each time the cycle passes trough a hyperbolic singularity. In particular $p$ is no longer a pseudovertex. Outside a collar of $\Gamma$ we require $\alpha=\alpha_1$.
\item[(iv)] $\Omega(\eta)$ is a hyperbolic singularity and $\alpha(p)$ is not part of a cycle. Then we place a corner on $\Gamma$ which corresponds to $\Omega(\eta)$. We continue with the unstable leaf $\eta'\subset\overline{B_\omega(\Gamma)}$ of $\Omega(\eta)$ and place corners or vertices on $\Gamma$ depending on the nature of the $\omega$-limit set of $\eta'$. One possible configuration is shown in the top right part of \figref{b:teardrop}.
\end{itemize}
\begin{figure}[htb]
\begin{center}
\includegraphics{teardrop}
\end{center}
\caption{\label{b:teardrop}}
\end{figure}
All unstable leaves of hyperbolic singularities in $F(\xi)$ which correspond to elements of $P_0\cap\Gamma$ can be treated in this way.
We iterate the procedure (starting from the choice of pseudovertices) until no new $1$-handles are added and we have treated all occurring boundary components. This process is finite because each hyperbolic singularity can induce the addition of at most one $1$-handle and there are only finitely many hyperbolic singularities on $F$. In the end we obtain a polygon $Q$. The existence of a finite set $V\subset \partial Q$ and the immersion $\alpha: Q\setminus V\longrightarrow F$ with the desired properties follows from the construction.
\end{proof}
\subsection{The elimination lemma}
There are several possibilities to manipulate the characteristic foliation on an embedded surface. Of course one can always perturb the embedding of the surface so that it becomes generic and that the singularities lie in the interior of the contact region $H(\xi)$ or in the interior of its complement. In addition to such perturbations we shall use two other methods.
The first method discussed in this section is called elimination of singularities and it is well known in the context of contact structures. The second method will be described in \secref{s:cutting}.
By a $C^0$-small isotopy of the surface $F$ one can remove a hyperbolic and an elliptic singularity which are connected by a leaf $\gamma$ of $F(\xi)$ if the signs of the singularities agree. The characteristic foliation before the isotopy is depicted in \figref{b:vor-elim}. The segment $\gamma$ corresponds to the thickened segment in the middle of \figref{b:vor-elim}.
\begin{figure}[htb]
\begin{center}
\includegraphics{vor_elim}
\end{center}
\caption{\label{b:vor-elim}}
\end{figure}
After the elimination of a pair of singularities as in \lemref{l:elim} the characteristic foliation on a neighbourhood of $\gamma$ looks like in \figref{b:nach-elim}.
\begin{figure}[htb]
\begin{center}
\includegraphics{nach_elim}
\end{center}
\caption{\label{b:nach-elim}}
\end{figure}
The elimination of singularities plays an important role in Eliashberg's proof of \thmref{t:TB Ungl tight} for tight contact structures.
Below we give a proof of the elimination lemma which applies to confoliations under a condition on the location of the singularities. Usually the elimination lemma is proved using Gray's theorem but this theorem is not available in the current setting (this is explained in \cite{Aeb} for example).
\begin{lem} \mlabel{l:elim}
Let $F$ be a surface in a confoliated manifold $(M,\xi)$. Assume that the characteristic foliation on $F$ has one hyperbolic singularity and one elliptic singularity of the same sign which are connected by a leaf $\gamma$ of the characteristic foliation.
If the elliptic singularity lies in $H(\xi)$, then then there is a $C^0$-small isotopy of $F$ with support in a small open neighborhood $U$ of $\gamma$ such that the new characteristic foliation has no singularities inside of $U$. The isotopy can be chosen such that $\gamma$ is contained in the isotoped surface.
\end{lem}
Note that if $\xi$ is a foliation, then the situation of the lemma cannot arise since all leaves of the characteristic foliations in a neighbourhood of an elliptic singularity are closed.
\begin{proof}[Proof of \lemref{l:elim}]
We assume that both singularities are positive. There is a neighbourhood $U$ of $\gamma$ with coordinates $x,y,z$ such that $\xi\eing{U}$ is defined by the $1$-form $\alpha=dz+a(x,y,z)dy$ such that the function $a$ satisfies $\partial_x a\ge0$. We assume that $\partial_z$ is positively transverse to $\xi$ and $F$, $\{z=0\}\subset F$ and the $x-$axis of the coordinate system contains $\gamma$.
It follows that $\xi\eing{U'}$ can be extended to a confoliation $\xi_c$ on $\mathbb{ R}^3$ which satisfies the assumptions of \lemref{l:neg-curv} if $U'\subset U$ is a ball and $\partial_x$ is tangent to $\partial U'$ along a circle. Since every step in the proof will take place in a fixed small neighbourhood of $\gamma$ we can apply \lemref{l:neg-curv} without any restriction. We choose $\varepsilon>0$ so that $x\subset(-\varepsilon,\varepsilon)\subset U'$ for all $x$ in a neighbourhood $V\subset U'$ of $\gamma$. For a path $\sigma\subset V$ we will consider the hypersurface $T_\sigma=\sigma\times(-\varepsilon,\varepsilon)$. By our choices $T_\sigma(\xi)$ is transverse to the second factor of $T_\sigma$.
Choose a smooth foliation $\mathcal{ I}$ of a small neighbourhood (contained in $U$) of $\gamma$ in $F$ by intervals $I_s, s\in[-1,1]$ as indicated by the dashed lines in \figref{b:vor-elim}. We choose $\mathcal{ I}$ such that it has the following properties.
\begin{itemize}
\item[(i)] Two intervals $I_{s_0},I_{s_1}$ pass through the singularities.
One of them is tangent to the closure of the unstable separatrices of the hyperbolic singularity.
\item[(ii)] All intervals intersecting the interior of $\gamma$ have exactly two tangencies with the characteristic foliation on $F$. The intervals which do not intersect the closure of $\gamma$ are transverse to the characteristic foliation.
\item[(iii)] Let $\sigma$ by a path in $F$ which is shorter than $\delta$ with respect to a fixed auxiliary Riemannian metric. If $\delta>0$ is small enough, then the image of $(\sigma(0),0 )$ under the holonomy along $T_\sigma$ is defined. We assume that the length of each $I_s$ is smaller than $\delta$.
\end{itemize}
We parameterize the leaf $I_s$ by $\sigma_s: [0,1] \longrightarrow F$ such that the intersection of $\gamma$ with $I_s$ is positive (or empty), ie. in \figref{b:vor-elim} the leaves of $\mathcal{ I}$ are oriented towards the upper part of the picture.
The following figures show neighbourhoods of $I_s$ in $T_s:=T_{\sigma_s}$ for certain $s\in[-1,1]$. In each of these figures the dotted line represents $I_s$, oriented from left to right. \figref{b:vorcrittrans} corresponds to a leaf $I_s$ which does not intersect $\gamma$. Then $I_s$ is nowhere tangent to the characteristic foliation on $T_s$. By our orientation conventions and the choice of $\mathcal{ I}$ the slope of $\xi\cap T_s$ is negative along $I_s$.
\begin{figure}[htb]
\begin{center}
\includegraphics{vorcrittrans}
\end{center}
\caption{\label{b:vorcrittrans}}
\end{figure}
The leaves $I_{s_0},I_{s_1}$ contain the singular points of the characteristic foliation on $F$. As shown in \figref{b:critpointtrans} there is exactly one tangency of $F$ and the characteristic foliation on $T_{s_0},T_{s_1}$. The slope of the characteristic foliation on $T_{s_0},T_{s_1}$ is negative along $I_{s_0},I_{s_1}$ except at the point of tangency.
\begin{figure}[htb]
\begin{center}
\includegraphics{critpointtrans}
\end{center}
\caption{\label{b:critpointtrans}}
\end{figure}
Finally, the leaves $I_s,s\in[s_0,s_1]$ intersect the interior of $\gamma$ and $I_s$ is tangent to $F(\xi)$ in exactly two points. This is shown in \figref{b:middletrans}. Between the two points of tangency, the slope of the characteristic foliation on $T_s$ is positive along $I_s$, it is zero at the tangencies and negative at the remaining points of $I_s$.
\begin{figure}[htb]
\begin{center}
\includegraphics{middletrans}
\end{center}
\caption{\label{b:middletrans}}
\end{figure}
We want to find a smooth family of isotopies of the intervals $I_s$ within $T_s$ such that
\begin{itemize}
\item[(i)] for all $s$ the isotopy is constant near the endpoints of $I_s$ and
\item[(ii)] after the isotopy, the intervals $I_s$ are transverse to the characteristic foliation on $T_s$.
\end{itemize}
This will produce the desired isotopy of $F$. Such a family of isotopies exists if and only if the following condition (s) is satisfied for all $s\in[-1,1]$:
\smallskip
{\bf Condition (s):} The image of $\sigma_s(0)\times\{0\}$ under the holonomy along $\sigma_s$ lies {\em below} the other endpoint $\sigma_s(1)\times\{0\}$ of $I_s$ or the leaf of $T_s(\xi)$ which passes through $(\sigma_s(0),0)$ exits $T_s$ through $(\sigma_s,-\varepsilon)\subset \partial T_s$.
\smallskip
Note that this condition is automatically satisfied for $s\in[-1,1]$ if $I_s$ does not intersect $\gamma$ or this intersection point is close enough to a singularity of the characteristic foliation.
If (s) is not satisfied for all $s$, then we will replace $\mathcal{ I}$ by another foliation $\mathcal{ I}'$ by intervals $I_s'$ (the corresponding embeddings of intervals are denoted by $\sigma_s'$) as follows:
\begin{itemize}
\item[(i)] If $I_s$ does not intersect $\gamma$, then $\sigma_s=\sigma'_s$. $I_s'$ intersects $\gamma$ if and only if $I_s$ does.
\item[(ii)] $I_s'$ is tangent to the characteristic foliation on $F$ along two closed intervals (which may be empty or points). The complement of these two intervals is the union of three intervals such that each of these intervals is mapped to a curve of length $\le\delta$.
\item[(iii)] $I_s$ and $I'_s$ coincide on those intervals where the characteristic foliation on $T_s$ has negative slope for all $s\in[-1,1]$.
\item[(iv)] $\overline{I}_s\cup I'_s$ bounds a positively oriented disc (here $\overline{I}_s$ denotes the interval $I_s$ with the opposite orientation).
\end{itemize}
In \figref{b:vor-elim2} the dashed line corresponds to $I_s'$ while the thick solid line represents $I_s$.
\begin{figure}[htb]
\begin{center}
\includegraphics{vor_elim2}
\end{center}
\caption{\label{b:vor-elim2}}
\end{figure}
For $s\in(s_0,s_1)$ we define a curve $I''_s$ by replacing the segment of $I_s$ lying between the tangencies with $F(\xi)$ by two segments of leaves of $F(\xi)$ whose $\mathcal{A}$-limit set is the elliptic singularity in $V$. Then the holonomy on $I''_s\times(-\varepsilon,\varepsilon)$ clearly satisfies the condition (s). This shows that for each $s$ one can choose $I'_s$ with the desired properties.
Moreover, whenever $I_s$ satisfies (s) then so does $I'_s$ by \lemref{l:neg-curv}. It follows that we can choose the foliation $\mathcal{ I}'$ such the leaf $I'_s$ of $\mathcal{ I}'$ satisfies (s) for all $s\in[-1,1]$. The desired isotopy of $F$ can be constructed such that the surface is transversal to $\partial_z$ throughout the isotopy.
\end{proof}
The following lemma is a partial converse of the elimination lemma. Because is only concerned with the region where $\xi$ is a contact structure we omit the proof. It can be found in \cite{El,giroux}.
\begin{lem} \mlabel{l:create}
Let $F\subset M$ be an embedded surface in a confoliated manifold and $\gamma\subset F$ a compact segment of a nonsingular leaf of the characteristic foliation on $F$ which lies in the contact region of $\xi$.
Then there is a $C^0$-small isotopy of $F$ with support in a little neighbourhood of $\gamma$ such that after the isotopy there is an additional pair of singularities (one hyperbolic and ons elliptic) having the same sign. The isotopy can be performed in such a way that $\gamma$ is still tangent to the characteristic foliation and connects the two new singularities.
\end{lem}
We end this section with mentioning a particular perturbation of an embedded surface $F$ which also appears in \cite{El}. Consider an injective Legendrian polygon $(Q,V,\alpha)$ such that there is an elliptic singularity $x$ of $F(\xi)$ such that $\alpha^{-1}(x)$ consists of more than one vertex of $Q$.
Then $F$ can be deformed by a $C^0$-small isotopy near $x$ into a surface $F'$ such that there is a map $\alpha' : Q \longrightarrow F'$ with the same properties as $\alpha$ which coincides with $\alpha$ outside a neighbourhood of $\alpha^{-1}(x)$ and $\alpha'$ maps all vertices in $\alpha^{-1}(x)$ to different elliptic singularities of $F'(\xi)$, cf. \figref{b:split}.
\begin{figure}[htb]
\begin{center}
\includegraphics{split}
\end{center}
\caption{\label{b:split}}
\end{figure}
\subsection{Modifications in the neighbourhood of integral discs} \mlabel{s:cutting}
The second method for the manipulation of the characteristic foliation on an embedded surface $F$ is by surgery of the surface along a cycle $\gamma$ which is part of an integral disc of $\xi$. The latter condition is satisfied when the confoliation is tight and $\gamma$ bounds a disc in $F$ (for example when $F$ is simply connected).
While the elimination lemma is used in the proof of the Thurston-Bennequin inequalities for embedded surfaces in tight contact manifolds, the following lemmas adapt lemmas appearing in \cite{rous, Th} (cf. also \cite{cc}) which are used in the proof the the existence of the Roussarie-Thurston normal form for surfaces in $3$-manifolds carrying a foliation without Reeb components. The existence of this normal forms implies the Thurston-Bennequin inequalities for such foliations.
\begin{lem} \mlabel{l:cut}
Let $F$ be a surface and $\gamma$ a closed leaf of the characteristic foliation on $F$ such that there is a disc $D$ tangent to $\xi$ which bounds $\gamma$ and has $F\cap D=\gamma$.
Then there is a surface $F'$ which is obtained from $F$ by removing an annulus around $\gamma$ and gluing in two discs $D_+,D_-$. The discs can be chosen such that the $D_+(\xi),D_-(\xi)$ have exactly one elliptic singularity in the interior of $D_+,D_-$.
If the germ of the holonomy $h_{\partial D}$ has non trivial holonomy along $\gamma$ on one side of $\gamma$, then we can achieve that the elliptic singularity on the disc on that side lies in the interior of the contact region and every leaf of the characteristic foliation on the new discs connects the singularity with the boundary of the disc.
\end{lem}
\begin{proof}
We will construct the upper disc $D_+$ in the presence of non-trivial holonomy on the upper side of $\gamma\subset F$. The construction of the other disc is analogous.
Fix a closed neighbourhood $U\simeq D\times(-2\varepsilon,2\varepsilon), \varepsilon>0$ of $D$ such that the fibers of $D\times(-\varepsilon,\varepsilon)$ are positively transverse to $\xi$. We assume $F\cap U=\partial D\times(-2\varepsilon,2\varepsilon)$ and we identify $D\times\{0\}$ with the unit disc in $\mathbb{ R}^2$.
By \lemref{l:neg-curv} there is $x\in D$ and $0<\eta<\eta'<\varepsilon$ such that $x\times[\eta,\eta']$ is contained in the interior of the contact region of $\xi$. On $D$ we consider the singular foliation consisting of straight lines starting at $x$. For $t\in[\eta,\eta']$ let $D_t$ be the disc formed by horizontal lifts of leaves of the singular foliation on $D$ with initial point $(x,t)$. By Gray's theorem we may assume that $\xi$ is generic near $x\times[\eta,\eta']$. Then $D_t(\xi)$ is homeomorphic to the singular foliation by straight lines on $D$ and the singularity is non-degenerate for all $t\in[\eta,\eta']$.
Let $\rho : [\eta,\eta']\longrightarrow[1/2,1]$ be a monotone function which is smooth on $(\eta,\eta']$ such that $\rho\equiv 1$ near $\eta'$ and the graph of $\rho$ is $C^\infty$-tangent to a vertical line at $(\eta,1/2)$. We denote the boundary of the disc of radius $\rho(t)$ in $D_t$ by $S_t$. The union of all $S_t,t\in[\eta,\eta']$ with the part of $D_\eta$ which corresponds to the disc with radius $1/2$ is the desired disc $D_+$. We remove the annulus $\partial D\times[0,\eta']$ from $F$ and add $D_+$.
By construction the only singular point of $D_+(\xi)$ is $(x,\eta)$, the singularity is elliptic and contained in the contact region. Its sign depends on the orientation of $F$.
In order to show that all leaves of $D_+(\xi)$ accumulate at the elliptic singularity it is enough to show that there are no closed leaves on $D_+$. Assume that $\tau$ is a closed leaf of $D_+(\xi)$. Let $D_\tau$ be the disc formed by lifts of the leaves of the radial foliation on $D$ with initial point on $\tau$.
The restriction of $\xi$ to $D\times[0,\varepsilon]$ extends to a confoliation $\widetilde{\xi}$ on $\mathbb{ R}^2\times\mathbb{ R}$ which is a complete connection. By \propref{p:complete connection} $\widetilde{\xi}$ is tight. Hence $\tau$ must bound an integral disc of $\xi'$. Now $D_\tau$ is the only possible candidate for such a disc. But $D_\tau$ cannot be an integral disc of $\widetilde{\xi}$ because it intersects the contact region of $\widetilde{\xi}$ (or equivalently $\xi$) in an open set. This contradiction finishes the proof.
\end{proof}
The following two lemmas are analogues to the elimination lemma in the sense that we will remove pairs of singularities. Note however that new singularities can be introduced. In particular in \lemref{l:cut3} we will obtain a surface whose characteristic foliation is not generic. However this will play no role in later applications since the locus of the non-generic singularities will be isolated from the rest of the surface by closed leaves of the characteristic foliation.
\begin{lem} \mlabel{l:cut2}
Let $F$ be a surface in a confoliated manifold, $D$ an embedded disc tangent to $\xi$ and $D\cap F=\gamma$ is a cycle containing exactly one hyperbolic singularity $x_0$.
Then there is a surface $F'$ which coincides with $F$ outside of a neighbourhood of $\gamma$ and is obtained from $F$ by removing a tubular neighbourhood of $\gamma$ and gluing in two discs $D_+,D_-$. The characteristic foliation of $F'$ has no singularities on $D_-$ and one elliptic singularity on $D_+$ whose sign is the opposite of the sign of $x_0$.
\end{lem}
\begin{proof}
The assumptions of the lemma imply that $x_0$ has a stable and an unstable leaf which do not lie on $D$.
Choose a simple curve $\sigma\subset D$ connecting $x_0$ to another boundary point $x_1$ of $D$ such that $\sigma$ is not tangent to a separatrix of $x$ and extend $\sigma$ to a Legendrian curve such that $x_0,x_1$ become an interior points of $\sigma$. Fix a product neighbourhood $U\simeq\widetilde{D}\times(-\varepsilon,\varepsilon)$ of $D$ with the following properties.
\begin{itemize}
\item[(i)] $D$ is contained in the interior of the disc $\widetilde{D}\times\{0\}$.
\item[(ii)] There is a simple Legendrian curve $\sigma\subset \widetilde{D}$ containing $x_0$ in its interior and intersecting $\partial D$ respectively $\partial \widetilde{D}$ in two points such that $\gamma$ is nowhere tangent to $\sigma$ respectively $\partial\widetilde{D}$ is transverse to $\sigma$.
\item[(iii)] The fibers of the projection $\pi:\widetilde{D}\times(-\varepsilon,\varepsilon)\longrightarrow \widetilde{D}$ are transverse to $\xi$.
\end{itemize}
Now consider $T_\sigma=\sigma\times(-\varepsilon,\varepsilon)$. The intersection $T_\sigma\cap F$ has a non-degenerate tangency with $T_\sigma(\xi)$ in $x_0$and meets $\sigma\times\{0\}$ transversely in $x_1$. We choose two points $y_0,y_1\in T_\sigma\cap F$ such that $x_0,x_1$ lie between $\pi(y_0)$ and $\pi(y_1)$, as indicated in \figref{b:cut2}.
\begin{figure}[htb]
\begin{center}
\includegraphics{cut2}
\end{center}
\caption{\label{b:cut2}}
\end{figure}
The points $y_0,y_1$ can be connected by a curve $\hat{\sigma}\subset T_\sigma$ transverse to the characteristic foliation on this strip provided that $y_0,y_1$ are close enough to $\widetilde{D}$. Moreover, we may assume that $\hat{\sigma}$ is tangent to $F$ near its endpoints (cf. the lower dashed curve in \figref{b:cut2}).
The curve $\hat{\sigma}$ is going to be part of $D_-$. In order to finish the construction of $D_-$ we choose a foliation of $\widetilde{D}$ by a family $I_s, s\in\sigma$ of intervals that connect boundary points of $\widetilde{D}$ and are transverse to $\sigma$. The characteristic foliation on $T_{I_s}$ consists of lines which are mapped diffeomorphically to $I_s$ by $\pi$.
If $\hat{\sigma}$ was chosen close enough to $\widetilde{D}$, then there is a smooth family of curves $\hat{I}_s$ in $I_s\times(-\varepsilon,\varepsilon)$ which
\begin{itemize}
\item[(i)] intersect $\hat{\sigma}$ and are tangent to $\xi$ in these points,
\item[(ii)] are transverse to $\xi$ elsewhere and
\item[(iii)] are tangent to $F$ near $y_0,y_1$.
\end{itemize}
The choices we made for $\hat{\sigma}$ and $\hat{I}_s, s\in\sigma$ ensure that the union of all curves $\hat{I}_s$ is a disc $D_-$ which is transverse to $\xi$.
The disc $D_+$ is obtained as in the proof of \lemref{l:cut}. The statement about the sign of the singularity of $D_+(\xi)$ follows from the construction.
\end{proof}
\begin{lem} \mlabel{l:cut3}
Let $F\subset M$ be an embedded surface in a manifold carrying a confoliation $\xi$ such that $F(\xi)$ contains a hyperbolic singularity $x$ and the stable and unstable leaves of $x$ bound an annulus $A\subset F$ which is pinched at $x$. We assume that the pinched annulus is bounded by an integral disc $D$ of $\xi$ such that $\partial A=F\cap D$.
Then there is an embedded surface $F'$ which is obtained from $F$ by removing a neighbourhood of $\gamma$ and gluing in an annulus $A'$ and a disc $D'$ such that $A'(\xi)$ has one of the following properties.
\begin{itemize}
\item[(i)] $A'(\xi)$ has no singularity.
\item[(ii)] The singularities of $A'(\xi)$ form a circle and a neighbourhood in $F'$ of this circle is foliated by closed leaves of $F(\xi')$.
\end{itemize}
The characteristic foliation on $D'$ has exactly one singularity which is elliptic and whose sign is opposite to the sign of $x$.
\end{lem}
\begin{proof}
The disc $D$ in the statement of the lemma is an immersed disc which is an embedding away from two points in the boundary. These two points are identified to the single point $x$. Let $S^1\simeq\sigma\subset D$ be a simple closed curve in $D$ which meets $x$ exactly once.
We choose a solid torus $C=\sigma\times[-1,1]\times[-1,1]$ such that $\sigma=\sigma\times\{(0,0)\}$ and the foliation corresponding to the second factor is Legendrian while the foliation corresponding to the third factor is transverse to $\xi$. For $s\in[-1,1]$ let $A_s=\sigma\times\{s\}\times[-1,1]$. The torus is chosen such that $D\subset\sigma\times[-1,1]\times\{0\}$ and $F$ intersects $A_-=\sigma\times[-1,1]\times\{-1\}$ in two circles while $F\cap (\sigma\times[-1,1]\times\{1\})$ is a circle which bounds is disc in $\sigma\times[-1,1]\times\{1\}$.
If $C$ is thin enough, then a disc $D'$ which bounds $F\cap (\sigma\times[-1,1]\times\{1\})$ with the desired properties can be constructed as in the proof of \lemref{l:cut}.
Let $P_s:=\sigma(s)\times[-1,1]\times[-1,0],s\in S^1$. The characteristic foliation on $P_s$ consists of lines transverse to the last factor of $P_s$ and $\sigma(s)\times[-1,1]\times\{0\}$ is a leaf of $P_s(\xi)$
If $\xi$ one of the annuli $\sigma\times\{t\}\times(-1,0], t\in(-1,1)$ has non-trivial holonomy along $\sigma\times\{(t,0)\}$ or if $\sigma\times\{(t,0)\}$ is not Legendrian, then one can choose a curve $\sigma'$ in that annulus which is transverse to $\xi$. The annulus $A'$ is the union of curves in $P_s, s\in S^1$ which connect the two points of $F\cap(\sigma(s)\times[-1,1]\times\{-1\}$ and pass through $\sigma'\cap P_s$. These curves can be chosen such that they are transverse to $P_s(\xi)$ everywhere except in $\sigma'\cap P_s$. By construction $A'(\xi)$ has the property described in (i) of the lemma.
This construction also applies if we choose $\sigma'$ in annuli which are $C^\infty$-close to $\sigma\times\{t\}\times[-1,0]$ for a suitable $t\in [-1,1]$. If all annuli of this type have trivial holonomy along their boundary curve which is close to $\sigma\times\{(t,0)\}$, then $\xi$ is a foliation on a neighbourhood of $\sigma$ in $\sigma\times[-1,1]\times[-1,0]$ by \lemref{l:neg-curv} whose holonomy along $\sigma$ is trivial. The same construction as in the previous case (with $\sigma'=\sigma$) yields an annulus $A'$ with the properties described in (ii).
\end{proof}
\lemref{l:cut} and \lemref{l:cut2} suffice for \secref{s:rigid} because the embedded surfaces in that section are going to be simply connected. Then one can apply \lemref{l:cut2} to one of the boundary components of the pinched annulus.
In the lemmas of this section we have assumed that $F\cap D=\gamma$. In general $F$ and $D$ may intersect elsewhere. Since all singularities of the characteristic foliation on $\gamma$ are non-degenerate or of birth-death type, there is a neighbourhood of $\gamma$ in $D$ such that $\gamma$ is the intersection of $F$ with this neighbourhood. After a small perturbation with support outside of a neighbourhood of $\gamma$ we may assume that $F$ is transverse to $D$ on the interior of $D$. Now we can apply \lemref{l:cut} a finite number of times to circles in $F\cap D$ in order to achieve that the resulting surface intersects $D$ only along $\gamma$. Then we can apply the lemmas of this section.
\section{Tight confoliations violating the Thurston-Bennequin inequalities} \mlabel{s:example}
The example given in this section shows that tightness (as defined in \defref{d:tight confol}) is a much weaker condition for confoliations compared to the rigidity of tight contact structures or foliations without Reeb components. It also shows that it may happen that {\em every} contact structure obtained by a sufficiently small perturbation of a tight confoliation is overtwisted. This is in contrast to the situation of foliations without Reeb components: According to \cite{colin pert} every foliation without a Reeb component can be approximated by a tight contact structure.
The starting point for the construction of a tight confoliation violating the Thur\-ston-Benne\-quin inequalities is the classification of tight contact structures on $T^2\times I$ such that the characteristic foliation on $T_t=T^2\times \{t\}, t\in\{0,1\}$ is linear (cf. \cite{giroux2}). We fix an identification $T^2\simeq \mathbb{ R}^2/\mathbb{ Z}^2$ and the corresponding vector fields $\partial_1,\partial_2$.
According to \cite{giroux2} (Theorem 1.5) there is a unique tight contact structure $\xi$ on $T^2\times I$ such that
\begin{itemize}
\item[(i)] the characteristic foliation on $\partial(T^2\times I)$ is a pair of linear foliations whose slope is $2$ respectively $1/2$ on $T_0$ respectively $T_1$,
\item[(ii)] the obstruction for the extension of the vector fields which span the characteristic foliation on $\partial (T^2\times I)$ is Poincar{\'e}-dual to $(2,2)\in H_1(T^2;\mathbb{ Z})\simeq\mathbb{ Z}^2$.
\end{itemize}
\figref{b:movie} shows the characteristic foliation on $T^2\times\{t\}$ at various times and its orientation. The two curves in $T^2\times\{1/2\}$ where the characteristic foliation is singular represent the homology class $(2,2)\in H_1(T^2;\mathbb{ Z})$.
\begin{figure}[htb]
\begin{center}
\includegraphics{movie}
\end{center}
\caption{\label{b:movie}}
\end{figure}
We may assume that the contact structure is $T^2$-invariant and tangent to $\partial_t$ on a neighbourhood of the boundary (cf. \cite{giroux}). Then there are smooth functions $f_i,g_i, i\in\{0,1\}$ on this neighbourhood such that $\xi$ is spanned by $\partial_t$ and
\begin{align} \label{e:confol repr}
\begin{split}
f_0(t)\partial_1+g_0(t)\partial_2 & \textrm{ near } T^2\times\{0\} \\
f_1(t)\partial_1+g_1(t)\partial_2 & \textrm{ near } T^2\times\{1\}.
\end{split}
\end{align}
Because $\xi$ is a positive contact structure, the functions $f_i,g_i$ satisfy the inequalities $f_i'(t)g_i(t)-g_i'(t)f_i(t)>0$ for $i\in\{0,1\}$ on their respective domains.
We now modify $\xi$ to a confoliation $\tilde{\xi}$ on $V=T^2\times[0,1]$. For this replace the functions $f_i,g_i$ in \eqref{e:confol repr} by $\tilde{f}_i,\tilde{g}_i$ such that for $i=0,1$
\begin{itemize}
\item $\tilde{f}_i,\tilde{g}_i$ coincide with $f_i,g_i$ outside of small open neighbourhoods of $T^2\times\{i\}$
\item there is $\tau>0$ such that $\tilde{f}_i'(t)\tilde{g}_i(t)-\tilde{g}_i'(t)\tilde{f}_i(t)>0$ if $t\in(\tau,1-\tau)$ and
\item $\tilde{f}_i'(t)\tilde{g}_i(t)-\tilde{g}_i'(t)\tilde{f}_i(t)\equiv 0$ for $t\in[0,\tau]\cup[1-\tau,1]$
\item $\tilde{f}_i,\tilde{g}_i$ coincide with $f_i,g_i$ at $t=0,1$.
\end{itemize}
\begin{rem} \mlabel{r:tight interior}
From the proof of Theorem 1.5 in \cite{giroux2} it follows that the contact structure $\tilde{\xi}$ on $T^2\times(\tau,1-\tau)$ is tight.
\end{rem}
We write $\xi$ for the confoliation constructed so far. In the next step we will extend $\xi$ to a smooth confoliation on $T^2\times[-1,2]$ such that the boundary consists of torus leaves.
Let $h$ be a diffeomorphism of $\mathbb{ R}^+_0$ such that $h(s)<s$ for $s>0$ and all derivatives of $h(s)-s$ vanish for $s=0$. The suspension of this diffeomorphism yields a foliation on $S^1\times\mathbb{ R}^+_0$ whose only closed leaf is $S^1\times\{0\}$ and all other leaves accumulate on this leaf. In this way we obtain a foliation on $S^1\times(S^1\times\mathbb{ R}^+_0)$ such that the boundary is a leaf and the characteristic foliation on $S^1\times (S^1\times \{\sigma\})\simeq T^2\times\{\sigma\}, \sigma>0$ corresponds to the first factor. In particular it is linear.
Using suitable elements of $\{A\in\mathrm{Gl}(2,\mathbb{ Z})|\det(A)=\pm 1\}$ we glue two copies of the foliation on $T^2\times[0,\sigma],\sigma>0$ to $T^2\times[0,1]$. We obtain an oriented confoliation on $T^2\times[-1,2]$ such that the boundary is the union of two torus leaves and we may assume the orientation of the boundary leaves coincides with the orientation of the fiber of $T^2\times[-1,2]$.
After identifying the two boundary components by an orientation preserving diffeomorphism, we get a closed oriented manifold $M$ carrying a smooth positive confoliation which we will denote again by $\xi$.
\medskip
{\it Claim: $\xi$ is tight.}
We show that the assumption of the contrary contradicts \remref{r:tight interior}. Let $\gamma\subset M$ be a Legendrian curve which bounds an embedded disc $D$ in $M$ such that $\xi$ is nowhere tangent to $D$ along $\gamma$ and violates the requirements of \defref{d:tight confol}. By construction $\xi$ has a unique closed leaf $T$. If $\gamma$ is contained in $T$, then $\gamma$ bounds a disc in $T$ because $T$ is incompressible. Thus we may assume that $\gamma$ lies in the complement of $T$ and we can consider the manifold $M\setminus T= T^2\times(-1,2)$.
By \remref{r:tight interior}, $\gamma$ cannot be contained in $T^2\times(\tau,1-\tau)$. If $\gamma$ lies completely in the foliated region $T^2\times\big((-1,\tau]\cup[1-\tau,2)\big)$, then it bounds a disc in its leaf because all leaves are incompressible cylinders.
It remains to treat the case when the $\gamma$ intersects the contact region and the foliated region. All leaves of $\xi$ in $M\setminus T= T^2\times(-1,2)$ are cylinders which can be retracted into the region $T^2\times[0,\tau)\cup(1-\tau,1]$. Hence we may assume that $\gamma$ is contained in $T^2\times[0,1]$.
First we show that there is a Legendrian isotopy of $\gamma$ such that the resulting curve is transverse to the boundary of the contact region $B=T^2\times\{\tau,1-\tau\}$. A similar isotopy will be used later, therefore we describe it in detail.
Let $T^2\times(0,\tau')$ with $0<\tau<\tau'$ be a neighbourhood of one component of $B$ where $\xi$ can be defined by the $1$-form
$$
\alpha_0=dx_1-\frac{\tilde{f}_0(t)}{\tilde{g}_0(t)}dx_2.
$$
We consider the projection $\mathrm{pr} : T^2\times[0,\tau']\longrightarrow S^1\times[0,\tau']$ such that the fibers are tangent to $\partial_1$. Note that $d\alpha_0$ is the lift of the $2$-form
$$
\omega=\frac{\tilde{f}_i'(t)\tilde{g}_i(t)-\tilde{g}_i'(t)\tilde{f}_i(t)}{\tilde{g}_0^2(t)}dx_2\wedge dt.
$$
The fibers of $\mathrm{pr}$ are transverse to $\xi$. Let $\hat{\gamma}$ be a segment of $\gamma$ which is contained in $T^2\times[0,\tau']$ and whose endpoints do not lie on $B$.
If $\hat{\gamma}$ is contained in the foliated part of $\xi$, then we isotope $\hat{\gamma}$ within its leaf such that the resulting curve is disjoint from $T^2\times\{\tau\}$ and the isotopy does not affect the curve on a neighbourhood of its endpoints.
Now assume that some pieces of $\hat{\gamma}$ are contained in the contact region of $\xi$. Then $\mathrm{pr}(\hat{\gamma})$ passes through the region of $S^1\times(\tau,\tau']$ where $\omega$ is non-vanishing. We consider an isotopy of the projection of $\hat{\gamma}$ which is fixed near the endpoints and the area of the region bounded by $\hat{\gamma}$ is zero for all curves in the isotopy. By Stokes theorem this implies that one obtains closed Legendrian curves when $\hat{\gamma}$ is replaced by horizontal lifts of curves of the isotopy (with starting point on $\gamma$).
Hence we may assume that $\gamma$ is transverse to $T^2\times\{\tau\}$ and $\gamma$ is decomposed into finitely many segments whose interior is completely contained in either the contact region or the foliated region of $\xi$.
Let $\gamma_0\subset\gamma$ be an arc with endpoints in the contact region of $\xi$ such that $\gamma_0$ contains a exactly one sub arc of $\gamma$ lying in the foliated region. Because $\gamma_0$ is embedded, it bounds a compact half disc in a leaf tangent to $\xi$ and we can choose $\gamma_0$ such that the half disc does not contain any other segment of $\gamma$.
Now we isotope $\gamma_0$ relative to its endpoints such that after the isotopy this segment lies completely in the contact region of $\xi$. As above we deform $\mathrm{pr}(\gamma_0)$ through immersions such that the resulting arc $\hat{\gamma}_0$ has the following properties
\begin{itemize}
\item the integral of $\omega$ over the region bounded by $\hat{\gamma}_0$ and $\mathrm{pr}(\gamma_0)$ is zero and the same condition applies to every curve in the isotopy,
\item $\hat{\gamma}_0$ is completely contained in $S^1\times(\tau,\tau']$.
\end{itemize}
Then the horizontal lift of $\hat{\gamma}_0$ can be chosen to have the same endpoints as $\gamma_0$ and we can replace $\gamma_0$ by this horizontal lift. The resulting curve is Legendrian isotopic to $\gamma$ but it the number of pieces which lie in the foliated region has decreased by one.
After finitely many steps we obtain a Legendrian isotopy between $\gamma_0$ and a closed Legendrian curve which lies completely in the interior of the contact region. The Thurston-Bennequin invariant of the resulting curve is still zero. But this is impossible because the contact structure on $T^2\times(\tau,1-\tau)$ is tight.
\medskip
{\it Claim: If $M=T^3$, then $\xi$ violates b) of \thmref{t:TB Ungl tight}.}
The trivialization of $\xi$ induced by the characteristic foliation on $T^2\times\{0,1\}$ extends to the complement of $T^2\times[0,1]$ in $T^3$. The obstruction for the extension of the trivialization from $T^2\times\{0,1\}$ to $T^2\times[0,1]$ is Poincar{\'e}-dual to $(1,1)\in H_1(T^2\times[0,1])$. Hence $e(\xi)$ is Poincare-dual to $(2,2,0)\in H^1(T^2)\oplus \mathbb{ Z}$ where the second factor corresponds to the homology of the second factor of $T^3\simeq T^2\times S^1$. This means that $\xi$ violates the Thurston-Benneuqin inequalities since these inequalities imply $e(\xi)=0$ because every homology class in $t^3$ can be represented by a union of embedded tori.
An example of a torus in $(T^3,\xi_T)$ which violates the Thurston-Bennequin inequality can be described very explicitly. Let $T_0$ be the torus which is invariant under the $S^1$-action transverse to the fibers and it intersects each fiber in a curve of slope $-1$, hence this curve represents $(1,-1)\in H_1(T^2)$ when $T_0$ is suitably oriented. It follows from the description of $\xi$ given above, that $\tau=T_0\cap (T^2\times\{1/2\})$ is Legendrian and the characteristic foliation on $T_0$ has exactly four singular points which lie on $\tau$ and have alternating signs.
Moreover, $T_0\cap T$ is a Legendrian curve and $\xi$ is transverse to all tori $T^2\times\{t\}, t\in(-1,2)$ except in the singular points on $T_0\cap(T^2\times\{1/2\})$. \figref{b:starfish} shows a singular foliation homeomorphic to the one on $T_0$.
\begin{figure}[htb]
\begin{center}
\includegraphics{starfish}
\end{center}
\caption{\label{b:starfish}}
\end{figure}
We choose the orientation of $T_0$ such that $e(T_0)=-4$. In order to find an example of a surface with boundary which violates the inequality c) from \thmref{t:TB Ungl tight} it suffices to remove a small disc containing one of the elliptic singularities in $T_0$.
Finally, note that according to \cite{confol} every positive confoliation can be approximated (in the $C^0$-topology) by a contact structure, it follows that tightness is {\em not} an open condition in the space of confoliations with the $C^0$-topology. Actually $\xi$ can be approximated by contact structures which are $C^\infty$-close to $\xi$. This can be seen by going through the proof of Theorem 2.4.1 and Lemma 2.5.1 in \cite{confol}: By construction the holonomy of the closed leaf on $T_0$ is attractive, therefore it satisfies conditions which imply the conclusion of Proposition 2.5.1, \cite{confol} (despite of the fact that the infinitesimal holonomy is trivial). The main part of this lemma is stated in \lemref{l:reminder on holonomy approx} together with an outline of the proof.
Thus tightness is not an open condition for confoliations in general. This answers question 1 from the section 3.7 in \cite{confol} (when tightness is defined as in \defref{d:tight confol}).
\section{Rigidity results for tight confoliations} \mlabel{s:rigid}
The example from the previous section shows that tight confoliations are quite flexible objects compared to tight contact structures and foliations without Reeb components. In this section we establish some restrictions on the homotopy class of plane fields which contain tight confoliations.
The first restriction is the Thurston-Bennequin inequality for simply connected surfaces. Note that this imposes no restriction on the Euler class $e(\xi)$ of a tight confoliation $\xi$ on a closed manifold $M$ unless the prime decomposition of $M$ contains $(S^1\times S^2)$-summands. The second restriction on the homotopy class of $\xi$ is a consequence of
\begin{thm} \mlabel{t:tight on balls}
Let $M$ be a manifold carrying a tight confoliation $\xi$ and $B\subset M$ a closed embedded ball in $M$. There is a neighbourhood of $\xi$ in the space of plane fields with the $C^0$-topology such that $\xi'\eing{B}$ is tight for every contact structure $\xi'$ in this neighbourhood.
\end{thm}
The proof of this theorem is given in \secref{s:perturb}. Let us explain an application of \thmref{t:tight on balls} which justifies the claim that \thmref{t:tight on balls} is a rigidity statement about tight confoliations.
By \thmref{t:El-Th approx} every confoliation on a closed manifold can be $C^0$-approximated by a contact structure unless it is a foliation by spheres. Hence \thmref{t:tight on balls} can be applied to every confoliation. Recall the following theorem.
\begin{thm}[Eliashberg, \cite{El}] \mlabel{t:ball class}
Two tight contact structures on the $3$-ball $B$ which coincide on $\partial B$ are isotopic relative to $\partial B$.
\end{thm}
It follows from this theorem that two tight contact structures on $S^3$ are isotopic and therefore homotopic as plane fields. In contrast to this every homotopy class of plane fields on $S^3$ contains a contact structure which is not tight. Thus the following consequence of \thmref{t:tight on balls} shows that there are restrictions on the homotopy classes of plane fields containing tight confoliations.
\begin{cor}
Only one homotopy class of plane fields on $S^3$ contains a positive tight confoliation.
\end{cor}
\begin{proof}
Let $\xi$ be a tight confoliation on $S^3$. It is well known that every foliation of rank $2$ on $S^3$ contains a Reeb component, cf. \cite{No}. Thus $H(\xi)$ is not empty. We choose $p\in H(\xi)$ and a ball $B\subset H(\xi)$ around $p$.
According to \cite{confol} $\xi$ can be $C^0$-approximated by a contact structure $\xi'$ on $S^3$ such that $\xi$ and $\xi'$ coincide on $B$. By \thmref{t:tight on balls} the restriction of $\xi'$ to $S^3\setminus B$ is tight and by a result from \cite{colin} $\xi'$ is a tight contact structure on $S^3$ which is homotopic to $\xi$.
\end{proof}
More generally, \thmref{t:tight on balls} together with \thmref{t:ball class} implies that the homotopy class of a tight confoliation $\xi$ as a plane field is completely determined by the restriction of $\xi$ to a neighbourhood of the $2$-skeleton of a triangulation of the underlying manifold.
\subsection{The Thurston-Bennequin inequality for discs and spheres} \mlabel{s:tb sphere disc}
In this section we prove the Thurston-Bennequin inequalities for a tight confoliation $\xi$ in the cases where $F$ is a sphere or a disc (with transverse boundary). For this we adapt the arguments in \cite{El}. We shall discuss why Eliashberg's proof cannot be adapted for non-simply connected surfaces in tight confoliations after the proof \thmref{t:discs and spheres}. Recall that the self-linking number $\mathrm{sl}(\gamma,F)$ of a null-homologous knot $\gamma$ which is positively transverse to $\xi$ with respect to a Seifert surface $F$ satisfies $e(\xi)[F]=-\mathrm{sl}(\gamma,F)$ where $e(\xi)[F]$ corresponds to the obstruction for the extension the characteristic foliation near $\partial F$ to a trivialization of $\xi\eing{F}$.
\begin{thm} \mlabel{t:discs and spheres}
Let $(M,\xi)$ be a manifold with a tight confoliation. Then
\begin{itemize}
\item[a)] $e(\xi)[S^2]=0$ for every embedded $2$-sphere $S^2\subset M$ and
\item[b)] $\mathrm{sl}(\partial D, D)\le -1$ for every embedded disc whose boundary is positively transverse to $\xi$.
\end{itemize}
\end{thm}
\begin{proof}
We perturb the surface such that it becomes generic and the elliptic singularities lie in the interior of $H(\xi)$ or in the interior of the foliated region. Furthermore, we will assume in the following that there are no connections between different hyperbolic singularities of characteristic foliations.
We show $e(\xi)[D]\ge 1$ for every disc as in b). By the Poincar{\'e} index theorem
\begin{align} \label{e:chie}
\begin{split}
\chi(D) & = e_+(D) + e_-(D) -h_+(D) - h_-(D) \\
e(\xi)(D) & = e_+(D) - e_-(D) - h_+(D) + h_-(D).
\end{split}
\end{align}
Subtracting these equalities we obtain $\chi(D)- e(\xi)[D]=2(e_--h_-)$. In order to prove the b) it suffices to replace $D$ by an embedded disc $D'$ with $e(\xi)[D]=e(\xi)[D']$ such that $D'$ contains no negative elliptic singularities.
Because $\xi$ is tight and $D$ is simply connected each cycle of $D(\xi)$ is the boundary of an integral disc. We can apply \lemref{l:cut} or \lemref{l:cut2} to such discs to obtain a new embedded disc $D'$. By (iii) of \defref{d:tight confol} $e(\xi)[D]=e(\xi)[D']$.
We now choose particular cycles of $D(\xi)$ to which we apply \lemref{l:cut} and \lemref{l:cut2}: Define $\gamma\le\gamma'$ for two cycles $\gamma,\gamma'$ of the characteristic foliation if $\gamma'$ bounds an embedded disc containing $\gamma$. We apply \lemref{l:cut} and \lemref{l:cut2} to cycles which are maximal with respect to $\le$. This means in particular that the holonomy of maximal cycles which are closed leaves of $D(\xi)$ is not trivial on the outer side of the cycle.
Hence we obtain a disc $D'$ whose characteristic foliation does not have closed cycles and all elliptic singularities are contained in $H(\xi)$. In particular there are no integral discs of $\xi$ which pass though elliptic singularities of the characteristic foliation of $D$. Moreover, $e(\xi)[D]=e(\xi)[D']$. From now on we will write $D$ instead of $D'$.
Adapting arguments from \cite{El} we eliminate one negative elliptic singularity $y$. Let $U$ be a disc such that $\partial U$ is transverse to $D(\xi)$ and $y\in U$. According to \lemref{l:leg poly} there is a Legendrian polygon $(Q,V,\alpha)$ covering $\overline{B(U)}$. In the present situation $V=\emptyset$ since $D(\xi)$ has no cycles or exceptional minimal sets.
Note that $B(U)\subset D$ because the characteristic foliation is pointing outwards along $\partial D$. After a small perturbation of $D$ we may assume that $\alpha$ identifies vertices of $\partial Q$ only if adjacent edges are also identified, for elliptic vertices this is illustrated in \figref{b:split}. In this situation all boundary components of $\partial\overline{B(y)}$ are embedded piecewise smooth circles.
Recall that $D(\xi)$ contains no cycles. Then every boundary component $\gamma_{o}$ of $\overline{B(y)}$ therefore contains an elliptic singularity (which has to be positive). If all singularities of $D(\xi)$ on $\gamma_{o}$ are positive, then we obtain a contradiction to the tightness of $\xi$. Hence $\gamma_{o}$ contains a negative singularity which has to be hyperbolic. According to our assumptions it is a pseudovertex of the Legendrian polygon, ie. its unstable leaf ends at $y$ while the other unstable leaf never meets $B(y)$.
Therefore the application of the elimination lemma (\lemref{l:elim}) does not create new cycles on the disc. We continue with the elimination of negative elliptic singularities until $e_-=0$. This finishes the proof of b)
Now we come to the prove of a). First we use \lemref{l:cut} and \lemref{l:cut2} in order to decompose $S$ into a disjoint union of embedded spheres such that there are no cycles which contain hyperbolic singularities. In the following we consider each sphere individually, so we continue to write $S$. If $S(\xi)$ contains a closed leaf, then the claim follows immediately from the definition of tightness: Let $D_1,D_2\subset S$ be the two discs with $\partial D_1=\gamma=\partial D_2$. Then there is an integral disc $D'$ of $\xi$ such that $\partial D'=\gamma$. We orient $D'$ such that $D_1\cup D'$ is a cycle and denote by $-D'$ the disc with the opposite orientation. Then $[S]=[D_1\cup D']+[(-D')\cup D_2]$ and the claim follows from (iii) of \defref{d:tight confol} applied to $D_1,D_2$:
$$
e(\xi)[S]=e(\xi)[D_1\cup D'] + e(\xi)[(-D')\cup D_2]=0.
$$
Finally if $S(\xi)$ has neither closed leaves or cycles, then one can prove a) using b) when one considers complements of small discs around positive or negative elliptic singularities.
\end{proof}
Consider a Legendrian polygon $(Q,V,\alpha)$ in $F\subset M$ when $\xi$ is a contact structure on $M$. Generically the characteristic foliation on $F$ is of Morse-Smale type (cf. \cite{giroux}). In particular there are no quasi-minimal sets. If the set of virtual vertices of the Legendrian polygon $(Q,V,\alpha)$ associated to $U$ is not empty, then by \lemref{l:create} one can create of a canceling pair of singularities along on $\gamma_v$ for $v\in V$ such that all leaves which accumulated on $\gamma_v$ now accumulate on an elliptic or a hyperbolic singularity.
For this reason the case $V\neq\emptyset$ plays essentially no role when $\xi$ is a contact structure. If the $\omega$-limit set of $\gamma$ is contained in the fully foliated part of $\xi$, then it not possible to apply \lemref{l:create} (cf. \secref{s:example}). It is at this point where the proof of the Thurston-Bennequin inequalities for tight contact structures fails when one tries to adapt the arguments from \cite{El} to tight confoliations and surfaces which are not simply connected.
We finish this section with a remark that will be useful later.
\begin{rem} \mlabel{r:d+}
Let $\xi$ be a tight confoliation. For an embedded surface $F\subset M$ we define $d_\pm(F)=e_\pm(F)-h_\pm(F)$ for open subsets of $F$. Note that if $F$ is a sphere, then $d_+(F)=d_-(F)=1$ by \thmref{t:discs and spheres} and $\chi(F)=2$.
Part b) \thmref{t:discs and spheres} can be strengthened: It is not only possible to replace $D$ be a disc with the same boundary and $e(\xi)[D]=e(\xi)[D']$ such that $D'(\xi)$ has no negative elliptic singularities. Consider $\alpha$-limit set of stable leaves of positive hyperbolic singularities of $D'$. Since $D'(\xi)$ contains no cycles the $\alpha$-limit set is generically a positive elliptic singularity. Thus we may eliminate all negative elliptic and all positive hyperbolic singularities from $D'(\xi)$. This implies the following inequalities:
\begin{align*}
d_-(D) & =e_-(D)-h_-(D)= e_-(D')-h_-(D')\le 0 \\
d_+(D) & =e_+(D)-h_+(D)= e_+(D')-h_+(D')\ge 0
\end{align*}
In a later application we shall consider discs such that $\partial D$ is negatively transverse to $\xi$. Then the two inequalities above will be interchanged.
\end{rem}
\subsection{Perturbations of tight confoliations on balls} \mlabel{s:perturb}
The proof \thmref{t:tight on balls} is given in the following sections. It has two main ingredients: First we generalize taming functions on spheres to confoliations. We show that the characteristic foliation on an embedded sphere $S$ can be tamed if $\xi$ is tight and that this remains true for contact structures $\xi'$ which are close enough to $\xi$. Then we apply arguments from \cite{giroux2} to conclude that $\xi'|B$ is tight if $\xi'$ is a contact structure.
In the following sections $\xi$ will always be an oriented tight confoliation on $M$ and $S$ denotes an embedded oriented sphere. We do not consider foliations by spheres.
\subsubsection{Properties of characteristic foliations on spheres}
The tightness of $\xi$ leads to restrictions on the signs of hyperbolic singularities on $\gamma$. \lemref{l:signs in cycles on spheres} is concerned with signs of hyperbolic singularities on cycles of $S(\xi)$ when $\xi$ is a tight confoliation. To state it we need the following definition:
\begin{defn}
A cycle connected $\gamma$ of $S(\xi)$ is an {\em internal subcycle} if there is another cycle $\gamma'$ of $S(\xi)$ such that $\gamma\cap\gamma'$ is not empty and the integral disc which bounds $\gamma'$ contains the integral disc which bounds $\gamma$.
A leaf $\gamma$ of $S(\xi)$ is called {\em internal} if there are two cycles of $S(\xi)$ which bound discs tangent to $\xi$ whose interiors are disjoint. We say that a hyperbolic singularity on $\gamma$ is {\em essential} if it is not lying on an internal subcycle of $\gamma$.
The union of singular points and cycles of $S(\xi)$ will be denoted by $\Sigma(S)$. This set is compact.
\end{defn}
An example of an internal subcycle is shown in \figref{b:fol-taming-ex}. Note that one can create internal cycles intersecting a fixed cycle of $S(\xi)$ with arbitrary sign using an inverse of the construction explained in \lemref{l:cut2}.
If a connected cycle $\gamma$ of $S(\xi)$ contains hyperbolic singularities, then the holonomy along $\gamma$ can be defined at most on one side. The one-sided holonomy is defined if and only if there is an immersion of a disc $D$ into $S$ which is an embedding on $\ring{D}$ and $\partial D$ is mapped onto $\gamma$ such that the image of $\ring{D}$ does not contain a stable or unstable leaf of a hyperbolic singularity on $\gamma$. We will say that $D$ is a disc in $S$ although some points on the boundary may be identified.
The singularities on $\gamma$ can be decomposed into two classes
\begin{align*}
A(\gamma) & = \{ \textrm{hyperbolic singularities on }\gamma \textrm{ such that } \gamma \textrm{ contains}\\
& \quad \textrm{ both stable leaves}\} \\
B(\gamma) & = \{ \textrm{hyperbolic singularities on }\gamma \textrm{ such that } \gamma \textrm{ contains}\\
& \quad \textrm{ only one of the two stable leaves}\}.
\end{align*}
Let $\gamma$ be a cycle of $S(\xi)$ and $D\subset S$ a disc with $\partial D=\gamma$ whose interior does not contain a stable leaf of a hyperbolic singularity on $\gamma$. Then the one-sided holonomy along $\gamma$ is well defined. Because $\xi$ is tight there is a disc $D'$ tangent to $\xi$ such that $\partial D' = \gamma$. We orient $D'$ using the orientation of $\xi$.
\begin{defn} \mlabel{d:pot}
We say that $\gamma$ is {\em potentially attracting} if
\begin{itemize}
\item[(i)] $D$ lies below respectively above $D'$ (with respect to the coorientation of $\xi$) in a neighbourhood of $D'$ and
\item[(ii)] the orientation of $\gamma$ is opposite respectively equal to the orientation of $\partial D'$.
\end{itemize}
In the opposite case, $\gamma$ is {\em potentially repulsive}.
\end{defn}
According to \lemref{l:neg-curv} the holonomy along potentially repulsive respectively attractive cycles is non-repelling respectively non-attracting. The terminology of \defref{d:pot} is introduced to deal with the case when the holonomy is trivial (and therefore non-repelling and non-attracting at the same time).
\begin{lem} \mlabel{l:signs in cycles on spheres}
Let $\gamma$ be a cycle of $S(\xi)$ containing a hyperbolic singularity and such that the one-sided holonomy is defined.
Then all essential singularities in $A(\gamma)$ have the same sign and all essential singularities in $B(\gamma)$ have the opposite sign. The one-sided holonomy is potentially attractive (respectively repulsive) if and only if all singularities in $A(\gamma)$ are negative (respectively positive) and all singularities in $B(\gamma)$ are positive (respectively negative).
The signs of the non-essential singularities in $A(\gamma)$ respectively $B(\gamma)$ is opposite to the sign of the essential singularities in $A(\gamma)$ respectively $B(\gamma)$.
\end{lem}
\begin{proof}
Let $D\subset S$ be the disc in $S$ with $\partial D=\gamma$ such that the one-sided holonomy is defined on the side of $\gamma$ where $D$ is lying. Because $\xi$ is tight, there is a disc $D'$ tangent to $\xi$ which bounds $\gamma$. Consider a tubular neighbourhood of $D'$ which contains a collar of $\partial D$ and the collars lies on one side of $D'$ in the tubular neighbourhood.
The statement about the signs of singularities now follows by looking how $D$ approaches $D'$ near the tangencies and the relation between the signs and the holonomy is a consequence of our orientation conventions and \lemref{l:neg-curv}. \end{proof}
The following proposition is a generalization of Lemma 4.2.1 in \cite{El}. It will play an important role in the proof of \thmref{t:tight on balls}.
\begin{prop} \mlabel{p:basins in spheres}
Let $\xi$ be a tight confoliation on $M$ and $S\subset M$ an embedded sphere such that the singularities of $S(\xi)$ are non-degenerate.
Let $U\subset S$ be a connected submanifold of dimension $2$ such that $\partial U$ is transverse to $S(\xi)$ and $S(\xi)$ points outwards along $\partial U$. Each connected component $\Gamma$ of the boundary the associated Legendrian polygon $(Q,V,\alpha)$ has the following properties.
\begin{itemize}
\item[(i)] If there is a negative elliptic singularity $x$ on $\alpha(\Gamma)$ such that $\alpha(Q)$ is not a neighbourhood of $x$ or a cycle $\gamma_v$ with $v\in V\cap \Gamma$ such that $\alpha(Q)$ is not a one-sided neighbourhood of $\gamma_v$, then $\alpha(\Gamma)$ contains a positive pseudovertex.
\item[(ii)] If $d_+(U)=1$ and $(Q,V,\alpha)$ identifies the edges $e_1,\ldots,e_l$ of $\Gamma$, then $\alpha$ maps the pseudovertices on $e_1,\ldots,e_l$ to negative hyperbolic singularities of $S(\xi)$.
\end{itemize}
\end{prop}
\begin{proof}
It was shown in \lemref{l:leg poly} that $\overline{B(U)}$ is covered by a Legendrian polygon $(Q,V,\alpha)$. Recall that $\alpha$ is defined only on $\Gamma\setminus(\Gamma\cap V)$, but we shall denote $\alpha(\Gamma\setminus(\Gamma\cap V))$ by $\alpha(\Gamma)$.
First we reduce the situation to the case when $V=\emptyset$. By the theorem of Poincar{\'e}-Bendixon, the $\omega$-limit sets corresponding to points of $V$ are cycles. Because $\xi$ is tight, these cycles bound integral discs of $\xi$ and we can apply \lemref{l:cut} or \lemref{l:cut2}.
Since the discs bounding these cycles may intersect $U$ it is also necessary to consider cycles in $U$.
Let $v\in V$ and $D_v$ the integral disc of $\xi$ which bounds $\gamma_v$ and $\gamma_i$ a cycle of $S(\xi)$ which is contained in $D_v$. We assume that the disc $D_i\subset D_v$ bounded by $\gamma_i$ intersects $S$ only along $\gamma_i$. The cycle $\gamma_{i}$ is either contained in $U$ or in the complement of $U$.
We begin with the case $\gamma_i\subset U$. In this case we obtain two embedded spheres $S',S''$ by cutting along $\gamma_{i}$. When we use \lemref{l:cut} for this the subset $U\subset S$ induces two subsets $U'\subset S', U''\subset S''$ such that $U'$ respectively $U''$ contains one positive respectively one negative singularity in addition to singularities which were already present in $S$, $\partial U'$ respectively $\partial U''$ is transverse to $S'(\xi)$ respectively $S''(\xi)$ and the characteristic foliation points outwards. The pseudovertices of the Legendrian polygons associated to the basins of $U',U''$ coincide with the pseudovertices of $(Q,\alpha,V)$.
If $d_+(U)=1$, then
\begin{align}
\begin{split} \label{e:d+ spaltung}
d_+(U')+d_+(U'')& = d_+(U)+1 \\
d_+(S'\setminus U')+d_+(U') & = d_+(S')=1 \\
d_+(S''\setminus U'')+d_+(U'') & = d_+(S'')=1.
\end{split}
\end{align}
Notice that $(S'\setminus U')\cup (S''\setminus U'')=S\setminus U$ and $\partial(S\setminus U)$ is negatively transverse to $S_\xi$. It follows from \remref{r:d+} that $d_+(S'\setminus U')\le 0$ and $d_+(S''\setminus U'')\le 0$. Together with \eqref{e:d+ spaltung} this implies $d_+(U')=d_+(U'')=1$.
If we applied \lemref{l:cut2} and the hyperbolic singularity was positive respectively negative, then $h_+(U'\cup U'')=h_+(U)-1$ respectively $e_+(U'\cup U'')=e_+(U)+1$ and one of the sets, say $U'$ coincides with $U$. Then $d_+(U)=1$ implies $d_+(U'')=1$.
When $\gamma_{i}$ lies in the complement of $U$, cutting along $\gamma_{i}$ will not affect $U$ or $d_+(U)$ but the basin of $U$ can change: We might remove a virtual vertex, or after the surgery process some boundary components of the Legendrian polygon might be mapped to a negative elliptic singularity while they were accumulated on a cycle before. The pseudovertices are not affected. Note also that if $\alpha(Q)$ is a one--sided neighbourhood of a cycle $\gamma_v$, then the Legendrian polygon which results from the surgery along $\gamma_v$ will be a neighbourhood of the negative elliptic singularity which results from surgery process. (Recall that $\gamma_v$ has well defined attractive one--sided holonomy on the side of $\alpha(Q)$).
After finitely many steps we obtain a finite union of embedded spheres $S_j$ and subsets $U_j$ with the same properties as $U$ such that the associated Legendrian polygon $(Q_j,V_j,\alpha_j)$ satisfies $V_j=\emptyset$. Therefore is suffices to prove the claim when $\overline{B(U)}$ is covered by a Legendrian polygon $(Q,V,\alpha)$ with $V=\emptyset$. Let $\Gamma$ be a boundary component of $Q$.
We now prove (i). Let $x\in\alpha(\Gamma)$ be an elliptic singularity such that $\overline{\alpha(Q)}$ is not a neighbourhood of $x$. Then the connected component of $\partial(\alpha(Q))$ containing $x$ is a piecewise smooth closed curve $c$. After a perturbation of the sphere we may assume that $c$ does not contain corners, $x\in H(\xi)$ and $c$ is embedded (cf. \figref{b:split}). If all singularities on $c$ were negative, then we would get a contradiction to the tightness of $\xi$ since no integral surface of $\xi$ can meet $x$. Since all elliptic singularities on $c\subset\alpha(\partial Q)$ are attractive and therefore negative there must be a positive pseudovertex on $c$.
It remains to prove (ii). Assume $d_+(U)=1$ and let $x_1,\ldots,x_l,l\ge 2$ be the pseudovertices on the edges $e_1,\ldots,e_l\subset\Gamma$.
When $\alpha(e_i)=\alpha(e_j)$ for $i\neq j$, then $l=2$. Let $\eta,\eta'$ be the two stable leaves of $\alpha(x_1)$. After a small perturbation of $S$ in the complement of $U$ we may assume that the $\alpha$-limit sets of $\eta,\eta'$ are contained in $U$.
If $\alpha(e_i)\neq\alpha(e_j)$ for all $i\neq j$, then let $\alpha(x_i),\alpha(x_j)$ be two hyperbolic singularities which lie on the cycle associated to identified edges (cf. \defref{d:identify}) and are connected by a piecewise smooth simple oriented path $\sigma$ in the complement of $U$ consisting of leaves of $S(\xi)$ and hyperbolic singularities (as corners) such that $\sigma$ starts at $\alpha(x_i)$ and ends at $\alpha(x_j)$ without passing through images of other pseudovertices. After a small perturbation of $S$ in the neighbourhood of $\alpha(x_j)$ we obtain a sphere $S'$ such that the $\alpha$-limit sets $\mathcal{A}(\eta),\mathcal{A}(\eta')$ of the two stable leaves $\eta,\eta'$ of $\alpha(x_i)$ are contained in $U$.
We may assume that neither $\mathcal{A}(\eta)$ or $\mathcal{A}(\eta')$ is a hyperbolic singularity or a singularity of birth-death type. By the Poincar{\'e}-Bendixon theorem $\mathcal{A}(\eta)$ is either an elliptic singularity or a cycle. The same is true for $\mathcal{A}(\eta')$. Using \lemref{l:cut} and \lemref{l:cut2} we can ensure that $\mathcal{A}(\eta)$ is an elliptic singularity, which has to be positive. Note that $\eta,\eta'$ lie in the same connected component of the two spheres obtained by the surgery along cycles in $U$.
For the same reason we may assume that the $\alpha$-limit set of each stable leaf of hyperbolic singularities in $U$ is an elliptic singularity in $U$. Under these conditions the hypotheses $d_+(U)=1$ implies that the graph formed by positive singularities (except birth-death type singularities) and stable leaves of hyperbolic singularities is a connected tree.
Both stable leaves of $\alpha(x_1)$ together with the simple path on the tree $\Gamma$ connecting $\mathcal{A}(\eta)$ with $\mathcal{A}(\eta')$ form a simple closed curve $\gamma$ on $S$ which is Legendrian. All singularities on $\gamma$ except $\alpha(x_i)$ are positive by construction. Moreover, $\gamma$ contains an elliptic singularities which lies in $H(\xi)$. If $\alpha(x_i)$ is positive we obtain a contradiction to the tightness of $\xi$ since $c$ cannot bound an integral disc of $\xi$.
\end{proof}
In order to apply the previous proposition efficiently it remains to show that either one of the two parts of \propref{p:basins in spheres} can be used or $\Gamma\subset\partial Q$ does not contain any pseudovertices at all. This is done in the following lemma.
\begin{lem} \mlabel{l:edges of poly}
In the situation of \propref{p:basins in spheres} $\partial Q$ has more connected components or one of the following statements holds for each connected component $\Gamma$ of $\partial Q$.
\begin{itemize}
\item[(i)] There is a connected component $\Gamma$ of $\partial Q$ such that $\alpha(\Gamma)$ is an elliptic singularity and $\alpha(Q)$ is a neighbourhood of $x$ or $\alpha(\Gamma)$ is a cycle and $\alpha(Q)$ is a one-sided neighbourhood of that cycle.
\item[(ii)] $\alpha(\Gamma)$ contains a cycle of $S(\xi)$ such that $\alpha(Q)$ is not a one-sided neighbourhood of $\alpha(\Gamma)$ or $\alpha(\Gamma)$ contains an elliptic singularity such that $\alpha(Q)$ is not a neighbourhood of $x$.
\item[(iii)] $\alpha$ identifies edges on $\Gamma$.
\end{itemize}
\end{lem}
\begin{proof}
After a small perturbation of $S$ we may assume that all negative elliptic singularities on $S$ lie in $H(\xi)$ or the interior of the complement of $H(\xi)$. As in the proof of the previous proposition the problem can be reduced to the case when $\Gamma\cap V=\emptyset$.
We show that if (i) and (ii) do not hold for $\Gamma$, then (iii) applies to $\Gamma$.
In the following discussion we ignore corners on $\alpha(\Gamma)$ if two of their separatrices lie in the complement of $\overline{\alpha(Q)}$.
Let $x_1\in\alpha(\Gamma)$ be an elliptic singularity. Since $\alpha(\Gamma)\neq x_1$ there is an unstable leaf $\eta_1'$ of a pseudovertex $y_1$ which ends at $x_1$. Let $\eta_1$ be the other unstable leaf of $y_1$.
If the $\alpha$-limit set of $\eta_1$ is a negative elliptic singularity, then $y_1$ is contained in the interior of $\alpha(Q)$ and the two edges of $\Gamma$ which correspond to $y_1$ are identified by $\alpha$. Otherwise the $\omega$-limit set of $\eta_1$ is a hyperbolic singularity $y_2$ and we can assume that $y_2$ is a pseudovertex of $\Gamma$. There is a unique unstable leaf $\eta_2$ of $y_2$ which is not contained in the interior of $\alpha(Q)$. In particular the $\omega$-limit set of $\eta_2$ cannot by an elliptic singularity. Thus the $\omega$-limit set of $\eta_2$ is the image $y_3$ of a pseudovertex of $Q$.
If $y_3=y_1$, then $\alpha$ identifies the edges corresponding to $y_1$ and $\eta_1,\eta_2$ form a non-trivial cycle of $S(\xi)$.
Otherwise we continue as above until a pseudovertex appears for the second time. This happens after finitely many steps since $\Gamma$ contains only finitely many pseudovertices. If we obtained a sequence $y_1,y_2,\ldots,y_r, r\ge 2$ with $y_1=y_r$, then $\alpha$ identifies the edges corresponding to the pseudovertices $y_1,\ldots,y_{r-1}$. Thus if (i) and (ii) do not apply, then (iii) is true.
\end{proof}
\subsubsection{Taming functions for characteristic foliations on spheres}
Taming functions for characteristic foliations were introduced by Y.~Eliashberg in \cite{El}. In this section we extend the definition of taming functions so that it can be applied to spheres embedded in manifolds carrying a tight confoliation.
Let $S$ be an embedded sphere in a confoliated manifold such that the singularities of the characteristic foliation $S(\xi)$ are non-degenerate or of birth-death type. This assumption holds in particular for spheres in a generic $1$-parameter family of embeddings. In addition we may assume that there are at most two different hyperbolic singularities which are connected by their stable/unstable leaves.
\begin{defn} \mlabel{d:taming fct}
Let $U\subset S$ be a compact submanifold of dimension $2$ in $S$ whose boundary is piecewise smooth and does not intersect $\Sigma(S)$. Moreover, we assume that every connected component $\Gamma\subset\partial U$ satisfies one of the following conditions:
\begin{itemize}
\item[(1)] $\Gamma$ is either transverse or tangent to $S(\xi)$.
\item[(2)] $\Gamma$ intersects one respectively two stable leaves of hyperbolic singularities of $S(\xi)$ (these singularities may be part of a cycle, cf. \figref{b:levelset} or $U$ is a neighbourhood of a hyperbolic singularity). Each smooth segment of $\Gamma$ intersects exactly one separatrix of a hyperbolic singularity in $U$ and each segment is transverse to $S(\xi)$.
\item[(3)] $U$ is disc and a neighbourhood of a birth-death type singularity of $S(\xi)$ such that $\partial U$ consists of two smooth segments transverse to $S(\xi)$.
\end{itemize}
A function $f: U\longrightarrow \mathbb{ R}$ is a {\em taming function} for $S(\xi)$ if it has the following properties.
\begin{itemize}
\item[(o)] If a component $\Gamma\subset\partial U$ belongs to the class (1), then $f$ is assumed to be constant along $\Gamma$. If $\Gamma$ is of class (2) or (3) we require that $f\eing{\Gamma}$ has exactly one critical point in the interior of each of the smooth segments of $\Gamma$.
\item[(i)] The union of the singular points of $S(\xi)$ with all points on internal leaves coincides with the set of critical points of $f$. The function is strictly increasing along leaves of $S(\xi)$ which are not part of a cycle and $f$ is constant along cycles of $S(\xi)$.
\item[(ii)] Positive respectively negative elliptic points of $S(\xi)$ are local minima respectively maxima of $f$.
\item[(iii)] If the level set $\{f=C\}$ contains only hyperbolic singularities, then as $C$ increases the number of closed connected components of $\{f=C\}$ changes by $h_-(\{f=C\})-h_+(\{f=C\})$.
\end{itemize}
\end{defn}
Requirement (i) in \defref{d:taming fct} is slightly more complicated than one might expect. \figref{b:fol-taming-ex} gives an example of a sphere $S$ in $\mathbb{ R}^3$ equipped with the foliation by horizontal planes. A part of the characteristic foliation is indicated in the right part of \figref{b:fol-taming-ex} where the cycle containing the internal subcycle is thickened. If one requires that singular points of $S(\xi)$ should coincide with critical points of the taming function, then $S(\xi)$ cannot be tamed although the confoliation in question is tight.
\begin{figure}[htb]
\begin{center}
\includegraphics{fol-taming-ex}
\end{center}
\caption{\label{b:fol-taming-ex}}
\end{figure}
Assume that $(X,\omega)$ is a symplectic filling of $(M,\xi)$ and a compatible almost complex structure on $M$ is fixed such that $\xi$ consists of complex lines. By Theorem 1 of \cite{hind} an embedded $2$-sphere $S\subset M$ can be filled by holomorphic discs when the embedding of $S$ satisfies several technical conditions. The singular foliation in the formulation of Theorem 1 in \cite{hind} is very similar to the singular foliation formed by level sets of a taming function. The appearance of internal cycles should be compared with Remark 2 in \cite{hind}.
\subsubsection{Construction and deformations of taming functions}
Let $S\subset M$ an embedded oriented $2$-sphere. The tightness of $\xi$ leads to several restrictions on the combinatorics of the cycles of $S(\xi)$ and their holonomy. This will be used to construct a taming function for $S(\xi)$.
Recall that the orientations of $S$ and $\xi$ induce an orientation of $S(\xi)$ and integral surfaces of $\xi$ are oriented by $\xi$. If $\gamma$ is a cycle of $S(\xi)$, then by tightness there is an integral disc $D_\gamma$ of $\xi$ such that $\partial D_\gamma=\gamma$ but the orientation of $\partial D_\gamma$ as boundary of $D_\gamma$ does not coincide with the orientation of $\gamma$ in general. Recall also that $D_\gamma$ is uniquely determined because $\xi$ is not a foliation by spheres.
For a $2$-dimensional submanifold $U\subset S$ with piecewise smooth boundary we define the following quantities:
\begin{align*}
d_+(U) & = e_+(U)-h_+(U) \\
N_-(U) & = \textrm{Number of connected components }\Gamma\textrm{ of }\partial U\textrm{ where }S(\xi)\\ & \quad\textrm{ points transversally into }U \textrm{ or } \Gamma \textrm{ is tangent to } S(\xi) \\
& \quad \textrm{ and }\Gamma \textrm{ is potentially repulsive on the side of }U. \\
N_s(U) & = \textrm{Number of boundary components of }\partial U \textrm{ through which}\\
& \quad\textrm{ stable leaves of negative hyperbolic singularities enter.}\\
P_s(U) & = \textrm{Number of stable leaves of positive hyperbolic singularities in }U\\
& \quad\textrm{ which intersect }\partial U.
\end{align*}
These quantities will be used in the construction of taming functions.
\begin{lem} \mlabel{l:taming functions near cycles}
For each path connected component $\Sigma_0$ of $\Sigma(S)$ there is a neighbourhood $U_0$ of $\Sigma_0$ and a taming function $f : U_0 \longrightarrow \mathbb{ R}$ such that no connected component of $\partial U_0$ is tangent to $S(\xi)$ and
\begin{equation} \label{e:d+}
d_+(U_0)=1-N_-(U_0)-P_s(U_0)-N_s(U_0).
\end{equation}
\end{lem}
\begin{proof}
We will construct $U_0$ and $f: U_0\longrightarrow\mathbb{ R}$ inductively. The starting point are connected cycles $\gamma$ and singularities of $S(\xi)$ in $\Sigma_0$ which belong to the following classes.
\begin{itemize}
\item[(i)] Positive elliptic singularities and hyperbolic or birth-death type singularities which do not belong to a cycle.
\item[(ii)] Closed leaves with sometimes attractive (non-trivial) one-sided holonomy.
\item[(iii)] Cycles $\gamma$ containing hyperbolic singularities which satisfy the following conditions:
\begin{itemize}
\item The only cycle of $S(\xi)$ containing $\gamma$ is $\gamma$.
\item If $\gamma_0\subset\gamma$ is a subcycle with potentially attractive one-sided holonomy, then this one-sided holonomy is not trivial.
\end{itemize}
\end{itemize}
If the positive elliptic singularity $y$ in (i) is dynamically hyperbolic, then it is a source and there is a taming function on a neighbourhood $U$ whose boundary is transverse to $S(\xi)$. If the elliptic singularity is not dynamically hyperbolic, then one obtains a taming function using the holonomy of an interval $[0,\eta), \eta>0$ which is transverse to $S(\xi)$ except at $y$ and $y$ corresponds $0$ (cf. \lemref{l:little discs}). If the holonomy is non-trivial, then we can choose the domain $U$ of the taming function such that $\partial U$ is transverse to $S(\xi)$. Otherwise we choose $U$ such that $\partial U$ is a closed leaf of $S(\xi)$. Moreover, $U$ satisfies \eqref{e:d+}.
If $x$ is a hyperbolic singularity or a singularity of birth-death type, then the existence of a taming function on a neighbourhood $U$ which satisfies \eqref{e:d+} is obvious.
For a closed leaf $\gamma$ of $S(\xi)$ as in (ii) we choose an embedded interval $(-\eta,\eta),\eta>0$ transverse to $S(\xi)$ such that $0$ corresponds to a point in $\gamma$ and $(-\eta,0]$ corresponds to the side where the holonomy of $\gamma$ is sometimes attractive. This choice determines $f$ along the transverse segment and $f$ can be extended to a taming function on a neighbourhood of $\gamma$. If the holonomy on the side $\{f\ge 0\}$ is non-trivial (respectively trivial) we choose $U$ to be an annulus with transverse boundary (respectively such that $\partial U\cap\{f>0\}$ is a leaf of $S(\xi)$ and the other component of $\partial U$ is transverse to $S(\xi)$). Thus $N_-(U)=1$ and $U$ contains no singular points of $S(\xi)$. This means that \eqref{e:d+} holds for $U$.
Now let $\gamma$ be a cycle containing hyperbolic singularities. For each subcycle with potentially attractive (respectively repelling) one-sided holonomy chose a transversal $(-\varepsilon,0]$ (respectively $[0,\varepsilon)$) with $0$ lying on $\gamma$ and construct taming functions on collars of discs bounding the subcycle. When the germ of the one-sided holonomy is nontrivial, then we can choose the boundary corresponding boundary component of the domain $U$ of $f$ to be transverse to $S(\xi)$, otherwise we can choose the boundary of the domain to be tangent to a leaf of $S(\xi)$.
If $\gamma$ contains a corner such that only one stable leaf of the hyperbolic singularity is part of $\gamma$, then the levelsets of $f$ near $\gamma$ can be chosen as suggested in \figref{b:levelset}. The thick curve represents a critical level of $f$ while the dashed curve corresponds to a regular level of $f$
\begin{figure}[htb]
\begin{center}
\includegraphics{levelset}
\end{center}
\caption{\label{b:levelset}}
\end{figure}
By construction $f$ is constant along cycles and increasing along leaves of $S(\xi)$ which are not part of cycles. Singular points of $S(\xi)$ clearly are critical points of $f$. In order to show that requirement (i) of \defref{d:taming fct} is satisfied by $f$ we consider an internal leaf $\gamma_0\subset\gamma$.
Let $D_{0,1},D_{0,2}\subset S$ be discs which lie on opposite sides of $\gamma_0$ and contain no subcycle of $\gamma$ in their interior. Because $\gamma$ is an internal leaf $\ring{D}_{0,1}$ respectively $\ring{D}_{0,2}$ can not contain a stable or unstable leaf of a hyperbolic singularity on $\partial D_{0,1}$ respectively $\partial D_{0,2}$. Therefore the one-sided holonomy along $\partial D_{0,1}$ and $\partial D_{0,2}$ is well defined and by \lemref{l:neg-curv} the holonomy along $\partial D_{0,1}$ is potentially attractive if and only if the same is true for the holonomy along $\partial D_{0,2}$. Hence $f$ has a local minimum respectively maximum at every point of $\gamma_0$ when the holonomy is potentially repulsive respectively attractive.
Using induction on the number of hyperbolic singularities in $\gamma$ we now prove requirement (iii) from \defref{d:taming fct} and \eqref{e:d+} for $f :U\longrightarrow\mathbb{ R}$. We have already treated the case when $\gamma$ contains no hyperbolic singularity.
Given a cycle $\gamma$ and a fixed hyperbolic singularity $x_0$ we isotope $S$ in a neighbourhood of $x_0$. We choose the isotopy such that segments of $S(\xi)$ in $S\cap S'$ which ended at $x_0$ before the perturbation are now connected be non-singular segments of $S'(\xi)$. In this way obtain a cycle $\gamma'$ on $S'$ which contains one singularity less than $\gamma$ and it may happen that $\gamma'$ is not connected.
In order to construct an isotopy with the desired properties one moves $x_0$ away from the integral surface of $\xi$ which contains the cycle $\gamma$. When $x_0$ is part of an internal cycle or not all stable/unstable leaves of $x_0$ are contained in $\gamma$ one has to move $x_0$ into the interior of an integral surface of $\xi$ and then slightly above or below the integral surface with respect to the coorientation of $\xi$. Choosing to push upwards or downwards one can make sure that on obtains a cycle on the perturbed surface which is contained in the interior of the integral surface of $\xi$ which contains $\gamma$. \figref{b:shift} shows one particular instance of the isotopy in a neighbourhood of $x_0$. In that figure, we move $x_0$ downwards. In the left part of the figure all lines are part of $S$ while in the right part they straight line do not belong to $S'$. The cycles $\gamma$ respectively $\gamma'$ correspond to the thickened lines in the left respectively right part of \figref{b:shift}.
\begin{figure}[htb]
\begin{center}
\includegraphics{shift}
\end{center}
\caption{\label{b:shift}}
\end{figure}
If there is a hyperbolic singularity $x_0\in\gamma$ such that $\gamma$ contains only one stable leaf of $x_0$, then $x_0$ is automatically an essential singularity on $\gamma$ and our orientation convention and the choice of the function in \figref{b:levelset} together with \lemref{l:signs in cycles on spheres} imply that the behavior of the level sets of $f$ near $x_0$ is compatible with requirement (iii) of \defref{d:taming fct}.
In order to prove \eqref{e:d+} we perturb $S$. After an isotopy of $S$ in a neighbourhood of $x_0$ we obtain a cycle $\gamma'$ which contains one singularity less than $\gamma$ and the singularity we removed had a stable leaf which was not part of $\gamma$. We construct the function $f'$ on $U'\supset\gamma'$ as above. When $x_0$ is positive, then
\begin{align*}
d_+(U') & = d_+(U) + 1 & N_-(U') & = N_-(U) \\
N_s(U') & = N_s(U) & P_s(U') & = P_s(U)-1.
\end{align*}
Therefore \eqref{e:d+} holds for $U$ if and only if it holds for $U'$. If $x_0$ is negative we have to distinguish two cases: In the first case, the stable leaf of $x_0$ is the only stable leaf of a negative hyperbolic singularity intersecting the connected component of $\partial U$. Then
\begin{align*}
d_+(U') & = d_+(U) & N_-(U') & = N_-(U)+1 \\
N_s(U') & = N_s(U)-1 & P_s(U') & = P_s(U).
\end{align*}
If there are other stable leaves of other hyperbolic singularities of $\gamma$ which intersect the same connected component of $U$ as the stable leaf of $x_0$, then
\begin{align*}
d_+(U') & = d_+(U) & N_-(U') & = N_-(U) \\
N_s(U') & = N_s(U) & P_s(U') & = P_s(U).
\end{align*}
Again the validity of \eqref{e:d+} for $U$ follows from \eqref{e:d+} for $U'$. For the proof of \eqref{e:d+} we may assume from now on that all stable and unstable leaves of all hyperbolic singularities on $\gamma$ are contained in $\gamma$. In particular $N_s=P_s=0$ in the sequel.
Let $x_0\in\gamma$ be an essential hyperbolic singularity. We shall discuss the configuration shown in the left part of \figref{b:shift}. The other configurations can be handled in the same manner. The vertical arrow in \figref{b:shift} indicates the coorientation of $\xi$, the other arrows indicate orientations of leaves of $S(\xi)$ and $S'(\xi)$. In addition we assume that the stable leaf on the right (resp. left) hand side is connected in $\gamma\setminus\{x_0\}$ to the unstable leaf on the right (resp. left) hand side.
In this situation $\gamma$ is split into two connected components $\gamma',\gamma''$ by the isotopy. For both connected components there is an integral disc of $\xi$ which bounds a cycle containing parts of one stable leaf of $x_0$. The two integral discs have disjoint interiors.
Therefore there is one disc $D_b\subset S$ with well defined one-sided holonomy below the integral surface of $\xi$ and $x_0\in D_b$ and by \lemref{l:neg-curv} this holonomy is potentially attractive. There are two discs with well defined one-sided holonomy lying above the integral surface and each of the upper discs contains exactly one stable leaf of $x_0$ in its boundary while the lower disc contains both stable leaves of $x_0$ in its boundary. The one-sided holonomies along the boundary of each of the two discs if potentially repulsive. This is exactly the behavior prescribed by (iii) of \defref{d:taming fct}.
We choose neighbourhoods $U',U''$ of $\gamma',\gamma''$ which satisfy \eqref{e:d+}. The relation between $d_+(U)$ and $d_+(U'),d_+(U'')$ is given by
\begin{align*}
d_+(U) & = d_+(U')+d_+(U'') & N_-(U) & = N_-(U')+N_-(U'')-1.
\end{align*}
Hence \eqref{e:d+} is true for $U$ because it is satisfied for $U',U''$. The other configurations can be handled in a similar manner.
Now we assume that $x_0$ is a hyperbolic singularity such that one stable leaf is part of an internal cycle and the other one is part of a subcycle of $\gamma$ which is not internal (if there are internal subcycles, then there must be singularities with this property because $\gamma$ is connected).
Let $\gamma_{0,1},\gamma_{0,2}$ be the stable and unstable leaves of $x_0$ which are internal. There is a disc $D_0\subset S$ whose boundary contains $\gamma_{0,1},\gamma_{0,2}$ such that the one-sided holonomy along $\partial D$ is well defined. If it is potentially attractive respectively repulsive, then $x_0$ is positive respectively negative by \lemref{l:signs in cycles on spheres}.
The remaining pair of separatrices is part of a cycle with well defined one-sided holonomy. It is potentially attractive if and only if the holonomy along $\partial D_0$ is potentially repulsive (cf. \lemref{l:signs in cycles on spheres}).
By a small isotopy we can obtain a connected cycle $\gamma'$ or two connected cycles $\gamma',\gamma''$ on the perturbed sphere $S'$ with one singularity less than $\gamma$ such that $\gamma_{0,1}, \gamma_{0,2}$ (ie. the segments lying outside of the support of the perturbation of $S$) are connected by a leaf of $S'(\xi)$ and the same is true for the other pair of separatrices of $x_0$. \figref{b:fol-taming-ex} shows a cycle which decomposes into a pair of connected cycles. The discussion above shows that $f:U\longrightarrow\mathbb{ R}$ satisfies (iii) of \defref{d:taming fct} if the same is true for $f' : U'\longrightarrow\mathbb{ R}$ and $f'':U''\longrightarrow\mathbb{ R}$.
We construct a taming function on a neighbourhood of the perturbed cycle. The following table summarizes the relations from \lemref{l:signs in cycles on spheres} between the invariants $d_+,N_-$ associated to $\gamma$ with the invariants for the perturbed cycle.
\smallskip
\begin{tabular}{|l|c|c|}
\hline
& $x_0$ is positive & $x_0$ is negative \\
\hline
$\gamma$ remains connected & \begin{tabular}{c} $d_+=d_+'-1$ \\ $N_-=N_-'+1$ \end{tabular}
& \begin{tabular}{c} $d_+=d_+'$ \\ $N_-=N_-'$ \end{tabular} \\
\hline
$\gamma$ splits into two cycles &\begin{tabular}{c} $d_+=d_+'+d_+''-1$ \\ $N_-=N_-'+N_-''$ \end{tabular} & \begin{tabular}{c} $d_+=d_+'+d_+''$ \\ $N_-=N_-'+N_-''-1$ \end{tabular} \\
\hline
\end{tabular}
\smallskip
Therefore \eqref{e:d+} holds for the neighbourhood $U$ of $\gamma$ and $f : U \longrightarrow \mathbb{ R}$ has the desired properties.
This finishes the first step in the construction of a taming function on a neighbourhood of $\Sigma_0$. If all components of $\partial U$ are transverse to $S(\xi)$, then $U_0:=U$ and $f$ tames $S(\xi)$ on $U_0$. Otherwise we iterate the above construction.
Assume we have constructed a taming function $f: U\longrightarrow\mathbb{ R}$ and $\Gamma\subset\partial U$ is a closed leaf of $S(\xi)$ with trivial holonomy. By construction the holonomy is potentially attractive on the side of $\Gamma$ which is contained in $U$. Then there is a cylinder $S^1\times(0,1)\subset S$ such that $S(\xi)$ corresponds to the foliation by the first factor and $\overline C$ consists of two cycles $\gamma_0, \gamma_1$ such that $\gamma_0\subset U$ and $\gamma_1$ lies in the complement of $U$. We choose $C$ maximal among cylinders with these properties. Then $\gamma_1$ can not be a closed leaf with trivial holonomy. Therefore $\gamma_1$ belongs to one of the following classes.
\begin{itemize}
\item[(i)] $\gamma_1$ is a negative elliptic singularity or a closed leaf such that the holonomy on the side which is not contained in $C$ is non-trivial and potentially repulsive. In this case it is easy to extend $f$ to a taming function on $U\cup \overline{C}$ such that \eqref{e:d+} is satisfied.
\item[(ii)] $\gamma_1$ is a cycle containing hyperbolic singularities. If we did not yet define a taming function near $\gamma_1$, then we apply the above procedure to construct a taming function $g: V\longrightarrow\mathbb{ R}$ on a set $V$ with $U\cap V=\emptyset$. In particular, $V$ satisfies \eqref{e:d+}. We add a constant to $g$ to ensure that $g\eing{\gamma_1}>f\eing{\Gamma}$. Then we extend $g\cup f: U\cup V\longrightarrow\mathbb{ R}$ to a taming function on $U\cup V\cup C$. Note that $N_-(U\cup V\cup C)= N_-(U)+N_-(V)-1$. From this it follows that \eqref{e:d+} holds for $U\cup V\cup C$.
\end{itemize}
After finitely many steps we have constructed a taming function on a neighbourhood $U_0$ of $\Sigma_0$ with the desired properties. It is clear how to adapt the construction in the presence of birth-death type singularities.
\end{proof}
The following lemma implies that the existence of a taming function on a neighbourhood $U$ of $\Sigma$ is a property which is stable under $C^0$-small perturbations of $\xi$ if $U$ is small enough. For the statement of \lemref{l:stab} recall that for a given cycle in $S$ there is a unique integral disc of $\xi$ whose boundary is the cycle.
\begin{lem} \mlabel{l:stab}
Let $\Sigma_0$ be a path connected component of $\Sigma(S)$ and $\widetilde{\Sigma}_0$ the union of all discs tangent to $\xi$ which bound cycles in $\Sigma_0$. There is a neighbourhood $\widetilde{\Sigma}_0\subset W\subset M$ and $\varepsilon>0$ such that for every confoliation $\xi'$ on $M$ which is $\varepsilon$-close (in the $C^0$-topology) there is a confoliation $\xi_c'$ on $\mathbb{ R}^3$ which is transverse to the fibers of $\mathbb{ R}^3\longrightarrow\mathbb{ R}^2$ and complete as connection together with an embedding
$$
\varphi : \left(W,\xi'\eing{W}\right) \longrightarrow \left(\mathbb{ R}^3,\xi_c'\right)
$$
such that $\varphi_*(\xi')=\xi_c'$. In particular, if $\xi'$ is a contact structure, then $\xi'\eing{W}$ is tight.
\end{lem}
\begin{proof}
Note that the integral discs which bound a cycle depend continuously on the cycle because the integral discs are uniquely determined. On $\widetilde{\Sigma}_0$ we define an equivalence relation as follows: $x\sim y$ for $x,y\in \widetilde{\Sigma}_0$ if and only if there is a piecewise smooth path in $\widetilde{\Sigma}_0$ tangent to $\xi$ which connects $x$ and $y$.
The space $T:=\widetilde{\Sigma}_0/\sim$ should be thought of as a directed graph: Discs bounding singular cycles and closed leaves with non-trivial holonomy correspond to vertices while edges of $T$ correspond to families of integral discs of $\xi$ which bound a maximal connected cycle in $\Sigma_0$. (Because a disc in $\widetilde{\Sigma}_0$ may be part of a bigger disc in $\widetilde{\Sigma}_0$, a point in $\widetilde{\Sigma}_0/\sim$ does not correspond to a unique cycle of $S(\xi)$ in general. This happens for example in \figref{b:fol-taming-ex}.) The orientation of an edge is induced by the coorientation of $\xi$.
$T$ is a connected tree because $\widetilde{\Sigma}_0$ is connected and $S$ is a sphere. We embed $T$ in the $y,z$-plane in $\mathbb{ R}^3$ such that $dz$ is consistent with the orientation of the edges of $T$.
Let $\mathcal{ L}$ be the foliation on $\mathbb{ R}^3$ by straight lines parallel to the $x$-axis and $\mathcal{ Z}$ the foliation by planes parallel to the $x,y$-plane.
We replace $T$ by a family of discs tangent to $\mathcal{ Z}$: For each vertex of $T$ we choose a collection of discs $D_i$ such that
\begin{itemize}
\item each $D_i$ is tangent to the leaf of $\mathcal{ Z}$ containing the vertex,
\item $\cup_i D_i$ is homeomorphic to the union of integral discs in $M$ which bound the corresponding cycle in $M$ and $\cup_i D_i$ intersects the original tree $T$ in exactly one point.
\end{itemize}
Then we connect the discs which correspond to vertices of $T$ by families of discs tangent to $\mathcal{ Z}$ as prescribed by the edges of $T$, ie. by the configuration of integral discs in $M$. This is done in such a way that outside of a small neighbourhood of the discs which correspond to vertices of the tree each leaf of $\mathcal{ L}$ intersects at most one disc and this intersection is connected. (In the presence of some configurations of critical points on cycles in $\Sigma_0$ it may be impossible to satisfy the last requirement everywhere without violating the requirement that each leaf of $\mathcal{ L}$ intersects at most one disc.)
So far we have obtained an embedding $\varphi_0: \widetilde{\Sigma}_0\longrightarrow\mathbb{ R}^3$ with $\varphi_{0*}(\xi)=\mathcal{ Z}$ and the Legendrian foliation $\varphi_{0*}^{-1}(\mathcal{ L})$ on $\widetilde{\Sigma}_0$. We extend this foliation to a Legendrian foliation $\mathcal{ L}_0$ on an open neighbourhood $\widetilde{\Sigma}$ of $\widetilde{\Sigma}_0$ and we extend the embedding $\varphi_0$ such that the extended Legendrian foliation is mapped to $\mathcal{ L}$, the extension of $\varphi_0$ is the desired embedding $\varphi : \widetilde{\Sigma}\longrightarrow\mathbb{ R}^3$
but we still have to find the right domain and the neighbourhood $W$.
We may assume that $\widetilde{\Sigma}$ was chosen such that the intersection of each leaf of $\mathcal{ L}$ with $\varphi(\widetilde{\Sigma})$ is connected and $\varphi_*(\xi)$ is transverse to $\partial_z$. By construction $\varphi_*\left(\xi\eing{\widetilde{\Sigma}}\right)$ is the kernel of the $1$-form $\alpha=dz+f(x,y,z)dy$ with $\partial_x f\ge 0$ and $f\equiv 0$ on $\widetilde{\Sigma}_0$.
By extending $f$ to a function on $\mathbb{ R}^3$ we can extend $\alpha$ to a $1$-form $\alpha_c$ on $\mathbb{ R}^3$ whose kernel is a confoliation $\xi_c$ with the desired properties: If we extend $f$ to a function on $\mathbb{ R}^3$ with $\partial_xf\ge 0$ and $f\equiv 0$ for $|z|$ big enough, then $\xi_c$ is a complete connection.
For each plane field $\zeta$ on $\varphi(\widetilde{\Sigma})$ such that $\zeta$ is transverse to $\partial_z$ we define a foliation $\mathcal{ L}(\zeta)$ which is tangent to the projection of $\partial_x$ to $\zeta$ along $\partial_z$. There is a neighbourhood $W\subset M$ of $\widetilde{\Sigma}_0$ and $\varepsilon>0$ with the following properties:
\begin{itemize}
\item If $\xi'$ is $\varepsilon$-close to $\xi$, then $\varphi_*(\xi)$ is transverse to $\partial_z$.
\item For every plane field $\xi'$ which is $\varepsilon$-close to $\xi$ there is an open set $W'$ with $\widetilde{\Sigma}_0\subset W\subset W'\subset U$ such that the intersection of $\varphi(W')$ with leaves of $\mathcal{ L}(\varphi_*(\xi'))$ is connected.
\end{itemize}
This implies the claim of the lemma: If a confoliation $\xi'$ is sufficiently close to $\xi$ in the $C^0$-topology, then we can extend $\varphi_*(\xi'\eing{W})$ by extending (as above) the confoliation $\varphi_*(\xi\eing{W'})$ along leaves of a foliation $\mathcal{ L}'$ of $\mathbb{ R}^3$ by lines transverse to the planes $\{x=\textrm{const}\}$ and which coincides with $\mathcal{ L}$ outside of $\varphi(\widetilde{\Sigma})$. Thus we have found a confoliation $\xi'_c$ on $\mathbb{ R}^3$ with the desired properties.
The statement about the tightness of $\xi'\eing{W}$ follows from \propref{p:complete connection}.
\end{proof}
Next we show that the taming functions which we have constructed on pieces of $S$ in \lemref{l:taming functions near cycles} can be combined to obtain a taming function on a given generically embedded sphere.
\begin{prop} \mlabel{p:taming functions on spheres}
If $(M,\xi)$ is tight and $S$ is an embedded sphere such that $S(\xi)$ has isolated singularities which are either non-degenerate or of birth-death type, then $S$ admits a taming function.
\end{prop}
\begin{proof}
We construct $f$ inductively in a finite number of steps. By \lemref{l:taming functions near cycles} we can cover the compact set $\Sigma(S)$ by a finite collection of open sets $\mathbb{U}_0=\{U_1,\ldots,U_l\}$ with $U_j\subset S$ such that there is a taming function $f_j$ on $U_j, j=1,\ldots,l$ and the sets $U_j$ are pairwise disjoint. Recall that
\begin{equation} \label{e:d+2}
d_+(U_j)=1-N_-(U_j)-P_s(U_j)-N_s(U_j)
\end{equation}
for all $j=1,\ldots,l$. For later applications we assume that each $U_j\in\mathbb{U}_0, j=1,\ldots,l$ has the property described in \lemref{l:stab} for $\varepsilon_j>0$.
We define a partial order $\preceq$ on $\mathbb{U}_0$ as follows: $U_{j}\preceq U_{k}$ if and only if either $j=k$ or $U_{k}$ has a boundary component which bounds a disc in $S$ not containing $U_k$ and a leaf of the characteristic foliation coming from $U_j$ enters $U_k$ through this boundary component.
By definition every cycle of $S(\xi)$ which intersects $U_j$ is completely contained in $U_{j}$. This implies that $U_{j}\preceq U_{k}$ and $U_{k}\preceq U_{j}$ if and only if $j=k$ and there is a set $U_j\in\mathbb{U}_0$ which is minimal with respect to $\preceq$.
All connected components of $\partial U_j$ are transverse to $S(\xi)$ and the characteristic foliation points outwards along the boundary. Moreover, \eqref{e:d+2} implies $d_+(U_j)=1$.
Let $f_j$ be a taming function on $U_j$ and consider the basin $B(U_j)$ of $U_j$. According to \lemref{l:leg poly} the closure of $B(U_j)$ is covered by a Legendrian polygon $(Q_j,V_j,\alpha_j)$. We consider four cases which correspond to the conclusion of \lemref{l:edges of poly}. Let us assume that there are no birth-death type singularities. This assumption will be removed below.
{\em Case (o)}: $Q_j$ has more boundary components than $U_j$. This means that in the construction of $(Q_j,V_j,\alpha_j)$ in \lemref{l:leg poly} we did attach $1$-handles to $U_j$ (recall that we used $U_j$ as a starting point for the construction of $Q_j$).
Let $\gamma_j$ be the stable leaf of a hyperbolic singularity $h_j$ such that $\gamma_j$ leaves $U_j$ and $h_j$ is a corner in a cycle $\eta$. This cycle is contained in one of the sets $U_{i(\eta)}\in\mathbb{U}_0$. Let $f_i$ be a taming function on $U_{i(\eta)}$. Now we extend $f_j$ to a taming function on a neighbourhood $U'_j$ of $\gamma_j\cup U_j\cup U_{i(\eta)}$ (it may be necessary to add a sufficiently large constant to $f_{i(\eta)}$).
The extended function tames the characteristic foliation on its domain and the new boundary component of $U'_j$ can be chosen transverse to $S(\xi)$. By construction
\begin{align*}
N_-\left(U'_j\right) & = N_-(U_{i(\eta)}) \\
P_s\left(U'_j\right) & = \left\{
\begin{array}{ll} P_s(U_{i(\eta)})-1 & \textrm{ if }h_j \textrm{ is positive} \\
P_s(U_{i(\eta)}) & \textrm{ if }h_j \textrm{ is negative} \\
\end{array}\right. \\
N_s\left(U'_j\right) & = \left\{
\begin{array}{ll} N_s(U_{i(\eta)}) & \textrm{ if }h_j \textrm{ is positive} \\
N_s(U_{i(\eta)})-1 & \textrm{ if }h_j \textrm{ is negative.} \\
\end{array}\right.
\end{align*}
This implies $d_+(U'_j) = 1 - N_-(U'_j)-P_s(U'_j)-N_s(U'_j)$.
In the following cases we consider a fixed connected component $\Gamma\subset \partial Q_j$ which was not covered in case (o).
{\em Case (i)}: $\alpha_j(\Gamma)$ is an elliptic singularity and $\alpha_j(Q_j)$ is a neighbourhood of $x$ or $\alpha_j(\Gamma)$ is a cycle and $\alpha_j(Q_j)$ is a one-sided neighbourhood of that cycle.
Let us start with the case when $\alpha_j(\Gamma)$ is an elliptic singularity. Because it is attractive, it must be negative and it is contained in $U_{i(\Gamma)}$ with $i(\Gamma)\neq j$. One can easily extend $f_j$ to a taming function on the union $U'_j$ of $U_j\cup U_{i(\Gamma)}$ with all leaves passing through $\Gamma$. Obviously \eqref{e:d+2} holds for $U'_j$.
If $\alpha_j(\Gamma)$ is a closed leaf or a cycle, then $\alpha_j(\Gamma)$ belongs to one of the sets $U_{i(\Gamma)}$ with $i(\Gamma)\neq j$. After eventually adding a constant to the taming function on $U_{i(\Gamma)}$ one obtains a taming function on the union of the flow lines leaving $U_j$ through $\Gamma$ with $U_j$ and $U_{i(\Gamma)}$. As before we denote the new domain by $U'_j$. From
\begin{align*}
N_-\left( U'_j \right) & = N_-(U_{i(\Gamma)})-1\\
P_s\left( U'_j \right) & = P_s(U_{i(\Gamma)}) \\
N_s\left( U'_j \right) & = N_s(U_{i(\Gamma)}).
\end{align*}
it follows that $d_+(U'_j) = 1 - U_-( U'_j) -P_s(U'_j)-N_s(U'_j)$.
{\em Case (ii)}: $\alpha_j(\Gamma)$ contains an elliptic singularity such that $\alpha_j(Q_j)$ is not a neighbourhood of this singularity or there is $v_j\in V_j\cap\Gamma$ such that $\gamma_{v_j}$ is a cycle of $S(\xi)$ and $\alpha_j(Q_j)$ is not a one sided neighbourhood of $\gamma_{v_j}$ or
According to \propref{p:basins in spheres} there is a positive pseudovertex $x$ on $\alpha_j(\Gamma)$ such that $\alpha_j(Q_j)$ is not a neighbourhood of $x$. Let $\eta$ be the stable leaf of $x$ which is not contained in $\alpha_j(Q_j)$. The $\alpha$-limit set of $\eta$ is contained in a set $U_{i(\eta)}$ while $x\in U_{i(x)}$. We obtain a taming function on the union of $U'_j$ of $U_j\cup U_{i(\eta)}\cup U_{i(x)}$ with a neighbourhood of the stable leaves of $x$ (after adding a constant to the taming function on $U_{i(x)}$).
Because $x$ is positive the requirements in the definition of taming functions are satisfied. Moreover, we can choose the domain $U'_j$ of the taming function such that its the new boundary component is transverse to $S(\xi)$. The equality $d_+(U'_j)=1-N_-(U'_j) - P_s(U'_j)- N_s(U'_j)$ follows from
\begin{align*}
N_-\left(U'_j\right) & = N_-\left(U_{i(\eta)}\right) \\
P_s\left(U'_j\right) & = P_s\left(U_{i(\eta)}\right) \\
N_s\left(U'_j\right) & = N_s\left(U_{i(\eta)}\right)
\end{align*}
and the fact that $x$ is positive.
{\em Case (iii)}: (0)-(ii) do not hold for $(Q_j,V_j,\alpha_j)$. Then $\alpha_j$ identifies edges on $\Gamma$ by \lemref{l:edges of poly}. We shall use the notation from the proof of that lemma.
Let $e_1,\ldots,e_l$ be edges on $\Gamma$ which are obtained as in the proof of \lemref{l:edges of poly}. The cycle $\eta\subset\alpha_j(e_1)\cup\ldots\cup\alpha_j(e_l)$ is contained in $U_{i(\eta)}\in\mathbb{U}_0$ and we denote the stable leaves of the pseudovertices on $\eta$ which are not part of $\eta$ by $\sigma_1,\ldots,\sigma_l$. Let $U_j'$ be the union of $U_j\cup U_{i(\eta)}$ with neighbourhoods of $\sigma_1,\ldots,\sigma_l$. No other stable leaves of hyperbolic singularities enter $U_{i(\eta)}$ and all pseudovertices on $\eta$ are negative. After we add a sufficiently big constant to $f_{i(\eta)}$ we obtain a taming function $f'_j$ on $U'_{j}$. By construction we have
\begin{align*}
N_-\left(U'_j\right) & = N_-\left(U_{i(\eta)}\right) \\
P_s\left(U'_j\right) & = P_s\left(U_{i(\eta)}\right) \\
N_s\left(U'_j\right) & = N_s\left(U_{i(\eta)}\right)-1.
\end{align*}
These equalities immediately imply \eqref{e:d+}.
We have now considered all cases occurring in \lemref{l:edges of poly}. Next we remove the assumption that there is not birth-death type singularity. Assume that in the step above we encounter a birth-death type singularity $x$. Then $x$ is contained in a set $U_{i(x)}$ from $\mathbb{U}_0$. In an intermediate step we extend $f$ to the union $U_j^{int}$ of $U\cup U_{i(x)}$ with the leaves of $S(\xi)$ which connect $U_{i(x)}$ to $U$. Then we continue as before with $U_j^{int}$ instead of $U_j$.
Now we remove $U_j$ together with all $U_i$ which are contained in $U'_j$ from the collection $\mathbb{U}_0$ and we add $U'_j$. This yields a new collection of of subsets $\mathbb{U}_1$ such that on each domain in $\mathbb{U}_1$ we have a defined a taming function. Notice that the number of sets in $\mathbb{U}_1$ is strictly smaller than the number of sets in $\mathbb{U}_0$.
We iterate the procedure after replacing $\mathbb{U}_0$ with $\mathbb{U}_1$. After finitely many steps we obtain a taming function on $S$.
\end{proof}
So far we have established the existence of a taming function on embedded spheres such that $S(\xi)$ has only non-degenerate or birth-death type singularities. Now we consider an embedding of a family of spheres $S^2\times[0,1]$ in $M$ and a $C^0$-approximation of $\xi$ by a confoliation $\xi'$. After a $C^\infty$-small perturbation of $S^2\times[0,1]$ each sphere $S_t=S^2\times\{t\}$ becomes generic. We want to show that the characteristic foliation $S_t(\xi')$ admits a taming function if the confoliation $\xi'$ is close enough to $\xi$ in the $C^0$-topology.
\begin{prop} \mlabel{p:deform taming fct}
There is a $C^0$-neighbourhood of $\xi$ such that for every confoliation $\xi'$ in that neighbourhood $S_t(\xi')$ admits a taming function for all $t\in[0,1]$ if $S_t$ is generic with respect to $\xi'$ for all $t$.
If $\xi'$ is a contact structure, then $S_t(\xi')$ admits a taming function which is strictly increasing along all leaves of $S_t(\xi')$.
\end{prop}
\begin{proof}
We show that if $\xi'$ is close enough to $\xi$ in the $C^0$-topology and $S_t(\xi)$ has only non-degenerate singularities or singularities of birth death type, then the iteration process used for the construction of a taming function in \propref{p:taming functions on spheres} can be carried out to yield a taming function for $S_t(\xi')$. For this we first reconsider the proof of \propref{p:taming functions on spheres} in order to show the existence of $\varepsilon>0$ with the desired properties for a fixed sphere $S_t$ and then we argue that $\varepsilon$ can be chosen independently from $t\in[0,1]$.
Recall that in the proof of \propref{p:taming functions on spheres} we required that all sets $U_j\in\mathbb{U}_0$ appearing in the initial stage of the construction are contained in a set $W_j$ with the stability property described in \lemref{l:stab} for $\varepsilon_j>0$: The restriction of $\xi'$ to $W_j$ is tight when $\xi'$ is $\varepsilon_j$-close to $\xi$.
Moreover, we chose the $U_j$ such that each smooth segment in $\partial U_j$ is transverse to $S(\xi)$. This remains true when $\xi'$ is $\varepsilon_j$-close to $\xi$ when $\varepsilon_j>0$ is small enough. The iteration process in the proof of \propref{p:taming functions on spheres} stops after finitely many steps and we choose $\varepsilon>0$ so small that each smooth segment contained in the boundary of a set in $\mathbb{U}_0,\mathbb{U}_1,\ldots$ is transverse to $S(\xi')$ when $\xi'$ is $\varepsilon$-close to $\xi$. This requirement ensures also that the combinatorics of the extensions of $f$ is the same for $S_t(\xi)$ and $S_t(\xi')$.
It remains to show that we can choose $\varepsilon>0$ independently from $t\in[0,1]$. For this note that $\Sigma=\cup_t\Sigma(S_t)$ is compact. Thus a finite number of sets $W_j$ obtained from \lemref{l:stab} suffice to cover $\Sigma$. If $\tau$ is sufficiently close to $t$, then $S_\tau(\xi)$ is very close to $S_t(\xi)$ in the $C^\infty$-topology and the combinatorics of extensions of a taming function for $S_t(\xi)$ and $S_\tau(\xi)$ coincide, ie. we connect subsets $U_j(t)$ of $S_t$ which are very close to subsets $U_j(\tau)$ of $S_\tau$ in the same order (with the possible but irrelevant exception of birth-death type singularities).
When the above procedure for the choice of $\varepsilon$ for $S_t$ yields $\varepsilon_t>0$, then $\varepsilon_t/2$ has the desired property with respect to the characteristic foliation on $S_{\tau'}$ when $\tau'$ is close enough to $t$. Since $[0,1]$ is compact, this proves the claim.
\end{proof}
\subsubsection{Proof of \thmref{t:tight on balls}}
For the proof of \thmref{t:tight on balls} we combine the results from the previous sections with results from \cite{giroux2}.
Let $B\subset B_1\subset M$ be an embedded closed ball in a manifold $M$ with a tight confoliation $\xi$. We assume that the interior of $B_1$ contains points where $\xi$ is a contact structure since otherwise \thmref{t:tight on balls} follows immediately from \lemref{l:stab}. Moreover, we assume that $\partial B_1$ is generic.
Let $B_0$ be a ball in the contact region whose characteristic foliation has exactly two singular points and the leaves of the characteristic foliation connect the two singularities. The existence of such a ball follows from the fact that every contact structure is locally equivalent to the standard contact structure $\mathrm{ker}(dz+xdy)$ on $\mathbb{ R}^3$. Moreover, there is an open neighbourhood of $\xi|_{B_0}$ such that every confoliation in this neighbourhood is tight on $B_0$.
Let $\xi'$ be a contact structure on $B_1$. If $\xi''$ is a contact structure and sufficiently close to $\xi'$ in the $C^\infty$-topology, then $\xi'|B$ is diffeomorphic to the restriction of $\xi''$ to a closed ball in $B_1$. Therefore it is enough to prove \thmref{t:tight on balls} for generic perturbations.
We fix a generic identification $B_1\setminus\ring{B}_0\simeq S^2\times[0,1]$ such that $\partial B_i=S_i, i=0,1$. Because the confoliation $\xi$ is assumed to be tight, $S_t(\xi)$ can be tamed for all $t$. By \propref{p:deform taming fct} this remains true for generic confoliations $\xi'$ which are sufficiently close to $\xi$ in the $C^0$-topology.
Recall that an embedded surface in a contact manifold is called {\em convex} if there is a vector field transverse to the surface such that the flow of the vector field preserves the contact structure. According to \cite{giroux} convexity is a $C^\infty$-generic property, so we may assume that $\partial B_0$ and $\partial B_1$ are convex with respect to $\xi'$.
We will show that $\xi'$ can be isotoped on $S^2\times[0,1]$ relative to the boundary such that all leaves of the product foliation on $S^2\times[0,1]$ become convex with respect to the isotoped contact structure. Since $\partial B_0$ is convex and $\xi'$ is tight on a neighbourhood of $\partial B_0$ this implies that $\xi'|_B$ is tight by Theorem 2.19 in \cite{giroux2} (and the gluing result in \cite{colin}).
In order to prove the existence of the desired isotopy of $\xi'$ we use the following lemma. Our formulation is a slight modification of Lemma 2.17 in \cite{giroux2} in the case $F\simeq S^2$.
\begin{lem} \mlabel{l:make convex}
Let $(M,\xi')$ be a contact manifold. Assume that the characteristic foliation on each sphere $S_t$ from the family $S^2\times[0,1]\subset M$ admits a taming function and $S_0,S_1$ are convex. Then there is a contact structure $\xi''$ such that
\begin{itemize}
\item $\xi'$ and $\xi''$ are isotopic relative to the boundary and
\item the characteristic foliation of $\xi''$ on $S_t$ has exactly $\chi(S)=2$ singular points and $S_t$ is convex with respect to $\xi''$ for all $t\in[0,1]$.
\end{itemize}
\end{lem}
The original statement of Giroux of this lemma contains tightness as an assumption. However the proof of Lemma 2.17 of \cite{giroux2} requires only properties of the characteristic foliation on $S_t,t\in[0,1]$ which follow from the existence of taming functions.
More specifically, the proof of Lemma 2.17 in \cite{giroux} yields a proof of \lemref{l:make convex} after the following modification: As we have already explained we may assume that the characteristic foliation of $\xi'$ on $S_t$ can also be tamed for all $t\in[0,1]$ by \propref{p:deform taming fct}. Moreover, because $\xi'$ is a contact structure, the taming functions are strictly increasing along leaves of the characteristic foliation. Therefore the following statements hold:
\begin{enumerate}
\item There is no closed cycle on $S\times\{t\}, t\in[0,1]$.
\item The graph $\Gamma_t^+$ ($\Gamma_t^-$) on $F\times\{t\}$ formed by positive (negative) singular points and stable (unstable) leaves of positive (negative) hyperbolic singularities is a tree.
\end{enumerate}
Using these two observations one obtains a proof of \lemref{l:make convex} from the proof of Lemma 2.17 in \cite{giroux2}. This finishes the proof of \thmref{t:tight on balls}.
\section{Overtwisted stars} \mlabel{s:discussion}
In this section we introduce overtwisted stars. Their definition is given in the next section and it is motivated by the discussion of the confoliation $(T^3,\xi_T)$ in \secref{s:example}. The absence of overtwisted stars in a tight confoliations implies all Thurston-Bennequin inequalities and we show that symplectically fillable confoliations do not admit overtwisted stars (in addition to the fact that they are tight).
\subsection{Overtwisted stars and the Thurston-Bennequin inequalities} \mlabel{s:ot star}
As we have already mentioned the point where Eliashberg's proof of the Thurston-Bennequin inequalities fails in the case of tight confoliations is the following: Given an embedded surface $F$ and a tight confoliation $(M,\xi)$, there may be leaves of $F(\xi)$ which come from an elliptic singularity and accumulate on closed leaves $\gamma$ (or on quasi-minimal sets) of the characteristic foliation such that $\gamma$ is part of the fully foliated set of $\xi$. Even if all singular points on $\partial B(x)$ have the same sign it may be impossible to construct a disc from $B(x)$ which has the properties of the disc $D$ appearing in \defref{d:tight confol}.
This suggests the following definition of overtwisted stars on generically embedded surfaces $F$
\begin{defn} \mlabel{d:overtwisted star}
An overtwisted star in the interior of a generically embedded compact surface $F\not\simeq S^2$ is the image of a Legendrian polygon $(Q,V,\alpha)$ with the following properties.
\begin{itemize}
\item[(i)] $Q$ is homeomorphic to a disc and $\alpha(\partial Q)$ contains singularities of $F(\xi)$
\item[(ii)] All singularities of $F(\xi)$ on $\alpha(\partial Q\setminus V)$ have the same sign. There is a single singularity in the interior of $\alpha(Q)$; it is elliptic and its sign is opposite to the sign of the singularities on $\alpha(\partial Q)$.
\item[(iii)] If $\gamma_v$ is a cycle, then it does not bound an integral disc of $\xi$ in $M$.
\end{itemize}
\end{defn}
The torus shown \figref{b:starfish} contains two overtwisted stars. Note that the polygon is not required to be injective. Requirement (i) implies that either $V\neq\emptyset$ or $\alpha(\partial Q)$ contains an elliptic singularity of $F(\xi)$ and we may assume that this singularity is contained in $H(\xi)$. (Note that the elliptic singularity cannot lie in the interior of $M\setminus H(\xi)$. After a small perturbation and by \lemref{l:cut} the elliptic singularity lies in $H(\xi)$). In particular discs with the properties of $D$ in \defref{d:tight confol} are not overtwisted stars.
If $\xi$ is a contact structure and $F\subset M$ is a generically embedded closed surface containing an overtwisted star $(Q,V,\alpha)$, then $\xi$ cannot be tight since $\xi$ is convex by the genericity assumption (therefore all $\gamma_v, v\in V$ are cycles) and has a homotopically trivial dividing curve (this terminology is standard in contact topology; because we shall not really use it we refer the reader to \cite{giroux} or \cite{honda}). This argument does not apply when $F\simeq S^2$. Since the definition of tightness in \defref{d:tight confol} can be applied efficiently to spheres and discs, the exceptional role of spheres in \defref{d:overtwisted star} will not play a role.
The following theorem is proved following Eliashbergs strategy from \cite{El} and \thmref{t:discs and spheres}.
\begin{thm} \mlabel{t:no stars imply tb}
Let $(M,\xi)$ be an oriented tight confoliation such that no compact embedded oriented surface contains an overtwisted star and $(M,\xi)$ is not a foliation by spheres.
Every embedded surface $F$ whose boundary is either empty or positively transverse to $\xi$ satisfies the following relations.
\begin{itemize}
\item[a)] If $F\simeq S^2$, then $e(\xi)[F]=0$.
\item[b)] If $\partial F=\emptyset$ and $F\not\simeq S^2$, then $|e(\xi)[F]|\le-\chi(F)$.
\item[c)] If $\partial F\neq\emptyset$ is positively transverse to $\xi$, then $\mathrm{sl}(\gamma,[F])\le -\chi(F)$.
\end{itemize}
\end{thm}
\begin{proof}
The claim a) was already covered in \thmref{t:discs and spheres}. For the proof of b) and c) we may assume that $F$ is a generic representative of the homology class $[F]$ which is incompressible (this means that the map $\pi_1(F)\longrightarrow\pi_1(M)$ which is induced by the inclusion $F\hookrightarrow M$ is injective). Recall that if $\partial F$ is positively transverse to $\xi$, then $F(\xi)$ points out of $F$ along $\partial F$. Recall that
\begin{equation*
\chi(F)-e(\xi)[F]=2(e_--h_-)
\end{equation*}
by \eqref{e:chie}. If there is no negative elliptic singularity, then this
implies $-e(\xi)[F]\le-\chi(F)$. If there is a negative elliptic singularity $x$, then we shall use the absence of overtwisted stars to eliminate $x$ without creating new negative elliptic singularities. Let $D_x$ be the maximal open disc in $F$ such that
\begin{itemize}
\item $\partial D_x=\overline{D}_x\setminus D_x$ is a cycle of $F(\xi)$ and
\item $x$ is the only singularity of $F(\xi)$ in the interior of $D$.
\end{itemize}
Unless $D_x\neq\emptyset$ there is an integral disc $D_x'$ of $\xi$ whose boundary is $\partial D_x$ because $\xi$ is tight. Moreover, the intersection of the interior of $D_x'$ with $F$ consists of homotopically trivial curves in $F$ (otherwise we get a contradiction to the incompressibility of $F$).
Thus we can cut $F$ using \lemref{l:cut}, \lemref{l:cut2} and \lemref{l:cut3} so that the resulting surface $F'$ is the union of spheres and a surface which is diffeomorphic to $F$ and incompressible. Because $e(\xi)[S]=0$ for embedded spheres $S$ we can ignore the spherical components and we denote the remaining surface by $F'$. It follows
that $e(\xi)[F]=e(\xi)[F']$.
If we used \lemref{l:cut2} or \lemref{l:cut3}, then we have reduced the number of negative elliptic singularities by one. Note that if we have applied \lemref{l:cut3}, then $F'$ might contain a circle of singularities. This means that $F'$ is non-generic near that circle. Since this circle is isolated from the rest of $F'$ by closed leaves of $F'(\xi)$ and the singularities on this circle do not contribute to $e(\xi)[F']$ or $\chi(F')$, these singularities will play no role in the following. Therefore we can pretend that $F'$ is generic and eliminate the remaining negative elliptic singularities.
If we used \lemref{l:cut}, then $F'$ contains a negative elliptic singularity $x'$. By construction $x'$ lies in $H(\xi)$. In the following we shall denote $x'$ again by $x$.
The basin of $x$ is covered by a Legendrian polygon $(Q',V',\alpha')$ on $F'$. By the maximality property of $D_x$ the boundary of $Q'$ is not mapped to a cycle of $F'(\xi)$. If $\partial Q'$ has more than one connected component, then there is a hyperbolic singularity $y$ on $\alpha'(\partial Q')$ which is the corner of a cycle $\gamma_y$. If $y$ is negative, then we can eliminate the pair $x,y$.
Now assume that $y$ is positive. If $\gamma_y$ does intersect $H(\xi)$, then we can perturb $F'$ in a small neighbourhood of a point on the cycle such that $y$ is no longer part of a cycle after the perturbation. If $\gamma_y$ does not intersect $H(\xi)$, then we push a part of the cycle into $H(\xi)$ by an isotopy of $F'$ without introducing new singularities of the characteristic foliation.
The isotopy is constructed as follows. Let $L$ be the maximal connected integral surface of $\xi$ which contains the cycle through $y$. We choose a simple curve $\sigma$ tangent to $\xi$ which connects the cycle to $H(\xi)$ and is disjoint from $F'$. This curve can be chosen close to the stable leaf of $y$ which is connected to $x\in H(\xi)$. We choose a vector field $X$ tangent to $\xi$ with support in a small neighbourhood of $\sigma$ such that $\sigma$ is a flow line of $X$ and $F'$ is transverse to $X$. We use the flow of $X$ to isotope $F'$ such that all unstable leaves of $y$ are connected to $H(\xi)$ after the isotopy. Since $X$ is transverse to $F'$ and tangent to $X$ the isotopy creates no new singular points of the characteristic foliation. \figref{b:slide} shows $L$ together with a part of the intersection $F'\cap L$. The curve $\sigma$ is represented by the thickened line while the shaded disc represents another part of $H(\xi)$ or non-trivial topology of $L$.
\begin{figure}[htb]
\begin{center}
\includegraphics{slide}
\end{center}
\caption{\label{b:slide}}
\end{figure}
By this process we modified the basin of $x$ and the surface. Note that there are finitely many hyperbolic singularities on $F$ and the procedure described above does not create new ones. Therefore finitely many applications lead to a surface $F''$ with $e(\xi)[F]=e(\xi)[F'']$ such that the hyperbolic singularities of $F''(\xi)$ are also hyperbolic singularities of $F(\xi)$ and the basin of $x$ is homeomorphic to a disc. Also, the number of negative elliptic singularities did not increase. Note that $F''$ is not a sphere because $F''$ and $F$ have the same genus. Moreover, $F''$ has the following properties.
The basin of $x$ is covered by a Legendrian polygon $(Q'',V'',\alpha'')$ on $F''$ such that $Q''$ is a disc and $\alpha''(Q'')$ is not an elliptic singularity or a cycle of $F''(\xi)$. If necessary, we eliminate all elements of $v''$ with the property that $\gamma_{v''}$ is null homotopic in $F''$.
Now the assumption of the theorem implies that $\partial Q''$ contains a negative pseudovertex. By \lemref{l:elim} we can isotope $F''$ to a surface containing less negative elliptic singularities than $F$ respectively $F''$. After finitely many steps we have eliminated all negative elliptic singularities. This finishes the proof of c) and one of the inequalities in b). The remaining inequality in b) can be proved by eliminating all positive elliptic singularities.
\end{proof}
\subsection{Overtwisted stars and symplectic fillings} \mlabel{s:symp fill ot star}
In this section we show that symplectically fillable confoliations do not admit overtwisted stars. In the proof we $C^0$-approximate a confoliation by another confoliation (cf. \thmref{t:El-Th approx}). Several techniques used in the proof are adaptations of constructions in \cite{confol}. Other useful references are \cite{pet} (where the proofs of Lemma 2.5.1 c) and Lemma 2.5.3 from \cite{confol} are carried out) and \cite{etnyre-notes}. For later use we summarize the proof of a lemma used to show \thmref{t:El-Th approx}.
\begin{lem}[Lemma 2.5.1 c) in \cite{confol}] \mlabel{l:reminder on holonomy approx}
Let $\gamma$ be a simple closed curve in the interior of an integral surface $L$ of $\xi$. If $\gamma$ has sometimes attractive holonomy, then in every $C^0$-neighbourhood of $\xi$ there is a confoliation $\xi'$ which
\begin{itemize}
\item[(i)] is a contact structure on a neighbourhood of $\gamma$ and
\item[(ii)] coincides with $\xi$ outside a slightly larger neighbourhood.
\end{itemize}
\end{lem}
\begin{proof}
We only indicate the main stages of the construction. Fix a neighbourhood $V\simeq S^1_x\times[-1,1]_y\times[-1,1]_z$ and coordinates $x,y,z$ such that the foliation by the second factor is Legendrian, $S^1\times[-1,-1]\times\{0\}\subset L$ and $S^1\times\{(0,0)\}$ corresponds to $\gamma$. We assume that $\gamma$ has sometimes attractive holonomy. As in Lemma 2.1.1 of \cite{pet} the coordinates can be chosen such that
\begin{itemize}
\item $\xi$ is defined by the $1$-form $\alpha=dz+a(x,y,z)\,dx$ with $\partial_ya\le 0$ and
\item
there are sequences $\zeta_n'<0<\zeta_n$ converging to zero such that $a(x,0,\zeta'_n)<0<a(x,0,\zeta_n)$ for all $x$.
\end{itemize}
At this point we use the assumption that the holonomy along $\gamma$ is sometimes attractive. We fix a pair $\zeta',\zeta$ of numbers from the sequences $(\zeta_n),(\zeta')_n$.
According to Lemma 2.2.1 in \cite{pet} and Lemma 2.5.3 in \cite{confol} there is a diffeomorphism $g: [-1,1]\longrightarrow[-1,1]$ such that
\begin{itemize}
\item[(i)] $g$ is the identity outside of $V:=(\zeta',\zeta)$ and
\item[(ii)] $g'(z)a(x,0,z)<a(x,0,g(z))$ for all $(x,0,z)\in S^1\times\{0\}\times V$.
\end{itemize}
It follows that $g$ converges uniformly to the identity as $\zeta,\zeta'\to 0$, but no claim is made with respect to the $C^1$-topology. The graph of $g$ is given in \figref{b:graph-f} (cf. \cite{pet}). The parameters $a,b$ with $\zeta'<a<0<b<\zeta$ are chosen such that $a(x,0,z)\neq 0$ for $z\in[\zeta',a]\cup[b,\zeta]$.
\begin{figure}[htb]
\begin{center}
\includegraphics{graph-f}
\end{center}
\caption{\label{b:graph-f}}
\end{figure}
In order to obtain the desired confoliation in a $C^0$-neighbourhood of $\xi$, one proceeds as follows.
{\em Step 1:} Replace $\xi$ on $S^1\times[-1/2,-1/4]\times V$ by the push forward of $\xi$ with the map $G$ which is defined by
$$
G(x,y,z):=(x,y,u(y)g(z)+(1-u(y))z)
$$
where $u$ is a smooth non-negative function on $[-1/2,-1/4]$ such that $u\equiv 0$ near $-1/2$ and $u\equiv 1$ near $-1/4$. We extend $G$ to $M\setminus(S^1\times[-1/4,1/2]\times V)$ by the identity. As $\zeta,\zeta'\to 0$ the corresponding diffeomorphism $G$ converges to the identity uniformly but not with respect to the $C^1$-topology in general. Therefore $G_{*}(\xi)$ might not be $C^0$-close to $\xi$ on $S^1\times[-1/2,-1/4]\times V$. This will be achieved in the third step (at this point we follow the exposition on \cite{pet} closely). In the following step we replace the confoliation on $S^1\times[-1/4,1/2]\times V$.
The dashed respectively the solid lines in \figref{b:reminder} show the characteristic foliations of $\xi'$ on neighbourhoods of $\gamma$ in $\{y=-1/4\}$ respectively on $\{y=1/2\}$ using dashed respectively solid lines in the simple case when $\gamma$ has attractive holonomy.
\begin{figure}[htb]
\begin{center}
\includegraphics{reminder}
\end{center}
\caption{\label{b:reminder}}
\end{figure}
{\em Step 2:} We extend $G_{*}(\xi)$ to a confoliation $\xi''$ on $M$ such that $\partial_y$ remains Legendrian: The plane field $\xi''$ rotates around the foliation $S^1\times[-1/4,1/2]\times V$ such that the characteristic foliation on $S^1\times\{-1/4,1/2\}\times V$ coincides with the characteristic foliation of $F_{n*}(\xi)$ on these annuli. This is possible by (ii) using the interpretation of the confoliation condition mentioned in \secref{ss:confolmeaning} (cf. \figref{b:reminder}). Note that $\xi''$ is a contact structure on the interior of $S^1\times[-1/4,1/2]\times V=:\widetilde{V}$.
{\em Step 3:} We want to construct a diffeomorphism $\phi$ of $M$ with support in $V$ such that $\phi_{*}\xi''$ is $C^0$-close to $\xi$. For this one has to choose $V$ more carefully. This is carried out on p. 31--33 of \cite{pet}. The argument can be outlined as follows; cf. p.~16 in \cite{pet}: Assume that $r$ is chosen such that $V\subset[-r/2,r/2]$ and $\xi$ is $\varepsilon$-close to the horizontal distribution on $S^1\times[-1,1]\times[-r,r]$. As we already mentioned $\xi''$ might be very far away from the horizontal distribution. Choose a very small number $\delta>0$ and a diffeomorphism $\varphi : [-r,r]\longrightarrow[-r,r]$ such that $\varphi([-r/2,r/2])\subset[-\delta,\delta]$. Then the push forward of the restriction of $\xi''$ to $S^1\times[-1/2,1/2]\times[-r,r]$ is $3\varepsilon$-close to the horizontal distribution. One has to extend $\varphi$ such that this property is preserved.
\end{proof}
We will need not only the statement of the lemma, but also the construction outlined in the proof since we need to understand how this modification of $\xi$ near a curve $\gamma$ with sometimes attractive holonomy affects the presence of overtwisted stars on embedded surfaces in $M$. The third step of the above proof is of course irrelevant at this point.
\figref{b:near-tentacle} shows $F(\xi'')$ near a closed curve of $F(\xi'')$ in an embedded surface $F$ transverse to $\gamma$ after the second step of the proof of \lemref{l:reminder on holonomy approx}. The dot in the center of the figure represents $F\cap\gamma$ while the left inner rectangle represents the support of $G$. Finally, $\xi''$ is a contact structure in the inner rectangle on the right (this rectangle corresponds to the region $\widetilde{V}\cap F$ in the proof of \lemref{l:reminder on holonomy approx}). Recall that the characteristic foliation $F(\xi)$ was nearly horizontal in the region shown in \figref{b:near-tentacle}.
\begin{figure}[htb]
\begin{center}
\includegraphics{near-tentacle}
\end{center}
\caption{\label{b:near-tentacle}}
\end{figure}
Note that if $\gamma$ even has non-trivial infinitesimal (or only attractive) holonomy, then the statement of \lemref{l:reminder on holonomy approx} can be sharpened in the sense that the lemma remains true for $C^\infty$-neighbourhoods of $\xi$ because the function $g : [-1,1]\longrightarrow[-1,1]$ can be chosen $C^\infty$-close to the identity. In the following we will consider only $C^0$-approximations. This allows us to choose the approximation of $\xi$ more freely. In particular we can preserve qualitative features of the characteristic foliation on surfaces transverse to $\gamma$.
\begin{lem} \mlabel{l:approx with control1}
Let $\xi$ be a $C^k$-confoliation, $k\ge 1$, and $\gamma$ a simple Legendrian segment such that both endpoints of $\gamma$ lie in the contact region and $\gamma$ intersects $F$ transversely and at most once.
Then every $C^k$-neighbourhood of $\xi$ contains a confoliation $\xi'$ such that $\xi'=\xi$ outside a neighbourhood of $\gamma$ and $\xi'$ is a contact structure on a neighbourhood of $\gamma$. Moreover, $F(\xi)=F(\xi')$.
\end{lem}
\begin{proof}
The case $\gamma\cap F=\emptyset$ corresponds to Lemma 2.8.2. in \cite{confol}, the case $\gamma\cap F=\{p\}$ is very similar and only this case uses the assumption that both endpoints of $\sigma$ lie in $H(\xi)$.
\end{proof}
The following lemma is standard in the setting of foliations: One can thicken a closed leaf to obtain a smooth foliation which is close to the original one and contains a family of closed leaves. Once there is such a family, one can modify the foliation such that a compact leaf whose holonomy was never sometimes attractive on one sides has sometimes attractive holonomy one one side after the modification.
The main difficulty in the context of confoliations is the fact that now compact leaves of $\xi$ may have boundary.
\begin{lem} \mlabel{l:thickening}
Let $(M,\xi)$ be a manifold with confoliation, $L\subset M$ a compact embedded surface tangent to $\xi$ and $F\subset M$ a closed oriented surface which is generically embedded and does not intersect $\partial L$. We require that each connected component of $\partial L$ can be connected to $H(\xi)$ by a Legendrian curve which is disjoint from $\ring{L}\cup F$.
Then there is a smooth confoliation $\xi'$ which is $C^0$-close to $\xi$ such that $F(\xi')$ is homeomorphic to the singular foliation obtained from $F(\xi)$ by thickening the closed leaves of cycles of $F(\xi)$ which are also contained in $L$.
\end{lem}
\begin{proof}
Let $I=[-1,1]$ and $J=[-1,0]$. We fix a tubular neighbourhood $U\simeq L\times I$ of $L=L\times\{0\}$.
For each boundary component $B_i$ of $L$ we choose $U_i\simeq S^1\times J\times I\subset M$ in the complement of $\ring{L}\cup F$. We assume that the third factor of $U_i$ is transverse to $\xi$ while the foliation $\mathcal{J}$ whose fibers correspond to the second factor is Legendrian and that $S^1\times\{(0,0)\}=B_{0,i}$ and $S^1\times\{(-1,0)\}=B_{-1,i}$ intersect $H(\xi)$. Let $A_{j,i}=S^1\times\{j\}\times I\subset \partial U_i$ for $j\in\{-1,0\}$.
Without loss of generality we may assume that $B_{-1,i}$ is completely contained in the contact region and transverse to $\xi$. Otherwise we apply \lemref{l:approx with control1} along segments of $B_{-1,i}$ and replace $U_i$ with a new set $U_i'$ with the desired property.
We will now construct a confoliation $\xi'$ on $U\cup \bigcup_i U_i$ which coincides with $\xi$ near $\partial U$ and has the desired properties.
The restriction of $\xi'$ to $U$ is defined in two steps. First we flatten $\xi$ in a neighbourhood $U\simeq L\times I$ using the push forward of $\xi$ using a smooth homeomorphism $g$ of $I$ which is $C^\infty$-tangent to the zero map and coincides with the identity outside a neighbourhood of $0$.
We push forward $\xi$ on $L\times[0,1]$ respectively $L\times[-1,0]$ using a diffeomorphism $[0,1]\longrightarrow[\varepsilon,1]$ respectively $[-1,-\varepsilon]$. The confoliation on $(L\times [-1,-\varepsilon])\cup (L\times [-\varepsilon,\varepsilon]) \cup (L\times[\varepsilon,1] )\simeq U$ (with $\varepsilon>0$), which is the product foliation on $L\times[-\varepsilon,\varepsilon]$, is smooth and contains a family of compact leaves. Moreover, we can choose the diffeomorphisms appearing in the construction such that $\xi\eing{U}$ is as close to $\xi'\eing{U}$ in the $C^0$-topology as we want.
We can choose $\xi'\eing{U}$ such that $A_{0,i}(\xi)$ and $A_{0,i}(\xi')$ coincide outside of the region where the slope of $A_{0,i}(\xi)$ is very small compared to the slope of $A_{-1,i}(\xi)$. By construction the slope of $A_{0,i}(\xi')$ is much smaller than the slope of $A_{-1,i}(\xi)=A_{-1,i}(\xi)$. As in the second step in the proof of \lemref{l:reminder on holonomy approx} (or Lemma 2.5.1. of \cite{confol}) one can extend $\xi'$ to a smooth confoliation on $M$ such that $\xi'$ is close to $\xi$ (the foliation $\mathcal{J}$ corresponds to the $y$-coordinate in \cite{confol}). The claim about $F(\xi')$ follows immediately from the construction.
\end{proof}
\begin{rem} \mlabel{r:force holonomy}
After a trivially foliated bundle $L\times[-\varepsilon,\varepsilon]$ is added to the confoliation, it is possible to replace the trivially foliated piece by a foliation on $L\times[-\varepsilon,\varepsilon]$ such that the boundary leaves $L\times\{\pm\varepsilon\}$ have sometimes attractive holonomy on side lying in $L\times[-\varepsilon,\varepsilon]$. The following statements follow from the construction explained in \cite{confol} on p. 39. (This construction carries over to surfaces with boundary after the surface is doubled.)
When the Euler characteristic of $L$ is negative, then one can replace the product foliation on $L\times[-\varepsilon,\varepsilon]$ by a foliation such that the holonomy along every homotopically non trivial curve in $L\times\{\varepsilon\}$ or $L\times\{-\varepsilon\}$ is sometimes attractive on one side.
If the Euler characteristic of the compact surface with boundary $L$ is not negative, then $L$ is diffeomorphic to $S^2,D^2,T^2$ or $S^1\times I$. The case $S^2$ will not occur unless the confoliation in question is actually a product foliation by spheres. But these are excluded. If $L\simeq S^1\times I$, then the suspension of a suitable diffeomorphism yields the same result as in the case of $\chi(L)<0$ (without doubling the surface). The case $L\simeq D^2$ will be excluded by the last requirement of \defref{d:overtwisted star} in the application we have in mind. Finally, the case $L\simeq T^2$ is exceptional because of Kopell's lemma (cf. the footnote on p.~39 of \cite{confol}). But if $L=T^2$, then it is easy to arrange that the holonomy is attractive along a given homotopically non-trivial curve.
This modification changes the characteristic foliation on $F$, but only an open set which was foliated by closed leaves and cycles before the perturbation. In particular overtwisted stars are not affected.
\end{rem}
The following proposition from \cite{confol} adapts a famous result of Sacksteder \cite{sacksteder} to laminations so that it can be applied to the fully foliated part of confoliations.
\begin{prop}[Proposition 1.2.13 in \cite{confol}] \mlabel{p:sacksteder}
Let $(M,\xi)$ be a $C^k$-confoliation, $k\ge 2$. All minimal sets of the fully foliated part of $\xi$ are either closed leaves or exceptional minimal sets. Each exceptional minimal set contains a simple closed curve along which $\xi$ has non-trivial infinitesimal holonomy.
In particular exceptional minimal sets are isolated and there are only finitely many of them.
\end{prop}
We denote the finite set consisting of the exceptional minimal sets of the fully foliated part of $\xi$ by $\mathcal{E}(\xi)$.
In the following $F$ will be an embedded surface containing an overtwisted star $(Q,V,\alpha)$. We write $\Omega_Q$ for $\cup_{v\in V}\gamma_v$. If $\gamma_v, v\in V$ is a cycle containing hyperbolic singularities of $F(\xi)$, then the confoliation $\xi$ can be modified such that the cycle has a neighbourhood which is foliated by closed leaves of the characteristic foliation of the modified confoliation (cf. \lemref{l:thickening}). We will therefore assume that $\gamma_v$ is either a closed leaf of $F(\xi)$ or a quasi-minimal set but not a cycle containing hyperbolic singularities. (By the definition of an overtwisted star, $\gamma_v$ is not an elliptic singularity.)
\begin{lem} \mlabel{l:approx with control2}
Let $\xi$ be a confoliation and $F$ an embedded connected surface containing an overtwisted star $(Q,V,\alpha)$ and $v\in V$.
\begin{itemize}
\item[a)] If $\gamma_v$ is contained in a closed leaf of $\xi$, then in every $C^0$-neighbourhood of $\xi$ there is a confoliation $\xi'$ such that $F(\xi')$ contains an overtwisted star $(Q',V',\alpha')$ which is naturally identified with $(Q,V,\alpha)$ and $\gamma'_v, (v\in V'\simeq V)$ passes through the contact region of $\xi'$.
\item[b)] Assume that $\gamma$ is contained in an exceptional minimal set, $\gamma$ has attractive linear holonomy, and $\gamma$ is transverse to $F$. Then every $C^0$-neighbourhood of $\xi$ contains a confoliation $\xi'$ such that $F(\xi')$ contains an overtwisted star which can be naturally identified with $(Q,V,\alpha)$
and $|\mathcal{E}(\xi')|<|\mathcal{E}(\xi)|$.
\end{itemize}
\end{lem}
\begin{proof}
First we prove a). Let $L$ be the closed leaf containing $\gamma_v$. Since $\gamma_v$ is the $\omega$-limit set of leaves in $F(\xi)$ it has attractive holonomy on one side and $F\cap L$ consists of a family of cycles. In particular, $L\cap\alpha(Q)=\emptyset$ because an overtwisted star with virtual vertices does not contain closed cycles of the characteristic foliation.
We use \lemref{l:thickening} and \remref{r:force holonomy} to ensure that $\gamma_v$ has sometimes attractive holonomy on both sides. Unfortunately this property
is not stable under arbitrary isotopies of $\gamma_v$ in general. But by \lemref{l:neg-curv} there is an annulus $A\simeq \gamma_v\times[0,1]$ such that $\gamma_v=\gamma_v\times\{0\}=F\cap A$ and all curves in $A$ have attracting holonomy on the side where $\alpha(Q)$ approaches $\gamma_v$ while isotopies do not change the nature of the holonomy on the other side of $L$ since there the confoliation is actually a foliation.
Therefore there is a small isotopy of $F$ which maps $(Q,V,\alpha)$ to an overtwisted star $(Q',V',\alpha')$ on the isotoped surface $F'$ such that $\gamma_v$ is mapped to $\gamma_v\times\{\varepsilon\}$ where $0<\varepsilon<1/2$. Then we can apply \lemref{l:reminder on holonomy approx} to $\gamma_v\times\{0\}$ and $\gamma_v\times\{2\varepsilon\}$.
After this there is a Legendrian arc intersecting $F'$ exactly once in a point of $\gamma_v$ and both endpoints of this arc lie in the contact region. Hence this arc satisfies the assumptions of \lemref{l:approx with control1}. Therefore there is a confoliation $\xi'$ with the desired properties such that $F'(\xi)=F'(\xi')$. This finishes the proof of a).
Now we prove b). We shall use notations from the proof of \lemref{l:reminder on holonomy approx}. In the proof we will use the freedom in the choice of the function $g$ in the proof of \lemref{l:reminder on holonomy approx}. For this we need the fact that $\gamma$ has non-trivial infinitesimal holonomy since then there are only very few restriction on $g$ in the proof of \lemref{l:reminder on holonomy approx}, cf. also Lemma 2.5.2 in \cite{confol}.
Fix a neighbourhood $U\simeq S^1_x\times[-1,1]_y\times[-1,1]_z$ such that $\gamma=S^1\times\{(0,0)\}$ and the coordinates $x,y,z$ have all the properties used in the proof of \lemref{l:reminder on holonomy approx}. In particular, the foliation by the second factor is Legendrian and coincides with $F(\xi)$ on $F\cap U$ while the third factor is positively transverse to $\xi$. We require that $U$ intersects $F$ only in neighbourhoods of points in $\gamma\cap\Omega_Q=:X$.
Let us make an orientation assumption in order to simplify the presentation: We assume that the orientation of the Legendrian foliation on $S^1\times[-1,1]\times[-1,1]$ given by the second factor coincides with the orientation of $F(\xi)$ near points of $\gamma\cap\gamma_v, v\in V$, ie. in \figref{b:near-tentacle} the foliation is oriented from left to right. When this assumption is not satisfied for some $y\in\gamma\cap\Omega_Q$, then one has to interchange the roles of $\hat{\tau}_-(y)$ and $\hat{\tau}_+(y)$ in some of the following arguments.
By transversality $\gamma$ intersects $F$ in a finite number of points. Since $\gamma$ is contained in the fully foliated part of $\xi$, $\gamma$ cannot intersect $\alpha(Q)$ since every point of $\alpha(Q)$ is connected to $H(\xi)$ by a Legendrian arc. We can ignore the points in $F\cap\gamma$ which do not belong to $\overline{\alpha(Q)}$ if we deform $\xi$ on a neighbourhood of $\gamma$ which is small enough.
Because $F$ is smoothly embedded and $\xi$ is $C^2$-smooth, $F(\xi)$ is also of class $C^2$. As we have already mentioned in \secref{ss:legpoly} the $\omega$-limit set $\gamma_v$ with $v\in V$ is either a quasi-minimal set or we may assume (after a small isotopy of $F$) that $\gamma_v$ is a closed leaf of $F(\xi)$. We distinguish the following cases.
\begin{itemize}
\item[(i)] $\gamma_v$ is quasi-minimal. Since there are interior points of $\alpha(Q)$ arbitrarily close to $\gamma_v$, there is no segment $\tau$ transverse to $F(\xi)$ such that $\tau\cap\gamma_v$ is dense in $\tau$. Then $\gamma_v\cap\tau$ is a Cantor set (cf. \cite{guiterrez}). The intersection between two different quasi-minimal sets cannot contain a recurrent orbit by Maier's theorem (Theorem 2.4.1 in \cite{flows}) and the number of quasi-minimal sets of $F(\xi)$ is bounded by the genus of $F$ according to Theorem 2.4.5. in \cite{flows}.
\item[(ii)] $\gamma_v$ is a closed leaf of $F(\xi)$ whose holonomy is attractive on the side from which $\alpha(Q)$ accumulates on $\gamma_v$ while it is repulsive on the other side and $\alpha(Q)$ spirals onto $\gamma_v$ on the attractive side. In this case, $\alpha(Q)$ cannot enter a one-sided neighbourhood of $\gamma_v$ on the side where the holonomy is repulsive.
\item[(iii)] $\gamma_v$ is a closed leaf of $F(\xi)$ whose holonomy is attractive on one side and either there is a sequence of closed leaves of $F(\xi)$ on the other side of $\gamma_v$ which converge to $\gamma_v$ or $\gamma_v$ has attractive holonomy on both sides.
\end{itemize}
If $\gamma_v$ belongs to class (iii) and $U$ is small enough (ie. contained in the interior of an annulus each of whose boundary is tangent to $F(\xi)$ or transverse to $F(\xi)$ such that $F(\xi)$ points into the annulus), then any modification of $F(\xi)$ with support in $U\cap F$ will result in a singular foliation on $F$ such that all leaves of the characteristic foliation which enter a neighbourhood of $\gamma_v$ containing $U$ will remain in $U$ forever even after the modification. When no singularities are created during the modification, then the modification replaces $(Q,V,\alpha)$ by an overtwisted star $(Q',V',\alpha')$ such that $|V|=|V'|$. In this case $\gamma_{v}\neq\gamma'_{v}$ but $\gamma_v'$ is a closed leaf of $F(\xi')$ which passes through $H(\xi')$ (by the proof of \lemref{l:reminder on holonomy approx}. We keep this case separated from the others although all three of them may occur in one single perturbation of $\xi$.
The following argument is complicated due to a difficulty in case (ii). If $\alpha(Q)$ accumulates on $\gamma_v$ and the holonomy of $\gamma_v$ is repulsive on the side where points of $\gamma$ are pushed to by the diffeomorphism $G$ appearing in the proof of \lemref{l:reminder on holonomy approx}, then it is impossible to say something about the new $\omega$-limit set of leaves in $\alpha(Q)$ which accumulated on $\gamma_v$ unless $G$ is chosen carefully: It is possible that leaves which accumulated on $\gamma_v$ accumulate on $\gamma_{v'}$ when the characteristic foliation is modified near $\gamma_{v}$. However it is possible that $\gamma_{v'}$ is also changed when $\xi$ is replaced by $\xi'$. Therefore one has to treat all $v\in V$ such that $\gamma_v$ belongs to (i),(ii) simultaneously.
For non-empty open intervals $\tau_-\subset[-1,0)$ and $\tau_+\subset(0,1]$ we write $\hat{\tau}_\pm(y):=\{y\}\times[-1,1]\times\overline{\tau_\pm}$ for $y\in\gamma$. We will fix $\tau_\pm$ in the following.
We require that $\tau_+$ is chosen such that the $\omega$-limit
of a leaf intersecting $\hat{\tau}_+(y)$ is never a hyperbolic singularity for all $y\in X$. Because
\begin{itemize}
\item there are only finitely many hyperbolic singularities on $F$ and
\item $\alpha(Q)$ intersects every interval transverse to $\gamma_v$ in an open set (note that there are singular folioations on surfaces with dense quasiminimal sets; in particular stable leaves of hyperbolic singularities in such quasi-minimal sets may be dense in the surface)
\item $\alpha(\partial Q)$ is disjoint from $\gamma_v$ which intersect $\gamma$ even if $\gamma_v$ is quasi-minimal (this is true because every point of $\alpha(Q)$ is connected to $H(\xi)$ by a Legendrian curve while $\gamma$ is part of the fully foliated set)
\end{itemize}
this condition can be satisfied.
Next we impose additional restrictions on $\tau_-$:
We choose $\tau_-$ such that no point in $\hat{\tau}_+(x), x\in X,$ is connected to $\hat{\tau}_-(y),y\in X,$ by a leaf of $F(\xi)$ which is disjoint from $\{(y,0)\}\times[\inf(\tau_-),\sup(\tau_+)]$. In other words, we require that leaves of $F(\xi)$ which come from $\hat{\tau}_+(x)$ do not intersect $\hat{\tau}_-(y)$ when they meet the piece of $\{(y,-1)\}\times[-1,1]\subset (U\cap F)$ which lies between the lower endpoint of $\hat{\tau}_-(y)$ and the upper endpoint of $\hat{\tau}_+(y)$ for the first time. In order to satisfy this condition it might be necessary to shorten $\tau_+$.
Obviously there is a choice for $\tau_+,\tau_-$ which satisfies these requirements for $x,y\in X$ whenever the limit set $\gamma_v$ which corresponds to $y$ is not the $\omega$-limit set of leaves intersecting $\hat{\tau}_+(x)$.
If $y$ is contained in a closed leaf of $F(\xi)$, then one can also satisfy the requirement for $x,y\in X$ provided that $\tau_+$ is so short that the translates of $\hat{\tau}_+(x)$ along leaves of $F(\xi)$ do not cover the segment $\hat{\tau}_-(y)$). We shorten $\tau_+$ whenever this is necessary. Finally, when $y$ is part of a quasi-minimal set and the leaves of $F(\xi)$ which intersect $\hat{\tau}_+(x)$ accumulate on this quasi-minimal set the above requirement can be satisfied by shortening $\tau_\pm$ again. Now one can construct $\tau_-$ in a finite number of steps and shortening $\tau_\pm$ at each step.
Let $t_-\in\tau_-$. We fix the diffeomorphism $g:[-1,1]\longrightarrow[-1,1]$ in the proof of \lemref{l:reminder on holonomy approx} such that $g$ maps the entire interval $(t_-,\sup(\tau_+))$ into $\tau_+$ and the support of $g$ is contained in $(\inf(\tau_-),\sup(\tau_+))$.
The role of the parameters $\zeta,\zeta'$ from the proof of \lemref{l:reminder on holonomy approx} is now played by $\sup(\tau_+),\inf(\tau_-)$.
If $\xi$ is modified by the procedure described in the proof of \lemref{l:reminder on holonomy approx} using the diffeomorphism $g$ chosen above, then one obtains a confoliation $\xi'$ such that all leaves of $F(\xi')$ starting at the elliptic singularity in the center of the original overtwisted whose $\omega$-limit set was $\gamma_v$ such that $\gamma_v\cap\gamma\neq\emptyset$ never meet a hyperbolic singularity of $F(\xi')$.
Since all elliptic singularities on the boundary of the basin of the elleiptic singularity in $\alpha(Q)$ are automatically negative and all hyperbolic singularities on the boundary of the basin where already present in $\alpha(\partial Q)$ there is an overtwisted star $(Q',V',\alpha')$ and $V'$ can be viewed as a subset of $V$ by construction. Moreover, $|\mathcal{E}(\xi')|<|\mathcal{E}(\xi)|$.
\end{proof}
Now we can finally show that there are no overtwisted stars when $\xi$ is symplectically fillable.
\begin{thm} \mlabel{t:no polygons if filled}
Let $(M,\xi)$ be a $C^k$-confoliation, $k\ge 2$, which is symplectically fillable. Then no oriented embedded surface contains an overtwisted star.
\end{thm}
\begin{proof}
Let $(X,\omega)$ be a symplectic filling of $\xi$. Assume that $F$ is an embedded surface containing an overtwisted star $(Q,V,\alpha)$. It is sufficient to treat only the case of closed surfaces when the elliptic singularity in the interior of $\alpha(Q)$ is positive.
In the first part of the proof we show how to reduce the number of virtual vertices. Because overtwisted stars are not required to be injective as Legendrian polygons, we show in a second step how to obtain an embedded disc violating \defref{d:tight confol} starting from an overtwisted star $(Q,\emptyset,\alpha)$. The confoliation is modified several times but all confoliations appearing in the proof will be $C^0$-close to $\xi$. In particular they are symplectically fillable. Therefore the assumption that $(M,\xi)$ admits an overtwisted star leads to a contradiction to \thmref{t:fillable confol are tight}.
Notice that in the presence of an overtwisted star $\xi$ cannot be a foliation everywhere. Therefore $M$ is not a minimal set of the fully foliated part of $\xi$ and $\xi$ is not a foliation without holonomy.
{\em Step 1:} If $V\neq\emptyset$, then $\xi$ can be approximated by a confoliation which admits an overtwisted star with less virtual vertices than $(Q,V,\alpha)$. We fix $v_0\in V$. If $\gamma_0:=\gamma_{v_0}$ intersects $H(\xi)$, then an application of \lemref{l:create} yields a surface carrying an overtwisted star with less virtual vertices after a $C^0$-small isotopy of $F$. Now assume $\gamma_0\cap H(\xi)=\emptyset$.
Let $L$ be the maximal connected open immersed hypersurface of $M$ which is tangent to $\xi$ and contains $\gamma_0$. If $L=\emptyset$, then there is a Legendrian segment $\sigma$ satisfying the hypothesis of \lemref{l:approx with control1}. After applying this lemma, $\gamma_v$ intersects the contact region of the modified confoliation and we are done.
Now assume $L\neq\emptyset$ and let $L^\infty$ be the space of ends of $L$. We say that an end $e\in L^\infty$ lies in $H(\xi)$ if for every compact set $K\subset L$ there is a Legendrian curve from $H(\xi)$ to the connected component of $L\setminus K$ corresponding to $e$.
{\em Step 1a:} If $L^\infty\neq\emptyset$, then we approximate $\xi$ such that all ends of $L$ lies in the contact region of the modified confoliation.
The set of ends in $H(\xi)$ is open in $L^\infty$, therefore its complement $L^\infty_{fol}$ is compact. To each $e\in L^{\infty}_{fol}$ we associate a minimal set $\mathcal{M}(e)\subset\lim_e L$ of the fully foliated part of $\xi$ (this is explained in \cite{cc}, p. 115). Recall that $M$ cannot be a minimal set of the fully foliated part of $\xi$. According to \cite{hh}, p.19, all minimal sets are either closed leaves or exceptional minimal sets. Note that we allow that $L$ is contained in $\mathcal{M}(e)$.
If $\mathcal{M}(e)$ is a closed leaf of $\xi$ whose holonomy along a curve $\gamma$ transverse to $F$ is sometimes attractive, then we can apply \lemref{l:approx with control2} (a) to $\gamma_v$ if there is $v\in V$ with $\gamma_v\subset \mathcal{M}(e)$. If $L$ contains no limit set of $\alpha(Q)$, then the procedure from the proof of \lemref{l:reminder on holonomy approx} can be applied directly to any curve $\gamma\subset \mathcal{M}(e)$ with sometimes attractive holonomy. We can ensure the existence of such a curve by \lemref{l:thickening} and \remref{r:force holonomy}.
If $\mathcal{M}(e)$ is an exceptional minimal set, then according to \propref{p:sacksteder} there is a simple closed curve $\gamma$ in a leaf $L_\gamma\subset \mathcal{M}(e)$ with non-trivial infinitesimal holonomy. Every curve in $L_\gamma$ which is isotopic to $\gamma$ through Legendrian curves has the same property by Lemma 1.3.17 in \cite{confol}. In particular we may assume that $\gamma$ is transverse to $F$.
Using \lemref{l:approx with control2} (b) we approximate $\xi$ by a confoliation $\xi'$ such that $L_\gamma$ meets $H(\xi')$.
If $\mathcal{M}(e)$ was an exceptional minimal set, this process might have changed the overtwisted star in the sense that type of the $\omega$-limit sets of virtual vertices may have changed. But recall that by the proof of \lemref{l:approx with control2} we can view $V'$ as a subset of $V$. We use $\gamma'_v$ to denote the $\omega$-limit set of leaves which start at the elliptic singularity in the center of the overtwisted star and accumulated on $\gamma_v, v\in V$ before the modification.
We iterate the procedure from the very beginning with $v_0\in V'$ and with an integral surface of $\xi'$ containing $\gamma'_0$. Since $\mathcal{E}(\xi)$ is finite and $|\mathcal{E}(\xi')|<|\mathcal{E}(\xi)|$ this phenomenon can occur only finitely many times.
After finitely many steps no exceptional minimal sets will occur in the above procedure. In later applications of the above construction $\gamma_0'=\gamma_0$ and the maximal integral surface of $\xi'$ containing $\gamma_0'$ is contained in the maximal integral surface of $\xi$ containing $\gamma_0$. Because the inclusion induces a continuous mapping between the spaces of ends and by the compactness of $L^\infty_{fol}$ we are done after finitely many steps. We continue to write $F$ for the embedded surface, $\xi$ for the confoliation, and $(Q,V,\alpha)$ for the overtwisted star etc.
{\em Step 1b:} We isotope $F$ such that all quasi-minimal sets of the characteristic foliation on the resulting surface pass through the contact region. As we have already noted in the proof of \lemref{l:approx with control2}, $F(\xi)$ has only finitely many quasi-minimal sets (this number is bounded by the genus of $F$). Let $\gamma_w,w\in V$ be a quasi-minimal set of $F(\xi)$ which is disjoint from $H(\xi)$.
According to Theorem 2.3.3 in \cite{flows} there is an uncountable number of leaves of $F(\xi)$ which are recurrent (in both directions) and dense in $\gamma_w$ while there is only a finite number of pseudovertices of $(Q,V,\alpha)$ and only finite number of virtual vertices. Therefore there is $p_w\in\gamma_w$ which can be connected to $H(\xi)$ by a Legendrian arc $\sigma$ transverse to $F$ such that $\sigma$ does not meet $\alpha(\partial Q)$ and $\sigma$ never intersects closed components of $\Omega_Q$. At this point we use the fact that every end of the union of integral hypersurfaces containing $\gamma_w$ lies in $H(\xi)$. If $\sigma$ intersects $\Omega_Q$ in some other quasi-minimal set $\gamma_{w'}, w'\in V$ before it meets $H(\xi)$, then we replace $\gamma_w$ by $\gamma_{w'}$. Thus we may assume that $\sigma$ meets $F$ in $p_w$ and nowhere else.
By Lemma 2.8.2 in \cite{confol} there is a confoliation $\xi'$ $C^k$-close to $\xi$ such that $F(\xi')=F(\xi)$, $\sigma$ is tangent to $\xi$ and $\xi'$ and a neighbourhood of $p_w$ in $F$ lies in $\overline{H(\xi')}$. We will denote $\xi'$ again by $\xi$.
Choose a neighbourhood $U\simeq\sigma\times[-1,1]\times[-1,1]$ of $\sigma$ such that $\sigma=\sigma\times\{(0,0)\}$ and $(\{p_w\}\times[-1,1]\times[-1,1])\subset F$. Moreover, we require that the foliation by the first factor is Legendrian while the foliation corresponding to the second factor is transverse to $\xi$ and $\ring{U}\subset H(\xi)$. Finally we assume that the foliation which corresponds to the second factor is Legendrian when it is restricted to $F$.
Now we apply an isotopy to $F$ whose effect on the characteristic foliation on $F$ is the same as the effect of the map $G$ appearing in the proof of \lemref{l:reminder on holonomy approx}. We explain this under the following orientation assumptions (the other cases can be treated in the same way):
The orientation of $F(\xi)$ coincides with the second factor of $U\simeq\sigma\times[-1,1]\times[-1,1]$ and the coorientation of $F$ points away from $U$. In \figref{b:near-tentacle} the left respectively right edge of the rectangle corresponds to $\{(p_w,-1)\}\times[-1,1]$ respectively $\{(p_w,1)\}\times[-1,1]$, the foliation is oriented from left to right, the coorientation of $\xi$ points upwards and the coorientation of $F$ points towards the reader.
Choose $-1<x<0<y<1$ such that the points $(p_w,-1,x), (p_w,1,y)\in F$
\begin{itemize}
\item[(i)] do not lie on a stable or unstable leaf of a hyperbolic singularity and they are not connected by a leaf of $F(\xi)$.
\item[(ii)] can be connected by a smooth Legendrian arc $\lambda$ in $U$ whose projection to $\sigma\times[-1,1]$ is embedded and $\lambda$ is $C^\infty$ tangent to $F$. Moreover, we assume that the projection of $\lambda$ to $\sigma\times[-1,1]$ is transverse to the first factor.
\end{itemize}
The curve $\lambda$ and $x,y$ exist because of the orientation assumptions and \lemref{l:neg-curv}. Now fix $x',y'$ close to $x,y$ such that $x<x'<0<y'<y$.
Using a flow along the first factor of $U$ we can move $\{p_w\}\times[-1,1]$ to a curve which is close to the projection of $\lambda$ to $\sigma\times[-1,1]$. When we apply this flow to $F$, the surface is pulled into $U$ and we obtain a surface $F'$ isotopic to $F$ which coincides with $F$ outside of $\{p_w\}\times(-1,1)\times(x,y)$.
By the assumptions on $\lambda$ we can choose $F'$ such that $F'((xi)$ compresses the transverse segment $\{(p_w,-1)\} \times (x',y)$ onto $\{(p_w,1)\}\times(y',y)$ such that no leaf of intersecting $\{(p_w,1)\}\times(y',y)$ is part of a stable or unstable leaf of $F(\xi)$. Moreover, we may assume that leaves which start at points of $\{(p_w,1)\}\times(y',y)$ meet the segment $\{(p_w,-1)\}\times[x',y]$ before the enter the region where $F'\neq F$ for the first time.
The new $\omega$-limit set is now a closed leaf of $F'(\xi)$ which passes through $\{(p_w,1)\}\times(y',y)$.
This modification may have created quasi-minimal sets on $F'$ which were not present in $F(\xi)$. But if this happens, then the new quasi-minimal sets intersect the contact region by construction. Thus after finitely many steps (this number is bounded by the genus of $F$) we have isotoped $F$ such that all quasi-minimal sets of the characteristic foliation on the resulting surface pass through the contact region. Now we apply \lemref{l:create}. We obtain a surface $F''$ containing an overtwisted star $(Q'',V'',\alpha'')$ such that there is a natural inclusion $V''\subset V$ and all $\gamma_v, v\in V''$ are cycles of $F''(\xi)$. In the next step we treat the remaining virtual vertices. We will denote $F''$ by $F$, $Q''$ by $Q$, etc.
{\em Step 1c:} Let $\gamma_0$ be the limit set which corresponds to the virtual vertex $v_0\in V$ of an overtwisted star $(Q,V,\alpha)$. We assume that $\gamma_v$ is a cycle for all $v\in V$ and
all ends of the maximal integral surface $L_0$ containing $\gamma_0$ lie in the contact region.
Choose a submanifold $L_0'\subset L_0$ of dimension $2$ such that $L_0'$ contains all closed components of $\Omega_Q\cap L_0$. Since each end of $L_0$ lies in $H(\xi)$ we can choose $L_0'$ so that each boundary component is connected to $H(\xi)$ by a Legendrian curve which does not intersect the interior of $L_0'$. After a $C^\infty$-small perturbation (we use again Lemma 2.8.1 from \cite{confol}) of $\xi$ we may assume that the boundary of $L_0'$ is contained in the contact region of the resulting confoliation $\xi'$. This perturbation might affect the characteristic foliation on $F$, but since the modification of the confoliation does not affect $\Omega_Q$ and all components of $\Omega_Q$ are cycles of $F(\xi)$ which are also present in $F(\xi')$, there still is an overtwisted star $(Q',V'\alpha')$ on $F$ together with a natural inclusion $V'\hookrightarrow V$.
Now we can apply \lemref{l:thickening} and \remref{r:force holonomy}. From \lemref{l:approx with control2} a) we obtain a confoliation $\xi''$ which is $C^0$-close to $\xi'$ such that $F(\xi'')$ contains an overtwisted star $(Q'',V'',\alpha'')$ with $V''\subset V'$ and all $\omega$-limit sets $\gamma_w'', w\in V''$ which were contained in $L_0$ now intersect the contact region of $\xi''$. After an application of \lemref{l:create} we can reduce the number of virtual vertices.
{\em Step 2:} We show that we can assume that the map $\alpha$ associated to the overtwisted star $(Q,\emptyset,\alpha)$ in $F$ is injective.
Assume that the Legendrian polygon $(Q,\emptyset,\alpha)$ is not injective. Then there are two edges $e_1,e_2$ of $Q$ such that $\alpha(e_1)=\alpha(e_2)$. (Recall that by our genericity assumption no two different hyperbolic singularities of $F(\xi)$ are connected by leaves. Therefore configurations like the one shown in \figref{b:identify} cannot appear.)
Let $y$ be the image of the pseudovertex on $e_1$ by the map $\alpha$. Then $y$ is a negative hyperbolic singularity of $F(\xi)$. The $\omega$-limit sets of the stable leaves of $y$ are negative elliptic singularities $y_1,y_2$ in $\alpha(\partial Q)$ and we may assume that these singularities are contained in $H(\xi)$ (because they are $\omega$-limit sets, they do not lie in the interior of the foliated part of $\xi$).
We eliminate $y_1$ and $y$ using \lemref{l:elim}. This reduces the number of edges of the polygon which are identified unless $y_1=y_2$. The case when $y_1=y_2$ requires slightly more work:
After perturbing the surface on a neighbourhood of $y_1$ we may assume that the two unstable leaves of $y$ form a smooth closed Legendrian curve $\gamma'$. We eliminate $y_1,y$ such that $\gamma'$ is a closed leaf of the characteristic foliation on the resulting surface. We obtained a Legendrian polygon $(Q',V',\alpha')$ on a surface $F'$ with $Q'\simeq D^2$ and $V'$ consists of all vertices of $Q'$ which were mapped to $y_1$ by $\alpha'$. By construction $\gamma_{v'}=\gamma'$ for all $v'\in V'$.
Since $y_1\in H(\xi')$ we can approximate $\xi'$ by a confoliation $\xi''$ which coincides with $\xi'$ outside a tubular neighbourhood of $\gamma'$ and is a contact structure near $\gamma'$. This can be done without changing the characteristic foliation on the surface by \lemref{l:approx with control1}.
Next we apply a standard procedure from contact topology called folding to $\gamma'$. This is described in \cite{honda} (on p. 325). We obtain a surface $F''$ which contains an overtwisted star $(Q'',V'',\alpha')$ such that $V'$ consists of two elements with $Q''\simeq Q'$, $V''=V'$ but now elements of $V''$ correspond to different $\omega$-limit sets depending on which side of $\gamma'$ the corresponding leaves of $\alpha(Q)$ accumulated.
In order to continue we create a pair of negative singularities along the closed leaves in $\overline{\alpha''(Q'')}$. We eliminate all pseudovertices successively and we obtain a confoliation $\widetilde{\xi}$ on $M$ together with an overtwisted star $(\widetilde{Q},\widetilde{V}=\emptyset,\widetilde{\alpha})$ on a surface $\widetilde{F}$ which has no virtual vertices and is injective as a Legendrian polygon. $\widetilde{\alpha}$ becomes injective after finitely many perturbations of $\widetilde{F}$ as in \figref{b:split}.
Because $\widetilde{\alpha}(\partial \widetilde{Q})$ passes through the contact region of $\widetilde{\xi'}$ the disc $D=\widetilde{\alpha}(\widetilde{Q})$ violates \defref{d:tight confol}. This concludes the proof of the theorem.
\end{proof}
This proof can be modified to yield a proof of \thmref{t:fillable confol are tight} using the well known fact that symplectically fillable contact structures are tight and without referring to results of R.~Hind in \cite{hind} which are used in \cite{confol}. Let us outline the argument.
Given a disc $D$ as in \defref{d:tight confol} assume first that the holonomy of $\partial D$ in $D$ is non-trivial. We try follow the construction above to find a confoliation $\xi'$ such that $\partial D$ remains Legendrian and $\xi'$ is $C^0$-close to $\xi$. This attempt must fail since otherwise we could continue to modify $\xi'$ into a symplectically fillable contact structure such that $D$ becomes an overtwisted disc. This contradicts the fact that symplectically fillable contact structures are tight.
The only point at which the above construction can break down is the application of \remref{r:force holonomy} in the case when $\partial D$ bounds a disc $D'$ in the maximal surface which contains $\partial D$ and is tangent to the confoliation. In order to show that $e(\xi)[D\cup D']=0$ one chooses an embedded sphere $S$ close (and homologous) to $D\cup D'$. Then $e(\xi)[S]=0$ follows from the tightness contact structures which are $C^0$-close to the original one.
It remains to treat the case when the holonomy of $\partial D$ in $D$ is trivial. Then one has to show that either $\partial D$ is a vanishing cycle (cf. Chapter 9 in \cite{cc2}) or one can replace $D$ by a smaller disc which has Legendrian boundary along which the holonomy of the characteristic foliation on the disc is not trivial. If $\partial D$ is a vanishing cycle, then one uses results due to S.~Novikov \cite{No} to establish the existence of a solid torus whose boundary $T$ is a leaf of the confoliation. This contradicts $\int_T\omega>0$ because this inequality means that $T$ represents a non-trivial homology class.
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"redpajama_set_name": "RedPajamaC4"
} | 8,493 |
In natural selection the fittest individuals survive and pass on their genes to the next generation
Animals' features are highly functional, otherwise they wouldn't survive. But what possible function could a peacock's tail have? The answer lies in another of Charles Darwin's great ideas – sexual selection.
Sexual selection is based on the theory that competition for a mate drives the evolution of certain characteristics. In nature males typically have to compete to be chosen by females. If females favour some attractive feature of a male, the genes for that feature will thrive, as will genetic changes that enhance it – until the benefits in the mating game are balanced by the cost of such extravagant and useless features.
But why do females choose decorated males? Possibly, showy features help females to choose a mate with the 'best' genes. An extravagant display, in beautiful condition, suggests that the male has managed to acquire plenty of food, and has defended himself well against predators and disease. While he might just have been lucky, more likely he has a fine set of genes.
Illustration showing sexual selection. A fancy decoration may attract the females, but eventually it could become a liability.
Illustration © Glen McBeth
This resource was first published in 'Evolution' in January 2006 and reviewed and updated in October 2014.
Genetics and genomics, Health, infection and disease
Evolution, Sex and Gender
How Darwin changed the world
Charles Darwin put forward a theory of evolution by natural selection – but he was not the only person to come up with such an idea
Caught in a drift
A random process of drift can also change the genetic make-up of a species | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 474 |
sfRenderWindow* sfRenderWindow_create_helper
(sfVideoMode* mode, const char* title, sfUint32 style, const sfContextSettings* settings)
{
return sfRenderWindow_create (*mode, title, style, settings);
}
void sfRenderWindow_getSettings_helper (const sfRenderWindow* renderWindow, sfContextSettings* settings)
{
*settings = sfRenderWindow_getSettings (renderWindow);
}
void sfRenderWindow_getPosition_helper (const sfRenderWindow* renderWindow, sfVector2i* position)
{
*position = sfRenderWindow_getPosition (renderWindow);
}
void sfRenderWindow_setPosition_helper (sfRenderWindow* renderWindow, sfVector2i* position)
{
sfRenderWindow_setPosition (renderWindow, *position);
}
void sfRenderWindow_getSize_helper (const sfRenderWindow* renderWindow, sfVector2u* size)
{
*size = sfRenderWindow_getSize (renderWindow);
}
void sfRenderWindow_setSize_helper (sfRenderWindow* renderWindow, sfVector2u* size)
{
sfRenderWindow_setSize (renderWindow, *size);
}
void sfRenderWindow_clear_helper (sfRenderWindow* renderWindow, sfColor* color)
{
sfRenderWindow_clear (renderWindow, *color);
}
void sfRenderWindow_getViewport_helper (const sfRenderWindow* renderWindow, const sfView* view, sfIntRect* rect)
{
*rect = sfRenderWindow_getViewport (renderWindow, view);
}
void sfRenderWindow_mapPixelToCoords_helper
(const sfRenderWindow* renderWindow, sfVector2i point, const sfView* targetView, sfVector2f* out)
{
*out = sfRenderWindow_mapPixelToCoords (renderWindow, point, targetView);
}
void sfMouse_getPositionRenderWindow_helper (const sfRenderWindow* relativeTo, sfVector2i* position)
{
*position = sfMouse_getPositionRenderWindow (relativeTo);
}
void sfMouse_setPositionRenderWindow_helper (sfVector2i* position, const sfRenderWindow* relativeTo)
{
sfMouse_setPositionRenderWindow (*position, relativeTo);
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,429 |
\section{Introduction}
The three heavily boron-doped semiconductors diamond \cite{ekimov04a}, cubic silicon \cite{bustarret06a}, and silicon carbide \cite{ren07a} belong to the newly discovered family of superconductors based on the diamond structure. The remarkable difference between them is the nature of the superconducting ground state: C:B and Si:B are type-II whereas SiC:B is a type-I superconductor. Silicon carbide itself is a well-known example for polytypism. More than 200 crystal modifications with energetically slightly different ground states are reported in literature. The most common ones are 3C-SiC, 2H-, 4H- and 6H-SiC, and 15R-SiC. The number in front of C (\,=\,cubic unit cell), H (\,=\,hexagonal), and R (\,=\,rhombohedral) indicates the number of Si\,--\,C bilayers stacking in the conventional unit cell. Whereas the cubic structure seems to be a precursor or precondition for the occurrence of superconductivity in the parent systems C:B and Si:B, in SiC:B hexagonal modifications contribute to the superconductivity, too, as we will discuss in this paper. We focus on two different polycrystalline samples. One, referred to as SiC-1, contains three different phase fractions: 3C-SiC, 6H-SiC, and Si and is identical to the sample used in Refs.\,\cite{ren07a} and \cite {kriener08a}, where the preparation details are given. The second sample, referred to as 6H-SiC and prepared in a similar way, is also a multiphase sample mainly consisting of hexagonal 6H-SiC \cite{muranakacomment}. In addition, we identified pure Si and 15R-SiC by x-ray diffraction, but there is no indication of a cubic 3C phase fraction in this sample. In spite of these differences both samples become superconducting at about $\ensuremath{T_{\rm c}}\approx 1.45$\,K and are type-I superconductors as indicated by the observation of a strong supercooling effect in finite magnetic fields in resistivity and AC susceptibility \cite{ren07a,kriener08a,muranakacomment}. The critical field strength was estimated to be about 115\,Oe (SiC-1) and 125\,Oe (6H-SiC) and the residual resistivity $\rho_0$ at \ensuremath{T_{\rm c}}\ amounts to $\sim 0.06$\,m$\Omega$cm (SiC-1) and $\sim 1.2$\,m$\Omega$cm (6H-SiC). The charge-carrier concentration is $1.91\cdot 10^{21}$\,cm$^{-3}$ for SiC-1 and $0.25\cdot 10^{21}$\,cm$^{-3}$ for 6H-SiC as estimated from Hall-effect measurements. The latter value is surprisingly low, only 1/10 of the value measured for SiC-1.
The specific-heat data presented in this paper was taken by a relaxation-time method using a commercial system (Quantum Design, PPMS).
\section{Specific heat}
\begin{figure}
\begin{center}
\includegraphics[width=14.5cm]{fig1.pdf}
\end{center}
\caption{\label{fig1} (Color online) Specific heat of the samples SiC-1 and 6H-SiC: The closed symbols in all panels denote data measured in zero field. Open symbols refer to data measured at $H=200\,{\rm Oe}>\ensuremath{H_{\rm c}}$ representing the normal-state specific heat. In panel (a) the specific heat $\ensuremath{c_{p}}/T$ as measured is shown. The dashed black curves are results of Debye fits to the data. Panels (b) (SiC-1) and (c) (6H-SiC) contain the electronic specific heat $\ensuremath{c_{\rm el}}/T$ and fit results, see text. For 6H-SiC the experimental data (triangles) was corrected (squares) due to experimental problems, see text.}
\end{figure}
In Fig.\,\ref{fig1} specific-heat data of the samples SiC-1 and 6H-SiC are shown. The solid symbols in all panels refer to data taken in zero field, the open symbols denote the normal-state specific heat achieved by applying an external magnetic DC field $\ensuremath{H_{\rm DC}}=200$\,Oe\,$>\ensuremath{H_{\rm c}}$. Both samples exhibit a clear jump at \ensuremath{T_{\rm c}}\ as seen in Fig.\,\ref{fig1}\,(a) indicating that the superconductivity in these compounds is a bulk feature. The respective transition in \ensuremath{c_{p}}\ is rather broad, reflecting their polycrystalline multiphase character. The in-field data of 6H-SiC exhibits an unusual upwards slope upon decreasing temperature below approximately 2\,K and around 0.4\,K an anomaly occurs. Currently both observations are believed to be the result of experimental problems with our PPMS since we find similar anomalies measuring different samples.
A fit to the data of SiC-1 in the temperature interval $0.6\,{\rm K} < T < 2$\,K applying the conventional Debye formula $\ensuremath{c_{p}}=\ensuremath{c_{\rm ph}}+\ensuremath{c_{\rm el}} = \ensuremath{\gamma_{\rm n}} T+\beta T^3$
yields the (normal-state) Sommerfeld parameter $\ensuremath{\gamma_{\rm n}}($SiC-1$)=0.29$\,mJ/molK$^2$ and the prefactor of the phononic contribution to the specific heat $\beta($SiC-1$) = 0.02$\,mJ/molK$^4$. For the sample 6H-SiC data at higher temperature $2\,{\rm K} < T < 10$\,K was chosen and a similar Debye fit yields $\ensuremath{\gamma_{\rm n}}($6H-SiC$)=0.35$\,mJ/molK$^2$ and $\beta($6H-SiC$) = 0.01$\,mJ/molK$^4$. Both results are displayed as dashed black lines in Fig.\,\ref{fig1}\,(a).
The Debye temperature evaluates to $\ensuremath{{\it \Theta}_{\rm D}}\approx 590$\,K for SiC-1 and $\approx 715$\,K for 6H-SiC somewhat higher than that found for SiC-1 reflecting the different slope above \ensuremath{T_{\rm c}}. For undoped SiC a Debye temperature of $\ensuremath{{\it \Theta}_{\rm D}}\approx 1200$\,K\,--\,1300\,K depending on the particular polytype is reported. Therefore the question arises which process is responsible for the strong suppression of \ensuremath{{\it \Theta}_{\rm D}}\ in this system. For superconducting diamond an earlier specific-heat study \cite{sidorov05a} reports a similar reduction of \ensuremath{{\it \Theta}_{\rm D}}, whereas a very recent study \cite{dubrovinskaia08a} does not find such a decrease questioning the speculation that a strong suppression of the Debye temperature and hence a strong softening of the corresponding phonon modes is a common effect in this family of superconductors.
Subtracting the phononic contribution from the experimental data yields the electronic specific heat $\ensuremath{c_{\rm el}}=\ensuremath{c_{p}}-\ensuremath{c_{\rm ph}}$ displayed in Fig.\,\ref{fig1}\,(b) (SiC-1) and (c) (6H-SiC) as $\ensuremath{c_{\rm el}}/T$ vs $T$.
Due to the mentioned experimental problems in the measurement of 6H-SiC a further analysis of the low-temperature data (black triangles in Fig.\,\ref{fig1}\,(c)) was difficult. Therefore we replaced the in-field electronic specific-heat data (open triangles) by the normal-state Sommerfeld parameter $\ensuremath{\gamma_{\rm n}}($6H-SiC$)=0.35$\,mJ/molK$^2$ as obtained from the Debye fit (solid red line in Fig.\,\ref{fig1}\,(c)). Next the difference between the in-field data and \ensuremath{\gamma_{\rm n}}(6H-SiC) was calculated and subtracted from the zero-field electronic specific-heat data (closed triangles) assuming that the same background signal is included to the zero-field data. The two data points below the anomaly in the in-field data in Fig.\,\ref{fig1}\,(a) were neglected in this process. This procedure yields the data given in red closed squares in Fig.\,\ref{fig1}\,(c) which will be the base for the analysis carried out next.
An entropy conserving construction (not shown) yields a jump height at \ensuremath{T_{\rm c}}\ of about 1 for both samples, clearly smaller than the BCS weak-coupling expectation 1.43.
We note that for superconducting diamond a jump height of only 0.5 is reported \cite{sidorov05a}.
For further analyzing the specific-heat data we choose two different approaches as described in detail in Ref.\,\cite{kriener08a}. Approach (i) assumes a BCS-type behavior of the electronic specific heat below \ensuremath{T_{\rm c}}\
\begin{equation}\label{GlBCS_res}
\ensuremath{c_{\rm el}}(T)/T = \ensuremath{\gamma_{\rm res}} + \ensuremath{\gamma_{\rm s}}/\ensuremath{\gamma_{\rm n}}\cdot \ensuremath{c_{\rm el}}^{\rm BCS}(T)/T.
\end{equation}
The samples used are multiphase samples. Hence it is possible that parts of the samples remain normal conducting allowing for an additional residual contribution to the specific heat below \ensuremath{T_{\rm c}}. To pay respect to this we include an additional residual term $\ensuremath{\gamma_{\rm res}}=\ensuremath{\gamma_{\rm s}}+\ensuremath{\gamma_{\rm n}}$ to Eq.\,\ref{GlBCS_res}. The prefactor \ensuremath{\gamma_{\rm s}}\ denotes the contribution of the superconducting parts of the samples. Please note that \ensuremath{\gamma_{\rm res}}\ is the only adjustable parameter in this scenario. Approach (ii) assumes a power-law behavior of the electronic specific heat with in principle three independent fitting parameters
\begin{equation}\label{Glpower}
\ensuremath{c_{\rm el}}(T)/T = \ensuremath{\gamma_{\rm res}} + a\cdot T^b.
\end{equation}
At low temperatures $b=1$ or 2 corresponds to line or point nodes. For sample SiC-1 both models describe the data reasonably well as can be seen in Fig.\,\ref{fig1}\,(b). The dashed green curve corresponds to approach (i), the dotted black curve to approach (ii). Approach (i) results in a residual contribution $\ensuremath{\gamma_{\rm res}}=0.5\times\ensuremath{\gamma_{\rm n}}$(SiC-1) corresponding to a superconducting volume fraction of approximately 50\,\%. However, the assumption of a $T$-linear behavior below \ensuremath{T_{\rm c}}\ yields a very good description of the data extrapolating to zero for $T\rightarrow 0$. The fit corresponding to the second approach was done with keeping the exponent $b=1$ in Eq.\,\ref{Glpower}. It is quite surprising that the linear behavior holds up to approximately 1.1\,K, i.\,e.\ up to the transition. In a nodal gap scenario it is expected that for $T\rightarrow \ensuremath{T_{\rm c}}$ the gap magnitude reduces and hence the electronic specific heat deviates from the linear extrapolation. Moreover the fit yields $\ensuremath{\gamma_{\rm res}}\approx 0$, i.\,e.\ the fit quality was the same with or without including a residual \ensuremath{\gamma_{\rm res}}\ factor emphasizing the surprising strict linear behavior and suggesting a volume fraction of about 100\,\%.
For sample 6H-SiC, as shown in Fig.\,\ref{fig1}\,(c), the fit corresponding to approach (i) yields a reasonable description, too, with a residual contribution of about 40\,\% of the normal-state Sommerfeld parameter. Approach (ii) reveals again a linear $T$ dependence of the electronic specific heat $\ensuremath{c_{\rm el}}/T$ in the superconducting state. However, the fit results in a negative value for \ensuremath{\gamma_{\rm res}}\ underlining that the rough correction of the data is very speculative. On the other hand the qualitative finding of a power-law behavior somewhat justifies the chosen way.
We note that an estimation of the superconducting jump height at \ensuremath{T_{\rm c}}\ paying respect to the result of approach (i), i.\,e.\ a finite residual contribution combined with a BCS-like behavior of the specific heat, yields for both specimen approximately 1.48, close to the BCS expectation.
\section{Conclusion}
With the present study we can comment on the question if either the cubic or the hexagonal or even both phase fractions participate in the superconductivity of heavily boron-doped silicon carbide, cf. Ref.~\cite{kriener08a}. Here we demonstrated that hexagonal boron-doped 6H-SiC is a bulk superconductor as indicated by a clear jump at \ensuremath{T_{\rm c}}. Moreover, approach (ii) of our analysis of the specific heat suggests that the cubic phase fraction in SiC-1 becomes superconducting, too. However, it is possible but would be rather surprising if both phase fractions of SiC-1 exhibit an identical critical temperature since we find only one single sharp transition in our AC susceptibility data of sample SiC-1 \cite{ren07a}. Therefore a comprehensive answer of this question needs further clarification.
In summary, we present a comparative specific-heat study on two different samples of heavily boron-doped SiC. One of them consists of cubic 3C- and hexagonal 6H-SiC whereas the other contains 6H-SiC but no cubic phase fraction. Both exhibit a similar critical temperature and field strength and are type-I superconductors. The electronic specific heat in the superconducting state can be described by either the assumption of a BCS-like exponential temperature dependence including a residual density of states due to non-superconducting parts of the sample or by a power-law behavior.
\section*{Acknowledgements}
This work was supported by a Grants-in-Aid for the Global COE ''The Next Generation of Physics, Spun from Universality and Emergence'' from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan, and by the 21st century COE program ''High-Tech Research Center'' Project for Private Universities: matching fund subsidy from MEXT. It has also been supported by Grants-in-Aid for Scientific Research from MEXT and from the Japan Society for the Promotion of Science (JSPS). TM is supported by Grant-in-Aid for Young Scientists (B) (No. 20740202) from MEXT and MK is financially supported as a JSPS Postdoctoral Research Fellow.
\section*{References}
\bibliographystyle{/PaperBase/bst/iopart-num}
| {
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{"url":"https:\/\/yurichev.org\/py_lambda\/","text":"## [Python][For noobs] What is anonymous\/lambda function?\n\nThese functions are JUST SHORT ONE-LINE functions to be used as an argument for other functions, like sorting (sorted()). Shorter than ~40 symbols.\n\nMore advanced Python developers\/programmers use them in map() and filter() functions.\n\nAS SIMPLE AS THAT. Most of the time, these are just short functions you don't want to define as a 'usual' functions. Often, used only once, so you won't separate them.\n\nWhy anonymous? Because they have no name.\n\nWhy lambda? This term inherited from Lisp, forget about it for a moment. (Lambda functions are also inherited from Lisp.)\n\nActually, in Python you can define function via lambda. For example, square root:\n\n>>> lambda x: x**2\n<function <lambda> at 0x7f356a3fe200>\n\n>>> f=lambda x: x**2\n\n>>> f(2)\n4\n\n>>> f(10)\n100\n\n\nI'm not a Lisp\/Scheme expert, but as far as I know, in toy Lisp interpreters, function definition is actually a syntactic sugar for assigning anonymous lambda function to a function's name. Of course, you can define 'usual' functions via lambda there.\n\n###### (the post first published at 20230313.)\n\nYes, I know about these lousy Disqus ads. Please use adblocker. I would consider to subscribe to 'pro' version of Disqus if the signal\/noise ratio in comments would be good enough.","date":"2023-03-25 10:01:09","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\": 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\": 0.3546591103076935, \"perplexity\": 3932.972140849149}, \"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\/1679296945323.37\/warc\/CC-MAIN-20230325095252-20230325125252-00114.warc.gz\"}"} | null | null |
Tired of your witch sims autonomously riding brooms all over town? So was I! =D And thanks to a request I got yesterday, I finally did something about it.
Witches, child age and older, all have hidden brooms in their inventories, which they will automatically use as their "preferred vehicle" whenever they go somewhere. | {
"redpajama_set_name": "RedPajamaC4"
} | 8,947 |
Q: Nothing can access internet except IE My partner's Computer is connect to internet and the network Icon shown on the taskbar is also shows it's working. He only use IE to connect to the Internet, nothing else.
Problem started when I install Kaspersky Internet Security on his computer. I try to active the software but it said check your internet connection.
I've downloaded Chrome to try visit some sites (IE still working, but I don't like to use it). After install Chrome, it's also cannot open any site and shown the problem with the DNS server (I use the Google DNS service 8.8.8.8 and 8.8.4.4).
I download Firefox also but again it's not working.
Additionally, I try to access the site "tinhte.vn" by enter the IP i got from Ping, both FF and Chrome show the Error from Cloudflare. Is there any explanation and solution for my case? Thank you.
The computer is Dell Inspiron One 2310 (AIO touch screen)
A: Remove all cookies and restart and check IE. If it is still working except other browser, check for firewall configuration settings. Disable all firewalls then check firefox or other browser.
| {
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Making a first impression is integral to creating a powerful message that turbo-charges your brand, but it's easy to overdo it and mess up your image. The last thing you want to do is send people the wrong impression.
Designing a good label is much more than just a graphic. Realistically there's a lot of practice and experience that goes into the design, and there's a huge list of things you should do when you're establishing your product label.
No matter what you're doing, it's important to start off small. Take the time to establish at least 20-30 different paper and pen drawings that establish a large variety of variations of your beginning ideas. If they don't seem to work it's important to start over with new sketches until you find the one that helps you establish your identity. A truly skilled designer or advertising professional will often spend as much or more time in the design step than actually making the label.
One of our brain's interesting mechanisms is that we create scales in our head that help us perceive ideas. This means that some aspects are appealing and pleasing to the way that we receive information. When you're developing your product label, you have to keep it balanced by enforcing that the "weight" of your finished product is equally balanced as your graphics, colour, and size. While you can tweak the rules as you see fit, your label will hopefully be seen by millions, so keeping it balanced is the way to go.
The same rules apply for logos. Logos MUST look good and be legible, no matter what size they are. Your logo instantly loses credibility when it's not as defined when scaled down. It also needs to be designed in such a way that it looks great in larger formats like on billboards, posters, and on the web.
It's tough to pick a colour scheme but it's always best when you use complementary colours, and colours that aren't too bright or graded. You also must ensure that your product label looks great in black and white, grayscale, and when made in just two colours.
Make sure you effectively research your client and your audience before you begin your preliminary work. When you're designing product labels, it should instantly provide background information to your client about the brand. Don't fall into the trap of going after "recent trends". Do what works for you by determining the best design style and work up a font that isn't distracting and gets your message across so you can get a design that works the first time. | {
"redpajama_set_name": "RedPajamaC4"
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Das Interface-Segregation-Prinzip oder Schnittstellenaufteilungsprinzip ist ein Begriff aus der Informatik. Es handelt sich um ein Prinzip des objektorientierten Entwurfs. Demnach sollen zu große Schnittstellen in mehrere Schnittstellen aufgeteilt werden, falls implementierende Klassen unnötige Methoden haben müssen. Nach erfolgreicher Anwendung dieses Entwurfprinzips müsste ein Modul, das eine Schnittstelle benutzt, nur diejenigen Methoden implementieren, die es auch wirklich braucht.
Zweck
Durch dieses Prinzip ist es möglich, die von Bertrand Meyer geforderten schlanken Schnittstellen zu realisieren, was eine verbesserte Wartbarkeit mit sich bringt, da Klassen nur noch die Methoden implementieren, die sie benötigen. Somit wird der Code kompakt und ist besser wiederverwertbar. Auch eine verbesserte Überprüfbarkeit ist gegeben.
Beispiele
C#
public interface IPerson
{
int Id { get; }
string FirstName { get; }
string LastName { get; }
// Andere Eigenschaften...
}
public interface ILoad
{
void Load(string path);
}
public interface ISave
{
void Save(string path);
}
public interface IToXmlString()
{
string ToXmlString();
}
public class Person : IPerson, ILoad, ISave, IToXmlString
{
public int Id { get; set; }
public string FirstName { get; set; }
public string LastName { get; set; }
// Andere Eigenschaften...
public void Load(string path)
{
// Lesen der Daten aus der Datei...
}
public void Save(string path)
{
// Speichern der Daten in die Datei...
}
public string ToXmlString()
{
// Zurückliefern der Daten als XML-Zeichenkette...
string xmlString = "...";
return xmlString;
}
}
Anwendung
// Irgendwo in eine andere Klassen/Code-Datei...
IPerson person = GetPersonById(123);
// Die Daten der Person (Eigenschaften) sollen aus einer Datei geladen werden.
(person as ILoad).Load(@"C:\dir1\file1.ext");
// Später soll die Daten der Person in einer Datei gespeichert werden.
(person as ISave).Save(@"C:\dir2\file2.ext");
// Etwas weiter im Code soll person als XML string bearbeitet werden.
string xml = (person as IToXmlString).ToXmlString();
Java
interface IPerson {
int getId();
void setId(int id);
String getFirstName();
void setFirstName(String firstName);
String getLastName();
void setLastName(String lastName);
// Andere Eigenschaften...
}
interface ILoad {
void load(String path);
}
interface ISave {
void save(String path);
}
interface IToXmlString {
String toXmlString();
}
class Person implements IPerson, ILoad, ISave, IToXmlString {
private int id;
private String firstName;
private String lastName;
// Andere Eigenschafts-Variablen...
@Override
public int getId() { return id; }
@Override
public void setId(int id) { this.id = id; }
@Override
public String getFirstName() { return firstName; }
@Override
public void setFirstName(String firstName) { this.firstName = firstName; }
@Override
public String getLastName() { return lastName; }
@Override
public void setLastName(String lastName) { this.lastName = lastName; }
// Andere Eigenschaften...
@Override
public void load(String path) {
// Lesen der Daten aus der Datei...
}
@Override
public void save(String path) {
// Speichern der Daten in die Datei...
}
@Override
public String toXmlString() {
// Zurückliefern der Daten als XML-Zeichenkette...
String xmlString = "...";
return xmlString;
}
}
Anwendung
// Irgendwo in eine andere Klassen/Code-Datei...
IPerson person = getPersonById(123);
// Die Daten der Person (Eigenschaften) sollen aus einer Datei geladen werden.
((ILoad) person).load("C:\\dir1\\file1.ext");
// Später soll die Daten der Person in einer Datei gespeichert werden.
((ISave) person).save("C:\\dir2\\file2.ext");
// Etwas weiter im Code soll person als XML string bearbeitet werden.
String xml = ((IToXmlString)person).toXmlString();
Einzelnachweise
Softwaretechnik
Softwarearchitektur
Objektorientierte Programmierung
Vorgehensmodell (Software) | {
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La chapelle Notre-Dame-des-Vertus est un édifice religieux catholique sis à Noblehaye, un hameau de Bolland (commune de Herve), en province de Liège (Belgique). Une première construction du est remplacée par la chapelle actuelle datant de 1707. Ancien centre de pèlerinage marial, la chapelle est classée au patrimoine de Wallonie depuis 1934. On y célèbre régulièrement l'Eucharistie.
Histoire
Selon la tradition - mêlée de légende - les origines de la chapelle remonteraient au début du . Des soldats qui bivouaquaient à Noblehaye, hameau de la seigneurie libre de Bolland, auraient eu l'attention attirée par une lumière éclatante émanant d'un arbre. S'en approchant ils virent une statuette de la Vierge Marie. Averti de la découverte, le curé du village se serait rendu sur les lieux en procession et aurait rapporté la statuette dans l'église du village. Le lendemain, à la surprise générale, la statuette se retrouve à l'endroit que la Vierge Marie avait choisi. Les villageois comprirent le message et s'empressèrent alors d'y bâtir une chapelle. Et bientôt de nombreux pèlerins lui rendent visite, d'autant plus qu'on lui attribue des propriétés miraculeuses.
Sous l'impulsion du curé de Bolland, Antoine de Sarémont, la chapelle actuelle fut construite en 1707, avec les dons des pèlerins et le soutien financier du seigneur de Bolland, le comte Adrien de Lannoy-Wignacourt. Le sanctuaire, un édifice de forme hexagonal surmonté d'une coupole, date de cette époque. Une nef voutée de deux travées fut ajoutée en 1745.
Après de longues années d'abandon la chapelle attire l'attention des amis du patrimoine de Wallonie et elle est classée en 1934. Il faut encore de nombreuses années avant qu'elle ne reçoive une restauration complète – ce sera de 1971 à 1973 - grâce à l'appui d'une association locale d'Amis de la chapelle de Noblehaye', qui obtient également qu'un prêtre la visite régulièrement pour y recevoir les pèlerins et célébrer l'Eucharistie.
Description
La nef voutée est longue de deux travées se prolonge en un sanctuaire hexagonal (avec sacristie) surmonté d'une coupole nervée. Le fronton de la chapelle est orné d'une niche où se trouve une statue de là Vierge Marie et porte les blasons du comte de Lannoy et de sa femme Constance de Wignacourt.. La date de 1707 y est indiquée.
Patrimoine
La statue, dite 'miraculeuse', de Notre-Dame-des-Vertus n'a pas plus de de hauteur. Elle trône au dessus du maître-autel.
Le maître-autel, au dessus duquel trône la statue de la Vierge Marie, est de style Louis XV et date de 1767. Il est œuvre d'Arnold d'Outrewe et Charles Antoine Galhausen. La table d'autel en marbre date de 1878
Les deux autels latéraux, également de style Louis XV, datent du troisième quart du .
La chaire de vérité, en bois de chêne, date d'environ 1750.
Plusieurs statues de saints, en bois polychrome (XVIIe siècle)-
Deux toiles de l'artiste Sébastien Wiart : 'Saint Antoine, abbé' et 'Marie avec l'Enfant-Jésus et Jean-Baptiste' (1782).
Notes et références
Liens externes
Chapelle dédiée à Notre-Dame
Chapelle dans la province de Liège
ChapelleNotreDameVertusNoblehaye
Chapelle construite au XVIIIe siècle
Chapelle transformée au XVIIIe siècle
Chapelle restaurée au XXe siècle | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,977 |
ROOT = ../../../../..
DIR = Providers/ManagedSystem/UNIXProviders/VoltageSensor
include $(ROOT)/mak/config.mak
LIBRARY = UNIX_VoltageSensorProvider
EXTRA_INCLUDES += -I/usr/local/include -I./..
SOURCES = \
../CIMHelper.cpp \
UNIX_VoltageSensorMain.cpp \
UNIX_VoltageSensor.cpp \
UNIX_VoltageSensorProvider.cpp
ifeq ($(OS), aix)
SOURCES += UNIX_VoltageSensor_AIX.cpp
endif
ifeq ($(OS), darwin)
SOURCES += UNIX_VoltageSensor_DARWIN.cpp
endif
ifeq ($(OS), freebsd)
SOURCES += UNIX_VoltageSensor_FREEBSD.cpp
endif
ifeq ($(OS), hpux)
SOURCES += UNIX_VoltageSensor_HPUX.cpp
endif
ifeq ($(OS), linux)
SOURCES += UNIX_VoltageSensor_LINUX.cpp
endif
ifeq ($(OS), solaris)
SOURCES += UNIX_VoltageSensor_SOLARIS.cpp
endif
ifeq ($(OS), tru64)
SOURCES += UNIX_VoltageSensor_TRU64.cpp
endif
ifeq ($(OS), vms)
SOURCES += UNIX_VoltageSensor_VMS.cpp
endif
ifeq ($(OS), win32)
SOURCES += UNIX_VoltageSensor_WIN32.cpp
endif
ifeq ($(OS), zos)
SOURCES += UNIX_VoltageSensor_ZOS.cpp
endif
ifeq (, $(filter aix,darwin,freebsd,hpux,linux,solaris,tru64,vms,win32,zos $(OS)))
else
SOURCES += UNIX_VoltageSensor_STUB.cpp
endif
LIBRARIES = \
pegprovider \
pegclient \
pegcommon \
pegquerycommon \
pegqueryexpression \
pegcql \
pegwql
EXTRA_LIBRARIES = \
-pthread \
-lutil \
-lgeom \
-lkvm \
-lcam
include $(ROOT)/mak/dynamic-library.mak
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,750 |
US NFP Preview: Will another good jobs release finally move the Fed?
James Chen, CMT September 1, 2016 12:32 PM
The Non-Farm Payrolls (NFP) employment report coming up on Friday will be an exceptionally critical one in relation to the Federal Reserve's monetary policy trajectory in late September and beyond. Fed members, most notably Fed Chair Janet Yellen, have repeatedly stressed that economic data takes center stage in the central bank's policy decisions, and the labor market is one of the most important components of that decision-making.
Yellen remarked in last week's Jackson Hole Economic Symposium that the case for a rate hike "has strengthened in recent months," and that this was largely due to "solid performance of the labor market and our outlook for economic activity and inflation." These remarks were followed shortly after by a televised appearance featuring Fed Vice Chair Stanley Fischer, in which he stated that Yellen's speech was consistent with the possibility of a rate hike in September and potentially more than one rate hike by the end of 2016. This statement was tempered as usual, however, by the statement that "these are not things we know until we see the data."
As a result of these relatively hawkish pronouncements, the market's expectations of a Fed rate hike increased markedly and the dollar sharply extended its recent surge. For the most part, this surge has continued this week in the run-up to Friday's critical jobs report.
The NFP reports for the past two months have painted a rosy picture of the US employment situation. June's data, released in early July, revealed an exceptionally positive 287,000 additional jobs versus prior expectations of 175,000. The actual number was subsequently revised even higher to 292,000. July's numbers, released early last month, similarly showed a much better-than-expected reading at 255,000 non-farm jobs added against forecasts of 180,000. Of course, those two stellar months followed a colossally disappointing reading for May (a dismal 11,000 jobs added), but the positive turnaround in the data since then has apparently been quite dramatic and has been acknowledged as such by Fed members.
Friday's jobs data will be the last major employment release before the next FOMC policy meeting and statement on September 21st. As it currently stands immediately prior to Friday's NFP release, the Fed Fund futures market is showing a 24% implied probability of a rate hike at the September meeting. This number could change immediately and drastically, however, depending on the outcome of Friday's release.
Clearly, another better-to-stellar outcome following the last two very positive months should increase the rate hike probability substantially, which should then further boost the recently surging dollar while further pressuring depressed gold prices. A surprise to the downside, however, should lead to a significant pullback for the dollar and rebound for gold.
Consensus expectations for Friday's NFP, which will be accompanied by key related data on the unemployment rate and average hourly earnings, are around 180,000 jobs added for the month of August. The August unemployment rate is expected to come in at 4.8%, while average hourly earnings are expected to have increased by 0.2%.
Wednesday's ADP employment report, which sometimes serves as a limited leading indicator for NFP Fridays, came in slightly better than expected at 177,000 jobs added in August against prior forecasts of 174,000. Additionally, July's ADP reading was revised substantially higher from the originally-reported 179,000 up to 194,000.
Other recent employment-related data for August have shown somewhat mixed results, including Thursday's ISM Manufacturing employment component. This key survey came out at a disappointing 48.3 contraction for August, which represents an acceleration of July's 49.4 contraction. The ISM Non-Manufacturing employment component for August comes out next week and is therefore not a factor as a pre-NFP input. As for August's weekly jobless claims data, they have all come out better-than-expected. Thursday's release covering the last week of August showed a slightly better-than-expected (lower) number of claims at 263,000 vs 265,000 expected. The preceding three weeks in August also showed numbers that were lower than forecast, indicating consistently positive jobless claims data.
Despite the discouraging ISM Manufacturing data, other leading employment data points are pointing to an actual NFP reading on Friday that could likely be somewhat better than the expected ~180,000 jobs added for August, with a target range around 185,000-200,000. However, one caveat should be stressed: for the past five years, August jobs data has disappointed expectations each and every year. Caution, therefore, should be exercised when trading potentially affected markets, as always. Any substantial deviation from consensus could make a significant market impact, primarily on the US dollar and commodities like gold. In particular, both EUR/USD and USD/JPY could make some substantial moves, as is often the case, depending on Friday's actual reading and its potential monetary policy implications.
NFP Jobs Created and Potential USD Reaction:
> 200,000
Strongly Bullish
180,000-200,000
Moderately Bullish
Moderately Bearish
< 160,000
Strongly Bearish
Central Banks dollar Fed Federal Reserve FOMC Fundamental Analysis Gold Interest rates Labor Market NFP Non-farm payrolls US Dollar USD | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 532 |
//
// UCXSDKInstance.h
// Pods
//
// Created by huyujin on 2017/8/17.
// Copyright © 2017年 ucarinc. All rights reserved.
//
#import <Foundation/Foundation.h>
/**
* The state of current instance.
**/
typedef NS_ENUM(NSInteger, UCXState) {//state.code
UCXWeexInstanceReady = 1000,
UCXWeexInstanceActived,
UCXWeexInstanceDeactived,
};
@interface UCXSDKInstance : NSObject
@end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,793 |
If you are unable to keep a scheduled appointment, please call to cancel so that that time can be reserved for another patient.
Please try to arrive 15 minutes prior to your appointment time so that you can complete your paper work.
We take patients according to their appointment time and not their arrival time. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,411 |
Home Hill Farm Medical Centre is open for business.
Wacky (as in wacko) the Indian Runner who spent the first few days following birth madly throwing its head backwards and falling over usually into water container is cured. For some days now there has been no fitting. Thanks to The Backyard Duck Book and its author Nyiri Murtagh. As often as possible we would put a few drops of sugared water into Wacky's tiny beak/bill. The apparent cause of the problem was lack of Glucose to the brain.
Wocky (as in wockeye) the Rhode Island Red arrived with a problem in one eye causing it to be shut and looking infected. Using a jeweller's eyepiece we trimmed away some suspect fur around the eye. An extremely difficult and delicate task. Jean regularly bathed the eye with a salt solution and for a few days it worsened then the swelling disappeared but the eye remained partially shut. It is now fine fully open to the point we had trouble picking which one is Wocky.
Tippy (tippy toe) the Rhode Island Red arrived with both sets of toes curled under. Using gaffer tape (after trying various other adhesive tapes) we have been binding Tippy's toes in various ways to maintain an extended position. Most of the toes now no longer curl under. They are not perfect and skew a little to the side but they are functional. The main toes still need binding but they are improving each day. Tippy does have a habit of slipping out of his orthopaedic shoes and requires a new pair at least once each day. We are optimistic that she will be fine if we persevere.
There is now a new collective noun for a gaggle of ducks - "A lap of ducks" They run across the grass and leap into a spare lap, hunker down and go all quiet. Occasionally one or more will climb up your body to get under your chin or into an armpit. Jean's productivity has plummeted as a result of much time spent "bonding" with her babies. | {
"redpajama_set_name": "RedPajamaC4"
} | 872 |
\section{Introduction}
\begin{quote}
Suit the action to the word, the word to the action, with this special observance, that you o'erstep not the modesty of nature: for any thing so o'erdone is from the purpose of playing, whose end, both at the first and now, was and is, to hold as 'twere the mirror up to nature: to show virtue her feature, scorn her own image, and the very age and body of the time his form and pressure.
--HAMLET Act 3, scene 2, 17-24
\end{quote}
The aim of this brief paper is unification, not just in the trivial sense of concatenation, but in the more general and aesthetic sense of union within an elegant framework. A strong effort has been made towards the graceful and concise exposition of the physical and mathematical formalism, as well as towards the fluid introduction of the physical concepts. The starting point is pseudo-Riemannian geometry, and the construction of an elegant minimal framework leads directly to the domain of Clifford algebra, a formalism allowing the seemingly facile manipulation of complex geometric entities. A Clifford algebra decomposition of the unit basis vector frame leads naturally to the appearance of a spinor field. A physically motivated constraint on the dynamics of the frame is suggested, that the unit time form of the frame be the gradient of a scalar time field. This constraint produces a much sought after clock on the manifold and appears as the addition of a spinor dependent term in the gravitational action, a term corresponding to the dynamics of matter. In this manner the unification of gravitation and matter is achieved within the most elementary framework of geometry conceivable.
\section{Manifold and Vielbein}
Assume that the universe is an $n$-dimensional pseudo-Riemannian manifold. The geometry of the manifold is completely described in any coordinate patch by a set of orthogonal unit vectors, the vielbein, frame, or tetrad,
\begin{equation}
\hat {e_\alpha } = {(e_\alpha )}^i \vec {\partial _i}
\end{equation}
that satisfy
\begin{equation}
\hat {e_\alpha } \cdot \hat {e_\beta } = {(e_\alpha )}^i {(e_\beta )}^j g_{ij} = \eta _{\alpha \beta }
\label{vielb}
\end{equation}
in which $\vec {\partial _i}$ is a coordinate basis vector, roman indices are coordinate indices, $g$ is the metric, $\eta$ is the Minkowski metric, and greek indices are labels raised and lowered by $\eta$. If a smoothly varying vielbein can be defined everywhere, the manifold is called a spin manifold. The vielbein naturally implies a set of basis 1-forms, the fielbein
\begin{equation}
\hat{e^\alpha} = \vec{dx^i} \, ({e^{\! - \!1}}_i)^\alpha
\end{equation}
with $\vec{dx^i}$ the coordinate 1-forms, that are dual to the vielbein vectors
\begin{equation}
{(e_\alpha )}^i {({e^{\! - \! 1}}_i )}^\beta = \delta _\alpha^\beta
\label{fielb}
\end{equation}
or, more compactly in matrix notation, $e {e^{\! - \! 1}} = I$, where the components of $e$ are ${(e_\alpha )}^i$. On a pseudo-Riemannian manifold the 1-forms may be identified with vectors via the metric, $\vec{dx^i} = g^{i j} \, \vec{\partial_j} = \vec{\partial^i} $ and $\hat{{e^{ - \! 1 \,}}^\alpha} = \eta^{\alpha \beta} \, \hat {e_\beta} = \hat {e^\alpha}$ , and often go under the name of covariant vectors. The only time a distinction need be drawn between vectors and 1-forms is when taking them to a submanifold, as 1-forms are the objects that may be pulled back to a submanifold. Any vector (the word now used interchangeably with ``form'') may be represented in terms of the coordinate or vielbein basis vectors
\begin{equation}
\vec{v} = v^i \vec{\partial _i} = v^\alpha \hat {e_\alpha } = (v^i ({e^{\! - \! 1}}_i)^\alpha) \hat {e_\alpha }
= v^i \, g_{i j} \, \vec{dx^j} = v_\alpha \hat{e^\alpha}
\end{equation}
The fielbein can be considered a factorization of the metric, since
\begin{equation}
{g}_{ij} = {({e^{\! - \! 1}}_i )}^\alpha \, \eta _{\alpha \beta } \, {({e^{\! - \! 1}}_j )}^\beta
\end{equation}
or $g = {e^{\! - \! 1}} \eta {e^{\! - \! 1}}^T$. However, the frame of orthogonal unit vectors tangent to a manifold seems a more satisfying intuitive description than the equivalent metric, and should be interpreted as being more fundamental. Also note that the vielbein describes an orientation on the manifold, information absent from the metric. The metric is, however, a more compact description of the geometry, having ${n(n+1) \over 2}$ degrees of freedom compared to the vielbein's $n^2$. The metric is invariant under local orthonormal ( Lorentz ) transformations of the fielbein,
\begin{equation}
\hat {e^\alpha} \mapsto \hat{e^\beta} {L^\alpha}_\beta
\label{lor}
\end{equation}
with ${L^\alpha}_\beta \, \eta_{\alpha \mu} \, {L^\mu}_\nu = \eta_{\beta \nu}$ ( or $L^T \eta L = \eta$ ), which leads to the natural unique decomposition of the fielbein matrix,
\begin{equation}
{({e^{\! - \! 1}}_i )}^\alpha = {(\gamma_i )}^\beta {L^\alpha}_\beta
\label{fac}
\end{equation}
in which $\gamma$ is symmetric and $L$ is restricted to be a proper ( ${\rm det} \, L > 0$ ) orthochronous ( ${L^0}_0 > 0$ ) Lorentz transformation taking timelike vectors to timelike vectors and spacelike vectors to spacelike vectors, so $\hat {e^\alpha } \cdot \hat {e^\beta } = \hat {\gamma^\alpha } \cdot \hat {\gamma^\beta }$ and the direction of time is preserved. This decomposition capitalizes on the metric invariance (\ref{lor}) to factor the fielbein into a gravitational part, the symmetric fielbein, $\hat{\gamma^\beta}$, which has ${n(n+1) \over 2}$ degrees of freedom and gives $g = {e^{\! - \! 1}} \eta {e^{\! - \! 1}}^T = \gamma \eta \gamma^T$, and the rotational part, $L$, which has ${n(n-1) \over 2}$ degrees of freedom.
\section{Spinors}
Since the 1-forms may be naturally identified with vectors via the metric, the vector dot product may be carried over this way and combined with the exterior algebra to produce a Clifford algebra with the symmetric fielbein vectors, $\hat{\gamma^\alpha}$, as 1-form basis elements satisfying the Clifford product relation,
\begin{eqnarray}
\hat{\gamma^\alpha} \hat{\gamma^\beta} & = & \hat{\gamma^\alpha} \cdot \hat{\gamma^\beta} + \hat{\gamma^\alpha} \wedge \hat{\gamma^\beta} \\
& = & \eta^{\alpha \beta} + \hat{\gamma^\alpha} \wedge \hat{\gamma^\beta}
\end{eqnarray}
with the dot product of two vectors, $\vec{a} \cdot \vec{b} = {1 \over 2}(\vec{a} \vec{b} + \vec{b} \vec{a})$, producing a scalar and the wedge product, $\vec{a} \wedge \vec{b} = {1 \over 2}(\vec{a} \vec{b} - \vec{b} \vec{a})$, producing a 2-vector ( aka bivector or 2-form ). Several excellent treatments of Clifford algebras and their application in physics have been made by David Hestenes and I recommend the reader to his work\cite{dh,dhgs} as an introduction. Readers unfamiliar with Clifford algebra but familiar with Dirac matrices should note the isomorphism between the basis 1-forms and Dirac matrices, $\hat{\gamma^\alpha} \sim \gamma^\alpha$, which form a basis for the matrix representation of Clifford algebra and satisfy the same multiplicative identities, such as $\gamma^\alpha \gamma^\beta + \gamma^\beta \gamma^\alpha = 2 \eta^{\alpha \beta}$ and anti-commutivity, $\gamma^\alpha \gamma^\beta = - \gamma^\beta \gamma^\alpha$ for $\alpha \neq \beta$.
The factoring of the fielbein in (\ref{fac}) is performed in a Clifford algebra as
\begin{equation}
\hat{e^\alpha} = \hat{\gamma^\beta} {L^\alpha}_\beta = \Psi \hat{\gamma^\alpha} \widetilde{\Psi}
\label{facv}
\end{equation}
where $\Psi$, an even or odd unitary Dirac-Hestenes spinor, is an even or odd graded multi-vector element of the Clifford algebra satisfying $\Psi \widetilde{\Psi} =1$, and $\widetilde{\Psi}$ denotes the reverse of the multi-vector, which reverses the products of all vectors in $\Psi$. The components of $L$ may be readily obtained from $\Psi$ since
\begin{equation}
L^{\alpha \mu} = \hat{e^\alpha} \cdot \hat{\gamma^\mu} = (\Psi \hat{\gamma^\alpha} \widetilde{\Psi}) \cdot \hat{\gamma^\mu} = \hat{\gamma^\alpha} \cdot (\widetilde{\Psi} \hat{\gamma^\mu} \Psi )
\label{rot}
\end{equation}
An even unitary spinor has ${n(n-1) \over 2}$ degrees of freedom and may be written as the exponential of a bivector, $\Psi = e^B$.
In four dimensional spacetime, $S$, an even spinor may be written out in terms of the basis as
\begin{eqnarray}
\psi & = & a_0 + b_\epsilon \hat{\gamma^0} \hat{\gamma^\epsilon} + a_\epsilon \hat{\gamma^1} \hat{\gamma^2} \hat{\gamma^3} \hat{\gamma^\epsilon} + b_0 \gamma \\
& = & a_0 + a_\epsilon \gamma \hat{\gamma^\epsilon} \hat{\gamma^0} + \gamma (b_0 + b_\epsilon \gamma \hat{\gamma^\epsilon} \hat{\gamma^0})
\label{psi}
\end{eqnarray}
in which $\epsilon$ here sums from $1$ to $3$, and the volume element ( pseudo-scalar ) is $\gamma = \hat{\gamma^0} \hat{\gamma^1} \hat{\gamma^2} \hat{\gamma^3} = dx^0 dx^1 dx^2 dx^3 \, {\rm det } \, \gamma = {e^{\! - \! 1}} $ ( both the volume-element, $\gamma$, and symmetric fielbein matrix, $\gamma$, appear in this expression, the distinction apparent via context ). Note that the quaternions, familiar from their use in 3-space rotations, are here equivalent to the spacelike bivectors $\gamma \sigma^\epsilon = \gamma \hat{\gamma^\epsilon} \hat{\gamma^0}$. An even non-unitary Dirac-Hestenes spinor, $\psi$, induces a conformal transformation, a Lorentz transformation by ${L}$ and scaling by $s$ ( aka Weyl or orthogonal transformation ), given by
\begin{equation}
s \hat{\gamma^\beta} {L^\alpha}_\beta = \psi \hat{\gamma^\alpha} \widetilde{\psi}
\label{orth}
\end{equation}
in which $\psi$ is an even multi-vector free of restrictions. An even non-unitary, non-null ( $\psi \widetilde{\psi} \neq 0$ ), spinor may be factored as $\psi = { s }^{1 \over 2} e^{\gamma {\phi \over 2}} \Psi$, which contains an even unitary spinor, $\Psi$, as well as a duality rotation, $e^{\gamma {\phi \over 2}}$, that does not effect the result of the vector transformation (\ref{orth}). An even unitary spinor factors into a boost along $\vec{v}$ and rotation around $\vec{r}$ as $\Psi = e^B = e^{v_\epsilon \sigma^\epsilon} e^{r_\epsilon \gamma \sigma^\epsilon}$.
This is the most important fact to understand in this paper: A unitary spinor field is defined and understood here as a Clifford algebra representation of a restricted Lorentz transformation. And the fielbein, $\hat {e^\alpha }$, factors uniquely into a unitary spinor part, $\Psi$, and a metric part, $\hat {\gamma^\alpha }$, via (\ref{facv}). The fielbein hence carries a spinor part and gravitational part -- spinors are already in General Relativity, they've just remained hidden in $\hat {e^\alpha }$. This is quite different then the way spinors are usually defined, but an isomorphism holds between this definition of spinor as transformation and the standard definition. Appendix A contains a translation to Dirac spinors and the conformal transformation matrix.
\section{Coordinate Transformations}
Although the fielbein vectors, $\hat{e^\alpha}$, are coordinate independent objects, the fielbein matrix, ${({e^{\! - \! 1}}_i )}^\alpha$, and it's decomposition, are not coordinate independent. A new set of $\hat{\gamma^\beta}$ and a new ${L^\alpha}_\beta$ and hence new $\Psi$ must be obtained after a coordinate transformation such that the new $\gamma$ matrix is symmetric. This is achieved as follows:
Consider a coordinate change $x^i \rightarrow {x'}^j (x)$ that gives $\vec{dx^i} = \vec{d{x'}^j} {\partial x^i \over \partial {x'}^j} = \vec{d{x'}^j} {L^i}_j $. The old symmetric $\hat{\gamma^\beta}$ are now given by $\hat{\gamma^\beta} = \vec{dx^i} \, (\gamma_i)^\beta = \vec{d{x'}^j} {L^i}_j \, (\gamma_i)^\beta$. The matrix ${L^i}_j \, (\gamma_i)^\beta$ is now not symmetric in $j$ and $\beta$. A new set of $\hat{\gamma^\beta}'$, the old set rotated by the same $L$, is needed so that the new $\gamma'$ is symmetric. This is
\begin{equation}
\hat{\gamma^\beta}' = \vec{d{x'}^j} \, ({\gamma'}_j)^\beta = \vec{d{x'}^j} {L^i}_j \, (\gamma_i)^\mu {L_\mu}^\beta = \hat{\gamma^\mu} {L_\mu}^\beta = \Phi \hat{\gamma^\beta} \widetilde{\Phi}
\end{equation}
giving a symmetric $\gamma' = L^T \gamma L$, and $\Phi$ the unitary spinor corresponding to transformation by $L$. Since $\hat{e^\alpha}$ remains the same but $\hat{\gamma^\beta}$ has changed, $\Psi$ must change as well so that
\begin{equation}
\hat{e^\alpha} = \Psi \hat{\gamma^\alpha} \widetilde{\Psi} = \Psi \widetilde{\Phi} \hat{{\gamma'}^\alpha} \Phi \widetilde{\Psi} = \Psi' \hat{{\gamma'}^\alpha} \widetilde{\Psi'}
\end{equation}
and the spinor $\Psi$ changes as expected under a coordinate transformation to $\Psi' = \Psi \widetilde{\Phi}$.
\section{Derivative}
The covariant derivative, $\nabla_{\vec{V}}$, is defined to have the following properties,
\begin{eqnarray}
\nabla_{ \vec{A} + f \vec{B}} C & = & \nabla_{ \vec{A}} C+ f \nabla_{ \vec{B}} C \\
\nabla_{ \vec{A}} (B + f C) & = & \nabla_{ \vec{A}} B + f \nabla_{ \vec{A}} C + (A^i \partial_i f) C \end{eqnarray}
where $\partial_i = {\partial \over {\partial x^i}}$ and $f$ is a scalar. The covariant derivative acting on vectors gives
\begin{eqnarray}
\nabla_i \vec{v} & = & \nabla_i ( v^k \vec{\partial_k} ) =
( \partial_i v^k ) \vec{\partial_k} + v^k ( \nabla_i \vec{\partial_k} ) \\
& = & \vec{\partial_j} \ [ \partial_i v^j + v^k g^{j m} \vec{\partial_m} \cdot ( \nabla_i \vec{\partial_k} ) ] \\
& = & \vec{\partial_j} \ [ \partial_i v^j + {\Gamma^j}_{ik} v^k ]
\end{eqnarray}
in which $\nabla_i = \nabla_{\vec{\partial_i}}$ and the affine connection is $\Gamma_{jik} = \vec{\partial_j} \cdot \nabla_i \vec{\partial_k}$.
Clifford algebra allows for the definition of the vector derivative, or gradient,
\begin{equation}
\vec{\nabla} = \hat{e^\alpha} \nabla_{\hat{e_\alpha}} = \hat{\gamma^\alpha} \nabla_{\hat{\gamma_\alpha}} = \hat{\gamma^\alpha} ({\gamma^{\! - \! 1}}_\alpha)^i \nabla_i = \vec{\partial^i} \nabla_i
\end{equation}
which gives, for example,
\begin{eqnarray}
\vec{\nabla} \vec{v} & = & \vec{\nabla} \cdot \vec{v}+ \vec{\nabla} \wedge \vec{v} \\
& = & \vec{\partial^i} \cdot \nabla_i \vec{v}+ \vec{\partial^i} \wedge \nabla_i \vec{v} \\
& = & g^{i k} (\partial_i v_k - {\Gamma^j}_{i k} v_j ) + \vec{\partial^i} \wedge \vec{\partial^k} \,(\partial_i v_k - {\Gamma^j}_{i k} v_j ) \\
& = & \hat{\gamma^\alpha} \cdot \nabla_{\hat{\gamma_\alpha}} \vec{v} + \hat{\gamma^\alpha} \wedge \nabla_{\hat{\gamma_\alpha}} \vec{v} \\
& = & ( \partial_\mu v^\mu + {\omega^\alpha}_{\alpha \mu} v^\mu ) + \hat{\gamma^\alpha} \wedge \hat{\gamma^\beta} \, ( \partial_\alpha v_\beta + {\omega}_{\beta \alpha \mu} v^\mu )
\end{eqnarray}
where the spin connection for the symmetric fielbein is ${\omega}_{\beta \alpha \mu} = \hat{\gamma_\beta} \cdot \nabla_{\hat{\gamma_\alpha}} \hat{\gamma_\mu} $ and $\partial_\alpha = {({\gamma^{\! - \! 1}}_\alpha )}^i \partial _i$ in this expression.
The covariant derivative acting on a symmetric vielbein vector may also be written as
\begin{equation}
{\nabla}_\mu \hat{\gamma_\nu} = \hat{\gamma^\alpha} \omega_{\alpha \mu \nu} = {1 \over 2} ( \omega_\mu \hat{\gamma_\nu} - \hat{\gamma_\nu} \omega_\mu )
\label{vderiv}
\end{equation}
in which the connection bivector is defined as $\omega_\mu = {1 \over 2} \omega_{\alpha \mu \nu} \, \hat{\gamma^\alpha} \wedge \hat{\gamma^\nu} $, and the shorthand ${\nabla}_\mu={\nabla}_{\hat{\gamma_\mu}}$. This expression may be applied to an arbitrary multivector, $A$, to obtain
\begin{equation}
{\nabla}_\mu A = \bar{\partial_\mu} A + {1 \over 2} ( \omega_\mu A - A \omega_\mu )
\label{deriv}
\end{equation}
where $\bar{\partial_\mu} = ({\gamma^{\! - \! 1}}_\mu )^i \bar{\partial_i} $ is the partial derivative acting only on coefficients in $A$. This naturally gives rise to the ``covariant spinor derivative'' when acting on objects composed of an even multiple of a spinor, for example
\begin{eqnarray}
\nabla_{\mu} \left( \Psi \hat{\gamma^0} \widetilde{\Psi} \right) & = & ( \bar{\partial_\mu} \Psi + {1 \over 2} ( \omega_\mu \Psi - \Psi \omega_\mu )) \hat{\gamma^0} \widetilde{\Psi} \\
& + & \Psi {1 \over 2} ( \omega_\mu \hat{\gamma^0} - \hat{\gamma^0} \omega_\mu ) \widetilde{\Psi} \\
& + & \Psi \hat{\gamma^0} ( \bar{\partial_\mu} \widetilde{\Psi} + {1 \over 2} ( \omega_\mu \widetilde{\Psi} - \widetilde{\Psi} \omega_\mu )) \\
& = & ( \nabla^s_{\mu} \Psi ) \hat{\gamma^0} \widetilde{\Psi} + \Psi \hat{\gamma^0} \widetilde{ ( \nabla^s_{\mu} \Psi )}
\end{eqnarray}
in which the middle terms cancel to give the covariant spinor derivative, $ \nabla^s_{\mu} \Psi = \bar{\partial_\mu} \Psi + {1 \over 2} \omega_\mu \Psi$, also known as the covariant Dirac operator in curved spacetime.
\section{Curvature and Gravitation}
Since the metric is independent of local Lorentz transformations of the fielbein, all traditional geometric objects derived from the metric may be written interchangeably in terms of the fielbein, $\hat{e^\alpha}$, or symmetric fielbein, $\hat{\gamma^\alpha}$, basis. Since the metric degrees of freedom are contained uniquely in $\hat{\gamma^\alpha}$ ( $\hat{e^\alpha}$ containing also the spin information of $\Psi$ ) traditional geometric objects will be written in terms of $\hat{\gamma^\alpha}$ except where noted.
The Ricci vectors and scalar curvature in Clifford notation are
\begin{eqnarray}
\vec{R_\alpha} & = & R_{\alpha \beta} \hat{\gamma^\beta} = ( \vec{\nabla} \wedge \vec{\nabla} ) \cdot \hat{\gamma_\alpha} \\
R & = & \hat{\gamma^\alpha} \cdot \vec{R_\alpha}
\end{eqnarray}
in which $R_{\alpha \beta}$ is the Ricci tensor in the symmetric fielbein basis. Integration over the scalar curvature gives the gravitational action,
\begin{equation}
S = \int{ \gamma \ R } = \int{ \gamma \ \left\{ \hat{\gamma^\alpha} \cdot ( \vec{\nabla} \wedge \vec{\nabla} ) \cdot \hat{\gamma_\alpha} \right\} }
\end{equation}
Requiring this action to be stationary with respect to independent variations of $\hat{\gamma_\alpha}$ and $\vec{\nabla}$, the Palatini method\cite{peldan}, gives the equations,
\begin{eqnarray}
\vec{R_\alpha} - {1 \over 2} \hat{\gamma_\alpha} R & = & 0 \\
\vec{\nabla} \wedge \hat{\gamma_\alpha} +\hat{\gamma^\mu} \wedge \hat{\gamma^\nu} \, \omega_{\nu \mu \alpha} & = & 0
\end{eqnarray}
The first is the vacuum Einstein equation and the second, solvable for $\omega_{\nu \mu \alpha}$ in terms of $\hat{\gamma_\alpha}$ and $\partial_i \hat{\gamma_\alpha}$, is the defining equation for the metric compatible torsionless spin connection.
\section{Time and Spinor Dynamics}
There is a long standing problem in General Relativity, and hence in approaches to quantum gravity, regarding the nature of time. One would like to evolve a spacelike submanifold in some coordinate time on the spacetime manifold, but the equations are invariant with respect to diffeomorphisms of the coordinates, so demanding a priori that the coordinate $x^0$ be time, a non-coordinate invariant statement, is clearly a poor option. One needs to come up with a coordinate invariant clock, a scalar field, $t$, that, on relevant patches of the manifold, corresponds to the time. One good option is to introduce $t$ as a separate physical scalar field on the manifold \cite{rovelli}, but consider the following alternative method:
Demand that, on relevant patches, the unit time fielbein vector, $\hat{e^0}$, be closed
\begin{equation}
\vec{\nabla} \wedge \hat{e^0} = 0
\label{closed}
\end{equation}
and hence that, on patches of the manifold for which every closed oriented curve is the boundary of some compact oriented surface\cite{frankel}, $\hat{e^0}$ is exact
\begin{equation}
\hat{e^0} = \vec{\nabla} t
\end{equation}
This method has several good attributes. The arrow of time, the coordinate invariant form, $\hat{e^0}$, gives rise naturally to the scalar time, $t$. Hence the clock field, $t$, is obtained in a coordinate invariant manner using geometric elements at hand. One may then naturally choose to transform to coordinates in which $x^0 = t$ and evolve a spacelike submanifold in Gaussian normal coordinates with $\hat{e^0}$ as the normal vector field.
The constraint equation, (\ref{closed}), is a bivector equation corresponding to the restriction of ${n(n-1) \over 2}$ degrees of freedom and determines the dynamics of $\Psi$ as follows
\begin{eqnarray}
0 & = & \vec{\nabla} \wedge \hat{e^0} \\
& = & \hat{\gamma^\mu} \wedge \nabla_{\mu} \left( \Psi \hat{\gamma^0} \widetilde{\Psi} \right) \\
& = & \hat{\gamma^\mu} \wedge [ ( \nabla^s_{\mu} \Psi) \hat{\gamma^0} \widetilde{\Psi} + \Psi \hat{\gamma^0} \widetilde{( \nabla^s_{\mu} \Psi )} ] \\
& = & 2 \hat{\gamma^\mu} \wedge < \! ( \nabla^s_{\mu} \Psi) \hat{\gamma^0} \widetilde{\Psi} \! >_1 \\
& = & 2 \hat{\gamma^\mu} \wedge \hat{\gamma^\nu} < \! \hat{\gamma_\nu} ( \nabla^s_{\mu} \Psi) \hat{\gamma^0} \widetilde{\Psi} \! >_0 \\
& = & 2 \hat{\gamma^\mu} \wedge \hat{\gamma^\nu} < \! \overline{\Psi} \hat{\gamma_\nu} ( \nabla^s_{\mu} \Psi) \! >_0 \\
& = & 2 \hat{\gamma^\mu} \wedge \hat{\gamma^\nu} \, T_{\mu \nu}
\end{eqnarray}
in which the operator $<>_n$ gives the grade $n$ elements of a multivector, $\overline{\Psi} = \hat{\gamma^0} \widetilde{\Psi}$, and the energy-momentum tensor for a spinor field, $T_{\mu \nu}$, has been recognized. The requirement that the unit time vector, $\hat{e^0}$, be closed is hence equivalent to the requirement that the anti-symmetric part of the spinor energy-momentum tensor, $T_{\mu \nu}$, vanish.
One natural way to enforce the vanishing of $T_{[\mu \nu]}$ is to construct the equations of motion to be
\begin{equation}
R_{\mu \nu} - {1 \over 2} \eta_{\mu \nu} R = T_{\mu \nu}
\end{equation}
in which the symmetry of the Ricci tensor will enforce the vanishing of $T_{[\mu \nu]}$. Since $T_{\mu \nu} = \, < \! \overline{\Psi} \hat{\gamma_\nu} {({\gamma^{\! - \! 1}}_\mu )}^i ( \nabla^s_i \Psi) \! >_0 $ is the energy-momentum tensor of the standard spinor action, these equations of motion will come from the action
\begin{equation}
S = \int{ \gamma \ \left\{ R + < \! \overline{\Psi} \vec{\nabla^s} \Psi \! >_0 \right\} }
\label{gmac}
\end{equation}
Thus it appears that the matter action arises from the geometric restriction that full fielbein gravity have a closed unit time vector. To vary $\Psi$ in (\ref{gmac}) in spacetime one may vary $\Psi$ over all even multi-vectors and enforce $\Psi \widetilde{\Psi} =1$ via the method of Lagrange multipliers. Introducing $m_s$ and $m_p$ as Lagrange multiplier scalar fields, (\ref{gmac}) is equivalent to
\begin{equation}
S = \int{ \gamma \ \left\{ R + < \! \overline{\psi} \vec{\nabla^s} \psi \! >_0 + < \! (m_s + \gamma m_p )(\psi \widetilde{\psi} - 1) \! >_0 \right\} }
\label{mgmac}
\end{equation}
with $\psi$ varied over it's eight degrees of freedom and the physical interpretation of $m$ clear. If $\psi$ is dynamically restricted to be unitary, as above, then one might also consider terms in the action such as $\psi R \widetilde{\psi}$ and address conformal symmetry.
An alternative to the inclusion of the term $< \! \overline{\Psi} \vec{\nabla^s} \Psi \! >_0$ in the action might be the direct restriction to $\vec{\nabla} \wedge \hat{e^0} = 0$ via the method of Lagrange multipliers, with the inclusion of a term such as $< \! B_2 \vec{\nabla} ( \Psi \hat{\gamma^0} \widetilde{\Psi} ) \! >_0$, with $B_2$ a Lagrange multiplier bivector field and dynamical selection of $B_2$ acting as a method of symmetry breaking.
\section{Gauge Symmetries}
A central proposal of this paper is that the ostensibly non-gravitational dynamics of the fielbein, the dynamics of $\psi$, are contained entirely in the geometric restriction $\vec{\nabla} \wedge \hat{e^0} = 0$. The dynamics imposed by (\ref{mgmac}) on $\psi$ are overly restrictive in this regard and need to be loosened by the addition of symmetries corresponding to the symmetries of $\vec{\nabla} \wedge \hat{e^0} = 0$. This is accomplished via the method of adding vector gauge fields and couplings to attain the necessary symmetries.
The first symmetries to notice in $\vec{\nabla} \wedge \hat{e^0} = \hat{\gamma^\mu} \wedge \nabla_{\mu} \left( \psi \hat{\gamma^0} \widetilde{\psi} \right) = 0$ are the invariance of this equation under duality and space rotations of $\hat{\gamma^0}$. The duality rotation invariance is invariance of $\hat{e^0}$ under the transformation $\psi \mapsto \psi e^{\gamma {\phi \over 2}}$. It corresponds to the group $U(1)$ and necessitates the addition of the corresponding vector gauge field in the standard manner to (\ref{mgmac}). The space rotation invariance is invariance of $\hat{e^0}$ under the transformations $\psi \mapsto \psi e^{r_\epsilon \gamma \sigma^\epsilon}$. It corresponds to the group $SU(2)$ and necessitates the addition of the three corresponding gauge fields.
One should consider the lifting of the restriction that $\psi$ in (\ref{mgmac}) be even. This raises the possibility that one might add to $\psi$ an odd multivector part, such as $\psi_{\! o} \, e_L$, in which $\psi_{\! o}$ is odd and $e_L = {1 \over 2} ( 1 + \hat{\gamma^3} \hat{\gamma^0} )$ is an idempotent projection operator. This ensures that the scalar and pseudo-scalar parts of $\psi \widetilde{\psi}$ remain unchanged, since $e_L \widetilde{e_L} = 0$. Note also that $e_L \hat{\gamma^0} \widetilde{e_L}$ is a null vector, so factoring $\psi$ into the left ideals of $e_L$ and $\widetilde{e_L} = e_R$ shows how $\psi$ is built from left and right chirality states and allows one to see the geometric meaning of $U(1) \times SU(2)_L$.
A possible symmetry of $\vec{\nabla} \wedge \hat{e^0} = 0$ to notice is the symmetry of transformations of the whole bivector equation, $B = \vec{\nabla} \wedge \hat{e^0} = 0$. This equation will be satisfied if and only if $< \! B \widetilde{B} \! >_0 \, = 0$. The scalar $< \! B \widetilde{B} \! >_0$ is invariant under the group $SU(3)$ of transformations of the bivector $B$, as described in \cite{hest3}, though it does not seem possible to incorporate this symmetry into $\psi$ as a gauge symmetry in the same manner as $U(1)$ and $SU(2)$. This difficulty suggests that it may be necessary to consider other dimensions from the four of spacetime in order to naturally obtain the $U(1) \times SU(2) \times SU(3)$ gauge symmetry of the standard model.
\section{Conclusion}
In this paper a step towards unification has been achieved, the unification of matter and gravity in a minimal geometric framework. Although others have recently proposed a similar unification scheme of obtaining gravitational dynamics from the Dirac operator \cite{connes}, the path proposed in the present exhibition goes in the other direction by obtaining the spinor field and Dirac operator from geometry.
A significant problem remaining in the current approach is the difficulty in satisfactorily accommodating $SU(3)$ symmetry. It seems plausible that $SU(3)$ could obtain with the addition of other dimensions to spacetime, perhaps in a Kaluza-Klein compactification scheme or in a holographic approach. And, of course, this program on the unification of matter and gravity would be incomplete without mention of the possibility of understanding quantum field theory within a geometric model. It is my greatest hope that this goal will be achieved, and that this work has furthered progress towards that end.
\newpage
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,656 |
{"url":"http:\/\/science.slc.edu\/mfrey\/post\/t1-t2-plotting\/","text":"# T1 and T2 Plotting\n\n(Written by Nicholas Torres)\n\nAn important aspect of conducting NMR analysis is finding two time-constants: T1 and T2. The T1 constant represents the longitudinal relaxation time or how long it will take for a proton that has been energized by a radiofrequency (RF) pulse to go back to realign with the magnetic field, whereas the constant T2 or transversal relaxation time tells us roughly how long it will take for a proton that has been struck with a 90\u00b0 RF pulse to dephase from its neighboring protons due to different local magnetic environments. It is important to stress the fact that these constants are not the exact times it will take for these processes to happen, simply a representation of how fast the process goes.\n\nBoth T1 and T2 are mathematically represented by these exponential functions: $V= V_0(1-e^{(-\\tau\/T_1)})$ and $V= V_0e^{(-t\/T_2 )}$, where $V$ and $V_0$ are the voltage we expect to measure with our TeachSpin setup. For T1, we use a relaxation recovery sequence (180\u00b0 pulse-$\\tau$-90\u00b0 pulse) and measure the voltage peak after the 90\u00b0 pulse for different $\\tau$ times. For T2, we use a CPMG sequence and take the voltage peak of the Hahn spin echoes. (The CPMG sequence using the Hahn spin echo to get rid of decoherence due to inhomogeneity of the external magnetic field, as well as changes the phases of the pulses to correct for pulse error.)\n\nBeing familiar with these constants is extremely advantageous for developing an MR image, for they provide special contrasting capabilities. For the purposes of the research the Sarah Lawrence Physics Department, we performed NMR analyses on zebrafish because discovering more about their biological makeup can elucidate important facts concerning neurodevelopmental diseases.\n\nIn order to collect T1 and T2 data, we utilized the oscilloscope and processed the data using Python. Below is our Python code for the data analysis: A Sample of T2 Data Analysis Python Script\n\nsamplingRate = 2500\ntau = 0.01\nnumEchoes = 20\nfullfilename = \"zebra fish middle body sample\" + '.csv'\nplt.plot(data[:,0], data[:,1])\nx2=len(data)\nmaxNum1=max(data[0:x2,1])\n\ncount=0\nwhile data[0+count,1] != maxNum1:\ncount +=1\ncount +=1\nfirstPeak=0+count\nprint(firstPeak)\n#Finds first peak value in Hahn Echo\nfirstPeak = 0\ninterval=int(2*tau*samplingRate)\nprint(interval)\n#If we know tau, then interval = 2*tau*samplingRate\nechoPeaks = [data[interval*j+firstPeak,1] for j in range(numEchoes)]\ntEchoes = [data[interval*j+firstPeak,0] for j in range(numEchoes)]\nplt.scatter(tEchoes,echoPeaks)\n\nfrom scipy.optimize import curve_fit\ndef fitfunc(x, p1, p2, p3):\nreturn p1*np.exp(-x\/p2) + p3\npoptB, pcovB = curve_fit(fitfunc, tEchoes, echoPeaks,p0=(12,0.01, 0.000001))\nperrB = np.sqrt(np.diag(pcovB))\npoptB\n#Prints array with T2 value and error\n\nfitData = [fitfunc(tEchoes[j], poptB[0], poptB[1], poptB[2]) for j in range(numEchoes)]\nplt.xlabel('Time (s)')\nplt.ylabel('Voltage (V)')\nplt.title('Fits with T2 = 44 +\/- 4 ms')\nplt.plot(tEchoes, echoPeaks,'.', label='Echo Peaks')\nplt.plot(tEchoes, fitData, label = 'Fit to Data')\nplt.legend(loc='upper center')\nplt.show()\n#Constructs and shows plot\n\n\nA Sample of T1 Data Analysis Python Script\n\ndef timearray(sampleRate, numPoints):\nsampleSpacing = 1.\/sampleRate\ntime = np.linspace(sampleSpacing, sampleSpacing*numPoints, numPoints)\nreturn time\ndef freqarray(sampleRate, numPoints):\nsampleSpacing = 1.\/sampleRate\nfreq = np.fft.rfftfreq(numPoints,sampleSpacing)\nreturn freq\ntime = timearray(1e7, 30000)\nfreq = freqarray(1e7, 30000)\n\nfilenums = [17, 18, 19, 20, 21, 22, 23, 24]\n#filenums corresponds tot the last two digits of each Excel file and is meant to be editted for each T1 Data Sample\ntauValues = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7,0.8]\n#tauValues should correspond to the Tau times set by the Pulse Programmer.\nmaxYValues = []\n\nn = 0\nfor n in filenums:\nfullfilename = 'TEK00' + str(n)+'.csv'\nmaxNumForEachDataSet = max(data[:,1])\nmaxYValues.append(maxNumForEachDataSet)\nn = n + 1\n#Iterates through our Excel files in a folder and finds peak values for each file\n\nfrom scipy.optimize import curve_fit\ndef fitfunc(x, p1, p2, p3):\nreturn p1*np.exp(-x\/p2) + p3\npoptB, pcovB = curve_fit(fitfunc, tauValues, maxYValues,p0=(12,0.01, 0.000001))\nperrB = np.sqrt(np.diag(pcovB))\npoptB\n#Prints array with T1 value and error\n\nfitData = [fitfunc(tauValues[j], poptB[0], poptB[1], poptB[2]) for j in range(len(filenums))]\nplt.scatter(tauValues, maxYValues)\nplt.xlabel('Tau')\nplt.ylabel('Voltage(V)')\nplt.title('Fits with T1 = 37 +\/- 2')\nplt.plot(tauValues, maxYValues,'.', label='T1 Peaks')\nplt.plot(tauValues, maxYValues, label = 'Fit to Data')\nplt.legend(loc='upper center')'\n#Constucts and shows plots\n\n\nWhat follows are the plots, constructed in Python, for our T1 and T2 data analysis:\n\n(Note: The extra peaks in the raw T2 data is coming from ringdown from the 180\u00b0 pulses.)","date":"2019-10-14 17:04:39","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\": 0.416466623544693, \"perplexity\": 4652.132211622818}, \"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-2019-43\/segments\/1570986653876.31\/warc\/CC-MAIN-20191014150930-20191014174430-00428.warc.gz\"}"} | null | null |
Collegio elettorale di Battipaglia – collegio elettorale della Camera dei deputati
Collegio elettorale di Battipaglia – collegio elettorale del Senato della Repubblica | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,444 |
I tested a lot of pillows outdoors since a good sleep is the basis of the hiking day. As often the simplest solutions are the best.
How can you use the T-shirt as pillow cover? Don't you wear it?
Do as you like. I usually have long sleep clothes in my pack, typically a pullover and a leggins made of type 100 fleece that also serve a spare warmth.
Is it for a reason that you turn the T-shirt inside out?
Yes, it's simply the skin-side of the shirt.
Doesn't the T-shirt smell to much to rest your head on it?
Well … no. I use a T-shirt made of merino-mix, that does not accumulate so much bad smells. When I take it off in the evening it ist mostly dry already and the smelly stuff has damped out.
What do you do if it gets really cold and you're need to wear your jacket inside the quilt?
I do what I always do: Improvise, vary, re-think. What's the worst thing to hapen? Just to sleep one night without a pillow. But before it comes that far you still have oportunities: Put your shoes under the mattress. Or the food bag instead. Or just use your day trousers instead of the jacket as pillow fill. Or two handful of leaves in a plastic bag. It will not be an emergency, just a small problem that is easy to solve.
What for are the black elastics on the sleeping mat that can be seen in the video?
They have nothing to do with the pillow and sevre as a quilt attachment. Details and my video about that can be found here (method B). | {
"redpajama_set_name": "RedPajamaC4"
} | 1,516 |
Q: Длина минимального слова Всем доброго времени суток. Можете ли помочь найти длину самого минимального слова в строке
разделенной пробелами на Java.
A: <script>
function find_min(str)
{
str=str.replace(/,/g, "");
arr = str.split(' ');
max_len = 0;
for(i=0;i<=arr.length-1;i++)
if(arr[i].length>max_len) {newstr=arr[i]; max_len=arr[i].length;}
return newstr;
}
alert(find_min("Yesterday, all my troubffffffles seemed so far away Now it looks as though they're here to stay Oh, I believe in yesterday."));
</script>
Блин, так ведь сначала нужна была реализация на JS ! Тьфу)
A: Примерно так на Java
String x="sdfds ds dsfsdf sdfs sdf sdf";
String[] xx=x.split(" ");
int min=1000000;
for (String i: xx){
if (i.length()>0 && i.length()<min) min=i.length();
}
P.S. Мини-реклама Python
x="sdfds ds dsfsdf sdfs sdf sdf"
minlen=min(map(len, filter(lambda y: y!='', x.split(' '))))
A: ИМХО, современный C# (3.0 и выше) ничем не уступает Пайтону по красоте и выразительности.
using System;
using System.Linq;
class Program
{
static void Main()
{
Console.WriteLine(Console.ReadLine().Split()
.OrderBy(x => x.Length).LastOrDefault());
// можно еще так, вроде выглядит попроще, но работает медленнее
Console.WriteLine(Console.ReadLine().Split().Max(x => x.Length));
}
}
A: Ловите студонята.. Писал 20 хв с вышеуказанным примером (лабораторная), макс и мин число..
package qq;
import java.util.Scanner;
public class alln {
public static void main(String[] args){
Scanner sc = new Scanner(System.in);
String x=sc.nextLine();
sc.close();
//String x="sdfds ds dsfsdf ds sdfs sdf sdf";
String[] xx=x.split(" ");
int min = 1000000;
int max = 0;
int bufmin = 0;
int bufmax = 0;
String temp;
String tempz;
for(int i = 0; i < xx.length; i++) {
temp = xx[i];
if (temp.length()<min){
min=temp.length();
bufmin=i;
}
}
for(int i = 0; i < xx.length; i++) {
tempz = xx[i];
if (tempz.length()>max){
max=tempz.length();
bufmax=i;
}
}
System.out.print("Min: "+min+" ("+xx[bufmin]+") ; Max: "+max+"
("+xx[bufmax]+") ;");
}
}
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,626 |
'''
Created on 2014年7月7日
@author: kerry
'''
from twisted.internet import reactor, protocol
from base.miglog import miglog
#from robot_chat_mgr import robot_chat_mgr
from base.net_work import NetData
import sys
import struct
class MIGChatBaseSchedulerClient(protocol.Protocol):
def connectionMade(self):
miglog.log().debug("Chat connection success")
self.transport.write(robot_chat_mgr.RobotChatLogin(self.platform_id, self.robotid,self.uid))
def dataReceived(self, data):
"As soon as any data is received, write it back."
#处理粘包问题
#pack_stream,result = self.net_work(data)
pack_stream,result = self.netdata.net_wok(data)
miglog.log().debug("result %d",result)
if(result==0):
return
packet_length,operate_code,data_length = robot_chat_mgr.UnpackHead(pack_stream)
miglog.log().debug("packet_length %d operate_code %d data_length %d data %d",packet_length,operate_code,data_length,len(pack_stream))
if(packet_length - 31 <> data_length):
return
if(packet_length<=31):
return
if(packet_length<>len(pack_stream)):
miglog.log().debug("===========")
return
if(operate_code==100):#心跳包回复
self.transport.write(pack_stream)
if(operate_code==1001):#登陆成功
self.transport.write(robot_chat_mgr.RobotJoinChat())
def connectionLost(self, reason):
print "connection lost"
def dataWrite(self,data):
self.transport.write(data)
def __init__(self):
print "MIGChatBaseSchedulerClient:init"
self.netdata = NetData()
def set_platform_id(self,platform_id):
self.platform_id = platform_id
def set_uid(self,uid):
self.uid = uid
def set_robotid(self,robotid):
self.robotid = robotid
class MIGChatBaseSchedulerFactory(protocol.ClientFactory):
def __init__(self,platformid,uid,robotid):
print "MIGChatBaseSchedulerFactory:__init__"
self.protocol = MIGChatBaseSchedulerClient
self.platformid = platformid
self.uid = uid
self.robotid = robotid
def clientConnectionFailed(self, connector, reason):
print "Connection failed - goodbye!"
reactor.stop()
def clientConnectionLost(self, connector, reason):
print "Connection lost - goodbye!"
#自行退出进程
reactor.stop()
sys.exit(0)
def buildProtocol(self, addr):
p = protocol.ClientFactory.buildProtocol(self, addr)
p.set_platform_id(self.platformid)
p.set_uid(self.uid)
p.set_robotid(self.robotid)
return p
class MIGChatInitialScheduler():
def Connection(self,host,port):
f = MIGChatBaseSchedulerFactory(self.platform_id,self.uid,self.robotid)
reactor.__init__() #因使用进程池,故工作进程会把主进程的reactor拷贝过来,reactor在主进程已经运行,故需要重新初始化
reactor.connectTCP(host, port, f)
def set_platform_id(self,platform_id):
self.platform_id = platform_id
def set_uid(self,uid):
self.uid = uid
def set_robotid(self,robotid):
self.robotid = robotid
def start_run(self):
reactor.run()
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,091 |
Q: Substitute R values Is there a faster way to do the following R substitution
for(i in 1:545082)
{
index = i*33
A[index,]$pred = B[index,]$pred
}
This loop seems to take forever in R. Thanks
A: Assuming you have a data.frame you can use data.table's set function to replace values by reference. That should be very fast since there are no copies being made.
library(data.table)
set(A, i=1:545082*33, j="pred", B[i:545082*33, "pred"])
A: Some benchmarks. data.table::set() is indeed a lot faster than regular data frame assignment, but the gigantic difference comes from vectorized assignment (avoiding the for loop). You can get about a 15000-fold speed increased by using vectorized assignment, or a 200,000-fold increase using data.table::set() (again in a vectorized way).
updated: added set within a for loop, which is intermediate in speed (much faster than doing assignment within a loop, and only 50 times slower than doing a vectorized assignment).
n <- 1e5
m <- 30
s <- as.integer(seq(1,n,by=m))
set.seed(101)
A <- B <- data.frame(x=runif(n),y=runif(n))
library("data.table")
library("rbenchmark")
benchmark(for(i in s) { A[i,]$y <- B[i,]$y },
for(i in s) { A[i,"y"] <- B[i,"y"] },
for(i in s) { set (A,i=i,j="y",B[i,"y"]) },
A[s,"y"] <- B[s,"y"],
set(A, i=s, j="y", B[s,"y"]),
replications=20,
columns = c("test", "elapsed", "relative"))
## test elapsed relative
## A[s, "y"] <- B[s, "y"] 0.027 13.5
## for (...) { A[i, "y"] <- B[i, "y"]} 94.797 47398.5
## for (...) { A[i, ]$y <- B[i, ]$y} 409.383 204691.5
## for (...) { set(A,i=i,j="y",B[i,"y"])} 1.283 641.5
## set(A, i = s, j = "y", B[s, "y"]) 0.002 1.0
A: Try:
n = 545083*33
A$pred[1:n] = B$pred[1:n]
| {
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} | 4,299 |
let webpack = require('webpack');
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loaders: ['style-loader', 'css-loader', 'less-loader']
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// For each one, we'll add a new Webpack rule and then prepare the necessary
// extract plugin to extract the CSS into its file.
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tap(new ExtractTextPlugin(outputPath), extractPlugin => {
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vueExtractPlugin = extractPlugins.length ? extractPlugins[0] : new ExtractTextPlugin('vue-styles.css');
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loader: 'vue-loader',
exclude: /bower_components/,
options: {
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loaders: Config.extractVueStyles ? {
js: {
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sass: vueExtractPlugin.extract({
use: 'css-loader!sass-loader?indentedSyntax',
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if (Config.extractVueStyles && ! extractPlugins.length) {
extractPlugins.push(vueExtractPlugin);
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return { rules, extractPlugins };
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| {
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} | 8,264 |
{"url":"https:\/\/stats.stackexchange.com\/questions\/237799\/are-marginals-of-a-jointly-gaussian-sequence-always-gaussian?noredirect=1","text":"# Are marginals of a jointly Gaussian sequence always Gaussian?\n\nAre marginal distributions of the random variables comprising a jointly gaussian random vector always Gaussian?\n\nThis stems from my confusion with the Central Limit Theorem which loosely states that sum of a sufficiently large number of independent random variables tends to be normal under mild constraints irrespective of the distributions of each random variable.\n\nThe second statement is that of a Gaussia Random process in time, which states that \"for any number n of samples, any sampling times $t_1,t_2\\ldots ,t_n$, and any scalar constants $a_1,a_2\\ldots a_n$, the linear combination $a_1X(t_1)+a_2X(t_2)+\\ldots +a_nX(t_n)$ is a jointly gaussian random variable.\"\n\nNow, for Jointly gaussian random variables $X_1,X_2,\\ldots,X_n$, any linear combination of these random variables is a gaussian random variable. Then, for all but one scalar coefficients $a_i$ set to zero, the resulting random variable would still be a Gaussian and hence, the marginal $X_i$ would be gaussian.\n\nBut, CLT states that it could be of any distribution!\n\nI am confused with these two lines of thought. Please remedy my confusion.\n\n\u2022 The CLT says absolutely nothing about finite linear combinations of random variables. It asserts a limiting distribution is Gaussian, not that it \"could be any distribution\"! Why don't you review our posts on the CLT? \u2013\u00a0whuber Sep 30 '16 at 19:10\n\u2022 It is worth adding that the converse statement need not be true: R.V.s can have marginal Normal distributions but their joint distribution might not Multivariate Normal. A simple example for Bivariate Normal: let $X$ be a standard Normal R.V. and $S$ be a random sign R.V. which is independent of $X$. $S$ takes on values $-1$ or $1$ with equal probabilities of $\\frac{1}{2}$. Now define $Y=SX$, which is also Normally distributed (by symmetry of the Normal distribution). Now, $P(X+Y=0)=P(S=-1)=\\frac{1}{2}$. ... ctd \u2013\u00a0slazien Sep 30 '16 at 19:40\n\u2022 ctd ... Since $X+Y$ is a linear combination of two standard Normal R.V.s which is not Normal, $(X,Y)$ is not Bivariate Normal. $\\:\\:\\:$ This neat example was taken from Blitzstein's Introduction to Probability book \u2013\u00a0slazien Sep 30 '16 at 19:40\n\u2022 \u2013\u00a0whuber Sep 30 '16 at 19:51\n\nThe assertion \"$a_1X(t_1)+a_2X(t_2)+\\ldots +a_nX(t_n)$ is a jointly gaussian random variable\" in your second statement is almost completely correct: $a_1X(t_1)+a_2X(t_2)+\\ldots +a_nX(t_n)$ is indeed a gaussian random variable but since it is just one variable all by itself, the adjective \"jointly\" is not needed.\n\nDefinition: A random process $\\{X(t) \\colon t \\in \\mathbb T\\}$is called a Gaussian random process if all the finite-dimensional distributions of the process are (multivariate) Gaussian distributions.\n\nA more prolix description is that each random variable $X(t), t \\in \\mathbb T$ is a Gaussian random variable, and for any integer $n \\geq 2$ time instants $t_1, t_2, \\ldots, t_n \\in \\mathbb T$, the $n$ random variables $X(t_1)$, $X(t_2)$, $\\ldots X(t_n)$, are jointly Gaussian random variables.\n\nDefinition: The random variables $X_1, X_2, \\ldots, X_n$ are said have a multivariate Gaussian distribution (or they are called jointly Gaussian random variables) if for all choices of real numbers $a_1, a_2, \\ldots, a_n$, the random variable $a_1X_1+a_2X_2+\\cdots+a_nX_n$ is a Gaussian random variable.\n\nAs the OP has noted, this implies that the marginal distributions of the $X_i$ are Gaussian. Note that also that when each $a_i$ is $0$, the sum is also $0$ and we are accepting this constant as a degenerate Gaussian random variable (cf. the extended discussion in the comments following this answer).\n\nInserting the latter definition into the former, we get the description of Gaussian random process used by the OP. Note that each random variable from a Gaussian random process is indeed a Gaussian random variable. That is, the answer to the OP's question\n\nAre marginal distributions of the random variables comprising a jointly gaussian random vector always Gaussian?\n\nis an unequivocal Yes.","date":"2019-12-15 04:54:04","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\": 0.7550734281539917, \"perplexity\": 202.05679399920194}, \"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-2019-51\/segments\/1575541301598.62\/warc\/CC-MAIN-20191215042926-20191215070926-00129.warc.gz\"}"} | null | null |
No Fun Aloud (1982)
I Found Somebody
I Volunteer
The Allnighter (1984)
Lover's Moon
Smuggler's Blues
Soul Searchin' (1988)
Some Kind of Blue
I Did It for Your Love
Strange Weather (1992)
Strange Weather
Love in the 21st Century
Before the Ship Goes Down
Part of Me, Part of You
Glenn Lewis Frey (; November 6, 1948 – January 18, 2016) was an American singer, songwriter, actor and founding member of the rock band the Eagles. Frey was the lead singer and frontman for the Eagles, roles he came to share with fellow member Don Henley, with whom he wrote most of the Eagles' material. Frey played guitar and keyboards as well as singing lead vocals on songs such as "Take It Easy", "Peaceful Easy Feeling", "Tequila Sunrise", "Already Gone", "James Dean", "Lyin' Eyes", "New Kid in Town", and "Heartache Tonight".
After the breakup of the Eagles in 1980, Frey embarked on a successful solo career. He released his debut album, No Fun Aloud, in 1982 and went on to record Top 40 hits "The One You Love", "Smuggler's Blues", "Sexy Girl", "The Heat Is On", "You Belong to the City", "True Love", "Soul Searchin'" and "Livin' Right". As a member of the Eagles, Frey won six Grammy Awards, and five American Music Awards. The Eagles were inducted into the Rock and Roll Hall of Fame in 1998, the first year they were nominated. Consolidating his solo recordings and those with the Eagles, Frey had 24 Top 40 singles on the Billboard Hot 100.
http://glennfreyafterhours.com/ | {
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} | 7,219 |
To all those who experience grace, humbleness, and satisfaction by stepping through life led by a sense of wonder.
CONTENTS
50 Hikes in Northern New Mexico at a Glance
Preface
Introduction
I. SANTA FE AREA
1.CABEZON PEAK
2.OJITO WILDERNESS
3.TENT ROCKS
4.SANTA FE BALDY LOOP
5.NAMBE LAKE
6.ATALAYA MOUNTAIN
7.TRUCHAS PEAK (EAST)
8.PECOS BALDY LAKE LOOP
9.APACHE CANYON TO GLORIETA BALDY
10.CAVE CREEK TRAIL
11.PECOS RUINS
12.HAMILTON MESA
13.MORA FLATS TO HAMILTON MESA LOOP
14.HERMIT PEAK
II. LOS ALAMOS AREA
15.SAN PEDRO PARKS LOOP
16.OJITOS TRAIL
17.MCCAULEY WARM SPRINGS TO JEMEZ FALLS
18.BOX CANYON
19.KITCHEN MESA
20.CERRO PEDERNAL
21.RIM VISTA TRAIL
22.VALLE CALDERA
23.CERRO GRANDE
24.BEARHEAD PEAK
25.DOME WILDERNESS
26.BANDELIER CANYON LOOP
27.RUINS TOUR
28.FRIJOLES FALLS
29.WINDOW ROCK
III. TAOS AREA
30.CRUCES BASIN WILDERNESS
31.RIM TO RIVER LOOP
32.LATIR LOOP
33.PLACER CREEK TO GOLD HILL LOOP
34.WHEELER PEAK
35.LOST LAKE TO HORSESHOE LAKE
36.WILLIAMS LAKE
37.SAN LEONARDO LAKES
38.TRUCHAS PEAK (WEST)
39.TRAMPAS LAKES AND HIDDEN LAKE
40.POWDERHOUSE CANYON
41.CLAYTON CAMP
42.SERPENT LAKE
43.RIO DE LA CASA LAKES LOOP
44.TOLBY CREEK MEADOWS
45.CAPULIN VOLCANO
IV. FARMINGTON AREA
46.SIMON CANYON RUIN
47.BISTI BADLANDS
48.DE-NA-ZIN WILDERNESS
49.PEÑASCO BLANCO
50.PUEBLO ALTO LOOP
Acknowledgments
Resources
References
Index
50 Hikes in Northern New Mexico at a Glance
Preface
Nearly ten years have elapsed since the first printing of this book. In that time, though on the surface all may look well, the life systems of northern New Mexico and the rest of the planet have been in the throes of human-caused climate change that has grown in volume, erratic nature, and intensity. Northern New Mexico has always been a place where geology, over spans of millions of years, has ushered in fantastical changes to geography, ecology, and human enterprise. But because of the excessiveness of destructive human enterprises, we see that people are not only redefining geography, ecology, and even the geology of places like northern New Mexico, but that the climate itself, the atmosphere that makes life possible on Earth, is gasping for air. All of these man-made, monumental shifts have occurred in a span of time that isn't even a nano-blip of a heartbeat when it comes to the Earth's existence and its recipe for change unfolding now for billions of years. Through this book, northern New Mexico awaits your companionship, and I sincerely hope you squeeze every precious drop from it, but be aware that this unique place also needs your care at a time when it and its people are at a crossroads of survivability.
NORTHERN NEW MEXICO HOLDS A SURPRISING NUMBER OF BEAUTIFUL HIGH MOUNTAIN LAKES
Introduction
Northern New Mexico is a unique place, recognizable by name and identifiable on a map, even without artificial lines boxing in its physical features. This is not a static setting, however, but one that is ever-changing. It is rich in names, events, and stories told and retold by the people who have roamed, settled, warred, prospered, suffered, and lived in communities across this region, but also in its varied landscape and the immense history it possesses. To understand northern New Mexico, you must realize that it is ancient in people and place. This region was once part of a great sea, and over millions of years layers of sedimentary rock have created a stratified history. Volcanic eruptions, the birth of mountains, and a dome of ice also helped create the complex, diverse geology and geography we experience today.
There have also been many human layers reaching as far back as 20,000 years ago. Clovis and Folsom man—named after the artifacts and animal bones found near Clovis and Folsom, New Mexico—moved along places like the Pecos River valley and the volcanic fields around Capulin. Their movement meant life in the game they tracked and the edible plants they gathered. The ancient human history here is recorded with an amazing depth of information, much more so than anywhere else in North America. The Anazazi people, descendants of Folsom man, crossed the Sangre de Cristo Mountains and were responsible for the very first cities in this country. What the land could provide in crops held these people in place—an agrarian culture was taking its first steps. They lived in pit houses in the beginning, digging large holes covered by roofs made from timber beams, tree bark, and soil. They lived this way for hundreds of years, hand farming and supplementing other needs with hunting and gathering, and eventually with trade.
In A.D. 850 an Atlantis of sorts arose inside a desert canyon called Chaco that had no visible means of providing for a society's survival, let alone the creation of the greatest ancient civilization in North America. Chaco Canyon had civil engineering projects that lasted for 150 years, driven by a kingless society without slaves. Thousands upon thousands of timbers had to be hauled from distances as far as 60 miles without the aid of horses or oxen. And tens of thousands of stone blocks were shaped with rudimentary hand tools as part of the meticulous process of constructing stone walls. These were dry fitted and mud mortared with laser-like precision. Corners came together seamlessly and the straight, level walls stood as high as five stories. Many thousands of tons of dirt were excavated to create regal kivas—predecessors to pit houses that became places of worship and elder council. The Chacoan people created multiple pueblos (mini-cities) without written plans and without tools for measurement. From what archeologists can tell, all this work was more for the purpose of ceremony and spiritual function than year-round habitation. The results, much still visible today, were palace villages set against stunning orange and red sandstone walls and alongside massive boulders that littered the canyon floor.
There are many mysteries about the people of Chaco: the way they lived, how they lived, the mecca for trade that this place was, and why their civilization collapsed in less than 300 years. Why did structures with hundreds of rooms contain only a handful with fireplaces for cooking and heat in the cold winter months? Why was a lunar and solar calendar built on top of Fajada Butte in a hard-to-reach place over half a mile from the nearest pueblo? Why did a society without horses or wagons build some 400 miles of super roadway spiraling out from Chaco Canyon? Why are there few to no burial sites in a place that had thousands of inhabitants over hundreds of years?
Descendants of the Chaco people lived on in Aztec and Salmon in New Mexico, Canyon de Chelly in Arizona, Hovenweep in Utah, and Mesa Verde in Colorado. A second migration occurred in A.D. 1300, with a group pushing south into places like Frijoles Canyon in what we know today as the cliff dwellings and structures of Bandelier. These people and others eventually resettled into the present-day pueblos of Cochiti, Taos, Pecos, and Zuni, and in the Hopi country of Arizona. Spanish conquistadors arrived in the 1500s, followed by Hispanic settlers and the beginnings of the Navajo nation in the 1600s. The migration of American homesteaders and merchants occurred in the 1800s, and the population of the region continues to grow today. The human history is much more complex than what I've presented here, and remains in constant flux between "the old ways" and the new.
The history of the landscape here is also diverse and complex, and infinitely more ancient than the presence of humans. In an arid region that struggles to survive on the meager supply of rain and snow, it is hard to imagine a time when northern New Mexico actually contained swampy ecosystems of cypress and sequoia-like trees with an understory of massive ferns. These coastal forests existed more than 100 million years ago and provided food for duckbilled and tyrannosaurid dinosaurs in a dank, humid climate. Sharks, rays, and crocodiles patrolled the salty waters that once existed here. Petrified cypress trees up to 40 feet tall still can be seen today in the Bisti Badlands, along with a variety of dinosaur fossils. Extraordinary full skeletons have been unearthed in places like Ghost Ranch and the Ojito Wilderness.
The sea and the dinosaurs retreated into oblivion, and for tens of millions of years volcanoes shaped and molded the landscape. The results are obvious today in the collection of volcanic necks around Cabezon Peak, in this continent's most perfectly preserved cinder volcano in Capulin, and in the Valle Caldera, where the earth-rumbling fury of the volcano transformed hundreds of square miles of terrain. Time, water, and wind shaped the Valle Caldera's lava and ash into stunning formations like Battleship Rock and the Tent Rocks.
There is tremendous variety in the canyon settings across northern New Mexico, from the deep chasm of the Rio Grande outside Taos to the broad, candy-striped walls of the upper Chama River to the steep, classic, V-shaped gorge of the Cimarron River. Where older Precambrian granite rock layers were thrust into the region's thin air—around Truchas Peaks and Wheeler Peak—frozen fingers of water (glaciers) created sharp summits and cirques.
Today hikers, backpackers, and other adventurers have the opportunity to explore a land full of geographical and ecological wonders. The high plateau desert zones—places like Tent Rocks, Window Rock, the Ojito Wilderness, and Ghost Ranch—are harsh yet delicately beautiful. On average, less than 9 inches of precipitation falls on this landscape of mesas and arroyos, creating a parched and prickly environment that will keep you constantly on guard. The prickly pear cactus blending into the ground like landmines, the forests of spiny cholla, the skin-piercing leaves of yucca plants, the whip-fast tails of scorpions, and the lightning release of the diamondback rattler are all obstacles you may face as you weave through stands of juniper and pinion pine. While encounters with scorpions and rattlesnakes are rare, they are possible.
Countering this desert ruggedness are the incredibly delicate flowers on the defensive cholla, the blankets of fleeting wildflowers that appear after a good rain, and the yellow puffballs of blooming chamisa in late summer. Nearly every morning and evening, sunlight illuminates the desert features with a tranquility powerful enough to convince you to make this wild place your home.
The desert is to be expected in this region, but perhaps one of the most surprising aspects here is the vast array of subalpine and alpine settings to explore in the Jemez and Sangre de Cristo Ranges. Even more amazing than the boundless mountainscapes are the number of brilliant backcountry lakes, many found in the Pecos Wilderness. Examples include Lake Katherine, pressed against the feet of regal Santa Fe Baldy; the rare specimen of Serpent Lake, with its unmolested, wildflower-rich wet meadows; and shallow Williams Lake, found beneath the state's highest mountain in one of the most striking cirques in the West. Other high-country treasures await too, such as the aspen zones along the western slopes of the Sangre de Cristos above Santa Fe and the trailless wilderness of the underexplored Cruces Basin. Amazing anomalies exist in the expansive wet-meadow parklands of San Pedro, the wildflower promenade of Hamilton Mesa, and the fusion of grassy highlands and marvelously scalloped subalpine basins deep in the Latir Wilderness.
Many of us seek solace and rejuvenation in the wilderness. A late fall backpacking trip to Pecos Baldy Lake, an early morning hike to Jemez Falls, an overnighter to the Trampas Lakes, or a day hike to the top of Cerro Pedernal can offer these qualities. But people and the landscape are connected in so many ways in this region. To walk the ruins of Pecos is to walk through a time when Pueblo people traded with Plains Indians in this area. To hike into the backcountry of Bandelier is to retrace the routes of the people of the Yapashi Pueblo. To move across the incredible landscape of the Valle Vidal is to follow the paths of countless generations of hunters. To work your way up Willow Creek into the secluded basin that holds its headwaters is to walk with prospectors of the 1800s. To stand on the summit of Atalaya and look down upon the city of Santa Fe and the high plateau and surrounding mountains is to look over thousands of years of human migration. People and place, through times of exploitation as well as stewardship, are intertwined in northern New Mexico. Now it is your time to add—with care, of course—to the layers of this ancient place.
CHACOAN PETROGLYPHS LINED WITH SWALLOW NESTS MARK THE PASSAGE OF A ONCE-VIBRANT COMMUNITY
THE HOW AND WHY OF THIS GUIDE
The hikes here were chosen first and foremost to reflect the diversity of what northern New Mexico has to offer in its respective regions, life zones, and collection of ancient ruins. It also was important for me to factor hiking distance, difficulty, aesthetics, flora, fauna, natural history, and human history. The Pecos Wilderness holds the largest number of hikes discussed, in part because of its size in relation to the greater region, but also because of its amazing attributes. The reality is that each hike—whether Tent Rocks, Chaco Canyon, the Latir Peak Wilderness, or Glorieta Baldy—is unique, interesting, and worthy of your time and effort.
The basic statistics for each hike include type (day, overnight, or multiday), season, distance, difficulty, elevation, location, and suggested accompanying maps. The difficulty rating (easy, moderate, and strenuous) is subjective, but not completely baseless. I tried to rate the hikes for the "average" hiker and how he or she would perceive the hike. The easy hikes and the majority of strenuous hikes were not difficult to rate; the moderate ones may have the greatest degree of variation in relation to your own judgment. Location is listed solely to help you find a hike when using a map application on your computer, phone, or printed road map.
I deliberately did not suggest hiking times because I believe they can be misleading. For example, you can complete a outing in the Bisti Badlands in a couple of hours, but more than likely you'll spend, pleasurably I think, a half day to an entire day exploring this alien-planet setting imagining the fantastical creatures that once lived here. Weather, available time, fitness, seasons, and interest in the physical surroundings all play a part in how long a hike will take each of us to complete. The more you hike the better you will be able to gauge how many hours it will take you to travel a specific distance over moderate terrain.
I recommend using a USGS map for each hike, although these do not always show a great level of detail. Still, the USGS 7.5-minute maps are very accurate as to the lay of the land, making them ideal for trailless areas and cross-country travel off designated trails. For areas like the Pecos Wilderness, the U.S. Forest Service produces large foldout maps that offer good detail of the landscape and indicate points of interest in a more hiker-friendly manner than the USGS maps.
The hike descriptions are meant to provide you with accurate details on distance, location of geographic features, campsites, trail features, and various flora and fauna. The idea was to weave these elements into a narrative that provided a sense of the aesthetics and personality of each of these places, along with interesting facts on the geography, geology, and history. The bonus section following each hike description varies from alternate routes to other interesting outings nearby to stories or short histories about the area.
50 Hikes in Northern New Mexico should provide you with a thorough overview of the vast possibilities of hiking and backpacking adventures across this region. I believe all guidebooks, including this one, are most useful for highlighting an aspect of a hike, discussing gear, or even examining the climate of a region. You should always feel like you have the freedom to break from the real and artificially imposed boundaries presented in this and other books and hike a region's trails however you please—not in a destructive manner, of course, but in balance with the surroundings. The most important thing is to make the time to venture out into the diverse, unique areas of northern New Mexico. Make sure to see these living and breathing places for what they are; let your aim be to move through them with an open and ready mind.
HAZARDS
Much of northern New Mexico, and really New Mexico as a whole, is quite rural. In a state covering 121,598 square miles, there are only 15.6 people per square mile. Even so, the road system allows for relatively easy access to the outings described here. But while you may not be far from good road access, in nearly every case you will be quite a distance from emergency services. The hazards you may confront in these remote and semi-remote places are generally knowable, relatively harmless, and/or rare, but you do need to be prepared for the worst-case scenario.
Rattlesnakes, scorpions, bears, mountain lions, and hantavirus are all realities in northern New Mexico. Lightning, flash floods, dehydration, altitude sickness, and threats from a vast collection of desert plant life with stickers, barbs, and thorns are also possible problems. The key hazards can be thought of in three categories: weather, geography, and animals.
WEATHER
Summer thunderstorms can be intense in northern New Mexico, whether you are hiking along grassy Latir Mesa or exploring the unique sandstone features of the De-na-zin Wilderness. These storms typically arrive in the afternoon, building incredible cloud banks that can unleash rapid-fire lightning strikes. Cells often will hover and send forth dozens of downstrikes in a concentrated area, particularly in areas like the Valle Caldera. New Mexico is one of the nation's leaders in lightning-caused injuries and deaths each year.
Do not take an approaching storm lightly, whether you are bound for the summit of Kitchen Mesa or hiking along the shoulder ridge of Truchas Peak. The best course of action is simple: Get yourself out of harm's way. In the mountains this usually means moving quickly to a lower elevation into the cover of the trees. You can also lessen your chances for trouble by checking the weather reports prior to your hike. And it's a good practice to be mindful of the time of day you start your hike and to scan for possible safety zones en route. On the high plateaus you should look for overhangs along cliffs and rock outcroppings or, better yet, return to your vehicle before bad weather arrives.
Temperatures can drop 20 to 30 degrees when a thunderstorm cell passes overhead. In the high plateau country this could mean going from 90 degrees to 65 degrees in an extremely short amount of time. Though this is a big swing, it isn't too severe a threat to your wellbeing. However, in the mountains a 20-degree drop could mean summer temperatures sinking into the 50s or 40s, where the threat of hypothermia is greater if you aren't properly prepared for rain. Temperatures often plummet to the freezing level and beyond in certain high elevations in the summer, turning rain into snow.
Of course, elevation always brings somewhat cooler temperatures. A simple equation to remember is that the higher you climb, the cooler the temperature. Always carry proper rain gear and clothing layers to stay dry and warm. The National Oceanic and Atmospheric Administration web site (www.weather.gov) provides accurate weather forecasts for any area you plan to visit. Local ranger stations and/or information centers also are key resources for obtaining weather forecasts. (See Resources for phone numbers and web addresses.)
Flash flooding in the high plateau is truly an amazing spectacle. In a matter of minutes trails can become raging creeks, and arroyos that were bone dry prior to a storm suddenly become swift-moving rivers. Avoid getting caught in any canyon settings when these sorts of storms are threatening. Also, fording creeks and arroyos that are running mad would not be wise. Even a smaller arroyo may be unsafe because you might be swept downstream into a larger one that could be running much faster and deeper. It's better to wait it out, preferably somewhere sheltered, than to chance it.
Make sure to have proper protection from the sun too, especially with the high-elevation UV intensity of northern New Mexico. And proper hydration is an absolute must, because summer temperatures are often more than 100 degrees in the high desert.
GEOGRAPHY
The two most prevalent hiking zones in northern New Mexico are the high plateau desert and the subalpine. Each has specific obstacles and considerations. In the high plateau you are faced with two primary concerns: exposure and dangerous plant life. Exposure plays itself out in the intensity of the sun and the power of thunderstorms. There are a number of plants with defensive measures—Russian olive thorns, prickly pear cactus spines, and the yucca's sharp points—that will keep you on constant guard, especially if you are moving off-trail. In the subalpine, negotiating downfall and scrambling up loose rockslides represent possible hazards. In both zones the altitude is surely a hazard, especially if you are not acclimated. Altitude sickness can strike you at an elevation of 8,000 feet and surely more so the higher you climb into the mountainous zones of northern New Mexico. Pulmonary and cerebral edema can also occur at elevations as low as 9,000 to 10,000 feet. The most important action to take if either occurs is to retreat to a lower elevation immediately. It is also critical to stay hydrated when at altitude.
Perhaps the most threatening hazard isn't being stuck by cholla or tripped up by a tree root, but rather being directionally challenged. The hikes here are mostly enjoyed via trail systems that mitigate this geographic risk. Some areas lack designated trails, and you must always be aware that trusting a trail alone isn't the best way to enter more remote backcountry settings, or even a relatively short day hike for that matter. A map and compass or GPS are invaluable allies in keeping you grounded in relation to your environment. Always carry one or the other, and check the map periodically to confirm your location.
ANIMALS
Our separation from wild animals in everyday life has come to mean that many of us fear desert, forest, and mountain inhabitants like the rattlesnake, bear, and cougar. But the reality is that the chance of a violent confrontation with an animal is extremely remote. Watching a black bear feeding in a high mountain meadow is a fantastic experience. If you feel the distance between you and the bear isn't far enough, make some noise to warn it of your presence. A bear will acknowledge you by moving away or keeping a watchful eye on you while it continues to feed. If you want to know more about how you can minimize an encounter with large wild animals, read Don't Get Eaten: The Dangers of Animals That Charge or Attack, by David Smith.
Rattlesnakes inhabit a number of places referenced in this book, so it's important to watch where you place your hands and feet. If you do encounter one, keep your distance and don't provoke it. Pay special attention when you are near overhangs and boulders or along arroyos. The same precaution goes for scorpions. If you are camping make sure to check your sleeping bag, tent, and shoes for either of these creatures.
The surest way to attract unwanted animals is food. Marmots, squirrels, mice, birds, pack rats, and other smaller, seemingly less threatening creatures actually may give you the most trouble. So keep your food stored properly. If you are camping in the mountains, be sure to secure all food off the ground if possible. Cook away from tents and try not to leave any food unattended inside your tent.
KEYS TO BEING PREPARED
The two most emphasized and hopefully adhered-to credos for hiking and backpacking are the Ten Essentials and Leave No Trace. You should also pay attention to planning, rules and regulations, equipment, and trail etiquette.
TEN ESSENTIALS
Maps and trail information
Compass
Flashlight/headlamp
Extra food
Extra clothing
Sunglasses
First-aid kit
Knife/multitool
Matches/lighter
Fire starter
LEAVE NO TRACE
Leave No Trace is the philosophy of minimal impact and removal of any obvious signs of human presence. Stay on trails, use existing campsites, camp 200 feet from water sources, pack out solid human waste or utilize cat holes, don't remove branches or cut down trees for firewood, don't disturb the plant and wildlife, and pack out what you pack in. The idea is a simple one—leave the wilderness as you found it or better. More information can be found at www.lnt.org.
PLANNING
It is always a good idea to find out the conditions of the area you plan to visit: weather, road access, and trail conditions. The Resources section at the end of this book lists the agencies that manage public land in northern New Mexico, and the people who work there should be able to answer all of your questions. Another important element of backcountry travel is to leave your plans with someone back home in case of an emergency. Provide them with dates, places, and contact numbers, along with a time frame for notifying the proper agencies if you don't return. Remember, it's better to be safe than sorry.
RULES AND REGULATIONS
The hikes discussed here run through national monuments, wilderness areas, state parks, wildlife refuges, private reserves, natural areas, and national forests. Each of these areas has its own rules and regulations. For instance, wilderness areas have maximum group sizes of twelve, allow a maximum of fourteen days at any one campsite, and have a rule against mechanized travel (cars, motorcycles, bikes, hang gliders, etc.). National monuments have restrictions on horse use, access for dogs, preservation of natural or archeological features, and typically require an entrance fee. It's a first-come first-served permit system to access Valle Caldera by car. The permit is free, but the preserve entrance fee is $20 per vehicle. Always verify the current rules and regulations with local management offices before hitting the trail. The information provided throughout this book is a basic overview, and should answer the questions of the average hiker or backpacker.
A CHOLLA BLOOM PROTECTED BY PRICKLY SPINES IN THE DESERT
EQUIPMENT
What should I wear? What should I bring? The answers to both of these questions obviously hinge on where you are going and for how long and your own personal tastes. No matter where you go, remember that function and comfort, not fashion, are the keys. The following is by no means a comprehensive list, but it does offer a few suggestions and reminders.
If it feels good, wear it. But try to select clothing made of wool, wool blends, or synthetic material, and try also to avoid cotton. The wool and synthetic materials will be more comfortable, breathe better, and retain their shape better. Synthetics also dry more quickly. Cotton, on the other hand, doesn't dry quickly, can cause hot spots, and will rob your body of heat when wet. Of course, the time you are out, the terrain you are in, and the distance you are going will also affect your decision about what to wear.
Good hiking socks are well worth the money. Most are made completely of synthetic material or a blend of synthetics and wool. Good socks pad your feet in the proper places, dry quickly, and hold their shape, a good characteristic when you're on a long trip.
When walking in rugged terrain, going cross country in the high deserts, in wet or snow conditions, or when carrying a backpack on a longer outing, hiking boots provide sound stability and reduce leg fatigue. However, low-cut hiking shoes, trail-running shoes, and even good running shoes are adequate for many of the hikes listed here. These types of footwear are far more comfortable than heavy hiking boots, and when you're carrying a light load or day-hiking, they'll make your legs feel much livelier during and after the trip.
PACKS
I recommend looking for a backpack the same way you should look for a new bicycle: focus on fit over everything else. The price range between specific packs is vast, differentiated by the quality of materials, design, and features offered. A moderately priced backpack should have enough adjustment points to gain a good fit, be constructed of reasonably good material that will last many hiking seasons, and be outfitted with features that make sense considering the demands of backpacking. I don't mean to steer you toward one kind of equipment store over another, but specialty outdoor stores are more apt to have personnel who actually hike and backpack and can help you find a pack for your specific body type.
Day packs, fanny packs, and larger hydration packs are great for day hikes. Most are big enough to carry a supply of water, food, clothing, and other provisions. Fit is still important, but it isn't as crucial because of the minimal amount of weight being carried.
HIKING POLES
There was a time, not too long ago, when the elderly were the only people you saw hiking or backpacking with walking sticks. But these days all age groups are enjoying the benefits of adjustable hiking poles with ergonomic grips that transform into a monopod for your camera. Whether or not the poles are cluttered with features or made of the latest lightweight alloy, their use makes sense for hikers and backpackers of all abilities.
Day-hiking or backpacking is much more enjoyable and energizing with poles (old ski poles do the job and cost a lot less). The poles keep a portion of your pack's weight off your legs, keep your arms swinging to aid circulation, and help pull you uphill and absorb some of the impact going downhill. And if you stumble, your extra set of "artificial legs" can help you avoid a face plant.
WATER PURIFICATION
Times have changed in the world of making water safe to drink. The options range from water purification tablets to filtration systems to UV light pens to water bottles with filters built right into them. There's also the old-fashioned method: boiling your water. Your choice of purification method will depend on how often you'll be using it, its weight, and the amount of water you need. The best first step would be to pop into a specialty outdoors store and talk through your options with a professional.
DUCT TAPE
This item should be the eleventh essential. Duct tape is perfect for everything from repairing a pack or a hole in a sock to a cracked flashlight case. It also can serve as a substitute for gaiters or to cover hot spots or blisters on your heel. You could carry a whole roll (somewhat heavy) or just wrap a decent amount around the shaft of your hiking pole or water bottle.
HEADLAMPS
Almost all the headlamps on the market today utilize an LED light that burns brighter and longer than conventional bulbs. But they still require AA or AAA batteries. When you aren't using your headlamp, or are storing it between hiking seasons, it's a good idea to reverse the battery positions (positive and negative). This way, if you accidentally turn on your headlamp while reaching into the top of your pack for candy, you won't drain the batteries.
MOUNTAIN FOOD
Buying dehydrated foods can be quite expensive. If you backpack a lot, then a food dehydrator and vacuum-sealing machine are well worth the investment. Fruits like apples, pears, plums, strawberries, peaches, and bananas make great trail snacks, and dehydrating them on your own saves money. Vacuum-sealing and freezing the food items will help keep them fresh two to four times longer.
Whole meals also can be dehydrated or just vacuum-sealed and frozen without dehydration. When you're ready to hike, just remove the non-dehydrated, premade meal from the freezer, and keep it frozen in a cooler as long as possible before you step onto the trail. These meals should be fine for a number of days after they have thawed as long as they're stored in a vacuum-sealed bag. To heat your dinner, just drop the package into boiling water. For more information on dehydrating different kinds of foods, check out the Complete Dehydrator Cookbook, by Mary Bell and Evie Righter, published by Morrow Cookbooks.
TRAIL ETIQUETTE
Your reasons for wanting to hike in the outdoors probably aren't much different from those of other people who may have chosen the same place you did. If you keep this in mind, it will be much easier to observe proper manners afield. When you encounter people on horseback or leading a pack line, you need to yield the right-of-way. Whether the riders see you first or you see them, make sure to say "hello" or "hiker up," not so much for the riders but so the horses know that the object in the trail ahead is a human. Give a horse plenty of room to pass; if the trail isn't wide enough, step off on the downslope side. If the horse gets spooked by you or something else while passing, it will turn away (upslope) from you, which should make it easier for the rider to gain control.
HIKE OFF-DAYS/SEASON
Weekdays, whether at the height of the season or on either end, are a great time to venture out while avoiding the additional weekend trail traffic. On the back half of the season, usually mid-September to the end of October, the summer crowds have disappeared back to their jobs and schools, leaving the wilderness open for much greater solitude. And the weather is usually stable and still plenty warm, even at the higher elevations. If you like to hike and backpack with minimal human contact, then just keep on walking. Basically, the longer and more difficult the hike, the greater the likelihood you'll avoid other people. There is no hard and fast rule, but typically if you hike at least 8 miles one way, you should find some space and solitude.
TRAVELING WITH TRAIL INFORMATION AND MAPS
Instead of lugging this entire book with you on the trail, just photocopy the necessary trail information and maps. Secure those pages and your more detailed USGS map(s) in a waterproof case or covering. Map and travel bookstores sell such cases, or you can simply use a large Ziploc bag. Some online map companies can also print waterproof maps for you.
Cabezon Peak
TYPE: Day hike
SEASON: March to November
TOTAL DISTANCE: 2 miles
RATING: Easy
ELEVATION GAIN: 150 feet
LOCATION: Cabezon Peak Wilderness Study Area, 27 miles northwest of Bernalillo
MAPS: USGS Cabez on Peak
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GETTING THERE
From Bernalillo, take US 550 24 miles northwest to San Ysidro. Approximately 18 miles north of San Ysidro (42 miles total), turn left onto CR 39 at a sign for San Luis. At 8.7 miles along CR 39, the road surface changes from pavement to dirt. At 13.1 miles (55.1 miles total), the road splits. Take the left fork, which crosses over a bridge in less than 1 mile. After the bridge crossing, drive another 2.2 miles to a sign for Cabezon Peak and the access road to the parking area and trail, another 0.9 mile (59.2 miles total).
THE TRAIL
As Cerro Pedernal (located near Ghost Ranch) scrapes the sky in distinctive fashion above the Chama River valley and beyond, so too does Cabezon Peak (7,786 feet), its gumdrop shape acting as the sacred beacon of the Rio Puerco valley. The Navajos tell the story of a giant who was slain on Mount Taylor (11,301 feet), with the lava flows and a collection of more than four dozen volcanic necks representing the aftermath. The area around Cabezon is part of the Mount Taylor volcanic field, which was created over millions of years as eruptions sent mud flows racing down the slopes of Taylor and lava out across the landscape from a number of outlets, including Cabezon Peak. The slopes run steeply off Cabezon as they transition from thick blankets of loose rock onto a pedestal base of juniper, yucca, and cholla before slipping steeply again to claw tracks of arroyos with open grassland radiating outward.
Cabezon Peak, literally "big head" in Spanish, is one of fifty volcanic necks in the area. These were formed by molten lava pushing through rock layers of an ancient sea. As is often the case with the amazing geology visible today, it took millions of years for the softer sedimentary rock to be broken down and carried away in order to expose the harder basalt that is Cabezon and the other headless necks in the area.
A trail, measuring approximately 1.75 miles, hugs the bottom end of the loose rock slopes as it circles the benched pedestal of Cabezon. The trail meets a fenceline on the northwest side of the mountain. Even from the benched area, you have high views across the Rio Puerco valley to the Sandia Mountains to the east, the southern end of the Jemez Mountains to the north, and to the west and south an encampment of the some fifty other volcanic memorials.
The entire wilderness study area encompasses 8,159 acres, which means there is plenty of cross-country exploring to do beyond the lower slopes of Cabezon. Following rainy periods in the warmer months of the year the sun-leathered ground will transform into a colorful scene, with cholla sprouting delicate fuchsia blooms, prickly pear showing yellow flowers, and a nice collection of desert wildflowers, from aster to sunflowers to penstemon, revealing other attractive shades.
CHOLLA BELOW CABEZON PEAK
BE THE HAIR ON "BIG HEAD"
Scramblers, you're in luck. Starting on the east side and moving slightly north at points via a number of steep scrambles, you can reach the top of Cabezon Peak. To do this you must be in good physical condition, have some knowledge of climbing in loose rock terrain, and have the smarts to wear a helmet. As you would expect, the sky and landscape shine with even greater brilliance from the summit.
Ojito Wilderness
TYPE: Day hike or overnight
SEASON: March to November
TOTAL DISTANCE: Variable
RATING: Easy
ELEVATION GAIN: 200 feet
LOCATION: Ojito Wilderness, 25 miles northwest of Bernalillo
MAPS: USGS Ojito Spring and Sky Village NW
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GETTING THERE
From Santa Fe, travel south on I-25 for approximately 40.5 miles to Exit 242, signed for Bernalillo and US 550 for Cuba. Take US 550 toward Cuba. At 21.2 miles turn left onto Cabezon Road (look for mile marker 21; there is also a sign for the Ojito Wilderness). The road surface is dirt and packed gravel. Stay left at the fork less than 0.1 mile down the road. At 4.5 miles (25.7 miles total) you reach the parking area and trailhead for White Mesa. After crossing a wide arroyo at 5.7 miles the road forks again; stay to the right. There is a sign for the Ojito Wilderness at 9.3 miles (30.5 miles total). There are a couple options for parking: Beyond the wilderness sign there is a small turnout about 0.2 mile down, and a parking area at 0.5 mile.
THE TRAIL
Seismasaurus once stepped across this area at an estimated height of more than 40 feet and weighing in excess of 70 tons. Fossilized remains were excavated from a location not too far from the parking area, and they are currently on display at the New Mexico Museum of Natural History and Science. Stone tools, pottery chards, and petroglyphs that date back to the Paleo-Indian period have been discovered in certain areas of the wilderness. Tamarisk chokes arroyos, delicate wildflowers spread themselves out in lacy whiteness between juniper and yucca, elk graze the grassy zones, and rattlesnakes hunt in the cool of the night. Cabezon Peak and a city of volcanic necks stand to the northwest, while sunflowers bloom across the often-parched earth. These are but a few of the many dimensions of the Ojito Wilderness.
The 10,903 acres of wilderness terrain are a mix of arroyos of various sizes, some with richer collections of plant species growing along the bottoms, along with rock outcroppings and mesas. The most prominent mesa is Bernalillito Mesa, which runs along the western edge of the wilderness area. The dominant vegetation consists of sage, chamisa, prickly pear cactus, juniper, yucca, cholla, and a range of wildflowers like aster, zinnia, and paintbrush. Rain always will bring things to life, sprouting meadows of desert wildflowers as well as the delicate fuchsia-colored cholla blooms.
The options for exploring this trailless zone, officially designated a wilderness in 2005, range from walking along sandy arroyo bottoms to cutting across open spaces landminded with cactus—please don't disturb the cryptobiotic soil—and decorated with hoodoos to clambering up the pinion pine mesas for a high view of the area. Multicolored rock bands are joined by colorful ground cover during the wildflower seasons.
There is very little relief from the intensity of the sun here in the desert, so hike early in the day and/or in the cooler months of the year. Animal life is vibrant, with mammals like the coyote, elk, pack rat, cottontail rabbit, and mountain lion calling the Ojito home. There are also many different kinds of insects and a handful of reptiles, the most notable being the western diamondback rattlesnake. Often you will find these snakes near water sources and in shaded places under rocks.
A RATTLESNAKE IN THE OJITO WILDERNESS
Water works the terrain in many ways: providing sustenance, reshaping arroyos by striping away the soft soil, and at points leaving behind rocks balancing on small towers of soil. When you reach some high ground, in the distance you can see the Sandia Mountains to the east, the southern end of the Jemez Mountains to the north, and the prominent rounded haystack-shaped feature to the west that is Cabezon Peak, a volcanic neck originally formed some 2 million years ago.
Tamarisk, also known as salt cedar, grows to heights of more than 15 feet tall in the arroyo bottoms and is distinguishable by the fuzzy, feathery, coral-like leaves and its 2-inch-long bottlebrush blooms, which show in summer. Along the edges of some of the arroyos you may find small barrel-like cactus clinging to boulders like mussels on shoreline rocks. The area is a mix of sedimentary rock, gypsum, volcanic ash, and volcanic rock. There are places where the white and red rock bands appear to have been carved out by a giant spoon. The Ojito Wilderness is an amazing place to wander and discover, whether you are searching for a fossil or pottery shard, or just the solitude of the desert.
DESERT DUATHLON
The White Mesa area is open to hikers and mountain bikers. A series of long, looping single-track and double-track pathways provide more than 15 miles of unique mountain biking here. The area has only recently been opened to mountain bikers, thanks in part to the efforts of a group called Friends of Otero, which is helping the Bureau of Land Management (BLM) maintain the trails and facilities. More information can be found at www.ambanm.org.
Tent Rocks
TYPE: Day hike
SEASON: Year-round
TOTAL DISTANCE: 3.3 miles
RATING: Easy to moderate
ELEVATION GAIN: 600 feet
LOCATION: Cochiti Pueblo (managed by the BLM), 25 miles west of Santa Fe
MAPS: USGS Cañada
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GETTING THERE
Take I-25 south from Santa Fe toward Albuquerque for approximately 17.5 miles to Exit 264. Then head west on NM 16, signed for the Cochiti Pueblo. At 26 miles total, or 8.5 miles along NM 16, you reach a T-intersection. Turn right, now driving north along NM 22. In approximately 0.2 mile you will see a brown recreation sign marked KASHA-KATUWE/TENT ROCKS. At 2.7 miles along NM 22 (28.7 miles total) you turn left, continuing now in a more westerly direction along NM 22. There are signs again for Tent Rocks. At 30.4 miles, turn right onto FS 266. The road surface changes from pavement to gravel in 0.3 mile. You reach the picnic area and trailhead for Tent Rocks 4.6 miles along FS 266 (35 miles total). There is a daily fee of $5 per vehicle or you can display your National Parks Pass.
THE TRAIL
No matter whether you harbor childhood thoughts of elaborate oceanside sand castles, visions of exotic treks in central Turkey, or fantasies of exploring distant planets, Tent Rocks will match anything you can imagine. What you see today took millions of years to form, and native peoples have appreciated the striking uniqueness of the area for more than 4,000 years. For you, it will take, at minimum, a full day to absorb and explore this national monument and magical jewel of northern New Mexico.
With the namesake teepee-shaped formations set about like an encampment, you have a couple of hiking options to consider. There are two official trails: the 1.1-mile Cave Loop and the 1.3-mile Canyon Trail (one-way). Here, we'll start on the Cave Loop, soon connect to the Canyon Trail to explore up to the mesa top, and then rejoin the Cave Loop trail back to the trailhead.
TENT ROCKS CANYON
A short distance down the Cave Loop trail to the left, you weave your way through a small cluster of tent rock formations. It will be tempting to run your fingers along the surface. Do so, but lightly, so as not to break loose any of the conglomerated materials. What you see today in this city of Turkish towers, or hoodoos, was originally a thick layer of ash, pumice, and tuff, at some points more than 1,000 feet deep, deposited from a series of volcanic eruptions that took place more than six to seven million years ago. Wind and water ate away at the soft layers to leave behind the tent rocks, canyons, and arroyos.
The area of Tent Rocks is a high desert zone home to plant species like yucca, juniper, Indian plume, and manzanita, as well as creatures like blue-tailed lizards, rattlesnakes, and jackrabbits. The trails throughout Tent Rocks are plenty wide, so avoid moving off-trail to help keep this resilient-but-fragile ecosystem unharmed. Tent Rocks also is known as Kasha-Katuwe, "white cliffs" in the traditional Keresan language of the local Pueblo people. Rocks, technically called boulder caps, balanced on hardened sand castle–like cones seem to defy gravity in many places along the hike.
At 0.5 mile along the Cave Loop trail you reach the cave itself. Set into the wall at the mouth of a tall slot canyon, a traditional pueblo ladder will put you at eye level with the small shelter. Past the cave the trail arches up to give you a view of the landscape leading back toward the trailhead. The mountain cluster you see in the distance is the Sandia Range, its highest point reaching 10,678 feet on the Sandia Crest. Tent Rocks is on Cochiti Pueblo land managed by the BLM and designated in 2001 as a national monument. Hollywood movies like Lonesome Dove and Young Guns II were filmed here.
The trail makes small dips and twists, connecting to the Canyon Trail at 0.8 mile. Head left for a fantastic journey into a narrow canyon and up to a highpoint with great vistas. To the right is the continuation of the Cave Loop, which travels 0.3 mile across the open zone back to the trailhead.
The mouth of the canyon is quite inviting, but as you reach deeper in, approximately 0.3 mile, you begin to feel the undulation of the canyon walls. It is as if they are breathing sandstone lungs, the exhales pinching the trail through narrow passages. The shaping of the rock is definitely a great wonder, done by tens of thousands of years of water and wind and the abrasive action of sand against the canyon walls. The trail twists through the canyon like a mountain stream seeking the easiest path down. Nature is more into motion, contortions, odd leanings, and spirals than straight lines, and the walk through the canyon is a testament to this.
This hike does not involve canyoneering, technically speaking or otherwise, yet it does create a sensation similar to that experience, but without the element of danger. Heavy rains sometimes cause water to rush through here, though, making travel more difficult or ill-advised.
At 0.7 mile along the Canyon Trail you are in the upper canyon in a much wider zone, having lazily wound your way beneath some more amazing tent rock formations. A natural rock staircase marks the beginning of the short climb to the top of the mesa. It is 0.3 mile to the top, the trail climbing steeply the whole way. At one point you must make a ladder-like move over a rock. It is not overly difficult, but small children and those in poor physical shape may need some assistance.
Once you've topped out, there are a couple of trails to follow, the main one leading to a point that overlooks the Cave Loop area. Winds can be strong up here, especially on the point, so be mindful. Still, it is a wonderful perch for taking in the immediate area, with additional views of all the major ranges in the area: the Jemez Mountains to the north, the Sangre de Cristos east-northeast, and the Sandia Mountains to the southeast. As tempting as it might be to seek an alternate route back to the trailhead from here, you must return the way you came because of the impassability of the terrain and the need to preserve the fragile features of Tent Rocks.
COCHITI PUEBLO
Archeological finds have shown the present-day Cochiti Pueblo to have been continually inhabited since A.D. 1225, making it one of the oldest communities in North America. Research also has supported the idea that the Pueblo people of Frijoles Canyon were the ancestors of the Cochiti people. Most of the surrounding Pueblo people speak either Tewa or Towa (Tanoan languages), but the Cochiti people speak an unrelated language called Keresan. The Cochiti people farmed along the Rio Grande for more than 700 years. They also were excellent craftspeople who created beautiful pottery, and the tradition is still alive today.
Santa Fe Baldy Loop
TYPE: Day or Overnight
SEASON: Late June to early October
TOTAL DISTANCE: 16.9 miles
RATING: Moderate to strenuous
ELEVATION GAIN: 2,700 feet
LOCATION: Pecos Wilderness, 13 miles northeast of Santa Fe
MAPS: USGS Aspen Basin and Cowles
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GETTING THERE
Off Paseo de Peralta in Santa Fe, take Bishops Lodge Road north. At the first stoplight (0.2 mile), turn right onto Artist/Hyde Park Road, the road for Santa Fe Ski Basin. From here, it is 14.6 miles to the large parking area for the Winsor Trail and Santa Fe Ski Basin. There are outhouses at the trailhead.
THE TRAIL
At 12,622 feet, Santa Fe Baldy is one of the premier highpoints of the southern Sangre de Cristo Mountains, and adding to the splendor of this classic northern New Mexico hike is the regal cirque situated at Lake Katherine. In autumn, the slopes leading up to the trailhead from Santa Fe and many points along this hike reveal brilliant golden-yellow pools of color floating above the green conifers—compliments of the thousands of acres of aspen trees.
The trail begins by diving into the trees, with a creek crossing immediately thereafter. Next you begin climbing up switchbacks through a mixed forest of fir and aspen groves ringed by a carpet of green grasses and decorated with a fantastic collection of wildflowers. At 0.6 mile, with the more strenuous climbing behind, you reach a gate, a sign-in area, and the Ravens Ridge Trail junction.
Once through the gate you are officially in the Pecos Wilderness. The trail eases up along this stretch as you glide across a long gentle arc on the high west slope of the Rio Nambe drainage. You are still immersed in the forest, passing by lichen-covered rocks and crossing through patches of aspen that shimmer in yellow come the beginning of September.
At 0.8 mile you pass the junction for the Rio Nambe Trail. And at 1.8 miles you reach a grassy open zone with views of a rocky basin to the south, as well as the infant Rio Nambe. This also is the junction for accessing Nambe Lake. Before you continue straight ahead to Santa Fe Baldy, take a break to absorb the scents of the forest and sounds of the creek. At 2.1 miles you pass the junction for the other end of the looping Rio Nambe Trail. The pleasant walk continues with an easy-going trail through mixed forest, with the added bonus of pocket meadows dotted with wildflowers. If you are paying attention and time it right, there are wild strawberries to be had, typically ripening around the end of July. There is also a nice glimpse of bare-topped Santa Fe Baldy at 2.3 miles.
The Sangre de Cristo Mountains of New Mexico are part of the southern Rocky Mountains, which extend into Colorado. In 1719, Spanish explorer Antonio Valverde y Cosio, noting the reddish hue of the high mountains at sunset, named the mountains the "Blood of Christ."
At 2.8 miles you cross a creek lined with globeflower and marsh marigold; past here the trail starts to climb. With the climbing, though, you also gain nice views of the surrounding landscape, including the Jemez Mountains to the west and Lake Peak (12,409 feet) and Penitente Peak (12,249 feet) in the near distance to the south, along with growing views of the shape and features of Santa Fe Baldy (12,622 feet) to the north.
You reach the Skyline Trail junction at 3.6 miles. It is set inside a broad, grassy, benched area lined with spruce trees, and when in bloom their cones have a noticeable raspberry color that complements the wildflower blooms growing in the meadow below. From the junction you take Skyline Trail 251, climbing through clusters of trees, and eventually above them, into a grass and rock zone that leads to a magnificent saddle at 4.9 miles. From here the trail climbs much more strenuously to gain the summit of Santa Fe Baldy. Continuing straight, the trail drops into the Lake Katherine basin and offers expansive views of the Pecos Wilderness.
It is a marvelous spin to the summit. The route is strenuous, but the exposed ridgeline trail snakes through wildflowers and a natural rock garden as it gains 1,000 feet. The beautiful scenery should keep you more than occupied with good thoughts. You'll reach a highpoint, but not the summit, at 1.3 miles. A short push 0.2 mile farther will have you standing on the windswept pinnacle of Santa Fe Baldy. As you would expect–and deserve after your efforts–the vistas are the best in the area, with a full view of the Jemez Mountains stretching from Abiquiu to Cochiti, the formidable cluster of the Truchas Peaks to the north, and the tree-choked expanse at the heart of the Pecos Wilderness to the east.
Even in the hottest days of summer it will be cool up here and the winds will ebb and flow from breezy to gale force depending on the threat of thunderstorms. Even in this harsh environment, the wildflowers are extremely vibrant, almost glowing—the bioluminescence of the subalpine and alpine—so be careful not to crush them. If you edge along the summit to the northeast you'll have an overlook of Lake Katherine nestled in a basin nearly 1,000 feet below.
To continue on to Lake Katherine, follow the trail back down the exposed ridge to the saddle and into the cover of trees, winding your way downslope to the southeast shoreline in 0.9 mile, or 8.8 miles total from the trailhead. The forest rims the southern end of the lake and the walls of the basin slide into the remaining shoreline, lush with grasses and wildflowers like columbine and alpine aven, which pop up en masse between and below craggy rock features. The lake is popular and has suffered somewhat due to the number of visitors that trample the understory near this end. Please be mindful. Northern New Mexico is in an extremely arid climate zone, so high-mountain lakes and the surrounding flora should be viewed as precious, fragile resources.
SANTA FE BALDY
Near the east shoreline, close to the lake's outlet, is the continuation trail for looping back along a section of the Skyline Trail to rejoin the Winsor Trail and pass Spirit Lake. The trail from the lake loses elevation quickly, and at 0.3 mile (9.1 miles total) it passes by a water garden of sorts, a small, boulder-strewn tarn decorated with striated paintings created by rising and dropping watermarks. The trail shadows the course of the stream, which eventually becomes Winsor Creek, keeping you in a diverse riparian plant zone before it breaks off into a drier forest environment dominated by fir trees.
At 10.5 total miles you reach the junction with the Winsor Trail. Heading left would lead you to Stewart Lake in 1.2 miles. The trail to the right moves through the trees, crossing a creek and alternately gaining and losing elevation on the way to a small break where quaint and isolated Spirit Lake sits at 11.5 miles. The lake is for day use only and no campfires are allowed.
Moving on from Spirit Lake the trail gains some elevation, but in a very casual manner. It makes a high-slope run through the trees 2,000 feet above the Holy Ghost Creek drainage, but with breaks here and there that show glimpses of the Pecos Wilderness to the east. At 12.7 total miles you reach a signed junction marking the intersections of the Skyline Trail, a branch of the Skyline, and the Winsor Trail. Continue straight on the Winsor Trail, entering a forested bench area. Follow the pleasant course back to the junction with the Skyline Trail at 13.3 miles. From here it is 3.6 miles back to the trailhead, or 16.9 miles total.
SHOOTING THE SKYLINE
No other trail in the Pecos Wilderness is adorned with as many natural splendors as the Skyline. The western end of the trail sits on 12,409-foot Lake Peak and the eastern end ceases near the Barillas Peak Lookout (9,362 feet), a distance of more than 60 miles. In between, this incredible scenic byway provides off-ramps to all the Pecos Wilderness giants, like Santa Fe Baldy, East Pecos Baldy, and the Truchas Peaks. The Skyline Trail also accesses backcountry gems like Horsethief Meadow, Rincon Bonito, Enchanted Lake, and Lost Lake.
Nambe Lake
TYPE: Day hike
SEASON: Late June to early October
TOTAL DISTANCE: 5.6 miles
RATING: Moderate to strenuous
ELEVATION GAIN: 1,400 feet
LOCATION: Pecos Wilderness, 13 miles northeast of Santa Fe
MAPS: USGS Aspen Basin
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GETTING THERE
From Paseo de Peralta in Santa Fe, take Bishops Lodge Road north. At the first stoplight (0.2 mile) turn right onto Artist/Hyde Park Road, the access road for Santa Fe Ski Basin. From here it is 14.6 miles to the large parking area for the Winsor Trail and Santa Fe Ski Basin. There are outhouses at the trailhead.
THE TRAIL
In the Tewa language, Nambe means "People of the Round Earth." Nambe Lake, at 11,400 feet, is a major feeder for the Rio Nambe, which flows down the western slopes of the Sangre de Cristo Mountains and along the Nambe Pueblo. It is believed that before the early 1500s small villages were scattered across the foothills below Nambe Lake, providing the hunting and gathering families access to the riches of the river valley, as well as the game and berries on the higher ground. Eventually pueblo living was established in a fertile zone along the Rio Nambe. This created an agrarian society that, like other pueblos of the greater Rio Grande corridor, was eventually catholicized by the Spanish.
To reach the high mountain lake, follow the Winsor Trail up through a mixed forest of fir and aspen that is carpeted with grasses and a diverse collection of wildflowers. At 0.6 mile you reach the Ravens Ridge Trail junction, along with the sign-in for the Pecos Wilderness Area. Lake Peak (12,409 feet), accessed by the Ravens Ridge Trail, is a worthy substitute for the much more distant Santa Fe Baldy (12,622 feet) when it comes to elevated views of the surrounding area. It requires, however, a similar strenuous push up to the summit, much like the one you face in reaching Nambe Lake.
You can first relax, though, because once through the gate the trail slides easily down through thick groves of aspen. After 1.8 miles of easy walking, you reach the trail junction for Nambe Lake. A complete change in scenery and challenge awaits you from this point forward. Gone are the aspen shimmer and the shadowy forest stroll, and in their place is a strenuous climb that parallels the lake's outlet, gaining serious chunks of elevation—1,000 feet—and offering open-air views of the twisted, steep-walled cirque that holds Nambe Lake.
In the beginning, you will see that the traffic of past human visitors has left behind an unnecessarily wide access trail, along with additional pathways most likely created during periods of receding snowpacks or when the trail was excessively wet. Drying out your hiking boots is far easier than rebuilding a subalpine ecosystem, so be careful to keep your feet on the most traveled path. Doing so will allow surrounding areas to recover more quickly.
After you alternately grunt and rest over the 0.9-mile climb (2.7 miles total) the trail relents as it passes by a marshy area set in a narrow section of what feels like a hanging valley. An additional 0.1 mile brings you to small, clear Nambe Lake, set in a big cirque with tall, loose rock walls. The two highpoints some 600 vertical feet above the head of the basin are Lake Peak (known by the Nambe and Tesuque Pueblos as Blue Stone Mountain) and Deception Peak (12,280 feet). As is the case with other cirque lakes of the Pecos Wilderness, wildflowers from marsh marigold to monkshood dot the lakeshore through the blooming season. Camping is not allowed in the Nambe Lake basin.
THE NAMBE LAKE OUTLET
SPLASHING THROUGH A GOLDEN SEA
A fire in the late 1800s ravaged thousands of acres of the western slopes of the Sangre de Cristo Mountains above Santa Fe. The thick fir and spruce forest was destroyed, but more sun-loving tree species like aspen soon began to appear. These aspen still claim a staggering amount of mountainscape that, come autumn, shows in the crisp shimmer of the leaves, which range from sundrop yellow to fire orange. Aspen Vista, located along the ski basin road a few miles before the ski resort, is a wonderful but also wildly popular jump-off point into this aspen sea.
Atalaya Mountain
TYPE: Day hike
SEASON: April to October
TOTAL DISTANCE: 6.6 miles
RATING: Strenuous
ELEVATION GAIN: 1,800 feet
LOCATION: Santa Fe National Forest, on the eastern edge of Santa Fe
MAPS: USGS Santa Fe and McClure Reservoir
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GETTING THERE
From Paseo de Peralta in Santa Fe, a couple of blocks east of the Plaza, turn left onto East Alameda. Drive 1.2 miles as the road bends over the Santa Fe River to Upper Canyon Road. Turn left onto Upper Canyon and drive 1.3 miles to the intersection with Cerro Gordo Road. Turn left—your only turn option—and then take the first right into the parking lot for the Dale Ball Trail System and Santa Fe Canyon Preserve.
THE TRAIL
Beyond the dozens of art galleries along Canyon Road is this book's most relentless hike, Atalaya Mountain (9,121 feet). It shows itself from far below (1,800 vertical feet of climbing) in the rugged cliff face that overlooks the city of Santa Fe and the broad plateau that separates the Sangre de Cristos from the blue-tinged Jemez Mountains to the west. An early evening hike will have you twisting through blocks of pink quartzite and an evergreen forest of pinion pine up into crimson sunlight that reveals why the Sangre de Cristo Mountains were named "Blood of Christ" in Spanish.
Another badge of distinction for the Atalaya hike is the splendor of the trailhead location. The Santa Fe Canyon Preserve, which is accessed from the same parking area, hosts a huge variety of bird life feeding and living among the trees and plants. The trail system that loops the area should not be missed. An additional attribute of the Atalaya hike is the incredibly thorough trail-junction marking system present throughout the Dale Ball Trail System. Each junction is numbered and has a map indicating its location in respect to other junctions in the vicinity, as well as the distances between each. Getting lost here would be a real accomplishment.
To begin, head through the gate at the opposite end of the parking lot, as if intending to wander through the preserve. Just past this fenceline another gate leads down into a swale and over the continuation of Upper Canyon Road to access the first section of trail up to Atalaya Mountain. The trail parallels the road overlooking the refuge before turning up a narrow ravine. Volcanic basalt and quartzite boulders litter the trailside as you climb up to the first of a half-dozen junctions at 0.7 mile.
The route continues to the left along the lower mid-slope of Picacho (8,577 feet). The local plant life consists of pinion pine, ponderosa pine, yucca, prickly pear cactus, and wildflowers like daisy and sunflower. At just before 1 mile you reach the second junction. Head left to start the corkscrew ascent of the steep west slope of Picacho. The views become bigger the higher you go.
By 1.9 miles you reach the short spur trail that takes you on to the summit of Picacho, with a high view over the preserve and out over the western slopes of the Sangre de Cristos below the Santa Fe Ski Basin. Stay straight to continue on one of the two trails heading for Atalaya. The spilt pathways meet up in less than 0.3 mile, the one to the left angling more directly cross slope and the right one making a few twisting bends that offer nice views of Atalaya.
The trail crosses a ridgeline saddle connecting the two highpoints, with a view down the beginning of Arroyo Mora to the west. At 2.7 miles you reach another junction, the fifth so far. Continue to the left, working along the arm and shoulder of Atalaya. The hiking is steep the whole way, but it really rockets straight up just beyond a cliff band around the 3-mile mark. By 3.3 miles you will be standing on the summit of Atalaya, most likely catching your breath yet also taking in views of Santa Fe, mountainscapes of the Sandias and the Jemez Mountains, and close-ups of the lower slopes of the Sangre de Cristos.
It is possible to make this a through hike by continuing down the steep west slope of Atalaya and into the Arroyo de Los Chamisos, then on to the campus of St. John's College. This route is approximately 4.5 miles. You would, of course, need to leave a vehicle on each end or be prepared to make the full loop along roads to return to the Dale Ball parking area, roughly 10.5 total miles.
FEELING FOWL?
It was only in 2000 that the Santa Fe Canyon Preserve (a series of land donations over the years have brought total acres up to 525) was nudged back into its natural state as a life-rich bosque fed by the Santa Fe River. Remnants of the original 1881 dam still can be seen. It retarded the river and began the decline of this amazing cottonwood and willow ecological zone, which today lures in bear, deer, the building talents of beaver, and more than 140 different species of bird life. A bosque, Spanish for "woodlands," is a low-lying zone (floodplain) where woodlands and riparian areas merge. Along the 1.5-mile interpretive trail, you can easily spot dozens of birds, from mallard or blue-winged teal to heron, western bluebird, and cedar waxwing. Find out more by visiting The Nature Conservancy web site at www.nature.org and linking to the preserve.
Truchas Peak (East)
TYPE: Overnight or multiday
SEASON: Late June to October
TOTAL DISTANCE: 24.6 miles
RATING: Moderate to strenuous
ELEVATION GAIN: 4,750 feet
LOCATION: Pecos Wilderness, 14 miles north of Pecos
MAPS: USGS Cowles and Truchas Peak
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GETTING THERE
From the town of Pecos, take NM 63 north, which is also signed as Main Street. On the way out of town, you pass a sign reading TERERRO 14 MILES, COWLES 20 MILES. At 11.4 miles the road forks; the left one goes toward Holy Ghost and the right one toward Cowles. Take the right fork, which crosses the Pecos River and enters the community of Tererro. At 19.4 miles, you reach a left turn for the Panchuela Campground. (A large recreation sign also indicates the Cowles Campground to the left.) Cross the Pecos River and bear right shortly thereafter in the direction of the Panchuela Campground. You arrive at the parking lot and trailhead for this hike at 20.9 miles. There is a $5 fee per day per vehicle for a campsite.
THE TRAIL
Cloud-scraping peaks, high-elevation mountain lakes, open ridgeline traverses, creekside pathways, aspen-forested slopes, and sweeping vistas are all part of a multiday backpacking adventure at Truchas Peak (east). It strikes that sweet balance between hard work and the rewards of backcountry serenity. The massiveness of this zone of the Pecos Wilderness provides comfort and reminds us that we are part of nature's systems, not separate. Standing on top of New Mexico's second tallest mountain, Truchas Peak (13,102 feet), can make you feel both powerful and minuscule.
The more popular approach from the heart of the Pecos Wilderness up to Pecos Baldy Lake is along Jack's Trail. Starting out on Panchuela Creek and continuing with a spectacular mid-slope run along the Dockweiler Trail, however, makes the other approach just as worthy and offers more solitude. For the latter, you slip through the picnic area below the parking lot to a footbridge to access the first section of the trail. Panchuela Creek runs with a healthy volume of water through the summer, providing both melody and the nutrients for a diverse riparian ecosystem. The trail stays creekside for short pieces but mainly runs higher on the slope to the junction with the Dockweiler Trail at 0.7 mile. Doses of steeper climbing are part of the recipe for the next 2 miles before the trail eases up along a slope of ancient aspen. The first grind lasts about 0.7 mile as you switchback above the Panchuela Creek drainage and bend around to the head of the Jacks Creek drainage.
VIEWS NORTH OF TRAILRIDERS WALL
The trail moves through some aspen along a more relaxed ascent before climbing again at 1.8 miles, slipping into a predominantly fir forest. By 2.4 miles your hard work is rewarded by a beautiful aspen-dotted slope carpeted in lush grasses and wildflowers like iris and lupine. The trail moves above Jacks Creek with views to the opposite, equally aspen-rich slope and farther beyond to the green-grass corridor of Hamilton Mesa.
The junction with the Rito Perro Trail arrives within a big, open, grassy zone at about 4 miles. Popping into the trees and then out into a small meadow delivers you to the Jacks Creek Trail junction at 4.3 miles. You head left, or northeast, moving upstream for the next 0.6 mile before the trail veers away on a more northerly course. The route is set mainly in the trees with one nice meadow crossing, and you take out chunks of elevation by stair-stepping along a rocky and tree-rooted trail.
You next cross the outlet of Pecos Baldy Lake and enter an open slope shortly before reaching another trail junction at 6.3 miles. You need to head left at the junction to reach Pecos Baldy Lake. Set below the east slope of East Pecos Baldy (12,529 feet), the small, round lake is an ideal home base for a day's exploration around the northwest section of the Pecos Wilderness. There are plenty of campsites up and off the lakeshore.
Once you have settled in at a campsite, your options are plentiful. You can reach the top of East Pecos Baldy by pushing up to a small saddle above the lake and then making a corkscrew ascent to the long summit, where the 360-degree vista spins from mountaintops to deep basins to blankets of forest. Another option, and the one you set out for originally on this hike, is the amazing promenade along the west side of a grassy mesa-like formation known as the Trailriders Wall, which feeds into the glacially shaped basins below the impressive Truchas Peaks triad.
To begin the Truchas approach, move around the northeast shoreline of Pecos Baldy toward a saddle about 150 vertical feet above and to the west of the lake. A whole new world opens up as you teeter above a huge basin and begin a 3-mile highline journey with growing views of the Truchas Peaks. The slope is a marvelous grassy playground that is a thrill in sunny weather, although it can feel a bit precarious when a thunderstorm is building. The nearest trees are a few hundred vertical feet below.
By 9.8 miles (the mileage is a continuation from Pecos Baldy Lake), you reach a collection of trail junctions. The first path to the left is an unmaintained trail that works down to a creekside run along the Rio Medio. The second left-side junction trail reaches the Rio Medio too, and also accesses Jose Vigil Lake, nestled in a steep and deep basin below the south slope of Truchas Peak and the Rio Quemado Trail. The junction to the right provides access to a number of other trails, including Trail 257, which works its way back to Pecos Baldy Lake along the forested side of the Trailriders Wall.
VIEW OVER TRUCHAS LAKES FROM TRUCHAS PEAK
This zone of junctions is a prime piece of real estate situated just beyond the north end of the Trailriders Wall, which comes up short in directly connecting East Pecos Baldy to the mountain string of the Truchas Peaks. From here you have two options depending on your objective. To gain the summit of Truchas Peak (13,102 feet) continue along the trail for about 0.2 mile before moving onto the shoulder ridgeline that is the southern approach to the top. There is an unofficial but discernible trail as you make your way higher, edging slightly to the west above the Jose Vigil Lake basin. From where the trail takes off it is about 1 mile to the summit, with an elevation gain of 1,400 vertical feet.
The summit of Truchas Peak is the most impressive of the high peaks in New Mexico. Gray rocky catwalks lead toward Middle Truchas Peak (13,066 feet) and North Truchas Peak (13,024 feet), as well as broad-shouldered Chimayosos Peak (12,841). The tightrope run could feasibly continue all the way to Jicarita Peak (12,835 feet) 8 miles to the northeast. Floating in the treed basin below and to the north are the Truchas Lakes. Virtually the whole Pecos Wilderness is at your feet, as is the Rio Grande valley as it slides into the Jemez Mountains. The Wheeler Peak Wilderness is faintly visible on the horizon to the north, and to the south are numerous highpoints along the backbone of the Sangre de Cristo Mountains.
Another option is to continue on the trail for 2.3 miles (12.3 miles total), bending in and out of the mini-basins below the steep east face of Truchas Peak. You move through white boulder fields while grabbing a handful or two of currants—ripe in September—on the journey up to the Truchas Lakes. The lakes are pressed against the 1,000-foot wall wrapping around from Truchas Peak to Chimayosos Peak and beyond, and the smaller one is stacked above the larger one. Below the lakes, a vein-like network of rivulets converges 1,000 feet below into the Rito de los Chimayosos, which eventually feeds the Pecos River near Beatty's Flats. No camping is allowed in the Truchas Lakes basin.
A SEA OF ICE
New Mexico has a history—albeit one that ended some 70 million years ago—with the sea, still visible today in the numerous sedimentary rock layers and fossilized sea life visible all across northern New Mexico. It is difficult enough to imagine this region as home to sharks and clams and even great cypress forests along salty shorelines, but then try adding the fact that New Mexico was once encased in ice. The results of the melting or retreating glaciers, which occurred from 1.5 million to 15,000 years ago, are the U-shaped valleys and basins of the Pecos Wilderness, along with the sharp edges of the Truchas Peaks and the highpoints and ridgelines around Wheeler Peak.
Pecos Baldy Lake Loop
TYPE: Overnight or multiday
SEASON: Late June to October
TOTAL DISTANCE: 16 miles
RATING: Moderate to strenuous
ELEVATION GAIN: 4,100 feet
LOCATION: Pecos Wilderness, 14 miles north of Pecos
MAPS: USGS Cowles and Truchas Peak
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GETTING THERE
From the town of Pecos, take NM 63 north, also signed as Main Street. On the way out of town you pass a sign reading TERERRO 14 MILES, COWLES 20 MILES. At 11.4 miles, the road forks. The left option is for Holy Ghost and the right for Cowles. Take the right fork, which crosses the Pecos River and enters the community of Tererro. At 19.4 miles you reach the left turn for the Panchuela Campground. (A large recreation sign also indicates Cowles Campground to the left.) Cross the Pecos River and bear to the right shortly thereafter in the direction of the Panchuela Campground. You reach the parking lot and trailhead for this hike at 20.9 miles. There is a $5 fee per day per vehicle for a campsite.
THE TRAIL
The terrain around East Pecos Baldy and Pecos Baldy Lake is by far the most dramatic in the realm between the subalpine and alpine, and the vistas are as good as any you will encounter in northern New Mexico. The triad of Truchas Peaks to the northwest; the stunning promenade of the Trailriders Wall, which separates two incredible basins and connects East Pecos Baldy and the Truchas Peaks; and the treed and meadow-pocked Pecos Wilderness make this setting a backpacker's must. The approach is also enhanced by the flower-filled meadows, lush creekside flora and fauna, aspen-lit slope, and cave exploration.
From the parking lot, walk into the picnic area to reach a footbridge across Panchuela Creek. You will be creekside for a number of miles as you move along Panchuela Creek and then Cave Creek. The tree mix is fir and aspen, with an active understory of wild rose (whose fruit we know as the rosehip), blankets of green grasses, and a broad variety of wildflowers, from aster and daisy to yarrow, harebell, and paintbrush. The official entry into the Pecos Wilderness is marked with a sign around 0.4 mile.
The trail gains a bit of high ground above the creek shortly past the wilderness boundary. It moves through an open tree zone before reaching the junction with Dockweiler Trail 259 at 0.8 mile. You continue straight on what is signed as Cave Creek Trail 288. The trail slides back down along the creek at 1.1 miles, with another beautiful arrangement of wildflowers, including scarlet gilia, sunflowers, thistle, and wild strawberry. At 1.4 miles the trail slips over Panchuela Creek via a footlog and enters the Cave Creek drainage. This drainage is a little tighter in the beginning, and it's more treed but still has very pleasant shades of green in the understory and splashes of color in the wildflowers. Keep your eye out because a number of caves can be accessed along this stretch. In fact, the creek flows right through a few. The trail stays creekside for a short distance before gaining elevation moderately.
By 2.6 miles the Cave Creek drainage begins to broaden, giving the trail a more open and airy feel as it gains elevation more steeply and then transitions to a rolling stair-step ascent. There is a view back down the tree-choked drainage, where Cave Creek slips down boulders and other obstructions in small, picturesque cascades. At 3.1 miles you reach the junction with Skyline Trail 251. Stay straight, continuing on the trail to Horsethief Meadow. The trail follows a small creek for about 0.3 mile before making a short, steep push up and away, leaving behind the sounds of rushing water that have been with you for more than 3 miles.
Ancient seas and the shrinking ice sheets did their part in shaping the upper Pecos landscape around this hike. Identifiable along Cave Creek and into Horsethief Meadow are extremely ancient sedimentary rocks—some 300 million years old—as well as bluffs of granite from the Precambrian era—the oldest geologic period.
If conditions are right, there will be numerous varieties of mushrooms, including edible kinds like boletus and chanterelles, along this stretch of forest. You pass through a small meadow before beginning to lose elevation in the approach to Horsethief Meadow at 4.4 miles. Horsethief is a beautiful meadow that runs for about 0.75 mile. Tall grasses, wildflowers, and Horsethief Creek make this an excellent camping spot. Indian artifacts dating from hundreds of years ago have been found in the area. The meadow's name comes from tales of stolen horses being brought here and run out in the meadow for a time, then rebranded and moved out westward across the Sangre de Cristos. The trail, marked with a sign for Pecos Lake, makes a relaxing run across most of the meadow, the edges torched with yellow aspen in the fall.
Aspens also light up the slopes across the way, and you encounter small sections of tree shade before sliding back into a more consistent forest environment at 4.9 miles. You gain elevation until 5.7 miles, where there is a slight drop to a crossing of Panchuela Creek at 6 miles. Panchuela's headwaters are about 2 miles north of here, below the lower west slope of Pecos Baldy. The Pecos Wilderness contains somewhere in the neighborhood of 150 miles of streams and 28 lakes.
CAVE ALONG CAVE CREEK
The trail crosses the creek and continues up and down on a cross-slope run along the Rito Perro drainage. At 7.3 miles you reach the junction with Rito Perro Trail 256 in a nice open zone that provides views of Pecos Baldy (12,500 feet). Head to the left crossing through the open area and on into a creek-fed ravine at 8.2 miles. This is the steepest, most strenuous section of the hike to this point, as you gain about 1,200 vertical feet in less than 2 miles. The trail crosses into a basin of sorts below the east slopes of Pecos Baldy before reaching the junction with the trail to the summit of East Pecos Baldy at 9.1 miles. This junction is set in an open zone/saddle with a great overlook of Pecos Baldy Lake.
The summit trail is 1 mile long and gains 800 vertical feet, zigzagging up the east slope to reach the long, bench-like peak of East Pecos Baldy (12,529 feet) and vistas galore. The most prominent views are of the Trailriders Wall just below and to the north. It runs into the signature peaks of the Pecos Wilderness in Truchas Peak (13,102 feet), Middle Truchas (13,066 feet), and North Truchas (13,024 feet). To the east-southeast, the long, open, green corridor is Hamilton Mesa. To the south you will see Redondo Peak and Santa Fe Baldy. The views are indeed big, as you see across so much of the Pecos Wilderness from here—all the gentle high valleys, steep creek drainages, and deep basins.
SUMMIT VIEW FROM EAST PECOS BALDY
Bypassing the trail to the summit of East Pecos Baldy, the trail works downslope to the lake in less than 0.3 mile (9.4 miles). The lake presses up against the sheer walls of East Pecos Baldy's north face, while the opposite shoreline welcomes a seemingly boundless stretch of forest and high open valleys to the north. There is a very relaxing feeling up here, with plenty of campsites up and off the shoreline. There also are plenty of opportunities for day hikes around Trailriders Wall, a summit outing to one of the glacially shaped Truchas Peaks, or various other explorations.
Looping back, the trail drops from here along Jacks Creek Trail 257, crossing an open slope and over the outlet for Pecos Baldy Lake before slipping into a forest. It is a mix of moderate and steeper descents along a rocky and tree-rooted trail at points. You pass through a forest of fir and aspen, with a slopeside meadow coming at 10.2 miles and the junction with the Dockweiler Trail 259 (northbound) at 11.1 miles. Continue on the Jacks Creek Trail, actually along the creek itself, for another 0.6 mile to reach the Dockweiler Trail junction to the south. Pass through a small meadow, duck into the trees, and pop back out onto a big open grassy slope to reach the Rito Perro Trail junction at 12 miles.
The sensational slopeside garden of iris and lupine continues as the trail contours along the drainage and slips between majestic aspen groves. You have views across to a similar slope of open meadow and aspen, as well as slivered views of Hamilton Mesa farther to the east. By 13.6 miles, the trail drops a little more steeply and enters a fir-dominated forest. It relaxes a bit after winding downslope at around 14.2 miles and then reenters the aspen zone, but with a sparse understory. At 14.6 miles the trail takes another steeper fall via some switchbacks as you make your way back into the Panchuela Creek drainage. The junction with the Dave's Creek Trail arrives at 15.3 miles. Another 0.7 mile or so and you are back at the trailhead (16 miles total).
JACK IT IS
Most backpackers looking to access Pecos Baldy Lake leave from the Jacks Creek trailhead located at the end of FS 555. (Instead of turning left for Panchuela Campground, continue straight to reach this trailhead.) The trail follows high along the east side of the Jacks Creek drainage, passing underneath Round Mountain (10,809 feet) before reaching the Dockweiler Trail junction and continuing up to the lake along the same route as the hike described above. The round trip for this hike is 14 miles.
Apache Canyon to Glorieta Baldy
TYPE: Day hike
SEASON: June to October
TOTAL DISTANCE: 9 miles
RATING: Moderate to strenuous
ELEVATION GAIN: 2,400 feet
LOCATION: Santa Fe National Forest, 9 miles east-southeast of Santa Fe
MAPS: USGS Glorieta and McClure Reservoir
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GETTING THERE
From Paseo de Peralta in downtown Santa Fe, take Old Santa Fe Trail Road south. In approximately 0.3 mile, turn left to stay on Old Santa Fe Trail Road (continuing straight would put you on Old Pecos Trail Road). Old Santa Fe Trail Road also is known as CR 67. At 8 miles, you bear left onto Canada Village Road (Old Santa Fe Trail Road continues straight). Pass through Canada Village, where the road surface transitions from pavement to packed dirt (8.8 miles). At 10.2 miles, take the left fork onto FR 79 at the sign for the Santa Fe National Forest. The parking area for this hike is at 12.9 miles. Follow the road to the right to begin hiking.
THE TRAIL
Glorieta Baldy offers the finest overview of the Pecos Wilderness and Galisteo Basin of any highpoint in the area. Throw in an approach that moves through a portion of Apache Canyon's majestic trees and also across fantastic subalpine slopes and ridges and you have one of the most challenging and memorable outings in the Santa Fe area.
After following the road from the parking area for 0.3 mile you pass through a gate and arrive at the official trailhead. There is a trail marker for Baldy Trail 175 and a sign that shows the route to Glorieta Baldy and explains how this trail came to be. The trail was created, with support from the forest service, in memory of Otto Gruninger, who loved these mountains. The trail moves along a ridge that provides views over Santa Fe and across the Pajarito Plateau before bending downslope to meet a logging road at 0.7 mile. A small arrow indicates that the route continues to the left. Follow the bending road for another 0.7 mile to a trail junction. This area is a blend of life zones, combining high plateau plants like yucca, pinion pine, and juniper with low-level subalpine flora like Gamble oak and ponderosa pine.
A small sign indicates that the path to the right heads to Glorieta Baldy on Baldy Trail 175. The trail drops into Apache Canyon, with views of Shaggy Peak (8,847 feet) across the way and then up the canyon itself. A marvelous natural arboretum is located along the canyon floor. Apache Creek is the life force nurturing a diverse mix of old and massive fir, pine, spruce, cottonwood, juniper, and aspen—definitely a rare treat for northern New Mexico. At 1.2 miles you reach another trail junction. Head right, or upslope, on the trail signed for Glorieta Baldy. An information sign here highlights the importance and interconnected nature of the Galisteo Creek watershed.
Once out of the canyon, the trail topography alternates between short climbs and ridge runs. By 2.5 miles you are high enough to enjoy views down Apache Canyon, to Shaggy Peak now below you, and to the expanse of Galisteo Basin. The trail climbs steeply through a ponderosa pine forest before easing up as it gains the southern ridgeline leading to Glorieta Baldy at 3.4 miles. It's smooth going from here as the trail moves across the ridgetop through fir and aspen trees, only climbing a little. Your first good view of the Glorieta Baldy lookout comes at 4.3 miles.
Shortly beyond this point you pass by Trail 272, which accesses the Glorieta Conference Center (5 miles one-way). The old lookout site, built in 1940, is reached at 4.5 miles. The views from Glorieta Baldy are nice from the ground but spectacular from the lookout, with picture-perfect looks toward the Truchas Peaks to the north and Galisteo Basin to the south. Unfortunately, the lookout is currently closed due to lack of maintenance.
GALISTEO BASIN PRESERVE
Spearheaded by the Commonweal Conservancy in 2003, the Galisteo basin Preserve was born out of the desire to keep the former Thornton Ranch site from being subdivided into multiple lots for private development. The aim, after 13 years, continues to be to combine conservation, restoration, and development for 13,000 acres (9,000 acres acquired so far, with 4,000 more under contract) in the central zone of the Galisteo Basin. When the vision is fully realized, the preserve will have 50 miles of trail accessible to hikers, bikers, and equestrians; development on only 4% of the total available land; and an extensive restoration project that will invigorate 12 miles of habitat to the benefit of animal and plant species. To learn more, visit www.galisteobasinpreserve.com.
Cave Creek Trail
TYPE: Day hike
SEASON: Late April to October
TOTAL DISTANCE: 4.6 miles
RATING: Moderate
ELEVATION GAIN: 600 feet
LOCATION: Pecos Wilderness, 16 miles north of Pecos
MAP: USGS Cowles
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GETTING THERE
From Santa Fe take I-25 east for 15 miles to Exit 299, which is the turnoff for Glorieta and NM 50. Take NM 50 east for 6 miles to reach the town of Pecos. At the intersection of NM 50 and NM 63, turn left or north onto NM 63 headed toward Tererro and Cowles. The scenery that the paved road up the Pecos River takes you through is quite beautiful, so enjoy the drive. At 13 miles there is a fork in the road. Stay to the right, crossing over the bridge following the signs for Iron Gate, Cowles, and Panchuela. Just over the bridge you'll enter into the little community of Tererro. At 18.8 miles (39.8 miles total) take a left turn onto Winsor Road towards the Winsor Trailhead. A short 0.1 mile up you'll reach a right hand turn that is signed for Los Pinos Guest Ranch and Panchuela Campground. Turn right onto the paved Panchuela Road (FR 305) that leads to the parking area and campground in 1.3 miles (41.2 miles). This is a fee facility. If you decide to camp it is $5 per vehicle, per day. If you are there for just the day, the fee is $2 per vehicle.
THE TRAIL
This area of the Pecos Wilderness is spiderwebbed by a series of creek drainages, of which the Cave Creek hike takes you along two in Panchuela and Cave Creek, all of which feed the life force of the young Pecos River at its very beginning stages of a 1000 mile journey to meet up with the Rio Grande near Comstock, Texas. This hike is of water, wildflowers, deep wilderness stillness, and a rare treat in a creekside cave. Thanks to the Pecos River and the road that carries you into the heart of the Pecos Wilderness, you can have a backcountry experience with very little effort.
The headwaters of the Pecos River spring forth at 12,000 feet, picking up steam as the various creek drainages add more and more water volume. The Cave Creek hike begins along the Panchuela Creek, which confluences with the Pecos River a short distance from trailhead at 8,100 feet. From the headwaters to the town of Tererro, the Pecos is a designated Wild and Scenic River. Northern New Mexico is a harsh place climate-wise, with most of the landscape baking under the high sun and requiring the need to conserve every precious drop of water. But here, in the center of the Pecos Wilderness, so long as snowpacks return in winter and don't rush off in spring, water and wetness bring forth both wonderful riparian and forest understory life along this hike.
From the parking area there is a sign for Cave Creek Trail #288 and a trail that will lead you down into a camp area and the short footbridge over the creek. Across the creek the trail takes a decent uphill path for 0.3 mile. At 0.4 mile you are officially entering into the Pecos Wilderness.
The Pecos Wilderness was ushered in with others in the United States as the first places to receive this federally protective status in 1964. Since then the total acres have grown, bringing the Pecos to 223,667 acres, the largest wilderness area in northern New Mexico. However, don't be fooled by the ease of access and the relatively pleasant stroll-like hike of Cave Creek; the Pecos is still big backcountry territory that if you want to fully experience it will require some serious effort, whether you want to summit East Truchas Peak, visit the open expanse of Hamilton Mesa, or touch the waters of the Rio de la Casa Lakes.
The trail shadows, close by and up above at points, Panchuela Creek for most of the hike. The tree mix is ponderosa pine and fir, providing some shadow play and relief from the sun, especially in the hot summer months. Wild turkey and deer consider this area home.
At 0.9 mile you reach the trail junction with the Duckweiler Trail #259. After gaining some elevation above the creek, by the 1 mile mark or so and after a quick downhill, you are once again walking close to the creek. It's quite pleasant down in the drainage where the views aren't of mountain peaks but of the splendors around you. The trail is set inside both a riparian and the drier forest environment, which means the wildflowers you may see range from water thirsty iris to drier-climate-adapted lupine, along with other blooms like columbine, rosehip, and wild strawberry.
Settlements dot various points along the Pecos River up to the Cave Creek, including the Los Pinos Guest Ranch you will pass on the way to the trailhead. The most famous settlement, though, is that of the Pecos Pueblo found a few miles south of the current day town of Pecos. Built in A.D. 1300, the pueblo was the easternmost outpost of the Puebloan people and was known as Cicuique. Over the years, under the Puebloan people and others, the Pecos Pueblo has been a small city (up to 2,000 people), fortress, Spanish mission, stagecoach stop, and now a national park.
At the junction with the Duckweiler Trail #259 you'll want to continue to your left, staying on Cave Creek Trail #288. At 1.8 miles there will be a footlog crossing of Panchuela Creek. Once across, the trail now is working its way along and up the Cave Creek drainage. From here it's 0.5 mile to reach the caves. Between 0.3 and 0.4 mile you'll pass by a sign stating no camping or campfires near the creek or trail. From here it's between 0.1 and 0.2 mile to reach a small clearing—your visual indicator that you are near the caves (2.3 miles total). Move off trail through that clearing toward the creek to come into full view of the caves.
These are limestone caves where a part of the creek flow diverts into them for further sculpting. You can definitely explore the entry of the caves, and depending on the water level and your nerves you can go a bit deeper with the exploring as well. Make sure to bring a headlamp or flashlight.
Other significant rock formations in this area include red shale, sandstone, quartzite, and granite. The backbone of the Pecos Wilderness are the 12,000-plus foot peaks just a few miles north of here made of granitic rock, thrust upward some 70 million years ago. As the waters of Cave Creek play at the limestone of the caves so too did the receding glaciers in bringing shape to East Pecos Baldy and the Truchas Peaks. The Cave Creek Trail continues past the caves for another 2.3 miles to reach Skyline Trail #251, which provides access to the high peaks of the Pecos.
MEADOW IN THE PECOS RIVER VALLEY
GLORIETA BATTLEFIELD
Numerous conflicts have taken place over the centuries in the vicinity of Glorieta, but the one best remembered today occurred at the Glorieta Battlefield. At the end of March 1862, a multiday Civil War battle commenced when regulars from Fort Union and a group of Colorado volunteers tried to halt the advance of Texas Confederates led by Brigadier General Henry H. Sibley. The Confederates had already taken Albuquerque and Santa Fe and were bound for the gold fields of Colorado, hoping to eventually control the whole Southwest all the way to the Pacific Ocean. Sibley's army was far superior in battle and had victory well in sight, but he signed a truce after only a few days of fighting upon learning that his ill-protected supply train had been completely destroyed by Union soldiers.
Pecos Ruins
TYPE: Day hike
SEASON: Year-round
TOTAL DISTANCE: 1 mile
RATING: Easy
ELEVATION GAIN: 35 feet
LOCATION: Pecos National Historic Park, 10 miles southeast of Santa Fe
MAPS: USGS Pecos
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GETTING THERE
From Santa Fe travel 16 miles southeast on I-25 to Exit 299, which is the first exit for Pecos and the access for Glorieta. Cross back over the interstate and look for signs directing you to the Pecos National Historic Park on the right. Approximately 6 miles down NM 50, turn right at a stop sign in the town of Pecos. There are signs again for the monument. After another 1.7 miles, you will see a sign on the right for the visitor center and park entrance. The parking area and visitor center are reached in 0.2 mile (23.9 miles total).
THE TRAIL
There was a time, not so long ago, that the Pecos people thrived in this area thanks to a well-established agricultural system and the trade that took place between area Pueblo farmers and Plains tribes. They exchanged items like pottery and textiles for buffalo hides and shells. This was also a place of bloodshed between Indian peoples, and later the Spanish. Going back even further, this area has been inhabited by humans for nearly 10,000 years, and small communities still exist here today. The Pecos Ruins embody what archeologists term the Rio Grande Classic Period (A.D. 1325–1600) and later the Spanish (A.D. 1540–1840).
The visitor center is well worth your time, as Pecos can be appreciated far more with a degree of historical context. The Pecos Pueblo and its incarnations under Spanish control, as well as that of the Union Army, have been of great significance to many cultures over different periods here. Physically the pueblo lies in the Pecos River valley, guarded to the south by the Glorieta Mesa and to the north by the Pecos Wilderness, which flows like green lava from the Sangre de Cristo high peaks, painted with winter snows well into June.
Water was much more readily available in the days of the active pueblo, originating from the high mountain snowpacks and running by the small rise, or mesa, upon which the bulk of the accessible ruins are built. To add to their water supply, the native people built check dams to catch rain runoff and irrigate their fields of beans, corn, and squash. Geologically speaking, the southern terminus of the Sangre de Cristos, the long wall of Glorieta Mesa, and the Tocolote Range meet to create a small gap at Glorieta Pass to the west. The Glorieta-Pecos Corridor runs east and then south, cut through an ancient seabed by the Pecos River over millions of years.
An easy-going gravel path loops by a number of pueblo and Spanish ruins. An interpretive guide, available at the visitor center, helps provide context. The loop first takes you by an open field that once held crops. It also was a campground for the buffalo hide tipis of trading Plains people. You will have two perspectives on the mission, built in 1717, the first coming from below. The structure is a combination of original and restored adobe bricks. "Original" is only true to a point, though, because what stands here is a much smaller and newer version of a church built in the 1620s. The first church was destroyed by the Pecos people in the Pueblo Revolt of 1680, which took place in many locations across northern New Mexico.
The loop continues past an accessible kiva, the south and north Pueblo ruins, and the ruins around the church. The North Pueblo ruins were, in their time, an incredibly well-conceived, well-built structure that reached heights of five stories and contained some 600 rooms connected by porches on the upper levels. It had a fortress-like feel due to its defensive design and its location on the highpoint of the area. Construction began in the 1400s and the structure was occupied for 200 years.
The area where the decaying church stands is called the Mission Complex. The first church was much bigger than the one standing here today. It stretched some 150 feet in length and its series of exterior buttresses and six bell towers were said to have included 300,000 adobe bricks weighing 40 pounds each. The other buildings and structures you see served as living quarters, classrooms, kitchen, dining room, and stables. There also was a garden. The kiva in the middle of the ruins was built during the Pueblo Revolt as an act of defiance. When the second church was built, this kiva was buried.
The Pecos National Historic Park occupies three separate sections in the surrounding area. Public access is not allowed in areas beyond the Pueblo and mission ruins, both because excavation of other ruins continues and to respect the sacred land of the Pecos people. (This also includes the Glorieta Battlefield, which is accessible by guided tour only.) The Pecos Ruins are set in a high plateau zone of tall grasses, juniper, cactus, rain-coaxed wildflowers, and rattlesnakes, and there is a healthy community of local and migratory bird species.
REST STOP, THEME PARK, AND TRAILSIDE DINER
During the 60-some years when the Santa Fe Trail experienced heavy use for commerce and migration, the Pecos Pueblo was used as a campsite, a place to replenish resources, and as an amusement park. Tales even were spun early on that the Aztec emperor Montezuma had resided here, which, of course, would have upped the ticket price if someone had been charging for a walk through the ruins. The Pecos people abandoned the pueblo by the late 1830s, so there was no one left to explain its history from the standpoint of both the Indians and the Spanish. Wood beams from the mission were pilfered in the 1850s to build houses and other outbuildings on the Kozlowski Ranch, now part of the park. It was a desired meal stop for passing stagecoaches.
THE PECOS RUINS
Hamilton Mesa
TYPE: Day hike
SEASON: Late June to October
TOTAL DISTANCE: 10.1 miles
RATING: Moderate
ELEVATION GAIN: 850 feet
LOCATION: Pecos Wilderness, 19 miles north of Pecos
MAPS: USGS Elk Mountain and Pecos Falls
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GETTING THERE
From Pecos, take NM 63 north. At 11.4 miles, the road forks. The left option is for Holy Ghost and the right for Cowles. Take the right fork, which crosses the Pecos River and enters the community of Tererro. You reach the right turn for FS 223 at 18 miles. This is the road for the Iron Gate Campground, and it's rough and rutted. A high-clearance, four-wheel-drive vehicle is recommended. You arrive at the parking area and small campground at 22 miles. There is a $5 fee per day per vehicle for a campsite.
THE TRAIL
Hamilton Mesa is an anomaly in a wilderness already filled with spectacularly unique geographic features. This Pecos Wilderness darling defies the encroachment of trees, maintaining its open, long grassy swath. It is a magnificent parkland for idle strolling on a grand scale, with wildflowers decorating the ground and regal mountains silhouetted against the big northern New Mexico sky. The Hamilton Mesa Trail stretches beyond the signature portion of the mesa an additional 4 miles to provide access to deeper backcountry locations like Pecos Falls or the rarely visited collection of high lakes in Santiago, Pacheco, and Enchanted.
From the campground, the trail moves through a wide-spaced forest zone and winds its way to the junction with Trail 240 at 0.3 mile. You continue north, heading left on the Hamilton Mesa Trail. The openness continues in the form of a long overlook across the Rio Mora valley. The next junction comes with Rociada Trail 250 at 0.8 mile. The Rociada descends Hamilton Mesa's east slope to reach Mora Flats.
GRASSY TOP OF HAMILTON MESA
Compared to the rewards, the work ahead is really nothing, however, there is some elevation to be gained. The trail climbs moderately across rocks and tree roots to a stock gate at 1.5 miles. Through the gate a slightly more rigorous ascent awaits, but so too do higher views across the Rio Mora valley. You'll have a front row seat for the mountainous backbone of the Pecos, anchored by Tesuque Peak (12,043 feet) in the south and capped by Jicarita Peak (12,835 feet) to the north. The anticipation builds as the trail flattens out and edges along a thick grove of aspen and the peaks are unveiled one at a time, starting with summit views of Santa Fe Baldy (12,622 feet) and more full views of Redondo Peak (12,357 feet) and eventually Pecos Baldy (12,500 feet), East Pecos Baldy (12,529 feet), and the 13,000-foot triplets in Truchas, Middle Truchas, and North Truchas.
The stroll through here is magnificent as all these peaks—including Chimayosos Peak (12,841 feet), the nearby and impressive neighbor to North Truchas—stay in sight for nearly 2 miles. In addition, colorful wildflowers like iris, paintbrush, cinquefoil, and bluebells do their best to steal your attention throughout the summer. By 3.5 miles, after a few very brief sections of trees, you reach the Larkspur Trail 260 junction. This trail descends into the Pecos River valley and accesses Beatty's Flats. In 1990 the Pecos River, from its headwaters in an unnamed basin south of Rincon Bonito to the town of Tererro, was protected as a Wild and Scenic River. To qualify, rivers must be free of man-made obstructions and have an untouched ecosystem along their banks.
The geographical treats and amazing flora continue for another 1.2 miles (4.7 miles total) before the Hamilton Mesa Trail enters a forested environment. For day-trippers this signals the end of the journey, but for those seeking deeper backcountry it is 3.2 miles to the trail junction for Pecos Falls and an additional 1.2 miles to the Gascon Trail, which connects with the Skyline Trail to access Santiago Lake and the cross-country-only treks to Pacheco and Enchanted Lakes.
"PLACE WHERE THERE IS WATER"
The Keresan Indian translation for the Spanish word pecos is "place where there is water." We see the word repeatedly in this region—Pecos Pueblo, Pecos River, Pecos Wilderness. The Pecos Wilderness was part of the first wave of wilderness designations in 1964. Today New Mexico is home to 25 designated wilderness areas, totaling 1.6 million acres. As the second largest wilderness area at 223,667 acres, the Pecos is the heart of backcountry adventures in northern New Mexico. It contains 445 miles of trails that lead to amazing settings like Hamilton Mesa, Santa Fe Baldy, Truchas Lakes, Trampas Lakes, Rincon Bonito, Pecos Falls, and Hermit Peak. The easy-traveling roads to the trailheads also make this area popular. And in a region that is poor in water, the Pecos has more than 100 miles of creeks and rivers, along with 28 lakes.
Mora Flats to Hamilton Mesa Loop
TYPE: Day hike
SEASON: Late June to October
TOTAL DISTANCE: 10.1 miles
RATING: Moderate
ELEVATION GAIN: 1,200 feet
LOCATION: Pecos Wilderness, 19 miles north of Pecos
MAPS: USGS Cowles, Elk Mountain, and Pecos Falls
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GETTING THERE
From Pecos, take NM 63 north. At 11.4 miles, the road forks. The left option is for Holy Ghost and the right for Cowles. Take the right fork, which crosses the Pecos River and enters the community of Tererro. You reach the right turn for FS 223 at 18 miles. This is the road for the Iron Gate Campground, and it's rough and rutted; a high-clearance, four-wheel-drive vehicle is recommended. The parking area and small campground are at 22 miles. There is a $5 fee per day per vehicle for a campsite.
THE TRAIL
This hike is a beautiful mix of wide-spaced forest settings, grassy meadows, and creek corridors, capped off by the spectacular open run of Hamilton Mesa—a natural runway to the most dramatic peaks of the Pecos Wilderness. In the height of the wildflower season, especially when the early summer explosion of iris occurs, it will be a struggle to decide whether to scan the natural beauty of the flora or revel in the geological artwork above and beyond the Pecos River valley.
From the parking area, the trail winds through the trees to a junction with Trail 240 at 0.3 mile. Head left, continuing on Hamilton Mesa Trail 249, and begin a canyon-rim stroll above the Rio Mora valley to the junction with Rociada Trail 250.
Follow this trail as it takes its time losing elevation to eventually reach the Rio Mora valley and Mora Flats. In the process you are treated to slopes covered in grass and wildflowers in summer, and displaying the yellow shimmer of aspen in the fall. Other plant and tree species include wild rose, ground juniper, oak and fir trees, and a small collection of stately ponderosa pines.
COLUMBINE IN BLOOM
The dead stand of trees across the valley and up the Rito los Esteros drainage is the result of a past wildfire. By 2.4 miles (1.6 miles down the Rociada Trail) you reach an overlook of Mora Flats and the Mora Canyon. Mora Flats stretches for approximately 1.5 miles, etched by the Rio Mora and decorated with clumps of grasses and wildflowers. Mora Flats is a boggy zone, but if you followed the creek downstream, you would eventually enter a deep, narrow gorge.
From here the trail quickly loses elevation on the way to the junction with Los Trampas Trail 240 and the entryway into Mora Flats (2.7 miles). You have to ford the river to reach Mora Flats. Stay straight to continue the loop, passing by a number of campsites on what can be a boggy section of trail. You remain in an open corridor up to the junction with Valdez Trail 224 (3.2 miles) and for a short while longer as you work your way up the Rio Valdez valley.
The Valdez Trail slips into greater tree cover and edges along the Rio Valdez on a more rugged trail for 1.2 miles. There are a number of creek crossings as the drainage constricts, the first at 3.6 miles with three others following shortly. Take your socks off through here or wear some water sandals. At 4.5 miles you reach the junction with Bob Grounds Trail 270. Follow this trail on an immediate zigzag course upslope through a brief barrier of trees to a clearing. Around 0.2 mile up (4.7 miles total), the trail splits. Stay left, continuing up along a tree line until the trail cuts hard to the left, the direction you just came from while working up the Rio Valdez drainage.
Because of the lack of foot traffic and trail markers and the well-defined and distracting cow paths, it is easy to get off course through here. The trail follows the tree line but stays out in the open for less than 0.2 mile before making a switchback upslope. If you lose the trail look for the prominent ravine, which should contain running water, even late into summer. On the top of this ravine you will spot a cattle trough and the trail heading to the top of Hamilton Mesa, with its amazing views of the string of high summits to the west and north. The unmarked junction with the Hamilton Mesa Trail comes at 5.4 miles. This point is recognizable by the nearby stand of trees along the trail heading north. However, you need to take the trail to the left, or south.
The silent giants that follow you for a number of miles are the three 13,000-foot Truchas Peaks, East Pecos Baldy (12,529 feet), Pecos Baldy (12,500 feet), and Redondo Peak (12,357 feet). Hamilton Mesa is a marvelous treat, offering open views in all directions and a long canvas of wildflowers in the summer months. You pass the Larkspur Trail 260 junction at 6.6 miles. The walking so far has been easy, with relatively flat terrain that even descends slightly at times. Past the junction, the trail crosses through a stand of trees and then pops back out into the open, continuing its very pleasant journey. By 7.8 miles the open feeling is still there, but views back up toward highpoints like the Truchas Peaks are obstructed by a stand of aspen.
There are views to the east over the Rio Mora valley and to other highpoints and valleys to the south. You pass through a stock gate at about 8.6 miles and make a steeper and rougher descent to the junction with Trail 250 (9.3 miles). From here you rejoin the same stretch you came in on to reach the trailhead at 10.1 miles.
FALLS FLAT
Hamilton Mesa is one of a few trails that will lead you to Beatty's Flats and Pecos Falls. Located 6 miles from Iron Gate, Beatty's Flats is a flower-painted meadow along the Pecos River that acts as the Grand Central Station for trails coming to and from numerous areas of the wilderness. Pecos Falls, 9.5 miles in, is a 50-foot waterfall located in one of the most remote and least visited zones. It is possible to follow a loop off Hamilton Mesa and down into the wild and scenic Pecos River valley to reach both of these natural beauties. Refer to the Pecos Falls USGS map.
Hermit Peak
TYPE: Day hike
SEASON: June to November
TOTAL DISTANCE: 9.2 miles
RATING: Moderate
ELEVATION GAIN: 2,700 feet
LOCATION: Pecos Wilderness, 18 miles west-northwest of Las Vegas
MAPS: USGS El Porvenir
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GETTING THERE
From Las Vegas, take Grand Avenue north, which is also NM 65. At 0.8 mile, you reach a controlled intersection with Railroad Road; turn left toward United World College, which is signed. At 1.1 miles, you reach another stoplight. Turn right onto Hot Springs Road, the continuation of NM 65. Shortly past the turn, you will see a sign for El Porvenir. Use this as a landmark to make sure you're on the right path, as the trailhead for Hermit Peak is in the same direction. At 12.1 miles, after winding through the river canyon and entering a valley of horse pasture and farmland, you pass through the town of Gallinas. Straight ahead is Hermit Peak, the rounded massif whose middle section stretches to more of a point. At 12.5 miles, the road forks. Bear right onto FS 261, which leads to El Porvenir Campground. Another 2.7 miles down (15.2 miles total), you reach a small parking area and the trailhead for Hermit Peak Trail 223.
THE TRAIL
Written about in an essay by Rick Bass and taken as the title of a novel by Michael McGarrity, Hermit Peak comes by its name thanks to an Italian recluse by the name of John Augustiani who lived on the mountain to stay out of the public eye. Today people visit this high, flat perch to take in the sharp contrast between the terminus of the Rocky Mountains protruding from the north and the beginnings of the Great Plains spreading to the eastern horizon.
The hike begins in a ponderosa pine and fir forest along Porvenir Creek. You cross over a road around 0.2 mile in and follow the sign for Hermit Peak Trail 223. The pathway is a bit uneven and rocky and gains elevation moderately. In spring and early summer you will find paintbrush, sunflowers, daisies, and buttercups. Much of the rest of the relatively sparse understory consists of shrubs like Gamble oak. The trail parallels a creek drainage for a half mile. At about 0.6 mile you cross the creek; stay to the left, continuing along the drainage. The short shrubs with red berries and spoon-shaped leaves are kinnikinnick. Native peoples used kinnikinnick leaves as a diuretic for urinary tract problems and made a form of tobacco that incorporated the dried leaves.
At 0.8 mile the trail arrives at another road. Head left about 40 yards to a sign for Hermit Peak and the continuation of the trail. As encouragement, there are filtered views of a portion of Hermit Peak—a granite batholith that originally pushed forth some 1.4 billion years ago.
After hiking some 2 miles and gaining about 1,000 feet of elevation through a sun-filled forest, you officially enter the 222,673-acre Pecos Wilderness. Tucked in the southeast corner, the hike to Hermit Peak (10,212 feet) is one of dozens available across New Mexico's second largest wilderness area. By 2.2 miles the trail begins to steepen as you approach what looks like an impassible gap. It soon becomes apparent, however, that you can indeed pass through the gap's two rock outcroppings via a couple of switchbacks. This gap will lead you to a plateau or benched section of the mountain for the final easy walk to the broad point of Hermit Peak's summit. Aspen and a few other deciduous trees and shrubs join the forest mix as you slowly gain on the plateau, passing by a small boulder field at the bottom of a sheer cliff at the 3-mile mark.
At 3.9 miles you reach the plateau. From here you can look across the south-central region of the Pecos Wilderness to the west or view the beginnings of the southwest edge of the Great Plains, stippled with mesas and extinct volcanoes, along the horizon to the east. A short distance down the trail you reach a junction. A covered spring is set in a small clearing here. Heading straight, the trail makes a slow arc to gain the summit. The more road-like path to the right climbs a bit more steeply but directly to reach the opposite end of the broad summit. It is along the summit that you will discover the Hermits' Cave. This is where Augustiani is reported to have lived during his time here.
Continuing straight away, you pass through a grove of aspen as the trail slowly bends along the western side of Hermit Peak. There are more views across the Pecos and a view over man-made Storrie Lake. You also come across another trail junction at 4.5 miles. The trail that makes a sharp downslope turn to the left leads to Lone Pine Mesa 5 miles away.
The summit (4.6 miles) is a great place to camp. There is a fantastic plateau environment up here with slightly higher views toward the Great Plains, and to the north you can see the southern flow of the Sangre de Cristo Mountains coming out of Colorado.
MONTEZUMA'S REVENGE
Rejuvenate sore muscles by soaking in the hot spring across from the United World College just outside Las Vegas along the road to the Hermit Peak trailhead. It occupies the grounds and castle-like structure of the old Montezuma Hotel. Just off the roadway and punched into what feels like a city sidewalk, pools of marvelously silky, mineral-rich springwater attract locals and tourists alike. The water temperature is ideal for a visit in late fall, winter, and early spring. By the time summer arrives, though, the pools are often unbearably hot.
ON THE TRAIL TO HERMIT PEAK
San Pedro Parks Loop
TYPE: Overnight or multiday
SEASON: June to October
TOTAL DISTANCE: 17.7 miles
RATING: Moderate
ELEVATION GAIN: 1,000 feet
LOCATION: San Pedro Parks Wilderness, 8 miles northeast of Cuba
MAPS: USGS Nacimiento
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GETTING THERE
From Cuba, take NM 126 east, which is signed for the San Pedro Parks Wilderness. At 10.2 miles, turn left at a sign for San Pedro Parks Wilderness and San Gregorio Lake. The road surface changes from pavement to packed dirt. At 12.5 miles, make sure to stay straight, continuing along FS 70 instead of turning left. You reach the trailhead and parking area at 12.8 miles.
THE TRAIL
The San Pedro is known for its natural park zones, lush boggy corridors of grassy meadow cut by slow-moving creeks dotted with whitish granite boulders. Wildflowers splash color on the green canvas in the summer months. Elk abound here, enjoying the bountiful food and ease of movement across this 41,132-acre wilderness. Hiking trails branch out in every direction, shadowing the numerous creeks—20 in all—that etch the parklands. What isn't readily apparent, though, is that this is actually a mountain range. The San Pedro Mountains sit like a flat block above the greater arroyo-fed Rio Puerco valley to the southwest, and they are a continuation of the Sierra Nacimiento uplift to the south and neighbor to the Jemez Mountains. You are in essence working across mountaintops, but without the effort normally required to do so.
This hike is a garden stroll, beginning as a wide, smooth, crushed-rock path through an open forest of fir and aspen with wildflowers like lupine, aster, daisy, and a large patch of false hellebore. During the moist times of spring and after summer rains, you will also spot a great variety of mushrooms. Granite boulders—compliments of the uplift of Precambrian granite hundreds of millions of years ago—are positioned in the forest as if hand placed by landscape artists. Popping up here and there are wild raspberry bushes, with berries ripening around the middle to end of August.
PARKLAND ON THE WAY TO SAN PEDRO PARKS
By 0.75 mile you reach man-made San Gregorio Reservoir, set in an open grassy zone colored here and there by the yellow of sneeze weed and the bluish-purple of harebell. Follow the trail to the right, edging around the upper east shoreline. You reenter the forest past the lake and continue the easy-going path you've been on since the trailhead, crossing over sections of elevated walkway where the ground is boggy.
At 1.7 miles you reach a creek crossing beyond a pleasant zone of wildflowers and aspen groves, the trail alternating between a wider path and a narrow hiker's trail. This is the junction for the Vacas Trail to San Pedro Park, which heads left. The trail makes a beautiful run along Clear Creek for 1.3 miles (3 miles total). You will see a path cutting back hard to the left and crossing the creek. Do not take this trail; instead, continue straight just a bit farther along Clear Creek.
About 0.2 mile up you enter the first of many parkland environments on this hike. The trail edges along a grassy, rocky mound, and slightly downslope a feeder creek knifes through the wildflower-lined corridor. By 3.7 miles you reenter the trees and gain a little elevation before starting a flat run that alternates between a corridor of fir trees and open grassy zones choked with false hellebore. You end up stepping across another boggy open parkland at 4.8 miles.
The alternating trees and parkland continue, along with a crossing of the Rio de las Vacas. A trail junction (5.2 miles) lies just a few strides past the other side of the creek. Head left on the Vacas Trail toward San Pedro Parks. In a little over 0.3 mile you reach yet another junction. Continue to the right, still on the Vacas Trail.
This marks the beginning of a beautiful grassy corridor run along the lazy and slightly curvy Rio de las Vacas. The creeks throughout San Pedro are home to native trout. The boggy and wildflower-flecked pocket parklands up to this point already have revealed the uniqueness of the wilderness, but the next phase of the hike definitely places San Pedro in a category all its own. All of these corridors, parklands, and vegas (Spanish for "meadows") remain treeless due in part to grazing animals—cattle grazing is still allowed throughout wilderness areas in New Mexico—but primarily because the overly moist ground is not conducive for tree growth.
After nearly a 2-mile run (7.2 miles total) along the Vacas Trail you reach a junction where the Penas Negras Trail goes right and the San Jose Trail to San Pedro Parks goes left. Heading straight will move you into the trees toward an old cabin site. It is approximately 0.7 mile to the cabin, and continuing on this unmaintained trail you can reconnect to the San Jose Trail at San Pedro Parks. Shortly before reaching the 0.7-mile mark, at a point where the trail makes a hard bend to the left away from the creek, there is a hunter's camp down along the creek bank that would make a good overnight spot.
To continue on the hike, take the San Jose Trail through another corridor environment to the wide-open zone a number of square miles in size that is San Pedro Parks (7.8 miles). This whole hike is prime elk country. Also, throughout the boggy zones, including in San Pedro Parks, you may notice a beautiful bluish-purple flower with a single bloom perched on a stem growing in patches among the grasses—this is fringed gentian. The Rio Puerco is nearby for a water source and there are campsites in the trees.
A couple of round posts mark the way across the boggy section beyond the park. It is difficult, as with other boggy sections along this hike, not to get your shoes wet. By 8 miles you reach the junction with the Los Pinos Trail, which follows the Rio Puerco down a gorgeous tight valley much different from the flat, broad corridor of the Rio de las Vacas. There is a great mix of more heavily treed, steeper-sided slopes with wildflowers, boulders, and broad gentle areas of boggy grasses. It is easy going because of the slight loss of elevation along the way. You have plenty of options for pitching a tent through here. By 9.5 miles, you cross over a creek and are on the edge of another open grassy expanse. But the trail stays in the trees to arrive at the junction with the Anastacio Trail at 9.8 miles. Head left (east) here.
You pass through another boggy section along here. Roughly a half mile along (10.3 miles total) you pass into a narrow corridor. Trails run along the left and right sides, but you should stay to the right, following the round posts. By 11 miles you reach a point where the corridor forks, with options to the right and straight ahead. Two or three round posts mark this spot and forest service blazes—a small round mark where the bark has been removed above a longer mark—on the trees indicate that you should head to the right. You will also notice the wide pathway leading into the trees.
By 12.2 miles you reach the junction with the Vacas Trail. Head to the right and retrace the 5.5 miles back to the trailhead (17.7 miles total). This hike is surely to become a favorite, whether you visit in the spring, summer, or fall.
COYOTES, BEARS, AND COWS, OH MY!
A less traveled portion of San Pedro Parks is reached off NM 96 near the town of Coyote. Take FS 103 and FS 93 to the Resumidero Campground. From the campground, you can make a loop of 12 miles or so through parklands like Vega Redondo (Round Meadow) and near Vega del Oso (Bear Meadow) on the way to San Pedro Parks. This hike utilizes a combination of different trails—including the Vaca Trail (vaca means "cow" in Spanish)—some of which fade out in the meadow areas, so a compass and topographic map are a must. The topographic map you would need is Arroyo Delagua.
Ojitos Trail
TYPE: Day hike or overnight
SEASON: June to October
TOTAL DISTANCE: 10.6 miles
RATING: Moderate
ELEVATION GAIN: 1,000 feet
LOCATION: Chama River Wilderness, 23 miles northwest of Abiquiu
MAPS: USGS Navajo Peak and Laguna Peak
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GETTING THERE
From Abiquiu, take US 84 north toward Chama. You pass by the turn for Ghost Ranch and the visitor center before reaching the signed left turn for FS 151 at 14 miles. Take this dirt road for 9.4 miles, passing by the Big Eddy boat ramp, to reach a steel bridge that spans the Chama River. There is a turnout for parking at 23.4 miles.
THE TRAIL
Known by boaters for its wild and scenic stretch of whitewater from below the El Vado Reservoir to Big Eddy, the Chama River Wilderness is much more than a strikingly beautiful canyon to view from a raft or kayak. Tall red, yellow, and brown mesas frosted by the green of ponderosa pines are separated by canyon bottoms that punch in at various points along the 18-mile river wilderness. Yucca and juniper and the delicate blooms of globemallow and tiny white daisies decorate the landscape. There is only one trail in the 50,300-acre wilderness area, which leaves an awful lot to be discovered by cross-country travel. The trail described here is a worthy experience by itself or as a springboard into the vast open country of the wilderness.
From the turnout along the road, cross over the bridge that spans the Chama River. You are in a beautiful, broad sagebrush valley edged by colored rock walls and jutting mesas that resemble fantastical birthday cakes. Approximately 0.2 mile along the road over the bridge you reach a ROAD CLOSED sign and a trail marker that points you straight ahead. At 0.5 mile you pass through a fence opening and by the official sign for the Chama River Wilderness. The trail continues to edge along the pastureland in the direction of a side canyon. The trail markers are round posts with pointed tops.
Chama ("red" from the mispronounced Tewa word tzama) surely is the correct name for the boldly colored rock and energetic river that define much of the physical aspect of this place. Another dimension here is the stillness, whether you hike the Ojitos Trail on an early morning in summer or strike out on a crisp autumn weekend. By 1 mile you reach a vague crossroads. The trail heads to the left along a smaller valley floor, through a thick community of sage. A fireworks explosion of small-headed wildflowers appears here after rainy periods. The trail then crosses into pinion pines, a nice treat as this species has suffered greatly throughout New Mexico during the many years of drought.
MULTICOLORED ROCK FORMATIONS IN THE CHAMA RIVER BASIN
Through a gap of sorts at 1.5 miles, the trail slings over and into a broader valley/canyon. It is a marvelous area of contrasts: red sandstone, forest-green pinion and juniper, olive-green sage, a rainbow of wildflowers, blue skies often stamped by puffy clouds, and white rocks (gypsum) strewn about like pottery shards. A gate crossing comes at 2 miles, and shortly beyond here you transition into a creekside combination zone of yucca and juniper with Gamble oak and the shade relief of ponderosa pine. The trail crosses from one side of the canyon to the other a number of times during a 2-mile stretch as you continue along a floor bookended by mesas colored in rose, tan, white, and taupe, their tops decorated with juniper and pinion. The life force of the creek also attracts a healthy bird population.
By the 4-mile mark, the trail bends upslope, regaining the canyon floor through a thicker zone of ponderosa pine. You pass by a decent campsite that's not too far from the creek. It is a good option for an overnight, because higher up you will need to pack water. You have growing views of the opposite canyon edge, as well as views across the west-northwest zones of the wilderness. By 5.3 miles you reach a benched zone beneath the short-walled Mesa del Camino. This is a good turnaround point for a day hike or a jump-off point into a cross-country exploration of the wilderness.
CHRIST LIVING OFF THE GRID
At the end of FS 151 you will find the Christ in the Desert Monastery. The sun, captured by solar panels, provides all its electrical needs. There are guest houses for those looking for spiritual retreats and a small church whose tall windows provide a stunning view of the red-rock cliff face. Just before reaching the grounds it is possible to take a short hike into Chavez Canyon. An unimproved trail leads into a slickrock slot canyon, offering a spectacular but easy Utah Canyonlands–type experience. You can find more information at www.christdesert.org.
McCauley Warm Springs to Jemez Falls
TYPE: Day hike
SEASON: April to November
TOTAL DISTANCE: 6.8 miles
RATING: Easy to moderate
ELEVATION GAIN: 1,100 feet
LOCATION: Jemez Mountains, 18 miles west of Los Alamos
MAPS: USGS Jemez Springs and Redondo Peak
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GETTING THERE
From Los Alamos, take NM 501 south for 4.5 miles to the junction with NM 4. Turn right onto NM 4, signed for the town of Jemez Springs. At 23.5 miles, you reach the junction with NM 126. Continue on NM 4 toward Jemez Springs. At 26.5 miles, turn into a large turnout/parking lot near a prominent rock outcropping known as Battleship Rock. There is an official campground and picnic area entrance a short distance down the road, but for a day hike this first lot is where you should park.
THE TRAIL
This outing to McCauley Warm Springs and on to Jemez Falls is a tale of fire and water. The fire originally came in the form of a number of eruptions that took place as recent as 1.1 million years ago, filling the entire Jemez Canyon with volcanic material. Today the fire continues in the geothermal heat that warms the water of McCauley Springs and a number of other springs in the area. A rapid release of water occurred when the natural dam of the Valle Caldera was breached by the push of the San Antonio and East Fork Jemez Rivers surfacing from artesian wells. This water cut the canyon and sculpted the tent rocks you see along the hike, as well as the dazzling water feature of Jemez Falls.
From the parking area you head downhill and through the picnic area to a bridge over the Jemez River. Trail 137 begins beyond a picnic shelter, edging against Battleship Rock and along the lush East Fork Jemez River. It is fairly easy to see how Battleship Rock came by its name. The sharp-edged prow appears to slice through the trees, as if an entire ship will be cast afloat for a canyon run on the Jemez River. The shape was created by a series of volcanic eruptions that deposited layer upon layer of volcanic ash, which under intensely high heat actually became welded together. This impressive rock formation stands more than 200 feet high.
The habitat is lush with locust, oak, wildflowers, and many other plant and shrub varieties feeding from and contributing back to the riparian life zone. Sandstone is the most prevalent rock, having been laid down nearly 300 million years ago when this area, and much of New Mexico, was sea bottom. There are also beautiful, oily black volcanic rocks called obsidian, monuments to the series of eruptions that created the Jemez River canyon and continue to feed the geothermal heat for at least 15 different hot and warm springs in the area.
Popularity has its price, and unfortunately human visitors wanting to blaze their own paths have created unnecessary trail options around the 0.2-mile mark. Follow the trail heading upslope and to the left. You climb for a short distance, gaining elevation over the river yet still within earshot of it. You also end up above Battleship Rock, which is framed nicely against the western wall of the Jemez River canyon.
Gaining elevation also means entering a different life zone, one more arid and dominated by ponderosa pine, yet decorated with asters and scarlet gilia. By 0.9 mile the trail levels off. It feels like you are walking along a canyon rim, but without any danger, as you move along the northern side of the East Fork Jemez River canyon. A wonderful attribute of this hike to McCauley Warm Springs and then on to Jemez Falls is that in a relatively short distance, with minimal energy output, you can experience a deep backcountry feeling. However, you will have to time your outing for early morning and avoid weekends and holidays to reap this reward.
BATTLESHIP ROCK
You arrive at McCauley Warm Springs at 1.5 miles. The water is naturally heated, but the pools are man-made. And the setting is quite nice, with the upper, larger, and more exposed pool feeding the smaller, more shaded pool. Remember, these are considered warm springs so their temperatures range between 85 and 95 degrees. The temperature range in hot springs normally runs from 100 to 115 degrees. Soak your feet or submerse yourself fully for some rejuvenation before the short push on to Jemez Falls.
The springs also provide an oasis for a number of plants and creatures in this particular life zone. Wild roses grow downstream from the bottom pool, creating sustenance for bees during blooming season and food for a variety of bird species in the form of rosehips. And the moss that covers many of the rocks along the warm-water stream is part of the diet for deer in the winter months. It is quite serene to watch the water bend and turn around smoothed boulders and downed trees, dropping in little cascades as it begins its journey to meet the East Fork Jemez River some 700 feet below.
To continue on to Jemez Falls, walk around the top end of the upper pool or follow one of the side trails below the lower pool to reach the main trail. It begins by losing a little elevation and then rises gently on the way to the falls. For most of this hike, the trailbed is level and has a surface of crushed rock. Approximately 0.3 mile past the springs (1.8 miles total), the slope opens up to provide a view across the canyon to some rock outcroppings that are pushing their way out from between the trees. The coloration of the rock varies from richer reds to brownish-tans to mustard yellow. At 2.5 miles, again across the canyon, another geologic feature displays itself in the form of cone-like conglomerate rock formations with sharp peaks, appropriately called tent rocks. Over time, volcanic eruptions deposited a mixture of ash, pumice, and what is known as tuff (fragmented rock material), then wind and water slowly sculpted the rock into its present form.
Jemez Falls is accessible off NM 4—if you drove to the trailhead from Los Alamos you passed this turnoff. It has a designated campground area that you reach along the trail at 3.1 miles. A few hundred yards downslope, the trail makes a dip and then meets up with a wider trail leading to the falls. A sign there indicates the downslope direction and the G-mile distance.
The East Fork Jemez River makes a very slow, lazy turn just before it drops in a stair-step. The final drop is the longest, a free fall of about 20 feet. The total height of the falls is 70 feet. About 20 feet down from the top, there is a beautiful side pool positioned like a watery balcony in the shade. The viewing area for the falls is on top of a whitish rock outcropping. Adding to the pleasantness of the area are views of Los Griegos (10,117 feet) to the west and the nearby ridgeline, which is covered in ponderosa pine and splashed with patches of aspen.
SPEND THE AFTERNOON IN RUINS AND THE EVENING RECOVERING
Continuing on NM 4 into the town of Jemez Springs, you pass the Jemez State Monument. It is a mixed site, with ruins of a 500-year-old pueblo known as Giusewa ("Place at the Boiling Waters") to the Jemez people and a 17th century Spanish mission. The town of Jemez Springs is populated with restaurants, specialty shops, motels, and bed & breakfast operations, all set in a gorgeous, tall red-rock canyon. The town also lives up to its name, offering public-accessible hot springs at Giggling Springs (gigglingsprings.com) and Jemez Springs Bath House (jemezspringsbathhouse.com).
Box Canyon
TYPE: Day hike
SEASON: Year-round
TOTAL DISTANCE: 3.8 miles
RATING: Moderate
ELEVATION GAIN: 100 feet
LOCATION: Ghost Ranch, 8 miles northwest of Abiquiu
MAPS: USGS Ghost Ranch
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GETTING THERE
From Abiquiu, drive 11.5 miles north on US 84 to the entrance for the Ghost Ranch Conference Center (the official visitor center is another 2 miles down on the right). The road surface changes from pavement to gravel as you drive into the Ghost Ranch. Approximately 1 mile up, you reach a sign indicating the headquarters to your left and the dining hall to your right. Stay to the right. After paralleling a large open field, in about 0.5 mile you pass through a parking lot behind the dining hall. A very short distance from here you come to a set of posts with various signs; follow the one to the right for Kitchen Mesa (Hike 19). Drive another 0.4 mile (39.9 miles total) to reach the trailhead parking area. Next to where the road is blocked off by a metal cable, you will see signs for Kitchen Mesa and Box Canyon. Park here for both hikes.
THE TRAIL
Vivid sandstone walls painted in bands the color of red chili powder, white gypsum, and tanned leather stand as blocky bookends at the beginning of an easy and short-but-adventurous journey along the spring-fed Arroyo del Yeso. The canyon narrows the farther up you travel, eventually reaching the walled-in hollow that gives this place the name Box Canyon.
Starting in the same location as the hike to the top of Kitchen Mesa, the trail forks to the left at the point where the Kitchen Mesa Trail crosses the arroyo. You pass by four or five small rounded adobe huts known as hogans (Navajo style homes). There are great views of Kitchen Mesa, Chimney Rock to the west, and the mouth of Box Canyon straight away along this portion of the hike. The sandy, road-like path moves through juniper and pinion pine and a prolific collection of saltbush or chamisa, which produces a soft yellow bloom that turns the shrub into an oversized pom-pom in late summer, lighting up the plateau in a colorful play off the red-rock walls. For those interested in high desert plant life, there are plenty of species to identify, from cholla to prickly pear cactus to greasewood.
By 0.3 mile you reach the junction for Camposanto. This memorial is set against the near cliff wall. It was built as a way for people to honor those who have departed in this place of wild beauty that is Ghost Ranch. Continuing on the Box Canyon Trail, you step into the creek bed at about 0.5 mile. As you make your way up the narrowing canyon the trail stays along, or actually in, the creek. Before moving on, look up at the near cliff to see a rock feature that resembles an incomplete sculpture of a human.
You cross under an old water pipe and around a bend in the creek before entering a small forest of sorts. You will see a series of eight coffee cans painted black and numbered through here. The first comes at the start of the pseudo-forest run. Pinion pine, juniper, and tall Gamble oak surround you before the trail slips back into the creek environment. This area also is known as Yeso Canyon (yeso means "gypsum" in Spanish). The route has been well-traveled and is marked at key places, so just relax and enjoy the experience. Water is present year-round. Sandals with or without neoprene socks wouldn't be a bad idea, although normal hiking footwear is perfectly fine. Be aware that during heavy rains the canyon is not passable, and it is downright dangerous during a flash flood.
THE ENTRANCE FOR BOX CANYON
Cottonwood trees also dot the canyon. They turn a rich yellow in the fall and, along with the red to rust-brown Gamble oak leaves, make for a welcoming scene. The Upper Camp Trail junction comes at about 1 mile, along with the fifth coffee can marker. The canyon becomes more rugged past here, and you're forced to do a lot of hopping back and forth from one side of the creek to the other. The canyon walls also grow taller, creating the feel of a more remote canyoneering experience.
A sign points upward to an eagle's nest perched high on the cliff wall just past the junction. Nests can measure 8 feet in diameter and weigh as much as 1,000 pounds. This one is most likely to be occupied in spring.
The canyon splits at about 1.5 miles. A couple of small, tranquil pools are set on top of one another and big blocks of rock begin to choke the flow of the creek at this point. The eighth marker is located here. It is possible to explore up either canyon; continue straight for access to the terminus of Yeso Canyon.
PAINTBRUSH RENEGADE
She was born in Wisconsin in 1887 and spent years working on her art in cities like Chicago and New York, but it wasn't until 1929 that the name Georgia O'Keeffe would become synonymous with northern New Mexico. Her sensual interpretation of the surrounding landscape through color and perspective put her work in an unofficial category called "almost abstract." The world was taken by her talents and unique style and paintings of hers like "Pedernal" and "Black Iris" were regarded with the same prestige as works by Picasso and Matisse. Extremely independent—not easy for a woman in her time—O'Keeffe eventually moved to this area, which was even more remote and cut off from the rest of the country than it is today. After the death of her husband, Arthur Steiglitz, in 1946, she continued to live in the area of Ghost Ranch until her death in 1986 at the age of 98.
Kitchen Mesa
TYPE: Day hike
SEASON: Year-round
TOTAL DISTANCE: 3.8 miles
RATING: Moderate
ELEVATION GAIN: 550 feet
LOCATION: Ghost Ranch, 8 miles northwest of Abiquiu
MAPS: USGS Ghost Ranch
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GETTING THERE
From Abiquiu, drive 11.5 miles north on US 84 to the entrance for the Ghost Ranch Conference Center (the official visitor center is another 2 miles down on the right). The road surface changes from pavement to gravel as you drive into the Ghost Ranch. Approximately 1 mile up, you reach a sign indicating the headquarters to your left and the dining hall to your right. Stay to the right. After paralleling a large open field, in about 0.5 mile you pass through a parking lot behind the dining hall. A very short distance from here, you come to a set of posts with various signs; follow the one to the right for Kitchen Mesa. Drive another 0.4 mile (39.9 miles total) to reach the trailhead parking area. Next to where the road is blocked off by a metal cable, you will see signs for Kitchen Mesa and Box Canyon (Hike 18). Park here for both hikes.
THE TRAIL
Ghost Ranch carries a fantastical history that flows from the birth of the great age of dinosaurs to a revolution in American painting to an Indiana Jones–style discovery of natural artifacts that put this fiercely unforgiving place on the world map. The stories are infused with wonderful names like Coelophysis, Chinle sand lands, Dr. Friedrich von Huene, Piedra Lumbre, Chama River, Georgia O'Keeffe, and, of course, the ominously named Ghost Ranch itself, whose symbol, the sun-bleached cow skull and horns, appeared in paintings by O'Keeffe. The journey to Kitchen Mesa is a journey across 200 million years.
On the other side of the cable are the access trails for Kitchen Mesa and Box Canyon. Both are short hikes, and even at a leisurely pace you can easily manage to see the geographic treats that define each in a single day. Start the Kitchen Mesa hike by crossing over the arroyo. The trail makes a tiny push uphill into an open zone of cactus, sage, chamisa, cholla, and yucca, with a bottom-up view of the layered, multicolored birthday cake that is Kitchen Mesa's southwest side.
The various blooming stages of wildflowers, cactus, cholla, and chamisa offer a dramatic contrast to the red-rock environment. A series of wildflowers bloom from spring into fall. Green pitaya cactus—barrel-shaped and usually growing in clusters—produces a scarlet bloom in May. Cholla (pronounced choi-a) has a delicate fuchsia-colored bloom in late summer. The chamisa or saltbush, with eight varieties in New Mexico, paints the ground in soft yellow puff balls. These plants and others are reminders of the vitality and diversity of life in a zone that sees just 9 inches of precipitation a year.
KITCHEN MESA
To the south is the incredibly prominent steep-sloped neck and flat top of Pedernal ("flint" in Spanish). Georgia O'Keeffe memorialized this mountain in numerous paintings, and in a way created the iconic symbol for the high desert of northern New Mexico. This trail has a unique marking system that mainly utilizes large coffee cans painted green with one vertical white stripe. You will see them on the ground, hanging off tree limbs, and capping posts. They are handy for the approach up to and across the first section of the mesa.
At 0.4 mile, the trail makes a steep push up a hill of red sand and down the other side. This is one of the places where excavations took place from the late 1940s into the 1950s, uncovering completely intact Coelophysis dinosaurs. This particular species isn't the missing link between the Triassic and Jurassic periods, but it is an extremely crucial one in determining the progression of the greater species.
The carnivorous Coelophysis was not very big, about the size of a small adult human. Thousands of complete skeletons were found, concentrated in layers near the point where the Kitchen Mesa Trail passes over, and 10 times that amount may still lie buried in the area. The process of preservation through fossilization is well-understood: Silts and soils carried by water buried the dinosaurs shortly after their demise, suggesting that flooding occurred. What can only be speculated about is how so many young and old Coelophysis died at the same time. The most likely theory comes from a more modern comparison with thousands of crocodiles that died along the Amazon after being attracted to a bountiful food source that disappeared because of drought. Perhaps a similar event occurred with the Coelophysis.
Once on the other side of the red hill, you are at the mouth of a small, dead-end valley bottom. The trail continues through a similar mix of plant life, passing by large, smooth sandstone boulders, across a couple of small arroyos, and under the beginnings of a deeper conchoidal arch—sandstone seemingly scooped out with a large spoon from the vertical wall on the northwest side of Kitchen Mesa. It doesn't appear that there is access to the mesa top, but by 0.8 mile you begin a steeper push up a loose rock trail. You will have to do some high-stepping over bigger rocks and eventually a small amount of scrambling. At 1.1 miles, guided by the green coffee cans, you are below a slot in the wall that requires some effort to make the short ascent to the top. This little climb may not be feasible for small children, older people, or those in poor physical condition.
Once atop the mesa, the trail stays close to the edge and then makes a short push to an upper shelf via a minor scramble. In the last section, before you step on a defined crushed rock trail, the path moves across a staircase-like collection of shale, hundreds of thin layers built up over thousands of years during the Mesozoic era about 150 million years ago.
Another feature here, and really throughout the high plateau desert, is the presence of a very large collection of organisms called cryptobiotic soil. It is clearly visible in the soot black, fistsized bumps or lumps on the ground. This is a living organism made up in large part by cyanobacteria, but it may also include soil lichens, mosses, green algae, micro-fungi, and bacteria. This crust plays an important role in the ecosystems in which it occurs, stabilizing the soil against the erosive nature of wind and water, absorbing water to the benefit of neighboring plants, and enriching the soil with nitrogen to create a livable environment for other plants. It has an armor-like appearance, but don't be fooled: Cryptobiotic soil is highly susceptible to damage by foot traffic. Depending on the conditions it could take up to 100 years for a section of ground to recover. So stay the course, and stay on the trail that leads across the mesa to a white rock field.
It is a brilliant, easy promenade of 0.7 mile (1.9 miles) to the trail's conclusion, 450 feet above the valley below. From the mesa top (7,077 feet) you can see Pedernal, Abiquiu Lake, Box Canyon, Chimney Rock, the mountains of the Chama River Wilderness, and the Sangre de Cristos to the east. The cream cheese spread of white rock covering Kitchen Mesa from edge to edge is gypsum—made up of sulfate minerals left behind by evaporated sea water.
Just as you should anywhere above tree line or out in the open, you must keep an eye out here for approaching thunderstorms in the summer months. In a matter of minutes, storm cells can build and seemingly collide with each other to create an explosion of lightning and torrential rain. Lightning strikes come in rapid succession and with surprising consistency, repeatedly hitting the ground in the same general area. And rain can fill a typical dry arroyo with 2 to 3 feet of water in 10 minutes. Don't try to outrun it either.
A BONE TO PICK
Besides the intact skeleton of a Coelophysis, the Ruth Hall Museum of Paleontology on the grounds of Ghost Ranch also offers fossils of the Rutiodon. A Photostat, the Rutiodon is a parallel ancestor of the crocodile that reached lengths of 16 feet. It was a menacing predator. The Coelophysis and Rutiodon existed some 200 million years ago during the Triassic period. For museum hours and other information about Ghost Ranch, visit www.ghostranch.org.
Cerro Pedernal
TYPE: Day hike
SEASON: May to October
TOTAL DISTANCE: 7 miles
RATING: Moderate to strenuous
ELEVATION GAIN: 1,900 feet
LOCATION: Santa Fe National Forest, 8 miles west-southwest of Abiquiu
MAPS: USGS Youngsville and Cañones
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GETTING THERE
From the town of Abiquiu, take US 84 for 7.2 miles west to the junction with NM 96, which is signed for Gallina, Coyote, and Abiquiu Lake. Turn left and follow NM 96 for 11.2 miles and then make a left turn onto FS 100. The gravel road climbs to reach FS 160 in 5.5 miles (23.9 total). Pull onto FS 160 and park in the open area on either side of the road.
THE TRAIL
Made into a symbol of the harsh beauty of the Chama River valley by painter Georgia O'Keeffe, Cerro Pedernal reveals its true shape on this hike. Viewed from the north in the Ghost Ranch area, the steep-shouldered, flat-topped basalt volcanic structure appears to be a long butte. Its secret is exposed during the approach, and even more so from the summit: Pedernal is really a narrow rock band formation, as dramatic as a Hollywood movie set. Unlike the big screen, however, Cerro Pedernal offers a visceral experience in the grassland approach, rock climb–like ascent, and tremendous views over a vast spread of the Chama River environment.
Although it doesn't happen often, it should be noted that the road is actually accessible to four-wheel-drive vehicles all the way to the base of the final hike, scramble, and climb to the top. Regardless, it's a nice hike all the way. You will enjoy shape-shifting takes of the mountain, crossing through a band of multicolored flint, and pausing in a meadow overlook of the Chama River valley. Pinion pine, ponderosa pine, juniper, Gamble oak, sagebrush, the late-summer-blooming chamisa (saltbush), and wildflowers blanket the first 0.6-mile stretch. The road bends west from its northeasterly course, climbing in view of the south face of Pedernal around the 1-mile mark.
TOP OF CERRO PERDERNAL AS SEEN FROM THE NORTH SIDE
The views grow as you climb, including ones over the Rito Encino valley and the Rio Cañones canyon located to the south. By 1.9 miles, the road meets a T-intersection of sorts. Follow the rocky road coming in sharply from the right, not the one bending to the left. After a steep ascent of 0.5 mile (2.4 miles total), you reach the first of a chain of meadows, with Pedernal looming larger and larger over you.
Keep an eye out for rock cairns placed along the road around 2.8 miles, close to the road's end. Following the cairns, you pass through some open space before setting foot on a good trail again. If you miss the start of the trail, you'll need to aim for the sharp western face of the mountain. Stay slightly to the right of center and you will hit the steep corkscrew trail that leads to a small boulder field at 3.3 miles. Scarlet gilia, wallflower, and lupine light up the grassy meadows.
Cairns guide you to the top of the boulder field and onto a trail that hugs the bottom end of the upper cliff bands around to the south side. In less than 0.2 mile, you pass under a leaning juniper tree. Shortly after, as you scan the wall, you will see a location that reveals the most sensible access to the top. This spot should be marked by a white arrow. If you reach the cave you observed on the hike up, you have gone too far. Just backtrack slowly and you will see this spot. There also may be a small platform of rocks that previous hikers have set up to begin the short climb.
To access the summit of Pedernal you have to climb. The tough section is less than 12 feet high and in climbing vernacular would be rated only about a 5.6 in difficulty. Use your own judgment about whether to try it. Once you are above this section, a rough trail moves along to the right. Another scramble/climb is necessary shortly before you reach a chute of sorts on your left. The surface is loose rock, so be careful as you clamber up, especially if there are others behind you.
As you go higher, you pass through some trees and into a small clearing on the top of Pedernal. The mountaintop is about 0.2 mile long and the true summit is on the western end. The vistas do not disappoint from any location up here, with a grand take on the Chama River valley, the Rio Puerco valley, the Jemez Mountains to the south, more distant mountain ranges like the Sangre de Cristos to the northeast, and others to the northwest.
THE MOUNTAIN GOD GAVE ME
Georgia O'Keeffe said that God should allow her to claim Cerro Pedernal as her own because of her numerous paintings of the landmark. Over her long, vibrant career she managed to create 20 different paintings of the mountain, many of which can be seen at the Georgia O'Keeffe Museum in Santa Fe (www.okeeffemuseum.org). The museum collection has other famous paintings of O'Keeffe's—1,148 paintings and drawings in total—like "Black Lines" and "Pelvis Series Red and Yellow."
Rim Vista Trail
TYPE: Day hike
SEASON: Year round
TOTAL DISTANCE: 4.6 miles
RATING: Moderate to strenuous
ELEVATION GAIN: 1250 feet
LOCATION: Carson National Forest, 36 miles northwest of Española
MAP: USGS Echo Amphitheater
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GETTING THERE
From Santa Fe take US 84/285 north to Española for 25 miles. After Española, in 7.4 miles, US 84/285 splits. Continue straight at the junction on US 84, headed towards the small community of Abiquiu. From Abiquiu (43.3 miles total) it is 12.5 miles to the entrance with Ghost Ranch. You will continue past the Ghost Ranch entrance 2.5 miles (58.3 miles total) to reach a left hand turn onto FR 151. Besides using the Ghost Ranch entrance as a warning of the upcoming turn, a closer notice of the turn will come by way of a brown recreational sign for Christ in the Desert Monastery. The pavement changes to dirt and gravel. At 0.6 mile down FR 151 you'll crest a small rise and will see a road to your right that should be marked with a sign that says TRAIL. Turn right onto that road and travel another 0.1 mile (59 miles total) to a lower parking area. You'll see an upper parking area another 0.1 mile uphill, which is next to the trailhead. Depending on the road conditions you may need a four-wheel-drive vehicle to reach that upper lot.
THE TRAIL
The Rim Vista Trail is a short hike set in the Chama Basin, a place that has a long, complex, and fascinating history that includes everything from dinosaurs to ancient seas to Hollywood to desert monks to a wild and scenic river. This hike includes spectacular vistas in a compact setting from the benched environment above the Rio Chama, home to cacti and rabbits, to a top balcony setting adorned with pinyon pine and home to elk and crystal clear views of Ghost Ranch, Abiquiu Lake, Cerro Perdenal, and the Rio Chama Wilderness. However, the bounty of the grand vista spot doesn't come until you commit to gaining 1,300 feet in elevation over 2.3 miles.
To start, the trail makes one quick downhill slide through the folds of the terrain before it turns upward and climbs all the way to the rim vista point 2.3 miles away. When you reach the 0.4-mile mark you'll start up a short, natural rock staircase. Though still gaining elevation the whole while, along with the vistas as they rise in greater and greater splendor, the trail does relax a bit at 0.9 mile. Be aware that the trail can be extremely slippery when wet as the clay becomes greasy, so if possible, try to hike this area when there are dry conditions.
Though you already started the hike with some great views around the Chama Basin, the higher you get the bigger the world becomes. This world belonged to dinosaur morphs, Triassic period dinosaurs, and more advanced dinosaurs of the late Triassic, 250 to 200 million years ago. The area around Ghost Ranch has been a gold mine for dinosaur firsts: everything from the discovery of a thousand Coelophysis skeletons to that of the gecko-looking (though it stood 3 feet tall) Dromomeron romeri, which, along with other species discovered at Ghost Ranch, showed that the transition to the dinosaur age was more gradual than originally thought. All animal life was occurring when the land mass of the planet was one super continent called Pangea, though it was in the midst of breaking apart.
LOWER SECTION OF RIM VISTA TRAIL
When you reach the 1.7 mile mark the trail tilts upward for a steep stretch to reach a benched area. Though it's unknown how often there is any trail maintenance out here, the trail is quite obvious, but in case you are in need of extra reassurance it is marked, here and there, with blue diamonds. The plant mix takes from the high plateau pallet and paints the landscape with pinyon-juniper, sage, a sporadic yucca, and a bold collection of wildflowers from purple locoweed to Indian paintbrush to aster depending on the season (spring is best). Also, you may notice a periodic pebble and sand mound near the trail; these are anthills.
The most mesmerizing views all along the hike, including from the rim vista point, are that of the multi-striped, multicolored sedimentary and sandstone rock formations of Ghost Ranch. You half expect to see dinosaurs walking along the top of Kitchen Mesa or down in the grasslands near the entry of Box Canyon. The rock formations and colors come over a long and complex geologic history that includes everything from tectonic shifts to ancient seas to great deserts to the action of water over the landscape, all of which spanned tens of millions of years.
Once you are through the benched area the trail works itself up a steeper incline starting at 2 miles. At 2.3 miles, shortly before topping out, the trail provides one last grunt across a steep, rocky trail to reach the rim and its stunning overlook. Between the layered cake of rock formations of Ghost Ranch to the iconic Cerro Perdenal with its anvil-like profile to Abiquiu Lake and the Rio Chama giving the expanse of the valley floor a shimmer, it is well worth the effort. Hollywood discovered the beauty of this place starting back in 1939 with a movie titled The Light That Failed and more recently with movies like No Country for Old Men and Cowboys & Aliens.
Once up top, the open mesa environment provides for some enticing exploring beyond the vista point if you're so inclined. Rabbit, elk, deer, and coyote call this area home. Other year-round inhabitants include the monks from Christ in the Desert Monastery located about 5 miles as the crow flies up the Rio Chama from here. You can visit the monastery by taking FR 151 to its end. It's also worth noting that a total of 24.6 miles of the Rio Chama, including where it slides by the monastery, has been given a federal Wild and Scenic River designation.
ECHO AMPHITHEATER
The vista point on the Rim Vista Trail is not only a key spot for grand views of the surrounding area, but it also sits on the same mesa that backdrops one of New Mexico's most impressive natural features: the Echo Amphitheater. Much easier and safer than attempting to scramble down from the mesa top to reach Echo Amphitheater would be to take US 84 north, 1.5 miles past the turn for FR 151. As the name indicates, you can hear your voice echo off the walls when you get close enough to what looks like a smooth scoop taken from a Neapolitan ice cream container. The rock layers, like those around Ghost Ranch, are a combination of the Jurassic and Triassic periods. Whether you are a rock hound or not, this place is a must see purely for its rare beauty.
Valle Caldera
TYPE: Day hike
SEASON: May to October
TOTAL DISTANCE: 6 miles
RATING: Moderate
ELEVATION GAIN: 1,100 feet
LOCATION: Valle Caldera Reserve, 5 miles west of Los Alamos
MAPS: USGS Valle San Antonio, Valle Toledo, Bland, and Redondo Peak
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GETTING THERE
From Los Alamos, take NM 501 south 4.5 miles to the junction with NM 4. Turn right onto NM 4 and head 10.8 miles west to the turn for the Valle Caldera Reserve (there is a sign). The gravel road leads to the staging area in the caldera in 1.3 miles (16.6 miles total). Vehicle access is on a first-come first-served basis. There are 35 permits issued per day from May 15th to September 30th to noncommercial vehicles, and they can be picked up at the Valle Grande Visitors Center. Though the access permit is free, there is a per vehicle entrance fee of $20. It's best to check out the full information on accessing the Valle Caldera by going to www.nps.gov/vall.
THE TRAIL
Violent volcanic eruptions in the lower 48 states have been few and far between in the last couple hundred years. The Mount St. Helens eruption in May 1980 took the country by surprise. Its display of force leveled hundreds of square miles of forest in a matter of seconds and reduced the mountain's height by 1,300 feet. Here in northern New Mexico, a hulking, towering mountain reaching a height somewhere near 11,000 feet erupted over a million years ago with 100 times the force of that Mount St. Helens eruption, completely rearranging the landscape for hundreds of square miles.
Like a skyscraper imploding, the volcano became a sea of volcanic rock. Some geologists believe you can still see a variety of this feldspar on the north slope of Redondo Peak. Volcanic domes formed inside the caldera, and these were eventually covered with grasses and forest growth. Two artesian wells bubble up inside the caldera, the headwaters of the East Fork Jemez River and the San Antonio River. The valley stays moist enough to keep the encroachment of trees at bay. It is a massive and strikingly beautiful open expanse—14 miles across—that is home to more than 5,000 elk. It also hosts a brilliant bloom of iris in early summer. Hikers are drawn to this unique landscape, which is enjoyed by a variety of creatures.
WEATHERED ELK SKULL IN THE VALLE CALDERA
There are currently three designated hikes in the reserve. The newest is Cerro de los Posos, which provides the highest overlook of the caldera. To hike in the reserve, you must first make a half-hour van ride through the caldera. (Information about reserving a date to hike and where to meet for the shuttle within the preserve is available at www.vallescaldera.gov.) On an early morning hike, you will more than likely spot many elk finishing up the last of their feeding before moving into the trees. It isn't unusual to see 80 to 100 head of elk. The Valle Caldera has been under some form of domesticated grazing for more than 130 years, beginning with huge flocks of sheep tended to by Basque shepherds and continuing today with cattle that still graze sections of the preserve, but in very small numbers.
The Cerro de los Posos hike follows an old logging road to the upper reaches of the north rim of the caldera. The outing is mostly about the tour across the caldera and the sweeping panoramic views. The hike itself is pretty straightforward, as you simply follow a road for 3 miles to a high overlook. For an even grander vista, climb to the open grassy ridgetop. The first 2 miles are set in the trees. At 2.2 miles the road breaks out onto the lower end of the open slope. From here it moves cross-slope, arriving at a gate at around 3 miles. Past the gate, you have access to the grassy slope that leads up to a higher overlook. The road continues on to another gate and the reserve boundary.
You will have approximately five hours to complete this hike and/or explore other areas around this trail. Currently, reserve rules require that you stay on the road because geologists and anthropologists are still assessing the caldera and want uninvestigated areas left undisturbed. The forest around the caldera is a mix of ponderosa pine, fir, spruce, and aspen. The aspen are magnificent in the fall, golden yellow puddles of light set on a canvas of green.
GOOD ENOUGH TO BE THE REAL THING
Hollywood has been to the Valle Caldera a number of times, with movies like The Gambler starring Kenny Rogers and The Missing starring Tommy Lee Jones shooting here. Near the entrance to the park sits a homestead that has never been lived in that was used for the movie The Fight Before Christmas. Another set was created for the movie The Shootout starring Gregory Peck, and it was used for other productions too. It was built well enough that the buildings are still used today for housing and storage. More recently the television series Longmire has used this amazing place as part of its set. Walt Longmire, the lead character, lives in what is supposed to be a valley in Wyoming, but his house is actually in the Valle Caldera.
Cerro Grande
TYPE: Day hike
SEASON: May to October
TOTAL DISTANCE: 4 miles
RATING: Moderate
ELEVATION GAIN: 1,200 feet
LOCATION: Bandelier National Monument, 5 miles west of Los Alamos
MAPS: USGS Bland
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GETTING THERE
From Los Alamos, take NM 501 south 4.5 miles to the junction with NM 4. Turn right onto NM 4 and head 6 miles (10.5 miles total) west to a parking area on your right, just before the left turn for FS 289.
THE TRAIL
This hike lives up to its name "Grande" with a high eastern rim overlook of the Valle Caldera and views across the heart of canyon-edged Bandelier and the fire-deforested peaks of the Dome Wilderness. Cerro Grande itself was part of a recent forest fire in 2011, and both the scars and rebirth will be visible. Sunrises and sunsets are spectacular from the easy-to-access peak.
You pass through a ponderosa pine forest and a loose collection of aspen trees at the beginning of this 2-mile trek. The area only recently was opened to the public, and even though no official trail was constructed, the amount of visitation has created a very pleasant approach. The "non-trail" follows a series of yellow diamonds mounted to the trees. The flat, benched zone ends at 0.3 mile and the trail then begins a rollercoaster run to the 1-mile mark. The trail gains the slopeside above young Frijoles Creek, which was one of the life forces to the Pueblo community of Bandelier 10 miles downstream. Across the way, thicker groves of aspen decorate the hillside and bluebell, paintbrush, and scarlet gilia brighten the terrain along the trail. Deer, elk, and coyote also make their home here.
The trail moves away from the drainage, slipping through the trees and gaining elevation. By 1.6 miles, the trail enters the bottom end of the grassy corridor that leads to the summit of Cerro Grande Peak (10,199 feet). The incline is steep through here, as you gain 600 feet in the next 0.4 mile. Your efforts are rewarded by the 2-mile mark, with balcony-style views across a vast amount of the Valle Caldera. The highpoint due west is Redondo Peak, standing 11,254 feet. The Sangre de Cristo Mountains loom large across the Rio Grande. The bulky mass in the distance to the southeast is the Sandia Mountains. A prominent cliff band is visible in the upper end of Frijoles Canyon, as the creek makes a dogleg bend to the left.
SLOPE LEADING TO CERRO GRANDE
DOME WILDERNESS FIRE
The fire began on April 25, 1996, and by the time it was finished, it had burned some 6,000 acres, most of the Dome Wilderness. The intensity of the fire took down a forest and left behind a charred wasteland—and innumerable treasures. Various scientific groups quickly flocked to the area to begin analysis and exploration. Some specialists were looking at the effects of the sediment runoff that would occur in the streams below the steep slopes now that the holding effect of a living forest was gone. And with the blanket of trees removed, archeologists were able to discover 69 new sites of interest.
Bearhead Peak
TYPE: Day hike
SEASON: June to October
TOTAL DISTANCE: 9.4 miles
RATING: Moderate
ELEVATION GAIN: 800 feet
LOCATION: Santa Fe National Forest, 12 miles southwest of Los Alamos
MAPS: USGS Redondo Peak, Bland, Canada, and Bear Springs Peak
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GETTING THERE
From Los Alamos, take NM 501 south 4.5 miles to the junction with NM 4. Turn right onto NM 4 and head 11.2 miles west to the left turn for FS 280. The dirt/packed-gravel road is not marked along NM 4 coming from Los Alamos. So as soon as you move beyond the edge of the Valle Caldera, watch for a FS 280 sign about 35 feet up on the left. If you pass the sign for the Jemez National Recreation Area on NM 4, you've gone too far. At 2.2 miles along FS 280, you reach a junction: FS 280 continues to the right and the road straight ahead is closed. The rocky road off to the left is FS 282, and this is your turn. This road is accessible only for high-clearance, four-wheel-drive vehicles. At 3.1 miles (21 miles total), you pass by an open area on your right that leads to a large meadow beyond. Park your vehicle in the first open area. The road continues for another 0.4 mile, but there isn't adequate parking farther along.
THE TRAIL
Ridge-running with access to two different peaks, vistas across the rugged backcountry terrain of the Jemez Mountains, and a crow's nest–style lookout all await you on this seldom visited hike. Bearhead Ridge rises above the volcanic cliff bands of Peralta Canyon to the west and the former mining community of Bland in Bland Canyon to the east. It curls from south to east to finish on the summit of Bearhead Peak, the site of an old fire lookout.
There are several trail options a short trek from where you parked. The trail to the right slips down into the canyon bottom of Peralta. The trail to the left moves across Woodward Ridge to an overlook of Bland. And straight away the trail leads pleasantly across Bearhead Ridge for the first 0.2 mile before it begins popping up and down—but mostly up. There are views of the Sangre de Cristo Mountains, the Dome Wilderness, and Cochiti Reservoir as you move through a mix of ponderosa, fir, and Gamble oak. Wildflowers from aster and bluebells to scarlet gilia and sunflowers grow along the ridge.
BEARHEAD PEAK RISES IN THE DISTANCE
At 0.8 mile you come to what looks like a fork in the trail. Stay to the right as you gain more of the northern slope of Aspen Peak (9,244 feet). The trail is rarely maintained, so there may be some downfall with which to contend, but the pathway is relatively easy to follow. Long, round-topped Aspen Peak is reached at 1.5 miles, and by 2 miles you are above an open slope of lichen-spotted volcanic rock and a healthy population of Gamble oak.
The route from here can be a little tricky. The key is to stay to the right, hugging the edge as a definitive trail does its best to steer clear of the oaks. By 2.3 miles, the trail begins to bend to the southeast, passing through the bottom end of the open slope and nearly down the middle of a stand of aspen. It then curls more to the south before turning southeast again and gaining some elevation to reach an open ridgetop with great views of some columnar volcanic cliff bands in Peralta Canyon at around 3.1 miles. You continue by dipping down to a small saddle before moving cross slope and punching up a steep section to a trail junction at 3.9 miles.
A sign indicates that Bearhead Peak stands to the left. The trail to the left of Bearhead leads down into Colle Canyon. The one to the right accesses Peralta Canyon. And a relatively easy 0.4-mile jaunt (4.3 miles total) leads you to the small clearing of Bearhead Peak (8,711 feet). Instead of the typical cabin-style structure, lookouts lived in wall tents and climbed a 25-foot tower to reach the crow's nest for a good view of the area. That tower still stands today, barely raising its chin above the ever-growing trees.
YOU TAKE THE HIGH ROAD, I'LL TAKE THE LOW ROAD
Instead of stepping along Bearhead Ridge, move downslope at the beginning of the hike into Peralta Canyon, following a spring-fed creek before turning upslope to gain the summit of Bearhead Peak. The trail, like many in this area, is unmaintained. Bring a map and compass or GPS and be prepared for some adventure along this alternate route.
Dome Wilderness
TYPE: Day hike
SEASON: June to November
TOTAL DISTANCE: 6 miles
RATING: Moderate
ELEVATION GAIN: 1,500 feet
LOCATION: Dome Wilderness, 10 miles south of Los Alamos
MAPS: USGS Bland, Frijoles, Cochiti Dam, Canada
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GETTING THERE
From Los Alamos, take NM 501 south 4.5 miles to the junction with NM 4. Turn right, or west, onto NM 4 and drive just over 6 miles (10.5 miles total) to FS 289, where you turn left (the road is signed). The road surface is gravel. Approximately 2.2 miles up you pass a parking area; continue straight on FS 289 toward the Dome Wilderness. At 7.2 miles (17.7 miles total), there is a sign for the Dome Wilderness and Dome Lookout, along with a list of trails. Turn left here onto FS 142. Because of the poor road condition, four-wheel or all-wheel drives are recommended, but you can continue, up to a point, with a high-clearance, two-wheel-drive vehicle. At 3.5 miles (21.2 miles total), you reach a small parking area just before a closed gate blocks the road to Dome Lookout.
THE TRAIL
On maps, the Dome Wilderness appears as an odd appendage to the 32,727-acre Bandelier Wilderness. And the 5,200-acre Dome Wilderness indeed was created in 1980 as the western extension of the more famous Bandelier. The Dome is its own unique place, however, set in a small sub-range called the San Miguel Mountains, with highpoints like St. Peters Dome (8,464 feet) and Cerro Picacho (8,113 feet). It is found low in Sanchez Canyon, which is 500 feet deep at points. The landscape was once known for its pine-covered slopes and hidden cliff outcroppings, but a fire in 1996 took down 75 percent of the trees. Today it is a stark place of openness and rebirth—still worthy, still its own environment, connected but separate from Bandelier.
Because the Dome ajoins Bandelier National Monument, there are access trails into that park at the beginning and turnaround point of this hike. Boundary Peak Trail 427 and Capulin Trail 116 are accessible at the start. To hike Dome, move past the barricade and follow the road 0.7 mile to the St. Peters Dome Trail, marked by a sky-blue post. This place is in transition, and it is estimated that it will take 150 years for a forest to regrow to pre-fire stature. Regardless, it is a stunning setting with wide views over the leathery folds of the Rio Grande canyon, a series of big basins, striking sharp-toothed Boundary Peak (8,300 feet) in the near distance to the northeast, and other mountainscapes of the Jemez Mountains.
THE FIRE-SCARRED LANDSCAPE SURROUNDING THE DOME WILDERNESS LOOKOUT
The lookout, visible from here, is accessed by continuing on the road another 0.6 mile. It is no longer regularly staffed, but it still offers a nice view of the surrounding area and you can explore the easy-to-follow ridgeline to the east. The St. Peters Dome Trail immerses you in the area's new growth. The current plant mix consists of grasses, wildflowers like harebell, sunflowers, and scarlet gilia, and a growing population of Gamble oak. The luscious growth has attracted larger mammals, like deer, elk, and bear, back into this zone.
The trail curves around the west slope of St. Peters Dome and through a rare stand of mature pine trees to reach the upper end of a long saddle at around 0.8 mile. The tall peak to the south is Cerro Picacho. A treeless basin stretches between the two peaks to the east. The scouring effect of the fire has made some of the basalt volcanic rock more prominent, so much so that at points it appears to be still cooling down from a recent eruption. Other wildflower blooms you may see include daisy, aster, nodding onion, and golden rabbit brush. As the area is open and arid, yucca and cactus are also common through here.
The trail fades, but barely, at points as you cross over the spine of the saddle in a southerly direction. Cairns set along here provide further reinforcement that you are on the right path. By 1.2 miles, you pass through a heavier collection of basalt rock before entering the beginnings of a thick cluster of Gamble oak along a midline trail that cuts across Cerro Picacho's east-northeast slope. By 1.6 miles, you enter a stretch of unusual, sometimes castle-like rock formations. Wind and water shaped this rock material, which is called tuff. There also is a broad mesa zone in the near distance that can be explored easily by dipping off-trail a short distance farther along.
At 2 miles, the trail switchbacks into a small canyon decorated with a nice collection of ponderosa pine. It is the only stretch on this hike that offers relief from the sun. By 2.3 miles, you reenter the open space of loose rock and the high Pajarito Plateau plant mix. The stout range you can see to the south-southwest is the Sandia Mountains. By 3 miles you reach a cholla and sunflower zone, along with the junction for Turkey Springs and the hike's turnaround point.
If you head to the left, you could work your way down to a canyon bottom before passing into Bandelier National Monument and on to Turkey Springs (dogs are not allowed in Bandelier). It is possible to pass through the park, which would be 6.5 miles, to make this a loop option for a longer day or an overnight hike. You could also venture up the arroyos into the basin between St. Peters Dome and Cerro Picacho, and back up to the ridge for a cross-country trip back to the trailhead. Of course, just heading back along the trail will make for a rewarding return hike, too.
SANCHEZ CANYON AND THE SUMMIT OF CERRO PICACHO
Cerro Picacho can be summited by following the trail to the right at the junction. It bends back to the north to work up Sanchez Canyon and past a waterfall. Then a steep off-trail ascent takes you to the top. The north slope offers another route up Cerro Picacho. From the saddle you crossed over on the trail from St. Peters Dome, you can scramble up the steep slope for nearly 1,000 vertical feet to the summit. As you can tell, there are plenty of cross-country options from which to choose, especially with the forest cover now gone—at least for the next century or so.
Bandelier Canyon Loop
TYPE: Overnight
SEASON: May to November
TOTAL DISTANCE: 19.1 miles
RATING: Moderate
ELEVATION GAIN: 1,500 feet
LOCATION: Bandelier National Monument, 12 miles south of Los Alamos
MAPS: USGS Frijoles and Bland
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GETTING THERE
From Los Alamos, take NM 501 south 4.5 miles to the junction with NM 4. Turn left onto NM 4 and travel 5.7 miles to the entrance for Bandelier. There is an entry fee of $20 per vehicle, which is good for seven days of access. You can also use your National Parks Pass if you have one. From the entry gate, the road descends into Frijoles Canyon to reach the parking area and visitor center in 3.1 miles. Be aware that between mid-May and mid-October from the hours of 9 a.m. to 3 p.m., you must take a shuttle bus to access the park. The shuttle bus leaves from the White Rock Visitor Center. Exceptions include those backpacking overnight. Check the most up-to-date entry information by going to www.nps.gov/band.
THE TRAIL
Bandelier National Monument is primarily a wilderness area. Only a small percentage of its 32,727 acres are outside this designation. The Bandelier Canyon Loop Hike takes you away from the bustle of civilization—present and past—of Frijoles Canyon and across open mesas to the rim of breathtaking Alamo Canyon, the doorstep of the once vibrant Yapashi Pueblo, and down through the wild and beautiful Upper Frijoles Canyon. Your sights will be set on the Yapashi Ruins, but there are some real treats along the way.
To begin, cross over the vehicle bridge by the visitor center and walk along the road for less than 0.1 mile to a trail that cuts uphill by some outhouses. Shortly after starting down this trail there is a signed junction. The Yapashi Trail continues uphill, eventually gaining the rim of the southwest wall of Frijoles Canyon. As you climb, views of the northeast wall grow bigger, as does the aerial view of the various ruins from Tyuonyi to Long House to Alcove House farther up canyon. Even though Dr. Edgar Lee Hewett is rightfully credited with being the energy behind the preservation of this area (established in 1916), the national monument takes its name from the Swiss-born archeological pioneer Adolph F. A. Bandelier, whose multiyear exploits of the Southwest included explorations of the ruins of Frijoles Canyon.
At 0.5 mile you reach the canyon rim. From here you have an excellent overview of the surrounding landscape: the forested rise of the Jemez Mountains to the northwest, the Sangre de Cristo Mountains to the northeast, and the stout Sandia Mountains to the east. To the southwest the terrain alternates from rim views to canyon bottoms, with a succession of seven different canyons in a 10-mile stretch. This hike crosses into three of these canyons. This greater geographic area is the edge of the Pajarito Plateau, densely layered by a collection of massive eruptions from what is known today as the Valle Caldera. The soft ash has been worn and shaped by the run of water over a million years, like a rake dragging tracks in a dirt hill.
YAPASHI RUINS
The trail edges the rim for another 0.5 mile or so before you reach an unexcavated site called Frijolito. It was occupied in the late 1200s and is estimated to have 70 to 80 rooms. A trail moves south to reach the Rio Grande in approximately 4.5 miles, but you want the trail that continues up canyon to reach a junction for the Yapashi Ruins at 1.3 miles. If you continued straight, you would stay along a beautiful rim trail that eventually drops back into Frijoles Canyon at the Upper Crossing.
The environment is definitely high and dry, with lots of juniper, yucca, cactus, cholla, and, of course, outrageously beautiful bursts of wildflowers in spring and after heavy periods of rain through the summer. As you approach shallow Lummis Canyon, the trees are in greater abundance, including some ponderosa pine in the bottom of the canyon. You make a quick turn and twist to cross into the canyon, stepping over a wet or dry creek bed and gaining open views again by the 2.3-mile mark. The stripped but still majestic highpoints to the east are part of the Dome Wilderness, hit hard by an intense, sweeping, 6,000-acre fire in 1996.
By 2.9 miles the trail noticeably changes to a pumice surface, a remnant of the volcanic blasts from a million years ago. As you round a corner, more than likely admiring the interesting rock formations along the trail, you are hit with a spectacular view of the chasm that is Alamo Canyon. The canyon is only 500 feet deep at this point, but it's broad—a quarter mile or so across—with ruggedly stark rock walls. Most of its physical impact comes in the seemingly sudden appearance of the canyon. A steep switchback trail takes you 0.5 mile to the canyon bottom. Again, depending on the winter snowpack, the creek may or may not have water. The trail passes by conical rock formations with boulders balancing on the tips before starting the ascent back out the canyon via the opposite wall. It is a strenuous push, but you reach the rim at the 4.2-mile mark.
JEMEZ MOUNTAINS
By 4.7 miles you have gained much closer views of the Dome Wilderness and arrived at a trail junction. The sign for Yapashi directs you to the right (northwest). In another 0.6 mile you reach the former Yapashi Pueblo. Short rock walls line out what used to be multistory buildings and homes. This community was made up of several hundred people who subsisted by hunting, gathering, and farming. Their most consistent water source was in Capulin Canyon. The most prolific community members today are the cholla, typically sprouting a magenta-colored bloom in summer and after heavy rains.
At 5.7 miles there is a junction for the Dome Lookout and Upper Crossing. Continue toward Upper Crossing in the direction of some large, rounded boulders that mark the entrance to a small side canyon. The trail climbs briefly before entering the ponderosa pine canyon at 6.2 miles. The scenery shifts to a combination grassy zone and pine forest for 0.5 mile. At 7.1 miles you reach the junction with Capulin Canyon. Head toward the canyon to reach a water source and campsite in 1 mile.
Doubling back to continue the loop, you reach the upper section of Alamo Canyon at 7.3 miles. The canyon here is much more treed than it was where you crossed previously, but it still has an impressive, expansive feel. The trail drops to the canyon bottom and a creek crossing at 8.1 miles. A shorter, far less steep ascent takes you back out of the canyon and through a forested section to a more open zone with views across Frijoles Canyon.
There are two junctions close to one another. The first, at 9 miles, is for the rim trail that leads back to the visitor center in 7 miles—this is an option if you want to shorten the hike. The next junction, at 9.2 miles, is a shortcut for hikers coming out of Frijoles Canyon who want to access the rim trail. Stay to the left to reach yet another junction at 9.5 miles, this one marking Alamo Spring and Ponderosa Campground. Continue toward Upper Crossing and the campground, descending into a lush, creek-fed zone with healthy ponderosa pines and a diverse collection of plant life.
At 11 miles you will have made Upper Crossing. Head to the right, downstream along Frijoles Creek in a fantastic canyon environment, to eventually reach Alcove House and the main canyon ruins and visitor center beyond. There are a number of creek crossings along the first 4 miles or so of this stretch, along with some campsites. The canyon expands and contracts through here, with blocky rock walls in alternating colors of orange, red, gray, and tan. There is a trail the whole way, but the setting creates the feeling that you're exploring a wild, unvisited place.
Alcove House is at 15.9 miles. The easy creekside trail continues for another mile or so back to the visitor center and parking area (17.1 miles).
STONE LIONS
A very short distance past the Yapashi Ruins is a sacred site of native peoples. The twin rocks are called the Stone Lions because of their resemblance to reclining lions, which guard the entrance to the dwelling of a supernatural being. It is extremely rare to come across sculptures of this size anywhere among tribes of the Southwest. Even today its spiritual significance is strong enough that Zuni males make journeys of 400 miles here as a rite of passage into manhood.
Ruins Tour
TYPE: Day hike
SEASON: April to November
TOTAL DISTANCE: 2.1 miles
RATING: Easy to moderate
ELEVATION GAIN: 135 feet
LOCATION: Bandelier National Monument, 10 miles south of Los Alamos
MAPS: USGS Frijoles
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GETTING THERE
From Los Alamos, take NM 501 south 4.5 miles to the junction with NM 4. Turn left and travel 5.7 miles east to the entrance to Bandelier. There is an entry fee of $20 per vehicle, which is good for seven days of access. You can also use your National Parks Pass if you have one. From the entry gate the road descends into Frijoles Canyon to reach the parking area and visitor center in 3.1 miles. Be aware that between mid-May and mid-October, from the hours of 9 a.m. to 3 p.m. you must take a shuttle bus to access the park. The shuttle bus leaves from the White Rock Visitor Center. Exceptions include those backpacking overnight. Check the most up-to-date entry information by going to www.nps.gov/band.
THE TRAIL
The Frijoles Canyon pueblos are a chapter in a bigger book of existence, preceded by places like Chaco, Canyon de Chelly, and Mesa Verde and followed by Cochiti, Zuni, Pecos, and Taos. Incredible architectural structures rose in multistory stone buildings like Tyuonyi, the mixed-use alcoves and walled structures in Long House, and the Otowi Ruins in Pueblo Canyon outside the national monument. For 200 years the places along the Ruins Loop made up a town, one that survived by hunting and gathering, along with hand farming—no machines or beasts of burden.
Slip behind the visitor center—it is worth stopping in to grab the "Main Loop Trail Guide" pocket guide—to access the trail, which reaches a junction approximately 0.1 mile down. Head to the right to access the Tyuonyi Pueblo, talus houses, and Long House. Past Long House you have the option of continuing the hike to Alcove House or returning to the visitor center.
At 0.3 mile you reach the first ruins. This is the Tyuonyi Pueblo, recognizable as the footprint of what was, some 600 years ago, a bustling village. There was a circular arrangement of rooms, some sections two or three stories high, built with stone and smoothed by a mud plaster coating. The roof structure for single or multiple levels was made possible by cross beams, or what were known as vigas. The rooms housed people, food supplies, and domesticated animals like turkeys. These were raised primarily for their feathers, which were used for blankets and ceremonial purposes. In the center of the small village were kivas, underground rooms used for council and ceremony.
A short distance beyond here you work your way along a catwalk of sorts with ladder access to one of the talus cliff dwellings. A traditional pine ladder is securely propped up against the rock wall for easy access to a two-chamber alcove/home. These rooms or small caves were hand dug in the soft volcanic canyon wall, although some existed naturally. The interior walls and ceiling of the cave are charred black from the warming and cooking fires of the ancestral Pueblo people, most closely linked to current-day peoples of the Cochiti Pueblo.
A second dwelling close by, known as Cave Kiva, was tall enough for a full-grown man to stand up in—not a concern for the peoples who inhabited this canyon, in that men stood 5 feet, 6 inches on average. The second junction of this short outing is at 0.4 mile for the Frey Trail, which leads to the Juniper Campground. At the next junction Long House is to the right, or there is an option to loop back to the visitor center.
Long House is a fascinating stretch of what can best be described as a cave/alcove and housing complex—an ancient mixed-use residential zone. The evenly spaced and bored round holes in the canyon wall once supported the ends of vigas, which were part of the roof structure for ground dwellings built of stone. The result was multiple residences in line with one another and rising two or three stories high. It is also here that you will find evidence of petroglyphs, and even a preserved example of a pictograph. These works of art were presumably created as a record of everyday life in the canyon, although more sacred representations are not understood fully by historians. Now empty of living humans, this area is said to be inhabited by the spirits—ancestors of today's Pueblo people. However, Long House is still inhabited by living beings in the form of two species of migrating bats that summer in the canyon to birth young and feed on the healthy population of insects. Bandelier National Monument is known to have up to eleven bat species.
At 0.6 mile the trail has curled away from Long House and crossed over Frijoles Creek to reach a trail junction. Heading to the left would bring you back to the visitor center. The trail to the right is the route to Alcove House, formerly known as Ceremonial Cave. You walk along the shaded creek, crossing over a footbridge to reach the approach for Alcove House at 1.1 miles. Be aware that you will gain more than 100 feet of elevation via stone steps and a series of ladders. Anyone afraid of heights or who cannot negotiate a collection of 25-foot ladders should avoid this section of the hike.
For those who are game, it is a fun ascent up the ladders to reach Alcove House. The natural alcove is about 50 feet wide and 30 feet deep. A traditional kiva has been reconstructed here, allowing you to better imagine what it must have been like to be part of a council or ceremony. It is worth noting that, historically, only men would have been allowed inside a kiva. The kiva's construction style and exclusivity can be attributed to a belief in what is termed Sipapu—the great emergence of men into this world from the underground.
On the return trip to the visitor center and parking lot, go past the junction for Long House and follow the creekside trail. It is marked with a series of informational and instructional signs that provide insight into the flora, fauna, and natural history of this area. The total distance of this hike is approximately 2.1 miles.
CLIFF DWELLING IN BANDELIER NATIONAL MONUMENT
TSANKAWI RUINS
Outside the main monument, at the junction of NM 4 and East Jemez Road, is the archeological site Tsankawi. The name is a contraction of a longer Tewa word meaning "village between two canyons at the clump of sharp, round cactus." This short hike, 1.5 miles round trip, exposes you to nearly a dozen kivas. It is an opportunity to walk with the ancients in "foot-carved" trails across the soft volcanic rock and explore cave dwellings. A pueblo with more than 350 rooms, several stories high, was inhabited for about 200 years starting in the early 1400s.
Frijoles Falls
TYPE: Day hike
SEASON: April to November
TOTAL DISTANCE: 3.8 miles
RATING: Moderate
ELEVATION GAIN: 700 feet
LOCATION: Bandelier National Monument, 10 miles south of Los Alamos
MAPS: USGS Frijoles
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GETTING THERE
From Los Alamos take NM 501 south 4.5 miles to the junction with NM 4. Turn left onto NM 4 and travel 5.7 miles to the entrance for Bandelier. There is an entry fee of $20 per vehicle, which is good for seven days of access. You can also use your National Parks Pass if you have one. From the entry gate the road descends into Frijoles Canyon to reach the parking area and visitor center in 3.1 miles. Be aware that between mid-May and mid-October, from the hours of 9 a.m. to 3 p.m., you must take a shuttle bus to access the park. The shuttle bus leaves from the White Rock Visitor Center. Exceptions include those backpacking overnight. Check the most up-to-date entry information by going to www.nps.gov/band.
THE TRAIL
Rain, snow, and wind helped create conditions conducive for alcove formation in the soft rock walls of Frijoles Canyon. Ancestors of the Chacoan people occupied these natural caves, created others, and crafted stone buildings. The Frijoles River helped sustain a thriving Pueblo community here for 200 years. So this hike passes through human history, as well as by unusual rock formations, the two beautiful Frijoles waterfalls, and a canyon bottom with a riverside view of the Rio Grande.
From the main parking area in front of the visitor center, cross over the bridge and turn left toward the backcountry parking lot. You can hop on a trail at this junction, but if you miss it just head toward the backcountry parking lot to pick it up. Check into the visitor center to obtain a walking guidebook for this hike. It includes some excellent information. Periodically along the trail you will see numbered posts that correspond to features of geologic, historic, or natural significance in this canyon area. The trail runs along the creek the entire time, and at the beginning there are also sections with some impressive ponderosa pine trees.
UPPER FRIJOLES FALLS
At 0.5 mile you come upon some interesting rock formations that are pocked with ragged-edged holes and capped with pointed hats. Volcanic eruptions millions of years ago deposited huge amounts of material. Over time, these formations, known as tent rocks, were shaped by constant exposure to the elements. Time and its partners—wind, water, and gravity—will, of course, continue to reduce the size of all these formations. This place is marked as No. 5 in the self-guided tour booklet.
Shortly beyond here the trail runs down to meet the creek and passes through a sanctuary of ponderosa pine, grasses, and rock decorations, exiting via a footbridge over the creek. You will again see a gallery of tent rock formations. At 0.8 mile the trail jumps to the other side of the creek and begins a steady, moderate, but short climb up toward a tall gap in the canyon. In less than 0.2 mile you are 100 feet above the creek, with a thrilling high view of the canyon and the Rio Grande in the distance to the southeast. After two switchbacks, you come face-to-face with 80-foot-high Upper Frijoles Falls. The canyon rock layers are nicely visible here. It appears to be a sandstone layering process, but once again it's really associated with volcanic activity, termed a maar volcano. In fact, you are actually standing at the mouth for this volcano.
The trail winds down to cross the creek. The vegetation is a mix of high plateau species like juniper, yucca, and cactus and a variety of riparian plants like canyon grape, poison ivy, and the rare yellow ladyslipper, along with trees like box elder and cottonwood higher up in the canyon. In large part because of the life force of Frijoles Creek, Bandelier National Monument has a surprising 700-plus plant species.
At 1.3 miles, after passing through a sandy zone shaded with cottonwood trees, you once again have a high-ledge sensation as you wrap down the left side of the canyon with a view of the smaller (40 feet) but equally beautiful Lower Frijoles Falls set among boulders. By 1.6 miles the trail has jumped back and forth over the creek a number of times, through a decently vegetated zone highlighted by horsetail, to reach a gate. Beyond here you walk into an open zone marking the exit from Frijoles Canyon and the entrance to the Rio Grande canyon.
At 1.9 miles you are strolling along the bank of the Rio Grande, which began its nearly 1,900-mile run to the Gulf of Mexico in the San Juan Mountains of southwest Colorado. (It's the fourth longest river in the U.S.) The return hike feels like an entirely new experience as you climb up from a more arid life zone into a rich water-fed zone. You also get to see both waterfalls from the bottom up and view the canyon from a different perspective, even though you are passing through the same exact areas. Two hikes for the price of one, so to speak.
SWISS CHEESE AND BEANS?
The national monument bears the name Bandelier in honor of Southwest anthropological pioneer Adolph F. A. Bandelier. He was born in Switzerland in 1840 and immigrated to America as a child. Forty years later, Bandelier finally set foot in New Mexico and began a frenzied 12-year intellectual investigation of the social systems, customs, and history of the various peoples of this region. Much of his work was dedicated to Frijoles Canyon, which was conserved in part through a novel he wrote entitled The Delight Makers. At its height, the canyon contained a population of 700 people, who subsisted by foraging and hunting and farming corn, squash, and frijoles (Spanish for beans).
Window Rock
TYPE: Day hike
SEASON: April to November
TOTAL DISTANCE: 8 miles
RATING: Easy to moderate
ELEVATION GAIN: 500 feet
LOCATION: Santa Fe National Forest, 12.5 miles north-northwest of Española
MAPS: USGS Medanales and Chili
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GETTING THERE
From Española, take US 285/84 north. Just beyond the 197-mile marker (7.5 miles), US 285 and US 84 split. Stay on US 84, heading toward Abiquiu and Chama. Be on the lookout for the 200-mile marker. Less than 0.2 mile past that marker you will find parking off the east side of the highway. Power lines cross the road near this spot, which is also directly across from an arroyo. There is no official parking area or sign for this hike.
THE TRAIL
Two bands of extruded, upturned igneous volcanic rock break up the scenery of cottonwood-lined sandy arroyos and juniper mesa tops on this hike. In one of the bands, a 12-foot-wide oval opening frames the Jemez foothills to the west and a high plateau desert that includes Black Mesa to the east. Created when an air bubble burst during the lava's cooling off process, Window Rock offers hikers the chance to visit a region of northern New Mexico that is more often seen through a car window.
The loose to firm sandy arroyo bottom moves you away from the highway through sage, chamisa, juniper, and tam-arisk (salt cedar). You come to a fork in the pathway at 0.5 mile. Stay to the right, continuing in the main channel of Arroyo de las Lamitas. Cottonwood and elm also grow in the arroyo bottom, sending a flow of golden color across the sun-bleached landscape in autumn. The cutbanks are fairly tall at points, exposing the extremely vulnerable sandstone to the punishment of the elements. Some of the walls hold clusters of round knobs, and a number of these knobs are covered in lichens. You also may discover fossil imprints, evidence of the ancient sea that submerged most of New Mexico.
At 1.3 miles you can gain a mesa top via a four-wheel-drive pathway or follow the arroyo as it pinches together and reaches a dead end. A short push pops you out on top of the finger mesa. Looming in the near distance to the east is the long Black Mesa, and farther off the 11,000-foot peaks of the Sangre de Cristo Mountains are visible. The mesa top provides a nice overview of the jumbled, various-sized arroyos, including Arroyo del Palacio to the south, and you can see the lower Chama River valley to the north and the north end of the Jemez Mountains to the west.
Around 2.1 miles the trail levels out at a point where the widening mesa has a noticeable blanket of grasses, juniper, and cholla. The mesa then narrows again and the trail drops slightly and bends to the northwest. You climb a rocky section to reach another wide, juniper-dense section of the mesa at 2.8 miles. Slightly farther on you have your first take on Window Rock. A volcanic rock band caps a skinny mesa here, and punched through the wall is an opening about 12 feet wide and 8 feet high. The broad meadow below Window Rock is a reservoir, filling to various depths depending on spring snowmelt and heavy periods of rain. The trail drops gradually over 0.7 mile to reach the reservoir. In the summer months, a large field of sunflowers blooms on the opposite side of the small earthen dam. Follow the road as it curls around the dam and continues to a dead end below Window Rock (4 miles).
About 0.1 mile before the end of the road, you can cut upslope, aiming to move in between the two parallel rock bands. The hillside is steep and loose so be careful. A faint trail leads to a more discernible one once you've gained that spot between the two rock bands. From here the trail leads directly to the Window. There are beautiful views of the surrounding area, including more of the Chama River valley toward Abiquiu.
THIRD LARGEST CITY IN NEW MEXICO
Santa Fe remains one of the three largest communities in New Mexico, but towns like Santa Cruz and Abiquiu are no longer the population giants they were in the 1790s. Abiquiu had a population of 1,300 (third-most in the state at that time), which swelled to 3,500 by the 1820s. The town was sanctioned by the Spanish in 1734 and acted as a significant trading center until the mid-1800s. The quaint town still has a wonderful church in Santo Tomas and retains the character and layout many villages in the region used to have 200 years ago.
Cruces Basin Wilderness
TYPE: Day hike or overnight
SEASON: June to October
TOTAL DISTANCE: Variable
RATING: Moderate to strenuous
ELEVATION GAIN: Variable
LOCATION: Carson National Forest, 50 miles northwest of Taos
MAPS: USGS Toltec
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GETTING THERE
From Taos, travel 4.5 miles north on NM 522 to US 64. Turn left at the light onto US 64 and travel another 27 miles northwest to the town of Tres Piedras and the junction with NM 285. Turn right at the junction, now traveling north on US 285. At 10.6 miles (42.1 miles total) you reach the left turn for FS 87. The recreation sign on FS 87 is for Lagunitas. The road surface is gravel or packed dirt the rest of the way. You remain on FS 87, always in the direction of Lagunitas, through a number of junctions before reaching the intersection with FS 572 at 15.2 miles (57.3 miles total). Turn onto FS 572 and continue 2.6 miles to the parking area and trailhead of sorts for the Cruces Basin Wilderness. When muddy, this road can be difficult to impassable without four-wheel drive.
THE TRAIL
Unbounded by designated trails, this 18,902-acre wilderness is approachable for anything from an easy stroll to a rugged adventure. The jump-off point is on the southeast side of the basin rim, set in the middle of an amazingly diverse environment. Depending on your direction of travel, you may find yourself on the rounded butte between the Osha Creek and Diablo Creek valleys, aimlessly wandering through a fantastic forest of aspen and eventually perching on a boulder that looms above the confluence of Osha, Diablo, and Beaver Creeks. You also can explore along the lush, low creek valleys. Osha Creek begins in a narrow slot canyon with 200-foot-high cliff walls and then runs down into a gentle valley to meet Beaver Creek, which flows northward to the Rio de los Pinos.
Once down in the creek valleys, you have options for gaining the high ground up along Osha Creek or toward the northwest corner of the wilderness onto Toltec Mesa. From the parking area, you can stay high by moving north-northeast on a vast open high-country grass zone that hugs the rim for 2 miles, interrupted by miniature forests of spruce or aspen, before reaching the tight, steep Lobo Creek canyon. This area is teeming with elk and deer, and you may see pronghorn, coyote, and bear. Flowers to identify include daisy, aster, paintbrush, scarlet gilia, fleabane, wild rose, and wild strawberries.
ALL ABOARD!
A significant former lifeline for the mining industry is memorialized today in the wonderful narrow-gauge rail line between Chama, New Mexico, and Antonito, Colorado. Stitching its route along the northern boundary of the Cruces Basin Wilderness, the Cumbres & Toltec Scenic Railroad is a section of the extended rail line that once connected Durango, Colorado, to Denver in the late 1800s. The railway moved minerals like silver and gold that were extracted from the various mining operations along the route. Today the train transports tourists from the middle of June to October. For more information, visit www.cumbrestoltec.com.
ELK ARE COMMON IN THE CRUCES BASIN WILDERNESS
Rim to River Loop
TYPE: Day hike or overnight
SEASON: Year round
TOTAL DISTANCE: 7.4 miles
RATING: Moderate
ELEVATION GAIN: 1,000 feet
LOCATION: Rio Grande del Norte National Monument, 20 miles north of Taos
MAP: USGS Guadalupe Mountain
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GETTING THERE
From Taos drive 24.4 miles via NM 522 to the town of Questa. From the center of Questa it's another 2.5 miles along NM 522 to the junction with NM 378. Turn left on to NM 378. You'll reach a sign for Rio Grande del Norte National Monument at 3.4 miles along NM 378. Drive another 7.5 miles (37.8 miles total) to a fork in the road. Stay to the right. In 0.8 mile you'll reach a right-hand turn for the Big Arsenic Campground. The parking area and trailhead are 0.3 mile (38.9 miles total) down a gravel road. Keep in mind that there is a $3 per vehicle day pass that can be purchased at the designated pay station you come by a few miles before the fork in the road.
THE TRAIL
The Rio Grande del Norte National Monument is a vast expanse of 242,500 acres stretching nearly 40 miles along the Colorado border and terminating to a fine point 50 miles to the south, downstream from the Rio Grande Gorge Bridge—a 1,280 foot steel span, 565 feet above the Rio Grande. Though the ink is barely dry on this new national monument (spring 2013) it contains fantastically old geologic relics in the ancient, warren shield volcanoes like Cerro de la Olla to the layers of lava flows laid down by millions of years of volcanic activity. Cracking open the plateau is the Rio Grande Gorge—part of the massive 166,000 square mile Rio Grande Rift—enticing the curious to stand on its edge to absorb the grand vistas while at the same time coaxing the adventurous to descend into the canyon bottom to the river's edge. The Rim to River Loop does not disappoint when it comes to immersing you in a Rio Grande del Norte experience.
The loop hike begins at the Big Arsenic Trailhead, which sits about 750 feet above the Rio Grande on the eastern rim of the canyon. Take a moment to absorb your surroundings from the river in the canyon below to the open plateau to the Sangre de Cristo mountains to the east and southeast. The Puebloan people called the Rio Grande Posoge, or P'Osoge, meaning "big river."
This first stretch of the Rim to River Loop is all downhill as the trail winds its way through a mix of sage, juniper, and pinyon pine. Though the pinyon pine and juniper are prolific and defining species of the high plateau in northern New Mexico, they are also extremely vulnerable in that they take 250–350 years to 500–1000 years, respectively, to reach maturity. So when you come across a 15–20 foot tall pinyon or juniper in this area you are looking at a living creature that has experienced hundreds of years of history.
By 0.3 mile down you will be out and away from the cliff wall of the upper rim. Along this stretch of the trail, passing through ponderosa pine, are a series of interpretive signs highlighting information about the trees, animals, and geology. This river gorge comes thanks to a continental rift that occurred millions of years ago, where the Earth's crust became thin enough and was eventually pulled apart by surrounding geologic activity to such a degree that valleys formed, mountains rose up, and deep fissures appeared like that of the Rio Grande Gorge. What you will see in the Rio Grande as a river today is one to two million years old, not having cut the gorge that contains it but merely flowing down a path of least resistance caused by the rift.
At 0.7 mile you will reach a trail junction. Heading right you'll reach the Big Arsenic spring which is located a little less than 0.4 mile down slope. Besides the coldwater spring there is a camp area complete with outhouses and camp shelters. There are also some nice lounging rocks along the river if you're interested in a snack break.
The Rim to River Loop heads left at the trail junction in the direction of Little Arsenic spring. We most likely equate arsenic found in rat poison, but the mined, poisonous mineral is also used industrially in the production of semiconductors, pesticides, and treated wood products. Arsenic is used in the mining of gold and has managed to pollute a number of rivers in New Mexico over the years. However, there is nothing toxic about the beautiful setting nor the fresh coldwater springs. The "arsenic" names may have come from a hermit who once lived in the area and informed others that the springs were poisonous to keep people away.
A touch over 0.3 mile from the junction, after an open stroll above the river, you reach a short, rocky set of switchbacks that lead you to another benched area, this one narrower, though, than what you just passed through. About 0.5 mile (1.2 miles total) there is another set of switchbacks that in less than 0.2 mile drops you down right alongside the dark olive green Rio Grande.
The Rio Grande is spawned from the San Juan Mountains of Colorado, where it then flows for nearly 1,900 miles to feed the Gulf of Mexico. However, just as other rivers all over the country, the Rio Grande is under tremendous stress from heavy consumption such that only 20 percent of the natural discharge actually reaches the Gulf.
By 1.8 miles total you'll be crossing over Little Arsenic Spring. Another 0.3 mile down you'll reach the trail junction for the Little Arsenic Rim Trail. Continue straight toward the campground and the La Junta Trail junction. Past the spring the trail goes up and away from the river, leaving that side-by-side experience with the river you'll have enjoyed. The Little Arsenic Campground has shelters, picnic tables, and outhouses.
CONFLUENCE POINT OF THE RIO GRANDE AND RED RIVERS
You are rewarded once again with a riverside stroll at 0.6 mile (2.7 miles total). Less than 0.5 mile farther along, the trail does climb up to a small plateau, and just after cresting you'll reach the trail junction for the La Junta Rim Trail. You'll have hiked approximately 3.2 miles total to this point.
To work your way down to touch the waters for both the Red River and the Rio Grande you will head to your right toward the La Junta campground. The trail moves along and down an ever-sharpening land point, which eventually gives way to the power of the rivers. It is 0.4 mile down to the upper campsite area and another 0.1 mile to the lower campsite area and then an easy scramble down to the confluence. There are some fantastic lounging rocks here to take in the water and surrounding canyon environment—downstream, upstream, and up to the canyon rims.
The Red River is a short river, its headwaters in the nearby Sangre de Cristo Mountains, but by being fed by numerous coldwater springs along the way it has good volume and an optimal temperature for trout. Fall is the perfect time to be down at the confluence to take your shot at a big brown trout as they work their way upstream to spawn.
Whether you make it to the water, choose to spend the night by the rivers, or are ready to head out of the canyon, the trail that gains the canyon rim heads to your left, working its way up the Red River Gorge. Get your legs and lungs ready because the trail climbs up dirt and loose rock from the beginning. At 0.4 mile you reach a natural rock staircase to ascend. Beyond that point the trail continues to work its way beneath the rock conglomerate that is La Junta Point via a couple of switchbacks before snaking along and up canyon.
A solid 0.6 mile up and after 14 switchbacks across a rocky, uneven trail, you will reach a set of metal stairs. The trail is pretty even-surfaced beyond the metal staircase, crossing along a short section of sidewalk and finishing up a man-made rock staircase. The total distance from river bottom to canyon rim is 0.9 mile, which—including the down and back to the confluence—brings the total distance of the loop hike to this point as 5.1 miles.
With the rivers flowing along 800 feet below, you will now be cruising along the rim of the Rio Grande Gorge and across a plateau grassland environment. From the top of the stone stairs you want to connect to the Rincon Loop Trail by heading left and starting along the Rio Bravo Nature Trail that works along the rim. In about 0.3 mile you'll meet up with the Rinconada Loop Trail, which is a wide crushed rock pathway. Continue heading north (to your left).
More of a path than a trail, the Rinconada is easygoing and flat. You'll have occasional vistas back into the Rio Grande river canyon and plenty of takes on the surrounding mountains, including a cluster of peaks to the southeast that includes New Mexico's highest in Wheeler Peak (13,159 feet). In the winter months the loop trail (6.1 miles) serves as a cross-country ski route. By 1.1 miles you will reach the Montoso Campground. Cross the road and continue on the gravel pathway trail.
The trail alternates from being in the open on the plateau to somewhat immersed in the small trees. At 1.4 miles (6.5 miles total) will be the Little Arsenic Campground. Don't go into the campground where it is signed, but bear to your right to stay on the gravel pathway. Another 0.9 mile along (7.4 miles total) you've completed the loop by arriving back at the Big Arsenic trailhead and campground.
IMMIGRANTS, ADAPTORS, SCOURGE, ASSIMILATORS
The story of the Jicarilla Apache is similar to that of other Native American tribes, their chronology ranging from peace and prosperity to near extinction to adopting entirely new ways of living. The Jicarilla arrived in New Mexico sometime in the 1400s and lived by hunting and gathering in the plains and mountainous zones around present-day Cimarron and Taos. Their roving lifestyle was first disrupted by the aggressive Comanche, restricting the Jicarilla more to the mountains. Trade with the Pueblo people taught the Jicarilla how to farm as a supplement to their hunting and gathering. Land grants and the U.S. government's poor treatment not only displaced the Jicarilla, but nearly killed them off. After clashes with the U.S. Army, many of the Jicarilla roamed the area around Chama. The Jicarilla were the last to receive a reservation—a poor agricultural zone around the town of Dulce—in 1887. An outbreak of tuberculosis in 1925 reduced the population to just 625. Through ranching, mining, and timber sales (products of the American westward expansion), the Jicarilla have made a life for themselves through the years on their 850,000-acre reservation. They once freely roamed a land of 9 million acres.
Latir Loop
TYPE: Overnight or Multiday
SEASON: June to early November
TOTAL DISTANCE: 13 miles
RATING: Moderate to strenuous
ELEVATION GAIN: 3,400 feet
LOCATION: Latir Wilderness, 25 miles north of Taos
MAPS: USGS Latir Peak
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GETTING THERE
From Taos, drive north on NM 522. At 0.4 mile, the road, which is signed for Pueblo del Norte, splits; stay to the left. Approximately 4 miles up you reach a stoplight. Continue straight on NM 522 toward Questa. You reach Questa and the junction with NM 38 at 25.4 miles. Turn right at the stoplight onto NM 38, going east toward Red River. In approximately 0.7 mile, turn left onto Kiowa Road, which eventually becomes FS 138. (The turn also is signed for Cabresto Lake.) One mile up, you come to a stop sign at a T-intersection. Turn right, again following the sign for Cabresto Lake. At 2 miles (29.1 miles total), the road surface transitions from pavement to gravel and you arrive at another stop sign. Turn right and continue down FS 138 for 3.4 miles (32.5 total miles) to the sign and turn left for FS 134A to Cabresto Lake. This road is rocky and somewhat steep and narrow. High-clearance, four-wheel-drive vehicles are recommended. In 2.2 miles (34.7 miles total) you reach a good-sized parking lot. The trailhead is located here, and there are picnic tables and outhouses.
THE TRAIL
The Latir Loop offers a hidden lake setting reminiscent of regions in Montana, marvels resembling the Scottish Highlands, and a network of alpine ridges connecting gorgeous basins similar to those found in the Colorado Rockies. Under-visited and undervalued, the Latir Wilderness holds backcountry experiences uniquely its own. Although man-made, Cabresto Lake is a beautiful gateway into the wilderness area. Most visitors drive up to the lake to picnic, fish, and take short walks. Very few venture up to Heart Lake, and even fewer continue beyond onto the Latir Mesa and eventually to the incredible alpine settings of pointed peaks and massive basins.
The trail leaves from the parking area and runs above the west shoreline of the lake. A number of spur trails, however, slip steeply down to lake level. It is 0.5 mile to the opposite end of the lake, a lush marshy zone of tall wavy grasses and other aquatic plants fed by Lake Fork Creek. The trail spends nearly all of the next 4.8 miles to Heart Lake edging along Lake Fork, the first portion through a rich riparian environment. There are a number of wildflowers like asters, cow parsnip, and buttercups as you move north up the drainage, immersed in a mixed forest of fir and aspen. At 0.7 mile, the trail reaches the official entrance into the 20,506-acre Latir Wilderness and a small creek crossing.
VIEWS ALONG LATIR LOOP
You may notice a short shrub with a cluster of shiny red berries growing along here; this is baneberry. The leaves, roots, and especially the berries are poisonous. The vegetation is less lush along this stretch, but no less interesting, with bluebells, scarlet gilia, wild strawberry, and wild raspberry bushes growing out from rock sections along the trail. And, as mushroom hunters know, in spring and after periods of heavy rain there are fungal treasures to be found along the forest floor.
At 1.8 miles, the trail enters a slightly more open zone that offers views of the southeast end of Latir Mesa. It is a nice reprieve from the tree cover. On your topographic map, the ridgeline and mountain system of Latir Mesa, Latir Peak, and Cabresto Peak resemble an amoebic subalpine and alpine mass. The Bull Creek Trail junction and the confluence of Bull Creek and Lake Fork come at 2.5 miles. Continue toward Heart Lake, crossing Lake Fork.
The trail starts a steady climb from here, cruising along the creek and taking occasional side trips upslope. At 4.1 miles, you reach the junction with the Baldy Mountain Trail. Baldy Mountain is a 3-mile journey that pushes steeply through the forest before breaking out above tree line. There are great views from the summit of this 12,046-foot peak.
From the junction it is 0.7 mile (4.8 miles total) to Heart Lake. The trail climbs somewhat steeply through the trees and then enters a wide grassy swath, where it parallels the outlet for Heart Lake. This is also the first point along our tour of Latir, where much larger views open up to blocky, grass-topped Latir Mesa beyond the lake, highpoints to the northwest, and Baldy Peak rising above a thick collar of trees. The lake is surrounded by trees and ringed by grasses and wildflowers like cinquefoil. There are campsites on the south end of the lake, and this quiet setting offers a very nice spot to spend the night.
Just before you reach the lake there is a sign to the left for Latir Mesa. After visiting the lake, you will backtrack briefly to this trail to continue the loop hike. The trail passes some large quarry-like piles of rock and takes a steep course through the trees before reaching the bottom end of a basin at 5.2 miles. There is a jumbled archipelago of rock and grass islands the whole way up to the basin rim and the edge of the Latir Mesa. The grassy zones are also home to daisy, paintbrush, and shrubby cinquefoil, providing a nice distraction to the steep, serpentine climb along with a growing overview of Heart Lake and the entire surrounding area. You reach the mesa at 5.6 miles.
The Latir Mesa setting is unique to New Mexico, especially if you arrive when a misty fog has settled in. The broad, slightly rounded mesa dead-ends to the southeast, but you can follow the route north and northwest to even more spectacular areas. The mesa is a mix of thick clumpy grasses, large and small rocks, and a variety of hardy-yet-delicate wildflowers.
This is the most difficult section of the hike to follow. The trail is often swallowed up by the grasses, and only by the aid of rock cairns are you able to find the way easily. A good topographic map and compass are a must. It also helps to know that you should stay more toward the crest of the mesa and follow along as it makes a gentle bend to the northwest. It then connects with a short rockslide section that leads to a sharp, narrow saddle between two beautiful basins.
HIGHLINE JUNCTION IN THE LATIR WILDERNESS
At 6.2 miles you reach a highpoint and then move down to a more discernible trail that crosses a rockslide at 6.6 miles. From the saddle, there are perfect views into the bottom of each basin and to the sharper highpoint of Virsylvia Peak (12,594 feet) and the sweeping alpine landscape. Both basins below you are decorated with small tarns, and easy slopes provide access to these and possible backcountry campsites. To the south, you can see the ski runs of Red River and portions of the Columbine-Hondo Wilderness.
Below Latir Peak, which is less than 0.5 mile to the north, lies a string of lakes arranged like polished stones on a silver bracelet. You can reach the Latir Lakes on a trail originating from the northeast, or by moving cross country below Latir Peak. From the saddle on which you're currently standing, the incredible highline run continues as the trail curls around the north side of a blocky rock outcropping to reach another saddle of sorts. There is a slow right-hand swing into a gentle, downsloping gully and a cross-slope run. The way continues to be marked by rock cairns and stretches of recognizable game-like trails.
From the second saddle you reach a cairn at 7.3 miles. Look downslope or down the gully to spot the next cairn and the route. There is a signed junction for Rito del Medo at approximately 7.6 miles. Continue cross-slope just above the tree line. The trail here is much more visible, and it makes an easy, beautiful run to the junction with the Bull Creek Trail and Cabresto Peak at 7.9 miles. Stop a moment to take it all in because from here you leave the phenomenal and glorious highline exposure and sink back into the sights, sounds, and rhythms of the forest.
The trail drops down a couloir and reaches a small campsite and the beginnings of Bull Creek at 8.2 miles. It makes a very nice run through the forest with a number of creek crossings. Lush riparian zones host tall yellow and purple flowers growing en masse. At 9.9 miles, you enter a small clearing with views of a couple rocky highpoints nearby. Shortly thereafter you cross over Bull Creek. The trail continues its pleasant slide downslope, passing close to the confluence of Lagunitas and Bull Creeks before crossing over Bull to reach the junction with the Heart Lake Trail at 10.5 miles. From here, retrace your steps back to the trailhead and parking area to complete the 13-mile hike.
WILD NEW MEXICO
As it stands today, New Mexico has 25 wilderness areas totaling some 1.6 million acres, which is only 2 percent of the land. The Gila Wilderness in the southwest corner of the state is the largest at 558,065 acres. The smallest is Dome Wilderness at 5,200 acres. The Pecos Wilderness is the largest in northern New Mexico at 222,673 acres. There are more than 57 areas classified as wilderness study areas across the state. Currently five of these are up for consideration by Congress for wilderness status.
Placer Creek to Gold Hill Loop
TYPE: Overnight
SEASON: June to October
TOTAL DISTANCE: 16 miles
RATING: Moderate to strenuous
ELEVATION GAIN: 5,000 feet
LOCATION: Carson National Forest, 14 miles north of Taos
MAPS: USGS Questa and Red River
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GETTING THERE
From Taos, take NM 522 approximately 25.5 miles north to the town of Questa. The junction for NM 38 is at the stoplight in Questa. Turn right, or east, toward Red River. Look for Columbine Campground on the right 5.2 miles (27.7 miles total) down NM 38. The campground road circles around to a small parking lot beside the trailhead. If you are coming from Red River, it is approximately 7 miles to the campground.
THE TRAIL
Gold Hill can be seen as the shorter, younger, and less popular brother to Wheeler Peak (Hike 34). But a down-the-boulevard view into the Williams Lake basin, vistas over the Cimarron Range, and close-up takes into the Latir Wilderness and beyond allow Gold Hill to compete with its older sibling any day of week. When you add in the approach up Placer Creek into the secluded Willow Creek basin and the slide across the grassy ridgebacks leading to the summit of Gold Hill, this experience may even exceed Wheeler's adventure and aesthetics.
The hike begins on Columbine Creek Trail 71, which runs along the creek of the same name. It crosses over three times via arcing footbridges on its way up a wide drainage toward the central ridgeline that runs through the 30,500-acre Columbine-Hondo Wilderness. Highpoints here include Lobo Peak (12,115 feet) and nearly a half-dozen others in the 12,000-foot range.
The highest protection for a special area and the creatures that inhabit it would be a refuge that restricts all human entry. The next level is a designated wilderness area, which allows low-impact human access but restricts potentially destructive practices like logging, mining, and, in most cases, grazing. Wilderness study areas like the one through which you are hiking can be thought of as leading candidates for wilderness area status. There is a wide range of benefits in allowing nature to maintain its own balance. And restricting resource extraction operations and mechanized travel in these special places also keeps new roads from being built.
You don't actually reach the central ridgeline on this hike, as you deviate up a different creek drainage to the east far before then. It is definitely an adventure, not a crazy one, but surely different from the maintained feel of more popular trails. You will hike up along the overgrown but very manageable Placer Creek Trail into a brilliant two-tiered basin that leads farther on to a fantastic highline run up to the summit of Gold Hill.
The first 1 mile along Columbine Creek is an open zone with aspen and fir trees and a mix of wildflowers that includes the area's namesake, the Colorado columbine. The large bloom has five pointy petals circling five cylinders, painted in a soft bluish-purple blended with ivory white. Columbine typically blooms by July. The first skip over the creek comes at 0.4 mile. Apparently wanting to show off each side of the creek equally, the trail makes another crossing at 0.6 mile and then at 0.9 mile–thimbleberry and wild raspberry bushes line portions of the trail along here—before reaching the junction with the Columbine-Twinning National Recreation Trail at 1.5 miles. This will be the return trail for our hike.
So even though the sign indicates that Gold Hill is to the left, continue straight along the Columbine Creek Trail toward Lobo Peak. You cross the creek again shortly past the junction and continue through similar riparian vegetation. At 3 miles you reach the Placer Creek junction. Head left, crossing Columbine Creek yet again, to begin working your way up this rarely visited drainage.
The trail can be overgrown, but it is quite easy to navigate, with numerous crossings of Placer Creek and a jungle path through a lush riparian zone and aspen groves. At 4.3 miles the trail makes a few slightly wider swings away from the creek and starts to angle more steeply uphill in a more open setting. At 4.8 miles, you reach the junction of Placer Creek and Willow Fork (also signed for Gold Hill). Take the Willow Creek Trail, which heads to the right, making one last crossing of Placer Creek. At the junction or just a little beyond along the Willow Fork, you will find a nice clearing in which to set up camp if you so desire.
A beautiful grove of aspen appears at 5.4 miles, and the forest floor is carpeted with thick grass and wildflowers. The trail is consumed somewhat by the setting so make sure you just maintain your course, not gaining or losing elevation, for approximately 50 yards before it shows itself again. The section of trail from the last junction has become more strenuous. In another 0.2 mile (5.6 miles total) you reach a similar aspen zone where the trail again can be difficult to follow. This time you cross an expanse of about 80 yards to pick up the trail.
At 5.9 miles you enter a small meadow where you must move through the wide-spaced trees near the edge in order to stay on the trail. At 6.3 miles you enter the bottom end of a fantastic basin. The headwaters of Willow Creek carve a line through this open grass and wildflower zone. Trees are thickly gathered along the south wall of the basin, as well as leading up to the ridge. There are great views of Flag Mountain (11,946 feet) to the west. This is an ideal location for an overnight campsite.
From here to the top of the basin, the route can be a little tricky, but don't be deterred. As you always should, just make sure to carry a good topographic map and compass. Move up through the lower basin along the creek, following a faint trail. If you lose the trail, just remember to follow the main creek more to the north. This leads you to the upper basin, which is decorated with large mounds of earth, at 6.8 miles. A side drainage cuts along the gentler slope to the left, and a trail takes you up toward the north rim of the basin. Once you're on the backbone of the ridge/rim, a trail leads to a cairn and post marking the highpoint and a picture-perfect view of Gold Hill to the east.
GOLD HILL LOOMING ABOVE THE TREE LINE
Move more toward the east to reach a trail (7.4 miles) that straddles the basin you just climbed out of and the beautiful Placer Fork basin set 500 feet below to the east. After climbing a ramp-like section of trail, you reach the highpoint on the east side of the basin. A cairn and fenceline mark the junction to Gold Hill at 7.8 miles. Be aware that the next 2 miles or so of this hike are above tree line, which can leave you exposed to lightning. Always watch for thunderstorms. Looking east, Gold Hill is the highest point. The trail that leads to Gold Hill runs down the near slope. Covering a distance of 0.4 mile (8.2 miles total), the trail reaches an area of patchy trees. It's not hard to lose the trail through here, so just work your way up the middle of this section. Once on top you will easily gain the trail again as it runs close to the Placer Fork basin rim.
Downslope a little to the southwest, a post marks the trail junction for Goose Lake and Bull-of-the-Woods Pasture. Goose Lake is an option for an overnight campsite, but be aware that an ATV road from Red River accesses this lake. To continue up to Gold Hill, angle more to the left to intersect the trail just before it crosses a rocky section. There are brilliant vistas of Taos Ski Valley through here, including the eastern ridgeline that runs up to the summit of Mount Walter (13,141 feet) and Wheeler Peak (13,161 feet) beyond. By 8.9 miles, you meet up with the Columbine-Twining National Recreation Trail. The trail moves up the west side of Gold Hill, with continually stunning views of the surrounding area, before slinking onto its east side for the last 0.1 mile to the summit. The views don't cease—the Taos Ski Valley in full splendor, the Cimarron Range to the east, the Latir Wilderness and southern end of the Sangre de Cristos to the north, and the high plateau cut by the Rio Grande. Take a rest and enjoy the scenery.
After winding down a rockier slope for 0.4 mile, the trail moves across a grassier ridgeline dotted with wildflowers. At approximately 9.7 miles, it bends to the left just above a patch of trees that could offer protection from a fast-moving thunderstorm. The trail stays out in the open for another 0.3 mile (10 miles total) before reentering the trees. At 10.5 miles, you reach the junction for the Red River Trail, which continues straight, and the Columbine-Twining Trail, which heads left. Continuing on the Columbine-Twining Trail, you will come onto an open slope that is the finger ridge dividing the Deer Creek and Placer Creek basins at 11 miles.
The trail winds its way down a series of long, looping switchbacks into the Deer Creek drainage. It passes through pine, aspen, and fir trees and eventually meets the creek around the 13.7-mile mark. It is also here that you cross over the creek for an easy 0.5-mile stretch to the junction with the Columbine Trail and the return to the trailhead (15.7 miles).
SEEING GOLD IN RED RIVER
The Red River valley from the town of Red River to Elizabethtown made a hard run at establishing mining operations starting in the mid-1890s. Even with successes, most activity came to a screeching halt within 25 years in large part because of the slow-arriving and poorly connected railroad. There were active claims in both the Placer and Willow Creek drainages, but the value of gold and silver extracted was minimal. The "gold" today in this area comes by way of tourists visiting in the summer to hike and run four-wheelers and in the winter to ski the Red River Ski & Ride Area—its first incarnations coming in 1940.
Wheeler Peak
TYPE: Day hike or overnight
SEASON: June to October
TOTAL DISTANCE: 13.2 miles
RATING: Moderate
ELEVATION GAIN: 3,800 feet
LOCATION: Wheeler Peak Wilderness, 12 miles north-northeast of Taos
MAPS: USGS Wheeler Peak
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GETTING THERE
From Taos, drive north on NM 522 toward Taos Ski Valley. Approximately 0.4 mile along (NM 522 is also signed for Pueblo del Norte), the road forks. The right fork leads to the Taos Pueblo, but you should stay to the left. At 4 miles, you turn right at a stoplight. The signs are for Arroyo Seco and Taos Ski Valley. You are now traveling on NM 150. At 18.6 miles, you reach the large parking area for Taos Ski Valley. Stay along the uppermost route, but don't worry if you miss it because each parking level meets up at the same point on the edge of the ski village. Travel another 0.3 mile to a Forest Service sign for the Wheeler Peak Wilderness, which sits next to a small picnic area. Park anywhere nearby.
THE TRAIL
The route to New Mexico's highest point, Wheeler Peak, takes you from a forested stream with an ensemble of wildflowers to a spectacular ridgeline that runs through subalpine and alpine areas—home to a healthy population of Rocky Mountain bighorn sheep. Of course, the grandest prize of all is eventually setting foot on Wheeler's summit at 13,161 feet. You will be rewarded with more amazing vistas than you can digest in a single day.
To start the journey, cross through the small picnic area and over Twining Road onto a fairly steep trail that leads to Bull-of-the-Woods Pasture in 2.1 miles, with 1,600 feet of elevation gain. Steep it is, but you will also be "steeped" in aspen trees briefly before the forest mix is quickly dominated by fir trees. The trail braids some along here, with markers indicating routes for hikers or horsemen. An unnamed creek drops through here, providing nourishment for paintbrush, sunflowers, and purple aster. You cross over the creek at 0.8 mile and then reach the junction with the Long Canyon Trail around the 1-mile mark. Shortly thereafter, you are on more of a road, which leads to the Bull-of-the-Woods Pasture. You remain near the creek the entire time, and views begin to open up the closer you get to the pasture at 2.1 miles.
THE SADDLE BETWEEN WHEELER PEAK AND SIMPSON PEAK
The pasture area, or wet meadow, lies straight ahead, but the continuation of the hike to Wheeler Peak heads right following the sign for La Cal Basin. You continue to climb for the next 2 miles, passing through sections of open space that tease you with marvelous views down the turning and twisting Taos Valley and out to the high plateau around Taos. You can also see Tusas Ridge across the valley and Gold Hill (12,711 feet), the prominent bare rounded mountain nearby to the north-northwest.
At 2.4 miles you reach a T-junction. Head to the right, continuing to ascend on a milder course. This point offers a beautiful overlook of the Middle and West Fork Red River drainages and of the western slope of the Cimarron Range to the east, standing tall over the Eagle Nest Valley. You reach a possible point of confusion around 2.6 miles, as a road-like trail cuts off to the left. Stay to the right to continue toward Wheeler Peak.
Another T-junction and grand vista arrive at the top of a short, steep section at the 3.1-mile mark. Head right again at the intersection, this time passing through a cattle fence a short distance down. You will be on more of a true hiker's trail the rest of the way. The path winds through the trees here before beginning the first of two spectacular open runs to Wheeler. This forest is home to deer and elk, but up in the open ridge country, there is a high likelihood of spotting Rocky Mountain bighorn sheep.
After making the rigorous ascent to this amazing zone, you are officially in the Wheeler Peak Wilderness at 3.8 miles. A short distance on, you begin a long, looping descent down into the oasis of La Cal Basin (4.2 miles). The bottom end of the basin holds a thick collection of trees and a vibrant riparian ecosystem, provided by the headwaters of the Middle Fork Red River. Above here there is a sweeping open area of grassy, rocky terrain that leads up to a long arc of ridgelines. There are tent sites and water in La Cal Basin, making it the ideal camping site for an overnighter on the approach to Wheeler Peak.
From here you climb steeply up a series of switchbacks that begin in the trees and break out into the open at 4.6 miles. You are now ascending the big basin you originally viewed as you entered the wilderness area. Bighorn sheep, marmots, and delicate wildflowers like buttercups and bistort dot the landscape. At 5.9 miles, you are on a short saddle along the ridgeline where you can see Horseshoe Lake sitting some 950 vertical feet below.
You are now on the final run to Wheeler Peak. The trail continues to climb, but in a much more relaxed way than the stretch out of La Cal Basin. In approximately 0.4 mile you reach Mount Walter (13,141 feet), marked by a sign. After a dip down and then up over another 0.3 miles (6.6 miles total) along a narrow section of the ridge, you will be standing on the blocky summit of Wheeler Peak. It is worth noting that you will pass a trail coming up the western slope between Mount Walter and Wheeler Peak. It originates at Williams Lake, visible far below, and in the event of a thunderstorm or other inclement weather, this is a good option for reaching lower, tree-covered terrain quickly.
As you would expect, the vistas are tremendous. A 360-degree spin starting to the south fills your eyes with Simpson Peak (12,976 feet), seemingly just an arm's distance away, and the Truchas Peaks (over 13,000 feet) 37 miles away in the Pecos Wilderness. Next you can see the high plateau beyond Taos and the Rio Grande canyon to the west, Gold Hill (12,711 feet) in the near distance, and the faint outline of the tall peaks of southern Colorado's Sangre de Cristo Range to the north, and the Cimarron Range to the east.
Enjoy the solitude of the experience, especially if you summit early in the morning. The marmots will keep you company, perhaps a little too close by as they've lost their natural suspicion of people thanks to being fed by too many previous visitors. Don't forget to sign the register in the big metal cylinder embedded in the rock monument. If you want to summit Simpson Peak, follow the trail that runs off Wheeler down to the narrow saddle between the two peaks and then back up (0.8 mile).
HORSESHOES ANYONE?
The route to Horseshoe Lake is a beautiful slopeside glide, with magenta paintbrush, cinquefoil, bighorn sheep, and mountain vistas. Although it may be a bit much to add to a day hike to Wheeler, Horseshoe Basin makes another good overnight option besides La Cal Basin. Campsites are located just down the trail past the lake and on the benched area above the lake. If you look over your maps, you will see that a one-way shuttle hike is possible if you leave a vehicle at either the West or East Fork Red River trailheads.
Lost Lake to Horseshoe Lake
TYPE: Overnight
SEASON: June to October
TOTAL DISTANCE: 14.5 miles
RATING: Moderate
ELEVATION GAIN: 2,400 feet
LOCATION: Wheeler Peak Wilderness, 4 miles south of Red River
MAPS: USGS Wheeler Peak
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GETTING THERE
From Taos, drive north on NM 522. At 0.4 mile, the road, which is signed for Pueblo del Norte, splits; stay to the left. Approximately 4 miles up you reach a stoplight. Continue straight on NM 522 toward Questa. You reach the town of Questa and the junction with NM 38 at 25.4 miles. Turn right at the stoplight onto NM 38, heading east toward Red River. Drive through the town of Red River (37.9 miles) then bear right, south, onto NM 578, which is also FS 58. (NM 38 continues on the left fork.) Drive 8.3 miles down FS 58 to the road's end at the parking area and West Fork trailhead (46.2 miles total).
THE TRAIL
Red River was a true frontier town, founded on the prospect of wealth. As with so many other towns scattered across the West in the mid to late 1800s, the shimmering mirage of minerals like silver and gold lured prospectors into the region around the Columbine-Hondo, Latir, and Wheeler Peak wilderness areas. The dreams faded quickly due to the small amounts of minerals and the expense of extracting them, which left behind wilderness for wilderness' sake. The shimmer still exists today, however, as people are lured here for the stellar views across the Moreno Valley, the access to two fantastic lakes in Lost and Horseshoe, and the chance to push across the broad eastern slope of Wheeler Peak while enjoying the incredible scenery in every direction from a perch at more than 13,000 feet.
Even though you start from the West Fork trailhead, you will spend more of your time along Middle Fork Creek, which drops from Middle Fork Lake (a 2-mile round trip if you choose to detour here). The valleys are tight and tall as you walk the 0.2 mile to the bridge crossing of the West Fork and begin the steep ascent up the thickly forested Middle Fork drainage. You twist up six switchbacks on the east side of the drainage along an old road before reaching a trail junction at 1.3 miles.
BEAUTIFUL LOST LAKE
Tucked into a nook in the ridgeline to the west, Middle Fork Lake is accessed by continuing straight at the junction. The route to Lost Lake and Horseshoe Lake follows a switchback ascent up the east side of the creek drainage along a hiker's trail. At 2.7 miles, the trail begins to make a slow bend from east to south. To the west, you have nice views of Bull-of-the-Woods Mountain (11,514 feet), Frazer Mountain (12,163 feet) farther to the south, and other features of the first section of the highline run for Wheeler Peak (accessed from the Taos Ski Valley).
The trees are spaced wider apart through here as you continue to gain elevation, although much more gradually. The trail follows a finger ridge that eventually leads along the bottom end of a steep-walled mountain jetty of sorts attached to the Wheeler Peak and Mount Walter ridgeline. This also forms the eastern wall of the La Cal Basin. Open rockslide slopes are colored in yellow groundsel and out below the run you have views over the wide Moreno Valley, which is edged by the Cimarron Range rising some 4,000 feet above the valley floor.
The trail alternates between tree cover and open slope, first to the East Fork Trail junction (4.2 miles) and then along the short run up to Lost Lake at 4.7 miles. You officially enter the Wheeler Peak Wilderness shortly before the lake. Lost is a small lake horseshoed by trees. Its western shoreline runs into a rocky slope dropping from a 12,400-foot ridgeline. There are plenty of campsites on the north and south sides of the lake. Just be mindful to not trample the vegetation.
The journey connecting Lost Lake to Horseshoe Lake is a short one. You gain about 600 vertical feet in 1 mile, mainly in the trees, and then tackle a couple of switchbacks. There are tent sites at the top of the last switchback, just before you step onto a huge open slope where Horseshoe Lake is the blue gem in a world of green (5.7 miles). The trail crosses over the lake's outlet and works up the rocky southeast corner of the basin to a benched area stippled with trees. This makes for an excellent high camp with views of Wheeler Peak as well as the protection of the trees. In 2006, a helicopter crash-landed on this bench during a search-and-rescue operation (pilot and passengers survived).
This area leads into a ridgeback ascent and then a beautiful, long arcing trail that bisects the east slope of Wheeler Peak. It aims for the mountain's south shoulder and the final approach to the summit. The slope, which forms one wall of another giant basin, is a collection of thick clumps of green grasses, flowering shrubs, and a virtual garden of wildflowers like lupine, paintbrush, cinquefoil, and many other vibrant varieties.
Two tarns are set in the bottom of the basin. And there is the possibility of meeting up with a healthy population of Rocky Mountain bighorn sheep as you make your cross-slope journey. It is about 0.7 mile from Horseshoe Lake to the ridgeback that leads to the broad slope. In another 0.8 mile, you move onto another ridgeline, this one connecting Simpson Peak and Wheeler Peak. Heading north (left), you finish the last 0.4 mile to the summit of Wheeler Peak. Here you can see another amazing basin and high-peak overlook to the west, along with a whole collection of other visual treats in the Truchas Peaks to the south and the Gold Hill area to the north. This is indeed a marvelous outing. The climb up and back from Wheeler Peak adds 3.8 miles to the hiking distance, making the total 15.2 miles.
EAST FORK RED RIVER ALTERNATIVE
This trail brings you by an old relic of the mining days in the Elizabethtown Ditch, which carried water from the mountains out across the Moreno Valley (a distance of 41 miles). The setting is similar to the West Fork approach except that the trail more closely shadows the creek drainage (the East Fork this time). This trail adds about 1.5 miles of total distance to the hike to Horseshoe Lake.
Williams Lake
TYPE: Day hike
SEASON: June to October
TOTAL DISTANCE: 4.8 miles
RATING: Moderate
ELEVATION GAIN: 750 feet
LOCATION: Wheeler Peak Wilderness, 12 miles north-northeast of Taos
MAPS: USGS Wheeler Peak
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GETTING THERE
From Taos, drive north on NM 522 toward Taos Ski Valley. Approximately 0.4 mile along (NM 522 is also signed for Pueblo del Norte), the road forks. The right fork leads to the Taos Pueblo, but you need to stay to the left. At 4 miles, turn right at a stoplight. The signs are for Arroyo Seco and Taos Ski Valley. You now are traveling on NM 150. At 18.6 miles, you reach the large parking area for Taos Ski Valley. Stay along the uppermost route, and don't worry if you miss it as each parking level meets up at the same point on the edge of the ski village. Travel another 0.3 mile to a Forest Service sign for the Wheeler Peak Wilderness, which sits next to a small picnic area. Take the road that cuts behind this spot, signed as Twining Road. At 0.9 mile (19.8 miles total) up Twining Road, you bear to the left, following the sign for Williams Lake. The road continues to wind and climb steeply to the turn for the Williams Lake parking area. At this point, the 20.7-mile mark, you are officially on Machine Road. Turn onto Deer Lane to access the parking area. A well-placed sign indicates the turn, so there is no need to be too concerned with road names.
THE TRAIL
This hike is New Mexico's equivalent to treks in the Alps of Austria or Italy. It is an absolutely beautiful setting among majestic peaks and rocky ridgelines, and contained in this dramatic high valley are a collection of homes and a Tyrolean-style restaurant. It has that European balance between civilization and wild nature. This short, pleasant journey leads to a neck-craning view of Wheeler Peak (13,161 feet), Lake Fork Peak (12,881 feet), and other highpoints along the sharp ridgeline that walls in a two-tiered cirque. The upper section of the basin is decorated with islands of hearty alpine grasses occasionally accented with stunted spruce trees. The lower level features a waterfall, wildflowers, campsites, and small, bean-shaped Williams Lake.
WILLIAMS LAKE
From the parking area, you follow a road around the bottom end of the farthest chair lift up the ski valley. You then pass by the restaurant before splitting off on a wide, wildflower-lined path that draws you more fully into the rhythms of the Wheeler Peak Wilderness (0.5 mile). In fact, by 1.1 mile, you already have passed a sign for Williams Lake and officially entered the wilderness area. The trail moves through trees and past the bottom end of avalanche chutes replete with a gorgeous collection of flowering shrubs, aster, daisy, and other yellow, pink, red, and purple blooms. The Wheeler Peak Wilderness was designated as part of the pioneering 1964 Wilderness Act.
By 1.8 miles your view of the peaks guarding the valley has shifted from Fraser Peak (12,663 feet) to the east to the ridgeline off an unnamed 12,000-foot peak to the west. After a short corkscrew ascent, the trail curls around the edge of a large field of lichen-covered boulders and reaches a crest of sorts at 2.3 miles—the gateway into the Williams Lake basin. You also have growing views of the wonderful surrounding landscape up and down valley.
The small, shallow lake is nestled against the foot of the steep western slope of Wheeler Peak, New Mexico's highest point. The tall basin wall continues all the way around from Wheeler, touching distinctive highpoints in Simpson Peak (12,881 feet) and Lake Fork Peak. The basin has a big, pleasant feel. In addition to the lake, there are rockslides holding wild raspberry bushes, collections of trees, and a waterfall a short distance beyond the lake. The benched area, or upper basin, includes small patches of alpine grasses, wildflowers like rose crown, and stunted spruce trees set just below the land of rock. A decent trail leads to a view of the small falls, which is 0.3 mile from the lake, and continues up into a portion of the upper basin. Campsites are available upslope to the west of the lake, set between the rocks and stands of trees.
Ambitious adventurers will discover a trail starting off the north end of the lake, where the outlet is located. It climbs steeply up a slope of loose rock and short grass to the ridgeline that leads to Wheeler Peak. This outing is a very pleasant day trip that could also turn into an enjoyable overnight experience.
THE FOUR W'S
The Wheeler Peak Wilderness, encompassing 19,150 acres, and Wheeler Peak are named for U.S. Army Major George M. Wheeler, who surveyed the vast majority of the state of New Mexico. Harold D. Walter's name lives on in Mount Walter, the highpoint just north of Wheeler Peak. It was named in honor of Walter's passion for this place, and because he was the catalyst for confirming that Wheeler Peak is indeed the state's highest point. The origin of the name for Williams Lake is unclear.
San Leonardo Lakes
TYPE: Day hike or overnight
SEASON: June to October
TOTAL DISTANCE: 7 miles
RATING: Moderate
ELEVATION GAIN: 2,000 feet
LOCATION: Pecos Wilderness, 18 miles south of Taos
MAPS: USGS El Valle
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GETTING THERE
From Taos, take NM 68 south for 3 miles to the junction with NM 518. Continue on NM 518 south toward Peñasco. In 17 miles (20 miles total), you reach the junction with NM 75; turn right, heading west. Drive through the town of Peñasco to reach the junction with NM 76 at 27.4 miles total. Turn left on NM 76 toward Las Trampas and Truchas. At 33.3 miles, the road makes a downhill bend to the right about a mile out of Las Trampas. The right turn for FS 207 is located at the elbow of the turn, marked with a sign. There is a short stretch of pavement before the road changes to packed dirt and gravel. At 41.2 miles (7.9 miles on FS 207) you reach the junction with FS 639. A sign indicates that the Trampas Lakes are straight ahead and that the San Leonardo Lakes are to the right. The road you want is just past this sign. Be advised that this last section of road to the trailhead is best accessed by high-clearance or four-wheel-drive vehicles. You must cross the river, and depending on the time of year, the water level may be fairly high. Use discretion. The road is rough and will be more challenging when wet. The parking area and trailhead are on your left at a bend in the road at 43.3 miles total.
THE TRAIL
The string of watery jewels begins with the San Leonardo Lakes on the northwest edge of the Pecos Wilderness. The quaint Trampas Lakes run along a similar creek valley, and they are followed by a great hike along the Middle Fork Rio Santa Barbara to the tiny, off-trail Santa Barbara Lakes. Finally come the Rio La Casa Lakes, set in a big, open basin. Two lakes make up the San Leonardo cirque, and with a short scramble above the upper lake you can pass a drowsy afternoon admiring the rugged basin walls, the shimmer of water below, and views out over the Rio Grande valley before a snooze among a blanket of subalpine wildflowers.
A former road paralleling the Rio San Leonardo kicks off the hike. It passes through the trees and across open grassy areas decorated with daisy, aster, and mountain bluebell during various parts of the summer. Also keep your eye out for shooting star and wild strawberry in this early stage of the hike. By 0.6 mile the trail is more immersed in the trees, gaining elevation at a moderate rate and still following the stream. At 0.9 mile you pass through a gate, and 0.1 mile farther, just after a creek crossing, you are officially in the Pecos Wilderness. Grazing is still permissible in many wilderness areas, the Pecos included, and on other federal lands. Groups like the Wild Earth Guardians (www.wildearthguardians.org) are working to limit livestock grazing in order to reestablish the natural balance of the various ecosystems in these areas.
The next 1.2 miles are very pleasant as the trail winds along the creek. Fairy slippers are hidden in the grass, patches of kinnikinnick cover the ground, and logjams create small cascades. The creek also provides sustenance for water-loving plants, such as sedge and globeflower, which grow along its banks. At 2.2 miles, after another creek crossing, the trail ascends more steeply. By 2.8 miles, the trail relents a bit as it enters an open area beneath a rocky slope. If you can take your eyes off the nice views of nearby craggy rock outcroppings, you may notice that the creek has disappeared underground.
In what feels like a quick 3.5 miles, you enter the bottom end of the basin that holds the lower and upper San Leonardo Lakes. The basin is steep walled, and its loose, craggy rock is laced with fingers of green in the grasses and spruce trees that push up from the lakeshores. Sprinkled between the clumps of grass is a rich variety of wildflowers. This place has a remote feel, yet doesn't require a huge effort to reach. Plus, the lakes see very few visitors, so your chances for solitude are quite good. Campsites are located between the two lakes and at the north end of the lower lake. Adventurous hikers can scramble up the basin and down into the Trampas Lakes basin or follow the ridgeline to the summits of the Truchas Peaks.
LAS TRAMPAS: A FRONTIER TOWN
Established in 1751, this small, enduring village was founded by a group of Hispanic families. Despite the decades of threats from raiding Comanches, the harsh weather of summer and winter, and eventually the land-grab mentality of early Anglo-Americans, the town has survived. The number of current residents is far fewer than it was 150 years ago and the fortress-style arrangement of houses is becoming less discernible, as are the fallow fields of the little valley. What has survived is the San Jose de Gracia Church, which is well worth a visit. Built in the 1770s, it has been extremely well-maintained inside and out, and it contains some beautiful wood carvings and paintings.
Truchas Peak (West)
TYPE: Overnight or multiday
SEASON: Late June to October
TOTAL DISTANCE: 19 miles
RATING: Moderate to strenuous
ELEVATION GAIN: 4,000 feet
LOCATION: Pecos Wilderness, 25 miles south of Taos
MAPS: USGS Sierra Mosca and Truchas Peak
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GETTING THERE
From Taos, take NM 68 south for 45 miles to the town of Española. Here you turn left (east) onto NM 76, signed for Chimayo. At 9.9 miles up NM 76—passing by the turn for Chimayo that heads in the direction of Truchas—you turn right onto NM 503. The road climbs, and approximately 0.4 mile after topping out, you turn left onto FR 306 (46.4 miles total). The correct turn is about 0.1 mile before the turn for Santa Cruz Lake. Follow FR 306 for 9 miles to a right turn onto FR 435. The road is passable in passenger cars for about 1.2 miles, and there are places to park off the road at this point. Whether walking from here or continuing in a four-wheel drive, you follow the road for 0.5 mile. Where the road bends to the left, another road heads to the right. Follow this road for another 0.5 mile to a very small parking area and the Rio Quemado trailhead (57.6 miles total).
THE TRAIL
Under-visited but overflowing with visual rewards, the western route to Truchas Peak rolls along the northern rim of the deep Rio Medio canyon en route to a stunning junction of trails located on an open, broad ridge between the Truchas Peaks and East Pecos Baldy. Beyond this marvelous trail junction, most likely in complete solitude, you will move through forests of fir and aspen, past four alpine lakes, and onto the summit of arguably the grandest peak in New Mexico.
The Rio Quemado Trail begins by edging along a large clearing, twisting through a stand of aspen trees. The trail climbs somewhat until the 0.4-mile mark, where it reaches a small ridgeline. You follow an easygoing stretch through a predominately fir forest before shifting to a more strenuous ascent at 0.8 mile and continuing to a trail junction at 1.6 miles. Heading right puts you on Trail 151 toward The Dome (11,336 feet) along a much less strenuous route. Views of the mountains across the broad Rio Medio drainage are possible through the trees along here. The forest understory is sparse, occasionally broken up by a wildflower or mushroom cap that adds color and character to the forest floor. The moderate climb lasts until the 2.4-mile mark, where you begin a steeper ascent toward The Dome. At 2.7 miles there is a fork in the trail. Stay to the right as the trail loses a little elevation before moving cross-slope just slightly below the summit of The Dome.
ROCKY MOUNTAIN BIG HORN SHEEP IN EARLY MORNING
In between the aspen trees along this stretch, you begin to have glimpses of East Pecos Baldy (12,529 feet) and the Truchas Peaks. The Truchas Peaks are made up of North (13,024 feet), Middle (13,066 feet), and Truchas (13,102 feet). Truchas is known by local Pueblo people as Stone Man Mountain. The trail drops and rises in easily digestible amounts, reaching a distinctive highpoint at 4.2 miles before dropping steeply to a cross-slope run. At 4.4 miles you reach a small clearing in the trees. One trail continues straight and another heads to the right. Follow the trail to the right, paying attention to the tree blazes through the next short, somewhat difficult-to-follow stretch.
THE TRUCHAS PEAKS AND CHIMAYOSOS PEAK
Soon after the clearing, the trail climbs 0.5 mile before flattening out and moving cross slope. By 5.2 miles, you are rewarded with your first big views of the Truchas Peaks. The west slopes are steep and lead into deep, tall basins, one of which cradles Jose Vigil Lake. The trail drops into and over the creek drainage to meet the Jose Vigil Trail junction at 6.6 miles. A steep climb of 1.2 miles brings you up into the Jose Vigil Lake basin. No camping is allowed in the basin itself.
To continue on the route to Truchas Peak, go straight. After losing some elevation, you meet Trail 351 at 7.1 miles. Take the trail to the left as it passes through a narrow meadow with campsites and then follows a creek up to a more open, circular meadow with a tarn set in the middle, another campsite option. From here the trail moves to the north, making a 0.7-mile push out of the trees and onto the spectacular north end of the Trailriders Wall (8.3 miles).
Trying to consume all the views that surround you in this open zone will make you dizzy—the Truchas Peaks in your face to the north, the spread of the Pecos Wilderness to the east, and East Pecos Baldy tethered to the Trailriders Wall to the south. You have two options at this point: head to the summit of Truchas Peak or into the small basin that holds the Truchas Lakes.
Head north (left) on Skyline Trail 251 to access the summit of Truchas Peak. After 0.2 mile, move off-trail to the left to gain the north shoulder of Truchas Peak. You will fall upon a trail that moves above the Jose Vigil Lake basin to reach the summit of Truchas Peak after 1,300 feet of elevation gain over 1.2 miles. The views are, of course, stunning from here, with the Jemez Mountains, the Wheeler Peak Wilderness, and so many splendors of the Pecos Wilderness within sight.
The trail—northbound Skyline Trail 251—to the Truchas Lakes hugs the bottom of the eastern slopes of the Truchas Peaks, moving through boulder fields, rockslides, and forested stretches while gaining elevation. The lakes are stacked on top of each other with the smaller of the two lakes taking the top bunk so to speak (10 miles total). No camping is allowed here. All along this hike there are opportunities to see deer, elk, coyote, marmot, and numerous species of bird, including the golden eagle.
BURNT WATER
It is possible to take an alternate route to Truchas Peak as an out-and-back or as part of a loop hike. Instead of turning onto Trail 151 you can continue straight on Rio Quemado Trail 153. The trail drops into and then up the North Fork Rio Quemado drainage, accessing the amazing Rio Quemado Falls before making a steep push up to a tiny saddle south of North Truchas Peak. This leads down to the Truchas Lakes. By the way, quemado means "it burned" in Spanish.
Trampas Lakes and Hidden Lake
TYPE: Day hike or overnight
SEASON: June to October
TOTAL DISTANCE: 11 miles
RATING: Moderate
ELEVATION GAIN: 2,350 feet
LOCATION: Pecos Wilderness, 18 miles south of Taos
MAPS: USGS El Valle and Truchas Peak
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GETTING THERE
From Taos, take NM 68 south for 3 miles to the junction with NM 518. Continue on NM 518 south toward Peñasco. In 17 miles (20 miles total), you reach the junction with NM 75; turn right, heading west. Drive through the town of Peñasco to the junction with NM 76 at 27.4 miles total. Turn left on NM 76 toward Las Trampas and Truchas. At 33.3 miles, the road makes a downhill bend to the right about a mile out of Las Trampas. The right turn for FS 207 is located at the elbow of the turn, marked with a sign. There is a short stretch of pavement before the road changes to packed dirt and gravel. Continue on FS 207 for 8.2 miles (41.5 miles total) to its end, where you reach the parking area and trailhead. There is an outhouse here as well. A sign indicates that this is the route to the Trampas Lakes and Hidden Lake.
THE TRAIL
This outing is rich with life. The trail winds its way up the Rio de las Trampas drainage to the small, quaint Trampas Lakes, held inside a basin created by retreating glaciers as recently as 10,000 years ago. Right from the beginning, you are treated to spectacular blooms in daisies, scarlet gilia, and a dozen other wildflowers, along with a prolific community of wild strawberries. The moderately inclined trail spends most of its time in the trees, and it's often lined by the broad-leafed thimbleberry shrub.
By 0.9 mile, the trail enters a small oasis—a grove of aspen with tall, thick grasses, buttercups, asters, and the fantasy-book false hellebore, with its stout leaf layers and straight cob-style bloom rocketing the entire plant to more than 6 feet in height. Another 0.2 mile down (1.1 miles total), you officially enter the Pecos Wilderness. The 6- to 8-inch-tall shrub growing thickly along this stretch is grouse whortleberry. The tiny, sweet berry is typically ripe by the middle of August, and it's a favorite of black bears.
WILDFLOWERS IN BLOOM ALONG THE LAKESHORE
At 1.7 miles you are at creek level near a rockslide as the trail maintains its easy to moderate gradient. Plant life thins out somewhat, but there is still a noticeable mix of wildflowers and large blankets of whortleberry. The diverse riparian environment returns at 2.2 miles with crossings of the Rio de las Trampas. There also are views of the slopes leading to the summits of Trampas Peak (12,170 feet) to the east and Jicarilla Peak (12,494 feet) to the south before the trees welcome you back into their care.
The trail starts to gain a little more elevation along this stretch, climbing higher above the creek drainage. You also begin the big swooping right-hand bend the trail makes around Jicarilla Peak in its approach to the Trampas Lakes basin. At 3.4 miles, you embark on a series of slack switchbacks that deliver better views of the two ridgelines and the creek drainage you hiked up. The forest is still thick through here, with a more ancient feel than the youthful zone along the creek. Next you enter a more open setting with views of cliff bands and rock outcroppings, and a creek crossing comes at 4.6 miles. The signed junction for the Trampas Lakes and Hidden Lake arrives at 5.3 miles. Follow the trail to the left, which takes you to Lower Trampas Lake and Trampas Lake in less than 0.2 mile.
A thin strip of forest separates the two lakes, which are approximately equal in size. You'll find this area a truly peaceful place. The upper lake is set a little deeper in the trees and rimmed by a beautiful, sharp-toothed ridgeline that is part of the broader cirque holding both lakes. Lower Trampas is edged on three sides by trees, but its east shoreline blends with a steep, loose rock slope that connects to the Trampas and Truchas Peaks ridgeline 1,100 feet above. Beautiful collections of wildflowers like marsh marigold, elephantella, and rose crown grow in the marshy zones along the lakeshores. There are campsites near each lake.
HIDING NOT IN PLAIN VIEW
It is a short jaunt to Hidden Lake along an easy trail that loses elevation and edges along the Rio de las Trampas drainage, providing a canyon rim–like sensation. The lake is just 0.7 mile from the junction. Smaller and shallower than the Trampas Lakes, Hidden Lake has its own personality. It is pressed between forest and a steep, loose rock slope blanketed in plant life and wildflowers. There are campsites along the benched area above the lake.
Powderhouse Canyon
TYPE: Day hike or overnight
SEASON: June to November
TOTAL DISTANCE: 12.9 miles (with shuttle)
RATING: Moderate
ELEVATION GAIN: 1,600 feet
LOCATION: Valle Vidal, 35 miles north-northeast of Taos
MAPS: USGS Comanche Point and Ash Mountain
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GETTING THERE
From Taos, drive 45 miles north on NM 522, passing through Questa, to reach the town of Costilla and the junction for NM 196. Turn right onto NM 196. At 55.7 miles, the road transitions from pavement to dirt and gravel, and is now marked as FS 1950. After continuing approximately 8 miles (63.6 miles total) on FS 1950, you reach a fork in the road. The left fork is FS 1900 (signed), which leads to Upper Costilla Creek. At 66.1 total miles you reach the road's gated end, a parking area, and the sign for the Powderhouse Canyon Trail.
To leave a shuttle vehicle at the endpoint, go right at the junction of FS 1950 and FS 1900 to continue along FS 1950. Approximately 2.2 miles down, you pass a pullout on the left. Continue another 0.8 mile to the small parking area on your right. There is a stock corral and a gated road with a ROAD CLOSED sign on the left.
THE TRAIL
The popularity of the Valle Vidal with anglers and elk hunters is no accident. In many places across this area, near-perfect trout streams push their way through thigh-high streamside grasses, the water bending and twisting and nearly doubling back on itself at points. The geography ranges from rolling open country to forest-stippled slopes to steeper drainages, creating a playground for New Mexico's largest population of elk.
This hike begins in an angler's paradise. Upper Costilla Creek presses the east side of a shallow valley here that is bookended by rounded and forested mountains. Follow the lower road up valley for 0.7 mile. Watch for a more grass-covered road to your right that leads down to the creek. Follow it. If you were to continue straight you would reach a gate and a NO TRESPASSING sign.
You may notice, as you pass through this short valley, that a lush riparian ecosystem feeds off the constant moisture of the creek. But a short distance beyond this swath, the plant life changes to a more semi-arid mix of wildflowers and bushes. After crossing the creek, the road makes a gentle bend to the right and reaches a gate at 1 mile. This marks the entry into Powderhouse Canyon. On the other side of a dam lies Costilla Reservoir and the 580,000-acre Vermejo Ranch.
Powderhouse Canyon begins as a shallow, grassy valley, narrower than the Upper Costilla valley. It soon constricts, though, and you'll notice the trees slipping closer to the creek and road as you move up valley. The area of the Valle Vidal ("Valley of Life" in Spanish) was roamed by hunter-gatherers as far back as 10,000 years. These people, known as Folsom people because of artifacts found near Folsom, New Mexico, were the ancestors of early Anazazi people who eventually spread across many regions of the Southwest. Today hikers wander the Valle Vidal in part by way of abandoned roads instead of trails. The hundreds of miles of roadway have a history in mining and timber operations, but their presence won't lessen the aesthetic beauty of the journey.
It is possible in the lower valleys, and even more likely as you head deeper into the hike, that you will encounter numerous elk. The countryside along the Valle Vidal is ideal elk habitat, with numerous open spaces, wide-spaced trees, and terrain that varies from rolling hills to steeper slopes leading up to highpoints like Little Costilla Peak (12,584 feet).
At 2 miles, you come to a road that splits off to the left. A small shack sits on the other side of the creek here, along with a water-control gate. Continue straight along the creek. Turn around at this point for a nicely framed view of the rugged Big Costilla Peak (12,739 feet) and ridgeline. Shortly past here you move above the creek and through more of a corridor of trees, marking the transition from valley to forest travel.
At 4 miles, you cross over the creek and enter a more open zone of the drainage, climbing a bit more as you go. You pass by two roads that cut off to the right before reaching a third such road at 4.5 miles. There is no sign here, although it may be marked by a cairn, but you'll recognize this spot because you will see a road making its way up the slope on the opposite side of the creek. Follow this road to the right for approximately 0.2 mile (4.7 miles total) to a creek crossing. If you happen to continue straight at this junction instead of heading to the right, you will reach another fork. Here the road continuing straight crosses over a faint, slightly overgrown road and the one to the left climbs steeply for a short stretch. If you reach this point you've made a mistake and need to turn around and make your way back to the left fork at the previous junction.
After crossing the creek, the old road winds its way up the near slope and out and around a highpoint. This area was heavily logged in the early to mid-20th century. Approximately 0.2 mile up there is another split in the road; stay to the right. Along here, and for most of the remaining hike, you have different takes on Little Costilla Peak. The scars of old logging roads are still somewhat visible on its western slope, but today it's thickly treed up to around 11,700 feet. The last 800 feet or so are treeless. Elk encounters, especially if you are out early, are very likely along much of the rest of this hike.
THE VALLE VIDAL HOLDS MANY TREASURES
By 5.2 miles, you reach a clearing of sorts and an intersection of logging roads. There are nice views across the Valle Vidal. The hike follows the road as it bends to the left and back into a corridor of trees. The road follows a curving ridgeline for 3.5 miles, sometimes walled in by trees and sometimes through clearings that provide views of Little Costilla as well as Tetilla Peak (10,600 feet) and Van Diest Peak (11,223 feet) off to the left, or south.
You have an easy glide for a number of miles before descending gradually back to the main valley floor. At 8.7 miles the road bends away from Little Costilla, but in its place there is a beautiful overlook of a lush meadow, an ideal location for a campsite. Another clearing and road intersection come at 9 miles. Stay on the road that makes a gentle bend to the right, which is noticeably the more traveled route. At 9.8 miles, there is a nice mix of forest and meadow, an ideal place to do a little exploring off the main path if you are feeling up to it.
The road already has met up with clearings at various points, and another arrives at 10.5 miles. Little Costilla puts on another worthy face from this vantage point, and the route stays straight before bending to the left and entering a more treed section. A broad open slope, dotted occasionally with trees, hangs like a landscape canvas across the drainage of a tributary that feeds Little Costilla Creek. There also are opening views of the eastern and northeastern slopes of the Cimarron Range.
After a promenade along the northeastern edge of the Valle Vidal, cut by Comanche Creek in the distance, the road turns once again toward Little Costilla at 11.6 miles. After a 0.4-mile stretch, the views return to the long gentle rolling valley, with the Cimarron Range as backdrop. In another 0.3 mile (12.3 miles total), you have walked by your last serious covering of trees—ponderosa pine instead of the previous aspen and fir—and are now in the expansive valley.
At 12.9 miles you reach FS 1950 and your shuttle vehicle. No shuttle vehicle? From here it is 5.5 miles back to the Powderhouse trailhead. If you would prefer to make this hike as an out-and-back, it will be much more engaging and scenic to start from this trailhead instead of the Powderhouse trailhead.
"LIFE GIVING" VALLEY HOLDING ON FOR DEAR LIFE
The Valle Vidal (vidal means "life giving" in Spanish) was donated to the American people by the Penzoil Corporation in 1982. Its 101,794 acres, managed by the Carson National Forest, were set aside so that hikers, horsemen, cross-country skiers, hunters, and anglers could enjoy this truly unique landscape. A 40,000-acre area has been coveted by mining interests for oil and natural gas extraction. But the Coalition for the Valle Vidal was formed by concerned citizens, businesses, and conservation groups like the Sierra Club to put a stop to any notions of violating the natural beauty of the Valle Vidal for short-term gains. In 2006, the Valle Vidal Protection Act, which would restrict all mining and operations in Valle Vidal, was signed into law by President George W. Bush.
Clayton Camp
TYPE: Day hike
SEASON: June to November
TOTAL DISTANCE: 3.4 miles
RATING: Moderate
ELEVATION GAIN: 100 feet
LOCATION: Valle Vidal, 35 miles north-northeast of Taos
MAPS: USGS Comanche Point
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GETTING THERE
From Taos, drive 45 miles north on NM 522, passing through Questa, to the town of Costilla and the junction for NM 196. Turn right onto NM 196. At 55.7 miles, the road transitions from pavement to dirt and gravel, and it's now marked as FS 1950. Approximately 8 miles (63.6 miles) along FS 1950, you reach a fork in the road. FS 1900 is straight ahead, but you stay to the right, continuing on FS 1950. In approximately 4.2 miles, you reach a road that splits off to the right just before FS 1950 starts to climb. At 0.4 mile down this unsigned road (68.2 miles total), you reach a small parking area and a gate across the road.
THE TRAIL
The Valle Vidal is in recovery. Heavy logging and devastating grazing practices—6,000 head of cattle ran at times in some areas—have damaged streamside habitats. But volunteers are working to restore a natural balance so native species like the Rio Grande cutthroat trout can thrive again. A major restoration project is under way along Comanche Creek, led by the Quivira Coalition. The hike to Clayton Camp edges along that creek, making this journey about the future and the past.
Comanche Creek moves quietly through this small, shallow canyon. There are interesting rock formations near the beginning of the hike and nice collections of grasses and wildflowers the entire way. Approximately 0.8 mile down, you cross the creek and pass through a gate. The creek bottom terrain also opens up through here into more of a dry grass environment. There are plenty of opportunities all along this hike to strike out across the rolling valley or head up into more forested sections. By 1.3 miles, the road has made a bend to the left, crossed the creek again, and entered a narrower valley bottom. You reach Clayton Camp at 1.7 miles.
CLAYTON CAMP
You pass a small stock pen and outbuilding before coming upon the main house. This point also marks the confluence of Comanche and Vidal Creeks. With a map and compass, you could continue on by exploring either creek drainage. Aster, giant thistle, cinquefoil, tiny daisies, and scarlet gilia paint the ground.
MCCRYSTAL RANCH
From the Clayton Camp trailhead, it is another 17.5 miles down FS 1950 to the start of the easy 3.5-mile walk through an open environment to the McCrystal Ranch, established in the late 1800s. Enjoy the creekside trail and visit an old sawmill along the way. Off NM 64, it is approximately the same distance to reach the McCrystal Ranch trailhead.
Serpent Lake
TYPE: Day hike
SEASON: June to October
TOTAL DISTANCE: 7.4 miles
RATING: Moderate
ELEVATION GAIN: 1,300 feet
LOCATION: Pecos Wilderness, 25 miles south of Taos
MAPS: USGS Holman and Jicarita
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GETTING THERE
From Taos, take NM 68 south 3 miles to the junction with NM 518. Continue south toward Peñasco on NM 518. In 17 miles (20 miles total), you reach the junction with NM 75; turn left toward the Sipapu Ski Area, continuing on NM 518. At 33.6 miles total you reach the right turn for FS 161. There is a sign for FS 161, but it helps to know the turn is 1.8 miles past Angostura Camp. There are a few rough spots at the beginning of the dirt road; otherwise, it is a decent 4.1-mile drive (37.7 miles total) to the road's end and the start of the hike.
THE TRAIL
Although it carries a menacing name, Serpent Lake is perhaps the most delicate and bashful high mountain lake in the Southwest. It is surrounded by boggy ground popping with water-thirsty wildflowers like marsh marigold and gentian. The tiny lake nests in the corner of a broad, kelly green basin.
The trail to this New Mexico gem begins along what used to be the continuation of FS 161. So you make a 0.3-mile, wildflower-lined stroll down a country road before reaching an actual trailhead for Trail 19 and slipping into the cover of trees. It is a pleasant trail, offering collections of wildflowers and a small cascade set in the trees off to your left at 0.6 mile. You cross a man-made canal another 0.1 mile down the trail.
Picture a snake digesting a couple of small creatures and you will gain a sense of how the trail is shaped. It remains road-width for much of the way, at points squeezing down somewhat closer to the size of a hiker's trail. The grade is steady and moderate throughout, but there are plenty of rocks and tree roots to keep your legs active up to the junction with Serpent Lake at 3.4 miles.
Approximately 0.4 mile before you reach the junction, you can feel the terrain begin to open up. Beyond the trees, seen with more clarity the closer you get to the junction, is the Divide Trail ridgeline, with its collection of nearly uniform basins scooped out of the eastern slope. The 8-basin chain begins with Jicarita Peak (12,835 feet) and runs south to the 12,626-foot highpoint above the Rincon Bonito basin. In fact, if you continue past the Serpent Lake junction in 1 mile, the trail climbs into the open alpine zone. Here you will find broad vistas of the Pecos Wilderness and trail access to both Jicarita and the high perch above Rincon Bonito.
The trail to Serpent Lake slides downslope through the trees before quickly entering the edge of a large, extremely lush basin choked with shrubs, thick blankets of grasses, and a fabulous community of wildflowers like marsh marigold, gentian, and buttercup (3.7 miles). Beyond this boisterous edge, picture-perfect Serpent Lake is set in the bottom of the basin. The lake is rimmed in a soft green bumper of grasses and other plant life.
A boggy meadow zone—considered wet tundra—sucks up the short section of trail that leads you closer to the lake. It is extremely unusual to find such a setting that is relatively undisturbed by human visitors, so please watch every step, touching dry ground as often as possible as you pass through this fragile landscape. It is a tranquil setting indeed—the peaceful shape and placement of the lake in relation to the green basin, whose loose rock slope rises to a 12,000-foot ridgeline. Camping and campfires are not allowed in the lake basin.
SERPENT LAKE
NO SURFING AND VOLLEYBALL IN THIS SANTA BARBARA
Starting from the Santa Barbara trailhead off FS 116 from the town of Peñasco, a long approach trail (10-plus miles) moves along the Rio Santa Barbara to the junction of the Middle and East Forks. Off the south end of the trail, before the climb onto the open Divide Trail, are three lakes known as the Santa Barbara Lakes. Various out-and-back trips, loops, and side trips can be taken in the surrounding area. This would be a very worthwhile weekend outing.
Rio de la Casa Lakes Loop
TYPE: Day hike or overnight
SEASON: June to October
TOTAL DISTANCE: 12.2 miles
RATING: Moderate to strenuous
ELEVATION GAIN: 2,800 feet
LOCATION: Pecos Wilderness, 31 miles north-northwest of Las Vegas
MAPS: USGS Jicarita Peak, Holman, Gascon, and Pecos Falls
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GETTING THERE
From Las Vegas, take NM 518 north toward Mora. If you are coming from I-25, in approximately 3 miles (still in Las Vegas) NM 518 north heads left from the stoplight intersection for Mills Road. At 3.5 miles you reach another stoplight, this time for Seventh Street and the continuation of NM 518 north to the right. Follow the sign for Storrie Lake and Mora. After passing through the town of Mora and into its immediate neighbor, Cleveland, look for a left turn onto CR 28 at 35.8 miles. The road is signed but easy to miss if you are traveling too fast. The road surface is packed dirt. After traveling 4.4 miles on CR 28 (40.2 miles total) and crossing a bridge, you have the option of bearing to the left (continuing to follow the river) or heading to the right on unsigned CR 29. Bear to the right and begin climbing up a rough, rocky, and rutted road. High-clearance and/or four-wheel-drive vehicles are recommended. At 44 miles total you reach the signed Walker Flats area and Viga area. Park here. Two roads split off to the left of the main road. The upper road, the one closest to the signed area, is Trail 269 and the start of this hike.
THE TRAIL
This hike runs through a tranquil, secluded, high mountain valley, set below a thickly forested mass of mountains that includes Pyramid Peak (10,597 feet) a few miles to the south. The dramatic, wedge-like opening of the Middle Fork Rio de la Casa canyon adds to the majesty of the surroundings. On your return, you will head down this canyon across a marvelous slopeside garden, as the river rushes forcefully below you toward its confluence with the North Fork. The two forks eventually merge with the South Fork to feed the Mora River in the town of Mora.
What is marked as Trail 269—signed 0.5 mile along—is also a vehicle accessible road. It moves through the gentle, open setting of Walker Flats, passing into tree cover and then dropping down to a clearing. It winds its way up to the junction with Trail 233 at 1.1 miles. Follow Trail 233 as it heads up a short, steep section. After a brief reprieve, you begin a strenuous push upslope. The trail passes through a fenceline and gains a small clearing at 1.9 miles, with views to the east where the mountains meet the plains.
The Great Plains are indeed great, encompassing some 1.4 million square miles. They gather mountain rivers flowing from the Rockies in the west and rivers like the White in Indiana to the east, all adding size to the 2,500-mile-long Mississippi River. Incredible wild grasslands once hosted large animals like mammoths and sabertooth tigers during the Paleo period. And up to 50 million buffalo roamed here up until the 1800s, when they were virtually eliminated by hide hunters as part of a federal plan to break the Plains Indians, who existed off the bounty of this animal.
Trees along the trail, and sometimes rocks on the trail itself, are tagged with orange spray paint to keep you on course. (A few well-used game trails mix with Trail 233.) At 2.2 miles, you're given a breather, as the trail mellows out in steepness and ruggedness. You are in the trees this whole time and continue to be until shortly before you reach the lake. Enjoy the break, because more climbing occurs between 2.4 and 3.1 miles. You also pass an unmarked junction with Trail 269 in this stretch. The trail pops out of the tree cover and onto an open slope around 4.3 miles, making a short push up and then leveling off for the final run to the shores of North Fork Lake at 4.7 miles.
After gaining nearly 3,000 vertical feet, you've certainly earned the big views far to the east. The semi-steep, grassy ridgeline provides a beautiful backdrop to the small, clear, shallow lake. There are campsites nearby and options for cross-country exploring. Up on the ridgeline, you can use the Divide Trail to access Horseshoe Lake, situated in the next basin to the north, and the Santa Barbara Lakes a few miles to the southwest.
The narrow-benched setting continues as you make an easy cross-slope move around the near highpoint to the south in the direction of the Middle Fork. At 0.8 mile (5.5 miles total), you reach an open slope covered in plantain, clearly recognizable by its banana tree–sized leaves, single stalk, and corncob-like collection of red blooms. There are expansive views again out toward the Great Plains and nearby to the east-southeast of Pyramid Peak, which shields a collection of lakes below its south slope. The junction with Trail 266 arrives at 5.9 miles.
From here it is an easy 0.4 mile to Middle Fork Lake, set in an environment similar to the North Fork, but with the bonus of an additional smaller lake set more in the trees and teetering above the Middle Fork Rio de la Casa drainage. There are some primitive campsites between the two lakes and more on the south end of the smaller lake. This is another excellent option for an overnight camp, with day-hike options to Rincon Bonito to the south and closer access to the Santa Barbara Lakes via some trail and cross-country walking.
Return to the Trail 266 junction and continue the loop back to the trailhead. Besides wild strawberries and mushrooms, you will come across a variety of currant bushes. The berries can be quite tasty off the bush when picked around the beginning of September, but usually they are reserved for jellies. This area also is home to elk and deer. After alternating between small open spaces and jaunts through the trees, all the while losing elevation, you reach a marvelous grass and wildflower slope at 7.5 miles (mileage includes the route to Middle Fork Lake). There are views of the crusty, rounded rock butte that forms part of the steeper canyon wall for the Middle Fork Rio de la Casa, and beyond to Walker Flats.
You work across the slope and wind down a steep section of trail to reach the river and the canyon run at 8.2 miles. The river rushes and drops the whole way, predominantly through aspens, as you go down short switchback sections and across a rockslide before beginning to move out of the canyon at 9.1 miles. The trail stays somewhat rough, but the corridor of aspen and the understory of oak, asters, and blankets of kinnikinnick make it quite pleasant.
By 9.9 miles, the trail will have made a move to the north and rolled over a finger ridge away from the river and into a forested zone of fir. Silence replaces the sound of rushing water. The trail is unmaintained but easily navigated to the gate at 10.4 miles. After the gate, you are on a trail for a short while longer before transitioning to old roads for the rest of the journey. At 10.6 miles, head left at the junction with the road. After cruising along the road for almost 1 mile (11.4 miles) you reach the North Fork Rio de la Casa. Head to the left as the road arcs over the river itself and begins a short climb and then a more level run back out to the trailhead at 12.2 miles.
NORTH FORK LAKE
"WATER OF THE DEAD," NEW MEXICO
In French, the area was called L'Eau des Morts ("water of the dead"), so named by beaver trappers attracted to the Mora Valley in the 1820s. The name later became assimilated into Spanish and shortened to Mora (muerte means death in Spanish). The town was primarily built by Hispanic pioneers who trapped, hunted, farmed, and established many mills in the area, the nicest today being La Cueva Mill a few miles east of Mora, which was operational until 1949. The name of the town is unfortunately appropriate thanks to a history of killing raids here by Indians, a devastating smallpox outbreak, a deadly standoff with U.S. soldiers, and a retaliation killing by a band of renegade Texan ranchers.
Tolby Creek Meadows
TYPE: Day hike
SEASON: Late April to October
TOTAL DISTANCE: 8.5 miles
RATING: Moderate (one strenuous section; alternate route available)
ELEVATION GAIN: 1350 feet
LOCATION: Colin Neblett Wildlife Area, 20 miles east-northeast of Taos
MAP: USGS Touch-Me-Not Mountain and Tooth of Time
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GETTING THERE
From the center of Taos drive 24.2 miles on US 64 east to Angel Fire. Continue on US 64 another 11 miles toward the town of Eagle Nest. Drive through Eagle Nest, still on US 64, and head east towards Cimarron Canyon State Park. In 3.4 miles (38.6 miles total) from Eagle Nest you'll enter the state park. There will be a sign for Tolby Creek Campground and pay station, which is located across the road from the Tolby Creek Trailhead. Turn into the campground but park in the day-use lot. To access this hike you need to have already or be ready to purchase one of the following: a valid State Park permit (day use, camping permit, or annual pass), valid hunting, trapping, or fishing license with a HMAV, or a GAIN permit with HMAV. If you're not a hunter or fisherman, the easiest and least expensive option is to use your annual State Park pass if you have one or purchase a day-use pass for $5 at the Tolby Creek Campground. Gaining Access Into Nature or GAIN permits can be purchased online at www.wildlife.state.nm.us/recreation/g-a-i-n.
THE TRAIL
The Tolby Creek Meadows hike follows a quaint creek drainage out of Cimarron Canyon into a spectacular broad, high mountain meadow nestled in a big country setting, one most often left to the wild creatures that inhabit both Cimarron Canyon State Park and the 33,000-acre Colin Neblett Wildlife Area. When people do venture into this part of New Mexico it is mainly to cast a line for trout on the Cimarron River or hunt deer, elk, bear, or turkey in the high country. Between the formidable barrier in the Palisades Sill up-canyon from Tolby Creek and the few trails that lead from the canyon bottom but a short distance into the rugged mountains, this country is as wild and untamed as the Spanish word cimarron has come to be understood.
BROAD AND PEACEFUL TOLBY CREEK MEADOW
The Tolby Creek Meadows Trailhead is across the road from the day-use parking area. You'll see by way of the large sign at the trailhead that the trail and surrounding area is closed to access from May 15th to July 31st for deer fawning and elk calving. To start the hike, pass through the gate that sits between the large sign and the horse corrals. The trail, which is really a roadbed at this point, works along Tolby Creek. A short 0.1 mile up you'll reach a junction that will be marked Upper and Lower Tolby. The Upper Tolby Trail cuts upslope and works its way through the forest and above Tolby Creek, eventually linking back up with the Lower Tolby Trail and into Tolby Creek Meadows.
However, this hike continues on the Lower Tolby, nicely in sync with the melodies of Tolby Creek. In this lower section of the creek drainage you'll be in a mix of evergreens and cottonwood trees. Another 0.1 mile up you'll pass along a house and some outbuildings. There's an access road/trail that cuts over the creek via a culvert. Just continue straight, upstream, where the roadbed pathway will eventually narrow to a footpath. It's a pleasant setting that will be a nice, cool reprieve from the hot sun in summer. Though clearly not in the same league as the Palisades, there are some impressive cliff bands as you move your way up the drainage.
As with so much of northern New Mexico there is a long, complex, and fascinating geologic history to this area. Significant periods range from as old as 1.9 billion years ago, from sedimentary and igneous rock coming from deep within the Earth's crust, to a period 300 to 66 million years ago when seas covered this area, contributing to the formation of other types of sedimentary rock, to the formation of the Palisades Sill 30 million years ago. As is often the case, the Palisades sculpting didn't just come about by geologic activity but by the action of water both in the flow of the Cimarron River and freezing and thawing events that broke away rocks and boulders from the cliff wall.
Approximately 0.7 mile up, the trail takes two switchbacks upslope, gaining some elevation above the creek. It's also here that you'll see you are in a setting of fir, pinyon pine, juniper, spruce, and groundcover like kinnikinnick. At 1 mile the trail tops out after some more noticeable climbing and starts rolling downhill slightly to two more switchbacks and then onto a nice footpath above the creek. You'll reach a creek crossing at 1.7 miles. The crossing requires a bit of puzzling out, and depending on the water volume in the creek, you may or may not be getting your feet wet.
Hitting the 2-mile mark, the trail punches uphill followed by a more relaxed incline and short pushes uphill. It's around here that groves of aspen make their presence, most spectacularly with their golden glow in the fall. At 2.5 miles you'll reach an opening where a feeder creek confluences with Tolby Creek. The path to the left, marked with a red diamond on a tree, is an easy-to-follow trail that takes a moderate climb up to the camp sites and into Tolby Meadows in a little over 2 miles.
If you're feeling adventurous, stay to the right or straight, following the trail alongside Tolby Creek. The trail eventually fades away and there will be a slight amount of orienteering and definitely some scrambling to reach the meadows. From the junction 0.4 mile up (2.9 total miles), you reach a small open area that has some campsite options. Past the open area the creek canyon narrows up considerably, coming across a few more dispersed camping options, and most of all the disappearance of the trail.
However, you'll be able to move fairly easily for another 0.2 mile before you'll want to get yourself on the left or east side of the creek, working your way to a comfortable height above the creek to avoid the brush and put yourself in a position to scramble along as easily as possible. This will most likely mean angling upslope across some steep terrain and scrambling over rocks and small boulders.
The cross-country work is over relatively quickly though, even if the going will be slow, because by 3.5 total miles you'll reach the lower end of Tolby Meadows. Depending on how high you've worked yourself upslope, you may need to slide down to the grassy benched area alongside the creek that acts as the runway into the broader expanse of the meadow itself.
Tolby Meadows is a beautiful circular parkland set in a thick forest at the feet of the Cimarron Range and decorated by a long band of aspen that creates a golden-yellow ribbon along the meadow's eastern edge in fall. It makes for a great spot for a snack and lounging if you're on a day hike or a short stop for further exploring up the creek and perhaps a summit attempt of Tolby Peak. Keep in mind that there is no camping or campfires allowed in the meadows.
The Colin Neblett Wildlife Area is one of thirty-eight wildlife management areas in northern New Mexico under New Mexico Game and Fish. The bigger chunk of the Colin Neblett is found south of the Cimarron River, but there is a rugged expanse to explore north of the river as well via such access points as the Maverick Falls Trail on the east side of Cimarron Canyon. These wildlife management areas are primarily conservation zones to protect the wildlife and ecosystems yet still allow for more primitive human recreation. Deer, elk, bear, grouse, turkey, and other wildlife call this place home.
To work your way out of the meadow and onto the rest of the hike, stay along the north side of the meadow, below the tree line, and toward the cluster of aspen ahead of you—most specifically where you see the aspen and evergreens pinch together. You'll come to a wide trail that will lead you out of the meadow (4.0 miles total) and down to the campsites.
About 0.1 mile out of the meadow, the trail meets up with a roadbed that continues downhill. Through the trees will be glimpses into the Eagle Nest valley and across toward Wheeler Peak and its accompanying cast of 12,000-plus-foot-high peaks. A 0.5 mile (4.6 miles total) from the meadow you'll reach the campsite area. If you're not staying the night, continue on downhill.
A touch over 0.5 mile from the campsite area the road-like trail will continue to the right, which is Upper Tolby. You will want to stay to your left on a footpath that edges alongside the creek. The trail will be marked with a red diamond. The trail follows the creek that eventually confluences with Tolby Creek down in the opening you passed through on your way up. Along the trail you'll pass by a little pond as you work your way down to the trail junction in about 0.9 mile. At the junction you'll head right to return to the trailhead in 2.5 miles (8.5 miles total).
BOTTOMS UP!
There are only four designated trails—a total distance of 15 miles—in this area, all of which originate from the narrow swath of Cimarron Canyon State Park and lead into different sections of the Colin Neblett Wildlife Management Area. They each start from the canyon floor and move their way upslope via different drainages that eventually feed into the Cimarron River. When coming from Eagle Nest, the Jasper and Agate Trails and the Maverick Canyon Trail are found up-canyon or on the east side. In between the up/eastside canyon trails and the Tolby Creek Meadows Trail you'll find the Clear Creek Canyon Trail, which is adorned with a couple of waterfalls. No backcountry camping is allowed in the Colin Neblett so as to protect the area for the sake of wildlife.
Capulin Volcano
TYPE: Day hike
SEASON: April to November
TOTAL DISTANCE: 1 mile
RATING: Moderate
ELEVATION GAIN: 275 feet
LOCATION: Capulin Volcano National Monument, 25 miles east of Raton
MAPS: USGS Folsom
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GETTING THERE
From Raton, take US 64/87 for 29 miles to the town of Capulin. Turn left onto NM 325 toward the Capulin Volcano National Monument. At 32.7 miles (2.7 miles from the junction), take a right into the entrance for the national monument. There is a visitor center a short distance into the park where you can stop for information and to pay the entry fee—$7 per vehicle, valid for seven days of access. Continue on the winding road toward the top to reach another parking area at 34.8 miles.
THE TRAIL
The eruptions that formed the Capulin Volcano some 60,000 years ago came in the third phase of volcanic development, which took place over a period of 9 million years. Even though there is a calm about this area today, giant bison and mammoths once roamed the wispy grasslands that radiate out in all directions. And bursts of fiery ash, miles of fast-flowing lava, and sky-shattering explosions were all part of the scene at various times. Today the Capulin Volcano is a natural pyramid, a pristine example of a cinder cone rarely seen in this country.
There are two ways to explore the extinct volcano. The first is a 1-mile rim trail that provides 360-degree views of the surrounding geography and four distinct lava flows that move out from the volcano's base. The second is a short trail that leads into the bottom of the volcano, next to where the vent became plugged by cooling lava. Capulin came under federal protection in 1891, very early in the conservation movement, and received national monument status in 1916 under President Wilson.
The paved rim trail is lined with a collection of vegetation from Gamble oak and mahogany to juniper and a variety of wildflowers. Chokecherry bushes—the berries edible fresh, in jams, or dried—also grow on Capulin. In fact, the word capulin means chokecherry in Spanish. As you probably noticed on the drive up to the parking area and again while circling the rim, the volcano has extremely steep slopes all around. The materials that make up the volcano are loose cinders, ash, and other rock debris brought up from deep underground during its eruption. The vegetation blanketing Capulin today has been key in stabilizing the fragile slopes.
Starting on the south side of the rim trail, you can look down on what are labeled the third and second lava flows. These are followed by the first lava flow, which comes off the southeast side of the volcano. The fourth lava flow, the largest, moved northward. All told they cover nearly 16 square miles. An interesting feature of the flows are the ripples that formed as the crust cooled with hotter lava still flowing underneath. Lava mounds formed when building pressure split the not-yet-hardened crust and lava bubbled up.
Sierra Grande (8,720 feet), the bulky flat-topped highpoint you can see to the southeast, is classified as a shield volcano. Shield volcanoes are built by highly fluid spreads of lava that create broad, gently sloped mountains. Mesas like Barilla, Raton, and Johnson and other highpoints dot the landscape in each direction. This area, covering some 8,000 square miles, is known as the Raton-Clayton Volcanic Field. Looking west, the long wall of 12,000-foot peaks running north to south is the Sangre de Cristo Mountains. There is much on which to ruminate as you circle the rim, and this hike will most likely spur you to learn more about this region of New Mexico. But looking inward can do the same.
CAPULIN VOLCANO
A trail dropping from the parking lot leads to an observation point in the crater bottom. Gamble oak has settled in this zone and grass coats the inside walls, with pinyon pine and juniper frosting the upper reaches. This is the point where the volcano was born, creating a 1,300-plus-foot mountain where nothing existed before in the blink of an eye. The only activity today can be seen and heard in the bird chatter, the scurry and chirp of ground squirrels, and the movement of deer foraging for food.
HUMAN FLOW
Off the east side of Capulin runs what is known as the Fort Union–Grande Road. Fort Union has gone through three different manifestations; what stands today was constructed in the 1860s. The fort was conceived by General Stephen Watts Kearny, and later followed through on by Colonel Edwin V. Sumner in 1851. Its mission was to protect area communities and travelers along the Santa Fe Trail from hostile tribes over a 40-year period. Its presence and defensive layout also helped thwart an attack by Texas Confederates in 1861. Fort Union is located between Las Vegas and Wagon Mound and is now a national monument. Granda, Colorado, is 200 miles away. The two northern routes of the Santa Fe Trail that converged on Fort Union are the Cimarron Cutoff, which moved to the south of Capulin and on into Oklahoma, and the Mountain Branch, which moved through the present-day town of Raton and then north into Colorado. The two trails passed through Kansas to reach Kansas City, Missouri, a distance of 800 miles from Fort Union.
Simon Canyon Ruin
TYPE: Day hike
SEASON: Year-round
TOTAL DISTANCE: 1.8 miles
RATING: Easy
ELEVATION GAIN: 150 feet
LOCATION: Simon Canyon, 30 miles east-northeast of Farmington
MAP: USGS Archuleta
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GETTING THERE
From Farmington take NM 516 into Aztec and the junction with NM 560 (12.3 miles). You will continue straight at the intersection, but will now be on NM 560 (also known as NE Aztec Blvd.). From the junction you'll travel on NM 560 for 1.4 miles to the junction with NM 173. Take a right turn onto NM 173. At 4.25 miles up on NM 173 the road splits—the left fork is NM 173 and the right fork is NM 575. Take the left fork, continuing on NM 173 for 13 miles. At a total distance of 31 miles you will reach County Road 4280. Turn left. The road is 3 miles of dirt and is perfectly passable when dry but can be difficult-going to impassable when wet. At 1.4 miles down the dirt road you'll reach a sign for Navajo Lake State Park. At 34 miles total you'll reach the parking area and trailhead for Simon Canyon. Outhouses and picnic tables are available.
THE TRAIL
The origin of Navajo pueblitos—of which Simon Canyon is the only "boulder type" remaining north of the San Juan River—came out of the Pueblo Revolt of 1680. An alliance of the Puebloan people drove the Spanish out of what is today northern New Mexico in 1680, only to see their return in 1692. Under heavy assault from the Spaniards, it is believed some of the Puebloan people moved into a region called Dinetah, home of the Navajo, whereby one-to-two room pueblitos were constructed, either by them or the local Navajos, in strategic locations for the sake of defense. A short hike up from the banks of the cottonwood-lined San Juan River and into the beautiful sandstone Simon Canyon will lead you to a one-room pubelito built in the 1700s, perched, like a rock nest, on top of a massive sandstone boulder.
SIMON CANYON PUEBLITO
The trail begins in a mix of riparian plants and trees and that of the high plateau, which means juniper, pinyon pine, cottonwoods, and sage. You'll cross over a stream, an occasional lifeblood to the area, in less than 0.1 mile from the trailhead. Once across you'll reach a trail junction. You'll want to stay straight or slightly left to continue into Simon Canyon. If you have the time, though, the trail to the right is a beautiful slow meander that hugs the San Juan River and cuts beneath rock walls, at points festooned with colonies of swallows' nests. This trail heads downriver about 1.5 miles and is great for bird watching and, if you happen to be a fisherman, some stellar trout fishing (all catch and release). Also at the junction you will discover a plant identification billboard, which contains plant pressings, descriptions of the plants (including their uses by native people), and a photograph of the plant or tree. Plants and trees highlighted include horsetail, cottonwood, tarragon, peachleaf willow, and stretchberry.
From the junction the trail makes its biggest gain in elevation by punching steeply up a rocky road above the stream wash over a distance of a quarter of a mile. When you top out you'll be next to a fenced-in area, which contains infrastructure from the gas drilling that takes place throughout this area of New Mexico.
Ironically, Simon Canyon is a 3,900-acre preserve categorized as an Area of Critical Environmental Concern, a special categorization for preserving places in the west of cultural and ecological significance, whereby only primitive forms of recreation are allowed—fishing, hiking, and backpacking—yet oil and gas fracking are allowed, both of which are proven to harm the natural environment and people at the local level, along with contributing more to the fossil fuel supply chain and the effects of climate change.
From the top of the steep climb (0.3 mile) there are some nice vistas back toward the San Juan River and up into Simon Canyon. Attached to the fence you should see a sign that says TRAIL with an arrow pointing up-canyon. You'll be on an actual trail (versus the road) from here on, as it takes you along a beautiful rim run all the way to the pueblito.
The trail alternates from wide to narrow, even-surfaced to making your way over and in between sandstone rocks. Joining you will be pinyon pine, juniper, cacti, yucca, and—if you time it right (spring and post-wet periods in the summer)—wildflower blooms like rough Indian paintbrush, fringed gromwell, wallflower, and other varieties. Mammals and birds that call Simon Canyon home include rabbit, deer, porcupine, beaver, golden eagle, and great horned owl.
By the time you reach about the 0.7-mile mark the canyon opens up with spectacular rock formations on each side, stippled with plenty of green from the pinyon-juniper. To your left is a short side canyon, and up the main canyon you get your first glimpse of the pueblito. Continue on for another 0.2 mile or so to reach the pueblito in a total of 0.9 mile.
The boulder that holds the pueblito takes on the look of an early era tank, with the pueblito as the turret. However, this pueblito did not serve so much as an armed defensive position but as an advance lookout for hostile forces. In this part of New Mexico during the reestablishment of Spanish control, that meant raids from allied Indian tribes like the Southern Ute of Colorado. The pueblito was under attack often enough that it was eventually abandoned.
There is plenty of scrambling to be done in the area either up from the pueblito or further up-canyon; however, be careful not to get yourself caught in a bad spot or damage the fragile ecosystem.
STEEPED IN RUINS
Depending on where you came from or where you are headed, there are two other ruins in the area worth checking out, both found in or around Aztec. Salmon Ruins, located in Bloomfield and built around A.D. 1100, was a pueblo of up to 300 buildings, some of which were three stories high, along with ceremonial kivas. The name comes from a late-1800s homesteader, George Salmon, whose still-visible home and outbuildings occupy the same ground as the abandoned pueblo. Visit www.salmonruins.com for more information. Aztec Ruins, in Aztec, contains a restored ruin that is made up of 400 rooms. In addition, the Great Kiva was reconstructed to how it may have looked in A.D. 1100. This part of the grounds is known as the West Ruin. Much of the old pueblo—occupied once by 700 to 1,000 people—remains unexcavated. The name "Aztec Ruin" is a misnomer, being that the Aztec people never set foot this far north. If there were a name for this pueblo it is said to be "A Place by Flowing Waters." Visit www.nps.gov/azru for more information.
Bisti Badlands
TYPE: Day hike
SEASON: April to November
TOTAL DISTANCE: 4 miles (minimum)
RATING: Easy
ELEVATION GAIN: 50 feet
LOCATION: Bisti Wilderness, 35 miles south of Farmington
MAPS: USGS Alamo Mesa West, Alamo Mesa East, and Huerfano Trading Post SW
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GETTING THERE
The Bisti Wilderness is located south of Farmington off NM 371, or what is known as the Bisti Highway. The left turn onto CR 7297 comes at approximately 37 miles. Watch for the BISTI WILDERNESS sign approximately 0.25 mile before the turn. The wide, gravel road heads east for 2 miles to a signed junction. Turn left here and travel another 1 mile north, crossing over a wash to reach the small parking area on the other side (40 miles).
THE TRAIL
Even if there was a trail system for the Bisti Wilderness, also known as Bisti or the Bisti Badlands, it would fail to do justice to how you should discover this fantastical world, which is like no other in New Mexico. The Bisti is perfect for aimless wandering, like water finding the path of least resistance. You will be in the midst of a stone garden—sandstone stems holding teetering stone mushroom caps at impossible, seemingly playful angles. A maze of side arroyos take you to surreal landscapes filled with rock towers, fossilized tree stumps, and marble-sized stones, which are splashed across the ground as if a child's bucket had been turned over. There also are mud mounds with a surface like cracked rhino skin and dusted in white, powdery gypsum.
The Bisti (3,946 acres) is an easy place to explore, but a good map and compass can be useful. Two washes come together at the start of the hike and later split, with the De-na-zin Wash bending more to the south and the Alamo Wash continuing nearly due east. The Alamo is the main route, and as long as you stay within the wash, or keep a sense of where it is when you're off exploring, it is difficult to get lost in the Bisti. When the weather is clear, you can see the Chuska Range some 37 miles to the west. These mountains are a good landmark for orienting yourself.
The various rock formations are the result of four different intervals of geologic history. This area is made up of what is known as Lewis Shale, which is more than 1,000 feet thick in locations within the San Juan Basin. One of the layers or intervals, the Fruitland Formation, is coal-bearing. The ocean was present here during all of these periods, and as it retreated the landscape was dominated by the surrounding mountains and the arid indentation of the San Juan Basin.
Spencer G. Lucas, in the book Bisti, writes about how this environment appeared in the beginning of the last geologic period where the sea was present with descriptions like, "Huge conifers... towered above a jungle of ferns, palms, and other flowering plants," and "Horned dinosaurs... browsed unencumbered," and "the top of the terrestrial food chain rested solidly in the grasp of the enormous jaws of tyrannosaurid dinosaurs." Swamps, crocodiles, sharks, and clams were also part of this place some 100 million years ago.
The evidence of this surreal diversity is all around you in dinosaur bone fragments, the fossilized imprints of jungle plants, and numerous petrified tree stumps and sections up to 40 feet long. These will remind you of the existence of duckbilled dinosaurs and massive cypress trees. Water still moves through this stark, alien place from time to time, often in flash floods—water rushing along every possible channel to feed the central wash. Once-active rivulets are noticeable in the snake belly–like imprints you see across the sandy ground. Water is surely scarce in the Bisti Badlands. Even so, a few small shrubs, tufts of grasses, and lonely wildflowers have taken root along the wash.
Take time to enjoy the magic of the formations and think about the incredible transformations that have resulted over millions of years. To reach the heart of the sculpted features, you need to walk up the wash about 2 miles. There is still more to discover beyond this point, however, including channels that knife through tall dark clay hummocks. You can scramble on top of one of these for an overlook of this natural amusement park.
TOADSTOOL FORMATIONS IN THE BISTI BADLANDS
BISTI COAL LAND
This name is not too far from the truth, evidenced by the mining operation just north of the Bisti Wilderness. An aerial overview of this region reveals the extensive and violent scarring of the landscape due to energy development. Those scars are the visible aspects of these operations, but the impacts go even farther, with groundwater pollution and the overuse of precious water. Thankfully, areas of geological, geographical, and cultural importance have been preserved within the Bisti Wilderness, but it is also important to preserve the surrounding landscape.
De-na-zin Wilderness
TYPE: Day hike
SEASON: April to November
TOTAL DISTANCE: Variable
RATING: Moderate
ELEVATION GAIN: 100 feet
LOCATION: De-na-zin Wilderness, 28 miles south-southeast of Farmington
MAPS: USGS Alamo Mesa East and Huerfano Trading Post SW
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GETTING THERE
The Bisti Highway (NM 371) runs south from Farmington to reach the left turn onto CR 7500, the signed access to the De-na-zin Wilderness, in 44.6 miles. The road surface changes from pavement to packed dirt and it can be difficult to drive here after periods of heavy rain. Travel on CR 7500 for 13.3 miles (57.9 miles total) to a small, signed parking area on your left. It is also possible to access the wilderness from the east off US 550. From the junction of US 550 and CR 7500, it is 11.2 miles.
THE TRAIL
The Bisti (Hike 47) and De-na-zin are actually one contiguous wilderness area, and have been since 1996, with a combined 47,800 acres. Connected they may be, but their environments and ecologies are quite different. The De-na-zin is a magical playground of unusual water- and wind-shaped sandstone formations set in the bottom of the broad De-na-zin Wash. Just like at Bisti, you will find blocky stone towers capped with teetering rocks and basketball-sized rocks perched on cutbanks, just waiting for the next heavy rain to send them tumbling. But the De-na-zin Wash has much more life in the collection of sage, cactus, yucca, juniper, pinyon pine, chamisa, grasses, wildflowers, and tamarisk. With the plants come creatures like the bull snake, lizard, cottontail rabbit, jackrabbit, deer, and coyote.
From the parking area, follow the old Jeep road north toward the wash. Just before the road drops into the wash, a spur road branches off to the left to trace the rim through a sea of sage. This place is made for wandering, but one idea would be to explore the wash as far to the north and west as you want and then loop back to the rim and along this rim road.
As with the Bisti, the Den-na-zin is defined by four distinct geologic periods. The most recent interval occurred some 70 million years ago. This last period was witness to the ebb and flow of oceans, swamps, and cypress trees, the fading of the dinosaur, and tectonic shifts that pushed forth mountain ranges and created the San Juan Basin. It is quite striking to imagine the ecology of this place millions of years ago compared to its present state of extremes—inhospitably intense summer heat and bitingly cold winter winds. This place was once a humid swamp environment with a massive cypress forest, and creatures like the armored ankylosaur and duckbilled hadrosaur foraged through the lush jungle foliage. It is quite common to find fossilized plants, petrified trees and tree stumps, and dinosaur fossils in the wash and along side channels.
ESKIMOS IN THE DESERT
There is truth to this title in that the Apache tribe, of which the Navajo are part, have a link to the Athabaskan people of interior Alaska. The Navajo Diné language is considered Southern Athabaskan (there are 23 related Athabaskan languages), part of a 4,000-mile language link joined through tribes along coastal California and Oregon, as well as western Canada. The Athabaskan people are said to have made eastern and southern migrations from their homeland around A.D. 500. The Navajo people are said to have arrived in New Mexico sometime in the 1400s.
A ROCK CITY IN THE DE-NA-ZIN WILDERNESS
Peñasco Blanco
TYPE: Day hike
SEASON: April to November
TOTAL DISTANCE: 7.1 miles
RATING: Moderate
ELEVATION GAIN: 200 feet
LOCATION: Chaco Canyon National Historic Park, 48 miles south-southeast of Farmington
MAPS: USGS Kin Klizhin Ruins and Pueblo Bonito
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GETTING THERE
From Farmington, travel 12 miles east on US 64 to the town of Bloomfield. Turn right onto US 550, heading south. At 39.2 miles down US 550, you reach the signed, right-hand turn for CR 7900. Plenty of signs along the way indicate the upcoming turn and deter you from taking other roads. In 5 miles (56.2 miles total), CR 7900 meets CR 7950, where you turn right onto CR 7950. Shortly after the turn 3 miles down, the road surface changes from pavement to packed dirt. The road can be difficult to navigate after heavy periods of rain. At 77.1 miles the road transitions from dirt to pavement again as you enter the outer boundary of the park. You pass by the campground before reaching the visitor center at 79.7 miles. The fee is $16 per vehicle, good for seven days. However, the entrance fee is scheduled to go up to $20 by 2017. The backcountry trail book you can obtain at the visitor center is quite handy to have on the hike, especially for explaining the various petroglyphs found along the way. Following the 8-mile loop road, you pass by Pueblo Bonito to the short spur road to reach the parking area directly across from Pueblo Arroyo (83.7 miles).
THE TRAIL
The Chaco Wash was the fickle lifeblood of the Chacoan people during their 300 years here, gathering and delivering water only during the spring thaw and after heavy summer rains. Attempts were made to enhance a natural dam at the confluence of the Chaco and Escavado Washes, most likely to create some predictability in this precious resource for farming and everyday life. The Chaco Wash may not have water coursing through it when you hike to Peñasco Blanco, but it will provide access to two Great Houses, petroglyphs created by the people of Chaco and more recent works by the Navajos, a down-canyon view of the area from one of the more sacred sites of Chaco, and a record of astronomical history.
Kin Kletso is visible 0.2 mile down the roadway, which parallels the wash the entire way before crossing it for the climb up to Peñasco Blanco. Kin Kletso was built in A.D. 1130 and included 54 ground-level rooms. Behind the ruin is the trail access for New Alto and Pueblo Alto. Because of the wash, cottonwood trees pop up along the route, the largest concentration gathered by a bend in the wash near the crossing. The whole Chaco Canyon area is home primarily to grease bush, sagebrush, yucca, cactus, and rain-sparked wildflowers. Other flora species include sumac, Indian rice grass, Gamble oak, and chamisa.
At 0.9 mile, just after a hairpin bend, you arrive at Casa Chiquita. The landscape appears to be slowly swallowing up the squat structure. Like most of the pueblos in Chaco Canyon, it was rarely inhabited, its rooms used for food storage and as a place for sacred ceremony. No more than 0.2 mile past Casa Chiquita, at another hairpin turn, there are petroglyphs behind a large boulder. The spirals were made somewhere around 1,000 years ago. The animal figure was more than likely made a few hundred years ago. Some of the other markings etched on the wall are from visitors of the very recent past who could not help themselves.
PEÑASCO BLANCO
The marked Petroglyph Trail, which parallels the main trail, is reached at 1.5 miles. There are six different panels along this 0.3-mile stretch. The most elaborate is Panel 6, with its collection of beings, bighorn sheep, and spirals. But the most significant is Panel 4, with its supernatural figure and Katsina mask. Most of the petroglyphs are 15 to 25 feet off the ground.
Back on the main trail you hike another 0.7 mile (2.5 miles total) to reach the Chaco Wash crossing. The trail dips down into the wash and crosses it at a left bend, shortly before the main channel bends back to the right. A cluster of trees is situated next to the crossing. If heavy rains have occurred recently, the wash may be too dangerous to cross. Make sure to check with the visitor center for the most up-to-date information. Across the main channel, the trail wanders a short distance through the wash before beginning the climb to Peñasco Blanco. At 2.9 miles the trail splits. The right fork accesses the Super Nova in approximately 0.7 mile. This brilliant work of art is set in a shaded overhang of the cliff wall. The belief is that this pictograph (rock painting) may be an astronomical record from A.D. 1054 of an exploding star that we know today as the Crab Nebula.
Continuing straight, the trail winds its way up to Peñasco Blanco at 3.6 miles. In the distance to the west-northwest, you can see the natural sand-dune dam of the two washes. Stepping more to the south, once on the grounds of the ruin, you can see down the Escavado Wash to Mount Taylor. There is also a great view down Chaco Canyon. The blocky structure silhouetted above Pueblo Bonito on the mesa top to the east is New Alto.
NO RELATION TO ELMO
Five distinct styles of masonry were used in Chaco Canyon. The oldest, as seen in much of Pueblo Bonito, consisted of a single layer of stones and a generous amount of mud mortar. When the Chacoans started building multistory structures, they employed thicker interior walls with a thin veneer. These walls tapered as they went higher to distribute the weight. The last buildings constructed in Chaco in the time period of New Alto used what is known as the McElmo style—a masonry technique in which a thinner interior wall was combined with the thicker veneer of shaped sandstone. Upon entering Peñasco Blanco, you can see three styles in one stretch of wall across to the right of the open area.
Pueblo Alto Loop
TYPE: Day hike
SEASON: April to November
TOTAL DISTANCE: 5.1 miles
RATING: Moderate
ELEVATION GAIN: 350 feet
LOCATION: Chaco Canyon National Historic Park, 48 miles south-southeast of Farmington
MAPS: USGS Pueblo Bonito
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GETTING THERE
From Farmington, travel 12 miles east on US 64 to the town of Bloomfield. Turn right at the junction with US 550, heading south. At 39.2 miles down US 550, you reach the signed right turn for CR 7900. Plenty of signs along the way indicate the upcoming turn and deter you from taking other roads. In 5 miles (56.2 miles total), turn right onto CR 7950. Three miles down the surface changes from pavement to packed dirt. This road can be difficult to navigate after periods of heavy rain. At 77.1 miles, the road transitions back to pavement as you enter the park boundary. You pass by the campground to reach the visitor center at 79.7 miles. The fee is $8 per vehicle, good for seven days. The backcountry trail book available at the visitor center is a handy companion on the hike. Following the 8-mile loop road, you pass by Pueblo Bonito to reach the short spur road and the parking area, which is directly across from Pueblo Arroyo (83.7 miles).
THE TRAIL
No less than six of Chaco Canyon's 14 pueblos are clustered around this walk through history. Chetro Ketl and Pueblo Bonito, the two largest and most impressive ancient structures in the United States, are situated a short way after the start of this journey. Pueblo del Arroyo and Kin Kletso are within 0.2 mile of one another, followed by New Alto and Pueblo Alto. This Anazazi (ancient Puebloan people) home tour also provides overlook vistas of the surrounding landscape, including a stretch of the nearly 400 miles of roadway the Chaco people built over 1,000 years ago.
A dirt road leads beyond the wilderness check-in box to Kin Kletso in slightly more than 0.2 mile. This pueblo was constructed in the early 11th century and reflects the later McElmo building style used on other pueblos like New Alto and Pueblo Alto, situated on the mesa top beyond. The trail leads behind Kin Kletso and begins what at first appears to be an impossible course up the sheer sandstone cliff wall. With some high stepping, the trail follows a natural staircase set in a long crack in the cliff, ending atop the mesa. This is somewhat physically demanding and may not be suitable for everyone.
Now perched on the canyon rim, you have a high view across and up and down Chaco Canyon. The trail hugs the rim for the next 0.75 mile to the junction for Pueblo Alto. As mentioned earlier, the backcountry trail book available at the visitor center is worth picking up. It points out features like small carved basins used for making offerings and the fossilized shrimp and clam shells noticeable in many places across this ancient solidified sea bed. The path along the entire loop hike is marked with cairns when need be, so it's easy to follow.
At the junction, you can either continue down to the next lower level of the canyon rim to overlooks of Pueblo Bonito and Chetro Ketl or save the bird's eye overview of the grandest Great Houses for the end on the loop back. The trail moves up off the rim and onto a more vegetated mesa top. This area is a full-on desert, receiving less than 10 inches of precipitation annually, but still home to yucca, sagebrush, grease bush, prickly pear, and desert wildflowers. The simple theory for why the most majestic civilization of its time was constructed in Chaco Canyon is that the climate was different, presumably with a higher amount of moisture. There may have been years of bountiful precipitation here, but there were also years of excessive drought, which led to one of only a few theories to explain why Chaco was left to the spirits after less than 300 years.
Climbing the Chacoan Stairs, you reach New Alto and Pueblo Alto at 1.6 miles. New Alto is off to the left. Built in A.D. 1100, its 58 rooms contained within two stories served as a seasonal residence. Straight ahead is the continuation of what is referred to as the North Road. The 30-foot-wide road leads 40 miles from here to the Salmon Ruins in present-day Bloomfield. As mentioned, the Chacoans built nearly 400 miles of roadways—this in a culture that had no domesticated beasts of burden to pull a wagon. Archeologists speculate that the roads were built for ceremonial purposes.
Pueblo Alto, next to New Alto, was only one story high and contained 70 rooms. The midden, or trash pile, roped off to the east of the ruin has been tremendously useful in determining both habits and the area's degree of use. The trail strikes out to the east, moving down canyon. Fajada Butte is visible in the distance. Toward the top of the butte is a sun calendar constructed from three large flat sandstone slabs, and a spiral petroglyph is etched in the wall behind the vertically situated stones. The spiral is struck with a shaft, or dagger, of sunlight that on the summer solstice splits the spiral down the middle. The calendar's location high on a butte over 0.5 mile from any pueblo has led archeologists to theorize that its use was more ceremonial than practical.
There are some fantastic vistas of prominent geographic features from the Pueblo Alto area, and more farther along as you move down the canyon rim. To the south, the flat-topped mesa is the now dormant, but once wildly violent Mount Taylor. The Navajo country of the Chuska Mountains lies to the west, the short La Plata Range is to the north, and the silhouetted outline of the Jemez Mountains is to the east. By 2.1 miles, the trail slips back onto the scalloped sandstone rim to make a big bend around a box canyon. In the canyon are massive sandstone boulders, cleaved from the walls by the slow action of wind and water.
Where the canyon pinches together, you are by the Jackson Staircase (2.5 miles). In the process of road construction there came points when the natural topography posed engineering challenges for the Chacoan people. The solution here was to carve out steps in the wall to reach the mesa top and areas beyond. For the modern traveler, the trail to follow passes this ancient pathway and continues along the opposite rim of the box canyon. An area called the Ramp is reached at 3 miles. A very narrow split in the mesa provides the first stage of access down to the lower rim of the canyon. The trail drops enough to give you the feeling that it will access Chetro Ketl. It doesn't actually drop that far, but it does provide a perfect overview of this 1,100-year-old pueblo ruin.
AN OVERVIEW OF PUEBLO BONITO
Bending around the small box canyon, the trail climbs slightly before shadowing the rim to reach the junction with Pueblo Alto at 4.1 miles. If you didn't peek over the edge and down onto the pueblo, now is your chance. To finish the hike, retrace the first 1 mile back down the natural rock staircase and by Kin Kletso to the parking area.
SOUTH MESA HIKE
Across the Chaco Wash from Pueblo Bonito is the ruin known as Casa Rinconada, which has a Great Kiva with a diameter of more than 63 feet. From here a 3.6-mile loop runs to another ruin in Tsin Kletzin. There are overviews of Chaco Canyon and views of New Alto to the north and one of the southern Chacoan roads.
Acknowledgments
This book has come into being by way of support and encouragement from the past and present. Looking to the past, there is still a deep appreciation for Kermit Hummel of The Countryman Press for agreeing to print this book originally; to Lars Huschke, Klaus Huschke, and Wren Farris for their companionship in exploring a number of the places featured in this book; and to a host of others from other corners of my life who were present during the original creation of this book. Fast forward nearly ten years and we have a new edition that has come into being, thanks to the continued support of The Countryman Press and my amazing family—Sagi, my wife, and my two boys, Jet and Pierre. Connection to place and to one another couldn't be any more important with the global climate crisis we are fully immersed in, and if I were to infuse any sense of hope into this book it would be that people's experiences with the amazing places featured here serve as a means to reinforce our obligation to defend and protect northern New Mexico, as well as our own backyards, wherever they may be.
Resources
SANTA FE AREA
BLM–Albuquerque/Rio Puerco Field Office
Bureau of Land Management
100 Sun Avenue NE
Pan American Building
Suite 330
Albuquerque, NM 87109
505-761-8700; www.nm.blm.gov
Cabezon Peak; Ojito Wilderness; Tent Rocks
Santa Fe National Forest Supervisor's Office
11 Forest Lane
Santa Fe, NM 87508
505-438-5300; www.fs.usa.gov/santafe
Santa Fe Baldy Loop; Nambe Lake; Atalaya Mountain; Apache Canyon to Glorieta Baldy
Pecos RS
P.O. Drawer 429
Pecos, NM 87552
505-757-6121
Truchas Peak (east); Pecos Baldy Lake Loop; Cave Creek Trail; Hamilton Mesa; Mora Flats to Hamilton Mesa Loop
Pecos NHP
P.O. Box 418
Pecos, NM 87552
505-757-7241; www.nps.gov/peco
Pecos Ruins
Las Vegas RS
1926 North 7th Street
Las Vegas, NM 87701
505-425-3534
Hermit Peak
LOS ALAMOS AREA
Cuba RD
P.O. Box 130
Cuba, NM 87013
505-289-3264
San Pedro Parks Loop
Coyote RD
HC 78 Box 1
Coyote, NM 87012
505-829-3535
Chama River Wilderness; Box Canyon; Kitchen Mesa; Cerro Pedernal; Rim Vista Trail
Jemez RD
P.O. Box 150
Jemez Springs, NM 87025
575-829-3535
McCauley Warm Springs to Jemez Falls
Valle Caldera National Preserve
P.O. Box 359
Jemez Springs, NM 87025
575-829-4100; www.nps.gov/vall
Valle Caldera
Los Alamos Office
475 20th Street B
Los Alamos, NM 87544
505-667-5120
Cerro Grande; Bearhead Peak; Dome Wilderness
Bandelier NM
15 Entrance Road
Los Alamos, NM 87544
505-672-3861 x517; www.nps.gov/band
Bandelier Canyon Loop; Ruins Loop; Frijoles Falls
Española RD
1710 N. Riverside Drive
Española, NM 87532
505-753-7331
Window Rock
TAOS AREA
Tres Piedras RD
P.O. Box 38
Tres Piedras, NM 87577
505-758-8678
Cruces Basin Wilderness
Questa RD
P.O. Box 110
Questa, NM 87556
505-586-0520
Latir Loop; Placer Creek to Gold Hill Loop; Powderhouse Canyon; Clayton Camp
Rio Grande del Norte NM
226 Cruz Alta Road
Taos, NM 87571
www.blm.gov/nm/riograndedelnorte
Rim to River Loop
Carson National Forest
208 Cruz Alta Road
Taos, NM 87571
505-758-6200; www.fs.fed.us/r3/carson
Wheeler Peak; Lost Lake to Horseshoe Lake; Williams Lake
Camino Real RD
P.O. Box 68
Peñasco, NM 87553
505-587-2255
San Leonardo Lakes; Truchas Peak (west); Trampas Lakes and Hidden Lake; Serpent Lake
Las Vegas RS
1926 North 7th Street
Las Vegas, NM 87701
505-425-3534
Rio de la Casa Lakes Loop
New Mexico Department of Game & Fish
1 Wildlife Way
Sante Fe, NM 87507
505-476-8000; www.wildlife.state.nm.us
Tolby Creek Meadows
Capulin Volcano NM
P.O. Box 40
Capulin, NM 88414
505-278-2201; www.nps.gov/cavo
Capulin Volcano
FARMINGTON AREA
BLM–Farmington Field Office
Bureau of Land Management
6251 College Boulevard
Suite A
Farmington, NM 87402
505-564-7600; www.blm.gov/nm
Bisti Badlands; De-na-zin Wilderness; Simon Canyon Run
Chaco Culture NHP
P.O. Box 220
Nageezi, NM 87037
505-786-7014; www.nps.gov/chcu
Peñasco Blanco; Pueblo Alto Loop
WEB SITES
Wild Earth Guardians: www.wildearthguardians.org
Leave No Trace: www.LNT.org
National Weather Service: www.weather.gov
New Mexico Wilderness Alliance: www.nmwild.org
USGS maps: www.usgs.gov
References
Arora, David. All That the Rain Promises, and More... : A Hip Pocket Guide to Western Mushrooms. Berkeley, Calif.: Ten Speed Press, 1991.
Julyan, Bob. New Mexico's Wilderness Areas: The Complete Guide. Englewood, Colorado: Westcliffe Publishers, 1998.
Noble, David Grant, ed. New Light on Chaco Canyon. Santa Fe, New Mexico: School of American Research Press, 1984.
Noble, David Grant. Pueblos, Villages, Forts, and Trails: A Guide to New Mexico's Past. Albuquerque: University of New Mexico Press, 1994.
Parent, Laurence. Hiking New Mexico. Guilford, Connecticut: The Globe Pequot Press, 1998.
Index
Page numbers listed correspond to the print edition of this book. You can use your device's search function to locate particular terms in the text.
* Italics indicate illustrations and maps.
A
Abiquiu, 43, 95, 103, 107, 112, 116, 150, 152
Abiquiu Lake, 107, 110, 112, 116, 119
Agate Trail, 221
The Alamo, 231–232
Alamo Canyon, 136, 138, 140
Alamo Spring, 140
Alamo Wash, 231
Albuquerque, 70–71
Alcove House, 137, 140, 142, 143
altitude sickness, 21
Anastacio Trail, 94
Anazazi people, 201
Angel Fire, 216
Angostura Camp, 207
animals, 17, 21–22
Antonito, Colorado, 156
Apache Canyon, 64, 65
Apache Canyon to Glorieta Baldy, 8–9, 64–66, 65
Apache Creek, 65
Apache people, 235
Area of Critical Environmental Concern, 229
Arroyo Delagua, 94
Arroyo de las Lamitas, 150
Arroyo de Los Chamisos, 51
Arroyo del Palacio, 151
Arroyo del Yeso, 103
Arroyo Mora, 51
Arroyos, 20–21, 22, 33
Arroyo Seco, 174, 183
Aspen Peak, 130
Aspen Vista, 48
Atalaya Mountain, 8–9, 17, 49–51, 50
Athabaskan people, 235, 236
Augustiani, John, 84, 86
Aztec people, 16, 226, 229
Aztec Ruins, 230
B
backpacking, 17, 24
Baldy Mountain, 166
Baldy Mountain Trail, 65, 166
Bandelier, 17, 125, 132, 134, 136, 146
Bandelier, Adolph F. A., 137, 149
Bandelier Canyon Loop, 8–9, 16, 136–140, 137, 138, 139
Bandelier National Monument, 135, 136, 143, 144, 149
Bandelier Wilderness, 132
Barilla Mesa, 223
Barillas Peak Lookout, 45
Bass, Rick, 84
Battleship Rock, 16, 99, 100, 101
Bearhead Peak, 8–9, 128–131, 129, 130
Bearhead Ridge, 128, 131
Beatty's Flats, 79, 83
Beaver Creek, 154, 155
Bell-of-the-Woods Mountain, 181
Bernalillito Mesa, 33
Bernalilo, 28
Big Arsenic Campground, 157
Big Arsenic Spring, 159
Big Arsenic Trailhead, 159
Big Costilla Peak, 201
Big Eddy, 95
Bisti, 232
Bisti Badlands, 10–11, 16, 19, 231–233, 232, 233
Bisti Wilderness, 231–233
Black Mesa, 150, 151
Bland, 128
Bland Canyon, 128
Bloomfield, 230, 237, 241, 243
Blue Stone Mountain, 48
Bob Grounds Trail, 82
boulder caps, 39
Boundary Peak, 134
Boundary Peak Trail, 134
Box Canyon, 8–9, 103–106, 104, 105, 107, 110, 119
Box Canyon Trail, 104
Bull Creek Trail, 166, 168
Bull-of-the-Woods Pasture, 172, 174, 175
Bureau of Land Management, 35, 39
Bush, George W., 203
C
Cabezon Peak, 8–9, 16, 28–31, 29, 30, 32, 34
Cabresto Lake, 163
Cabresto Peak, 166, 168
Canyon de Chelly, 16, 141
Canyon Trail, 36, 38, 39
Capulin, 222, 223, 224
Capulin Canyon, 139
Capulin Trail, 134
Capulin Volcano, 10–11, 15, 16, 222–224, 223, 224
Capulin Volcano National Monument, 222
Carson National Forest, 203
Casa Chiquita, 238
Casa Rinconada, 244, 244
Cave Creek, 58, 61, 67, 69
Cave Creek Trail, 8–9, 59, 67–71, 68, 69, 70, 71
Cave Kiva, 143
Cave Loop, 36, 38, 39
cerebral edema, 21
Ceremonial Cave, 143
Cerro de la Olla, 157
Cerro de los Posos, 124
Cerro Grande, 8–9, 125–127, 126, 127
Cerro Pedernal, 8–9, 17, 28, 112–115, 113, 114, 116, 119
Cerro Picacho, 132, 134, 135
Chaco, 141
Chacoan people, 15–16, 237, 239, 243
petroglyphs of, 18
Chacoan Stairs, 243
Chaco Canyon, 15, 16, 18, 238, 239, 241, 242, 243, 244, 244
Chaco Wash, 237–238, 244
Chama, New Mexico, 95, 150, 156, 162
Chama Basin, 116, 117
Chama River, 16, 28, 95, 107, 112, 115, 151
Chama River Wilderness, 95–96, 110
Chavez Canyon, 98
Chetro Ketl, 241, 242, 243
Chimayo, 190
Chimayosos Peak, 57, 78, 193
Chimney Rock, 103, 110
Chinle sand lands, 107
Cholla, 23, 30
Christ in the Desert Monastery, 98, 116, 119
Chuska Mountains, 243
Chuska Range, 232
Cimarron, 162
Cimarron Canyon, 216
Cimarron Canyon State Park, 216, 221
Cimarron Cutoff, 224
Cimarron Range, 169, 173, 178, 202, 202, 220
Cimarron River, 17, 181, 216, 219, 221
Civil War, Glorieta battlefield in, 70–71, 74
Clayton Camp, 10–11, 204–206, 205, 206
Clea Creek Canyon Trail, 221
Cleveland, 211
Clovis, New Mexico, 15
Clovis man, 15
Coalition for the Valle Vidal, 203
Cochiti, 43
Cochiti people, 36, 40, 141
Cochiti Pueblo, 16, 39, 40, 143
Cochiti Reservoir, 130
Coelophysis dinosaurs, 107, 109, 110, 111, 117
Colin Neblett Wildlife Area, 216, 220, 221
Colle Canyon, 131
Columbine, 82
Columbine Campground, 169
Columbine Creek, 169, 171
Columbine Creek Trail, 171
Columbine-Hondo Wilderness, 167, 169, 178
Columbine-Twinning National Recreation Trail, 171, 173
Comanche Creek, 202, 202, 204, 206
Comanche people, 162
Commonweal Conservancy, 66
Compasante, 104
Costilla, 199, 204
Costilla Creek, 202, 202
Costilla Reservoir, 201
Cougas, 21
Cowles, 52, 58, 76, 80
Cowles Campground, 52, 58, 67
Coyote Lake, 94, 112
Crab Nebula, 239
Cruces Basin Wilderness, 8–9, 17, 154–156, 155, 156, 156
cryptobiotic soil, 110
Cuba, 32, 90
Cumbres & Toltec Scenic Railroad, 156
D
Dale Ball Trail System, 49, 51
Dave's Creek Trail, 63
day-hiking, 24
Deception Peak, 48
Deckweiler Trail, 59
Deer Creek, 173
De-na-zin Wash, 231, 234
De-na-zin Wilderness, 10–11, 20, 234–236, 235, 236
Denver, 156
Diablo Creek, 154
Dinetah, 226
Divide Trail, 208, 210, 213
Dockweiler Trail, 52, 55, 63
The Dome, 192
Dome Mountains, 139
Dome Wilderness, 8–9, 125, 130, 132–135, 133, 134, 138, 168
fire at, 127
Dome Wilderness Lookout, 132, 134
Dromomeroni romeri, 117
Duckweiler Trail, 69
duct tape, 25
Dulee, 162
Durango, Colorado, 156
E
Eagle Nest, 176, 216, 220–221
East Fork, 210
East Fork Jamez River, 99, 102, 124
East Fork Red River, 177, 182
East Fork Trail, 181
East Pecos Baldy, 55, 57, 58, 61, 63, 70, 78, 83, 190, 192, 193
summit view from, 62
East Truchas Peak, 69
Echo Amphitheater, 119–120
Elizabethtown, 173
Elizabethtown Ditch, 182
El Porvenir Campground, 84
El Vado Reservoir, 95
Enchanted Lake, 45, 76, 79
equipment, 23–24
Escavado Wash, 237, 240
Española, 116, 150, 190
F
Fajada Butte, 16, 243
Farmington, 226, 231, 234, 237, 241
Flag Mountain, 171
flash flooding, 20–21, 105, 232
Folsom people, 15, 201
Fork Creek, 164
Fort Union, 70, 224
Fraser Peak, 185
Frazer Mountain, 181
Frey Trail, 143
Friends of Otero, 35
Frijoles Canyon, 16, 127, 136, 137, 138, 140, 141, 143, 146, 149
Frijoles Creek, 125, 149
Frijoles Falls, 8–9, 146–149, 147, 148
Frijoles River, 146
Frijolito, 138
Fruitland Formation, 232
G
Gaining Access Into Nature (GAIN) permits, 216
Galisteo Basin, 64, 65, 66
Galisteo Creek, 65
Gallina Lake, 112
Gallinas, 84
Gascon Trail, 79
geography, 21
Ghost Ranch, 16, 17, 28, 95, 103, 104, 106, 107, 111, 112, 116, 117, 119, 120
Conference Center, 103, 107
Giggling Springs, 102
Gila Wilderness, 168
Giusewa, 102
Glorieta Baldy, 18, 64, 65, 66, 72
Glorieta battlefield, 70–71, 74
Glorieta Conference Center, 66
Glorieta Mesa, 73
Glorieta Pass, 73
Glorieta-Pecos Corridor, 73
Gold Hill, 169, 171, 172, 173, 176, 177, 182
Goose Lake, 172
Granda, Colorado, 224
Great House, 242–243
Great Kiva, 230, 244, 244
Great Plains, 86, 212, 213
Gregorio Reservoir, 93
Gruninger, Otto, 64
H
Hamilton Mesa, 8–9, 17, 61, 63, 69, 76–79, 77, 78, 80, 83
Hamilton Mesa Trail, 76, 79, 83
Havenweep, 16
hazards, 19–20
headlamps, 25
Heart Lake, 164, 166
Heart Lake Trail, 168
Hermit Peak, 8–9, 79, 84–88, 85, 87
Hermit Peak Trail, 86
Hermits' Cave, 86
Hewett, Edgar Lee, 137
Hidden Lake, 10–11, 195–198, 196, 197, 198
high mountain lakes, 14
hike off-days/season, 26
hiking poles, 24
Holy Ghost, 52, 58, 76, 80
Holy Ghost Creek, 45
Hopi people, 16
Horseshoe Basin, 177
Horseshoe Lake, 177, 178, 181, 182, 213
Horsethief Creek, 59
Horsethief Meadow, 45, 59
Huene, Friedrich von, 107
I
Iron Gate Campground, 67, 76, 80, 83
J
Jacks Creek, 55
Jacks Creek Trail, 55, 63
Jackson Staircase, 243
Jack's Trail, 52
Jasper Trail, 221
Jemez Falls, 17, 99, 100, 102
Jemez Mountains, 17, 29, 34, 40, 43, 49, 51, 57, 90, 115, 128, 134, 137, 139, 150, 151, 194
Jemez National Recreation Area, 128
Jemez River, 100
Jemez Springs, 99, 102
Bath House, 102
Jemez State Monument, 102
Jicarilla Apache, 162
Jicarita Peak, 57, 78, 198, 208
Johnson Mesa, 223
Jose Vigil Lake, 55, 57, 193, 194
Juniper Campground, 143
K
Kansas City, Missouri, 224
Kasha-Katuwe, 39
Kearny, Stephen Watts, 224
Kin Kletso, 238, 241–242
Kitchen Mesa, 8–9, 20, 103, 107–111, 108, 109, 119
Kitchen Mesa Trail, 103
Kivas, 15
Kozlowski Ranch, 74
L
La Cal Basin, 176, 177, 181
La Cueva Mill, 215
Lagunita Creek, 168
Lagunitas, 154
La Junta Point, 161
La Junta Trail, 160
Lake Fork, 164, 166
Lake Fork Creek, 164
Lake Fork Peak, 185, 186
Lake Katherine, 17, 41, 43–44
Lake Peak, 43, 45, 46, 47–48
Larkspur Trail, 83
Las Trampas, 187, 189, 195
Las Vegas, 84, 211, 224
Latir Lakes, 167
Latir Loop, 10–11, 163–168, 164, 165, 167
Latir Mesa, 20, 164, 166
Latir Peak, 166, 167
Latir Peak Wilderness, 18
Latir Wilderness, 17, 163, 166, 169, 173
L'Eau des Morts, 215
Lewis Shale, 232
Little Arsenic Campground, 160, 162
Little Arsenic Rim Trail, 160
Little Arsenic Spring, 160
Little Costilla Peak, 201, 202, 202
Lobo Peak, 169, 171
Logo Creek canyon, 155
Long Canyon Trail, 176
Long House, 137, 141, 142, 143
Los Alamos, 99, 102, 121, 125, 128, 136, 141, 146
Los Griegos, 102
Los Pinos Guest Ranch, 67, 69
Los Pinos Trail, 94
Lost Lake, 45, 178, 181
Lost Lake to Horseshoe Lake, 10–11, 178–182, 179, 180
Los Trampas Trail, 82
Lower Frijoles Fall, 149
Lower Tolby Trail, 218, 219
Lower Trampas, 198
Lucas, Spencer G., 232
Lumbre, Piedra, 107
Lummis Canyon, 138
M
Maverick Falls Trail, 220
McCauley Warm Springs, 99, 100–101
McCauley Warm Springs to Jemez Falls, 8–9, 99–102, 100, 101
McCrystal Ranch, 206
McElmo style, 239, 242
McGarrity, Michael, 84
Mesa del Camino, 98
Mesa Verde, 16, 141
Middle Fork Creek, 178
Middle Fork Lake, 181, 213
Middle Fork Red River, 176, 177, 178
Middle Fork Rio de la Casa, 211, 213
Middle Fork Rio Santa Barbara, 187
Middle Truchas Peak, 57, 61, 78
Mission Complex, 74
Montezuma, 74
Montezuma Hotel, 88
Montoso Campground, 162
Mora, 211, 212, 215
Mora Canyon, 82
Mora Flats, 76, 80, 82
Mora Flats to Hamilton Mesa Loop, 8–9, 80–83, 81
Mora River, 212
Mora Valley, 215
Moreno Valley, 178, 181, 182
Mountain Branch, 224
mountain food, 25
Mount St. Helens eruption, 121
Mount Taylor, 28, 240, 243
Mount Walter, 173, 177, 181, 186
N
Nambe Lake, 8–9, 43, 46–48, 47, 48
Nambe Pueblo, 46
national monuments, 22
National Oceanic and Atmospheric Administration, 20
National Parks Pass, 36, 136, 141, 146
Nature Conservancy, 51
Navajo Diné language, 235–236
Navajo Lake State Park, 226
Navajo people, 16, 28, 226, 235, 236, 238
New Alto, 238, 239, 242, 243, 244, 244
New Mexico Game and Fish, 220
New Mexico Museum of Natural History and Science, 32
North Fork Lake, 212, 213, 214
North Fork Rio de la Casa, 215
North Fork Rio Quemado, 194
North Truchas Peak, 57, 61, 78, 194
O
Ojitos Trail, 8–9, 95–98, 96, 97
Ojito Wilderness, 8–9, 16, 17, 32–35, 33, 34
O'Keeffe, Georgia, 106, 107, 109, 112, 115
O'Keeffe, Georgia, Museum, 115
Osha Creek, 154, 155
Otowi Ruins, 141
P
Pacer Creek, 169
Pacheco Lake, 76, 79
Pajarito Plateau, 64, 135, 137
Palisades, 216
Palisades Sill, 219
Panchuela Campground, 52, 58, 63, 67
Panchuela Creek, 52, 55, 58, 59, 63, 67, 68, 69
Pangea, 118
Paseo de Peralta, 41, 46, 49, 64
Pecos, 16, 17, 52, 58, 67, 76, 80, 86, 141, 189
Pecos Baldy, 59, 61, 78, 83
Pecos Baldy Lake, 17, 52, 55, 57, 58, 61, 63
Pecos Baldy Lake Loop, 8–9, 58–63, 60, 61, 62
Pecos Falls, 76, 79, 83
Pecos Lake, 59
Pecos National Historic Park, 72, 74
Pecos Pueblo, 69, 72, 79
Pecos River, 15, 52, 67, 68, 69, 73, 79, 80, 83
Pecos Ruins, 8–9, 72–74, 73, 75
Pecos Wilderness, 17, 18, 19, 41, 43, 45, 46, 48, 52, 55, 57, 59, 61, 64, 67, 68, 69, 70, 73, 76, 79, 80, 86, 168, 177, 187, 189, 193, 194, 198, 208
Pedernal, 109, 110
Peñasco, 187, 195, 207, 210
Peñasco Blanco, 10–11, 237–240, 238, 239
Penas Negras Trail, 93
Penitente Peak, 43
Penzoil Corporation, 203
Peralta Canyon, 128, 130, 131
petroglyphs, 18, 32
Petroglyph Trail, 239
Picacho, 50
Placer Creek to Gold Hill Loop, 10–11, 169–173, 170, 172
Placer Creek Trail, 171
Placer Fork, 172
plains people, 17, 74, 212
plants, 17, 21
Ponderosa Campground, 140
Porvenir Creek, 86
Powderhouse Canyon, 10–11, 199–203, 200, 202
Powderhouse Canyon Trail, 199
precambrian granite rock layers, 17
Prijoles Canyon, 40
Pueblo Alto, 238, 241–242, 243, 244
Pueblo Alto Loop, 10–11, 241–244, 242, 244
Pueblo Arroyo, 237, 241
Pueblo Bonito, 241, 242, 244, 244
Pueblo Canyon, 141
Pueblo del Arroyo, 241–242
Pueblo del Norte, 163, 178, 183
Pueblo people, 17, 159, 192
Pueblo Revolt (1680), 74, 226
pueblos, 15
pulmonary edema, 21
Pyramid Peak, 211, 213
Q
Questa, 157, 163, 169, 178, 199, 204
Quivira Coalition, 204
R
racks, 24
Raton, 222
Raton-Clayton Volcanic Field, 224
Raton Mesa, 223
rattlesnakes, 21–22, 33, 34
Ravens Ridge Trail, 41, 46
Redondo Peak, 61, 78, 83, 121, 127
Red River, 160, 160, 161, 163, 167, 169, 172, 178
Red River Gorge, 161
Red River Ski & Ride Area, 173
Red River Trail, 173
Resumideo Campground, 94
Rim to River Loop, 10–11, 157–162, 158, 160, 161
Rim Vista Trail, 8–9, 116–120, 117, 118, 119
Rinconada Loop Trail, 161
Rincon Bonito, 45, 79, 208, 213
Rincon Loop Trail, 161
Rio Bravo Nature Trail, 161
Rio Cañones, 115
Rio Canyon, 149
Rio Chama Wilderness, 116, 119
Rio de la Casa Lakes Loop, 10–11, 69, 211–215, 212, 214
Rio de las Trampas, 198
Rio de las Vacas, 93, 94
Rio de los Chimayosos, 57
Rio de los Pinos, 155
Rio Grande, 16, 40, 57, 67, 127, 134, 138, 146, 149, 157, 159, 160, 160, 162, 173, 189, 204
Rio Grande del Norte National Monument, 157
Rio Grande Gorge, 157, 159
Rio Grande Gorge Bridge, 157
Rio Grande Rift, 157
Rio La Casa Lakes, 187
Rio Medio, 55, 190, 192
Rio Mora valley, 76, 78, 80, 82
Rio Nambe, 41, 43, 46
Rio Nambe Trail, 43
Rio Puerco, 29, 94, 115
Rio Quemado Falls, 194
Rio Quemado Trail, 57, 190, 192, 194
Rio San Leonardo, 189
Rio Santa Barbara, 187, 195, 207, 210
Rio Valdez drainage, 83
Rito del Medo, 168
Rito Encino, 115
Rito los Esteros drainage, 82
Rito Perro drainage, 61
Rito Perro Trail, 55, 61, 63
Rociada Trail, 76, 80, 82
Rocky Mountains, 43
Round Mountain, 63
Ruins Tour, 8–9, 141–145, 142, 144
Ruth Hall Museum of Paleontology, 111
Rutlodon, 111
S
St. Peters Dome, 132, 134, 135
St. Peters Dome Trail, 134
Salmon, George, 230
Salmon people, 16
San Antonio River, 99, 124
Sanchez Canyon, 132
Sandia Crest, 39
Sandia Mountains, 29, 34, 39, 40, 127, 135, 137
Sangre de Cristo Mountains, 15, 17, 40, 41, 43, 46, 48, 49, 50, 51, 57, 59, 73, 86, 110, 127, 130, 137, 151, 161, 173, 177, 224
San Gregorio Lake, 90
San Jose de Gracia Church, 189
San Jose Trail, 93
San Juan Basin, 232, 235
San Juan Mountains, 149, 159
San Juan River, 226, 228, 229
San Leonardo Lakes, 10–11, 187–189, 188
San Luis, 28
San Miguel Mountains, 132
San Pedro Mountains, 90
San Pedro Parks Loop, 8–9, 17, 90–94, 91, 92
San Pedro Parks Wilderness, 90
Santa Barbara, 210
Santa Barbara Lakes, 187, 210, 213
Santa Cruz, 152
Santa Cruz Lake, 190
Santa Fe, 17, 32, 36, 46, 64, 67, 71, 152
Santa Fe Baldy, 17, 41, 43, 44, 46, 61, 78, 79
Santa Fe Baldy Loop, 8–9, 41–45, 42, 44
Santa Fe Canyon Preserve, 49, 51
Santa Fe National Forest, 64
Santa Fe River, 51
Santa Fe Ski Basin, 41, 46, 48, 50
Santa Fe Trail, 224
Santiago Lake, 76, 79
Santo Tomas, 152
San Ysidro, 28
scorpions, 22
Serpent Lake, 10–11, 207–210, 208, 209
Shaggy Peak, 65
Sibley, Henry H., 70, 71
Sierra Club, 203
Sierra Grande, 223
Sierra Nacimiento uplift, 90
Simon Canyon, 226, 228, 229
Simon Canyon Pueblito, 228
Simon Canyon Ruin, 10–11, 226–230, 227, 228
Simpson Peak, 177, 182, 186
Sipapu Ski Area, 207
Skyline Trail, 43, 44, 45, 59, 70, 79, 193–194
South Fork, 212
South Mesa Hike, 244
Spanish conquistadors, 16
Spirit Lake, 44, 45
Steiglitz, Arthur, 106
Stewart Lake, 44
Stone Lions, 140
Stone Man Mountain, 192
Storrie Lake, 86, 211
Summer, Edwin V., 224
Super Nova, 239
T
Taos, 16, 141, 154, 157, 162, 163, 169, 174, 176, 177, 178, 183, 187, 190, 199, 204, 207, 216
Taos Pueblo, 174, 183
Taos Ski Valley, 172, 173, 174, 181, 183
Tent Rocks, 8–9, 16, 17, 18, 36–40, 37, 38, 102
Tererro, 52, 58, 67, 68, 79
Tesuque Peak, 78
Tesuque Pueblos, 48
Tetilla Peak, 202, 202
Thornton Ranch, 66
Tocolote Range, 73
Tolby Creek, 210, 219, 221
Tolby Creek Campground, 216
Tolby Creek Meadows, 10–11, 216–221, 217, 218, 219
Tolby Creek Meadows Trail, 216, 218, 221
Tolby Meadows, 220
Toltec Mesa, 155
trail etiquette, 25
trail information and maps, 26
Trailriders Wall, 55, 57, 58, 61, 63
views north of, 53
Trampas Lakes, 10–11, 17, 79, 187, 189, 195–198, 196, 197, 198
Trampas Peak, 198
Tres Piedras, 154
Truchas, 190, 192, 195
Truchas Lakes, 56, 57, 78, 79, 187, 194
Truchas Peak (East), 8–9, 52–57, 53, 54, 56
Truchas Peak (West), 10–11, 190–194, 191, 192, 193
Truchas Peak, 20, 43, 61, 63
Truchas Peaks, 17, 58, 70, 83, 177, 182, 189, 192
Tsankawi ruins, 144–145
Tsin Kletzin, 244, 244
Turkey Springs, 135
Tusas Ridge, 176
Tyuonyi, 137, 141
Tyuonyi Pueblo, 142
U
U.S. Forest Service, 19
Upper Camp Trail, 105
Upper Canyon, 46
Upper Costilla Creek, 199
Upper Costilla valley, 201
Upper Crossing, 138, 139, 140
Upper Frijoles Canyon, 136
Upper Frijoles Falls, 148, 149
Upper Tolby Trail, 218, 220–221
Utah Canyonlands, 98
V
Vacas Trail, 93, 94
Valdez Trail, 82
Valle Caldera, 8–9, 16, 20, 99, 121–124, 122, 123, 125, 127, 128, 138
Valle Vidal, 17, 199, 201, 202, 202–203, 204
Valle Vidal Protection Act, 203
Valverde y Cosio, Antonio, 43
Van Diest Peak, 202, 202
Vega del Oso, 94
Vega Redondo, 94
Vermejo Ranch, 201
Vidal Creek, 206
Viga, 211
Virsylvia Peak, 167
W
Wagon Mound, 224
Walker Flats, 211, 212, 213
Walters, Harold D., 186
water purification, 24–25
weather, 20–21
West Fork Red River, 176, 177, 178, 181
West Ruin, 230
Wheeler, George M., 186
Wheeler Peak, 10–11, 17, 57, 162, 169, 173, 174–177, 175, 176, 181, 182, 185, 220
Wheeler Peak Wilderness, 57, 174, 177, 178, 181, 183, 185, 186, 194
White Mesa, 32, 34–35
White Rock Visitor Center, 136, 141, 146
Wild and Scenic Rivers, 68, 79, 119
Wild Earth Guardians, 189
Williams Lake, 10–11, 17, 169, 177, 183–186, 184, 185
Willow Creek, 17, 169, 171, 173
Willow Creek Trail, 171
Willow Fork, 171
Wilson, Woodrow, 222
Window Rock, 8–9, 17, 150–152
Winsor Creek, 44
Winsor Trail, 41, 44–45, 46, 67
Woodward Ridge, 128
Y
Yapashi Pueblo, 17, 139
Yapashi Ruins, 138, 138, 139, 140
Yapashi Trail, 136–137
Yeso Canyon, 105
Z
Zuni people, 16, 140, 141
OTHER BOOKS IN THE 50 HIKES SERIES
50 Hikes Around Anchorage
50 Hikes in Washington
50 Hikes in Oregon
50 Hikes in the Sierra Nevada
50 Hikes in Utah
50 Hikes in Orange County
50 Hikes in the Ozarks
50 Hikes in Michigan
50 Hikes in Michigan's Upper Peninsula
50 Hikes on Michigan & Wisconsin's North Country Trail
50 Hikes in Ohio
50 Hikes in West Virginia
50 Hikes in the North Georgia Mountains
50 Hikes in South Carolina
50 Hikes in Northern Virginia
50 Hikes in Eastern Pennsylvania
50 Hikes in New Jersey
50 Hikes in the Lower Hudson Valley
50 Hikes in the Berkshire Hills
50 Hikes in the White Mountains
50 Hikes in Vermont
50 Hikes in Coastal & Inland Maine
Over time trails can be rerouted and signs and landmarks altered. If you find that changes have occurred on the routes described in this book, please let us know so that corrections may be made in future editions. The author and publisher also welcome other comments and suggestions. Address all correspondence to:
50 Hikes Editor
The Countryman Press
P.O. Box 748
Woodstock, VT 05091
© 2007 by Kai Huschke
Second Edition
All rights reserved. No part of this book may be reproduced in any form or by any electronic or mechanical means, including information storage and retrieval systems, without permission in writing from the publisher, except by a reviewer, who may quote brief passages.
ISBN 978-0-88150-680-8
ISBN 978-1-58157-546-0 (e-book)
Cover and interior photographs by the author
Series cover design by Steve Attardo
Cover photograph © Ralph Lee Hopkins/National Geographic/Getty Images
Back cover photograph © Kai Huschke
Published by The Countryman Press, P.O. Box 748, Woodstock, VT 05091
Distributed by W. W. Norton & Company, Inc., 500 Fifth Avenue, New York, NY 10110
| {
"redpajama_set_name": "RedPajamaBook"
} | 3,154 |
Q: Regular Expression to parse Query Output I have a need to execute a metadata query which will dump a list of tables into a file. However, I need a way to eliminate all formatting besides the tableId itself. Can this be done through a regex? Appreciate all help in advance.
+-------------------------------------+-------+
| tableId | Type |
+-------------------------------------+-------+
| t_margins | TABLE |
| t_rev_test | TABLE |
| t_rev_share | TABLE |
A: You have some options, but I would suggest something like this:
^\| (\S+)
It will match on the line from the start, a pipe, a space and then all non-spaces. The non-spaces will be your tableId. Here is a little example in Python:
import re
my_string = '''| t_margins | TABLE |
| t_rev_test | TABLE |
| t_rev_share | TABLE |'''
my_list = my_string.split('\n')
for line in my_list:
match = re.search("^\| (\S+)", line)
print (match.group(1))
This will give you:
t_margins
t_rev_test
t_rev_share
A: The following regexp captures just the column values of the first column:
^\| (\w+)
https://regex101.com/r/gODhra/3
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,137 |
An opportunity wasted
Amna Umar Khan
At the Organisation of Islamic Cooperation (OIC) in Makkah, Pakistani Prime Minister Imran Khan started off his first ever OIC speech, emphasising the issue he deems the most urgent and compelling concern facing Muslims of the world. He said, "I would raise, first and foremost, the most important question, about whenever in the Western countries, people blaspheme our Prophet (Peace Be Upon Him), I always felt that the response from the Muslim Ummah, and the OIC, was lacking. Therefore I wanted to use this platform (to say) that the OIC owes a responsibility to the Muslim world that when anyone in the Western world blasphemes the Prophet (PBUH), it is a failure of the OIC that we have not been able to explain to the western people the amount of pain they cause us."
The rest of Prime Minister Imran Khan's speech centred upon the oppression the Muslims are facing in Palestine and Kashmir by being deprived of their right to a state and to self-determination. He also said that the Muslim world was not paying much attention to science and technology, despite being on the verge of another industrial revolution with the artificial intelligence and new technologies coming in, and urged more emphasis on education and science.
As with all things to do with Imran Khan, the reception to this speech has been divided. Those who were his fans lauded his speech and the rare occurrence of a Muslim leader headlining the topic of blasphemy in front of the OIC, the second largest intergovernmental body after the UN. Yet his speech has received some criticism, not all from PTI haters or partisan groups, but from some in the international and Arab community as well. The platform, that of the OIC which represents the Muslim collective of the world, is a very meaningful and significant one; thus it would not be out of place to make some constructive criticism of the Prime Minister's speech.
For one, bringing up blasphemy by Western actors as the first and foremost topic in his maiden speech at the OIC begs us to answer the question as to whether that is the most pressing issue facing Muslims currently. Certainly, blasphemy and casual disrespect of Islam in the West is a concern for Muslims; it leads to further marginalisation of the Muslim community in the Western world and causes anti-Muslim radicalisation, leading to the kinds of disasters that we saw in the Christ Church mosque massacre in March. The organised instances of blasphemy against the Prophet (PBUH) in the West also cause unrest and instability in the Muslim-majority countries, which is perhaps precisely what those bad-faith actors intended. Truly, it is an issue that causes distress and damage to the Muslim world, and we need to better communicate to the West the severe harm that occurs due to Islamophobic speech and actions.
Yet, though we recognise that blasphemy is an issue, is it truly such an urgent problem that the Prime Minister of Pakistan should identify it as a failure of the OIC? The last major incident of blasphemy in the West had been that of Geert Wilders, an obscure politician in the Netherlands, who had proposed an extremely disrespectful competition to be held in order to insult Muslims. This had last occurred in August of 2018 and was rightfully cancelled after the Muslim world registered their protest to it. This was nearly a year ago, and since then, although the environment in Western countries may have become increasingly hostile towards Muslims, no such incident which can be called "blasphemous" or disrespectful to the Prophet (PBUH), has occurred that would warrant the kind of urgency implied in the Prime Minister's speech.
The argument could be made that even with the rare incidents of blasphemy in the West, there was a need to emphasise communication with the West due to the progressively hostile environment for Muslims. This argument holds weight but is ignoring the context behind why the OIC meeting was called, and the very significant geopolitical position Pakistan finds itself in today. Tensions between Iran and the Gulf allies of the United States have escalated to the point that war is not too far off if conciliation and peace efforts are not held by neutral stakeholders. Preceding the OIC conference were two emergency Arab meetings the night before in Makkah criticising Iran's behaviour and influence in countries like Syria, Iraq and Lebanon. This clearly indicates that the goal of the OIC conference was to deal with the extremely crucial question of tensions with Iran, which could boil over to a devastating conflict across the entire Middle East and sub-continent area.
Pakistan, being a neighbour of Iran, and an ally of Saudi Arabia, is in a precarious situation and could be the country that could facilitate de-escalation between the two. It appears Iran thinks so too, evidenced by Imran Khan's visit to Tehran right before the OIC. With this context in mind, it would perhaps been more appropriate had our Prime Minister emphasised the importance of peace and brotherhood among Muslims and started off the OIC conference on an anti-war and harmonious note. Instead, while our Prime Minister's speech was certainly impactful and reflected the sentiments of Muslims everywhere, it felt somewhat of a waste of an opportunity to de-escalate a conflict which is right on our doorstep, a conflict which, if exacerbated, could result in complete devastation of our region.
The OIC has been criticised in the past for lack of solutions for Muslim countries in crises. By setting the tone for peace and resolution, Imran Khan could have used the OIC's influence to shape the Muslim body for a more engaging, instrumental role in the geopolitics of today. Prioritising blasphemy cases in the West is definitely a crowd-winner and will appeal to Muslims in Pakistan; yet even after the speech, there is little that the OIC can and will do to combat such incidents other than through condemnation. Our Prime Minister's speech was certainly impactful, yet in the grand scheme of things, will likely have little impact at all.
9:08 AM | September 22, 2018
India's back down wasted opportunity of peace: FO
I wouldn't have wasted my time on Trump, says Greta Thunberg
Nation's precious time wasted in aimless protests, says CM Buzdar
JUI-F sit-in becomes opportunity for some businesses
Content for June 03, 2019 is not available×
IF IT'S SO EXPENSIVE STOP EATING IT!!
Durdana Najam
Has BJP ended dynastic politics in India?
Senator (R) Sehar Kamran
National Action Plan: bigger responsibilities lie ahead
The Nuances Of Nepotism
New Trade War
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Children with HIV
Sindh under attack of AIDS | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,618 |
\section{Introduction}
In quark-diquark models, baryons are assumed to be composed of a constituent quark, $q$, and a constituent diquark, $Q^2$ \cite{Ida:1966ev,lich}.
The effective degree of freedom of diquark, introduced by Gell-Mann in his original paper on quarks \cite{GellMann:1964nj}, has been used in a large number of studies, from one-gluon exchange to lattice QCD calculations \cite{Jakob:1997,Brodsky:2002,Gamberg:2003,Jaffe:2003,Wilczek:2004im,Jaffe:2004ph,Selem:2006nd,DeGrand:2007vu,BacchettaRadici,Forkel:2008un,Anisovich:2010wx} and, more recently, also in tetraquark spectroscopy \cite{Maiani:2004vq,Santopinto:2006my}.
Up to an energy of 2 GeV, the diquark can be described as two correlated quarks with no internal spatial excitations \cite{Santopinto:2004hw,Ferretti:2011zz}.
Then, its color-spin-flavor wave function must be antisymmetric.
Moreover, as we consider here only light baryons, made up of $u$, $d$, $s$ quarks, the internal group is restricted to SU$_{\mbox{sf}}$(6).
If we denote spin by its value, flavor and color by the dimension of the representation, the quark has spin $s_2 = \frac{1}{2}$, flavor $F_2={\bf {3}}$, and color $C_2 = {\bf {3}}$.
The diquark must transform as ${\bf {\overline{3}}}$ under SU$_{\mbox{c}}$(3), hadrons being color singlets. Then, one only has the symmetric SU$_{\mbox{sf}}$(6) representation $\mbox{{\boldmath{$21$}}}_{\mbox{sf}}$(S), containing $s_1=0$, $F_1={\bf {\overline{3}}}$, and $s_1=1$, $F_1={\bf {6}}$, i.e., the scalar and axial-vector diquarks, respectively \cite{Wilczek:2004im,Jaffe:2004ph}. If we indicate the possible diquark states by their constituent quark content in square (scalar diquarks) or brace brackets (axial-vector diquarks), then the possible scalar diquark configurations are $[n,n]$ and $[n,s]$ (where $s$ is a strange quark, while $n = u,d$) , while the possible axial-vector diquark configurations are $\{n,n\}$, $\{n,s\}$ and $\{s,s\}$ \cite{Jaffe:2004ph}.
In this contribution, we discuss the relativistic interacting quark-diquark model of Refs. \cite{Santopinto:2004hw,Ferretti:2011zz,DeSanctis:2011zz,qD2014a,qD2014b}, which is a potential model for strange and nonstrange baryon spectroscopy constructed within the point form formalism \cite{Klink:1998zz,Pavia-Graz,Sanctis:2007zz}.
In our model, baryon resonances are described as two-body quark-diquark bound states, thus the relative motion between the two constituents and the Hamiltonian of the model are functions of the relative coordinate $\vec r$ and its conjugate momentum $\vec q$.
The Hamiltonian contains a Coulomb plus linear confining interaction and an exchange one, depending on the spins and isospins of the quark and the diquark.
The strange and nonstrange spectra are computed and the results compared to the existing experimental data \cite{Nakamura:2010zzi}.
\section{The Mass operator}
\label{The Model}
We consider a quark-diquark system, where $\vec{r}$ and $\vec{q}$ are the relative coordinate between the two constituents and its conjugate momentum, respectively.
The baryon rest frame mass operator we consider is
\begin{equation}
\begin{array}{rcl}
M & = & E_0 + \sqrt{\vec q\hspace{0.08cm}^2 + m_1^2} + \sqrt{\vec q\hspace{0.08cm}^2 + m_2^2}
+ M_{\mbox{dir}}(r) \\
& + & M_{\mbox{ex}}(r)
\end{array} \mbox{ },
\label{eqn:H0}
\end{equation}
where $E_0$ is a constant, $M_{\mbox{dir}}(r)$ and $M_{\mbox{ex}}(r)$ respectively the direct and the exchange diquark-quark interaction, $m_1$ and $m_2$ stand for diquark and quark masses, where $m_1$ is either $m_{[q,q]}$ or $m_{\{q,q\}}$ according if the mass operator acts on a scalar or axial-vector diquark.
The direct term we consider,
\begin{equation}
\label{eq:Vdir}
M_{\mbox{dir}}(r)=-\frac{\tau}{r} \left(1 - e^{-\mu r}\right)+ \beta r ~~,
\end{equation}
is the sum of a Coulomb-like interaction with a cut off plus a linear confinement term.
We also have an exchange interaction, since this is the crucial ingredient of a quark-diquark description of baryons \cite{Santopinto:2004hw,Lichtenberg:1981pp}.
In the nonstrange sector we have \cite{Santopinto:2004hw,Ferretti:2011zz}
\begin{equation}
\begin{array}{rcl}
M_{\mbox{ex}}(r) & = & \left(-1 \right)^{L + 1} \mbox{ } e^{-\sigma r} \left[ A_S \mbox{ } \vec{s}_1
\cdot \vec{s}_2 \right. \\
& + & \left. A_I \mbox{ } \vec{t}_1 \cdot \vec{t}_2
+ A_{SI} \mbox{ } \vec{s}_1 \cdot \vec{s}_2 \mbox{ } \vec{t}_1 \cdot \vec{t}_2 \right]
\end{array} \mbox{ },
\label{eqn:Vexch-nonstrange}
\end{equation}
where $\vec{s}$ and $\vec{t}$ are the spin and the isospin operators, while for strange baryons we consider a G\"ursey-Radicati inspired interaction \cite{Gursey:1992dc,qD2014b}.
In the nonstrange sector, we also have a contact interaction
\begin{equation}
\begin{array}{rcl}
\label{eqn:Vcont}
M_{\mbox{cont}} & = & \left(\frac{m_1 m_2}{E_1 E_2}\right)^{1/2+\epsilon} \frac{\eta^3 D}{\pi^{3/2}}
e^{-\eta^2 r^2} \mbox{ } \delta_{L,0} \delta_{s_1,1} \\
& \times & \left(\frac{m_1 m_2}{E_1 E_2}\right)^{1/2+\epsilon}
\end{array} \mbox{ },
\end{equation}
introduced in the mass operator of Ref. \cite{Ferretti:2011zz} to reproduce the $\Delta-N$ mass splitting.
\section{Results and discussion}
In this section, we show our results for the non-strange baryon spectrum from Ref. \cite{Ferretti:2011zz}. See Fig. \ref{fig:Spectrum-ND}.
While the values of the diquarks masses $m_n$, $m_{[n,n]}$ and $m_{\{n,n\}}$ almost coincide in the "strange" and "nonstrange" fits \cite{Ferretti:2011zz,qD2014b}, there is a certain difference between the values of a few model parameters used in the two fits. This is especially evident in the case of the exchange potential parameters, $A_S$ and $A_I$. This difference is due to the substitution of the spin-isospin term in the exchange potential with the $SU(3)$ flavor-dependent, which also determines a change in the values of the spin and isospin, $A_S$ and $A_I$, parameters.
Moreover, and most important, some parameters are present in one fit and not in the other, such as the contact interaction ones, because the potential of Eq. (\ref{eqn:Vcont}) was introduced to reproduce the $\Delta-N$ mass splitting, and thus it is inessential in the strange sector.
It is also interesting to note that in our model $\Lambda(1116)$ and $\Lambda^*(1520)$ are described as bound states of a scalar diquark $[n,n]$ and a quark $s$, where the quark-diquark system is in $S$ or $P$-wave, respectively \cite{qD2014b}. This is in accordance with the observations of Refs. \cite{Jaffe:2004ph,Selem:2006nd} on $\Lambda$'s fragmentation functions, that the two resonances can be described as $[n,n]-s$ systems.
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=7cm]{fig4.eps}
\end{center}
\caption{Comparison between the calculated masses (black lines) of the $3^*$ and $4^*$ $N$ and $\Delta$ resonances (up to 2 GeV) and the experimental masses from PDG \cite{Nakamura:2010zzi} (blue boxes).}
\label{fig:Spectrum-ND}
\end{figure}
It is interesting to compare the present results to those of the main three-quark quark models \cite{IK,CI,HC,GR,LMP}. It is clear that a larger number of experiments and analyses, looking for missing resonances, are necessary because many aspects of hadron spectroscopy are still unclear \cite{Hugo}.
The present work can be expanded to include charmed and/or bottomed baryons \cite{FS-inprep}, which can be quite interesting in light of the recent experimental effort to study the properties of heavy hadrons.
| {
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