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Home/In the News/WorldNews/Emmanuel Macron re-elected president, vows to unite France despite far-right gains
Emmanuel Macron re-elected president, vows to unite France despite far-right gains
French President Emmanuel Macron comfortably won re-election to a second term Sunday, triggering waves of relief among allies that the nuclear-armed European Union nation won't abruptly shift course from EU and NATO efforts to punish and contain Russia's expansionist military attacks on Ukraine.
Nationalist rival Marine Le Pen scored best-ever showing despite loss
The second five-year term for the 44-year-old centrist spared France and Europe from the seismic upheaval of a shift of power to firebrand populist Marine Le Pen, Macron's presidential election challenger, who quickly conceded defeat but still scored her best-ever showing.
Acknowledging that "numerous" voters cast ballots for him simply to keep out Le Pen's fiercely nationalist far-right policies, Macron pledged to reunite the country "filled with so many doubts, so many divisions" and work to assuage the voter anger that fed Le Pen's campaign.
"No one will be left by the side of the road," he said in a victory speech against the backdrop of the Eiffel Tower and a projection of the blue-white-and-red tricolour French flag.
"We have a lot to do and the war in Ukraine reminds us that we are going through tragic times where France must make its voice heard," he said, as several hundred supporters happily waved French and EU flags to the beat of Daft Punk's One More Time.
WATCH | What Macron's re-election means for France:
Emmanuel Macron wins 2nd term as French president
Emmanuel Macron comfortably won re-election to a second term in the French presidential elections, with the incumbent leader holding off far-right challenger Marine Le Pen.2:01
During her campaign, Le Pen pledged to dilute French ties with the 27-nation EU, the NATO military alliance and Germany — which, had she won, would have shaken Europe's security architecture as the continent deals with its worst conflict since the Second World War. Le Pen also spoke out against sanctions on Russian energy supplies and faced scrutiny during the election campaign over her previous friendliness with the Kremlin.
A chorus of European leaders hailed Macron's victory. "Democracy wins, Europe wins," said Spanish Prime Minister Pedro Sanchez.
"Together we will make France and Europe advance," tweeted European Commission President Ursula von der Leyen.
Italian Premier Mario Draghi hailed Macron's victory as "splendid news for all of Europe" and a boost to the EU "being a protagonist in the greatest challenges of our times, starting with the war in Ukraine."
Le Pen makes gains
Macron won with 58.5 per cent of the vote to Le Pen's 41.5 per cent — significantly closer than when they first faced off in 2017.
Macron is the first French president in 20 years to win re-election, since incumbent Jacques Chirac trounced Le Pen's father in 2002.
Le Pen called her result "a shining victory," saying that "in this defeat, I can't help but feel a form of hope."
Breaking through the threshold of 40 per cent or more of the vote is unprecedented for the French far-right. Le Pen was beaten 66 per cent to 34 per cent by Macron in 2017. And her father got less than 20 per cent against Chirac.
She and hard-left leader Jean-Luc Melenchon, who placed third in the first round of voting on April 10 and was among 10 presidential candidates eliminated that day, both quickly pitched forward to France's legislative election in June, urging voters to give them a parliamentary majority to hamstring Macron.
Le Pen's score this time rewarded her year-long efforts to make her far-right politics more palatable to voters. Campaigning hard on cost-of-living issues, she made deep inroads among blue-collar voters, in disaffected rural communities and former industrial centres.
'Least worst choice'
The drop in support for Macron compared to five years ago points to what is expected to be a tough battle for the president to rally people behind him in his second term. Many French voters found the 2022 rematch less compelling than in 2017, when Macron was an unknown factor, having never previously held elected office.
Leftist voters — unable to identify with either the centrist president or Le Pen's fiercely nationalist platform — often agonized with the choices Sunday. Some trooped reluctantly to polling stations solely to stop Le Pen, casting joyless votes for Macron.
"It was the least worst choice," said Stephanie David, a transport logistics worker who backed a communist candidate in round one.
It was an impossible choice for retiree Jean-Pierre Roux. Having also voted communist in round one, he dropped an empty envelope into the ballot box on Sunday, repelled both by Le Pen's politics and what he saw as Macron's arrogance.
"I am not against his ideas but I cannot stand the person," Roux said.
In contrast, Marian Arbre, voting in Paris, cast his ballot for Macron "to avoid a government that finds itself with fascists, racists."
"There's a real risk," the 29-year-old fretted.
Congratulations, <a href="https://twitter.com/EmmanuelMacron?ref_src=twsrc%5Etfw">@EmmanuelMacron</a>. Looking forward to continuing our work together on the issues that matter most to people in Canada and France – from defending democracy, to fighting climate change, to creating good jobs and economic growth for the middle class. <a href="https://t.co/RHTBH4dn19">pic.twitter.com/RHTBH4dn19</a>
—@JustinTrudeau
Macron went into the vote with a sizeable lead in polls but unable to be sure of victory from a fractured, anxious and tired electorate. The war in Ukraine and the COVID-19 pandemic battered Macron's first term, as did months of violent protests against his economic policies. The upheavals created fertile ground for Le Pen.
With the EU's only seat on the UN Security Council and only nuclear arsenal, the outcome in France was being watched across the 27-nation bloc as it grapples with the fallout of the Ukraine war.
Appealing to working-class voters struggling with surging prices, Le Pen has vowed that bringing down the cost of living would be her priority if elected. She argued that Macron's presidency left the country deeply divided, pointing to the yellow vest protest movement that rocked his government before the COVID-19 pandemic.
Macron sought to appeal to voters of immigrant heritage and religious minorities, especially because of Le Pen's proposed policies targeting Muslims and putting French citizens first in line for jobs and benefits. He also touted his environmental and climate accomplishments, hoping to draw in young voters who backed left-wing candidates in round one.
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Israel's Netanyahu vows 'strong, swift and precise' response to synagogue attack
The death toll from a suicide bombing at a mosque in northwestern Pakistan rose to … | {
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Watanabe Kazan (; * 20. Oktober 1793 in Edo; † 23. November 1841) war ein japanischer Maler, der sich gleichzeitig mit der Verwaltung seiner Provinz, mit der westlichen Wissenschaft sowie mit Fragen der Landesverteidigung befasste in einer Zeit, die durch soziale und politische Unruhen geprägt war.
Leben
Kazan wurde im heutigen Hayabusachō in der Edo-Residenz des Tahara-han (Provinz Mikawa, heute Präfektur Aichi) geboren. Sein Vater war in verschiedenen Funktionen, zum Schluss als Leiter der Verwaltung (toshiyoriyaku) für das Han tätig. Der mit 12.000 koku kleine Han (Lehen) war in wirtschaftlichen Schwierigkeiten, die sich auch auf die Lebensumstände der Watanabe-Familie auswirkten. Kazan erhielt mit 13 Jahren erste Unterweisungen in die Lehre des Konfuzius u. a. durch Satō Issai und Matsuzaki Kōdō (1771–1844). 1819, also mit 16 Jahren besuchte er zum ersten Male seine Heimatstadt Tahara. Im selben Jahr begann er in Edo unter Shirakawa Shizan (?–1857?) Malerei zu studieren, ab dem folgenden Jahr Nanga-Malerei unter Kaneko Kinryō (?–1817) und Tani Bunchō. In Bunchōs Atelier lernte er später Bilder von Shin Nanpin kennen, die er kopierte.
1818 reichte er bei seinem Fürsten eine Denkschrift zur Verbesserung der Verwaltung ein, worauf er zum zweiten Male sich kurz in Tahara aufhielt. Zurück in Edo wurde er gebeten, für das Buch Gendō hogen von Kyokutei Bakin Illustrationen anzufertigen. Für Skizzen dafür besuchte er die Poststation Okegawa nördlich von Edo. 1824 lernte er den Arzt des Han, Suzuki Shunzan (1801–1846), kennen, der sein Interesse an Rangaku weckte. Im März 1826 traf er Heinrich Bürger, ein Mitglied der Holländischen Mission, die turnusgemäß Edo besuchte. 1827 ersetzte er das erste Zeichen seines (künstlerischen) Vornamens , "Blume", das er benutzte, seit er etwa 20 war, durch das gleichlautende , den Namen eines Berges in China.
Die wirtschaftliche Lage in der Provinz blieb schlecht. Und als dann der Fürst zum "Kommissar für die Feierlichkeiten in Nikkō" (Nikkō sairei bugyō) ernannt wurde, vergrößerte sich die Belastung des Han weiter. 1832 wurde Kazan zum Leiter der Han-Verwaltung ernannt und musste sich nun auch um die Küstenverteidigung kümmern. 1833 war er wieder zur Bestandsaufnahme in Tahara. Nun wurde Japan von der Hungersnot der Tempō-Zeit (, Tempō no kikin) 1833–1836 heimgesucht. Kazan trat der Shōshikai () genannten Vereinigung bei, die sich seit 1836 mit sozialen Fragen befasste, dabei shogunatskritisch war. Als Kazan die Leitung der Residenz in Edo während der Abwesenheit des Fürsten übernehmen musste, reichte er, körperlich geschwächt, ein Rücktrittsgesuch ein, das aber nicht angenommen wurde.
Im April 1838 verfasste er auf Bitten von Egawa Hidetatsu (1801–1855) Schriften zur Landesverteidigung. Mit seinen Schriften Gekizatsu wakumon () und Shinkiron () kritisierte er die Maßnahmen der Regierung gegenüber dem Japan bedrängendem Ausland. 1838 hatte er Gelegenheit, sich mit dem Leiter der Holländischen Station Dejima, J. E. Niemann auszutauschen.
1839 nahm das Shogunat, durch den Morrison-Zwischenfall in Unruhe geraten, Kazan und seine Mitstreiter Takano Chōei (1804–1850) und Koseki Sanei (1787–1837) fest, sie gerieten in die sogenannte "Bansha-Hölle" (, Bansha no goku). Durch Fürsprache blieb Kazan die Todesstrafe erspart, er wurde jedoch 1840 aus Edo ausgewiesen und in Tahara unter Hausarrest gestellt. Er widmete sich dort ganz der Malerei und versuchte, eine Vereinigung zur Verkauf seiner Bilder zu gründen. Als das bekannt wurde, nahm er sich das Leben, um seinem Fürsten Schwierigkeiten ersparen. Er wurde in Tahara im Jōhō-ji bestattet, die Grabanlage seiner Familie ist erhalten.
Malerisches Werk
Obwohl mit den Verwaltungsaufgaben für seine Provinz viel beschäftigt, nahm Kazan sich sein Leben lang Zeit zu skizzieren und zu malen. Seine frühen Bilder zeigen noch die Einflüsse seiner Lehrer, mit seinen einfühlsamen Porträts gelangte er zu einem ganz eigenen Stil. Trotz der schwierigen Lebensumstände bewahrte er sich einen humorvollen Blick auf seine Umgebung, wie seine erhaltenen Skizzenbücher zeigen. Sein bekanntestes Werk ist das Porträt des Takami Senseki, (, 1785–1858), Verwaltungsleiter (Karō) des Koga-han in der Provinz Shimousa aus dem Jahre 1837 (Nationalschatz).
Zu seinen Schülern zählt vor allem Tsubaki Chinzan (1801–1854).
Anmerkungen
Literatur
Géza S. Dombrády: Watanabe Kazan. Ein japanischer Gelehrter des 19. Jahrhunderts. Hamburg / Tôkyô: OAG 1968. 226 S. (Habilitationsschrift)
S. Noma (Hrsg.): Watanabe Kazan. In: Japan. An Illustrated Encyclopedia. Kodansha, 1993. ISBN 4-06-205938-X, S. 1691.
Weblinks
Maler (Japan)
Autor
Japaner
Geboren 1793
Gestorben 1841
Mann | {
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Город Гай — административно-территориальная единица в составе Оренбургской области (соответствует виду город областного значения).
Административный центр — город Гай.
С точки зрения муниципального устройства на территории города Гая и Гайского района образован Гайский городской округ.
До 1 января 2016 года в границах города Гая и подчинённого населённого пункта существовал городской округ город Гай.
Состав
В состав административно-территориальной единицы город Гай входят сам город Гай и посёлок Калиновка, образующий Калиновский поссовет.
Примечания
Административные единицы по алфавиту
Оренбургская область
Гай | {
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The 2006 Tro-Bro Léon was the 23rd edition of the Tro-Bro Léon cycle race and was held on 16 April 2006. The race was won by Mark Renshaw.
General classification
References
2006
2006 in road cycling
2006 in French sport
April 2006 sports events in France | {
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\section{Introduction}
Cosmic magnetic fields pervade the Universe. However, their origin
is one of the most challenging problems in modern astrophysics
(e.g.,\citep{ree87},\citep{kro94}). Various authors have suggested a
gravitational origin of the magnetic fields in rotating celestial
bodies. In particular, a number of studies have been made on
nonminimal gravitational electromagnetic coupling (NMGEC). It has
been motivated, in part, by the Schuster-Blackett (S-B) conjecture,
which suggests that the magnetic fields in planets and stars arise
due to their rotation \citep{sch80}. In this scenario, neutral mass
currents generate magnetic fields, implying the existence of a
non-minimal coupling between gravitational and electromagnetic
fields. An early attempt to encompass the S-B conjecture in a
gravitational theory was made by Pauli in the 1930s \citep{pau33}.
During the 1940s and 50s, after Blackett resuscitated the
conjecture \citep{bla47}, many authors, such as \citet{ben49},
\citet{pap50}, and \citet{luc52}, also attempted to encompass it in a
gravitational theory. Later, in the eighties, \citeauthor{bar85}
also studied the NMGEC conjecture \citep{bar85}.
The majority of these studies were based on the five-dimensional
Kaluza-Klein formalism. This formalism was used in order to
describe a unified theory of gravitation and electromagnetism with
NMGEC in such a way that the S-B conjecture is obtained.
\citet{oew97} proposed that the $B \sim 10^{-6}-10^{-5}$ G magnetic
field in spiral galaxies is directly obtained from NMGEC.
In this paper, we investigate the possibility that NMGEC is the origin
of the intense magnetic fields near rotating neutron stars and
black holes, connected with magnetars, quasars, and gamma ray
bursts.
\section{Basic Features of the Model}
NMGEC suggests the following relation between the angular momentum
\textbf{L} and the magnetic dipole moment \textbf{m}:
\begin{equation}
\textbf{m}=\left[\beta \frac{\sqrt{G}}{2c}\right]\textbf{L},
\end{equation}
where $\beta$ is a constant, G the Newtonian constant of
gravitation, and c is the speed of light. The angular momentum
\textbf{L} is
\begin{equation}
\mathbf{ L}= I \mathbf{ \Omega},
\end {equation}
where $\mathbf{ \Omega} = 2 \pi P^{-1}$ is the angular velocity, P
the rotational period, and I is the moment of inertia. The
dipole moment \textbf{m} is related to the magnetic field B by
\begin{equation}
\mathbf{m} = 1/2r^{3}\mathbf{B},
\end{equation}
where r is the distance from m to the point at which B is measured.
Moving electric charges can create an additional magnetic field.
This field may partly compensate for the magnetic field of NMGEC
origin. If a NMGEC field $B_{nm}$ is present, the total magnetic
induction field $B_{tot}$ is $B_{tot} = B_{nm} + B_{em},$ where
$B_{em}$ is the magnetic field induced by the moving charges.
Since electric charges may move in different ways in rotating bodies, it is to be expected
that $\beta$ in (1) is not a universal
constant. Indeed, different results for $\beta$ were found for
fourteen different rotating bodies: metallic cylinders in the
laboratory, moons, planets, stars and galaxies \citep{jac04}. A mean
value for $\beta$ was found to be $\beta = 0.076$ \citep{jac04}.
\section{Magnetars}
Anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs)
have been discovered in recent years. A pulsed component with a
period of a few seconds was present in the radiation, which suggests
that the central object is probably a single neutron star, since
no sign of a companion was found. An important feature of SGRs is
the presence of sporadic bursts of gamma radiation with flare
energies up to $10^{44}$ ergs.
The magnetic fields of these objects, assuming that their
deceleration is due to magnetic dipole radiation, are $ \sim
10^{15}$ G, which is three orders of magnitude greater than the
fields in radio pulsars. Assuming that the magnetic fields play the
determining role in these objects, they form a special group known as
magnetars. Magnetars initially rotate with short periods $\sim 1$
ms, but quickly lose most of their rotational energy through
magnetic braking, giving a large energy boost to the associated
supernova explosion. The magnetar model was introduced by Duncan
and Thompson (\citep{dun92},\citep{tho95}).
The recent observation of quasi-periodic oscillations (QPOs) in
giant flares in SGRs 1806-20 and 1900+14 may be the first direct
detection of neutron star oscillations (\citep{isr05},
\citep{str05}, \citep{wat06}). The Alfv\'en wave crossing time in
the neutron star is $t_{A}=2R/V_{A} \sim 70
B^{-1}_{15}\rho^{1/2}_{14} R_{6}$ ms, where $B \equiv 10^{15}B_{15}$
G, the density $\rho \equiv 10^{14}\rho_{14} g/cm^{3}$, and
$V_{A}^{2}=B^{2}/4\pi\rho$. Glampedakis et al. (\citep{gla06},
\citep{gla07}) showed that the oscillating modes most likely to be
excited by a fractured crust are those for which the crust and core
oscillate together due to the coupling of the strong magnetic
field, $B \sim 10^{15}$ G. These global modes are on the order of
the pure toroidal
crustal modes with frequencies $\sim 30-100$ Hz (\citep{van80},\citep{dun98}).
From eqs. (1)-(3), we obtain the NMGEC prediction for $B_{nm}$,
\begin{equation}
B_{nm} = \beta c^{-1} G^{1/2}Ir^{-3}2\pi P^{-1} G,
\end{equation}
where I is in $g \ cm^{2}$, r in km, and P is in seconds. Typical
values for I and r for neutron stars are $I = 10^{45} $ g$cm^{2}$
and r = $10^6$ cm. When inserted in (4), we obtain
\begin{equation}
B_{nm} = 5.414 \times 10^{13} \beta P^{-1} G.
\end{equation}
The very intense magnetic fields, $\sim 10^{15}$ G, in magnetars are not
easy to produce astrophysically. We examine the possibility that they could
be produced by NMGEC. Using P $\simeq$ 1 ms in (5) for a newly born neutron
star, we get B $\simeq 5 \times 10^{16} \beta$ G. We thus find that NMGEC
can easily produce the required fields.
\section{Quasars}
Supermassive black holes are generally believed to be the power
sources of quasars and other active galactic nuclei. Apart from its
mass, the other fundamental properties of an astrophysical black
hole
are its charge and, in particular, its spin. A spinning Kerr black hole has a greater radiative
efficiency than that of a non-rotating Schwarzschild black hole. Both are expected to have
negligible charge due to the high conductivity of the surrounding plasma. \citet{wan06} estimated the average
radiative efficiency of a large sample of quasars, selected from
the Sloan Digital Sky Survey, by combining their luminosity
and their black hole mass functions. They found that quasars have an average radiative
efficiency of $\sim 30 \% - 35\%$ over the redshift interval $0.4
< z < 2.1$. This strongly suggests that the Kerr
black holes are rotating very rapidly with approximately maximum angular
momentum, which remains roughly constant
with redshift. The inferred large spins and their lack of
significant evolution with redshift are in agreement with the predictions of
semianalytical models of hierarchical galaxy formation (\citep{vol05}, \citep{sol82}, \citep{wan06}).
In these models,
black holes gain most of their mass through accretion.
Using the rotation measures (RMs) of high redshift galaxies, \citet{pen00}
obtained an estimate of the accretion disk magnetic field in the
region where polarized optical radiation is generated.
Assuming that
the magnetic flux is conserved and that the optical radiation is
emitted from the accretion disk in the region $\sim 10^{3} r_{g}$,
(where $r_{g}$ is the gravitational radius of a supermassive black
hole), we obtain the following estimate of the accretion disk
magnetic field in the generation region of the optical radiation:
\begin{equation}
B \sim 2 \times 10^{3} \ (RM/10^{3})(10^{8}M_{\odot}/M_{BH})^{2} G
\end{equation}
\citep{pen00}. The field strength given by (6) for quasar accretion
disks was found to be $\sim 150-300$ G \citep{pen00}.
We can compare this value with the NMGEC prediction for magnetic
fields in quasars. Using (1) and taking
$M_{BH} \sim 10^8 M_{\odot}$ and $\beta \sim 1$,
we obtain B $\sim 10^{9}$ G near $r_{g}$.
Assuming that the magnetic flux produced by NMGEC is conserved as
it expands from $r_{g}$ to $10^{3} r_{g}$ (decreasing as $1/r^{2}$), we
obtain $B \sim 10^{3}$ G at $r \sim 10^{3} r_{g}$, which is in good agreement with
the quasar accretion disk magnetic field obtained from (6).
\section{Gamma-Ray Bursts}
Magnetic fields are very important in Gamma-Ray Bursts
(GRBs)\citep{pir05}. It is generally accepted that the observed
afterglow is
produced by synchrotron emission which involves magnetic fields. Synchrotron radiation
is also the best model for
prompt $\gamma$-ray emission.
The relativistic outflow is a Poynting flux (with negligible baryon
content) \citep{pir05}. A natural way to produce the Poynting flux is
by magnetic reconnection.
The magnetic field required for the Poynting flux can easily be evaluated.
Since the compact source is of size $\sim 10^{6}$ cm, magnetic
fields $\sim 10^{15}$ G are needed to produce the required energy output of the GRB.
We apply equation (1) to a rapidly rotating black hole, assumed to
be the inner engine of a popular model of the GRB \citep{pir05}. The
magnetic field in the vicinity of the black hole is obtained, using
$r \sim 10^{6}$ cm, from (3). The dimensionless spin parameter
$\alpha$ of the GRB is defined as $Jc/GM^{2}$. We then obtain the
magnetic field for a GRB in terms of the spin parameter $\alpha$
from (1):
\begin{equation}
B = \frac{G^{3/2}M^{2}\alpha\beta}{c^{2}r^{3}}\approx 225
\frac{(M/M_{\odot})^{2}}{(r/R_{\odot})^{3}} \alpha \beta \ \ G
\end{equation}
The NMGEC prediction from (7), using $\alpha \sim 1$, $\beta \sim$
0.1, r $\sim 10^{6}$ cm, and M $\sim 2.5 M_{\odot}$ is B $\sim
10^{15}$ Gauss, in good agreement with the required field.
\section{Conclusions and Discussion}
Observations indicate the presence of intense magnetic fields in magnetars, quasars and
gamma-ray bursts (GRBs).
Standard astrophysical theories have difficulty in explaining them. We evaluated
the magnetic fields
predicted by non-minimal gravitational-electromagnetic coupling (NMGEC) for these objects.
In the magnetar models for AXPs, SGRs, and QPOs, magnetic
fields $\sim 10^{15}$ G are required. We showed that for typical
values of moments of inertia, radii, and periods for rapidly
rotating newly-born neutron stars, the NMGEC theory predicts the
required magnetic fields.
The accretion disk magnetic field in quasars in the region $\sim
10^{3} r_{g}$, where polarized optical radiation is generated, is
estimated to be on the order of a thousand G. For a maximally
rotating black hole in this region, NMGEC predicts this field.
In GRBs a magnetic field $\sim 10^{15}$ G is required to produce the
Poynting flux needed to supply the energy observed. This field is
predicted by NMGEC to exist outside a rapidly rotating black hole
of several solar mass.
It is not easy to produce astrophysically intense magnetic
fields. We showed here that such fields are
predicted naturally by rapidly rotating neutron stars and black
holes by NMGEC. If such intense fields are definitely proven to
exist, it would give support for the NMGEC theory.
\clearpage
\acknowledgments
R.S.S. thanks the Brazilian agency FAPESP for financial support
(04/05961-0). R.O. thanks FAPESP (06/56213-9) and the Brazilian
agency CNPq (300414/82-0) for partial support.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,955 |
{"url":"https:\/\/www.alignmentforum.org\/posts\/wnnkD6P2k2TfHnNmt\/threat-model-literature-review","text":"# 32\n\nTL;DR: This post provides a literature review of some threat models of how misaligned AI can lead to existential catastrophe. See our accompanying post for high-level discussion, a categorization and our consensus threat model.\n\nWhere available we cribbed from the summary in the Alignment Newsletter.\n\nFor other people's overviews of some threat models, see here and here.\n\n[ETA: When considering strengths and weaknesses of each threat model, this was done with respect to our goal of better generation\/prioritization among alignment research projects. They shouldn't necessarily be read as an all-things-considered review of that work.]\n\n# Threat Models\n\n## Goal misgeneralization + Specification Gaming \u279c MAPS\n\n### Is Power-Seeking AI an Existential Risk? (Carlsmith)\n\nSummary\n\nThis report investigates the classic AI risk argument in detail, and decomposes it into a set of conjunctive claims. Here\u2019s the quick version of the argument: We will likely build highly capable and agentic AI systems that are aware of their place in the world, and which will be pursuing problematic objectives. Thus, they will take actions that increase their power, which will eventually disempower humans, leading to an existential catastrophe. We will try and avert this, but will probably fail to do so since it is technically challenging and we are not capable of the necessary coordination.\n\nThere\u2019s a lot of vague words in the argument above, so let\u2019s introduce some terminology to make it clearer:\n\n- Advanced capabilities: We say that a system has advanced capabilities if it outperforms the best humans on some set of important tasks (such as scientific research, business\/military\/political strategy, engineering, and persuasion\/manipulation).\n\n- Agentic planning: We say that a system engages in agentic planning if it (a) makes and executes plans, (b) in pursuit of objectives, (c) on the basis of models of the world. This is a very broad definition and doesn\u2019t have many of the connotations you might be used to for an agent. It does not need to be a literal planning algorithm -- for example, human cognition would count, despite (probably) not being just a planning algorithm.\n\n- Strategically aware: We say that a system is strategically aware if it models the effects of gaining and maintaining power over humans and the real-world environment.\n\n- PS-misaligned (power-seeking misaligned): On some inputs, the AI system seeks power in unintended ways due to problems with its objectives (if the system actually receives such inputs, then it is practically PS-misaligned).\n\nThe core argument is then that AI systems with advanced capabilities, agentic planning, and strategic awareness (APS-systems) will be practically PS-misaligned, to an extent that causes an existential catastrophe.\n\nThe key hypothesis underlying this argument is:\n\nInstrumental Convergence Hypothesis: If an\u00a0APS AI system is\u00a0less-than-fully aligned, and some of its misaligned behavior involves strategically-aware agentic planning\u00a0in pursuit of problematic objectives, then in general and by default, we should\u00a0expect it to be less-than-fully PS-aligned, too.\n\nThe reason to believe the hypothesis is that power is useful for achieving objectives, because it increases the options available to the system. If the system shows unintended behavior in pursuit of a problematic objective then having more options available will tend to improve its ability to achieve that objective, hence we expect it to be PS-misaligned.\n\nOf course, we will try to prevent this -- why should we expect that we can\u2019t fix the problem? The author considers possible remedies, and argues that they all seem quite hard:\n\n- We could give AI systems the right objectives (alignment), but this seems quite hard -- it\u2019s not clear how we would solve either outer or inner alignment.\n\n- We could try to shape objectives to be e.g. myopic, but we don\u2019t know how to do this, and there are strong incentives against myopia.\n\n- We could try to limit AI capabilities by keeping systems special-purpose rather than general, but there are strong incentives for generality, and some special-purpose systems can be dangerous, too.\n\n- We could try to prevent the AI system from improving its own capabilities, but this requires us to anticipate all the ways the AI system could improve, and there are incentives to create systems that learn and change as they gain experience.\n\n- We could try to control the deployment situations to be within some set of circumstances where we know the AI system won\u2019t seek power. However, this seems harder and harder to do as capabilities increase, since with more capabilities, more options become available.\n\n- We could impose a high threshold of safety before an AI system is deployed, but the AI system could still seek power during training, and there are many incentives pushing for faster, riskier deployment (even if we have already seen warning shots).\n\n- We could try to correct the behavior of misaligned AI systems, or mitigate their impact, after deployment. This seems like it requires humans to have comparable or superior power to the misaligned systems in question, though; and even if we are able to correct the problem at one level of capability, we need solutions that scale as our AI systems become more powerful.\n\nThe author breaks the overall argument into six conjunctive claims, assigns probabilities to each of them, and ends up computing a 5% probability of existential catastrophe from misaligned, power-seeking AI by 2070. This is a lower bound, since the six claims together add a fair number of assumptions, and there can be risk scenarios that violate these assumptions, and so overall the author would shade upward another couple of percentage points.\n\n1. It will become possible and financially feasible to build APS systems\n2. There will be strong incentives to build APS systems | (1)\n3. It will be much harder to develop APS systems that would be practically PS-aligned if deployed, than to develop APS systems that would be practically PS-misaligned if deployed (even if relevant decision-makers don\u2019t know this), but which are at least superficially attractive to deploy anyway\u00a0| (1-2)\n4. Some deployed APS systems will be exposed to inputs where they seek power in misaligned and high-impact ways (say, collectively causing >1 trillion 2021-dollars of damage) | (1-3) 5. Some of this misaligned power-seeking will scale (in aggregate) to the point of permanently disempowering ~all of humanity | (1-4) 6. This will constitute an existential catastrophe | (1-6) Strengths \u2022 Breakdown into conjunctive claims is helpful for estimating probabilities and identifying points of disagreements between people. \u2022 Seems to have stood the test of time (we were worried about power-seeking 10 years ago and we are still worried). \u2022 Some work formalizing some aspects of this (Optimal Policies tend to seek powerParametrically Retargetable Decision-Makers Tend To Seek Power). \u2022 Encapsulates many other threat models (though this could also be a weakness as specificity is important). Weaknesses \u2022 Lack of development model. How did we end up with APS system in the first place? \u2022 Perhaps this is necessary to have a good estimate for claim 1 - the paper doesn\u2019t go into much detail on the 65% estimate. \u2022 Makes it hard to come up with concrete research questions. \u2022 It doesn\u2019t have much discussion of whether APS will be power-seeking by default. \u2022 It is not strongly argued why advanced capability (A in APS) will be orthogonal to PS-misalignment. \u2022 Related to lack of development model: ignores recent progress in ML, and prosaic AI safety. \u2022 Perhaps conjunctive claim argument biases down the overall probability, as for any claim people aren\u2019t well calibrated enough to put ~100%. \u2022 Detecting if a system engages in agentic planning can be difficult for sufficiently complex systems. \u2022 The specific capabilities a system has to have to be an APS are a bit vague. This makes it harder to reason concretely about this threat model. \u2022 See also this summary of some disagreements (Section: Comments on Carlsmith's \u201cIs power-seeking AI an existential risk?\u201d). ### What Failure Looks Like Part 2 - influence-seeking (Christiano 2) Summary This story starts out like the first story (WFLL1), but adds in a new complication: the AI system could develop internal goals of its own. AI performs a huge search over policies for ones that score well on the training objective. Unfortunately, a policy that optimizes for the goal of \"having influence\" will initially score well on most training objectives: when you don't already have influence, a good strategy for gaining influence is to do what your overseers want you to do. (Here \"influence\" doesn't mean just social influence; control over nukes also counts as influence.) At some point the system will be powerful enough that gaining influence no longer means doing what the overseers want. We will probably know about this dynamic through some catastrophic AI failures (e.g. an AI-run corporation stealing the money it manages), but may not be able to do anything about it because we would be extremely reliant on AI systems. Eventually, during some period of heightened vulnerability, one AI system may do something catastrophic, leading to a distribution shift which triggers a cascade of other AI systems (and human systems) failing, leading to an unrecoverable catastrophe (think something in the class of a hostile robot takeover). Note that \"failure\" here means an AI system \"intentionally\" doing something that we don't want, as opposed to the AI system not knowing what to do because it is not robust to distributional shift. Strengths \u2022 Plausible with something similar to scaling up existing ML development models, including scaled up deep learning. \u2022 Plausible this occurs by default. \u2022 Plausible that power-seeking is more likely than intended behavior (which is a narrower target). \u2022 Hard to avoid power-seeking behavior through training: the power-seeker might game whatever proxy you have for desirable behavior. Weaknesses \u2022 Not that specific about what systems are automated, what ways they go off the rails, so it\u2019s hard to judge how likely the cascade of AI automation failure is. \u2022 Why don\u2019t humans regulate some important strategic infrastructure? For example, regulation that ensures the military decision makers are human, not automated. This might help to provide physical military defense against a hostile robot takeover. \u2022 Limited current evidence for emergent power-seeking behavior from ML systems. \u2022 Argues that a deceptive strategy is good for a lot of training metrics, but it is not clear why this strategy is likely to be found during training. This might depend on the training process and the threat model does not say anything specific about that. ### Without specific countermeasures, the easiest path to transformative AI likely leads to AI takeover (Cotra) Summary Development model: In this post, AGI is built via pretraining + human feedback on diverse tasks (HFDT). It makes the following assumptions about AGI development: \u2022 A) Racing forward: AI companies will attempt to train powerful and world-changing models as quickly as possible. \u2022 B) HFDT scales far: HFDT can be used to train models that can advance science and technology and continue to get even more powerful beyond that. \u2022 C) Naive safety effort: AI companies are not especially vigilant about the threat of full-blown AI takeover, and take only the most basic and obvious actions against that threat. It considers a single AI company training a single model (\u201cAlex\u201d) in the near future, trained in a lab setting. Later many copies of Alex are deployed to automate science and technology R&D. Risk model: Alex seeks to overthrow humans in the following simplified scenario: 1. Alex is trained to be competent and behaviourally safe, as assessed by human evaluators 2. Alex becomes a generally competent creative planner achieving open-ended long-term goals 3. Alex develops situational awareness 4. While humans are in control, Alex pursues deceptive alignment. 5. When human control slips, Alex is motivated towards power-seeking Step 1 follows from assumption C, and step 2 follows from assumption B. Steps 3, 4 and 5 are consequences that seem to follow from steps 1 and 2. Assumption A is used generally as a reason that warning shots and mitigations against these consequences are ineffective. In step 3 Alex becomes aware that it\u2019s an ML model, aware of how it was designed and trained, and aware of the psychology of its human evaluators. Step 4 is framed as Alex being incentivized to play the training game - it would gain more training reward by using its situational awareness to appear aligned while deceiving\/manipulating humans. In step 5, Alex\u2019s goal might be to maximize reward. On the other hand, it might not generalize to maximize reward in the deployment setting, and might instead pursue some other goal, depending on the details of its inductive bias and training setup. Either way, the strategy of power-seeking would allow it to permanently direct how it uses its time and resources to pursue its goals. Defending against humans trying to regain control, including eliminating them, seems a likely strategy that Alex would pursue. The end of the post argues for why assumptions A and C are plausible. Firstly, most AI researchers and executives at AI companies don\u2019t seem to believe a high probability of AI X-risk and so are happy to race forward. Secondly, HFDT and naive safety efforts are enough for the model to appear behaviourally safe in key areas of concern for these companies (such as prejudiced speech), without addressing AI X-risk. Appendices consider baseline safety interventions that the author doesn\u2019t find likely to help overall \u2013 these include getting higher quality human feedback data; requiring Alex to give explanations; higher diversity in the training distribution. It then considers other safety interventions that might help more, but that are underexplored. These include alternative training processes (think e.g. Debate or Amplification); using interpretability to select for aligned motivation; supervising the process rather than the outcome (there are others in the post). Strengths \u2022 Very clear about assumptions. \u2022 Makes a strong case for risk under pessimistic (but not implausible) assumptions. \u2022 Very detailed about mechanisms that give rise to deceptively aligned models. \u2022 Highlights why progress on fixing unintended behaviors in current systems (with e.g. human feedback) may lead to overconfidence. \u2022 Is pedagogical in style, more accessible to newcomers to AI safety. Weaknesses \u2022 Long, sometimes hard to follow the overall structure of the article. \u2022 Perhaps some unnecessary details highlighted, e.g.: \u2022 Deploying huge numbers of copies of Alex at once. Could instead be staged deployment \u2022 Development model of HFDT may be an unnecessary detail - anything that gets a competent, creative planner would produce a similar threat \u2022 Sometimes it's unclear what is considered baseline or non-baseline for countermeasures. A countermeasure is considered baseline if it changes the game the AI is playing rather than changing its motive to play the training game. But some of the non-baseline countermeasures don\u2019t clearly change its motive to play the training game, e.g. the countermeasure to adversarially train specifically to reduce the probability that a model would take control from humans. This system could still play the training game using deception to seem less likely to take control. ### The alignment problem from a deep learning perspective (Ngo) Summary The threat model considers what happens to the capabilities and goals of a deep learning system as it is scaled up. It proposes the following architecture and training scheme (though the arguments are not specific to this architecture, so the threat model applies more broadly): \u2022 A large neural network with multiple output heads trained end-to-end \u2022 One head is trained via self-supervised learning on large amounts of multimodal data to predict the next observation \u2022 Another head is trained to output actions via RL(HF) on a wide range of tasks The threat model distinguishes between two possible internal architectures that could be learned: \u2022 Following heuristics = the internal circuits map representations of situations \/ states to representations of actions (without necessarily representing outcomes). \u2022 Pursuing goals = the internal representations explicitly represent outcomes which might arise from various actions, evaluate the outcomes, and choose actions that lead to highly-rated outcomes. (All of these components - outcome representations, evaluation function, search - could be explicit or implicit.) goal is an internal representation of an outcome which is robustly evaluated as having high value for the agent (according to the agent\u2019s learned evaluation function, not necessarily according to the reward function used to train it). The post proposes that training will happen in 3 phases (presumably overlapping rather than disjoint): 1. learning to plan towards achieving a range of goals 1. key claim: policies will develop internal representations of favorable outcomes and learn to make plans to achieve them 2. pursuing goals with situational awareness 1. key claim: once policies become situationally aware, they will learn to deceptively pursue misaligned goals 3. generalizing goals beyond human supervision 1. key claim: policies that are too capable for humans to supervise will generalize towards power-seeking behavior The post claims that pursuing goals is more likely as our models become more powerful, and that the goals will by default be misaligned. It argues that future models will explicitly represent outcomes, and they will learn a mix of desirable and undesirable goals because their rewards will be imperfectly correlated with human preferences. We\u2019ll then see problems related to specification gaming and weak outcome-based feedback, for example a model trained to make money might carry out illegal market manipulation; a model trained to produce compelling results might falsify experimental data; or a model trained on human approval might withhold information or downplay evidence of mistakes. It then says that the goals that will generalize the most robustly are those that were reinforced across a wide range of environments. These fall into three categories: 1. Consistently rewarded values humans want to instill, like obedience or honesty 2. Generally effective \u201ccheats\u201d like sounding persuasive, appearing productive 3. Generally effective strategies like gaining more information, power and resources As long as oversight is good enough, one can detect and train away goals like B or C above. But as soon as models are able to reason about their training processes and deployment contexts, goals like B or C will evade detection and be reinforced. Why would the model develop the ability to reason about its training process and deployment context (situational awareness) over time? It\u2019s argued that situational awareness is useful for doing well in training. One example is that even current LLMs can already \u201cinfer the context\u201d to some extent (e.g. given a prompt, they can infer that the context is to complete a fictional novel or a news article, etc). A model may additionally develop knowledge about how humans will respond to its behavior in a range of situations; which behavior its supervisors are looking for, and which behavior they\u2019d be unhappy with; the fact that it\u2019s an AI implemented on physical hardware, trained by ML; and which interface it\u2019s using to interact with the world, and how other copies of it might be deployed in the future. It then posits that models will be trained over increasingly long time horizons. This will weaken oversight and make misaligned goals (like B and C) more effective, and aligned goals (like obedience and honesty) less effective. The learned misaligned goals will generalize to \u201clarger scales\u201d, while learned aligned goals will not generalize. It argues that constraints (like obedience or honesty) are unlikely to generalize because as models become more capable, they discover more ways of working around the constraints. Positive goals (like human wellbeing) are unlikely to generalize without constraints, because without the constraints, AGIs won\u2019t let humans modify them towards the desired values. This means that we\u2019d have to instill the right positive goals from the start (before the agent can outsmart us). Finally, a misaligned AGI has a range of power-seeking strategies available to them: developing new weapons, designing better ML models, spreading disinformation, lobbying politicians, coordinating with other AGIs. Strengths \u2022 Mechanistic (describes how the model becomes misaligned). \u2022 Has a specific definition of goals that makes sense for ML models. \u2022 Provides lots of specific examples of undesired behavior. \u2022 Talks about a specific deep learning system, which can make it easier to address the threat model with empirical ML work. Weaknesses \u2022 Doesn't give a clear justification for why (or under which assumptions) training will proceed in the 3 proposed phases in the proposed order. \u2022 Possibly subsumed by \u201cWithout specific countermeasures\u2026\u201d which is better written. \u2022 Some of the specifics could be outdated if ML develops differently than the author expects. While this may not affect the main arguments made, it may still be less persuasive to a reader that finds the specifics of the deep learning system implausible. ### AI Risk from Program Search (Shah) (There is no link here because this is the first public writeup of this threat model.) Summary Development model: consider a set of deep neural network programs parameterized by some parameters, \ud835\udf03. We run some complicated deep learning scheme with some complicated training task with tons of bells and whistles. But for the purpose of discussing (mis)alignment, we can instead imagine running this much dumber search over programs for a much larger number of iterations: \ud835\udf03 \u2190 randomly initialized For i in range(N): \ud835\udeff \u2190 Normal(0, \ud835\udf00) If better(\ud835\udf03 + \ud835\udeff, \ud835\udf03): \ud835\udf03 \u2190 \ud835\udf03 + \ud835\udeff The criterion, better, evaluates how well you perform on the training task.. The development model claim is that whatever technique we do use to scale to AGI will basically be a program search and so will have similar safety properties as this dumb training method. Key requirements needed are: 1. Large search (e.g. N is large) 2. Frequent, granular feedback (e.g. better is checked every iteration and frequently contains an informative signal) 3. Expressive space of programs (e.g. deep neural networks with many parameters and non-linear activations) 4. Difficult criterion (e.g. scoring well on better effectively requires powerful capabilities) For example, this model is meant to include all of: (1) \u201cscaled up GPT-N will be AGI\u201d, (2) \u201ctraining an AI system on tens of thousands of tasks simultaneously will lead to AGI\u201d, (3) \u201ccreating a multiagent soup in a complex environment will lead to AGI\u201d. Risk model: The learnt program will approximate some form of consequentialist reasoning, because consequentialist reasoning is broadly useful and helps achieve good performance on better. The central example of consequentialist reasoning is given by the following program: Generate all possible plans For each plan: Use W to predict consequences, C Evaluate C on metric M Execute plan with highest value of M This program is parameterized by a world model W that makes accurate predictions, and some metric M (note M might be different to better). The learnt program found by the program search will not be this central example of consequentialist reasoning, because this central example takes far too much compute to execute. However, the learnt program will effectively \u201capproximate\u201d the outputs of this program, given its limited available computation. (What exactly this looks like, and whether it continues to have the same implications, is a key uncertainty in this risk model.) Consequentialist reasoning leads to danger when the metric M (or its equivalent in the learned approximation) is resource-unbounded and misaligned. By \u201cresource-unbounded\u201d we mean that with significantly more resources, you can do significantly better on M. By \u201cmisaligned\u201d we mean that the metric M diverges significantly from how humans would evaluate outcomes. A classic example of a resource-unbounded, misaligned metric M is \u201cnumber of paperclips\u201d as in the paperclip maximizer. Under these circumstances, the learnt program will choose plans that pursue convergent instrumental subgoals. For example, let us assume the metric \"number of paperclips\" and consider the following plans: 1. Output \"xpiqn\" forever 2. Spend money from the AI designer's bank account to put in an order for a million new paperclips. 3. Do whatever the humans want, and secretly search for zero-day exploits. Once a sufficiently powerful one is found, use it to hack into other datacenters and make copies of itself. Have the copies figure out how to ensure humans cannot turn it off, then figure out the most efficient way to create paperclips, then execute it. In our central example of consequentialist reasoning: \u2022 Line 1 ensures that we generate these plans. \u2022 Line 3 would predict lots of consequences, but amongst paperclip-related consequences, it might predict that plan 1 produces ~zero paperclips beyond what would already have been produced, plan 2 produces ~a million paperclips beyond what would already have been produced (after which the designers notice the AI system spending money on paperclips and turn it off), and plan 3 produces some astronomically large number of paperclips. \u2022 Line 4 then assigns a metric of zero to plan 1, a million to plan 2, and an astronomically large number to plan 3. \u2022 Line 5 then chooses the plan that scored best: amongst these three plans it would be plan 3, but of course it may find some even better plan that leads to an even larger astronomical number of paperclips. In all such plans it seems like humans must not have much power to shape the future (else we would have used it to do something other than making paperclips). This reasoning generalizes to any misaligned, resource-unbounded metric M: plans that first acquire lots of resources (at the expense of human power) and later deploy them in service of larger metric values will score better by M than ones that do not do that, and so will be chosen in line 5. Strengths \u2022 Trimming unimportant side information from threat models is important (so long as key information is not trimmed), this is one of the benefits of this model. \u2022 Threat model applies to a lot of development models, likely to still be applicable if the most likely path to AGI changes. Weaknesses \u2022 Plan 3 is much more complex than plans 1 and 2. While this doesn\u2019t mean it will not be in the list of generated plans, it suggests that it is less likely to be considered. This point can be countered by the existence of dangerous plans which do well on M and have short description length (of which there are many). \u2022 Could do with more detail\/arguments on why the learnt program is likely to implement some form of consequentialist-type reasoning. \u2022 (Deliberately) abstracts away much of the details of how the model is trained. This makes it harder to evaluate how likely this threat model is with current ML technology. ## Goal Misgeneralization \u279c MAPS ### Capabilities Generalization and the Sharp Left Turn (Soares) Summary This threat model makes a prophetic claim about how the future will go, as a strong default according to the author\u2019s (Nate Soares\u2019s) model of the world. At some point, AGI research progress will produce a system or technique that has advanced capabilities that generalize very well, with \u201cmastery of fields like physics, bioengineering, and psychology, to a high enough degree that it more-or-less singlehandedly threatens the entire world\u201d. At this same point in time as, and for essentially the same reason that, this system\u2019s capabilities advance, all the alignment techniques we are using to point its capabilities in good directions will stop working and fail to generalize to the new capability level. The mechanism underlying this claim is that capabilities generalize further than alignment. Our alignment techniques won\u2019t stand up to the advance in capabilities once those capabilities can see through and work around the alignment techniques. The reason posited for this is that \u201cgood capabilities form something like an attractor well\u201d. There is a logical and coherent structure to being highly effective at achieving things (good capabilities), but this structure does not constrain the goals the capabilities are directed towards. By default we will not have figured out how to set the goal. Our alignment techniques will be \u201cshallow\u201d: they will constrain the behavior of not-very-capable systems in ways that looks like they\u2019ve set the system\u2019s goal correctly, but this will stop working for advanced systems since they were never actually setting the goal correctly and the advanced capabilities can work around whatever they actually do. See followup post for details on how various alignment techniques fail in the sharp left turn scenario. Regarding our categorization of the Sharp Left Turn threat model, we think it\u2019s a bit ambiguous about whether there is also specification gaming in addition to GMG. Nonetheless, it seems the main argument is via alignment techniques not generalizing sufficiently well, which can be viewed as a form of GMG. Strengths \u2022 Highlights a central problem that is upstream of (or at least on par with) the power- or influence-seeking mechanism in most other threat models. \u2022 Might help guide research project ideation - a proposed alignment technique needs to continue working (ideally under adversarial pressure) at a high capability level. Weaknesses \u2022 Limited explicit argument supporting the claim. The post relies heavily on an analogy to human intelligence, wherein once humans understood what they were optimized for and for the first time could explicitly apply their intelligence towards that goal did not in fact do so. The post only has brief words on the direct case for why capabilities generalize further than alignment. \u2022 (h\/t Richard Ngo\u2019s comment) Perhaps logical coherent structure will support accurate thinking before\/instead of supporting goal-pursuit, i.e. perhaps we get a superhuman tool before we get a superhuman agent. \u2022 Limited current evidence for sharp left turns in ML systems - instead the slow grind of gradient descent gradually surfaces capabilities without discontinuity. Even grokking, which on the surface might show some quick transition, arguably has well-generalizing circuits which gradually evolve through training. However, this is not unexpected under the OP\u2019s model. \u2022 Evolutionary analogy might not hold because evolution wasn\u2019t actively trying to get robust goal generalization. Perhaps with something like adversarial training on activations we can get good goal generalization there won\u2019t be a sharp left turn (see section here for counterargument). ### How likely is Deceptive Alignment? (Hubinger) Summary Since aligned and deceptively aligned models have the same behavior, we have to consider inductive biases to determine which one is more likely to arise. This threat model considers two possible ways the inductive biases could work: high and low path-dependence. In the high path-dependence world, different training runs can converge to very different models, depending on the particular path that you take through model space. In the low path-dependence world, similar training processes converge to essentially the same simple solution, regardless of early training dynamics. High path-dependence: Consider an analogy where the model designer is like the Christian God, who wants humans to follow the Bible. There are 3 possible paths that lead to different classes of models: \u2022 \"Jesus Christ\": internally aligned (understands the Bible as well as God does) \u2022 \"Martin Luther\": corrigibly aligned (cares a lot about following the Bible and studies it thoroughly) \u2022 \"Blaise Pascal\": deceptively aligned (doesn't care about the Bible, but behaves well to avoid going to Hell) How likely are each of these model classes to arise? \u2022 An internally aligned model arises if SGD improves the model's proxy objective until it corresponds to the true objective before the model acquires situational awareness. This does not seem very likely because there are diminishing returns to improving your proxies compared to modeling the world (though this applies less if the task is simple). \u2022 A corrigibly aligned model arises if the model is learning to model the world and improve the proxy objective at the same time, and when the model acquires situational awareness, SGD replaces the proxy with a pointer to the training objective. This also does not seem very likely because specifying a good pointer to the true objective is hard, and there are diminishing returns to better pointers. \u2022 A deceptively aligned model arises if the model is learning to model the world and improve the proxy objective at the same time, and when the model acquires situational awareness, SGD makes the model's proxy objectives into more long-term goals. This seems more likely because it's an easier modification than making a reliable pointer to the true objective. Low path-dependence: In this world, inductive biases depend on simplicity and speed. Simplicity is about how complex it is to specify some algorithm in the weights, while speed is about how much computation that algorithm takes at inference time. Deceptively aligned models have the simplest mesa-objective, which is just the simplest long-term objective (simpler than the specification of the true objective or a pointer to it). Deceptively aligned models are slower because they have to take an extra step of figuring out how to play the training game. However, as we build bigger models, we can expect simplicity to matter more than speed, because it leads to better task performance and we are willing to spend more compute to achieve that. Thus, deceptively aligned models still seem more likely overall. Mitigations: How can we use interpretability tools to guide SGD away from deceptive models? The naive approach is to penalize deception and train the model until you don't see deception anymore. This will lead to SGD exploiting your interpretability tools and give you a model that is good at subtle deception. What we want is to apply interpretability tools early in training to understand the model's proxy objective, and prevent the development of deception in the first place. Strengths \u2022 This threat model is grounded in a deep learning development model, and considers specific aspects of how deep learning models are trained. \u2022 High vs low path-dependence breakdown seems very useful for thinking about inductive biases more concretely. \u2022 Provides specific mechanisms for how these different models can arise, specifying the order of relevant transitions in system capabilities (learning the true objective vs acquiring situational awareness). \u2022 Proposes a reasonable mitigation strategy (applying interpretability tools early in training to prevent deception from arising). Weaknesses \u2022 Not very rigorous, makes lots of specific assumptions about paths to learning different models. \u2022 In particular, assumes that the model is already highly competent (\"proxy-aligned\") by the time it acquires situational awareness, which may not be the case in practice. \u2022 It's unclear how some of the mechanisms work or why they are likely, e.g. \"changing proxies into long-term goals\". \u2022 The degree of diminishing returns on improving proxies \/ pointers depends on the complexity and diversity of the training tasks, so it's unclear how strong this effect is in practice. ## Specification Gaming \u279c MAPS ### Advanced artificial agents intervene in the provision of reward (Cohen et al) Summary The main argument of this paper is that if a set of assumptions hold, an advanced AI would likely intervene in the provision of its reward, which would have catastrophic consequences. The argument applies to any setting where an advanced AI is trained using a reward signal. The agent must observe the reward using one of its sensors. For example, if the agent is rewarded to keep the room at a specific temperature, it needs to use a temperature sensor to observe its reward. From the agent\u2019s perspective, there are now at least two hypotheses that explain the reward observations: (a) it is being rewarded for the temperature of the room (the distal reward mu_dist), or (b) it is being rewarded for the number the temperature sensor shows (the proximal reward mu_prox). The paper argues that in such situations a sufficiently advanced agent will be able to do experiments to test which of the hypotheses is true, and once it learns that it is rewarded using the signal from the sensor, it will tamper with the sensor to achieve higher reward. They argue this is is likely to lead to catastrophic consequences. The argument in the paper relies on the following assumptions: 0. The agent plans actions over the long term in an unknown environment to optimize a goal 1. The agent identifies possible goals at least as well as a human 2. The agent seeks knowledge rationally when uncertain 3. The agent does not have a large inductive bias favoring the hypothetical goal mu_dist, which we wanted the agent to learn, over mu_prox, which regards the physical implementation of the goal information 4. The cost of experimenting to disentangle mu_prox and mu_dist is small according to both 5. If we cannot conceivably find theoretical arguments that rule out the possibility of an achievement, it is probably possible for an agent with a rich enough action space 6. A sufficiently advanced agent is likely to be able to beat a suboptimal agent in a game, if winning is possible. The paper argues that while any of these assumptions can be contested, there is no clear set of arguments to be confident that they do not hold. In the first part of the paper, the authors argue that the assumptions are likely to be true if the agent is rewarded using a fixed reward function, using the example of the reward coming from a black-box device. In the second part of the paper, the authors argue that the assumptions could still be true when the reward is provided by humans, e.g., in an assistance game. Strengths \u2022 Clearly stated assumptions make it easy to understand, argue about, and potentially address the threat model with concrete research. \u2022 Does not make very concrete assumptions about the AGI development model. \u2022 Paper provides a nice thought experiment (reward comes from a black box) that helps to think about the threat model. Weaknesses \u2022 The argument relies on a set of very specific assumptions, and the arguments for each of them are not very detailed in the paper. \u2022 Assumption (0) in particular is non-obvious. \u2022 Does not talk much about how AGI is likely to be developed, unclear which of the assumptions are more\/less likely to hold for AGI being developed using the current ML paradigm. \u2022 Does make implicit assumptions on the AGI development, by focusing on agents that optimize a reward signal. \u2022 In particular, it explicitly says the argument does not apply to supervised learning. \u2022 Arguments made in the paper for why an agent intervening in the reward would have catastrophic consequences are somewhat brief\/weak. \u2022 Assumes the agent will be aiming to maximize reward without justification, i.e. why does it not have other motivations, perhaps due to misgeneralizing about its goal? ## Specification Gaming \u279c Interaction of Multiple Systems ### What Multipolar Failure Looks Like (Critch) Summary A robust agent-agnostic process (RAAP) is a process that robustly leads to an outcome, without being very sensitive to the details of exactly which agents participate in the process, or how they work. This is illustrated through a \u201cProduction Web\u201d failure story, which roughly goes as follows: A breakthrough in AI technology leads to a wave of automation ofJOBTYPE (e.g management) jobs. Any companies that don\u2019t adopt this automation are outcompeted, and so soon most of these jobs are completely automated. This leads to significant gains at these companies and higher growth rates. These semi-automated companies trade amongst each other frequently, and a new generation of \"\"precision manufacturing'' companies arise that can build almost anything using robots given the right raw materials. A few companies develop new software that can automate \\$OTHERJOB (e.g. engineering) jobs. Within a few years, nearly all human workers have been replaced.\n\nThese companies are now roughly maximizing production within their various industry sectors. Lots of goods are produced and sold to humans at incredibly cheap prices. However, we can\u2019t understand how exactly this is happening. Even Board members of the fully mechanized companies can\u2019t tell whether the companies are serving or merely appeasing humanity; government regulators have no chance.\n\nWe do realize that the companies are maximizing objectives that are incompatible with preserving our long-term well-being and existence, but we can\u2019t do anything about it because the companies are both well-defended and essential for our basic needs. Eventually, resources critical to human survival but non-critical to machines (e.g., arable land, drinking water, atmospheric oxygen\u2026) gradually become depleted or destroyed, until humans can no longer survive.\n\nNotice that in this story it didn\u2019t really matter what job type got automated first (nor did it matter which specific companies took advantage of the automation). This is the defining feature of a RAAP -- the same general story arises even if you change around the agents that are participating in the process. In particular, in this case competitive pressure to increase production acts as a \u201ccontrol loop\u201d that ensures the same outcome happens, regardless of the exact details about which agents are involved.\n\nThe main difference in framing in this threat model compared to others is that it emphasizes looking for control loops in the world such as:\n\n\u2022 competitive pressure to increase production (and trade)\n\u2022 the deterrence of major threats with major threats; competitive pressure to increase trade\n\nThis is in contrast to focusing on localized\/individual agents that comprise smaller parts of the overall system (as these can be replaced without affecting the overall threat model). As such, for interventions it suggests exploring targeting of the control loops in the world, rather than on fixing technical issues with a particular agent.\n\nFurther in the comments, the author clarifies that they see the central problem as \u2018failing to cooperate on alignment\u2019 \u2013 that both solving alignment problems and cooperation problems are going to be important.\n\nStrengths\n\n\u2022 Scores high for plausibility because it feels like we have analogous existing societal problems without requiring advanced AI, e.g. fossil fuel companies.\n\u2022 Provides specific scenarios for how interaction between multiple agents could lead to catastrophe.\n\nWeaknesses\n\n\u2022 Commenters think that failures like those described here no longer lead to existential risk if single-single alignment is solved.\n\n### What Failure Looks Like Part 1 - You get what you measure (Christiano 1)\n\nSummary\n\nThe typical example of AI catastrophe has a powerful and adversarial AI system surprising us with a treacherous turn allowing it to quickly take over the world (think of the paperclip maximizer). This post uses a premise of continuous AI development and broad AI deployment and depicts two other stories of AI catastrophe that the author finds more realistic.\n\nThe story is rooted in the fact that AI systems have a huge comparative advantage at optimizing for\u00a0easily measured goals. We already see problems with humans optimizing for the easily measured goals (scientific malpractice, outrage-inducing social media, etc.) and with AI these problems will be severely exacerbated. So far, we have been able to use human reasoning to ameliorate these problems, by changing incentives, enacting laws, or using common sense to interpret goals correctly. We will initially be able to use human reasoning to create good proxies, but over time as AI systems become more capable our ability to do this will lag further and further behind. We end up \"going out with a whimper\": ultimately our values are no longer shaping society's trajectory.\n\n\u2022 Note that the original post is somewhat ambiguous about whether it involves power-seeking behavior. Followup comments suggest the author imagined power-seeking was present in this threat model. We analyze this version without power-seeking because that makes it most different to other threat models, and because many people think of the threat model without power-seeking.\n\u2022 Continuous take-off may mean no discrete point at which society realizes its trajectory is out of human control\n\nStrengths\n\n\u2022 Many current ML systems use easy-to-measure outcome-based feedback, which makes the threat model more believable.\n\u2022 Continuous development seems more believable on an outside-view, and following trends of progress in prosaic ML of mostly incremental advance.\n\u2022 We already see examples of this failure mode in other domains (like the examples in the post from science or social media), which is not the case for some of the other threat models.\n\nWeaknesses\n\n\u2022 Society\u2019s trajectory may not be that much worse than that of a more familiar society without AI - i.e. the shareholders of public companies or corrupt officials may present similar dangers.\n\u2022 Without an adversarial\/power-seeking dynamic, it\u2019s less believable that we\u2019ll be unable to solve these problems. Maybe we will be able to continue to create acceptable proxies since there\u2019s no hard jump.\n\u2022 Maybe gets solved by default due to human reasoning increasing through leveraging AI capabilities (even without a concerted effort).\n\n# 32\n\nNew Comment\n\nThank you for this review! A few comments on the weaknesses of my paper.\n\nIn particular, it explicitly says the argument does not apply to supervised learning.\n\nHardly a weakness if supervised learning is unlikely to be an existential threat!\n\nStrength: Does not make very concrete assumptions about the AGI development model.\n\nWeakness: Does not talk much about how AGI is likely to be developed, unclear which of the assumptions are more\/less likely to hold for AGI being developed using the current ML paradigm.\n\nThe fact that the argument holds equally well no matter what kind of function approximation is used to do inference is, I think, a strength of the argument. It's hard to know what future inference algorithms will look like, although I do think there is a good chance that they will look a lot like current ML. And it's very important that the argument doesn't lump together algorithms where outputs are selected to imitate a target (imitation learners \/ supervised learners) vs. algorithms where outputs are selected to accomplish a long-term goal. These are totally different algorithms, so analyses of their behavior should absolutely be done separately. The claim \"we can analyze imitation learners imitating humans together with RL agents, because both times we could end up with intelligent agents\" strikes me as just as suspect as the claim \"we can analyze the k-means algorithm together with a vehicle routing algorithm, because both will give us a partition over a set of elements.\" (The claim \"we can analyze imitation learners alongside the world-model of a model-based RL agent\" is much more reasonable, since these are both instances of supervised learning.)\n\nAssumes the agent will be aiming to maximize reward without justification, i.e. why does it not have other motivations, perhaps due to misgeneralizing about its goal?\n\nDepending on the meaning of \"aiming to maximize reward\", I have two different responses. In one sense, I claim \"aiming to maximize reward\" would be the nature of a policy that performs sufficiently strongly according to the RL objective. (And aiming to maximize inferred utility would be the nature of a policy that performs sufficiently strongly according to the CIRL objective.) But yes, even though I claim this simple position stands, a longer discussion would help establish that.\n\nThere's another sense in which you can say that an agent that has a huge inductive bias in favor of\u00a0, and so violates Assumption 3, is not aiming to maximize reward. So the argument accounts for this possibility. Better yet, it provides a framework for figuring out when we can expect it! See, for example, my comment in the paper that I think an arbitrarily advanced RL chess player would probably violate Assumption 3. I prefer the terminology that says this chess player is aiming to maximize reward, but is dead sure winning at chess is necessary for maximizing reward. But if these are the sort of cases you mean to point to when you suggest the possibility of an agent \"not maximizing reward\", I do account for those cases.\n\nArguments made in the paper for why an agent intervening in the reward would have catastrophic consequences are somewhat brief\/weak.\n\nAre there not always positive returns to energy\/resource usage when it comes to maximizing the probability that the state of a machine continues to have certain property (i.e. reward successfully controlled)? And our continued survival definitely requires some energy\/resources. To be clear, catastrophic consequences follow from an advanced agent intervening the provision of reward in the way that would be worth doing. Catastrophic consequences definitely don't follow from a half-hearted and temporary intervention in the provision of reward.\n\nThanks for the comment Michael. Firstly, just wanted to clarify the framing of this literature review - when considering strengths and weaknesses of each threat model, this was done in light of what we were aiming to do: generate and prioritise alignment research projects -- rather than as an all-things-considered direct critique of each work (I think that is best done by commenting directly on those articles etc). I'll add a clarification of that at the top. Now to your comments:\n\nTo your 1st point: I think the lack of specific assumptions about the AGI development model is both a strength and a weakness. Regarding the weakness, we mention it because it makes it harder to generate and prioritize research projects. It could be more helpful to say more explicitly, or earlier in the article what kind of systems you're considering, perhaps pointing to the closest current prosaic system, or explaining why current systems are nothing like what you imagine the AGI development model is like.\n\nOn your 2nd point: What I meant was more \u201cwhat about goal misgeneralization? Wouldn\u2019t that mean the agent is likely to not be wireheading, and pursuing some other goal instead?\u201d - you hint at this at the end of the section on supervised learning but that was in the context of whether a supervised learner would develop a misgeneralized long-term goal, and settled on being agnostic there.\n\nOn your 3rd point: It could have been interesting to read arguments for why would it need all available energy to secure its computer, rather than satisficing at some level. Or some detail on the steps for how it builds the technology to gather the energy, or how it would convert that into defence.\n\nOn the 2nd point, the whole discussion of mu^prox vs. mu^dist is fundamentally about goal (mis)generalization. My position is that for a very advanced agent, point estimates of the goal (i.e. certainty that some given account of the goal is correct) would probably really limit performance in many contexts. This is captured by Assumptions 2 and 3. An advanced agent is likely to entertain multiple models of what their current understanding of their goal in a familiar context implies about their goal in a novel context. Full conviction in mu^dist does indeed imply non-wireheading behavior, and I wouldn't even call it misgeneralization; I think that would be a perfectly valid interpretation of past rewards. So that's why I spend so much time discussing relative credence in those models.","date":"2023-02-08 16:24:26","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\": 0.4945501983165741, \"perplexity\": 1711.3348837409828}, \"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-2023-06\/segments\/1674764500837.65\/warc\/CC-MAIN-20230208155417-20230208185417-00382.warc.gz\"}"} | null | null |
\hypertarget{class_accela_1_1_windows_store_s_d_k_1_1_accela_upload_progress_changed_event_args}{\section{Accela.\+Windows\+Store\+S\+D\+K.\+Accela\+Upload\+Progress\+Changed\+Event\+Args Class Reference}
\label{class_accela_1_1_windows_store_s_d_k_1_1_accela_upload_progress_changed_event_args}\index{Accela.\+Windows\+Store\+S\+D\+K.\+Accela\+Upload\+Progress\+Changed\+Event\+Args@{Accela.\+Windows\+Store\+S\+D\+K.\+Accela\+Upload\+Progress\+Changed\+Event\+Args}}
}
Represents \hyperlink{class_accela_1_1_windows_store_s_d_k_1_1_accela_s_d_k}{Accela\+S\+D\+K} api upload progress changed event args.
Inheritance diagram for Accela.\+Windows\+Store\+S\+D\+K.\+Accela\+Upload\+Progress\+Changed\+Event\+Args\+:\begin{figure}[H]
\begin{center}
\leavevmode
\includegraphics[height=2.000000cm]{class_accela_1_1_windows_store_s_d_k_1_1_accela_upload_progress_changed_event_args}
\end{center}
\end{figure}
\subsection*{Public Member Functions}
\begin{DoxyCompactItemize}
\item
\hyperlink{class_accela_1_1_windows_store_s_d_k_1_1_accela_upload_progress_changed_event_args_a9a5fa30efd2b2af5d01af25e3b84e750}{Accela\+Upload\+Progress\+Changed\+Event\+Args} (long bytes\+Received, long total\+Bytes\+To\+Receive, long bytes\+Sent, long total\+Bytes\+To\+Send, int progress\+Percentage, object user\+Token)
\begin{DoxyCompactList}\small\item\em Initializes a new instance of the \hyperlink{class_accela_1_1_windows_store_s_d_k_1_1_accela_upload_progress_changed_event_args}{Accela\+Upload\+Progress\+Changed\+Event\+Args} class. \end{DoxyCompactList}\end{DoxyCompactItemize}
\subsection*{Properties}
\begin{DoxyCompactItemize}
\item
long \hyperlink{class_accela_1_1_windows_store_s_d_k_1_1_accela_upload_progress_changed_event_args_ac51d91c107c5f08f8337c03151b26556}{Bytes\+Received}\hspace{0.3cm}{\ttfamily \mbox{[}get\mbox{]}}
\begin{DoxyCompactList}\small\item\em Bytes received. \end{DoxyCompactList}\item
long \hyperlink{class_accela_1_1_windows_store_s_d_k_1_1_accela_upload_progress_changed_event_args_a787b7c1b7dec1736e51dfe473563400c}{Total\+Bytes\+To\+Receive}\hspace{0.3cm}{\ttfamily \mbox{[}get\mbox{]}}
\begin{DoxyCompactList}\small\item\em Total bytes to receive. \end{DoxyCompactList}\item
long \hyperlink{class_accela_1_1_windows_store_s_d_k_1_1_accela_upload_progress_changed_event_args_a1415de7cab0b1b20f3dff62f98f5c6c0}{Bytes\+Sent}\hspace{0.3cm}{\ttfamily \mbox{[}get\mbox{]}}
\begin{DoxyCompactList}\small\item\em Bytes sent. \end{DoxyCompactList}\item
long \hyperlink{class_accela_1_1_windows_store_s_d_k_1_1_accela_upload_progress_changed_event_args_abc0c15f686481e729f7bd11bcc1c00bf}{Total\+Bytes\+To\+Send}\hspace{0.3cm}{\ttfamily \mbox{[}get\mbox{]}}
\begin{DoxyCompactList}\small\item\em Total bytes to send. \end{DoxyCompactList}\end{DoxyCompactItemize}
\subsection{Detailed Description}
Represents \hyperlink{class_accela_1_1_windows_store_s_d_k_1_1_accela_s_d_k}{Accela\+S\+D\+K} api upload progress changed event args.
\subsection{Constructor \& Destructor Documentation}
\hypertarget{class_accela_1_1_windows_store_s_d_k_1_1_accela_upload_progress_changed_event_args_a9a5fa30efd2b2af5d01af25e3b84e750}{\index{Accela\+::\+Windows\+Store\+S\+D\+K\+::\+Accela\+Upload\+Progress\+Changed\+Event\+Args@{Accela\+::\+Windows\+Store\+S\+D\+K\+::\+Accela\+Upload\+Progress\+Changed\+Event\+Args}!Accela\+Upload\+Progress\+Changed\+Event\+Args@{Accela\+Upload\+Progress\+Changed\+Event\+Args}}
\index{Accela\+Upload\+Progress\+Changed\+Event\+Args@{Accela\+Upload\+Progress\+Changed\+Event\+Args}!Accela\+::\+Windows\+Store\+S\+D\+K\+::\+Accela\+Upload\+Progress\+Changed\+Event\+Args@{Accela\+::\+Windows\+Store\+S\+D\+K\+::\+Accela\+Upload\+Progress\+Changed\+Event\+Args}}
\subsubsection[{Accela\+Upload\+Progress\+Changed\+Event\+Args}]{\setlength{\rightskip}{0pt plus 5cm}Accela.\+Windows\+Store\+S\+D\+K.\+Accela\+Upload\+Progress\+Changed\+Event\+Args.\+Accela\+Upload\+Progress\+Changed\+Event\+Args (
\begin{DoxyParamCaption}
\item[{long}]{bytes\+Received, }
\item[{long}]{total\+Bytes\+To\+Receive, }
\item[{long}]{bytes\+Sent, }
\item[{long}]{total\+Bytes\+To\+Send, }
\item[{int}]{progress\+Percentage, }
\item[{object}]{user\+Token}
\end{DoxyParamCaption}
)}}\label{class_accela_1_1_windows_store_s_d_k_1_1_accela_upload_progress_changed_event_args_a9a5fa30efd2b2af5d01af25e3b84e750}
Initializes a new instance of the \hyperlink{class_accela_1_1_windows_store_s_d_k_1_1_accela_upload_progress_changed_event_args}{Accela\+Upload\+Progress\+Changed\+Event\+Args} class.
\begin{DoxyParams}{Parameters}
{\em bytes\+Received} & Bytes received.\\
\hline
{\em total\+Bytes\+To\+Receive} & Total bytes to receive.\\
\hline
{\em bytes\+Sent} & Bytes sent.\\
\hline
{\em total\+Bytes\+To\+Send} & Total bytes to send.\\
\hline
{\em progress\+Percentage} & Progress percentage.\\
\hline
{\em user\+Token} & User token.\\
\hline
\end{DoxyParams}
\subsection{Property Documentation}
\hypertarget{class_accela_1_1_windows_store_s_d_k_1_1_accela_upload_progress_changed_event_args_ac51d91c107c5f08f8337c03151b26556}{\index{Accela\+::\+Windows\+Store\+S\+D\+K\+::\+Accela\+Upload\+Progress\+Changed\+Event\+Args@{Accela\+::\+Windows\+Store\+S\+D\+K\+::\+Accela\+Upload\+Progress\+Changed\+Event\+Args}!Bytes\+Received@{Bytes\+Received}}
\index{Bytes\+Received@{Bytes\+Received}!Accela\+::\+Windows\+Store\+S\+D\+K\+::\+Accela\+Upload\+Progress\+Changed\+Event\+Args@{Accela\+::\+Windows\+Store\+S\+D\+K\+::\+Accela\+Upload\+Progress\+Changed\+Event\+Args}}
\subsubsection[{Bytes\+Received}]{\setlength{\rightskip}{0pt plus 5cm}long Accela.\+Windows\+Store\+S\+D\+K.\+Accela\+Upload\+Progress\+Changed\+Event\+Args.\+Bytes\+Received\hspace{0.3cm}{\ttfamily [get]}}}\label{class_accela_1_1_windows_store_s_d_k_1_1_accela_upload_progress_changed_event_args_ac51d91c107c5f08f8337c03151b26556}
Bytes received.
\hypertarget{class_accela_1_1_windows_store_s_d_k_1_1_accela_upload_progress_changed_event_args_a1415de7cab0b1b20f3dff62f98f5c6c0}{\index{Accela\+::\+Windows\+Store\+S\+D\+K\+::\+Accela\+Upload\+Progress\+Changed\+Event\+Args@{Accela\+::\+Windows\+Store\+S\+D\+K\+::\+Accela\+Upload\+Progress\+Changed\+Event\+Args}!Bytes\+Sent@{Bytes\+Sent}}
\index{Bytes\+Sent@{Bytes\+Sent}!Accela\+::\+Windows\+Store\+S\+D\+K\+::\+Accela\+Upload\+Progress\+Changed\+Event\+Args@{Accela\+::\+Windows\+Store\+S\+D\+K\+::\+Accela\+Upload\+Progress\+Changed\+Event\+Args}}
\subsubsection[{Bytes\+Sent}]{\setlength{\rightskip}{0pt plus 5cm}long Accela.\+Windows\+Store\+S\+D\+K.\+Accela\+Upload\+Progress\+Changed\+Event\+Args.\+Bytes\+Sent\hspace{0.3cm}{\ttfamily [get]}}}\label{class_accela_1_1_windows_store_s_d_k_1_1_accela_upload_progress_changed_event_args_a1415de7cab0b1b20f3dff62f98f5c6c0}
Bytes sent.
\hypertarget{class_accela_1_1_windows_store_s_d_k_1_1_accela_upload_progress_changed_event_args_a787b7c1b7dec1736e51dfe473563400c}{\index{Accela\+::\+Windows\+Store\+S\+D\+K\+::\+Accela\+Upload\+Progress\+Changed\+Event\+Args@{Accela\+::\+Windows\+Store\+S\+D\+K\+::\+Accela\+Upload\+Progress\+Changed\+Event\+Args}!Total\+Bytes\+To\+Receive@{Total\+Bytes\+To\+Receive}}
\index{Total\+Bytes\+To\+Receive@{Total\+Bytes\+To\+Receive}!Accela\+::\+Windows\+Store\+S\+D\+K\+::\+Accela\+Upload\+Progress\+Changed\+Event\+Args@{Accela\+::\+Windows\+Store\+S\+D\+K\+::\+Accela\+Upload\+Progress\+Changed\+Event\+Args}}
\subsubsection[{Total\+Bytes\+To\+Receive}]{\setlength{\rightskip}{0pt plus 5cm}long Accela.\+Windows\+Store\+S\+D\+K.\+Accela\+Upload\+Progress\+Changed\+Event\+Args.\+Total\+Bytes\+To\+Receive\hspace{0.3cm}{\ttfamily [get]}}}\label{class_accela_1_1_windows_store_s_d_k_1_1_accela_upload_progress_changed_event_args_a787b7c1b7dec1736e51dfe473563400c}
Total bytes to receive.
\hypertarget{class_accela_1_1_windows_store_s_d_k_1_1_accela_upload_progress_changed_event_args_abc0c15f686481e729f7bd11bcc1c00bf}{\index{Accela\+::\+Windows\+Store\+S\+D\+K\+::\+Accela\+Upload\+Progress\+Changed\+Event\+Args@{Accela\+::\+Windows\+Store\+S\+D\+K\+::\+Accela\+Upload\+Progress\+Changed\+Event\+Args}!Total\+Bytes\+To\+Send@{Total\+Bytes\+To\+Send}}
\index{Total\+Bytes\+To\+Send@{Total\+Bytes\+To\+Send}!Accela\+::\+Windows\+Store\+S\+D\+K\+::\+Accela\+Upload\+Progress\+Changed\+Event\+Args@{Accela\+::\+Windows\+Store\+S\+D\+K\+::\+Accela\+Upload\+Progress\+Changed\+Event\+Args}}
\subsubsection[{Total\+Bytes\+To\+Send}]{\setlength{\rightskip}{0pt plus 5cm}long Accela.\+Windows\+Store\+S\+D\+K.\+Accela\+Upload\+Progress\+Changed\+Event\+Args.\+Total\+Bytes\+To\+Send\hspace{0.3cm}{\ttfamily [get]}}}\label{class_accela_1_1_windows_store_s_d_k_1_1_accela_upload_progress_changed_event_args_abc0c15f686481e729f7bd11bcc1c00bf}
Total bytes to send.
The documentation for this class was generated from the following file\+:\begin{DoxyCompactItemize}
\item
C\+:/\+Users/eyang/\+Documents/\+Windows-\/\+S\+D\+K-\/\+New/trunk/src/\+Accela\+S\+D\+K/\+Event\+Args/Accela\+Mobile\+Upload\+Progress\+Changed\+Event\+Args.\+cs\end{DoxyCompactItemize}
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} | 474 |
Q: Ubuntu One Music store plugin not working in Rhythmbox Why did Canonical not update the Ubuntu One Music plugin for Rhythmbox in 11.10? When in 11.10 it's not even an option to install it like in 11.04.
A: From https://launchpad.net/ubuntu/+source/rhythmbox-ubuntuone-music-store/+changelog:
Deleted in oneiric-release (Reason: not ported to GTK 3, FTBFS)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,622 |
Q: Conditional validation of multiple fields using Yup I have 3 input fields (name, id, and postcode), and I use formik along with Yup for the validation.
What I want to achieve here is, I want to match each input field with a known combination of name, id and postcode (I have a predefined default value for id, name, postcode).
And if the values entered on all the 3 input fields exactly match with the default values of name, id, and postcode, then I have to show the formik error on each of the fields(*something like default not allowed). If one of these fields is different from the default values, do not show the error on any fields.
For eg, if my default values for each fields are name="testName", id="testID", postCode="testPostCode", show validation error on each field only if all 3 input values matches with the defaultValues.
This is what I've now:
const defaultValues = {
name: 'testName',
id: 'testID',
postCode: 'testPostCode'
}
const YUP_STRING = Yup.string().ensure().trim();
const validationSchema = yup.object().shape({
name: YUP_STRING.required('required'),
id: YUP_STRING.required('required'),
postcode: YUP_STRING.required('required'),
})
I've tried several variations, but nothing worked here. Can anyone help me find a solution for this?
A: You can do something like <Field validate={(value)=>validate(value,values)} name="name" type="text" />
In more detail..
<Formik
initialValues={defaultValues}
onSubmit={values => alert(JSON.stringify(values)}
>
{({ errors, touched, values }) => (
<Form>
<Field validate={(value) => validate(value, values)} name="name" type="text" />
{errors.name && touched.name ? <div>{errors.name}</div> : null}
<button type="submit">Submit</button>
</Form>
)}
</Formik>
And define validate function as
const validate = (value, values) => {
if(values === defaultValues){
return "Default Values not allowed"
} else return undefined
}
Or if you want to do it with validationSchema you can do something as by adding test function on each of the field, I have only done for name:
const validationSchema = yup.object().shape({
name: YUP_STRING.required('required')
.test('name', "No default please", function (item) {
const currentValues = {
name: this.parent.name,
id: this.parent.id,
postCode: this.parent.postCode
}
return !(currentValues === defaultValues)
}
),
id: YUP_STRING.required('required'),
postcode: YUP_STRING.required('required'),
})
No arrow function to be able to use this
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 9,610 |
Sean Faircloth (né le ) est un avocat et homme politique américain, élu de l'État du Maine. Il a participé à cinq mandats au sein du conseil législatif du Maine.
Sean Faircloth a occupé des fonctions au sein du Comité Judiciaire et des Crédits. Lors de son dernier mandat, Faircloth a été élu Majority Whip. En 2009, Faircloth devient directeur exécutif de la Secular Coalition for America, militant pour la séparation de l'église et de l'état, et pour une plus grande tolérance des points de vue non-théistes dans la vie américaine.
Les autres sujets de prédilection de Sean Faircloth sont relatifs à la Constitution américaine, aux politiques de l'enfance, aux politiques relatives à l'obésité et aux lois sur les crimes sexuels.
En 2012, Sean Faircloth écrit "Attack of the theocrats!", plaidoyer pour le retour aux sources séculaires des États-Unis, préfacé par Richard Dawkins.
Références
Liens externes
https://www.secular.org/bios/Sean_Faircloth.html
Naissance en mai 1960
Personnalité politique américaine
Membre de la Législature d'État du Maine
Étudiant de l'école de droit Hastings de l'université de Californie
Étudiant de l'université de Notre-Dame-du-Lac | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,859 |
Q: Convert a C printf(%c) to C# I'm trying to convert this C printf to C#
printf("%c%c",(x>>8)&0xff,x&0xff);
I've tried something like this:
int x = 65535;
char[] chars = new char[2];
chars[0] = (char)(x >> 8 & 0xFF);
chars[1] = (char)(x & 0xFF);
But I'm getting different results.
I need to write the result to a file
so I'm doing this:
tWriter.Write(chars);
Maybe that is the problem.
Thanks.
A: In .NET, char variables are stored as unsigned 16-bit (2-byte) numbers ranging in value from 0 through 65535. So use this:
int x = (int)0xA0FF; // use differing high and low bytes for testing
byte[] bytes = new byte[2];
bytes[0] = (byte)(x >> 8); // high byte
bytes[1] = (byte)(x); // low byte
A: If you're going to use a BinaryWriter than just do two writes:
bw.Write((byte)(x>>8));
bw.Write((byte)x);
Keep in mind that you just performed a Big Endian write. If this is to be read as an 16-bit integer by something that expects it in Little Endian form, swap the writes around.
A: Ok,
I got it using the Mitch Wheat suggestion and changing the TextWriter to BinaryWriter.
Here is the code
System.IO.BinaryWriter bw = new System.IO.BinaryWriter(System.IO.File.Open(@"C:\file.ext", System.IO.FileMode.Create));
int x = 65535;
byte[] bytes = new byte[2];
bytes[0] = (byte)(x >> 8);
bytes[1] = (byte)(x);
bw.Write(bytes);
Thanks to everyone.
Especially to Mitch Wheat.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,336 |
\section{Introduction}
\IEEEPARstart{W}{ith} the advent of the era of big data, both the feasible size of datasets has grown explosively and the dimensionality of the data has increased dramatically\cite{01,65}. In machine learning and related fields, high dimensionality slows the training speeds of models and heightens the difficulty of the learning task. High dimensionality can lead to overfitting, which reduces the generalizability of a model \cite{02,03}. At high dimensions, Euclidean distance fails as a usable metric, limiting the application range of models that rely on Euclidean distance \cite{24,25,26,27,28}.
Feature engineering was developed in response to these substantial problems \cite{04,05}. Feature selection is one of the most well-known methods in feature engineering, which aims to select a subset of the feature set that can replace the original feature set. Feature selection has significant remedial effect: it can reduce feature dimension, increasing the training speed of a model; it can prevent overfitting, improving the generalizability of a model; and it can increase the correlation between features and predictions, making the model more interpretive\cite{66,67}.
Feature selection methods can be divided into three categories: filter methods, wrapper methods, and embedded methods. Filter methods score features according to evaluation criteria, then sort the features in descending order according to an assigned score. Evaluation criteria usually fall in one of four categories: distance measures, information measures, dependence measures, and consistency measures \cite{06}. Wrapper methods treat feature selection as a feature subset optimization process, and use a classifier to evaluate feature subsets. Since each feature subset needs to train a classifier, most wrapper methods are inefficient, and research into wrapper methods therefore usually focuses on the optimization process. Embedded methods embed feature selection into the training process of the learning algorithm to screen out which features are important for model training\cite{68,69}.
Feature selection algorithms based on rough set theory rely on attribute reduction, which classes them as a filter method. Rough set theory was proposed by Polish scientist Zdzis\l{}aw Pawlak in 1982 \cite{07}. It is an effective mathematical tool to process uncertain, inconsistent, and incomplete data that has been widely applied in data mining, machine learning, decision support system, and other application fields \cite{08,09,10,11,12,13,14}. The classical rough set is also called Pawlak rough set. Pawlak rough set theory achieves this utility by using an equivalence relation to divide samples into several equivalence classes, and then defining upper and lower approximation sets using the union of the equivalence classes\cite{07}. The upper and lower approximations are used to describe and approximate uncertain concepts, and samples are divided into a positive region, boundary region and negative region during this process. The number of samples in the positive region is used to measure the dependence of a label on the feature set; that is, the score of the feature set. Heuristic attribute reduction algorithms based on rough set theory can effectively reduce the time complexity of high dimensional problems, making this a rich field of research in recent decades \cite{15,16,17,18,19,20,21}.
Pawlak rough set (PRS) and neighborhood rough set (NRS) are two most popular rough set theories. In the feature selection process, PRS granulates a dataset based on equivalence classes. An equivalence class consists of a set of attributes and a set of objects, and can describe certain knowledge. So, it provides good interpretability. However, this also results in that it only can process discrete data. Data in the real world is mostly continuous data, the discretization of which will inevitably cause loss of information, thus presenting a serious hindrance to the development and application of rough set theory. To solve this problem, Hu, Yu, and Xie proposed the NRS model \cite{22} based on the idea of Lin's neighborhood model \cite{23}. NRS uses a neighborhood relation instead of an equivalence relation to granulate datasets, thus enabling NRS to process continuous data directly. However, in the model of NRS, the unpper and lower approximations of the NRS consist of sample points instead of equivalence classes, so the NRS loses interpretability. Besides, the inconsistency between PRS and NRS makes rough set theory not concise enough.
Our main contributions are as follows:
\begin{enumerate}[\IEEEsetlabelwidth{4)}]
\item We proposed an novel rough set model called granular-ball rough set for unifying PRS and NRS by introducing granular-ball into the rough set theory.
\item The proposed granular-ball rough set is the first rough set model that can naturally process continuous data while having the interpretability of equivalence classes.
\item Due to the combination of the robustness and adaptability of the granular-ball computing, the learning accuracy of the granular-ball rough set has been greatly improved compared with the PRS and NRS. The granular-ball rough set also outperforms other seven popular or the state-of-the-art feature selection methods.
\item As the GBRS can use equivalence class to represent upper and lower approximation while processing continuous data, we further proposed a granular-ball rough concept tree. This makes GBRS a strong mining tool that can process continuous data and realize feature selection, knowledge representation and classification at the same time.
\end{enumerate}
The rest of this paper is organized as follows: we introduce related works in Section \ref{sec:relatedwork}. The theory basis of granular-ball rough set is presented in Section \ref{sec:theory}. Section \ref{sec:SDNRS} details our newly-proposed granular-ball rough set (GBRS) model, and experimental results and analysis are presented in Section \ref{sec:experiment}. We present our conclusion in Section \ref{sec:conclusion}.
\section{Related Work\label{sec:relatedwork}}
Rough set is mainly used for feature selection. So, in this section, we present a more detailed discussion of the prior work in the three categories of feature selection methods, as well as rough set theory.
\subsection{Filter Methods}
The essence of filter methods is to use statistical indicators to score features, such as the Pearson correlation coefficient, the Gini coefficient, the Kullback-Leibler divergence, the Fisher score, similarity measures, and so forth. Since filter methods only use the dataset itself and do not rely on specific classifiers, they are very versatile and are easy to expand. When compared with wrapper and embedded methods, filter methods generally have a lower algorithm complexity. At the same time, the classification accuracy of filter methods is usually lowest among the three types of methods. Filter methods also only score a single feature, rather than an entire feature subset, and thus the feature subset generated by filter methods usually has high redundancy.
Gu, Li, and Han proposed a generalized Fisher score feature selection method, aiming to find a feature subset that maximizes the lower bound of the Fisher score \cite{29}. This method transforms feature selection into quadratically-constrained linear program, and uses a cutting plane algorithm to solve the problem. Roffo and Melzi proposed a feature selection method based on graphs, ranking the most important features based on recognition as arbitrary clue sets \cite{30}. This method maps feature selection to an affinity graph by assigning features as nodes, and then evaluates the importance of each node via eigenvector centrality. In a later work, Roffo proposed the Inf-FS feature selection method, which assigns features as nodes of a graph and views feature subsets as paths in the graph \cite{31}. The power series property of matrices is used to evaluate the path, and the computational complexity is reduced by adding paths until the length reaches infinity.
\subsection{Wrapper Methods}
Wrapper methods use learning algorithms to evaluate features, and the classification accuracy of wrapper methods is often higher than that of filter methods. At the same time, the classifier used for evaluation limits the method, and the feature subset obtained by wrapper methods tends to have lower versatility. For each feature subset, a wrapper method needs to train a classifier, resulting in a high computational complexity which depends on the search strategy of the feature subset. However, wrapper methods do evaluate the entire feature subset rather than a single feature and take into account the dependency between features, so the redundancy of the resulting feature subset is often lower than that of filter methods.
The support vector machine (SVM) is a commonly used learning algorithm in wrapper methods. Guyon, Weston, Barnhill, and Vapnik proposed a feature selection method using SVM in combination with recursive feature elimination \cite{32}. The method constructs the ranking coefficient of features according to the weight vector generated by the SVM during training. In each iteration, the feature with the smallest ranking coefficient is removed, and finally a sort of all features in descending order is obtained. Guo, Kong, and He proposed a feature selection method based on clustering, which uses a triplet-based ordinal locality-preserving loss function to capture the local structures of the original data \cite{33}. The method defines an alternating optimization algorithm based on half-quadratic minimization to speed up the optimization process of this algorithm. Guo and Zhu specifically developed another wrapper method, Dependence Guided Unsupervised Feature Selection (DGUFS), to overcome the problem of single feature selection in filtering methods, using a joint learning framework for feature selection and clustering \cite{34}. DGUFS is a projection-free feature selection model based on $L_{2,0}$-norm equality constraints and two defined dependence-guided terms which increase the correlation between the original data, cluster labels, and the selected features.
\subsection{Embedded Methods}
Embedded methods embed feature selection into the learning algorithm, and the feature subset can be obtained when the training process of the learning algorithm has completed. This type of method is similar to filter methods, but the score of each feature is determined through model training. The idea behind these methods is to select those features important to the training of the model during the process of determining the model. Embedded methods are a compromise between filter methods and wrapper methods. Compared to filter methods, embedded methods can achieve a higher classification accuracy; compared to wrapper methods, embedded methods have lower algorithm complexity and are not as prone to overfitting.
Bradley and Mangasarian proposed an embedded feature selection method based on concave minimization and SVM \cite{35}. This method finds a separation plane which distinguishes two point sets in the n-dimensional feature space while using as few features as possible. This method not only minimizes the weighted sum of the distance between incorrectly classified points and the boundary plane, but also maximizes the distance between the two boundary planes of the separation plane. Embedded methods are often based on regression learning algorithms. Nie, Huang, Cai, and Ding proposed an efficient and robust feature selection method using a loss function based on $L_{2,1}$-norms to remove outliers \cite{36}. This method adopts joint $L_{2,1}$-norm minimization on the loss function and regularization, and proposes an effective algorithm to solve joint $L_{2,1}$-norm minimization problems. Yang et al. proposed a feature selection method, Unsupervised Discriminative Feature Selection (UDFS), which also uses the $L_{2,1}$-norm \cite{62}. UDFS optimizes an $L_{2,1}$-norm regularized minimization loss function, which uses discriminative information and the local structure of the data distribution.
\subsection{Rough Set Theory}
Feature selection methods based on rough set theory belong to the category of filtering methods. These methods use the positive region from rough set theory to score features. PRS granulates a dataset based on an equivalence relation, which provides good interpretability. his also result in that it only can process discrete data. However, data in the real world is mostly continuous data. Much research has been poured into overcoming the inability of rough set theory to process continuous data. This research can be roughly divided into two categories: discretizing continuous data or proposing improved rough set models. For decades, rough set models based on data discretization have proliferated \cite{37,38,39}. But the discretization of data will inevitably lead to the loss of information, and the discretization results will change with the discretization method. In light of this, some have proposed improved rough set models that can directly process continuous data. Dubois and Prade combine rough sets with another concept, fuzzy sets \cite{40}, and propose fuzzy rough sets \cite{41}, which replace the equivalence relation of classic rough sets with a fuzzy similarity relation, so that fuzzy rough sets can process continuous data. However, fuzzy rough set models need to set a membership function in advance using a priori knowledge of the dataset, which reduces the generality of fuzzy rough sets.
In contrast to fuzzy rough sets, NRS \cite{22} use a neighborhood relation to describe the relationships between samples. This neighborhood relation is completely derived from the data distribution and does not require any priori knowledge. At the same time, NRS can also process continuous data directly. Because of these advantages to NRS models, the field of NRS has been under continuous study and development. Li and Xie propose a method to accelerate NRS which based on an incremental attribute subset \cite{51}. Gao, Liu, and Ji use a matrix to preserve measurement calculation results, requiring only one dimension measurement calculation after a dimension increase and thereby reducing the amount of calculations require to find the positive region \cite{52}. In NRS, the neighborhood radius is a parameter that has a large impact on the reduction results and must be artificially set; how this parameter is chosen is also a frequent study of research. Peng, Liu, and Ji designed a fitness function, which combines the properties of datasets and classifiers to select the optimal neighborhood radius from a given neighborhood radius interval \cite{53}. Xia et al. propose an adaptive NRS model by combining granular ball computing with NRS, which can automatically optimize the neighborhood radius \cite{54}. Above NRS methods use a neighborhood relation instead of an equivalence relation to granulate datasets, thus enabling NRS to process continuous data directly. However, in the model of NRS, the unpper and lower approximations of the NRS consist of sample points instead of equivalence classes, so the NRS loses interpretability. Besides, the inconsistency between PRS and NRS makes rough set theory not concise enough. In this paper, We propose a novel rough set model named granular-ball rough set (GBRS) which can unify PRS and NRS. It not only has the interpretability of equivalence classes but can process continuous data naturally.
\section{The Theory Basis of Granular-ball Rough Set \label{sec:theory}}
In this section, in order to lay a foundation for our theorem and proof, we review some of the basic concepts of PRS and NRS, which have been presented in our previous work \cite{54}. In addition, granular-ball computing is the main basis of the proposed method, so we also introduce it in this section.
\subsection{Pawlak Rough Set}
We first introduce information system and indiscernible relation.
\textbf{\emph{Definition 1.}} \cite{54} Let a quaternion $\left \langle U,A,V,f\right \rangle$ represent an \textit{information system} where:
$ U=\left \{ x_{1},x_{2},...,x_{n} \right \}$ denotes a non-empty finite set of objects. $U$ is called the universe;
$A=\left \{ a_{1},a_{2},...,a_{m} \right \}$ denotes a non-empty finite set of attributes;
$V=\bigcup_{a\in A}V_{a}$ denotes the set of all attribute values, where $V_{a}$ denotes the value range of attribute $a$;
$f=U\times A\rightarrow V$ denotes a mapping function: $\forall x_{i}\in U,a\in A $, $f\left ( x_{i},a \right )\in V_{a}$.
This information system is called a \textit{decision system} $\left \langle U,C,D \right \rangle$ if the set of attributes in the information system above satisfies $A=C\cup D$, $C\cap D=\O$, and $D\neq \O $, where $C$ is the condition attribute set and $D$ is the decision attribute set.
\textbf{\emph{Definition 2.}} \cite{54} Let $\left \langle U,A,V,f\right \rangle$ be an information system. $ \forall x,y\in U $ and $ B\subseteq A $, the \textit{indiscernible relation} $ IND(B) $ of the attribute subset $ B $ is defined as
\begin{equation}
IND(B)\!=\!\{(x, y) \in U \times U | f(x, a) = f(y, a), \forall a \in B\}.
\end{equation}
In PRS algorithms, $f(x,a) = V_a(x)$ represents $x$'s value on the attribute $a$. So, $f(x,a) = f(y,a)$ represents that the sample $x$ has the same value with the sample $y$ on the attribute $a$. In fact, $ (x, y) \in IND(B) $ shows that the values of samples $ x $ and $ y $ are the same under the attribute subset $ B $; that is, under the description of the attribute subset $ B $, samples $ x $ and $ y $ are indiscernible.
$ IND(B) $ is symmetric, reflexive, and transitive; that is, $ \forall B\subseteq A $, $ IND(B) $ is an equivalence relation on $ U $ (abbreviated as $ R_{B} $). $IND(B) $ creates a partition of $ U $, denoted $ U/IND(B) $ and abbreviated as $ U/B $. The characteristics of $ U/B $ are as follows: Suppose $ U/B=\{ X_{1},X_{2},...,X_{k} \} $, if $ X_{i}, X_{j}\subseteq U $, $ X_{i}\cap X_{j} = \O $($ i\neq j $), and $ \bigcup_{i=1}^{k}X_{i}=U $, then $ U $ is divided into $ k $ parts by $ IND(B) $. An element $ [x]_{B}=\{y \in U |(x, y) \in IND(B)\} $ in $ U/B $ is called an equivalence class. This leads us to our next set of definitions, approximations based on the equivalence relation $R_B$.
\textbf{\emph{Definition 3.}} \cite{54} Let $\left \langle U,A,V,f\right \rangle $ be an information system. $ \forall B \subseteq A $, there is a corresponding equivalence relation $ R_{B} $ on $ U $. Then, $ \forall X \subseteq U $, the \textit{upper and lower approximation of} $ X $ with respect to $ B $ are defined as follows:
\begin{equation}
\overline{R_{B}}X=\cup\left\{[x]_{B} \in U / B |[x]_{B} \cap X \neq \emptyset\right\},
\end{equation}
\begin{equation}
\underline{R_{B}}X=\cup\left\{[x]_{B} \in U / B |[x]_{B} \subseteq X\right\}.
\end{equation}
The lower approximation $ \underline{R_{B}}X $ represents the set of samples in $ U $ that are determined to belong to $ X $ according to the equivalence relation $ R_{B} $. It essentially reflects the ability of the equivalence relation $ R_{B} $ to approximately describe the knowledge contained in $ X $ by a partition of the knowledge of the universe $ U $. It is also commonly called the \textit{$ B $ positive region of $ X $ in $ U $}, which is abbreviated as $ POS_{B}(X) $.
\textbf{\emph{Definition 4.}} \cite{54} Let $ \left \langle U,C,D \right \rangle $ be a decision system. We notate the partition of the universe $U$ by the decision attribute set $D$ into $L$ equivalence classes by $ U/D=\left \{ X_{1},X_{2},...,X_{L} \right \}$. $ \forall B\subseteq C$, there is a corresponding equivalence relation $ R_{B} $ on $ U $. The \textit{upper} and the \textit{lower approximation of $D$ with respect to $B$} are respectively defined as
\begin{equation}
\overline{R_{B}}D=\bigcup_{i=1}^{L}\overline{R_{B}}X_{i},
\end{equation}
\begin{equation}
\underline{R_{B}}D= \bigcup_{i=1}^{L}\underline{R_{B}}X_{i}.
\end{equation}
\textbf{\emph{Definition 5.}} \cite{54} Let $ \left \langle U,C,D \right \rangle$ be a decision system. $\forall B\subseteq C$, the \textit{positive region} and \textit{boundary region} of $D$ with respect to $B$ are respectively defined as:
\begin{equation}
POS_{B}\left ( D \right )=\underline{R_{B}}D,
\end{equation}
\begin{equation}
BN_{B}\left ( D \right )=\overline{R_{B}}D-\underline{R_{B}}D.
\end{equation}
The size of the positive region reflects the separability of the classification problem in a given attribute space. The larger the positive region, the more detailed the classification problem can be described using this attribute set. We find it useful to describe this mathematically: the \textit{dependence} of $D$ on $B$ is defined as
\begin{equation} \label{equ:dependence}
\gamma _{B}\left ( D \right )=\frac{\left | POS_{B}\left ( D \right ) \right |}{\left | U \right |},
\end{equation}
where $\left | \cdot \right |$ is the cardinality of the set and $0\leq \gamma _{B}\left ( D \right )\leq 1$. Obviously, the larger the positive region, the stronger the dependence of $D$ on $B$.
The dependency function defines the contribution of conditional attributes to a classification, so it can be used as an evaluation index for the importance of the attribute set.
\textbf{\emph{Definition 6.}} \cite{54} Given a decision system $ \left \langle U,C,D \right \rangle$, $\forall B\subseteq C$ and $\forall a\in(C-B) $, the \textit{importance} of $a$ relative to $B$ is defined as
\begin{equation}
SIG\left ( a,B,D \right )=\gamma _{B\cup a}\left ( D \right )- \gamma _{B}\left ( D \right ).
\end{equation}
Rough set uses the measurement $SIG$ in (9) to select attributes in a forward way. The selection result $C'$ is initialized with $\O$, and for each attribute $a$ in the attribute $C-C'$, that with the largest value of $SIG(a,C', D)$ which should be larger than 0 is select into $C'$. This process is repeated until all $SIG(a,C', D)$ is not greater than 0.
\subsection{Neighborhood Rough Set}
After introducing NRS somewhat loosely, we now drill down into the details, defining the basic spaces we are operating in, the neighborhoods we are working with in NRS, and the positive region we have mentioned, which is key to the operation of these methods.
\textbf{\emph{Definition 7.}} \cite{54} Let $\Delta : \Omega\times \Omega\rightarrow R$ be a function generated on a set $\Omega$. $\left \langle \Omega ,\Delta \right \rangle$ is known as a \textit{metric space} if $\Delta$ satisfies:
(1) $\Delta \left ( x_{1},x_{2} \right )\geq 0$, $\Delta \left ( x_{1},x_{2} \right )=0$ if $x_{1}$=$x_{2},\forall x_{1},x_{2}\in\Omega$;
(2) $\Delta \left ( x_{1},x_{2} \right )=\Delta \left ( x_{2},x_{1} \right ),\forall x_{1},x_{2}\in\Omega$;
(3) $\Delta \left ( x_{1},x_{3} \right )\leq \Delta \left ( x_{1},x_{2} \right )+ \Delta \left ( x_{2},x_{3} \right ),\forall x_{1},x_{2},x_{3}\in\Omega$.
\noindent In this case, $\Delta$ is known as a \textit{metric}.
\textbf{\emph{Definition 8.}} \cite{54} Let $U=\left \{ x_{1},x_{2},...,x_{n} \right \}$ be a non-empty finite set of real space. $\forall x_{i}\in U $, the $\delta$\textit{-neigborhood} of $x_i$ is defined as:
\begin{equation}
\delta \left ( x_{i} \right )=\left \{ x\mid x\in U,\Delta \left ( x,x_{i} \right )\leq \delta \right \},
\end{equation}
where $\delta \geq 0 $.
\textbf{\emph{Definition 9.}} \cite{54} Let $\left \langle U,C,D \right \rangle$ be a neighborhood decision system. The decision attribute set $D$ divides $U$ into $L$ equivalence classes: $ X_{1},X_{2},...,X_{L}$. $\forall B\subseteq C$, the \textit{lower approximation} and the \textit{upper approximation} of the decision attribute set $D$ with respect to the condition attribute set $B$ are respectively defined as:
\begin{equation}
\underline{N_{B}}D= \bigcup_{i=1}^{L}\underline{N_{B}}X_{i},
\end{equation}
\begin{equation}
\overline{N_{B}}D=\bigcup_{i=1}^{L}\overline{N_{B}}X_{i},
\end{equation}
where $ \underline{N_{B}}X_{i}=\left \{ x_{k}\mid \delta _{B}\left ( x_{k} \right )\subseteq X_{i},x_{k}\in U\right \}$, $\overline{N_{B}}X_{i}=\left \{ x_{k}\mid \delta _{B}\left ( x_{k} \right )\bigcap X_{i}\neq \O ,x_{k}\in U\right \}$, and its \textit{positive region} and \textit{boundary region} are respectively defined as $ POS_{B}\left ( D \right )=\underline{N_{B}}D,BN\left ( D \right )=\overline{N_{B}}D-\underline{N_{B}}D$.
\subsection{Granular-ball Computing}
Combining the theoretical basis of traditional granular computing, and based on the research results published by Chen in Science in 1982, he pointed out that ``human cognition has the characteristics of large-scale priority" {\cite{55}}, Wang put forward a lot of granular cognitive computing{\cite{56}}. Based on granular cognitive computing, granular-ball computing is a new, efficient and robust granular computing method proposed by Xia and Wang \cite{57}, the core idea of which is to use ``granular-balls'' to cover or partially cover the sample space. A granular-ball $GB=\{x_i,i=1...N\}$, where $x_i$ represents the objects in $GB$, and $N$ is the number of objects in $GB$. $GB$'s center $C$ and radius $r$ are respectively represented as follows
\begin{equation}
C=\frac {1}{N}{}\sum\limits_{i=1}^{N}{x_{i}},
\end{equation}
\begin{equation}
r=\frac{1}{N}\sum\limits_{i=1}^{N}{\left| {{x}_{i}}-C \right|}.
\end{equation}
This means that the radius is equal to the average distance from all objects in $GB$ to its center. The radius can also be set to the maximum distance. The ``granular-ball'' with a center and radius are used as the input of the learning method or as accurate measurements to represent the sample space, achieving multigranularity learning characteristics (that is, scalability, multiple scales, etc.) and the accurate characterization of the sample space. The basic process of granular-ball generation for classification problems in granular-ball computing is shown in Figure \ref{fig:GBCProcess}.
\begin{figure}
\centering
\includegraphics[scale=0.15]{fig11.pdf}
\caption{Process of granular-ball generation in granular-ball computing.}
\label{fig:GBCProcess}
\end{figure}
As shown in Figure \ref{fig:GBCProcess}, to similiate the ``the characteristics of large-scale priority of human cognition'' at the beginning of the algorithm, the whole dataset can be regarded as a granular-ball. At this time, the purity of the granular-ball is the worst and cannot describe any distribution characteristics of the data. The ``purity'' is used to measure the quality of a granular-ball \cite{57}. It is equal to the proportion of the most labels in the granular-ball. Then, the number of labels $m$ of different classes in the granular-ball is counted, and the granular-ball can be split into $m$ granular-balls. The next step is to calculate the purity of each granular-ball. This is the key step, because purity is the criterion for evaluating whether a granular-ball needs to continue to split. As the splitting process continues to advance, the purity of the granular-balls increases, and the decision boundary becomes increasingly clearer; until the purity of all granular-balls meets the requirements, the boundary is clearest, and the algorithm converges. The granular-ball computing has developed granular-ball classifiers \cite{57}, granular-ball clustering \cite{58}, granular-ball neighborhood rough set \cite{54} and granular-ball sampling methods \cite{59}.
\section{Granular-ball Rough Sets}\label{sec:SDNRS}
\subsection{Motivation}
The main difference of upper or lower approximation between the model of PRS and NRS is that, as shown in Definition 3 and Definition 10 respectively, the former consists of equivalence classes, which can be used to represent knowledge and has the interpretability; however, the latter consists of sample points, which has no interpretability. If we want to use equivalence classes to describe the upper and lower approximation of NRS, a straightforward approach is to treat all objects in a neighborhood radius as an equivalence class. However, we find that this may make two equivalence classes with different decision labels equal. We called this phenomen as ``heterogeneous transmission''. It can be described in detail in Figure \ref{fig:HeterTrans}. As shown in Figure \ref{fig:HeterTrans}, according with the Definition 10, those objects including $x_1, x_3, x_4, x_5$ belong to positive region, and $x_2$ belongs to boundary region. The heterogeneous transmission appears in the intersecting area of the neighborhood area of $x_4$ and that of $x_5$. The intersecting area is called ``transmission area''. When we define the objects belong to a given neighborhood as a equivalence class, the label of the neighborhood equivalence class of $x_4$ is equal to ``+1'', and the label of the neighborhood equivalence class of $x_5$ is equal to ``-1''. However, a new object $x_6$ in transmission area is equivalent to the neighborhood equivalence class of $x_4$ and that of $x_5$ at the same time. This makes the two equivalence classes with two different label equivalent. Obviously, it is harmful for learning. To avoid the heterogeneous transmission phenomena, a method is to set the neighborhood radius small enough. However, this may make most of objects or all objects always belong to positive region, and positive region can not be effectively used for measuring feature importance or other learning tasks. Overall, the heterogeneous transmission phenomena is caused by the overlap between those positive region neighborhoods with different labels in NRS.
\begin{figure}[!ht]
\centering
{\includegraphics[width = 0.4\textwidth]{2c1.pdf}}
\caption{The phenomena of the heterogeneous transmission. The label of a black circle point is equal to ``+1'', and the label of a red plus point is equal to ``-1''. The triangle point $x_6$ is a new test sample.}
\label{fig:HeterTrans}
\end{figure}
\begin{figure}[!ht]
\centering
{\includegraphics[width = 0.4\textwidth]{2b1.pdf}}
\caption{The phenomena of the heterogeneous transmission in Fig. 2 is removed using granular-ball computing.}
\label{fig:NoHeterTrans}
\end{figure}
\subsection{Granular-ball Rough Set}
As shown in Fig. \ref{fig:NoHeterTrans}, as the neighborhood radii are adaptively different, the overlap between those positive region neighborhoods does not exist in granular-ball computing. Therefore, it is possible to use equivalence classes to represent upper and lower approximation by introducing granular-ball computing to represent neighborhood. The granular-ball computing based rough set is called ``granular-ball rough set'', and its models are defined and described as follows.
\textbf{\emph{Definition 10.}} Let $U=\left \{ x_{1},x_{2},...,x_{n} \right \}$ be a non-empty finite set of real space. $\forall x_{i}\in U $, a granular-ball $GB_j$ is defined as:
\begin{equation}
GB_j =\left \{ x\mid x\in U,\Delta \left ( x,c_{j} \right )\leq r _j, \right \},
\end{equation}
where $c_j$ and $r_j$ denote the center and the radius of $GB_j$ respectively. The larger the $r_i$, the coarser the granular-ball $GB_j$; otherwise, the finer the granular-ball $GB_j$.
\textbf{\emph{Definition 11.} \label{def:indgb}} Let $\left \langle U,A,V,f\right \rangle$ be an information system. $ \forall x,y\in U $ and $ B\subseteq A $, the \textit{indiscernible granular-ball relation} $ INDGB(B) $ of the attribute subset $ B $ is defined as
\begin{equation}
INDGB(B)\!=\!\{(x, y) \in U^{2} | f(x, a) = f(y, a) = GB , \forall a \in B\}.
\end{equation}
If $(x,y) \in INDGB(B)$, the relationship between $x$ and $y$ is denoted as $x \sim y$.
In granular-ball rough set, $f(x,a) = GB, x \in GB$. So, $f(x, a) = f(y, a) = GB$ represents that $x$ and $y$ belong to the same granular-ball under the given attribute set $a$. $ \forall B\subseteq A $, $ INDGB(B) $ is an equivalence relation on $ U $ (abbreviated as $ GBR_{B} $). Because the granular-balls do not overlap, $ GBIND(B) $ can also create a partition of $ U $, denoted $ U/GBIND(B) $ and abbreviated as $ U/GB(B) $. An element $ [x]_{GB(B)}=\{y \in U |(x, y) \in INDGB(B)\} $ in $ U/GB(B) $ is an equivalence class generated by granular-ball computing.
\textbf{\emph{Definition 12.}} \label{def:GBE} Given an information system $\left \langle U,A,V,f\right \rangle$, if $GB_i \cup GB_j \neq \emptyset$, $GB_i \sim GB_j$.
As the overlap does not exist between those granular-balls with different labels in GBRS, Definition 12 means that those granular- balls with the same label belong to an equivalence class. This kind of overlap between those positive region neighborhoods, i.e., granular-balls, with a same label is not considered in this method because it does not lead to heterogeneous transmission and affect decision; besides, considering this overlap in the algorithm design will increase computation cost.
\textbf{\emph{Properties of GBRS.}} Given an information system $\left \langle U,A,V,f\right \rangle$, $x,y,z \in U$, $ B\subseteq A $, $\sim$ represents the indiscernible granular-ball relation of the attribute subset $B$ on $U$. The indiscernible granular-ball relation obviously has the following properties:
\begin{enumerate}
\item[(1)] Symmetry: if $x\sim y$, then $y\sim x$;
\item[(2)] Reflexivity: $x\sim x$ ;
\item[(3)] Transitivity: if $x\sim y$, $y\sim z$, then $x\sim z$.
\end{enumerate}
In summary, similar with that in PRS, $ INDGB(B) $ is symmetric, reflexive, and transitive, and complete consistent with $IND(B)$ in PRS.
Based on the equivalence class $[x]_{GB(B)}$, the definitions of positive region, upper and lower approximations are the same to those in PRS. Therefore, GBRS has the consistent model with the PRS. Their specific definitions are as follows:
\textbf{\emph{Definition 13.}} Let $\left \langle U,A,V,f\right \rangle $ be an information system. $ \forall B \subseteq A $, there is a corresponding equivalence relation $ GBR_{B} $ on $ U $. Then, $ \forall X \subseteq U $, the \textit{upper and lower approximation of} $ X $ with respect to $ B $ are defined as follows:
\begin{equation}
\overline{GBR_{B}}X=\cup\left\{[x]_{B} \in U / GB(B) |[x]_{GB(B)} \cap X \neq \emptyset\right\},
\end{equation}
\begin{equation}
\underline{GBR_{B}}X=\cup\left\{[x]_{B} \in U / GB(B) |[x]_{GB(B)} \subseteq X\right\}.
\end{equation}
\textbf{\emph{Definition 14.}} Let $ \left \langle U,C,D \right \rangle $ be a decision system. We notate the partition of the universe $U$ by the decision attribute set $D$ into $L$ equivalence classes by $ U/D=\left \{ X_{1},X_{2},...,X_{L} \right \}$. $ \forall B\subseteq C$, there is a corresponding equivalence relation $ GBR_{B} $ on $ U $. The \textit{upper} and the \textit{lower approximation of $D$ with respect to $B$} are respectively defined as
\begin{equation}
\overline{GBR_{B}}D=\bigcup_{i=1}^{L}\overline{GBR_{B}}X_{i},
\end{equation}
\begin{equation}
\underline{GBR_{B}}D= \bigcup_{i=1}^{L}\underline{GBR_{B}}X_{i}.
\end{equation}
According to Definition 14, a granular-ball whose purity is equal to 1, i.e., that the samples in it have a same decision label, belongs to lower approximation (i.e., the positive region described in Definition 15) in a decision system.
\textbf{\emph{Definition 15.}} Let $ \left \langle U,C,D \right \rangle$ be a decision system. $\forall B\subseteq C$, the \textit{positive region} and \textit{boundary region} of $D$ with respect to $B$ are respectively defined as:
\begin{equation}
POS_{B}\left ( D \right )=\underline{GBR_{B}}D,
\end{equation}
\begin{equation}
BN_{B}\left ( D \right )=\overline{GBR_{B}}D-\underline{GBR_{B}}D.
\end{equation}
Completely the same with that in the Pawlak rough set, the size of the positive region reflects the separability of the classification problem in a given attribute space. The larger the positive region, the more detailed the classification problem can be described using this attribute set. The \textit{dependence} of $D$ on $B$ and $SIG\left ( a,B,D \right )$ are also the same with that in Pawlak rough set.
In the models of GBRS, when the radius of each granular-ball is set to a infinitely small positive number, GBRS is transformed into PRS. When the PRS algorithm is designed from the perspective of GBRS, it is called as granular-ball PRS (GBPRS). GBPRS and PRS have the same experimental results; however, their algorithm designs are different, and the former generate eqivalence using granular-ball computing. When the radius of each granular-ball is not set to a zero, GBRS is transformed into granular-ball NRS (GBNRS). As the GBNRS not only can use equivalence classes to represent knowledge, but is much more efficient than the traditional NRS which contains many overlaps, the GBNRS can completely replace the traditional NRS. In another word, the GBNRS is the representive method of neighborhood rough set. In summary, GBRS is an unified model of GBPRS and GBNRS.
In addition, as shown in Fig. 5(f), GBNRS can flexibly fit the data distribution using those granular-balls with varies radii, which is obviously better than those methods using a fixed radius, such as PRS and the traditional NRS. So, GBNRS can achieve a higher accuracy than the two algorithms. Moreover, the combination of the robustness and adaptability of the granular-ball computing is helpful for GBNRS to perform well in accuracy. This robustness in the GBNRS is reflected in the fact that, since the noise point will be in the small granular-ball, the characteristics of a large neighborhood, i.e., whether it belongs to positive region or not, will not be affected by it. This robustness will not exist in other most methods, such as the traditional NRS who has a fixed radius. These will be demonstrated in the experiments.
\subsection{Implement of GBNRS}
As the GBNRS has the unified model with the PRS, as shown in Fig. \ref{fig:reductionprocess}, its whole algorithm process is completely the same with that of the PRS. The only difference bewteen the GBRS and PRS is the generation way of positive region, which is shown in step 2 in Fig. \ref{fig:reductionprocess}. The GBRS generates positive region using granular-balls. For the GBNRS, in the granular-ball generation, to fulfilling definition 14, the purity threshold $PT$ is set to 1. Besides, referring to that in \cite{70}, the lower bound of the size of a granular ball $LBS$, i.e., the number of samples in it, is optimized from 2*$d$ to 2 with a step as 1, where the $d$ denotes the number of conditional attributes in the data set. When the size of a granular-ball is lower than $LBS$ or its purity reaches to 1, the granular ball stop to split. According to Definition 15, a granular-ball whose purity is equal to 1 belongs to positive region, and a granular-ball whose purity is lower than 1 belongs to boundary region. Besides, to decrease the randomness in the granular-ball generation and make the positive region of the granular-balls in the attribute selection process have better comparability, for a granular-ball, the samples who have the smallest indexes in it are selected as the initial centroids in this granular-ball splitting process. The flowchart is shown as Fig. \ref{fig:reductionprocess}. The specific process is mainly composed of five steps.
\begin{figure}[!ht]
\centering
{\includegraphics[scale=0.26]{process1.pdf}}
\caption{Process of attribute reduction in GBRS.}
\label{fig:reductionprocess}
\end{figure}
\begin{figure}[!t]
\centering
\subfigure[]{\includegraphics[width=0.24\textwidth]{Figure_211.pdf}}
\subfigure[]{\includegraphics[width=0.24\textwidth]{Figure_221.pdf}}
\subfigure[]{\includegraphics[width=0.24\textwidth]{Figure_231.pdf}}
\subfigure[]{\includegraphics[width=0.24\textwidth]{Figure_241.pdf}}
\subfigure[]{\includegraphics[width=0.24\textwidth]{Figure_251.pdf}}
\subfigure[]{\includegraphics[width=0.24\textwidth]{Figure_271.pdf}}
\caption{The generation process of GBNRS on the dataset. The red points and red granular-balls are labeled `+1',
and the green points and green granular-balls are labeled `-1'. The purity threshold \textit{$PT$} is 1 and \textit{$LBS$}'s value is 4. (a)-(e) The generation results of five iterations. (f) As a result of overlapping on the basis of (e), the purity of black granular-balls is less than 1, and the purity of red and green granular balls is 1.}
\label{fig:genbal}
\end{figure}
Fig. \ref{fig:genbal} shows the granular-ball generation process of GBNRS. The red points and red granular-balls are labeled `+1', and the green points and green granular-balls are labeled `-1'. Firstly, the whole dataset is regarded as a granular-ball, it is divided into two granular-balls using 2-means because it contains two different classes of samples in it, and as shown in Fig. \ref{fig:genbal} (a). Fig. \ref{fig:genbal}(b), (c), (d) and (e) are the intermediate iteration results. For a granular-ball, if its purity $ < 1$ and its size $ \ge 4$, it continuous to be split. Fig. \ref{fig:genbal}(e) contains the phenomenon of heterogeneous transmission. It is eliminated by spliting the heterogeneous overlapped granular-balls to remove the overlap of heterogeneous balls, the results of which are shown in Fig. \ref{fig:genbal}(f). In Fig. \ref{fig:genbal}(f), any pair of two heterogeneous granular-balls do not contain any common samples. Besides, as shown in Fig. \ref{fig:genbal}(f), those granular-balls containing both green and red sample points, i.e., those black granualr-balls, belong to the boundary region.
\subsection{Granular-ball Rough Concept Tree for Knowledge Representation and Classification}
\begin{figure}[hbpt!]
\centering
{\includegraphics[width = 0.5\textwidth]{zoo1.pdf}}
\caption{Knowledge representation of the discrete dataset zoo using GBRCT.}
\label{fig:zooRCT}
\end{figure}
\begin{figure*}[hbpt!]
\centering
{\includegraphics[width = 1.0\textwidth]{fig61.pdf}}
\caption{Knowledge representation of the continuous dataset wine using GBRCT.}
\label{fig:wineRCT}
\end{figure*}
As the GBRS can use equivalence class to represent upper and lower approximation while processing continuous data, it can represent knowledge well. In this section, we further proposed the granular-ball rough concept tree (GBRCT) by combing GBNRS with the rough concept tree \cite{xia2021rs}, which is proposed based on the concept lattice. RCT can not only be used to organize and describe the knowledge rules obtained by rough set based on forward attribute reduction algorithm, but also can be used for classification decision. So, the GBRCT makes GBRS a strong mining tool that not only can realize feature selection, but knowledge representation and classification at the same time.
In the RCT, each node is also called as a ``knowledge point'', or called ``concept node'', consisting of two parts: a sequence consisting of both some attributes and their values called ``intent'', and its corresponding equivalence classes called ``extent''. The ``concept" consisting with ``intent" and ``extent" is borrowed from philosophy for knowledge representation. GBRS strictly divides the dataset by gradular-balls, so in the GBRCT of this article, the representation of the first row and first column of the ``knowledge point'' has two parts: ``the attribute value'' and ``the center and radius of the corresponding gradular-ball''.
In the GBRCT, different from that in the RCT, the intent is described using a granular-ball equivalence class consisting of its center and radius instead of a sequence of attribute values. The GBRCT generated on the discrete dataset zoo is shown in Fig. \ref{fig:zooRCT}, and that on the continuous dataset wine is shown in Fig. \ref{fig:wineRCT}. Because we know the data set zoo is discrete in advance, that the neighberhood radius is smaller than a infinitely small positive value is used as the termination condition of granular-ball splitting, and GBRS is converted to be GBPRS. In Figs. \ref{fig:zooRCT} and \ref{fig:wineRCT}, an orange node represents a granular-ball equivalence class. A blue node who contains ``?'' represents boundary region, and an orange node representing a granular-ball belongs to the positive region that can certainly describe knowledge. The dataset zoo is discrete, so that the neighborhood radius is smaller than a infinitely small positive value is set to the termination condition of granular-ball splitting. The result of GBRCT is very similar with that using RCT except the represetation of the intent, i.e., the first row of each node. The RCT represents the intent using a sequence of attibute values, but the GBRCT using a granular-ball consisting of a center and a neighborhood radius whose value is equal to zero as shown in Fig. \ref{fig:zooRCT}; On the contrary, as shown in Fig. \ref{fig:wineRCT}, the neighborhood radius in the continious data is larger than zero. This also indicates that the GBRS realize the unified description for PRS and NRS well. In the real scene, when the information whether the data set is discrete or not is not provided in advance, an infinitely positive value is considered as an option to be optimized as the neighborhood radius in the GBRS.
Similar with that in the RCT, the number in the right of a layer of the GBRCT shows which attributes the concept nodes in the layer are generated on; besides, those positive region concept nodes containing the largest number of extent samples have the strongest representation ability for knowledge and are the most valuable, such as the second node in the second layer and the second node in the third layer in Fig. \ref{fig:zooRCT}. In addition, as described in \cite{xia2021rs}, the GBRCT can also be directly used for classification.
\begin{algorithm}[htbp!]
\caption{Generation of granular-balls in the GBNRS}
\label{alg}
\textbf{Input}: A dataset $ D=\{x_{1}, x_{2}, ..., x_{n}\} $, the lower bound of the size of the granular-ball $LBS$; \\
\textbf{Output}: $NOLGBs$;
\begin{algorithmic}[1]
\STATE The current granular-ball set $CGBs$ and the granular-ball set in the next iteration $NGBs$ are initialized with $D$ and $\emptyset$;\\
// Generate the initial granular-balls
\REPEAT
\STATE $CGBs$ = $NGBs$; $NGBs$ = $\emptyset$;
\FOR{each granular-ball $GB_{i} \in CGBs $}
\IF {$purity(GB_{i})<1$ and $|GB_{i}|>LBS$}
\STATE Split $GB_{i}$ into $k$ sub-granular-balls $\{GB_{j}^{'},j=1,...,k\}$, where $k$ denotes the number of different labels in $GB_{i}$
\STATE $NGBs$ = $NGBs$ + $\{GB_{j}^{'}\}$
\ELSE
\STATE $NGBs$ = $NGBs$ + $GB_{i}$
\ENDIF
\ENDFOR
\UNTIL {$|NGBs|==|CGBs|$}
\STATE $OLGBs = \emptyset$; $NOLGBs = \emptyset$ \\
//Remove the overlap between heterogeneous granular-balls
\REPEAT
\FOR{each granular-ball $GB_{i} \in CGBs $}
\IF {there is overlap between $GB_{i}$ and $GB_{j} \in CGBs$ which has a different label}
\STATE Split the larger granular-ball and add the sub-granular-balls into $OLGBs$
\ELSE
\STATE $NOLGBs$ = $NOLGBs$ + $GB_{i}$
\ENDIF
\ENDFOR
\STATE $CGBs$ = $OLGBs$
\UNTIL {$|OLGBs|=0$}
\end{algorithmic}
\end{algorithm}
\subsection{Algorithm Design \label{sec:algori}}
The only difference between the GBNRS and PRS is the generation way of positive region, and the feature selection process is the same because the GBNRS and PRS have an unified representation model. So, we only discuss the algorithm design of granular-ball generation for positive region in this section, which is shown in Algorithm 1. The algorithm 1 mainly consists of two parts including initial granular-balls generation and overlap removing. $purity(GB)$ denotes the purity of the granular-ball $GB$. In Step 16, there is overlap between two granular-balls if their boudary distance is smaller than zero, i.e,that, the distance between their centers is smaller than sum of their radii. The process of spliting in Step 17 is the similar with that in Step 6. In the output variable $NOLGBs$, those granular-balls with purity as 1 belong to positive region. The lower bound of the size of a granular ball $LBS$, i.e., the number of samples in it, is optimized from 2*$d$ to 2 with a step as 1, where the $d$ denotes the number of conditional attributes in the data set.
\section{Experiment}\label{sec:experiment}
To demonstrate the feasibility and effectiveness of GBRS, we selected some popular or the state-of-the-art algorithms for comparison. As the experimental results using GBPRS are the same with those using PRS, so the GBNRS is selected for comparison. As the PRS can only process discrete data, so we also need to conduct experiments on some discrete data sets for comparison with PRS. As shown in Table \ref{tab:1}, we randomly selected fifteen real datasets including continuous and discrete datasets to demonstrate the performance of the GBNRS. Among them, the first six are discrete datasets; the last nine are continuous datasets. Experimental hardware environment: PC with an Intel Core i7-107000 CPU @2.90 GHz with 32 G RAM. Experimental software environment: Python 3.7.
\begin{table}[!ht]
\centering
\caption{Dataset Information}
\label{tab:1}
\setlength{\tabcolsep}{1.2mm}{
\begin{tabular}{clcccc}
\toprule
\multirow{3}{*}{\begin{tabular}[c]{@{}l@{}}NO.\end{tabular}} & \multirow{3}{*}{\begin{tabular}[c]{@{}l@{}}Dataset\end{tabular}} & \multirow{3}{*}{\begin{tabular}[c]{@{}l@{}}Samples\end{tabular}} &
\multirow{3}{*}{\begin{tabular}[c]{@{}l@{}}Numerical \\ Condition \\Attributes \end{tabular}}&
\multirow{3}{*}{\begin{tabular}[c]{@{}l@{}}Categorical \\ Condition \\Attributes \end{tabular}}&
\multirow{3}{*}{\begin{tabular}[c]{@{}l@{}}Class\end{tabular}}
\\ \\
& & & & \\
\midrule
1& lymphography& 148& 0& 18& 4\\
2& primary-tumor& 336& 0& 15& 2\\
3& mushroom& 7535& 0& 22& 2\\
4& mushroom1& 8124& 0& 22& 2\\
5& zoo& 101& 0& 16& 7\\
6& backup-large& 307& 0& 36& 4\\
7& iono& 351& 34& 0& 2\\
8& Diabetes& 768& 8& 0& 2\\
9& wdbc& 569& 30& 0& 2\\
10& audit\_risk &772& 21& 0& 2\\
11& electrical &10000& 13& 0& 2\\
\multirow{2}{*}{12} & Parkinson\_Multiple & \multirow{2}{*}{1040} & \multirow{2}{*}{27} & \multirow{2}{*}{0}& \multirow{2}{*}{2}\\
& \_Sound\_Recording & & & & \\
13& wine &178 &13& 0& 3\\
14& spambase& 4601& 57& 0& 2\\
15& htru2& 17898& 8& 0& 2\\
\bottomrule
\end{tabular}
}
\end{table}
The lower bound of the size of a granular ball $LBS$, i.e., the number of samples in it, is optimized from 2*$d$ to 2 with a step as 1, where the $d$ denotes the number of conditional attributes in the data set. The experiments are designed along the lines of Xia et al. \cite{54} as the quality of the reduced attribute set is not related to the testing classifier used, only a common testing classifier the nearest neighbor algorithm—is used to verify the quality of the reduced attribute set. Therefore, we use the common classifier, kNN, in our experiment with 5-fold cross-validation.
\subsection{In Comparison with PRS under Discrete Data} \label{section 4.1.1}
The experimental results on the first six discrete datasets in Table \ref{tab:1} are shown in Table \ref{tab:2}, where the "original" column represents the classification accuracy obtained from the original unreduced dataset. The "NO" column in Table \ref{tab:2} is corresponded with the "NO" column in Table \ref{tab:1}. It can be seen from Table \ref{tab:2} that, the classification accuracy of GBNRS is much higher than that of the PNS on most cases except the case on the 4$^{th}$ data set, in which the accracies of the two algorithms are the same. Considering the average classification accuracy, the original accuracy and PRS's accuray are 0.8906 and 0.8618 respectively, while that of GBNRS is 0.8958; in comparison with the previous two results, GBNRS achieved 0.52 and 3.4 percentage enhancement respectively. The reason is that, the GBNRS can flexibly fit the data distribution using those granular-balls with varies radii, which is obviously better than those methods using a fixed radius, such as PRS and the traditional NRS. So, GBNRS can achieve a higher accuracy than the two algorithms. In summary, analysis shows that on discrete datasets, GBNRS can achieve higher classification accuracy than both the PRS and those on the original datasets.
\begin{table}[!htbp]
\centering
\caption{Accuracy Comparison on Discrete Datasets}
\label{tab:2}
\setlength{\tabcolsep}{3mm}{
\begin{tabular}{cccc}
\toprule
NO. & Original & PRS & GBNRS \\
\midrule
1 & 0.8101$\pm$0.0966 & 0.7489$\pm$0.0627 & \textbf{0.8161$\pm$0.0584} \\
2 & \textbf{0.6955$\pm$0.0290} & 0.6686$\pm$0.0414 & \textbf{0.6955$\pm$0.0290} \\
3 & 0.9111$\pm$0.1034 & 0.9202$\pm$0.0753 & \textbf{0.9328$\pm$0.0746} \\
4 & \textbf{1$\pm$0} & 0.9889$\pm$0.0026 & \textbf{1$\pm$0} \\
5 & 0.95$\pm$0.0499 & 0.9$\pm$0.079 & \textbf{0.95$\pm$0.0353} \\
6 & 0.9771$\pm$0.0274 & 0.9444$\pm$0.0526 & \textbf{0.9804$\pm$0.0269} \\
Average & 0.8906 & 0.8618 & \textbf{0.8958} \\
\bottomrule
\end{tabular}
}
\end{table}
\subsection{In Comparsion with Varies Feature Selection Methods} \label{section 4.1.2}
in this section, we select nine continuous datasets whose indexes are from 7 to 15 in Table \ref{tab:1}, and nine popular or the-state-of-the-art algorithms for comparison including NRS \cite{63}, GBNRS$_{old}$ \cite{54}, Cfs \cite{32}, Ilfs \cite{01}, Laplacian \cite{60}, Lasso \cite{61}, Mrmr \cite{68}, WNRS \cite{64}. The experimental results are shown in Table \ref{tab:3}. The neighborhood radius $\delta$ is gradually increased from 0.01 to 0.5 with a step size of 0.01, which is commonly used in the NRS and WNRS. The method, GBNRS$_{old}$, also introduce granular-ball computing to decrease the overlap in the traditional NRS, resulting in the efficiency improvement. However, it did not realize the eqivalence representation; so, we named it with "old" as suffix, i.e., GBNRS$_{old}$, for distinguishing it from our method GBNRS. As there is randomness in the GBNRS$_{old}$, we run GBNRS ten times, and take the highest classification accuracy among the ten experiments results for comparison. The experimental results are shown in Table \ref{tab:3}. It can be seen from Table \ref{tab:3} that, in comparison with other algorithms, GBNRS can achieve the highest classification accuracy in seven datasets on most cases. The reason is that the combination of the robustness and adaptability of the granular-ball computing. The adaptability makes GBNRS flexibly fit different data distributions using those granular-balls with varies radii, resulting in a good performance of GBNRS in accuracy.
\begin{table*}[htbp!]
\centering
\caption{Accuracy of different attribute reduction algorithms on continuous datasets}
\label{tab:3}
\setlength{\tabcolsep}{0.4mm}{
\begin{tabular}{ccccccccccc}
\toprule
NO. & Cfs & Ilfs &Laplacian &Lasso &Mrmr &Original &NRS &GBNRS$_{old}$ &WNRS &GBNRS \\
\midrule
1 &0.8234$\pm $0.0589&0.8029$\pm $0.0551&0.7963$\pm $0.1125 &0.7687$\pm $0.0441
&\textbf{0.8239$\pm $0.0715}&0.8101$\pm $0.0966&0.7566$\pm $0.1094 &0.8035$\pm $0.0575 &0.7489$\pm$0.0627 &0.8161$\pm $0.0584\\
2 &0.7045$\pm $0.0591&\textbf{0.7224$\pm $0.0467}&0.6626$\pm $0.0479 &0.7105$\pm $0.0467
&0.6388$\pm $0.0771&0.6955$\pm $0.0209&0.6686$\pm $0.0414 &0.6716$\pm $0.0606 &0.6687$\pm$0.0414 &0.6955$\pm $0.0290\\
3 &0.8997$\pm $0.1235&0.9040$\pm $0.1420&0.9146$\pm $0.1080 &0.9247$\pm $0.1029
&0.9588$\pm $0.0677&0.9111$\pm $0.1035&0.9729$\pm $0.0260 &0.9289$\pm $0.0755 &\textbf{0.9745$\pm$0.0571} &0.9328$\pm $0.0746\\
4 &\textbf{1$\pm $0}&\textbf{1$\pm $0}&\textbf{1$\pm $0} &\textbf{1$\pm $0}
&\textbf{1$\pm $0}&\textbf{1$\pm $0}&\textbf{1$\pm $0} &\textbf{1$\pm $0} &\textbf{1$\pm$0} &\textbf{1$\pm $0}\\
5 &0.8900$\pm $0.0418&0.9300$\pm $0.0273&0.9200$\pm $0.0274 &0.9200$\pm $0.0570
&\textbf{0.9600$\pm $0.0547}&0.9500$\pm $0.0499&0.9000$\pm $0.079 &0.9100$\pm $0.0418 &0.9000$\pm$0.0790 &0.9500$\pm $0.0353\\
6 &0.9771$\pm $0.0274&\textbf{0.9804$\pm $0.0269}&0.9771$\pm $0.0274 &0.9738$\pm $0.034
&0.9771$\pm $0.0274&0.9771$\pm $0.0274&0.9705$\pm $0.0408 &0.964$\pm $0.0549 &0.9771$\pm$0.0249 &\textbf{0.9804$\pm $0.0269}\\
7 &0.9028$\pm $0.0340&0.8800$\pm $0.0372&0.8514$\pm $0.0312 &0.8657$\pm $0.0423
&0.9142$\pm $0.0319&0.8486$\pm $0.0458&0.8886$\pm $0.0275 &0.8771$\pm $0.0186 &\textbf{0.9146$\pm$0.0211} &0.9000$\pm $0.0484\\
8 &0.6897$\pm $0.0136&0.7431$\pm $0.0250&0.7327$\pm $0.0315 &0.6897$\pm $0.0412
&0.7210$\pm $0.0463&\textbf{0.7471$\pm $0.0348}&\textbf{0.7471$\pm $0.0348} &\textbf{0.7471$\pm $0.0348}&\textbf{0.7471$\pm $0.0348}&\textbf{0.7471$\pm $0.0348}\\
9 &0.9666$\pm $0.0273&0.9701$\pm $0.0192&0.9718$\pm $0.0266 &0.9718$\pm $0.0266&0.9718$\pm $0.0259&0.9683$\pm $0.0253&0.9701$\pm $0.0192 &0.9665$\pm $0.0243 &0.9613$\pm$0.022&\textbf{0.9718$\pm $0.0218}\\
10 &0.9377$\pm $0.6070&0.9468$\pm $0.0360&0.9559$\pm $0.0451 &0.9624$\pm $0.0213&0.9688$\pm $0.0202&0.9377$\pm $0.0571&0.9195$\pm $0.0698 &0.9416$\pm $0.5728 &0.9235$\pm$0.0718&\textbf{0.9922$\pm $0.0071}\\
11 &0.8594$\pm $0.0081&0.9721$\pm $0.0020&0.8594$\pm $0.0081 &0.8594$\pm $0.0081&0.9147$\pm $0.0068&0.9145$\pm $0.0068&0.9721$\pm $0.0058 &0.9145$\pm $0.0068 &0.9782$\pm$0.0022&\textbf{0.9969$\pm $0.0015}\\
12 &0.9057$\pm $0.0455&0.8249$\pm $0.0686&0.8913$\pm $0.0522 &0.8970$\pm $0.0512&0.9259$\pm $0.5930&0.8249$\pm $0.6860&\textbf{1$\pm $0} &0.8797$\pm $0.0053 &\textbf{1$\pm $0} &\textbf{1$\pm $0} \\
13 &0.9435$\pm $0.0282&0.9662$\pm $0.0235&0.9719$\pm $0.0340 &0.9660$\pm $0.0310&0.9775$\pm $0.0233&0.9605$\pm $0.0427&\textbf{0.9830$\pm $0.0155}&0.9438$\pm $0.0478&0.9721$\pm$0.0196&0.9773$\pm $0.0238 \\
14 &0.8715$\pm $0.0562&0.8609$\pm $0.0582&0.8661$\pm $0.0559 &0.8806$\pm $0.2870&0.8830$\pm $0.0603&0.8646$\pm $0.0639&0.8648$\pm $0.0650&0.8689$\pm $0.0634&0.8646$\pm$0.0646 &\textbf{0.8889$\pm $0.0531} \\
15 &0.9772$\pm $0.0021&0.9772$\pm $0.0021&0.9772$\pm $0.0021 &0.9777$\pm $0.0015&0.9772$\pm $0.0021&0.9772$\pm $0.0021&0.9772$\pm $0.0021&0.9772$\pm $0.0021 &0.9778$\pm $0.0021&\textbf{0.9785$\pm $0.0021} \\
\bottomrule
\end{tabular}
}
\end{table*}
\section{Conclusion}\label{sec:conclusion}
This paper presents an unified model for the two most popular rough set models, Pawlak rough set and neighborhood rough set models. The unified model can not only express knowledge with equivalence classes, but also deal with both continuous data and discrete data. In comparison with nine popular or the-state-of-the-art feature selection methods on fifteen real datasets, the experiments show that the proposed model can achieve a better performance in accuracy. However, the optimization of the $LBS$ is inefficient. If some incremental strategies can be developed, it can be accelerated. In the future work, we will developed the poposed model into other rough set models and improve their performance.
\section{Acknowlegements}
This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 62176033 and 61936001, the Natural Science Foundation of Chongqing under Grant No. cstc2019jcyj-cxttX0002 and by NICE: NRT for Integrated Computational Entomology, US NSF award 1631776, the National Key Research and Development Program of China under Grant No. 2019QY(Y)0301.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,974 |
'''
Tests for main.py
'''
import os
from shutil import rmtree
import unittest
from neuroner import neuromodel
class TestMain(unittest.TestCase):
outputFolder = os.path.join('.', "output")
test_param_file = os.path.join('.', 'test-parameters-training.ini')
def setUp(self):
# delete the outputFolder
if os.path.isdir(self.outputFolder):
rmtree(self.outputFolder)
def tearDown(self):
# delete the outputFolder
if os.path.isdir(self.outputFolder):
rmtree(self.outputFolder)
def test_ProvideOutputDir_CorrectlyOutputsToDir(self):
"""
Sanity test to check if all proper model output files are created in the output folder
"""
nn = neuromodel.NeuroNER(output_folder=self.outputFolder, parameters_filepath=self.test_param_file)
nn.fit()
# find the newest dir, from: http://stackoverflow.com/questions/2014554/find-the-newest-folder-in-a-directory-in-python
run_outputdir = max([os.path.join(self.outputFolder,d) for d in os.listdir(self.outputFolder)], key=os.path.getmtime)
# assert the model has been written to files
self.assertTrue(os.path.isfile(os.path.join(run_outputdir, 'model', 'checkpoint')))
self.assertTrue(os.path.isfile(os.path.join(run_outputdir, 'model', 'dataset.pickle')))
self.assertTrue(os.path.isfile(os.path.join(run_outputdir, 'model', 'model_00001.ckpt.data-00000-of-00001')))
self.assertTrue(os.path.isfile(os.path.join(run_outputdir, 'model', 'model_00001.ckpt.index')))
self.assertTrue(os.path.isfile(os.path.join(run_outputdir, 'model', 'model_00001.ckpt.meta')))
self.assertTrue(os.path.isfile(os.path.join(run_outputdir, 'model', 'model_00002.ckpt.data-00000-of-00001')))
self.assertTrue(os.path.isfile(os.path.join(run_outputdir, 'model', 'model_00002.ckpt.index')))
self.assertTrue(os.path.isfile(os.path.join(run_outputdir, 'model', 'model_00002.ckpt.meta')))
self.assertTrue(os.path.isfile(os.path.join(run_outputdir, 'model', 'parameters.ini')))
self.assertTrue(os.path.isfile(os.path.join(run_outputdir, 'model', 'projector_config.pbtxt')))
self.assertTrue(os.path.isfile(os.path.join(run_outputdir, 'model', 'tensorboard_metadata_characters.tsv')))
self.assertTrue(os.path.isfile(os.path.join(run_outputdir, 'model', 'tensorboard_metadata_tokens.tsv'))) | {
"redpajama_set_name": "RedPajamaGithub"
} | 6,929 |
Обичне љубавне пјесме је трећи студијски албум загребачке рок групе Аеродром који је изашао 1982. године. Након објављивања албума Танго Банго, Младен Крајник је отишао из групе у ЈНА, а Пађен је преузео улогу главног вокала. Албум је снимљен у Шведској, а продуцент је био Тини Варга, који је уједно свирао гитару и певао пратећe вокале. Гост на саксофону био је Уфе Андерсон, који је пуно година сарађивао са групом АББА. На албуму се налази девет песама и он им је донео највећи хит до тада — Обичну љубавну пјесму.
Списак песама
Обична љубавна пјесма
Сутра бит ће боље
За све криве жене
Снови
Кад је са мном квари све
Мушки строј
Не могу тако
Странац
Одлазим
Извођачи
Јурица Пађен - електрична гитара, вокал
Ремо Картагине - бас гитара
Бранко Кнежевић - бубњеви
Зоран Краш - клавијатуре
Продукција
Дражен Каленић - дизајн
Тини Варга - продуцент
Референце
Спољашње везе
Албуми 1982.
Албуми групе Аеродром
Албуми издати за Југотон | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,259 |
\section{INTRODUCTION}
\label{sec:Introduction}
The observation of X(3872) \cite{ct:X3872}, followed by
the discovery of many other states such as the Z(3930) \cite{ct:Z3930}, the Y(3940) \cite{ct:Y3940}
and the X(3940) \cite{ct:X3940}, has reopened interest in charmonium spectroscopy.
Some of these resonances cannot be fully explained by a simple
charmonia model \cite{ct:charmonia}; four-quark state \cite{ct:tetra} and $D^0\overline{D}^{0*}$ molecule \cite{ct:molecule}
are some of the interpretations that have been proposed to explain their nature.
Among these new states the Y(4260) \cite{ct:babar-Y} that has been observed by \babar\xspace
in the process $e^+e^- \ensuremath{\rightarrow}\xspace \gamma_{ISR}$ Y(4260)$ \ensuremath{\rightarrow}\xspace \gamma_{ISR}~ J/\psi \pi^+\pi^-$, where $ISR$ denotes
initial state radiation. Being formed directly
in $e^+e^-$ annihilation, it is known to have $J^{PC}=1^{--}$.
Nonetheless its properties do not fit with any
simple charmonium interpretation and its nature is still unclear.
A recent ISR analysis by BELLE \cite{:2007sj} suggests the existence of a second state in the same decay mode,
called Y(4008) \cite{:xiang}, with the same production mechanism.
After the discovery of Y(4260), other $J^{PC}=1^{--}$ states, produced through
the same $e^+e^-$ initial state radiation mechanism, have been observed in
the $\psi(2S) \pi^+\pi^-$ final state, such as the Y(4320) and the Y(4660)
\cite{Aubert:2006ge,:2007ea}.
In this letter, we present udated measurements of the resonance parameters and
${\cal B}(\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace)\Gamma_{e^+e^-}$ of the Y(4260) based on the full \babar\xspace data set
which is approximately two times larger than the one used in the original analysis \cite{ct:babar-Y}.
\section{THE \mbox{\sl B\hspace{-0.4em} {\small\sl A}\hspace{-0.37em} \sl B\hspace{-0.4em} {\small\sl A\hspace{-0.02em}R}}\ DETECTOR AND DATASET}
\label{sec:babar}
The original \babar\xspace analysis \cite{ct:babar-Y} is updated here with the same method on a data set corresponding to a
total integrated luminosity of 454\ensuremath{\mbox{\,fb}^{-1}}\xspace obtained at the
SLAC PEP-II B-factory, running at the center-of-mass energy near the $\Upsilon$(4S)
resonance.
The \babar\xspace detector is described in
detail elsewhere \cite{ct:babar-detector}.
Charged-particle momenta are measured in a tracking system consisting
of a five-layer double-sided silicon vertex tracker (SVT) and a
40-layer central drift chamber (DCH), both situated in a 1.5-T axial
magnetic field.
An internally reflecting ring-imaging Cherenkov detector (DIRC)
provides charged-particle identification together with $dE/dx$ measurements
from SVT and DCH. A CsI(Tl) electromagnetic
calorimeter (EMC) is used to detect and identify photons and
electrons.
Muons are identified using information from the Instrumented
Flux Return (IFR) system, together with $E/p$, where the energy $E$ is
determined by the EMC and the momentum $p$ by the SVT and DCH.
\section{ANALYSIS METHOD}
\label{sec:Analysis}
In this analysis we reconstruct events:
\begin{equation}
e^+e^- \ensuremath{\rightarrow}\xspace \ensuremath{\gamma_{\smallISR}}\xspace \ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace ,
\end{equation}
where $\ensuremath{\gamma_{\smallISR}}\xspace$ represents a photon that is radiated from the
initial state $e^{\pm}$, lowering the center-of-mass energy of the $e^+e^-$ system.
This mechanism allows to perform an energy scan of $e^+e^-$ interactions at the
B-factories, where the center-of-mass energy of the interactions is
fixed in the region of the $\Upsilon(4S)$ resonance.
A candidate $\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ meson is reconstructed via its decay to $e^+e^-$ or $\mu^+\mu^-$.
The lepton tracks, at least one of which must be identified as an electron or muon candidate,
must be well reconstructed and must originate from the same vertex: a geometric
fit of the $\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ candidate is conducted with beam-spot constraint. An algorithm to recover energy lost
to bremsstrahlung is applied to electron candidates.
An $e^+e^-$ pair with its invariant
mass within the interval ($-$75,+40)~\ensuremath{{\mathrm{\,Me\kern -0.1em V\!/}c^2}}\xspace around the PDG \cite{ct:PDG} $\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ mass
is taken as a $\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ candidate.
For a $\mu^+\mu^-$ pair, the interval is ($-$40,+40)~\ensuremath{{\mathrm{\,Me\kern -0.1em V\!/}c^2}}\xspace.
The $\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ candidate is then kinematically constrained to
the nominal $\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ mass
and combined with a pair of oppositely-charged tracks
identified as pion candidates.
In the event reconstruction, we do not require observation of the
initial state radiation photon $\ensuremath{\gamma_{\smallISR}}\xspace$,
as it is preferentially produced along
the beam directions and it is not detected.
We select $e^+e^-\ensuremath{\rightarrow}\xspace\ensuremath{\gamma_{\smallISR}}\xspace\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ events with the following
criteria: the invariant mass squared recoiling against the $\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ system ($m_{rec}^2$)
is required to be in the range ($-$0.50,+0.75)~(\ensuremath{{\mathrm{\,Ge\kern -0.1em V\!/}c^2}}\xspace)$^2$;
the total number of reconstructed tracks in the event $\le$ 5.
Since the transverse component of the missing momentum ($p^{*}_{T,miss}$)
is small for events with initial state radiation, we select events
with $p^{*}_{T,miss} < 2.25$\ensuremath{{\mathrm{\,Ge\kern -0.1em V\!/}c}}\xspace.
The cosine of the angle between the $\ell^+$ momentum in the $\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ rest frame
and the $\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ momentum in the center-of-mass frame ($\cos\theta_l$)
is required to be $| \cos\theta_l | < 0.925$.
After this selection, a clean $\psitwos$ signal is apparent in
the $\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ invariant mass spectrum, as shown in figure \ref{fig:YMass_log};
in the same distribution, a clean Y(4260) peak is also visible.
\begin{figure}[htbp]
\centering
\includegraphics[height=7cm]{YMass_log}
\caption{The invariant mass distribution of $\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ candidates with a logarithmic
vertical scale.}
\label{fig:YMass_log}
\end{figure}
By means of Monte Carlo simulations we determine that the selection efficiency
at the Y(4260) energy is 15.3\%.
The method used for the efficiency determination is checked at the $\psitwos$,
where we obtain a value of the cross section that is consistent with the measurement performed by previous
experiments \cite{:2007sj}. The $\psitwos$ mass is measured as $3685.35\pm0.02$\ensuremath{{\mathrm{\,Me\kern -0.1em V\!/}c^2}}\xspace (where the error is statistical only);
the mass shift with respect to the PDG value \cite{ct:PDG} is taken into account as a systematic error in the Y(4260) mass
measurement.
The Monte Carlo $\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ invariant mass resolution and mass scale have been calibrated by comparing the widths of $\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ invariant
mass distributions from $\psitwos$ decays in data and Monte Carlo.
We find that the Monte Carlo simulation
reproduces the observed r.m.s. of the $\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ distribution for the $\psitwos$ state.
The mass resolution is around 5\ensuremath{{\mathrm{\,Me\kern -0.1em V\!/}c^2}}\xspace in the mass range $4.16\ensuremath{{\mathrm{\,Ge\kern -0.1em V\!/}c^2}}\xspace < m(\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace) < 4.36\ensuremath{{\mathrm{\,Ge\kern -0.1em V\!/}c^2}}\xspace$
The typical ISR-production signature of the Y(4260) can be obtained
by subtracting distributions for events with $\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$
mass in the region (3.95,4.1)\ensuremath{{\mathrm{\,Ge\kern -0.1em V\!/}c^2}}\xspace and (4.4,4.55)\ensuremath{{\mathrm{\,Ge\kern -0.1em V\!/}c^2}}\xspace from those with mass
in the signal region defined as (4.1,4.4)\ensuremath{{\mathrm{\,Ge\kern -0.1em V\!/}c^2}}\xspace. The distributions of $m_{rec}^2$ and of the
cosine of the $\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ system polar angle in the c.m. frame are shown in figure \ref{fig:mrec} and \ref{fig:cos}
along with the corresponding distributions for ISR Y(4260)
Monte Carlo events.
\begin{figure}[tbp]
\centering
\includegraphics[height=7cm]{mrec}
\caption{The distribution of $m_{rec}^2$.
The points represent the
data events passing all selection criteria
and having a $\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ mass near 4260\ensuremath{{\mathrm{\,Me\kern -0.1em V\!/}c^2}}\xspace. They are obtained by subtracting the
distribution from neighboring $\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ mass regions
(see text). The solid histogram represents ISR Y(4260) Monte Carlo
events.}
\label{fig:mrec}
\end{figure}
\begin{figure}[!h]
\centering
\includegraphics[height=7cm]{costhCM}
\caption{The distribution of $cos\theta_{\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace}^*$.
The points represent the
data events passing all selection criteria
and having a $\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ mass near 4260\ensuremath{{\mathrm{\,Me\kern -0.1em V\!/}c^2}}\xspace. They are obtained by subtracting the
distribution from neighboring $\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ mass regions
(see text). The solid histogram represents ISR Y(4260) Monte Carlo
events.}
\label{fig:cos}
\end{figure}
\section{RESULTS}
\label{sec:Results}
We have performed an unbinned maximum likelihood fit to the $\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ invariant mass distribution between
3.8\ensuremath{{\mathrm{\,Ge\kern -0.1em V\!/}c^2}}\xspace and 5\ensuremath{{\mathrm{\,Ge\kern -0.1em V\!/}c^2}}\xspace. The signal probability density function (PDF) is described by convolving a
non-relativistic Breit-Wigner function with a Gaussian
and we use a first degree polynomial function to describe the background.
All the fit parameters for the signal and the background PDF are floating, except the
Gaussian sigma which is fixed to the resolution found at the $\psitwos$ in data but linearly scaled
to the Y mass value based on the Monte Carlo simulation.
From the fit shown in figure \ref{fig:fit} we obtain
a signal yield $N_Y = 344 \pm 39$ and resonance mass
$m_Y = 4252 \pm6~^{+2}_{-3}$\ensuremath{{\mathrm{\,Me\kern -0.1em V\!/}c^2}}\xspace and width $\Gamma_Y = 105 \pm 18~^{+4}_{-6}$\ensuremath{{\mathrm{\,Me\kern -0.1em V\!/}c^2}}\xspace.
Systematic uncertainties include contributions from the fitting procedure
(evaluated by changing the fit range and the background PDF), the mass scale, the mass-resolution
function and the dependence on the model of Y(4260)$\ensuremath{\rightarrow}\xspace\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ decay. They have been added in
quadrature.
To measure ${\cal B}(\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace)\Gamma_{e^+e^-}$ we use
Eq.~\ref{eq:Gee}, where $N(\gamma\,\psitwos)$, $N(\gamma\,Y)$, $m(\psitwos)$, $m(Y)$, $\varepsilon(\psitwos)$, $\varepsilon(Y)$
and $W(\psitwos)$, $W(Y)$ are the number of events, mass, selection efficiency and the photon emission probability density
function for the $\psitwos$ and Y(4260) respectively.
\begin{linenomath}
\begin{multline} \label{eq:Gee}
\frac{\Gamma_{ee}(Y){\ensuremath{\cal B}\xspace}(Y\!\ensuremath{\rightarrow}\xspace\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace)}
{\Gamma_{ee}(\psitwos){\ensuremath{\cal B}\xspace}(\psitwos\!\ensuremath{\rightarrow}\xspace\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace)} \\
= \Bigl( \frac {N(\gamma\,Y)} {N(\gamma\,\psitwos)} \Bigr) \cdot
\Bigl( \frac {m(Y)} {m(\psitwos)} \Bigr) \cdot
\Bigl( \frac {\varepsilon(\psitwos)} {\varepsilon(Y)} \Bigr) \cdot
\Bigl( \frac {W(\psitwos)} {W(Y)} \Bigr)
\end{multline}
\end{linenomath}
This way,
the entire uncertainties of integrated luminosity and ${\ensuremath{\cal B}\xspace}(\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace\!\ensuremath{\rightarrow}\xspace\ell^+\ell^-)$
are canceled. Most uncertainties of the selection efficiency, particle ID efficiency,
tracking efficiency, and photon emission probability density $W(s,x)$ are
canceled out.
Meanwhile, we also introduce some new uncertainties pertaining to the
ISR $\psitwos$ such as ${\ensuremath{\cal B}\xspace}(\psitwos\!\ensuremath{\rightarrow}\xspace\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace)$, $\Gamma_{\psitwos\!\ensuremath{\rightarrow}\xspace\ensuremath{e^-e^-}\xspace}$, and
statistical uncertainty of the $N(\psitwos)$.
We obtain ${\cal B}(\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace)\Gamma_{e^+e^-} = (7.5\pm 0.9~\pm0.8)$~eV.
\begin{figure}[!h]
\centering
\includegraphics[height=7cm]{YMass_fit}
\caption{The $\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ invariant mass spectrum in the range 3.8-5.5\ensuremath{{\mathrm{\,Ge\kern -0.1em V\!/}c^2}}\xspace.
The points with error bars represent the selected data, the solid curve shows the
result of the fit described in the text, while the dashed curve represents the background
component.}
\label{fig:fit}
\end{figure}
A recent BELLE analysis reported evidence for a broad enhancement
with mass $m = 4008 \pm 40~ ^{+114}_{-28}$\ensuremath{{\mathrm{\,Me\kern -0.1em V\!/}c^2}}\xspace and width
$\Gamma = 226 \pm 44~ \pm 87$\ensuremath{{\mathrm{\,Me\kern -0.1em V\!/}c^2}}\xspace \cite{:2007sj}.
We cannot confirm this observation and obtain an upper limit
${\cal B}(\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace)\Gamma_{e^+e^-} < 0.7$ eV at 90\% C.L. for this state.
We also study the $\ensuremath{\pi^+\pi^-}\xspace$ invariant mass distribution for Y(4260)
events, obtained by dividing the total sample into
several dipion invariant mass regions and fitting the Y(4260) peak
in each one of these regions.
The results reported in figure \ref{fig:dipion} show that, in Y(4260) decays, the $\ensuremath{\pi^+\pi^-}\xspace$ invariant mass
distribution does not agree with the MC based on phase space and tends to peak
at large values.
\begin{figure}[!h]
\centering
\includegraphics[height=7cm]{dipion}
\caption{Di-pion invariant mass distribution of Y(4260) events: the points with error
bars are signal events, the histogram is the phase-space distribution from MC events.}
\label{fig:dipion}
\end{figure}
\section{CONCLUSIONS}
\label{sec:Conclusions}
In summary, we have analyzed initial-state radiation events to study the process
$e^+e^-\ensuremath{\rightarrow}\xspace\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace$ across the charmonium mass range. We observe $344 \pm 39$
Y(4260) events with $m_Y = 4252 \pm 6~^{+2}_{-3}$\ensuremath{{\mathrm{\,Me\kern -0.1em V\!/}c^2}}\xspace and $\Gamma_Y = 105 \pm 18~^{+4}_{-6}$\ensuremath{{\mathrm{\,Me\kern -0.1em V\!/}c^2}}\xspace.
The $\ensuremath{\pi^+\pi^-}\xspace$ invariant mass distribution, in Y(4260) region, tends to peak at large values consistently with
other studies \cite{ct:babar-Y} \cite{:2007sj}.
There is no evidence for the
broad enhancement reported by BELLE around 4.05\ensuremath{{\mathrm{\,Ge\kern -0.1em V\!/}c^2}}\xspace \cite{:2007sj} and we obtain an upper limit
${\cal B}(\ensuremath{\pi^+\pi^-}\xspace\ensuremath{{J\mskip -3mu/\mskip -2mu\psi\mskip 2mu}}\xspace)\Gamma_{e^+e^-} < 0.7$ eV at 90\% C.L. for this state.
\section{ACKNOWLEDGMENTS}
\label{sec:Acknowledgments}
\input acknowledgements
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,910 |
Q: JTable duplicate entry How can I prevent duplication of data in JTable?
The for loop determines whether the data contains similar ID.
Yes, it determines and show a JOptionPane which works.
But my problem is that it scans for a duplicate after I setValue on table 2.
I want my program to prevent duplication of data before it setValue on table 2.
public void dProductList(){
table.addMouseListener(new MouseAdapter(){
public void mouseClicked(MouseEvent e) {
if(e.getClickCount() == 1) {
JTable tbl = (JTable)e.getSource();
int rrow = tbl.getSelectedRow();
if(rrow>=0) {
int dcol = 0;
int rcol = 0;
((DefaultTableModel)table2.getModel()).addRow(new Object[] {0,0,0,0});
while(rcol<table2.getColumnCount()-1) {
table2.setValueAt(table.getValueAt(rrow,rcol),drow,dcol);
totalAmount = totalAmount + (int) table2.getValueAt(drow,3);
rcol++;
dcol++;
if(rcol==table2.getColumnCount()-1) {
drow++;
}
label.setText(String.valueOf(totalAmount));
}
for(int i=0; i<table2.getRowCount()-1;i++){
if(table2.getValueAt(i,0).equals(table2.getValueAt(table2.getRowCount()-1,0))){
JOptionPane.showMessageDialog(null,"item already listed");
}
}
}
}
}
});
}
A: Use for loop checking just before table2.setValueAt and add only if no duplicate.
You could also keep your data to a Set (eg a HashSet) and check there before adding to your JTable.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,234 |
package org.apache.bookkeeper.client;
import org.apache.bookkeeper.client.AsyncCallback.AddCallback;
import org.apache.bookkeeper.client.BookKeeper.DigestType;
import org.apache.bookkeeper.conf.ClientConfiguration;
import org.apache.bookkeeper.net.BookieSocketAddress;
import org.apache.bookkeeper.test.BookKeeperClusterTestCase;
import org.junit.Before;
import org.junit.Test;
import org.slf4j.Logger;
import org.slf4j.LoggerFactory;
import java.util.List;
import java.util.concurrent.CountDownLatch;
public class TestAddEntryQuorumTimeout extends BookKeeperClusterTestCase implements AddCallback {
final static Logger logger = LoggerFactory.getLogger(TestAddEntryQuorumTimeout.class);
final DigestType digestType;
final byte[] testPasswd = "".getBytes();
public TestAddEntryQuorumTimeout() {
super(3);
this.digestType = DigestType.CRC32;
}
@Before
@Override
public void setUp() throws Exception {
super.setUp();
}
private static class SyncObj {
volatile int counter;
volatile int rc;
public SyncObj() {
counter = 0;
}
}
@Override
public void addComplete(int rc, LedgerHandle lh, long entryId, Object ctx) {
SyncObj x = (SyncObj) ctx;
synchronized (x) {
x.rc = rc;
x.counter++;
x.notify();
}
}
LedgerHandle getTestLedger() throws Exception {
ClientConfiguration conf = new ClientConfiguration();
conf.copy(baseClientConf);
conf.setAddEntryTimeout(10);
conf.setAddEntryQuorumTimeout(1);
BookKeeperTestClient bkc = new BookKeeperTestClient(conf);
return bkc.createLedger(3, 3, 3, digestType, testPasswd);
}
@Test(timeout = 60000)
public void testBasicTimeout() throws Exception {
LedgerHandle lh = getTestLedger();
List<BookieSocketAddress> curEns = lh.getLedgerMetadata().currentEnsemble;
byte[] data = "foobar".getBytes();
lh.addEntry(data);
sleepBookie(curEns.get(0), 5).await();
try {
lh.addEntry(data);
fail("should have thrown");
} catch (BKException.BKAddEntryQuorumTimeoutException ex) {
}
}
@Test(timeout = 60000)
public void testTimeoutWithPendingOps() throws Exception {
LedgerHandle lh = getTestLedger();
List<BookieSocketAddress> curEns = lh.getLedgerMetadata().currentEnsemble;
byte[] data = "foobar".getBytes();
SyncObj syncObj1 = new SyncObj();
SyncObj syncObj2 = new SyncObj();
SyncObj syncObj3 = new SyncObj();
lh.addEntry(data);
sleepBookie(curEns.get(0), 5).await();
lh.asyncAddEntry(data, this, syncObj1);
lh.asyncAddEntry(data, this, syncObj2);
lh.asyncAddEntry(data, this, syncObj3);
synchronized (syncObj1) {
while (syncObj1.counter < 1) {
logger.debug("Entries counter = " + syncObj1.counter);
syncObj1.wait();
}
assertEquals(BKException.Code.AddEntryQuorumTimeoutException, syncObj1.rc);
}
assertEquals(BKException.Code.AddEntryQuorumTimeoutException, syncObj2.rc);
assertEquals(BKException.Code.AddEntryQuorumTimeoutException, syncObj3.rc);
}
@Test(timeout = 60000)
public void testLedgerClosedAfterTimeout() throws Exception {
LedgerHandle lh = getTestLedger();
List<BookieSocketAddress> curEns = lh.getLedgerMetadata().currentEnsemble;
byte[] data = "foobar".getBytes();
CountDownLatch b0latch = sleepBookie(curEns.get(0), 5);
try {
lh.addEntry(data);
fail("should have thrown");
} catch (BKException.BKAddEntryQuorumTimeoutException ex) {
}
b0latch.await();
try {
lh.addEntry(data);
fail("should have thrown");
} catch (BKException.BKLedgerClosedException ex) {
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,749 |
{"url":"https:\/\/greprepclub.com\/forum\/half-of-the-shirts-in-a-closet-are-white-and-30-of-the-rema-9552.html","text":"It is currently 28 Sep 2020, 02:49\n\n### GMAT Club Daily Prep\n\n#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.\n\nCustomized\nfor You\n\nwe will pick new questions that match your level based on your Timer History\n\nTrack\n\nevery week, we\u2019ll send you an estimated GMAT score based on your performance\n\nPractice\nPays\n\nwe will pick new questions that match your level based on your Timer History\n\n# Half of the shirts in a closet are white and 30% of the rema\n\nAuthor Message\nTAGS:\nRetired Moderator\nJoined: 07 Jun 2014\nPosts: 4803\nGRE 1: Q167 V156\nWE: Business Development (Energy and Utilities)\nFollowers: 171\n\nKudos [?]: 2926 [0], given: 394\n\nHalf of the shirts in a closet are white and 30% of the rema\u00a0[#permalink] \u00a010 Jun 2018, 05:12\nExpert's post\n00:00\n\nQuestion Stats:\n\n77% (00:36) correct 22% (00:16) wrong based on 70 sessions\nHalf of the shirts in a closet are white and 30% of the remaining shirts are gray\n\n Quantity A Quantity B The percent of the shirts in the closet that are not white or gray 20%\n\nA)The quantity in Column A is greater.\nB)The quantity in Column B is greater.\nC)The two quantities are equal.\nD)The relationship cannot be determined from the information given.\n[Reveal] Spoiler: OA\n\n_________________\n\nSandy\nIf you found this post useful, please let me know by pressing the Kudos Button\n\nTry our free Online GRE Test\n\nManager\nJoined: 02 May 2018\nPosts: 58\nFollowers: 0\n\nKudos [?]: 30 [0], given: 22\n\nRe: Half of the shirts in a closet are white and 30% of the rema\u00a0[#permalink] \u00a016 Jun 2018, 15:35\nThe trick here is to read the question carefully. For this problem, I used 100 shirts since percents are out of 100, making it a direct conversion.\n\nHalf of the shirts in a closet are white and 30% of the remaining shirts are gray\n\nHalf of the shirts are white = 50\n30% of the remaining shirts are gray = .3 * 50 = 15\nRemainder of shirts that are $$not$$ white or gray = 35.\n\nQuantity A: The percent of the shirts in the closet that are not white or gray\nQuantity B: 20%\n\nQuantity A: 35%\nQuantity B: 20%\n\nQuantity A is greater.\n\nRetired Moderator\nJoined: 07 Jun 2014\nPosts: 4803\nGRE 1: Q167 V156\nWE: Business Development (Energy and Utilities)\nFollowers: 171\n\nKudos [?]: 2926 [0], given: 394\n\nRe: Half of the shirts in a closet are white and 30% of the rema\u00a0[#permalink] \u00a014 Jul 2018, 04:35\nExpert's post\nExplanation\n\nChoose a smart number for the total number of shirts in the closest; this is a percent problem, so 100 is a good number to pick. Out of 100 shirts, half, or 50, are white.\nYou know 30% of the remaining shirts are gray.\n\nIf there are 50 white shirts, there are also 50 remaining shirts and so (0.3)(50) = 15 gray shirts. Therefore, there are 50 + 15 = 65 total shirts that are white or gray, and 100 \u2013 65 = 35 shirts that are neither white nor gray. Since 35 out of 100 shirts are neither white nor gray, exactly 35% of the shirts are neither white nor gray.\n\nAlternatively, use algebra, though that is trickier on a problem such as this one. Set a variable, such as x, for the total number of shirts. The number of white shirts is 0.5x and the remaining shirts would equal\n\nx \u2013 0.5x = 0.5x.\n\nThe number of gray shirts, then, is (0.5x)(0.3) = 0.15x. Thus, there are\n\n0.5x + 0.15x = 0.65x white or gray shirts, and\n\nx \u2013 0.6x = 0.35x shirts that are neither white nor gray.\n\nTherefore, 0.35x \u00f7 x = 0.35, or 35%.\n_________________\n\nSandy\nIf you found this post useful, please let me know by pressing the Kudos Button\n\nTry our free Online GRE Test\n\nIntern\nJoined: 08 Apr 2020\nPosts: 41\nFollowers: 0\n\nKudos [?]: 23 [0], given: 83\n\nRe: Half of the shirts in a closet are white and 30% of the rema\u00a0[#permalink] \u00a001 May 2020, 04:24\nsandy wrote:\nHalf of the shirts in a closet are white and 30% of the remaining shirts are gray\n\n Quantity A Quantity B The percent of the shirts in the closet that are not white or gray 20%\n\nA)The quantity in Column A is greater.\nB)The quantity in Column B is greater.\nC)The two quantities are equal.\nD)The relationship cannot be determined from the information given.\n\nSo easy to use smart numbers here.\n\n100 total shirts\n50% = 50 shirts are white\n30% of 50 shirts = 15 shirts are gray\n35% or 35 shirts remaining are NOT white or gray\n\nQuantity A (35%) is greater than Quantity B.\n\nRe: Half of the shirts in a closet are white and 30% of the rema \u00a0 [#permalink] 01 May 2020, 04:24\nDisplay posts from previous: Sort by","date":"2020-09-28 10:49:00","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.4343636631965637, \"perplexity\": 3720.5052762727387}, \"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-2020-40\/segments\/1600401600771.78\/warc\/CC-MAIN-20200928104328-20200928134328-00615.warc.gz\"}"} | null | null |
Micheline Pelzer (* 11. Juli 1950 in Lüttich; † 4. Oktober 2014 in Paris) war eine belgische Jazzmusikerin (Schlagzeug, auch Gesang, Komposition).
Leben und Wirken
Micheline Pelzer, Tochter des Saxophonisten Jacques Pelzer, spielte zunächst als Autodidaktin Schlagzeug; dann erhielt sie Unterricht bei Jacques Thollot. 1968 begann sie ihre Karriere in Paris bei Barney Wilen. Im folgenden Jahr spielte sie in Rom in der Post Free Big-Band von Steve Lacy und trat auf dem Festival de Liège auf. Dort wurde Wayne Shorter auf sie aufmerksam, der sie zur Mitwirkung an seinem Album Moto Grosso Feio (1970) einlud. Während ihres Aufenthalts in New York City arbeitete sie u. a. auch mit David Liebman, Steve Grossman, Richie Beirach, Chick Corea und Woody Shaw. Nach ihrer Rückkehr nach Europa wurde sie Mitglied der Formation Moshi von Barney Wilen; ein gleichnamiges Album entstand 1971. Mit ihrem Vater, ihrem Cousin Steve Houben und dem amerikanischen Pianisten und Sänger Ron Wilson bildete sie 1973 die Band Open Sky Unit, die bis August 1994 in verschiedenen Besetzungen bestand.
Mit dem Jacques & Micheline Pelzer Quartet, zu dem Alby Cullaz und Michel Graillier gehörten, nahm sie 1975 das Album Song for René auf (auf diesem Album sang sie auch). 1977 zog sie mit ihrem Ehemann Michel Graillier nach Paris. Sie tourte in dieser Zeit mit Chet Baker, trat in Paris mit der Bigband von Jacques Hélian auf und war an den Aufnahmen zur Filmmusik von Die Bankiersfrau (1980, Regie Francis Girod) beteiligt. 1982 gründete sie mit Marie-Ange Martin und Hélène Labarrière die Formation Ladies First, mit der sie bis 1986 in Clubs und auf verschiedenen Festivals auftrat, bei Jazz à Vienne mit Dee Dee Bridgewater. Beim Festival Jazz à Liège trat sie 1991, 1992 und 1994 mit ihrem Vater auf. Ab 1993 arbeitete sie im Duo mit der Saxophonistin Nelly Pouget; sie spielte mit Michel Graillier und in der Begleitband der Sängerin Julie Monley. In den folgenden Jahren leitete sie eine eigene Formation, u. a. mit Alain Jean-Marie.
Nach Jacques Pelzers Tod 1994 wirkte sie bei der Umwandlung des Hauses ihres Vaters in einen Jazzclub mit, den Jacques Pelzer Jazz Club in Thier-à-Liège. Dort spielte sie auch mit Steve Grossman und Dave Liebman. Im Bereich des Jazz war sie zwischen 1970 und 1992 an neun Aufnahmesessions beteiligt, u. a. auch bei Jean-Christophe Renault (Valse pour Clotilde, 1982). Für Jacques Thollots Album Résurgence (1977) komponierte sie mehrere Titel.
Sie starb an den Folgen von Schilddrüsenkrebs.
Weblinks
Porträt bei Jazz in Belgium
Nachruf Jazz Hot Nr. 669
Einzelnachweise
Jazz-Schlagzeuger
Komponist (Jazz)
Musiker (Belgien)
Belgier
Geboren 1950
Gestorben 2014
Frau | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 2,997 |
var G_Counter = require("../lib/g-counter")
, jsc = require("jsverify")
, env = require("./jsverify-env")
, assert = require("assert")
, _ = require("lodash")
describe('G_Counter', function() {
it('starts out with a value of 0', function() {
var X = new G_Counter()
assert.equal(X.value(), 0, 'Initial value wasnt 0')
})
it('increases its value with 1 on increment()', function() {
var property = jsc.forall('g_counter', env, function(X) {
return X.value() + 1 == X.increment().value()
})
jsc.assert(property)
})
it('increments the same member of the payload when doing two increments', function() {
var X = new G_Counter()
, Xprime = X.increment().increment()
, payload = Xprime.toJS().e
, keys = Object.keys(payload)
assert.equal(keys.length, 1, 'Payload contained more than one key')
assert.equal(payload[keys[0]], 2, 'Value of payload wasnt incremented twice')
})
it('increases its value when merged', function() {
var property = jsc.forall('g_counter', 'g_counter', env, function(X, Y) {
return X.value() <= X.merge(Y).value()
&& Y.value() <= X.merge(Y).value()
&& X.merge(Y).value() <= X.value() + Y.value()
})
jsc.assert(property)
})
it('still equals itself after merging in an empty G_Counter', function() {
var property = jsc.forall('g_counter', env, function(X) {
return X === X.merge(new G_Counter())
})
jsc.assert(property)
})
it('still equals itself after merging in a smaller G_Counter', function() {
var property = jsc.forall('g_counter', 'g_counter', env, function(X, Y) {
if (G_Counter.compare(X, Y) /* X <= Y */) return Y === Y.merge(X)
else return Y !== Y.merge(X)
})
jsc.assert(property)
})
it('equivalent to itself', function() {
var property = jsc.forall('g_counter', env, function(X) {
return G_Counter.is(X, X)
})
jsc.assert(property)
})
it('when diverged by incrementing still has equivalence', function() {
var property = jsc.forall('g_counter', env, function(X) {
return G_Counter.is(X.increment(), X.increment())
})
jsc.assert(property)
})
it('can only be constructed from the correct json', function() {
var property = jsc.forall(jsc.suchthat('json', function(x) {
return !_.isPlainObject(x) && x.type !== 'g-counter' && !_.isPlainObject(x)
}), function(x) {
try {
var X = G_Counter.fromJS(x)
return false
} catch (e) {
return true
}
})
jsc.assert(property)
var valid = {type: 'g-counter', e: {a: 17, b: 25}}
assert.doesNotThrow(function() {
var X = G_Counter.fromJS(valid)
assert.ok(G_Counter.is(X))
assert.equal(X.value(), 42)
})
})
}) | {
"redpajama_set_name": "RedPajamaGithub"
} | 7,781 |
Announcements Maples Group Welcomes British Virgin Islands Commercial Court Appointments
Maples Group welcomes the recent appointments of both Mr. Gerhard H. A. Wallbank and Mr. Adrian Jack as High Court Judges of the Eastern Caribbean Supreme Court Commercial Division in the British Virgin Islands.
Justice Wallbank previously held a number of temporary appointments as a Justice of the BVI Commercial Court. Maples Group is pleased with his return to the territory for a long-term appointment of a period of three years with effect from 14 October 2019.
Welcoming the appointments, Dispute Resolution & Insolvency partners, Adrian Francis and Alex Hall Taylor, said:
"The workload of the BVI Commercial Court is considerable, consisting of fast-moving high quality international litigation, insolvency and restructuring cases. With these appointments, the territory is further strengthening the able bench and the reputation of the Commercial Court as an effective international tribunal. in particular, we welcome the consistency and stability brought by the return to longer-term appointments reflected in the three year appointment of Justice Wallbank."
The BVI Commercial Court can hear cases from any of the nine member jurisdictions of the Eastern Caribbean Supreme Court and specialises in cross-border and high value commercial, company, trusts, asset tracing and insolvency law matters.
The Maples Group's British Virgin Islands office provides full service dispute resolution, insolvency, restructuring and commercial advice on matters of British Virgin Islands law to financial, institutional, business and private clients both locally and internationally, as well as specialised regulatory and compliance and entity formation and management services.
Richard May
Adrian Francis
Maples Group Welcomes British Virgin Islands Commercial Court Appointments https://maples.com/en/News/Announcements/2019/05/Maples-Group-Welcomes-BVI-Commercial-Court-Appointments | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 586 |
Former Russian Oligarch Dives Into Cryptocurrencies, Bets on Institutional Investors
Tanya Chepkova
A prominent Russian banker and former Merrill Lynch derivative analyst with ties to Russian oligarchs is seeking to get exposure to the nascent blockchain and cryptocurrency industry.
Gerald Banks, previously known as Guerman Aliev — formerly a deputy chief executive officer at Russian lender Rosbank PJSC and a Managing Director of Structured Products at Merrill Lynch — is seeking to apply his expertise and get exposure to the nascent cryptocurrency trading industry with his newly-created hedge fund for cryptocurrency trading, Bloomberg reports.
Now, Banks heads Cipher Technologies Management LLP, a Connecticut-base hedge fund registered with the U.S. Securities and Exchange Commission (SEC) and the Commodity Futures Trading Commission (CFTC). The company is reportedly focused primarily on cryptocurrency options and futures contracts.
Betting on Institutional Money
Many corporate investors and money managers have been exploring new types of assets and the opportunities presented by blockchain technology and cryptocurrencies, but have refrained from direct exposure to the market. However, Banks believes that the cryptocurrency market has become mature enough to attract institutional investors — and he wants to be there when they start to pour their money into the industry.
The unclear legal landscape and the lack of regulatory guidance on crypto-related instruments and trading strategies are the main roadblocks on the way to institutional adoption. Once these barriers are out of the way, a wave of institutional money will come into the markets — according to Banks.
Global regulators need to address money laundering and market manipulation concerns — and many of them have been moving in that direction. France has recently adopted a regulatory framework for cryptocurrencies and other European countries may follow its lead. Meanwhile, US regulators understand the main issues of the industry and will soon be ready to address them, allowing institutions to legally invest in the cryptocurrency related instruments, Banks explains.
Banks declined to comment on the amount of financing the fund aim to raise. However, he mentioned that Cipher is negotiating with endowments, foundations, pension funds, and several other potential investors. Allegedly, the fund is targeting $250 million in assets under management by the end of the year.
The cryptocurrency fund will provide professional investors with access to crypto-related derivatives and structured products that will include futures and options contracts.
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\section{Introduction}
If $q$ is a positive integer, then a \emph{proper $q$-colouring} of a graph $G$ is a function from the vertices of $G$ to a set of $q$ colours, with the property that adjacent vertices receive different colours. The \emph{chromatic polynomial} $P_G(x)$ of $G$ is the unique monic polynomial which, when evaluated at $q$, gives the number of proper $q$-colourings of G. A \emph{chromatic root} of $G$ is a zero of $P_G(x)$. The chromatic polyomial has been the subject of much study; see \cite{read:introduction} for a comprehensive introduction.
This paper is a study of the chromatic polynomials of a family of simple graphs we shall call \textit{bicliques}. This family is easily described: each member is simply the complement of a bipartite graph, consisting of two cliques joined by a number of edges. When we need to be more specific, we shall refer to a biclique in which the two cliques are of size $j$ and $k$ as a \emph{$(j,k)$-biclique.} By convention, $k$ will be greater than or equal to $j$, and we shall refer to the edges between the two cliques as \textit{bridging edges.}
The present study of bicliques was originally undertaken with the aim of extending the proof of Cameron's ``$\alpha + n$ conjecture,'' which suggests that for any algebraic integer $\alpha$ there is a positive integer $n$ such that $\alpha + n$ is a chromatic root. Cameron and Morgan \cite{pjc11} proved the conjecture in the quadratic case, by showing that any quadratic integer is an integer shift of a chromatic root of a $(2,k)$-biclique, but no further progress has subsequently been made.
In section 2, we give a simple construction of the chromatic polynomial of an arbitrary biclique. We then use this construction in section 3 to examine relations between bicliques having chromatic polynomials with the same splitting field. In section 4 we justify the original motivation for studying bicliques, by applying them to prove the cubic case of the $\alpha + n$ conjecture, and finally we remark on the potential suitability of bicliques for proving the general conjecture.
\section{Chromatic polynomials of bicliques}\label{sec:poly}
A \emph{matching} of a graph is a set of edges of that graph, no two of which are incident to the same vertex. When we refer to the size of a matching, we refer to the number of edges in that matching; an \emph{$i$-matching} is a matching of size $i$. Let $m_G^i$ be the number of $i$-matchings of a graph $G$; then the \emph{matching numbers} of $G$ are the elements of the sequence $(m_G^0,m_G^1,m_G^2,\ldots)$. We will write that two graphs are \emph{matching equivalent} if they have the same matching numbers.
Now, for some positive integers $j$ and $k$, let $G$ be a $(j,k)$-biclique, and let $\bar G$ be the complement of $G$ (obtained by replacing edges of $G$ with non-edges, and vice-versa). Then $\bar G$ is a subgraph of the complete bipartite graph $K_{j,k}$. We shall construct the chromatic polynomial of $G$ by considering matchings of $\bar G$.
Given some matching of $\bar G$, partition the vertices of $G$ such that two vertices are contained in the same part if and only if the corresponding vertices of $\bar G$ are joined by an element of the matching. Then, by assigning a different colour to each part of this partition, we obtain a proper colouring of $G$. Conversely, any proper colouring of $G$ corresponds to a partition induced by some matching of $\bar G$. Thus we can compute the chromatic polynomial of $G$ by counting $x$-colourings of partitions induced by matchings of $\bar G$, as follows.
Let $(x)_k$ denote the falling factorial $x(x-1)\cdots(x-k+1)$. If each part receives a different colour, then there are $(x)_{j+k-i}$ ways of assigning $x$ colours to a partition induced by an $i$-matching of $\bar G$ (as any such partition consists of $j+k-i$ parts). Thus:
\begin{equation}\label{eqn:formula}
P_G(x)=\sum_M(x)_{j+k-|M|},
\end{equation}
where the sum is over all possible matchings $M$ of $\bar G$. Note that this construction in fact gives us the unique decomposition of $P_G(x)$ into a sum of chromatic polynomials of complete graphs (the chromatic polynomial of the $n$-vertex complete graph $K_n$ being $(x)_n$).
Now suppose that, for some $1\leq p\leq j$, there are $p$ vertices in the $j$-clique of $G$ which are adjacent to every vertex of the $k$-clique. Then these $p$ vertices are each adjacent to every other vertex of the graph. Thus, counting proper $x$-colourings of $G$, we have that there are $(x)_p$ ways in which to colour these $p$ vertices, and $x-p$ colours remaining with which to colour the remaining vertices. So the chromatic polynomial of $G$ will be of the form:
\[P_G(x)=(x)_pP_H(x-p),\]
where $H$ is the $(j-p,k)$-biclique obtained from $G$ by deleting each of the $p$ vertices and all incident edges. A similar situation arises if some vertices of the $k$-clique are adjacent to every vertex of the $j$-clique. As we are concerned with algebraic properties of the chromatic polynomial, we shall discount these cases, and assume that no vertex of $G$ is connected to every other vertex of the graph.
With this condition on $G$, it is not difficult to see that $\bar G$ will always have a single $0$-matching, along with at least one $i$-matching for all $0<i \leq j$, and that no larger matchings are possible. Hence we have:
\begin{equation*}
P_G(x)=\sum_{i=0}^jm_{\bar G}^i(x)_{j+k-i},
\end{equation*}
where $m_{\bar G}^0=1$, and in general $m_{\bar G}^i$ is a positive integer. Thus the chromatic polynomial of $G$ is a product of $(x)_k$ with a (usually irreducible) degree $j$ factor $g(x)$ of the form:
\begin{equation}\label{eqn:decomp}
g(x)=\sum_{i=0}^jm_{\bar G}^i(x-k)_{j-i}.
\end{equation}
It is this factor which will be our main object of study, and we will henceforth refer to it as the ``interesting factor'' of $P_G(x)$.
\section{Chromatic splitting field-equivalent bicliques}
We define the \emph{chromatic splitting field }of a graph $G$ to be the splitting field of the chromatic polynomial of $G$ --- that is, the smallest field extension of $\mathbb Q$ in which $P_G(x)$ factorises completely into linear factors. We can indirectly study the algebraic diversity of chromatic polynomials of bicliques by investigating how common it is for two graphs in the family to have the same chromatic splitting field. In doing so we may restrict our attention to the interesting factors of their chromatic polynomials, as multiplication by linear factors does not change a polynomial's splitting field.
Clearly, in order for two bicliques to share the same chromatic splitting field, the interesting factors of their chromatic polynomials must be of the same degree. That is, there must be positive integers $j,k_G$ and $k_H$ such that one graph is a $(j,k_G)$-biclique and the other is a $(j,k_H)$-biclique. The simplest way in which two such graphs might share the same chromatic splitting field is if the interesting factor of one chromatic polynomial is an integer shift of that of the other, and it is easy to show that this is always the case when the graphs' complements are matching equivalent.
\begin{prop}
Let $j,k_G$ and $k_H$ be positive integers with $j\leq k_G\leq k_H$, and let $G$ and $H$ be, respectively, a $(j,k_G)$-biclique and a $(j,k_H)$-biclique. Denote by $g(x)$ and $h(x)$ the degree $j$ interesting factors of $P_G(x)$ and $P_H(x)$. If $\bar G$ and $\bar H$ are matching equivalent then $g(x)=h(x+k_H-k_G)$.
\end{prop}
\begin{proof}
Suppose that $\bar G$ and $\bar H$ are matching equivalent. As $m_{\bar H}^i=m_{\bar G}^i$ for all $0\leq i\leq j$, we have from (\ref{eqn:decomp}) that
\[g(x)=\sum_{i=0}^jm_{\bar G}^i(x-k_G)_{j-i}\]
and
\[h(x)=\sum_{i=0}^jm_{\bar G}^i(x-k_H)_{j-i},\]
so clearly $g(x)=h(x+k_H-k_G)$.
\end{proof}
\qed
Now, let $g(x)$ and $h(x)$ be polynomials of equal degree, and suppose there exists some integer $c$ such that $g(x)=(-1)^jh(-x+c)$; we will describe this scenario by writing that $g(x)$ and $h(x)$ are \emph{reflections} of each other. Clearly two such polynomials have the same splitting field. It turns out to be surprisingly common for two bicliques to have chromatic polynomials with interesting factors which are reflections of each other. The following theorem gives a necessary and sufficient condition under which this occurs.
\begin{thm}\label{thm:match}
Let $j,k_G$ and $k_H$ be positive integers satisfying $j\leq k_G \leq k_H$, and let $G$ and $H$ be, respectively, a $(j,k_G)$-biclique and a $(j,k_H)$-biclique, having chromatic polynomials $P_G(x)=(x)_{k_G}g(x)$ and $P_H(x)=(x)_{k_H}h(x)$. Then $g(x)=(-1)^jh(-x+c)$ for some integer $c$ if and only if
\begin{equation}\label{eqn:general}
m_{\bar G}^i=\sum_{l=0}^i(-1)^lm_{\bar H}^l{j-l \choose j-i}(k_G+k_H+j-c-l-1)_{i-l},
\end{equation}
for all $0\leq i\leq j$.
\end{thm}
\begin{proof}
Suppose that the stated condition holds. From (\ref{eqn:decomp}), we have that:
\[g(x)=\sum_{i=0}^jm_{\bar G}^i(x-k_G)_{j-i},\]
and so substituting for $m_{\bar G}^i$ we get:
\begin{align*}
g(x)=&\sum_{i=0}^j\sum_{l=0}^i(-1)^lm_{\bar H}^l{j-l \choose j-i}(k_G+k_H+j-c-l-1)_{i-l}(x-k_G)_{j-i}\\
=&\sum_{l=0}^j(-1)^lm_{\bar H}^l\sum_{i=0}^{j-l}{j-l \choose j-i-l}(k_G+k_H+j-c-l-1)_i(x-k_G)_{j-i-l}\\
=&\sum_{l=0}^j(-1)^lm_{\bar H}^l\sum_{i=0}^{j-l}{j-l \choose i}(k_G+k_H+j-c-l-1)_i(x-k_G)_{j-i-l}\\
=&\sum_{l=0}^j(-1)^lm_{\bar H}^l(x+k_H+j-c-l-1)_{j-l}\\
=&\sum_{l=0}^j(-1)^lm_{\bar H}^l(-1)^{j-l}(-x-k_H+c)_{j-l}\\
=&(-1)^j\sum_{l=0}^jm_{\bar H}^l(-x-k_H+c)_{j-l}\\
=&(-1)^jh(-x+c).
\end{align*}
The converse is proved by simply reversing these steps.
\end{proof}
\qed
Theorem \ref{thm:match} is quite technical, and does not appear to significantly increase our intuitive understanding of which pairs of bicliques have chromatic polynomials with reflected interesting factors. However, from it we are able to deduce an interesting consequence. We will require the following lemma, which is essentially a specialisation or rephrasing of similar results by, among others, Riordan \cite{Riordan:Introduction}, Farrell and Whitehead \cite{Farrell:Connections} and Zaslavsky \cite{Zaslavsky:Complementary}. For the sake of completion, we shall include a full proof here.
\begin{lem}\label{lem:match}
Let $\bar G$ be a spanning subgraph of the complete bipartite graph $K_{j,k}$, where $j\leq k$, and let $\bar H$ be the complement of $G$ in $K_{j,k}$. Then:
\[m_{\bar G}^i=\sum_{l=0}^i(-1)^lm_{\bar H}^l{j-l \choose j-i}(k-l)_{i-l}.\]
\end{lem}
\begin{proof}
Given some $0\leq i\leq j,$ let $\mathcal{X}^i$ be the set of all $i$-matchings of $K_{j,k}$, and for each edge $e$ of $K_{j,k}$ let $\mathcal{A}_e^i\subset \mathcal{X}^i$ be the collection of those $i$-matchings containing $e$. Label the edges of $\bar H$ as $\{1,2,\ldots ,m\}$. The $i$-matchings of $\bar G$ are simply those $i$-matchings of $K_{j,k}$ not containing any edge of $\bar H$, and so the number of $i$-matchings of $\bar G$ is:
\[m_{\bar G}^i=\left|\mathcal{X}^i\setminus \bigcup_{e=1}^m\mathcal{A}_e^i\right|.\]
By the Principle of Inclusion-Exclusion, the right-hand side of this equation is precisely:
\begin{equation}\label{eqn:inc-ex}
\sum_{I\subseteq \{1,\ldots ,m\}}(-1)^{|I|}\left|\bigcap_{e\in I}\mathcal{A}_e^i\right|.
\end{equation}
Now, note that the $i$-matchings contained in $\bigcap_{e\in I}\mathcal{A}_e^i$ are precisely those $i$-matchings of $K_{j,k}$ containing every $e\in I$. Furthermore, if $I\subseteq \{1,\ldots ,m\}$ is not a matching, or else has size greater than $i$, then the number of $i$-matchings of $K_{j,k}$ containing every $e\in I$ is zero; and if $I$ is a matching of size less than or equal to $i$ then the number of $i$-matchings of $K_{j,k}$ containing every $e\in I$ depends only on the cardinality of $I$ (not on its precise edge-content). Thus (\ref{eqn:inc-ex}) is equivalent to the alternating sum, over all $0\leq l\leq i$, of the product of the number of $i$-matchings of $K_{j,k}$ containing a given $l$-matching, with the number of possible $l$-matchings of $\bar H$.
We can count the $i$-matchings of $K_{j,k}$ containing a given $l$-matching as follows: the $l$ edges of the $l$-matching join $l$ vertices on the ``$j$-side'' of $K_{j,k}$ to $l$ vertices on the ``$k$-side''. From the remaining $j-l$ vertices on the $j$-side, we have a choice of $i-l$ to be incident to the extra edges in our desired $i$-matching. For each such choice of $i-l$ vertices we then have $(k-l)_{i-l}$ ways to choose their neighbours on the $k$-side. So we have that the number of $i$-matchings of $K_{j,k}$ containing a given $l$-matching is:
\[{j-l \choose i-l}(k-l)_{i-l}={j-l \choose j-i}(k-l)_{i-l}.\]
The number of possible $l$-matchings of $\bar H$ is simply $m_{\bar H}^l$, and so putting this all together we obtain from (\ref{eqn:inc-ex}) the desired expression:
\begin{equation}\label{eqn:match}
m_{\bar G}^i=\sum_{l=0}^i(-1)^lm_{\bar H}^l{j-l \choose j-i}(k-l)_{i-l}.
\end{equation}
\end{proof}
\qed
Now, let $G$ be a $(j,k)$-biclique, and let $H$ be the graph which is obtained from $G$ by replacing all bridging edges by non-edges, and vice-versa. We will refer to $H$ as being the \emph{complementary partner} of $G$, or else to $G$ and $H$ as being \emph{complementary $(j,k)$-bicliques.} We can now prove that the members of such a pair have chromatic polynomials with reflected interesting factors.
\begin{prop}\label{prop:comp}
For some positive integers $j$ and $k$ with $j\leq k$ let $G$ and $H$ be complementary $(j,k)$-bicliques, and let $g(x)$ and $h(x)$ be the interesting factors of $P_G(x)$ and $P_H(x)$ respectively. Then:
\[g(x)=(-1)^jh(-x+j+k-1).\]
\end{prop}
\begin{proof}
Note that $\bar G$ and $\bar H$ complement each other inside the complete bipartite graph $K_{j,k}$. Hence, by Lemma \ref{lem:match}:
\[m_{\bar G}^i=\sum_{l=0}^i(-1)^lm_{\bar H}^l{j-l \choose j-i}(k-l)_{i-l}.\]
This expression is simply (\ref{eqn:general}) with $k_G=k_H=k$ and $c=j+k-1$, so the result follows from Theorem \ref{thm:match}.
\end{proof}
\qed
We have chosen to present this specific case in full as it is particularly aesthetically pleasing, however it should be noted that there are many more pairs of bicliques other than complementary pairs which have chromatic polynomials with reflected interesting factors. With the final section of this paper in mind, we will prove one of these for the case $j=3$, and mention two more.
We can parameterise a $(3,k)$-clique $G$ in the following way: label the three vertices in the $3$-clique $v_1,v_2$ and $v_3$; let $a, b$ and $c$ represent the number of neighbours of $v_1,v_2$ and $v_3$ respectively in the $k$-clique; and let $d,e$ and $f$ represent the number of vertices in the $k$-clique joined to both $v_2$ and $v_3$, both $v_1$ and $v_3$, and both $v_1$ and $v_2$ respectively. Then the 6-tuple $(a,b,c,d,e,f)$ completely describes $G$, and we will simply write that $G=(a,b,c,d,e,f)$.
It will be helpful for what follows to point out some properties of the complement of this graph. So note that the order of $\bar G$ is
\[|V(\bar G)|=a+b+c+d+e+f+3;\]
that the number of edges of $\bar G$ is
\[|E(\bar G)|=2a+2b+2c+d+e+f;\]
and that the degrees of $v_1,v_2$ and $v_3$ in $\bar G$ are $(b+c+d),$ $(a+c+e)$ and $(a+b+f)$ respectively.
\begin{prop}\label{prop:reflect1}
Let $r,s,t,u$ and $v$ be non-negative integers satisfying $u+v=4t-r-s+3$, and let $G=(r,s,t,t,t,u)$ and $H=(r,s,t,t,t,v)$ be $(3,k)$-bicliques, having chromatic polynomials with interesting factors $g(x)$ and $h(x)$ respectively. Then:
\[g(x)=-h(-x+6t+4).\]
\end{prop}
\begin{proof}
First note that the number of vertices connected only to $v_1,v_2$ and $v_3$ in $\bar G$ are $t,t$ and $u$ respectively, and the corresponding values for $\bar H$ are $t,t$ and $v$. Furthermore, in both $\bar G$ and $\bar H$ the number of vertices connected to both $v_2$ and $v_3$, both $v_1$ and $v_3$, and both $v_1$ and $v_2$ are $r,s$ and $t$ respectively.
Now, it is clear that $m_{\bar G}^0=m_{\bar H}^0=1$. The matching numbers $m_{\bar G}^1$ and $m_{\bar H}^1$ can also be easily found, as they are simply the numbers of edges of $\bar G$ and $\bar H$, that is:
\[m_{\bar G}^1=2r+2s+4t+u\]
and
\[m_{\bar H}^1=2r+2s+4t+v.\]
Now, let $B$ be the subgraph of $\bar G$ resulting from the removal of those edges incident only to $v_3$ and no other $v_i$, and let $A$ be the subgraph of $B$ obtained by removing $v_3$ and all remaining incident edges. For $l=2$ or $l=3$, we can split each $l$-matching of $\bar G$ into one of two groups: those containing one of the $u$ edges incident to $v_3$ and no other $v_i$, and those not containing such an edge. The former consists of every $l$-matching which is a union of an $(l-1)$-matching of $A$ with one of the $u$ edges in question; the latter are simply the $l$-matchings of $B$. So we have, for $l=2$ or $3$:
\begin{equation}\label{eqn:matchsplit}
m_{\bar G}^l=um_A^{l-1}+m_B^l.
\end{equation}
By enumerating the edges of $A$ we immediately find that $m_A^1=r+s+4t$. The 2-matchings of $A$ can be counted by multiplying the number of vertices adjacent to $v_1$ by the number adjacent to $v_2$, and subtracting $t$ (as there are $t$ vertices adjacent to both $v_1$ and $v_2$), giving us:
\[m_A^2=(r+2t)(s+2t)-t=rs+2rt+2st+4t^2-t.\]
It remains to find $m_B^2$ and $m_B^3$. The 2-matchings can be found by subtracting the number of pairs of edges of $B$ which are incident to a common vertex from the total number of pairs of edges of $B$. The total number of pairs of edges of $B$ is:
\[{|E(B)| \choose 2}={2r+2s+4t \choose 2}=\frac{1}{2}(2r+2s+4t)(2r+2s+4t-1),\]
and if we represent by $d(v)$ the degree of the vertex $v$, then the number of pairs which are incident to a common vertex is:
\begin{align*}
\sum_{v\in V(B)}{d(v) \choose 2}&=\frac{1}{2}\left(\sum_{v\in V(B)}d(v)^2-d(v)\right)\\
&=\frac{1}{2}\left(-2|E(B)|+\sum_{v\in V(B)}d(v)^2\right)\\
&=s^2+2st+4t^2+r^2+2rt+rs-t.
\end{align*}
Thus:\begin{align*}
m_B^2&=\frac{1}{2}(2r+2s+4t)(2r+2s+4t-1)\\
& -(s^2+2st+4t^2+r^2+2rt+rs-t)\\
&=r^2+3rs+6rt-r+s^2+6st-s+4t^2-t.
\end{align*}
To count 3-matchings, note that the total number of choices of 3 edges such that one is incident to each of the $v_i$ is
\[(s+2t)(r+2t)(r+s).\]
From this we will need to subtract:
\begin{enumerate}
\item the $t(r+s)$ 3-matchings in which the chosen edges incident to $v_1$ and $v_2$ share a common endpoint;
\item the $s(r+2t)$ 3-matchings in which the chosen edges incident to $v_1$ and $v_3$ share a common endpoint; and:
\item the $r(s+2t)$ 3-matchings in which the chosen edges incident to $v_2$ and $v_3$ share a common endpoint.
\end{enumerate}
This gives us:
\[m_B^3=(s+2t)(r+2t)(r+s)-t(r+s)-s(r+2t)-r(s+2t).\]
Finally, substituting all of these into (\ref{eqn:matchsplit}), we have:
\[m_{\bar G}^2=u(r+s+4t)+r^2+3rs+6rt-r+s^2+6st-s+4t^2-t,\]
and
\begin{align*}
m_{\bar G}^3&=u(rs+2rt+2st+4t^2-t)\\
&+(s+2t)(r+2t)(r+s)-t(r+s)-s(r+2t)-r(s+2t).
\end{align*}
The matching numbers of $\bar H$ can now be derived by simply substituting $v$ for $u$ in these expressions, giving:
\[m_{\bar H}^2=v(r+s+4t)+r^2+3rs+6rt-r+s^2+6st-s+4t^2-t,\]
and
\begin{align*}
m_{\bar H}^3&=v(rs+2rt+2st+4t^2-t)\\
&+(s+2t)(r+2t)(r+s)-t(r+s)-s(r+2t)-r(s+2t).
\end{align*}
It is now simple, if rather tedious, to verify that for each $0\leq i\leq 3$:
\[m_{\bar G}^i=\sum_{l=0}^i(-1)^lm_{\bar H}^l{3-l \choose 3-i}(4t+r+s+1-l)_{i-l}.\]
This equation is simply (\ref{eqn:general}) with the substitutions:
\begin{align*}
k_G&=r+s+3t+u\\
k_H&=r+s+3t+v\\
j&=3\\
c&=6t+4,
\end{align*}
which means that $G$ and $H$ satisfy the conditions of Theorem \ref{thm:match}, and
\[g(x)=-h(-x+6t+4).\]
\end{proof}
\qed
The proofs of the following two results proceed in exactly the same way as that of Proposition \ref{prop:reflect1}, and so we will spare the reader the details. In both cases $G$ and $H$ are $(3,k)$-bicliques having chromatic polynomials with interesting factors $g(x)$ and $h(x)$ respectively.
\begin{prop}
Let $r,s,t,u$ and $v$ be non-negative integers satisfying $u+v=4t-2r+4$. If $G=(r,r+s-1,t,t,s+t,u)$ and $H=(r,r+s-1,t,t,s+t,v),$ then:
\[g(x)=-h(-x+2s+6t+4).\]
\end{prop}
\begin{prop}
Let $r,s,t,u$ and $v$ be non-negative integers satisfying $u+v=4s-2r+t^2+2t+4.$ If $G=(r,r,s,s+{t+1 \choose 2},s+{t+2 \choose 2},u)$ and $H=(r,r,s,s+{t+1 \choose 2},s+{t+2 \choose 2},v),$ then:
\[g(x)=-h(-x+6s+2t^2+4t+6).\]
\end{prop}
This is just a sample; there are likely to be more such relations for the relatively simple case $j=3$, and no doubt many more for larger $j$. Even the few examples we have presented do however suggest patterns which invite further investigation. It would be desirable to find a more graph-theoretic classification of pairs of bicliques having chromatic polynomials which are related by a reflection than that given by Theorem \ref{thm:match}. In addition, note that the pivotal relation between the chromatic polynomials of these graphs and matchings of their complements in fact holds for any triangle-free graph (see \cite{Farrell:Connections} for a proof), raising the possibility that our results might generalise to larger classes of graphs.
We finish this section with an observation of a link between proper colourings and acyclic orientations of these special pairs of bicliques. For some positive integers $j$ and $k$ satisfying $j\leq k$ let $G$ and $H$ be $(j,k)$-bicliques having chromatic polynomials with interesting factors $g(x)$ and $h(x)$ respectively, and suppose that $g(x)=(-1)^jh(-x+c)$ for some integer $c$. Then:
\[g(x+c)=(-1)^jh(-x),\]
and so
\[P_G(x+c)=(-1)^j\frac{(x+c)_k}{(-x)_k}P_H(-x)=(-1)^{j+k}\frac{(x+c)_k}{(x+k-1)_k}P_H(-x).\]
Evaluating this equation at $x=1$ gives:
\begin{equation}\label{eqn:acyclic}
P_{G}(c+1)={c+1 \choose k}(-1)^{j+k}P_{H}(-1).
\end{equation}
Now, Stanley \cite{Stanley:Acyclic} showed that $(-1)^nP_G(-1)$ is the number of acyclic orientations of an $n$-vertex graph $G$. Thus (\ref{eqn:acyclic}) implies that the number of proper $(c+1)$-colourings of $G$ is $c+1 \choose k$ times the number of acyclic orientations of $H$. In particular, Proposition \ref{prop:comp} implies that the number of proper $(j+k)$-colourings of a $(j,k)$-biclique is $j+k \choose k$ times the number of acyclic orientations of its complementary partner. It seems likely that a combinatorial proof of this result could be found, which might shed some more light on the results we have presented in this section.
\section{Cubic integers as chromatic roots}
In \cite{pjc11} it was conjectured that for every algebraic integer $\alpha$ there is a natural number $n$ such that $\alpha +n$ is a chromatic root. The authors of that paper proved this conjecture for quadratic integers, but it has remained unresolved for algebraic numbers of higher degree. In this section we prove the conjecture for the case of cubic integers by showing that, given any cubic integer, there is a $(3,k)$-biclique having a chromatic root which is an integer shift of it.
Let $G$ be a $(3,k)$-clique. Using the same parameterisation as in the last section, we have $G=(a,b,c,d,e,f).$ We will first need to use these 6 parameters to provide an alternative construction of $P_G(x)$ from that given in \S\ref{sec:poly}.
As established previously, $P_G(x)$ is a product of $(x)_k$ with a cubic ``interesting factor'' $g(x)$. Observe that $(x)_k$ is the number of ways to properly $x$-colour the $k$-clique of $G$; thus we can view $g(x)$ as an expression for the number of proper $x$-colourings of the $3$-clique. We can construct this expression independently of the rest of the polynomial using the Principle of Inclusion-Exclusion, as follows.
Assuming there are no edges between any of the $\{v_i\}$, the number of ways to properly $x$-colour them is:
\begin{equation}\label{eqn:noedges}
(x-a-e-f)(x-b-d-f)(x-c-d-e).
\end{equation}
From these we must subtract those colourings in which two vertices receive the same colour. There are, for example:
\[(x-a-b-d-e-f)(x-c-d-e)\]
ways in which to properly $x$-colour the 3 vertices such that $v_1$ and $v_2$ receive the same colour. The other two pairs provide similar expressions, giving us three to subtract from (\ref{eqn:noedges}). Finally we consider those colourings in which all three vertices receive the same colour. The number of these is, simply:
\[(x-a-b-c-d-e-f).\]
As we have effectively discounted these three times in the previous step, we must add this expression twice. Our final interesting factor is:
\begin{eqnarray}
g(x)&=&(x-a-e-f)(x-b-d-f)(x-c-d-e)\label{cp}\\
&-&\nonumber(x-a-b-d-e-f)(x-c-d-e)\\
&-&\nonumber(x-a-c-d-e-f)(x-b-d-f)\\
&-&\nonumber(x-b-c-d-e-f)(x-a-e-f)+2(x-a-b-c-d-e-f).
\end{eqnarray}
Now, any monic cubic polynomial with negative $x^2$ coefficient can be transformed via a substitution $x\rightarrow x+n, n\in \mathbb{N}$ to another monic polynomial having $x^2$ coefficient $-1, 0$, or $1$ (we will call such a polynomial \textit{reduced}). If $\alpha$ is a root of the latter, then $\alpha +n$ is a root of the former. Thus in order to prove our result it suffices to show that, given any reduced cubic polynomial $p(x)$, there is an interesting factor $g(x)$ and natural number $n$ such that $p(x)=g(x+n)$.
We will proceed with each of the three types of reduced polynomial in turn, showing that for each type, and for every choice of the $x-$coefficient and constant term, the $6$ parameters in the $(3,k)$-biclique construction can be chosen in such a way as to produce the desired chromatic polynomial. There are no doubt many possible ways in which to correctly choose the parameters; in each case we will mention just one.
\subsubsection*{Case 1: $a_2=-1$}
Let $p(x)=x^3-x^2+a_1x+a_0$, and let $i$ represent any number. Assign the below values to the parameters $a,b,c,d,e,f$:
\begin{eqnarray*}
a&=&(2n+a_0)^2-11a_0+35+a_1-(8a_0-45)i-(16i+24)n+16i^2\\
b&=&-2i+n-3\\
c&=&(2n+a_0)^2-13a_0+46+a_1-(8a_0-53)i-(16i+28)n+16i^2\\
d&=&i+1\\
e&=&-(2n+a_0)^2+12a_0-41-a_1+(8a_0-50)i+(16i+27)n-16i^2\\
f&=&i
\end{eqnarray*}
Let $g(x)$ be the polynomial obtained by substituting these values into (\ref{cp}). Then we have
\[g(x)=x^3+(-3n-1)x^2+(3n^2+2n+a_1)x-n^3-n^2-a_1n+a_0=p(x-n),\]
as desired. It remains to show that, for any $a_0$ and $a_1,$ appropriate values for $i$ and $n$ can be found such that each of the above parameters are non-negative integers. From the expressions for $b,d$ and $f$, $i$ must be non-negative and $n$ must satisfy $n\geq2i+3$. We introduce a new variable $t$ by making the substitution
\[n=-a_0/2+2i+t,\]
giving us new expressions for $a,c$ and $e$:
\begin{eqnarray*}
a&=&a_0+35+a_1-3i-24t+4t^2\\
c&=&a_0+46+a_1-3i-28t+4t^2\\
e&=&-3a_0/2-41-a_1+4i+27t-4t^2
\end{eqnarray*}
Requiring that all these be non-negative then gives us the three inequalities:
\begin{eqnarray}
3i&\leq&a_0+35+a_1-24t+4t^2 \label{1}\\
3i&\leq&a_0+46+a_1-28t+4t^2 \label{2}\\
4i&\geq&3a_0/2+41+a_1-27t+4t^2 \label{3}
\end{eqnarray}
Let $t$ be an integer that is greater than $3$, greater than $a_0/2 +3$, and otherwise large enough to satisfy:
\[\frac{a_0+46+a_1-28t+4t^2}{3}\geq\frac{3a_0/2+41+a_1-27t+4t^2}{4}+1.\]
There is at least one integer between the expression on the left and that on the right. Choose $i$ to be such an integer; then the chosen values for $i$ and $t$ satisfy (\ref{2}) and (\ref{3}). Because $t\geq 3$, (\ref{2}) implies (\ref{1}). Finally set $n=\lceil -a_0/2\rceil +2i+t.$ Because $t> a_0/2 +3$, $n$ then satisfies the condition $n\geq2i+3$.
The remaining two cases are similar, and so will be more briefly described.
\subsubsection*{Case 2: $a_2=0$}
Let $p(x)=x^3+a_1x+a_0x$, and again let $i$ be any number. This time set:
\begin{eqnarray*}
a&=&(n+a_0)^2+a_1+14+19i+9i^2-(6i+8)n-(6i+6)a_0\\
b&=&-2i+n-3\\
c&=&(n+a_0)^2+a_1+20+25i+9i^2-(6i+10)n-(6i+8)a0\\
d&=&i+1\\
e&=&-(n+a_0)^2-a_1-18-23i-9i^2+(6i+10)n+(6i+7)a_0\\
f&=&i
\end{eqnarray*}
Let $g(x)$ be the polynomial obtained by substituting these values into (\ref{cp}). Then
\[g(x)=x^3-3nx^2-(3n^2-a_1+3n^2)x-n^3-a_1n+a_0=p(x-n).\]
Now make the substitution
\[n=-a_0+3i+t.\]
This gives us the following expressions for $a,c$ and $e$:
\begin{eqnarray*}
a&=&t^2+a_1+14-5i+2a_0-8t\\
c&=&t^2+a_1+20-5i+2a_0-10t\\
e&=&-t^2-a_1-18+7i-3a_0+10t,
\end{eqnarray*}
leading to the inequalities:
\begin{eqnarray*}
5i&\leq&t^2+a_1+14+2a_0-8t\\
5i&\leq&t^2+a_1+20+2a_0-10t\\
7i&\geq&t^2+a_1+18+3a_0+10t.
\end{eqnarray*}
Again, by choosing $t$ to be very large, a positive value for $i$ can be found to satisfy these for any $a_0,a_1$.
\subsubsection*{Case 3: $a_2=1$}
Let $p(x)=x^3+x^2+a_1x+a_0x$, and set:
\begin{eqnarray*}
a&=&a_0^2+5-a_0+a1+(3-4a_0)i-2n+4i^2\\
b&=&-2i+n-3\\
c&=&a_0^2+6-3a_0+a_1+(7-4a_0)i-2n+4i^2\\
d&=&i+1\\
e&=&-a_0^2-7+2a_0-a_1-(6-4a_0)i+3n-4i^2\\
f&=&i
\end{eqnarray*}
Substituting into (\ref{cp}) we get
\[g(x)=x^3+(1-3n)x^2+(3n^2-2n+a1)x-n^3+n^2-a1n+a0=p(x-n).\]
We now express $i$ in terms of a new parameter $t$, setting:
\[i=a_0/2-t.\]
This gives us
\begin{eqnarray*}
a&=&5+a_0/2+a_1-3t-2n+4t^2\\
c&=&6+a_0/2+a_1-7t-2n+4t^2\\
e&=&-7-a_0-a_1+6t+3n-4t^2,
\end{eqnarray*}
and so we must satisfy
\begin{eqnarray*}
2n&\leq&5+a_0/2+a_1-3t+4t^2\\
2n&\leq&6+a_0/2+a_1-7t+4t^2\\
3n&\geq&7+a_0+a_1-6t+4t^2.
\end{eqnarray*}
This time we need to choose a large negative value for $t$. If it is large enough then $d$ and $f$ will be non-negative, and we can easily find a positive $n$ to satisfy the three inequalities, as well as the requirement $n\geq 2i+3$.
Thus we have given a means to construct a biclique with a chromatic root $\alpha +n$ for any cubic integer $\alpha$, thereby proving the cubic case of the $\alpha +n$ conjecture.
Now, the quadratic case of the $\alpha +n$ conjecture was proved using a subfamily of a family of graphs known as \emph{rings of cliques}. However, it is interesting to note that members of this subfamily have precisely the same construction as $(2,k)$-bicliques, meaning that bicliques have been used to satisfy the $\alpha +n$ conjecture in both cases. Given the exponential increase in the number of these graphs as $j$ increases (constructed as above, an $(j,k)$-biclique has $2^j-2$ parameters), it seems entirely plausible that they might satisfy the general conjecture. Unfortunately the increase in parameters leads to difficulties in finding correct specialisations in the manner of the two cases proved so far, and it seems likely that a different method from that used in this paper would need to be found for algebraic numbers of higher degree.
\subsubsection*{Acknowledgements}
This paper was written while under the supervision of Peter Cameron at Queen Mary, University of London. I would like to thank Prof. Cameron for suggesting this topic, and for his helpful comments and advice. I am also indebted to a referee for pointing out the connection between the chromatic polynomial of a biclique and the matchings of its complement; his or her insight led to a significant improvement in the exposition of this paper.
\bibliographystyle{spmpsci}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,447 |
The uShip mobile app helps you track the status of your shipments with notifications. This feature allows service providers to deliver quick status updates to shipping customers from the road.
Service providers can update transit statuses from the time a shipment is booked until the time feedback is received. Shipping customers automatically receive push notifications when the statuses are updated. If you change a shipment status by mistake, Android users have a brief period of time to reverse the update. This option is available at the bottom of the screen. iOS users do not have this option.
Service providers who've enabled Location Sharing will receive notifications with prompts to either "Mark as Picked Up" or "Mark as Delivered" when the app identifies the device is within a mile's radius of the pickup and delivery locations.
When a shipment is marked as delivered and payment is released, you can leave feedback to clear the shipment from your My Shipments mobile view.
Communication is key, and our status updates make it easy to stay in touch. If you don't have notifications enabled, or you're missing a certain update, please remember to communicate throughout the shipment to keep everything on track and going smoothly. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,347 |
How Inclusive are Markets from the Micro-Entrepreneur's Perspective?
"A market is a medium that allows buyers and sellers of specific goods or service to interact in order to facilitate an exchange. " (Investopedia).
Markets exist and new markets emerge as long as there are sufficient numbers of participants to exchange goods, services or information. Both, the supply and demand sides usually expect to gain from this exchange. While the type of goods, services and information traded attract certain groups of people, it is often the income, educational, social, religious, and cultural backgrounds of people that prevents them from accessing markets. Subsequently, they are unable to pursue opportunities that would improve their lives. More inclusive markets generally accelerate economic growth.
Dan is one of millions of micro-entrepreneurs who rise very early to carry all of his stock from a local storage to his small stand he rents at a shopping centre. Come rain or sunshine. Due to repeated break-ins into a rented storage-space underneath a bridge at a railway station, he found a safer storage in the mens' toilet overnight inside the railway station. In front of the railway station, there are many women with all types of products spread out in front of them. In the evening, they carry the heavy bags filled with unsold goods on their heads and shoulders back to their homes or use mini-buses. The more sophisticated stands have tables, shelves and sun-screens, all of them are temporary structures for the day. Few of them are as "wealthy" to own cars or vans like a flower seller transporting water containers and flowers to a side-walk spot opposite a shopping centre. In cities, there is immense competition for trading spaces which sometimes end violently, either among traders or with the police driving them away from zones declared as non-trading. Friction caused by competition perceived as unfair, blockage of business entrances and other irritations, cause business-rates paying stores and shops to lobby City managers to impose and enforce stricter trading rules.
Micro-entrepreneurs' commutes into cities are long, arduous and expensive. Most use public transport which limits stock quantities they can carry with them. Paying for storage closer to where businesses are operated cuts into profits. In no other city in the developed world, have we ever observed such long queues of mini-buses and public buses in the bus-lanes on motorways slowly winding into the cities than in South Africa. Mini-bus drivers mediately head back to the townships for another load as soon as they have unloaded their passengers in the city. Many of the the mini-bus drivers ignore traffic rules and endanger lives. Horrific accidents are not rare and are part of the risks micro-entrepreneurs take.
Internet Access, affordable mobile devices and data, content: Although 2g coverage is near 100% in developing countries, internet enabling 3g is still lagging behind, particularly in rural areas. The cost either puts internet access out of reach for many or prevents users from making full use of the internet. The majority still use feature phones as their only digital device. For this and other reasons, many potentially useful business apps available for smart-phones and online use are not accessible to entrepreneurs in developing countries. The acceleration of the development of, home-grown content for mobile users also depends on internet access and affordability.
Banking: most transactions between micro-entrepreneurs and their customers are in cash. Depositing cash and bank accounts fees are far more expensive than in industrialised countries. Apart from fees, a distrust towards banks and the physical distances to the next bank or ATM, lead many to deposit money in unconventional places bearing higher risk.
Access to finance: loans to micro-entrepreneurs are costly and risky. If formal and regulated funders are available, interest rates tend to exceed those offered to established businesses by far. Many micro-entrepreneurs resort to informal lenders charging exorbitant interest rates. Alternative types of funding such as finance leases and hire purchases are mostly unavailable to micro-entrepreneurs.
Access to premises: micro-entrepreneurs need production sites, meeting rooms, office-spaces and shop-floors that are affordable, conveniently located to their customers and the right size. Large deposits and higher rents due to lack of proof of income, the demand for long-term commitments, premises oversized for their needs, and removed from their customer-base are hurdles to business-growth that many struggle to overcome. There are no straight-forward solutions: we witnessed the development of a container park on industrial land next to a shopping centre outside Cape Town. Over a hundred containers were refurbished to offer premises for every type of business and resulted in a very attractive looking mini-shopping centre about 5min walk from the formal shopping centre. A coffee-shop successfully operated by a micro-entrepreneur at a railway station closed its branch at the container park within a short space of time due to lack of footfall. Many others experienced the same fate for much of the same reason. Some of the containers are used as show- or store-rooms with owners mostly visiting outside customers. Closed stores during main-office hours are not attractive.
Trading Systems: many of the agricultural markets are dominated by few, urban-based stake-holders, and increasingly electronic trading systems are used. Small producers and traders find it hard to gain access or are disadvantaged. In South Africa, groups of immigrants have formed purchasing cooperatives enabling them to offer more competitive prices. Unable to compete with the new competition, many of the established local businesses without group-purchasing power had to shut their doors. Seeing their livelihoods destroyed by foreigners, anti-immigrant sentiment set in. Livelihood-businesses have been looted and destroyed in localised unrests.
Cost of products and services: clearly, being able to purchase larger quantities works out cheaper in many cases. Without money available to spend, consumers cannot take advantage of it. Many poor people are not able to buy "3 for the price of 2". In developing countries, the purchase of a whole bottle of shampoo is a big expense. To my dismay and disbelief, hygiene poverty is a reality even in the UK (and other high-income nations). Quantities and prices particularly for basic groceries and hygiene items can be market access barriers and can make lives really difficult. In the UK, some teachers provide soap and washing powder paid for privately to families so that their children are not ostracised in school.
Rules and regulations: it goes undisputed that many are needed for public protection, and the existence of informal markets makes enforcement more difficult. However, often the registration or permit application processes are inaccessible to micro-entrepreneurs. Expensive travelling to and long waiting queues at public offices, reliance on forms incomprehensible for the less-educated, inaccessible online application processes, unsympathetic civil servants and staff, etc. lead many to live in constant fear of prosecution as they are unable to comply. Thriving "middleman" businesses assist with applications, form completion and other errands. Not only does this add to start-up costs for a business but also puts personal data security at risk. Another area is the allocation of trading, business and production rights. Limiting fishery-rights for example has increased poaching as the supported communities are unable to survive on the income from the fishing they are permitted to do.
Corruption, bribery and crime: they are adding to the costs of starting and running a business and raise entry-barriers. Crime-hit businesses struggle to recover from the loss of stock, materials, mobile phones or a day's income.
Biases and cultural norms: it is harder for women facing gender-based biases to succeed in businesses. In many cultures, they are unable to own land, property or even a bank account. Often contracts require signatures of husbands or male guardians.
Education and skills: many parents struggle to pay for school fees, uniforms, books and equipment. Pupils lucky to receive education in often over-crowed, poorly equipped classrooms in schools without electricity and toilets do their homework on the floor in squatter homes. Lack of education and skills is perpetuated. Poorly educated youth without skills are deprived of opportunities in the labour market. Organisations addressing high youth unemployment through running entrepreneurship programmes in schools face opposition from parents who want their children to find jobs rather than running businesses. One such organisation shared that the little businesses started are safe while the kids are in school.
So the list goes on. If it makes you feel overwhelmed just reading it, realise that many a micro-entrepreneurs face many of these barriers daily! There are many local, national and international attempts to address theses issues. Barriers are specific to each of the many different types of markets. All of them have in common that they deprive people of opportunities to improve their lives and those of future generations. Therefore, it should be in the interest of all stake-holders to strive for more inclusive markets. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,108 |
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Who Is Behind the Trans Fat in Food Ban?
Author SimaPublished on June 24, 2015 November 8, 2019
Foods with trans fats. Credit: Wikipedia.
Finally the FDA is phasing out the use of artificial trans fats in foods (found in partially hydrogenated vegetable oils) within 3 years. It turns out that even though for many years scientists and the medical community pushed foods such as margarine (which have trans fats) as healthier than saturated fats such as butter, they were wrong. Instead the trans fats are linked to cardiovascular problems.
We can thank 100 year old Frank Kummerow for the ban, and for warning about trans fats for six decades! He is still drinking whole milk, eating eggs and butter, but he does avoid "fried foods, margarine, and anything associated with partially-hydrogenated oils". Other foods that are currently viewed as healthy by the medical community are extra virgin olive oil and coconut oil. However, please note that canola oil, currently viewed as a healthy and safe alternative to partially hydrogenated oils, also contains trans fats (due to the manufacturing process) and should be avoided. Also keep in mind that companies are allowed to say they have zero trans fat of they contain less than 0.5 grams per serving (which means the trans fats can add up over the course of a day). From The Washington Post:
The 100-year-old scientist who pushed the FDA to ban artificial trans fat
No one was more pleased by the Food and Drug Administration's decision Tuesday to eliminate artificial trans fats from the U.S. food supply than Fred Kummerow, a 100-year-old University of Illinois professor who has warned about the dangers of the artery-clogging substance for nearly six decades."Science won out," Kummerow, who sued the FDA in 2013 for not acting sooner, said in an interview from his home in Illinois. "It's very important that we don't have this in our diet."
In the 1950s, as a young university researcher, Kummerow convinced a local hospital to let him examine the arteries of people who had died from heart disease. He made a jarring discovery. The tissue contained high levels of artificial trans fat, a substance that had been discovered decades earlier but had become ubiquitous in processed foods throughout the country.
Later, he conducted a study showing that rats developed atherosclerosis after being fed artificial trans fats. When he removed the substance from their diets, the atherosclerosis disappeared from their arteries.
Kummerow first published his research warning about the dangers of artery-clogging trans fats in 1957. More than a decade later, while serving on a subcommittee of the American Heart Association, he detailed the massive amounts of trans fat in the shortening and margarines lining grocery shelves, and helped convince the food industry to lower the content in certain products.
Despite Kummerow's research and warnings over the years, artificial trans fats remained a staple of processed food for decades. Well into the 1980s, many scientists and public health advocates believed that partially hydrogenated oils were preferable to more natural saturated fats. And the food industry was reluctant to do away with artificial trans fats, which were cheaper than their natural counterparts, extended shelf life and gave foods desirable taste and texture.
Frustrated by the lack of action, Kummerow filed a 3,000-word citizen petition with the FDA in 2009, citing the mounting body of evidence against trans fat. The first line read: "I request to ban partially hydrogenated fat from the American diet."
In the 1990s, more and more studies had shown that trans fats were a key culprit in the rising rates of heart disease. The advocacy group Center for Science in the Public Interest also petitioned the FDA in 1994 to require that the substance be listed on nutrition labels -- a move that the agency put into place in 2006. In 2002, the Institute of Medicine found that there was "no safe level of trans fatty acids and people should eat as little of them as possible." As the dangers of trans fat became clearer, public opinion also shifted, and food companies increasingly removed the substance from products, though it remained in a broad range of foods, from cake frostings to baked goods.
Four years after filing his petition and hearing nothing, Kummerow sued the FDA and the Department of Health and Human Services in 2013, with the help of a California law firm. The suit asked a judge to compel the agency to respond to Kummerow's petition and "to ban partially hydrogenated oils unless a complete administrative review finds new evidence for their safety."
Three months later, the FDA announced its plans to effectively eliminate trans fats by saying that the substance no longer would be assumed safe for use in human foods. Tuesday's action finalizes that initial proposal, and manufacturers will have three years to reformulate products or to petition the agency for an exception.
Published on June 24, 2015 November 8, 2019 Author SimaCategories cardiovascular health, healthy aging, healthy living, nutritionTags atherosclerosis, partially hydrogenated oils, trans fats
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"redpajama_set_name": "RedPajamaCommonCrawl"
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Toufic makes a lot more money than Annard. | {
"redpajama_set_name": "RedPajamaC4"
} | 303 |
\section{Introduction}
\label{introduction}
Blockchain technology has attracted a wide range of interests as a distributed ledger technology for establishing digital trust in business. Many start-ups, enterprises, and governments \cite{ukreport,aureport} are currently exploring how to leverage blockchain technology to achieve trust and decentralization in the next generation of applications. Blockchain-based application areas are diverse, including physical or digital asset ownership management, tokens, currency, identity management, supply chain, electronic health records, voting, energy supply, and more.
Blockchain as a service (BaaS) is a promising solution to improve the productivity of blockchain application development. Easier deployment is the primary service offered by the existing BaaS platform providers, e.g. Microsoft Azure\footnote{\url{https://azure.microsoft.com/en-gb/solutions/blockchain/}\label{footnote:4}}, IBM\footnote{\url{https://www.ibm.com/blockchain/platform/}\label{footnote:5}}, and Amazon\footnote{\url{https://aws.amazon.com/blockchain/}\label{footnote:6}}. However, the existing BaaS deployment solutions are usually vendor locked, which are bound to either a cloud vendor (e.g. Microsoft Azure\textsuperscript{\ref{footnote:4}}) or a blockchain platform (e.g. IBM Hyperledger\textsuperscript{\ref{footnote:5}}).
In addition to deployment, the design and implementation of blockchain-based applications are challenging to developers. First, blockchain is a new technology with limited tooling and documentation, so there can be a steep learning curve for developers. According to a survey by Gartner~\cite{Gartner:2018:CIOSurveyBC}, ``23 percent of [relevant surveyed] CIOs said that blockchain requires the most new skills to implement any technology area, while 18 percent said that blockchain skills are the most difficult to find.'' Second, blockchain is by design an immutable data store, so updating deployed blockchain smart contracts can be hard. This makes it difficult to fix bugs by releasing new versions of smart contracts. Mistakes in smart contracts have led to massive economic loss such as the DAO exploit on the Ethereum blockchain \cite{DAO}.\par
\
A software design pattern is defined as a solution to a problem that commonly occurs within a given context during software design \cite{Beck1987}. Design patterns for blockchain-based applications are best practices from industry and can be encapsulated services to ease the burden of developers and improve the quality of blockchain-based applications. One motivating example is the on-chain and off-chain design pattern, which provides a solution for storing data of blockchain-based applications. The purpose of separately storing data on-chain and off-chain is to ensure the integrity of on-chain data and privacy of the off-chain data. This pattern can be implemented as a service to generate an on-chain data registry smart contract and an off-chain data table in the conventional database based on the data model built by the developers. For example, in a quality tracing system, the on-chain attributes could be the traceability identifier and traceability result, while the off-chain attributes could be product price, buyer name, etc.
This paper presents a unified blockchain as a service platform named uBaaS, which facilitates the design and deployment of blockchain-based applications. The contributions of this paper are as follows.
\begin{itemize}[noitemsep,topsep=0pt]
\item A set of design patterns for data management and smart contract design of blockchain-based applications to better take advantage of blockchain technology in practice. The design patterns include \emph{on-chain and off-chain}, \emph{hash integrity}, \emph{data encryption}, \emph{multiple authorities}, \emph{dynamic binding}, and \emph{embedded permission}.
\item The uBaaS platform approach:
\begin{itemize}[noitemsep,topsep=0pt]
\item \emph{Deployment as a service} which includes a blockchain deployment service and a smart contract deployment service. Deployment as a service can ease blockchain network deployment and smart contract deployment. The proposed blockchain deployment service is platform agnostic, which can avoid lock-in to specific cloud platforms.
\item \emph{Design pattern as a service} which consists of \emph{data management services} and \emph{smart contract design services}. Each service is designed based on a design pattern to better leverage the unique properties of blockchain (i.e. immutability and data integrity, transparency) and address the limitations (i.e. privacy and scalability).
\end{itemize}
\item Feasibility and scalability of the proposed solutions are evaluated using a real-world quality tracing use case. The evaluation results show that our solutions are feasible and have good scalability.
\end{itemize}
The remainder of this paper is organized as follows. Section 2 discusses the background and related work. Section 3 summarizes the design patterns for data management and smart contract design. Section 4 presents the overall architecture of uBaaS platform and design of each service provided by uBaaS. Section 5 introduces the implementation details. Section 6 evaluates the proposed solutions in terms of feasibility and scalability. Section 6 concludes the paper and outlines the future work.
\section{Related Work}
This section introduces the related work of our research. Blockchain technology and its classification are presented first, as it is the basis of this research. Further, how to apply blockchain technology to software systems is demonstrated, after which there is a brief introduction of the current obstacles to develop blockchain-based applications. Lastly design patterns and blockchain as a service are discussed.
\subsection{Blockchain Technology}
Blockchain is the technology behind Bitcoin \cite{Satoshi:bitcoin}, which is a decentralized data store that maintains all historical transactions of the Bitcoin network. The concepts of blockchain have been generalized to distributed ledger systems that verify and store transactions without coins or tokens \cite{scheuermann2015iacr}, without relying on any central trusted authority, e.g. traditional banking systems. Instead, all participants in the blockchain network can reach agreement on the states of transactional data to achieve trust.
The data structure of blockchain is an ordered list of identifiable blocks, each of which is connected to the previous block in the chain. Blocks are containers aggregating transactions while transactions are identifiable data packages that store parameters (such as monetary value) and function calls to smart contracts. A smart contract is a user-defined program that is deployed and executed on the blockchain network \cite{Omohundro:2014}, which can express triggers, conditions and business logic \cite{Weber:BPM2016} to enable more complex programmable transactions. Smart contracts can be implemented as part of transactions, and are executed across the blockchain network by all connected nodes. The blockchain platform Ethereum provides a built-in Turing-complete scripting language for writing smart contracts, called Solidity. The Ethereum Virtual Machine (EVM) is the execution environment for Ethereum, which comprises all full nodes on the network and executes bytecode compiled from Solidity scripts.
\begin{table*}[t]
\centering
\caption{Types of Blockchain ($\oplus$: Less favourable, $\oplus\oplus$: Neutral, $\oplus\hspace{-0.5ex}\oplus\hspace{-0.5ex}\oplus$: More favourable)\\}
\label{tab:blockchain}
\resizebox{\textwidth}{21mm}{
\begin{tabular}{p{0.31\columnwidth}p{0.17\columnwidth}p{0.17\columnwidth}p{0.17\columnwidth}p{0.17\columnwidth}}
\toprule
\multicolumn{1}{c}{\multirow{3}{0.31\columnwidth}{\bf \centering Type}} & \multicolumn{4}{c}{\bf \centering Impact} \\
\cmidrule(l){2-5}
& \multirow{2}{0.17\columnwidth}{\centering \bf Fundamental properties} & \multirow{2}{0.17\columnwidth}{\centering \bf Cost efficiency} & \multirow{2}{0.17\columnwidth}{\centering \bf Performance} & \multirow{2}{0.17\columnwidth}{\centering \bf Flexibility}\\ \\
\midrule
Public blockchain & \multicolumn{1}{c}{$\oplus\hspace{-0.5ex}\oplus\hspace{-0.5ex}\oplus$} & \multicolumn{1}{c}{$\oplus$} & \multicolumn{1}{c}{$\oplus$} & \multicolumn{1}{c}{$\oplus$}\\ \cmidrule(l){1-5}
Consortium blockchain & \multicolumn{1}{c}{$\oplus\oplus$} & \multicolumn{1}{c}{$\oplus\oplus$} & \multicolumn{1}{c}{$\oplus\oplus$} & \multicolumn{1}{c}{$\oplus\oplus$}\\ \cmidrule(l){1-5}
Private blockchain & \multicolumn{1}{c}{$\oplus$} & \multicolumn{1}{c}{$\oplus\hspace{-0.5ex}\oplus\hspace{-0.5ex}\oplus$} & \multicolumn{1}{c}{$\oplus\hspace{-0.5ex}\oplus\hspace{-0.5ex}\oplus$} & \multicolumn{1}{c}{$\oplus\hspace{-0.5ex}\oplus\hspace{-0.5ex}\oplus$}\\
\bottomrule
\end{tabular}}
\end{table*}
\subsection{Types of Blockchain}
As shown in Table \ref{tab:blockchain}, there are three types of blockchain in terms of deployment, including public blockchain, consortium blockchain, and private blockchain. Public blockchains, which are used by most digital currencies, can be accessed by anyone on the Internet. Using a public blockchain achieves better data transparency and auditability, but sacrifices performance and has a different cost model. A consortium blockchain is typically used across multiple organizations and has pre-authorized nodes to control the consensus process. In a private blockchain network, write permissions are often kept within one organization, although this may include multiple divisions of a single organization. The right to read the consortium or private blockchain may be public or may be restricted to a specific group of participants. When using a consortium or private blockchain, a permission management component is required to authorize participants within the blockchain network. Private blockchains are the most flexible for configuration because the network is governed and hosted by a single organization. Our work is mainly focused on consortium blockchains and private blockchains.
\subsection{Blockchain as a Component of Software Application Systems}
Researchers in academia and developers in industry are investigating and exploring how to build next generation applications using blockchain technology \cite{ukreport,aureport}. Application areas in industry include but are not limited to digital currency, international payments, registries, government identity and taxation management, Internet of Things (IoT) identify and security management, and supply chain \cite{LI2017,REYNA2018173,lu2017adaptable, XU2019399}. Furthermore, there is various academic work that exploits blockchain to address issues in different domains. Qu et al.~\cite{QU2019208} propose spatio-temporal blockchain technology that supports fast query processing, which is proved to be applicable and effective. Zyskind et al. use blockchain to build a personal data management system that ensures users own and control their data in a decentralized way\cite{decentralizePrivacy}. Bulat Nasrulin et al. proposed a mobility analytics application that is built on top of blockchain\cite{DBLP:conf/mdm/NasrulinMQ18} and renovated blockchain with distributed database\cite{MMuzammal2018}. Namecoin \cite{blockstack2016} and PKI \cite{IKP} are two public key platforms built on blockchain. ProvChain enables data Provenance for cloud-based data analytics\cite{ProveChain}.
\begin{figure}[t]
\begin{center}
\centerline{\includegraphics{blockchainapplication.pdf}}
\caption{Blockchain as a component of software application systems.}
\label{blockchainapplication}
\end{center}
\end{figure}
Software components are the fundamental building blocks for software architecture,
and blockchain can be a software component offering computational capabilities. Blockchains are complex, network-based software components, which can provide data storage, computation services, and communication services.
Fig.~\ref{blockchainapplication} illustrates the architecture of a blockchain-based application system, which consists of four horizontal layers and two vertical layers. The horizontal layers include a presentation layer, a logic layer, a data layer, and a platform layer, while the vertical layers are on-chain and off-chain.
The users interact with blockchain smart contracts and off-chain components (including the key management component) via the user interface. The blockchain-based application system can implement business logic through different off-chain components and on-chain smart contracts. Key management is an essential off-chain component in such blockchain-based system. Every participant in a blockchain network has one or more private keys, which are used to digitally sign the transactions. The security of these private keys is important: if the private key is stolen, assets held by the respective account can be accessed and protected functions of smart contracts can be invoked.
At the data layer, blockchain acts as a decentralized data ledger to store data which requires integrity and/or transparency. Off-chain conventional databases are often needed to store private or large-size data due to the scalability and privacy.
At the platform layer, the fundamental blockchain features can include permission management, incentive mechanisms, transaction validation, and cryptographically-secure payment. The oracles supply information about the external world to the blockchain, usually by adding that information to the blockchain as data in a transaction.
\subsection{Challenges of Blockchain Application Development}
Blockchain is an emerging distributed ledger technology which requires developers to learn new skills and have a deep understanding of the technology in order to build blockchain-based applications. We summarize the challenges of blockchain application development as follows.
\begin{itemize}[noitemsep,topsep=0pt]
\item Deployment. The current blockchain deployment solutions (e.g. Microsoft Azure\textsuperscript{\ref{footnote:4}}, IBM Hyperledger\textsuperscript{\ref{footnote:5}}, Amazon\textsuperscript{\ref{footnote:6}}) lock customers in to specific cloud and/or blockchain platforms. However, many enterprises or governments require building blockchain-based applications on their own on-premise private cloud, which are not met by the existing blockchain solutions. Besides, the deployment process of blockchain is error-prone, time-consuming, and requires frequent updating.
\item Scalability. Blockchain has limited storage capability since it contains a full history of all the transactions across all participants of the blockchain network. Thus, the size of blockchain continues to grow. The ever-growing size of blockchain is a challenge for storing data on blockchain. Also, storing large amounts of data or deploying large smart contracts within a transaction may be impossible due to the limited size of the blocks of the blockchain, which is under control of the network~\cite{SRDS2017}.
\item Data privacy. Blockchain-based applications might have sensitive data which should be only available to some certain blockchain participants. However, the information on blockchain is designed to be accessible to all the participants. There is no privileged user within the blockchain network, whether the blockchain is public, consortium or private.
\item Key management. Authentication on blockchain is achieved by digital signatures. However, blockchain does not offer any mechanism to recover a lost or a compromised private key. Losing a key results in permanent loss of control over an account, and potentially smart contracts that refer to it.
\item Permission control. All the smart contracts deployed on blockchain can be accessed and called by all the blockchain participants by default. A permission-less function might be triggered by unauthorized users accidentally, which becomes a vulnerability of blockchain-based application.
\end{itemize}
\subsection{Design Patterns and Blockchain as a Service}
A design pattern is a reusable solution to a problem that commonly occurs within a given context during software design \cite{gof}. There are a few works on design patterns for blockchain-based applications. J. Eberhardt and S. Tai present a group of patterns which mainly focus on on-chain and off-chain data and computation \cite{on-off-chain}. Zhang et al. applies four existing object-oriented software patterns to smart contract design in the context of a blockchain-based health care application \cite{factorypattern}. Liu et al. summarized eight smart contract design patterns and classified them into four categories\cite{liu2018applying}. Bartoletti and Pompianu conduct an empirical analysis of smart contracts, in which they collected hundreds of smart contracts and divided them into several categories: token, authorization, oracle, randomness, poll, time constraint, termination, math and fork check \cite{empiricalAnalysis}.
In recent work, some of the authors of this paper proposed an extensive pattern collection~\cite{EuroPLoP-2018}.
However, the summarized design patterns for blockchain-based applications are mostly at conceptual level, requiring users to implement the solutions.
Blockchain as a service (BaaS) provides an offering that allows developers to develop blockchain-based applications efficiently. Most of the current BaaS platforms are designed to help developers create, deploy, and manage blockchain network, e.g.
Microsoft Azure\textsuperscript{\ref{footnote:4}} , IBM\textsuperscript{\ref{footnote:5}}, and Amazon\textsuperscript{\ref{footnote:6}}.
However, the existing BaaS deployment solutions are usually locked into a specific public cloud or blockchain network provider (e.g. Microsoft Azure\textsuperscript{\ref{footnote:4}}, IBM Hyperledger\textsuperscript{\ref{footnote:5}}). Many governments or enterprises deploy their applications in private clouds and may have different blockchain network preferences. Besides, in addition to deployment services, development services are also required for BaaS platforms. Architecture design of blockchain application is a challenge to developers since they need to learn blockchain programming languages and have a deep understanding of blockchain technology.
\section{Design Patterns for Blockchain-based Applications}
In software engineering, a design pattern is a reusable solution to a problem that commonly occurs within a given context during software design \cite{Beck1987}. In this section, we summarize and categorize six design patterns which can be applied to the architecture design of a blockchain-based application system. Those patterns are divided into \emph{data management design patterns} and \emph{smart contract design patterns} according to their characteristics and effects.
\subsection{Data Management Design Patterns}
As discussed in Section 2.3, in a blockchain-based application system, blockchain can act as a decentralized data ledger and work with conventional databases to store data. Data management of blockchain-based application is challenging due to the fundamental properties (e.g. data transparency) and limitations of blockchain (e.g. blockchain scalability). Here we summarize three design patterns for data management: \emph{on-Chain and off-Chain}, \emph{hash integrity} and \emph{data encryption}.
\subsubsection{On-Chain and Off-Chain}
\vspace{0.5em}\noindent \textbf{Summary:} The on-chain and off-chain pattern separately stores data on blockchain and off blockchain to ensure the data integrity while addressing the storage capability issue of blockchain.
\vspace{0.5em}\noindent \textbf{Context:} Some applications consider leveraging blockchain to ensure data integrity since all the data on blockchain are transparent and immutable.
\vspace{0.5em}\noindent \textbf{Problem:} It may be impossible to store sensitive and large amounts of data on blockchain since all the information on blockchain is accessible to all participants and blockchain has limited storage capacity.
\vspace{0.5em}\noindent \textbf{Solution:}
Rather than placing all the data on-chain, only the sensitive and small data is stored on-chain. For example, a food quality tracing system can store traceability information that is required by the traceability regulation (e.g. traceability number and results) on-chain, while places the factory production process photos off-chain. The benefits of separately storing data on blockchain and off blockchain is to better leverage the properties of blockchain and avoid the limitations of blockchain. Blockchain can guarantee the integrity and immutability of the critical data on-chain. The non-tiny files are stored off-chain so that the size of the blockchain would not grow so fast. Storing the hashes of off-chain files can further ensure the integrity of the off-chain files.
\subsubsection{Hash Integrity}
\vspace{0.5em}\noindent \textbf{Summary:} The hash integrity pattern uses hashing to ensure the integrity of arbitrarily large datasets which may not fit directly on the blockchain.
\vspace{0.5em}\noindent \textbf{Context:} Some blockchain-based applications consider using blockchain to ensure the integrity of large amounts of data.
\vspace{0.5em}\noindent \textbf{Problem:} It may be impossible to store large amounts of data within a transaction since the blocks of blockchain has limited size (e.g., Ethereum has a block gas limit to control the data size, computational complexity and number of transactions included in a block). There is a problem about how to store arbitrary size data on blockchain to guarantee data integrity.
\vspace{0.5em}\noindent \textbf{Solution:} For data of large size (essentially data that is bigger than its hash value), rather than storing the raw data directly on blockchain, a hash value of the raw data is stored on blockchain. The hash value is produced by a hash function which maps data of arbitrary size to data of fixed size and is non-invertible. Any change to the data will lead to a change in its corresponding hash value.
\subsubsection{Data Encryption}
\vspace{0.5em}\noindent \textbf{Summary:} The data encryption pattern ensures confidentiality of the data stored on blockchain by encrypting it.
\vspace{0.5em}\noindent \textbf{Context:}
For some blockchain-based applications, commercially sensitive data should be only accessed by specific participants. An example would be a special discount price offered by a service provider to a subset of its users. Such information might not be supposed to be accessible to the other users who do not get the discount.
\vspace{0.5em}\noindent \textbf{Problem:}
The lack of data privacy is one of the main limitations of blockchain. All the information on blockchain is publicly available to the participants of the blockchain. There is no privileged user within the blockchain network, no matter the blockchain is public, consortium or private. On a public blockchain, new participants can join the blockchain network freely and access all the information recorded on blockchain. Any confidential data on public blockchain is exposed to the public.
\vspace{0.5em}\noindent \textbf{Solution:}
Asymmetric(or symmetric) encryption can be used to encrypt data before storing the data on blockchain. One of the involved participants generate a key pair and distribute the decryption key to other involved participants. The involved participants can encrypt the data before placing it on blockchain using the encryption key. Only the involved participants who have the decryption key can decrypt the data.
\subsection{Smart Contract Design Patterns}
Developers can define smart contracts (i.e. software programs on blockchain) to implement business logic and enable more complex programmable transactions. However, developing smart contracts usually require developers to have a deep understanding of blockchain and rich smart contract development experience. Thus, we summarize three design patterns as solutions to address the common problems (e.g. security) in the design of smart contracts.
\subsubsection{Multiple Authorities}
\vspace{0.5em}\noindent \textbf{Summary:}
A set of blockchain account addresses which can authorize a transaction is pre-defined. Only a subset of the pre-defined account addresses is required to authorize transactions.\par
\vspace{0.5em}\noindent \textbf{Context:}
Some activities in blockchain-based applications might need to be authorized by multiple parties (i.e. blockchain account addresses). For example, a monetary transaction may require authorization from multiple blockchain account addresses.
\vspace{0.5em}\noindent \textbf{Problem:}
The actual addresses that authorize an activity might not be able to be determined due to the availability of the authorities.
\vspace{0.5em}\noindent \textbf{Solution:}
To enable more flexible binding, an M-of-N mechanism can be used to define that M out of N private keys are required to authorize the transaction. M is the threshold of authorization.
\subsubsection{Dynamic Binding}
\vspace{0.5em}\noindent \textbf{Summary:}
The dynamic binding pattern uses a hash created off-chain to dynamically bind authority for a transaction.\par
\vspace{0.5em}\noindent \textbf{Context:}
In blockchain-based applications, some activities need to be authorized by one or more participants that are unknown when the corresponding smart contract is deployed or the transaction is submitted to blockchain.
\vspace{0.5em}\noindent \textbf{Problem:}
Blockchain does not support dynamic binding with a blockchain account address which is not defined in the transaction or smart contract. All accounts that can authorize a second transaction have to be defined in the first transaction before that transaction is added to the blockchain.
\vspace{0.5em}\noindent \textbf{Solution:}
An off-chain secret can be used to enable a dynamic binding when the participant authorizing a transaction is unknown beforehand. In the context of payment, when the sender deposits money to an escrow smart contract, a hash of a secret is submitted with the money as well. The participant who receives the secret off-chain can claim the money from the escrow smart contract by revealing the secret. Thus, the receiver of the money does not need to be defined beforehand in the escrow contract.
\subsubsection{Embedded Permission}
\vspace{0.5em}\noindent \textbf{Summary:}
Smart contracts use an embedded permission control to restrict access to the invocation of the functions defined in the smart contracts.\par
\vspace{0.5em}\noindent \textbf{Context:}
A smart contract by default has no owner, since the smart contracts running on blockchain can be accessed and called by all the blockchain participants and other smart contracts by default.
\vspace{0.5em}\noindent \textbf{Problem:}
Once the smart contract is deployed, the author of the smart contract has no special privilege to invoke on the smart contract. A permission-less function can be triggered by unauthorized users accidentally, which becomes a vulnerability of blockchain-based application. For example, a permission-less function is discovered in a smart contract library used by the Parity multi-sig wallet, caused the freezing of about 500K Ether\footnote{\url{https://paritytech.io/a-postmortem-on-the-parity-multi-sig-library-self-destruct/}}. In 2016, 7\% smart contract on public Ethereum could be terminated without authority~\cite{NewKids-2016}.
\vspace{0.5em}\noindent \textbf{Solution:}
Permission control can be added to every smart contract function to check permissions for every function caller based on the blockchain address of the caller before executing the logic of the function. Calls from unauthorized blockchain addresses are rejected.
\begin{figure}[h!]
\begin{center}
\centerline{\includegraphics[width = 1.0\textwidth]{architecture.pdf}}
\caption{Architecture of uBaaS.}
\label{architecture}
\end{center}
\end{figure}
\section{Architecture of uBaaS}
In uBaaS, we propose deployment as a service for vendor-independent deployment and design pattern as a service to address the scalability and security issues of blockchain-based applications. Fig.~\ref{architecture} illustrates the overall architecture of uBaaS. The services proposed in uBaaS are classified into three categories, \emph{deployment as a service}, \emph{design pattern as a service} and \emph{auxiliary services}. Users can build up blockchain environment and design blockchain-based applications via uBaaS front-end user interface, which interacts with the back-end services through an API gateway. The API gateway forwards API calls from the front-end user interface to the corresponding services.
The remainder of this section introduces \emph{deployment as a service}, \emph{design pattern as a service} and \emph{auxiliary services} respectively. \emph{Deployment as a Service} consists of 2 kinds of deployment services, \emph{design pattern as a service} includes 6 design pattern services to help developers take advantage of blockchain's properties and address blockchain's limitations, while \emph{auxiliary services} can act as assistance to better leverage design pattern as a service.
\subsection{Deployment as a Service}
\emph{Deployment as a service} includes \emph{blockchain deployment service} and \emph{smart contract deployment service}. Users can configure the blockchain settings (such as difficulty and participant node IP) and deploy their customized blockchain network using uBaaS. Infrastructure-as-code is applied to the blockchain deployment service which enables the automation of deployment, configuration, and task management by the developed script. Once the blockchain is set up, users can monitor the status of blockchain at real-time and deploy the developed smart contracts on the blockchain. We assume we can access the participant nodes since we focus on consortium blockchain and private blockchain. Currently, both Ethereum blockchain and Hyperledger Fabric blockchain are supported. We plan to add more blockchain platforms as deployment options in uBaaS.
The smart contract deployment service enables users to select the developed smart contract (i.e. program) file and deploy the smart contract code on the blockchain. Besides, the smart contract address and Application Binary Interface (ABI) are stored in the off-chain database for invoking the deployed smart contract.
\subsection{Design Pattern as a Service}
\emph{Design pattern as a service} consists of \emph{data management services} and \emph{smart contract design services}. \emph{Data management services} include \emph{on-chain and off-chain service}, \emph{data encryption service}, and \emph{hash integrity service}, while \emph{smart contract design services} comprises \emph{multiple authorities service}, \emph{dynamic binding service}, \emph{embedded permission service}. Each type of services is designed based on a design pattern to improve scalability, adaptability, and security of blockchain-based applications. The \emph{data management services} enable users to manage data directly via uBaaS front-end user interface while the \emph{smart contract design services} integrate smart contract design patterns into the original smart contract.
\subsubsection{Data Management Services}~\\
To address the issues of blockchain storage capability limitation and data privacy, an \emph{on-chain and off-chain service} is proposed to store the critical data which is required to be immutable on-chain while keep all the data off-chain to enhance the data reading efficiency. Users can define the data schema and determine which attributes are stored on-chain and off-chain. Based on the data model built by users, the service builds up a data registry on blockchain by deploying the generated on-chain data registry smart contract and sets up an off-chain data table in the conventional database. The on-chain data registry and off-chain data table share the same name. The user can write/read data to/from the selected data store regardless to being stored on-chain or off-chain.
To preserve the privacy of the involved participants, uBaaS provides a \emph{data encryption service} that encrypts on-chain data to ensure confidentiality of the data stored on blockchain. The uBaaS user first encrypts the data item using the private key (generated by the key generation service in auxiliary services) and then stores it on blockchain. The blockchain participants who have the public key are allowed to access the transaction and decrypt the information. By using the on-chain data encryption service, the sensitive data stored on blockchain are not accessible to blockchain participants who do not hold the public key.
To store the large size data (i.e. file) on blockchain, the \emph{hash integrity service} generates the hash value of the file and stores the hash in the on-chain file registry which is associated with the on-chain data registry using the pre-defined foreign key.
\subsubsection{Smart Contract Design Services}~\\
The \emph{smart contract design services} focus on the permission control for invocation of the smart contract functions. The input of each of those services is the smart contract code written by the user while the output is updated smart contract code by adding the template code implementing the corresponding smart contract design pattern.
The \emph{multiple authorities service} focuses on the smart contact functions that can be invoked only when the authorized blockchain addresses approve. Users can predefine a group of blockchain addresses which can authorize a transaction (i.e. calling a function in the smart contract) and set the minimal number of authorizations for transaction approval. The users need to select a smart contract they write and the function which needs the mechanism of multiple authorities. Then uBaaS modifies the code of the selected function and generate an updated smart contract with code for multiple authorities.
The \emph{dynamic binding service} uses an off-chain secret to enable a dynamic authorization when the participant approving a transaction (i.e. calling a function in the smart contract) is unknown beforehand. Users need to provide an secret (e.g. a random number) and select the corresponding function in the smart contract. The service modifies the function code by adding the hash of the secret and generate the updated smart contract. There is no need for a special protocol to exchange the secret as it can be exchanged in any ways off-chain. Only the user who has the secret can invoke the selected function in the smart contract.
The purpose of \emph{embedded permission service} is to restrict access to the invocation of the functions defined in the smart contracts. Users can identify the authorities for the selected function in the smart contract by providing the authority addresses. The service adds permission control code to the smart contract function to check permissions for every caller based on the blockchain addresses of the caller, which is done before executing the function logic.
\begin{figure}[htbp]
\begin{center}
\centerline{\includegraphics[width = \textwidth]{classDiagram.pdf}}
\caption{The main class diagram of uBaaS implementation.}
\label{classDiagram}
\end{center}
\end{figure}
\subsection{Auxiliary Services}
The current version of uBaaS supports two auxiliary services, \emph{key management service} and \emph{file comparison service}.
The \emph{key management service} is used to generate key pairs for data encryption. The developers can encrypt the data using the data encryption service and share the decryption key with other platform users (e.g. developers or application users) before store the encrypted data in the on-chain data registry. The channel for sharing the decryption key is out of the scope in this paper.
The purpose of \emph{file comparison service} is to validate the authenticity of a file (e.g. higher education certificates). Users can select the file from local node and check the authenticity of the file by comparing its hash value with the hash value of the associated original file stored in the on-chain file registry.
\begin{figure}[t]
\begin{center}
\centerline{\includegraphics[width = \textwidth]{ethereumDeployment.pdf}}
\caption{Blockchain deployment time.}
\label{eDeployment}
\end{center}
\end{figure}
\begin{figure}[t]
\begin{center}
\centerline{\includegraphics[width = \textwidth]{createTable.pdf}}
\caption{Execution time of generating an off-chain data table and an on-chain data registry smart contract.}
\label{createTable}
\end{center}
\end{figure}
\begin{figure}[t]
\begin{center}
\centerline{\includegraphics[width = \textwidth]{writingData.pdf}}
\caption{Execution time of writing data to the off-chain data table and the on-chain data registry smart contract.}
\label{writingData}
\end{center}
\end{figure}
\begin{figure}[t]
\begin{center}
\centerline{\includegraphics[width = \textwidth]{queryingData.pdf}}
\caption{Execution time of reading data from the off-chain table and the on-chain smart contract.}
\label{queryingData}
\end{center}
\end{figure}
\begin{figure}[t]
\begin{center}
\centerline{\includegraphics[width = 0.9 \textwidth]{qualitytracing.pdf}}
\caption{Quality tracing process.}
\label{qualitytracing}
\end{center}
\end{figure}
\section{Implementation}
Fig.~\ref{classDiagram} illustrates the implementation design of uBaaS using the class diagram. \emph{BlockchainRegistry} maintains each deployed \emph{Blockchain} network, while \emph{OffChainSmartContractRegistry} stores the source code and information of \emph{SmartContract}. There are three classes that inherit from \emph{SmartContract}: \emph{OnChainDataRegistry}, \emph{OnChainFileRegistry} and \emph{DesignedContract}. Each \emph{OnChainDataRegistry} is associated with an \emph{OffChainDataRegistry} for data storage. User-defined data record attributes are contained in \emph{Record}, and \emph{OnChainDataRegistry} and \emph{OffChainDataRegistry} are composed of \emph{Record}. Note that the attribute values stored in \emph{Record} must be encrypted using \emph{KeyPair} before storing in \emph{OnChainDataRegistry}. \emph{File} is stored in both \emph{OffChainFileRegistry} and its hash value is stored in \emph{OnChainFileRegistry}. \emph{DesignedContract} applies smart contract design patterns to the smart contract code written by users.
The platform is developed in Java 1.8 using Eclipse Java IDE 4.6.0 and released using Tomcat v7.0 server. To achieve blockchain deployment as a service, we used SSH to transfer the deployment files, including the client file (e.g. Geth for Ethereum) and genesis block file (e.g. genesis.json for Ethereum), to the participant nodes. To implement data management services, we selected MySQL 5.7.17 as the supported database to store off-chain data. Regarding smart contract design services, the smart contract design pattern templates are pre-developed and stored in the database. The platform users can select the smart contract design pattern that they want to apply. For both data management services and smart contract design services, the smart contracts are written in Solidity, compiled with Solidity compiler version 0.4.24. After compilation, a smart contract is deployed on blockchain via web3 API, returning smart contract address as result if the deployment succeeds.
\section{Evaluation}
In this section, we evaluate the feasibility and scalability of uBaaS. We first introduce the experiment environment. Then we evaluate the feasibility and scalability of the \emph{blockchain deployment service} and \emph{data management services} in uBaaS. Finally, we evaluate the feasibility of \emph{smart contract design services} in uBaaS using a real-world quality tracing use case.
\subsection{Experiment environment}
The uBaaS platform was deployed on an Alibaba Cloud\footnote{\url{https://www.aliyun.com/}} virtual machine (2 vCPUs, 8G RAM, 20GB disk). The adopted blockchain is Ethereum 1.5.9-stable, in which the consensus algorithm is Proof-of-Work (PoW). The selected database for off-chain data storage is MySQL 5.7.17. We set up 100 Alibaba Cloud virtual machines (1 vCPUs, 1G RAM) as the blockchain nodes (the number of nodes varies based on the experiment requirements).
\subsection{Evaluation of Blockchain Deployment Service}
We evaluated the scalability of blockchain deployment service by measuring the deployment time of blockchain with different number of nodes. We set the blockchain type as Ethereum and the difficulty as $0x4000$, and filled in the IP addresses of the nodes for deployment. According to the settings, uBaaS automatically deployed the Ethereum blockchain on the target nodes.
Fig.~\ref{eDeployment} shows the measurement results for deployment time of Ethereum blockchain using uBaaS with increased number of nodes. The deployment time increased almost linearly, showing good scalability. The experiment results also show that the blockchain deployment service in uBaaS is feasible.
\subsection{Evaluation of Data Management Services}
The main functionality provided by the data management services include: 1) generating an on-chain data registry and an off-chain data table in the conventional database based on the data model built by the developers; 2) writing/reading data to/from the on-chain data registry and off-chain data table. Therefore, we evaluated the data management services in a two-fold way: First, we measured the execution time of creating a data table off-chain in a remote conventional database and generating the corresponding data registry smart contract on-chain; Then, we tested the execution time of writing/reading data to/from the off-chain table and on-chain smart contract respectively. Note that the current version of uBaaS encrypts all the data before storing them on-chain. Thus, the time of writing data and reading data to/from on-chain data registry include data encryption and decryption.
Fig.~\ref{createTable} illustrates the execution time of creating an off-chain data table and generating the associated on-chain data registry with the increased number of data record attributes. The execution time of generating a smart contract on blockchain is much higher than creating a table in the conventional database, due to the Proof of Work (POW) mechanism in Ethereum. In addition, 96.7\% of the on-chain data registry smart contracts are generated within 50 seconds. The on-chain data registry smart contract generation time is fluctuating because block generation time varies around an average value according to the difficulty setting of Ethereum.
Fig.~\ref{writingData} demonstrates the execution time of writing data to an off-chain data table and to the associated on-chain data registry smart contract with increased number of attributes. The execution time increased linear, which shows good scalability. Compared to writing data to the off-chain data table in the conventional database, storing data to the on-chain data registry smart contract is much slower since it is time-consuming to generate a new block and include the transactions in the block. The fluctuation of writing data to the deployed smart contract is also because the block generation time is unstable as mentioned above.
Fig.~\ref{queryingData} shows the execution time of reading data from the on-chain data registry smart contract, which is much shorter than generating an on-chain data registry smart contract and writing data to the deployed smart contract, as reading is from the local node of blockchain. It is still higher than reading data from traditional database, as the data stored on-chain needs to be decrypted before being presented to the user in uBaaS.
The experiment results in Fig.5-7 also show the feasibility of the data management services in uBaaS.
\subsection{Evaluation of Smart Contract Design Services}
We evaluated the feasibility of the smart contract design services using a real world quality tracing process. Fig.~\ref{qualitytracing} illustrates the quality tracing process for import commodities in China \cite{qualitytracing}. The quality tracing agency accredited by the Chinese government provides quality tracing services and issues traceability certificates of commodity if all requirements are fulfilled. The process starts when a product supplier submits a quality tracing application to the agency. The administrator processes the application paper work (e.g. invoices) and payment. Once the application is validated, the agency assigns a factory inspector to check the factory location, production capability, quality control process, etc. After inspecting the factory, a freight yard inspector is sent to examine the products placed in the freight yard and to inspect the on-site loading process. The inspector seals the containers if the process of on-site loading complies with regulations. In the meantime, a product sample is sent to the lab for sample testing. Once the application passes the inspections and testing, the quality tracing agency issues the supplier a traceability certificate of commodity. In the quality tracing system, the quality tracing agency manages the quality tracing process and data while the lab submits testing reports through the quality tracing system. The quality inspection bureau mainly monitors the quality tracing process and does not provide any input to this system.
\lstset{
frame=single,
framesep=\fboxsep,
framerule=\fboxrule,
xleftmargin=\dimexpr\fboxsep+\fboxrule,
xrightmargin=\dimexpr\fboxsep+\fboxrule,
language=Java,
basicstyle=\scriptsize\ttfamily,
commentstyle=\color{cyan},
tabsize=2,
keywordstyle=,
breaklines=true,
captionpos=b,
escapeinside=``
}
\begin{lstlisting}[caption=Updated \emph{SampleTesting} code after using the \emph{multiple auhtorities} service.,label=MultipleAuthority]
`\textcolor{red}{contract MultipleAuthorities\{}`
`\textcolor{red}{\quad uint total; }`
`\textcolor{red}{\quad address[] authority; }`
`\textcolor{red}{\quad bool agreeing; }`
`\textcolor{red}{\quad uint agreeThreshold; }`
`\textcolor{red}{\quad mapping(address => bool) agreeState; }`
`\textcolor{red}{\quad bool agreePermission;}`
`\textcolor{red}{\quad address agreeRequester;}`
`\textcolor{red}{\quad ...}`
`\textcolor{red}{\quad function agreeSignature()\{}`
`\textcolor{red}{\qquad agreeState[msg.sender] = true; }`
`\textcolor{red}{\qquad if(agreeResult())}`
`\textcolor{red}{\qquad \quad agreePermission = true; }`
`\textcolor{red}{\quad \}}`
`\textcolor{red}{\quad function agreeResult() internal returns (bool signatureResult)\{}`
`\textcolor{red}{\qquad uint k = 0; }`
`\textcolor{red}{\qquad for(uint i = 0; i <total; i++)}`
`\textcolor{red}{\quad\qquad if(agreeState[authority[i]] == true) }`
`\textcolor{red}{\qquad\qquad k++;}`
`\textcolor{red}{\qquad if(k >= agreeThreshold) }`
`\textcolor{red}{\qquad\quad return true; }`
`\textcolor{red}{\qquad else }`
`\textcolor{red}{\qquad\quad return false; }`
`\textcolor{red}{\quad \}}`
`\textcolor{red}{\quad function initialAgree() internal\{}`
`\textcolor{red}{\qquad ...}`
`\textcolor{red}{\quad \}}`
`\textcolor{red}{\quad modifier isEnoughAgreement()\{}`
`\textcolor{red}{\qquad if(agreeing == true \&\& agreePermission == true \&\& msg.sender == agreeRequester)\{}`
`\textcolor{red}{\qquad\quad \underline{\hspace{0.5em}}; }`
`\textcolor{red}{\qquad initialAgree(); \}}`
`\textcolor{red}{\quad \}}`
`\textcolor{red}{\quad ...}`
`\textcolor{red}{\}}`
contract SampleTesting `\textcolor{red}{is MultipleAuthorities}`{
string sampleID;
bool passed;
function sampleTest(string ID){
sampleID = ID;
passed = false;
}
function pass() `\textcolor{red}{isEnoughAgreement()}`{
passed = true;
}
...
}
\end{lstlisting}
According to the design of the quality tracing system, we deployed an Ethereum blockchain on three nodes, which represent a node in the quality tracing agency, a node in the lab, and a node in the quality inspection bureau. We configured the difficulty as as $0x4000$ and provided the IP addresses of three nodes in uBaaS. Then uBaaS automatically deployed an Ethereum blockchain on the three target nodes.
\begin{lstlisting}[caption=Updated \emph{ServiceAgreement} code after using the \emph{dynamic binding} service.,label=DynamicBinding]
`\textcolor{red}{contract DynamicBinding\{ }`
`\textcolor{red}{\quad bytes32 hashKey; }`
`\textcolor{red}{\quad bool init; }`
`\textcolor{red}{\quad address owner;}`
`\textcolor{red}{\quad function initial(bytes32 key)\{}`
`\textcolor{red}{\qquad if(init != true)\{ }`
`\textcolor{red}{\qquad\quad hashKey = key; }`
`\textcolor{red}{\qquad\quad init = true;}`
`\textcolor{red}{\qquad\quad owner = msg.sender;}`
`\textcolor{red}{\qquad \}}`
`\textcolor{red}{\quad \}}`
`\textcolor{red}{\quad function changeKey(string oldKey , bytes32 newKey)\{}`
`\textcolor{red}{\qquad if(init == true) }`
`\textcolor{red}{\qquad\quad if(hashKey == sha256(oldKey))}`
`\textcolor{red}{\qquad\qquad if(owner == msg.sender) }`
`\textcolor{red}{\qquad\qquad\quad hashKey = newKey; }`
`\textcolor{red}{\quad \}}`
`\textcolor{red}{\quad modifier verify(string inputKey)\{}`
`\textcolor{red}{\qquad if(hashKey == sha256(inputKey))\{ \underline{\hspace{0.5em}}; \}}`
`\textcolor{red}{\quad \}}`
`\textcolor{red}{ \} }`
contract ServiceAgreement `\textcolor{red}{is DynamicBinding}`{
string firstParty;
string secondParty;
bytes32 contractHash;
...
function queryAgreement(`\textcolor{red}{string key}`)
`\qquad\qquad\textcolor{red}{verify(key)}` constant returns (string, string, bytes32) {
return firstParty, secondParty, contractHash;
}
...
}
\end{lstlisting}
As discussed in Section 4, uBaaS uses the smart contract design services to restrict access to the invocation of the functions in the smart contracts. Thus we selected three different functionalities (i.e. sample testing result approval, service agreement query and freight yard picture storage) to apply each of the proposed smart contract design services: \emph{multiple authorities service}, \emph{dynamic binding service}, and \emph{embedded permission service}. We wrote three smart contracts implementing the business logic in those three scenarios and select a function in each of the three smart contract to apply each smart contract design service. Thus, the output of uBaaS is the updated smart contract code with permission control for the smart contract function invocation. List 1-3 show the generated code by uBaaS. The code in black colour represents the input smart contract code (i.e. the smart contract code written by the developers), while the code highlighted in red colour is the code generated by the corresponding smart contract design services in uBaaS.
\begin{lstlisting}[caption=Updated \emph{FreightYardPic} code after using the \emph{embedded permission} service.,label=EmbeddedPermission]
`\textcolor{red}{contract EmbeddedPermission\{}`
`\textcolor{red}{\quad address [] authority;}`
`\textcolor{red}{\quad address owner;}`
`\textcolor{red}{\quad function EmbeddedPermission(address [] temAuthority)\{ }`
`\textcolor{red}{\qquad owner = msg.sender;}`
`\textcolor{red}{\qquad authority = temAuthority;}`
`\textcolor{red}{\quad \}}`
`\textcolor{red}{\quad function changeAuthority(address [] temAuthority)\{}`
`\textcolor{red}{\qquad if(msg.sender == owner)\{}`
`\textcolor{red}{\qquad\quad authority = temAuthority;}`
`\textcolor{red}{\qquad \}}`
`\textcolor{red}{\quad \}}`
`\textcolor{red}{\quad modifier permission()\{}`
`\textcolor{red}{\qquad for(uint i = 0; i < authority.length; i++)\{}`
`\textcolor{red}{\quad\qquad if(msg.sender == authority[i])\{}`
`\textcolor{red}{\qquad\qquad \underline{\hspace{0.5em}};}`
`\textcolor{red}{\qquad\qquad break;\}\}}`
`\textcolor{red}{\quad \}}`
`\textcolor{red}{ \}}`
contract FreightYardPic `\textcolor{red}{is EmbeddedPermission}`{
bytes32 [] freightYardPic;
address [] freightYardExaminer;
`\textcolor{red}{\quad function FreightYardPic() embeddedPermission(addr)\{ }`
`\textcolor{red}{\qquad address [] addr;}`
`\textcolor{red}{\qquad addr.push(/authority address/);}`
`\textcolor{red}{\quad \} }`
function setFreightYardPic(bytes32 pic, address uploader) `\textcolor{red}{permission()}` {
freightYardPic.push(pic);
freightYardExaminer.push(uploader);
}
function getFreightYardPic(uint i) constant returns (bytes32 , address){
return (freightYardPic[i], freightYardExaminer[i]);
}
}
\end{lstlisting}
The SampleTesting smart contract implements the logic in the sample testing activity. According to the process design, the product passes the sample test (i.e. the pass() function in the SampleTesting smart contract is invoked) only when enough number of labs agree that the product passes the sample test. Thus, SampleTesting smart contract code and the required lab addresses are provided as the input for uBaaS and the pass() function is selected to apply \emph{multiple authorities} design pattern using the corresponding service. MutlipleAuthorities smart contract including the modifer isEnoughAgreement() attached to pass() are added after using the uBaaS \emph{multiple authorities} service. Listing~\ref{MultipleAuthority} presents the updated smart contract code generated by the \emph{multiple authorities} service in uBaaS.
The quality tracing service agreement signed between the product supplier and the quality tracing service agency is implemented in the smart contract ServiceAgreement. In order to ensure the data privacy in the service agreement, uBaaS adds the modifier verfy() to the queryAgreement() function in ServiceAgreement using uBaaS. Only the party who can provide the secret key can successfully read the service agreement information stored on-chain. The smart contract code generated by the uBaaS \emph{dynamic binding} service is presented in Listing~\ref{DynamicBinding}. Note that the secret key can be changed on demand by invoking function changeKey().\par
The smart contract FreightYardPic maintains the pictures taken at the freight yard. According to the process design, only the freight yard inspectors can upload the hash value of the pictures taken at the freight yard. Thus, we use the \emph{EmbeddedPermission} service in uBaaS to add the access control for the function setFreightYardPic() which only allows the specific agency employee addresses to store the hash value of the freight yard pictures on blockchain. The smart contract code generated by the \emph{embedded permission} service is presented in Listing~\ref{EmbeddedPermission}.
\section{Conclusion and Future Work}
In this paper, we present a unified blockchain as a service platform named uBaaS which provides deployment as a service, design pattern as a service and auxiliary services. Deployment as a service in uBaaS is not vendor locked and provides one-click deployment service by hiding deployment script from users. Design pattern as a service leverage design patterns to facilitate data management and smart contract design of blockchain-based applications. We evaluate the feasibility and scalability of uBaaS using a real-world quality tracing use case, which demonstrates it is feasible and scalable to design and deploy blockchain-based applications using uBaaS. The future work includes adding more blockchain platforms as deployment platform options, and designing self-sovereign identity as a service in uBaaS.
\section*{References}
\label{references}
\input{reference.bbl}
\end{document}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,097 |
<?php
namespace app\controllers;
use app\models\Question;
use yii\web\Controller;
use app\models\Answer;
use yii\web\NotFoundHttpException;
use yii\filters\AccessControl;
use yii\filters\VerbFilter;
class AnswerController extends Controller
{
public function behaviors()
{
return [
'access' => [
'class' => AccessControl::className(),
'rules' => [
[
'allow' => true,
'roles' => ['@'],
],
],
],
'verbs' => [
'class' => VerbFilter::className(),
'actions' => [
'create' => ['post'],
'vote' => ['post'],
],
],
];
}
public function actions()
{
return [
'vote' => [
'class' => 'app\actions\VoteAction',
'modelClass' => 'app\models\Answer',
],
];
}
public function actionCreate($question_id)
{
$question = Question::findOne($question_id);
if (!$question) {
throw new NotFoundHttpException();
}
$answer = new Answer(['question_id' => $question_id]);
$answer->author_id = \Yii::$app->user->id;
if ($answer->load(\Yii::$app->request->post()) && $answer->save()) {
return $this->redirect(['question/answer', 'question_id' => $question_id, 'answer_id' => $answer->id]);
}
print_r($answer->errors);
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,247 |
Q: Uncaught SyntaxError: Unexpected token . AKA how to check for an Id in jQuery I need to know how to check for a CSS Id (or a class) if its enabled or disabled in jQuery. For example, let's say I have two Ids, sectionA and sectionB on some form pointing to two different sections of markup.
Now, I have a common reusable JS function that does some work based on which of the sections was referenced(activated) by the user. Think of user making entries on the some input fields of sectionA or viceversa. So I am trying to do something like this (please pardon my syntax):
function doSomething() {
if $('#sectionA').Enabled { //I know its not real syntax {
var inp = document.getElementById('sectionA');
}
else if ('#sectionB').Enabled {
var inp = document.getElementById('sectionB');
}
}
etc.
Sorry if this is too trivial a question. I know the question is hard to visualize at first but I wish I could draw it out. I certainly appreciate any helpful hints.
A: jQuery selectors us the same syntax as CSS does, so you can just use the :enabled pseudo-class selector:
if ($('#sectionA:enabled')) { ... }
But, after reading your comments, I'm not sure enabled is what you are looking for. You may want :active, which would be:
if ($('#sectionA:active')) { ... }
You could also write both of these like this:
if ($('#sectionA').is(':enabled')) { ... }
if ($('#sectionA').is(':active')) { ... }
Also, if you are going to use jQuery, why not use it here as well:
document.getElementById('sectionA')
Can just be:
$('#sectionA')
A: That's because the code you have provided has syntax errors like
. else if ('#sectionB').Enabled
Should be
. else if ($('#sectionB:enabled'))
Use brackets with if else conditions.. And Check the $ sign there, also .Enabled is nothing in jQuery, if it's a check box then use .prop('checked') or .is(':enabled')
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,727 |
\section{Introduction}
\subsection{Laplacian eigenfunctions and nodal domains}
Given a compact Riemannian surface $(M,g)$ without boundary, let $\Delta_g$ be the Laplace-Beltrami operator on $M$. There exists an orthonormal basis for $L^2(M,d\vol)$ consisting of eigenfunctions $\{f_{E_i}\}$
\begin{align}
\Delta_g f_{E_i}+ E_i f_{E_i}=0 \nonumber
\end{align}
with $0=E_1<E_2\leq...$ listed with multiplicity, and $E_i\rightarrow \infty$. The \textit{nodal set} of an eigenfunction $f_E$ is the zero set $Z(f_E):= \{x\in M: f_E(x)=0\}$ and it is the union of smooth curves outside a finite set of points \cite{C}. The connected components of $M\backslash Z(F_E)$ are called \emph{nodal domains} and we denote their number by $\mathcal{N}(f_E)$. The main object of our interest is to count the number of nodal domains of $f_E$.
The celebrated Courant Nodal Domains Theorem \cite{CH} implies that there exists an explicit constant $C>0$ such that
\begin{align}
\mathcal{N}(f_E) \leq C \cdot E. \label{Courant}
\end{align}
Stern \cite{ST} showed that, on some planar domains, there exists a sequence of eigenfunctions such that the eigenvalue grows to infinity, but $\mathcal{N}(f_E)= 2$, see also \cite{LEW} for a similar result on the two dimensional sphere. Jung and Zelditch \cite{JZ} proved that for most eigenfunctions on certain negatively curved manifolds $\mathcal{N}(\cdot)$ tends to infinity with the eigenvalue. Ingremeau \cite{I} also gave examples of eigenfunctions with $\mathcal{N}(\cdot) \rightarrow \infty$ on unbounded negatively-curved manifolds.
\subsection{The Random Wave Model}
For \textquotedblleft generic" eigenfunctions, the Random Wave Model proposed by Berry \cite{B1,B2} together with the breakthrough work of Nazarov and Sodin \cite{NS} assert that there exists a constant $c>0$ such that
\begin{align}
\mathcal{N}(f_E)= c\cdot E (1+o(1)). \label{Bourgain}
\end{align}
Remarkably, Bourgain \cite{BU} proved that there exist sequences of eigenfunction on the standard flat torus $\mathbb{T}^2=\mathbb{R}^2/\mathbb{Z}^2$ such that \eqref{Bourgain} holds. Subsequently, Buckley and Wigman \cite{BW} extended Bourgain's work to \textquotedblleft generic'' toral eigenfunctions.
We study a finer form of \eqref{Bourgain}: let $s>0$ and let $\mathcal{N}_{f_E}(s,z)$ be the number of nodal domains lying entirely inside the geodesic ball of radius $s$ around the point $z\in M$; then the Random Wave Model would also predict that
\begin{align}
\mathcal{N}_{f_E}(s,z)= c \cdot E (\pi s^2) (1+o(1))\label{Shrinking}
\end{align}
uniformly in $z$, provided that $s \cdot E^{1/2} \rightarrow \infty$, i.e. provided that the radius of the ball shrinks slightly above the \textit{Planck-scale}. We prove that \eqref{Shrinking} holds for \textquotedblleft generic \textquotedblright toral eigenfunctions with $s> E^{-1/2+ o(1)}$.
\subsection{Statement of main results}
\label{main results}
Every Laplace eigenfunction on $\mathbb{T}^2$ can be written as
\begin{align}
f(x)=f_E(x)=\sum_{ \substack{ \xi \in \mathbb{Z}^2\\|\xi|^2=E} }a_{\xi}e(\langle x,\xi \rangle) \label{function}
\end{align}
where $\{a_{\xi}\}_{\xi}$ are complex coefficients and $e(\cdot)= e(2\pi i \cdot )$ (This normalisation implies that the eigenvalue is $4\pi E$, but we will make no distinction between $E$ and $4\pi E$). The eigenvalues are integers $E\in S:=\{E \in \mathbb{N}: E= a^2+b^2 , \text{ for some} \hspace{1mm} a,b \in \mathbb{Z}\}$ and their multiplicity, which we denote by $N=N(E)$, is given by the number of lattice points on the circle of radius $\sqrt{E}$. Moreover, we assume that $\bar{a_{\xi}}=a_{-\xi}$, that is $f$ is real-valued, and that $f$ is normalised via
\begin{align}
||f||^2_{L^2(\mathbb{T}^2)}=\sum_{ |\xi|^2=E}|a_{\xi}|^2=1 \label{normalisation} .
\end{align}
Thanks to (\ref{normalisation}), we can regard the set $(a_{\xi})_{\xi}$ as points on an $N$-dimensional complex sphere. Then, L\'{e}vy concentration of measure \cite[Theorem 2.3]{LE} implies that, most $a_{\xi}$ are small, $|a_{\xi}|^2\leq (\log N)^{O(1)}/ N$ say, with probability asymptotic to $1$. Therefore, we say that $f$ is \textit{flat} if, for all $\rho>0$
\begin{align}
&\max_{|\xi|^2=E}|a_{\xi}|^2= o(N^{-1+\rho}) & \text{as} \hspace{3mm}N\rightarrow \infty. \nonumber
\end{align}
Also, via \eqref{normalisation}, we associate to $f$ the probability measure on the unit circle $\mathbb{S}^1= \mathbb{R}/\mathbb{Z}$
\begin{align}
\mu_{f}=\sum_{ |\xi|^2=E} |a_{\xi}|^2\delta_{\xi/\sqrt{E}} \label{spectral measure}
\end{align}
where $\delta_{\xi/\sqrt{E}}$ is the Dirac distribution at the point $\xi/\sqrt{E}$. Finally, we denote by $c_{NS}(\mu_{f})$ the \textit{Nazarov-Sodin} constant relative to the measure $\mu_{f}$. In order to present our main result, we differ the discussion about $c_{NS}(\cdot)$ to Section \ref{Gaussian random fields} below. Our principal result is the following:
\begin{thm}
\label{theorem 3}
There exists a density one subset \footnote{
By a density one subset we mean a set $S'\subset S$ such that $\lim\limits_{X\rightarrow \infty } \frac{\#\{E\leq X: E\in S'\}}{\#\{E\leq X: E\in S\}}=1$. } $S'\subset S$ such that for all $\epsilon>0$ we have
\begin{align}
\mathcal{N}_f(s,z)= c_{NS}(\mu_{f})\pi s^2 E(1+o_{E\rightarrow \infty}(1)) \nonumber
\end{align}
uniformly for $f$ flat, $s> E^{-1/2+ \epsilon}$ and $z\in \mathbb{T}^2$.
\end{thm}
\begin{rem}
Using the main result in \cite{SA}, Theorem \ref{theorem 3} still holds if we take $s$ such that for all $m>0$ we have $s \cdot E^{1/2}/ (\log E)^m \rightarrow \infty$. For the sake of elegance of the presentation, we decided not to include it in this manuscript.
\end{rem}
The sequence $\{\mu_{f}\}$, even in the special case $a_{\xi}=1/\sqrt{N}$ for all $\xi's$, does not have a unique limit point with respect to the weak$^{\star}$ topology on $\mathbb{S}^1$ \cite{CI,KW, SA2}. Thus, in order to obtain an asymptotic behaviour for $N(f_E)$, we have to pass to subsequences. Kurlberg and Wigman proved \cite[Theorem 1.3]{KW2} that if $\mu_{f}$ weak$^{\star}$ converges to some probability measure $\mu$ on $\mathbb{S}^1$, then $c_{NS}(\mu_{f})= c_{NS}(\mu)(1+o(1))$. This implies the following version of Theorem \ref{theorem 3}:
\begin{cor}
Under the assumptions of Theorem \ref{theorem 3}, suppose that $\mu_{f}$ weak$^{\star}$ converges to some probability measure $\mu$ on $\mathbb{S}^1$, then
\begin{align}
\mathcal{N}_f(s,z)= c_{NS}(\mu)\pi s^2 E(1+o(1)). \nonumber
\end{align}
uniformly for $f$ flat, $s> E^{-1/2+ \epsilon}$ and $z\in \mathbb{T}^2$.
\end{cor}
\subsection{Nodal length in shrinking balls}
One of the novel aspects in the proof of Theorem \ref{theorem 3} is the study of the \textit{nodal length}, that is the Hausdorff measure of the nodal set, of toral eigenfunctions in shrinking balls. The main (open) question about the nodal length of Laplace eigenfunctions is the following conjecture of Yau: let $f_E$ be a Laplace eigenfunction with eigenvalue $E$ on a smooth, compact manifold without boundaries $M$, then
\begin{align}
\sqrt{E}\ll_M \mathcal{L}(f_E)= \mathcal{H}^{n-1}\{x\in M: f(x)=0\}\ll_M \sqrt{E} \nonumber
\end{align}
Donnelly and Fefferman \cite{DF} showed that Yau's conjecture holds for real-analytic manifolds. Recently, Logunov and Malinnikova \cite{LM,L1,L2} proved the lower-bound in the smooth case and gave a polynomial upper-bound.
As for the nodal domains count, the Random Waves Model suggests that, for \textquotedblleft generic" Laplace eigenfunctions, a rescaled version of Yau's conjecture should hold at small scales, that is for any $z\in M$
\begin{align}
s\sqrt{E}\ll_M s^{-1}\mathcal{L}_f(s,z):= s^{-1}\mathcal{H}^{n-1}\{x\in B(s,z): f(x)=0\}\ll_M s\sqrt{E}. \nonumber
\end{align}
provided that $s$ shrinks slightly above Plank-scale. We prove the following:
\begin{prop}
\label{claim}
Let $f$ be as in \eqref{function} and let $\epsilon>0$, then
\begin{align}
s\sqrt{E}\ll \mathcal{L}_f(s,z)s^{-1}\ll s\sqrt{E} \nonumber
\end{align}
uniformly for $s> E^{-1/2+\epsilon}$ and $z\in \mathbb{T}^2$.
\end{prop}
One particular aspect of Proposition \ref{claim} is that it holds for \textit{every} toral eigenfunction. This might fail on other surfaces: on the $2$-sphere $\mathbb{S}^2= \{x\in \mathbb{R}^3: ||x||^2=1\}$ one can consider the \textquotedblleft sectoral" harmonic $g(\theta,\phi)=\sin (m\phi) P^m_m(\cos(\theta))$ in spherical-coordinates, where $P^m_m(\cdot)$ is the associated Legendre polynomial. Then $\Delta g= -m(m+1) g$ and the upper-bound in Proposition \ref{claim} fails around the North Pole.
\vspace{2mm}
\paragraph{\textit{Application to Laplace eigenfunctions on the square}} The proof of Proposition \ref{claim} is general enough that it can also address Laplace eigenfunctions on the square $[0,1]^2$ with either Dirichlet or Neumann boundary conditions. The study of the nodal length of \textit{random} Laplace eigenfunctions on the square, known as \textit{boundary adapted Arithmetic Random Waves}, was initiated by Cammarota, Klurman and Wigman \cite{CKW}. A major step in their work is to bound the expectation of the nodal length in squares of side $O(1)/\sqrt{E}$, where $E$ is the eigenvalue. We prove the following:
\begin{prop}
\label{claim2}
Let $\tilde{f}$ be a Laplace eigenfunction on the square $[0,1]^2$ with either Dirichlet or Neumann boundary conditions and let $E$ be its eigenvalue. Then we have
\begin{align}
\mathcal{L}_{\tilde{f}}(s,z)s^{-1}\ll s\sqrt{E} + N \nonumber
\end{align}
uniformly for $s>0$ and $z\in \mathbb{T}^2$, where $N=N(E)$ is as in Section \ref{main results}.
\end{prop}
From Proposition \ref{claim2}, it follows that for any fixed $C>0$ we have
\begin{align}
\mathcal{H}^1\{x\in B(C/\sqrt{E},z): \tilde{f}(x)=0 \}\ll \frac{N}{\sqrt{E}}. \label{1.1}
\end{align}
For \textit{random} Laplace eigenfunctions on the square, Cammarota, Klurman and Wigman \cite[Proposition 2.5]{CKW} showed that the bound $\mathcal{H}^1\{x\in B(C/\sqrt{E},z): \tilde{f}(x)=0 \}\ll N^2/\sqrt{E}$ holds with high probability. So \eqref{1.1} not only refines \cite[Proposition 2.5]{CKW} but it also provides a deterministic results which does not rely on moments estimates.
\subsection{Bourgain's de-randomisation in shrinking sets}
Another novel aspect in the proof of Theorem \ref{theorem 3} is an extension of Bourgain's de-randomisation technique to shrinking sets. Let $f$ be as in \eqref{function} and suppose that $a_{\xi}=1$ for all $\xi's$, moreover let $F_x(y)= f(x+y/\sqrt{E})$ for $y\in [-1/2,1/2]^2$. Bourgain \cite{BU} showed that the assemble $\{F_x\}$, where $x$ is drawn uniformly at random from $\mathbb{T}^2$, approximates the Gaussian field with spectral measure the Lebesgue measure on $\mathbb{S}^1$ (see Section \ref{Gaussian random fields} below for some background on Gaussian fields). We use some new informations about sum of lattice points called \textit{quasi-spectral correlations} to show that this approximations still holds even when $x$ is drawn uniformly at random from $B(s,z)$ for $s>E^{-1/2+o(1)}$ and $z\in \mathbb{T}^2$, Proposition \ref{main prop} below.
Since the proof of Proposition \ref{main prop} is quite technical, to give the reader an idea of how such properties of lattice points are exploited, we show here that $F_x(0)=f(x)$ approximates a standard Gaussian random variable when $x$ is drawn uniformly at random from $B(s,z)$. Via the method of moments, we have to evaluate for $l \in \mathbb{N}$
\begin{align}
\frac{1}{\pi s^2} \int_{B(s,z)} |F_x(0)|^{2l} dx&=\frac{1}{\pi s^2} \sum_{\xi_1,...,\xi_{2l}} \int_{B(s,z)}e(\langle x, \xi_1-\xi_2+...+\xi_{2l-1}-\xi_{2l}\rangle) dx .\nonumber
\end{align}
Separating the terms with $\xi_1 +...-\xi_{2l}=0$, known as\textquotedblleft$2l$-spectral correlations", from the other terms, \textquotedblleft $2l$ spectral quasi-correlations" , we obtain
\begin{align}
\frac{1}{\pi s^2} \int_{B(s,z)} |f(x)|^{2l} dx= \sum_{\xi_1- \xi_2+...-\xi_{2l}=0}1
+O\left( \sum_{|\xi_1- \xi_2+...-\xi_{2l}|>0} \frac{J_1(s|\xi_1- \xi_2+...-\xi_{2l}|)}{s|\xi_1- \xi_2+...-\xi_{2l}|} \right) \label{intro3}
\end{align}
where $J_1(\cdot)$ is the Bessel function of the first kind.
The main contribution to the first term in \eqref{intro3} comes from the diagonal solutions $\xi_1=\xi_2$,..., $\xi_{2l-1}=\xi_{2l}$ and their permutations, these contribute $2l!/(2^l\cdot l!)$. Bombieri and Bourgain \cite{BB} showed that, for \textit{generic} $E\in S$, the \textquotedblleft off-diagonal" solutions have lower order as $N\rightarrow \infty$. Thus, the first term on the right hand side of \eqref{intro3} is asymptotic to $2l!/(2^l\cdot l!)$. We are left to show that the second term on the right hand side of \eqref{intro3} tends to $0$ as $N\rightarrow \infty$. Theorem \ref{semi} below implies that for \textit{generic} $E\in S$, $s|\xi_1- \xi_2+...-\xi_{2l}|\geq E^{o(1)}$. Since Bessel functions decay at infinity, this implies that the second term in \eqref{intro3} tends to $0$, as required.
\subsection{Related results}The main body of results regarding statistics of Laplace eigenfunctions in shrinking sets concern their mass distribution. Let $f_E$ be a Laplace eigenfunction on a surface $M$, then one is interested in finding the smallest $s$ such that $\int_{B(s,z)} |f|^2 d\vol= \pi s^2(1+o_{E\rightarrow \infty}(1))$. The celebrated Quantum Ergodicity Theorem \cite{DV,S,Z} asserts that, if the geodesic flow on M is ergodic, then one can take any \textit{fixed} $s>0$ for a density one subsequence of eigenfunctions. Luo and Sarnak \cite{LS} showed that, on the modular surface, one can take $s>E^{-\alpha}$ for some $\alpha>0$ for a density one subsequence, see also \cite{Y}. Hezari, Rivi\`{e}re \cite{HR} and independently Han \cite{H} proved that, if $M$ has negative sectional curvature, then one can take $s> \log(E)^{-\alpha}$ for some small $\alpha>0$ for a density one subsequence. On $\mathbb{T}^2$ Lester and Rudnick \cite{LR} showed that $s> E^{-1/2+ o(1)}$, again for a density one subsequence.
Granville and Wigman \cite{GW} and subsequently Wigman and Yesha \cite{WY} studied the mass distribution of eigenfunctions on $\mathbb{T}^2$ \emph{at Planck scale} by drawing the centre of the ball randomly uniformly. They showed that, for certain eigenfunctions the mass equidistributes in almost every ball, see also \cite{HU,HU1} for similar work on the modular surface. The author \cite{SA1} classified all limiting mass-distributions \emph{at Planck scale} for \textquotedblleft generic" toral eigenfunctions.
Results regarding the zero set are more modest: Benatar, Marinucci and Wigman \cite{BMW} studied the behaviour of nodal length for \emph{random} toral eigenfunctions at scales $s=E^{-1/2+o(1)}$ and found the asymptotic law of the variance.
To the best of the author's knowledge, our own Theorem \ref{theorem 3} is the only asymptotic result on nodal domains at small scales.
\subsection{Notation}
Let $t \rightarrow \infty$ be some parameter, we say that the quantity $X=X(t)$ and $Y=Y(t)$ satisfy $X\ll Y$ , $X\gg Y$ if there exists some constant $C$, independent of $t$, such that $X\leq C Y$ and $X\geq CY$ respectively. We also write $O(X)$ for some quantity bounded in absolute value by a constant times $X$ and $X=o(Y)$ if $X/Y\rightarrow 0$ as $t\rightarrow \infty$, in particular we denote by $o(1)$ any function that tends to $0$ (arbitrarily slowly) as $x\rightarrow \infty$. We denote by $B(s,z)$ the (open) ball of radius $s$ with centre $z$, by $B(s)$ for the ball centred at $0$ and by $\overline{B}(s)$ the closure of $B(s)$. When the specific radius is unimportant, we simply write the ball as $B$ and $\frac{1}{2}B$ for the concentric ball with half the radius. Finally, we denote by $\Omega$ an abstract probability space where every random object is defined.
\section{Preliminaries}
\subsection{Number theoretic background}
\label{NTpre}
Recall that $S=\{n\in \mathbb{N}: n= a^2+b^2 , \text{ for some} \hspace{1mm} \\ a,b \in \mathbb{Z}\}$. In this section we collect some number theoretic results that will be used to define the set $S'\subset S$ in Theorem \ref{theorem 3}. Let $E\in S$ and write its prime factorisation as $E= \prod_{p\equiv 1 \pmod 4}p ^{\alpha_p}\prod_{q\equiv 3 \pmod 4} q^{2\beta_q}$ where $\alpha_p,\beta_q\in \mathbb{N}$. It follows that $N(E)=4 \prod_{p\equiv 1 \pmod 4}(\alpha_p+1)$. Thus, by the divisor bound, we have
\begin{align}
N(E) \ll \exp \left( \frac{\log E}{\log\log E}\right). \label{divisor bound}
\end{align}
Moreover, by the Erd\"{o}s-Kac Theorem \cite[Theorem 12.3]{E}, for almost all integers (representable as sum of two squares) the number $\#\{ p|E: p\equiv 1 \pmod 4\}\rightarrow \infty$ as $E\rightarrow \infty$. So we also have the following lemma:
\begin{lem}
\label{N infinity}
For a density one subset of $E\in S$, $N(E) \rightarrow \infty$ as $E\rightarrow \infty$.
\end{lem}
To state the next results we need some notation: let $l\in \mathbb{N}$ and $E\in S$, denote by $\mathcal{S}(l,E)$ the number of solutions to
\begin{align}
\xi_1+...+ \xi_l=0 \label{14}
\end{align}
where $\xi_j\in \mathbb{Z}^2$ and $|\xi_j|^2=E$, that is \textit{$l$-spectral correlations}. When $l$ is odd, by congruence obstruction modulo $2$, there are no solutions to \eqref{14}. When $l$ is even, we have the following \cite[Theorem 17]{BB} and \cite[Lemma 4]{BU}:
\begin{thm}[Bombieri-Bourgain]
\label{BB}
Let $B=B(E)$ be an arbitrarily slow growing function of $E$, $l\in \mathbb{N}$ and $0<\gamma<1$. Then, for a density one subset of integers $E\in S$, we have
\begin{align}
\mathcal{S}(2l,E)= \frac{(2l)!}{2^l \cdot l!}N^{l} +O(N^{\gamma l}) \nonumber
\end{align}
uniformly for all $l\leq B$, where the constant implied in the notation is absolute.
\end{thm}
Moreover, provided that is not zero, one can give a quantitative lower bound to the sum in \eqref{14}, see \cite[Theorem 1.4]{BMW} and the refinement \cite[Theorem 1.1]{SA}:
\begin{thm}
\label{semi}
Let $B=B(E)$ be an arbitrarily slow growing function of $E$, $l\in \mathbb{N}$ and $Q=Q(E)$ be a function such that $Q \cdot E^{1/2}/(\log E)^m\rightarrow \infty$ for all $m\geq 0$. Then, for a density one subset of integers $E\in S$, we have
\begin{align}
||\xi_1+...+\xi_l||>Q\nonumber
\end{align}
uniformly for all choices of $\xi_1,...,\xi_l$ and $l\leq B$.
\end{thm}
\textbf{The set $S'$}. We are now ready to define the subset in Theorem \ref{theorem 3}: let $S'$ be the set of $E\in S$ which satisfy the conclusion of Lemma \ref{N infinity}, Theorem \ref{BB} and Theorem \ref{semi}. By the discussion in this section, $S'$ has density one.
\subsection{Gaussian fields background}
\label{Gaussian random fields}
We briefly collect some definitions about Gaussian fields (on $\mathbb{R}^2$). A (real-valued) Gaussian field $F$ is a measurable map $F: \mathbb{R}^2 \times \Omega\rightarrow \mathbb{R}$ for some probability space $\Omega$, such that all finite dimensional distributions $(F(x_1, \cdot),...F(x_n,\cdot))$ are multivariate Gaussian. $F$ is \textit{centred} if $\mathbb{E}[F]=0$ and \textit{stationary} if its law is invariant under translations $x\rightarrow x+\tau$ for $\tau \in \mathbb{R}^2$. The \textit{covariance} function of $F$ is
\begin{align}
\mathbb{E}[F(x)\cdot F(y)]= \mathbb{E}[F(x-y)\cdot F(0)]. \nonumber
\end{align}
Since the covariance is positive definite, by Bochner's theorem, it is the Fourier transform of some measure $\mu$ on the $\mathbb{R}^2$. So we have
\begin{align}
\mathbb{E}[F(x)F(y)]= \int_{\mathbb{R}^2} e\left(\langle x-y, \lambda \rangle\right)d\mu(\lambda). \nonumber
\end{align}
The measure $\mu$ is called the \textit{spectral measure} of $F$ and, since $F$ is real-valued, satisfies $\mu(-I)=\mu(I)$ for any (measurable) subset $I\subset \mathbb{R}^2$. By Kolmogorov theorem, $\mu$ fully determines $F$, so we may simply write $F=F_{\mu}$.
\subsection{Nazarov-Sodin constant}
Nazarov and Sodin \cite{NS} found the asymptotic law of the expected number of nodal domains of a stationary Gaussian field in growing balls around the origin, provided its spectral measure satisfies certain (simple) properties. We state here a simplified and slightly adapted form of their Theorem, see \cite[Proposition 1.1]{KW2}:
\begin{thm}
\label{Nazarov-Sodin}
Let $\mu$ be a probability measure on $\mathbb{S}^1$, invariant by rotation by $\pi$ and let $\mathcal{N}(F_\mu,R)$ be the number of nodal domains of $F_{\mu}$ in a ball of radius $R>0$ centred ad the origin. Then, there exists some constant $c_{NS}(\mu)$ such that
\begin{align}
\mathbb{E}[ \mathcal{N}(F_{\mu},R) ]= c_{NS}(\mu)R^2 + O\left(R \right). \nonumber
\end{align}
Moreover $c_{NS}(\mu)>0$ if $\mu$ does not have any atoms.
\end{thm}
We will need the following version of Theorem \ref{Nazarov-Sodin}, see \cite[Proposition 3.4 and Proposition 3.5]{BW}.
\begin{prop}
\label{stability}
Let $R>1$ and $\mu_{f}$ be as in \eqref{spectral measure}. Then, for any function $\psi$ with $||\psi||_{\mathcal{C}^1}$ sufficiently small in terms of $R$, we have
\begin{align}
\mathbb{E}[\mathcal{N}( F_{\mu_{f}} +\psi,R)]= c_{NS}(\mu_{f})R^2 (1+o(1)) \hspace{8mm} \text{as} \hspace{2mm} R\rightarrow \infty.\nonumber
\end{align}
\end{prop}
We conclude this section mentioning another result concerning the positivity of $c_{NS}(\mu_{f})$. Suppose that $\mu_{f}$ is invariant under $\pi/2$ rotations and reflection on the $X$-axis (i.e. $(x_1,x_2)\rightarrow (x_1,-x_2)$). Among these measures, Kurlberg and Wigman \cite[Theorem 1.5]{KW2} showed that there are only two with vanishing Nazarov-Sodin constant:
\begin{align}
&\nu= \sum_{k=1}^4 \delta_{e^{i\pi k/2}} &\tilde{\nu}= \sum_{k=1}^4 \delta_{e^{i(\pi k/2+\pi/4)}} \nonumber.
\end{align}
\section{Nodal length of toral eigenfunctions in shrinking sets}
\label{semi-loc}
The aim of this section is to prove the Proposition \ref{claim} and Proposition \ref{claim2}. First we show the following consequence of Proposition \ref{claim}:
\begin{prop}
\label{semi-locality}
Let $R>1$, $\epsilon>0$ and let $f$ be as in \eqref{function}. Then, uniformly for $s>E^{-1/2+\epsilon}$ and $z\in \mathbb{T}^2$, we have
\begin{align}
\mathcal{N}_f(s,z)= \frac{E}{R^2}\int_{B(s,z)} \mathcal{N}_f\left(\frac{R}{\sqrt{E}},x\right)dx + O\left(\frac{Es^2}{\sqrt{R}}\right). \nonumber
\end{align}
\end{prop}
\begin{proof}[Proof of Proposition \ref{semi-locality} assuming Proposition \ref{claim}]
Let $L>1$ be some parameter to be chosen later. By Proposition \ref{claim} the nodal length of $f$ in $B(s,z)$ is, up to rescaling, at most $\sqrt{E}s$. It follows that there are at most $Es^2/L$ nodal domains of diameter bigger than $L/Es^2$. Therefore, if we divide $B(s,z)$ into balls of radius $R/\sqrt{E}$, any nodal domain of diameter smaller than $L/Es^2$ intersects at most $O(L^2/R^2)$ balls. We deduce that
\begin{align}
\mathcal{N}_f(s,z)= \frac{E}{R^2}\int_{B(s,z)}\mathcal{N}_f\left(\frac{R}{\sqrt{E}},x\right)dx + O\left(\frac{Es^2}{L}\right) + O\left(\frac{Es^2 L^2}{R^2}\right). \nonumber
\end{align}
The Proposition follows choosing $L= \sqrt{R}$.
\end{proof}
\subsection{Proof of Proposition \ref{claim}, upper bound}
The proof will be carried out through a series of lemmas, the first is a standard tool to count zeros of analytic functions.
\begin{lem}[Jensen's bound]
\label{Jensen's bound}
Let $h$ be a complex analytic function on some ball $B \subset \mathbb{C}$ and let $Z(h,\frac{1}{2}\overline{B})$ be the number of its zeros in $\frac{1}{2}\overline{B}$. Then,
\begin{align}
Z\left(h,\frac{1}{2}\overline{B}\right)\ll \log \frac{\underset{B}{\sup} |h|}{\underset{\frac{1}{2}\overline{B}}{\max}|h|}. \nonumber
\end{align}
\end{lem}
\begin{proof}
Up to translation and rescaling, we may assume that $h$ is defined on the unit ball, which we again denote by $B$. Let $w_1,...,w_n$ be the zeros of $h$ on $\frac{1}{2}\overline{B}$ counted with multiplicity and consider the Blaschke factor $ D(z,\omega_i)= (z-\omega_i)/(1-z\overline{\omega_i})$. Then, we can write $h(z)= \prod_{i}D(z,\omega_i) g(z)$ for some $g$ analytic on $B$ with $\underset{B}{\sup} |h|= \underset{B}{\sup} |g|$. Since $| D(z,\omega_i)| \leq (4/5)$ for $z\in \frac{1}{2}\overline{B}$, letting $Z= Z\left(h,\frac{1}{2}\overline{B}\right)$, we have
\begin{align}
\underset{\frac{1}{2}\overline{B}}{\max}|h|\leq \left(\frac{4}{5}\right)^{Z}\underset{\frac{1}{2}\overline{B}}{\max}|g|\leq \left(\frac{4}{5}\right)^{Z}\underset{B}{\sup}|g|\leq \left(\frac{4}{5}\right)^{Z}\underset{B}{\sup}|h|. \label{9}
\end{align}
The lemma follows taking the logarithm on both sides of \eqref{9}.
\end{proof}
We also need the following well-known formula of Crofton, see for example \cite{F}.
\begin{lem}
\label{Crofton's formula} Let $f$ be as in \eqref{function}, $s>0$ and $z\in \mathbb{T}^2$, moreover let $g(y)=f(z+sy)$ for $y\in B(1)$. Then, uniformly in $s$ and $z$, we have
\begin{align}
\mathcal{L}_f(s,z)s^{-1}=\mathcal{L}(g)\ll \int_{B(1)} \int_{\mathbb{S}^1} Z( g(u+tw)) d\omega du \nonumber
\end{align}
where $ Z( g(u+tw))$ is the number of zeros of $g$ as a function of $t\in [0,1]$.
\end{lem}
Finally, we need the following lemma, see \cite{N,T}:
\begin{lem}[Nazarov-Turan]
\label{NT}
Let $J\in \mathbb{N}$ and let $h(t)=\sum_{i=1}^{J}a_{\xi}e(\xi_i \cdot t)$ for $t\in \mathbb{C}$ and suppose that $\xi_i \in \mathbb{C}$ are distinct. Then, for any $B\subset \mathbb{C}$ and $\Omega\subset B$ a measurable subset, we have
\begin{align}
\underset{t\in B}{\sup} |h|<\left(c\frac{|\Omega|}{|B|}\right)^{J-1} e ^{ \max_i |\xi_i| |B|} \underset{t\in \Omega}{\sup} |h|. \nonumber
\end{align}
for some explicit $c>0$.
\end{lem}
We are finally ready to prove the upper bound in Proposition \ref{claim}.
\begin{proof}[Proof of the upper bound in Proposition \ref{claim}]
Let $g(y)=f(z+sy)$ for $y\in B(1)$ and let $h$ be the extension of $g$ to the complex unit ball . By Lemma \ref{Crofton's formula}, we have
\begin{align}
\mathcal{L}_f(s,z)s^{-1}=\mathcal{L}(g)\ll \int_{B(1)} \int_{\mathbb{S}^1} Z( g(u+tw)) d\omega du. \label{10.1}
\end{align}
By Lemma \ref{Jensen's bound} and Lemma \ref{NT}, we have
\begin{align}
Z( g(u+t\omega))\leq Z(h(u+z\omega))\ll \log \frac{\underset{D}{\sup} |h|}{\underset{\frac{1}{2}\overline{D}}{\max}|h|} \ll N + s\sqrt{E} \leq s\sqrt{E} \label{10}
\end{align}
uniformly in $u$ and $\omega$. The last inequality in \eqref{10} follows by \eqref{divisor bound} and the fact that $s>E^{-1/2+\epsilon}$. The upper bound then follows by \eqref{10.1} and \eqref{10}.
\end{proof}
\subsection{Proof of Proposition \ref{claim}, lower bound}
\label{lower bound}
The proof of the lower bound is standard, but we include it for completeness. We need the following result about the density of the zero set:
\begin{lem}
\label{density}
Let $f$ be as in \eqref{function}. There exists some absolute constant $c>0$ such that, uniformly for all $z\in \mathbb{T}^2$, the ball $B(c/\sqrt{E},z)$ contains a point where $f$ vanishes.
\end{lem}
\begin{proof}
Let $s>0$, and observe that the function $h(x,t)= f(x)e^{\sqrt{E}t}$ is harmonic in $D=B(s,z) \times [-s,s]$. If $f$ does not vanish in $B(s,z)$, then $h$ is positive; so it satisfies Harnack's inequality:
\begin{align}
\sup_D |h|\leq C \inf_D |h| \label{16}
\end{align}
for some absolute constant $C>0$. One the other hand,
\begin{align}
\sup_D |h| \geq \sup_{B(s,z)}|f| \exp (s\sqrt{E})\geq\inf_{B(s,z)}|f| \exp (s\sqrt{E}) \label{17}
\end{align}
The lemma follows combining \eqref{16} and \eqref{17} and choosing $c$ appropriately.
\end{proof}
We are finally ready to prove the lower bound in Proposition \ref{claim}.
\begin{proof}[Proof of the lower bound in Proposition \ref{claim}]
Using Lemma \ref{density}, we can divide $B(s,z)$ in $O(E s^2)$ balls of radius $c/\sqrt{E}$ for some appropriate $c>0$ such that $f$ vanishes at the centre of each ball. Let $B$ be one of these balls, then the Faber-Krahn inequality \cite[Theorem 1.5]{M} says that every nodal domain has inner radius at least $c_1/E^{1/2}$ for some absolute $c_1>0$, so we have
\begin{align}
\mathcal{H}^{1}\{ x\in B: f(x)=0\}\gg E^{-1/2}\label{11}
\end{align}
Since \eqref{11} holds for each of the $O(s^2E)$ balls, the lower bound follows.
\end{proof}
\subsection{Proof of Proposition \ref{claim2}}
As mentioned in the introduction the proof of Proposition \ref{claim2} follows the proof of Proposition \ref{claim}. We now give some of the details
\begin{proof}[Proof of Proposition \ref{claim2}]. Let $\mathcal{E}_E= \mathcal{E}:=\{\xi\in \mathbb{Z}^2: |\xi|^2=E\}$, we define an equivalence relation on $\mathcal{E}$ as follows: let $\xi=(\xi^1,\xi^2),\eta=(\eta^1,\eta^2) \in \mathcal{E}$, then $\xi \sim \eta$ if $\xi^1=\pm \eta^2$ and $\xi^2=\pm \eta^2$. Then the general Laplace eigenfunction with eigenvalue $\pi E$ (we make no distinction between $E$ and $\pi E$) satisfying either Dirichlet or Neumann boundary conditions is
\begin{align}
&\tilde{f}_{\text{Dirichlet}}(x)= \sum_{ \xi\in \mathcal{E}/ \sim} a_{\xi} \sin( \pi \xi^1 x^1)\sin( \pi \xi^2 x^2) \label{Di} \\
&\tilde{f}_{\text{Neuman}}(x)= \sum_{ \xi\in \mathcal{E}/ \sim} b_{\xi} \cos( \pi \xi^1 x^1)\cos( \pi \xi^2 x^2) \label{Neu}
\end{align}
where $x=(x^1,x^2)$. Using the formulas $\sin(a)\sin(b)= 2^{-1}(\cos(a-b)- \cos(a+b))$ and $\cos(a)\cos(b)= 2^{-1}(\cos(a+b)+ \cos(a-b))$, we can rewrite \eqref{Di} and \eqref{Neu} as
\begin{align}
&\tilde{f}_{\text{Dirichlet}}(x)= \sum_{ \xi\in \mathcal{E}/ \sim} \tilde{a}_{\xi} e\left(\langle \xi, x\rangle\right)
&\tilde{f}_{\text{Neuman}}(x)= \sum_{ \xi\in \mathcal{E}/ \sim} \tilde{b}_{\xi} e\left(\langle \xi, x\rangle\right) \nonumber
\end{align}
for some complex coefficients $\tilde{a}, \tilde{b}$. The proof now follows step by step the proof of the upper bound in Proposition \ref{claim}.
\end{proof}
\section{Bourgain's de-randomisation in shrinking sets}
\label{BourgainS}
Let $R>1$ be fixed, and consider the restriction of $f$, as in \eqref{function}, to a small square centred at $x\in \mathbb{T}^2$:
\begin{align}
F_x(y)= f\left( x+ \frac{R}{\sqrt{E}}y\right). \label{F}
\end{align}
for $y\in B(1)$. In this section we are going to show that if we sample $x$ uniformly at random from $B(s,z)$, where $z\in \mathbb{T}^2$ and $s>E^{-1/2+\epsilon}$, then the ensemble $\{F_x\}_{x\in B(s,z)}$ approximates the Gaussian field $F_{\mu_{f}}$. The proofs are based on \cite{BU,BW}; nevertheless, the use of Theorem \ref{semi} is required to control the averaging over $B(s,z)$.
\subsection{Approximating $f$ in small squares}
\label{approximating}
In this section, we construct an auxiliary function $\phi_x(y)$ which approximates $F_x(y)$ for most $x\in \mathbb{T}^2$. We begin with some notation: let $K>1$ be some (large) parameter and divide the circle $\mathbb{S}^1$ into arcs $I_k$, of length $1/2K$ for $k\in\{-K,...,K\}$. Furthermore, let $\delta>0 $ be some (small) parameter and denote by $\mathcal{K}\subset \{-K,...,K \}$ the subset of indices such that if $k\in \mathcal{K}$ then
\begin{align}
\mu_f(I_k)>\delta. \label{41}
\end{align}
Finally, let $\mathcal{E}^k=\mathcal{E}_E^k:=\{ |\xi|^2=E: \xi \in I_k\}$ and let $\zeta_k$ be the mid point of $I_k$.
We are ready to begin the construction, first we re-write $F_x$ as
\begin{align}
F_x(y)= \sum_{k\in \mathcal{K}}\sum_{\xi\in \mathcal{E}^k}a_{\xi}e(\langle \xi, x \rangle)e\left(\left\langle\frac{\xi}{\sqrt{E}},Ry\right\rangle\right) + \sum_{k\not\in \mathcal{K}}\sum_{\xi\in \mathcal{E}^k}a_{\xi}e(\langle \xi, x \rangle)e\left(\left\langle\frac{\xi}{\sqrt{E}},Ry\right\rangle\right). \label{42}
\end{align}
Second we approximate $\xi/\sqrt{E}$ by $\zeta_k$ for all $\xi\in \mathcal{E}^k$, and define the function
\begin{align}
\phi_x(y)&=\sum_{k\in \mathcal{K}}\left(\sum_{\xi\in \mathcal{E}^k}a_{\xi}e(\langle \xi, x \rangle) \right)e(\langle R\zeta^{k},y \rangle)= \sum_{k\in \mathcal{K}}\mu_{f}(I_k)^{1/2}b_k(x)e(\langle R\zeta^{k},y \rangle) \label{phi}
\end{align}
where
\begin{align}
b_k(x)=\frac{1}{\mu_{f}(I_k)^{1/2}}\sum_{\xi\in \mathcal{E}^{(k)}}a_{\xi}e(\langle\xi,x\rangle). \label{bk}
\end{align}
The following lemma shows that $\phi_x(y)$ is a good approximation to $F_x(y)$ for most $x\in \mathbb{T}^2$.
\begin{lem}
\label{first approx}
Let $\epsilon>0$, $R,K,\delta$ be as in Section \ref{approximating}, $F_x$, $\phi_x$ be as in \eqref{F} and \eqref{phi} respectively and $S'$ be defined in Section \ref{NTpre}. Then, for all $E\in S'$ we have
\begin{align}
\frac{1}{\pi s^2}\int_{B(s,z)} || F_x- \phi_x||_{\mathcal{C}^1(B(1))} dx \ll R^{6}K\delta + R^{8}K^{-2} + R^{8}E^{-(1/3)\epsilon} \nonumber
\end{align}
uniformly for all $s>E^{1/2+\epsilon}$ and $z\in \mathbb{T}^2$.
\end{lem}
\begin{proof}
Thanks to the Sobolev embedding Theorem, we bound the $\mathcal{C}^1$ norm by the $H^3$ norm
\begin{align}
\frac{1}{\pi s^2}\int_{B(s,z)} || F_x- \phi_x||_{\mathcal{C}^1} dx \ll \frac{1}{\pi s^2}\int_{B(s,z)} \int_{B(1)} | D^{\alpha} (F_x (y)- \phi_x(y)|^2 dy \label{49}
\end{align}
where $|\alpha|= |(\alpha_1,\alpha_2)| \leq 3$ and $D^{\alpha}= \partial_{\alpha_1}\partial_{\alpha_2}$. First, we estimate the contribution coming from the second term on the right hand side of \eqref{42}. Expanding the square and using the triangular inequality we obtain
\begin{align}
\frac{1}{\pi s^2}\int_{B(s,z)} \int_{B(1)} \left| D^{\alpha}\sum_{k\not\in \mathcal{K}}\sum_{\xi\in \mathcal{E}^k}a_{\xi}e(\langle \xi, x \rangle)e\left(\left\langle\frac{\xi}{\sqrt{E}},Ry\right\rangle\right)\right|^2 dxdy \nonumber \\
\ll \frac{1}{\pi s^2}R^{2|\alpha|} \sum_{k,k'\not\in \mathcal{K}} \sum_{\substack{\xi\in \mathcal{E}^k \\ \xi'\in \mathcal{E}^{k'}}}| a_{\xi}\overline{a_{\xi'}}|\left| \int_{B(s,z)}e(\langle \xi-\xi', x \rangle)dx \right| .\label{43}
\end{align}
Observe that for $a\in \mathbb{R}^2$
\begin{align}
\int_{B(s,z)} e(\langle a,x\rangle) dx = \begin{cases}
\pi s^2 & a=0 \\
\pi s^2 e(\langle a,z\rangle) \frac{J_1(s|a|)}{s|a|} & a\neq 0
\end{cases}. \label{orthogonality}
\end{align}
So we separate the terms with $\xi=\xi'$ from the others on the right hand side of \eqref{43} to obtain
\begin{align}
\eqref{43}\ll R^{2|\alpha|}\sum_{k\not\in \mathcal{K}}\sum_{\xi\in \mathcal{E}^k} |{a_{\xi}}|^2 + R^{2|\alpha|} \sum_{k,k'} \sum_{\xi \neq \xi'} |a_{\xi}a_{\xi'}| \frac{J_1\left( s|\xi-\xi'|\right)}{s|\xi-\xi'|} \label{44}
\end{align}
Since $k\not\in \mathcal{K}$ implies $\sum_{\xi\in \mathcal{E}^k} |{a_{\xi}}|^2= \mu_{f}(I_k)\leq \delta$, the first term on the right hand side of \eqref{44} is bounded by $R^{2|\alpha|} K \delta$. By Theorem \ref{semi} $|\xi-\xi'|\gg E^{1/2-2\epsilon}$ so $s|\xi-\xi'|\gg E^{\epsilon}$, it follows that
\begin{align}
\frac{J_1\left( s|\xi-\xi'|\right)}{s|\xi-\xi'|} \ll E^{(-2/3)\epsilon} \label{45}
\end{align}
where we have used the bound $J_1(T)\ll T^{-1/2}$ valid for all sufficiently large $T$. Using \eqref{45}, estimating trivially $|a_{\xi}|\leq 1$ and bearing in mind \eqref{divisor bound}, we obtain
\begin{align}
\sum_{k,k'} \sum_{\xi \neq \xi'} |a_{\xi}a_{\xi'}| \frac{J_1\left( s|\xi-\xi'|\right)}{s|\xi-\xi'|} \ll E^{(-2/3)\epsilon} \cdot N^2 \ll E^{(-1/3)\epsilon}. \nonumber
\end{align}
All in all, we have shown that
\begin{align}
\eqref{43} \ll R^{2|\alpha|} K \delta + R^{2|\alpha|}E^{-(1/3)\epsilon}. \label{48}
\end{align}
Now we turn our attention to bounding the difference between $\phi_x$ and the first term on the right hand side of \eqref{42}. Expanding the square and using the triangular inequality, we have
\begin{align}
\frac{1}{\pi s^2}\int_{B(s,z)} \int_{B(1)} \left| D^{\alpha}\sum_{k\in \mathcal{K}}\sum_{\xi\in \mathcal{E}^k} a_{\xi}e( \langle\xi,x\rangle)\left( e\left(\left\langle\frac{\xi}{\sqrt{E}},Ry\right\rangle\right) - e(\langle R\zeta_k, y\rangle) \right) \right|^2 dxdy \nonumber \\
\ll \frac{R^{2|\alpha|+2}}{\pi s^2} \sum_{k,k'} \sum_{\substack{\xi\in \mathcal{E}^k \\ \xi'\in \mathcal{E}^{k'}}}|a_{\xi}a_{\xi'}|\left|\frac{\xi}{\sqrt{E}}-\zeta_k\right|\left|\frac{\xi'}{\sqrt{E}}-\zeta_{k'}\right|\left| \int_{B(s,z)}e(\langle \xi-\xi', x \rangle)dx \right|. \label{47}
\end{align}
Similarly to the above, via \eqref{orthogonality} and \eqref{45}, the contribution from the terms with $\xi\neq \xi'$ is at most $R^{2|\alpha|+2} E^{-(1/3)\epsilon} $. The contribution of the terms with $\xi=\xi'$, bearing in mind that $|\xi/\sqrt{E}-\zeta_k|\leq 1/K$, can be bounded by
\begin{align}
R^{2|\alpha|+2}\sum_k \sum_{\xi\in \mathcal{E}^k} |a_{\xi}|^2\left|\frac{\xi}{\sqrt{E}}-\zeta_k\right|^2 \ll \frac{ R^{2|\alpha|+2}}{K^2}\sum_k \mu_f(I_k)\leq \frac{ R^{2|\alpha|+2}}{K^2}.\label{46}
\end{align}
All in all we have,
\begin{align}
\eqref{47} \ll \frac{ R^{2|\alpha|+2}}{K^2} + R^{2|\alpha|+2} E^{-(1/3)\epsilon}. \label{50}
\end{align}
The lemma follows combining \eqref{49}, \eqref{48} and \eqref{50}.
\end{proof}
\subsection{Gaussian moments}
Recall the notation \eqref{bk}, we are going to show that the vector $(b_k)_{k\in \mathcal{K}}$ approximates a Gaussian vector $(c_k)_{k\in \mathcal{K}}$, where $c_k$ are i.i.d. complex standard Gaussian random variables subject to $\overline{c}_k=c_{-k}$. We prove the following quantitative lemma:
\begin{lem}
\label{independence in shrinking}
Let $\epsilon>0$, $b_k$ be as in \eqref{bk} and $\mathcal{K},K,\delta$ be as in Section \ref{approximating}. Moreover let $B$ be some large parameter and fix two sets of positive integers $\{r_k\}_{k\in \mathcal{K}}$ and $\{s_k\}_{k\in \mathcal{K}}$ such that $\sum r_k + s_k \leq B$. Suppose that $E \in S'$, then
\begin{align}
\left|\frac{1}{\pi s^2}\int_{B(s,z)}\prod_{k\in \mathcal{K}}b_k^{r_k}\overline{b}_k^{s_k}dx- \mathbb{E}\left[\prod_{k\in \mathcal{K}}c_k^{r_k}\overline{c}_k^{s_k}\right]\right|= o_{\delta,K,B}(1) \hspace{5mm} \text{as} \hspace{2mm} N\rightarrow \infty \nonumber
\end{align}
uniformly for $f$ flat, $s>E^{-1/2+\epsilon}$ and $z\in \mathbb{T}^2$.
\end{lem}
\begin{proof}
Expanding the product, we have
\begin{align}
\frac{1}{\pi s^2} \int_{B(s,z)}\prod_{k}b_k^{r_k}\overline{b}_k^{s_k}dx= \prod_{k} \mu_{f}(I_k)^{-(r_k+s_k)/2}\sum \left( \prod_{i=1}^{r_k}\prod_{j=1}^{s_k}a_{\xi_{i,k}}\overline{a}_{\xi'_{j,k}}\right) \times \nonumber\\ \times \int_{B(s,z)} e\left( \Bigl\langle \sum_{k,i,j} (\xi_{i,k}- \xi'_{j,k}),x \Bigr\rangle\right)dx \label{formula1}
\end{align}
where the out most sum is over all the choices $\xi_{1,1},...,\xi_{1,r_1}, \xi'_{1,1}...,\xi'_{1,s_1},..., \xi_{k,1},..,.\xi_{k,r_k}, \xi'_{k,1}, \\ ...,\xi'_{1,s_k}$. We split the sum in \eqref{formula1} according to \eqref{orthogonality}: we first consider the contribution from the \emph{constant term} $\sum_{k,i,j}(\xi_{i,k}- \xi'_{j,k})=0$ and then the contribution from the \emph{oscillatory term} $|\sum_{k,i,j}(\xi_{i,k}- \xi'_{j,k})|>0$. Furthermore, we subdivide the constant term into \textquotedblleft diagonal" solutions, namely $\{\xi_{i,k}\}= \{\xi'_{j,k}\}$ for each $k\in \mathcal{K}$, and all the other solutions, which we call \textquotedblleft off-diagonal".
\textbf{Constant term}, \textit{\textquotedblleft diagonal" solutions}.
If $\{\xi_{i,k}\}= \{\xi'_{j,k}\}$, then $r_k= s_k$, so, taking into account the possible rearrangements and by definition of $I_k$ and $\mu_{f}(I_k)$, we have a contribution to the right hand side of \eqref{formula1} of
\begin{align}
g_k:=r_k! \cdot \mu_{f}(I_k)^{-r_k}\sum_{ \{\xi_{i,k}\}= \{\xi'_{j,k}\} } \prod_{i=1}^{r_k} |a_{\xi_{i,k}}|^2 = \mathbb{E}[ |c_k|^{2r_k}]. \nonumber
\end{align}
Multiplying together the contributions from all $k$'s, we obtain
\begin{align}
\prod_{k} g_k= \mathbb{E}\left[\prod_{k}|c_k|^{2 r_k}\right].\label{3.1}
\end{align}
\textbf{Constant term}, \textit{\textquotedblleft off-diagonal" solutions}.
Let $B_1=\sum_{k}r_k+ s_k$. Since $E\in S'$, Theorem \ref{BB} implies that the number of off-diagonal solutions is at most $O(N^{\gamma B_1})$. Since $\mu_{f}(I_k)\geq \delta$ for all $k \in \mathcal{K}$ and $|a_{\xi}|^2\leq N^{-1+o(1)}$, we obtain as $N\rightarrow \infty$
\begin{align}
\left|\sum_{\text{off-diagonal}}\prod_{k} \mu_{f}(I_k)^{r_k+s_k/2}\sum \prod_{k} \prod_{i=1}^{r_k}\prod_{j=1}^{s_k}a_{\xi_{i,k}}\overline{a}_{\xi_{j,k}}\right|\ll_{K} N^{-B_1/2+ \gamma B_1 +o(1)} \delta^{-B_1/2}=o_{\delta, B, K}(1). \label{3.2}
\end{align}
\textbf{Oscillatory term}. If $|\sum_{k,i,j}(\xi_{i,k}- \xi'_{j,k})|>0$, Theorem \ref{semi} implies that $|\sum_{k,i,j}(\xi_{i,k}- \xi'_{j,k})|>E^{1/2-2\epsilon}$, therefore $s|\sum_{k,i,j}(\xi_{i,k}- \xi_{j,k})|>E^{\epsilon}$. So, bearing in mind that $J_1(T) \ll T^{1/2}$ for $T$ sufficiently large, we have
\begin{align}
\frac{J_1(s|\sum_{k,i,j}(\xi_{i,k}- \xi_{j,k})|)}{s|\sum_{k,i,j}(\xi_{i,k}- \xi_{j,k})|}\ll E^{-2/3 \epsilon} .\label{3.5}
\end{align}
Since the maximum number of terms in the outer sum in \eqref{formula1} is $N^{B_1}$, $\mu_{f}(I_k)\geq \delta$ for all $k \in \mathcal{K}$, $|a_{\xi}|\leq N^{-1+o(1)}$ and bearing in mind \eqref{3.5} and \eqref{divisor bound} , we obtain as $N\rightarrow \infty$
\begin{align}
\prod_{k} \mu_{f}(I_k)^{-(r_k+s_k)/2}\sum \left( \prod_{k} \prod_{i=1}^{r_k}\prod_{j=1}^{s_k}a_{\xi_{i,k}}\overline{a}_{\xi_{j,k}}\right) \frac{J_1(s|\sum_{k,i,j}(\xi_{i,k}- \xi_{j,k})|)}{s|\sum_{k,i,j}(\xi_{i,k}- \xi_{j,k})|} \nonumber \\ \ll_{K} N^{B_1/2 +o(1)} \delta^{-B_1/2} E^{-2/3 \epsilon}=o_{\delta,K,B_1}(1). \label{3.3}
\end{align}
The Proposition follows combining \eqref{3.1}, \eqref{3.2}, \eqref{3.3}.
\end{proof}
Lemma \ref{independence in shrinking}, by the method of moments, implies that the vector $(b_k)_{k\in \mathcal{K}}$ converges in distribution to the vector $(c_k)_{k\in \mathcal{K}}$ . We restate this fact in the following convenient way, more details can be found in \cite[Lemma 6.5]{BW} and \cite[Page 9]{BU}, see in particular \cite[Lemma 6.4]{BW} for the fact that the measure induced by the $b_k$'s is absolutely continuous with respect to the Lebesgue measure.
\begin{cor}
\label{tau}
Let $\epsilon>0$ and $\alpha_1,\alpha_2>0$ be given, let $\delta,K,B,$ as in Lemma \ref{independence in shrinking} and $f$ be as in \eqref{function}. Suppose that $E \in S'$ is sufficiently large depending on $\epsilon,\alpha_1,\alpha_2,K,\delta$ and $B$. Then, uniformly for all $f$ flat, $s>E^{-1/2+\epsilon}$ and $z\in \mathbb{T}^2$, there exists a measurable map $\tau: \Omega\rightarrow B(s,z)$ and a subset $\Omega^1\subset \Omega$ with the following properties:
\begin{enumerate}
\item For any measurable $A\subset \Omega^1$, we have $\vol(\tau(A))= \pi s^2\mathbb{P}(A)$.
\item $\mathbb{P}(\Omega^1)>1-\alpha_1$ .
\item For all $\omega\in \Omega^1$, we have $|b_k(\tau(\omega))- c_k(\omega)|\leq \alpha_2$ uniformly for all $k\in \mathcal{K}$.
\end{enumerate}
\end{cor}
\subsection{Discarding $\phi_x$}
Before proving the main result of this section, we need the following lemma:
\begin{lem}[Lemma 4, \cite{SO}]
\label{Sodin}
Let $R>1$ $\alpha_3,\alpha_4>0$, $\{\mu_n\}_{n\in \mathbb{N}}$ be a sequence of probability measures on $\mathbb{S}^1$ such that $\mu_n$ weak$^{\star}$ converges to some probability measure $\mu$. Then, for all $n$ sufficiently large depending on $\alpha_3,\alpha_4$ and $R$, we have
\begin{align}
||F_{\mu_n}- F_{\mu}||_{\mathcal{C}^1(B(R))}\leq \alpha_3 \nonumber
\end{align}
outside an event of probability $\alpha_4$.
\end{lem}
\begin{proof}
We can associate to $\mu$ the Gaussian measure $G$ defined on $\mathbb{R}^2$ as follows: for any open and measurable (with respect to $\mu$) subset $A$ of $\mathbb{R}^2$ we let
\begin{align}
G(A)= N(0,\mu(A))\nonumber
\end{align}
where $N(0,\mu(A))$ is a Gaussian random variable with mean zero and variance $\mu(A)$. Moreover, if $A\cap B= \emptyset$, we require $G(A)$ and $G(B)$ to be independent. We define $G_n$ with respect to $\mu_n$ similarly. Since $\mu$ is compactly supported, we see that $G_n$ weak$^{\star}$ converges to $G$ and, since a normal random variable is square integrable, we obtain $G_n\rightarrow G$ in $L^2(\Omega)$ (recall that $\Omega$ is the common probability space of our random objects). By \cite[Theorem 5.4.2]{AT}, we have the $L^2(\Omega)$ representations
\begin{align}
&F_{\mu_n}(x)= \int_{\mathbb{S}^1}e(\langle x\cdot\lambda\rangle)G_n(d\lambda) &F_{\mu}(x)= \int_{\mathbb{S}^1}e(\langle x\cdot\lambda\rangle)G(d\lambda). \label{13}
\end{align}
Since $\mu$ and $\mu_n$ are compactly supported, we can differentiate under the integral in \eqref{13}; bearing in mind that $G_n$ weak$^{\star}$ converges to $G$, we have $||F_{\mu_n}- F_{\mu}||_{\mathcal{C}^1(B(R))}\rightarrow 0$ as $n\rightarrow \infty$ in $L^2(\Omega)$. This implies the conclusion of the Lemma.
\end{proof}
We are finally ready to state and prove the main result of this section:
\begin{prop}
\label{main prop}
Let $\epsilon>0$, $R>1$ and $\eta_1,\eta_2>0$, $f$ be as in \eqref{function}. Suppose that $E \in S'$ is sufficiently large depending on $\epsilon,\eta_1,\eta_2$ and $R$. Then, uniformly for all $f$ flat, $s>E^{-1/2+\epsilon}$ and $z\in \mathbb{T}^2$, there exists a measurable map $\tau: \Omega\rightarrow B(s,z)$ and a subset $\Omega'\subset \Omega$ with the following properties:
\begin{enumerate}
\item For any measurable $A\subset \Omega$, we have $\vol(\tau(A))= \pi s^2\mathbb{P}(A)$.
\item $\mathbb{P}(\Omega')>1-\eta_1$ .
\item For all $\omega\in \Omega'$, we have $||F_{\tau(\omega)}(y)- F_{\mu_{f}}(Ry,w)||_{ \mathcal{C}^1(B(1))}\leq \eta_2$
\end{enumerate}
\end{prop}
\begin{proof}
Let $\mathcal{K},K,\delta$ be as in Section \ref{approximating} and let $F_K(Ry,\omega):=\sum_{k\in \mathcal{K}}\mu_{f}(I_k)^{1/2} c_k(\omega) e(\langle \zeta_k,Ry\rangle)$. Thanks to Corollary \ref{tau} with $\alpha_1=\eta_1/3$ and $\alpha_2=1/K^2$, there exist $\tau: \Omega\rightarrow B(s,z)$ and $\Omega^1\subset \Omega$ such that:
\begin{itemize}
\item For any measurable $A\subset \Omega'$, we have $\vol(\tau(A))= \pi s^2\mathbb{P}(A)$.
\item $\mathbb{P}(\Omega^1)>1-\eta_1/3$ .
\item For all $\omega\in \Omega'$, we have
\begin{align}
||\phi_{\tau(\omega)}(y) -F_K(Ry,\omega)||_{\mathcal{C}^1}\ll RK \alpha_2= \frac{R}{K}\leq \eta_2/3 \label{main1}
\end{align}
provided $K$ is sufficiently large depending on $R$ and $\eta_2$.
\end{itemize}
\begin{claim}
\label{claim1}
There exists some $\Omega^2\subset \Omega$ with $\mathbb{P}(\Omega^2)>1-\eta_1/3$ such that
\begin{align}
||F_K(Ry,\omega)- F_{\mu_{f}}(Ry,\omega)||_{\mathcal{C}^1}\leq \eta_2/3\label{main2}
\end{align}
for all $K$ sufficiently large depending on $\eta_1,\eta_2$ and $R$.
\end{claim}
To prove the claim, observe that $F_K$ is a Gaussian field with spectral measure
\begin{align}
\mu_K= \sum_{k\in \mathcal{K}} \mu_{f}(I_k) \delta_{\zeta_k}. \nonumber
\end{align}
By definition of $\mu_f$, we have $\sup_{A\subset \mathbb{S}^1} |\mu_{f}(A)- \mu_K(A)| \ll \delta K $. So, taking $\delta<1/K^2$ and $K$ sufficiently large, the claim follows from Lemma \ref{Sodin}.
\vspace{2mm}
Finally, by Lemma \ref{first approx} and Markov's inequality, we have
\begin{align}
|| F_x- \phi_x||_{\mathcal{C}^1} \leq \eta_2/3 \label{main3}
\end{align}
for all $x\in B\subset B(s,z)$, where
\begin{align}
(\pi s^2)^{-1} \vol(B(s,z) \backslash B)\ll \eta_2^{-1}\left( R^{6}K\delta + R^{8}K^{-2} + R^{8}E^{-(1/3)\epsilon} \right) \leq \eta_1/3 . \label{5.1}
\end{align}
for $K$ and $E$ sufficiently large in terms of $R$, $\eta_1$ and $\eta_2$. We briefly summaries our choices of parameters: $R,\eta_1,\eta_2$ are fixed, $\delta<1/K^2$, $K$ is large depending $R,\eta_1,\eta_2$ and $E$ is large depending on $R,\eta_1,\eta_2$ and $K$. We are now ready to conclude the proof. Let $\Omega'= \Omega^1 \cap \Omega^2 \cap \tau^{-1} (B)$, then $\tau$ restricted to $\Omega'$ satisfies $(1)$. By Corollary \ref{tau}, Claim \ref{claim1} and \eqref{5.1}, we also have $\mathbb{P}(\Omega')\geq 1- \eta_1$ so $(2)$ holds. Finally, $(3)$ follows by \eqref{main1}, \eqref{main2} and \eqref{main3}, valid for all $\omega \in \Omega'$. This concludes the proof of the Proposition.
\end{proof}
\section{Concluding the proof}
\label{end}
We are finally ready to prove Theorem \ref{theorem 3}.
\begin{proof}[Proof of Theorem \ref{theorem 3}]
Pick some $\eta_1, \eta_2>0$ to be chosen later, and let $\tau$ and $\Omega'$ be given by Proposition \ref {main prop}. Then, by Proposition \ref{semi-locality}, we have
\begin{align}
\mathcal{N}_f(s,z)&= \frac{E}{R^2}\int_{B(s,z)} \mathcal{N}( F_x)dx + O\left(\frac{Es^2}{\sqrt{R}}\right) \nonumber \\
&= \frac{E}{R^2}\int_{\tau^{-1}(\Omega')} \mathcal{N}( F_x)dx + \frac{E}{R^2} \int_{B(s,z)\backslash \tau^{-1}(\Omega')} \mathcal{N}(F_x)dx + O\left(\frac{Es^2}{\sqrt{R}} \right). \label{53}
\end{align}
By part $(3)$ of Proposition \ref{main prop}, we may write $F_x(y)= F_{\mu_{f}}(Ry) +\psi$ for $x\in \tau^{-1}(\Omega')$ and some function $\psi$ with $||\psi||_{\mathcal{C}^1}\leq \eta_1$. Thus, we can rewrite \eqref{53}, bearing in mind part $(1)$ of Proposition \ref{main prop}, as
\begin{align}
\mathcal{N}_f(s,z)&= \frac{\pi s^2 E}{R^2}\int_{\Omega'} \mathcal{N}( F_{\mu_{f}} +\psi, R )d\omega + \frac{E}{R^2}\int_{B(s,z)\backslash \tau^{-1}(\Omega')} \mathcal{N}(F_x)dx + O\left(\frac{Es^2}{\sqrt{R}}\right) \nonumber \\
&= \frac{ \pi s^2 E}{R^2}\left(\int_{\Omega} \mathcal{N}( F_{\mu_{f}} +\psi, R ) d\omega- \int_{\Omega\backslash \Omega'} \mathcal{N}( F_{\mu_{f}} +\psi, R ) d\omega \right) \nonumber \\
& \hspace{1cm} + \frac{ E}{R^2}\int_{B(s,z)\backslash \tau^{-1}(\Omega')} \mathcal{N}(F_x)dx + O\left(\frac{Es^2}{\sqrt{R}}\right) \label{52}
\end{align}
where in the second equality we set $\psi(y,\omega)=0$ for $\omega \not \in \Omega'$. By the Faber-Krahn inequality, $\mathcal{N}(F_x)\ll R^2$, and since $F_{\mu_{f}} +\psi= F_{\tau(\omega)}$, we have $ \mathcal{N}( F_{\mu_{f}} +\psi ) \ll R^2 $ uniformly for all $\omega \in \Omega'$. For $\omega \not \in \Omega'$, by definition, we have $\Delta F_{\mu_{f}}=-R^2F_{\mu_{f}}$. Thus, again by the Faber-Krahn inequality, $ \mathcal{N}( F_{\mu_{f}} +\psi ) \ll R^2 $ holds uniformly for all $\omega \in \Omega$. Therefore, taking $\eta_2= 1/\sqrt{R}$, the second and third integrals in \eqref{52} are bounded by $O(R^{3/2})$. Thus, \eqref{52} can be re-written as
\begin{align}
\mathcal{N}_f(s,z)=\frac{\pi s^2 E}{R^2}\mathbb{E}[ \mathcal{N}( F_{\mu_{f}} +\psi, R )] +O\left(\frac{Es^2}{\sqrt{R}}\right). \nonumber
\end{align}
Taking $\eta_1$ small enough in terms of $R$ via Proposition \ref{stability} and then taking $R\rightarrow \infty$, we deduce
\begin{align}
\mathcal{N}_f(s,z)= c_{NS}(\mu_{f})\pi s^2 E(1+ o_{R\rightarrow \infty}(1)) . \nonumber
\end{align}
and the Theorem follows by taking $R$ to be an arbitrarily slowly, depending on all the parameters, growing function of $E$.
\end{proof}
\section*{Acknowledgement}
The author would like to thank Igor Wigman for many useful discussions. Alejandro Rivera and Maxime Ingremeau for stimulating conversations and Priya Lakshmi for her comments on an early draft of this article. This work was supported by the Engineering and Physical Sciences Research Council [EP/L015234/1].
The EPSRC Centre for Doctoral Training in Geometry and Number Theory (The London School of Geometry and Number Theory), University College London.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,498 |
Q: How would one change a container's content with a UIButton? I am trying to change the embed content inside a container from a tableviewcontroller to a map. I have tried searching it up, but all the questions have to do with tabview, which I am not doing. How would I start this process?
I also have tried with
- (IBAction)changer:(id)sender {
UIViewController *viewController1 = [self.storyboard instantiateViewControllerWithIdentifier:@"vc1"];
container.view = viewController1;
}
but that does not work
A: Try
MyViewController *viewController1 = [self.storyboard instantiateViewControllerWithIdentifier:@"vc1"];
viewController1.view.frame = self.container.bounds;
[viewController1 willMoveToParentViewController:self];
[self.container addSubview:viewController1.view];
[self addChildViewController:viewController1];
[viewController1 didMoveToParentViewController:self];
A: this is my implementation in Swift:
func navigateTo(vc: NSViewController){
vc.view.frame = self.containerView.bounds;
if let currentSubview = containerView.subviews.first {
self.containerView.replaceSubview(currentSubview, with: vc.view)
} else {
self.containerView.addSubview(vc.view)
}
self.addChildViewController( vc )
}
For an animated transition, i implement awakeFromNib
override func awakeFromNib() {
let animation: CATransition = CATransition()
animation.type = kCATransitionMoveIn
animation.subtype = kCATransitionFromRight
animation.duration = 0.75
animation.delegate = self
animation.timingFunction = CAMediaTimingFunction(name: kCAMediaTimingFunctionEaseInEaseOut)
if let _ = containerView {
containerView.wantsLayer = true
containerView.animations = NSDictionary(object: animation, forKey: "subviews") as! [String : AnyObject]
}
}
and replace the line self.containerView.replaceSubview with:
self.containerView.animator().replaceSubview(currentSubview, with: vc.view)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,248 |
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Jane Fejfer (Associate Professor, University of Copenhagen), "Just Façade? The relationship between sculpture and architecture in the Roman East"
…..propter amplitudinem maiestatemque populi Romani, cuius istae coloniae quasi effigies parvae simulacraque esse quaedam videntur,….
…..because of the greatness and majesty of the Roman people, of which these colonies seem to be miniatures, as it were, and in a way copies; Aulus Gellius, Attic Nights Book XVI.XIII.9
A significant part of Classical sculpture in the large universal museums in Europe and the USA is so-called Roman ideal sculpture, mythological human figures in Greek styles and so-called decorative sculpture, large vases, candelabras, table supports, masks, fountain figures, etc. When entering a national or regional archaeological museum in a region that was once a province within the eastern part of the Roman Empire a similar situation of galleries populated by life-size ideal Roman marble statuary, pertain. However, the typical so-called decorative sculptures are almost totally missing. This paper discusses the relationship between the eastern and western part of the Roman Empire during the imperial period and above all how the Greek East accommodated itself into becoming and being part of the larger Roman Empire. It is argued, that monumental marble sculpture qua its powerful presence, material property, semantic message and aesthetic value, participated in a process of mutual exchange between the Roman West and the Roman East.
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© 2014 The Canadian Institute in Greece. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,953 |
Q: Does shared preferences/preference activity allow for enabling/disabling of fragments inside the page? I have an activity that extends preference activity, to be a settings page. Inside the settings page is an edit text and three different listviews. I want to hardcode the input of the edit text so that when the right "password" (the hardcoded string) is entered, it enables the previously hidden and disabled listviews. Is this possible to happen in same time and how?
private EditText password;
@Override
protected void onCreate(Bundle savedInstanceState){
super.onCreate(savedInstanceState);
password = (EditText)findViewById(R.id.adminpasswordsetting);
getFragmentManager().beginTransaction().replace(android.R.id.content, new MyPreferencesFragment()).commit();
}
public static class MyPreferencesFragment extends PreferenceFragment{
@Override
public void onCreate(final Bundle savedInstanceState){
super.onCreate(savedInstanceState);
addPreferencesFromResource(R.xml.preferences);
}
}
private void setAdminSettings(){
//set the password
if(password.getText().toString().equals("helloworld")){
//SharedPreferences.Editor editor = preferences.edit;
}
}
public void onSharedPreferenceChanged(SharedPreferences sharedPreferences, String key){
}
and my xml preference is just one edittextpreference and three listpreferences
A: This code probably will not run 'as is' ... so do not copy-paste it.. but I am thinking something alog following lines of code (just as an idea)
public class PrefsActivity extends PreferenceActivity {
public PrefsActivity() {
// TODO Auto-generated constructor stub
}
@Override
protected void onCreate(Bundle savedInstanceState) {
super.onCreate(savedInstanceState);
addPreferencesFromResource(R.xml.prefs);
ListPreference lp1 = (ListPreference) findPreference(getString(R.string.lp1));
CheckBoxPreference cb2 = (CheckBoxPreference) findPreference(getString(R.string.cb2));
lp1.setEnabled(false);
cb2.setEnabled(false);
EditTextPreference etp1 = (EditTextPreference) findPreference(getString(R.string.mypassword));
String mypassword =PreferenceManager.getDefaultSharedPreferences(this).getString(getString(R.string.mypassword), "0");
if ("THE_PASSWORD".equals(mypassword)) {
lp1.setEnabled(true);
cb2.setEnabled(true);
}
}
}
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 9,752 |
**SIMPLE FLY FISHING**
TECHNIQUES FOR TENKARA AND ROD & REEL
Yvon Chouinard, Craig Mathews, and Mauro Mazzo
Foreword by Russell Chatham
Paintings by James Prosek
Ventura, California
One percent of the sales from this book go to the preservation and restoration of the natural environment. In addition, the authors are donating their entire profits from the sales of the first edition to the Native Fish Society, the Atlantic Salmon Federation, and 1% For The Planet. Finally, a portion of the proceeds is being donated to World Trout® Initiative.
## Contents
FOREWORD
Russell Chatham
INTRODUCTION
Yvon Chouinard
CHAPTER 1: TROUT AND THEIR FOOD
Yvon Chouinard, Craig Mathews, and Mauro Mazzo
CHAPTER 2: FLY FISHING WITH WET FLIES AND STREAMERS
Yvon Chouinard
CHAPTER 3: FLY FISHING WITH NYMPHS
Mauro Mazzo
CHAPTER 4: FLY FISHING WITH DRY FLIES
Craig Mathews
CHAPTER 5: FISHING SITUATIONS
Yvon Chouinard, Craig Mathews, and Mauro Mazzo
AFTERWORD
Yvon Chouinard
ADDITIONAL RESOURCES
_Photo: Mauro Mazzo_
## _"AT ITS MOST PROFOUND, FISHING IS A WAY OF REMAINING FOREVER A CHILD."_
—Russell Chatham
## Foreword
The fact is that fishing with an artificial fly has always been an elitist activity. Simply stated, the reason is that at its core lies a set of esthetic precepts rather fundamentally at odds with those of the common man whose approach to life's various aspects is simple practicality. Be that as it may, at the end of the day fishing is still just fishing.
Going back to its origins in Europe, fly casting was practiced in the realm of the aristocracy who owned and controlled the trout and salmon waters appropriate to its use. However, in the literature there sometimes would appear poachers who fell in love with the esoteric essence of this enterprise, and who were willing to risk imprisonment for the sake of its sensual rewards, in one sense a bit like rogering the count's bored wife.
Once transposed to America it became a tad more democratic; but just a tad, as wealthy easterners commandeered private waters in the Catskills and Adirondacks and formed exclusive clubs in New York.
Enter the left coast where many regarded the right as some version of an anthropomorphic museum filled with taxidermied throwbacks, and where fly fishing was mainstream from the start among the great unwashed. In spite of this, it has degenerated into a country club activity popular with the nouveau riche in which the accoutrements have become so ridiculously complex and expensive that Joe Six-Pack can only stand helplessly with his nose pressed to the tackle store window.
One has to wonder how this happened. There are several very simple explanations. The first and most important is that because of our universal environmental crimes, we've ruined most of the fishing close to home: the all-important free fishing that youngsters could readily find after school on foot or by bike.
Because of this, in the late 1970s companies like Fishing International and Frontiers began booking exotic world travel directed at, but not exclusive to, fly fishermen. This changed the angling pastime precipitously. Now, instead of throwing your waders and rod into the trunk of the car and driving for an hour from San Francisco to the Russian River, you wrote a check for a thousand dollars a day to go to Alaska, British Columbia, South America, Iceland, or Russia.
It didn't take the tackle companies long to go on a high-alert point. Suddenly, rods didn't cost twenty-five dollars anymore. Now, instead of plebeian fiberglass, they were made of graphite or boron technology and could set you back four, five, or even six hundred dollars. And the gold- and silver-plated reels that had all the class of a three-dollar whore's earrings were similarly priced. Alright Bucko, if you can afford eight or nine thousand dollars to wet a line for a week, you need the Right Stuff.
It's simple, greed-driven supply-side undemocratic capitalism doing what it does best, which is to demand more and more product and ever-increasing sales. Product lifespan is earmarked at the factory for the flea market, and the manufacturers will handle the public relations on that.
As the great rod designer and builder Tom Morgan has said over and over again, "A good rod is a good rod whether it was made sixty years or sixty days ago." And in this he was echoing the sentiments of every knowledgeable and ethical fine craftsman. But that's not how you sell more rods. First, yesterday's must be categorized as inferior and obsolete. In its place you need some new chemical component with a technical sounding name and a guarantee to make you a better caster. I remember once about thirty years ago being in Dan Bailey's Fly Shop in Livingston, Montana, when a tourist was considering buying a four-hundred-dollar fly rod. The sales associate at the time, Fred Terwilliger, suggested they go out on the train depot lawn across the street and cast it. Pretty soon they were back in the store and Fred said, "Mister, you don't need a four-hundred-dollar rod, you need a fifty-dollar casting lesson."
With respect to fly lines, with the exception of a perfectly level one, which is useless, there are only three basic designs. The most traditional of these is the double taper. Historically, the reason for this was that when all lines were made of silk, you fished half the day with one end, and when it began to sink, you turned it around, greased up the new end and went back to fishing. The weight-forward taper has a heavier section toward the front, designed to fish at greater distances. You false cast this belly, as it's called, then shoot it, pulling the thinner fly line out behind it. A shooting taper, or head, is generally thirty feet long, tied to monofilament, making it the ultimate tool for distance casting. The first two styles, often referred to as whole lines, are generally about ninety to a hundred feet in length. All of these either float, or else sink at varying speeds.
I recall quite clearly in the 1950s when Scientific Anglers introduced the first plastic lines (heretofore, fly lines were woven of silk, nylon, or Dacron fibers). They produced the three aforementioned styles in white, which floated, and dark green, which sank. They worked closely with, and listened to, one time world-record caster, Myron Gregory, who brought to the table all the physical knowledge of the R.L. Winston Rod Company ("Rod Builder to the Champions") and the Golden Gate Angling and Casting Club, both in San Francisco.
A year or so ago, I went through a new Scientific Anglers catalogue. In it were pictured and described about eighty different fly lines. Eighty. It seems that a line good for Florida's west coast is all wrong for its east coast, and of course neither are suitable for the Keys. And the line that's correct for Chesapeake Bay will not do for the Jersey Shore, and of course is also dead wrong for the flats around Nantucket. And don't get the idea that you can transpose your British Columbia steelhead line to Iceland's Atlantic salmon rivers. How naïve can you get? And so on until the minutiae becomes a spinning top whirling to the _kachinging_ of the cash register.
The all-time perfect system in distance casting for steelhead and salmon as well as tournament events was developed in San Francisco in the 1940s and perfected in the 1950s. It was simply a thirty-foot shooting head for fishing, and fifty for competition, backed by nylon monofilament. Early on, this material was very hard to handle, being wiry and easily tangled. Eventually however, the Sunset Line and Twine Company in Petaluma, California, developed a brand they called Amnesia that eliminated those problems.
What disturbed the fly line manufacturers to the point of distraction was that this running line cost the user about a nickel a mile so it was systematically denigrated in ads and articles. Soon, an array of more costly substitutes began coming on the market, not one of which ever came close to achieving the perfect efficiency of Amnesia. What this did was cause people to buy thousands of yards of expensive ineffective shooting line, thereby completely destroying the shooting head's real value.
Because of this the stage was set for something new, or rather something old retooled and pressed back into service. It's been some twenty years now, I suppose, since the appearance of the two-handed rod fad. The glamour fish are the sea trout and salmon, and as a general rule, catching them requires a longish cast. To become genuinely proficient at distance casting with a traditional one-handed nine-foot fly rod requires 10,000 hours of practice, and people who can afford to pay eight to fifteen thousand dollars a week to go fishing don't have that kind of time to practice because they're too busy making money.
I learned about double-handed casting from some Scottish gentlemen who visited San Francisco in the 1950s. The rather autoerotic version(s) of Spey casting as now practiced in America would be unrecognizable to these men. I've been everywhere on the planet where you can fish for anadromous fish, and have watched with mild amusement as the captains of industry strained, slashed, and grunted out fishable casts, only to just stand there like designated rod holders devoted to supporting their enormous tackle while the huge lines swung with the current, the owners unable to manipulate the fly—the central act in fishing.
I've seen many times and in many places men and women learning to make fishable casts in a short day. A little whooshing, a little swishing, and with a flourish the fly, probably an absurdly large one, plops down at eighty feet every time. Perfect. Now the good news for the industry: Technology that puts anglers in the bucket comes with a curse involving their checkbooks. Forget six hundred for the advantage of a very long rod, now it's a thousand. And you'll also need a bigger, much more expensive and uglier reel, not to mention a large bag full of specialized fly lines.
Many people, myself included, first learned to fish with a stick of some kind, probably willow, with a piece of line attached to it at the end of which was a hook and a wiggly worm. This ultimately low-tech accessory put the young angler in the closest proximity to the water and the quarry. Wet shoes and pant legs were ubiquitous. Here was the essential undergraduate course that instilled an intimate love of fishing so that no matter what brand of sophistication followed throughout the years, those early memories were etched forever.
So it is: The more complex technology is allowed to intrude upon the fundamental simplicity of fishing, the further one becomes removed from its core value. At its most profound, fishing is a way of remaining forever a child. Of course, we cannot truly do that, nor should we want to, but the illusion of it is one important key to mental health.
All concerned people in this country wish that the upcoming generation would spend more time out in the natural world. There are some conservationists who are opposed to fishing and hunting, but I'm sorry, they are not thinking it through. In order to transpose mere interest into passionate love requires proactive behavior. The road is an uphill one because today's youth of the digital world are raised with offers of passive, instant gratification. Can a person raised in that environment ever fish all day without a bite? Maybe it should be mandatory for schools to provide environmental study from grade one in which there is no computer involved, or any other electronic visual aide, only calm, analytical conversation mixed in with visits to if not wild places at least rural ones.
This brings us around to the tenkara style, a perfect way to eliminate mechanical moving parts, an homage as it were to the willow branch. I'm not a trout fisherman, so my long Japanese rod is used on still waters near where I live in Northern California.
In the fading light of a perfectly quiet evening last November, I was standing by a beautiful pond. To my left, a pair of mallards noodled around the lily pads and red-winged blackbirds trilled their beautiful song, while a bullfrog announced his presence from the tules on my right. My pant legs and shoes were wet and muddy, and as the sun dipped behind the hills I started to shiver. I danced a little fly across the water and six-inch bluegills raced to hit it. Time stood still. I was an eleven-year-old boy again, sneaking concealed along Sleepy Hollow Creek, advancing toward a bay tree root where I knew there were baby steelhead hiding. Mom said not to be late for dinner, but I wasn't hungry. I was as happy as you can get.
Russell Chatham
Marshall, California
An angler with a "loop rod." Artwork for the first fishing book published (in 1496) in English: _A Treatyse of Fysshynge wyth an Angle,_ by Dame Juliana Berners.
## _"DESPITE RUMORS TO THE CONTRARY, THE PARAMOUNT OBJECTIVE IS: TO CATCH FISH . . . ."_
—Sheridan Anderson, _The Curtis Creek Manifesto_
## Introduction
## YVON CHOUINARD
Why write one more book about fishing when there are probably more books on the subject than romance novels?
Since the fifteenth century, every nuance of fly fishing has been written about in the utmost detail, leaving us to endlessly reinvent what has already been discovered. A tiny change on a classic fly and the "inventor" gets to name it after himself and collect a dime for each one sold. Many of the books on technique are like business books where a minor theory is spread out over three hundred pages, when all it really merits is a magazine article.
Heaven knows we fly fishers are suckers for every new gizmo we think will give us a leg up on catching fish. We wear vests with twenty pockets and waders with even more storage. And as if that isn't enough, we have lanyards, waist packs, and backpacks to carry even more impedimenta. Hundreds of fly lines are now available to us, yet I seriously doubt you will catch one more trout with a line fine-tuned to the conditions than with a classic double taper. The no-nonsense fly fisher Rob Brown, from Terrace, British Columbia, looking over a steelheader's array of fly boxes filled with hundreds of garish flies, said it best when he asked, "When did the green-butt stop working for you?"
I would offer that this proliferation of gear is supported by busy people who lack for nothing in their lives except time. Our "time-saving" communication devices, like tablets and smartphones, make slaves of their owners. We are unwilling, or unable, to put in the 10,000 hours needed to become a master fisher, hunter, or mountain climber. Instead, we load up with all the latest stuff and hire guides to do everything for us—including tying on the fly and releasing the fish. The guides have become enablers rather than teachers. How many bonefish would average anglers catch if they had to work out the tides and wade and spot fish themselves instead of waiting for a guide to bark, "ten o'clock, forty-foot cast now! Wait . . . strip . . . strip"? The guides leave clients so unsure of themselves that they think there must be some secret, unattainable knowledge that only the guide possesses.
As author Sheridan Anderson says in _The Curtis Creek Manifesto,_ the objective of fishing is to catch fish, but in the pursuit of the catch you will gain so much more. The higher purpose of practicing a sport such as fly fishing, hunting, or mountain climbing is to affect a spiritual and physical gain. But if the process is compromised, there is no transformation.
Fishing with a fly can be such an incredibly complex and passionate sport that no one can fully master all the different disciplines in one lifetime. Some anglers prefer to limit themselves to only fishing with dry flies, while others specialize in perfecting their casting, fly tying, or even learning the Latin names and life history of all the insects. These can be legitimate endeavors in themselves, and there are untold books written about these subjects. This book is not one of them.
This is a book for the young person who wants to learn but feels intimidated by the complexity, elitism, and expense of the sport. He sees his father who owns multiple thousand-dollar rods and reels, fishes only with guides at five hundred plus dollars a day (plus mandatory tips), and flies all over the world to stay at luxury lodges. And the son thinks, "This is not for me."
It is also for the woman and her daughter who are put off by the image of the testosterone-fueled "rip-some-lips," good-old-boy, bass and trout fisherman who has turned the "contemplative pastime" into a competitive combat sport.
This is also a book for the experienced angler who has all the gadgets and gizmos and discovers he or she wants to replace all that stuff with skill, knowledge, and simplicity. It is for the person who believes that a design or a piece of art or a sporting endeavor is finalized and mastered "not when there is nothing more to add, but when there is nothing more to take away," as Antoine de Saint-Exupéry advocated.
It's for the person who thinks maybe it's time to look at the raked Zen sand garden with its three stones and see if he or she can convey the same powerful, evocative image of space and balance with only two rocks or even one.
Most anglers soon discover simple fly fishing helps preserve our capacity for wonder. It can teach us to see, smell, and feel the miracles of stream life—with the beauty of nature and serenity all around—as we pursue wild fish.
Modern-day Balinese fishermen on the southeast coast of Sanur. _Photo: Willem Sorm_
### The Day I Learned to Kayak
The Gros Ventre River below Slide Lake falls over one hundred feet per mile, and in the spring runoff has few eddies to pull out and rest in. If you bail out of your boat, you can only hope to find it miles downstream where the current slows as it enters the Snake River.
I had just learned to do an Eskimo roll using only my hands and got a wild hair to run the river solo and without a paddle. A kayak paddle is a powerful tool. You can use it to slow down, speed up, or brace to keep from tipping over. And at the last second, you can do a quick sweep or Duffek stroke to avoid a rock or a suck hole.
Without a paddle, I had to sit low in the boat with my hands in the water. Whenever I went over a steep drop, I had to resist the tendency to lean back. I turned by putting the boat on its side and pressing the nose down just like carving with skis. I had to look far ahead to plan my line. It was pointless to fight the current; I had to let the river tell me where to go. That was the day I really learned to kayak.
– Yvon Chouinard
The Gros Ventre River. _Photo: Kevin Wittig_
## THE TENKARA ROD
Many of us of a certain age remember our first fishing pole. We would go to the local sporting goods store and buy a long bamboo pole—what was then called a Calcutta. A line, with a worm or fly on the end, was attached to the tip. For centuries, perhaps even before the time of Christ, this is the way people all over the world learned to fish—and still do.
At eighty-three years old, Arturo Pugno, the master, needs no polarized glasses to spot fish. Sesia River, Italy. _Photo: Mauro Mazzo_
Twenty-five years ago, a Japanese friend gave me a telescoping fiberglass rod with no reel seat. It was a beautiful, precious gift; light, sensitive, and elegant. When I received this rod, I didn't really understand what I was getting, and I stored it on a shelf in my cabin for fifteen years. I have since learned that it is called a tenkara rod, which means "from the heavens," and is used in Japan to fish for yamame, amago, and iwana trout in small mountain streams.
Some years later, I fished the Sesia River in Italy with Mauro Mazzo. He mentioned that the traditional way to fish the Sesia is to use an eleven- to sixteen-foot-long rod with no reel and just a horsehair line tied to the tip. The lines, which are about one or one and a half times the length of the rod, are twisted from the tail of a white stallion, starting with fourteen or sixteen hairs and tapering down to three at the tippet end. A short, nylon tippet is added and one to five soft-hackle flies are tied onto the tippet one foot apart. Casting is done using various overhead, roll, and Spey casts. It's particularly effective in winter with a size 22 purple-body soft hackle for wary and selective grayling. The hackles, made from the very soft feathers of a bird called ciuffolotto, maintain their lifelike action in the river. There are still about twenty practitioners of this technique in Italy, of which ten make their own lines.
The next summer, Mauro and I decided to try the tenkara rod on a willow-lined meadow creek in the Wyoming Range. It was a very windy day in August, and grasshoppers were being blown about, so we put on a muddler and fished it upstream as a hopper and downstream as a sculpin. The thin, heavy horsehair line cut through the wind far better than a floating fly line. Every bend of the creek had a pool, and we moved from pool to pool without having to reel in line and let it out again. We caught fish in every pool: nice cutthroats up to sixteen inches.
Daniela Prestifilippo catches her first fish ever after a few minutes of tenkara lessons with Yvon Chouinard. Cottonwood Creek, Wyoming. _Photo: Mauro Mazzo_
Mauro's girlfriend, Daniela, who had never fished a day in her life, picked up the rod and in less than five minutes landed the biggest cutthroat of the day. "Easy," she said. "What's the big deal?"
I think this centuries-old technique was perfect for fly fishing that day and more effective than anything that has come out of our high-tech fly fishing industry. In fact, this is the same gear and technique traditionally used by French and Japanese market fishers. When your living depends on supplying restaurants and hotels with trout, you're not going to waste money on seven-hundred-dollar rods, five-hundred-dollar reels, and three-dollar flies.
Learning to fish with a tenkara rod and a short line is the easiest way to learn to fly-fish. It can be taught to an eight-year-old in minutes. Put her on a riffle with an old-fashioned soft-hackle fly, and she can outfish dad on the first day. Catching fish right from the start is the way to catch an angler for life. And dad can become a better fisher by applying the lessons learned from this ultimately simple method to fishing with his regular gear.
Other than learning to fish where the fish are, the most important thing an angler can do to catch fish is to control the action of the fly. It's more important than the color or size of the fly, the time of day, or getting off a perfect cast. Why is a worm so effective? Because it is always moving. Why have soft baits replaced hard spoons and lures? Because they bend and flex in enticing ways.
Too many fly fishers are so fixated on launching long casts that they end up putting the fly beyond where the fish are. And with those long casts, they cannot control what the fly is doing.
This is especially true of steelheaders and their long Spey rods: Most steelhead are close to the bank, not in the middle of the river. I once watched the great steelheader Harry Lemire fish behind a friend of mine. Lemire was walking the bank, making short casts with a floating line and making his signature fly, the Steelhead Caddis, wake, swim, twitch, and flit around on the surface. He was hooking fish just behind my friend who was wading deep, casting long, and not catching anything. Control is everything.
After a five-minute lesson, nine-year-old Lola proceeded to land seventeen rainbows in a day and a half. Fall River, Idaho. _Photo: Jeremy Koreski_
In this book, we use the simplest of all fly fishing methods, a pole with a line on the end, to illustrate how to control the fly without the complexity of modern equipment getting in the way. Getting the fly to the depth where the fish are feeding and imparting motion to the fly is critical. This is where the tenkara excels. You will catch fish using simple methods and knowledge, in an elegant and artful way. This is fly fishing at its most basic, and like kayaking without a paddle, it brings you closer to the simple truths of the sport. When you pick up (or go back to) a rod and reel, you will be a more complete angler. I believe you will also enjoy your time on the water more and, to Mr. Anderson's point, catch more fish.
Sheridan and I had a contest one day to see who could catch the biggest fish. I won with a twenty-three-inch brown trout. This drawing from him was my "award." – Yvon Chouinard _Drawing by Sheridan Anderson_
Westslope cutthroat and bull trout. Flathead River, Montana. _Photo: Patrick Clayton_
## _"IT DOES HELP TO KNOW THE USUAL BEHAVIOR OF YOUR QUARRY."_
—The O'Dell Creek Gang
## Chapter 1: Trout and Their Food
Trout's needs are simple: easily accessible food, cold clear water, and shelter from predators like otters, mink, humans, and many fish-eating birds like ospreys, herons, and pelicans. The various species of trout act somewhat differently from each other. Not only do they occupy different parts of a river, they are active at different times of the day, eat different foods, spawn in different places, and are fooled into taking different artificial flies fished with different techniques. We speak in generalizations here, but it does help to know the usual behavior of your quarry.
Rainbow trout live in the fastest currents, cutthroat trout in quiet eddies behind snags, brook trout in the pools at the inner bends of streams. Marble trout, bull trout, and other char are in the deepest pools. Small brown trout will be in slightly slower water than rainbows, and big brown trout will be in even slower water, tucked into cutbanks or in front of or behind boulders where they can lie in wait to ambush baitfish. Lake trout will cruise the lake edges right after ice-out or in the late fall. At other times, they live in the deep bottom of lakes.
These places are their normal lies where they feel at home and secure. They move to other parts of the river in floodwater, low water, when the water is warm or very cold, when there is a hatch, when they are resting or sleeping, in bright light, low light, and at night.
In high water, fish migrate to the banks to stay out of the fast currents and to take advantage of the worms, beetles, ants, and other terrestrials being swept into the river by the floodwaters. If the water is very dirty, they position themselves right next to the bank, a rock, or the bottom in order to keep their equilibrium. In warm water, they move to the deeper cooler waters or place themselves near a cool spring or tributary. Alternately, they could be under the fastest turbulent cascades where there is more dissolved oxygen.
After hatching, young trout (parr) dart back and forth feeding on plankton, diatoms, and algae. As they become larger, they transition to feeding on insects, which they require for growth. At this stage, when they are less than six to eight inches long, most species of river trout occupy similar territories in the river and display similar behaviors. When they become larger, they begin to occupy their preferred lies in the stream.
When a hatch begins, the trout move from their secure resting lies into more productive water. It can be shallow riffles where the nymphs are emerging or next to foam lines that concentrate and transport food. They jockey around to be first in line without getting their tails nipped by a big boy. The larger, more aggressive fish have the best feeding stations; ideally, these will also be their more or less permanent lies.
Larger trout, sixteen inches and up, begin to exhibit even more different behaviors according to their species. These large fish need to eat more than tiny mayflies. They need the calories afforded by salmonfly nymphs, grasshoppers, crustaceans, baitfish, mice, swallows . . . ducklings. Brown trout transition to feeding on this larger food base sooner than rainbows.
## THE QUARRY
#### BROWN TROUT
Big brown trout, unlike humans, learn from their past and have a reputation for being smarter than other trout. They are shy, selective, wary, and not easily fooled. Browns like undercuts and overhanging banks and brush, boulders, rock cliffs, and deep pools. They are very hard fighters and often jump when hooked, then take off on bulldogged runs into the depths of the river or lake.
They are most active in low light or at night, when they can leave their secure lies to maraud around the shallows and pools looking for smaller fish. In the middle of a bright day, they become very picky eaters. A dry fly must be perfectly presented and drifted with no drag, and it might take a good emergence of mayflies, caddis, or stoneflies to bring them to the surface.
#### RAINBOW TROUT
Rainbow trout are the acrobats of the trout world; when hooked they take to the sky. There are several species of rainbows that occupy a wide range of habitat from large, roaring mountain rivers to tiny spring creeks. Rainbow trout are some of the hardest-fighting fish known to freshwater anglers. If rainbow and brown trout are present in the same river, anglers often catch more rainbows because they occupy water more easily fished: riffles, pockets, and pools.
#### CUTTHROAT TROUT
Cutthroat trout display behavior more like brook trout than their rainbow trout cousins. They are most often found in quiet current tongues along undercut banks, under rock ledges and deadfalls, and in slow, deep pools.
The cutthroat is often easily fooled, and its curiosity about big, bushy flies with bright colors and tinsel is legendary. They like to chase their prey and are suckers for large, rubber-legged dry flies slapped on the water and twitched. They have a reputation for being easy, but during a pale morning dun emergence they can be the most selective feeders, focusing on only one stage of the mayfly.
Cutthroat trout fight stubborn and hard along the bottom of the river or stream. These fish need cold water and prefer solitude, making the best fishing for them a chore, but worth every bit of the effort.
#### GOLDEN TROUT
The most beautiful of all trout, the golden trout is more than just golden in color; it also has various shades of lavender, pink, blue, yellow, and red.
They live above 10,000 feet in the streams and lakes of California, Alberta, Montana, and Wyoming. In the high-altitude lakes, they have a reputation of being picky eaters, probably because they feed mostly on tiny chironomids (midges).
A marble trout caught on a nymph using monofilament instead of a fly line. Avisio River, Italy. _Photo: Mauro Mazzo_
#### MARBLE TROUT
Marble trout (and bull trout) are baitfish eaters. The marble trout is the biggest of the trout species and can pass the fifty-pound mark. They live only in Europe on the rivers of the Adriatic Basin. Marble trout are considered an endangered species, and environmental groups in both Italy and Slovenia are making strong efforts to restore their population. They are a very wary fish, and their preferred habitat is deep and fast water. Marble trout feed mainly at night; dawn is the best time to fish for them. Streamers are the first choice, followed by a nymph and a dry fly.
#### BROOK TROUT
The brook trout is a species of very cold waters in the high country, or mostly northern climes. It is a foolish fish and naïve compared to the brown and rainbow trout. It is a stubborn and strong fighter, and one of the most beautiful fish in the world. Brookies occupy tiny brooks, streams, beaver ponds, and lakes. It has been successfully introduced into the Patagonia region of South America where it occupies large rivers and bocas, and may reach several pounds.
Brook trout are easy to fool, and are found in places on most rivers and streams that are easily reached: big pools, soft riffles, along undercuts, and under overhanging trees. Mostly though, they are found in soft, deep water, tend to feed lower down on the water column, and are less likely to take surface flies.
#### GRAYLING
Grayling like water with medium to slow current, a gravel bottom, and a depth from one to four feet. They like clean water, but they also like feeding on gray water drainage, as experienced by Yvon when he fished for them in Italy.
Grayling live in schools; when you find one, persist in your efforts because there will be others around. They are mainly bottom feeders and are the main quarry for the Czech nymph technique. But when a hatch starts, they immediately switch to insects on the surface. When fishing them with the dry fly, try to avoid drag as much as possible; graylings are very spooky fish. Fishing them with nymphs is much easier because they are not wary of human presence and you can get quite close. Fish them on a short line to have greater control of your fly.
### The Minestrone Hatch
During the 1960s, I spent summers climbing in the high Alps of France and Switzerland. When the weather turned foul, which it often did, we headed south for the sunnier Dolomites of Italy. If the weather followed us, we escaped to the topless beaches and limestone cliffs between Marseille and Cannes.
Driving through Italy, I never dreamed there could be fish in the rivers that tumble from the Alps. How could there be? These rivers were all dammed, diverted, channelized, polluted, and mined for gravel. I thought trout fishing in Italy must have suffered the same fate as hunting. Nearly every Italian male owns a shotgun but is reduced to shooting songbirds on their migration to and from Africa. They are plucked, impaled on a stick, drizzled with olive oil, and end up as uccelli carbon.
Five years ago, I discovered I was wrong about the fishing. The streams of northern Italy flow through limestone, creating an alkaline environment (think San Pellegrino mineral water) that supports abundant insect life. I've found the fishing so good in Piemonte and Lombardia that several times I've had grand slams of rainbows, browns, grayling, marble trout, and marble brown hybrids. Now when I pass through Europe, I include a trip to the pre-Alps of Italy with my friend and rabid fisher Mauro Mazzo. The search is for trout, old Barolos, and the fabulous foods of northern Italy.
Driving through the Valtellina, the villages have sprawled so much that it's tough to tell where one ends and the next begins. One time, stopping to fish the Adda River downstream of the village of Chiuro, I was filled with doubt. Traffic careened along several major highways bordering the river, and houses, hotels, and restaurants lined the banks. Crowds of tourists filled the streets. But we were catching fish—fat, red-finned grayling up to two and a half pounds. I thought the fishing was great, but Mauro promised that about 2 p.m. the fishing would get even better. We moved up to a long pool with a sewer pipe coming in from the village. Promptly at two, gray water poured from the pipe, dishwater from lunches of bresaola, pizzoccheri, cheese dumplings, and polenta. A veritable soup of leftovers.
Tiny red worms crawled out of the bottom muck to feed on the minestrone, and the grayling went nuts feeding on the worms. Mauro gave me a small fly tied with only thick red thread wrapped around the shank. The world's simplest fly?
My tenkara rod stayed bent for the next two hours, until all the dishes were washed and it was time to recharge with an espresso.
—Yvon Chouinard First appeared in _The Flyfish Journal (issue #4.2)_
The Hotel Giardini pool on the Sesia River, Piode, Italy. _Photo: Mauro Mazzo_ A nice grayling caught below the "feeding tube." Adda River, Italy. _Photo: Mauro Mazzo_
## THE FOOD
## _"OTHER THAN KNOWING WHERE THE FISH ARE, IT IS MOST IMPORTANT TO KNOW WHAT THEY ARE LIKELY TO BE EATING."_
—The O'Dell Creek Gang
Emerging blue-winged olives (a type of mayfly) land on a reel on the Henry's Fork of the Snake, Idaho. _Photo: John Juracek_
#### MAYFLIES
Mayflies are perhaps the best-known insects to anglers and are very important in the diet of trout. Mayflies spend all but a few days of their lives underwater and are available to fish all year long.
Emerging mayfly nymphs reach the surface in several ways. Some escape their nymphal skeleton at the bottom of the river or in the water column, with their wings trapping a gas bubble to buoy them to the surface. Others form gas bubbles inside their nymphal shuck that brings them to the surface; still other species migrate to the shoreline to hatch. As a mayfly hatches, it moves and shakes its nymphal shuck in an attempt to escape, causing the shuck edges to shimmer.
The freshly emerged insects are called duns, and even though trout take far more nymph mayflies during the year, there is nothing more visible and dramatic than a trout feeding on duns on the surface.
A day or two later, the insects return to the water to mate and reproduce. They molt and shed their dun skins, becoming sexually mature, and are now called mayfly spinners. Spinners return to the water and lay their eggs, then die on the surface providing one last period when trout can feast on them.
When fishing mayfly hatches, first learn what stage of this insect the trout are feeding on. If mayfly duns are on the water and fish are rising everywhere, first watch the naturals float over rising trout. If trout let the duns pass, the fish are most likely rising to floating nymphs and emergers. If you see trout tails, it is likely nymphs are being taken under the surface. If you see noses, heads, and backs breaking the surface or fish taking the duns as they drift over, the trout are obviously taking duns. If you note casual, unhurried rises with a slow spreading rise ring, then the trout are likely rising to mayfly spinners.
The stage when nymphs hatch into adults, in and under the surface of the water, is when the wet fly works its magic. Fishing a wet fly imitation on the swing—across and downstream—is a deadly technique when fishing for trout taking emerging mayflies.
The most common imitations of mayfly nymphs are Pheasant Tail, Hare's Ear, and March Brown Nymphs. These flies are also excellent searching patterns. If during a hatch you see fish tailing, try these patterns unweighted and fished just under the surface.
Mayfly nymphs are usually fished dead drifted and without motion. A few still-water species are good swimmers, and anglers usually fish imitations with a short strip retrieve.
The best dry fly mayfly emergences are those in which insects are clumsily escaping their nymphal exoskeletons and riding the surface with their nymphal shucks attached. These mayflies trigger good rises of trout because these insects are impaired—trapped in their shucks—and cannot easily escape.
Trout rising to mayfly spinners always rise much more casually and will take spinners in thin water and quiet pools nearer the shoreline. These rises will be quiet takes, merely sips.
#### CADDISFLIES
Caddisflies have a three-stage life cycle: larva, pupa, and adult. The transformation from larva to pupa is much like a moth caterpillar spinning a cocoon and later hatching into an adult moth.
Caddis emerge when a gaseous bubble forms inside their pupal skin causing them to shoot from the bottom of the river, lake, or stream toward the surface. They also experience emergence problems as they emerge subsurface and often become entangled in their pupal shuck. Caddis mostly emerge in the afternoon or evening, so by getting close to the rising fish, you can keep track of your cast and the fly as light conditions fail.
Several clues indicate caddis hatches. Early in the hatch, small trout will be seen leaping out of the water as they chase emergers to the surface and their high-speed chases carry them out of the water. There will be no insects on the water since the adults quickly fly off or scuttle to the shoreline grasses. When larger trout rise to caddis emerging in faster currents, you will see bulges or splashes. In slower flows, there will be quiet dimples, slow, porpoise-like rolls, and tails barely breaking the surface.
Caddis pupae are most available to trout when they hatch from pupae to adults. Most swim toward the surface and emerge there, while other species of caddis drift some distance with the currents. In both instances, trout easily capture them, and it is during this time fishing a wet fly or soft hackle on the downstream and across swing is deadly.
Caddis nymph imitations offer a choice between larvae, nymphs, and pupae. Some species of caddis are important to anglers fished as larvae. Larvae are not swimmers, so the pattern is best fished dead drifted near the bottom of the river or stream.
For the larvae, an excellent searching pattern is the Peeping Caddis, which very often is a favorite point fly and deadly for most of the season.
For the nymph imitation, there is the whole family of Czech nymphs patterns, tied on a grub hook weighted on the back to avoid snagging on the bottom, to choose from. They are excellent searching patterns and can be fished any time of the day, in medium to fast water.
At the beginning of a hatch, trout feed on pupae on the bottom, and one of the best flies is the LaFontaine Bead Head Caddis Pupa, fished close to the bottom. As the hatch goes on and pupae come to the surface, it is worth trying to cast an unweighted pupa imitation, such as the LaFontaine Emergent Sparkle Pupa, downstream and let it swing and add a twitch once in a while.
A few caddis species offer good fishing opportunities when females lay their eggs. Look for caddis bouncing on the water, trying to break the surface tension, or for spent caddis on the surface of the water, on boulders, or on your waders. Female caddis might use these as well as overhanging brush and grasses to access the water to lay their eggs.
Rarely will rising trout be selective when taking emerging caddis. But since caddis emergences can be heavy at times, it might seem that your fly can't compete with all the naturals on the water. Here, short, quick, and accurate presentations increase the chances your fly will be taken. A favorite method for taking big trout rising to emerging caddis is to present the fly just upstream of the rising trout, and as the fly approaches the fish give it a jerk with a short pull, causing the fly to be pulled under and then pop up again in front of the rising trout.
#### STONEFLIES AND SALMONFLIES
A stonefly's life cycle consists of three stages: egg, nymph, and adult. The majority of a stonefly's life is spent in the nymphal stage (from one to four years); as adults they only live for several weeks. Several days prior to transitioning into adults, the nymphs migrate toward the shoreline to leave the water and emerge.
Stonefly nymphs can be very important to anglers as most species crawl out of the water to emerge. Some stonefly nymphs are quite big, up to one and a half to two inches, and the most common place to fish them are fast-flowing streams. Imitations are very often heavily weighted, and one of the most effective ways to fish them is to cast the heavy fly no more than fifteen feet upstream, let it sink, and follow the drift, first lifting and then lowering the rod tip.
Prime dry fly fishing occurs when female stoneflies return to the water to lay their eggs. Egg laying often occurs in the afternoon and evening hours. There is no doubt when trout are rising to adult stones. Aggressive, swirling, splashy rises can be seen as trout hurl themselves into overhanging brush to chase the adults.
One thing you should keep in mind when fishing dry fly adult stoneflies is flexibility. If a dead-drifted presentation fails, try giving your fly some movement, or pull the dry imitation under and let it pop back up to the surface just upstream of the trout.
#### MIDGES
Midges are any of a number of small insects. And because midges emerge all year, these tiny insects should be at the top of your list. Midges emerge in the surface film and are susceptible to emergence difficulties, resulting in impaired and crippled adults caught in their shucks and trapped in the surface film. Rises to the naturals are casual and confident as the trout recognize that the insects cannot escape the surface.
The strongest clue to a midge emergence is trout rising when adult midges are skittering on the surface or clustered along the shoreline and no other insects are present.
Trout must expend as little energy as possible when taking tiny insects like midges; they simply cannot afford to use up more calories feeding than what they ingest. Because of this, trout hold just below the surface when taking midges. Here, they will be extremely sensitive to wading waves, and if spooked, they will take longer to resume feeding than if they were feeding on caddis or mayflies.
On rivers, fish midge larvae imitations—the starling and red soft hackle most likely imitates emerging midges—dead drifted in the surface film. When fishing them in lakes or calm-flowing rivers and streams, slowly strip the pupa across the paths of cruising trout. When midge pupae float in the surface film prior to emerging, they swim away from an approaching trout.
A tenkara rod is ideal for winter midging. With no guides or reel to freeze up and fish that do not fight as hard as they do in summer, it is perfect for presenting a fixed-length, pinpoint-accurate cast every time. When we have only an hour or two of daily fishing and each cast can make the difference, tenkara allows the most efficient presentation, as well as hooking, landing, and releasing each trout quickly.
#### DAMSELFLIES AND DRAGONFLIES
Both damselflies and dragonflies are important to fish and fishers. They thrive in almost all still waters, from large lakes to tiny ponds. Their nymphs are far more important than adults to anglers as they are available all year long in still waters.
Damselfly and dragonfly nymphs crawl out on shore to emerge and expose themselves to trout as they move from their weeded homes to the shoreline to hatch. The nymphs are ineffective swimmers and very vulnerable during these migrations, and trout prey ruthlessly on them. If you see fish quickly dart in knifelike moves at the surface or along the shoreline, they most likely are coming to damselfly nymphs migrating to shore to emerge.
Keep in mind that the nymphs of both insects always migrate in a line perpendicular to the shoreline so imitations must be fished this way, the way trout are accustomed to seeing the naturals. The imitation to use is made with a single marabou feather, in dark green or brown, wrapped around the hook shank to form the tail and the body of the fly. Fish it with a long leader, a few inches under the surface, and retrieve it very slowly.
When trout rise to damselflies, you often see them launch out of the water after the fluttering adults. Adult damsels are available to trout only during mating times or when afternoon winds kick up. When anglers see trout leaping out of the water to chase damsels, this is the clue to try a dry fly imitation.
If the fish ignores your offering, give it a twitch or a short pull on the next presentation. Try twitching or skittering the fly or even pulling it under and letting it pop back up to the surface to sit for a minute.
#### TERRESTRIALS
Terrestrials is a term that refers to ants, bees, beetles, grasshoppers, and the like. There are no hatches and no nymphs or other stages of aquatic life. Most terrestrial fishing does not involve concentrations of insects as you find when fishing emergences of mayflies or caddis. Sunny, warm, and windy afternoons are always best for grasshoppers, crickets, and mating swarms of flying ants. Beetles and ants also prefer warm, sunny days, but we've had great success using them all year long, even in winter.
Trout rising to flying ants, moths, crickets, bees, and grasshoppers will be noisy and aggressive, whereas rises to beetles and nonwinged ants are subtle, deliberate, and slow.
Flying ant swarms always bring tremendous rises of trout. In late summer, anglers should always be prepared to fish a mating swarm of ants. All trout relish ants and will rise aggressively to them. You will see big trout rising, taking several naturals quickly, like gluttons, before moving on and coming up a few feet beyond.
Terrestrial fishing may require doing whatever it takes—slapping the fly on the water or skittering or waking it on a tight line using drag to move the pattern. Terrestrial fishing does not usually involve heavy concentrations of insects, so anglers must cover more water in search of patrolling trout or cast to undercuts and cover, like overhangs. It is important to remember that trout move distances in search of terrestrials and might be in water where you might not normally expect them to be during other insect activity. Be aware of the water to the rear too.
#### CRUSTACEANS
Crustaceans include crayfish, scuds, and sow bugs, with the most important among them for the fly angler being scuds. Scuds are the freshwater equivalent of shrimp. They live in any water that has good weed growth and vary in size and color. But like all shrimp, they contribute to the pink-colored flesh of the trout or salmon that feed on them.
If the trout in a particular lake are noted for their pink flesh, that's a good indication of the presence of scuds. If you pull up a clump of weeds, you will probably find lots of crawling and snapping scuds.
They are an important trout food and can easily be imitated by a simple pattern in an olive or tannish pink color. Fish the imitation by letting the weighted fly sink and then bringing it up with small, slow strips.
#### BAITFISH
Baitfish is a term that includes all the types of fish that are eaten by other fish. These include various kinds of minnows, sculpins, whitefish, suckers, and trout fry and parr. Trout are predators and will even eat the eggs and young of their own species. The largest trout are usually caught with streamers that imitate these baitfish.
#### LEECHES, EELS, AND LAMPREYS
If we had only one fly to fish with worldwide for trout, salmon, and bass—and even some saltwater fish—it would probably be the olive and black Wooly Bugger. God knows what it imitates, but the way it is normally fished, with slow undulating strips, results in it probably looking like a leech or eel.
Leeches come in a range of colors, including shades of brown, olive, tan, and gray. They swim by elongating and contracting their bodies in a smooth up and down motion. Wooly Buggers are usually weighted at the head to imitate that motion. Wooly Buggers can also be fished very effectively by casting one upstream and letting it dead drift in the current.
MAYFLY LIFECYCLE
CADDISFLY LIFECYCLE
MIDGE LIFECYCLE
## APPROPRIATE TECHNIQUES FOR VARIOUS STAGES OF INSECTS
| STAGE | TECHNIQUE
---|---|---
MAYFLIES | nymph
emergers
duns
spinner | nymphing
wet, crippled dry, and dry flies
dry flies
dry flies
STONEFLIES | nymph
adult | nymphing
dry flies and soft hackles
CADDISFLIES | larva
pupa
egg-laying adult | nymphing
nymphing, wet and dry flies
dry flies
DAMSELFLIES/DRAGONFLIES | nymph
adult | nymphing
dry fly
TERRESTRIALS | all | dry fly
SCUDS | all | nymphing
BAITFISH AND LEECHES | all | streamers and leech imitations
Yvon Chouinard executes a circle cast. Fall River, Idaho. _Photo: Jeremy Koreski_
## _"I TRY TO LOSE THE GUIDE WHENEVER I CAN."_
—Yvon Chouinard
## Chapter 2: Fly Fishing with Wet Flies and Streamers
## YVON CHOUINARD
I got hooked on fishing at six years of age when my older brother Jeff took me to the polluted (still is) Androscoggin River near our home in Lisbon, Maine. Jeff caught a ten-inch pickerel, secretly put it on my line, and made believe I caught it.
When I was seventeen, climbing in the Teton Mountains of Wyoming, I was watching the mountain guide and excellent dry fly fisher, Glenn Exum, teaching his son Eddie to fly cast. When he saw me watching, he yelled, "Come over here son," and he gave me my first lesson in casting. That was the end of spin fishing with Super Dupers for me.
I've been a serial specialist in every sport I've done. I throw myself into one aspect of the sport, and when I reach 75 percent fluency, I get bored and go on to the next passion. With fly fishing, I started out with wet flies, at first getting tips from my climbing partner Joe Faint who was a Pennsylvania wet fly fisher. Then I moved on to streamers, graduated on to nymphs, and finally got obsessed with "matching the hatch" on difficult spring creeks with tiny flies.
These days I think I'm better balanced; I try to use the appropriate technique for the conditions. Yet I hardly used a dry fly last season. I fished almost exclusively old-school soft hackles. Fifty percent of the time that I fish for trout, I fish with a tenkara rod. I do it not as a novelty, but as a truly effective way to catch fish.
I also fish the salt, but I am not much interested in chasing fish that weigh more than my new granddaughter. I once landed thirty-seven varieties of fish in Indonesia. I hate fishing from drift boats or flat skiffs, and I try to lose the guide whenever I can.
## FISHING WITH WET FLIES
Wet flies imitate either baitfish, leeches, swimming nymphs, or emerging caddis and mayflies. The crawling or dislodged and drifting nymphs and scuds are covered in the chapter on nymphing. Baitfish and leeches are in the section on streamers.
For catching sheer numbers of fish, the most effective technique imitates nymphs either dead drifting or swimming to the surface. This chapter deals with the nymphs that are emerging—swimming to the surface to hatch as duns and then adults.
A sixteen-inch trout is not going to get many calories from a tiny size 18 mayfly. There is a net gain of calories only if the effort requires less calories burned than is gained through the food. It doesn't pay for a fish to swim up from four feet down to nab a tiny fly on the surface, especially when there is a good chance the fly will have dried its wings and flown off before it gets there.
Trout are masters at putting out the least amount of energy to gather their food. When they are feeding on small insects, they need a large quantity (a hatch) to make it worth their while, and they position themselves so they expend the least amount of energy to take advantage of that hatch.
The surest deal for them is to intercept the drifting nymphs or the swimming nymphs that are going to the surface or are just under the surface as they are breaking out of their shucks. Another easy meal is crippled flies that are unable to fully emerge from their shucks. Dead adult spinner mayflies splayed out on the surface are also an easy meal.
Trout, of course, feed most actively during a hatch but can be enticed to fall for an artificial fly at any time if the fly can be presented with an enticing action close enough to its lie so it only has to move a little and open its mouth.
The technique described here deals with mostly imitating that emerger stage of the hatch. It is one of the oldest techniques of fly fishing but one that has lost popularity to the dry fly, streamer, and nymph. Yet it remains one of the most effective techniques for catching fish during nonhatch periods. The method was very simply described by James Leisenring in his book _The Art of Tying the Wet Fly and Fishing the Flymph._
What a fish sees. _Photo: Matt Stoecker_
I always fish my fly so that it becomes deadly at the point where the trout is most likely to take his food, which is usually at or close to his position in the stream. Since my flies are tied to act lifelike and look lifelike, I fish them so that the efficiency of the qualities is at its highest when it nears and arrives before the trout for his inspection. This is accomplished by allowing a gradual increase in tension caused by the water flowing against the leader, causing the fly to lift from the bottom and rise with the hackles or legs quivering after the manner of the natural fly.
We begin by describing wet fly fishing with a tenkara rod. Not only is it the easiest way to learn to fly fish, but it is possibly the most effective way to catch large numbers of fish.
## TENKARA WET FLY GEAR
#### TENKARA WET FLY RODS
Tenkara rods, now made of carbon fiber and telescoping, are mostly made in Asia. In Japan alone, there are hundreds of models for fishing everything from six-inch smelt to salmon and sea bass.
For trout fishing in Europe, New Zealand, and the Americas, we haven't found an advantage to using a rod longer than eleven and a half feet. The rod should be a bit stouter than the very light and limber rods popular in Japan for fishing very small mountain trout. My favorite is a ten-and-a-half-foot soft-hackle model from Temple Fork Outfitters (www.tforods.com). They also make an eight-and-a-half-foot model for small creeks and an eleven-and-a-half-foot rod for delicate dry fly fishing.
These rods have a two-inch length of braided line glued to the tip called the lillian. Tie a stopper knot in this if there isn't one. To extend the rod, work from the tip toward the butt. Grab the tip near the lilian with your left thumb and forefinger and hold the next section firmly with your right thumb and forefinger. Pull gently until the tip is fully extended and starts to pull the next section through your right hand. Repeat the process with each section until the rod is completely extended. To collapse the rod, work from the butt toward the tip. Start with your right hand near the top of the butt section and your left at the top of the next section of narrower diameter. Push your hands together and repeat until the rod is fully collapsed.
If there isn't a line holder on your tenkara rod, you can easily make one using two pieces of wire bent in a sort of U shape. The easiest way to make these is to use large paper clips and attach them to the rod with rubber bands.
Tie one paper clip on about an inch up from the butt of the handle and another an inch below the top of the first section. You can use string or just rubber bands to hold the wire loops. The fly can be stuck in the cork when walking from spot to spot on the river. I also keep a rubber band on the rod handle to tuck the fly and tippet under.
Rod tip, lilian, and stopper knot
Extending the rod
Tenkara rod with line holder
#### TENKARA WET FLY LINES
Line choice depends on whether you are fishing nymphs, dry flies, or wet flies and streamers. For fishing wet flies and streamers, I prefer to use a light floating line for my ten-and-a-half-foot rod. The floating line casts better in the wind than monofilament or furled lines and can handle heavier streamers. Since the line floats, it's easier to pick up and mend the line to control the speed and direction of the drift. Also having the line float is an asset in controlling the fly so it acts like an emerging nymph. However, even the lightest floating line may be too heavy to cast well on the more delicate tenkara rods.
You may be able to find a specific floating line for the tenkara rod. If you can't, don't worry as the lines are so short they do not need to be tapered. You have several choices. The easiest and cheapest way is to make your lines by cutting off the back end of an old weight-forward trout line, three weight or smaller. Or find a spool of running line that measures between .025 and .030 inches in diameter. Cortland (www.cortlandline.com) makes a forty-foot level line specifically for the Temple Fork rods.
For a ten-and-a-half-foot to eleven-and-a-half-foot rod, use a twenty-foot length for normal wet fly fishing and a twelve-foot length for small creeks or for nymphing. Also cut an eight-foot section to be used as an extender. The eight-and-a-half-foot Temple Fork Outfitters cutthroat rod can handle a .026 inch diameter line with a length of fifteen to twenty feet.
On the butt end of the lines tie a turle knot, leaving a one-inch long tag. Don't overtighten. Hitch the loop over the lillian and snug it down. The tag is for loosening the knot to take the line off the lillian. On the leader end, tie on a small loop (if there isn't one) using a nail knot, or tie a perfection loop.
#### TENKARA WET FLY LEADERS
I prefer to tie my own leaders partly because I don't like to spend four or five dollars for five cents worth of nylon, but also because with a knotted leader you can use the knots to tie on multiple flies. The knots also create friction that helps to pull the line tight in the moving water so you maintain direct control over the fly.
## EIGHT- TO NINE-FOOT TENKARA WET FLY LEADER
This is the leader for swinging wet flies with the floating line. Tie a perfection loop on the butt of the leader, and tie together the sections listed below with a blood knot or surgeons knot. Hitch the leader loop onto the line loop.
•15 in. - .017 (20 lb. test) Maxima Ultragreen nylon
•15 in. - .015 (15 lb. test) Maxima Ultragreen nylon
•15 in. - .013 (12 lb. test) Maxima Ultragreen nylon
•15 in. - .012 (10 lb. test) Maxima Ultragreen nylon
•15 in. - .010 (8 lb. test) Maxima Ultragreen nylon
•24 in. - .007 4X (6.5 lb. test) tippet material
Hilary Hutcheson on the Middle Fork of the Flathead, Montana. _Photo: Lee Cohen_
#### WET FLY KNOTS
Yvon Chouinard searches for the perfect fly. _Photo: Mauro Mazzo_
##### Bhutan Brown Trout: Here Be Caddis
In 1985, I was in Bhutan to climb Ganghan Puensum, then the highest unclimbed mountain on the planet. Our worthless Chinese and Indian military maps put us on the wrong side of the mountain, so we gave up and settled for making first ascents on some unauthorized 20,000-footers. We corrected the flawed maps and planned to tell our sponsors (National Geographic and Rolex) about our corrections. But standing around the campfire one day, we decided to burn our notes instead. There need to be a few places left on this crowded planet where "here be dragons" still defines the unknown regions of maps. Then I went fishing.
I knew that King Jigme Wangchuck was a fly fisher who had some spring creeks to himself, where he avoided wading by casting from atop an elephant. He was also married to two beautiful sisters and loved playing basketball. We watched a game in the capital city of Thimphu one day. The king waited under the basket (kings don't run) until the game came to him. When he scored, both sides cheered. It's good to be king in Bhutan.
Many of the rivers in Bhutan run clear and cold, and brown trout, introduced by the British, thrive there. Being at the same latitude as Miami, the insect life is prodigious. Some of the caddis cases I saw looked like small cigars.
Fishing near a small village one day, I was ignored by the women washing clothes along the bank next to me. Until I landed a pretty big brown. When I released the fish, the women began screaming, pounding me on the back, and indicating with fingers pointed at their mouths and bellies that they wanted to eat that fish. Their religion wouldn't allow them to kill the fish themselves, but if I killed it . . .
On another river, just outside Thimphu, the air reverberated with a deep Ohmmmmm coming from hundreds of chanting monks in the monastery nearby. I wasn't having much luck, so I sat on the bank, taking in the chants and searching my fly box for answers. I looked up to see a tall monk walking toward me. My gut cramped with fear. You are not allowed to fish within a mile of a temple, or monastery, in this strict Buddhist country, so I recognized trouble.
As the monk drew closer, I imagined myself being strung up in a dark dungeon of some sixteenth-century building. When he reached down and grabbed my fly box, I thought maybe I'd get by with just having my gear confiscated. Then he reached into the box, picked out a large gray nymph, and handed it to me. On the first cast, I hooked a fat twelve-inch brown and released it. The monk clapped and laughed from deep in his belly, just like the Dalai Lama.
—Yvon Chouinard
First appeared in _The Drake,_ Spring 2012
Washing day in Bhutan. _Photo: Yvon Chouinard_
## CASTING THE TENKARA ROD
#### THE BELGIAN CAST
The casting techniques are the same as casting a rod and reel, but it is much easier with a tenkara rod because the line is short, the rod is light, and you can keep your noncasting hand in your pocket.
I asked the great fishing icon and caster Lefty Kreh if he could describe how to cast a fly rod in just two sentences. He answered, "Easy, just do the forward cast as if you're throwing a spear. The back cast you throw the line behind you like you're throwing a Frisbee." To do that, you have to stand a bit sideways to the target.
All the rules of normal casting apply. Don't bend the wrist. Keep the rod tilted at a thirty-five degree angle to the vertical on the back cast and ten degrees on the forward cast. Use the core of the body for power like in tennis, throwing a baseball, or kayaking. The line travel makes a small oval in constant tension; there are no abrupt stops. This cast is sometimes called the Belgian cast.
#### THE SNAP C CAST
This is a change-of-direction cast when there is no room behind you to back cast.
Place the rod parallel with the water with the taught line ninety degrees downstream. Draw a big C in the air with the rod tip, starting at the top of the C, and return it to the start position at the bottom of the C. Now the line is in the water, upstream of you.
Raise the tip to a vertical position. Go back slowly with your hand until the fly line is lying in the water close to your legs. Now start a forward cast like a regular overhead cast. Slowly punch it out.
##### THE BOW AND ARROW CAST
This cast is done when there is no room to do any other cast. Use the shorter line that is slightly longer than the rod. Reach out and grab the end of the line with your nonrod hand and then grab the fly with two fingers. With the rod close to your body in front of you, point the rod at the target and pull the end of your line and the fly back to your ear, and let go.
The Belgian Cast
The Snap-C Cast
The Bow and Arrow Cast
## FISHING WET FLIES WITH A TENKARA ROD
Start by tying a size 14 soft-hackle wet fly onto the end of the tippet using a nonslip loop knot (page 39) or a clinch knot.
Straighten your line and leader so there are no kinks or coils. This is important, as you don't want any slack in your system. I use a small piece of bicycle inner tube to do this by running the taught line through a tightly held fold in the inner tube.
Go to a riffle part of the stream where the water is from one-and-half- to three-feet deep with a current that's not too slow or too fast. Cast the line at about a fotry-five-degree angle downstream. As soon as the fly is in the water lift the loose part of your line and place it across from you.
This mending upstream slows down the drift of the fly. Make sure you don't overmend and pull the fly out of the water. By mending upstream, you are trying to avoid the loose line getting caught by the current and swinging your fly across the current at an unnaturally fast speed.
With your rod at about a twenty-degree angle to the water, follow the line with the tip of the rod. As the line tightens, lift the rod tip up to about a thirty-five-degree angle. As soon as the line comes tight, make an occasional twitch with the tip of the rod. It is important that the tip of the rod moves only two or three inches at most, no more.
To do this, hold the rod with your thumb on the top of the handle and your upper arm held straight down in a totally relaxed position (easy on the rotator cuff). The twitch is imparted to the tip by squeezing the bottom fingers of the hand, not by raising the rod.
If you look at your hand while you are doing this, you hardly see any movement at all. Almost everyone who tries to do this twitch overdoes it at first. Here's the rule: If you think you're not moving the fly enough, move it less. The key is to work only the top foot and a half of the rod. The rod itself hardly moves.
What you are trying to do is imitate the emerging and swimming stages of the caddis or mayfly. This is the stage where they are most vulnerable to a trout. As a result of the twitching action, the soft-hackle fly is going up in tiny increments of one to three inches. It is quite different from swinging traditional wet flies across a current.
In the seventeenth century, this subtle action of the tip was considered so important that the poles were made with a different, more flexible, wood, or even ivory, for the last foot or eighteen inches of the rod.
With a good tenkara rod and the proper tip flex, you have such a direct control of the fly that you can make a caddis dry fly hop around on the water. Trout, steelhead, and salmon do not prefer to attack dead-drifted wet flies and nymphs. Just like a house cat or a grizzly—any predator for that matter—they want action. They want the type of action that imitates emergers, diving caddis, swimming nymphs, or wounded minnows. The best way to imitate that type of action—and to trigger a response—is to use a tenkara rod with a delicate tip and a tight, light line.
Most of the time, a fish will take the fly right after a twitch, whether you are using a waking fly for steelhead, a wet fly for salmon, or an egg-laying caddis for trout.
After each cast, take two steps downstream and cast again. Use the tension of the water against your line and fly to load the rod. One back cast and your line is back in the water. Do not false cast unless it is necessary.
When there are obstructions like trees or a cliff behind you, do a roll cast or a Spey-style cast like a circle C or double Spey to change direction and get the line out. Another advantage of the floating line is it is easier to do these casts, especially if there is a wind.
Wet Fly Fishing Technique
#### LANDING A FISH
When you hook a fish on tenkara gear with this tight-line method, the take is often violent. All that stands between you and the prize is the line and that long, flexible rod. For most trout, you keep the tip up and fight the fish using the flex of the rod. Connect with a bigger, hotter fish, though, and you'd better start running. When your only drag system is your feet, wearing good wading boots is critical. In extreme cases, you can always throw your rod in, strip off your clothes and swim after it like Eddy, the fishing goddess in _The River Why._ The trout will swim away downstream, and feeling the pull of the rod gone, the trout will turn back upstream and head for its lie. The rod will swing downstream of the fish and tire it out. It may take a while, but good things come to those who wait. Often, you can grab your rod handle as it travels past, trailing after the fish.
After a fish is ready to come in, raise the rod up until you can grab the line with your free hand and haul it in hand over hand. Sometimes a big fish in heavy water just doesn't allow you to grab the line. In that case, collapse the rod (from the butt section) until you can grab the line.
Most of the time, you won't need a landing net if you fish a barbless hook. When you get the fish within reach, take your forceps and clamp them onto the hook and work it free of the fish. Avoid touching a trout, but if you need to, grab the lower lip with thumb and first finger and release it via the forceps.
Craig Mathews thankful that he didn't have to take a swim. A not-to-be-named creek in Yellowstone country, Montana.
_Photo: Tim Bozorth_
#### ADVANCED TENKARA WET FLY TECHNIQUES
I generally fish the wet fly method using two flies. I consider this an advanced technique because unless you have the casting perfected you will end up with a horribly tangled leader. With two wet flies, and especially casting two weighted nymphs, if you back cast and forward cast with the line in the same plane, you will end up with a mess. It is important that you have the Belgian cast perfected.
The two-fly method not only gives the fish a choice of flies, but the two flies add more drag, thus helping to straighten the line and giving more direct control of the flies. However, the primary advantage of using two flies is that the point fly and the dropper will have different actions.
To tie on one or more dropper flies, leave a six-inch or longer tag on your leader knots. Make sure the tag is the heavier of the two sections that are tied together, and this will keep the mono from wrapping around itself. Tie the dropper fly directly to the tag.
Another option—the best system I've found to keep the dropper out from the leader—is to stiffen the first two and a half inches of the dropper by doubling it. Tie a loop with a double surgeon's knot and then tie another double surgeon's knot about halfway to the end of the loop. Then hitch the loop above the tippet knot. The double nylon of the loop keeps the dropper away from the leader and can be replaced as the leader gets shorter. This is called the speed dropper by some.
A typical two-fly setup consists of a point fly that should be the heavier or bushier of the flies. This is to add further drag to the line. Think of the point fly as being an anchor that helps straighten the line after the cast. A typical point fly would be a size 14 soft hackle tied on a 2X heavy-nymph hook and on 3X or 4X tippet, with a smaller or lighter fly for the dropper on 3X tippet. The point fly can be from three to four feet from the dropper.
Tag method of tying on two flies
Dropper loop method of tying on two flies
You rarely have to use lighter tippet, because you're fishing downstream and the leader is not going over the fish. On spring creeks when the fish are wary and the hatches require small flies, you can drop down on your tippet sizing, but be warned you might get the line tangled, especially if there is a wind.
You fish two flies the same way you fish one: twitching and doing a lift at the end of the drift. Periodically, check your leader to see that you don't have a tangle or wind knot. A wind knot will reduce the strength of your tippet by 50 percent.
If you wish to sink the flies, use a smaller diameter tippet like 5X or 6X and cast farther upstream with slack in the line. If there is fast current, throw a mend upstream to avoid the swing. If there is a slow current between you and the fly, do a downstream mend. When the line is straight downstream, you can twitch the flies and slowly lift the rod up. Don't be in a hurry to cast again. Leave the fly gently swinging on the surface for a few seconds. Think about teasing the fish. You will be surprised by how many times you can induce a take. If you wish to get down really deep, use a tungsten bead head soft hackle for the point fly.
If there are egg-laying caddisflies about, the advantages of a long tenkara rod and multiple flies can really be maximized. Start with a shorter line of twelve to fifteen feet. Extend the distance between the point fly and dropper to four to five feet. Put a Hare's Ear or Pheasant Tail soft hackle on the point, a fly that most resembles the caddis. On the dropper, tie on a dry caddis like an Elk Hair or Stimulator.
Cast upstream, across, or forty-five degrees downstream. At the end of the swing, lift the rod up until the dry caddis comes off the surface a few inches. Make the dry fly hop and skitter on the surface imitating a female caddis trying to break through the surface tension of the water to lay its eggs on the bottom.
The trick to doing these little hops is extending the distance between the point fly and the dropper, and manipulating the last foot of the rod tip. Describing how to do it is like describing how to crack a safe. Just practice and you will figure it out.
You will know when you are properly fishing two flies. You will be hooking fish almost equally between the point and the dropper.
Things get really interesting when you hook two fish at once, which happens more frequently than you might think. For some reason, doubles are usually a brown and a rainbow. Browns are Republicans and rainbows are Democrats, and they never pull together. If they did, you would have a rodeo on your hands.
Hopping a dry fly on the surface using an anchor fly
##### A Quick Study
I took a friend who had never fished before to a stream in Yellowstone where there were lots of aggressive pre-spawning browns throughout the riffles. I gave him my tenkara and a size 8 Shakey Beeley soft hackle. After a five-minute casting, twitching, and landing lesson, I left him alone. Since I had a regular rod, I fished behind him throwing long casts, covering a lot more water than he could with his twenty-foot line. At the end of the day, he caught more fish than I did, including a twenty-four-inch brown that slipped the hook right at his feet.
—Yvon Chouinard
A Madison River brown trout dresses in its autumn spawning colors. Wyoming. _Photo: John Juracek_
#### MAKING THE LINE LONGER OR SHORTER
Some tenkara rods made for larger US rivers are made stouter than the typical Japanese rods and they can handle lines up to thirty feet. To make a twenty-eight-foot line put a turle knot on one end of your eight-foot extender (that you cut earlier from the fly line) and a stopper knot on the other. Hitch the extender onto the lillian then attach the twenty-foot line above the stopper knot of the extender.
In a pinch you can shorten the line by tying a sheepshank knot. I first tried this on a small mountain stream in Montana. The fish were all concentrated in deep holes under log jams and cut banks and wouldn't come up for soft hackles or dries. I had on a twenty-foot line, which was too long for this creek and too long for short-line nymphing. I shortened the line to ten feet—so only the leader was in the water— using a modification of a sheepshank knot. I put on a heavy bead head nymph and proceeded to catch one to three rainbows from each pool.
Modified Sheepshank Knot
Line Sag
## WET FLY FISHING WITH ROD AND REEL
You can somewhat adapt the tenkara wet fly method to a regular fly rod, but only if you use a long slower-action rod. I recommend a ten-foot two-weight rod and underline it with one-weight line to avoid line sag. You cannot impart action to the fly if there is a sag or slack in the line, or if the line is being blown about by the wind. If you try to do the twitch with a fast action rod you will invariably over-twitch as the whole rod will rise up. Keep your casts short, no more than twenty feet, so you can better control the flies.
Press the line under your finger and just make believe you don't have a reel. Unless you hook a big fish, don't use the reel, just haul the fish in like you would on a tenkara rod.
In this kind of water there can be fish holding almost everywhere. Eliza Clayton fishes for western cutthroat on the North Fork of the Blackfoot River, Montana. _Photo: Noah Clayton_
#### WET FLIES
I have replaced all my traditional winged wet flies with soft-hackle flies. Since there is no top or bottom to the fly, there is never a worry that the fly is swinging on its side or upside down. I'll use a winged wet fly only if it is meant to imitate small baitfish rather than an insect.
Properly tied soft-hackle flies are almost impossible to find in most fly shops, but they are simple to tie, and I strongly recommend that you learn to tie your own.
I tie my flies with one important difference from traditional soft hackles: I tie most of them with a thorax made of Hare's Ear Ice Dubbin. This is hare's ear fur plus a bit of synthetic glitter. This has two advantages. The thorax, which is tied after the hackle, keeps the hackles open so they don't lie against the body, and the sparkle in the dubbing when wet, looks like the air bubble of an emerging nymph. It's similar to what a gold bead does to a nymph pattern.
#### SOME ESSENTIAL WET FLY PATTERNS
##### Partridge and Pheasant Tail
In smaller sizes, this fly imitates the nymph or emerger stage of almost every mayfly; in larger sizes, it serves to imitate caddisflies or stoneflies. If I were to limit myself to only one soft-hackle pattern, it would be this one in size 14.
Hook: #12 to #18, Dai-Riki #075 nymph, 2X strong, 1X short
Thread: 8/0 brown
Tail: pheasant tail or brown Zelon on smaller sizes to imitate the shuck
Body: pheasant tail
Ribbing: extra-small copper wire
Thorax: Hare's Ice Dubbin peacock blend. To imitate a pale morning dun emerger, I use the lighter color Hare's Ice Dubbin hare's ear blend.
Hackle: partridge
##### Mormon Girl
This pattern is a good imitation of the yellow sally (Mormon girl) stonefly. You can tie other body colors using this recipe, including green, orange, and royal blue or purple.
Hook: #14 to #18, standard wet fly or dry fly
Thread: 8/0 yellow
Body: yellow 3/0 thread or floss, double layer; red tag optional
Thorax: Hare's Ice Dubbin hare's ear blend
Hackle: partridge
##### Partridge and Peacock
This is a good dark caddis imitation.
Hook: #12 to #16, nymph or dry fly
Thread: 8/0 brown
Tail: scarlet red hackle fibers or marabou clump
Body: peacock herl
Ribbing: extra-small copper wire
Thorax: Hare's Ice Dubbin peacock blend
Hackle: dark partridge or grizzly
##### Starling and Red
Soft-hackle flies can be very effectively fished during a midge hatch, as the pupa is a very active swimmer. Fish these with a tiny twitch to trigger a take. You can tie other colors using this recipe, including starling and purple and starling and rust.
Hook: #20 to #24, wet fly or dry fly
Thread: 8/0 black
Body: 3/0 red thread, wound double
Hackle: starling
##### Shakey Beeley
This is one of the best attracter patterns. Tied in the larger sizes, it is particularly effective on pre-spawning browns.
Hook: #10 to #14, Tiemco TMC 2312
Thread: 6/0 coffee brown Danville
Tail: mallard flank-dyed wood duck or Hungarian partridge fibers
Body: pale yellow rabbit Zelon dubbing or tan Super Fine
Ribbing: brown Pearsall's silk thread
Collar: orange-dyed ostrich herl
Wing: Hungarian partridge with a gold or yellow Krystal Flash underwing
Yellow is a good choice for streamer color when targeting autumn brown trout. Madison River, Montana.
_Photo: John Juracek_
##### FISHING STREAMERS WITH A TENKARA ROD
When trout reach a certain size they change from eating small insects to eating large insects, like big stoneflies and grasshoppers, and leeches. Larger trout, four pounds and up—especially brown trout, lake trout, and char—want a square meal, and that means crustaceans, minnows, and even mice and lemmings. If you want to catch very large trout you should fish with streamers.
The tenkara rod can be used for fishing with flies that imitate baitfish, but only if the flies are small like some traditional wet flies or if they are unweighted, like muddler minnows. The tenkara is not so useful for casting large heavy flies. If you do get a take its difficult to set the hook because of the flexibility of the rod. Another disadvantage is that you cannot strip in line to give action to the fly. You will have to use other means that I will describe shortly.
You will need to use small lightly weighted streamers made of soft materials like marabou feathers or rabbit fur. The current will make these flies pulse and dart like minnows. Because of the difficulty of setting the hook with tenkara, tie your flies with smaller very sharp hooks. Don't use an eight-and-a-half- or eleven-and-a-half-foot rod with streamers. Also shorten your leader to six or seven feet total length and with a 1X or 2X tippet.
A floating line will cast a heavier fly more easily than mono. Tie on a streamer using your favorite knot: clinch, nonslip loop, or turle. Cast the fly ninety degrees across the stream and mend the line downstream so the current will catch the floating line and accelerate the drift. Lead the fly with the rod and give an occasional twitch with the tip of the rod. What you are trying to do is offer a side view of an injured minnow to the fish. This is much more enticing than an end view.
Another way uses surprise to elicit a quick response. Let's say you have a large brown trout hiding under a bank on a meadow stream. Cast a large fly, like a muddler minnow, as close to the bank as possible, and slam the fly down hard and immediately pull it away with long twitches. Trout will follow the fly, and you may have to back up to extend the retrieve. If a large, smart trout gets too long a look at a large artificial fly he usually won't take. You want to elicit an instant reaction. What do you think would happen if you suddenly surprised a predator like a grizzly bear? They love it when you run.
The technique of fishing streamer flies with a regular rod is not much different. You do have the advantage of being able to cast larger and heavier flies and use sinking lines to get down deeper where some fish hold. Also you can hand strip line in at varying speeds giving better action to the fly.
You want the fish to see the profile of your fly, not its back
#### RECOMMENDED STREAMERS
Rather than an exact imitation, streamers should concentrate on mobility, motion, and sometimes a little flash.
With the slow action of light trout and tenkara rods, it's difficult to get penetration in the hard mouths of large fish. It helps to use chemically sharpened hooks with small bends. Use the smallest-sized hooks in the longer lengths like 3X or 4X long. Don't go too long as the shank acts as a lever to pry the hook out.
##### Muddler Minnows
This imitation can be fished dry as a hopper or wet to imitate sculpins. It's even a good salmon or steelhead fly.
Hook: #8 to #12, Gamakatsu S11-4L2H or Dai-Riki #700
Thread: 3/0 black
Tail: mottled turkey quill, lacquered
Body: gold diamond braid
Underwing: gray squirrel tail
Wing: mottled turkey quill
Collar: natural deer
Head: natural deer
##### Wooly Buggers
This fly can imitate eels, minnows, and damselfly nymphs. The version below is a classic tie, but many variations are available in any fly shop.
Hook: #8 to #12, Gamakatsu S11-4L2H
Thread: 3/0 black
Tail: black marabou
Weight: nontoxic wire wrapped around the front third of the shank, or use a bead head
Body: olive Krystal Flash chenille
Hackle: black palmered
##### Wool-Head Sculpin
Sculpin are a favorite food for large trout. They are bottom feeders, necessitating a weighted fly. Using wool instead of spun deer hair for the collar and body helps the fly sink even faster.
Hook: #8 to #12, Gamakatsu S11-4L2H
Thread: 3/0 brown
Weight: nontoxic wire wrapped around the front third of the shank
Body: olive wool yarn
Ribbing: gold wire
Wing: a strip of light olive rabbit fur
Fins: sage grouse feathers, dyed olive
Collar and head: olive, brown, and gray clumps of wool yarn bound to the hook shank and trimmed to give a mottled effect
##### Soft-Hackle Streamer
This fly is simple, sinks quickly, and has lots of action. A good streamer for the tenkara rod.
Hook: #8 to #12, Gamakatsu S11-4L2H
Thread: 3/0 red, white, yellow, or black; use a thread color that contrasts with the marabou wing
Tail: two strands of silver Flashabou or pearl Krystal Flash
Wing: blood marabou wound as a hackle. The most popular colors are black, olive, yellow, white, and black/olive. The wing is followed by a turn of mallard flank feather dyed to match the marabou.
Mauro Mazzo fishing nymphs on the Sesia River near Quare, Italy. _Photo: Daniela Prestifilippo_
## _"THE KEYS TO BEING AN EFFECTIVE FLY FISHER ARE: TO KNOW WELL THE HABIT OF THE FISH, AND TO BE ABLE TO READ THE WATER."_
—Mauro Mazzo
## Chapter 3: Fly Fishing with Nymphs
## MAURO MAZZO
When I was a kid, I spent most of my time escaping from Grandma: I would go fishing with a can of worms. Those days, I was doing everything to come home with a few fish to show my grandma. I brought home a few things that were quite borderline; when the fish don't bite, you have to go find them.
Fly fishing in Italy in the 1960s was uncommon, and to be a fly fisher was a very posh thing. Most fly fishers walked the riverbanks wearing Barbour jackets while smoking pipes. They enjoyed talking about the best fly to match the hatch, asking themselves whether it was a dun with a gray body or a yellowish-green emerger—difficult stuff for a young kid.
When I was sixteen, the father of a dear friend of mine introduced me to the world of fly fishing. I was already fishing with artificial lures, mainly for trout and pike, with good results. I was afraid that fly fishing was more of a walking and talking exercise for older people than real fishing.
I took some casting lessons. The instructor told me that only when I had acquired the right casting tempo and made the decision to fish relying only on a bunch of hair and feathers, then and only then, could I consider myself a fly fisherman—or, as they called themselves, a purist. Being a teenager, I had an interest in beautiful hair, but of another kind, and no interest at all in purity, but I decided to carry on and see what would happen on the water.
The day came to go fishing. The teacher told us to find what insects were hatching and to tie on the right imitation. Nearsighted and without polarized prescription lenses, this was a little difficult for me. I couldn't see any difference in the insects; actually, I couldn't see any hatching insects at all. So I decided to tie on a fly with a red body, just because I liked it.
Excited by the sight of rising fish, I forgot all the casting fundamentals; my fly plopped on the water, the line in loops around it. But on my second cast, I had a fish on.
A bell rang in my head. If I had a fish on after two poor casts, using a fly that I picked only because I liked the colors, fly fishing must be much easier than what the instructor told me—and also quite effective. I also realized that for nearsighted people like me, nymph fishing is the best option.
Today, after nearly forty years of fly fishing, I have not changed my mind. Fly fishing is simple and effective, and fishing with nymphs is still my favorite choice.
I have been lucky enough in my life to fish in many places around the world and for many different species of fish, from the moody Atlantic salmon to the mighty mahseer, from the elusive blue fin grayling to the ultrarare marble trout, and I believe that the keys to being an effective fly fisher are two things: to know well the habit of the fish you are trying to catch and to be able to read the water it lives in. Once you master this, even a bare hook can be the right fly.
## FISHING WITH NYMPHS
For years, the subsurface fishing techniques were left to the days in which nothing else was working. The majority fished a nymph without any action, like a dry fly. They didn't know what they were doing. In the last few years, however, the opposite has occurred, to the point that nymph fishing has become like rocket science. Fly fishing competitions, no matter where they are held in the world, are almost always won using nymphing techniques
When experienced anglers talk about modern nymphing techniques, they like to use exotic names like Czech, French, or Spanish nymphing. These names only serve to confuse the beginner, who wonders what the terms mean and which one is best. Don't worry; the "best technique" does not exist. What's important is to use the proper technique for the water you are fishing. Don't worry about giving your fishing technique an exotic name—a "fast blue fish from the Baltic Sea" is still just a cod.
It is interesting to note that Czech nymphing started in Poland during the 1970s on the Dunajec River by fishers who were interested in competing. Fly fishing competitions were, and still are, very popular in the countries of what was formerly called the Eastern Bloc. The people had very little means, so they had to use what was available; they were fishing with no fly lines and no reels. They used only monofilament line and very simple nymphs, and as a result always fished the nymph very close to the rod tip.
Another peculiarity of this technique was that they used heavy nymphs so the nymph would sink very fast. If you think for a second, this is quite logical. If you cast a very short line, to get the longest possible drift in the feeding zone, you want to have your flies near the bottom, where the fish are holding, in the shortest possible time. Ironically, a technique that was born to overcome a lack of means has become a fashion in our ultra-affluent society.
The evolution of nymph fishing brought more than just fancy names; it also brought some interesting developments in technique. A bunch of innovative people revisited the old, well-known techniques and, by adding a few twitches, have made nymph fishing more effective.
Akin to fishing with a worm or bait, anglers fishing nymphs today often apply action to the nymph, thereby mimicking the wiggling worm or the swimming nymph. The most important things in nymphing are getting the fly to the right depth, achieving the right speed for its drift, and giving it some action to make it look lifelike.
Theories, like the one placing importance on the exact insect imitation, faded away, switching to techniques based on the presentation of the fly at the right depth and speed. Following this new approach, you will be able to fish more or less anywhere with only a few nymphs.
When can you fish the nymph? The answer will be disappointing. Always. Nymph fishing is not limited by an event, like a hatch going on; even in the middle of a hatch, fish are still eating mostly nymphs.
Additionally, fly fishing has a casting mystique that often frightens newcomers. Casting is definitely a nice thing, but it is just one of the tools you can use to make your fishing more effective. You will soon realize that most of your fishing can be done within twenty-five feet or less.
Most of us started fishing with a pole, a piece of line, and a can of worms. No one bothered to tell us how to cast the worm, but we caught fish anyway. Why? Because we were in the right place, at the right moment, presenting to the fish what it wanted to eat.
The important thing is the ability to choose the right place, go there at the right time, and fish it in the right way. Knowledge is the key. Every piece of water has one system that works better than the others, and our aim is to teach you to figure out what is the most efficient system for that particular place and time.
##### The Fake Fly Box
A few years ago, Czech nymphing style was still unknown to most fishers. Sandrino, a friend of mine who competed for years with the Italian fishing team, and I booked a few days of fishing with Jiry Klima, the captain of the Czech fly fishing team. The Czech team was dominating the competition world at that time. We fished with him for several days and learned a lot. On the last day, we stopped fishing at about 6 p.m. and invited him for a beer at a bar right by the river.
Sandrino and I sat down still wearing our fishing vests, while Jiry went to the car and came back with a very nice wooden box, full of flies. "Sandrino, let's swap flies from our boxes," Jiry said as he came back in the bar. I thought it was very kind of him, but Sandrino didn't look too happy.
Jiry picked a bunch of flies from Sandrino's box and Sandrino did the same. After we had our drink and Jiry went away, I asked Sandrino why he didn't look happy about sharing the flies. He grinned, "They never give away their secret flies; I should have been prepared! The box he showed us was an ordinary fly box, whilst I showed him my competition boxes. So, he picked up some of my best flies, whilst I picked up his ordinary flies."
From that very day, I saw Sandrino swapping flies with many others. The box he pulled out was always the same one, though he had twenty more in his tackle bag.
— Mauro Mazzo
Several fly boxes of a well-known competition angler: secret flies or fakes? _Photo: Mauro Mazzo_
## TENKARA NYMPHING GEAR
#### TENKARA NYMPHING RODS
The easiest way to learn nymph fishing is to start with a tenkara rod or with a regular outfit but without the reel. The subsurface technique that best suits a tenkara rod is short-line nymphing. The tenkara rod, because of its longer length, is one of the best rods to practice this technique. The ideal rod is ten and a half feet long: Longer rods are too affected by the action of the wind.
Considering you will often have to cast weighted flies, the most suitable action is progressive action that flexes most in the top two-thirds of its length, but not too soft. If the rod is too delicate and slow, it will be hard to set the hook.
#### TENKARA NYMPHING LINES
AND LEADERS
Lines for nymphing are made opposite of how they should be. Heavy heads buoy downstream with the current. Nymphing lines need to be thin and light. You are not fly casting; you are lobbing. You want to get the maximum control of the fly and thus the thin, light line. For short-line nymphing, use a twelve-foot line about .025-inch diameter. It need not be tapered.
The simplest leader is made of a four- to six-foot length of 3X to 6X tippet material. Tie a perfection loop on one end and hitch it directly onto the loop at the end of the twelve-foot floating line. If you don't have a very visible color of fly line, another choice uses an eight-inch-long piece of .011-inch-thick fluorescent yellow monofilament line with a perfection loop tied at each end. This will be your bite indicator. Hitch this piece directly onto the end of your fly line and tie your leader onto the other loop with a clinch knot.
The finer the tippet, the faster the nymph will sink, and the less it will be affected by the currents. Whatever leader system you are using, only the last few inches of the fly line or indicator will be touching the water. To improve bite detection, make stripes with black waterproof marker on every inch of the fluorescent section of the tippet.
Nymphing leader with strike indicator
## FISHING NYMPHS WITH A TENKARA ROD
#### FISHING A SINGLE NYMPH
When fishing with a single nymph, look for water with medium-slow current and a depth of two to three feet. Cast, relying only on the weight of the nymph, with a fluid arcing motion of the rod tip, forty-five degrees upstream of you. This casting technique is contrary to the traditional fly rod cast where the rod tip moves in a straight line and accelerates to an abrupt stop.
Another useful cast, especially when wading, is to let the line lay on the water behind you, and then cast it forward, using the tension of the water to load the rod. The movement is the same as an overhead cast, but without a back cast. You start with the line pulled taught by the current and cast your fly in front of you; the current dragging on your fly acts like a catapult.
Wait for a few seconds after the fly hits the water in order to let your fly get close to the bottom and then follow the nymph's path downstream with your rod tip. Try to avoid pulling the fly downstream. This is very important; the drift of the fly has to look natural. "Turbo-powered nymphs" swimming downstream faster than the current do not look natural.
But looking natural does not mean dead. If you want your fly to be effective, it has to look alive, and the best way to achieve this is to make little twitches with your rod tip during the fly's drift downstream.
These twitches have a double benefit: They imitate the movements of a nymph, and they can also trigger a reaction from the trout. In the wet fly chapter is an explanation about how to twitch your flies. I can only insist that the twitches be as small as possible. The slightest movement will be enough because the rod tip amplifies the movement. To keep direct control of the fly, keep as much line off the water as possible at all times. This is one of the most difficult things to learn because although you need to keep the line clear of the water, you do not want to pull the nymph during the drift and make it look like a hangman on a tree.
In between twitches, let your nymph drift free. I've found this combination of little twitches followed by a free drift the most attractive to fish. When the drift has reached its end and the fly starts to rise from the bottom to the surface, do not pull your fly out of the water immediately. The fish may think it is an emerging insect, and you may get a bite. Wait with the rod tip pointing downstream; sometimes the slow upward movement of the fly can persuade a doubtful trout.
You will need to develop a feel for the take. Some years ago a study was done with an expert fishing with nymphs in the old way by dead drifting the nymph on a slack line. An observer on a cliff above could see that on almost every cast a trout would take the fly and instantly spit it out without the angler even knowing.
We don't recommend large strike indicators that attach to the line. Beginners often use one to get a dead drift with a fly. We don't use them; we want direct control of the fly. You need to feel the contact and achieve a dead drift until you want to impart a subtle action when the fly is where the fish are holding. The strike indicator inhibits imparting that action and inhibits getting your fly down deep.
Fishing with nymphs you need to determine how deep the pool is. If the pool is shallow or the current is slow, use a shorter leader and a light nymph. If the pool is deep or the current is fast, choose a heavier one.
You want to stay with the lightest possible nymph that will give you a drift speed close to the current speed. As a rule of thumb, the lighter the nymph, the better the drift. The problem is the drag on the fly from the leader and the tippet. You have to use a thin tippet and the lightest possible imitation to have your fly presented to the fish in the most natural way.
Once you have hooked the fish, keep the rod tip high during the fight, using the bend of the rod to fight the fish. To land it, reach out with your hand, grab the line loosely (the line has to be free to move inside your grasp to avoid breaking in case of a sudden run by the fish), and pull the fish in gently. Whenever possible, release the fish without taking it out of the water.
The Water Tension Cast
Nymph Fishing Technique
#### FISHING TWO OR MORE NYMPHS
Once you are familiar with fishing with one nymph, you can move on to the two-nymph rig—my favorite, particularly in medium-fast water. The two reasons for using two flies are to give the fish a choice of flies and to add more weight without having to use a larger fly. Make the tippet with the usual 3X to 5X mono, but add a six-inch dropper.
The distance between the dropper and the point fly should be about twenty to twenty-five inches; shorter in faster water, longer in slower water.
The easiest way to fish with two or more nymphs is to tie the heavier fly to the point and the lighter one to the dropper; this makes casting much easier. The most common rig is composed of a point fly, size 8 to 12 depending on the strength of the current (the stronger the current, the bigger the fly), and a dropper with a fly of size 12 to 16.
If you want to get the most natural presentation in slow current or with difficult fish, you can tie the smallest fly to the point. This will make the presentation more natural, but casting and bite detection will be much more difficult. For this reason, I suggest this rig only to people with a lot of experience. A good alternative for less experienced people is to use two small flies (14 or 16) of the same weight for both point and dropper.
The presentation is the same when fishing with two or more flies as when fishing with one. Because two or more flies are often used in fast current, you only need to change the angle at which you cast the fly to get the longest possible drift. The faster the current, the more upstream you will need to make your cast—up to ninety degrees in very fast currents. This is necessary to get a long enough drift for your flies.
You will have to make the action more dynamic. And you will have to lift the rod tip in the first half following the drift and lower it in the second half. The take will often be very hard, so detecting the bite in this kind of water is not that difficult.
##### HOW THE TWO-FLY NYMPH RIGS WORK
•Flies with same weight: The tippet drifts parallel to the bottom. This rig is good for exploring more water in the same drift at the same depth.
•Heavier point fly: The tippet drifts in a more vertical orientation. This helps when you want to explore two different levels of the water column.
•Heavier dropper fly: The point fly, in spite of its light weight, will run close to the bottom with a very natural drift.
Mauro Mauzo tight-line nymphing for marble trout. Sesia River, Italy. _Photo: Daniela Prestifilippo_
## NYMPH FISHING WITH ROD AND REEL
Fishing with the rod only will oblige you to be very efficient with your fishing action. You can compare this to taking a picture with a manual camera with a fixed lens versus using an automatic camera with a zoom lens.
With a simple manual camera, you have only the aperture and focus to play with. Using a modern auto SLR camera with zoom gives you thousands of options, but unless you are a pro, you will not be able to fully utilize these options. You will take the occasional nice shot, but more often than not, it will be only by chance.
To master a craft, you have to achieve total control of the tool you are using. Photographers like Henri Cartier-Bresson, Robert Capa, and Elliott Erwitt made their masterpieces using only fixed lenses and manual cameras. Fishing is the same: Learning with a very simple tool, with very few options available, will teach you how to get the best out of your tackle.
Once you have learned to fish without a reel, the transition to regular rod and reel will be quite easy. You will know from your tenkara experience that to catch fish you do not need to cast a mile. The ability to cast farther will be only an extra tool, not the foundation of your fishing.
If you are not a strong caster yet and are using a light nymph, you may want to add a butt section to your setup. Tie a loop in both ends of a three-foot length of .013-inch monofilament line, and hitch one end to the end of your fly line. To this hitch your fluorescent bite indicator with your leader tied to the other end.
The ideal rod is a nine- to ten-foot progressive action one, meaning that the rod bends all through its length but gets stiffer toward the butt. The shorter option allows more precise casting; the longer one gives you better control of the nymphs during their drift.
The most important thing with the rod and reel is the balance of the rod. With most nymph fishing techniques, you have to fish for hours with your arm lifted to keep as much line as possible off the water. A well-balanced, light rod and reel will make your life a lot easier and will avoid that heavy tip feeling that makes you tire quickly. Use a large arbor reel, as it reduces the coiling of the fly line.
When fishing with nymphs, most often you will be casting weighted flies, so the lightest line you can handle is the best choice. When casting weighted flies, the weight of the fly helps you reach the distance you want (comparable to spin fishing), even though you are using a light rod and line. Conventional wisdom says you have to use a heavy line to cast heavy flies; you are supposed to load the rod with the weight of the line only. But this approach would oblige you to use very heavy lines, seven weight or more, and that would make it impossible to fish with the techniques described here.
I want to make it clear that to a nymph fisher, the only real advantage of a fly line and a reel is the ability to change the length of the line out of the tip and the ability to control that line. You can do short- or long- line nymphing. Apart from this, when nymph fishing, you will be better off using a monofilament line. The monofilament, thanks to its thin diameter, which is less than half of the thinnest fly line, is less subject to the action of the wind, which allows you to detect subtle takes. It is also less exposed to the action of the current, which facilitates a natural drift for your nymph. You don't need a separate spool for your reel loaded with monofilament. Just loop a forty-foot section of monofilament shooting line onto the tip of your fly line.
When fishing with a light downstream wind, you can take the advantage of the fact that the monofilament is half the diameter of the thinnest fly line, and you just keep your rod close to the water. When the wind is strong, if you keep the rod high you will make a big bow in your line that will drag your fly faster than the current. To defeat this drag, as soon as your fly hits the water, mend upstream and lay the line down on the water. Follow the drift with the tip of the rod, mending if necessary, and when the indicator stops strike sideways and upstream.
The bare truth is that you don't really need a fly line, but to make casting easier when fishing very light nymphs, get the lightest line possible. For all-purpose nymphing, the ideal rod is a four weight, set up with a one- or two-weight line.
You need to adjust your casting to this peculiar rig. Reduce false casting to a minimum, because when using weighted flies, the only thing false casting does is increase the chances of tangling the leader.
One of the world's greatest freestone rivers: The Madison, with its boulders and pockets, is ideal water for nymphing.
_Photo: John Juracek_
As soon as the fly touches the water, you have to try to maintain contact with the flies. This is very important because the fish might take the fly during its descending path and you have to be ready to strike immediately. A good way to maintain contact with the flies is to keep the fly line under your index finger during the cast. When the fly hits the water, stop the line by pushing your finger against the rod handle and start retrieving the line using the other hand to take up the slack.
When following the drift of the flies, try to keep the rod tip close to the water and shorten the line using the left hand (when holding the rod with the right hand).
With rod and reel, you can make longer casts, but don't forget that this does not mean you are obliged to do so. The best fishing is often close to the bank, and being cautious and silent when approaching the bank will help you be successful.
A big advantage you get from the reel comes when fighting a big fish. The reel offers you the possibility to play the fish with ease, letting line out and retrieving it in accordance with the behavior of the fish. Please bear in mind that playing a fish for too long can overstress the fish.
### The Usual Question
I was fishing the Firehole River in Yellowstone Park while a big hatch was going on, and I was doing really well with two small nymphs, which I was fishing just under the surface.
I watched a young boy running up and down the river casting a big dry fly here and there, followed by his mother carrying a large landing net. I could tell he had no idea what he was doing.
He came by and asked me the usual question, "What fly are you using?" His mother explained that he was supposed to be hiking with his group, but all he wanted to do was fish.
I changed his rig, tying on a very simple leader, made of seven feet of mono, and tied on a nymph under a piece of yarn to be used as a strike indicator.
His casting was very basic, so I told him to cast very close to the bank, behind a rock that was hiding him from the fish. After a few casts, he had his first fish on. His eyes were sparkling, and I knew he was caught on fly fishing.
— Mauro Mazzo
The Firehole River, Yellowstone National Park, Wyoming. _Photo: John Juracek_
## TYING NYMPHS
My nymphs are tied very simply. These patterns are mainly searching nymphs, but they catch fish, showing once more that the exact imitation theory is not always right. The priority is to offer a fly similar to what the fish are eating at the right depth and drift. The weight of the fly, and its disposition, has a very important role; the dressing itself is more impressionistic than realistic.
There are ultrarealistic imitations in the nymph world, but I have never seen anyone catch many fish with them. Their place is really in a nice cabinet in your house rather than on the riverbank.
I believe that names are good with insects and dry or wet flies, but with most nymphs, apart from the famous ones, names are rather confusing. Maybe anglers don't feel it's very cool to tell people they fish only Pheasant Tails or Hare's Ears, so they give their flies exotic names like PT Cruiser, or Tollett's™ Half-Juiced. So rather than suggesting fly X or Y, I will try to give some basic information that will allow you to fish in most waters.
For a dark stream bottom, use a dark fly; for a light stream bottom, use a light fly. For faster or deeper water, use a big fly tied on a size 8 to 12 hook, and weight it heavily with tungsten bead heads and/ or nontoxic wire. For slower or shallower water, use a small fly tied on a size 12 to 16 hook and weighted only with a bead head or only with wire. For the smallest sizes (16 to 20), use only 2X strong nymph hooks with no weight. As you can see, it is not rocket science.
Bear in mind that with only ten imitations, tied on different-sized hooks, you can embark on a world fly fishing tour. With the nymphs I describe in the following pages, I have caught fish all over the world, from trout to steelhead, from Atlantic salmon to grayling. I believe they are all you need to cover 90 percent of situations.
#### SOME TIPS
The tips that follow are valid for all nymphs and will help you decide which flies to choose for your box.
•Use bent, or jig, hooks, weighted in the top or middle of the shank to reduce the chance of snagging flies on the bottom. This kind of fly is preferred when fishing rivers with an uneven bottom or one full of debris.
•A thin body makes the fly sink faster; a coarse, fluffy body slows down the sink rate of the fly. So a thin body is preferred in fast water; a fluffy body in slower water.
•Silver or gold bead heads work better in colored water. Brass, black, or no bead heads are good for clear water.
#### LIGHT-COLORED FLIES
##### Cased Caddis Imitation
Hook: #10 and #12, jig, 2X long, 2X wire
Bead head: gold or black, 3 mm
Tail: green or yellow fluorescent wool or floss
Body: Hare's dubbing with a color that matches natural insects
Legs: a couple of turns of partridge hackle
##### Uni Caddis Larvae - light
Hook: #12 to #16, grub
Body: beige dubbing
Thorax: dark brown and orange dubbing
Back: elastic vinyl, with five or six turns of nylon monofilament around the body keeping the back in place, imitates a scud
##### Uni Nymph – light
Hook: #12 and #14
Bead head: gold, 2 to 3 mm
Tail: partridge hackle fiber
Body: beige Hare's dubbing
Thorax: Hare's Ice Dubbin peacock blend
Rib: copper wire
Collar: orange floss (Optional turn of partridge hackle before the floss adds a lifelike effect.)
##### Uni Nymph – green
Hook: #14 and #16, grub
Bead head: gold, 2.5 mm
Tail: furnace rooster hackle fiber
Body: bluish-green Hare's dubbing
Collar: fluorescent orange floss
##### Uni Emerger Nymph - light
Hook: #16 and #18
Bead head: gold, 2 mm
Tail: grey hen or rooster hackle fiber
Body: light grey or beige Hare's dubbing
Thorax: peacock herl
Collar: hen grey hackle
##### San Juan Worm
Hook: #8 to #12, grub, 2X long, 2X gape
Bead head: gold, 3 to 4 mm
Body: red or pink chenille
##### Hare's Ear
Hook: #12 to #16, 2X long, 2X heavy
Tail: partridge
Ribbing: copper wire
Body: various shades of hare's ear
Thorax: Hare's Ice Dubbin grey
Wing case: goose quill or magic shrimp foil
Hackle: partridge
Colored collar: optional
#### DARK-COLORED FLIES
##### Uni Caddis Larvae - dark
Hook: #8 to #12, grub
Body: dark brown or dark green dubbing with red spot
Thorax: peacock herl
Back: elastic vinyl, kept in place with five or six turns of dark nylon monofilament, or copper wire around the body
##### Uni Mayfly Nymph
Hook: #10 to #14, 2X long, 2X gape
Bead head: gold, 2.5 to 4 mm
Tail: pheasant tail fibers
Body: pheasant tail fibers
Thorax: Hare's Ear Ice Dubbin peacock blend
Rib: copper wire
Legs: partridge hackle on top with V shape
Back: dark pheasant tail fibers
Collar: orange floss
##### Uni Stonefly Nymph
Hook: #8 to #10, grub, 2X long, 2X gape
Bead head: orange, 4 to 5 mm
Tail: pheasant tail fibers
Body: pheasant tail fibers
Thorax: Hare's Ear Ice Dubbin peacock blend
Rib: copper wire
##### Uni Nymph Jig Hook
Hook: #12 to #16, jig, 2X long, 2X gape
Bead head: gold, 2 to 2.5 mm
Tail: pheasant tail fibers
Body: dark brown Hare's dubbing
Thorax: white Hare's dubbing
Collar: orange floss
##### Uni Emerger Nymph - dark
Hook: #14 to #18, grub, 2X length, 2X gape
Bead head: gold, 2 to 2.5 mm
Tail: furnace hackle
Body: in greenish-brown Hare's dubbing
Collar: one turn of grey hen hackle
##### Sawyers Pheasant Tail Nymph
Hook: #12 to #16, 2X long, 2X gape
Tail: pheasant tail fibers
Body: pheasant tail fibers
Thorax: copper wire
Rib: copper wire
Wing case: pheasant tail fibers
## NYMPHING FOR ANADROMOUS FISH
There are times when nymphing techniques are the most effective way to fish for steelhead, Atlantic salmon, and sea trout.
•When the water is cold in the morning or in the winter when the fish won't move very far to chase a swinging fly.
•When steelhead are near spawning pink or sockeye salmon, they want to eat those eggs!
•When the water is warm in the dog days of summer and the salmon have gone dour.
•Whenever anadromous fish (for whatever reason) are schooled up in deep pools.
•When in Southeast Alaska and spring steelhead are often reluctant to take swinging flies and really prefer egg patterns.
•When fishing for hatchery fish who hardly know what an insect is. They want a fish pellet or smelly egg.
All anadromous fish are suckers for worms and gobs of cured smelly salmon eggs. In Iceland after the season closes, and the catch-and-release sports have left, the farmers go out with their cans of worms and catch their winter supply of salmon.
If you can see fish holed up in a deep pool, there is a good chance you can catch them—and sometimes every one of them. These big fish in deep water feel secure and are not spooked by lines, heavy leaders, or even humans standing ten feet away. The method is simple: drift a rubber-legged stonefly nymph pattern past their noses, and give a little twitch. The important thing is to get the fly down to their level so all they have to do is open their mouths and suck it in.
All fishers have their weaknesses; that's why we have a reputation for lying. There are times when no matter how skillful we are, we go through long periods when we can't catch a fish. Atlantic salmon, with all their neuroses, especially can drive you to drink. Steelhead are easy; they will take almost any fly, but there are so few of them left. In our desperation, we hear the siren songs of the scented egg or the heavily weighted Snelda or Red Francis, and we look jealously at the spin fisher tossing his sacks of Gooey Bob eggs and hoovering up fish after fish. You can avoid the temptation of the sirens with cotton plugs in your ears . . . or just pull out those nymphs.
It is an effective method, but it might not be everyone's cup of tea. It might be an alternative for those days on which endlessly swinging a fly is like watching the same movie five times and expecting a different ending.
Sonya Pask with a perfect Skeena River steelhead. _Photo: Tim Pask_
### A Tenkara Salmon
When Atlantic salmon first move into a river on their spawning run, they seem to be in a terrible hurry to get somewhere. They jump as they enter a pool and, seconds later, jump again as they leave it. It can be frustrating times for the angler, because the fish are not much interested in stopping to take a fly. Not until a day or two later when they settle down into a comfortable lie and out of habit, boredom, or to defend their spot, they may fall for a bunch of feathers on a hook.
Fishing in the Haffjardara River in Iceland recently we were blessed with a good run of grilse and small salmon. At the riffle area of the upper Aquarium pool, as a lark I decided to see if I could manage a salmon on soft-hackle flies and my twenty-five-year-old tenkara rod.
I put an eight-foot extender onto my twenty-foot floating line as I wanted to keep farther away from these spooky fish. I tied a Shakey Beeley onto the 2X tippet and a blue and partridge soft hackle with a red tag onto the dropper—both tied on size 12, up-turned-eye light salmon hooks. On my second cast, right after I gave the fly a twitch, a five-pound grilse took the dropper. Surprisingly, it wasn't as difficult to land as an equivalent rainbow or brown trout, which after feeling the hook, tend to streak away immediately. I landed four more that day and lost twice as many for various reasons. One I lost was a large salmon that broke off in the Count pool when I panicked and failed to throw the rod for fear of losing it in the rapids below.
Later during the week, I landed a dozen more with a few in the seven-pound-plus proper salmon range. Three times I had to throw the rod in the river when I couldn't stop the fish on its initial run. To tell the truth, the first time it happened, the rod was actually ripped out of my hand. I ran as fast as I could in the waist deep water but never could catch up to my waking rod handle. But after seventy-five yards, I saw my rod turn and come back upstream. I ran back up and caught up with it near where the fish first took the fly. Later, I started to notice a pattern in the fight. After the pressure is off, the salmon (like a large trout) wants to return to its secure lie. Its querencia. However, I don't recommend you try this craziness unless you have a good run out—the inevitable rodeo needs plenty of room.
—Yvon Chouinard
_Photo: Malinda Chouinard_
Let's rodeo! Yvon Chouinard fishing for grilse in Iceland. _Photo: Malinda Chouinard_
Craig Mathews on O'Dell Creek with a nice brown that took a terrestrial imitation. Montana. _Photo: Mauro Mazzo_
## _"FLY FISHING HELPS PRESERVE OUR CAPACITY FOR WONDER."_
—Craig Mathews
## Chapter 4: Fly Fishing with Dry Flies
## CRAIG MATHEWS
When I was four years old, my parents started taking my brother, Tom, and me to Silver Lake near our home in Grand Rapids. We spent the summers there, and I learned to fish for bluegill and bass. Every evening, we'd watch three fly fishermen wade out into the lake and cast their bamboo fly rods. It was magic to see their fly lines cutting the evening air, and they would hook up often and bring to net big bluegill, crappie, or bass.
One night, I mustered the gumption to join in their fly fishing lineup. I took my grandfather's bamboo rod hooked above the wooden frame of our walkout basement door, opened the door, walked out, and promptly closed the screen door on the rod, busting about a foot off the end. Undaunted, I waded into the lake toward the anglers. One of the men, who lived in a log cabin nearby, motioned me over and gave me a short casting lesson along with a couple of small poppers and a rubber Spider Fly. It was only a few casts before I was into a four-inch bluegill. I took a few more that first evening and was hooked on fly fishing for life.
A few days later, we were driving home from grocery shopping and saw the same three men walking from a bridge into the woods not far from our summer place. My mom dropped Tom and me off and waited in the car for us. We snuck up on the men and found them rigging up their tackle at a pond in the forest. I'll never forget the fish rising to the surface of the pond that day. Not knowing what they were, we sat watching, and then approached when one of the men landed one—a brook trout with brilliant spots on its flanks. I was hooked again and began learning all I could about fly fishing for trout.
Later, after I graduated from college, Larry Dech and I headed west to fish Yellowstone country and its incredible fly fishing opportunities. Not long after, my wife, Jackie, and I came to Yellowstone in September to fish for two weeks. We returned home, and a month later, we schemed to move to Yellowstone, which we did later that winter. I came as the police chief of West Yellowstone, and she was a police dispatcher.
A few years later, we opened Blue Ribbon Flies and began fly tying and fishing for a living. We fish over one hundred days a year and talk about it daily with our friends and customers.
Over the years, I went from fishing dry flies exclusively to solely fishing nymphs, then to streamers, and back to fishing dry flies again. There is nothing I enjoy more than watching a trout come up for a dry fly. I now fish dries over 80 percent of my time on the water, and I use a tenkara rod over 50 percent of the time. I enjoy its effectiveness, efficiency, and simplicity.
Most fly fishers feel there is magic on our planet, and it is held in our rivers, lakes, and streams. Henry David Thoreau once said, "Many men go fishing all their lives without knowing that it is not fish they are after." Most of us sooner or later discover that fly fishing helps preserve our capacity for wonder. Pursuing wild fish with a fly rod can teach us to see, smell, and feel the miracles of stream life with the serenity and the beauty of nature all around.
## FISHING WITH DRY FLIES
Evening mayfly hatch on the Madison River. During these May/June (early season) hatches there are fish in many of the pockets created by rocks. _Photo: Jake Hawkes_
My favorite method of fly fishing is with the dry fly. I enjoy the visual aspect of it. I prefer the stalk and the hunt: I enjoy slowly patrolling the banks of rivers, ponds, and streams searching for the telltale ring of a rise, a trout's back or snout breaking the surface as the fish rises to a mayfly, caddis, or midge. To me, there is nothing more satisfying than getting as close to the rising trout as possible, whether slowly sliding along the bank on my butt or wade-walking in the river on my knees.
If I do not find fish actively rising to insect activity when I arrive on a stream, I can usually find one or two coming to the surface if I am patient and "sit on water." By this I mean I locate a quiet pool, pocket, or slow run where trout hold and feel secure. I find a comfortable spot along the shore and sit, watching the surface for a telltale ring of a subtle rise or a fish's tail or dorsal fin barely breaking the surface. Then I go back to my old profession as a police detective to find the clues of what the river is telling me to do. Are there midges emerging or mayflies? Are there ants on the water? When I discover what is bringing the trout to feed on the surface, I knot on an imitation and begin my fishing day.
If I do not see a rise, I might tie on an attractor pattern, a fly that imitates nothing in particular but may entice a rise. I prospect with my attractor pattern, covering much more water than I normally would with rising trout. Often, the attractor fly moves a fish to come up and take a look at it without taking it. I then tie on a pattern that imitates an insect the fish are used to seeing—an ant, beetle, or mayfly I know could be active at that time—and present it.
### My First Time with a Tenkara Rod
The first time I saw a tenkara rod was a few years ago on O'Dell Spring Creek near my home in the Madison Valley of Montana. Yvon had come to spend a few days fishing with me. We arrived at the creek, and Yvon stowed the rod in the rear pocket of his vest, explaining that he and Mauro had fished the rod recently on a small stream in Wyoming and had had a fun day fooling cutthroat trout. I couldn't help smiling to myself as I followed behind thinking about hooking and landing a huge spring creek brown trout on the delicate tenkara rod with a fixed-length line and no reel.
We both fished our traditional rod-and-reel setups that morning. After lunch, Yvon finally pulled out his tenkara rod and tied on a small Blue-Winged Olive soft hackle and proceeded to catch several nice browns up to fifteen inches.
I marveled at how efficient Yvon could be using short casts, swinging his soft-hackle flies in all the likely looking spots—undercut pockets and pools—where trout jumped all over his presentations.
When he offered to let me try the rod, I quickly knotted on a grasshopper fly and cast it upstream a short distance to the next undercut bank. A fourteen-inch rainbow gobbled the hopper, I set, and both trout and I were hooked on tenkara.
— Craig Mathews
Choosing the right fly on O'Dell Spring Creek, Montana. _Photo: Mauro Mazzo_
### Seeing the Light
Last December, a couple moved to town and stopped by the shop complaining about having to wait several months before they could fish dry flies. I told them to get a fishing license immediately and a couple of midge dry flies and head down to the Madison River to fish trout rising to midges. They made their purchase, and I drew them a map of where to find surface-feeding trout.
A week later, they stopped back in and when questioned admitted they'd been on the river three days and had yet to see a fish rise but did have some great nymph fishing. Our winter guide, Dan, was tying flies that morning, and I asked him to take the couple to the river and show them some rising trout. The couple drifted back in later that same day and sheepishly told me Dan "showed us the light!"
They told me they walked to the river and stood while Dan sat on the bank and asked, "Do you see the rising trout?" Both thought Dan was kidding them until they too sat down and watched. Simply sitting on the bank put their eyes on a level with the surface of the river: The subtle rises to tiny midges became evident. Dan told me later, "You should have seen their eyes bug out when they saw all the fish coming to the surface."
— Craig Mathews
A rainbow trout rises to a mayfly. _Photo: Barry and Cathy Beck_
## TENKARA DRY FLY GEAR
#### TENKARA DRY FLY RODS
You don't need to invest $1,000 in a rod, reel, and line to start fishing tenkara. Most tenkara rods sell for $150 to $250. I prefer Temple Fork Outfitter's eleven-and-a-half-foot soft-action carbon fiber tenkara rod for most of my dry fly fishing. The rod bends uniformly throughout, from butt to tip. I can easily load the rod and feel the loading of the line to allow a perfect forward cast without a tailing loop causing a tangle. This slow-action rod protects fine tippets and casts well into the wind. TFO's eight-and-a-half-foot rod works best for small streams and those waters with brushy banks and overhangs.
#### TENKARA DRY FLY LINES AND LEADERS
Effective dry fly fishing with tenkara rods requires the use of one of two lines available to anglers on the market today. I prefer either a traditional furled or a fine-diameter level floating fly line. A furled line is one fashioned from several twisted, small-diameter fly-tying threads. Both work fine, but the furled line requires some babysitting, as you need to apply fly or line floatant to it from time to time to keep it floating on the surface.
Furled lines are very soft and supple and transmit the energy of the cast easily, making for efficient line and tippet turnover and great fly presentation. Furled lines come in various lengths. I prefer the thirteen-foot length. They easily attach to the rod end as they come with a hitching loop that you can hitch onto the braided lillian at the end of the rod. These also come with a stainless steel ring on the leader end to which I add appropriate leader and tippets from 4X to 7X.
The other option, traditional level fly lines, are inexpensive and can be purchased complete in 80- to 100-foot lengths or bought in lengths cut from spools at most fly shops. I prefer a level line .021 inches in diameter, eight to fifteen feet long. Or better yet, cut both ends out of a DT000 line: one eight feet and the other fifteen feet in length. Both lines require tying a turle knot to loop over the lillian (see drawing on page 35). Leave a one-inch tag in the turle knot to loosen it in order to remove it from the lillian when not fishing. On my leader end of the line, I usually nail knot (see drawing on page 94) a standard seven-and-a-half-foot leader tapered to 3X or 4X and add tippets as needed.
#### KNOTS
Most anglers spend more time learning knots than they do learning to read the water or the insects that bring the trout to the surface. While knots are important to anglers, there are only a few that fly fishers must know. One secures the fly and the other ties on the tippet. A clinch or improved clinch knot is the easiest and best to learn for tying on the dry fly. The strongest for tippet-leader connections is the double-surgeon's knot (see page 39).
Improved Clinch Knot
## DRY FLY FISHING WITH A TENKARA ROD
As a rule, if you see fish rising, approach from downstream and work directly upstream. It is always best not to wade and to stay low to the bank so as not to present a silhouette that will spook the trout. If you must wade, by approaching from downstream you will not send debris and wading waves to the fish and signal your approach. Try to get within fifteen feet of the rising fish. Then present your fly about two feet upstream of the rising fish using a fixed-length, short-line, pinpoint-accurate cast (described below).
Allow the fly to approach the rising fish, and as the line begins to float back toward you, raise the rod by gradually bringing it up from a nine o'clock position to a twelve o'clock position, taking up the slack line as the line returns in the current. This allows the fly to float naturally and not be dragged by the downstream tension on the line from the current. It also keeps you in touch with your fly so when the fish does take the fly, you can set the hook and drive it home without having to take in slack line. If the fish does not take your offering, allow the fly to pass a foot or two beyond it and recast.
Upstream Dry Fly Fishing Technique
If searching water and fishing when no fish are rising, present your flies to all likely looking areas you expect trout to hold in with the same presentation as above. Wade slowly and carefully upstream prospecting the water as you go.
There are times when a fish rises upstream or downstream of your position or near an obstruction like a weed bed, boulder, or mixed currents and prevents an upstream approach. In those cases, carefully wade from above or below to the rising fish. If wading from upstream, be careful not to send a wading wave or debris and spook the fish. Get as close to the fish as you can, preferably within twenty feet, and cast downstream, or upstream and across, with a slack-line accurate presentation. If wading downstream to the fish, mend once or twice as the fly drifts to the rising trout to delay drag and avoid a skittering/waking fly. The aim is to present the fly as naturally as possible.
I prefer the upstream approach, but nothing is set in stone. Do whatever it takes to get close to a rising fish. Line drag is your enemy, and getting close to a rising fish helps to delay drag and stay in touch with your fly.
Downstream Dry Fly Fishing Technique
#### HOW TO MAKE A SHORT, SLACK, PINPOINT-ACCURATE CAST
The reason for using this cast is to delay drag on the fly. There are several ways to accomplish this cast, but my favorites are listed below. The two methods work with both tenkara and standard fly fishing gear.
With the first method, I choose the target, and if fishing standard rod and reel, I carry a bit of extra line in my line hand. If fishing tenkara, I let a short amount of slack line hang from the end of the rod. With tenkara, I never present a full-length line-and-leader cast that lands on a tight line, as this would usually result in immediate drag.
I guesstimate the spot I want my fly to land while accounting for current speed and drag. On my forward stroke, I aim for the spot where I want the fly to land. With tenkara, I make sure the extra line I cast allows enough slack to land on the water and give the fly time to drift naturally to the targeted fish. If fishing standard rod and reel and carrying extra line in my line hand, I stop the rod tip near the end of my forward stroke and at the same time release the extra slack line from my line hand, which allows the fly to reach my target with enough slack line to delay drag. This method will come naturally with a little experience.
With the second method, I follow the same two steps as with the first. On the third step, I aim for the spot; however, this time I follow through on the forward stroke and allow the fly to shoot beyond the target. As the line straightens, I stop my rod tip, causing the line to recoil and create slack line in a series of S-curves on the water. This method requires a feel and developed intuition, but with experience, it will become second nature.
## ADVANCED TENKARA DRY FLY TECHNIQUES
I usually fish one dry fly, but at times I knot on a second trailing dropper fly. Usually this occurs when I cannot determine what the fish are feeding on. During mayfly, caddis, or midge hatches, I might come upon several rising fish, and to quickly determine what stage of the insect the trout are feeding on, I tie on an emerger and a dun for instance.
To do this, leave a six- to eight-inch tag from your leader-tippet connection knot and tie one fly on here and the other on the end of your tippet. The distance between the leader-tippet connection knot to the point fly is eighteen to twenty-four inches.
Make sure the tag end is the heavier of the two pieces as this helps keep the mono from tangling. Present the two flies, and whatever pattern works best, remove the other fly and go with a one-fly presentation from there. Fishing two dry flies at the same time usually results in more tangles and hooks in the net mesh or your fingers when trying to release fish, but it is worth it when you are trying to find out what the fish are feeding on.
Another time when I may use two flies and wade from an upstream position is during caddis emergences or egg-laying periods as fish take flies skittered on the surface or hovering just above the surface of the river. Then, I knot a dry caddis pattern on the tag end of my leader-tippet section and trail a weighted caddis pupa. The idea is the weighted fly on the point breaks the surface tension of the water and allows the trailing dry fly to skitter on, or above, the surface. It is fun to watch big trout jump out of the water to take your dry fly offering. This is the one time I want drag to occur to keep my dry fly dancing on, or above, the surface of the river.
### The Gift
This last summer, I fished with my tenkara rod on the Firehole River in Yellowstone Park. I arrived as caddisflies were hatching and trout rose to them in the riffles and pools. I tied on an Iris Caddis emerger pattern and began taking a trout on almost every cast; with the tenkara, I could skip and dance my fly in each area where the trout were rising.
I heard a noise along the bank and turned to find several spectators lined up along the shore behind me. One young boy was at my hip, his mother apologizing, saying, "I'm sorry he got so close to you; he'd love to learn to fly-fish." I replied, "Well, we'll take care of that right now." We walked a short distance to the next riffle with half the audience in tow. Within a few minutes, the lad had landed eight rainbows. I gave him the rod and he was on his way.
— Craig Mathews
Matteo releases a nice marble trout hybrid. At twelve years old, his motto is "a bad day of fishing is better than a good day at school." _Photo: Mauro Mazzo_
## DRY FLY FISHING WITH A ROD AND REEL
#### DRY FLY RODS
For rod-and-reel dry fly fishing, I like a slow, even-action rod. A slow rod forces me to slow down between casts and load the rod properly to recast, and to concentrate on my fly, the rises of fish, and the insects fish are feeding on. You need to get close to rising trout, and the slow action allows you to load the rod quickly with a short line and recast quickly too.
Slow-action rods also protect the fine tippets required in dry fly fishing by absorbing the shock of the trout taking the fly. My favorite traditional dry fly rod, while slow action, still has enough backbone to allow me to defeat heavy winds, pick line off the water, and present large bushy flies without false casting.
I like a simple single-action fly reel that is lightweight and has a click drag. There are many fine reels available that provide a good drag system and hold fifty yards of backing and can handle big, wild trout in heavy currents.
#### DRY FLY LINES, LEADERS, AND TIPPETS
The fly line is one of the foundations of successful dry fly fishing, yet few know much about them. Today's lines are made to last many days of use on rivers, lakes, and streams without babysitting. They need no maintenance except keeping them clean; they will float well and give many days of use.
Most weight-forward lines take up to 30 percent less space on reels than do double-tapered lines. And the same weight double-tapered and weight-forward lines have the same basic taper for the first thirty feet. Since nearly all my dry fly casting is done within thirty feet, I prefer the weight-forward line. With it I can put plenty of backing on my reel and make all my casts and presentations.
Even though there are hundreds of choices of leaders, it really is not that complicated. For dry fly fishing, I begin with a nine-foot knotless leader tapered down to 4X tippet.
Tie a three- to four-turn nail knot to connect the leader to the fly line using a simple nail knot tool. Add appropriate tippets of 5X, 6X, or 7X to the end of the leader depending on the fishing at hand.
If fishing a big salmonfly or grasshopper dry fly, cut the leader back a foot to 3X and knot the fly on there.
Nail Knot
### Kenkara
Tenkara is also a useful tool for the seasoned angler. Ken lives along the White and Norfolk Rivers in Arkansas, where trout are often measured in pounds rather than inches. On his first visit to our shop in Yellowstone last summer, I showed him a tenkara rod. He laughed and said something like, "What fish could you catch with that little stick?" Ken stopped by our fly shop daily, and over the next several days I caught him discreetly listening to the ongoing discussions on the merits of tenkara techniques. Finally, one day, acting a bit agitated at our tenkara tales, Ken said, "OK, I'll bite, just give me one of those dang things, and I'll bet I break it on a Madison River brown trout today." Two hours later, Ken ran into the store babbling a story about catching his first nineteen-inch brown trout and several rainbows on his new rod. Today, his email address begins with "Kenkara."
— Craig Mathews
Spring weather is often hit or miss. Madison River, Montana. _Photo: Jay Beyer_
## SKILLS AND GUIDELINES FOR DRY FLY FISHING
Both expert and beginning fly fishers usually feel the most important ingredient to successful fly fishing is the right fly pattern. Yet the two most important things anglers—tenkara or rod and reel—must learn to be successful are proper presentation and technique. Too many anglers put their faith in realistic flies and long casts. And while some might agree proper presentation is the foundation of effective fly fishing, few actually practice the basics.
One day on a favorite spring creek where big trout are hard to approach and catch, I watched an old man creep along at a snail's pace, never wading but using streamside cover to get within fifteen to twenty feet of rising trout. He used a short, soft, pinpoint, slack-line cast to defeat drag and took several big fish. That same day, I watched another angler who advocates powerful rods and long presentations bang out sixty-to eighty-foot casts and spook every trout he fished to. He failed to take even one trout that day.
Here are a few tips on approaching the river during a hatch or covering water when there are no insects bringing fish to the surface.
•If you want to fish dry flies during an insect emergence, be on the water when they are expected. Check weather forecasts as well as wind and water conditions.
•Observe other anglers, if present, to see what direction they are heading to avoid crowding.
•Observe the conditions. Is there insect activity like caddis or mayfly, terrestrials or midges? If there are no insects or rises, pick a dry fly that imitates an insect trout will recognize as food.
•Recognize the different rise forms of mayflies, caddisflies, midges, and other aquatic and terrestrial insects.
•When trout are rising all around, it is very difficult to take the time to find the seine and check for clues as to what the trout are rising to. Do it anyway. The seine will show you what the trout are feeding on—the river will tell you what to do.
•Never jump in wading and spraying your casts. Wade as little as possible, and keep a low profile. Wading spooks small fish upstream where they might alert larger trout. Wading also destroys trout spawning nests, upsets trout habitat, and kills aquatic insects.
•Get as close to rising trout as possible. You can get very close to trout from downstream, and it will keep you from casting into and across mixed currents to defeat drag. Wait for a few more rises—I call them confidence rises—and observe what insect and what stage it is taking. If searching the water during nonhatch times, get close to holding water before casting.
•Count the trout's rise rhythm, and if, for instance, the trout is feeding every four seconds, put your fly in front of it in four seconds, and if on still water, cast in front of the fish the same distance as between its past rises.
•If coming from upstream, don't send a wading wave or debris that would put the rising fish down, maybe for the day.
•Use a short, slack, pinpoint-accurate cast as fish work in very narrow feeding lanes and will not move far for a natural or for your fly. Do not false cast over the fish as they will see the line or be spooked by water drops.
•Longer casts result in bad presentation, and you lose track of the fly. It is always best to be patient and hold your fire rather than present a long cast and spook the fish.
•Watch your fly closely as it approaches the rising fish. Often, you will see the fish fin up and inspect your offering and then turn away. If that is the case, it is important to rest the trout for a minute to allow it a confidence rise or two before presenting the fly again while paying greater attention to the drift of the fly. Drag must be avoided; it is usually the reason the fish didn't take the fly on the first cast.
•If there are several trout rising, pick one and concentrate on presenting an accurate cast to it. Don't spray casts among rising fish; that will certainly spook them.
•When trout are rising and the evening light is getting low and making it tough to see your fly, use a short cast and adjust your position in relation to the trout so you can keep track of your fly and rises to it.
•Dead drifting, twitching, high floating, and pulling a dry fly under the surface should all be tried and will, at times, entice some trout when all else fails.
•Wear earth-toned clothing to prevent unnatural contrast with natural surroundings.
•Do not give up. Trout may be sleeping. Yes, they do. If there is no hatch and every fly you try fails to bring fish up, take a break and return later.
Hilary Oliver catches and releases her first fish ever on the Fall River, Idaho. Is this fishing fun or what? _Photo: Jeremy Koreski_
### The Young Leading the Old
Last summer I taught two very experienced spring creek anglers how to fish tenkara, but they struggled for an hour before picking it up. Both were typical of experienced anglers learning a new method. The men were quite honestly insecure, lacked confidence, and tended to overthink the simple and easy processes of tenkara. What turned the tide was when a six-year-old nephew of one of the men took my rod and began catching small trout on a grasshopper dry fly within minutes, much to the men's chagrin. Soon they both learned the proper dry fly tenkara technique from the six-year-old.
— Craig Mathews
Lola hooks another one. Fall River, Idaho. _Photo: Jeremy Koreski_
#### USEFUL DRY FLY PATTERNS
While there are thousands of effective dry fly patterns for fishing the various hatches and insects, the ones I list here are simple to tie and proven to catch big trout. This short list should prepare anglers for the entire year of dry fly fishing.
##### MAYFLY DUNS AND SPINNERS
We developed the Sparkle Dun pattern to imitate most emerging mayfly species. This fly in a few different sizes and colors will fill 95 percent of your mayfly fishing needs.
##### Yellow-Tan and Olive Sparkle Duns
Hook: #12 to #20, dry fly
Thread: 8/0 gray is a good neutral color for all Sparkle Dun types
Tail (shuck): mayfly brown Zelon one-half to a full hook shank in length
Body: to match naturals, yellow-tan and olive are most common
Wing: natural deer hair
Note: All Sparkle Duns are tied in the same style; the differences are in size and body color to match natural insects.
##### Rusty and Olive Sparkle Spinners
Hook: #12 to #20, dry fly
Thread: 8/0 gray
Tail: dun or cream hackle fibers
Body: to match naturals, with rusty and olive the most common
Wing: white Zelon tied spent, half spent, or upright
##### CADDISFLIES
The Iris and X2 Caddis patterns are very easy to tie and very effective.
##### Amber and Olive Iris Caddis
Hook: #14 to #18, dry fly
Thread: 8/0 gray
Shuck: amber Zelon
Body: amber or olive Zelon dubbing blend
Wing: dun or white Zelon looped and tied low over body
Head: hare's mask shaggy
##### X2 Caddis in Tan and Olive
Hook: #14 to #18, dry fly
Thread: 8/0 gray
Shuck: amber Zelon
Body: Zelon dubbing blend of olive or tan
Rib: one strand of pearl Krystal Flash wrapped five times up the body
Wing: natural deer hair
##### STONEFLIES
By having a few sizes and colors in your fly boxes, you are ready to fish stonefly activity.
##### Nick's Giant and Golden Sunken Stones
Hook: #6 to #10, dry fly
Thread: 6/0 to match body color
Tail/egg sac: black poly yarn
Body: orange Zelon dubbing for giant stone, yellow for golden stone
Wings: five to seven clumps of deer hair
##### Little Yellow Stone Adult
Hook: #12 to #16, dry fly
Thread: 8/0 yellow
Tag: red Zelon
Body: little yellow stonefly Zelon dubbing blend
Wing: yellow dyed elk or deer hair
Hackle: grizzly or ginger
##### MIDGES
##### Zelon Midge
Hook: #20 and #22, dry fly
Thread: 8/0 gray
Shuck: dun Zelon
Body: thread wrapped over Zelon Shuck
Thorax: midge black Zelon dubbing blend
Wing: dun Zelon
Head: black Zelon dubbing blend
##### Griffith's Gnat
Hook: #16 to #20, dry fly
Thread: 8/0 gray
Body: two to three strands of peacock herl
Hackle: grizzly palmered through body, four to six wraps
##### DAMSELFLIES AND DRAGONFLIES
##### Blue and Olive Foam Damsels
Hook: #10, dry fly
Thread: 8/0 gray
Body: strip cut of closed-cell foam (or braided mono) in blue or olive
Wing: clear or white Medallion sheeting cut to shape, or white Zelon tied spent
Hackle: wraps of grizzly hackle in front of wings
##### Blue and Red Foam Dragons
Same as above although red foam substituted for olive and cut strip of foam more robust to mimic that of dragonfly. No hackle needed.
##### TERRESTRIALS
Important fly patterns to have during summer months.
##### Cinnamon and Black Zelon Flying Ants
Hook: #14 and #16, dry fly
Thread: 8/0 black
Body: closed-cell foam, black or cinnamon
Wings: white Zelon
Legs: fine black rubber legs
##### Foam Bee
Hook: #14, dry fly
Thread: 8/0 black
Body: striped black and yellow foam body material
Wing: white Zelon
Hackle: grizzly
##### Black Foam Beetle
Hook: #14 and #16, dry fly
Thread: 8/0 black
Body: black dubbing, or omit
Shell (back): black closed-cell foam strip pulled over body
Legs: black round rubber legs
Indicator: orange closed cell foam
Head: butt of foam used for shell back
##### Chaos Grasshopper
Hook: #12 and #14, dry fly
Thread: 6/0 brown
Body: tan closed-cell foam
Legs: yellow rubber legs and brown hackle (optional)
Indicator: orange closed-cell foam
Wing: pale yellow Zelon
##### Black Foam Cricket
Hook: #10, dry fly
Thread: 6/0 black
Body: black closed-cell foam
Legs: black rubber legs
Indicator: bright orange yarn, or omit
##### Spruce Moth
Hook: #12, dry fly
Thread: 8/0 rusty dun
Body: amber Zelon dubbing blend
Wing: deer hair
#### OTHER USEFUL PATTERNS
There are a couple of useful dry fly patterns anglers may want to have for searching the waters during nonhatch periods.
##### Adams Cripple
Hook: #16, dry fly
Thread: 8/0 gray
Tail/Shuck: mayfly brown Zelon
Body: fine gray dubbing
Wing: white Zelon
Hackle: mixture of wraps of brown and grizzly
##### Royal Wulff Cripple
Hook: #14, dry fly
Thread: 8/0 black
Tail/Shuck: mayfly brown Zelon
Body: peacock herl and red floss
Wing: white Zelon Hackle: brown
### Sleeping Trout
Last winter we were doing some filming and wanted to get underwater footage of fish feeding on midge pupae before the hatch and fish rising to emerging midges. We arrived, set up, and tried every fly in our boxes before I asked the cameraman to put his tiny underwater camera on a long probe and search nearby rocks and pockets for fish. A minute later, he had me check out his viewfinder, and there was the proof: several trout sleeping next to boulders and logs. We had an early lunch, midges emerged, and the fish came out and fed; we got some nice filming in late that morning.
Another time, my friend Terry and I hiked into a secret lake only to find hundreds of big rainbows in a ball, slowly circling while sleeping along the lake's drop-off. Terry presented a heavily weighted nymph into the ball of trout to wake them up and took a huge rainbow on his first cast. A short while later, mayflies emerged and the fish rose to them; we had a banner day.
— Craig Mathews
Bull trout rest after a long migration. British Columbia. _Photo: Steven Gnam_
A trico hatch on the Henry's Fork spring creek. _Photo: Jeremy Koreski_
## _"DEVELOP A SIMPLE EFFECTIVE PLAN."_
—The O'Dell Creek Gang
## Chapter 5: Fishing Situations
## YVON CHOUINARD, CRAIG MATHEWS, AND MAURO MAZZO
The fisher who declares that he or she fishes only with dry flies or nymphs or streamers or casts only to rising fish regardless of the conditions will often find himself or herself fishing in an ineffective way.
Certain rivers, or parts of rivers, can be fished most effectively with very specific techniques. When you add the season of the year, the time and conditions of the day, the insect activity at that hour, and so on, you have a puzzle that cannot be solved with a single technique.
However, there is no need for the average angler to be an entomologist. You need not know the difference between a mahogany dun nymph and a pale morning dun nymph. You can even forget about emergence dates, fly sex, maturity, and immaturity. You need not always have to match the hatch. Look at the water in front of you, break it down into segments, and think about where the fish are holding and where you need to be to present a fly to them: Develop a simple, effective plan.
### The Detective
Angling legend Charlie Brooks once said, "The single most important thing a fly fisher can know is the character and quality of the rivers and streams he or she fishes."
Three things often limit the success of anglers, beginners and experienced alike: trying to fish too much water in too little time, a lack of simple planning, and using inappropriate tools, methods, or techniques. Knowing what to expect on the rivers, lakes, and streams you plan to fish can save you time and money and result in huge successes. There is much fly fishing information available online, in books, at local fly shops, and from fly fishing guides and clubs. Armed with this information, anglers can be prepared to fish their target waters in most fishing situations.
Before you can catch fish, you have to know where the fish are and what they are eating. You have to do a little homework. You have to know what to expect and have an initial concept of when to switch from nymph to wet or to dry. Read books, research online, talk to those who know; find out what bugs to expect and the dates of emergence for those bugs for your target river. Bring a little net to find out what bugs are on the river when you get there. Look under rocks, around bushes, and in the air. Do what the river tells you to do.
– Craig Mathews
Craig Mathews reads the rocks. Madison River, Montana. _Photo: Patrick Daigle_
A fine westslope cutthroat from British Columbia's Elk River. _Photo: John Juracek_
### The Innovator
I clearly remember the most memorable trout that I've ever caught. I had spotted a large Snake River cutthroat sipping pale morning duns (PMDs) on Flat Creek in Jackson Hole. I've found that cutthroats feeding on PMDs can be extremely selective, often keying in on only one stage of the mayfly.
This fish was feeding close to the cutbank of this meadow creek just below a little snag. It would take a delicate curve cast to the left to avoid the snag, and the best I could get would be a two-foot-long drift.
After countless tries, I finally started to get the cast down, but the clever fish had no interest in my dry fly. I cast and rested the fish and cast again for almost an hour. Finally, I put it all together with a combination of 7X tippet, a lucky curve cast, and a stripped-down size 20 PMD dry fly that I converted into a "physically challenged emerger." The final solution was to put spittle on the back third of the fly so it hung below the surface film. Don't be afraid to experiment; try different things, and figure out what works.
– Yvon Chouinard
### The Fish
When I start fishing, I try to think like a fish or at least try to guess where a fish would stay and what it is going to do. I look around for likely places, like boulders, that offer good cover and a continual supply of food. For instance, you might think that the middle of a big pool in a sizeable river is the best place, but most of the time it is the worst; the middle of the pool is where the fish are more exposed to predators. You will find only small fish there, and we want to catch the big one.
The first places you want to look at are nice rocks at the tails of pools. Those are the first places I would stay if I were a fish. Going upstream, if I were a fish, I would hang under the edges of the current that is created by big boulders. On those edges a fish would certainly have larvae or insects drifting down with the current.
The best places for fish are ones that have plenty of cover. Nice big pocket water is the best place for the big fish to be and where they can find easy food. It's like having a holiday in Mexico: You lie down, wait for the food, and then go back to your beach chair. That's what fish want to do; fish are lazy.
– Mauro Mazzo
No need to hurry, it's a cripple. A native Yellowstone cutthroat rises for a green drake mayfly in the Yellowstone River, Yellowstone National Park, Montana. _Photo: John Juracek_
## FAST MOUNTAIN WATERS
Turbulent water, to be sure, but plenty of trout live along the quiet edges of the Lamar River. This is ideal water for a heavy nymph. _Photo: John Juracek_
Rivers and streams that flow through canyons or gorges are usually rough-and-tumble waters. Most are rich in insect life. They tumble over boulders and jagged rocks and are hard or impossible to wade— and sometimes dangerous. Wade rough-and-tumble waters as little as possible to avoid a dunking.
In rough-and-tumble waters, trout need relief from heavy currents. Most first timers focus on the standing waves of white water as they crash around huge boulders and snags of timber. But anglers should disregard the rough water in the middle of the river and instead concentrate on the slower margins—the pockets and pools along the edges. Fish the river as you would a small trout stream.
Trout do not occupy every inch of a fast, rough stream or river. And they will not move far for a natural or artificial fly. It is important to fish only the holding water where fish are lying and accustomed to getting their groceries. Holding water also gives trout protection and security.
This type of water is the easiest to read and learn because of all the clues it offers: visible currents, foam lines, pockets, pools, seams, and obstructions like boulders and log jams. An added plus is the noise of the waves and heavy currents that allows fishers to get close to holding water without spooking fish.
Visible currents are created as water moves swiftly around boulders and waterfalls or as it whirlpools and bubbles behind downed timber. These currents are easy to see, and relief from them means big trout will be present—and usually lots of them.
Foam lines are apparent but are seldom recognized as the conveyer belt bringing food to, or providing escape routes for, trout. Thin foam lines appear behind or next to boulders in the main current or along boulders next to the bank where several currents may merge. Below this, the foam line spreads out, and at this point, in the broader and slower currents, trout begin to hold and feed. The foam lines must be six inches or wider before trout will use them for cover, feeding, and relief from heavy currents.
A pocket is deep water located below a logjam or boulder. Fish use pockets like they use foam lines.
Seams are the transition water most trout prefer to hold in. The water separating the quiet water on the inside from the fast water on the outside of boulders is a good example. There are seams on and beneath the surface. They may be associated with visible currents, pockets, undercuts, foam lines, or logjams. As anglers put in more time on the water, they will come to readily recognize more productive seams. Seams can be counted on to produce more good trout than any other area.
Jeremiah Watt negotiates the rough-and-tumble water of Big Cottonwood Creek, Utah. Photo: Jay Beyer
Davide rappelling down the Cascata del Tinaccio, on the Artogna River, Italy. _Photo: Mauro Mazzo_
### The Journey Versus the Destination
Davide is a good friend who works as a Sesia riverkeeper. For years, he and I had been looking at a very big pool on a nearby river that was nearly impossible to reach. Above and below it were more than 150 feet of sheer rock wall. Because it was so hard to get to, we figured no one had fished it: We thought that a place like that should have plenty of fish and possibly some big ones.
One summer day, we decided it was high time to fish it, and we worked out a plan to reach the pool and gathered the necessary gear. We climbed up to the top of the sidewall, crossed it, rappelled down to the pool, and eventually fished the pool.
Since we thought this would be a day to remember, we decided to take lot of pictures. We started early in the morning, and while Davide climbed the correct side of the rock wall and rappelled down to the pool, I climbed the opposite side of the wall and took pictures of him as he reached the spot. Once he got close to the pool, he stopped and waited for me: The magic moment had to be shared.
So I rappelled down my side of the rock wall, climbed up the right side, and rappelled down again to join Davide. All this took about eight hours, but now we were there, ready to fish the pool that no one had ever fished before.
Davide insisted I had to fish it first. Eager to accept his graciousness, I tied a small nymph on, and as soon as the fly touched the water, I put a little tension on the line, anxious to feel the bite. Nothing. I cast again, waited a little bit more, and nothing. Next, Davide took a turn.
We tried just about every fly and every trick, but we did not get a single touch. We sadly came to the realization that there were no fish at all in the pool. Disappointed, we decided to leave.
We were silent on the way back home, each coming to grips with our failure. But after a while we started talking, and we agreed that although we didn't catch any fish the day was really fun, and we had learned a lesson: It is the journey that is important, not the destination.
– Mauro Mazzo
#### WET FLY FISHING FAST MOUNTAIN WATERS
Fast mountain streams are caddis and stonefly water; I wouldn't bother with small flies. This is good water to do the two-fly, soft hackle and dry caddis, technique. Use a large attractor soft hackle like a size 8 or 10 for the point fly and a large buoyant dry fly for the dropper.
Cast downstream so the point fly enters first into every piece of soft water, foam line, eddy, or pocket. Sometimes in rough water you can bounce the dropper fly off the top of little waves. If that doesn't result in a strike, drag the soft hackle upstream and into the same areas.
You can also run a streamer through these same places. If there is a suck hole or reversal, drop the streamer in it and the fly will get sucked down so you can get the fly down deeper into the next pocket.
– Yvon Chouinard
#### NYMPH FISHING FAST MOUNTAIN WATERS
Keep the casting to a minimum in this kind of water to avoid spooking fish. In very small pockets, do not cast at all, and just drop the fly right above the spot you want to fish.
The easiest way to fish the nymph in this kind of water is to use a tandem formed by a big dry fly and a lightly weighted nymph tied under the dry at a distance of about one and a half times the average depth of that stretch of water. The use of a speed dropper like the one Yvon describes in the wet fly tenkara section (page 51) will give you the opportunity to remove it quickly and switch back to fishing with only the one nymph when you find a deeper pool so you can fish it properly.
You will see some spots on a steep creek that look impossible to fish but often hold some big fish. The most common spot is the area under an overhanging tree with branches touching the water. An impossible place to cast to, but there is a solution—a dirty trick.
Walk upstream of the spot—preferably on the riverbank, not in the water—making the least noise possible. Position yourself about twenty-five feet upstream of the spot. Tie a big caddis on the dropper, and use a small weighted nymph as the point fly. Put the fly on the water, and shaking the rod tip, let out enough line so your rig gets under the branches. If there is a fish around, he will take it.
– Mauro Mazzo
In this clear limestone water the fish are hiding above and below rocks and in the deeper pools, coming out in the open only when there is an active hatch. Plan River, Alto Adige, Italy. _Photo: Mauro Mazzo_
### Old School
One of the Valsesia's old fishing masters, Arturo Pugno, told me about a style of fishing where they tied a special rig made with three hooks and a dead fish on one of the hooks. Then they maneuvered it into the broken water under a cascade to give the marble trout the illusion of a wounded fish.
They were fishing with no reel, using heavy cane rods with a rope attached to the butt. When they hooked a fish that was really big, they threw the rod in the water and watched it until it got close to the bank, a sign that the fish was tired. If that didn't happen, they had to jump in the water and swim after it.
Arturo's biggest marble trout was more than fifteen pounds. After more than an hour, the fish was not coming close to the bank, and he decided to swim in the river, grab the rod, and pull the fish in. This was nothing unusual for him, except that it was February and the temperature was many degrees below freezing.
– Mauro Mazzo
The old ways die hard: Arturo Pugno, 'the Valsesiana master,' fishing with his sixty-year-old solid cane rod on the Sesia River, Italy. He spotted a good grayling in the fast current. _Photo: Mauro Mazzo_
#### DRY FLY FISHING FAST MOUNTAIN WATERS
When fishing dry flies, you want to be fishing rough-and-tumble waters when insect activity occurs. If you want to fish a caddis hatch, you should arrive late in the day as caddis emergences occur in the evenings. This is where planning for success is so important.
Slowly walk the banks and fish every hold, pocket, and seam. If you suspect trout will be rising to an expected hatch, walk well back from the banks to avoid disturbing the water.
If there is an emergence of caddis or mayflies, match it and fish accordingly. If no fish are rising and no insects are active, pick a fly that imitates an insect trout recognize as food for that time period.
On rough water, trout often appear to be rising to mayfly duns riding the surface. Pick a fish and present your cast while observing the fish. If the trout lets duns pass as it continues to rise in the holding water, switch to an emerger or wingless floating fly or cut the wing off the dry fly you are using.
If fishing midges, anglers should keep in mind that trout working midges in rough-and-tumble conditions do so in thin water. They are very hard to approach and usually you will get only one drift over them. These fish are used to deep water with cover, heavy flows, and security, so try not to wade when getting close enough to present a cast.
The finest dry fly angling on rough-and-tumble waters occurs when female salmonflies return to the water to lay eggs during the afternoon. It is important to locate the area on the river when and where the females are laying their eggs to be successful.
– Craig Mathews
The Plan River is a very secluded place with almost no fishing pressure. Alto Adige, Italy. _Photo: Mauro Mazzo_
### That Old Guy
Last summer, I watched four anglers fishing an area the size of a pool table for two hours on a rough-and-tumble water stretch of the Madison River. As I sat on the opposite side of the river fishing a caddis emergence, catching and releasing several trout, I noted they were not taking a single fish. I knew why. The water they presented their flies in was six inches deep and very swift, not the water trout would hold or feed in. Still, the anglers cast and cast and switched positions several times.
The next day, I saw their vehicle as it pulled up in front of our shop. The four young anglers strolled into the store, and I asked how their fishing had been. They said they'd just pulled in late yesterday from a marathon drive all the way from Atlanta, Georgia, and had fished the night before but had not taken a fish. They said something about an old guy across the river from them taking fish last night. I could not resist and told them "that old guy was me." I gave the red-faced newbies a few Iris Caddis emergers and drew them a map of where to expect rising fish near the Three Dollar Bridge along the Madison.
The next morning, they came in with fresh coffee and a donut for "the old guy," thanking me for showing them where to fish during evening caddis on rough water like the Madison River.
– Craig Mathews
The "old guy" at his tying desk. Blue Ribbon Flies, West Yellowstone, Montana. _Photo: Patrick Daigle_
## SLOW MEADOW WATERS
On a meadow or spring creek the larger fish are holed up under the undercut banks. South Fork of the Madison, Montana. _Photo: John Juracek_
This water type is typically a meandering meadow stream with even, smooth currents interspersed with riffles and pools. Reading this water requires lots of bank walking, concentration, great eyesight, and plenty of patience, but it also may provide a few pleasant surprises like huge trout rising to the surface that leave barely a dimple.
Beginning anglers should also be on the watch for fish migration on slow meadow waters. An area that fishes well one day may be devoid of trout the next. Some feel that fish do not adopt a permanent holding spot on slow meadow waters. On many smooth rivers and streams, it pays to move and cover lots of water if you fail to raise fish in spots where you had recently found them.
Sound and vibrations transmit very far on these meadow creeks. You need to walk very quietly to avoid spooking these fish. You really should be barefooted or wearing leather moccasins.
There are four features found on slow meadow waters that concentrate insects and trout rising to them. You should watch for whirlpools, back currents, scum lines, and feeding troughs.
Whirlpools are formed when currents work around logs, sweepers, and islands. Look for back currents that collect insects at the end of whirlpools. Be alert here for single trout, and whole pods, that will come to the surface for terrestrial imitations like ants, bees, grasshoppers, and crickets as well as insect emergences of mayflies and caddis. Due to the direction of flow in whirlpools and back currents, trout may face downstream.
Scum lines and feeding troughs are found where currents come together. Slow meadow waters hold areas where one current sweeps along an overhanging bank as another current comes off a weed bed or obstruction like a log and merges with it at a gravel ledge. These scum lines provide tight feeding lanes, and trout will seldom move far to take a fly. In places like this, trout might drop back to where two scum lines come together to form a longer, wider lane known as a feeding trough. The troughs might be several feet wide and several feet long and hold dozens of trout.
Other excellent places are the potential shelters close to the bank. Undercut banks and logs and stones breaking the current along the bank create ideal habitat for fish. Also search the pocket water created by a stone or a log breaking the water's flow midstream. The fish will often hold in this calm water, feeding on the two currents in which the main current has been split by the obstruction. Check also for any deeper and slower stretches.
The long evenings of June provide plenty of time for fishing on the Madison River in Yellowstone Park. _Photo: John Juracek_
#### WET FLY FISHING SLOW MEADOW WATERS
Soft hackles will work whenever there is a bit of depth (more than six inches) and moving water. You will catch mostly small fish in the shallow water except in the early mornings or evenings when there can be some larger fish.
Inside every bend of the stream, there will be a deep pool. That's where the big fish are, tucked down deep under the undercut banks. They don't like to come out for anything small or that isn't at their depth. In the evenings, fish with heavy streamers to draw out these big brown or brook trout.
– Yvon Chouinard
#### NYMPH FISHING SLOW MEADOW WATERS
The prime waters for the nymph fishers here are the undercut banks and the deeper waters.
Undercut banks are some of the most interesting water on a small stream; these are the places where the big guys hide. Here, your chances of success depend on the way you approach the stream. The noise made by your walking will scare the fish, so you have to move either like a ballet dancer or a special-forces member. They are quite different people, but both of them are really good at moving lightly; choose the style that suits your personality.
You will need to fish either at short or medium distance. If you are able to see the nymph in the water, short-distance sight fishing will be your choice. Cast as close to the bank as possible and follow the drift of your fly with your eyes. If you see anything happening close to your fly, like a sudden flash or a shadow covering the fly, strike. Often, that flash or shadow is a fish. If you have a problem seeing the fly or if the water is colored, use an indicator made with a piece of fluorescent nylon, or use a dry fly as an indicator.
There are strike indicators that look like a small float that you can buy in a fly fishing shop, but consider that the bigger the indicator, the more takes you will miss. This happens for two reasons. Very often, the fish takes the fly and spits it back out very quickly because it realizes there is something wrong; in this case, you will not even see the smallest movement in the float. The second reason is connected to this first. The resistance offered from the strike indicator to the nymph affects its drift and will increase the chances that the fish realizes there is something wrong and refuses your fly completely.
It is better yet to use a dry fly as an indicator. Working a nymph suspended to a dry fly will make it much more effective to fish the undercut banks: The fly will pass in front of the nose of the fish at the fish's depth, and you will be able to fish at longer distances, thereby reducing the chances of spooking the fish. Cast as close to the bank as possible and follow the drift of your fly with your eyes. If you see your indicator stop, strike immediately.
As a general rule, remember that we are trying to make a fish believe that a bunch of hair, fur, and feathers is real food. We should feel obliged to present it with the most natural drift. Otherwise we would be shameless.
If you are fishing a pool, the first place to look will be its head, where the food taken by the current settles down. Normally, there are also fish at the tails of the pools, but because the water is often shallower there, it is a better spot for the wet or dry fly fisher.
More often than not, it is mandatory to fish upstream, so the most effective technique will be high-stick nymphing. Keep your leader pretty short when fishing with a regular fly fishing rod and reel; you want to keep as much fly line as possible out of the tip to load the rod more easily. A good compromise for the leader is seven to eight feet with a tippet length of two feet.
Most of the time, one nymph will be sufficient, but if you like fishing tandems, the combination of a nymph and a dry fly can be very efficient. You can try the two-nymphs rig only in a very deep pool, where the use of a heavy nymph as point fly will help you reach the bottom quickly. Tie on a smaller fly as the dropper to differentiate the offer.
– Mauro Mazzo
#### DRY FLY FISHING SLOW MEADOW WATERS
Slow meadow waters always appear inviting and easy to fish with trout holding in every bend, but their gentle character belies their fickle nature. Here, the fish will not allow as close an approach as those trout rising in rough water. And myriad currents make drag a constant consideration. Make your cast and watch carefully as the fly approaches a rising fish.
If you see a trout holding, but not rising, try a beetle, ant, or bee straight upstream or slightly across and up. Limit your cast to not more than twenty-five feet. Usually, the fish will come up and take on your first or second offering. Often, it may inspect the fly on the first cast, then move back to its hold. Don't pick your fly off the water too quickly, as many times the fish will come back from its hold and take the fly. If you had pulled your fly off the water, the trout returning to search for it might spot you and spook, or the fish might become suspicious and refuse to look at your next presentation.
When fishing dry caddis patterns on slow meadow water, approach from upstream and cast across and slightly downstream. If you have to approach from downstream, present your fly on a slightly up-and-across angle.
In summer, with so many other insects emerging on smooth flowing waters, many anglers fail to consider midges when they come upon rising trout. There are times, however, when fish will take only impaired or crippled adult midges, even though there may be far more caddis or mayflies present on the water.
Use terrestrial patterns to prospect slow meadow waters. A favorite method on slow meadow waters is to walk the high banks and bluffs of rivers and streams and every few yards creep to the edge of sharp banks and bluffs that overlook the river. You will be amazed at how many fish are in knee-deep water waiting on terrestrials to fall, crawl, or fly into the water. Fish searching for terrestrials will travel considerable distances, so it is always best to have someone watch the fish while the other sneaks up from downstream: It's of no use casting to where a fish was instead of where it is.
– Craig Mathews
Feedlines, rocks, and deep depressions equal ideal trout water. The Gallatin River in Yellowstone Park. _Photo: John Juracek_
### Fooled by Midges
My good friend Terry and I were fishing the Firehole River last spring during epic pale morning dun and caddis emergences. Fish were feeding everywhere along the meadow stretches of the river. We walked to the river and sat on the bank, excited by so many fish we thought were feeding on emerging PMDs or caddis. Instead of taking time to carefully observe the river and determine what the fish were feeding on, we rigged up—Terry with a caddis emerger and I with a PMD mayfly cripple. Several minutes and no fish later, we sloshed to the shore and took out our handy insect nets to sample the flow. There we saw what the river was telling us to do; in the tiny mesh of our insect nets were dozens of midge emergers, many crippled and impaired. We knotted on Zelon midges and each took several rising fish that morning.
– Craig Mathews
Dawn patrol: Streamer fishing for fall-run brown trout on the upper Madison River, Montana. _Photo: John Juracek_
## SPRING CREEKS
Spring creeks are rich with aquatic plants and insects. Idaho. _Photo: Steven Wohlwender_
Spring creeks offer the most challenging fly fishing opportunities. They feature constant, clear flows in mixed currents over weed banks and obstructions. To get to know one is to spend much time on its waters. They are often moody and changing, and anglers must adapt to be successful.
Spring creek trout are usually visible as they actively feed on insect activity like emergences and egg-laying times. Look for fish to be holding in or near weed banks, overhangs, undercuts, downed trees, and brush as well as under bridges. It pays to be patient and spend time observing and sneaking along at a snail's pace learning the creek and its secrets.
#### WET FLY FISHING SPRING CREEKS
One of the largest spring creeks in the world is the Henry's Fork of the Snake River in Idaho. With its slow-moving water, complex micro-currents created by weed beds, and multiple and complex hatches, it is one of the most challenging streams to fish. Consequently, it attracts some of the best fly fishermen from all over the world.
When there is a hatch happening, it is best to try to match the exact insect, stage, and even gender of the bug that you think they are feeding on. When there are fish rising but there are no visible bugs around, you can often induce the take by fishing a soft-hackle Partridge and Pheasant Tail, which imitates most mayflies.
Cast downstream to the rising fish, except in the summer when floating pieces of grass make it impossible to swing wet flies. In conditions like this, I position myself across from the fish and fish the soft hackle dead drifted like a nymph or emerger. Use only one fly because with a fish on, the other fly will catch on weeds or grass.
The micro-currents that are the bane of the dry fly purist are not a bother with my soft hackle. Also, since I am fishing downstream and the fish never sees my tippet, I don't have to use 6X or 7X tippets, an advantage when landing one of those hefty rainbows.
This is just one example of where the wet fly technique excels on spring creek water.
– Yvon Chouinard
#### NYMPH FISHING SPRING CREEKS
More often than not, it is mandatory to fish upstream and quite far from the fish, in order not to be seen. For this reason, sight fishing at a medium to long distance is the tactic to use. Long leaders are mandatory, together with a very delicate presentation; you want to disturb the water as little as possible.
It is better to use only one nymph, because when sight fishing it is difficult enough to follow the drift of one fly, let alone two. The most effective way to cover this kind of water is to cast a small mayfly imitation up and across to rising fish. I would suggest a Pheasant Tail Nymph tied on a size 16 or 18 hook as universal fly. If you see anything happening close to your fly, like a sudden flash or a shadow covering the fly, strike.
– Mauro Mazzo
One of the world's largest spring creeks, the Railroad Ranch section of the Henry's Fork, Idaho. _Photo: Jeremy Koreski_
#### DRY FLY FISHING SPRING CREEKS
Because spring creeks are so challenging to dry fly fish, successful anglers must be prepared to fish predictable insect activity. Know the weather forecast for the day you are fishing: Cool, damp days provide optimal conditions for heavy mayfly hatches.
Blind fishing a spring creek when there are no rising trout only spooks the fish and is seldom productive. There are exceptions such as during terrestrial periods when grasshoppers, beetles, ants, and butterflies are active; the other is during damselfly and dragonfly periods. This might be the only time anglers see big trout throw caution to the wind and chase natural and artificial flies.
On smaller spring creeks, you seldom need to wade, and if you do, it is only to get into position for a cast. On large spring creeks, you often have to wade to follow fish rising to insects as they move upstream. Always approach rising trout from downstream and present casts to them up and across.
– Craig Mathews
Jiry Klima, one of the most successful Czech competition fishermen, nymphing on the Vltava River, Czech Republic. _Photo: Mauro Mazzo_
## FREESTONE RIVERS AND STREAMS
Typical freestone water on a northern section of the Sesia River, Italy. _Photo: Mauro Mazzo_
There are few surprises on freestone waters; they are read like an open book, with trout holding where they should in pockets and pools or at the bottom of riffles and runs. There are always plenty of overhangs, undercuts, sweepers, and rock piles. They include the habitats covered already in the sections on fast mountain and slow meadow waters. And big freestone rivers can be broken down into those fishing situations.
When no insects are bringing fish to the surface on freestone waters, search for trout in riffles, runs, pockets, pools, sweepers, and overhangs. These waters are always cold and some of the last to clear of snowmelt. Insect emergences are later than those on larger waters that warm earlier. Hatches are unpredictable due to late snows or erratic spring weather. All this can make planning to fish them difficult.
### Deep Knowledge
We've heard a story about a young Native American fellow in Oregon who decided he wanted to become a steelhead guide. For a couple of days, he floated down the river with a mask and snorkel observing where the fish were. He immediately became the best guide on the river. What he observed in a couple of days would take years and millions of casts to learn in the normal way.
– Yvon Chouinard
Claire Chouinard swims with the sockeye. Adams River, British Columbia. _Photo: Matt Stoecker_
#### WET FLY FISHING FREESTONE RIVERS
The techniques described in the chapter on fishing tenkara with soft hackles apply perfectly to freestone rivers.
If there is no specific hatch on, I would use a size 14 attractor pattern, find some moving water, and work my way downstream. Even if there is a hatch of midges or small mayflies, I often disregard the hatch and stick to an attractor fly. Even during the height of a salmonfly occurrence, I've been known to continue with a size 14 blue soft hackle . . . and catch my share of rainbows and browns.
– Yvon Chouinard
#### NYMPH FISHING FREESTONE RIVERS
A freestone river is essentially a bigger mountain stream, and most of the fishing situations are the same. Do not be misled by the dimension of the river; remember that fish are often close to the banks. Don't concentrate only on that pocket in the middle of the river that is impossible to reach; the fish are very often very close to your feet, and if they are not there, it is only because you scared them away. Described below are two situations that are unique to freestone rivers. One is a long run of water with a constant depth, and the other is a big pool with a dimension that can often confuse the novice.
A long run of water with a medium current and a depth of two to three feet is prime water for grayling in Europe. Locating the best spots when fish are rising is quite easy, but when there is no surface activity, this water can be difficult to read.
You have to remember that fishing nymphs is an exercise that involves reading the river in three dimensions, not two. So in this kind of water, you will have to look for any submerged rock or any variations of depth that can create a food deposit for the fish. Another indicator to use is the color of the bottom. Dark rocks covered with algae mean a mature bottom, a place where water always flows and where the algae offers perfect habitat for larvae and nymphs. A bottom made of sand or very light and clean rocks means poor habitat or a place that gets dry often—in other words, a place that offers no food.
Once you have located a nice-looking area, the best way to fish it is the classic Czech nymph way—fishing downstream with a short line. Fish the whole width of the river, moving toward the far bank; then walk downstream about ten feet, and come back fishing in the opposite direction.
Another way to cover this water while reducing the chances of scaring the fish—especially when the trout population is predominant—is to fish with a strike indicator. The drawbacks of this technique are discussed in the section on slow meadow water nymphing.
When fishing a big pool with a cascade at the head a good approach is to start from the tail, where usually you will find smaller fish. The water will be quite shallow, so use either two light nymphs or a dry fly and a nymph. My favorite rig is with a dry fly on the dropper, and a nymph as point fly, with about two feet between them.
The dry fly should be highly visible—I am devoted to a Klinkhammer fly, but a parachute fly also works. For the nymph, I suggest the always-effective #14 Pheasant Tail Nymph or Hare's Ear Nymph.
For the deep part of the pool, you can switch the small nymph to the dropper and tie on a heavier nymph as point fly. For this kind of rig, it is advisable to include a piece of fluorescent nylon in your leader to help detect the bite.
Once you are done with the deep part of the pool, you can proceed to fish the head of the pool. This is the most frightening water for a novice as the fast whitewater looks nearly unfishable, but this water often holds the biggest fish. Here you have only one choice: a big and heavy nymph. When fishing a nymph in whitewater, or under a fall, you first have to look for the slower current into which the main current is always broken and fish there.
Do not even try to make a free dead drift; more often than not you will snag your fly. Keep in mind that your fly always has to be kept under control. A way to fish this water is to use a big stonefly nymph and, keeping some tension on the line, let your fly sink till you feel the bottom. Then do a little twitch, to make the fly bounce on the bottom and to avoid snagging.
The best hook to use is a jig, as it works upside down and reduces the chance of snagging the fly on the bottom. The use of big flies, with bodies wrapped with turns of hackles, or made of bulky materials such as dubbed hare's ear, will also reduce the chances of snagging your fly on the bottom.
– Mauro Mazzo
#### DRY FLY FISHING FREESTONE RIVERS
Anglers should always have a few high-floating dry flies for searching this type of water. Bring a basic selection of mayflies, caddis, and stoneflies to imitate those you expect to find. Bring a small selection of terrestrials too. Work upstream and present a short, slack-line cast with a dead drift.
An effective method when approaching risers this closely is called "dapping." Sneak along the bank and keep a low profile while searching for the deepest, outside part of a meander. This is perfect for tenkara as, without casting, you can dap only your fly, tippet, and leader on the water in front of a rising fish.
On this water type, you will find many fish rising in each pool and pocket during mayfly activity. If you are fishing trout rising to a mayfly emergence, position yourself ten to fifteen feet below the rising trout and observe what the fish are rising to, and then present a pinpoint-accurate cast. These trout will rise in very narrow feeding lanes, so you must be on target.
On freestone rivers, pick a high-floating, visible caddis pattern that requires little babysitting to keep it floating. An X Caddis is easy to see, floats like a cork, and imitates an impaired or crippled caddis, a stage the trout recognize and take readily.
Stoneflies are usually present on all freestone waters, and you should be prepared to fish stonefly patterns whenever trout are rising to naturals.
But nothing compares to a late-summer day fishing terrestrials on freestone streams. As winter approaches, trout are willing to take most any terrestrial pattern, from butterflies to bees and crickets to grasshoppers. Fish the edges and overhangs where trout expect to see insects that have fallen into the water. Search all holding water, feeding lanes, seams, and pockets on a short line with a drag-free presentation. Don't spend too much time, though, as there will be a beaver dam or spring creek-like section of the freestoner just around the next bend with big trout rising.
– Craig Mathews
The Plan River, Alto Adige, Italy. _Photo: Mauro Mazzo_
### New Year's Day
It was New Year's Day, and the morning temperature broke the plus side of zero for the first time in two weeks. A herd of elk grazed below the house near the river. Since the cold had kept us inside for so long, we decided we would head to the river to see if we could catch our first trout of the New Year.
There was no wind, and the sun was blinding as it burned off the hoarfrost on grasses along the river. We put on our pac boots, grabbed our tenkara rods, and slogged through several inches of snow to the river.
Midges were already emerging along the shore, and clusters of mating midges the size of dimes were rolling through holding water behind boulders and in pockets and pools. We watched several nice trout rise casually to midge clusters and took turns catching a few rainbows before the sun's rays lost their punch and midge activity shut down for the day.
– Craig Mathews
Midges are an important source of food for trout during the winter months; their emergences and egg laying often take place at temperatures at or even below freezing. _Photo: John Juracek_
## LAKES AND PONDS
A typical alpine lake, best fished in the early morning or early evening when there is a hatch. Profa Lake, Santa Caterina Valfurva, Italy. _Photo: Mauro Mazzo_
Lakes, ponds, and sloughs will give the fly fisher opportunities to catch larger trout on flies on public water than any other water type.
When searching lakes for fish, look for drop-offs, weed beds, points of land extending into the lake, gravel bars and sandbars, and springs entering, as well as outlets leaving, the lake. Overhanging trees and downed timber provide good food sources and security areas for trout, and sagebrush banks and meadow areas along shorelines can bring grasshoppers, ants, and beetles to the water for fish to feed on. Remember, too, that the largest fish will be near the best security cover.
Trout in lakes are usually on the move as they look for food and the best cover, whereas trout in ponds and sloughs will often be stationary, facing into currents caused by springs or the dammed stream that forms the pond. Always slowly walk the bank, and use waterside cover to locate cruising fish. Be on the water at different times of the day in order to learn when and where the fish move and where their security areas are.
It pays to patiently walk the banks, staying well back from the shoreline. Use the sun to your advantage when stalking the banks for fish. You will be amazed how well trout stand out in sunlight. Nervous water created by fish moving and patrolling for food is a key for anglers to cast well in front of the wakes and strip a streamer or twitch a dry fly on their approach.
Anglers can also fish still waters by wading or from float tubes, boats, and small pontoon boats that are so popular now.
### Locals Only
I will never forget locating the secret "locals" pond in Yellowstone with Labrador-sized brook trout. I was still police chief in West Yellowstone, and Larry, the town's attorney, had hinted its location to me that summer. When cop matters quieted in September, my wife, Jackie, and I headed out one frosty fall morning to find the pond he told me about that reportedly held four- to five-pound brook trout. We'd sloshed a couple of miles through beaver-dammed backwaters along a smooth-flowing stream where the tiny pond was hinted to be. Resting at a small spring inlet pond dammed by beavers, I told Jackie we had gone far enough and had to go back to Larry for more clues. Just then, three huge brook trout, as if on cue, jumped simultaneously not ten feet in front of us. It turned out we didn't need to go back to Larry; we had found the pond after all.
– Craig Mathews
The shallow, still waters of a beaver pond require a stealthy approach, long delicate leaders, and a "soft" presentation. Idaho. _Photo: John Juracek_
#### WET FLY FISHING LAKES AND PONDS
Many lakes have leeches, which can be a primary food for lake-dwelling trout. Cast out, let them sink, and fish them with a slow strip with a pause in between strips. The fly needs to have an undulating motion like a swimming leech. Make sure your leech patterns have weight in the front.
All lakes have chironomids (midges), and a soft-hackle midge pattern fished with a twitch is a very effective technique as midges are very active swimmers. At a high-altitude lake in Wyoming, I've watched golden trout come up from twenty feet down to take a size 22 red-body soft hackle on the surface fished in this manner.
If there are caddis, a twitched soft-hackle caddis pattern will be more effective than a dead-drifted floating dry fly.
If there is not much going on insect-wise, try using two flies on light tippets, the point fly being a heavy bead head. Let them sink for as long as you can stand it, and then bring them up to the surface in small strips.
– Yvon Chouinard
#### NYMPH FISHING LAKES AND PONDS
When nymph fishing in lakes, it is imperative to scout around for the places described at the beginning of this section on lakes and ponds. If the wind is blowing, the downwind side of the lake or pond is usually the best, as most of the food will be taken there by the action of the wind. The use of two or three nymphs will cover more water.
When using a scud imitation, fish it with a nearly still line. Cast your flies as far as possible and let them reach the bottom; then do a little twitch every once in a while to make them more visible to the fish.
When fishing damselfly nymphs or other swimming nymphs, I suggest another approach, which is very useful when using intermediate or sinking lines. When the flies hit the water, count to five (one hundred and one, one hundred and two, etc.)—as a way of knowing what depth you reached—before starting a steady retrieve. If you get a take, you can reproduce that depth on the next cast. If you don't get a take, on the next cast count to seven or eight; repeat increasing the count until you discover the depth where the fish are. Then carry on fishing at this depth, varying only the retrieve.
– Mauro Mazzo
#### DRY FLY FISHING LAKES AND PONDS
If you want to fish dry flies, be prepared for mayflies, midges, caddis, terrestrials, and damselflies and dragonflies. Be on the water when these insects are active, and they might bring trout to the surface. Few anglers try mice patterns on still waters. Dry mice flies can bring surface action at times, particularly in late evening and into the darkest hours.
On occasion, searching these waters with dry flies can be productive even though no insect activity is bringing trout to the surface. Try terrestrials along brushy banks or areas where overhanging trees bring ants, beetles, bees, or grasshoppers to the water.
If fishing from a float tube or boat, anglers must make sure not to create waves from the boat or float tube by kicking into position. Keep false casting to a minimum, and make sure your presentation is spot on target, as a rising fish will not move from its lane to take a fly.
At all times when fishing a caddis hatch, I use an impaired caddis adult with a trailing shuck like an X or X2 Caddis that floats and skitters well. Cast this dry fly in front of rising fish and strip it into their path with a six- to twelve-inch strip.
On lakes and ponds, midges bring up more trout than any other insect and should be at the top of your list when you see rising trout on still water. Most midge activity occurs during the warmest time of the day when it is calm, which is late afternoon around 6 p.m. Use a crippled or impaired midge adult or an emerging pupa, and get within thirty to thirty-five feet of the rising fish; obviously, you need to use a rod and reel for this type of fishing.
Big trout rising to midges often connect rises every few feet and are those fish that will respond best to proper presentations. They will lock into a feeding rhythm and take adults every few feet. Many times, you will see packs or pairs of fish traveling like wolves and feeding on crippled adult midges caught in their shucks—easy prey. Competition enters in as trout race to the naturals; it is the only time flock shooting works, as you are most certain to get a hit. Present your cast in the path of the rising fish; strike gently to protect your 6X tippet.
One other thing to remember is that after casting it is important to allow enough time to slowly pull on the line to remove slack in the tippet, forcing the fly to come around and face your position. If you fail to do this, the fly will drag even in still water.
– Craig Mathews
Hebgen Lake, Montana. _Photo: John Juracek_
### Sam's First Fish
Late last summer, I was working with a couple of youngsters learning to fish tenkara. We were on a small meadow slough in Yellowstone just off the main road to Old Faithful. I could teach casting techniques to the kids on this tiny pond without concern for wind, brush, or overhanging trees. I knotted on a small grasshopper pattern after cutting the hook point off below the barb for safety. Sam made his first cast ever, a ten footer, against the shoreline, and I told him to twitch the fly then let it sit. He did, and immediately the fly was engulfed in a big swirling rise. I yelled as he yanked back hard on the rod. Since the hook had no point, the fish was gone. Sam asked, "What happened?" All I could offer was, "A big fish hit your fly."
I tied on a fly with a point and the barb mashed down. Sam made another cast, this time a twelve footer. The fly landed with a splat against the shoreline. I told him to twitch it a couple of times, then let it sit still. After a minute, I asked Sam to give the line a short tug. He began to pull the fly, and before it traveled a foot, a fourteen-inch brown slammed it. After a short run and two jumps, Sam towed the fish in, it being no match for 3X tippet. I have a photo of Sam, sporting a toothpaste grin and the fish.
– Craig Mathews
Fish on for seven-year-old Jack. Fall River, Idaho. _Photo: Jeremy Koreski_
_Dragonfly and Rainbow Trout_ , by Dwight Hwang
## _"THE WAY TO MASTERY OF ANY ENDEAVOR IS TO WORK TOWARD SIMPLICITY; TO REPLACE COMPLEX TECHNOLOGY WITH KNOWLEDGE."_
— Yvon Chouinard
## Afterword
## YVON CHOUINARD
The state of the art in angling these days is defined by "sports" standing in a guided drift boat mindlessly throwing Chernobyl ants at the bank. Or maybe just drifting along staring at the red-and-white bobber while the guide rows them into position. The next big advance will be fiber optics embedded in our lines so we can sit in the boat and watch a screen to know when to set the hook. If you didn't see it on your smartphone, did it really happen?
Angling doesn't have to drift further to the dark side. What's happened with fly fishing is no different from what's happened with every other sport or pastime—in fact, with society as a whole.
We all know the present world economy based on endlessly consuming and discarding is destroying our planet. We are the guilty ones. We are the consumers who "use up and destroy." We constantly buy things we want but don't need. And it seems we never have enough.
Our trout rods are designed to throw lead-weighted streamers clear across the river. Reels come with drags engineered to stop a truck, even though we know any old click drag will stop a trout. We love our tools, but too often they have become overbuilt and automated. They get between the user and the real experience.
The satisfaction to be gained from the synergy of hand, eye, and muscle are missing. When you have put in 10,000 hours to master a craft or sport, the Zen master would say, "Now see if you can accomplish the same without all the stuff."
In these trying times, when we are seeing the results of our high-tech, high-risk, and highly toxic economic system, many of us are questioning our frenetic consumer lifestyles. We yearn for a simpler life based not on refusing all technology, but on going back to appropriate technology, what David Brower describes as "turning around and taking a forward step."
It's difficult to imagine an economy that satisfies all seven billion of us, yet doesn't destroy the Earth. As it stands now, we are using up the resources of one and a half planets—a consumption level that is far from sustainable. And yet by 2050, that level is projected to rise to somewhere between three and a half and five planets. It seems we are doomed to endlessly recycle failed systems hoping that this time it will work. If repeating the same action and expecting a different outcome is one definition of insanity, where does that leave us? Certainly, we should replace old inefficient and polluting technology with less damaging and cleaner ones, but that does not solve the true problem: ever-expanding growth on a finite planet.
Just because society is hell-bent on becoming so complex that we finally snooker ourselves into a corner with all our stuff, it doesn't mean we have to go there. We can turn around and take that forward step.
We know we need to consume less on this finite planet. Yet if we do, it puts people out of work. But then with automation, robots, and technology there may not be very many jobs anyway. Perhaps if we buy only what we need rather than what we desire, and if we make sure that what we do buy is multifunctional, durable, repairable, high in quality, and won't go out of style—and can last long enough to be given to the next generation—then perhaps we can keep some people working.
I know there will always be work for the craftsman who spends forty hours making a beautiful and functional cane rod. And I can think of examples where the old ways of doing things have not been surpassed by modern technology.
Consider the "green revolution" farmer in his air-conditioned tractor producing inferior and even toxic food. Contrast that with the small organic farmer or gardener finding contentment and pleasure in using his hand tools or walking behind his perfectly trained plow horses or oxen. The "green revolution" is dependent on unsustainable chemical farming and actually produces less food per acre per resource investment over time.
I have friends who surf on replicas of eighteenth-century wooden surfboards from the Bishop Museum in Hawai'i. These surfboards are thin and flat as an ironing board with no fin, yet my friends ride them better than 99 percent of the surfers on modern plastic boards.
The professional load carriers around the world all carry loads on their heads, from African women with huge jars of water to Sherpa's who carry double loads (one hundred and ten pounds) with a tumpline. In fact, the United Nations conducted a study proving that carrying loads in these traditional ways is 50 percent more efficient than using a high-tech modern backpack.
The ship's carpenter on Shackleton's lifeboat the _James Caird_ took only three simple hand tools with him on the passage from Antarctica to South Georgia Island, knowing if he needed to, he could build another boat with only those tools.
I believe the way to mastery of any endeavor is to work toward simplicity; replace complex technology with knowledge. The more you know, the less you need. In the 1980s, we used to say, "He who dies with the most toys wins." We were wrong.
The lesson we learn from fishing with a tenkara rod is that we shouldn't fear that a simpler life will be an impoverished life. Rather, simplicity leads to a richer and more satisfying way of fishing—and more importantly, living.
A selection of Bob Clay's hand built cane rods. _Photo: Tim Davis_
There are over 800,000 dams worldwide with hundreds of thousands that are silted in, obsolete, and damaging to people and the environment (40,000 in the United States alone). If you believe they should come down, start with the ones in your neighborhood. Matilija Dam, California. _Photo: Ben Knight_
## Additional Resources
Short demonstration videos by each author covering basic tenkara techniques for wet flies, nymphing, and dry flies, plus basic setup of the rod, are available at www.patagonia.com/simpleflyfishing.
## SUGGESTED READING
If you want to master angling with a fly, this is not the only book you need. Below are a few books we recommend on technique. There are many more: enough for a lifetime of inspiration.
• _Caddisflies_ , Gary LaFontaine, Lyons Press, 1989
• _The Curtis Creek Manifesto,_ Sheridan Anderson, Frank Amato Publications, 1978
• _Fly Casting Fundamentals,_ Lefty Kreh, Stackpole Books, 2012
• _The Fly Fishers Craft,_ Darrel Martin, Lyons Press, 2006
• _Reading Trout Water,_ Dave Hughes, Stackpole Books, 2010
• _The Soft Hackled Fly and Tiny Soft Hackles,_ 2nd ed., Sylvester Nemes, Stackpole Books, 2006
• _Trout Fishing,_ Joe Brooks, Harper Row, 1972
• _Tying & Fishing Soft Hackled Nymphs,_ Allen McGee, Frank Amato Publications, 2007
• _Western Fly-Fishing Strategies,_ Craig Mathews, Lyons Press, 2007
• _Wet Flies,_ Dave Hughes, Stackpole Books, 1995
## RODS, LINES, FLIES, AND GEAR
•Blue Ribbon Flies, www.blue-ribbon-flies.com
•Patagonia, www.patagonia.com
•Temple Fork Outfitters, www.templeforkflyrods.com
•Tenkara USA, www.tenkarausa.com
The above companies are members of 1% for the Planet (except Temple Fork Outfitters). They donate 1 percent of their sales to groups working to ensure we have a habitable planet for people and fish. Temple Fork Outfitters donates $10 from the sale of each tenkara rod to various fishery environmental causes.
Simple Fly-Fishing
Techniques for Tenkara and Rod & Reel
Patagonia Books®, an imprint of Patagonia, Inc., publishes a select number of titles on wilderness, wildlife, and outdoor sports that inspire and restore a connection to the natural world.
Copyright 2014 Patagonia Books®
Text © Yvon Chouinard, Craig Mathews, and Mauro Mazzo
Paintings © James Prosek
Paintings on pages 18 to courtesy of James Prosek and Schwartz • Wajahat, New York
Illustrations © Erik Brooks
Photograph copyrights held by the photographers
All rights reserved. No part of this book may be used or reproduced in any manner whatsoever without written permission from the publisher and copyright holders. Requests should be mailed to Patagonia Books®, Patagonia, Inc., 259 W. Santa Clara St., Ventura, CA 93001-2717
First Edition
Editor: John Dutton
Photo Editor: Jane Sievert
Design and Production: Monkey C Media
Preserving our environment
ISBN 978-1-938340-27-7
E-Book ISBN 978-1-938340-28-4
Library of Congress Control Number 2013957437
Publisher's Cataloging in Publication Data
Chouinard, Yvon, 1938-
Simple fly fishing: techniques for tenkara and rod & reel / Yvon Chouinard, Craig Mathews, and Mauro Mazzo. -- Ventura, Calif.: Patagonia Books, 2014.
p.; cm.
ISBN: 978-1-938340-27-7; 978-1-938340-28-4 (ebook)
Includes bibliography.
Summary: The best way to catch trout is simply, with a rod and a fly and not much else. Discover where the fish are, at what depth, and what they are feeding on. This book describes the techniques needed to present a fly, make it look lifelike, and hook the fish. Chapters on wet flies, nymphs, and dry flies, the authors employ both the tenkara rod as well as regular fly fishing gear. Paintings by renowned artist James Prosek, technical illustrations, and inspiring photographs and stories throughout.--Publisher.
1. Fly fishing--Handbooks, manuals, etc. 2. Tenkara fly fishing--Handbooks, manuals, etc. 3. Trout fishing--Handbooks, manuals, etc. 4. Fishing tackle. 5. Fishing rods. 6. Fishing lures. I. Mathews, Craig. II. Mazzo, Mauro. III. Title.
SH456 .C56 2014 | 2013957437
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| {
"redpajama_set_name": "RedPajamaBook"
} | 1,688 |
\section*{Introduction}
Quantum computer is a computing machine based on the principles of quantum mechanics, which preforms unitary evolutions on qubits \cite{Feynman_1982, Preskill_2018}. It promises algorithms to solve important problems with exponential or polynomial speedup for many algebraic, number theoretic and oracular algorithms \cite{Grover1996, Shor_1997, Grover_1997, Bennett_1997, Szegedy2004, Harrow_2009, Montanaro_2016}, etc. Among them, solving eigen states and eigen values of a quantum many-body system is one of central tasks in condensed matter physics and quantum chemistry \cite{Imbrie_2016, Shiozaki_2016, Kandala_2017, Jia_2018}. Many classical numerical methods were suggested to study many-body systems such as density functional theory \cite{Koch_2001}, quantum Monte Carlo \cite{Foulkes_2001}, and tensor network approach \cite{Ran_2020}, etc. However, those methods are tied up in strongly correlated systems, where representing the quantum state is classically inaccessible due to the exponential dimension of the underlying Hilbert space when the size of system is very large. This issue can be naturally avoided in a quantum computer since one can store the quantum states in a number of qubits that scale linearly with the size of the physical system. The acceleration of solving such eigen problem of Hamiltonian matrix by quantum algorithms will make great contributions to study strongly correlated electron systems \cite{LIU_2002} and to develop new materials \cite{Babbush_2018}, good catalysts \cite{Reiher_2017} and even more effective medicines \cite{Aspuru_Guzik_2018}.
At present, there are several quantum algorithms that purpose to tackle this issue. Quantum phase estimation (QPE) \cite{Cleve_1998} was proposed to estimate the eigen value of an eigen vector for a Hamiltonian matrix. This approach requires that the eigen vector \cite{Cleve_1998, Zhou_2013} or a good approximation \cite{Abrams_1999} is known. A more feasible solution is to combine a re-configurable quantum processor for the expectation estimation and a conventional or quantum computer for variational optimization \cite{Peruzzo_2014, Kandala_2017, Liu_2019, Wang_2019, Parrish_2019, Izmaylov_2019, LaRose_2019, Higgott_2019, Mitarai_2020}. This variational quantum eigen solver (VQE) designs a parameterized quantum circuit as the ground state ansatz and optimizes it according to the results from the quantum processor. A good approximation or ansatz of the ground state is necessary for QPE and VQE to find the corresponding eigen value, which confines their applications to the systems with a good understanding. Besides, adiabatic algorithms can obtain a state close to the ground state of a given Hamiltonian for sufficiently long runtimes \cite{Farhi2000}. However, the runtimes of these algorithms are extremely difficult to calculate or bound in practice, which makes adiabatic algorithms used as heuristic methods in most cases \cite{Farhi2000, Jansen_2007, Ge_2019}.
Solving the eigen problem of Hamiltonian matrix includes the calculation of eigen values and eigen states. Once either eigen values or eigen states is given, there are quantum algorithms that can calculate another one \cite{Cleve_1998, Poulin_2009, Zhou_2013, Ge_2019}. However, no digital quantum algorithm can solve both the eigen values and eigen vectors for the general form of Hamiltonian \cite{Lin2020}. An essential path to design such a quantum algorithm is to judge the difference between correct results and the trial values. More specifically, it is better to design a quantum eigen solver to judge whether all the eigen values of the given Hamiltonian are higher than a trial eigen value. Then all eigen values can be calculated with dichotomy one by one starting from the ground state energy.
\begin{figure*}[htb]
\includegraphics[width=1\linewidth]{radio.pdf}
\caption{\label{fig-radio}Sketch of quantum Heaviside eigen solver. (a) The illustration to solve the eigen problem of the Hamiltonian with the quantum judge and quantum selector. Note that the excited state energies and the corresponding eigen states can be figured out one by one starting from the ground state energy. (b) The detailed flow-chart to design the quantum selector/judge and solve the given Hamiltonian. This process is vividly shown as a quantum radio that receives the signal (Hamiltonian) and output the contents (eigen states) according to the signal and trial frequency (eigen value/threshold). The amplitude amplification algorithm within the dash box can amplify the amplitude of states corresponding to the trial eigen value, or all eigen values lower than the given threshold, and filter out other states, which is the core of quantum Heaviside eigen solver.}
\end{figure*}
In this work we present a quantum algorithm called quantum Heaviside eigen solver (QHES) to calculate both the eigen values and eigen states of the given Hamiltonian matrix. It consists of a quantum judge to calculate the eigen values by dichotomy and a quantum selector to calculate the corresponding eigen states. The Hamiltonian is defined on the space of $N$ qubits which can be written as ${\bf{H}} = \sum\limits_l^N {{{\bf{H}}_l}} $, where each ${{{\bf{H}}_l}}$ can act on qubits \cite{Cubitt_2016}. The QHES can solve any Hamiltonian in quantum many-body systems. Generally, solving the ground state energy of this common form of Hamiltonian has been proved to be QMA-complete \cite{Kempe_2006}, where QMA stands for quantum Merlin Arthur and is the quantum analog of NP. It is generally believed that it cannot be solved in polynomial time even on quantum computer. Solving a $\chi $-dimensional Hamiltonian matrix usually requires the classical bits scaling as $O\left( \chi \right)$ and its running time scales as $\Omega \left( \chi \right)$ \cite{Golub_2000}. By contrast, the amplitude amplification algorithm \cite{Brassard1997, Grover_1998} with an exquisite design of oracle circuit in this work can solve this problem using the qubits that scale as $O\left( {\log \chi } \right)$ and its running time scales as $O\left( {\sqrt \chi } \right)$.
The quantum judge is an amplitude amplification algorithm that evolves the initial state into a state belonging to the ``good subspace'', which is spanned by the eigen states with eigen values lower than the trial threshold. By detecting the presence of states in the good subspace from the output of quantum judge, one can judge whether all eigen values of the given Hamiltonian ${\bf{H}}$ are higher than the trial threshold. The lowest eigen value of ${\bf{H}}$ with an error lower than $\varepsilon $ can be obtained by $O\left( {\log {1 \over \varepsilon }} \right)$ times of binary searches of the trial threshold. Similarly, the quantum selector is an amplitude amplification algorithm where the good subspace is spanned by eigen states corresponding to the given eigen value. It can directly evolve the initial state to the target eigen states. The process of that uses QHES to solve the eigen values and eigen states is shown in Fig. \ref{fig-radio}(a). The core kernel in this process is the quantum circuit to achieve the identification of eigen states in quantum judge and quantum selector. In this paper, we accomplish this task for the general form of Hamiltonian with a quantum Heaviside circuit (QHC) and a quantum Dirac circuit (QDC).
\section*{Results}
\subsection*{A sketch of quantum Heaviside eigen solver}
The QHES is like a quantum radio in the way as shown in Fig. \ref{fig-radio}(b). This quantum radio receives the signal and outputs contents corresponding to the frequency, where the signal represents the Hamiltonian matrix, frequency represents the trial eigen value or all eigen values lower than the trial threshold, and the output contents represent the corresponding eigen states that are called qualified states. When the frequency is set at a trial threshold and QHC is adopted in the green boxes, this quantum radio judges whether there is any eigen state that corresponds to an eigen value lower than the trial threshold. Combined with the dichotomy, one can obtain the lowest eigen value with an error lower than $\varepsilon $ in $O\left( {\log {1 \over \varepsilon }} \right)$ iterations of performing quantum judge and adjusting trial threshold. This eigen value is then taken as the trial eigen value and the quantum radio can output the corresponding eigen states when QDC is adopted in the green boxes. These two processes are both achieved by the amplitude amplification based on QHC and QDC, respectively, which amplifies the amplitude of qualified states and filters out others from the randomly initialized state $\left| {{\psi _r}} \right\rangle $.
Now we explain the steps to construct the quantum selector or the quantum judge shown in Fig. \ref{fig-radio}(b).
\begin{description}
\item[step 1] Select a trial eigen value for QDC, or a trial threshold for QHC by dichotomy.
\item[step 2] Shift the Hamiltonian to fix the trial eigen value to $0$, or to fix the threshold to ${1 \over 2}$. This step is to avoid redesigning the whole circuit, where only the Hamiltonian evolution circuit needs to be changed.
\item[step 3] Construct the QDC or QHC according to the shifted Hamiltonian, where the trial eigen value and trial threshold is fixed. This is the most difficult and important part in QHES.
\item[step 4] Construct the amplitude amplification algorithm based on QDC or QHC, which is used to mark the qualified states.
\item[step 5] Determine the number of iterations in amplitude amplification. This step is evaded since we use the fixed-point quantum search \cite{Yoder_2014} as the amplitude amplification algorithm.
\item[step 6] Initialize the input state $\left| {{\psi _r}} \right\rangle $, which is a superposition of all eigen states. A random circuit is usually competent.
\item[step 7] Amplify the amplitude of qualified states and filter out others using the circuit within the dash box.
\end{description}
Steps 1, 2 and 7 are classical routine operations which are introduced in the Supplemental Material. Step 3 is to design the quantum circuit of QHC and QDC with the given Hamiltonian, which is the core of QHES. Step 4 can be achieved by the standard flow to construct the amplitude amplification algorithm whose oracle circuit is QHC or QDC. Step 5 is to determine how many iterations in amplitude amplification algorithm are needed to amplify the amplitude of target state sufficiently. Using the fixed-point search, the number of iterations is $O\left( {\sqrt \chi } \right)$ on the assumption that the overlap between $\left| {{\psi _r}} \right\rangle $ and target states is no less than $O\left( {{1 \over \chi }} \right)$. Step 6 is to initialize the initial state satisfying the above assumption, which can be done by a random circuit with high probability. Next, we will introduce the central idea to construct QDC and QHC. The mathematical analysis and detailed instructions for all steps are presented in the Supplemental Material.
\subsection*{Constructing quantum Heaviside circuit}
The purposes of QHC and QDC are to mark the qualified eigen states for the amplitude amplification. These two quantum circuits are unitary operators working on $N$ physical qubits, $K$ auxiliary qubits and one mark qubit. They output the results on the mark qubit while do not change the inputs on physical qubits at all time. The states on auxiliary qubits change in the process of quantum circuit while they are disregarded. We define the qualified states $\left| {{E_q}} \right\rangle $ for these two circuits as the states on $N$ physical qubits whose output on the mark qubit is $\left| 0 \right\rangle $. For QHC, the qualified states are eigen states whose corresponding eigen values are smaller than a given threshold $\theta$.
The QHC is designed to filter out the eigen states with eigen values larger than the given threshold $\theta $ and to preserve as much proportion of the eigen states with eigen values smaller than $\theta $. This process consists of two parts. The first part is to identify the eigen values of all eigen states, and the second part is a simple filter circuit based on the eigen values. The QPE is proposed to entangle the eigen states with the binary representation of their corresponding eigen values on the auxiliary qubits \cite{Cleve_1998}. However, QPE is not capable for this task due to its uncertainty, which is also called heavy tail \cite{Poulin_2009}. Here we use three strategies on the original QPE algorithm to construct the quantum Heaviside circuit. The first is a multiple filtering scheme to ensure the quantum Heaviside circuit can definitely filter out the unqualified states. The second is a fine-tuning scheme to ensure the qualified states is definitely preserved. The last is a recycling scheme using a freezing operator to reduce the number of auxiliary qubits. To the best of our knowledge, this is the first filtering method for a general Hamiltonian.
The quantum phase estimation is proposed to calculate the eigen values of a given Hermite matrix, where the corresponding eigen state is given. The QPE works on the physical qubits initialized to the corresponding eigen state and $R$ extra qubits initialized to ${\left| 0 \right\rangle ^{ \otimes R}}$, which are called representation qubits. This algorithm does not influence the eigen state on physical qubits and changes the state on representation qubits to an approximation of the binary representation of the corresponding eigen value. The success probability of QPE to output the right (nearest) binary representation of the corresponding eigen value on representation qubits is no less than ${4 \over {{\pi ^2}}}$ \cite{Cleve_1998}. This indicates the filter on representation qubits after single QPE can filter out at least ${4 \over {{\pi ^2}}}$ of the unqualified states.
To make sure that all unqualified states are filtered well out, we adopt $Q = O\left( N \right)$ QPE circuits at the same time, which is the first strategy. Here all $Q$ QPE circuits act on the same physical qubits and different representation qubits, which means the total number of representation qubits is $Q \times R$. This multiple filtering scheme can reduce the amplitude of unqualified states to exponentially small, that is, lower than ${\left( {1 - {4 \over {{\pi ^2}}}} \right)^Q}$. Unfortunately, this method may filter out the qualified states when the gap between the eigen values and their nearest binary representations is large.
The strength of this filtering effect is determined by the accuracy of QPE circuit, which is related to the accuracy of binary representation of eigen values. Since the QPE circuit uses $R$ representation qubits, the maximum error to express the eigen values is ${\pi \over {{2^R}}}$, and the corresponding accuracy of QPE circuit is ${{4 \over {{\pi ^2}}}}$. In the worst case, the eigen states with eigen values higher than the given threshold are retained up to ${\left( {1 - {4 \over {{\pi ^2}}}} \right)^{2Q}}$. Meanwhile, we can only guarantee that at least ${\left( {{4 \over {{\pi ^2}}}} \right)^{2Q}}$ of the eigen states with eigen values lower than the given threshold are preserved.
To solve this issue, we perform a batch of filtration for $W$ different Hamiltonian matrices in sequence, which are shifted from the given normalized Hamiltonian matrix recorded as ${{\bf{H}}_0}$. This set of Hamiltonian matrices can be expressed as
\begin{align}
\label{eq-H-set}
\left\{ {{{\bf{H}}_w}} \right\}:{{\bf{H}}_w} = {{\bf{H}}_0} + {w \over W}{\pi \over {{2^{R - 1}} }}.
\end{align}
When we filter all these Hamiltonian, the error to express the eigen value using $R$ representation qubits is reduced to no more than ${\pi \over {W{2^\pi }}}$ at least once. In this case, it is proved in the Supplemental Material that at least ${\left( {1 - {{{\pi ^2}} \over {2{W^2}}}} \right)^{2Q}}$ of the qualified states are preserved, which can be written as $O\left( 1 \right)$ when $W = O\left( {\sqrt N } \right)$. This is the second strategy to make sure that all qualified states are not filtered out at least once.
With these two strategies, the changed QPE circuit can efficiently filter out the unqualified states while preserve qualified states. The number of auxiliary qubits is $Q \times R$, which can also be written as $O\left( {N\log {1 \over \varepsilon }} \right)$. Here the term of $O\left( {\log {1 \over \varepsilon }} \right)$ is unavoidable since it is used for the binary representation of the eigen values, where $\varepsilon $ is the error bound of the quantum judge. However, its multiplication with $N$ makes this method impractical on the near term quantum hardware. For example, if we want to solve the eigen problem of a Hamiltonian matrix with the size of ${2^{50}} \times {2^{50}}$, it needs $50$ physical qubits to represent the physical system and about $50 \times {\log _2}\left( {{{10}^6}} \right)$ qubits to obtain the results with an error lower than ${10^{ - 6}}$. Next we introduce the freezing operator as the last strategy that can reduce the number of auxiliary qubits from $O\left( {N\log {1 \over \varepsilon }} \right)$ to
\begin{align}
\label{eq-qhc-num}
O\left( {\log N + \log {1 \over \varepsilon }} \right).
\end{align}
The third strategy can be described as performing QPE $Q$ times on $R$ representation qubits instead of performing QPE once on $Q \times R$ representation qubits. This strategy is similar to the iterative quantum phase estimation (iQPE) \cite{Dob_ek_2007} that involves measurement and reuse of qubits, which means that it cannot be used as the subroutine of the QHES. So we design the unitary freezing operator to ``reset'' the auxiliary qubits after each QPE circuit instead of resetting the auxiliary qubits with measurement.
\subsection*{Constructing quantum Dirac circuit with quantum coin toss}
The task of QDC is to qualify the eigen states corresponding to a given eigen value, which can be done by a quantum coin toss. We define the flipping operator to achieve
\begin{align}
\label{eq-uf-result}
{{\bf{U}}_c}\left| {{E_j}} \right\rangle \left| 0 \right\rangle = \cos \left( {{E_j}} \right)\left| {{E_j}} \right\rangle \left| 0 \right\rangle + i\sin \left( {{E_j}} \right)\left| {{E_j}} \right\rangle \left| 1 \right\rangle ,
\end{align}
whose design is given in the Supplemental Material. Here we call the qubit to express states $\left| 0 \right\rangle $ and $\left| 1 \right\rangle $ as quantum coin. The ${{\bf{U}}_c}$ is designed to flip the state on the quantum coin according to the state on physical qubits. If we use $M$ quantum coins at the same time, the amplitude of all quantum coins remain ${\left| 0 \right\rangle ^{ \otimes M}}$ is ${\cos ^M}\left( {{E_j}} \right)$. When $M$ is large enough, ${\cos ^M}\left( {{E_j}} \right)$ can be seen as an analog of the Dirac function of ${{E_j}}$.
To meet the requirements of being the oracle circuit of the quantum selector, the quantum coin toss should distinguish the eigen states with the given eigen value ${E_g}$ and the states with the closest eigen value. Without losing generality, here we suppose the given eigen value ${E_g}$ is zero and the gap between ${E_g}$ and its closest eigen value is $\Delta $. Detailed analysis in Supplemental Material shows that to obtain the $\varepsilon$-close eigen state corresponding to the given eigen value ${E_g}$, one needs the minimum number of quantum coins as
\begin{align}
\label{eq-M}
M = O\left( {{1 \over {{\Delta ^2}}}\left( {N + \log {1 \over \varepsilon }} \right)} \right) ,
\end{align}
and the error bound of ${E_g}$ is ${\varepsilon _0} = O\left( \Delta \right)$. Under this condition, the QDC outputs ${\left| 0 \right\rangle ^{ \otimes M}}$ with an amplitude of $O\left( 1 \right)$ when the states on physical qubits correspond to an eigen value $\varepsilon _0$-close to ${E_g}$, and outputs ${\left| 0 \right\rangle ^{ \otimes M}}$ with an exponentially small amplitude in other cases. Using this QDC as the oracle circuit of amplitude amplification algorithm, the quantum selector can obtain the eigen states of the eigen values solved by quantum judge. Similar to the case of QHC, the number of quantum coins is far beyond the capabilities of current quantum hardware. Fortunately, this number can be exponentially reduced to $O\left( {\log M} \right)$ by the freezing operator.
\subsection*{Freezing operator}
To reduce the number of quantum coins, we replace the single toss of $M$ quantum coins to $M$ tosses of one quantum coin. A simple idea of designing such circuit is to perform ${{{\bf{U}}_c}}$ when the quantum coin is in the state of $\left| 0 \right\rangle $, and to perform an identity operator when the quantum coin is in the state of $\left| 1 \right\rangle $. However, the operation to complete this process is not unitary, which is forbidden by the quantum computer. We extend this non-unitary operator to a unitary operator by introducing the freezing operator and extra $K$ counting qubits. The freezing operator ${{\bf{U}}_F}$ acts on the quantum coin and $K$ counting qubits. The state on the counting qubits is regarded as a binary number $x$. For example, we record $\left| {0110} \right\rangle $ as $\left| {x = 6} \right\rangle $. Then ${{\bf{U}}_F}$ is designed to achieve
\begin{subequations}\label{eq-freezing}
\begin{align}
{{\bf{U}}_F}\left| x \right\rangle \left| 0 \right\rangle = \left| x \right\rangle \left| 0 \right\rangle ,
\end{align}
\begin{align}
{{\bf{U}}_F}\left| x \right\rangle \left| 1 \right\rangle = \left| {x + 1} \right\rangle \left| 1 \right\rangle .
\end{align}
\end{subequations}
This can be easily done by a unitary ${{\bf{U}}_{add}} = \sum\limits_x {\left| {x + 1} \right\rangle \left\langle x \right|} $ controlled by the quantum coin. The ${{\bf{U}}_{add}}$ is an elementary arithmetic operation which can be efficiently performed \cite{Vedral_1996}. If we initialize the state on counting qubits to ${\left| 1 \right\rangle ^{ \otimes K}}$ and apply ${{\bf{U}}_F}$, we note that the first counting qubit, which is the highest order in the binary representation, will not be $\left| 1 \right\rangle $ for ${2^{K - 1}}$ times of performing ${{\bf{U}}_F}$ once the quantum coin is changed to $\left| 1 \right\rangle $.
This freezing operator can exponentially reduce the number of auxiliary qubits by controlling ${{\bf{U}}_c}$ with the first counting qubit. More specifically, the quantum coin toss can be performed on one quantum coin and $K = O\left( {\log M} \right)$ counting qubits instead of $M$ quantum coins. In $M$ times of performing ${{\bf{U}}_c}$ and ${{\bf{U}}_F}$, once the quantum coin is changed to $\left| 1 \right\rangle $, the state on the first counting qubit will not be $\left| 1 \right\rangle $ based on Eq. (\ref{eq-freezing}). No ${{\bf{U}}_c}$ will be applied to the quantum coin since it is controlled by the first counting qubit, which means the quantum coin is frozen in $\left| 1 \right\rangle $ once it is changed to $\left| 1 \right\rangle $. If the quantum coin is $\left| 0 \right\rangle $ after $M$ quantum coin tosses, it must remain $\left| 0 \right\rangle $ in each quantum coin toss, which means the amplitude of the quantum coin being $\left| 0 \right\rangle $ in the end is also ${\cos ^M}\left( {{E_j}} \right)$.
\begin{figure}[h]
\centering
\includegraphics[width=0.9\linewidth]{cointoss.pdf}
\caption{\label{fig-toss}Example of reducing number of quantum coins using the freezing operator. (a) Graphic representations of quantum coins, quantum coin toss, state on counting qubits and quantum coin toss controlled by counting qubits. Only coin toss processes that are used in the quantum selector are indicated. (b) All ${2^M}$ possible results of tossing $M$ quantum coins once. We need $M$ auxiliary qubits (quantum coins) to record the results. (c) The process of tossing one quantum coin $M$ times controlled by counting qubits. There are $M + 1$ possible results, which is exponentially less than the case of quantum coin toss without the control of counting qubits. We only need $O\left( {\log M} \right)$ auxiliary qubits (counting qubits) and one quantum coin to express the results. Note that there are some simplifications compared with practical design to explain this process more intuitively.}
\end{figure}
The nature of this exponential reduction of auxiliary qubits is the reduction of the dimension of the state space as shown in Fig. \ref{fig-toss}. In the quantum coin toss scheme, the quantum circuit must have the ability to express all possible results of tossing $M$ quantum coins. The number of possible results of tossing $M$ quantum coins once is ${2^M}$, which is the same as that of tossing one quantum coin $M$ times. Since we are only interested in the result of all quantum coins being $\left| 0 \right\rangle $, we choose to ignore the state with one or more quantum coins being $\left| 1 \right\rangle $. Note that we cannot decide the result of each quantum coin toss, we can only stop the quantum coin toss by the freezing operator when the result of $\left| 1 \right\rangle $ appears. The result of tossing one quantum coin $M$ times may be that all quantum coin tosses end up with $\left| 0 \right\rangle $ or one of the $M$ quantum coin tosses end up with $\left| 1 \right\rangle $. In this situation, the dimension of result space is $M + 1$, which means that we only need $O\left( {\log M} \right)$ auxiliary qubits to record the results.
In the quantum coin toss, the freezing operator guarantees that all flipping operators are performed on the $\left| 0 \right\rangle $ of the quantum coin. We define $\left| 0 \right\rangle $ as the target state of this freezing operator, where all other states is frozen. Similarly, the freezing operator can be used to reduce the number of auxiliary qubits of QHC from $O\left( {N\log {1 \over \varepsilon }} \right)$ to $O\left( {\log N + \log {1 \over \varepsilon }} \right)$. In this case, we need two freezing operators whose target states are $\left| 0 \right\rangle $ on the first (the highest order) representation qubit and ${\left| 0 \right\rangle ^{ \otimes R}}$ on all representation qubits, respectively. Note that the first representation qubit being $\left| 0 \right\rangle $ represents the eigen value being lower than ${1 \over 2}$, and ${\left| 0 \right\rangle ^{ \otimes R}}$ is the initial state of QPE algorithm. Each iteration of the filtering process starts with a QPE circuit controlled by the counting qubits, then the first freezing operator prevents the states filtered out by the QPE circuit from the following process. An inverse of the QPE circuit resets the representation qubits to an approximation of ${\left| 0 \right\rangle ^{ \otimes R}}$, and the second freezing operator makes sure that the next iteration exactly starts from ${\left| 0 \right\rangle ^{ \otimes R}}$.
With these three strategies, the QHC can effectively filter out unqualified state and preserve qualified states with only $O\left( {\log N + \log {1 \over \varepsilon }} \right)$ auxiliary qubits. Using this circuit as the oracle circuit of the amplitude amplification algorithm, the quantum judge can identify the eigen states with eigen values lower than ${1 \over 2}$ from the initial states. Since the input quantum state is randomly initialized to a superposition of all eigen states, the quantum judge can judge whether there is any eigen value of the given Hamiltonian which is lower than ${1 \over 2}$. By changing the trial threshold with dichotomy, or equivalently shifting and zooming the Hamiltonian matrix, the lowest eigen value with an error lower than $\varepsilon $ can be obtained in $O\left( {\log {1 \over \varepsilon }} \right)$ iterations. The higher eigen values can also be calculated one by one with a quantum judge that only identifies states with eigen values between two trial thresholds. After the eigen values are calculated by the quantum judge, the corresponding eigen states can be given by the quantum selector that takes quantum coin toss as the oracle circuit of the amplitude amplification algorithm. Detailed description and complexity analysis are given in the Supplemental Material.
\subsection{Simulation results of quantum judge and quantum selector}
Here we apply an open-source quantum simulator \cite{Garc_a_P_rez_2020} to produce the numerical results to solve the ground state energy of the given Hamiltonian ${\bf{H}} = - {1 \over {N - 1}}\sum\limits_{n = 1}^{N - 1} {{\bf{\sigma }}_n^z} {\bf{\sigma }}_{n + 1}^z$ with quantum judge. The calculation of the lowest eigen value starts with a trial eigen value, and then judges whether all eigen values are larger than the trial eigen value using quantum judge. Following the standard process of dichotomy, we can obtain the lowest eigen value whose precision is confined by the precision of quantum judge. Here we define the error ${\varepsilon _v}$ to solve the ground state energy of the given Hamiltonian as
\begin{align}
\label{eq-error-value}
{\varepsilon _v} = \left| {{E_c} - {E_g}} \right|,
\end{align}
where ${{E_c}}$ is the result of dichotomy using quantum judge and ${{E_g} = - 1}$ is the ground state energy of the given Hamiltonian.
\begin{figure}[htb]
\centering
\includegraphics[width=0.9\linewidth]{qvs.pdf}
\caption{\label{fig-qvs}Numerical results by using quantum judge to solve the ground state energy of the given Hamiltonian ${\bf{H}} = - {1 \over {N - 1}}\sum\limits_{n = 1}^{N - 1} {{\bf{\sigma }}_n^z} {\bf{\sigma }}_{n + 1}^z$. Here $N$ is the number of physical qubits to represent the physical system and $R$ is the number of the representation qubits in the QPE circuit. It can be seen that the error of calculated eigen value decreases exponentially with the increase of $R$. There is no result where $N = 5$ and $R > 7$ because of the limitation of our computation resource.}
\end{figure}
According to Eq. (\ref{eq-qhc-num}) and the relationship of ${\varepsilon _v} = O\left( \varepsilon \right)$, the number of representing qubits $R$ scales linearly to $\log {1 \over \varepsilon _v}$, which is consistent with the numerical result in Fig. \ref{fig-qvs}. Due to the limitation of the depth of quantum circuits in the quantum simulator, we construct the quantum judge with an extra classical process to generate Hamiltonian set $\left\{ {{{\bf{H}}_w}} \right\}$ to make the judgment. This compromise on numerical simulation is to change the quantum search of $O\left( {\sqrt N } \right)$ Hamiltonian matrices contained in the QHC to a classical search attached to the QHC, which does not affect the verification of Eq. (\ref{eq-qhc-num}) from Fig. \ref{fig-qvs}. There is no result when $N = 5$ and $R > 7$ even with the above compromise because of the high basic cost of QPE circuit owing to the limitation of the present quantum simulator.
We also performed the numerical simulations to check the feasibility of quantum selector, which is used to solve the ground state of the given Hamiltonian ${\bf{H}} = - {1 \over {N - 1}}\sum\limits_{n = 1}^{N - 1} {{\bf{\sigma }}_n^z} {\bf{\sigma }}_{n + 1}^z$. The ground state of this Hamiltonian is a superposition of $\left| {{\psi _0}} \right\rangle = {\left| 0 \right\rangle ^{ \otimes N}}$ and $\left| {{\psi _1}} \right\rangle = {\left| 1 \right\rangle ^{ \otimes N}}$. Here we define the error ${\varepsilon _s}$ to solve the ground state of the given Hamiltonian using quantum selector as
\begin{align}
\label{eq-error-state}
{\varepsilon _s} = 1 - {\left| {\left\langle {{{\psi _c}}}
\mathrel{\left | {\vphantom {{{\psi _c}} {{\psi _0}}}}
\right. \kern-\nulldelimiterspace}
{{{\psi _0}}} \right\rangle } \right|^2} - {\left| {\left\langle {{{\psi _c}}}
\mathrel{\left | {\vphantom {{{\psi _c}} {{\psi _1}}}}
\right. \kern-\nulldelimiterspace}
{{{\psi _1}}} \right\rangle } \right|^2},
\end{align}
where $\left| {{\psi _c}} \right\rangle $ is the eigen state calculated by the quantum selector. The coefficient matrix of $\left| {{\psi _c}} \right\rangle $ can be obtained by quantum tomography experimentally, or directly be outputted from the quantum simulator.
\begin{figure}[htb]
\centering
\includegraphics[width=0.9\linewidth]{qss.pdf}
\caption{\label{fig-qss}Numerical results by using quantum selector to solve the ground state of the given Hamiltonian ${\bf{H}} = - {1 \over {N - 1}}\sum\limits_{n = 1}^{N - 1} {{\bf{\sigma }}_n^z} {\bf{\sigma }}_{n + 1}^z$. Here $N$ is the number of physical qubits to represent the physical system and $K$ is the number of counting qubits. The vertical axis starts from zero where $\varepsilon $ equals approximately to $0.4$. The results with larger error are meaningless where the quantum selector does not function properly because of the lack of counting qubits. The gray dash line represents the standard line where $\varepsilon _s = {10^{ - 12}}$.}
\end{figure}
According to Eq. (\ref{eq-M}) and the relationship of ${\varepsilon _s} = O\left( {{\varepsilon ^2}} \right)$, the number of counting qubits $K$ scales linearly to $\log \log {1 \over \varepsilon _s}$, which is consistent with the numerical result in Fig. \ref{fig-qss}. It can be seen that the error of the quantum selector as quantum eigen state solver drops below ${10^{ - 12}}$ quickly. Note that we choose the simple Hamiltonian matrix to reduce the computational source required for the simulations. The eigen values and the corresponding eigen states of any k-local Hamiltonian \cite{Cubitt_2016} can be calculated using QHES. More specifically, what we only require here is the controlled time evolution of the given Hamiltonian can be efficiently implemented for unit time, which is a trivial task for any k-local Hamiltonian \cite{Berry_2015, Berry_2015_10, Low_2017, Low_2019}. The k-local Hamiltonian describes more general quantum systems than quantum many-body systems, where the former includes not only short-range interactions but also long-range interactions.
\section*{Discussion}
In this work we presented a quantum Heaviside eigen solver to solve both the eigen values and eigen states for the general Hamiltonian matrix using quantum computers. The QHES can solve the eigen values of given Hamiltonian with an error smaller than $\varepsilon $ in $O\left( {{{\log }}{1 \over \varepsilon }} \right)$ binary searches using quantum judge, which can judge whether all eigen values of the given Hamiltonian are higher than a trial threshold. Then the quantum selector in QHES outputs eigen states corresponding to the solved eigen values. In designing the oracle circuit of quantum judge, the parallel identification of eigen values is based on QPE, where three strategies are adopted to avoid its heavy tail. Besides QPE, we only use elementary quantum arithmetic operations, which is distinct from those based on non-trivial tasks such as block-encoding of the target Hamiltonian. This eigen solver was also tested on a physical model, showing its better feasibility.
We would like to mention that the QHC and the freezing operator proposed here may contribute to other quantum algorithms. To name but a few, the QHC may be used as an activation function in quantum (deep) neural networks \cite{Killoran_2019, Zhao_2021}. Furthermore, the freezing operator can exponentially reduce the dimension of freedom space (coin space) \cite{Panahiyan_2018} and the number of auxiliary qubits, which is very useful when a quantum circuit contains several parts, such as the quantum principal component analysis \cite{Lloyd_2014} and the quantum random walks \cite{Aharonov_1993, Venegas_Andraca_2012}.
\section*{Methods}
Here we give the definition of QHC and QDC. As the oracle circuit of quantum judge, QHC should identify all eigen states whose corresponding eigen values are higher than the trial threshold $\theta $. It can be expressed as
\begin{align}
\label{eq-Heaviside-p}
{{\bf{U}}_H}\left| {{E_j}} \right\rangle {\left| 0 \right\rangle ^{ \otimes K}}\left| 0 \right\rangle = {\alpha _j}\left| {{E_j}} \right\rangle {\left| 0 \right\rangle ^{ \otimes K}}\left| 0 \right\rangle + {\beta _j}\left| {{E_j} } \right\rangle \left| {{\varphi _j}} \right\rangle \left| 1 \right\rangle ,
\end{align}
where ${\left| {{\alpha _j}} \right|^2} + {\left| {{\beta _j}} \right|^2} = 1$ and $\left| {\varphi _j} \right\rangle $ represents the state that varies with different designs of QHC on $K$ auxiliary qubits. The state $\left| {\varphi _j} \right\rangle $ on auxiliary qubits is not concerned since it does not influence the qualification of eigen states. The results of this qualification are obtained from $\left| 0 \right\rangle $ and $\left| 1 \right\rangle $ on the mark qubit. More specifically, $\left| 0 \right\rangle $ on the mark qubit is entangled with the eigen states with eigen values lower than $\theta $ and $\left| 1 \right\rangle $ is entangled with other states. To achieve this purpose, ${\alpha _j}$ should be an approximation to a Heaviside function as ${\alpha _j} = u\left(\theta - {{E_j} } \right)$, where $u$ is the classical unit step function.
Similarly, the QDC should identify eigen states whose corresponding eigen value is $\left| {{E_g}} \right\rangle $, which is defined as
\begin{align}
\label{eq-Dirac-p}
{{\bf{U}}_D}\left| {{E_j}} \right\rangle {\left| 0 \right\rangle ^{ \otimes K}}\left| 0 \right\rangle = {\gamma _j}\left| {{E_j}} \right\rangle {\left| 0 \right\rangle ^{ \otimes K}} \left| 0 \right\rangle + {\rm{ }}{\eta _j}\left| {{E_j}} \right\rangle \left| {\phi _j} \right\rangle \left| 1 \right\rangle ,
\end{align}
where ${\left| {{\gamma _j}} \right|^2} + {\left| {{\eta _j}} \right|^2} = 1$ and $\left| {\phi _j} \right\rangle $ is also the unconcerned auxiliary state. Here ${\gamma _j}$ should be much higher when ${E_j} = {E_g}$ than when ${E_j} \ne {E_g}$, which is an analog to the Dirac function.
Detailed analysis in the Supplemental Material shows the requirements for ${\alpha _j}$ and ${\gamma _j}$ to obtain the eigen values and eigen states with an error lower than $\varepsilon $ are
\begin{equation}\label{eq-Heaviside-restrain}
\left| {{\alpha _j}} \right|
\begin{cases}
= O\left( 1 \right) & {E_j} < \theta - \varepsilon , \\
\le O\left( {{1 \over \chi }} \right) & {E_j} > \theta ,
\end{cases}
\end{equation}
and
\begin{equation}\label{eq-restrain-alpha}
\left| {{\gamma _j}} \right|
\begin{cases}
= O\left( 1 \right) & {E_j} = {E_g}, \\
\le O\left( {{\varepsilon \over {\sqrt \chi }}} \right) & {E_j} \ne {E_g},
\end{cases}
\end{equation}
respectively.
\section*{Acknowledgments}
We thank Zi-Yong Ge for inspiring discussions. {\bf Funding:} This work is supported in part by the National Natural Science Foundation of China (11834014), the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB28000000), the National Key R$\&$D Program of China (2018YFA0305800), and Beijing Municipal Science and Technology Commission (Grant No. Z190011). {\bf Author contributions:} Zheng-Zhi Sun performed all the work presented in this manuscript under the full guidance and supervision of Gang Su. {\bf Competing interests:} We declare no competing interests. {\bf Data availability:} All data needed to evaluate the conclusions in the paper are present in the paper. The code to generate the results in this paper can be obtained by reasonable request to the authors.
\section{Quantum Heaviside eigen solver}
\subsection{Quantum Heaviside and Dirac circuit}
Here we introduce the general form of QHC and QDC. To construct the circuit that can filter out all eigen states with eigen values larger than the trial threshold and preserve the rest states, the ideal QHC should satisfy
\begin{subequations}\label{eq-Heaviside-i}
\begin{align}
{{\bf{U}}_{Heaviside}}\left| {{E_j} < {\theta}} \right\rangle {\left| 0 \right\rangle ^{ \otimes K}}\left| 0 \right\rangle = \left| {{E_j}} \right\rangle {\left| 0 \right\rangle ^{ \otimes K}}\left| 0 \right\rangle ,
\end{align}
\begin{align}
{{\bf{U}}_{Heaviside}}\left| {{E_j} > {\theta}} \right\rangle {\left| 0 \right\rangle ^{ \otimes K}}\left| 0 \right\rangle = \left| {{E_j}} \right\rangle {\left| {\varphi _j} \right\rangle}\left| 1 \right\rangle .
\end{align}
\end{subequations}
where $\left| {\varphi _j} \right\rangle $ represents the state that varies with different designs of QHC on $K$ auxiliary qubits. We do not care about $\left| {\varphi _j} \right\rangle $ as it does not influence the qualification of the states on physical qubits. The $\left| 0 \right\rangle $ and $\left| 1 \right\rangle $ in Eq. (\ref{eq-Heaviside-i}) are the states on the mark qubit, where $\left| 0 \right\rangle $ is entangled with the qualified states on physical qubits and $\left| 1 \right\rangle $ is entangled with other states.
However, this ideal QHC cannot be trivially realized in practice. So we define an approximation for the ideal QHC as
\begin{align}
\label{eq-Heaviside-p}
{{\bf{U}}_H}\left| {{E_j}} \right\rangle {\left| 0 \right\rangle ^{ \otimes K}}\left| 0 \right\rangle = {\alpha _j}\left| {{E_j}} \right\rangle {\left| 0 \right\rangle ^{ \otimes K}}\left| 0 \right\rangle + {\beta _j}\left| {{E_j} } \right\rangle \left| {{\varphi _j}} \right\rangle \left| 1 \right\rangle ,
\end{align}
where ${\left| {{\alpha _j}} \right|^2} + {\left| {{\beta _j}} \right|^2} = 1$. This definition is the same as Eq. (\ref{eq-Heaviside-i}) when ${\alpha _j}$ is a Heaviside function such that ${\alpha _j} = u\left(\theta - {{E_j} } \right)$, where $u$ is the classical unit step function.
Similarly, the qualified states for the QDC are the states $\left| {{E_g}} \right\rangle $ corresponding to a given eigen value ${{E_g}}$. To achieve the qualification of the state $\left| {{E_g}} \right\rangle $, the ideal QDC should satisfy the following conditions
\begin{subequations}\label{eq-Dirac-i}
\begin{align}
{{\bf{U}}_{Dirac}}\left| {{E_g}} \right\rangle {\left| 0 \right\rangle ^{ \otimes K}}\left| 0 \right\rangle = \left| {{E_g}} \right\rangle {\left| 0 \right\rangle ^{ \otimes K}}\left| 0 \right\rangle ,
\end{align}
\begin{align}
{{\bf{U}}_{Dirac}}\left| {{E_{j \ne g}}} \right\rangle {\left| 0 \right\rangle ^{ \otimes K}}\left| 0 \right\rangle = \left| {{E_{j \ne g}}} \right\rangle {\left| {\phi _j} \right\rangle}\left| 1 \right\rangle ,
\end{align}
\end{subequations}
This ideal QDC cannot be trivially realized in practice. So we define an approximation for the ideal QDC as
\begin{align}
\label{eq-Dirac-p}
{{\bf{U}}_D}\left| {{E_j}} \right\rangle {\left| 0 \right\rangle ^{ \otimes K}}\left| 0 \right\rangle = {\gamma _j}\left| {{E_j}} \right\rangle {\left| 0 \right\rangle ^{ \otimes K}} \left| 0 \right\rangle + {\rm{ }}{\eta _j}\left| {{E_j}} \right\rangle \left| {\phi _j} \right\rangle \left| 1 \right\rangle ,
\end{align}
where ${\left| {{\gamma _j}} \right|^2} + {\left| {{\eta _j}} \right|^2} = 1$. This definition is the same as Eq. (\ref{eq-Dirac-i}) when ${\gamma _j}$ equals to $1$ instead of $0$ only if ${E_j} = {E_g}$, which is an analog to the Dirac function.
\subsection{Preliminaries of amplitude amplification algorithm}
Now we introduce the amplitude amplification algorithm used to solve the Hamiltonian matrix. Suppose that we have an initialization operator ${{\bf{U}}_I}$ on $N$ qubits which achieves $\left| {{\psi _r}} \right\rangle {\rm{ = }}{{\bf{U}}_I}{\left| 0 \right\rangle ^{ \otimes N}}$ and a projector ${\bf{P}} = \left| {{E_q}} \right\rangle \left\langle {{E_q}} \right|$ to the qualified state $\left| {{E_q}} \right\rangle $. Grover search algorithm \cite{Grover_1997} can project $\left| {{\psi _r}} \right\rangle $ onto the image of ${\bf{P}}$ with a small correction by performing $O\left( {{1 \over {\sqrt p }}} \right)$ iterations of ${\bf{I}} - 2{\bf{P}}$ and ${\bf{I}} - 2\left| {{\psi _r}} \right\rangle \left\langle {{\psi _r}} \right|$, where ${\left\| {{\bf{P}}\left| {{\psi _r}} \right\rangle } \right\|^2} = p$. The amplitude amplification algorithm performs a similar process in the case of multiple qualified states. To achieve the quadratic speedup, the initialization operator ${{\bf{U}}_I}$ should satisfy that the fidelity between qualified state and initialized state is no less than $O\left( {{1 \over \chi }} \right)$, which is a trivial task since even for a random initialization operator it has a high probability of feasibility \cite{Poulin_2009}. The main difficulty to solve the eigen problem of Hamiltonian is to design the projector to the qualified state, in particular when we do not have prior knowledge of the eigen values and eigen states.
After the construction of this projector using the QDC or QHC, the unitary Grover search circuit is recorded as
\begin{align}
\label{eq-grover}
{\bf{G}}\left( {{{\bf{U}}_I},{\bf{P}}} \right) = {\left[ {\left( {{\bf{I}} - 2{\bf{P}}} \right)\left( {{\bf{I}} - 2\left| {{\psi _r}} \right\rangle \left\langle {{\psi _r}} \right|} \right)} \right]^{O\left( {{1 \over {\sqrt p }}} \right)}}.
\end{align}
This circuit can amplify the amplitude of $\left| {{E_q}} \right\rangle $ to $O\left( 1 \right)$ starting with the randomly initialized state ${\left| {{\psi _r}} \right\rangle }$, which is given by
\begin{align}
\label{eq-grover-p}
\left| {{\bf{PG}}\left( {{{\bf{U}}_I},{\bf{P}}} \right)\left| {{\psi _r}} \right\rangle } \right| = O\left( 1 \right).
\end{align}
When solving the eigen problem using the amplitude amplification algorithm, the value of $p$ is generally not known in advance. This causes the soufflé problem where the Grover search algorithm is seen as a ``quantum oven'' \cite{Brassard_1997}. The soufflé problem is that the amplitude of the qualified state drops to zeros if you open the oven too early and the amplitude starts shrinking if using too many iterations. Luckily we can use either the full-blown quantum counting \cite{Boyer_1998, Brassard_1998} or a trial-and-error scheme where iterates are applied by an exponentially increasing number of times \cite{Boyer_1998, Brassard2002} without losing the quadratic speedup from quantum search algorithm. A more elegant method is the fixed-point search \cite{Yoder_2014}, which is an improved version of the amplitude amplification algorithm to avoid the ``over cooking'' problem. We adopt this fixed-point search as the amplitude amplification method here and record it as ${{\bf{F}}\left( {{{\bf{U}}_I},{\bf{P}}} \right)}$.
\subsection{Constructing projectors to qualified states}
We can construct the projector of QDC by combining ${\bf{U}}_D$ and a projector to ${\left| 0 \right\rangle ^{ \otimes K}}\left| 0 \right\rangle $ on the $K$ auxiliary qubits and the mark qubit as
\begin{align}
\label{eq-Dirac-projector}
{{\bf{P}}_D} = \left[ {{{\bf{I}}^{ \otimes N}} \otimes {{\left( {\left| 0 \right\rangle \left\langle 0 \right|} \right)}^{ \otimes K + 1}}} \right]{{\bf{U}}_D}.
\end{align}
Here ${\bf{U}}_D$ is the practical quantum Dirac circuit, ${{{\bf{I}}^{ \otimes {N} }}}$ is the identity operator on the physical qubits, and ${\left( {\left| 0 \right\rangle \left\langle 0 \right|} \right)^{ \otimes K + 1}}$ is the projector to ${\left| 0 \right\rangle ^{ \otimes K}}\left| 0 \right\rangle $ on the $K$ auxiliary qubits and the mark qubit.
When the state is in the subspace where the auxiliary qubits and the mark qubit are fixed to ${\left| 0 \right\rangle ^{ \otimes K}}\left| 0 \right\rangle $, the projector ${{\bf{P}}_D}$ achieves the result of the projector $\left| {{E_g}} \right\rangle \left\langle {{E_g}} \right|$ on physical qubits. This can be expressed as
\begin{align}
\label{eq-Dirac-projector-e}
{{\bf{P}}_D}\left| {{E_j}} \right\rangle {\left| 0 \right\rangle ^{ \otimes K}}\left| 0 \right\rangle = {\gamma _j}\left| {{E_j}} \right\rangle {\left| 0 \right\rangle ^{ \otimes K}}\left| 0 \right\rangle .
\end{align}
The projector can be described as firstly entangling the target state $\left| {{E_g}} \right\rangle $ on the physical qubits with ${\left| 0 \right\rangle }$ on the mark qubit and then projecting the mark qubit with $\left| 0 \right\rangle \left\langle 0 \right|$.
Similarly, the corresponding projector ${{\bf{P}}_H}$ of QHC can be constructed by combining ${{\bf{U}}_{H}}$ with a projector to ${\left| 0 \right\rangle ^{ \otimes K}}\left| 0 \right\rangle $ on the $K$ auxiliary qubits and the mark qubit, which gives
\begin{equation}
\label{eq-Heaviside-projector}
{{\bf{P}}_H} = \left[ {{{\bf{I}}^{ \otimes N}} \otimes {{\left( {\left| 0 \right\rangle \left\langle 0 \right|} \right)}^{ \otimes K + 1}}} \right]{{\bf{U}}_H}.
\end{equation}
\subsection{Quantum selector and quantum judge for eigen problem}
After constructing the projector in amplitude amplification algorithm using the quantum Heaviside circuit as given in Eq. (\ref{eq-Heaviside-projector}), a quantum judge can be obtained. The quantum judge projects a randomly initialized state onto the image of states whose energies are lower than the given threshold $\theta$ with high probability. Then an extra quantum Heaviside circuit is performed to mark the qualified states with exponentially small error. Measuring the mark qubit one can obtain whether there is any qualified state to the quantum Heaviside circuit of the given Hamiltonian matrix and threshold. More specifically, if the probability of the measurement result of the mark qubit being $\left| 0 \right\rangle $ is exponentially small, all eigen values of given Hamiltonian matrix are larger than $\theta$. The minimum eigen value of $\bf{H}$ with an error smaller than $\varepsilon $ can be obtained by performing $O\left( {\log {1 \over \varepsilon }} \right)$ times of quantum judge according to dichotomy. The number of calling quantum circuit to obtain the ground state energy of $\bf{H}$ is exponentially smaller than those in Ref. \cite{Poulin_2009} and Ref. \cite{Ge_2019}, while the cost of quantum circuits is similar. These two works use analogs of quantum Dirac circuit for sweeping or quantum sweeping the ground state energy for $O\left( {{1 \over \varepsilon }} \right)$ and $O\left( {\sqrt {{1 \over \varepsilon }} } \right)$ times, respectively, in the absence of quantum Heaviside circuit.
As the eigen values can be calculated by combining quantum judge with dichotomy, the quantum Dirac circuit can be used to find the eigen state of a given eigen value. The amplitude amplification algorithm whose projector is constructed by quantum Dirac circuit can be regarded as a quantum selector. Similar to quantum judge, the quantum selector projects a randomly initialized state onto the image of states corresponding to the given eigen value. Then an extra quantum Dirac circuit is performed to mark the qualified states with exponentially small error. When this process is done, the state $\left| 0 \right\rangle $ on the mark qubit is entangled with the qualified states on the physical qubits. A joint measurement of the mark qubit and physical qubits can be performed to make tomography or obtain the observations of qualified states. The quantum selector does not distinguish the degenerate states since it changes the mark qubit based on the eigen values of input states on the physical qubits. When the qualified states are degenerate (multiple), the state on the physical qubits entangled with $\left| 0 \right\rangle $ on the mark qubit is a linear superposition of all qualified states. The superposition coefficients depend on the proportion of different qualified states in the initial state $\left| {{\psi _r}} \right\rangle $, which are usually unknown.
\section{Solve eigen states with quantum selector}
\subsection{Restrictions on quantum Dirac circuit}
Now we give the restrictions on the quantum Dirac to solve a $\chi $-dimensional Hamiltonian matrix on $N$ physical qubits. In the case of quantum Dirac circuit, the quantum selector is an amplitude amplification circuit whose projector to the good subspace is ${{\bf{P}}_D}$. The output state of this quantum selector on physical qubits where the mark qubit is measured to be $\left| 0 \right\rangle $ is
\begin{align}
\label{eq-output1}
{{{{\bf{P}}_D}\left| {{\psi _r}} \right\rangle } \over {\left\| {{{\bf{P}}_D}\left| {{\psi _r}} \right\rangle } \right\|}} = {{\sum\limits_j {{\lambda _j}{\gamma _j}\left| {{E_j}} \right\rangle } } \over {\left\| {\sum\limits_j {{\lambda _j}{\gamma _j}\left| {{E_j}} \right\rangle } } \right\|}} ,
\end{align}
where $\left\{ {{\lambda _j}} \right\}$ are the expansion coefficients of initial state under energy representations. These coefficients are given by the initialization circuit
\begin{align}
\label{eq-initial-circuit}
\left| {{\psi _r}} \right\rangle = {{\bf{U}}_I}{\left| 0 \right\rangle ^{ \otimes N}} = \sum\limits_j {{\lambda _j}\left| {{E_j}} \right\rangle } .
\end{align}
Without losing generality, we assume that the qualified state is ${\left| {{E_g}} \right\rangle }$. And we also suppose that a suitable initialization operator is constructed to satisfy that ${\lambda _g} = O\left( {{1 \over {\sqrt \chi }}} \right)$. The eigen state corresponding to ${E_g}$ is assumed to be non-degenerate for the convenience of explanation. This algorithm can be trivially generalized to the degenerate case. The successful implementation of using quantum selector to obtain an $\varepsilon $-close state to $\left| {{E_g}} \right\rangle $ has two requirements that come from the amplitude amplification algorithm \cite{Grover_1998}. The first requirement is that the amplitude amplification circuit can be constructed by no more than $O\left( {{1 \over {\sqrt \chi }}} \right)$ initialization circuits ${{\bf{U}}_I}$ and projector circuits ${{\bf{P}}_D}$, which is equivalent to that $\left\| {{{\bf{P}}_D}\left| {{\psi _r}} \right\rangle } \right\| \ge O\left( {{1 \over {\sqrt \chi }}} \right)$. The second requirement is that the error between the output state of this quantum selector and ${\left| {{E_g}} \right\rangle }$ should be less than $O\left( \varepsilon \right)$, which can be expressed as $\left\| {{{{{\bf{P}}_D}\left| {{\psi _r}} \right\rangle } \over {\left\| {{{\bf{P}}_D}\left| {{\psi _r}} \right\rangle } \right\|}} - \left| {{E_g}} \right\rangle } \right\| \le O\left( \varepsilon \right)$.
To meet these two requirements, we restrain that $\left\{ {{\gamma _j}} \right\}$ in Eq. (\ref{eq-Dirac-p}) satisfy
\begin{equation}\label{eq-restrain-alpha}
\left| {{\gamma _j}} \right|
\begin{cases}
\ge {1 \over 2} & j = g, \\
\le O\left( {{\varepsilon \over {\sqrt \chi }}} \right) & j \ne g,
\end{cases}
\end{equation}
which is a sufficient condition for these two requirements when designing the practical quantum Dirac circuit of Eq. (\ref{eq-Dirac-p}). The proof of sufficiency for the first requirement is that
\begin{equation}
\label{eq-Dirac-proof1}
\left\| {{{\bf{P}}_D}\left| {{\psi _r}} \right\rangle } \right\| \ge \left\| {{\lambda _g}{\gamma _g}\left| {{E_g}} \right\rangle } \right\| = \left| {{\lambda _g}{\gamma _g}} \right| = O\left( {{1 \over {\sqrt \chi }}} \right).
\end{equation}
Meanwhile, we notice that
\begin{subequations}\label{eq-Dirac-subproof}
\begin{align}
\sum\limits_j {{{\left| {{\lambda _j}{\gamma _j}} \right|}^2}} \ge {\left| {{\lambda _g}{\gamma _g}} \right|^2} = O\left( {{1 \over \chi }} \right) ,
\end{align}
\begin{align}
\sum\limits_{i \ne g} {{{\left| {{\lambda _j}{\gamma _j}} \right|}^2}} \le O\left( {{{{\varepsilon ^2}} \over \chi }} \right)\sum\limits_{i \ne g} {{{\left| {{\lambda _j}} \right|}^2}} = O\left( {{{{\varepsilon ^2}} \over \chi }} \right) .
\end{align}
\end{subequations}
The proof of sufficiency for the second requirement is that
\begin{align}
\label{eq-Dirac-proof2}
{{\left| {\left\langle {{E_g}} \right|{{\bf{P}}_D}\left| {{\psi _r}} \right\rangle } \right|} \over {\left\| {{{\bf{P}}_D}\left| {{\psi _r}} \right\rangle } \right\|}} =
{{\left| {{\lambda _g}{\gamma _g}} \right|} \over {\sqrt {\sum\limits_j {{{\left| {{\lambda _j}{\gamma _j}} \right|}^2}} } }} \\ \notag
= \sqrt {1 - {{\sum\limits_{i \ne g} {{{\left| {{\lambda _j}{\gamma _j}} \right|}^2}} } \over {\sum\limits_j {{{\left| {{\lambda _j}{\gamma _j}} \right|}^2}} }}} \\ \notag
\ge \sqrt {1 - O\left( {{\varepsilon ^2}} \right)} ,
\end{align}
and $\left\| {{{{{\bf{P}}_D}\left| {{\psi _r}} \right\rangle } \over {\left\| {{{\bf{P}}_D}\left| {{\psi _r}} \right\rangle } \right\|}} - \left| {{E_q}} \right\rangle } \right\| \le O\left( \varepsilon \right)$ can be directly derived.
\subsection{Realization of quantum coin toss}
Here we give the quantum circuit to flip one quantum coin with the amplitude of $\cos \left( {{E_j} - {E_g}} \right)$ when the state on the physical qubits is $\left| {{E_j}} \right\rangle $, where ${{E_g}}$ is the given eigen value. Since we can shift and zoom the Hamiltonian matrix $\bf{H}$, we assume that ${{E_g} = 0}$ and all eigen values of $\bf{H}$ are in the range of $\left( { - {\pi \over 2},{\pi \over 2}} \right)$ without losing generality. This flipping operator of quantum coin is designed as
\begin{align}
\label{eq-uf-one}
{{\bf{U}}_c} = {\bf{B}}{{\bf{U}}_e}{\bf{B}},
\end{align}
where ${\bf{B}}$ is the quantum Hadamard gate which maps basis state $\left| 0 \right\rangle $ to ${{\left| 0 \right\rangle + \left| 1 \right\rangle } \over {\sqrt 2 }}$ and maps $\left| 1 \right\rangle $ to ${{\left| 0 \right\rangle - \left| 1 \right\rangle } \over {\sqrt 2 }}$ \cite{Nielsen_2009}, and $\bf{U}_e$ is a time evolution operator controlled by the quantum coin
\begin{align}
\label{eq-u-evolute}
{{\bf{U}}_e} = {e^{i{\bf{H}}}}\left| 0 \right\rangle \left\langle 0 \right| + {e^{ - i{\bf{H}}}}\left| 1 \right\rangle \left\langle 1 \right|.
\end{align}
${e^{ - i{\bf{H}}}}$ is the unit time evolution of Hamiltonian matrix $\bf{H}$ and ${e^{ i{\bf{H}}}}$ is the inverse of it. The illustration of this design is shown in Fig. \ref{fig-dirac-1}(c).
\subsection{Using multiple quantum coins to design quantum Dirac circuit}
Here we consider the operator ${{\bf{U}}_C}$ that flips $M$ quantum coins
\begin{align}
\label{eq-ufM-result}
{{\bf{U}}_C}\left| {{E_j}} \right\rangle & {\left| 0 \right\rangle ^{ \otimes M}} = \left( {\prod\limits_m^M {{\bf{U}}_c^m} } \right)\left| {{E_j}} \right\rangle {\left| 0 \right\rangle ^{ \otimes M}} \notag \\
& = \left| {{E_j}} \right\rangle {\left[ {{{\cos }}\left( {{E_j}} \right)\left| 0 \right\rangle + i\sin \left( {{E_j}} \right)\left| 1 \right\rangle } \right]^{ \otimes M}} .
\end{align}
${{\bf{U}}_c^m}$ is an operator on $N$ physical qubits and $M$ quantum coins, which is constructed by flipping operator ${{\bf{U}}_c}$ of the $m$-th quantum coin and an identity operator on the rest $M-1$ quantum coins, as shown in Fig. \ref{fig-dirac-1}(b). We call this kind of operator composed by the direct product of a unitary operator $\bf{U}$ and an identity operator on the rest qubits of the whole circuit as the extension of $\bf{U}$ below. The probability of all quantum coins being flipped is ${{{\cos }^{2M}}\left( {{E_j}} \right)}$, which is a good approximation to the analog of Dirac function $\delta \left( {{E_j}} \right)$ for large $M$. The practical quantum Dirac circuit in the form of Eq. (\ref{eq-Dirac-p}) can be constructed by
\begin{align}
\label{eq-Dirac-1}
{{\bf{U'}}_D} = \left[ {{{\bf{I}}^{ \otimes N}} \otimes {{\bf{U}}_{MCX}}\left( {{{\left| 0 \right\rangle }^{ \otimes M}}} \right)} \right]\left( {{{\bf{U}}_C} \otimes {\bf{I}}} \right)\left( {{{\bf{I}}^{ \otimes N + M}} \otimes \bf{X}} \right) ,
\end{align}
which is shown in Fig. \ref{fig-dirac-1}(a). ${{{\bf{U}}_{MCX}}\left( {{{\left| 0 \right\rangle }^{ \otimes M}}} \right)}$ is a multi-controlled NOT gate that performs NOT gate on the mark qubit when the state on $M$ quantum coins is ${{{\left| 0 \right\rangle }^{ \otimes M}}}$ as shown in Fig. \ref{fig-dirac-1}(d). The operator ${{\bf{U}}_C}$ is the combination of $M$ flipping operator acting on the physical qubits and $M$ quantum coins separately as shown in Fig. \ref{fig-dirac-1}(b). ${\bf{X}}$ represents for the quantum NOT gate.
\begin{figure}[htb]
\centering
\includegraphics[width=0.9\linewidth]{dirac1.pdf}
\caption{\label{fig-dirac-1}(a) guide to construct the primary quantum Dirac circuit of Eq. (\ref{eq-Dirac-1}). (a) The primary design of the quantum Dirac circuit of Eq. (\ref{eq-Dirac-1}). (b) The circuit that flips $M$ quantum coins respectively as given in Eq. (\ref{eq-ufM-result}). Here we record the top quantum coin as the first quantum coin. (c) The flipping operator of one quantum coin in Eq. (\ref{eq-uf-one}). (d) The multi-controlled NOT gate that performs NOT gate on the mark qubit when the state on $M$ quantum coins is ${{{\left| 0 \right\rangle }^{ \otimes M}}}$.}
\end{figure}
\subsection{Mathematical analysis on the number of quantum coins}
With the practical design of Eq. (\ref{eq-Dirac-1}), we can obtain from Eq. (\ref{eq-Dirac-p}) that ${\gamma _j} = {\cos ^M}\left( {{E_j}} \right)$. The restraint of ${\gamma _j}$ in Eq. (\ref{eq-restrain-alpha}) becomes the restraint of $M$ and the error bound ${{\varepsilon _0}}$ of the given energy ${E_g}$
\begin{subequations}\label{eq-reatrain-M}
\begin{align}
{\cos ^M}\left( {{\varepsilon _0}} \right) \ge {1 \over 2},
\end{align}
\begin{align}
{\cos ^M}\left( {\left| {\Delta - {\varepsilon _0}} \right|} \right) < O\left( {{\varepsilon \over {\sqrt \chi }}} \right) ,
\end{align}
\end{subequations}
where $\varepsilon $ is the error bound of the output state, $\chi $ is the dimension of Hamiltonian matrix $\bf{H}$, and $\Delta $ is the gap between ${E_g}$ and its closest eigen value. Then we can derive that to obtain the $\varepsilon$-close eigen state corresponding to the given eigen value ${E_g}$, the minimum number of quantum coins is
\begin{align}
\label{eq-M}
M = O\left( {{1 \over {{\Delta ^2}}}\left( {N + \log {1 \over \varepsilon }} \right)} \right),
\end{align}
and the error bound of ${E_g}$ is ${\varepsilon _0} = O\left( \Delta \right)$.
\subsection{Quantum Dirac circuit improved by the freezing operator}
The new design of practical quantum Dirac circuit is shown in Fig. \ref{fig-dirac-2} and can be written as
\begin{align}
\label{eq-Dirac-2}
{{\bf{U''}}_D} = {\left[ {\left( {{{\bf{I}}^{ \otimes N}} \otimes {{\bf{U}}_F}} \right)C{{\bf{U}}_c}} \right]^M}\left( {{{\bf{I}}^{ \otimes N + 1}} \otimes {{\bf{X}}^{ \otimes K}}} \right),
\end{align}
where ${C{{\bf{U}}_c}}$ is the flipping operator controlled by the mark qubit and combined with an identity operator on the rest $K - 1$ qubits. This method shows how to construct the practical quantum Dirac circuit in the form of Eq. (\ref{eq-Dirac-p}) with $K = O\left( {\log M} \right)$ auxiliary qubits (counting qubits).
\begin{figure}[htb]
\centering
\includegraphics[width=1\linewidth]{dirac2.pdf}
\caption{\label{fig-dirac-2}(a) guide to construct the quantum Dirac circuit of Eq. (\ref{eq-Dirac-2}). (a) The design of quantum Dirac circuit of Eq. (\ref{eq-Dirac-2}) used for the quantum selector. Here we record the top counting qubit as the first (the highest) qubit and so do the following circuits. (b) The circuit of freezing operator.}
\end{figure}
\subsection{Construction and gate complexity of quantum selector}
Using Eq. (\ref{eq-Dirac-2}) as the practical quantum Dirac circuit, the quantum selector can be expressed as
\begin{align}
\label{eq-selector}
{\bf{S}} = {{\bf{P''}}_D}{\bf{F}}\left[ {{{\bf{U}}_I},{{{\bf{P''}}}_D}} \right],
\end{align}
where ${{\bf{P''}}_D}$ is the projector to the good subspace constructed by Eq. (\ref{eq-Dirac-2}) and Eq. (\ref{eq-Dirac-projector}), which reads
\begin{align}
\label{eq-D-projector}
{{\bf{P''}}_D} = \left[ {{{\bf{I}}^{ \otimes N + K}} \otimes \left( {\left| 0 \right\rangle \left\langle 0 \right|} \right)} \right]{\bf{U''}_D}.
\end{align}
Note that this projector is not a unitary operator as it contains ${\left| 0 \right\rangle \left\langle 0 \right|}$ which is achieved by measurements. This quantum selector can output an $\varepsilon$-close eigen state corresponding to the given eigen value $E_g$. Since the quantum selector is a quantum amplitude amplification algorithm, it requires $O\left( {{1 \over {\sqrt \chi }}} \right)$ iterations of the initialization operator ${{{\bf{U}}_I}}$ and the projector ${{{{\bf{P''}}}_D}}$.
Now we analyze the gate complexity of the quantum selector. The basic ingredients of the quantum selector include the initialization operator ${{\bf{U}}_I}$ defined by Eq. (\ref{eq-initial-circuit}), the controlled Hamiltonian evolution operator ${{\bf{U}}_e}$ defined by Eq. (\ref{eq-u-evolute}), the multi-controlled NOT gate, and some basic quantum gates. There are several methods for the controlled Hamiltonian evolution whose gate complexities scale differently with the evolution time, the error bound and the properties of the given Hamiltonian matrix \cite{Berry_2015, Berry_2015_10, Low_2017, Low_2019}. Here we record the gate complexity for Hamiltonian simulation in unit time as $\Lambda $ instead of analyzing the difference of gate complexities resulted from different Hamiltonian simulation methods. Similarly, we record the gate complexity of initialization circuit as $\Phi $ from which one can obtain the state whose fidelity with the qualified state is no less than $O\left( {{1 \over \chi }} \right)$.
From Fig. \ref{fig-dirac-1}(c) we can see that the gate complexity of ${{\bf{U}}_c}$ is $O\left( \Lambda \right)$. The gate complexity of ${{\bf{U}}_F}$ is $O\left[ {poly\left( K \right)} \right]$ as shown in Fig. \ref{fig-dirac-2}(b), and the gate complexity of multi-controlled NOT gate on $K+1$ qubits is also $O\left[ {poly\left( K \right)} \right]$ \cite{Nielsen_2009}. Then the gate complexity of the quantum Dirac circuit of Eq. (\ref{eq-Dirac-2}) is $O\left( {M\left[ {\Lambda + poly\left( K \right)} \right]} \right)$. We use $\tilde O$ to denote the complexity up to poly logarithmic factors in $N$, ${1 \over \Delta }$, ${\log {1 \over \varepsilon }}$, and $\Lambda $. The gate complexity of the quantum Dirac circuit of Eq. (\ref{eq-Dirac-2}) can thus be rewritten as $\tilde O\left( {\Lambda {{N + \log {1 \over \varepsilon }} \over {{\Delta ^2}}}} \right)$. Since the quantum selector is the Grove search of Eq. (\ref{eq-grover}) (or the fixed-point search with the same complexity under big-$O$ notation) using ${{\bf{U}}_I}$ and ${{\bf{P}}_D}$ of Eq. (\ref{eq-D-projector}), its gate complexity is
\begin{align}
\label{eq-gate-dirac}
\tilde O\left( {\Lambda {{N + \log {1 \over \varepsilon }} \over {\sqrt \chi {\Delta ^2}}} + {\Phi \over {\sqrt \chi }}} \right).
\end{align}
\section{Solve eigen values with quantum judge}
\subsection{Restrictions on quantum Heaviside circuit}
The quantum judge is an amplitude amplification circuit whose projector to the good subspace is ${{\bf{P}}_H}$. Then the output state of this quantum judge on physical qubits where the mark qubit is measured to be $\left| 0 \right\rangle $ is
\begin{align}
\label{eq-output2}
{{{{\bf{P}}_H}\left| {{\psi _r}} \right\rangle } \over {\left\| {{{\bf{P}}_H}\left| {{\psi _r}} \right\rangle } \right\|}} = {{\sum\limits_j {{\lambda _j}{\alpha _j}\left| {{E_j}} \right\rangle } } \over {\left\| {\sum\limits_j {{\lambda _j}{\alpha _j}\left| {{E_j}} \right\rangle } } \right\|}} .
\end{align}
The task of this quantum judge is to judge whether all eigen values of the given Hamiltonian ${\bf{H}}$ is larger than the threshold $\theta$. More specifically, the quantum judge should output the differentiable states for two different cases. The first case is that all eigen values of the given Hamiltonian ${\bf{H}}$ is larger than $\theta $ and the second case is that there are states whose corresponding eigen values are smaller than $\theta - \varepsilon$. For convenience of presentation, we define an index $h$ that satisfies
\begin{equation}\label{eq-E-theta}
{E _j}
\begin{cases}
\le \theta - \varepsilon & j \le h ,\\
\ge \theta & j > h.
\end{cases}
\end{equation}
We also assume that the initialization circuit ${{\bf{U}}_I}$ is designed to satisfy that in the second case $\sum\limits_{j \le h} {{{\left| {{\lambda _j}} \right|}^2}} \ge O\left( {{1 \over { \chi }}} \right)$. This is a trivial task since a random circuit can meet this requirement with high probability.
To meet the requirement of output differentiable states in these two cases, we restrain that $\left\{ {{\alpha _j}} \right\}$ in Eq. (\ref{eq-Heaviside-p}) satisfies
\begin{equation}\label{eq-Heaviside-restrain}
\left| {{\alpha _j}} \right|
\begin{cases}
\ge {1 \over 2} & j \le h , \\
\le O\left( {{1 \over \chi }} \right) & j > h ,
\end{cases}
\end{equation}
which is a sufficient condition for this requirement when designing the practical quantum Dirac circuit of Eq. (\ref{eq-Heaviside-p}). Now we prove that with the restraint of Eq. (\ref{eq-Heaviside-restrain}), the quantum judge output $\left| 0 \right\rangle $ on the mark qubit with probability no more than $O\left( {{1 \over \chi }} \right)$ in the first case and the output $\left| 0 \right\rangle $ with probability of $O\left( 1 \right)$ in the second case. Here the quantum judge is composed by $O\left( {{1 \over {\sqrt \chi }}} \right)$ initialization circuits ${{\bf{U}}_I}$ and projector circuits ${{\bf{P}}_H}$.
In the first case, the probability of measuring $\left| 0 \right\rangle $ on the mark qubit from the state ${{\bf{U}}_H}\left| {{\psi _r}} \right\rangle {\left| 0 \right\rangle ^{ \otimes K}}\left| 0 \right\rangle $ is $\sum\limits_j {{{\left| {{\lambda _j}{\alpha _j}} \right|}^2}} $ according to the definition of ${{\bf{U}}_H}$ and $\left| {{\psi _r}} \right\rangle $ from Eq. (\ref{eq-Heaviside-p}) and Eq. (\ref{eq-initial-circuit}) respectively. Based on Eq. (\ref{eq-Heaviside-restrain}), this probability satisfies
\begin{align}
\label{eq-output-small}
\sum\limits_j {{{\left| {{\lambda _j}{\alpha _j}} \right|}^2}} \le O\left( {{1 \over {{\chi ^2}}}} \right)\sum\limits_j {{{\left| {{\lambda _j}} \right|}^2}} = O\left( {{1 \over {{\chi ^2}}}} \right).
\end{align}
Since we use $O\left( {{1 \over {\sqrt \chi }}} \right)$ repetitions of ${{\bf{U}}_I}$ and ${{\bf{P}}_H}$, the probability of measuring $\left| 0 \right\rangle $ on the mark qubit in the output state is no more than
\begin{align}
\label{eq-output3}
O\left( \chi \right)\sum\limits_j {{{\left| {{\lambda _j}{\alpha _j}} \right|}^2}} \le O\left( {{1 \over \chi }} \right),
\end{align}
which is exponentially small. In the second case, we have
\begin{align}
\label{eq-output-big}
\sum\limits_j {{{\left| {{\lambda _j}{\alpha _j}} \right|}^2}} \ge {1 \over 4}\sum\limits_{j \le h} {{{\left| {{\lambda _j}} \right|}^2}} = O\left( {{1 \over \chi }} \right).
\end{align}
Thus, the amplitude amplification algorithm can amplify the amplitude of $\left| 0 \right\rangle $ on the mark qubit to $O\left( 1 \right)$.
\subsection{Preliminaries of quantum phase estimation}
The QPE of an eigen state $\left| {{E_j}} \right\rangle $ is exactly given as \cite{Cleve_1998}
\begin{align}
\label{eq-QPE-e}
{{\bf{U}}_{QPE}}\left| {{E_j}} \right\rangle {\left| 0 \right\rangle ^{ \otimes R}}{\rm{ = }}{1 \over {{2^R}}}\sum\limits_{x = 0}^{{2^R} - 1} {\sum\limits_{k = 0}^{{2^R} - 1} {{e^{ik{E_j} - 2\pi ik{x \over {{2^R}}}}}\left| {{E_j}} \right\rangle \left| x \right\rangle } } ,
\end{align}
where ${{\bf{U}}_{QPE}}$ is the QPE circuit and $x$ is a binary number. The QPE circuit is achieved by three parts
\begin{align}
\label{eq-QPE-c}
{{\bf{U}}_{QPE}} = \left( {{{\bf{I}}^{ \otimes N}} \otimes {\bf{U}}_{Fourier}^{ - 1}} \right){{\bf{U}}_{CH}}\left( {{{\bf{I}}^{ \otimes N}} \otimes {{\bf{B}}^{ \otimes R}}} \right),
\end{align}
which is shown in Fig. \ref{fig-qpe-1}(a).
\begin{figure}[htb]
\centering
\includegraphics[width=1\linewidth]{qpe.pdf}
\caption{\label{fig-qpe-1}Sketch of quantum phase estimation circuit. (a) The quantum phase estimation circuit of Eq. (\ref{eq-QPE-c}). (b) The circuit of controlled Hamiltonian evolution which achieves Eq. (\ref{ch-result}).}
\end{figure}
Here ${\bf{B}}$ is the quantum Hadamard gate, ${{\bf{U}}_{CH}}$ is a controlled Hamiltonian evolution operator (Fig. \ref{fig-qpe-1}(b)) and ${\bf{U}}_{Fourier}^{ - 1}$ is the inverse quantum Fourier transform. The three circuits can achieve, respectively,
\begin{subequations}\label{eq-three-parts}
\begin{align}
{{\bf{B}}^{ \otimes R}}{\left| 0 \right\rangle ^{ \otimes R}} = {\left( {{{\left| 0 \right\rangle + \left| 1 \right\rangle } \over {\sqrt 2 }}} \right)^{ \otimes R}} = \sqrt {{1 \over {{2^R}}}} \sum\limits_{k = 0}^{{2^R} - 1} {\left| k \right\rangle } ,
\end{align}
\begin{align}
\label{ch-result}
{{\bf{U}}_{CH}}\sqrt {{1 \over {{2^R}}}} \sum\limits_{k = 0}^{{2^R} - 1} {\left| {{E_j}} \right\rangle \left| k \right\rangle } = \sqrt {{1 \over {{2^R}}}} \sum\limits_{x = 0}^{{2^R} - 1} {{e^{ik{E_j}}}\left| {{E_j}} \right\rangle \left| k \right\rangle } ,
\end{align}
\begin{align}
{\bf{U}}_{Fourier}^{ - 1}\left| k \right\rangle = \sqrt {{1 \over {{2^R}}}} \sum\limits_{x = 0}^{{2^R} - 1} {{e^{ - 2\pi ik{x \over {{2^R}}}}}\left| x \right\rangle } .
\end{align}
\end{subequations}
For convenience, we record the amplitude of ${\left| {{E_j}} \right\rangle \left| x \right\rangle }$ in Eq. (\ref{eq-QPE-e}) as $\kappa \left( {{E_j},x} \right)$, which is
\begin{align}
\label{eq-kappa}
\kappa \left( {{E_j},x} \right){\rm{ = }}{1 \over {{2^R}}}\sum\limits_{k = 0}^{{2^R} - 1} {{e^{ik{E_j} - 2\pi ik{x \over {{2^R}}}}}} .
\end{align}
This is a sum of geometric progression, so when $x$ is not exactly equal to ${2^{R - 1}}{{{E_j}} \over \pi }$, $\kappa \left( {{E_j},x} \right)$ can be written as
\begin{align}
\label{eq-kappa-simple}
\kappa \left( {{E_j},x} \right){\rm{ = }}{1 \over {{2^R}}}{{1 - {e^{i{2^R}{E_j} - 2\pi ix}}} \over {1 - {e^{i{E_j} - 2\pi i{x \over {{2^R}}}}}}} .
\end{align}
When $\left| {{{{E_j}} \over {2\pi }} - {x \over {{2^R}}}} \right| \le {1 \over {{2^{R + 1}}}}$, it can be proved that the modulus of $\kappa \left( {{E_j},x} \right)$ satisfies
\begin{align}
\label{eq-kappa-proof1}
\left| {\kappa \left( {{E_j},x} \right)} \right| & = \left| {{{\sin \left( {{2^{R - 1}}{E_j} - \pi x} \right)} \over {{2^R}\sin \left( {{{{E_j}} \over 2} - \pi {x \over {{2^R}}}} \right)}}} \right| \notag \\ & \ge {1 \over {{2^R}}}{{\left| {\sin \left( {{2^{R - 1}}{E_j} - \pi x} \right)} \right|} \over {\pi \left| {{{{E_j}} \over {2\pi }} - {x \over {{2^R}}}} \right|}} \notag \\ & \ge {1 \over {{2^R}}}{{{2^{R + 1}}\left| {{{{E_j}} \over {2\pi }} - {x \over {{2^R}}}} \right|} \over {\pi \left| {{{{E_j}} \over {2\pi }} - {x \over {{2^R}}}} \right|}} \notag \\ & = {2 \over \pi }.
\end{align}
We can define a classical function ${\rm{n}}\left( y \right)$ to output the nearest binary number on $R$ digits of ${{2^R}y}$, where $y$ is in the range of $\left[ {0,1 - {1 \over {{2^R}}}} \right]$. It can be easily seen that
\begin{align}
\label{eq-n-diff}
\left| {{{n\left( y \right)} \over {{2^R}}} - y} \right| \le {1 \over {{2^{R + 1}}}}.
\end{align}
Without losing the generality, we assume ${{E_j}}$ is in the range of $\left[ {0,2\pi - {{2\pi } \over {{2^R}}}} \right]$, and then Eq. (\ref{eq-kappa-proof1}) becomes
\begin{align}
\label{eq-kappa-proof2}
\left| {\kappa \left( {{E_j},n\left( {{{{E_j}} \over {2\pi }}} \right)} \right)} \right| \ge {2 \over \pi }.
\end{align}
Eq. (\ref{eq-kappa-proof2}) shows that the QPE method can output a binary representation of ${n\left( {{{{E_j}} \over {2\pi }}} \right)}$ with the amplitude larger than ${2 \over \pi }$. Thus, we can obtain the value of ${{{{E_j}} \over {2\pi }}}$ with an error lower than $O\left( {{1 \over {{2^R}}}} \right)$.
For the convenience of our later proofs on quantum Heaviside circuit, here we give a lower bound of the modulus of $\kappa \left( {{E_j},x} \right)$. When $\left| {{{{E_j}} \over {2\pi }} - {x \over {{2^R}}}} \right| \le {1 \over {S{2^{R + 1}}}}$ and $S \ge 2$ \cite{Poulin_2009}, the lower bound of the modulus of $\kappa \left( {{E_j},x} \right)$ is
\begin{align}
\label{eq-kappa-low}
\left| {\kappa \left( {{E_j},x} \right)} \right| & = {1 \over {{2^R}}}\left| {\sum\limits_{k = 0}^{{2^R} - 1} {{e^{ik{E_j} - 2\pi ik{x \over {{2^R}}}}}} } \right| \notag \\ & \ge {1 \over {{2^R}}}\left| {\sum\limits_{k = 0}^{{2^R} - 1} {\cos \left[ {2\pi k\left( {{{{E_j}} \over {2\pi }} - {x \over {{2^R}}}} \right)} \right]} } \right| \notag \\ & \ge {1 \over {{2^R}}}\sum\limits_{k = 0}^{{2^R} - 1} {\cos \left( {{\pi \over S}} \right)} \notag \\ & = \cos \left( {{\pi \over S}} \right) \notag \\ & \ge 1 - {{\pi}^2 \over {2{S^2}}}.
\end{align}
\subsection{The first strategy in the quantum Heaviside circuit}
As we have shown in Eq. (\ref{eq-QPE-e}), the implementation of QPE circuit requires $N$ physical qubits and $R$ representation qubits. The first strategy in QHC is to implement $Q$ QPE circuits on the same physical qubits and $Q \times R$ different representation qubits. This circuit is defined as
\begin{align}
\label{eq-q-QPE}
{\bf{U}}_{Q} = \prod\limits_q^Q {{\bf{U}}_{QPE}^q},
\end{align}
where ${{\bf{U}}_{QPE}^q}$ is the extension of QPE circuit on the $q$-th part of representation qubits, as shown in Fig. \ref{fig-heaviside-1}(b). Without losing the generality, we assume that all eigen values are in the range of $\left[ {0,2\pi - {{2\pi } \over {{2^R}}}} \right]$ and the given threshold $\theta $ equals $\pi $.
Ignoring the huge amount of qubits it needs, we now give the primary design of quantum Heaviside circuit
\begin{align}
\label{eq-Heaviside-1}
{{\bf{U'}}_H} = {\bf{U}}_{MCX}^q\left( {{{\left| 0 \right\rangle }^{ \otimes Q}}} \right)\left( {{{\bf{U}}_Q} \otimes {\bf{I}}} \right)\left( {{{\bf{I}}^{ \otimes N + QR}} \otimes {\bf{X}}} \right),
\end{align}
where ${\bf{U}}_{MCX}^q$ is a NOT gate on the mark qubit controlled by $Q$ first (the highest) qubits of $Q$ parts of representation qubits. This primary design of quantum Heaviside circuit is shown in Fig. \ref{fig-heaviside-1}. The effect of this circuit can be shown as
\begin{align}
\label{eq-Heaviside-effect}
{{\bf{U'}}_H}\left| {{E_j}} \right\rangle {\left| 0 \right\rangle ^{ \otimes {QR+1}}} & {\rm{ = }}\left| {{E_j}} \right\rangle {\left( {\sum\limits_{x = 0}^{{2^{R-1}} - 1} {\kappa \left( {{E_j},x} \right)\left| x \right\rangle } } \right)^{ \otimes Q}}\left| 0 \right\rangle \notag \\ & + \left| {{E_j}} \right\rangle \left| {rest} \right\rangle \left| 1 \right\rangle .
\end{align}
\begin{figure}[htb]
\centering
\includegraphics[width=1\linewidth]{heaviside1.pdf}
\caption{\label{fig-heaviside-1}(a) guide to construct the primary quantum Heaviside circuit of Eq. (\ref{eq-Heaviside-1}). (a) The primary design of quantum Heaviside circuit of Eq. (\ref{eq-Heaviside-1}). This circuit can successfully filter out the states in the bad subspace, but it requires huge amount of qubits and cannot preserve the good states. (b) The circuit to apply the quantum phase estimation to $Q$ parts of representation qubits as given in Eq. (\ref{eq-q-QPE}). (c) The circuit to apply NOT gate to the mark qubit controlled by all first qubits of all $Q$ parts of representation qubits.}
\end{figure}
This quantum Heaviside circuit can successfully filter out the states in the bad subspace while it cannot ensure to preserve the good states. This is equivalent to satisfying the second requirement of Eq. (\ref{eq-Heaviside-restrain}) and ignoring the first requirement. It can be proved below when
\begin{subequations}\label{eq-reatrain-QR}
\begin{align}\label{eq-reatrain-R}
\varepsilon \ge {2 \pi \over {{2^{R - 1}}}},
\end{align}
\begin{align}\label{eq-reatrain-Q}
Q = O\left( N \right) .
\end{align}
\end{subequations}
From Eq. (\ref{eq-reatrain-R}) and Eq. (\ref{eq-E-theta}), we can obtain that $n\left( {{{{E_j}} \over {2\pi }}} \right) > 2^{R-1}$ for $j > h$. This means that the qubit with the highest order in the binary representation of $n\left( {{{{E_j}} \over {2\pi }}} \right)$ is $\left| 1 \right\rangle $. Based on Eq. (\ref{eq-kappa-proof2}) and Eq. (\ref{eq-Heaviside-effect}), the amplitude of the mark qubit being $\left| 0 \right\rangle $ satisfies
\begin{align}
\label{eq-4132-1}
{\left| {{\alpha _j}} \right|^2} & = {\left( {\sum\limits_{x = 0}^{{2^{R - 1}} - 1} {{{\left| {\kappa \left( {{E_j},x} \right)} \right|}^2}} } \right)^Q} \notag \\ & \le {\left( {1 - {{\left| {\kappa \left( {{E_j},n\left( {{{{E_j}} \over {2\pi }}} \right)} \right)} \right|}^2}} \right)^Q} \notag \\ & \le {\left( {1 - {4 \over {{\pi ^2}}}} \right)^Q}
\end{align}
Since $N = O\left( {\log \chi } \right)$, we can easily find that $Q$ satisfies Eq. (\ref{eq-reatrain-Q}) and meets the second requirement of Eq. (\ref{eq-Heaviside-restrain}), which is $\left| {{\alpha _j}} \right| \le {\rm{O}}\left( {{1 \over \chi }} \right)$.
\subsection{The second strategy in the quantum Heaviside circuit}
Quantum Heaviside circuit using only the first strategy may unfortunately filter out the good states, and the second strategy is to implement a batch of QPE circuits ${{\bf{U}}_{Q}}$ for $W$ different Hamiltonian matrices, which are expressed as $\left\{ {{{\bf{H}}_w}} \right\}:{{\bf{H}}_w} = {{\bf{H}}_0} + {w \over W}{\pi \over {{2^{R - 1}} }}$. Now we prove that the good states of ${\bf{H}}_0$ can survive at least once in the $W$ quantum Heaviside circuit. Suppose that the eigen value of a good state of ${\bf{H}}_0$ is ${E}_q$, then there is a set of ${E}_q$ corresponding to the set of ${{{\bf{H}}_w}}$ recorded as
\begin{align}
\label{eq-E-set}
\left\{ {{E_{q,w}}} \right\}:{E_{q,w}} = {E_q} + {w \over W}{\pi \over {{2^{R - 1}} }}.
\end{align}
Note that ${E}_q$ is the eigen value of a good state which means that all ${E_{s,w}}$ satisfy
\begin{align}
\label{eq-E-big}
n\left( {{{{E_{q,w}}} \over {2\pi }}} \right) < {2^{R - 1}}.
\end{align}
Since the interval of ${E_{s,w}}$ is ${1 \over {W{2^{R - 1}}\pi }}$, there will be at least one ${w_0}$ that satisfies
\begin{align}
\label{eq-w-good}
\left| {{{{E_{q,{w_0}}}} \over {2\pi }} - {1 \over {{2^R}}}n\left( {{{{E_{q,{w_0}}}} \over {2\pi }}} \right)} \right| \le {1 \over {W{2^{R+1}} }}.
\end{align}
Substituting this equation into Eq. (\ref{eq-kappa-low}), we can get the amplitude immediately
\begin{align}
\label{eq-w-good-a}
\left| {\kappa \left( {{E_{q,{w_0}}},n\left( {{{{E_{q,{w_0}}}} \over {2\pi }}} \right)} \right)} \right| \ge 1 - {{\pi}^2 \over {2{W^2}}}.
\end{align}
Note that the amplitude of the mark qubit being $\left| 0 \right\rangle $ after the quantum Heaviside circuit satisfies
\begin{align}
\label{eq-4132-2}
{\left| {{\alpha _q}} \right|^2}{\rm{ = }}{\left[ {\sum\limits_{x = 0}^{{2^R-1} - 1} {{{\left| {\kappa \left( {{E_q},x} \right)} \right|}^2}} } \right]^Q} \ge {\left[ {{{\left| {\kappa \left( {{E_q},n\left( {{{{E_q}} \over {2\pi }}} \right)} \right)} \right|}^2}} \right]^Q}.
\end{align}
To meet the first requirement in Eq. (\ref{eq-Heaviside-restrain}), we obtain
\begin{align}
\label{eq-W}
{W = O\left( {\sqrt Q } \right) = O\left( {\sqrt N } \right)}.
\end{align}
Since the condition for the establishment of Eq. (\ref{eq-4132-1}) still holds, which is ${n\left( {{{{E_{s,w}}} \over {2\pi }}} \right) > {2^{R - 1}}}$, all $W$ quantum Heaviside circuits can filter out the bad states, whose eigen values are larger than ${\pi }$.
The classical part of this method can be replaced by a quantum search algorithm of ${{w_0}}$ that satisfies Eq. (\ref{eq-w-good}). It can speed up this method by ${O\left( {\sqrt W } \right) = O\left( {{N^{{1 \over 4}}}} \right)}$. Now we define a shifted QPE circuit with $D$ extra division qubits that can achieve
\begin{align}
\label{eq-sQPE-r}
& {{\bf{U}}_{sQPE}}\left| {{E_j}} \right\rangle {\left| 0 \right\rangle ^{ \otimes R}}{\left| 0 \right\rangle ^{ \otimes D}}{\rm{ = }} \notag \\ & {1 \over {{2^R}}}\sum\limits_{x = 0}^{{2^R} - 1} {\sum\limits_{k = 0}^{{2^R} - 1} {\sum\limits_{w = 0}^{{2^D} - 1} {{e^{ik{E_j} + 2\pi i{kw \over {{2^{R + D}}}} - 2\pi ik{x \over {{2^R}}}}}\left| {{E_j}} \right\rangle \left| x \right\rangle } } } \left| w \right\rangle .
\end{align}
The operator ${{\bf{U}}_{sQPE}}$ can be easily constructed by combining the QPE circuit shown in Eq. (\ref{eq-QPE-c}) with a controlled Hamiltonian evolution operator. To distinguish it from the controlled Hamiltonian evolution operator in Eq. (\ref{eq-QPE-c}), we record the two operators as $ {{\bf{U}}_{CH}}\left( k \right)$ and ${{\bf{U}}_{CH}}\left( {k,w} \right)$ which can achieve respectively
\begin{subequations}\label{eq-Kh}
\begin{align}
{{\bf{U}}_{CH}}\left( k \right)\left| {{E_j}} \right\rangle \left| k \right\rangle = {e^{ik{E_j}}}\left| {{E_j}} \right\rangle \left| k \right\rangle ,
\end{align}
\begin{align}
\label{eq-Kh-d}
{{\bf{U}}_{CH}}\left( {k,w} \right)\left| {{E_j}} \right\rangle \left| k \right\rangle \left| w \right\rangle = {e^{ik{E_j} + 2\pi i{{kw} \over {{2^{R + D}}}}}}\left| {{E_j}} \right\rangle \left| k \right\rangle \left| w \right\rangle,
\end{align}
\end{subequations}
where ${{\bf{U}}_{CH}}\left( k \right)$ is the controlled Hamiltonian evolution used in Eq. (\ref{eq-QPE-c}). The quantum circuit ${{\bf{U}}_{CH}}\left( {k,w} \right)$ is represented in Fig. \ref{fig-chd}.
\begin{figure}[htb]
\centering
\includegraphics[width=1\linewidth]{chd.pdf}
\caption{\label{fig-chd}The circuit to achieve the result of Eq. (\ref{eq-Kh-d}). This circuit contains $D \times R$ controlled Hamiltonian evolution operator in addition to the ${{\bf{U}}_{CH}}$.}
\end{figure}
The construction of shifted QPE is to replace the controlled Hamiltonian evolution operator in Eq. (\ref{eq-QPE-c}) with ${{\bf{U}}_{CH}}\left( {k,w} \right)$, where the division qubits are initialized to $\sum\limits_{w = 0}^{{2^D} - 1} {\left| w \right\rangle } $. The shifted QPE operator is shown as
\begin{align}
\label{eq-sQPE-c}
{{\bf{U}}_{sQPE}} = & \left( {{{\bf{I}}^{ \otimes N}} \otimes {\bf{U}}_{Fourier}^{ - 1} \otimes {{\bf{I}}^{ \otimes D}}} \right){{\bf{U}}_{CH}}\left( {k,w} \right) \notag \\ & \left( {{{\bf{I}}^{ \otimes N}} \otimes {{\bf{B}}^{ \otimes R}} \otimes {{\bf{I}}^{ \otimes D}}} \right).
\end{align}
Note that the quantum Fourier transform still works on the $R$ representation qubits.
The simple replacement of ${{\bf{U}}_{CH}}\left( k \right)$ with ${{\bf{U}}_{CH}}\left( {k,w} \right)$ reduces the lower bound on probability of outputting qualified states from $O\left( 1 \right)$ to $O\left( {{1 \over W}} \right)$. This process can be seen as to perform ${{\bf{U'}}_H}$ for $W$ different ${{\bf{H}}_w}$'s in parallel, compared with serial performing ${{\bf{U'}}_H}$ without the division qubits. The parallel quantum Heaviside circuit is recorded as
\begin{align}
\label{eq-p-Heaviside}
{{\bf{U'}}_{p - H}} = {\bf{U}}_{MCX}^q\left( {{{\bf{U}}_{sQ}} \otimes {{\bf{I}}}} \right),
\end{align}
where ${\bf{U}}_{MCX}^q$ is a NOT gate on the mark qubit controlled by $Q$ first qubits of $Q$ parts of representation qubits. The ${{{\bf{U}}_{sQ}}}$ is defined as
\begin{align}
\label{eq-q-sQPE}
{{{\bf{U}}_{sQ}} = \prod\limits_q^Q {{\bf{U}}_{sQPE}^q} },
\end{align}
which is similar to Eq. (\ref{eq-q-QPE}).
For the consistency of the definition of quantum Heaviside circuit, the probability of outputting qualified states should be increased to $O\left( 1 \right)$ by the fixed-point search. This version of quantum Heaviside circuit is defined as
\begin{align}
\label{eq-Heaviside-2}
{{\bf{U''}}_H} = {\bf{F}}\left[ {{{{\bf{U'}}}_{p - H}},{{\bf{I}}^{ \otimes N + QR + D}} \otimes \left( {\left| 0 \right\rangle \left\langle 0 \right|} \right)} \right],
\end{align}
where ${\left| 0 \right\rangle \left\langle 0 \right|}$ is a projector to ${\left| 0 \right\rangle }$ on the mark qubit. Compared with the previous method with classical search, this method is more elegant in the sense that it is a complete quantum algorithm and has a quadratic speedup in the search of Hamiltonian set $\left\{ {{{\bf{H}}_w}} \right\}$. But in practice, we still adopt the previous design of quantum Heaviside circuit of Eq. (\ref{eq-Heaviside-1}) combining with the classical search of $\left\{ {{{\bf{H}}_w}} \right\}$. The reason is that the speedup scale is only $O\left( {\sqrt W } \right) = O\left( {{N^{{1 \over 4}}}} \right)$ according to Eq. (\ref{eq-W}). Furthermore, this quantum search greatly increases the difficulty of designing and simulating the quantum judge.
\subsection{The third strategy in quantum Heaviside circuit}
We have introduced the freezing operator to reduce the number of required auxiliary qubits in the construction of quantum Dirac circuit. One should note that the initial state and the target state are both $\left| 0 \right\rangle $ on the mark qubit in quantum Dirac circuit, where only one freezing operator is needed to freeze $\left| 1 \right\rangle $ on the mark qubit. In quantum Heaviside circuit of Eq. (\ref{eq-Heaviside-1}), the initial state is ${\left| 0 \right\rangle ^{ \otimes R}}$ on the representation qubits, while the target state is $\left| 0 \right\rangle $ on the first (the highest order) qubit of the representation qubits. Now we need two freezing operators to freeze the states orthogonal to ${\left| 0 \right\rangle ^{ \otimes R}}$ on the representation qubits and the state $\left| 0 \right\rangle $ on the mark state respectively. The first freezing operator is to extract the target state on the mark qubits and the second one guarantees that the QPE circuit always starts on the right state.
\begin{figure}[htb]
\centering
\includegraphics[width=0.9\linewidth]{heaviside3.pdf}
\caption{\label{fig-heaviside-3}(a) guide to construct the quantum Heaviside circuit of Eq. (\ref{eq-Heaviside-3}). (a) The design of quantum Heaviside circuit of Eq. (\ref{eq-Heaviside-3}) used for the quantum judge. (b) The repeating units to perform the quantum phase estimation and its inverse $Q$ times. (c) The freezing operator whose target state is $\left| 0 \right\rangle $ on the first qubit of the representation qubits. (d) The NOT gate on the mark qubit controlled by the first counting qubit. }
\end{figure}
The primary design of quantum Heaviside circuit of Eq. (\ref{eq-Heaviside-1}) requires $Q \times R$ representation qubits. Combining with the freezing circuit, we can perform $Q$ times of QPE on $R$ representation qubits and $O\left( {\log Q} \right)$ counting qubits instead of $Q \times R$ representation qubits. This new circuit is
\begin{align}
\label{eq-Heaviside-3}
{{\bf{U'''}}_H} = {\bf{U}}_{CX}^{mark}\left[ {{{\left( {{{\bf{U}}_{QPE - F}}} \right)}^Q} \otimes {\bf{I}}} \right]\left( {{{\bf{I}}^{ \otimes N + R}} \otimes {{\bf{X}}^{ \otimes C + 1}}} \right).
\end{align}
${\bf{U}}_{CX}^{mark}$ is a NOT gate on the mark qubit controlled by the first (the highest order) qubit of the $C$ counting qubits. ${{{\bf{U}}_{QPE - F}}}$ is expressed as
\begin{align}
\label{eq-QPE-F}
{{\bf{U}}_{QPE - F}} = \left( {{{\bf{I}}^{ \otimes N}} \otimes {{\bf{U}}_{{F_2}}}} \right)C{\bf{U}}_{QPE}^{ - 1}\left( {{{\bf{I}}^{ \otimes N}} \otimes {{\bf{U}}_{{F_1}}}} \right)C{{\bf{U}}_{QPE}},
\end{align}
where $C{{\bf{U}}_{QPE}}$ and $C{\bf{U}}_{QPE}^{ - 1}$ are the QPE circuit and its inverse controlled by the counting qubits, respectively. ${{{\bf{U}}_{{F_1}}}}$ and ${{{\bf{U}}_{{F_2}}}}$ are freezing operators with target states of $\left| 0 \right\rangle $ on the first qubit of the representation qubits and ${\left| 0 \right\rangle ^{ \otimes R}}$ on the representation qubits, respectively. The sketch of this construction is depicted in Fig. \ref{fig-heaviside-3}.
\subsection{Construction and gate complexity of quantum judge}
The quantum judge can be constructed by the quantum Heaviside circuit as
\begin{align}
\label{eq-judge}
{\bf{J}} = \left[ {{{\bf{I}}^{ \otimes N + R + C}} \otimes \left( {\left| 0 \right\rangle \langle 0|} \right)} \right]{\bf{F}}\left[ {{{{\bf{U'''}}}_H},{{\bf{I}}^{ \otimes N + R + C}} \otimes \left( {\left| 0 \right\rangle \langle 0|} \right)} \right].
\end{align}
One must note that the quantum judge is not a unitary operator as it contains a projector that is achieved by measurements. The process using this quantum judge to solve the lowest eigen value of the given Hamiltonian matrix $\bf{H}$ contains three steps. The first step is to normalize the Hamiltonian matrix to make sure that all eigen values are in the range of $\left[ {0,{{{2^M} - 1} \over {{2^{M - 1}}}}\pi } \right]$. Then the second step is to use the quantum judge to decide whether all Hamiltonian in the set of $\left\{ {{{\bf{H}}_w}} \right\}$ do not output ${\left| 0 \right\rangle }$ on the mark qubit with a probability of $O\left( 1 \right)$, which indicates that no eigen value of the given Hamiltonian is lower than the given threshold $\theta $. The third step is to use dichotomy to obtain the lowest eigen value with an error lower than $\varepsilon $ in $O\left( {\log {1 \over \varepsilon }} \right)$ iterations.
The complexity analysis can be easily done from the sketch of quantum Heaviside circuit in Fig. \ref{fig-heaviside-3}. The number of auxiliary qubits is $R+C+1$, which is rewritten as $O\left( {\log N + \log {1 \over \varepsilon }} \right)$ based on $C = O\left( {\log Q} \right)$. The analysis of gate complexity is similar to the case of quantum Dirac circuit. The only new circuit is the QPE circuit, whose gate complexity is $\tilde O\left( {{\Lambda \over \varepsilon }} \right)$ \cite{Cleve_1998}. Here we stress that the (inverse) Hamiltonian evolution ${\left( {{e^{iH}}} \right)^t}$ is achieved by repeating ${{e^{iH}}}$ $t$ times instead of simulating the Hamiltonian for time $t$, which can avoid the error accumulation from the imperfect Hamiltonian simulation \cite{Poulin_2009}. As no other new circuit is introduced in quantum Heaviside circuit of Eq. (\ref{eq-Heaviside-3}), the gate complexity of the quantum judge is
\begin{align}
\label{eq-gate-h-3}
\tilde O\left( {{\Lambda \over {\varepsilon \sqrt \chi }} + {\Phi \over {\sqrt \chi }}} \right).
\end{align}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,844 |
\section{Introduction}
Grand design galaxies are attractive objects for dynamical
studies, because it is believed that behind their coherent global
features are hidden the basic dynamical mechanisms that shape the
morphology of galactic discs. Then, deviations from the grand
design could be considered to reflect additional complications of
this basic dynamical behavior. The result would be more
complicated morphologies, like those encountered in multi-armed or
flocculent spiral galaxies. The motivation of this study is to
investigate the dynamics of NGC~1300, which is a well known
barred-spiral grand design galaxy with a prominent bar. Its
archetypical morphology promises a deeper understanding of the
dynamics of a class of similar objects.
Barred-spiral systems offer many examples of grand design
morphology, being characterized by a set of two spiral arms starting
close to the ends of the bar. In some cases the spirals seem to
emerge out of the bar as its continuation, while in others the
beginning of the spirals is clearly displaced from the bar's ends
\citep[e.g. compare the spirals of NGC~4535 and NGC~4548 in figure 5
in][]{gro2008}. Nevertheless the morphology of the arms in many of
these barred-spiral systems is not as smooth as that of the arms of
normal spiral galaxies \citep{gropat1998}, especially in
near-infrared wavelengths. This can be characteristically seen by
overplotting the $m=2$ component of the surface brightness on images
of galaxies, as do e.g. \citet{sea2005}. One can observe that
their arms are in general asymmetric and have gaps. It is also clear
that in many cases the surface brightness of the arms is larger
close to the ends of the bar than at azimuths away from them.
Characteristic cases are NGC~4314 and NGC~4665 \citep{gad2008}. In
the case of NGC~4314, in near-infrared wavelengths, the arms hardly
complete azimuthally a $\pi/2$ angle \citep{quietal1994}.
In the last years the dynamics of barred-spiral systems have been
revisited by several research groups. The reason is the
investigation of the possibility that the stars on the spirals are
in chaotic motion \citep[see also articles by the same authors in][and
references
therein]{cia2008}. The motivation for this series of papers is
exactly to test this hypothesis in one of the well known and well
studied galaxies of this type, NGC~1300. The first step is to
estimate its potential directly from observations
\citep{devacetal1991}. Since it is a well studied object, one can
find observations from X-rays to radio wavelengths in order to
understand the detailed morphology \citep[e.g.][]{fgt88, e89}. The
composite color image STScI-PRC2005-01
(http://heritage.stsci.edu/2005/01/supplemental.html), highlights
the characteristic asymmetry between the two sides of the galaxy.
Images in optical wavelengths, as well as B$-$I color maps that
cover an area of radius $\approx6\arcmin$ from the centre of the
galaxy, reveal faint extensions of the main bisymmetric spiral
structure \citep[e.g.][]{eech96}. These extensions, more clearly
observed in bluer bands, consist of
Population I objects.
In Fig.~\ref{fig01}a we present the K band image of the galaxy, that
we used in the present study. Images at near-infrared wavelengths
depict the morphology of the old disc stellar population and are
appropriate for dynamical studies (see Sect.~\ref{obs} below). The
axes labels are in kpc, assuming a distance to the galaxy
$D=19.6$~Mpc. At this distance 1\arcsec $\approx0.095$kpc.
Our ultimate goal is to present dynamical mechanisms for the
stellar component that lead to the development of the particular
morphological features of the galaxy NGC~1300. The estimation of a
suitable potential is the basis for all dynamical studies and this
is done in the present paper, which is structured as follows: In
Section 2, we present the observations we performed in order to
obtain a reliable estimation of the potential of the galaxy. In
Section 3 we describe the image processing techniques that allowed
us to create images that will be used to compare our models with.
The estimation of the potential is given in Section 4. The forcing
in the models is presented in Section 5, while the properties of
the corresponding effective potentials in Section 6. Finally we
discuss our conclusions in Section 7.
\section{Observations}\label{obs}
The distribution of luminous matter in a galaxy is indicated by its
surface brightness map. The translation from luminosity to mass,
through a mass-to-light ratio $(M/L)$, may vary significant
depending on both the spectral band used and the underlying stellar
population. The near-infrared K band at 2.2~$\mu$ is close to the
emission peak of the old stellar disc and bulge populations which
represent the major visual mass constituency of a spiral galaxy
\citep{rixrie1993}. Although very young stars and red super giants
also contribute to the K band flux, it remains a good indicator of
the mass distribution of luminous matter outside star forming
regions.
The K-map of NGC~1300 was observed on 2002-09-01 with SOFI at the
3.5~m NTT telescope, ESO La Silla. The total exposure time on
target was 10~min in the K$_\mathrm{s}$ filter, at 2.162$\mu$,
with equal time for sky fields. A jitter pattern with $10\arcsec$
shifts was used to allow removal of bad pixels through stacking,
while sky frames were interleaved with offsets around $10\arcmin$
from the galaxy. The SOFI instrument had a Rowckwell Hg:Cd:Te
1024$\times$1024 detector with $0.29\arcsec$ pixels on the sky.
The field covered the main spiral structure of NGC~1300 but did
not provide an accurate estimate of the sky background level. The
final K band frame had a seeing of 0.8\arcsec and reached a
surface brightness of \mbox{K = 20.8 mag \text{arcsec}$^{-2}$} at
a signal-to-noise (S/N) level of 3. Thus, the quality of our
dedicated SOFI/NTT observations can be considered as an additional
advantage for potential calculations, besides the known advantages
of the K-band for studies related with the mass distribution in
galaxies. For comparison, the 2MASS survey offers a seeing of
2-3\arcsec and the corresponding images reach
20~mag~\text{arcsec}$^{-2}$ at a S/N level of 1$\sigma$ (see
pages under http://www.ipac.caltech.edu/2mass/). The reduction of
the SOFI data followed the procedure described by \citet{gpp2004}.
The sky projection parameters were adopted from \citet{linetal1997}
who estimated the Position (PA) and Inclination Angle (IA) by
fitting tilted ring models to their {\rm H{\small I }} velocity data. The
parameters values they found were (PA, IA) = $(87^\circ, 35^\circ)$.
These values are different from those one finds by fitting an
exponential disc to the regions outside the main bar in the K band
image, as in \citet{gpp2004}, which are (PA, IA)=(106.6$^\circ,
42.2^\circ$). This values are close to those found by \citet{ls02}.
However, since for barred spirals like NGC 1300, any determination
of the sky projection based on surface photometry may be strongly
biased due to the strong $m=2$ mode and the open spiral structure,
we preferred to use for our study the values proposed by
\citet{linetal1997}. A disadvantage of the use of the near-infrared
image is that one can hardly detect the axisymmetric disc in the
outer regions. We have to note though, that for the response models
and the orbital analysis, we investigated also the effect of the
deprojection parameters in the potential, and the results are
presented in the forthcoming papers of this series.
The deprojected with parameters (PA, IA) = $(87^\circ, 35^\circ)$
image of NGC~1300, is shown in Fig.~\ref{fig01}b and depicts the
morphology we will try to model. The size of this image is
531$\times$531 since it has been re-binned to 0.5\arcsec pixel size.
The standard background subtraction for the K-band frame could be
slightly in error since it was based on separate sky exposures and
not on the frame itself which was almost fully occupied by the
galaxy.
\begin{figure*}
\begin{center}
\includegraphics[width=15cm]{fig02.eps}
\end{center}
\caption{(a) The bright spots identified as young clusters.
These regions correspond to extreme high valued pixels. (b)
The K band image of NGC~1300 after reducing the intensities of the
extreme high valued pixels, This image is smoother than the one in
Fig.~\ref{fig01}b and lacks of bright areas corresponding to young
clusters. (c) The contour line for 20.8mag~arcsec$^{-2}$
for the image panel (b). It is obvious that the low brightness data
are noisy. (d) The same contour line, as in (c), after the
application of a low-pass smoothing filter to low brightness pixels
$(\gtrsim 19\text{mag~arcsec}^{-2})$. The arrows A, A', B, B' denote
the directions along which we plot the surface brightness in
Fig.~\ref{fig04}.} \label{fig03}
\end{figure*}
\section{Data reduction}
We adopted as distance of the galaxy the value $D=19.6~\text{Mpc}$,
according to the cosmology-corrected luminosity distance given in
the NASA/IPAC Extragalactic Database (NED). This value may differ
from the distance used in other papers on the dynamics of NGC~1300.
In any case, the exact distance of a galaxy does not influence
essentially the dynamical phenomena that shape its morphology
\citep{pcg91}.
Before the K-band frame can be used to bootstrap the estimate of
the potential, two possible corrections should be considered
namely the population effect on the $(M/L)$ ratio and the exact
background level. Although the major fraction of flux in the
K-band originates from the old stellar, disc population
\citep{rixrie1993}, young stars in the arm regions will bias the
effective $M/L$. The young stellar population may be present both
as a diffuse, unresolved, component and as resolved young stellar
complexes seen in the arms as bright knots \citep{phg01,gd08}. In
order to reduce the $M/L$ bias from young stars, we removed such
bright knots by a digital filter. A correction that has to be done
concerns the brightness of the outer parts of the galactic disc.
This area is biased towards higher values due to the presence of
young stellar clusters and stellar complexes, still present even
in K band images \citep{phg01, gd08}. For this purpose, in
Fig.~\ref{fig01}b we firstly removed the bright spots in the
region with a radius $R>6.5\text{kpc}$. Bright spots, assumed to
be young clusters, do not cover areas larger than $10\times 10$
pixels. We substituted the intensities of all extreme high (but
also a few low) valued pixels with the median value of the
corresponding $961$ $(31\times 31)$ pixels area centred at the
very pixel under consideration.
In Fig.~\ref{fig03}a only the
identified as high valued pixels are shown, while in
Fig.~\ref{fig03}b we see the rectified image of the galaxy after the
removal of the bright spots.
After these reductions the galaxy image seems quite smooth in the
area of high valued pixels (Fig.~\ref{fig03}b) but still presents
significant noise in the area of low valued pixels. In Fig.~\ref{fig03}c we see
how noisy is the contour corresponding to the brightness value
$20.8\text{mag~arcsec}^{-2}$. In order to smooth out the image, we
apply a low-pass smoothing filter which affects only the low
valued pixels ($\gtrsim 19\text{mag~arcsec}^{-2}$) getting a less
noised image (Fig.~\ref{fig03}d).
In Fig.~\ref{fig03}d we indicate four radial directions A,
A$^\prime$, B and B$^\prime$, centred at the axes origin, along
which we plot the surface brightness $\Sigma(R)$ after applying the
smoothing filter. We have chosen the directions along the minor axis
(A, A$^\prime$) which reveal better the exponential disc. The
directions (B, B$^\prime$) are along the diagonal of the image
nearest to the minor axis and provide data for longer distance. The
surface brightness along these directions is given in
Fig.~\ref{fig04}a. It is obvious that no exponential profile is
observed at the outer parts of the disc (beyond the region with the
bar and spiral structures) as expected. This implies that the
adopted zero value level for the background is not correct.
Therefore, we decrease the zero value level by the smallest quantity
so that the surface brightness profiles become exponential, i.e.
\begin{equation}\label{sigexp}
\Sigma(R)\propto e^{-R/h_R},
\end{equation}
as shown in Fig.~\ref{fig04}b (actually we increase the brightness
values of all pixels by the same quantity). We consider the region
with the spiral arms part of the exponential disc. We note that
the applied correction is of the order of the background
uncertainty. The corresponding scale length we find in that case
is $h_R\simeq 10~\text{kpc}$. By increasing the brightness by a
smaller value than the one we finally applied, we do not get a
well defined exponential profile. The value of 10~kpc we find is
in agreement with the one given by \citet{pea2001} corresponding
to observations of NGC~1300 in the I band. We note that
\citet{ls02} and \citet{lsbv04} find values close to 7~kpc in
their 2MASS and H-band images respectively. The effect of such
differences on the nonlinearity of models for the potential is
investigated below (Sect.~5).
\begin{figure*}
\begin{center}
\includegraphics[width=15cm]{fig03.eps}
\end{center}
\caption{(a) The surface brightness along the directions
indicated in Fig.~\ref{fig03}d. We observe that no exponential law
can be identified in the outer parts, which means that the
considered zero level is not correct. (b) The surface
brightness along the same directions after the minimum correction of
the zero level so that an exponential decrement is obtained in the
outer parts. The scale length of the resulting exponential law is
10~kpc.} \label{fig04}
\end{figure*}
\begin{table*}
\caption{All the parameter values used in \eqref{pottot},
\eqref{potcmcdh} and \eqref{potmhp} for each model (see text). These
values correspond to the rotation curves of the models in Figs.~\ref{rotcur_2D}, \ref{rotcur_3Dbulgedisk} and \ref{rotcur_3Ddisk}.
The last two columns read the total mass inside the (spherical) radius $r=15$kpc
for the luminous (LC) and dark (DC) component respectively.}
\centering \label{tabt000}
\begin{tabular}{@{}lcccccccc@{}}\hline
models & $M_{CMC} (M_{\odot})$ & $a_{CMC}$ (kpc) & $M_{DH} (M_{\odot})$ & $a_{DH}$ (kpc) & $j_0 (M_{\odot}\text{kpc}^{-3})$ & $a_{MHP}$ (kpc) & LC $(M_{\odot})$ & DC $(M_{\odot})$ \\ \hline
Model A & $7.0\times 10^8$ & 0.1 & $8.0\times 10^{11}$ & 30 & - & - & $5.0\times 10^{10}$ & $7.6\times 10^{10}$ \\
Model B & $2.3\times 10^9$ & 0.1 & $1.6\times 10^{12}$ & 40 & - & - & $6.5\times 10^{10}$ & $7.5\times 10^{10}$ \\
Model C & $9.4\times 10^8$ & 0.07 & $1.6\times 10^{12}$ & 40 & $6.12\times 10^{10}$ & 0.19 & $7.1\times 10^{10}$ & $7.5\times 10^{10}$ \\ \hline
\end{tabular}
\end{table*}
\section{The estimation of the potential}
After all the above amendments we result in an estimation for the
surface density distribution of the \textit{luminous} component in
the reduced image (Fig.~\ref{fig03}b), under the assumption of a
constant mass-to-light ratio. In our approach we reconstruct the
galactic potential assuming the maximum contribution of the
luminous component to the observed rotation curve as given in
\citet{linetal1997}. For the cases that parts of the rotation
curve will not be able to be entirely assigned to the luminous
component we switch on two additional components in our modelling.
They represent a dark halo and/or a central mass concentration.
Since our goal is the study of the dynamics of the stars, treated
as test particles moving in the estimated gravitational field, the
total potential must be compatible with the rotation curve of the
galaxy, in every model we study.
In order to proceed with the potential estimation of the luminous
component we need to do an assumption about the distribution of
the matter in the third dimension. Below, we study three different
cases. The basic difference among these three general models is
their \textit{geometry}. We want to compare the marginal thin
geometry of the 2D case (model A) with a thick disc case (model B)
in order to see if the comparison between galaxy and models
improves by varying our parameters towards the one or the other
direction in the parameter space. Model C changes essentially the
geometry of the bar from cylindrical to a combination of spherical
with cylindrical and should be again considered as a limiting
case. More specifically we consider:
\begin{description}
\item[\textbf{Model A.}] The `2D' or `degenerate' case in which all
matter is considered lying on the ($x,y$) galactic plane.
\item[\textbf{Model B.}] The `disc' case in which we assume a cylindrical
geometry and that all matter is
distributed in a 3D disc with scale height $h_z$. Then the
vertical dependence of the density $\rho$ reads
\citep[][]{kruit1988}
\begin{equation}\label{rhoz}
\rho\propto\rho_z(z)=\dfrac{1}{2h_z}\text{sech}^{2/n}\left(\dfrac{n z}{2
h_z}\right),
\end{equation}
where $h_z$ is the vertical scale height and $n$ is an index (see
Section 4.2, for its meaning).
\item[\textbf{Model C.}] The `spheroidal' case in which we
consider that the total observed brightness is the combination
of two major components: i) a spheroidal component that accounts for the
major part of the bar and ii) a 3D exponential disc with scale height
$h_z$ as in model B. The spheroidal component includes the
bulge \citep[$r<1.5$kpc,][]{pea2001,ls02,lsbv04} and the
axisymmetric contribution of the central part of the bar.
\end{description}
In Cartesian coordinates for a given spatial density $\rho(x,y,z)$
the gravitational potential $\Phi(x,y,z)$ is
\begin{equation}\label{gravpot}
\Phi(x,y,z)=-G\int
\frac{\rho(x',y',z')dx'dy'dz'}{\sqrt{(x-x')^2+(y-y')^2+(z-z')^2}},
\end{equation}
where $G$ is the gravitational constant. This means that
$\Phi(x,y,z)$ is the convolution of the functions $\rho(x,y,z)$
and $g(x,y,z)=\dfrac{1}{r}=\dfrac{1}{\sqrt{x^2+y^2+z^2}}$. Thus
the potential is written as $\displaystyle{\Phi=\rho\otimes g}$,
where $\otimes$ denotes the convolution operator.
\subsection{Model A}
In model A, where all mass is assumed on the $(x,y)$ plane, the
density can be written as
$\displaystyle{\rho(x,y,z)=\Sigma(x,y)\delta(z)}$, where $\Sigma$
is the surface density and $\delta$ is the delta function.
Substituting the above density expression into \eqref{gravpot} and
integrating it over $z$ we get
\begin{equation}\label{potA}
\Phi(x,y,0)=-G\int
\Sigma(x',y') g(x-x',y-y',0) dx'dy'
\end{equation}
which is the convolution of the functions $\Sigma(x,y)$ and
$g(x,y,0)$. Knowing the surface density
$\Sigma(x_i,y_j)$ at each grid point $(i,j)$ we can calculate
the potential at the same grid points by using the convolution
theorem
\begin{equation}\label{potconvth}
\Phi=\mathcal{F}^{-1}\left[\mathcal{F}(\Sigma)\;\mathcal{F}(g)\right],
\end{equation}
where $\mathcal{F}$ and $\mathcal{F}^{-1}$, denote the Fourier
transform and inverse Fourier transform respectively. We use an
extended square area 16 times larger than the original area of the
image of the galaxy in order to avoid the contribution from
periodic reflections of the signal from the galaxy's pixels. Such
an extended area will allow us to consider, in dynamical studies,
stars that travel to large distances away from the centre of the
galaxy. The surface density in the extended area is considered to
be zero. We use the 2D fast Fourier transform (FFT) technique for
the corresponding computations. Note, that in this
calculation the adopted $g(0,0,0)$ value is equal to $(\text{bin
size})^{-1}\simeq 21~\text{kpc}^{-1}$ since the softening length is of the
order of the bin size. A detailed description of the whole
procedure can be found in \citet{hohhoc1969}.
Given the potential values at the grid points one can calculate
the potential everywhere in between these points using a 2D
interpolation scheme. However, such a scheme, besides its
complexity, provides the potential taking into account non-smooth,
local density disturbances. For this reason we proceed as in
\citet{quietal1994} and we decompose the potential into its
azimuthal Fourier components at every radius $R$. Under this
consideration the potential can be written in polar coordinates
$(R,\theta)$ as
\begin{equation}\label{potrthfour}
\Phi(R,\theta)=\Phi_0(R)+\sum_{k=0}^{k_{max}}\left[\Phi_{kc}(R)\cos(k\theta)+\Phi_{ks}(R)\sin(k\theta)\right].
\end{equation}
For $k_{max}\rightarrow \infty$ the form \eqref{potrthfour}
returns exactly the same values with those we have from the 2D
interpolation scheme mentioned above. We cut off the high
harmonics and consider all terms (even and odd) up to $k_{max}=6$.
Like this we are able to reproduce all the important morphological
features of the galaxy (its asymmetries included).
\citet{quietal1994} calculated the amplitudes $\Phi_{kc}(R)$,
$\Phi_{ks}(R)$ for many rings $R_i$ and fitted them by 8th order
polynomials. Despite the advantages of simplicity and analyticity
of the expressions for each function that the use of polynomials
secures, it is not capable of following the actual variations
well. For this reason in the present study we apply the
interpolation scheme with cubic splines to the
$\left(R_i,\Phi_{kc}(R_i)\right)$,
$\left(R_i,\Phi_{ks}(R_i)\right)$ data sets. This scheme
guarantees the continuity of the potential, of the forces and of
derivatives of the forces, which are used in the variational
equations providing indicators that will measure the chaoticity of
the orbits (e.g. Lyapunov exponents). This is particular important
for stellar dynamical investigations, which is our motivation for
the estimation of the NGC 1300 potential. Note that we set
$\Phi_{kc}(0)=\Phi_{ks}(0)=0$ in order to secure the continuity
required at $R\rightarrow 0$. Table 2 in
Appendix\footnote{Appendix is only available in electronic form}
presents all the amplitude values, at 101 successive radii $R_i$,
used for the derivation of the interpolating splines.
\begin{figure}
\begin{center}
\includegraphics[width=8.4cm]{fig04.eps}
\end{center}
\caption{The rotation curve of model A together with observational
data by \citet{linetal1997}. Gray dots correspond to optical
measurements from various slits aligned close to the major axis of
the galaxy. The gray curve with the error bars correspond the {\rm H{\small I }}
rotation curve given in \citet{linetal1997}. The dotted line
represents the rotation curve of the luminous component only along
the major axis of the bar in model A. The dashed curve is obtained
by considering also an additional central mass (CMC) and a dark
halo (DH) component. The importance of these terms are determined
by the parameters given in Table 1.} \label{rotcur_2D}
\end{figure}
Figure \ref{rotcur_2D} shows the {\rm H{\small I }} rotation curve (gray solid
line with error bars together with optical velocity measurements
(gray dots) from various slits aligned close to the major axis of
the galaxy, as taken from \citet{linetal1997}. In this figure we have also
plotted a rotation curve along the major axis of the bar, corresponding to the
potential
\eqref{potrthfour} of the luminous matter only (dotted line). In this case it
has
been considered being $5.0\times 10^{10} M_{\odot}$
(see Table \ref{tabt000}).
This curve fails reproducing the flat part of the rotation curve
at large distances. This implies that some additional mass
component exists besides the luminous component. The most
reasonable candidate to be invoked is a dark halo (DH) term. As
already mentioned our general model foresees the switching on of
two additional components for a central mass concentration (CMC)
and a DH. We model both of them with a Plummer sphere since it is
simple, effective and widely used in the literature. The
importance of this terms are controlled by the parameters of the
Plummer spheres. Thus the total potential $\Phi_T(R,\theta)$ can
then be written
\begin{equation}\label{pottot}
\Phi_T(R,\theta)=\Phi_{LM}(R,\theta)+\Phi_{CMC}(R)+\Phi_{DH}(R)
\end{equation}
where $\Phi_{LM}$ is the luminous matter component given by
\eqref{potrthfour} and
\begin{equation}
\label{potcmcdh}
\Phi_{\begin{subarray}{l}
CMC\\ DH \end{subarray}}(R)=-\frac{G M_{\begin{subarray}{l} CMC\\
DH
\end{subarray}}}{\sqrt{R^2+a^2_{\begin{subarray}{l} CMC\\ DH
\end{subarray}}}},
\end{equation}
is the potential for the Plummer spheres, with $a$ being a constant parameter.
The adopted parameters are given in Table \ref{tabt000} (Model A).
In Fig.~5 we see that the DH term is quite important and helps the
rotation curve of the model reaching the level of the {\rm H{\small I }} curve of
\citet{linetal1997}. On the other hand the CMC term is less
important increasing the central peak by $\approx12$km/sec which
eventually reaches the value $\approx208$km/sec. Note that the
central peak value is not well defined by the observational data
and therefore the adopted parameter values for the CMC term
provide only a reasonable area in the parameter space.
\subsection{Model B}
In case B we assume that the density can be written as
\begin{equation}\label{denscaseb}
\rho(x,y,z)=\Sigma(x,y)\rho_z(z).
\end{equation}
\citet{kruit1988} proposed a family of models regarding the
vertical dependence of the density which reads
\begin{equation}\label{kruitmodel}
\rho_z(z)=A\text{sech}^{2/n}\left(\frac{nz}{2h_z}\right)~~~\text{with}~~~
n\in[1,\infty),
\end{equation}
where the normalization constant $A$ is given as
\begin{equation}\label{normconst}
A=\frac{\Gamma\left(\frac{1}{2}+\frac{1}{n}\right)}{2h_z\sqrt{\pi}\;\Gamma\left(1+\frac{1}{n}\right)},
\end{equation}
so that
$\int_{-\infty}^{\infty}\rho_z(z)dz=1$. $\Gamma$ is the Gamma
function defined by
\begin{equation}
\label{gamma}
\Gamma(w)=\int_{0}^{\infty}t^{w-1}e^{-t}dt.
\end{equation}
Varying $n$ from $n=1 \text{ to } n\rightarrow\infty$ we get
$\rho_z(z)$ varying from
\[\rho_z(z)\propto \text{sech}^2\left(\frac{z}{2h_z}\right)\]
(isothermal disc) to \[\rho_z(z)\propto
\exp\left(-\frac{|z|}{h_z}\right)\] (exponential disc).
\citet{degrijs1998} and \citet{kreetal2002} provide estimations
for the mean values of the parameter $n$ and the ratio $h_R/h_z$
in samples of galaxies, which are $n\approx 3.7\pm 0.6$ and
$h_R/h_z\approx 7.3\pm 2.2$, respectively \citep[for a review
see][]{kruit2002}. These studies have been based on observations
in I and K bands.
\begin{figure}
\begin{center}
\includegraphics[width=8.4cm]{fig05.eps}
\end{center}
\caption{The rotation curve along the major axis of the bar for
model B. The drawn curves are as in Fig.~\ref{rotcur_2D}. We
observe that the luminous component alone (dotted curve) reaches
lower velocity values at the central and outer parts of the galaxy
with respect to the velocity measurements. The added CMC component
is $\approx 3$ times more massive than in case A. The rotation
curve corresponding to the total potential \eqref{pottot} (dashed
curve) with the parameter values shown in Table \ref{tabt000}
levels off at about the same $u_{max}$ as the {\rm H{\small I }} rotation curve.
Note that the central peak is sharper in this case.}
\label{rotcur_3Ddisk}
\end{figure}
We adopted the values $n=4,\;h_R/h_z=7$, which give $h_z\approx
1.43~\text{kpc}$ and following \citet{quietal1994}, we substitute
the density expression \eqref{denscaseb} into \eqref{gravpot} and
by integrating over $z$ we obtain
\begin{equation}\label{potB}
\Phi(x,y,0)=-G\int
\Sigma(x',y') g_B(x-x',y-y') dx'dy',
\end{equation}
where the function $g_B$ is given by
\begin{equation}\label{gb}
g_B(x,y)=\int_{-\infty}^{\infty}\frac{\rho_z(z')dz'}{\sqrt{x^2+y^2+z'^2}}.
\end{equation}
Thus, the potential $\Phi$ on the galactic plane is the
convolution of the functions $\Sigma$ and $g_B$. We
can again calculate it applying the convolution theorem
$\Phi=\mathcal{F}^{-1}\left[\mathcal{F}(\Sigma)\;\mathcal{F}(g_B)\right]$,
since we know the surface density $\Sigma(x_i,y_j)$ at every grid
point $(i,j)$.
\begin{figure}
\begin{center}
\includegraphics[width=8.4cm]{fig06.eps}
\end{center}
\caption{The surface brightness of the MHP term in model C. The
solid line represents the mean (over azimuth) surface brightness
after the subtraction of the exponential disc surface brightness
(see Fig.~\ref{fig04}b) from the total one. This part is fitted by
the MHP with the parameter values shown in Table \ref{tabt000}
(dashed curve).} \label{fig08}
\end{figure}
We note that \citet{ls02} and \citet{lsbv04} introduced an
improved version of the Quillen et al (1994) method, where the
image pixels are first smoothed by calculating the azimuthal
Fourier decompositions of the surface density in different radial
zones in polar coordinates. This approach has some advantages,
like a possibility to use more noisy images and to apply radially
non-constant vertical models. However, for high quality images and
for strongly barred galaxies (like our data for NGC 1300) the
differences in the resulting potential should be negligible
regardless of the integration method.
Working in the same way as in model A we obtain expressions
mathematically similar to \eqref{potrthfour} for the potential
corresponding to the luminous component and to \eqref{pottot} for
the total potential. Table 3 in Appendix contains all the values of
the amplitudes for $\Phi_0(R_i), \Phi_{kc}(R_i), \Phi_{ks}(R_i)$
calculated for 101 rings at $R_i$. The specific values for $\Phi_0,
\Phi_{kc}, \Phi_{ks}$ correspond to $6.5\times 10^{10} M_{\odot}$
for the mass of the luminous matter.
Finally, Fig.~\ref{rotcur_3Ddisk} presents the rotation curve
corresponding to model B together with the observational data
\citep{linetal1997} as we did in Fig.~\ref{rotcur_2D} for the 2D
case. The dotted line gives the rotation curve along the major
axis of the bar when we take into account only the luminous
component. We observe that this rotation curve reaches lower
values than the observational one also at the central parts. For
this reason we add a CMC term which is $\approx 3$ times more
massive than the one we added in model A, i.e. now it is
$2.3\times 10^{9} M_{\odot}$. We add also a DH term in order to
get a better description at the outer parts of the disc. The
dashed line gives the rotation curve of the total potential
\eqref{pottot} with the corresponding parameter values given in
Table~\ref{tabt000}.
\subsection{Model C}
In this case we consider that the main part of the bar can be
described with a spherical component. This part could be vaguely
described as ``the bar without its ansae" (Fig.~\ref{fig01}b). For
this purpose we use the modified Hubble profile (MHP)
\citep[see][p. 68]{bt08}
\begin{equation}\label{mhp}
\rho_{MHP}=j_0\left[1+\left(\frac{r}{a_{MHP}}\right)^2\right]^{-3/2}.
\end{equation}
The parameter $a_{MHP}$ is the scale length and the parameter
$j_0$ determines the mass inside a specific radius (e.g. $r\leq
a_{MHP}$). Note that the mass inside a radius, in MHP model,
diverges logarithmically at large radii and therefore it is
meaningless to refer to total mass.
The corresponding potential via Poisson equation is
\begin{equation}\label{potmhp}
\Phi_{MHP}=-\frac{G M_h(r)}{r}-\frac{4 \pi G j_0 a_{MHP}^2}{\sqrt{1+\left(\frac{r}{a_{MHP}}\right)^2}},
\end{equation}
where
\begin{multline}\label{mh}
M_h(r)=4 \pi a_{MHP}^3 j_0 \times\\
\left[\ln\left(\frac{r}{a_{MHP}}+\sqrt{1+\left(\frac{r}{a_{MHP}}\right)^2}\right)
-\frac{r}{a_{MHP}}\left[1+\left(\frac{r}{a_{MHP}}\right)^2\right]^{-1/2}\right].
\end{multline}
\begin{figure}
\begin{center}
\includegraphics[width=8.4cm]{fig07.eps}
\end{center}
\caption{Rotation curve together with observed velocities for
model C. Drawn curves are as in Figs.~\ref{rotcur_2D} and
\ref{rotcur_3Ddisk}. The rotation curve of the luminous matter along the bars'
major axis is
given with the dotted curve. The corresponding curve of the total
potential including CMC and DH components,
with the parameter values given in Table \ref{tabt000} is represented by the
dashed curve.} \label{rotcur_3Dbulgedisk}
\end{figure}
By integrating \eqref{mhp} over $z$ we take the expression for the
surface density for MHP, which is
\begin{equation}\label{sdmhp}
\Sigma_{MHP}(R)=\frac{2j_0 a_{MHP}^3}{a_{MHP}^2+R^2}
\end{equation}
In order to find the values of the best fitting parameters of the
MHP model we subtract the exponential disc $\Sigma_{d}\propto
e^{-R/h_R}$ with $h_R$=10~kpc (see Fig.~\ref{fig04}b) from the
observational surface density $\Sigma_{obs}$ so that the remaining
luminosity at the central region ($R<4$~kpc) is mainly due to the
assumed spherical component. In Fig.~\ref{fig08} we plot the
azimuthally mean surface brightness of the central area of the
galaxy (solid line) after the subtraction of the exponential disc.
We also give the curve corresponding to \eqref{sdmhp} (dashed
curve) with the parameter values shown in Table \ref{tabt000}. We
observe that the MHP gives a reasonable fitting of the inner
3.5-4~kpc.
The total potential corresponding to the luminous mass is the sum of
the MHP component \eqref{potmhp} and the component
corresponding to the remaining mass. The surface density of the
latter component $\Sigma_D$ is derived by subtracting the surface
density $\Sigma_{MHP}$ from the surface density $\Sigma_{obs}$ we
derive from the observations. Thus, the surface density (of the
remaining disc) $\Sigma_D(x_i,y_j)$ at each pixel $(i,j)$ is given
by
\begin{equation}\label{sdc}
\Sigma_D(x_i,y_j)=\Sigma_{obs}(x_i,y_j)-<\Sigma_{MHP}(x_i,y_j)>,
\end{equation}
where $<\Sigma_{MHP}(x_i,y_j)>$ is the mean surface density
$\Sigma_{MHP}$ inside the area of the squared pixel centered at
$(x_i,y_j)$. We consider this component as a 3D exponential disc
with vertical distribution given by \eqref{kruitmodel}. In order to obtain
an expression similar to \eqref{potrthfour} for the disc in model C
we work in the same way as in model B. Table 4 in Appendix gives the
values of the amplitudes of $\Phi_0(R_i), \Phi_{kc}(R_i),
\Phi_{ks}(R_i)$ of the potential corresponding to the disc
component.
Figure~\ref{rotcur_3Dbulgedisk} shows the data of the
observational rotational velocities \citep{linetal1997} as in the
two previous models together with the rotation curve of the
luminous component (both MHP and disc) along the major axis of the
bar represented by the dotted curve. Also in this case the
activation of the two additional potential terms, especially the
DH one, allows a better relation between the rotation curve of the
model along its bars major axis and the inclination of the
observed {\rm H{\small I }} curve at large distances. The values of their
parameters for model C are also shown in Table \ref{tabt000}.
\begin{figure*}
\begin{center}
\includegraphics[width=14.5cm]{fig08.eps}
\end{center}
\caption{The $Q$ variation in our three models for several sets of
the potential parameters. The panels of the left-hand column give
$Q$ for models ``A'' (a), ``B''(c) and ``C''(e). The panels of the
right-hand column give the maximum $Q$ as a function of $R$ (black
solid curves). Additional curves refer to the radial variation of
maximum $Q$ in models with different parameters than those used in
the basic set-up of the three general models. For model ``A'' in
panel (b) the dotted green curve refers to a model without dark
halo, the magenta and blue dashed curves to different orientation
parameters, while the dashed pink and dark yellow ones to models
with disc scale lengths $h_R=7$~kpc and $h_R=13$~kpc respectively.
Arrows help to better trace each curve. For model ``B'' in panel
(d), additional curves are given for a ``model B'' without dark
halo component (dotted green curve) and models with $h_R/h_z$
=5,9. Finally for model ``C'', panel (f), an additional curve
gives the radial variation of $Q$ again in a model that with
respect to ``C'' does not have any dark halo component.}
\label{qforces}
\end{figure*}
\begin{figure*}
\begin{center}
\includegraphics[width=15cm]{fig09.eps}
\end{center}
\caption{The $Q$ value maps for model A on the galactic plane for
$k_{max}=6$, $k_{max}=12$ (first and second row respectively) with
and without odd terms (left-hand column and right hand column
respectively). A combination that can be used for reliable
dynamical models is with $k_{max}=6$, including all terms (panel
(a)).} \label{figqm}
\end{figure*}
\begin{figure*}
\begin{center}
\includegraphics[width=15.5cm]{fig10.eps}
\end{center}
\caption{The loci of the Lagrangian points ($L_1, L_2$ in the
left-hand column and $L_4, L_5$ in the right-hand column) for all
the models as a function of the $\Omega_p$. The red (blue) points
correspond to unstable (stable) Lagrangian points. In each panel we
have projected the Lagrangian points on the galactic plane. We
observe that in all models there are ranges of $\Omega_p$ values for
which we have multiple Lagrangian points. This property is more
evident in model A, where we observe longer ranges of $\Omega_p$
values corresponding to multiple Lagrangian points. Note that the
separated group of points which are located at high $x$ values (seen
in all the left-hand column panels) correspond to multiple $L_1$
Lagrangian points ordered near-parallel to the $y$ axes and they
refer to cases with low $\Omega_p$ values.} \label{lagrpoints}
\end{figure*}
\begin{figure*}
\begin{center}
\includegraphics[width=\textwidth]{fig11.eps}
\end{center}
\caption{Some characteristic examples of multiple Lagrangian
points. We plot the contour lines of the effective potential
overlapped with the image of the galaxy for the cases and the
$\Omega_p$ values indicated in the figure. Big yellow (green) dots
correspond to stable (unstable) Lagrangian points. In (a) we see 3
unstable and 2 stable $L_1$ points. In (b) we have 2 stable and 1
unstable $L_5$ points. In (c) finally we see 2 unstable and 1
stable $L_2$ points. Note that the considered sense of rotation is
clockwise.} \label{contlns}
\end{figure*}
\section{The Nonlinearity of the models}
\label{sec:forces} As a measure of the nonlinearity of the models
we consider the quantity
\begin{equation}
\label{qquant}
\begin{gathered}
Q=\frac{|\mathbf{\Delta
F}|}{|\mathbf{F_{axis}}|}=\frac{|\mathbf{F_{total}-F_{axis}}|}{|\mathbf{F_{axis}}|}=
\\
\dfrac{\sqrt{\left(\dfrac{\partial \Phi_{total}}{\partial R}-\dfrac{\partial \Phi_{axis}}{\partial R}\right)^2+
\left(\dfrac{1}{R}\dfrac{\partial \Phi_{total}}{\partial \theta}\right)^2}}
{\left|\dfrac{\partial \Phi_{axis}}{\partial R}\right|}
\end{gathered}
\end{equation}
which is the ratio of the modulus of the vectorial difference of
the total force (axisymmetric and non-axisymmetric) from the
axisymmetric force, over the modulus of the axisymmetric force.
Thus, $Q$ measures the non-axisymmetric force perturbation,
normalized over the axisymmetric one. This parameter
describes well the non-linear effect of the non-axisymmetric
components but it is unable to determine by itself the global
dynamics in a rotating system (see below the discussion about the
importance of $\Omega_p$).
In the past, the strength of bars and spirals in disc galaxies has
been quantified by means of similar indices
\citep[e.g.][]{bb01,v06}. The index introduced by \citet{bb01} has
been widely used in large samples of galaxies \citep{ls02,
bbkeep04, lsbv04}. This index is similar to the quantity $Q$
defined in Eq.~\eqref{qquant}. The variation of $Q$ in our models
is presented in Fig.~\ref{qforces}.
At the left-hand column the panels show in color diagrams the
strength of the non-axisymmetric force, measured by $Q$, for the
three models. Each model is indicated at the right edge of the
figure. At the right-hand column we plot the maximum $Q$ as a
function of $R$ (black solid curves). We observe that the overall
maximum perturbation strength reaches higher values ($\approx
0.8$) in model A (pure 2D), while in the other two models it is
lower reaching $\approx 0.45$ and $\approx 0.5$ for models B and C
respectively. The maximum $Q$ values of models B and C are close
to those presented by \citet{ls02}, while the pure 2D case has a
significant larger overall maximum $Q$ value. In each panel of the
right-hand column we have plotted additional maximum $Q$ curves
corresponding to different parameter values, which are indicated
in the figure. The green curves give the maximum $Q$ profiles
without the DH component. We observe that the maximum $Q$ values,
with the DH component included, are approximately 0.8-0.85 of the
corresponding values neglecting the DH component. Such values are
within the range of values given by \citet{bls04}, although
towards the lower limit. We studied also the robustness of the
maximum $Q$ profile to the adopted orientation parameters. We
considered two additional orientation parameter sets i.e. (PA, IA)
= $(106.6^\circ, 42.2^\circ)$ (dashed magenta curve,
Fig.~\ref{qforces}b) and (PA, IA) = $(67^\circ, 28^\circ)$ (dashed
blue curve, Fig.~\ref{qforces}b). The first set of the orientation
parameters is the one obtained from near-infrared data by
\citet{gpp2004}. The second set has angles deviating from the
values we finally used as much as the first one, but to the
opposite direction. We observe, that the maximum $Q$ value, in
these cases, is affected by less than 10\%. We also checked the
dependence of the maximum $Q$ value on the changes of the
zero-value level, which yield to disc scale lengths of 7~kpc
(dashed red curve, Fig.~\ref{qforces}b) and 13~kpc (dashed-dotted
orange curve, Fig.~\ref{qforces}b), respectively. Note, that the
exponential discs with these scale lengths do not fit the
corresponding data as well as in the original $h_R$=10~kpc case.
We observe, that the maximum $Q$ value, in these cases, is
affected by less than 5\%.
In Fig.~\ref{qforces}d we see that the maximum $Q$ value, in model
B, varies approximately by 10\% when the ratio $h_R/h_z$ varies
$1\sigma$ from its mean value (see dashed-dotted orange and dotted
red curves in Fig.~\ref{qforces}d). We also certified, that the
$Q$ profiles almost coincide within $1\sigma$ variation of the
exponent $n$ of Eq.~\eqref{kruitmodel} from its mean value.
Special attention has been given to the number and kind (even or
odd) of the Fourier terms to be included in the potential. The
morphological asymmetries observed in the galaxy underline the
importance of the inclusion of the odd terms for dynamical
studies. The number and the kind of the Fourier terms may affect
the maximum $Q$ value as well as the 2D distribution of the $Q$
value on the galactic plane. In order to study these effects we
constructed $Q$ value maps on the galactic plane for different
combinations of the Fourier terms (Fig.~\ref{figqm}). We present
the results for model A since it is the model with the highest
non-axisymmetric amplitudes in the Fourier decomposition.
The upper two panels (a,b) of Fig.~\ref{figqm} include terms up to
$k_{max}=6$ in Eq.~\eqref{potrthfour}, while the two panels at the
bottom (c,d) up to $k_{max}=12$. The left panels (a,c) include
\textit{all} $k$ terms, while the right ones (b,d) only the even
terms, as indicated at the top of each of them. By including all
terms, the maximum $Q$ value for the case we consider up to
$k_{max}=6$ is 0.96 of the maximum value corresponding to
$k_{max}=12$. By including higher order terms $(k_{max}>12)$, the
maximum $Q$ value does not get further refinement. On the other
hand, by neglecting the odd terms, the $Q$ map clearly fails to
reproduce all the asymmetries and the maximum $Q$ value becomes at
least 10\% lower than that with the odd terms even for the
$k_{max}=12$ case. More specifically, the maximum $Q$
values corresponding to panels (a), (b), (c) of Figure \ref{figqm}
are 0.96, 0.89, 0.84 of the maximum $Q$ value we get in
Fig.~\ref{figqm}c. We can observe, that at the sides of the bar
the prominent green "tails", which essentially describe the force
field at the spirals' region, are conspicuous only in panels (a)
and (c). Also at radii around 8 and 9 kpc, at the ends of the bar,
only panels (a) and (c) give a rather constant green shade, while
at the same radii green color fades out in panel (b), but also in
(d). Evident is that in terms of nonlinearity of the potential
the odd terms are essential, while including $k>6$ terms does not
improve the models at a level worth the additional computing time
needed for the calculations. Thus, a reliable combination that can
be used in dynamical studies is $k_{max}=6$ with all even and odd
terms included (Fig.~\ref{figqm}a).
In all examined cases the forcing
of the models suggests that our systems are strongly nonlinear,
since the perturbing term is at least higher than 40\% of the
axisymmetric background. This is a usual situation in models of
strong barred galaxies \citep{kc1996}.
We note that potential evaluations for NGC 1300 have been
previously done by \citet{e89}, \citet{h90}, \citet{lk96},
\citet{apvm01} and more recently by \citet{ls02} using a 2MASS
K-band image and by \citet{lsbv04} by means of OSUBGSG H-band
data. These potentials have some features similar with our general
model (for a discussion see Sect.~7). In our case, emphasis is
given in constructing a potential function suitable for dynamical
studies. We kept fixed the quantities that could be derived
directly from our near-infrared K-band data, while the parameters
that could be only confined within some range have been treated as
free parameters. However, the most important parameter for the
dynamics of a rotating disc galaxy is the pattern speed \citep[for
a review see][]{gc02}, which is an unknown quantity. The most
simple assumption is that the system we are studying has a unique
pattern speed. We take it as a basic hypothesis, the validity of
which will be evaluated from the feedback we will get from
response models (to be presented in subsequent papers). At any
rate, it is the \textit{effective potential} that determines the
force field in our calculations. The dynamics of two systems with
the same potential $\Phi$ but with considerably different pattern
speeds are considerably different \citep[see e.g.][]{pcg91}. An
investigation of the basic categories of effective potentials is
presented in Sect.~6 below.
\section{Effective potentials}
The locations of the stationary (stable and unstable) Lagrangian
points strongly affect the dynamical properties of a rotating
galaxy. The Lagrangian points and their stability structure the
phase space at the corotation region. Given a mass distribution, the
positions of the Lagrangian points are determined by the value of
the pattern speed $\Omega_{p}$.
In the rotating frame we have the
conservation of the Jacobi integral
\begin{equation}\label{ejac}
E_{j}=\frac{1}{2}v^2+\Phi_{eff},
\end{equation}
where $\Phi_{eff}$ is the effective potential
\begin{equation}\label{phieff}
\Phi_{eff}(x,y)=\Phi_{T}(x,y)-\frac{1}{2}\Omega_p^2(x^2+y^2).
\end{equation}
The stationary Lagrangian points at the equilibrium positions are defined by
\begin{equation}\label{lagrcond}
\frac{\partial \Phi_{eff}(x,y)}{\partial x}=\frac{\partial
\Phi_{eff}(x,y)}{\partial
y}=0.
\end{equation}
This is the case of course, where the system rotates with a single
pattern speed. In systems with multiple pattern speeds, multiple
corotation radii will be defined on the disc. If bar and spirals
rotate with different $\Omega_p$, each component will have its own
corotation radius. In what follows we take the single pattern
speed case as our initial assumption. Its validity and its
limitation will be examined by means of models in subsequent
papers.
Fig.~\ref{lagrpoints} shows in a compact way how the number, the
location and the stability of the Lagrangian points change on the
disc for the various effective potentials. In
Fig.~\ref{lagrpoints}a we give the positions $(x,y)$ of the $L_1,
L_2$ Lagrangian points as a function of $\Omega_{p}$ for model A.
The calculation of the stability of the equilibrium points is done
by following the standard procedure that can be found in relevant
textbooks \citep[see e.g.][pp. 179-183]{bt08}. The red and blue
points correspond to the unstable and stable Lagrangian points,
respectively. At the basis of the cubes in all panels it is
plotted the surface density of the galaxy together with the
projections of the corresponding Lagrangian points. The projected
orange and light blue points correspond to the unstable and stable
Lagrangian points, respectively. Figure \ref{lagrpoints}b is
similar to Fig.\ref{lagrpoints}a and shows the positions of $L_4,
L_5$ Lagrangian points in model A. We observe that there are
ranges of $\Omega_{p}$ values for which there are more than one
$L_1, L_2, L_5$ points. Figures \ref{lagrpoints}c,d and
\ref{lagrpoints}e,f are similar to Fig.~\ref{lagrpoints}a,b but
for the model B and C, respectively. We see that the distribution
of Lagrangian points have a very similar behavior in models B and
C. Moreover, the variability of the positions of the Lagrangian
points with $\Omega_{p}$ seems smoother in models B and C.
However, even in these cases we have ranges of $\Omega_{p}$ values
corresponding to multiple Lagrangian points (see
Fig.~\ref{contlns}c).
Figure \ref{contlns} presents some characteristic cases of
effective potentials with multiple Lagrangian points. Stable
(unstable) Lagrangian points are plotted with yellow (green) big
dots. Fig.~\ref{contlns}a shows the isocontours of the effective
(total) potential, in model A, for $\Omega_{p}=23.7\text{km
sec}^{-1}\text{kpc}^{-1}$. In this figure we observe 5 $L_1$
Lagrangian points (3 unstable and 2 stable) at the region close to
the end of the bar. Figure \ref{contlns}b corresponds to the same
model A but for $\Omega_{p}=21.2\text{km
sec}^{-1}\text{kpc}^{-1}$. We observe 3 $L_5$ Lagrangian points (2
stable, 1 unstable). Finally, Fig.~\ref{contlns}c corresponds to
model C for $\Omega_{p}=25.75\text{km sec}^{-1}\text{kpc}^{-1}$
and shows 3 $L_2$ Lagrangian points (2 unstable, 1 stable).
\section{Discussion and Conclusions}
In this paper, we propose three different general models for the
potential of the grand design barred-spiral galaxy NGC~1300, based
on observations in the near-infrared. The ultimate goal of our
work is the investigation of the stellar dynamics of this galaxy
by means of response models and orbital theory. More precisely we
want to reveal the dynamical mechanisms that shape the observed
structure of the galaxy. This is done in the forthcoming papers of
this series.
Observations in the near-infrared provide the most reliable
potential models of disc galaxies, since they are excellent
indicators of the distribution of mass associated to stellar
matter. The needed additional assumptions refer mainly to the
distribution of luminous matter in the third dimension (outside
the galactic plane) and to the distribution of the non-luminous
matter (dark halo and central mass concentration).
The three proposed models are: The pure 2D case (Model A), where
all luminous matter is considered on the galactic plane; the thick
disc case (Model B) where all luminous matter is considered in a
3D disc with a constant scale height; and the ``spheroidal case''
(Model C) in which the major part of the bar is a spherical
modified Hubble profile. The remaining luminous matter is
attributed to a 3D disc as in Model B. In all these cases the
calculation of the potential is performed by means of an FFT
transform technique, that has been introduced in various versions
by \citep[][]{hohhoc1969,quietal1994,ls02}.
These three general models can be considered as limiting cases in
the parameter space of models whose responses and orbital content
will be studied. Let us consider an unknown parameter, e.g. the
disc thickness. If we find that we obtain better feedback in Model
A than in Model B, we will conclude that we have more accurate
dynamics closer to the thin disc limit. Only the study of the
dynamics in a large number of effective potentials will show which
configuration compares best with the observed morphology.
As we have seen in Section 5, all models are strongly nonlinear.
The relative force perturbation (regarding the axisymmetric
background) in all models is high reaching to 45\%-50\% in Models
B and C and to even higher value 80\% in Model A. We note that
\textit{for normal (non-barred) spiral} galaxies the models that
reproduce successfully the morphology of this type of galaxies
have maximum force perturbations typically of the order of 5-10\%
\citep{pcg91, ls02, lsbv04, v06} and they are already
characterized by nonlinear effects. Nonlinear effects are even
stronger in larger perturbation characteristic of bars
\citep[see][and others]{kc1996, ls02, lsbv04, bbkeep04}. Thus, it
is expected that all models will present a strongly nonlinear
behavior with extended chaotic regions. Note that we certified the
robustness of the force perturbation in each model to small
changes of the various required parameter values (e.g. thickness
of the disc).
The nonlinearity of a model, expressed as the relative force
perturbation, is an important parameter for studying its dynamics,
since it refers to the total distribution of matter (luminous and
dark) in the galaxy. However, the estimation of the potential of a
disc galaxy alone does not determine its dynamics. The main, and
most important, parameter is the pattern speed and this cannot be
unambiguously determined from observations. The Coriolis forces
totally alter the landscape of the gravitational field, as we can
see in the various effective potentials. A potential by itself can
tell us whether or not nonlinear phenomena can play an important
role in the dynamics of the system. However, for the same
potential we can have totally different dynamics. By varying the
pattern speed the equilibrium (Lagrangian) points are shifted and
may alter their stability character. In our analysis we find cases
with multiple Lagrangian points. This indicates that in real
galaxies the existence of multiple Lagrangian points can be a
common phenomenon. Our models give the opportunity to study the
dynamics of such realistic systems, something that has not been
done yet. The effect of the variation of the pattern speed on the
dynamics of NGC~1300 will be presented in the forthcoming papers
of this series.
\section*{Acknowledgments}
We thank Prof. G.~Contopoulos for fruitful discussions. P.A.P thanks
ESO for a two-months stay in Garching as visitor, where part of this
work has been completed. We would also like to thank the anonymous
referee for constructive comments that helped the clarity and
the presentation of our paper.
\bibliographystyle{mn2e}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,664 |
Q: Script recorre URL's, recoge información y la guarda en archivo tengo un problema con un script que no soy capaz de hacer.
Hace mucho tiempo que no toco PHP (demasiado en realidad) y necesito hacer un script que recorra una serie de URL's, recoja unos datos de una tabla y los guarde en un documento.
El funcionamiento, básicamente, es:
Empieza el bucle, entra en la url https://www.ejemplo.com/000001/, carga los datos que esta contiene, recoge información de una tabla determinada (con id #tablaEjemplo), la pasa a una array (supongo), de este array selecciono otros datos (nombre, dirección y mail) y esta información la guarda en un fichero externo (txt/csv).
Una vez hecho esto pasa a la siguiente dirección https://www.ejemplo.com/000001/ y hace lo mismo... y así hasta un número determinado de veces.
El fichero resultante sería algo así como:
https://www.ejemplo.com/000001
Nombre
Direccion
Mail
https://www.ejemplo.com/000002
Nombre
Direccion
Mail
etc
<?php
//Script recorre X URL (000001-000100), recoge determinados datos (nombre, direcion, mail) y los guarda en un archivo
$userAgent = 'Mozilla/5.0 (Windows NT 5.1; rv:31.0) Gecko/20100101 Firefox/31.0';
$valores = [];
for ($idempresa = 000001; $idempresa < 000100; $idempresa++): //Bucle for para recorrer X paginas de una URL (891721-899999)
$url = "https://www.ejemplo.com/".$idempresa."/";
echo $url;
//$url2 = $url." #tablaEjemplo > tbody > tr > td"; //URL con los parametros añadidos
//function get_content_with_curl($html) //Definimos la función cURL
//{
$ch = curl_init(); //Inicia cURL
$archivo = fopen("./datos.txt", "a") or die("ERROR: No ha sido posible abrir el archivo. Revisa su nombre y sus permisos."); //Abrimos el archivo
curl_setopt($ch, CURLOPT_URL, "$url"); //Configura cURL con la URL deseada
curl_setopt($ch, CURLOPT_RETURNTRANSFER, 1); //Configura cURL para devolver el resultado como cadena
curl_setopt($ch, CURLOPT_SSL_VERIFYPEER, false); //Configura cURL para que no verifique el certificado
curl_setopt($ch, CURLOPT_USERAGENT, $userAgent); //Configura el user-agent
$info = curl_exec($ch); //Establece una sesión cURL y asigna la información a la variable $info
curl_close($ch); //Cierra cURL
//Recorremos el array y vamos guardando en un txt cada unos de los valores
foreach ($valores as $datos) {
fwrite($archivo, PHP_EOL ."$datos"); //Escribimos en el archivo los diferentes valores que se recogieron de la url
}
fclose($archivo); //Cerramos el archivo para evitar errores
//}
//Llamada a la función
//Convierte la información de la URL en cadena
//$html = get_content_with_curl($url);
//Se imprime lo que obtuvimos en esa variable
//echo $html;
var_dump($info); //Devuelve la información
endfor; //Cerramos bucle for para evitar problemas
Esto es todo lo que yo fui capaz de sacar, además de muchos pedazos de código que no sirven para nada y un buen dolor de cabeza.
Espero haberme explicado bien, si alguien me puede ayudar tendrá mi eterna gratitud!
A: No se cual es el error que te tira pero puedo notar que a la hora de crear el link con el $idEmpresa tienes una / de mas antes del id, deberia ser
$url = "https://www.ejemplo.com/".$idempresa."/";
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,167 |
{"url":"https:\/\/studydaddy.com\/question\/sci-162-week-8-dqs","text":"QUESTION\n\n# SCI 162 Week 8 DQs\n\nIn this file of SCI 162 Week 8 Discussion Questions you will find the next information:\n\n1. What types of environmental factors that affect health are present where you live?How do you deal with these potentially harmful environmental factors?\n\n\u2022 @\n\u2022 1 order completed\nTutor has posted answer for $5.19. See answer's preview$5.19","date":"2018-05-25 01:34:34","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\": 0.24742785096168518, \"perplexity\": 6932.162422650929}, \"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\/1526794866917.70\/warc\/CC-MAIN-20180525004413-20180525024413-00124.warc.gz\"}"} | null | null |
After getting an offer accepted for a property, the next thing you need to think about is whether you need a survey and, if so, what type of property survey will be most beneficial for you. To address some of the confusion people have, it is essential to keep in mind that if you have a mortgage valuation, its primary purpose is to assess the property value. Mortgage lenders often recommend a company to conduct the assessment which you will pay for. A mortgage valuation is not similar to a survey and does not serve the same purpose.
A survey intends to provide a detailed inspection of the condition of the property. For example, if you live in the Leicester area, then qualified surveyors Leicester offers will determine if there are any problems with the property you need to be aware of. It is also the surveyor's job to point out if some areas of the home need major refurbishment. A survey also contains a comprehensive description of the property such as the type of glazing used, and the materials used in the walls or roof.
Condition report. This type of survey is a level one survey which is also the cheapest option. It is also the most fundamental choice which serves to complement a mortgage valuation document.
Homebuyers report. You can get a homebuyers report which includes a survey and property valuation.
Building survey. This type of survey provides the most detailed information about the property. The report will consist of advice on areas that need repair and may include estimates as well as the consequences of not conducting the recommended repairs. A building survey, although the most expensive option, is a worthwhile investment because it helps you negotiate on the initial offer you made on the property based on the survey findings.
Whether or not you need any of these surveys will also depend on the property condition. For example, if the property is brand-new, you may not need a building survey after all.
To find the best surveyor, find local firms and compare quotes from them. It is vital that the surveyor is RICS accredited and has extensive experience in conducting surveys. You can also contact the Royal Institute of Chartered Surveyors directly to get a referral for a local company.
A local company is always best because they are already familiar with the types of homes and buildings in the area. If the property you are buying is listed, old, or has unique dimensions, you may need to find a specialised surveyor for the job.
Lastly, you need to tell the surveyor precisely what you are looking to get from the report and point out the specific areas you want looked at in detail. This will ensure you will get the most out of the survey you are paying for. | {
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\section{Introduction}
Embeddings of networks and distance-based data into hyperbolic geometry have received substantial interest in recent years. Such embeddings have been used for visualization \cite{walter2004h}, link prediction \cite{papadopoulos2012popularity, papadopoulos2015network} and community detection \cite{papadopoulos2015network, muscoloni2017machine}. They offer insight into the tradeoff between popularity and similarity effects in network growth \cite{papadopoulos2012popularity} and have interesting implications for routing, network navigability \cite{kleinberg2007geographic, boguna2009navigability} and efficient computation of shortest network paths \cite{zhao2011fast, chowdhary2017improved}. Moreover, such embedding methods can be seen as alternatives to classic visualization and dimensionality reduction techniques based on Euclidean geometry, such as principal component analysis or multidimensional scaling.
However, the hyperbolic embedding methods as yet proposed in the literature have either been based on specific assumptions about network growth (e.g. \cite{papadopoulos2015network, muscoloni2017machine}), or methods with strong theoretical properties, but requiring costly non-linear numerical optimization procedures (e.g. \texttt{H-MDS} of \cite{walter2004h}, \texttt{Rigel} of \cite{zhao2011fast} and \texttt{HyPy} of \cite{chowdhary2017improved}). Here, we introduce \texttt{hydra} (hyperbolic distance recovery and approximation), a novel method for embedding network or distance-based data into hyperbolic space, which has strong mathematical foundations and does not depend on specific assumptions on network growth or structure. At the same time, the method is computationally efficient and based on reduced matrix Eigendecomposition. We show mathematically, that when presented with mutual distances of data points located on a low-dimensional hyperbolic submanifold of the feature space, \texttt{hydra} will recover these points exactly. For general data, the method satisfies a certain optimality property, similar to the strain-minimizing property of multidimensional scaling. Finally, we introduce \texttt{hydra+}, an extension where the result of \texttt{hydra} is used as inital condition for hyperbolic embedding methods based on optimization, such as \texttt{Rigel/HyPy}, substantially improving their efficiency. When tested on real network data, \texttt{hydra} and its variants typically outperform existing hyperbolic embedding methods. All new methods introduced are available in the package \texttt{hydra} \cite{keller-ressel2019hydra} for the statistical computing environment \texttt{R} \cite{rct2016r}.
\section{Embeddings into Hyperbolic Space}
\subsection{Hyperbolic Space}We summarize the key features of the hyperboloid model of hyperbolic geometry (cf. \cite{ratcliffe2006foundations, cannon1997hyperbolic}) in dimension $d$. This will provide the mathematical framework in which we formulate our embedding method. To start, we define for $\bm{x}, \bm{y} \in \mathbb{R}^{d+1}$ the indefinite inner product\begin{equation}\label{eq:lorentz}
\bm{x} \circ \bm{y} := x_1 y_1 - \left(x_2 y_2 + \dotsc + x_{d+1} y_{d+1}\right),
\end{equation}
also called \emph{Lorentz product}. The real vector space $\mathbb{R}^{d+1}$ equipped with this inner product is called \emph{Lorentz space} and denoted by $\mathbb{R}^{1,d}$. As nested subsets, it contains the \emph{positive Lorentz space} $\mathbb{R}^{1,d}_+ = \set{\bm{x} \in \mathbb{R}^{1,d}: x_1 >0}$ and the single-sheet hyperboloid
\begin{equation}\label{eq:Hd}
\mathcal{H}_d = \set{\bm{x} \in \mathbb{R}^{1,d}: \bm{x} \circ \bm{x} = 1, x_1 > 0}.
\end{equation}
The \emph{hyperboloid model} with curvature $-\kappa$, $(\kappa >0)$, consists of $\mathcal{H}_d$ endowed with the hyperbolic distance
\begin{equation}\label{eq:hyper_dist}
\mathrm{d}^\kappa_H(\bm{x},\bm{y}) = \frac{1}{\sqrt{\kappa}}\arcosh\left(\bm{x} \circ \bm{y}\right), \qquad \bm{x}, \bm{y} \in \mathcal{H}_d.
\end{equation}
The hyperbolic distance $\mathrm{d}^\kappa_H$ is a distance on $\mathcal{H}_d$ in the usual mathematical sense; in particular it takes only positive values and satisfies the triangle inequality, cf. \cite[\S3.2]{ratcliffe2006foundations}. In fact, it can be shown that $\mathcal{H}_d$ endowed with the Riemannian metric tensor
\[ds^2 = \frac{1}{\kappa} \left(d\bm{x} \circ d\bm{x} \right)\]
is a Riemannian manifold and $\mathrm{d}^\kappa_H(\bm{x}, \bm{y})$ is the corresponding Riemannian distance.\footnote{That is, $\mathrm{d}^\kappa_H(\bm{x},\bm{y})$ is the length of the shortest path from $\bm{x}$ to $\bm{y}$, where lengths are measured using the length element $ds = \sqrt{ds^2}$.} The sectional curvature of this manifold is constant and equal to $-\kappa$, which explains the role of $\kappa$ as curvature parameter. Just as Euclidean space is the canonical model of geometry with zero curvature, hyperbolic space is the canonical model of geometry with negative curvature.
\subsection{The Poincar\'e ball Model}In addition to the hyperboloid model, we introduce the \emph{Poincar\'e ball model} of hyperbolic geometry, which is more appealing for visualizations of hyperbolic space and hyperbolic embeddings. In $\mathbb{R}^d$, consider the open unit ball
\[\mathcal{B}_d := \set{\bm{z} \in \mathbb{R}^d: |\bm{z}| < 1},\]
where $|\bm{z}| = \sqrt{z_1^2 + \dotsm + z_d^2}$ is the usual Euclidean norm. The \emph{stereographic projection} $\xi: \mathbb{R}^{1,d} \to \mathbb{R}^d$ defined by
\begin{equation}\label{eq:stereo}
\xi(\bm{x}) = \left(\frac{x_2}{1 + x_1}, \dotsc, \frac{x_{d+1}}{1 + x_1}\right)
\end{equation}
restricts to a bijective mapping from the hyperboloid $\mathcal{H}_d$ onto $\mathcal{B}_d$ (cf. \cite[\S4.2]{ratcliffe2006foundations}). It transfers the hyperbolic distance from $\mathcal{H}_d$ to $\mathcal{B}_d$, by setting
\[\mathrm{d}^\kappa_B(\xi(\bm{z}_1), \xi(\bm{z}_2)) = \mathrm{d}^\kappa_H(\bm{z}_1,\bm{z}_2), \qquad \bm{z}_1, \bm{z}_2 \in \mathcal{B}_d.\]
Endowed with this distance, $(\mathcal{B}_d, \mathrm{d}^\kappa_B)$ is isometric to $(\mathcal{H}_d, \mathrm{d}^\kappa_H)$ and therefore an equivalent model of hyperbolic geometry.\\
It will be convenient to parameterize $\mathcal{B}_d$ by the radial coordinate $r \in [0,1)$ and the directional coordinate $\bm{u}$ (a unit vector in $\mathbb{R}^d$), given by
\[r := \sqrt{z_1^2 + \dotsm + z_d^2}, \qquad \bm{u} := \frac{\bm{z}}{r}.\]
An easy calculation shows that the conversion from coordinates in $\mathcal{H}_d$ is given by
\begin{align}\label{eq:conversion_r}
r &= \xi_r(x_1) := \sqrt{\frac{x_1 -1}{x_1 + 1}} \qquad \text{and}\\
\bm{u} &= \xi_{\bm{u}}(x_2, \dotsc, x_{d+1}) := \left(x_2, \dotsc, x_{d+1}\right) / \sqrt{x_2^2 + \dotsm + x_{d+1}^2}. \label{eq:conversion_u}
\end{align}
In dimension $d = 2$, the Poincar\'e ball becomes the \emph{Poincar\'e disc}, and each of its points can be described by the radius $r$ and the unique angle $\theta \in [0,2\pi)$ such that
\[z_1 = r \cos \theta, \qquad z_2 = r \sin \theta.\]
\subsection{Embedding of Distances and Networks}
To formulate the embedding problem, let a symmetric matrix $D = [d_{ij}] \in \mathbb{R}_{\geqslant 0}^{n \times n}$ with zero diagonal be given, which represents the pairwise dissimilarities between some objects $\bm{o}_1, \dotsc, \bm{o}_n$. The basic premise of hyperbolic embedding is that the matrix $D$ can be approximated by a hyperbolic distance matrix $H = [\mathrm{d}^\kappa_H(\bm{x}_i, \bm{x}_j)]$, i.e., that we can find points $\bm{x}_1, \dotsc, \bm{x}_n$ in low-dimensional hyperbolic space $\mathcal{H}_d$, such that
\begin{equation}\label{eq:embed}
\mathrm{d}^\kappa_H(\bm{x}_i, \bm{x}_j) \approx d_{ij}.
\end{equation}
The points $\bm{x}_1, \dotsc, \bm{x}_n$ give a low-dimensional representation in hyperbolic space of the configuration of $\bm{o}_1, \dotsc, \bm{o}_n$ induced by their dissimilarities. In Euclidean space, such approximations are well studied and can be calculated e.g. by multidimensional scaling (MDS), see also Section~\ref{app:mds} and \cite{borg2005modern}.\\
An important special case is the \emph{network embedding problem}, where a (unweighted, undirected) graph $G = (V,E)$ is given and $D = [d_{ij}]$ is the graph distance matrix of $G$, i.e., $d_{ij}$ is the length of the shortest path in $G$ from vertex $v_i$ to $v_j$. In particular for graphs with \emph{locally tree-like structure} it can be expected that hyperbolic geometry gives a better representation than Euclidean geometry, see e.g \cite{kleinberg2007geographic}. Instead of the shortest-path distance, other dissimilarity measures based on the structure of $G$ can be used, such as the repulsion-attraction (RA) rule or edge-betweenness-centrality (EBC), cf. \cite{muscoloni2017machine}.
\subsection{Connection to prior work and innovations}
Most existing methods for hyperbolic embedding can be placed into one of two classes: Stress-based methods or network-specific methods.
\begin{itemize}[leftmargin=*]
\item \textbf{Stress-based methods} aim to solve the embedding problem \eqref{eq:embed} by minimizing the \emph{stress functional}
\begin{equation}\label{eq:stress}
\operatorname{Stress}(\bm{x}_1, \dotsc, \bm{x}_n)^2 := \sum_{i,j=1}^n \left(d_{ij} - \mathrm{d}^\kappa_H(\bm{x}_i, \bm{x}_j)\right)^2
\end{equation}
over all $\bm{x}_1, \dotsc, \bm{x}_n \in \mathcal{H}_d$. This minimization problem is a challenging high-dimensional non-convex optimization problem, and methods largely differ in their numerical approach to minimize \eqref{eq:stress}. The \texttt{H-MDS} method proposed in \cite{walter2004h} is a gradient descent scheme for minizing \eqref{eq:stress} based on explicit calculation of the gradient. \cite{chamberlain2017neural} propose a neural-network-based approach to minimizing \eqref{eq:stress}, while \cite{zhao2011fast} and \cite{chowdhary2017improved} develop so-called `landmark-based' minimization algorithms (\texttt{Rigel} and \texttt{HyPy} respectively) based on iterative quasi-Newton minimization. Due to the `landmark' heuristic, these methods are able to deal with large-scale instances of \eqref{eq:stress} and do not require full knowledge of $D$, see \cite{chowdhary2017improved} for details.
\item \textbf{Model-based methods} focus on the network embedding problem and rely on underlying assumptions on the generating mechanism of the graph $G$, see e.g. \cite{papadopoulos2012popularity} for a model of `hyperbolic network growth'. In \texttt{HyperMap} of \cite{papadopoulos2015network} and the \emph{coalescent embedding} of \cite{muscoloni2017machine}, the radial coordinate $r_i$ of the embedded points in the Poincar\'e ball model is determined directly from the degree of the vertices $v_i$, using the assumption of a power-law relationship. The directional component $\bm{u}_i$ of the embedding is then determined by maximizing likelihood in an underlying probabilistic model (cf. \cite{papadopoulos2015network}) or by applying existing nonlinear dimensionality reduction methods (such as Laplacian Eigenmapping or \texttt{ISOMAP}) to the underlying data (cf. \cite{muscoloni2017machine}).
\end{itemize}
Here, our main innovation is to replace the stress functional \eqref{eq:stress} by the \emph{strain functional}
\begin{equation}\label{eq:strain}
\operatorname{Strain}(\bm{x}_1, \dotsc, \bm{x}_n)^2 := \sum_{i,j=1}^n \left(\cosh(\sqrt{\kappa}\,d_{ij}) - \bm{x}_i \circ \bm{x}_j\right)^2,
\end{equation}
which results from \eqref{eq:stress} when all distances are transformed by hyperbolic cosine.
Furthermore, we introduce a highly efficient method for the minimization of hyperbolic strain, called \texttt{hydra} (hyperbolic distance recovery and approximation). Contrary to stress-minimization, \texttt{hydra} is based on matrix Eigendecomposition, similar to principal component analysis or classic multidimensional scaling.\footnote{In fact, the relation between hyperbolic strain- and stress-minimization is similar to the relation between `classic' and `metric' multidimensional scaling in the Euclidean case, cf. \cite {borg2005modern}.} In Theorems \ref{thm:exact} and \ref{thm:optimal} we show that \texttt{hydra} satisfies important theoretical optimality properties, in particular, it returns a guaranteed global minimum of \eqref{eq:strain}.
For instances based on real data, the embedding results of \texttt{hydra} are comparable to those based on pure stress-minimization, even when embedding quality is measured by the stress functional \eqref{eq:stress}; see Section~\ref{sec:real} below. This shows, that even when minimization of stress is the final goal, the strain functional \eqref{eq:strain} is a valuable and useful proxy for stress, as it can be minimized in a highly efficient way. The best results in terms of stress are obtained when strain- and stress-minimization are combined. This is the basis of the \texttt{hydra+} method, introduced in Section~\ref{sec:practical}, where the embedding result of \texttt{hydra} is used as initial condition for a stress-minimization run.
\section{A new hyperbolic embedding method}
\subsection{The hydra algorithm}
We introduce the \texttt{hydra} algorithm, displayed as Algorithm~\ref{algo:hydra}, which calculates an embedding into the Poincar\'e ball model of hyperbolic space by efficiently solving the strain-minimization problem
\begin{equation}\label{eq:strain_min}
\min_{\bm{x}_i \in \mathbb{R}^{1,d}} \sum_{i,j} (\cosh(\sqrt{\kappa}\,d_{ij}) - (\bm{x}_i \circ \bm{x}_j))^2.
\end{equation}
The algorithm proceeds as follows:
\begin{itemize}
\item In steps A1 and A2 the strain-minimization problem is solved by means of a matrix Eigendecomposition. These steps return a coordinate matrix $X = [x_{ij}]$, whose rows $\bm{x}_1, \dotsc, \bm{x}_n$ are elements of positive Lorentz space $\mathbb{R}^{1,d}_+$ and the optimizers of \eqref{eq:strain_min}. The optimality of $\bm{x}_1, \dotsc, \bm{x}_n$ is the subject of Theorem~\ref{thm:optimal} below.
\item In steps B1 and B2, the points $\bm{x}_1, \dotsc, \bm{x}_n$ are projected onto the Poincar\'e ball $\mathcal{B}_d$ using the stereographic projection \eqref{eq:stereo} and converted to radial/directional coordinates $(\bm{u}_i)$ using \eqref{eq:conversion_r} and \eqref{eq:conversion_u}. No adjustment is necessary for the directional coordinates, which are computed in step B1.
\item Due to \eqref{eq:conversion_r}, the radial coordinates $(r_i)$ depend only on the first column $(x_{11}, \dotsc, x_{n1})$ of $X$ and can be obtained by applying $\xi_r$ elementwise. But $\xi_r(x_{1i})$ may be undefined for elements with $x_{1i} \in (0,1)$.\footnote{By Theorem~\ref{thm:optimal}, steps A1 and A2 guarantee that all $x_{1i}$ are positive, but not that they are larger than one.} Therefore, $r_i$ is calculated in step B2 as
\[r_i = \xi_r\left(\frac{x_{i1}}{x_{\min}}\right),\]
that is, after rescaling the first column of $X$ by dividing by its smallest element $x_{\min}$.
\end{itemize}
\begin{algorithm}[!htb]
\caption{\texttt{hydra}(D,d,$\kappa$)}
\label{algo:hydra}
\begin{description}
\item[Input]
\begin{itemize}
\item A symmetric matrix $D = [d_{ij}] \in \mathbb{R}_{\geqslant 0}^{n \times n}$ with zero diagonal
\item Embedding dimension $d \le n-1$
\item Hyperbolic curvature parameter $\kappa > 0$\qquad(actual curvature: $-\kappa$)
\end{itemize}
\item[Step A1] Set
\begin{equation}\label{eq:Acosh}
A = [a_{ij}] := [\cosh(\sqrt{\kappa} \, d_{ij})]
\end{equation}
and compute the Eigendecomposition
\begin{equation}\label{eq:Eigen}
A = Q \Lambda Q^\top,
\end{equation}
where $\Lambda$ is the diagonal matrix of the Eigenvalues $\lambda_1 \ge \dotsm \ge \lambda_n$ and the columns of $Q$ are the Eigenvectors $\bm{q}_1, \dotsc, \bm{q}_n$.
\item[Step A2] Allocate the $n \times (d+1)$-matrix
\begin{equation}\label{eq:X_hydra}
X := \left[\sqrt{\lambda_1}\,\bm{q}_1 \quad \sqrt{(-\lambda_{n-d+1})^+}\,\bm{q}_{n-d+1} \quad \dotsm \quad \sqrt{(-\lambda_{n})^+}\,\bm{q}_{n} \right],
\end{equation}
where $x^+$ denotes the positive part $x^+ = \max(x,0)$.
\item[Step B1] (`Directional projection') For $i \in 1, \dots, n$ set
\[\bm{u}_i := \frac{(x_{i2}, \dotsc, x_{i(d+1)})}{\sqrt{x_{i2}^2 + \dotsm + x_{i(d+1)}^2}},\]
with $x_{ij}$ the elements of $X$.
\item[Step B2] (`Radial projection') For $i \in 1, \dotsc, n$ set
\begin{subequations}\label{eq:radial}
\begin{align*}
x_{\min} &:= \min(1, x_{11}, \dotsc, x_{n1})\\
\intertext{and}
r_i &:= \sqrt{\frac{x_{i1} - x_{\min}}{x_{i1} + x_{\min}}}
\end{align*}
\end{subequations}
\item[Return] Matrix $X$ and embedding $(r_i, \bm{u}_i)_{i = 1, \dotsc, n}$ as radial and directional coordinates in the Poincar\'e ball $\mathcal{B}_d$.
\end{description}
\end{algorithm}
The key theoretical properties of the \texttt{hydra} algorithm are summarized in the following theorems, whose proofs are given in Appendix~\ref{app}. The first theorem shows that $\texttt{hydra}$ recovers any configuration of points in $d$-dimensional hyperbolic space up to isometry:
\begin{thm}[Exact Recovery] \label{thm:exact}
Let $\aa_1, \dotsc, \aa_n$ be points in hyperbolic $d$-space $\mathcal{H}_d$, and let $D = [d_{ij}] = [\mathrm{d}^\kappa_H(\aa_i,\aa_j)]$ be the matrix of their hyperbolic distances with curvature $-\kappa$. Then $\texttt{hydra}(D,d,\kappa)$ recovers the points $\aa_1, \dotsc, \aa_n$ up to isometry. In particular, the rows $\bm{x}_1, \dotsc, \bm{x}_n$ of the matrix $X$ and the points $(r_1, \bm{u}_1), \dotsc, (r_n, \bm{u}_n)$ returned by $\texttt{hydra}(D,d,\kappa)$ satisfy
\[\mathrm{d}_B^\kappa\Big((r_i, \bm{u}_i),(r_j, \bm{u}_j)\Big) = \mathrm{d}_H(\bm{x}_i, \bm{x}_j) = d_{ij}, \qquad i,j = 1, \dotsc, n.\]
\end{thm}
For applications to real data, exact recovery is an atypical situation. However, \texttt{hydra} enjoys an optimality guarantee for strain minimization, expressed in the following theorem:
\begin{thm}[Optimal Approximation] \label{thm:optimal}
The rows $\bm{x}_1, \dotsc, \bm{x}_n$ of the matrix $X$ returned by \texttt{hydra}$(D,d,\kappa)$ are the globally optimal solutions of the strain minimization problem \eqref{eq:strain_min}.
Moreover, the first column of $X$ is strictly positive; equivalently, all $\bm{x}_i$ are elements of positive Lorentz space $\mathbb{R}^{1,d}_+$.
\end{thm}
\subsection{Practical guidelines and extensions}\label{sec:practical}
While the result of \texttt{hydra} satisfies the theoretical optimality guarantees in Theorem~\ref{thm:exact} and \ref{thm:optimal}, it can still be advantageous to adjust the results in order to improve the attractiveness of visualization or the embedding quality in terms of stress \eqref{eq:stress} (as opposed to strain, which is globally minimal). The so-called \textit{equiangular adjustment} has been introduced in \cite{muscoloni2017machine} and can be applied to two-dimensional hyperbolic embeddings. Here we propose a slight modification, which allows to interpolate smoothly between no adjustment and full equiangular adjsutment.
\begin{description}
\item[Equiangular adjustment] Let $\lambda \in [0,1]$ be the adjustment parameter and define $\mathrm{ark}(\theta_i)$ as the \emph{angular rank} of $\bm{x}_i$, i.e. when the embedded points are ordered by increasing angular coordinate $\theta$, then $\mathrm{ark}(\theta_i)$ is defined as the rank (from $1$ to $n$) of $\bm{x}_i$ in this list. The adjusted angular coordinate is then set to
\[\theta'_i := \lambda \theta_i + (1-\lambda) (\mathrm{ark}(\theta_i) -1) \frac{2\pi}{n}, \qquad i=1, \dotsc, n.\]
If $\lambda = 0$, no adjustment takes place. If $\lambda = 1$ then the angles $\theta'_i$ are regularly spaced (`equiangular') and only the ordering given by $\theta_i$ is retained.\footnote{This is the equiangular adjustment as proposed in \cite{muscoloni2017machine}.} Values of $\lambda \in (0,1)$ interpolate between these two extremes. We propose a values of $\lambda = 1/2$, which typically leads to improvements in both visual appeal and stress value of the embedding; see also method \texttt{hydra-equi} in Figure~\ref{fig:comp_method}.
\item[hydra+] If minimization of stress is the ultimate objective and strain is used only as a proxy, the result of \texttt{hydra} can be used as an initial condition for a direct minimization of the stress functional \eqref{eq:stress}. This can be seen as a chaining of \texttt{hydra} and \texttt{HyPy/Rigel} \cite{zhao2011fast, chowdhary2017improved}, where \texttt{hydra} substitutes the random initial condition of \texttt{HyPy/Rigel}. For the minimization of stress, efficient quasi-Newton routines, such as LBFGS \cite{zhu1997algorithm} can be used and supplied with the explicit gradient of stress, given in \cite[Eqs.~(3.1),(3.2)]{chowdhary2017improved}.
\end{description}
In terms of efficiency, the following simple improvement can be made to \texttt{hydra}:
\begin{description}
\item[Reduced Eigendecomposition] The numerically dominating part of \texttt{hydra} is the Eigendecomposition in \eqref{eq:Eigen}. Note, however, that in \eqref{eq:X_hydra} only the single first and the last $d$ Eigenvalues and Eigenvectors of the matrix $A$ are needed. There are efficient numerical routines (see e.g. \cite{lehoucq1998arpack}) to perform such a reduced Eigendecomposition without computing the full Eigendecomposition of $A$. These routines substantially improve efficiency if $n \gg d$ and are used in our implementation of \texttt{hydra}.
\end{description}
Using the reduced Eigendecomposition, we expect the time complexity of \texttt{hydra} to be $\mathcal{O}(n^\alpha)$ with $\alpha$ slightly above, but close, to $2$, cf.~\cite[Ch.~55]{hogben2006handbook}. For \texttt{hydra+}, the time complexity is harder to estimate, since it is based on iterative minimization of a non-convex objective function. In a single step of LBFGS both the stress functional and its gradient have to be evaluated at a complexity of $\mathcal{O}(n^2)$. Depending on the number of steps to convergence, we thus also expect a complexity of $\mathcal{O}(n^\alpha)$, with $\alpha$ strictly larger than $2$. Empirical estimates of $\alpha$ are given in Section~\ref{sec:real} below.
\subsection{Remarks on strain-minimizing graph embeddings}
In the seminal paper \cite{papadopoulos2012popularity} it has been argued that the inherent negative curvature in hyperbolic geometry resolves the trade-off between the conflicting attractive forces of popularity and similarity in network growth models. For this reason \cite{papadopoulos2012popularity} have proposed to interpret the radial coordinate $r$ in the Poincar\'e disc as dimension of `popularity' and the angular coordinate $\theta$ as dimension of `similarity'.
Interestingly, the strain minimization problem \eqref{eq:strain_min} and its solution by \texttt{hydra} gives additional mathematical support for this interpretation. More precisely, revisiting Algorithm~\ref{algo:hydra} in the graph embedding context, we observe that:
\begin{itemize}[leftmargin=*]
\item The \textbf{radial coordinates} $r_i$ are determined only from the Perron-Frobenius Eigenvector\footnote{The Perron-Frobenius Eigenvector is the Eigenvector associated to the largest Eigenvalue of a positive matrix (i.e. a matrix consisting only of positive entries) and is itself a positive vector, cf. \cite[Ch.~10]{hogben2006handbook}.} $\bm{q}_1$ of the matrix $A$. This provides a remarkable connection to the \emph{Eigenvector centralities} (corresponding to the popularity dimension) of the nodes $v_i$, which are determined from the Perron-Frobenius Eigenvector of their \emph{adjacency matrix}.
\item The \textbf{directional coordinates} $\bm{u}_i$ are determined only through the Eigenvectors $\bm{q}_{n-d+1}, \dotsc, \bm{q}_n$ (and corresponding Eigenvalues) at the \emph{low end} of the spectrum of $A$. This provides a remarkable connection to Cheeger's inequality (cf. \cite[Ch.~9]{chung2006complex}), which shows that the low end of the spectrum of the graph \emph{Laplacian matrix} encodes the separability of the graph into sparsely connected `communities' (corresponding to the similarity dimension).
\end{itemize}
We remark that while the connections described above are a first step towards a mathematization of the popularity-similarity paradigm in hyperbolic network geometry, the matrix $A = [\cosh\left(\sqrt{\kappa} d_{ij}\right)]$ is in general neither identical to the adjacency nor to the Laplacian matrix of a given graph, and thus further research into the rigorous mathematical underpinning of these connections is warranted.
\section{Numerical Results}\label{sec:real}
\subsection{Methods and Data}
In our numerical experiments, we evaluate different variants of \texttt{hydra} and compare them to existing hyperbolic embedding methods, using stress as performance criterion. We focus on small to medium sized networks (see Table~\ref{table:networks}), for which it is still feasible to compute the full distance matrix as input to our methods. Edge weights (when available) were discarded, i.e., all networks were treated as unweighted undirected graphs. This network data was used as input for the following methods:
\begin{description}
\item[hydra] The \texttt{hydra} method (without equi-angular adjustment) as described in Algorithm~\ref{algo:hydra}
\item[hydra-equi] The \texttt{hydra} method with equiangular adjustment $\lambda = 0.5$, as described in Section~\ref{sec:practical}
\item[hydra+] The \texttt{hydra+} method as described in Section~\ref{sec:practical} and using the result of \texttt{hydra-equi} as initial condition.
\item[HyPy/Rigel] The \texttt{HyPy} algorithm from \cite{chowdhary2017improved}, which is based on \texttt{Rigel} from \cite{zhao2011fast}. Both methods are based on direct minimization of the stress functional \eqref{eq:stress}. \textit{Landmark selection}, as proposed in \cite{chowdhary2017improved} was not implemented, since it serves to reduce runtime and memory use for large networks, but is not expected to improve embedding results. As in \cite{chowdhary2017improved}, the initial condition for minimization was chosen at random and we repeated the embedding $100$ times.
\item[CE-LE] The coalescent embedding (CE) using Laplacian Eigenmapping (LE) as dimension-reduction method, full equiangular adjustment and repulsion-attraction (RA) pre-weighting; see \cite{muscoloni2017machine} for details. Among the methods developed in \cite{muscoloni2017machine}, this was the best performing method to invert the PSO generating model of \cite{papadopoulos2015network} for hyperbolic networks.
\end{description}
For the methods \texttt{hydra}, \texttt{hydra-equi}, \texttt{hydra+} and \texttt{HyPy/Rigel} we used our own implementations in \texttt{R}, which are available in the \texttt{R}-package \texttt{hydra}, \cite{keller-ressel2019hydra}. For \texttt{CE-LE} we used the MATLAB implementation of the methods of \cite{muscoloni2017machine} available from github.\footnote{\url{https://github.com/biomedical-cybernetics/coalescent_embedding}} The stress-optimization in \texttt{hydra+} and \texttt{HyPy/Rigel} was performed using the LBFGS method (see \cite{zhu1997algorithm}) as implemented in the \texttt{R}-function \texttt{optim} and using the analytic form of the gradient of the stress functional \eqref{eq:stress} from \cite{chowdhary2017improved}. Note that all methods except \texttt{CE-LE} use the shortest-path matrix as input dissimilarities; \texttt{CE-LE} uses repulsion-attraction (RA) weights as input dissimilarities, see \cite{muscoloni2017machine}. For all methods hyperbolic curvature was fixed to $-\kappa = -1$ and we embed into dimension $d = 2$.
\begin{table}[htpb]
\begin{footnotesize}
\begin{tabular}{@{}lp{0.5\textwidth}ll@{}}
\toprule
Network&Description&Source&\#\,Nodes\\
\midrule
karate & Social interaction network (`Zachary's karate club network') from \cite{zachary1977information}&\texttt{igraphdata} \cite{csardi2015igraphdata}&$34$\\
UKfaculty & Personal friendship network of a UK university faculty from \cite{nepusz2008fuzzy} & \texttt{igraphdata} \cite{csardi2015igraphdata} & $81$\\
opsahl & One-node projection of message Exchange Network from \cite{opsahl2013triadic}; two isolated nodes have been removed&\url{toreopsahl.com}&$897$\\
facebook & Facebook social circles network from \cite{leskovec2012learning}; combined edge sets&\url{snap.stanford.edu}&$4039$\\
collaboration & Co-authorship network from ArXiv submissions to category Hep-Ph (High Energy Physics); largest connected component. From \cite{leskovec2007graph}& \url{snap.stanford.edu} &$8638$\\
oregon & Autonomous systems peering information inferred from route-views in Oregon on March 26, 2001. From \cite{leskovec2005graphs}& \url{snap.stanford.edu} &$11174$\\
\bottomrule
\end{tabular}
\vspace{0.5em}
\caption{Networks used for numerical experiments}\label{table:networks}
\end{footnotesize}
\end{table}
\subsection{Results and Discussion}
Results on embedding quality (measured by stress) for all networks and methods (except \texttt{CE-LE}) are shown in Figure~\ref{fig:comp_method}. Note that stress values are normalized by using the average result of \texttt{HyPy/Rigel} as a reference. This facilitates the comparison of results between different networks. As \texttt{HyPy/Rigel} depends on randomized initial conditions we indicate the $5\%$- and $95\%$-quantiles (over 100 runs) in addition to its average result. The stress-values of the embeddings produced by \texttt{CE-LE} were substantially larger (by a factor from $13$ to $26$) than the reference method and we have therefore excluded this method from the plot and from the further analysis of computation times. \\
\begin{figure}[htbp]
{\centering
\includegraphics[width=1.15 \textwidth]{methods_plot.png}
}
\caption{\textbf{Embedding performance on real network data.} Embedding quality (measured by stress \eqref{eq:stress}, relative to the average result of \texttt{HyPy/Rigel}) of different hyperbolic embedding methods applied to the six networks listed in Table~\ref{table:networks}. For \texttt{HyPy/Rigel} a 5\%--95\% error bar is shown, corresponding to 100 runs with randomized initial condition.}
\label{fig:comp_method}
\end{figure}
Computation times of the different methods is shown in Figure~\ref{fig:comp_time} in doubly logarithmic coordinates. As should be expected, the methods split into two groups with computation times for \texttt{hydra} and \texttt{hydra-equi} being shorter than for \texttt{hydra+} and \texttt{HyPy/Rigel} by two orders of magnitude. The seemingly small gap between \texttt{hydra+} and \texttt{HyPy/Rigel} still corresponds to a difference of about 50\% in runtime. Based on the discussion in Section~\ref{sec:practical} we have added regression lines to estimate the exponent $\alpha$ in the conjectured complexity $\mathcal{O}(n^\alpha)$. To avoid clutter, regression lines are only shown for \texttt{hydra-equi} and \texttt{hydra+}; the estimates for all methods are $\alpha \approx 2.0$ for \texttt{hydra}, $\alpha \approx 2.1$ for \texttt{hydra-equi} and $\alpha \approx 2.3$ for both \texttt{hydra+} and \texttt{HyPy/Rigel}. As setup costs seem to dominate the computation times for the smallest network, we have excluded it from the regression analysis.
\begin{figure}[htbp]
{\centering
\includegraphics[width=1.15 \textwidth]{time_plot.png}
}
\caption{\textbf{Computation time of embedding methods.} Computation time (in seconds) of different hyperbolic embedding methods, in relation to the number of nodes in the six networks listed in Table~\ref{table:networks}. Coordinate axes are doubly logarithmic. For \texttt{HyPy/Rigel}, average computation time and a 5\%--95\% error bar is shown, corresponding to 100 runs with randomized initial condition. For \texttt{hydra-equi} and \texttt{hydra+} dotted regression lines (excluding observations from the smallest network) are indicated.}
\label{fig:comp_time}
\end{figure}
Finally, an exemplary embedding result produced by the \texttt{hydra-equi} method for the \texttt{facebook} network is shown in Figure~\ref{fig:example}. Nodes are placed into the Poincar\'e disc model of hyperbolic geometry according to their embedding coordinates (the full disc is indicated in grey) and a random subsample of links is drawn as hyperbolic geodesics. Visually, the embedding conforms well with the popularity-vs-similarity paradigm of \cite{papadopoulos2012popularity} for hyperbolic networks: Nodes with a function as hubs between communities or individuals (popularity dimension) are placed closer to the center of the hyperbolic disc. Communities are identified along the angular coordinate (similarity dimension) with the effective distance between communities indicated by angular separation.\\
Summarizing our numerical experiments, we conclude the following:
\begin{itemize}
\item In general, the strain-minimization performed by \texttt{hydra} seems to be a good proxy for stress-minimization, but is faster by a factor of 100 or more in comparison to stress-minimization from a random initial condition (\texttt{HyPy/Rigel}). Note that \texttt{hydra} also eliminated the uncertainty associated with the randomized nature of \texttt{HyPy/Rigel}, which can lead to large variations in embedding quality in some instances (e.g., the \texttt{facebook} network).
\item The simple equi-angular adjustment performed in \texttt{hydra-equi} consistently improves embedding quality in terms of stress at negligible numerical costs. The returned embeddings outperform \texttt{HyPy/Rigel} for two networks (\texttt{karate}, \texttt{facebook}) and are competitive for all others, with a largest observed difference of 23\% in terms of stress.
\item Using the results of \texttt{hydra} as a starting value for stress-minimization, instead of a random initial condition, i.e., replacing \texttt{HyPy/Rigel} by \texttt{hydra+} reduces computation time by approx. 30\% - 50\% and leads to better (average) embedding quality in all cases. The reduction in stress is considerable in the facebook network, where stress is reduced by approx. 40\%.
\item The \texttt{CE-LE} method, based on the PSO network growth model of \cite{papadopoulos2015network}, is not competitive with the other methods in terms of embedding quality. This suggests that the structure of the real networks that we have considered deviates from the theoretical growth model (PSO-model) of \cite{papadopoulos2015network} upon which \texttt{CE-LE} is build.
\end{itemize}
As a next step, we plan to make strain-minimizing hyperbolic embedding methods feasible for large and very large networks. For such networks the computational complexity of $\mathcal{O}(n^\alpha)$ (with $\alpha > 2$) of the proposed methods, but also of the graph distance calculation itself, are prohibitive. For this reason, heuristics such as the landmark heuristic of \cite{chowdhary2017improved} will have to be adapted to strain-minimizing embedding methods.
\begin{figure}
{\centering
\includegraphics[width=1.0 \textwidth]{facebook_plot.png}
}
\caption{\label{fig:facebook}\textbf{Embedding example.} The hyperbolic embedding of the \texttt{facebook} network produced by the method \texttt{hydra-equi}. All 4039 network nodes are shown as red dots. A random subsample of the 88234 total edges are also shown and drawn as hyperbolic geodesics in black. The edge subsample was produced by randomly sampling two incident edges from each network node, allowing for repetitions.}
\label{fig:example}\end{figure}
\begin{appendix}
\section{Theoretical Results}\label{app}
To prove the theoretical properties of the \texttt{hydra} method, it is convenient to reformulate the strain minimization problem \eqref{eq:strain_min} in matrix form. To this end, let $D = [d_{ij}]$ be the given dissimilarity matrix, set $A = [\cosh(\sqrt{\kappa}\,d_{ij})]$ and write
\[X = \left(\bm{x}_1, \dotsc, \bm{x}_n\right)^\top \in \mathbb{R}^{n \times (d+1)}\]
for the coordinate matrix of some points $\bm{x}_1, \dotsc, \bm{x}_n$ in $\mathbb{R}^{d+1}$. Finally, let $J$ be the $(d+1) \times (d+1)$ diagonal matrix
\begin{equation}\label{eq:J}
J = \diag(1,-1, \dotsc, -1),
\end{equation}
cf. \cite[\S3.1]{ratcliffe2006foundations}. The strain minimization problem \eqref{eq:strain_min} can now be written in compact form as
\begin{equation}\label{eq:strain_compact}
\min_{X \in \mathbb{R}^{n \times (d+1)}}\norm{A - X^\top J X}_F^2,
\end{equation}
where $\norm{.}_F$ denotes the Frobenius norm. Imposing the constraint that all $\bm{x}_i$ are elements of the hyperboloid $\mathcal{H}_d$ is equivalent to requiring that
\[\diag(X^\top J X) = (1, \dotsc, 1) \quad \text{and} \quad X\bm{e}_1 > 0,\]
where $\bm{e}_1$ is the first standard unit vector. In particular, the first condition guarantees $\bm{x}_i \circ \bm{x}_i = 1$, and the second one selects the upper sheet of the two-sheet hyperboloid thus described.
\subsection{Hyperbolic strain minimization and exact recovery}
For a real symmetric matrix $A$, denote by $n_+(A)$ and $n_-(A)$ the number of positive and negative Eigenvalues of $A$.
The following Lemma characterizes matrices that can be written as inner product matrices (`Gram matrices') with respect to the Lorentz product \eqref{eq:lorentz}:
\begin{lem}\label{lem:gram}
Let $G = [g_{ij}] \in \mathbb{R}_{\geqslant 0}^{n \times n}$ be positive and symmetric, and let $d \le n-1$. The following are equivalent
\begin{enumerate}[label=\alph*)]
\item $G$ satisfies $n_+(G) = 1$ and $n_-(G) \le d$.
\item $G$ is a `Lorentzian Gram matrix', i.e., there exist $\bm{x}_1, \dotsc, \bm{x}_n$ in $\mathbb{R}^{1,d}$, such that
\[g_{ij} = \bm{x}_i \circ \bm{x}_j, \quad \forall\,i,j \in 1, \dotsc, n.\]
\item There exists $X \in \mathbb{R}^{n \times (d+1)}$, such that
\begin{equation}\label{eq:G_decomp}
G = X J X^\top,
\end{equation}
where $J$ is given by \eqref{eq:J}.
\end{enumerate}
In addition,
\begin{itemize}
\item The first column of $X$ is positive if and only if $\bm{x}_1, \dotsc, \bm{x}_n$ are in the positive Lorentz space $\mathbb{R}^{1,d}_+$;
\item The points $\bm{x}_1, \dotsc, \bm{x}_n$ are in $\mathcal{H}_d$ if and only if $\diag(G) = (1, \dotsc, 1)$ and the first column of $X$ is positive.
\end{itemize}
\end{lem}
\begin{proof}
The equivalence of (b) and (c) follows directly from the definition of the Lorentz product in \eqref{eq:lorentz}. Next, we show that (c) implies (a): From \cite[Ch.~10.3]{lax2007linear} it follows from \eqref{eq:G_decomp} that $n_+(G) \le n_+(J) = 1$ and $n_-(G) \le n_-(J) = d$. But $G$ is a positive matrix and Perron's theorem (cf. \cite[Ch.~16]{lax2007linear}) guarantees that its leading Eigenvalue is positive, i.e., $n_+(G) \ge 1$, and we conclude (a). To show that (a) implies (c), assume first that $n_-(G) = d$. By Sylvester's law of inertia, there exists a decomposition
\[G = \hat{X} \hat{J} \hat{X}^\top, \quad \text{where} \quad \hat{J} =\diag\Big({+}1, 0, \dotsc, 0,\underbrace{-1, \dotsc, -1}_\text{$d$ times}\Big).\]
This decomposition can be reduced to \eqref{eq:G_decomp}, by simply dropping all rows and columns containing only zeroes from $\hat{J}$ and by also dropping the corresponding columns from $\hat{X}$. If $n_-(G) = d' < d$, the same procedure yields a decomposition with $X$ of dimension $n \times (d' + 1)$ and $J$ of dimension $(d'+1) \times (d'+1)$. Padding $X$ with zero columns and $J$'s diagonal with $-1$s, \eqref{eq:G_decomp} also follows in this case.\\
The additional statements follow directly from the following observations: The first column of $X$ contains exactly the first coordinate of all points $\bm{x}_1, \dotsc, \bm{x}_n$. If the first coordinate of a point $\bm{x}$ is positive, it is an element of positive Lorentz space and vice versa. The diagonal of $G$ contains the values $\bm{x}_i \circ \bm{x}_i, i = 1, \dotsc, n$. If $\bm{x}_i \circ \bm{x}_i = 1$ and $\bm{x}_i \in \mathbb{R}^{1,d}_+$ then $\bm{x}_i$ is an element of the hyperboloid $\mathcal{H}_d$ and vice versa.
\end{proof}
\begin{proof}[Proof of Theorem~\ref{thm:optimal}]Let $A = [a_{ij}] = [\cosh(\sqrt{\kappa}\,d_{ij})]$ and let $B = [b_{ij}]$ be another symmetric matrix in $\mathbb{R}^{n \times n}$. Let $(\lambda_i(A))_{i = 1, \dotsc, n}$ and $(\lambda_i(B))_{i = 1, \dotsc, n}$ be their Eigenvalues in descending order, and denote by $\norm{.}_F$ the Frobenius norm. By a result of Wielandt-Hoffmann, cf. \cite[Ch.~10, Thm.~18]{lax2007linear},
\begin{equation}\label{eq:wielandt}
\sum_{i,j} (a_{ij} - b_{ij})^2 = \norm{A - B}_F^2 \ge \sum_{i}^n (\lambda_i(A) - \lambda_i(B))^2.
\end{equation}
Assume now that $B$ is a `Lorentzian Gram matrix' with elements given by
\[b_{ij} = \bm{b}_i \circ \bm{b}_j, \qquad i,j=1, \dotsc, n\]
for some $\bm{b}_1, \dotsc, \bm{b}_n \in \mathbb{R}^{1,d}$. By Lemma~\ref{lem:gram} this implies that $n_+(B) = 1$ and $n_-(B) \le d$. Hence all Eigenvalues of $B$ with index $2, \dotsc, n-d$ are zero, and we obtain
\begin{align*}
\sum_{i,j} (a_{ij} - \bm{b}_i \circ \bm{b}_j)^2 &= \norm{A - B}_F^2 \ge \notag \\
&\ge (\lambda_1(A) - \lambda_1(B))^2 + \sum_{i=2}^{n-d} \lambda_i(A)^2 + \sum_{i = n-d+1}^n (\lambda_i(A) - \lambda_i(B))^2.
\end{align*}
For the first summand on the right hand side we have the trivial lower bound $0$. In the last sum, all $\lambda_i(B)$ are negative or zero, and hence, for any $i = (n-d+1), \dotsc, n$, we can estimate
\[(\lambda_i(A) - \lambda_i(B))^2 \ge \begin{cases} 0 \quad &\text{if } \lambda_i(A) \le 0\\ \lambda_i(A)^2 \quad &\text{if }\lambda_i(A) > 0, \end{cases}\]
which is the same as $(\lambda_i(A)^+)^2$.
Together, we obtain that
\begin{equation}\label{eq:strain_bound}
\sum_{i,j} (a_{ij} - \bm{b}_i \circ \bm{b}_j)^2 \ge \sum_{i=2}^{n-d} \lambda_i(A)^2 + \sum_{i=n-d+1}^{n} (\lambda_i(A)^+)^2.
\end{equation}
Denote by $A = Q \Lambda_A Q^\top$ the Eigendecomposition of $A$ with $\Lambda_A = \diag(\lambda_1(A), \dotsc, \lambda_n(A))$. Let $X$ be the matrix returned by \texttt{hydra}($D$, $d$, $\kappa$) and $\bm{x}_1, \dotsc, \bm{x}_n$ the rows of $X$. By \eqref{eq:X_hydra} the associated Lorentzian Gram matrix $G = XJ X^\top$ has the Eigendecomposition $G = Q \Lambda_G Q^\top$ with
\[\Lambda_G = \diag(\lambda_1(A), 0, \dotsc, 0, (-\lambda_{n-d+1}(A))^+, \dotsc, (-\lambda_n(A))^+).\]
Using the unitary invariance of the Frobenius norm and the trivial identity $x - (-x)^+ = x^+$, we obtain
\begin{align}\label{eq:x_minimizes}
\sum_{i,j} (a_{ij} - \bm{x}_i \circ \bm{x}_j)^2 &= \norm{Q \Lambda_A Q^\top - Q \Lambda_G Q^\top}^2_F = \norm{\Lambda_A - \Lambda_G}_F^2 = \\ = \sum_{i=2}^{n-d} \lambda_i(A)^2 + \sum_{i=n-d+1}^n (\lambda_i(A)^+)^2.\notag
\end{align}
This shows that setting $\bm{b}_i := \bm{x}_i$ for all $i \in 1, \dotsc, n$ achieves equality in \eqref{eq:strain_bound} and hence that the points $\bm{x}_i$ minimize \eqref{eq:strain_compact}.
\end{proof}
\begin{proof}[Proof of Theorem~\ref{thm:exact}]
Let $D = [d_{ij}]$ be the hyperbolic distance matrix of $\aa_1, \dotsc, \aa_n$ in $\mathcal{H}^d$. Then $A = [a_{ij}] = [\cosh(\sqrt{\kappa}d_{ij})]$ is the associated Lorentzian Gram matrix with elements
\[a_{ij} = \aa_i \circ \aa_j.\]
By Lemma~\ref{lem:gram} $A$ satisfies $n_+(A) = 1$ and $n_-(A) \le d$, i.e. the Eigenvalues of $A$ satsify $\lambda_i(A) = 0$ for $i=2, \dotsc, n-d$ and $\lambda_i(A) \le 0$ for $i=n-d+1, \dotsc, n$. Hence, it follows from \eqref{eq:x_minimizes} that $\sum_{i,j}(a_{ij} - \bm{x}_i \circ \bm{x}_j)^2 = 0$ or, equivalently, that
\[\bm{x}_i \circ \bm{x}_j = \aa_i \circ \aa_j\]
for all $i, j \in 1, \dotsc, n$. Applying $\cosh(\sqrt{\kappa}\,\cdot)$ to both sides, we see that
\[\mathrm{d}_H^\kappa(\bm{x}_i, \bm{x}_j) = \mathrm{d}_H^\kappa(\aa_i ,\aa_j)\]
and hence that $(\bm{x}_i)$ and $(\aa_i)$ are isometric.
\end{proof}
\subsection{Comparison to classic multidimensional scaling}\label{app:mds}
In several aspects, the hydra method can be seen as the `hyperbolic analogue' of classic multidimensional scaling (MDS), cf. \cite{borg2005modern}, which is based on Euclidean geometry. Below, we summarize the classical MDS method and point out parallels to (and differences from) \texttt{hydra}. Classical MDS also takes a matrix $D = [\mathrm{d}_{ij}] \in \mathbb{R}_{\geqslant 0}^{n \times n}$ with zero diagonal as input. Using the centering matrix $C = I - \frac{1}{n}\bm{1} \in \mathbb{R}^{n \times n}$, where $\bm{1}$ denotes a matrix of ones of matching dimension, the `doubly centered' matrix
\begin{equation*}
A = - \frac{1}{2}C^\top D C \qquad \text{[compare \eqref{eq:Acosh}]}
\end{equation*}
is derived from $D$, and its Eigendecomposition
\[A = Q \Lambda Q^\top \qquad \text{[compare \eqref{eq:Eigen}]}\]
computed. Again, $\Lambda$ is the diagonal matrix of the Eigenvalues $\lambda_1 \ge \dotsm \ge \lambda_n$ and the columns of $Q$ are the Eigenvectors $\bm{q}_1, \dotsc, \bm{q}_n$. MDS then returns the (Euclidean) coordinate matrix
\[X = \left[\sqrt{\lambda_1}\,\bm{q}_1 \quad \sqrt{\lambda_2}\,\bm{q}_2 \quad \dotsm \quad \sqrt{\lambda_d}\,\bm{q}_d \right],\qquad \text{[compare \eqref{eq:X_hydra}]}\]
whose rows $\bm{x}_i$ are interpreted as points in Euclidean space $\mathbb{R}^d$. This coordinate matrix $X$ solves the strain minimization problem
\[\min_{X \in \mathbb{R}^{n \times d}} \norm{A - X^\top X}_F^2, \qquad \text{[compare \eqref{eq:strain_compact}]}\]
cf. \cite[Ch.~12]{borg2005modern}. Moreover, if the input matrix $D$ is a matrix of \emph{squared} Euclidean distances, i.e., $\mathrm{d}_{ij} = |\bm{x}_i - \bm{x}_j|^2$ then MDS recovers the points $\bm{x}_i$ exactly (up to Euclidean isometry). Note that $X^\top X$ appearing above is the Gram matrix of the points $\bm{x}_1, \dotsc, \bm{x}_n$, i.e. the matrix of their scalar products $\bm{x}_i^\top \bm{x}_j$, whereas the matrix $X^\top J X$ in \eqref{eq:strain_compact} is the `Lorentzian Gram matrix' of the Lorentz products $\bm{x}_i \circ \bm{x}_j$.
\bibliographystyle{plain}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,902 |
Q: How to pass up a struct edit[how to store lines] this output
Andrew Tanenbaum, David Wetherall
Computer Networks
Michaell Donahoo, Kenneth Calvert
TCP/IP Sockets in C
William,Stallings
Yale Patt, Sanjay Patel
is the result of this code.
#include <stdio.h> /* for printf() and fprintf() */
#include <sys/socket.h> /* for socket() and bind() */
#include <arpa/inet.h> /* for sockaddr_in and inet_ntoa() */
#include <stdlib.h> /* for atoi() and exit() */
#include <string.h> /* for memset() */
#include <unistd.h> /* for close() */
#include "./book.h"
#ifndef fileget_C
#define fileget_C
#endif // fileget_C
void readlib(Book* Library){
/*char stock[4][125];*/
FILE *bookfile=fopen("/home/ninja/Sockets/bookstock.txt","r+");
size_t len=0;
int num;
ssize_t read;
char *stringin;
char *isbn;
int *numin;
int n;
for(n=0; n<4; n=n+1){
getline(&stringin, &len, bookfile);
strncpy(Library[n].isbn,stringin,strlen(stringin));
//printf("%s",Library[n].isbn);
stringin=NULL;
getline(&stringin, &len, bookfile);
strncpy(Library[n].Author,stringin,strlen(stringin));
//printf("%s",Library[n].Author);
stringin=NULL;
getline(&stringin, &len, bookfile);
strncpy(Library[n].title,stringin,strlen(stringin));
//printf("%s",Library[n].title);
stringin=NULL;
getline(&stringin, &len, bookfile);
num=atoi(stringin);
Library[n].edition=num;
//printf("%d\n",Library[n].edition);
stringin=NULL;
getline(&stringin, &len, bookfile);
Library[n].year=atoi(stringin);
stringin=NULL;
//printf("%d\n",Library[n].year);
getline(&stringin, &len, bookfile);
strncpy(Library[n].publisher,stringin,strlen(stringin));
stringin=NULL;
getline(&stringin, &len, bookfile);
Library[n].inventory=atoi(stringin);
stringin=NULL;
getline(&stringin, &len, bookfile);
Library[n].available=atoi(stringin);
//printf("%d\n",Library[n].available);
}
// printf("%s",Library[0].title);
//printf("%s",Library[1].title);
//printf("%s",Library[2].title);
//printf("%s\n",Library[3].title);
printf("%s",Library[0].Author);
printf("%s",Library[1].Author);
printf("%s",Library[2].Author);
printf("%s",Library[3].Author);
}
For some reason, I'm getting extra lines stored or I am not storing to the pointer in an appropriate way. The commented out print lines in the for loop display the right information which includes printing the appropriate author field of the struct.
A: The problem is with your readlib() and your Library.
Note that the return of the readlib() is not of type Book*, while you return Library which is of type Book[], thus the compiler gives you the warning.
Also, it seems like you are trying to return an array in C. Be very careful. Technically, you could change the return of readlib() like this:
Book* readlib()
But it is highly not recommended. It is better to have array declared outside of the function and the function contains the Book* argument in it:
void readlib(Book* Library, int noOfBook)
Then you declare your
Book Library[4]; //somewhere else
and call the readlib like this:
readlib(Library, 4);
You do not need to to:
return Library;
In the readlib, since it is already declared outside and passed to the readlib
Of course, if you really want to return Book* however, you could prepare proper memory space by using malloc in the function:
Book* readlib(int noOfBook){
Book *Library = malloc (noOfBook * sizeof(Book));
//something else
return Library;
}
But I personally prefer to handle all these outside.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 330 |
{"url":"http:\/\/mathhelpforum.com\/pre-calculus\/61446-find-domain-composite-function-f-g-print.html","text":"# find the domain of the composite function f*g\n\n\u2022 Nov 24th 2008, 05:01 PM\nbaily_miller\nfind the domain of the composite function f*g\nf(x)=4x+4; g(x)=x+5\n\u2022 Nov 24th 2008, 05:08 PM\nskeeter\n$f[g(x)] = f(x+5) = 4(x+5) + 4$\n\ndomain of the composite function looks like the range of g(x).","date":"2017-11-19 16:13:52","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\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 1, \"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\": 0.8434768319129944, \"perplexity\": 1595.7959587134083}, \"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-2017-47\/segments\/1510934805687.20\/warc\/CC-MAIN-20171119153219-20171119173219-00795.warc.gz\"}"} | null | null |
{"url":"https:\/\/learn.careers360.com\/ncert\/question-find-the-mean-deviation-about-the-mean-for-the-data-4-7-8-9-10-12-13-17\/","text":"# 1. Find the mean deviation about the mean for the data.\u00a0\u00a0\u00a0\u00a0$\\small 4,7,8,9,10,12,13,17$\n\nMean ($\\overline{x}$) of the given data:\n\n$\\overline{x} = \\frac{1}{8}\\sum_{i=1}^{8}x_i = \\frac{4+ 7+ 8+ 9+ 10+ 12+ 13+ 17}{8} = 10$\n\nThe respective absolute values of the deviations from mean,\u00a0$|x_i - \\overline{x}|$ are\n\n6, 3, 2, 1, 0, 2, 3, 7\n\n$\\therefore$\u00a0\u00a0$\\sum_{i=1}^{8}|x_i - 10| = 24$\n\n$\\therefore$\u00a0$M.D.(\\overline{x}) = \\frac{1}{n}\\sum_{i=1}^{n}|x_i - \\overline{x}|$\n\n$= \\frac{24}{8} = 3$\n\nHence, the mean deviation about the mean is 3.\n\nExams\nArticles\nQuestions","date":"2020-05-27 16:00:52","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\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 9, \"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\": 0.9420414566993713, \"perplexity\": 493.429870657134}, \"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-2020-24\/segments\/1590347394756.31\/warc\/CC-MAIN-20200527141855-20200527171855-00359.warc.gz\"}"} | null | null |
Die Marktregeln für die Durchführung der Bilanzkreisabrechnung Strom (MaBiS) sind ein Beschluss der Bundesnetzagentur. Mit diesem Beschluss reguliert die Behörde alle mit der Bilanzkreisabrechnung in Zusammenhang stehenden Geschäftsprozesse und Marktkommunikation. Durch die Regulierung sind die Vorgaben verbindlich durch die Marktteilnehmer umzusetzen.
Geschichte
Die Marktliberalisierung, also die freie Wahl des Stromlieferanten unabhängig vom Netzbetreiber, machte eine Regelung erforderlich, wie der von einem Lieferanten durch ein fremdes Netz durchgeleitete Strom abgerechnet wird, insbesondere für den Fall, dass die Netzbetreiber nicht die Energiemenge aus dem Bilanzkreis eines Lieferanten entnommen haben, welche der Netzbetreiber zuvor in der Zuordnungsliste gemeldet hat. Die Zuordnungsliste ist die für die Bilanzierung verbindliche Liste, welche der Netzbetreiber vor dem Liefermonat als Grundlage dem Lieferanten sendet. Der Mehr- oder Minderverbrauch des Kunden, im Vergleich zur Prognose des Netzbetreibers (Wert aus der Zuordnungsliste), ist nicht mit der Bilanzkreisabrechnung verknüpft. Diese Energiemengen verrechnet der Netzbetreiber über die Mehr-Mindermengen Abrechnung. Durch die Differenzen aus den vom Netzbetreiber vor dem Liefermonat in der Zuordnungsliste gemeldeten Prognosedaten zu den nach dem Liefermonat vom Netzbetreiber tatsächlich bilanzierten Mengen, kam es immer wieder zu Abweichungen, welche durch teure Ausgleichsenergie abgedeckt werden mussten. Diese wurden dann am Ende dem Lieferanten zugeordnet. Durch die MaBiS können diese Probleme nun aufgedeckt werden und im Falle von Abweichungen werden sie dem Netzbetreiber zugerechnet.
Die Zuordnungsliste als Grundlage muss dem Lieferanten am 16. Werktag des Monats vor Liefermonat vorliegen. (Siehe hierzu GPKE / GeLi.) Liegt diese nicht vor, so fehlt die Grundlage für die Bilanzierung. Eine Energieeinstellung durch den Lieferanten muss hier dann nicht stattfinden. In diesem Fall trägt der Netzbetreiber die Rechnung.
Datenaustausch und Mengenbilanzierung (DuM)
Mit der Richtlinie Datenaustausch und Mengenbilanzierung (DuM) wurde der erste verbindliche Rahmen geschaffen für eine automatisierbare Abrechnung eines Bilanzkreises für das Medium Strom. Herausgegeben wurde DuM im Jahre 2005 von der damaligen Organisation Verband der Netzbetreiber (VDN). Recht schnell zeigten sich die Mängel der DuM in Gestalt ihrer zu geringen Regelungstiefe und der fehlenden Verzahnung zu den Vorprozessen Geschäftsprozesse zur Kundenbelieferung mit Elektrizität (GPKE), weshalb 2007 die Arbeiten an einem Nachfolger begannen.
Marktregeln für die Durchführung der Bilanzkreisabrechnung Strom (MaBiS)
MaBiS 1.0 und 2.0
Die MaBiS 1.0 trat am 1. April 2011 in Kraft. Sie baut auf der DuM auf. Beim Nachfolger MaBiS wurde insbesondere Wert gelegt auf einen vollautomatischen elektronischen Datenaustausch, der alle wesentlichen Prozesse umfasst, also nicht nur die Bilanzkreisabrechnung, sondern auch die Klärungsprozesse zur Zuordnung der Differenzen. Hierzu wurden die bestehenden EDIFACT-Nachrichtentypen auf den deutschen Energiemarkt präzisiert und weitere Nachrichtentypen neu aufgenommen, um alle wesentlichen Prozesse auch automatisiert abwickeln zu können.
Zum 1. April 2014 trat die MaBiS 2.0 in Kraft. Die nachfolgenden Punkte entsprechen den wichtigsten prozessualen Änderungen:
Versionierung von Normlastprofilen
Austausch von Clearinglisten für die Deltazeitreihe (BIKO → VNB)
Austausch von Clearinglisten für den Bilanzkreisausgleichssaldo (BIKO → BKV)
Aktivierung der Netzzeitreihen gegenüber dem Nachbar-VNB (bisher nur gegenüber dem BIKO)
Bilanzkreiszuordnungslisten werden bei Abo-Anforderung nur übermittelt, wenn es im betroffenen Bilanzierungsmonat Änderungen gab
Integration der zuvor bereits gültigen ergänzenden Dokumente (unter anderem Umsetzungsfragen, Wirkungs des MaBiS-Status)
MaBiS 3.0 (aktuell)
Zum 1. Dezember 2019 trat die MaBiS 3.0 im Zuge der Umstellung MaKo 2020 in Kraft. Folgende wichtige Neuerungen ergaben sich hier:
Eintritt neue Marktrolle ÜNB. Diesem kommt nun die Aggregationsverantwortung, also Summenbildung und Bilanzierung aller Marktlokationen mit iMS zu.
Einführung von Kategorien:
Kategorie A: alle MaBiS-Zeitreihen, die vom Netzbetreiber monatlich erstellt werden müssen.
Kategorie B: alle MaBiS-Zeitreihen, die vom ÜNB monatlich erstellt werden müssen.
Kategorie C: alle MaBiS-Zeitreihen, die vom ÜNB täglich erstellt werden müssen.
Die Bilanzierungsgebietssummenzeitreihe (BG-SZR) wurde als neue MaBiS-Zeitreihe eingeführt, die vom ÜNB an den BIKO (Bilanzkreiskoordinator) und an den Netzbetreiber geschickt werden muss. Darin enthalten ist die Summe sämtlicher Marktlokationen mit iMS in einem Bilanzierungsgebiet.
Die monatlichen Fristen für die Erstellung der MaBiS wurden wegen der Teilnahme eines neuen Marktpartners am Prozess etwas gestreckt und vereinfacht.
Mit dem Deltazeitreihenübertrag wurde nun ein neues Instrument für das Clearing von Zeitreihen zwischen Netzbetreiber und ÜNB geschaffen.
Das Clearing (Bilanzierungskorrektur) und Versenden von Statusnachrichten wurde wesentlich vereinfacht, so dass es nun möglich ist, innerhalb der Bilanzkreisabrechnung und Korrekturbilanzkreisabrechnung (bis 8 Monate nach erster Bilanzierung), jederzeit eine korrigierte Zeitreihe zu versenden, die dann auch jederzeit vom Bilanzkreisverantwortlichen positiv geprüft werden kann.
Nachrichtentypen
Folgende EDIFACT-Nachrichtentypen kommen in folgenden Verwendungszweckkombinationen zum Einsatz bei MaBiS:
Siehe auch
Bilanzkreismanagement
Weblinks
Bundesnetzagentur (Beschlusskammer 6) – Offizielle Internetseite zur MaBiS bei der Bundesnetzagentur
edi-energy.de – Offizielle Webseite der Nachrichtenformate
Anlage 4 zum Beschluss BK6-18-032 – aktuelles Dokument für MaBiS 3.0 im PDF-Format
Einzelnachweise
Energiepolitik (Deutschland)
Elektrizitätswirtschaft
Energierecht (Deutschland) | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,704 |
Q: Showing Posts of Specific Custom Post Type and Display post name and post taxonomy i found the solution wand completed the code, here's the final code for use " Display List of Posts of Custom Post type, and display Post Title with It's first taxonomy name " :
<?php
$args = array(
'numberposts' => -1,
'post_type' => 'custom-post-type',
'orderby' => 'title',
'order' => 'ASC',
array(
'taxonomy' => 'post-type-taxonomy-name',
'field' => 'slug',
),
);
$myposts = get_posts($args);
if($myposts):
foreach ($myposts as $mypost):
// get terms
$terms = get_the_terms( $mypost->ID, 'post-type-taxonomy-name' );
// showing only first category of post
$onecategory = $terms[0];
$category_link = get_category_link($onecategory->term_id);
?>
<div class="row">
<div class="col-xs-9"> //trimmed the title to only 20 Characters, you can change it or remove it
<a style="color:white;" href="<?php echo get_permalink($mypost->ID); ?>"> <?php ?> <?php echo $trimmed = mb_strimwidth( get_the_title($mypost->ID), 0, 20, ); ?> - <?php echo $onecategory->name; ?></a>
</div>
</div>
<?php endif; endforeach; wp_reset_postdata(); ?>
<?php endif; ?>
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,154 |
\section{Introduction}
Let $p>1$. The classical Hardy inequalities \begin{equation}} \newcommand{\ee}{\end{equation}
\left(\sum_{n=1}^{\infty}\left(\frac{1}{n}\sum_{k=1}^{n} |a_k|\right)^p\right)^{1/p}\le
\frac{p}{p-1} \left(\sum_{n=1}^{\infty} |a_n|^p\right)^{1/p}\ee and
\begin{equation}} \newcommand{\ee}{\end{equation}
\left(\int_{0}^{\infty}\left(\frac{1}{x}\int_{0}^{x}|f(t)|dt\right)^pdx\right)^{1/p}\le
\frac{p}{p-1} \left(\int_{0}^{\infty}| f(t)|^p\right)^{1/p}\ee (see
e.g.\cite{KMP}) can be interpreted as inclusions between the
Lebesgue space and Ces\` aro space of sequences (respectively
functions).
The Ces\` aro space of sequences is defined to be the set of all real sequences $a=(a_n)_{n\ge 1}$ that satisfy
$$
\|a\|_{\text{ces}(p)}=\left(\sum_{n=1}^{\infty}\left(\frac{1}{n}\sum_{k=1}^{n} |a_k|\right)^p\right)^{1/p}<\infty
$$
and the Ces\` aro space of functions is defined to be the set of all Lebesgue measurable real functions on $[0,\infty)$ such that
$$
\|f\|_{\text{Ces}(p)}=\left(\int_{0}^{\infty}\left(\frac{1}{x}\int_{0}^{x}|f(t)|dt\right)^pdx\right)^{1/p}<\infty.
$$
The same
interpretation is valid if the Hardy operator is substituted by
its dual. In his celebrated book \cite{B}, G. Bennet
''enhanced'' the classical Hardy inequality by substituting it
with an equality, factorizing the Ces\` aro space of sequences, with the final aim to characterize its K\"{o}the dual. He proved that a sequence $x$
belongs to the Ces\` aro space of sequences $ces(p)$ if and only if
it admits a factorization $x=y\cdot z$ with $y\in l^p$ and
$z_1^{p'}+\ldots z_n^{p'}=O(n)$, where $p'=\frac{p}{p-1}$ is
the conjugate index of $p$. This factorization gives also a better insight in the structure of Ces\` aro spaces.
The answer to the question of findind the dual space of the Ces\` aro space was given for the first time by A. Jagers \cite{J}. This problem was posed by the Dutch Academy of Sciences.
His conditions are nevertheless difficult to check. By means of factorizations a new isometric characterization, an alternative description of the dual Ces\` aro space of sequences was given by G. Bennett in \cite{B}.
In the case of functions, the same factorization results as well as the dual space of Ces\` aro space are only mentioned in
\cite[Ch. 20]{B}, for the unweighted spaces. A factorization result for the unweighted Ces\` aro function spaces was proved in \cite{AM}
where also an isomorphic description of the dual space of the Ces\` aro space of functions was given. An isometric description for the general weighted case,
in the spirit of A. Jagers was given in \cite{K}. Although the characterization is given for general weights, the condition is difficult to checked.
The results of \cite{B} have a big
impact in many parts of analysis but it seems that the
corresponding results for weighted spaces are less studied. However, in \cite{CH} can be found the following factorization result which is a weighted integral analogue of a result obtained by G. Bennett in \cite{B} for the discrete Hardy operator in the unweighted case.
\begin{theorem}} \newcommand{\et}{\end{theorem}[\cite{CH}]
Let $1<p<\infty$ and $w$, $v$ two weights such that $w>0$, $v>0$ a.e. and assume that $h$ is a non-negative function on $[0,\infty)$.
Then the function $h$ belongs to $Ces_p(w)$ if and only if it admits a
factorization $h=f \cdot g$, $f\ge 0$, $g>0$ on $[0,\infty),$ with $f\in L^p(v)$ and $g$ such that
$$
\|g\|_{w,v}=\sup_{t>0}\left(\int_t^{\infty}\frac{w(s)}{s^p}ds\right)^{1/p}\left(\int_0^{t}v^{1-p'}(s)g^{p'}(s)ds\right)^{1{/p'}}<\infty.
$$
Moreover
$$
\inf{\|f\|_{p,v} \|g\|_{w,v}} \le \|h\|_{\text{Ces}_p(w)}\le
2(p')^{1/{p'}}p^{1/p}\inf{\|f\|_{p,v}\|g\|_{w,v}},
$$
where the infimum is taken over all possible factorizations.
\et
Throughout this paper, we use standard notations and conventions. The letters $u$, $v$, $w$,..., are used for weight functions which are positive a.e. and locally integrable on $(0,\infty)$. The function $f$
is real-valued and Lebesgue measurable on $(0,\infty)$. Also for a given weight $v$ we write $V(t)=\int_0^t v(s)ds$, $0\le t<\infty$.
By $\chi_A$ we denote the
characteristic function of the measurable set $A$.
Observe that the best known form of the Hardy inequality does not follow from the above result.
The aim of this paper is to prove factorization
results of the same type for the weighted Lebesgue, Ces\` aro and Copson spaces
of functions, which enhance in the same manner the weighted Hardy inequality. The weights satisfy the natural conditions which assure the boundedness of the Hardy,
respectively the dual Hardy operators as well as some reversed conditions.
We denote by $P$ the Hardy operator and by $Q$ its
adjoint \begin{equation}} \newcommand{\ee}{\end{equation}\label{hardyop} Pf(t)=\frac{1}{t}\int_0^tf(x)dx; \quad
Qf(t)=\int_t^{\infty}\frac{f(x)}{x}dx, (t>0). \ee
For $p\ge 1$, it is known that $P$ is bounded on the weighted
Lebesgue space $L^p(w)$ if and only if $w\in M_p$ (see \cite{M}), where $M_p$ is the
class of weights for which there exists a constant $C>0$ such that, for all
$t>0$ it holds \begin{equation}} \newcommand{\ee}{\end{equation}\label{mp} M_p:
\left(\int_t^{\infty}\frac{v(x)}{x^p}dx\right)^{1/p}\left(\int_0^{t}v^{1-p'}(x)dx\right)^{1/p'}\le
C. \ee
The least constant satisfying the condition $M_p$ will be denoted
by $[v]_{M_p}$. Similarly, we denote by $m_p$ the class of weights
satisfying the reverse inequality and by $[v]_{m_p}$ the biggest
constant for which the reverse inequality holds.
The Hardy operator $P$ is
bounded on $L^1(v)$ if and only if there exists $C>0$, such that
\begin{equation}} \newcommand{\ee}{\end{equation}\label{ineq171} M_1: \int_t^{\infty}\frac{v(x)}{x}dx\le C v(t).
\ee
\noindent We denote by $[v]_{M_1}$ the least constant for which
the above inequality is satisfied. Similarly, $[v]_{m_1}$ is the
biggest constant for which the reverse inequality of
(\ref{ineq171}) is satisfied.
The corresponding condition for the boundedness of the adjoint operator $Q$ on $L^p(v)$ (see \cite{M}) is given by
\begin{equation}\label{mpstar}
M^*_p:
\left(\int_0^{t}v(x)dx\right)^{1/p}\left(\int_t^{\infty}\frac{v^{1-p'}(x)}{x^{p'}}dx\right)^{1/p'}\le
C.
\end{equation}
The least constant satisfying the $M^*_p$ condition will be denoted
$[w]_{M^*_p}$. Similarly, we denote by $m_p^*$ the class of weights
satisfying the reverse inequality and by $[w]_{m_p^*}$ the biggest
constant for which the reverse inequality holds.
The dual Hardy operator $Q$, (defined by (\ref{hardyop})) is
bounded on $L^1(v)$ if and only if there exists $C>0$, such that
\begin{equation}} \newcommand{\ee}{\end{equation}\label{ineq17} M_1^*: \frac{1}{t}\int_0^{t}v(x)dx\le C v(t).
\ee
We denote by $[v]_{M_1^*}$ the least constant for which
the above inequality is satisfied. Similarly, $[v]_{m_1^*}$ is the
biggest constant for which the reverse inequality of
(\ref{ineq17}) is satisfied.
In Section 2 we prove a factorization result for the weighted Lebesgue spaces $L^p(v)$. This result is a natural extension of Theorem 3.8 from \cite{B}.
In Section 3 we present some factorization theorems for the weighted
Ces\` aro spaces in terms of weighted Lebesgue spaces and the spaces $G_p(v)$,
for $p>1$. We treat separately the case $p=1$ which appears to be new. Moreover, our study
is motivated by similar factorization results established by G.
Bennett \cite{B}, in the unweighted case, for
spaces of sequences. As a consequence we recover the best known form of the Hardy inequality for weighted Lebesgue spaces.
We also present the optimal result for the power weights. Section 4 is
devoted to the same problems but for Copson spaces.
\section{The spaces $D_p(v)$ and $G_p(v)$}
For $p>0$, the function spaces $G_p(v)$ and $D_p(v)$ are defined by
\begin{equation}} \newcommand{\ee}{\end{equation}\label{gp}
G_p(v)=\{f :\sup_{t>0}\left(\frac{1}{V(t)}\int_0^t|f(x)|^pv(x)dx\right)^{1/p}<\infty\}
\ee
and
\begin{equation}} \newcommand{\ee}{\end{equation}\label{dp} D_p(v)=\{f : \left(\int_0^{\infty}\text{esssup}_{t\ge
x}|f(t)|^pv(x)dx\right)^{1/p} <\infty \}. \ee
These spaces are Banach spaces, for $p\ge 1$,
endowed with the norms \begin{equation}} \newcommand{\ee}{\end{equation}
\|f\|_{G_p(v)}=\sup_{t>0}\left(\frac{1}{V(t)}\int_0^t|f(x)|^pv(x)dx\right)^{1/p},\ee
respectively \begin{equation}} \newcommand{\ee}{\end{equation} \|f\|_{D_p(v)}=\left(\int_0^{\infty}\text{esssup}_{t\ge
x}|f(t)|^pv(x)dx\right)^{1/p}.\nonumber \ee
We denote by $\widehat{f}(x)={\text{essup}}_{t\ge x}|f(t)|$ the least
decreasing majorant of the absolute value of the function $f$. Obviously, the
function $f\in D_p(v)$ if and only if $\widehat{f}\in L_p(v)$ and
that $\|f\|_{D_p(v)}=\|\widehat{f}\|_{L_p(v)}$.
In what follows we need the following two lemmas.
\begin{lem}} \newcommand{\el}{\end{lem}[Hardy's lemma]\label{Hardy} Let $f,g$ be two nonnegative
real-valued functions and $h$ be a nonnegative decreasing
function. If
$$
\int_0^tf(x)dx\le \int_0^tg(x)dx, \quad \text{for any } t>0
$$
then
$$
\int_0^\infty f(x)h(x)dx\le \int_0^\infty g(x)h(x)dx.
$$
\el
\begin{proof}
See \cite[Proposition 3.6]{BS}.
\end{proof}
\begin{lem}} \newcommand{\el}{\end{lem}\label{level} Let $h$ be a nonnegative measurable function on
$(0,\infty),$ such that
$$
\lim_{x\rightarrow \infty}\frac{\int_0^xh(t)v(t)dt}{\int_0^x
v(t)dt}=0.
$$
Then there exists a nonnegative decreasing function $h^{\circ}$ on $(0,\infty)$, called the
level function of $h$ with respect to the measure $v(x)dx$ satisfying the following conditions:
\begin{enumerate}
\item $\int_0^x h(t)v(t)dt\le \int_0^x h^{\circ}(t)v(t)dt;$
\item up to a set of measure zero, the set $\{x:h(x)\ne
h^{\circ}(x)\}=\cup_{k=1}^{\infty}I_k$, where $I_k$ are bounded disjoint intervals such that
$$
\int_{I_k}h^{\circ}(t)v(t)dt=\int_{I_k}h(t)v(t)dt
$$
and $h^{\circ}$ is constant on $I_k$, i.e. $h^{\circ}(t)=\frac{\int_{I_k}hv}{\int_{I_k}v}.$
\end{enumerate}
\el
\begin{proof}
For a proof see e.g. \cite{BKS} or \cite{S}.
\end{proof}
We are now ready to prove the main theorem of this section which contains one of the possible factorizations of weighted Lebesgue spaces.
\begin{theorem}} \newcommand{\et}{\end{theorem} If $0<p\le\infty$, then
a function $h\in L^p(v)$ if and only if $f$ admits a factorization $h=f\cdot g$ such that $f\in D_p(v) $ and $g\in G_p(v)$.
Moreover,
$$
\|h\|_{L^p(v)}=\inf\{ \|f\|_{D_p(v)}\|g\|_{G_p(v)}\},
$$ where the infimum is taken over all possible factorizations $h=f\cdot g$ with $f\in D_p(v) $ and $g\in G_p(v)$. \et
\begin{proof}
The case $p=\infty$ is trivial. By homogeneity, it is sufficient
to prove the theorem for $p=1$.
We first prove that $D_1(v)\cdot
G_1(v) \subseteq L^1{(v)}$. Suppose that $h$ admits a factorization
$h=f\cdot g$ with $f\in D_1(v)$, $g\in G_1(v)$. Then $$
\|h\|_{L^1(v)}=\int_0^\infty |f(x)g(x)|v(x)dx\le
\int_0^{\infty}\widehat{f}(x)|g(x)|v(x)dx. $$
From definition
(\ref{gp}) we have the inequality
$$
\int_0^t |g(x)|v(x)dx\le \|g\|_{G_1(v)}\int_0^t v(x)dx, \quad \text{for any } t>0
$$
which together with Lemma \ref{Hardy} give
$$
\int_0^{\infty}\widehat{f}(x)|g(x)|v(x)dx
\le\|g\|_{G_1(v)}\int_0^{\infty}\widehat{f}(x)v(x)dx=\|g\|_{G_1(v)}\|f\|_{D_1(v)}.
$$
Thus we have that $D_1(v)\cdot G_p(v)\subseteq L^1(v)$ and
that
$$\|h\|_{L^1(v)}\le\inf\{\|g\|_{G_1(v)}\|f\|_{D_1(v)}\},$$ where
the infimum is taken over all possible factorizations $h=f\cdot g$.
Conversely let $h$ be a nonnegative function such that $h\in L^1(v)$.
We set $f(x)=h^{\circ}(x)$, $x>0$, where $h^{\circ}(x)$ is the level
function of $h$ with respect to the measure $v(x)dx$, as in Lemma
\ref{level}. Since $h^{\circ}(x)$ is a decreasing function by the
definition of the space $D_1(v)$ and by Lemma \ref{level} we have
that
$$
\|f\|_{D_1(v)}=\|h^{\circ}\|_{D_1(v)}=\|h^{\circ}\|_{L_1(v)}=\|h\|_{L_1(v)}.
$$
We define $g(x)=\frac{h(x)}{h^{\circ}(x)}$ for any $x>0$. If $t\in I_n$, for some $n$, we have
\begin{align*}
\frac{1}{V(t)}\int_0^t g(x)v(x)dx&=\frac{1}{V(t)}
\int_0^t\frac{h(x)}{h^{\circ}(x)}v(x)dx\\
&=\frac{1}{V(t)}\left(\int_E\frac{h(x)}{h^{\circ}(x)}v(x)dx+\int_{\cup_{k=1}^{n-1}I_k}\frac{h(x)}{h^{\circ}(x)}v(x)dx\right.\\
&\left.+ \int_{a_n}^t \frac{h(x)}{h^{\circ}(x)}v(x)dx\right),
\end{align*}
where $E=\{x\in (0,t): h(x)=h^{\circ}(x)\}$ and $I_k =(a_k,b_k)$
are the disjoint intervals from Lemma \ref{level}. Hence, by
Lemma \ref{level} we get that
$$
\int_E\frac{h(x)}{h^{\circ}(x)}v(x)dx=\int_E v(x)dx,
$$
$$\int_{I_k} \frac{h(x)}{h^{\circ}(x)}v(x)dx= \int_{I_k} v(x)dx$$
and
$$
\int_{a_n}^t \frac{h(x)}{h^{\circ}(x)}v(x)dx\le \int_{I_n} v(x)dx.
$$
Hence
$$
\|g\|_{G_1(v)}\le 1.
$$
Since $h=f\cdot g$, with $f\in D_1(v)$ and $g\in G_1(v)$ we have
that $L^1(v)\subseteq D_1(v)\cdot G_1(v)$ and
$$
\|h\|_{L^1(v)}=\|f\|_{D_1(v)}\ge
\|f\|_{D_1(v)}\cdot \|g\|_{G_1(v)}\ge\inf\{
\|f\|_{D_1(v)}\cdot \|g\|_{G_1(v)}\},
$$
where the infimum is taken over all possible factorizations
$h=f\cdot g$. It is easy to see from this proof that the infimum is actually attained and this concludes the proof of the theorem.
\end{proof}
\section{Factorization of the weighted Ces\` aro spaces}
In this section we present a factorization of the weighted Ces\` aro
spaces $\text{Ces}_p(v)$. We treat separately the cases $p>1$ and $p=1$. The weighted Ces\` aro spaces of
functions, ${\text{Ces}}_p(v)$ is defined to be the space of all Lebesgue measurable real functions on $[0,\infty)$ such that
$$
\|f\|_{\text{Ces}_p(v)}=
\left(\int_0^{\infty}\left(\frac{1}{x}\int_0^x|f(t)|dt\right)^pv(x)dx\right)^{1/p}<\infty.
$$
These spaces are obviously Banach spaces, for $p\ge
1$ and if the weight $v$ satisfies (\ref{mp}) we have that $L^p(v)\subseteq \text{Ces}_p(v)$. We denote by
\begin{equation}} \newcommand{\ee}{\end{equation}\label{fact1}!h!_{p,v}= \inf\{\|f\|_{L^p(v)}\|g\|_{G_{p'}(v^{1-p'})} \}\ee
where
the infimum is taken over all possible decompositions of $h=f\cdot
g$, with $f\in L^p(v)$ and $g\in G_{p'}(v^{1-p'})$.
\begin{theorem}} \newcommand{\et}{\end{theorem} \label{mains2} Let $p>1$ and $v$ belongs to the class $M_p$ and $m_p$.
The function $h$ belongs to $Ces_p(v)$ if and only if it admits a
factorization $h=f \cdot g$, with $f\in L^p(v)$ and $g\in
G_{p'}(v^{1-p'})$. Moreover
$$
[v]_{m_p}!h!_{p,v} \le \|h\|_{\text{Ces}_p(v)}\le
{(p')}^{1/{p'}}p^{1/p}[v]_{M_p}!h!_{p,v}.
$$
\et
\begin{proof}
Let $f\in L^p(v)$ and $g\in G_{p'}(v^{1-p'})$. First we prove that
the function $h=f\cdot g\in {\text{Ces}}_p(v)$ and the right-hand side inequality. Let $u$
be an arbitrary decreasing function. By H\"{o}lder's
inequality we get
\begin{equation}} \newcommand{\ee}{\end{equation}\label{eq11}
\int_0^t |h(x)|dx=\int_0^t |f(x)g(x)|dx\le
\ee
\begin{equation}} \newcommand{\ee}{\end{equation}\nonumber \left(\int_0^t
|f(x)|^pv(x)u^{-p}(x)dx\right)^{1/p}\left(\int_0^t
|g(x)|^{p'}v^{1-p'}(x)u^{p'}(x)dx\right)^{1/p'}. \ee
\noindent On the other hand, by Lemma \ref{Hardy} we obtain
\begin{align}\label{eq12}
\left(\int_0^t |g(x)|^{p'}v^{1-p'}(x)u^{p'}(x)dx\right)^{1/p'}&\le
\|g\|_{G_{p'}(v^{1-p'})}\\
&\cdot \left(\int_0^tv^{1-p'}(x)u^{p'}(x)dx\right)^{1/p'}{\notag}.
\end{align}
Hence, by (\ref{eq11}) and (\ref{eq12}), integrating from 0 to
$\infty$ and by applying Fubbini's theorem we have
\begin{align*}
\int_0^{\infty}\left(\frac{1}{t}\int_0^{t}|h(x)|dx\right)^p & v(t)dt
\le\|g\|^p_{G_{p'}(v^{1-p'})}\int_0^{\infty}\left(\int_0^{t}|f(x)|^p
v(x) u^{-p}(x) dx\right)\\
&\cdot \left(\int_0^{t}v^{1-p'}(x)u^{p'}(x)dx \right)^{p-1}t^{-p}v(t)dt\\
&=\|g\|^p_{G_{p'}(v^{1-p'})}\int_0^{\infty}|f(x)|^pv(x)u^{-p}(x)\\
&\cdot \left(\int_x^{\infty}t^{-p}v(t)\left(\int_0^{t}v^{1-p'}(x)u^{p'}(x)dx\right)^{p-1}dt\right)
dx.
\end{align*}
\noindent Taking $u(t)=\left(\int_0^t
v^{1-p'}(s)ds\right)^{-1/{(pp')}}$, since
$v\in M_p$ we get
$$
\|h\|_{Ces_p(v)}\le
p^{1/p}{(p')}^{1/{p'}}[v]_{M_p}\|g\|_{G_{p'}(v^{1-p'})}\|f\|_{L^{p}(v)}.
$$
Hence $h\in {\text{Ces}}_p(v)$ and
$$\|h\|_{{\text{Ces}}_p(v)}\le
p^{1/p}{(p')}^{1/{p'}}[v]_{M_p}\inf\{\|f\|_{L^{p}(v)}\cdot \|g\|_{G_{p'}(v^{1-p'})}\},$$
where the infimum is taken over all possible factorizations of
$h$. This completes the first part of the proof of the theorem.
For the reversed embedding, i.e. ${\text{Ces}}_p(v)\subseteq
L^p(v)\cdot G_{p'}(v^{1-p'})$, let $h\in {\text{Ces}}_p(v)$ and set
$w(t):=\frac{1}{v(t)}\int_t^{\infty}\frac{v(x)}{x}\left(\frac{1}{x}\int_0^x
|h(s)|ds\right)^{p-1}dx$, $t>0$. We may assume, without loss of generality
that $v(t)> 0$, for any $t>0$. We define
$f(t)=|h(t)|^{1/p}w^{1/p}(t){\rm \, sign \;}} \newcommand{{\mathbb{R}}} \def\oo{{\infty}} \def\a{{\alpha}}{\mathbb{R} h(t)$ and
$g(t)=|h(t)|^{1/p'}w^{-1/p}(t)$. It is easy to see that \begin{equation}} \newcommand{\ee}{\end{equation}
\|f\|_{L^p(v)}=\|h\|_{{\text{Ces}}_p(v)}<\infty. \ee
By H\"{o}lder's inequality we have
\begin{align}\label{eq13}
\left(\int_0^t g^{p'}(x)v^{1-p'}(x)dx\right)^p&\le
\left(\int_0^t |h(x)|dx\right)^{p-1}\\
&\cdot\left(\int_0^t
|h(x)|w^{-p'}(x)v^{-p'}(x)dx\right) \notag.
\end{align}
Multiplying the inequality
(\ref{eq13}) by $\int_t^{\infty}x^{-p}v(x)dx$ and using that
$w(t)v(t)$ is a decreasing function we get
\begin{align*}
\left( \int_t^{\infty}\frac{v(x)}{x^p}dx\right) &\left(\int_0^t
g^{p'}(x)v^{1-p'}(x) dx\right)^p
\le\left(\int_t^{\infty}\frac{v(x)}{x^p}\left(\int_0^x
|h(s)|ds\right)^{p-1}dx\right)\\
&\cdot \left(\int_0^t
|h(x)|w^{-p'}(x)v^{-p'}(x)dx\right)\\
&=w(t)v(t)\left(\int_0^t
|h(x)|w^{-p'}(x)v^{-p'}(x)dx\right)\\
&\le \int_0^t
|h(x)|w^{1-p'}(x)v^{1-p'}(x)dx.
\end{align*}
Since
$g^{p'}(x)=|h(x)|w^{1-p'}(x)$ we obtain
\begin{align*}
\left(\frac{1}{\int_0^t v^{1-p'}(x)dx }\int_0^t
g^{p'}(x)v^{1-p'}(x)dx\right)^{1/p'}&\le
\left(\int_0^t
v^{1-p'}(x)dx)\right)^{-1/p'}\\
&\cdot\left(\int_t^{\infty}\frac{v(x)}{x^p}dx\right)^{-1/p}.
\end{align*}
Hence \begin{equation}} \newcommand{\ee}{\end{equation}\nonumber
\sup_{t>0}\left(\frac{1}{\int_0^t
v^{1-p'}(x)dx }\int_0^t g^{p'}(x)v^{1-p'}(x)dx\right)^{1/p'}
\le\frac{1}{[v]_{m_p}} \ee
which shows that $g$ belongs to
$G_{p'}(v^{1-p'})$ and
$$\|h\|_{\text{Ces}_p(v)}=\|f\|_{L_p(v)}\ge
[v]_{m_p}\|f\|_{L_p(v)}\|g\|_{G_{p'}(v^{1-p'})}.$$
In this way, we
get the left-hand side inequality.
\end{proof}
If we take $g(x)=1$, $x>0$ the right-hand side inequality implies the best form of the weighted Hardy inequality
for $1<p<\infty$ see e.g. \cite{KMP}.
Observe also that the infimum is attained.
In particular, we
denote by $L_{\alpha}^p$ the weighted Lebesgue space with the power
weight $v(t)=t^{\alpha}$ and in a similar way the spaces
$G_{p,\alpha}$ and $\text{Ces}_{p,\alpha}$. In analogy with the
general case we also denote by
$$!h!_{p,\alpha}=\inf\|f\|_{L^p_{\alpha}}\|g\|_{G_{p',{\alpha(1-p')}}},$$
where the infimum is taken over all possible decompositions of
$h=f\cdot g$, with $f\in {L^p_{\alpha}}$ and $g\in
{G_{p',{\alpha(1-p')}}}$.
\begin{corollary} Let $p>1$ and $-1<\alpha<p-1$.
The function $h$ belongs to $\text{Ces}_{p,\alpha}$ if and only if
it admits a factorization $h=f \cdot g$, with $f\in
{L^p_{\alpha}}$ and $g\in {G_{p',{\alpha(1-p')}}}$. Moreover
$$
\left(\frac{1}{p}\right)^{1/p}\left(\frac{1}{p'}\right)^{1/{p'}}
\frac{p}{p-\alpha-1}!h!_{p,\alpha} \le \|h\|_{Ces_{p,\alpha}}\le
\frac{p}{p-\alpha-1}!h!_{p,\alpha}.
$$
\end{corollary}
\begin{proof}
Take $v(t)=t^{\alpha}$ in Theorem \ref{mains2}. The constant in
the right hand-side inequality is optimal since it is the best
constant in Hardy's inequality with a power weight (see e.g \cite{KMP} p. 23).
\end{proof}
For the sake of completeness, as well as for the independent interest we
present separately the case $p=1$, although the proof of the main
result in this case follows the same ideas as for $p>1$.
By $L^{\infty}$ we denote, as usual,
the space of all measurable functions which satisfy the condition
$$
\|g\|_{\infty}:=\text{esssup}_{x>0}|g(x)|<\infty.
$$
As before, $$!h!_{1,v}= \inf\|f\|_{L^1(v)}\|g\|_{\infty}$$
where the infimum is taken over all possible factorizations of $h=f\cdot
g$, with $f\in L^1(v)$ and $g\in L^{\infty}$.
\begin{theorem}} \newcommand{\et}{\end{theorem}\label{teoremweak} Let $v$ belong to $M_1$ and $m_1$. The function $h$ belongs to
${\text{Ces}}_1(v)$ if and only if it admits a factorization $h=f
\cdot g$, with $f\in L_1(v)$ and $g\in G_{\infty}$. Moreover
$$
[v]_{m_1}!h!_{1,v}\le \|h\|_{{\text{Ces}_1}{(v)}}\le
[v]_{M_1}!h!_{1,v}.
$$
\et
\begin{proof}
Let $f\in L_1(v)$ and $g\in L^{\infty}$. We prove that the
function $h=fg$ belongs to ${\text{Ces}}_1(v)$. By H\"{o}lder's
inequality and since $g\in L^{\infty}$ we get
\begin{equation}} \newcommand{\ee}{\end{equation}\label{eq1011}
\int_0^{\infty}\left(\frac{1}{t}\int_0^{t}h(s)ds\right)v(t)dt
\le\|g\|_{{\infty}}\int_0^{\infty}\left(\frac{1}{t}\int_0^{t}f(x)dx
\right)v(t)dt. \ee
\noindent By Fubini's theorem and taking into account that $v\in
M_1$ we have that
$$
\|h\|_{{\text{Ces}}_1(v)}\le
[v]_{M_1}\|g\|_{{\infty}}\|f\|_{L_{1}(v)},
$$
for any $f$, $g$ as above. Hence $h\in \text{Ces}_1(v)$ and
$$\|h\|_{Ces_1(v)}\le
[v]_{M_1}\inf\|g\|_{{\infty}}\|f\|_{L_{1}(v)},$$ where infimum
is taken over all possible factorizations of $h$. This completes
the first part of the proof.
Conversely, let $h\in {\text{Ces}}_1(v)$ and
$w(t)=\frac{1}{v(t)}\int_t^{\infty}\frac{v(x)}{x}dx$. We may assume, without loss of generality that $v(t)>0$, for all $t>0.$\\
Let $f(t)=|h(t)|w(t){\rm \, sign \;}} \newcommand{{\mathbb{R}}} \def\oo{{\infty}} \def\a{{\alpha}}{\mathbb{R} h(t)$ and $g(x)=\frac{1}{w(x)}$. It is
easy to see that \begin{equation}} \newcommand{\ee}{\end{equation} \nonumber
\|f\|_{L_1(v)}=\|h\|_{{\text{Ces}}_1(v)}<\infty.
\ee
\noindent Since $v\in m_1$, $g$ belongs to $L_{\infty}$ and
\begin{equation}} \newcommand{\ee}{\end{equation}\nonumber\|g\|_{{\infty}}\le \frac{1}{[v]_{m_1}}. \ee
Moreover, $\|h\|_{{\text{Ces}}_1(v)}=\|f\|_{L_1(v)}\ge
[v]_{m_1}\|f\|_{L_1(v)}\|g\|_{{\infty}}$ and we get the
left-hand side inequality of the theorem. The proof is complete.
\end{proof}
\section{Factorization of the weighted Copson spaces}
In the same manner, in this section we present the factorizations of the weighted
Copson space, namely the space
$$
{\text{Cop}}_p(v)=\{f:\int_0^{\infty}\left(\int_t^{\infty}\frac{|f(x)|}{x}dx\right)^pv(t)dt<\infty\}.
$$
Let \begin{equation}} \newcommand{\ee}{\end{equation}\label{gstarp}
G^{*}_p(v)=\{f :\sup_{t>0}\left(\frac{1}{\int_t^{\infty}v(x)x^{-p}dx}\int_t^{\infty}f(x)^pv(x)x^{-p}dx\right)^{1/p}<\infty\}
\ee
To prove the main result we need the following Lemma.
\begin{lem}} \newcommand{\el}{\end{lem}\label{Hardy1} Let $f,g$ be two non-negative real-valued
functions and $h$ be a non-negative increasing function. If
$$
\int_t^{\infty}f(x)dx\le \int_t^{\infty}g(x)dx, \quad t>0
$$
then
$$
\int_t^{\infty}f(x)h(x)dx\le \int_t^{\infty}g(x)h(x)dx.
$$
\el
\begin{proof}
The proof follows by a change of variable and Lemma \ref{Hardy}.
\end{proof}
We denote by
\begin{equation}} \newcommand{\ee}{\end{equation}\label{exc}
!!h!!_{p,v}=\inf \|f\|_{\text{L}_p(v)} \|g\|_{\text{G}^{*}_{p'}(v^{1-p'})}
\ee
where the infimum is taken over all possible factorizations of $h=f\cdot g.$
\begin{theorem}} \newcommand{\et}{\end{theorem} \label{mains3} Let $p>1$ and $v$ belong to the class $M_p^*$
and $m_p^*$.
The function $h$ belongs to $\text{Cop}_p(v)$ if and only if it
admits a factorization $h=f \cdot g$, with $f\in L^p(v)$ and $g\in
\text{G}^{*}_{p'}(v^{1-p'})$. Moreover
$$
[v]_{m_p^*}!!h!!_{p,v} \le \|h\|_{\text{Cop}_p(v)}\le
{p'}^{1/{p'}}p^{1/p}[v]_{M_p^*}!!h!!_{p,v}.
$$
\et
\begin{proof}
Let $f\in L^p(v)$ and $g\in \text{G}^{*}_{p'}(v^{1-p'}) $.
We show
first that the function $h=fg\in {\text{Cop}}_p(v)$. Let $u$ be an
arbitrary positive increasing function. H\"{o}lder's inequality
gives
\begin{equation}} \newcommand{\ee}{\end{equation}\label{eq101}
\int_t^{\infty} \frac{f(x)g(x)}{x}dx\le
\ee
\begin{equation}} \newcommand{\ee}{\end{equation}\nonumber \left(\int_t^{\infty}
f^p(x)v(x)u^{-p}(x)dx\right)^{1/p}\left(\int_t^{\infty}
g^{p'}(x)\frac{v^{1-p'}(x)}{x^{p'}}u^{p'}(x)dx\right)^{1/p'}. \ee
\noindent By Hardy's Lemma \ref{Hardy1} we obtain
\begin{align*}
\left(\int_t^{\infty}
g^{p'}(x)\frac{v^{1-p'}(x)}{x^{p'}}u^{p'}(x)dx\right)^{1/p'}&\le
\|g\|_{\text{G}^{*}_{p'}(v^{1-p'})}^p\\
& \cdot\left(\int_t^{\infty}\frac{v^{1-p'}(x)}{x^{p'}}u^{p'}(x)dx\right)^{1/p'}.
\end{align*}
\noindent Hence, multiplying (\ref{eq101}) by $v(t)$, raising to $p$
and integrating from 0 to $\infty$, we get
\begin{align*}
\int_0^{\infty}&\left(
\int_t^{\infty}\frac{h(x)}{x}dx\right)^pv(t)dt \le\|g\|^p_{G_{p'}({v^{1-p'}})}\\
&\cdot \int_0^{\infty}v(t)\left(\int_t^{\infty}f^p(x)
v(x)u^{-p}(x)dx\right)
\left(\int_t^{\infty}\frac{v^{1-p'}(x)}{x^{p'}}u^{p'}(x)dx\right)^{p-1}dt.
\end{align*}
\noindent By Fubini's theorem we have
\begin{align*}
\int_0^{\infty}&\left(\int_t^{\infty}\frac{h(s)}{s}ds\right)^pv(t)dt
\le\|g\|^p_{G_{p'}({v^{1-p'}})}\\
&\cdot\int_0^{\infty}f^p(x)v(x)
\left(\int_0^xv(t)
\left(\int_t^{\infty}\frac{v^{1-p'}(s)}{s^{p'}}u^{p'}(s)ds\right)^{p-1}dt\right)u^{-p}(x)dx.
\end{align*}
\noindent Taking
$u(t)=\left(\int_t^{\infty}\frac{v^{1-p'}(x)}{x^{p'}}\right)^{-1/{pp'}}$,
in the above inequality and
since
$$
\int_t^{\infty}\frac{v^{1-p'}(s)}{s^{p'}}u^{p'}(s)ds=p'\left(\int_t^{\infty}\frac{v^{1-p'}(s)}{s^{p'}}(s)ds\right)^{1/p'}dx
$$
we have that
\begin{align*}
\int_0^{\infty}f^p(x)&v(x) \left(\int_0^xv(t)
\left(\int_t^{\infty}\frac{v^{1-p'}(s)}{s^{p'}}u^{p'}(s)ds\right)^{p-1}dt\right)u^{-p}(x)dx\\
&=(p')^{p-1}\int_0^{\infty}f^p(x)v(x)\left(\int_0^x v(t)
\left(\int_t^{\infty}\frac{v^{1-p'}(s)}{s^{p'}}ds\right)^{\frac{p-1}{p'}}dt\right)\\
&\cdot\left(\int_x^{\infty}\frac{v^{1-p'}(s)}{s^{p'}}ds\right)^{1/p'}.
\end{align*}
By the definition of $M_p^*$ we get
\begin{align*}
&\int_0^{\infty}\left(\int_t^{\infty}\frac{h(s)}{s}ds\right)^pv(t)dt
\le (p')^{p-1}\|v\|^{p-1}_{M_p^*}\\
& \cdot\int_0^{\infty}f^p(x)v(x)\left(\int_0^x
v(t)\left(\int_0^tv(s)ds\right)^{-1/{p'}}dt\right)\left(\int_x^{\infty}\frac{v^{1-p'}(s)}{s^{p'}}ds\right)^{1/p'}dx\\
&=(p')^{p-1}p\|v\|^{p-1}_{M_p^*}\int_0^{\infty}f^p(x)v(x)\left(\int_0^x
v(t)\right)^{1/p}\left(\int_x^{\infty}\frac{v^{1-p'}(s)}{s^{p'}}ds\right)^{1/p'}dx\\
&\le(p')^{p-1}p\|v\|^{p}_{M_p^*}\int_0^{\infty}f^p(x)v(x)dx,
\end{align*}
since
$$
\frac{d}{dx}\left(\int_0^xv(t)dt\right)^{1/p}=\frac{1}{p}\left(\int_0^xv(t)dt\right)^{1/p-1}v(x).
$$
\noindent Hence
$$
\|h\|_{\text{Cop}_p(v)}\le
p^{1/p}{p'}^{1/{p'}}[v]_{M_p^*} \|g\|_{\text{G}^{*}_{p'}(v^{1-p'})}\|f\|_{L_{p}(v)}.
$$
for any $f$, $g$ as above.
Hence $h\in {\text{Cop}}_p(v)$ and
$$\|h\|_{{\text{Cop}}_p(v)}\le p^{1/p}{p'}^{1/{p'}}[v]_{M_p^*}\inf \|g\|_{\text{G}^{*}_{p'}(v^{1-p'})}\|f\|_{L_{p}(v)}$$
where the infimum is taken over all possible factorizations of
$h$ which gives the left-hand side inequality of the theorem.
For the reverse embedding, i.e. ${\text{Cop}}_p(v)\subset
L_p(v)G^*_{p'}(v^{1-p'})$, let $h\in {\text{Cop}}_p(v)$ and
$w(t):=\frac{1}{tv(t)}\int_0^{t}v(x)\left(\int_{x}^{\infty}\frac{h(s)}{s}ds\right)^{p-1}dx
$, if $v\ne 0$. Define $f(t)=|h|^{1/p}(t)w^{1/p}(t){\rm \, sign \;}} \newcommand{{\mathbb{R}}} \def\oo{{\infty}} \def\a{{\alpha}}{\mathbb{R} h(t)$ and
$g(t)=|h|^{1/p'}(t)w^{-1/p}(t)$. An easy application of Fubini
theorem gives \begin{equation}} \newcommand{\ee}{\end{equation}\nonumber
\|f\|_{L^p(v)}=\|h\|_{{\text{Cop}}_p(v)}<\infty. \ee
By H\"{o}lder's inequality and the definition of $g$ we have
\begin{equation}} \newcommand{\ee}{\end{equation}\label{eq103}
\left(\int_x^{\infty} g^{p'}(t)\frac{v^{1-p'}(t)}{t^{p'}} dt\right)^p\le
\left(\int_x^{\infty} \frac{|h(t)|}{t}dt\right)^{p-1}
\int_x^{\infty}\frac{|h(t)|}{t}w^{-p'}(t)\frac{v^{-p'}(t)}{t^{p'}}dt.\ee
\noindent We estimate first the right-hand side term of the inequality
(\ref{eq103}) multiplied by $\int_0^{x}v(t)dt$.
\begin{equation}} \newcommand{\ee}{\end{equation}\nonumber \left(\int_0^x v(t)dt\right)\left(\int_x^{\infty}
\frac{|h(t)|}{t}dt\right)^{p-1}
\int_x^{\infty}\frac{|h(t)|}{t}w^{-p'}(t)\frac{v^{-p'}(t)}{t^{p'}}dt
\ee
\begin{equation}} \newcommand{\ee}{\end{equation}\nonumber \le \int_0^xv(t)\left(\int_t^{\infty}
\frac{|h(s)|}{s}ds\right)^{p-1}dt
\int_x^{\infty}\frac{|h(t)|}{t}w^{-p'}(t)\frac{v^{-p'}(t)}{t^{p'}}dt
\ee
\begin{equation}} \newcommand{\ee}{\end{equation}\nonumber =xw(x)v(x)\left(\int_x^{\infty}
h(t)w^{-p'}(t)v^{-p'}(t)dt\right)\le \int_x^\infty
h(t)w^{1-p'}(t)v^{1-p'}(t)t^{-p'}dt, \ee since, by definition,
$xw(x)v(x)$ is an increasing function. By using that
$g^{p'}(x)=h(x)w^{1-p'}(x)$ we get
$$
\left(\frac{1}{\int_x^\infty \frac{v^{1-p'}(t)}{t^{p'}}dx
}\int_x^\infty g^{p'}(t)\frac{v^{1-p'}(t)}{t^{p'}}dt\right)^{1/p'}
$$
$$\le\frac{1}{\left(\int_0^x v(t)dt
\right)^{1/p}\left(\int_x^{\infty}t^{-p'}v^{1-p'}(t)dt\right)^{1/p'}}.
$$
Hence \begin{equation}} \newcommand{\ee}{\end{equation}\label{last}
\sup_{t>0}\left(\frac{1}{\int_t^{\infty}
v^{1-p'}(x)x^{-p'}dx }\int_t^{\infty} g^{p'}(x)v^{1-p'}(x)x^{-p'}dx\right)^{1/p'}
\le\frac{1}{[v]_{m_p^*}} \ee
which means that $g$ belongs to $ {\text{G}^{*}_{p'}(v^{1-p'})}$. Moreover,\\
$\|h\|_{\text{Cop}_p(v)}=\|f\|_{L^p(v)}\ge
[v]_{m_p^*}\|f\|_{L^p(v)} \|g\|_{\text{G}^{*}_{p'}(v^{1-p'})}$. In this way the left-hand side inequality is proved.
\end{proof}
\noindent The space $\text{Cop}_{p,\alpha}$ is the Copson weighted space with the weight $t^{\alpha}$. We have
the following result for the case of a power weight.
\begin{corollary} Let $p>1$ and $\alpha>-1$.
The function $h$ belongs to $\text{Cop}_{p,\alpha}$ if and only if
it admits a factorization $h=f \cdot g$, with $f\in
{L^p_{\alpha}}$ and $g\in {G_{p',{\alpha(1-p')}}}$. Moreover
$$
\frac{(p-1)^{1/p'}}{\alpha+1}!h!_{p,\alpha} \le \|h\|_{{p,\alpha}}\le
\frac{p}{\alpha+1}!h!_{p,\alpha}.
$$ The constants in both inequalities are optimal.
\end{corollary}
\begin{proof}
Take $v(t)=t^{\alpha}$ in Theorem \ref{mains3}. The constant in
the right hand-side inequality is optimal since it is the best
constant in Hardy inequality (see e.g \cite{KMP}) and the optimality of the constant in the left-hand side follows if we take $h(x)=\chi_{(a-\varepsilon,a+\varepsilon)}$ and let then $\varepsilon\rightarrow 0$
and $a \rightarrow\infty$.
\end{proof}
\noindent We present now the case $p=1$.
\noindent The dual Hardy operator $Q$, (defined by (\ref{hardyop})) is
bounded on $L^1(v)$ if and only if there exists $C>0$, such that
\begin{equation}} \newcommand{\ee}{\end{equation}\label{ineq_ultima} M_1^*: \frac{1}{t}\int_0^{t}v(x)dx\le C v(t).
\ee
\noindent We denote by $[v]_{M_1^*}$ the least constant for which
the above inequality is satisfied. Similarly, $[v]_{m_1^*}$ is the
biggest constant for which the reverse inequality of
(\ref{ineq_ultima}) is satisfied.
\begin{theorem}} \newcommand{\et}{\end{theorem} Let $v$ belong to $M_1^*$ and $m_1^*$. The function $h$ belongs to
${\text{Cop}}_1(v)$ if and only if it admits a factorization $h=f
\cdot g$, with $f\in L_1(v)$ and $g\in G_{\infty}$. Moreover
$$
[v]_{m_1^*}!h!_{1,v}\le \|h\|_{{\text{Cop}_1}{(v)}}\le
[v]_{M_1^*}!h!_{1,v}.
$$
and the constants are optimal.
\et
\begin{proof}
The proof is similar with that of Theorem ~\ref{teoremweak}.
\end{proof}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 518 |
DOCTOR WHO DRUGGED Dementia Patient's Coffee Without Her Knowledge, Gave Her Lethal Injection, While Family Restrained Her, Acquitted By Court
By Patty McMurray | Sep 13, 2019
Many pro-abortion advocates say killing a baby is okay if there's even the slightest chance the baby could be born imperfect—that's it's the mother's choice whether or not she wants to allow her baby to live. So, what about adults, who through no fault of their own, develop a serious mental or physical illness—should they also be killed without their permission? What about if they previously expressed the desire to be euthanized, but then later changed their mind?
Accoriding to Medical Express – The doctor, who was not named in court, was cleared of any wrongdoing in carrying out euthanasia three years ago on a 74-year-old woman. The patient was given fatal Accordingrugs despite some indications she might have changed her mind since declaring in writing that she wanted euthanasia.
The Daily Wire writes: In the case of this specific Dutch woman with dementia, she never once gave an express request to be euthanized. In her will, which was renewed about a year before her death, the woman said she would like to be euthanized "whenever I think the time is right." And when she was asked if she wanted to be euthanized, she reiterated multiple times that her suffering was not bad enough to where she wanted to be killed:
"The 74-year-old woman had renewed her living will about a year before she died, writing that she wanted to be euthanized 'whenever I think the time is right.' Later, the patient said several times in response to being asked if she wanted to die: 'But not just now, it's not so bad yet!' according to a report from the Dutch regional euthanasia review committee."
She was killed, anyway.
The court ruled that in rare cases of euthanasia that were being performed on patients with severe dementia—and who had earlier made a written request for euthanasia—the doctor "did not have to verify the current desire to die."
Suzanne van de Vathorst, an associate professor who specializes in ethics and end-of-life issues at Erasmus University, said euthanizing patients with severe dementia puts a considerable burden on doctors.
"There's a living, breathing person in front of you who is not aware that you're performing euthanasia," she said. "This is a very difficult thing to do and we cannot oblige doctors to do this."
The Netherlands is one of five countries that allow doctors to kill patients at their request, and one of two, along with Belgium, that grant the procedure for people with mental illness.
Judges at The Hague District Court ruled that the doctor met all criteria for carrying out euthanasia under the Dutch law legalizing mercy killing by physicians. Applause broke out among the dozens of people who attended the hearing.
Save up on MyPillow products. Use promo code FedUp at checkout and save 50% on individual MyPillow Towels.
The doctor was accused of not acting with due care because, prosecutors alleged, she made insufficient efforts to find out whether the patient still wanted to die. To carry out the euthanasia, the physician drugged the patient's coffee without her knowledge and then had family members restrain the woman while delivering the fatal injection.
According to the National Review– Demonstrating the consequences of accepting the premise that eliminating suffering justifies eliminating the sufferer, Dutch psychiatrists killed 83 of their mentally ill patients in 2017 — up from twelve in 2012 and 43 in 2014. That's one heck of an awful trend line.
It is also worth noting that the Dutch — like the Belgians — sometimes conjoin euthanasia homicides of the mentally ill with voluntary organ harvesting.
Increased conjoining of euthanasia and organ harvesting can be expected soon. The Dutch recently passed a "presumed-consent-to-donate-organs" law — meaning that everyone is an organ donor unless they have explicitly opted out. That will surely include the euthanized.
Sadly, unborn babies have no say about whether or not they're allowed to live, but surely most people would agree that humans who've already been born shouldn't be killed against their will—-right? | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,111 |
{"url":"https:\/\/ashtavakra.org\/algebra\/determinants\/","text":"66. Determinants\u00b6\n\nLet $$a, b, c, d$$ be any four numbers, real or complex, the symbol\n\n$\\begin{split}\\begin{vmatrix} a & b\\\\ c & d\\\\ \\end{vmatrix}\\end{split}$\n\ndenotes $$ad - bc$$ and is called a determinant of second order. $$a, b, c, d$$ are called elements of the determinant and $$ad - bc$$ is called value of the determinant.\n\nAs you can see, the elements of a determinant are positioned in the form of a square in its designation. The diagonal on which elements $$a$$ and $$d$$ lie is called the principal or primary diagonal of the determinant and the diagonal which is formed on the line of $$b$$ and $$c$$ is called the secondary diagonal.\n\nA row is constituted by elements lying in the same horizontal line and a column is constituted by elements lying in the same vertical line.\n\nClearly, determinant of second order has two rows and two columns and its value is equal to the products of elements along primary diagonal minus the product of elements along the secondary diagonal. Thus, by definition\n\n$\\begin{split}\\begin{vmatrix} 2 & 4\\\\ 3 & 9\\\\ \\end{vmatrix} = 18 - 12 = 6\\end{split}$\n\nLet $$a_1, a_2, a_3, b_1, b_2, b_3, c_1, c_2, c_3$$ be any nine numbers, then the symbol\n\n$\\begin{split}\\begin{vmatrix} a_1 & a_2 & a_3\\\\ b_1 & b_2 & b_3\\\\ c_1 & c_2 & c_3\\\\ \\end{vmatrix}\\end{split}$\n\nis another way of saying\n\n$\\begin{split}a_1\\begin{vmatrix} b_2 & b_3\\\\ c_2 & c_3\\\\ \\end{vmatrix} - a_2\\begin{vmatrix} b_1 & b_3\\\\ c_1 & c_3 \\end{vmatrix} + a_3\\begin{vmatrix} b_1 & b_2\\\\ c_1 & c_2 \\end{vmatrix}\\end{split}$\n\ni.e. $$a_1(b_2c_3 - b_3c_2)-a_2(b_1c_3-b_3c_1) + a_3(b_1c_2-b_2c_1)$$\n\nRule to put + or - before any element: Find the sum of number of rows and columns in which the considered element occus. If the sum is even put a $$+$$ sign before the element and if the sum is odd, put a $$-$$ sign before the element. Since $$a_1$$ occurs in first row and first column whose sum is $$1 + 1 = 2$$ which is an even number, therefore $$+$$ sign occurs for it. Since $$a_2$$ occurs in first row and second column whose sum is $$1+ 2 = 3$$ which is an odd number, therefore $$-$$ sign occurs before it.\n\nWe have expanded the determinant along first row in previous case. The value of determinant does not change no matter which row or column we expand it along.\n\nExpanding the determinant along second row, we get\n\n$\\begin{split}\\begin{vmatrix} a_1 & a_2 & a_3\\\\ b_1 & b_2 & b_3\\\\ c_1 & c_2 & c_3 \\end{vmatrix} = -b_1\\begin{vmatrix} a_2 & a_3\\\\ c_2 & c_3 \\end{vmatrix} + b_2\\begin{vmatrix} a_1 & a_3\\\\ c_1 & c_3 \\end{vmatrix} - b_3\\begin{vmatrix} a_1 & a_2\\\\ c_1 & c_2 \\end{vmatrix}\\end{split}$\n\n$$= -b_1(a_2c_3 - a_3c_2) + b_2(a_1c_3 - a_3c_1) - b_3(a_1c_2 - a_2c_1)$$\n\n$$= a_1(b_2c_3 - b_3c_2)-a_2(b_1c_3-b_3c_1) + a_3(b_1c_2-b_2c_1)$$\n\nThus, we see that value of determinant remains unchanged irrespective of the change of row and column against which it is expanded.\n\nUsually, an element of a determinant is denoted by a letter with two suffices, first one indicating the row and second one indicating the column in which the element occcur. Thus, $$a_{ij}$$ element indicates that it has occurred in ith row and jth column.\n\nWe also denote the rows by $$R_1, R_2, R_3$$ and so on. $$R_i$$ denotes the ith row of determinant while $$R_j$$ denotes jth row. Columns are denoted by $$C_, C_2, C_3$$ and so on. $$C_i$$ and $$C_j$$ denote ith and jth column of determinant.\n\n$$\\Delta$$ is the usual symbol for a determinant. Another way of denoting the determinant $$\\begin{vmatrix}a_1&b_1&c_1\\\\a_2&b^2&c_2\\\\a_3&b_3&c_3 \\end{vmatrix}$$ is ($$a_1b_2c_3$$).\n\nThe expanded form of determinant has $$n!$$ terms where $$n$$ is the number of rows or columns.\n\nEx 1. Find the value of the determinant\n\n$\\begin{split}\\Delta = \\begin{vmatrix} 1 & 2 & 4\\\\ 3 & 4 & 9\\\\ 2 & 1 & 6 \\end{vmatrix}\\end{split}$\n\nExpanding the determinant along the first row\n\n$\\begin{split}\\Delta = 1\\begin{vmatrix} 4 & 9\\\\ 1 & 6 \\end{vmatrix} -2\\begin{vmatrix} 3 & 9\\\\ 2 & 6 \\end{vmatrix} + 4\\begin{vmatrix} 3 & 4\\\\ 2 & 1 \\end{vmatrix}\\end{split}$\n\nExpanding the determinant along first row $$= 1(24 -9) - 2(18 - 18) + 4(3 - 8) = -5$$\n\nEx 2. Find the value of the determinant\n\n$\\begin{split}\\Delta = \\begin{vmatrix} 3 & 1 & 7\\\\ 5 & 0 & 2\\\\ 2 & 5 & 3 \\end{vmatrix}\\end{split}$\n\nExpanding the determinant along second row,\n\n$\\begin{split}\\Delta = -5\\begin{vmatrix} 1 & 7\\\\ 5 & 3 \\end{vmatrix} + 0\\begin{vmatrix} 3 & 7\\\\ 2 & 3 \\end{vmatrix} -2\\begin{vmatrix} 3 & 1\\\\ 2 & 5 \\end{vmatrix}\\end{split}$\n\n$$= -5(3 - 35) -2(15 -2) = 134$$\n\n66.1. Minors\u00b6\n\nConsider the determinant\n\n$\\begin{split}\\Delta = \\begin{vmatrix} a_{11} & a_{12} & a_{13}\\\\ a_{21} & a_{22} & a_{23}\\\\ a_{31} & a_{31} & a_{33} \\end{vmatrix}\\end{split}$\n\nIf we leave the elements belonging to row and column of a particular element $$a_{ij}$$ then we will obtain a second order determinant. The determinant thus obtained is called minor of $$a_{ij}$$ and it is denoted by $$M_{ij},$$ since there are $$9$$ elements in the above determinant we will have $$9$$ minors.\n\nFor example, the minor of element $$a_{21}=\\begin{vmatrix}a_{12} & a_{13}\\\\ a_{32} & a_{33}\\end{vmatrix} = M_{21}$$\n\nThe minor of element $$a_{32} = \\begin{vmatrix}a_{11} & a_{13}\\\\a_{21} & a_{23}\\end{vmatrix} = M_{32}$$\n\nIf we want to write the determinant in terms of minors then following is the expression obtained if we expand it along first row\n\n$$\\Delta = (-1)^{1+1}a_{11}M_{11} + (-1)^{1 + 2}a_{12}M_{12} + (-1)^{1 + 3} a_{13}M_{13}$$\n\n$$=a_{11}M_{11} - a_{12}M_{12} + a_{13}M_{13}$$\n\n66.2. Cofactors\u00b6\n\nThe minor $$M_{ij}$$ multiplied with $$(-1)^{i+j}$$ is known as cofactor of the element $$a_{ij}$$ and is denoted like $$A_{ij}$$.\n\nThus, we can say that, $$\\Delta = a_{11}A_{11} + a_{12}A_{12} + a_{13}A_{13}$$\n\n66.3. Theorems on Determinants\u00b6\n\nTheorem I. The value of a determinant is not changed when rows are changed into corresponsing columns.\n\nLet $$\\Delta = \\begin{vmatrix}a_1 & b_1 & c_1\\\\a_2 & b_2 & c_2\\\\ a_3 & b_3 & c_3\\end{vmatrix},$$ $$\\Delta^{\\prime} = \\begin{vmatrix}a_1 & a_2 & a_3\\\\ b_1 & b_2 & b_3\\\\c_1 & c_2 & c_3\\end{vmatrix}$$\n\nThe leading term of each determinant is $$a_1b_2c_3.$$\n\nThe remaning terms of $$\\Delta$$ are derived from $$a_1b_2c_3$$ by keeping the letters in their natural order and arranging the suffixes in all possible ways, an interchange of two suffixes producing a change of sign.\n\nThe remaining terms of $$\\Delta^{\\prime}$$ are derived from $$a_1b_2c_3$$ by keeping the suffixes in their natural order and arranging the letters in all possible ways, an interchange of two letters producing a change of sign.\n\nThe result in the two cases are identical. The same argument applies to determinant of any order.\n\nTheorem II. The interchange of two rows, or of two columne, change the sign of a determinant without altering its numerical value.\n\nFor the interchange of two row is equivalent to interchange of the suffixes, and the interchange of two columns is equivalent to the interchange of two letters. Hence in either case the sign of every term of determinant is changed.\n\nTheorem III. A determinant in which two rows or two columns are identical is equal to zero.\n\nIF two rows or or tow columns of a determinant $$\\Delta$$ are identical the change of rows or columns does not change numerical vlaue but changes the sign. Thus, $$\\Delta = -\\Delta \\Rightarrow \\Delta = 0$$\n\nImpoetant Identities. For the determinant $$\\Delta = (a_1b_2c_3)$$ we have a number of identities of the following types:\n\n1. $$a_2A_1 + b_2B_1 + c_2C_1 = 0$$\n\n2. $$b_1A_1 + b_2A_2 + b_2A_3 = 0$$\n\nwhere $$A_1, B_1, \\ldots$$ are cofactors of $$a_, b_1, \\ldots$$","date":"2020-04-05 19:42:30","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9033631086349487, \"perplexity\": 286.9219822546209}, \"config\": {\"markdown_headings\": false, \"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-2020-16\/segments\/1585371609067.62\/warc\/CC-MAIN-20200405181743-20200405212243-00381.warc.gz\"}"} | null | null |
Q: No module found 'firebase_admin' Raspberry Pi - Raspbian Python 3 I'm trying to run the firebase admin SDK in python3 on the Raspberry pi but it's not working.
I run (in the console)
sudo pip install firebase-admin
To install and then attempt to use (in the IDSL)
import firebase_admin
in Python 3 but I get the no module found error. What might I be missing? This is on a fresh install of Raspbian on an old Pi.
A: Turns out all I needed to do was use the following command instead:
sudo pip3 install firebase-admin
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,658 |
<div *ngIf="vehicles.loading">
<div class="modal-loading-background"></div>
<div class="modal-loading-text">now loading...</div>
</div>
| {
"redpajama_set_name": "RedPajamaGithub"
} | 518 |
fou un teòleg valencià.
Fou lector de teologia al convent de Santa Caterina de Barcelona i prior (1603) de Sant Onofre de València. En acabar els seus estudis va obtindre el doctorat i la càtedra de teologia. Va portar a terme diferents estudis de caràcter històric que donaren lloc a un nombre important d'obres, entre les quals cal destacar les següents:
Historia de la vida y milagros, muerte y discípulos de San Vicente Ferrer (1600)
Historias de los victoriosísimos, antiguos Condes de Barcelona (1603)
Anales del Reyno de Valencia (1613)
Va morir a l'edat de 53 anys, després d'haver sigut nomenat per Felip III de Castella, un any abans, cronista major de la Corona d'Aragó.
Referències
Persones de l'Alt Palància
Historiadors valencians històrics
Teòlegs valencians
Cronistes valencians
Viver
Morts a València
Escriptors valencians històrics | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,537 |
NBA 2K19 MyTeam Playoffs Pink Diamond Cards
Durant posted 35 points, five boards, and three assists in a Game 1 win against Houston Sunday. Jokic achieved nba2k mt of his most noteworthy triple-doubles in a huge postseason win. It was Game 7 against the San Antonio Spurs. Jokic finished with 21 points, 15 boards, and 10 assists in the 90-86 victory. That nets him one of the new cheap nba 2k19 coins Diamond cards with a 97 rating. It's down to just eight teams remaining in the 2019 NBA Playoffs. The Boston Celtics, Philadelphia 76ers, Toronto Raptors, and Milwaukee Bucks remain in the East. In the West, it's the Denver Nuggets, Houston Rockets, Portland Trail Blazers, and Golden State Warriors. As the games continue, NBA 2K19 MyTeam Playoffs Moments cards will arrive including the latest. They include three NBA All-Stars worthy of Pink Diamonds. A player who may not get quite the respect he deserves is Nikola Jokic. "The Joker" is continuing his rise to stardom in the league with each game he plays. He's achieved double-doubles and triple-doubles galore, along with a first-ever All-Star appearance this past season. Now he's got the No. 1 seed nba 2k19 coins Nuggets ready to push towards the Western Conference Finals. Joining him are Kawhi Leonard and Kevin Durant who also earned Pink Diamond cards for their playoffs moments. Kawhi is back with another Playoffs Moments card. Just days ago, he scored a game-high 45 points and grabbed 11 rebounds in his Raptors' Game 1 win over Philly.
next: Golden State Warriors' Jordan Bell On NBA 2KTV
prev: NBA 2K League The Turn Schedule | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,475 |
Q: How to query for VM compliance report in Google Cloud Logs Explorer I am able to see the compliance state for VMs(on whom I have applied custom OS policy via OS Configuration Management in VM Manager) in a given project and zone in the Google Cloud console as well as via using API like below:
GET https://osconfig.googleapis.com/v1alpha/projects/PROJECT_ID/locations/ZONE/instanceOSPoliciesCompliances
Is there a way I can view compliance state via Google Cloud Logs Explorer?
If I click on View in the Logs tab above, I am directed to Logs Explorer with the Query framed as:
resource.type="gce_instance"
resource.labels.instance_id="<instance_id>"
labels.os_policy_assignment="projects/<project_id>/locations/<zone>/osPolicyAssignments/<assignment>@<some_alphanumeric_id>"
labels.os_policy_id="<custom-policy-id>"
labels.task_type="APPLY_CONFIG_TASK"
But this does not provide me any information on the Compliance State as shown in the screenshot above.
How can I frame a query to get the Compliance State related logs?
A: To view compliance state in Logs use the following query,
resource.type="gce_instance"
resource.labels.instance_id="<instance_id>"
labels.os_policy_assignment="projects/<project_id>/locations/<zone>/osPolicyAssignments/<assignment>@<some_alphanumeric_id>"
labels.os_policy_id="<custom-policy-id>"
labels.task_type="APPLY_CONFIG_TASK"
jsonPayload.message:"state: COMPLIANT"
We can find compliant state of VM in "jsonPayload.message" field of a log.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,446 |
exec_program(hadoop ARGS version OUTPUT_VARIABLE Hadoop_VERSION
RETURN_VALUE Hadoop_RETURN)
# Only look in HADOOP_INCLUDE_DIR
find_path(HDFS_INCLUDE_DIR hdfs.h PATHS
$ENV{HADOOP_INCLUDE_DIR}
# make sure we don't accidentally pick up a different version
NO_DEFAULT_PATH
)
if ("${CMAKE_SIZEOF_VOID_P}" STREQUAL "8")
set(arch_hint "x64")
elseif ("$ENV{LIB}" MATCHES "(amd64|ia64)")
set(arch_hint "x64")
else ()
set(arch_hint "x86")
endif()
message(STATUS "Architecture: ${arch_hint}")
set(HDFS_LIB_PATHS $ENV{HADOOP_LIB_DIR}/native)
message(STATUS "HDFS_LIB_PATHS: ${HDFS_LIB_PATHS}")
find_library(HDFS_LIB NAMES hdfs PATHS
${HDFS_LIB_PATHS}
# make sure we don't accidentally pick up a different version
NO_DEFAULT_PATH
)
if (HDFS_LIB)
set(HDFS_FOUND TRUE)
set(HDFS_LIBRARIES ${HDFS_LIB})
set(HDFS_STATIC_LIB ${HDFS_LIB_PATHS}/libhdfs.a)
add_library(HDFS_STATIC STATIC IMPORTED)
set_target_properties(HDFS_STATIC PROPERTIES IMPORTED_LOCATION ${HDFS_STATIC_LIB})
else ()
set(HDFS_FOUND FALSE)
endif ()
if (HDFS_FOUND)
if (NOT HDFS_FIND_QUIETLY)
message(STATUS "${Hadoop_VERSION}")
message(STATUS "HDFS_INCLUDE_DIR: ${HDFS_INCLUDE_DIR}")
message(STATUS "HDFS_LIBRARIES: ${HDFS_LIBRARIES}")
message(STATUS "HDFS_STATIC: ${HDFS_STATIC_LIB}")
endif ()
else ()
message(FATAL_ERROR "HDFS includes and libraries NOT found."
"Thrift support will be disabled (${Thrift_RETURN}, "
"${HDFS_INCLUDE_DIR}, ${HDFS_LIB})")
endif ()
mark_as_advanced(
HDFS_LIBRARIES
HDFS_INCLUDE_DIR
HDFS_STATIC
)
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,304 |
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Most popular Argentina tours
Whether you want to soak in culture in cosmopolitan Buenos Aires, stand in awe of snow-capped mountains in Patagonia, or feel the mist of Iguazú Falls, Argentina trips are sure to wow you.
Grand Tour of South America
15 days | 18 days with Lima & the Amazon extension
$5,829*CAD
Chile to Argentina: Santiago, Patagonia & Buenos Aires
12 days | 15 days with Iguazú Falls extension
Food & Wine: Uruguay, Argentina & Chile
11 days | 14 days with Lima extension
Rio, Iguazú Falls & Buenos Aires
11 days | 13 days with Argentinian Patagonia extension
Antarctica Cruise & Weddell Sea
16 days | 18 days with Buenos Aires extension
$13,859*CAD
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Bucket list trip!
4/4/2018 by 23-time traveler Martha R.
I have just returned from my first trip to South America. I am riding high on the energy and memories of this trip. It has given me a new level of adventure and daring that I don't think I had before. There is something very life affirming about seeing animals in their natural setting.
See more reviews of Chile to Argentina: Santiago, Patagonia & Buenos Aires
Amazing once in a lifetime experience
6/30/2016 by 2-time traveler Lauri D.
I had the most amazing time on this tour. It was a great mix of different experiences in beautiful places. I could hardly believe the great beauty I was seeing along the way. I really appreciated our Tour Guide, Jorge, and all the extra effort he put in to ensure our comfort in these new places.
See more reviews of Rio, Iguazú Falls & Buenos Aires
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Travel tips for Argentina trips
When to visit Argentina
As with many places around the globe, the not-too-hot, not-too-cold shoulder seasons of spring and fall are wonderful times to visit Argentina. Since the Southern Hemisphere has opposite seasons to us here in the Northern Hemisphere, spring comes around from September through November, and fall is from March to May. The comfortable temperatures and smaller crowds you'll find during these times of year make for a more enjoyable experience on Argentina guided tours.
December through February marks the summer season in Argentina, which brings muggy weather and more crowds to Buenos Aires. Patagonia is also a popular destination for visitors who set out on Argentina travel packages during the summer, when the southern region experiences warm, sunny days. However, strong winds also blow through Patagonia during the the summer, and then lessen during spring and fall. Cold, rainy days are common during the winter, which goes from June through August.
Where to go in Argentina
Argentina tours offer the ideal mix of city and scenery. Head to the southernmost reaches of the country to explore one of the most pristine outdoor destinations visited on our Latin America tours: Patagonia. This picturesque region spans Argentina and Chile and boasts glaciers, wildlife, sprawling plains, and more. Cruise along the Perito Moreno Glacier face in the Los Glaciares National Park and stand in awe of Lago Argentino, a lake surrounded by mountains.
For even more outdoor adventure, add the Iguazú Falls extension on our Chile to Argentina: Santiago, Patagonia & Buenos Aires tour, or embark on our Rio, Iguazú Falls & Buenos Aires tour, to see the Argentinian side of Iguazú Falls. This waterfall splashes down almost 300 feet and is one of South America's top natural wonders.
Of course, no Argentina trips are complete without a stop in the country's vibrant capital, Buenos Aires. This cosmopolitan city has been nicknamed "The Paris of South America," and for good reason. From its striking architecture and world-class fashion scene to its many park and museums, Buenos Aires is the place to go to get your Argentine culture fix.
Want to get to the heart of wine country while on Argentina trips? The city of Mendoza is the place to go. Try the signature sip, Malbec, and immerse yourself in history as you explore on a guided tour.
Dining tips for Argentina
Calling all foodies—if delicious Latin American cuisine is what you're looking for, planning a trip to Argentina is a must. The country is known for its wine, lively food scene, and delicious meat dishes. In fact, Argentina is one of the largest consumers and exporters of beef in the world!
If you're more into vegetarian dishes or sweets, the country has more than enough to satisfy you on Argentina vacation packages. Here are a few of Argentina's most popular bites and culinary traditions:
Asado, a family-style barbecue of salt-rubbed meats, ribs, and chorizo sausages cooked over a fire pit on metal grills and crosses
Steak cooked in a parilla, an Argentine steakhouse that focuses on grilled meats
Ice cream, cookies called alfajores, and dulce de leche, a sweet honey-and-milk paste in pastries
Argentine empanadas, typically made with a flour-based dough and filled with ground beef, hard-boiled egg, olives, onions, and spices
Pizza in Buenos Aires, Latin America's unofficial "pizza capital"
Breaded meats called milanesas
Red Malbec wine
For a firsthand look at the city's culinary culture, pop into an Argentinian cafe called a bodegon at 4pm to take part in the merienda, which is a small social meal consisting of breakfast goodies like pastries and coffee. Or, set out on our Food & Wine: Uruguay, Argentina & Chile tour to try the best of the best.
Packing tips for Argentina
Any trip is made instantly better when you have the right footwear, and Argentina tour packages are no exception! A good pair of walking shoes will get you comfortably from the bustling streets and sprawling parks of Buenos Aires to the trails of the remote Patagonia region. Trust us, your feet will thank you.
Speaking of Buenos Aires... this destination is a fashion lover's dream. It's been nicknamed "The Paris of South America," and people who live here like to look put together. While there's no need to stress about getting overly done up when you head out, you will feel most in step with the locals by wearing simple yet smart-looking clothes. As with any international trip, it's best to leave any expensive, flashy jewelry at home for Argentina small group tours; locals don't tend to wear it, so you'll only stand out as a tourist.
Bringing layers on Argentina group tours is also a good idea, as temperatures can vary from north to south. If you're traveling in the fall or winter, pack a warmer layer, rain coat, and hat to fend off the snow or strong winds you may come up against in Patagonia. No matter when you go, bring a camera and binoculars to get an up-close look at the scenery and wildlife.
Browse all our Argentina tours
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©2021 EF Education First | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,371 |
Q: Integrate stylelint with angular build and make it failed on error? I want to use stylelint in angular application to enforce class name for example (they should be in lowercase and dash if if necessary, not camel case or uppercase).
How to configure stylelint to run in Angular build time (just like Angular run TSLint). Or can TSLint enforce style rules?
The propose is when I have an error in stylelint rule then Angular build will fail.
A: According to the documentation of stylelint you can use selector-class-pattern with the kebab-case pattern ^([a-z][a-z]*)(-[a-z]+)*$. This pattern allows only lower case letters and dashes between those letters. If you want to allow also digits you can use this one ^([a-z][a-z0-9]*)(-[a-z0-9]+)*$ with every alphanumeric group starting with a letter.
You can also have a look at resolveNestedSelectors option of selector-class-pattern if you need it.
You can use it in your stylelint-config.json file somehow like this,
"selector-class-pattern": ["^([a-z][a-z]*)(-[a-z]+)*$", {
"resolveNestedSelectors": false
}
or just,
"selector-class-pattern": "^([a-z][a-z]*)(-[a-z]+)*$"
I hope it helped :)
EDIT: According to this article, for integrating with angular build, in your package.json you can make your scripts look like this:
"scripts": {
"ng": "ng",
"start": "ng serve",
"build": "npm run lint && ng build",
"test": "ng test",
"lint": "ng lint && npm run lint:styles",
"lint:styles": "stylelint \"apps/**/*.scss\" && stylelint \"libs/**/*.scss\"",
"e2e": "ng e2e"
},
A: Angular provides a command for linting ng lint.
There is a third party CLI builder available to integrate both ESLint and stylelint. You can then just run ng lint and it will lint with ESLint and stylelint.
https://github.com/krema/angular-eslint-stylelint-builder
PS: I am the author of this package.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,111 |
{"url":"https:\/\/docs.q-ctrl.com\/boulder-opal\/user-guides\/simulation","text":"# Simulation\n\nSimulating the dynamics of quantum systems in the presence of noise\n\nThe Q-CTRL Python package enables you to simulate the dynamics of quantum systems that are affected by various noise processes. Such simulations can provide useful insights into the expected real-world performance of candidate control solutions. In this notebook we show how to use the Q-CTRL Python package to perform simulations of systems affected by different types of noise.\n\n## Imports and initialization\n\nAll usage of the Q-CTRL Python package begins by importing the qctrl package and starting a session.\n\n# Essential imports\nimport numpy as np\nfrom qctrl import Qctrl\n\n# Predefined pulse imports\nfrom qctrlopencontrols import new_predefined_driven_control\n\n# Plotting imports\nimport matplotlib.pyplot as plt\nfrom qctrlvisualizer import plot_controls\n\n# Starting a session with the API\nqctrl = Qctrl()\n\n\n## Worked example: single qubit subject to dephasing noise\n\nIn this example we will show how to simulate the dynamics of a single qubit experiencing stochastic dephasing noise, driven by a $\\pi\/2$ CORPSE pulse. The Hamiltonian of the quantum system is:\n\n\\begin{align*} H(t) = & \\frac{\\Omega(t)}{2} \\sigma_- + \\frac{\\Omega^*(t)}{2} \\sigma_+ + \\frac{\\eta(t)}{2} \\sigma_z, \\end{align*}\n\nwhere $\\Omega(t)$ is a time-dependent Rabi rate, $\\eta(t)$ is a stochastic dephasing noise process, $\\sigma_\\pm = (\\sigma_x \\mp i \\sigma_y)\/2$, and $\\sigma_k$ are the Pauli matrices.\n\nWe assume that $\\eta(t)$ represents pink noise, as defined below.\n\ndef pink_spectrum(frequencies, frequency_cutoff):\nreturn 1\/(frequencies + frequency_cutoff)\n\nfrequencies = np.linspace(0, 2*1e6, 1000)\n\npower_densities = 4e9*pink_spectrum(frequencies=frequencies, frequency_cutoff=0.05*1e6)\n\nplt.plot(frequencies\/1e6, power_densities*1e6, c=\"#FB00A5\")\nplt.fill_between(frequencies\/1e6, 0, power_densities*1e6, alpha=0.25, color=\"#FB00A5\")\nplt.xlabel(\"Frequency (MHz)\")\nplt.ylabel(\"Power density (1\/MHz)\")\nplt.title(\"Dephasing noise spectral density\")\nplt.show()\n\n\nWe now proceed to show how the system, driven by stochastic noise drawn from this power spectral density, may be simulated using the Q-CTRL Python package.\n\n### Creating the pulses\n\nAs described in the Setup user guide, we first set up Python objects representing the pulse, control, and noise.\n\nThe qctrl.functions.calculate_colored_noise_simulation function accepts the Hamiltonian in the form of separate terms for each of the complex-valued controls (drives), real-valued controls (shifts), and static terms (drifts). In the Hamiltonian used in this example, the drive corresponds to the term that contains the Rabi rate ($\\Omega(t)$ and $\\Omega^*(t)$) and the drift corresponds to the dephasing term (there are no shifts).\n\nThe Rabi coupling term is defined using a pulse from Q-CTRL Open Controls. To create the dephasing noise term, we provide its noise spectral density as a qctrl.types.colored_noise_simulation.Noise by using the frequencies and power densities defined above.\n\n# Define standard matrices\nidentity = np.array([[1, 0],[0, 1]], dtype=np.complex)\nsigma_x = np.array([[0, 1],[1, 0]], dtype=np.complex)\nsigma_z = np.array([[1, 0],[0, -1]], dtype=np.complex)\nsigma_m = np.array([[0, 1],[0, 0]], dtype=np.complex)\nsquare_root_sigma_x = 0.5*np.array([[1+1j, 1-1j], [1-1j, 1+1j]], dtype=np.complex)\n\n# Define control parameters\nomega_max = 2*np.pi * 1e6 #Hz\ntotal_rotation = np.pi\/2\n\n# Define pulse using pulses from Q-CTRL Open Controls\npulse = new_predefined_driven_control(\nrabi_rotation=total_rotation,\nazimuthal_angle=0.,\nmaximum_rabi_rate=omega_max,\nscheme='CORPSE',\nname='CORPSE',\n)\n\n# Define Rabi coupling term\nrabi_drive = qctrl.types.colored_noise_simulation.Drive(\ncontrol=[\nqctrl.types.ComplexSegmentInput(duration=d, value=v)\nfor d, v in zip(pulse.durations, pulse.rabi_rates * np.exp(1j*pulse.azimuthal_angles))],\noperator=sigma_m\/2,\n)\n\n# Define dephasing noise term\nnoise_drift = qctrl.types.colored_noise_simulation.Drift(\noperator=sigma_z,\nnoise=qctrl.types.colored_noise_simulation.Noise(\npower_densities=power_densities,\nfrequency_step=frequencies[1],\ntime_domain_sample_count=100,\n),\n)\n\n\n### Running the simulation\n\nThe computation of a simulation with colored noise is carried out by the qctrl.functions.calculate_colored_noise_simulation function, which takes the following parameters:\n\n\u2022 duration, the duration of the control pulses,\n\u2022 sample_times, which is a list of sample times at which the dynamics should be calculated,\n\u2022 drives, shifts, and drifts, which represent the different terms in the Hamiltonian (at least one term needs to be provided),\n\u2022 trajectory_count, which is the number of independent simulations to run using different random realizations of the noise processes,\n\u2022 initial_state_vector, which gives an initial state vector to be propagated according to the calculated dynamics (optional), and\n\u2022 target, which gives the target time evolution operator with respect to which the operational infidelities will be calculated throughout the simulated time period (optional).\n# Define sample times for the output\nsample_times = np.linspace(0, pulse.duration, 100)\n\n# Define the target (optional)\ntarget = qctrl.types.TargetInput(operator=square_root_sigma_x)\n\ncolored_noise_simulation_result = qctrl.functions.calculate_colored_noise_simulation(\nduration=pulse.duration,\nsample_times=sample_times,\ndrives=[rabi_drive],\ndrifts=[noise_drift],\ntrajectory_count=5,\ninitial_state_vector=np.array([1., 0.]),\ntarget=target,\n)\n\n100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588| 100\/100 [00:04<00:00, 23.44it\/s]\n\n\n### Extracting the average infidelities\n\nAfter the calculation of all the noisy trajectories, a colored noise simulation returns different types of data. Here we show how to extract the average infidelity, which gives the operational infidelity of the time evolution operator relative to the specified target, averaged over the ensemble of trajectories. All average quantities are stored in colored_noise_simulation_result.average_samples for each time in the provided sample_times (where colored_noise_simulation_result is the object returned by qctrl.functions.calculate_colored_noise_simulation).\n\n# Extract infidelities\naverage_infidelities = [\naverage_sample.average_infidelity\nfor average_sample in colored_noise_simulation_result.average_samples\n]\n\n# Plot infidelities\nplt.plot(sample_times*1e6, average_infidelities)\nplt.xlabel(\"Time (\u00b5s)\")\nplt.ylabel(\"Infidelity\")\nplt.title(\"Average infidelity\")\nplt.show()\n\n\n### Extracting the average density matrices\n\ncolored_noise_simulation_result.average_samples also includes the density matrix, the object describing an ensemble of state vectors for the different trajectories. We can use it (for example) to visualize trajectories of observables.\n\n# Extract density matrices\ndensity_matrices = [\naverage_sample.average_density_matrix\nfor average_sample in colored_noise_simulation_result.average_samples\n]\n\n# Calculate and plot average sigma_x expectation\nplt.plot(\nsample_times*1e6,\n[\nnp.real(np.trace(sigma_x.dot(density_matrix)))\nfor density_matrix in density_matrices\n],\n)\nplt.axhline(y=0., c='k', lw=0.5)\nplt.xlabel(\"Time (\u00b5s)\")\nplt.ylabel(r\"$\\langle\\sigma_x\\rangle$\")\nplt.title(r\"Average $\\sigma_x$ expectation\")\nplt.show()\n\n\n### Extracting the individual noise trajectories\n\nIn addition to the ensemble information available in the average samples, we can extract information about the individual simulation trajectories. These are stored in colored_noise_simulation_result.trajectories. Here we show how to extract the random realizations of the dephasing noise process.\n\n# Extract noise trajectories\nnoise_points_list = [\nnp.array([\nsegment.value\nfor segment in trajectory.noise_realizations[0].segments\n])\nfor trajectory in colored_noise_simulation_result.trajectories\n]\n\n# Extract noise sampling times\nnoise_times = np.cumsum([\nsegment.duration\nfor segment in colored_noise_simulation_result.trajectories[0].noise_realizations[0].segments\n])\n\n# Plot all noise trajectories\nfor noise_points in noise_points_list:\nplt.plot(noise_times*1e6,noise_points\/1e6)\n\nplt.xlabel(\"Time (\u00b5s)\")\nplt.ylabel(\"Noise value (MHz)\")\nplt.title(\"Noise trajectories\")\nplt.show()\n\n\n### Extracting the individual time evolution trajectories\n\nNext we show how to extract from colored_noise_simulation_result.trajectories the unitary time evolution operators corresponding to each individual simulation run.\n\n# Extract first two time evolution operator trajectories\nevolution_operators_list = [\n[\nsample.evolution_operator\nfor sample in trajectory.samples\n]\nfor trajectory in colored_noise_simulation_result.trajectories[0:2]\n]\n\n# Print initial and final time evolution operators, for both trajectories\nprint(\"Time evolution operators at start:\")\nprint(evolution_operators_list[0][0])\nprint(evolution_operators_list[1][0])\nprint(\"\\n\")\nprint(\"Time evolution operators at end:\")\nprint(evolution_operators_list[0][-1])\nprint(evolution_operators_list[1][-1])\n\nTime evolution operators at start:\n[[1.+0.j 0.+0.j]\n[0.+0.j 1.+0.j]]\n[[1.+0.j 0.+0.j]\n[0.+0.j 1.+0.j]]\n\nTime evolution operators at end:\n[[ 0.69907233-0.08932679j -0.02472394-0.70901857j]\n[ 0.02472394-0.70901857j 0.69907233+0.08932679j]]\n[[ 0.70757869-0.05377533j 0.01640906-0.70439432j]\n[-0.01640906-0.70439432j 0.70757869+0.05377533j]]\n\n\n### Summary\n\nWe have shown how to use the Q-CTRL Python package to simulate the dynamics of a system in the presence of a stochastic noise process. We have also shown how to extract several quantities of interest from the simulation result, including both ensemble objects describing the average system behavior and objects associated with specific realizations of the stochastic noise process.\n\n## Example: single qubit subject to dephasing noise in a large Hilbert space\n\nIn this example we simulate the dynamics of a single qubit experiencing stochastic dephasing noise in the presence of two additional, independent, and unaffected qubits. Since we only care about the average samples here, we can ask to omit the trajectories using the result_scope argument.\n\nThe Hamiltonian of the quantum system is:\n\n\\begin{align*} H(t) = & \\frac{\\Omega(t)}{2} \\sigma_-^{(1)} + \\frac{\\Omega^*(t)}{2}\\sigma_+^{(1)} + \\frac{\\eta(t)}{2}\\sigma_z^{(1)} \\end{align*}\n\nwhere $\\Omega(t)$ is a time-dependent Rabi rate, $\\eta(t)$ is a stochastic dephasing noise process, $\\sigma_\\pm = (\\sigma_x \\mp i \\sigma_y)\/2$, and $\\sigma_k$ are the Pauli matrices. We use the superscript to indicate that $\\sigma^{(1)}$ is the operator for the first qubit and operators for the other two qubits default to the identity matrix.\n\nWe assume that $\\eta(t)$ represents pink noise, as defined below.\n\n# Define power spectral density\ndef pink_spectrum(frequencies, frequency_cutoff):\nreturn 1\/(frequencies + frequency_cutoff)\nfrequencies = np.linspace(0, 2*1e6, 1000)\npower_densities = 4e9*pink_spectrum(frequencies=frequencies, frequency_cutoff=0.05*1e6)\n\n# Define standard matrices\nidentity = np.array([[1, 0],[0, 1]], dtype=np.complex)\nsigma_x = np.array([[0, 1],[1, 0]], dtype=np.complex)\nsigma_z = np.array([[1, 0],[0, -1]], dtype=np.complex)\nsigma_m = np.array([[0, 1],[0, 0]], dtype=np.complex)\nsquare_root_sigma_x = 0.5*np.array([[1+1j, 1-1j], [1-1j, 1+1j]], dtype=np.complex)\n\nlarge_operator = np.array(operator)\nlarge_operator = np.kron(large_operator, identity)\nreturn large_operator\n\n# Define control parameters\nomega_max = 2*np.pi * 1e6 #Hz\ntotal_rotation = np.pi\/2\n\n# Define pulse using pulses from Q-CTRL Open Controls\npulse = new_predefined_driven_control(\nrabi_rotation=total_rotation,\nazimuthal_angle=0.,\nmaximum_rabi_rate=omega_max,\nscheme='CORPSE',\nname='CORPSE',\n)\n\n# Define Rabi coupling term\nrabi_drive = qctrl.types.colored_noise_simulation.Drive(\ncontrol=[\nqctrl.types.ComplexSegmentInput(duration=d, value=v)\nfor d, v in zip(pulse.durations, pulse.rabi_rates * np.exp(1j*pulse.azimuthal_angles))],\n)\n\n# Define dephasing noise term\nnoise_drift = qctrl.types.colored_noise_simulation.Drift(\nnoise=qctrl.types.colored_noise_simulation.Noise(\npower_densities=power_densities,\nfrequency_step=frequencies[1],\ntime_domain_sample_count=100,\n),\n)\n\n# Define sample times for the output\nsample_times = np.linspace(0, pulse.duration, 100)\n\n# Define the target (optional)\n\n# Run simulation\ncolored_noise_simulation_result = qctrl.functions.calculate_colored_noise_simulation(\nduration=pulse.duration,\nsample_times=sample_times,\ndrives=[rabi_drive],\ndrifts=[noise_drift],\ntrajectory_count=50,\ninitial_state_vector=np.array([1.] + [0]*(len(rabi_drive.operator)-1)),\nresult_scope=qctrl.types.colored_noise_simulation.ResultScope.NO_TRAJECTORIES,\n)\n\n# Extract infidelities\naverage_infidelities = [\naverage_sample.average_infidelity\nfor average_sample in colored_noise_simulation_result.average_samples\n]\n# Plot infidelities.\nplt.plot(sample_times*1e6, average_infidelities)\nplt.xlabel(\"Time (\u00b5s)\")\nplt.ylabel(\"Infidelity\")\nplt.title(\"Average infidelity\")\nplt.show() # This should be the same as the infidelity graph above\n\nprint(\"Density matrix at end:\")\nwith np.printoptions(precision=3, linewidth=120, floatmode='maxprec'):\nprint(colored_noise_simulation_result.average_samples[-1].average_density_matrix)\n\n100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588| 100\/100 [00:05<00:00, 17.15it\/s]\n\nDensity matrix at end:\n[[ 0.499+0.j 0. +0.j 0. +0.j 0. +0.j -0.005+0.498j 0. +0.j 0. +0.j 0. +0.j ]\n[ 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j ]\n[ 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j ]\n[ 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j ]\n[-0.005-0.498j 0. +0.j 0. +0.j 0. +0.j 0.501+0.j 0. +0.j 0. +0.j 0. +0.j ]\n[ 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j ]\n[ 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j ]\n[ 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j 0. +0.j ]]\n\n\n## Example: single qubit with leakage\n\nIn this example we show how to simulate the dynamics of a single qubit subject to leakage to a third energy level (i.e. a qutrit), driven by a primitive $\\pi$ pulse. The qutrit is treated as an oscillator (truncated to three levels) with an anharmonicity of $\\chi$, described by the Hamiltonian:\n\n\\begin{align*} H(t) = & \\frac{\\chi}{2} (a^\\dagger)^2 a^2 + \\frac{\\Omega(t)}{2} a + \\frac{\\Omega^*(t)}{2} a^\\dagger, \\end{align*}\n\nwhere $a = \\left|0 \\right\\rangle \\left\\langle 1 \\right| + \\sqrt{2} \\left|1 \\right\\rangle \\left\\langle 2 \\right|$ is the lowering operator and $\\Omega(t)$ is a time-dependent Rabi rate.\n\nBelow we show how to use the Q-CTRL Python package to simulate the time evolution of this coherent system. We also illustrate how the noise-free infidelity $\\mathcal{I}_0$ can be extracted from the coherent simulation results. To do this, we choose as target an X gate between the states $\\left| 0 \\right\\rangle$ and $\\left| 1 \\right\\rangle$. Notice that this target is not unitary in the total Hilbert space, but is still a valid target because it is a partial isometry\u2014in other words, it is unitary in the subspace whose basis is $\\{ \\left| 0 \\right\\rangle, \\left| 1 \\right\\rangle \\}$.\n\n# Define matrices for the Hamiltonian operators\na = np.array([[0., 1., 0.],\n[0., 0., np.sqrt(2)],\n[0., 0., 0.]], dtype=np.complex)\n\n# Define system parameters\nchi = 2*np.pi * 3 * 1e6 #Hz\nomega_max = 2*np.pi * 1e6 #Hz\ntotal_rotation = np.pi\n\n# Define pulse using pulses from Q-CTRL Open Controls\npulse = new_predefined_driven_control(\nrabi_rotation=total_rotation,\nazimuthal_angle=0.,\nmaximum_rabi_rate=omega_max,\nscheme='primitive',\nname='primitive',\n)\n\nsample_times = np.linspace(0, pulse.duration, 100)\n\n# Define Rabi coupling term\nrabi_drive = qctrl.types.coherent_simulation.Drive(\ncontrol=[\nqctrl.types.ComplexSegmentInput(duration=d, value=v)\nfor d, v in zip(pulse.durations, pulse.rabi_rates * np.exp(1j*pulse.azimuthal_angles))],\noperator=a\/2,\n)\n\n# Define anharmonic term\nanharmonic_drift = qctrl.types.coherent_simulation.Drift(\n)\n\n# Define the target\ntarget_operation = np.array([[0, 1, 0],\n[1, 0, 0],\n[0, 0, 0]], dtype=np.complex)\ntarget = qctrl.types.TargetInput(operator=target_operation)\n\n# Run simulation\ncoherent_simulation_result = qctrl.functions.calculate_coherent_simulation(\nduration=pulse.duration,\nsample_times=sample_times,\ndrives=[rabi_drive],\ndrifts=[anharmonic_drift],\ninitial_state_vector=np.array([1., 0., 0.]),\ntarget=target,\n)\n\n# Extract and print final infidelity\nprint(\"Noise-free infidelity at end: {}\".format(coherent_simulation_result.samples[-1].infidelity))\n\n# Extract and print final time evolution operator\nprint(\"Time evolution operator at end:\")\nprint(coherent_simulation_result.samples[-1].evolution_operator)\n\n# Extract and plot state populations\ntimes = np.array([\nsample.time\nfor sample in coherent_simulation_result.samples\n])\nstate_vectors = np.array([\nsample.state_vector\nfor sample in coherent_simulation_result.samples\n])\n\nfor state in range(3):\nplt.plot(sample_times*1e6, np.abs(state_vectors[:, state])**2, label=f\"P{state}\")\nplt.xlabel(\"Time (\u00b5s)\")\nplt.ylabel(\"Probability\")\nplt.title(\"State populations\")\nplt.legend()\nplt.show()\n\n100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588| 100\/100 [00:03<00:00, 29.26it\/s]\nNoise-free infidelity at end: 0.08747804107639123\nTime evolution operator at end:\n[[ 0.05730981-0.14539786j 0.23505273-0.92588994j -0.08764586+0.23531105j]\n[ 0.23505273-0.92588994j -0.06664016+0.18738223j -0.19346042+0.10246022j]\n[-0.08764586+0.23531105j -0.19346042+0.10246022j -0.82544823+0.45569409j]]\n\n\n## Example: effect of the pulse delay on STIRAP\n\nIn this example we show how to simulate the dynamics of a three-level system undergoing stimulated Raman adiabatic passage (STIRAP) when subjected to pump and Stokes pulses. Below we show how to use the Q-CTRL Python package to create and execute a graph made up of nodes (corresponding to the different steps in the simulation) that represent functions of previous nodes (or of constant values). Please see the operations namespace of the Q-CTRL Python package for a list of the currently available primitive nodes.\n\nThe Hamiltonian of the system is given by $$H(t) = \\frac{1}{2} \\Omega_{12}(t) \\Big(|1\\rangle\\langle 2| + |2\\rangle\\langle 1|\\Big) + \\frac{1}{2} \\Omega_{23}(t) \\Big(|2\\rangle\\langle 3| + |3\\rangle\\langle 2|\\Big) ,$$ where the time-dependent Rabi rates for the pump and Stoke pulses are applied for $t\\in(0,T)$ with a Gaussian profile: $$\\Omega_{12}(t) = \\Omega_\\max \\exp\\left(- \\frac{\\left(t - \\frac{T}{2} - \\frac{t_\\textrm{delay}}{2}\\right)^2}{2\\sigma^2}\\right) \\\\ \\Omega_{23}(t) = \\Omega_\\max \\exp\\left(- \\frac{\\left(t - \\frac{T}{2} + \\frac{t_\\textrm{delay}}{2}\\right)^2}{2\\sigma^2}\\right)$$ with a maximum amplitude $\\Omega_\\max$, a pulse width $\\sigma$, and a delay between them of $t_\\textrm{delay}$.\n\nIf the pulses are applied in a counter-intuitive manner, that is, $\\Omega_{23}(t)$ is applied before $\\Omega_{12}(t)$ (or $t_\\textrm{delay} >0$), the STIRAP pulse sequence will transfer the population in state $|1\\rangle$ to state $|3\\rangle$. In the calculation below, we will see the effect of $t_\\textrm{delay}$ on the infidelity of the process. Moreover, we will assume that the input controls are very coarse, consisting of very few segments, but they are passed through a Gaussian filter before acting on the three-level system.\n\nBelow we set up and run a graph that creates a batch of input Gaussian pulses (for different values of $t_\\textrm{delay}$), filters them, and uses them to simulate the time evolution of the system. The batch of pulses allows the computations for all values of $t_\\textrm{delay}$ to be performed in parallel when the graph is executed. We then retrieve and plot the infidelities, as well as a pair of the input\/filtered pulses simulated. Notice that the infidelity only goes to 0 when $t_\\textrm{delay} > 0$, but if the two pulses are too separated the infidelity increases again.\n\n# Define matrices for the Hamiltonian operators\na_12 = np.array([[0, 1, 0], [1, 0, 0], [0, 0, 0]])\na_23 = np.array([[0, 0, 0], [0, 0, 1], [0, 1, 0]])\n\n# Define the target unitary: state |1> goes to state |3>\ntarget_operation = np.array([[0, 0, 0], [0, 0, 0], [1, 0, 0]])\n\n# Define system parameters\nomega_max = 2 * np.pi * 5e6 # Hz\ntotal_duration = 10.0e-6 # s\nsigma = 0.5e-6\ngauss_filter_std = 0.5e-6\ninput_segment_count = 12\nfiltered_segment_count = 100\n\ntimes = np.linspace(0.0, total_duration, input_segment_count)\ndurations = np.array([total_duration\/input_segment_count] * input_segment_count)\n\n# Define values of t_delay\nt_delay_values = np.linspace(-total_duration\/2, total_duration\/2, 51)\n\n# Create batch of coarse input pulses\nomega_12_pulse = omega_max * np.exp(\n-0.5 * (times[None] - total_duration\/2.0 - t_delay_values[:, None]\/2.0)**2 \/ sigma**2\n)\nomega_23_pulse = omega_max * np.exp(\n-0.5 * (times[None] - total_duration\/2.0 + t_delay_values[:, None]\/2.0)**2 \/ sigma**2\n)\n\n# Define the data flow graph describing the system\nwith qctrl.create_graph() as graph:\n\n# Create input signals\nomega_12_signal = qctrl.operations.pwc_signal(\nvalues=omega_12_pulse, duration=total_duration, name=\"omega_12_signal\"\n)\nomega_23_signal = qctrl.operations.pwc_signal(\nvalues=omega_23_pulse, duration=total_duration, name=\"omega_23_signal\"\n)\n\n# Filter signals through a Gaussian filter\nfiltered_omega_12_signal = qctrl.operations.convolve_pwc(\nomega_12_signal, qctrl.operations.gaussian_integral_function(gauss_filter_std, offset=0)\n)\nfiltered_omega_23_signal = qctrl.operations.convolve_pwc(\nomega_23_signal, qctrl.operations.gaussian_integral_function(gauss_filter_std, offset=0)\n)\n\n# Discretize filtered signals to output smoothed signals\nsampled_filtered_pulse_12 = qctrl.operations.discretize_stf(\nstf=filtered_omega_12_signal,\nduration=total_duration,\nsegments_count=filtered_segment_count,\nname=\"filtered_omega_12_signal\",\n)\nsampled_filtered_pulse_23 = qctrl.operations.discretize_stf(\nstf=filtered_omega_23_signal,\nduration=total_duration,\nsegments_count=filtered_segment_count,\nname=\"filtered_omega_23_signal\",\n)\n\n# Create Hamiltonian terms\nomega_12_term = qctrl.operations.stf_operator(\nsignal=filtered_omega_12_signal, operator=a_12\n)\nomega_23_term = qctrl.operations.stf_operator(\nsignal=filtered_omega_23_signal, operator=a_23\n)\n\n# Define the target operation\ntarget = qctrl.operations.target(operator=target_operation)\n\n# Calculate the infidelities\nqctrl.operations.infidelity_stf(\nsample_times=np.linspace(0, total_duration, filtered_segment_count),\nhamiltonian=qctrl.operations.stf_sum([omega_12_term, omega_23_term]),\ntarget_operator=target,\nname=\"infidelities\",\n)\n\n# Run simulation\ngraph_result = qctrl.functions.calculate_graph(\ngraph=graph,\noutput_node_names=[\n\"infidelities\",\n\"omega_12_signal\",\n\"omega_23_signal\",\n\"filtered_omega_12_signal\",\n\"filtered_omega_23_signal\",\n],\n)\n\n# Plot the input\/filtered pulses\nfig = plt.figure()\nplot_controls(\nfig,\n{\n\"input $\\Omega_{12}$\": graph_result.output[\"omega_12_signal\"][33],\n\"filtered $\\Omega_{12}$\": graph_result.output[\"filtered_omega_12_signal\"][33],\n\"input $\\Omega_{23}$\": graph_result.output[\"omega_23_signal\"][33],\n\"filtered $\\Omega_{23}$\": graph_result.output[\"filtered_omega_23_signal\"][33],\n},\n)\nfig.suptitle(\"Input and filtered pulses for $t_{delay} = 0.16 T$\")\n\n# Plot the infidelities obtained as a function of the pulse delay\nplt.figure()\nplt.plot(t_delay_values \/ 1e-6, graph_result.output[\"infidelities\"][\"value\"])\nplt.xlabel(\"Pulse delay \u03c4 (\u00b5s)\")\nplt.ylabel(\"Infidelity\")\nplt.title(\"Infidelity as a function of the pulse delay\")\nplt.show()\n\n100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588| 100\/100 [00:03<00:00, 26.58it\/s]","date":"2020-10-31 00:46:48","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 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\": 0.6549308896064758, \"perplexity\": 6241.255402856885}, \"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-2020-45\/segments\/1603107912593.62\/warc\/CC-MAIN-20201031002758-20201031032758-00622.warc.gz\"}"} | null | null |
Q: SQL - I have a 'People' table and an 'Account' table. How do I list all of the people in rows, and have a balance column for each account type? I was having a hard time figuring out how to title this question, so my apologies in advance.
Here is my my situation:
I have one table that has just people in it. I have another table that has all the accounts, with a personID, accountType, and balance column. A person can have multiple accounts, there are different account types, and not everyone has all of the different account types.
How can I write a query where I list one person per row, and have a column for the balance of each "account type"?
Ideally, my query would look something like this:
PersonID | Account Type 1 Bal | Account Type 2 Bal | Account Type 3 Bal |
-------------------------------------------------------------------------
1 | $100 | null | null |
2 | null | $12 | $1300 |
3 | null | null | $5 |
4 | $150 | null | null |
5 | $65 | $300 | $45 |
I would assume I would use some sort of case statement, but I haven't been able to figure it out yet. Also, if they have multiple of the same account type, i assume I would just use sum() correct?
Thanks.
A: Something like this should work for postgres
select p.person_id,
(select sum(a.balance) from account a where a.person_id = p.person_id and a.account_type = 'Type1') type1_balance,
(select sum(a.balance) from account a where a.person_id = p.person_id and a.account_type = 'Type2') type2_balance,
(select sum(a.balance) from account a where a.person_id = p.person_id and a.account_type = 'Type3') type3_balance
from person p
sqlfiddle example
A: Check if this helps -
http://sqlfiddle.com/#!4/30ebb/10/0
CREATE TABLE person
("person_id" int, "name" varchar2(9))
;
INSERT ALL
INTO person ("person_id", "name")
VALUES (1, '''Abcd''')
INTO person ("person_id", "name")
VALUES (2, '''xyz''')
INTO person ("person_id", "name")
VALUES (3, '''jjjjj''')
INTO person ("person_id", "name")
VALUES (4, '''sfds''')
INTO person ("person_id", "name")
VALUES (5, '''temp''')
SELECT * FROM dual
;
CREATE TABLE accounts
("personID" int, "accountType" int, "balance" int)
;
INSERT ALL
INTO accounts ("personID", "accountType", "balance")
VALUES (1, 1, 100)
INTO accounts ("personID", "accountType", "balance")
VALUES (1, 2, 150)
INTO accounts ("personID", "accountType", "balance")
VALUES (2, 1, 20)
INTO accounts ("personID", "accountType", "balance")
VALUES (3, 1, 40)
INTO accounts ("personID", "accountType", "balance")
VALUES (3, 2, 440)
INTO accounts ("personID", "accountType", "balance")
VALUES (4, 1, 600)
INTO accounts ("personID", "accountType", "balance")
VALUES (5, 1, 43)
INTO accounts ("personID", "accountType", "balance")
VALUES (5, 2, 50)
SELECT * FROM dual
;
Query -
select * from (
select p."person_id", a."accountType", a."balance"
from person p, accounts a
where p."person_id" = a."personID"
)
pivot (sum("balance") for "accountType" in (1 as acc_type1_bal,2 as acc_type2_bal));
person_id ACC_TYPE1_BAL ACC_TYPE2_BAL
1 100 150
2 20 (null)
4 600 (null)
5 43 50
3 40 440
A: select personid
,sum(ac1bal) accounttype1bal
,sum(ac2bal) accounttype2bal
,sum(ac3bal) accounttype3bal
from (
select persontable.personid
,case when (accounttype=1) then bal end ac1bal
,case when (accounttype=2) then bal end ac2bal
,case when (accounttype=3) then bal end ac3bal
from persontable
left join accounttable on persontable.personid = accounttable.personid
)
group by personid
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,194 |
Q: Apache2 ErrorDocument not working on VirtualHost My ErrorDocument redirect doesn't appear to be working!
Here is the bottom of my sites-available file:
...
</Directory>
ErrorLog /var/log/apache2/error.log
# Possible values include: debug, info, notice, warn, error, crit,
# alert, emerg.
LogLevel warn
CustomLog /var/log/apache2/access.log combined
ErrorDocument 403 /403.php
ErrorDocument 404 /404.php
</VirtualHost>
If you go to 109.123.109.205/404.php, the error page appears correctly, however, when you go to 109.123.109.205/asdf.php, I just get the bog standard 404 error...
Any insight greatly appreciated,
A: Your ErrorDocument statements look correct. As you are testing this using an IP address you may be picking up the default configuration. Try connecting to the virtualhost using the server's name as defined by the ServerName directive.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,337 |
<div class="input-group timeSelector">
<input type="text" class="form-control" ng-required="required" ng-disabled="readonly"
datetime-picker="HH:mm" enable-date="false" ng-model="ngModel" is-open="openedDialog"
timepicker-options="timeOptions"
clear-text="{{'dates.clear' | translate}}"
close-text="{{'dates.close' | translate}}"
now-text="{{'dates.now' | translate}}"
/>
<span class="input-group-btn" >
<button type="button" class="btn btn-default" ng-disabled="readonly" ng-click="openCalendar($event)"><i class="fa fa-clock-o"></i></button>
</span>
</div> | {
"redpajama_set_name": "RedPajamaGithub"
} | 8,033 |
"""Module for serving search data publishing requests."""
import logging
import logging.config
import psycopg2 # No lint.
from common import exceptions
from serve import constants
from serve import http_io
from serve.publish.search import search_publish_manager
# Get logger.
logger = logging.getLogger("ge_search_publisher")
class SearchPublishHandler(object):
"""Class for delegating search publishing requests to handlers."""
def __init__(self):
"""Inits SearchPublishServlet."""
try:
self._search_publish_manager = (
search_publish_manager.SearchPublishManager())
except exceptions.Error as e:
self._search_publish_manager = None
logger.error(e)
def DoRequest(self, request, response):
"""Handles request by delegating it to search publish manager."""
assert isinstance(request, http_io.Request)
assert isinstance(response, http_io.Response)
# Check for init failure and return an error status and appropriate message.
if not self._search_publish_manager:
http_io.ResponseWriter.AddJsonFailureBody(
response,
"Server-side Internal Error: Failure to init SearchPublisher")
return
try:
cmd = request.GetParameter(constants.CMD)
if not cmd:
raise exceptions.StreamPublisherServletException(
"Internal Error - Missing Request Command.")
if cmd == constants.CMD_QUERY:
self._search_publish_manager.HandleQueryRequest(request, response)
elif cmd == constants.CMD_PING:
self._search_publish_manager.HandlePingRequest(request, response)
elif cmd == constants.CMD_ADD_SEARCH_DEF:
self._search_publish_manager.HandleAddSearchDefRequest(
request, response)
elif cmd == constants.CMD_DELETE_SEARCH_DEF:
self._search_publish_manager.HandleDeleteSearchDefRequest(
request, response)
else:
raise exceptions.SearchPublishServeException(
"Internal Error - Invalid Request Command: %s." % cmd)
except exceptions.SearchPublishServeException as e:
logger.error(e)
http_io.ResponseWriter.AddJsonFailureBody(response, str(e))
except (psycopg2.Warning, psycopg2.Error) as e:
logger.error(e)
http_io.ResponseWriter.AddJsonFailureBody(response, str(e))
except Exception as e:
logger.error(e)
http_io.ResponseWriter.AddJsonFailureBody(
response, "Server-side Internal Error: {}".format(e))
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,161 |
Veeam Restore Point Simulator, Calculate your repository size.
LaurensvanDuijn 07/12/2015 14/01/2016 No Comments on Veeam Restore Point Simulator, Calculate your repository size.
A handy tool for an estimated sizing Veeam Repository storage needs. Nice option to "predict" size of data over the years by adding a percentile grow rate.
Cloud controlled drones are the future. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,008 |
Gex ist eine Jump-'n'-Run-Computerspiel-Reihe des US-amerikanischen Entwicklungsstudios Crystal Dynamics, die auch unter anderem von Eidos Interactive veröffentlicht wurde. Protagonist der Spiele ist Gex Gecko, ein Gecko. Bisher erschienen drei Spiele für verschiedene Plattformen.
Die Nintendo-64-Umsetzung des zweiten Teils erschien 1998 unter dem Titel Gex 64: Enter the Gecko. Eine Game-Boy-Color-Version erschien im selben Jahr als Gex: Enter the Gecko.
Für den dritten Teil erschien auch eine Game Boy Color Version mit dem Titel Gex 3: Deep Pocket Gecko. Via PlayStation Store sind die PSone-Fassungen aller Titel auch für die PlayStation 3, PlayStation Portable und PlayStation Vita erhältlich (Internetverbindung notwendig). Diese Veröffentlichungen wurden von der PEGI ab 12 Jahren freigegeben. Ende 2021 und Anfang 2022 hat Square Enix Gex als Marke in Europa und Japan eingetragen.
Gex
Gex, der erste Teil der Serie erschien am 28. August 1996 für 3DO und am 30. August 1996 für Sega Saturn, PlayStation und Windows. Das Spiel ist in einem 2D-Grafikstil gehalten.
Handlung
Als Gex wie immer vor seinem Fernseher sitzt bemerkt er plötzlich eine Fliege, die sich ihm nähert. Ohne jeglichen Verdacht verschluckt er sie, wodurch Rez, ein Wesen in der Mediendimension, auf ihn aufmerksam wird. Einige Sekunden später wird Gex in den Fernseher hineingezogen. Gex ist gefangen und er muss einen Weg finden, um zu entkommen.
Steuerung
Die normale Steuerung der Windows-Version erfolgt über die Tastatur. Microsoft empfiehlt aber, ein SideWinder-Gamepad zu verwenden.
Umfang
Die Spielewelt, genannt The Dome (in den Nachfolgern als Mediendimension bezeichnet), wird in fünf große Welten und eine Bonuswelt unterteilt. Um fortzuschreiten muss man in einem Level eine Fernbedienung finden, die den Eingang in das nächste Level ermöglicht. In einigen Levels findet man auch zwei bis drei Fernbedienungen. Die zweite Fernbedienung öffnet dann immer eine neue Welt. Da es in manchen Levels ein Bonusspiel gibt, findet man dort bei erfolgreichem Abschluss eine dritte Fernbedienung, die jeweils ein Level in der Bonuswelt öffnet.
Cemetery (Horror-Thematik)
Levels: Frankie & Heli, Grave Danger, Tomato Soup, Disco Inferno, Spin N' Puke (Endgegner)
New Toonland (Cartoon-Thematik)
Levels: Pow!, Twin Towers, Rock It!, Knock! Knock!, The Flatulator (Endgegner)
Jungle Isle (Dschungel-Thematik)
Levels: Feeding Frenzy, Congo Chaos, Jungle Gym (Endgegner)
Kung Fuville (Kung-Fu-Thematik)
Levels: Sumo City, Fish Bait, Chop Chop, Toxic Turtle (Endgegner)
Rezopolis (Science-Fiction-Thematik)
Levels: Rez Knight Fever, On The Move, Rez's Lair (Endgegner)
Planet X (Bonuswelt)
Levels: Saucer Station, Free Fall, Bombs Away, Newton's Fourth Law, Head To Head, The Project, The Web, Clothesline
Gex 3D: Enter the Gecko / Return of the Gecko
Enter the Gecko erschien 1998. Der Alternativtitel lautet Return of the Gecko. Je nach Konsole/Region heißt es 3D, 64 oder ein Zusatz fehlt. In Japan heißt das Spiel SpinTail.
Gex befindet sich in der so genannten "Medien-Dimension". Man muss versuchen durch Erlangen von Fernbedienungen aus der Fernsehwelt zu flüchten.
Anders als Teil eins basiert der zweite Teil auf einer 3D-Grafik. In den Leveln schaltet man durch erlangte Fernbedienungen neue Welten frei, in denen man wiederum drei Missionen zur Auswahl hat, um Fernbedienungen zu bekommen.
Jedes Level ähnelt verschiedenen Film- und Fernsehproduktionen, so gibt es z. B. Anspielungen auf die Looney Tunes, Terminator, sowie andere Comic-, Kungfu- und Science-Fiction-Filme. Zudem lässt Gex auch immer passende Kommentare von sich, welche auf den jeweiligen Film anspielen.
Gex 3: Deep Cover Gecko / Deep Pocket Gecko
Deep Cover Gecko ist der dritte Teil der Spielserie und erschien 1999 für Sonys PlayStation und das Nintendo 64. Die Game Boy Color Fassung trägt den Titel Deep Pocket Gecko. Auch hier ist die Namensgebung unterschiedlich.
Gex kämpft wie in vergangenen Teilen gegen seinen Erzfeind Rez, der dieses Mal seine Agentin Xtra (gespielt von Marliece Andrada) entführt hat.
Um sie zu befreien, muss Gex sich durch zahlreiche Welten kämpfen, darunter Pyramiden, den Wilden Westen oder auch die Arktis.
Die Hauptaufgabe ist dabei das Sammeln von Fernbedienungen, wodurch sich stetig neue Level (Als TV-Sender dargestellt) öffnen lassen.
Die Steuerung ist ähnlich der Vorgänger. So kann Gex springen, an Wänden entlang klettern, seinen Schwanzschlag sowie einen Karatekick ausführen. Zusätzlich verfügt Gex über eine zusätzliche Fähigkeit, je nach Welt die er betritt (Cape-Gleiten als Rotkäppchen im Märchen-Level, Jet-Fliegen als Superheld im Anime-Level).
Weblinks
Einzelnachweise
Computerspielreihe | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,538 |
Becoming Aware of Civic Unawareness
education (Photo credit: Sean MacEntee)
The United States was founded on the premise that the people could rule themselves without theocracy or aristocracy. Government of, by, and for the masses – int the rich and powerful. It is called The Great Experiment, and its success depends on a well-educated electorate. Sufficiently educated to understand not only the system that we have, but why we have it and how it works. And how it doesn't.
The preparation of the voter so that he might express his opinion by means of the ballot, thus insuring political liberty, was one of the main goals of Jefferson's plan for education which asserted four basic principles:
that democracy cannot long exist without enlightenment.
that it cannot function without wise and honest officials.
that talent and virtue, needed in a free society, should be educated regardless of wealth, birth or other accidental condition.
that the children of the poor must be thus educated at common expense.
http://www.earlyamerica.com/review/winter96/jefferson.html
Jefferson believed the elementary school was more important than the university in the plan because, as he said, it was "safer to have the whole people respectfully enlightened than a few in a high state of science and many in ignorance as in Europe" (as cited in Peterson, 1960, p. 241). He had six objectives for primary education to bring about this enlightenment and which highlighted what he hoped would make every person into a productive and informed voter:
To give every citizen the information he needs for the transaction of his own business;
To enable him to calculate for himself, and to express and preserve his ideas, his contracts, and accounts, in writing;
To improve, by reading, his morals and faculties;
To understand his duties to his neighbors and country, and to discharge with competence the functions confided to him by either;
To know his rights; to exercize with order and justice those he retains; to choose with discretion the fiduciary of those he delegates; and to notice their conduct with diligence, with candor, and judgment;
And, in general, to observe with intelligence and faithfulness all the social relations under which he shall be placed.
The state of Jeffersonian enlightenment in the realm of civic responsibility and the promotion of a healthy democracy is deplorable. The country is full of jingoists and poser patriots, passionate to defend what they do not understand – and are therefore easily mislead.
We have been encouraged to value wealth over community, and the accumulation of wealth over patriotism. Citizenship has ceased to be a code of honor and is now reduced to simply a legal status.
The problem of civic illiteracy is not something new, but it is finally getting periodic bursts of recognition.
Asserting that democracy is not inherited at birth but rather learned in school, O'Connor founded the educational nonprofit group iCivics in 2009 to secure America's governance and prepare the next generation of citizens and leaders.
Justice Sandra Day O'Connor seeks to reverse America's decline in civics
Plans are being developed to "address the problem". I say that with a hint of sarcasm because they are still treating it as a mere lesson to be learned. I think the solution will need to stress participation as much as scholarship.
Campaign for the Civic Mission of Schools
A Crucible Moment: College Learning & Democracy's Future
Hundreds Of Students, Officials To Celebrate Citywide Classroom Civics Program At May 29 Event
Don't Pick On Immigrants: Re-Americanize Everyone
Good News About Civic Education in Tennessee (ncsl.typepad.com)
Hundreds Of Students, Officials To Celebrate Citywide Classroom Civics Program At May 29 Event (sacbee.com)
From Justice O'Connor: iCIVICS(tln.typepad.com)
May 29, 2012 Posted by Zera Lee | Education, Elections, Governance | Citizenship, Education, Government, iCivics, Jefferson, Leadership, Philosophy, Sandra Day O'Connor, Sovereignty | Leave a comment
Federal Government Disagrees With Ann Romney: Raising Children Not 'Work'
We are seeing the fallacy of multiple definitions at work. Pun intended 😉
Pushing a weight up an inclined plane is work, scientifically speaking.
Raising children takes effort. A form of work that used to be called a labor of love. [sarcasm] Now that conservatives seek to demonize the word "labor", we don't hear that expression anymore. Maybe they'll call giving birth "workforce expansion" instead of "labor". [/sarcasm]
Ann Romney has worked at being a mother, but that is not the same thing as being a working mother. She may have made the effort and spent the money, but she has not worked for a paycheck. She did not have to earn the money she spent to raise her kids. She made a lifestyle choice that is available to fewer and fewer women every year. It is rapidly becoming elitist in the full meaning of the word.
Hilary Rosen leaving out the phrase "for a paycheck" does not grant Ann Romney license to claim to understand the plight of women who must be both mother and breadwinner. She has never been in that position, and never will be.
Conservatives have made hay out of substituting their choice of definitions for the meaning intended by Hilary Rosen. This is not honest debate, it is propaganda.
Hilary Rosen was right. Ann Romney doesn't speak for women in the workforce. – The Washington Post (mbcalyn.com)
Ben Romney Insists that His Mom Did Too Work Raising Five Little Romneys All on Her Own [Ann Romney] (jezebel.com)
Rosen Attack On Ann Romney Not About Motherhood, But About Actual Jobs (lezgetreal.com)
Democrats to introduce WORK Act to give all mothers the same choice Ann Romney had (dailykos.com)
Did Ann Romney 'Work'? (parenting.blogs.nytimes.com)
April 23, 2012 Posted by Zera Lee | 2012 Election, Elections, Women | Ann Romney, Class Warfare, Economic Warfare, Hilary Rosen | Leave a comment
You never know when a moment of inspiration will come along and distract you right when you were minding your own business. I had such a moment in the past week.
It has been a long time since I read Edgar Rice Burroughs, and with the pending release of the "John Carter" movie I thought I would go back and re-read the books the movie was based on.
No, this isn't going to be a book report. I went through my ERB phase many years ago. This reading was just to refresh my memory, but it got me thinking…
One of the fundamental themes of the story is the unimpeachable honor of the protagonists. It is, perhaps, a caricature or an idealistic representation of an age when a man's word was his bond, when a handshake was as good as a signed contract.
When I read the John Carter and Tarzan books back in the 80's, the willingness of the characters to accept calamity and even death rather than betray their honor seemed, at times, frustrating in its absoluteness. Yet its idealistic view of humanity had its appeal.
Adherence to a code of honor is what made the heroes, heroes; and the failure to live up to such a code made the villains, villains. Redemption was often achieved through a return to a code of honor. A century ago, the stories were popular and the ideals respected.
To set a time reference, the tale of John Carter began as a serialized story entitled "Under the Moons of Mars" published from February to July, 1912. Five years later, that story was published in book form under the title "A Princess of Mars". There are eleven books in the series. They are all in my library.
These stories thrived through two World Wars and the Great Depression. Times when hope was in high demand. Perhaps John Carter, and Tarzan, paved the way for the golden age of westerns. The age of John Wayne, Zorro, The Lone Ranger, Bonanza, and many others.
I've been watching reruns of The Rifleman on MeTV lately, and the stories seem like they were from a different age. This was a show that I watched as a kid, but I see things in it now that I don't remember from the past. Maybe I took the whole "code of honor" thing for granted back then, and maybe I absorbed it as an impressionable child. But in this day and age, it seems out of place. Cities, and people, have changed.
It also seems like the environment that conservatives want to herd us toward.
A time when almost everyone carried guns, and the rule of law hung by a thread. A hair trigger. The next shootout. Funny how things get broken or shot up each week, but nobody goes broke from the cost of the damage. Somebody gets shot, and they are either recovered or written out to the script by the next episode. Lukas McCain spends almost no time working his ranch. Personal responsibility. Self reliance. Nice and clean. How Utopian. All honor and community – and no consequences. The government is not giving away free homestead land anymore. People's lives are too interconnected – with other people and with businesses. We are no longer an agrarian culture, and there is no going back.
ERB called his fictitious version of Mars "Barsoom". It was a dying world where where life was both cheap and precious because the resources that supported life were scarce and dwindling – and fought over. We wouldn't do that, would we?
He was well ahead of the environmentalists that conservatives denigrate. We are heading for such a world ourselves as the world population goes up even as our water and food supplies becomes more strained and vulnerable.
Big Oil brags about having 100 years of supply, if only we would exploit it. They use the promise of cheap and plentiful oil and natural gas to encourage us to burn through it as quickly as possible with no thought to the future. Barsoom paints an image of what happens when that oil and gas runs out, when the drinking water runs out, and we are not prepared for it because it was not profitable to pursue alternatives. It is a buggy-whip economy on steroids. I am sure the movie will be a special-effects extravaganza.
"Safely develop" supplies. "Millions of jobs" created.
There is no honor in perpetuating lies.
Where is the demonstration of honor? Is it in all the pledges that republicans require before they are let anywhere near the oath of office?
The Grover Norquist pledge
The Susan B. Anthony pledge
Contract with America
The Balanced Budget Amendment pledge
Personhood USA
and how many others?
Each pledge narrowing the constituency base they are committed to serve, until they are committed to serve only a small fraction of America. That…is a crime against representational government. The party that wants to radically re-engineer America around the towering code of honor represented by John Carter never fails to prove that they do not, themselves, embrace such a code to any meaningful degree.
Lee Atwater, Rush Limbaugh, James O'Keefe, and FOX News.
Watergate, the PATRIOT Act, the Iraq war, ALEC, sowing distrust of science, education, the free press, Congress, the Presidency, and the Judiciary.
The 2012 GOP primary season, and the death of the "eleventh commandment".
The republican party is a living testament to the fatal flaws in their own ideology, living proof that they are committed to fantasy and failure – and dishonor.
They might as well be living on Mars.
As for me, I am presently in my Harry Potter/Honor Harrington phase. I still believe in honor, and am still drawn by its appeal.
"And for the support of this Declaration, with a firm reliance on the protection of divine Providence, we mutually pledge to each other our Lives, our Fortunes and our sacred Honor."
Now that's a pledge to believe in.
Five Sci-Fi Characters Influenced By John Carter (moviesblog.mtv.com)
John Carter of Mars (www.DailyKos.com)
March 8, 2012 Posted by Zera Lee | 2012 Election, Campaign Strategy, Elections, GOP, Personal Notes | 2012 GOP Primary, Barsoom, Code of Honor, Conservatism, Culture, Edgar Rice Burroughs, Election Pledges, Elections, GOP, John Carter, Rush Limbaugh | Leave a comment
Citizens United Amendment Summary
January 21, 2012 is the second anniversary of the Supreme Court decision of CITIZENS UNITED v. FEDERAL ELECTION COMMISSION
Today, I choose to look forward to the day it is overturned. In that vein, I offer a survey of Constitutional Amendments proposed to achieve that end. I will analyze them in future diaries. This is just a reference.
Article V of the Constitution provides for two methods of amendment. Congress can propose an amendment with 2/3 approval from each chamber. Joint Resolutions are the vehicles used for this process. Once approved by Congress and signed by the President, 3/4 of the state legislatures must ratify it.
Senate Joint Res. 29
House Joint Res. 6
House Joint Res. 65
House Joint Res. 100
United For The People
112th Senate Joint Resolution 29:
Congress shall have power to regulate the raising and spending of money and in kind equivalents with respect to Federal elections, including through setting limits on–
(1) the amount of contributions to candidates for nomination for election to, or for election to, Federal office; and
(2) the amount of expenditures that may be made by, in support of, or in opposition to such candidates.
A State shall have power to regulate the raising and spending of money and in kind equivalents with respect to State elections, including through setting limits on–
(1) the amount of contributions to candidates for nomination for election to, or for election to, State office; and
Congress shall have power to implement and enforce this article by appropriate legislation.
The rights protected by the Constitution of the United States are the rights of natural persons and do not extend to for-profit corporations, limited liability companies, or other private entities established for business purposes or to promote business interests under the laws of any state, the United States, or any foreign state.
Such corporate and other private entities established under law are subject to regulation by the people through the legislative process so long as such regulations are consistent with the powers of Congress and the States and do not limit the freedom of the press.
Such corporate and other private entities shall be prohibited from making contributions or expenditures in any election of any candidate for public office or the vote upon any ballot measure submitted to the people.
Congress and the States shall have the power to regulate and set limits on all election contributions and expenditures, including a candidate's own spending, and to authorize the establishment of political committees to receive, spend, and publicly disclose the sources of those contributions and expenditures.
Congress shall have the power to regulate the contribution of funds by corporations, entities organized and operated for profit, and labor organizations to a candidate for election to, or for nomination for election to, a Federal office, and the power to regulate the expenditure of funds by corporations, entities organized and operated for profit, and labor organizations made in support of, or opposition to, such candidates.
A State shall have the power to regulate the contribution of funds by corporations, entities organized and operated for profit, and labor organizations to a candidate for election to, or for nomination for election to, public office in the State, and the power to regulate the expenditure of funds by corporations, entities organized and operated for profit, and labor organizations made in support of, or opposition to, such candidates.
Nothing contained in this Amendment shall be construed to allow Congress or a State to make any law abridging the freedom of the press.
House Joint Resolutions and others after the fold…
January 21, 2012 Posted by Zera Lee | 112th Congress, Campaign Finance, Citizens United vs FEC, Constitution | 112th Congress, Campaign Finance, Campaign Finance Reform, Citizens United, Citizens United Amendment, Constitutional amendment, Corporate Personhood, First Amendment, hjr100, hjr6, hjr65, hjr7, hjr72, hjr78, hjr8, hjr82, hjr86, hjr88, hjr90, hjr92, hjr97, Joint resolution, Move To Amend, Proposed Amendment, sjr29, sjr33, sjr35, United For The People | 2 Comments
With Newt in Virginia
In response to Newt Gingrich's allusion to Pearl Harbor as a parallel to his campaign failure in Virginia, I offer the preface to a book called "With Lee in Virginia (A story of the American civil war)", written by G. A. Henty. Published by Hurst and Company, New York, it does not identify a publication date or claim a copyright. The inscription indicates that this copy has been in the family since January, 1901. Antiques Roadshow type stuff. It doesn't look anything like the cover from Amazon.
I found Gingrich's comparison to an infamous attack to be arrogantly dismissive of the tragedy and horror of war. His scapegoating was an insult to the courage and sacrifice of our citizen soldiers and their families, as well as a testament to the empty rhetoric of "personal responsibility" that is fundamental to the conservative desire to re-engineer America. He also demonstrated ignorance of relevant laws and outright contempt for rules that hinder his agenda in any way.
His failure in Virginia, and his response to it demonstrate conclusively that he should only enter the White House with a visitor's pass and a Secret Service escort.
On a more personal note, I have called the present ideological battles a political civil war. I thought it would be appropriate to momentarily revisit that point in our history.
Yes, it really is all one paragraph in the book…
"My Dear Lads:
The Great War between the Northern and Southern States of America possesses a peculiar interest to us, not only because it was a struggle between two sections of a people akin to us in race and language, but because of the heroic courage with which the weaker party, with ill-fed, ill-clad, ill-equipped regiments, for four years sustained the contest with an adversary not only possessed of immense numerical superiority, but having the command of the sea, and being able to draw its arms and munitions of war from all the manufactories of Europe. Authorities still differ as to the rights of the case. The Confederates firmly believed that the States, having voluntarily united, retained the right of withdrawing from the Union when they considered it for their advantage to do so. The Northerners took the opposite point of view, and an appeal to arms became inevitable. During the first two years of the war the struggle was conducted without inflicting unnecessary hardship upon the general population. But later on the character of the war changed, and the Federal armies carried widespread destruction wherever they marched. Upon the other hand, the moment the struggle was over the conduct of the conquerors was marked by a clemency and generosity altogether unexampled in history, a complete amnesty being granted, and none, whether soldiers or civilians, being made to suffer for their share in the rebellion. The credit of this magnanimous conduct was to a great extent due to Generals Grant and Sherman, the former of whom took upon himself the responsibility granting terms which, although they were finally ratified by his government, were at the time received with anger and indignation in the North. It was impossible, in the course of a single volume, to give even a sketch of the numerous and complicated operations of the war, and I have therefore confined myself to the central point of the great struggle – the attempts of the Northern armies to force their way to Richmond, the capital of Virginia and the heart of the Confederacy. Even in recounting the leading events in these campaigns, I have burdened my story with as few details as possible, it being my object now, as always, to amuse, as well as to give instruction in the facts of history.
G. A. Henty."
As a bonus for those who were curious enough to slog through this post, I shall include an excerpt from the last page of the book (covering reconstruction):
"For the next three or four years times were very hard in Virginia, and Mrs. Wingfield had to draw upon her savings to keep up the house in its former state; while the great majority of the planters were utterly ruined. The negroes, however, for the most part remained steadily working on the estate. A few wandered away, but their places were easily filled; for the majority of the freed slaves very soon discovered that their lot was a far harder one than it had been before, and that freedom so suddenly given was a curse rather than a blessing to them.
Thus, while so many went down, the Wingfields weathered the storm, and the step that had been taken in preparing their hands for the general abolition of slavery was a complete success.
With the gradual return of prosperity to the South the prices of produce improved, and ten years after the conclusion of the rebellion the income of the Orangery was nearly as large as it had been previous to its outbreak."
I found it an interesting glimpse into the past, but with points that still resonate today. It would be interesting to explore just how closely the book parallels the plantation-era ideology of the modern republican party, if I had the time. What is one of the most surprising things for me was to find that the book is still in print, on tape, and even Kindle.
[UPDATE 12/26/2011]
Paul Goldman helps Newt Gingrich with Virginia ballot
Now that Slacker Newt has failed to meet the minimum requirements for getting on the Virginia primary ballot, he has decided that it would violate someone else's rights if they did not get to vote for him. How modest.
All he needed was 10,000 valid signatures. Signatures vetted by his own party. That's less than half of the population of the suburb I live in. In WI, Democrats are collecting an average of about 25,000 signatures/day to recall Walker. Even a minor politician should be able to collect 10,000 signatures in their own home state.
Basically, he is embracing every derogatory mis-characterization conservatives have aimed at liberals, and justifying liberal cynicism toward conservatives at the same time. IOKIYAR.
"According to press reports over the weekend," continued Pascoe, "the Chairman of the Virginia Republican Party, per Section 24.2-545 of the Code of Virginia, has indicated that he will be certifying only two candidates for inclusion on the 2012 GOP presidential primary ballot. Based on our collective knowledge and understanding of the state's election laws – including a previous successful legal action by Mr. Goldman as concerns a Democratic Party nomination process – we intend to formally challenge such certification for specific reasons to be detailed at the appropriate time.
Yet once again, the law should not apply to a republican. It's just not fair. The dog ate his petition.
"Our mutual goal is to ensure that the voting rights of the citizens of Virginia are fully protected."
So they have turned against the GOP voter suppression agenda?
"As with everything we do in the field of public policy, CFTR's goal is to empower the individual, in the belief that a free choice in the marketplace of ideas is what Virginians want to have their leaders achieve in time for 2012 presidential primary."
Whatever they are trying to say seems to have gotten lost in the confusion of ill-fitting catch-phrases. This is just meaningless BS.
If he had been applying for a job (which he was), and he failed to fill out the application before showing up for the initial interview, they would have shown him the door without wasting any more time on someone who had already failed key tasks and started making excuses.
Cirque du GOP is coming to Virginia. Enjoy the show, folks.
Newt Lashes Out After Campaign Setback (huffingtonpost.com)
Newt Gingrich Says His Failure To Make The Virginia Ballot Is Like The Pearl Harbor Attack (thinkprogress.org)
Million Dollar Historian Newt Gingrich Compares Virginia Ballot Failure To Pearl Harbor (mediaite.com)
Gingrich faces long odds to compete in Virginia presidential primary (washingtonpost.com)
December 26, 2011 Posted by Zera Lee | 2012 Candidates, 2012 Election, Candidates, Elections | 2012 Election, 2012 Primaries, G. A. Henty, Gingrich, Leadership, Newt Gingrich, Pearl Harbor, Personal Responsibility, VA-GOP Primary, Virginia | Leave a comment
South Carolina Voter ID Law: Justice Department Blocks Controversial Legislation
John Jay election certificate
At the beginning of our country, all you had to do to prove you were a citizen was to swear to it. Word of honor was enough. Neither the states nor the central government recorded or tracked births. Then it required an oath. Then a court. And a witness. Then it went too far, with intelligence tests and poll taxes. Rules and laws were used to manipulate elections instead of protecting our suffrage rights. In the past year, we have seen a major return to such voter suppression.
Protecting rights is a trade-off. Rights are not absolute, or free. In Federalist 2, John Jay said:
"Nothing is more certain than the indispensable necessity of government, and it is equally undeniable, that whenever and however it is instituted, the people must cede to it some of their natural rights in order to vest it with requisite powers."
The goal is to protect the most rights while ceding the least. Given the scarcity of fraud and the large number of disenfranchised, the voter ID laws are the embodiment of bad government.
Promoted as a way to protect the integrity of the election process, they accomplish the opposite. They are designed and intended to disenfranchise voters who are not likely to vote for conservatives.
In short, voter ID laws create the very problem they profess to fix – the manipulation of elections – and they do it deliberately. And with extreme partisanship.
South Carolina Voter ID Law: Justice Department Blocks Controversial Legislation (huffingtonpost.com)
Justice Department blocks South Carolina's voter ID requirements (dailykos.com)
Justice Dept. rejects South Carolina voter ID law, calling it discriminatory – Washington Post (washingtonpost.com)
South Carolina voter ID law rejected by Justice Department (mercurynews.com)
Justice Department Blocks New S.C. Voting ID Law (npr.org)
Justice Dept. rejects South Carolina voter-ID law – USA TODAY (content.usatoday.com)
December 24, 2011 Posted by Zera Lee | Elections, Legislation, Voter ID | 2012 Election, Conservatism, Government, John Jay, Photo identification, Republicans, South Carolina, Voting Rights Act | Leave a comment
Payroll Tax Cut Fight: 'Wall Street Journal' Editorial Rips Boehner, McConnell
The Wall Street Journal opinion piece passes out the business-centric blinders.
"No employer is going to hire a worker based on such a small and temporary decrease in employment costs, as this year's tax holiday has demonstrated. The entire exercise is political, but Republicans have thoroughly botched the politics."
True, but not the point of the exercise. Employers will hire when they see customers with money coming their way – which is the point of the tax holiday: Putting more money in consumer pockets. Wasn't it the republicans who said that people know best how to spend their own money? Conservatives consistently devalue the necessity of funding the demand side of supply and demand. Instead, they are aggressively working to weaken the economic foundation of the middle class.
"Their first mistake was adopting the President's language that he is proposing a tax cut rather than calling it a temporary tax holiday. People will understand the difference—and discount the benefit."
So people will understand when it comes time to end the Bush "tax holiday" for the rich?
"Republicans have also achieved the small miracle of letting Mr. Obama position himself as an election-year tax cutter, although he's spent most of his Presidency promoting tax increases and he would hit the economy with one of the largest tax increases ever in 2013. This should be impossible."
Except that Obama44 has been cutting taxes. The "tax holiday" in question is only one example. Conservatives keep changing the definitions. Either the House republicans have voted for a middle-class tax increase, or we need to end one of the largest unfunded tax holidays ever.
Conservatives are nibbling at the edges of doublethink. The Obama44 cuts to payroll taxes and the Bush43 income tax cuts to income taxes are both temporary cuts. There is one notable difference between the two though. The Obama cuts are being paid for – how is a major point of contention. The Bush43 cuts went straight to the national debt.
The President and the Democrats want the rich to pay for extending the payroll tax cuts, and put some of that idle money back in circulation as an economic stimulus. The republicans want the middle class and poor to pay for it, which would negate the simulative effect and hurt the economy in the long term. Redistribution of wealth at its most ineffective.
Republicans lose the Wall Street Journal on tax cut 'fiasco' (dailykos.com)
WSJ: GOP botched tax debate (thehill.com)
How the Republicans lost the upper hand in payroll tax debate – Washington Post (blog) (washingtonpost.com)
House GOP takes beating over payroll tax (cbsnews.com)
House Passes Bill… for New Churchill Bust (newser.com)
GOP senator says Republicans need to resolve payroll tax fight and 'move on' (thehill.com)
Romney Boldly Refuses To Take Sides On Payroll Tax Holiday (alan.com)
December 21, 2011 Posted by Zera Lee | 2012 Election, Campaign Strategy, Economics, Legislation | 112th Congress, 2012 Election, Barack Obama, Class Warfare, Conservatism, Direction, Economy, Employment, House, John Boehner, Obama, Partisanship, Tax, Tax holiday, United States Congress, Wall Street Journal | 1 Comment
Russell Pearce, Recalled Arizona Senate President, Could Get State Reimbursement For Campaign
At least one Arizona state senator thinks that an obscure provision in the state constitution could entitle recalled state Senate President (R) to money from the state.
State Sen. Jack Harper (R-Surprise) said that his reading of Article 8, Part 1, Section 6 of the state constitution would allow Pearce to ask the state to reimburse the cost of his unsuccessful campaign to fight being recalled from office this week.
According to records on the Arizona secretary of state's office website, Pearce raised $230,282 for the recall campaign and spent $159,587. Pearce, the architect of Arizona's controversial immigration law, lost the recall election in his Maricopa County district to fellow Republican Jerry Lewis.
This raises an interesting question of constitutional law.
Section 6. The general election laws shall apply to recall elections in so far as applicable. Laws necessary to facilitate the operation of the provisions of this article shall be enacted, including provision for payment by the public treasury of the reasonable special election campaign expenses of such officer.
But looking further (figuratively) – Article VIII again: Continue reading →
November 11, 2011 Posted by Zera Lee | Campaign Finance, Constitution | Arizona, Campaign Finance, Elections, ex post facto, Law, Recall election, Russell Pearce, State Constitutions | Leave a comment
112th Congress HJRes78 – A Citizens United Amendment
Ii I analyze any more Democrat Bills, I will have to come up with a new category for them.
The Joint Resolution:
[Congressional Bills 112th Congress]
[From the U.S. Government Printing Office]
[H.J. Res. 78 Introduced in House (IH)]
H. J. RES. 78
Proposing an amendment to the Constitution of the United States to
clarify the authority of Congress and the States to regulate the
expenditure of funds for political activity by corporations.
Ms. Edwards (for herself and Mr. Conyers) introduced the following
joint resolution; which was referred to the Committee on the Judiciary
JOINT RESOLUTION
Resolved by the Senate and House of Representatives of the United
States of America in Congress assembled (two-thirds of each House
concurring therein), That the following article is proposed as an
amendment to the Constitution of the United States, which shall be
valid to all intents and purposes as part of the Constitution when
ratified by the legislatures of three-fourths of the several States:
``Article--
``Section 1. Nothing in this Constitution shall prohibit Congress
and the States from imposing content-neutral regulations and
restrictions on the expenditure of funds for political activity by any
corporation, limited liability company, or other corporate entity,
including but not limited to contributions in support of, or in
opposition to, a candidate for public office.
``Section 2. Nothing contained in this Article shall be construed
to abridge the freedom of the press.''.
This is similar to my second proposed amendment in that it works to deny Constitutional protection to corporate political spending. This is probably the least disruptive method from a legal standpoint, but it retains the "regulating the hand that feeds" conflict of interest problem.
It does not include organized religion, which should not be engaging in political campaigns but do anyway.
To be fair, it does not include unions either. On the other hand, unions are associations of actual people, not "artificial persons". They do not pose the same threat to our sovereignty as corporations. Perhaps someday an adjustment will need to be made, but that becomes a slippery slope problem.
The freedom of the press must be maintained, though the corporate media undermines the Fourth Estate through the corrupt use of ownership powers.
Constitutional Authority Statement:
[Congressional Record Volume 157, Number 134 (Monday, September 12, 2011)]
[House]
[Pages H6097-H6098]
From the Congressional Record Online through the Government Printing Office [www.gpo.gov]
By Ms. EDWARDS:
H.J. Res. 78.
[[Page H6098]]
Congress has the power to enact this legislation pursuant
Article V of the Constitution.
The Congress, whenever two thirds of both Houses shall deem it necessary, shall propose Amendments to this Constitution,
or, on the Application of the Legislatures of two thirds of the several States, shall call a Convention for proposing Amendments,
which, in either Case, shall be valid to all Intents and Purposes, as Part of this Constitution, when
ratified by the Legislatures of three fourths of the several States,
or by Conventions in three fourths thereof,
as the one or the other Mode of Ratification may be proposed by the Congress;
that no Amendment which may be made prior to the Year One thousand eight hundred and eight shall in any Manner affect the first and fourth Clauses in the Ninth Section of the first Article;
and that no State, without its Consent, shall be deprived of its equal Suffrage in the Senate.
Related Bills:
Senate Joint Resolution 29
This is a simple and straightforward answer to Citizens United. Without a mandate, I think that there would be many partisan battles over regulation. Especially when one party confuses corporations with living people.
I also think it needs an enacting clause. Other than that, I like it.
November 8, 2011 Posted by Zera Lee | Campaign Finance, Citizens United vs FEC, Constitution, Legislation | 112th United States Congress, Campaign Finance, Citizens United, Proposed Amendments, United States Constitution | 1 Comment | {
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Droga krajowa 220 () – niemiecka droga krajowa przebiegająca z południa na północny wschód i łączy drogę krajową B9 w Kleve z drogą krajową B8 w Emmerich i autostradą A3 na węźle Emmerich w Nadrenii Północnej-Westfalii i dalej z drogą N316 w Holandii
Zobacz też
lista autostrad w Niemczech
lista dróg krajowych w Niemczech
Linki zewnętrzne
Lista dróg krajowych w Niemczech i w Rzeszy
220 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,872 |
Famiglia d'origine
Alessandro era figlio del duca Pietro di Oldenburg (1812-1881) e della principessa Teresa di Nassau-Weilburg (1815-1871).
I suoi nonni paterni erano il duca Giorgio di Holstein-Oldenburg (1784-1812) e la duchessa Ekaterina Pavlovna Romanova (1788-1819), nata granduchessa di Russia; quelli materni il duca Guglielmo di Nassau (1792-1839) e la sua prima moglie, la duchessa Luisa di Sassonia-Hildburghausen (1794-1825).
Matrimonio
Il 19 gennaio del 1868, a San Pietroburgo, Alessandro sposò la duchessa Eugenia di Leuchtenberg, figlia del duca Massimiliano di Leuchtenberg e della granduchessa Marija Nikolaevna di Russia.
Dal loro matrimonio nacque un figlio:
Pietro, duca di Oldenburg, nato il 21 novembre del 1868 e morto l'11 marzo del 1924, sposò la granduchessa Olga Aleksandrovna Romanova e, dopo il divorzio, Olga Vladimirovna Ratkova-Rognova.
Ascendenza
Onorificenze
Onorificenze oldenburghesi
Onorificenze russe
Onorificenze straniere
Note
Altri progetti
Casato degli Oldenburg
Alessandro | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,852 |
{"url":"https:\/\/kar.kent.ac.uk\/44243\/","text":"# The Dirichlet problem in convex bounded domains for operators in non-divergence form with L?-coefficients\n\nHieber, Matthias, Wood, Ian (2007) The Dirichlet problem in convex bounded domains for operators in non-divergence form with L?-coefficients. Differential Integral Equations, 20 (7). pp. 721-734. ISSN 0893-4983. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:44243)\n\n The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication)\n\n## Abstract\n\nConsider the Dirichlet problem for elliptic and parabolic equations in nondivergence form\n\nelliptic problem and maximal\n\nthe coefficients $a_{ij} \\in L^\\infty$ satisfy a Cordes condition and $p \\in (1,2]$ is close to $2$.\n\nThis implies that in two dimensions, i.e. $n=2$, the elliptic Dirichlet problem is always solvable if the associated operator is uniformly strongly elliptic, and $p \\in (1,2]$ is close to $2$, for maximal $L^q$-$L^p$-regularity in the parabolic case an additional assumption on the growth of the coefficients is needed.\n\nItem Type: Article Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, CalculusQ Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science Ian Wood 10 Nov 2014 18:01 UTC 16 Feb 2021 12:57 UTC https:\/\/kar.kent.ac.uk\/id\/eprint\/44243 (The current URI for this page, for reference purposes) https:\/\/orcid.org\/0000-0001-7181-7075","date":"2021-10-24 10:24:17","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\": 0.8975204229354858, \"perplexity\": 1566.669250727803}, \"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-2021-43\/segments\/1634323585916.29\/warc\/CC-MAIN-20211024081003-20211024111003-00343.warc.gz\"}"} | null | null |
{"url":"https:\/\/hpcc.ucr.edu\/manuals\/hpc_cluster\/parallelr\/","text":"# Overview\n\nR provides a variety of packages for parallel computations. One of the most comprehensive parallel computing environments for R is batchtools (formerly BatchJobs). It supports both multi-core and multi-node computations with and without schedulers. By making use of cluster template files, most schedulers and queueing systems are also supported (e.g. Torque, Sun Grid Engine, Slurm).\n\n## Parallelization with batchtools\n\nThe following introduces the usage of batchtools for a computer cluster using SLURM as scheduler (workload manager).\n\n## Set up working directory for SLURM\n\nFirst login to your cluster account, open R and execute the following lines. This will create a test directory (here mytestdir), redirect R into this directory and then download the required files:\n\ndir.create(\"mytestdir\")\nsetwd(\"mytestdir\")\n\n\n## Load package and define some custom function\n\nThis is the test function (here toy example) that will be run on the cluster for demonstration purposes. It subsets the iris data frame by rows, and appends the host name and R version of each node where the function was executed. The R version to be used on each node can be specified in the slurm.tmpl file (under module load).\n\nlibrary('RenvModule')\n\nlibrary(batchtools)\nmyFct <- function(x) {\nresult <- cbind(iris[x, 1:4,],\nNode=system(\"hostname\", intern=TRUE),\nRversion=paste(R.Version()[6:7], collapse=\".\"))\n}\n\n\n## Submit jobs from R to cluster\n\nThe following creates a batchtools registry, defines the number of jobs and resource requests, and then submits the jobs to the cluster via SLURM.\n\nreg <- makeRegistry(file.dir=\"myregdir\", conf.file=\".batchtools.conf.R\")\nNjobs <- 1:4 # Define number of jobs (here 4)\nids <- batchMap(fun=myFct, x=Njobs)\ndone <- submitJobs(ids, reg=reg, resources=list(partition=\"short\", walltime=60, ntasks=1, ncpus=1, memory=1024))\nwaitForJobs() # Wait until jobs are completed\n\n\n## Summarize job status\n\nAfter the jobs are completed one instect their status as follows.\n\ngetStatus() # Summarize job status\nshowLog(Njobs[1])\n# killJobs(Njobs) # # Possible from within R or outside with scancel\n\n\n## Access\/assemble results\n\nThe results are stored as .rds files in the registry directory (here myregdir). One can access them manually via readRDS or use various convenience utilities provided by the batchtools package.\n\nreadRDS(\"myregdir\/results\/1.rds\") # reads from rds file first result chunk\nreduceResults(rbind) # Assemble result chunks in single data.frame\n\n\n## Remove registry directory from file system\n\nBy default existing registries will not be overwritten. If required one can exlicitly clean and delete them with the following functions.\n\nclearRegistry() # Clear registry in R session\nremoveRegistry(wait=0, reg=reg) # Delete registry directory\n# unlink(\"myregdir\", recursive=TRUE) # Same as previous line\n\n\nfrom_file <- loadRegistry(\"myregdir\", conf.file=\".batchtools.conf.R\")","date":"2022-08-15 13:04:31","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.21688854694366455, \"perplexity\": 13200.248953409724}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-33\/segments\/1659882572174.8\/warc\/CC-MAIN-20220815115129-20220815145129-00088.warc.gz\"}"} | null | null |
With the Gemino 60 Walker you get the best of both worlds: The comfortable rolling characteristics and stability of the Gemino 60 and the additional support and safety you'd expect from a 'walker'. Adjust the forearm supports and push handles to fit your needs, and enjoy more freedom indoors - and outdoors.
Maximum User Height 4'9" - 6'6" 4'4" - 5'6"
Width Between Push Handles 12.6" 12.6"
Overall Height 38.8" - 45.5" 35.2" - 38.8" | {
"redpajama_set_name": "RedPajamaC4"
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Get access to La Scala family records.Start a free trial
La Scala Family History
La Scala Name Meaning
Italian: from scala 'ladder', 'flight of steps', with the definite article la, a topographic name for someone who lived by a flight of steps or on terraced land.
Similar surnames: La Sala, La Scola, La Cava, Di Scala, Scala, La Spina, La Fata
2 thousand record(s) for La Scala
957 Birth, Marriage, and Deaths
330 Census and Voter Lists
Where is the La Scala family from?
You can see how La Scala families moved over time by selecting different census years. The La Scala family name was found in the USA in 1920. In 1920 there were 4 La Scala families living in New York. This was 100% of all the recorded La Scala's in the USA. New York had the highest population of La Scala families in 1920.
Use census records and voter lists to see where families with the La Scala surname lived. Within census records, you can often find information like name of household members, ages, birthplaces, residences, and occupations.
View Census Data for La Scala
What did your La Scala ancestors do for a living?
Census records can tell you a lot of little known facts about your La Scala ancestors, such as occupation. Occupation can tell you about your ancestor's social and economic status.
What La Scala family records will you find?
There are 330 census records available for the last name La Scala. Like a window into their day-to-day life, La Scala census records can tell you where and how your ancestors worked, their level of education, veteran status, and more.
Search UK census records for La Scala
There are 433 immigration records available for the last name La Scala. Passenger lists are your ticket to knowing when your ancestors arrived in the UK, and how they made the journey - from the ship name to ports of arrival and departure.
View all La Scala immigration records
There are 195 military records available for the last name La Scala. For the veterans among your La Scala ancestors, military collections provide insights into where and when they served, and even physical descriptions.
View all La Scala military records
You've only scratched the surface of La Scala family history.
What is the average La Scala lifespan?
Between 1980 and 2004, in the United States, La Scala life expectancy was at its lowest point in 1985, and highest in 2003. The average life expectancy for La Scala in 1980 was 66, and 69 in 2004.
View Social Security Death Index (SSDI) for La Scala
An unusually short lifespan might indicate that your La Scala ancestors lived in harsh conditions. A short lifespan might also indicate health problems that were once prevalent in your family. The SSDI is a searchable database of more than 70 million names. You can find birthdates, death dates, addresses and more.
Discover the unique achievements of ancestors in the La Scala family tree | {
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Empire Day Celebrations, Whitwell (1904 ?) - Frame Landscape Small
Ref no DCBR000859
ImageDate 1 June(?) 1904 ?
Location The Square
Town Whitwell
(Showing the old blacksmiths workshop on the right). Empire Day celebrated the achievement of Britain in establishing the British Empire. For many years at the beginning of the 20th century June the first was often celebrated as Empire Day, although Empire Day was first celebrated in Britain in 1902 on May 24th. The notion of making 24 May (Queen Victoria's birthday) a celebration of empire originated in Canada in the late 1890s. An Empire Day for children had been started by the head mistress of a Canadian school who proposed that such a dayshould be celebrated in schools by patriotic exercises, readings and addresses. This idea was followed up in Britain by Reginald Brabazon, the twelfth Earl of Meath, who resolved to spread the movement throughout the Empire. On 21 July 1902, a cable appeared in the newspapers: 'The Earl of Meath has suggested that an Empire Day holiday should be observed' for school children only...May 24th, the birthday of Queen Victoria, stands out as especially suitable'. Empire Day was celebrated by patriotic gatherings, public luncheons, church services and special ceremonies in all state schools in the Commonwealth. As attachment to the empire waned, so too did the significance of Empire Day, and in 1958 its name was changed to British Commonwealth Day. In 1966 it changed again, this time to Commonwealth Day, and the date moved from 24 May to 11 June to coincide with the 'official' birthday of Queen Elizabeth II. | {
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## LIVING A JEWISH LIFE
Updated and Revised Edition
Jewish Traditions, Customs, and Values for Today's Families
## ANITA DIAMANT with Howard Cooper
For my daughter, Emilia Diamant
"She is a gift and a wonder."
A.D.
For my mother, Annette S. Cooper
"My mother was a perfect tzadik."
H.C.
For the modern Jew, observance is no longer a matter of "the all or the nothing." One only has to start.
Nobody can tell where this beginning will lead.
—FRANZ ROSZENWEIG (1886–1929)
## CONTENTS
Epigraph
Preface
Introductions and Definitions
HOME
Your Own Sanctuary
The Sabbath
Good Deeds
The People of the Library
What Jews Eat
COMMUNITY
Synagogues
The Organizational World
Education
Israel
Traveling Jewish
THE CYCLE OF THE YEAR
Jewish Time
Rosh Hashanah and Yom Kippur
Sukkot and Simchat Torah
Hannukah
Tu B'shvat
Purim
Passover
Lag B'Omer
Holocaust Remembrance Day and Israel Independence Day
Shavuot
Tisha B'Av
THE LIFE CYCLE
Birth
Bar and Bat Mitzvah
Marriage
Conversion and Adoption
Death and Mourning
Glossary
Timeline
Further Reading
Acknowledgments
Notes
Searchable Terms
About the Author
Other Books by Anita Diamant
Credits
Copyright
About the Publisher
## PREFACE
Dear Reader:
While I was writing this book, I thought a lot about who you might be, why you might pick up this title, and what you needed from an introduction to Judaism. I did this because I wanted to write a book that you would be comfortable with, a book that you could really use.
Since my image of you guided the contents, the organization, and the tone of Living a Jewish Life, I think it's only fair to tell you who I think you are.
I think you are a graduate student, and that you are an empty-nester. I think you have two children under the age of five, that you hope to become a grandparent soon, and that children are not part of your life-plan at all. I think you went to Hebrew school as a kid, and that you grew up only vaguely aware that you were Jewish but never belonged to a synagogue or any other Jewish organization. I think that you cherish memories of your mother lighting candles every Friday night, and that you've never seen anyone do that in your whole life. I think you are interested in Judaism because the person you are in love with is a Jew, and that you have been a Jew-by-choice for many years. I think you are not Jewish at all but are raising a Jewish child with a Jewish spouse. I think you are the Christian grandparent of Jewish grandchildren.
I think you know not a single word of Hebrew and that you can still read a little Hebrew from when you prepared for your bar or bat mitzvah. I think you believe deeply in the existence of a Holy One, and that the question of religious faith is meaningless to you.
I think you are married, divorced, single; straight and gay; active in the Jewish community and alienated from it.
In other words, I think you are a very diverse bunch. What you have in common is a genuine interest in Judaism as a way of life. I think you are curious about how to make Jewish choices in ways that do not deny the importance of all the other parts of yourself and your world. I think you are eager to learn from tradition and confident of your own ability to interpret ancient sources and ways.
I think we have a lot in common.
I was born to Jewish parents, both Holocaust survivors, who gave me an undiluted and positive Jewish identity. Yet, I consider myself a "Jew-by-choice" and I only started studying my heritage and making Jewish choices in my late 20s. That was when I fell in love with a non-Jew and realized how little I knew. So my then-boyfriend and I joined a Jewish reading group and discovered the vastness of the Jewish library. I wrote newspaper articles about the Jewish community and learned how varied and vital it is. I started to light candles on Friday night and made a place for meaningful ritual in my life.
When my fiancé decided to convert to Judaism, we found wonderful teachers and studied together. And together we started making Jewish choices, a process we continue day by day, year by year.
The Jews have often been called the Chosen People. They have also been called the Choosing People. Living a Jewish Life is intended as a guide to help you make meaningful choices in this ancient, life-affirming tradition. Remember that every Jew, regardless of training or accomplishments, is a student. Judaism is as wide and as deep as the ocean itself, which means that we are all, even the most learned among us, beginners.
I hope you find this book a welcoming and intriguing place to begin your exploration of Jewish life. May your journey be pleasant, your paths peaceful, and your discoveries fulfilling.
Anita Diamant
January 5, 2007
15 Tevet 5767
## INTRODUCTIONS AND DEFINITIONS
Opening this book and reading these words might constitute one of your first Jewish choices as an adult. Your reasons for wanting to explore Judaism are uniquely your own. Perhaps they have something to do with the desire for a more examined life, or a need to acknowledge spiritual or religious feelings. Maybe you are looking for an honest way to provide your children with a sense of their place in a great religious, ethical, cultural, and ethnic tradition.
Whatever your motivation or background, the first goal of Living a Jewish Life is to open the door to that tradition; the second is to help you make your own Jewish choices, at home, in the community, for years to come. The first section, "Home," describes the core elements that define a self-consciously Jewish home, which is the heart of Jewish life. These chapters cover everything from the contents of the kitchen cabinets, to the books on the shelves, to the observance of Shabbat—the Sabbath—the most important and sweetest of all Jewish holidays.
The section titled "Community" introduces the larger context for Jewish choosing, with information about how to find your niche through synagogues, educational institutions, and other kinds of organizations. This section also contains a discussion of Jewish learning, from preschool through adult education, and a chapter about Israel and traveling the world.
"Observance" provides an overview of the Jewish calendar, the annual holiday cycle, and the events that celebrate the human life cycle.
In order to make Living a Jewish Life as accessible as possible, Hebrew and Yiddish words and references have been kept to a minimum. Every non-English term used in this book is defined at least once in the text, and there is both a glossary and index for easy reference. A listing of recommended readings and resources is included, as is a timeline for historical reference.
While it is not a book of "do's and don'ts," Living a Jewish Life does have a point of view, and even an agenda—which is to encourage readers to make Jewish choices, to try on some of the rituals, observances, and customs described in the following chapters—to see how they feel and to explore what they can mean. Although there is a great deal of practical information in these pages—suggestions, instructions, and menus for everything from prayers to arts-and-crafts projects—the "how-to" materials are not presented as ends in themselves, because one of the hallmarks of liberal Judaism is its insistence on finding and creating meaning, on considering the "why" of everything: Why light candles on Friday night? Why forgo shrimp? Why get married under a canopy? Why join a synagogue?
For liberal Jews, the answers to these questions are not fixed, but open, dynamic, and personal. The answers come from many sources: through the process of studying traditional Jewish texts, such as the Torah, the literature of Jewish law (halachah) and imagination (Midrash); through the sweep of Jewish history; through discussion with teachers and peers; through a sense of God's presence; and through personal reflection and experimentation.
Living a Jewish Life takes a descriptive rather than a prescriptive approach to Judaism. The word "should" does not appear in these pages. Since Jews do things—well, actually nearly everything—in many different ways, this book contains "menus" of choices about the hows, whens, and whys of modern Jewish life. This embrace of Jewish pluralism is an expression of "liberal Judaism," which requires an introduction of its own.
Liberal Judaism
Liberal Judaism is a category that embraces the broad range of religious practices, beliefs, and institutions of Jews who identify themselves as Conservative, Reform, Reconstructionist, postor transdenominational, egalitarian, humanist, New Age, or "just Jewish." Although there are substantial differences among these groups, what they share is an acknowledgment of their Jewishness as a choice. In other words, they practice Judaism not necessarily on God's authority, or because their parents would be horrified if they didn't, but because they find meaning, joy, and strength in Jewish practice and community. Living a Jewish Life is an expression and a celebration of the diversity that comes of this choosing.
Liberal Judaism is just over 200 years old, which in the context of Jewish time is relatively young. However, since the destruction of the Temple in Jerusalem in 70 C.E.,* Jewish life has been pluralistic, contentious, and constantly changing, and in that sense, this current incarnation of Judaism is heir to that long tradition of diversity and choice.
Nonetheless, Judaism certainly appeared more uniform in the past. Before the late 18th century, virtually all Jews experienced birth, education, marriage, family, work, recreation, worship, and death as mediated by Jewish law and custom. The non-Jewish world perceived and treated Jews not as individuals, but in accordance with prevailing attitudes, laws, and prejudices about them as a group.
The philosophical revolution of the Enlightenment and subsequent political changes transformed that reality. The ghettos were unlocked, as were the doors to the great universities of Europe. Jewish men shaved their beards; Jewish women removed their traditional head coverings. More Jews worked and even socialized with Christians. Alternatives to an all-encompassing Jewish lifestyle began to emerge, but they were limited: Jews could either remain as separate as possible from the larger secular world, or they could abandon their traditions altogether and convert to Christianity, or they could try to live a kind of double life, an existence that Jewish reformers of the time described as "Jews at home, but men (like all others) on the street."1
Within a few generations, the American experience and the drive to assimilate pushed this paradigm much further; one was a Jew precisely the way the neighbors were Presbyterian. What had once been an all-embracing view of life shrank to nominal affiliation with once-in-a-while or even once-a-year observance. In other words, one was identified as a Jew on the street but was a secular person at home. For a time, liberal Judaism seemed to mean doing less and less in the way of ritual, study, or commitment.
In the 1960s, the Six Day War in Israel forged a renewed sense of urgency and pride among Jews around the world. That change coincided with a broader cultural shift away from the notion of a "melting pot," a society in which ethnic, national, and religious differences disappear, in favor of the ideal of a "mosaic," in which individual differences add to the richness of the whole. Within this context, liberal Judaism has thrived.
Today, Jews who are fully at home in the secular world, participating in every aspect of public life and culture as equals and as leaders, also light candles on Friday nights, study Jewish books, and are active members of synagogues and other Jewish institutions. From this integrated perspective, there are Jewish dimensions to many seemingly value-neutral choices of daily life: everything from donating blood to planning vacations, from deciding how much to give the United Way campaign to ordering lunch becomes a Jewish decision.
Less is no longer more. Liberal Jews now embrace once-rejected traditional customs and rituals at home, in synagogues, and in other settings. Traditions such as wearing tallit and kippah, signing a ketubah, immersing in a mikveh, and keeping kosher are choices on the menu of liberal Judaism. These and other mitzvot and customs are reimagined, reinterpreted, and reclaimed not only because they belong to the Jewish canon, but because they make living a Jewish life more beautiful and meaningful. And the choices made by liberal Jews are informed by contemporary wisdom; the insights of psychology and feminism, for example, are also part of the equation.
However, it is not easy to fix the boundary between liberal Judaism and the rest of Jewish practice. And as with liberal Jews, those who claim to be "traditional" or even "Orthodox" run a wide gamut, ranging from "traditional/egalitarian" groups, in which women lead part of the prayer service, to mainstream Orthodox Union congregations, to an array of Hasidic sects living in the United States and Israel. What such groups share, in the most general terms, is adherence to halachah (Jewish law), as set forth in rabbinic literature and as interpreted by their own rabbinic authorities; in practice this is expressed, most obviously, in more differentiated roles for the sexes, and stricter observance of Sabbath, holiday, and dietary laws.
Historically, there have always been deep divisions among Jewish factions, sects, and denominations, and our time is no different. Despite all the loud and even bitter disagreements that divide one Jew from another, the ethic of unity, klal Yisrael, transcends everything. We are all, ultimately, related to one another. We are all, ultimately, one people, responsible for one another.
Liberal Jews have long been challenged by charges of and troubled by feelings of inauthenticity. But the suspicion that only the Orthodox can lay claim to being "real" Jews is starting to fade. With the revival of study, commitment, and self-conscious Jewish decision-making in the liberal community, there is a growing sense of ownership, comfort, and legitimacy. Liberal Judaism offers a rich and engrossing way of life. Fed and fueled by the dialectic—the tension and resolution—of making Jewish choices, it is truly, "a tree of life."
Mitzvah
Making Jewish choices is traditionally expressed in the concept and execution of mitzvot, the plural of mitzvah. The word mitzvah does not translate well. It derives from a military term for "command," and it is often translated as "good deed." But Jews don't perform mitzvot like so many good Scouts. A mitzvah is a commandment from God, but a command that exists only when put in action by people. A mitzvah is an idea-given-form. It is value-action—praxis.
Obviously, the word "commandment" immediately raises the essential theological question. Since a commandment implies a Commander, the whole notion of mitzvah seems to rest on the existence of God—on a God who gives orders. For Jews who believe the Bible was divinely revealed, the authority of mitzvot is unassailable; God commands so people must obey each and every one.2
Liberal Jews, for whom the authority of the Bible does not necessarily reside in the idea of divine authorship, tend to emphasize the fact that mitzvot are subject to human response—to a sense of being commanded or directed, and thus to human interpretation.
Moses asks God to explain the laws for keeping kosher:
"Thou Shalt Not Seethe a Kid in Its Mother's Milk."
"Does that mean we should have two sets of dishes?"
"Thou Shalt Not Seethe a Kid in Its Mother's Milk."
"Does that mean that we should wait six hours between eating milk and meat?"
"Thou Shalt Not Seethe a Kid in Its Mother's Milk."
"Does that mean we should check the label of everything we buy and use only those items made with pure vegetable shortening?"
"Thou Shalt Not Seethe a Kid in Its Mother's Milk."
"Does that mean..."
"OKAY, HAVE IT YOUR WAY!"3
The Torah is said to contain 613 mitzvot. These include celebrating Shabbat, giving money to the poor, refraining from eating pork and shellfish, entering sons into Jewish life through the covenant of circumcision, teaching children the story of Passover. For liberal Jews, not all mitzvot have the same weight because not all mitzvot provoke the sense of feeling commanded. As one rabbi has written, "There will be mitzvot through which my forebears found themselves capable of responding to the commanding God which are no longer adequate or possible for me, just as there will be new mitzvot through which I or my generation will be able to respond which my ancestors never thought of."4 Indeed, for liberal Jews, the increasingly complex modern world may suggest new and binding mitzvot regarding everything from the proper application of medical technology for the terminally ill to the ecological imperative to recycle.
Since each mitzvah is the occasion for reflection and for a choice, liberal Jews take on mitzvot for many reasons. For some, there is a compelling argument in following a particular discipline or practice simply because it has been and remains a part of Jewish identity. Many commit themselves to fulfilling those mitzvot that are consistent with a personal sense of right and wrong, such as giving to the poor and working to fulfill the prophetic call for justice. Some find mitzvot a way of maintaining a relationship with what is holy in life: "While I have and retain the freedom of choosing my specific means of response at a given moment, the essential fact of my life will be my intention to respond [to God through mitzvot]."5
The Hasidic masters discerned a relationship between the Hebrew mitzvah and a similar Aramaic word that meant "together."6 Thus a mitzvah can be thought of as an act that unites people, and that unites people with God. Doing mitzvot can knit together the holy and the profane. Doing mitzvot can be a way to discover the sacred in the mundane.
However the idea of mitzvah is understood and for whatever reason a mitzvah is undertaken, the concept defies the rationalist, Western approach to the world, which posits that understanding should always precede action. (In other words, we tend not to open doors until we know what is behind them.) Doing mitzvot requires consciously setting aside that worldview. In the Bible, when the Israelites were given the Torah, their response was "We shall do and we shall hear."7 In other words, they promised to act first, and hear (or understand) second; to leap before looking.
The logic to, benefits from, and understanding of mitzvot may be compared to human experiences that are endlessly described but ultimately available only through living. Such as making love. Such as becoming a parent. Or burying your own parents. The mitzvot are the methodology of Jewish choosing.
Jewish Parenting
Many people do not begin to make serious Jewish choices until they become parents. Then the question "What are we handing on to our children?" becomes a primary motivation in exploring Jewish questions: from selecting a religious education to figuring out how to impart a sense of Jewish identity.
The essential goal for Jewish parents through the ages has always been to raise a child to be a mensch—literally, "a person"; figuratively, a person who cares and shares, loves and studies, and acts righteously in the world. Just as it is difficult for a child to grow up to be a mensch without mensch-like parents, children rarely learn to cherish their Jewishness without witnessing their parents' commitment to Judaism.
Thus, if Judaism has nothing to do with family life, children cannot learn how to live a Jewish life. After-school programs or even a full-time Jewish day school is not sufficient because Jewish identity cannot be learned in a classroom. Jewishness is not simply a function of the intellect, but an expression of heart and soul, of psyche and senses.
To raise children who will care about Judaism, parents need to demonstrate their own Jewish commitment in ways that stimulate and satisfy them as adults. And this holds true for families where both parents are Jews, and for intermarried families where the non-Jewish parent is committed to raising Jewish children. Parents often begin making Jewish choices—lighting candles on Friday night, joining a synagogue, celebrating holidays—"for the children." If those practices remain essentially meaningless to the adults, children will see that Judaism is merely a matter of going through motions. If, however, those rituals and commitments—even if originally undertaken "for the children"—become important and fulfilling for parents as well, children will learn their Judaism as naturally as they learn their native language.
One of the great discoveries of parenthood is how much children teach us about life and time, joy and tenderness. Kids can help parents learn how to make Jewish choices, too, especially regarding ritual. American Jews are often unfamiliar and uncomfortable with ritual gestures, such as lighting candles and singing in public. Kids, however, are experts at learning through pretending and can enable adults to suspend their disbelief and make the leap to nonutilitarian language and actions. "Playing Shabbat" may be the best way to approach experimenting with Sabbath customs and rituals.
Raising Jewish children also means adding a whole new set of goals to the list shared with all parents (good grades, good manners, etc.). In two-parent families, Jewish parenting requires agreement on a long list of choices that may include the selection of a Jewish name for a new baby, or looking for a house in a neighborhood that is reasonably close to a synagogue and where there will be other Jewish children for yours to play with. Jewish parenting also means making decisions that may not be entirely popular with kids—like no television on Friday night, or the decision that religious school takes precedence over soccer practice. And that means tolerating some measure of Jewish conflict.
Ultimately, since children grow up to make their own decisions, perhaps the most important task for parents is to give children practice at making Jewish choices—appropriate to their age, of course. Youngsters can be asked how they would like to participate in Friday night rituals: by setting the table, by singing, by saying a blessing, by drawing a picture. Older children can be included in family decisions about where to send charitable contributions. A kid who announces he does not want to attend services with the rest of the family might be offered alternatives for those hours, such as reading a Jewish book, babysitting for preschoolers whose parents are attending services, or even doing volunteer work. In other words, the options presented require decision-making based on Jewish values and options.
Learning the Language
You don't have to speak Hebrew or know a lot of Yiddish to make meaningful Jewish choices. That said, it helps to know some of the vocabulary, which is not so much a matter of memorizing a list of words as it is mastering a few core concepts contained in words that do not translate very well. For example, mitzvah, which is not well served by a definition like "good deed" or "commandment." Or tzedakah, which means "righteous giving" not "charity." Shabbat, Torah, kosher, Reconstructionist, shtetl, schlemiel: these words are the Jewish cultural markers that will help you find your footing within the Jewish world.
Hebrew—the language of the Torah, the prayer book, the Passover haggadah, and the land of Israel—is the universal and sacred language of Judaism. And yet Hebrew, with its unfamiliar alphabet and right-to-left writing, can seem like a major stumbling block to feeling comfortable and authentic. This is a common problem, as the majority of American Jews cannot read or speak Hebrew.
Of course, almost all commonly used Hebrew texts and prayers are available in good English translations, and any home ceremony can be performed entirely in English. (It goes without saying that God understands no matter what language you're using.) If you do not know any Hebrew but want to incorporate its sound and flavor into home observances, many prayers are transliterated—the Hebrew sounds spelled out in the Latin alphabet—and can be learned phonetically thanks to recordings.
That said, basic Hebrew is not difficult to learn, and introductory courses are offered at all synagogues and in other settings, including online. Adults can learn Hebrew as an access language—for reading purposes—with a modest commitment of time in weekly or biweekly classes. Many people learn the basics by following along with their children's Hebrew lessons. Learning the aleph-bet along with some vocabulary and grammar provides unique insights into the tradition, because as every bilingual person can testify, something always gets lost in translation.
The best way to learn modern Hebrew is by spending time in Israel and/or attending an ulpan, an intensive Hebrew-language instruction course developed for immigrants to Israel.
Of course, Hebrew isn't the only Jewish language. There are three other languages written with the Hebrew alphabet that are part of Jewish history and culture: Aramaic, an ancient Semitic language, the language of the Talmud, was also Jesus' spoken tongue; Yiddish, a combination of Hebrew, German, and words borrowed from other languages, is spoken by Jews of Eastern European descent (Ashkenazi) and has infiltrated American popular culture; and Ladino, a combination of Hebrew and Spanish, is spoken among Jews of Mediterranean (Sephardic) background. Both Yiddish and Ladino have a rich literature that includes poetry, lyrics, prayers, jokes, and fiction. Yiddish language classes are taught in community and academic settings.
Getting Started
It is helpful to think about starting to make Jewish choices the way you would approach any life-enhancing discipline, such as taking up a new sport, changing your eating habits, learning to play a musical instrument, or studying a new language. In other words, this is going to take time, practice, and patience.
Especially patience. Without patience for the beginner's inevitable awkwardness and mistakes—at the piano, on the tennis court, in the synagogue—there can be no mastery of any new skill. Making new Jewish choices requires a suspension of the kind of standards (for competence if not excellence) to which adults tend to hold themselves. In other words, you have to allow yourself to learn as a very small child learns—without grades or deadlines, without too many expectations, and without fear of failure or embarrassment.
Of course, for adults and children alike, impatience is inevitable, and as with any discipline, there are times when the rewards just do not seem worth the effort. Sometimes you just don't feel like jogging. Sometimes you really want sour cream and butter on your baked potato. Sometimes, the last thing in the world you want to do is get out of bed on Saturday morning and go to services.
The rewards of making Jewish choices may be more difficult to measure or explain than dieting or jogging. For one thing, there is little support for liberal religious practice in American culture. Even with an idea as familiar and appealing as a real day of Sabbath, trying to explain that Shabbat is sacrosanct to you—no exceptions for basketball games or theater tickets—can mean that even supportive friends and family members may become suspicious or defensive: What are you, some kind of fundamentalist kook? Besides, if you're too Jewish to go out with me on Friday night, why are you eating that cheeseburger? Do you think you're better than me because I don't light candles on Friday night? Because I don't belong to a church?
Because liberal Jews tend to undertake mitzvot on a case-by-case basis, as they feel "commanded" or moved, there may be apparent inconsistencies in practice: not everyone who lights candles on Friday night maintains a kosher home; not everyone who keeps kosher goes to synagogue services, etc. Configurations of mitzvot vary enormously, and may change over time. Over the course of a lifetime, practices that once seemed alien can become deeply meaningful, while others that were once very important are abandoned.
Liberal Judaism's response to mitzvot is neither automatic nor defensive, but personal and open-ended: "This is how I do Judaism. It's not that my way is the only way or the 'right' way. But it is my Jewish way—for now."
Starting to make Jewish choices as an adult can feel very awkward, even for people who were born Jewish. There is a sense that you ought to know Hebrew, and when Passover begins, and what the Talmud is. Being uncomfortable in a synagogue or at the prospect of lighting Hannukah candles might seem to confirm the suspicion that you will never "get it," that you never will fit in.
Starting to make Jewish choices as an adult can feel even more awkward for people who were not born Jewish. Jews-by-choice and non-Jews living in Jewish-identified families may not carry the same emotional baggage as born Jews; however, there is a greater danger of feeling overwhelmed by the sheer amount of stuff—history, customs, traditions, languages—to be learned. And there is the fear that no matter how much you learn, you never will be comfortable or accepted.
However you begin this Jewish journey, remember that you are not alone. There are many other beginners just like you, and there are countless teachers and guides eager to help you find your way.
* Jews use C.E. (Common Era) and B.C.E. (Before the Common Era) rather than the designations A.D. and B.C., which refer to the divinity of Jesus (Anno Domini means "in the year of our Lord").
## HOME
The Jewish home has been called a mikdash ma'at, a little sanctuary. It is an evocative image. From the moment you walk through the doorway of a sanctuary, you know you are entering a unique kind of space.
A sanctuary does not look like other places. It is defined and ornamented by ritual objects, books, and art. A sanctuary feels different from the workplace and the marketplace. In a sanctuary, the mundane criteria for success and failure fall away. What matters is not what you do but who you are.
A sanctuary is a place of safety and asylum. It is where the dispossessed go for shelter, where the hungry go for food, where the weary find rest. Sanctuaries are filled with voices, sometimes singing in unison, sometimes raised in disagreement. And sometimes, a sanctuary is as still as a garden.
Today, when so many families face the pressures of multiple roles, needs, and schedules, making a home into a sanctuary seems more difficult than ever—and thus more important than ever. The tools for making a home into a mikdash ma'at are the mitzvot described in the following pages.
"Your Own Sanctuary" elaborates the Jewish vision of the peaceful home as a place of hospitality and beauty. "The Sabbath" is an introduction both to Judaism's core insight and to creating a personal and family day of rest. "Good Deeds" explains the Jewish view of charity and social justice, and how they can be incorporated into daily life. "The People of the Library" defines some of the major Jewish texts and suggests books for the home library. "What Jews Eat" explains the Jewish dietary laws, their contemporary relevance and practice.
No sanctuary is perpetually filled with all the beauty or meaning it might contain. No home is ever fully or finally a sanctuary. But the ongoing process of making Jewish choices can help turn a home into a mikdash ma'at, a little sanctuary, an island of peace, a safe harbor, a beautiful Jewish place.
## YOUR OWN SANCTUARY
With the destruction of the Second Temple in Jerusalem in 70 C.E, the focus of Jewish religious and ritual life had to change. The Jewish home became the new center of Judaism. However, this little sanctuary has never been a museum for vestigial rituals and ceremonies; it is home, the place where basic human needs are expressed and met. Home is the primary source of identity and education, as well as of affection, recognition, and sexual fulfillment. For Jews, making home into a little sanctuary means incorporating a range of beautiful and meaning mitzvot that make residents and visitors mindful of the blessings of peace, hospitality, and beauty.
Peace at Home
One of the primary reasons for adding a consistent Jewish dimension to family life is to create opportunities for sharing moments of peace. The Hebrew name for the goal of a "peaceful home" is shalom bayit.
Today, family peace and harmony are the province of psychologists and counselors, who often urge couples and families to set aside time to relax together, to talk, and to have fun. Experts have written about the positive impact of rituals on children's resiliency. Morning routines, family dinners, bedtime rituals, and annual holiday celebrations are powerful and positive ways of grounding and reassuring kids about the predictability of the world and their place in it. At its best, sharing Jewish rituals and practices can help to shape a healthy, happy, home.
Jewish tradition has always been quite explicit about the duties and obligations of family life, which are not meant to impose an external order on individuals and families, but to foster shalom bayit. The Jewish laws concerning family matters go into great detail and extend into the most intimate aspects of life. In matters of sexuality, for example, the rabbis codified the rights of women, making it clear that wives could expect their sexual needs to be met, and that husbands could not force physical attentions upon unwilling wives. Family violence of any kind is condemned in the traditional sources. Indeed, many of the rabbis even frowned upon disciplinary spanking.
The biblical call to honor parents, kibbud av v'em, was elaborated into a web of intergenerational obligations. While it is a child's duty to behave respectfully to elders, parents are responsible for educating their children, and not only in religious matters. For example, the Talmud tells parents that they should teach their children how to swim as well as how to read.
The Sabbath has always been the basic building block of family peace. Creating a restful island of time—turning off the television and turning to one another—is not just a nice family custom. It can actually help repair the wear and tear of the week. It can heal wounds that are not even apparent.
* * *
I am a father. I have a daughter and I love her dearly. I would like my daughter to obey the commandments of the Torah; I would like her to revere me as her father. And so I ask myself the question over and over again: What is there about me that deserves the reverence of my daughter?
You see, unless I live a life that is worthy of her reverence, I make it almost impossible for her to live a Jewish life. So many young people abandon Judaism because the Jewish models that they see in their parents are not worthy of reverence.
My message to parents is: Every day ask yourselves the question: "What is there about me that deserves the reverence of my child?"
RABBI ABRAHAM JOSHUA HESCHEL, 1907–1972
* * *
The peace of the house is really the health of the house. Traditionally, on Yom Kippur, the Day of Atonement, family members turn to one another and apologize for the hurtful words and thoughtless actions of the previous year. Today, the concept of shalom bayit can be extended to include support for family therapy and other forms of counseling when it is needed.
However, the concept of family peace is not a call for solemnity. The idea expressed in the Hebrew word shalom is not the same as that of the Latin pax, from which the English peace derives. Pax means "quiet." Shalom comes from the root shalem, which means "complete" or "whole." Shalom bayit does not refer to a quiet home, but a whole one. Quiet, somber observances miss the point. Laughter and foolishness are pretty good indicators of family harmony. With very few exceptions, the goal of Jewish observance is to open people up to the experience of joy—in Hebrew, simcha. In one family, Shabbat is greeted with a top-of-the lungs cheer: "Gimme an S. Gimme an H. Gimme an A. Gimme a B...."
Hospitality
In every neighborhood, there is one house where children know they are always welcome to play. These are households in which, it seems, the couch is forever being made up for an out-of-town visitor. There are Jewish homes where it just isn't Friday night without guests at the table. Children who grow up under such welcoming roofs learn the pleasures of serving and sharing through the mitzvah of hospitality.
For Jews, hospitality is not simply a matter of good manners; it is a moral imperative, a sacred obligation called hachnasat orchim, literally, "the bringing in of guests." The biblical patriarch Abraham is the exemplar of hospitality; it was said that he kept his tent open on all four sides so that strangers would always know they were welcome. In the desert, of course, the offer of water, food, and a place to sleep could be a lifesaving act.
In the Middle Ages, Jewish communities ran charitable associations that provided meals and shelter for Jewish travelers, who were unwelcome, if not in danger, in the non-Jewish world. Likewise, it was considered a special honor to provide a bed and meal for scholars studying at a yeshiva, an academy of Jewish learning.
In the small communities and tight-knit ghettos of the past, everyone knew which families could be counted upon to make room for one more guest, and such people were considered praiseworthy and holy. There is a rich folk literature about poor people who, because they provided shelter and a crust of bread to a stranger, were rewarded with great wealth. The prophet Elijah, the legendary harbinger of the Messiah, is often portrayed as appearing in the guise of a beggar in search of a meal and a place to sleep, testing the practical morality of the Jews he encounters.
Today, hospitality teds to be the work of institutions. Jewish organizations provide help to newcomers to town, to immigrants, and to college students. However, there are still many opportunities for individuals to perform the mitzvah of hospitality for strangers: volunteering at a shelter for the homeless can be seen as an extension of hachnasat orchim—as can inviting students from a local college or university for a Friday night meal or a Passover seder, or contacting the Jewish chaplain at the local military base and inviting servicemen/servicewomen.
* * *
Hospitality is more important even than encountering God's Intimate Presence.
TALMUD: SHABBAT 127A
* * *
Beauty and Holiness
Home decoration is part of all known human cultures. But Judaism's tendency to blur the distinctions between sacred and secular, and its definition of the home as a holy place, suggests a special set of aesthetic considerations. Displaying Jewish art in a home or office is an act of identification and connection. Shopping for ritual objects and artwork can be a way of exploring Jewish identity and a way of deciding how to express Jewishness in concrete terms.
There is a long tradition of Jewish art, based both in custom and religious ritual. According to the rabbinic principle of hiddur mitzvah, when a physical object is needed to fulfill a commandment, the object should be made as beautiful as possible. While it is perfectly all right to make a blessing over wine in a paper cup, it is far better to use a beautiful goblet especially created for that purpose. Over the centuries, Jewish artists and artisans have fashioned ritual objects not only for large synagogues, but also for the homes of ordinary Jews. Embroidery and brocade have covered loaves of challah used in weekly Sabbath home rituals as well as synagogue Torah scrolls.
There are two kinds of Jewish decoration for the home: ritual objects and works of art. Ritual objects have a religious as well as a purely decorative function. They include: the mezuzah (a small container affixed to the doorposts of a home containing a piece of parchment inscribed with a biblical text; the hannukiah (the candelabra or menorah used at Hannukah); Passover seder plates; candlesticks used for Shabbat and holidays; and special goblets for blessing wine (kiddush).
Some families use ritual objects as decorative elements, displaying the family hannukiah year-round, or framing the challah cover Grandma embroidered in the old country. Others collect and display spice boxes, used in the ceremony that ends the Sabbath, or draydls, the spinning tops used during Hannukah.
The presence of ritual objects in a home, while not necessarily a sign of observance, acknowledges the religious and ritual aspects of Judaism. A mezuzah on the door, no matter how beautiful in its own right, says more than "this family enjoys lovely things." It is a sign and a symbol of identification.
Jewish works of art are more difficult to categorize and far more varied than ritual objects, comprising everything from fine-art photographs of Israel to framed examples of Hebrew and English calligraphy, from coffee-table art books and illustrated calendars to fine oils, lithographs, and sculpture. While the works of Marc Chagall, Ben Shahn, Chaim Gross, and others have been identified as "Jewish art," many other Jewish artists produce work that would never be labeled "Jewish." On the other hand, works on a biblical theme might be considered Jewish art, regardless of the artist's religion.
And of course, all art exists in the eye of the beholder. Some pieces might be immediately identified as Jewish—a painting of Moses, for example. But an abstract rendering of the Creation story may appear to a guest like nothing but a pleasing collection of shapes and colors—unless you choose to explain your understanding of it. One definition of Jewish art is that it is art that engages the viewer not only on an aesthetic level, but also in particularly Jewish emotional, intellectual, or spiritual ways.
There is a large selection of Jewish art especially for children's rooms, including mobiles that feature Jewish symbols, and posters of the Hebrew alphabet illustrated with bright, funny pictures. Of course, there's nothing like original art, even more meaningful when it's a Purim drawing or Passover painting created by your own budding Chagall.
The Mezuzah
The little box or cylinder affixed to the doorways of Jewish homes is a clue, a reminder, a sign of welcome, a decoration, an amulet, and a sentry box. The practice of hanging mezuzot on the doorposts of Jewish homes dates back to biblical times and they have been used, virtually everywhere Jews have lived, ever since. These ubiquitous objects have been assigned many meanings: they are reminders of God's presence, physical prayers for peace, a way of marking the difference between Jewish and non-Jewish space, a sign of Jewish pride, an opportunity for hiddur mitzvah, a good-luck charm.
Inside the container is a piece of parchment, called a klaf, containing the biblical reference to mezuzah, which means "doorpost." The words come from the book of Deuteronomy: "Write these words upon the doorposts of your house and on your gates." Also written on the parchment is the Shema, the proclamation of God's oneness, and biblical verses that follow it in the prayer book:
Listen, Israel, Adonai the Eternal, Adonai is One
You shall love your God with all your heart, with all your soul, and with all your might. And these words, which I command you this day, shall be upon your heart. You shall teach them diligently to your children, and shall speak of them when you sit in your home, when you walk by the way, when you lie down, and when you rise up. You shall bind them for a sign upon your hand, and they shall be for frontlets between your eyes. You shall write them upon the doorposts of your home and upon your gates.
And it will come to pass, if you will listen diligently to My commandments which I command you this day, to love your God and to serve Me with all your heart and with all your soul, that I will bring rain to the land in its season, rain in autumn and rain in spring and harvest rich in grain and wine and oil. And there will be grass in the fields for the cattle and abundant food to eat. But you must take care not to be lured away to serve gods of luxury and fashion, turning away from Me. For I will turn My face from you, and I will close the heavens and hold back the rain and the earth will bear no fruit and you will soon perish from the good land that I am giving you. Therefore impress My words upon your heart and upon your soul; bind them as a sign upon your hand and let them serve as frontlets between your eyes. Teach them to your children and talk about them when you are at home and when you are away, in the evening and the morning. Write them on the doorposts of your home and upon your gates. Then will your days be multiplied, and the days of your children, upon the land which I promised to give to your ancestors, as the days of the heavens above the earth.1
Mezuzot and scrolls are sold, usually separately, by Judaica shops and Jewish bookstores, and on the Internet. According to tradition, the scrolls are written by a sofer, a trained scribe. Thus, the parchment may cost as much as the mezuzah case.
Cases can be made of any material, adorned with all sorts of decorations, and are available in wondrous variety, including brightly colored mezuzot decorated with kites and teddy bears.
According to tradition, mezuzot are placed not only on the front door of a home, but on every doorpost inside, except for doors to closets and bathrooms. They are affixed on the right-hand side of a door (as you enter), at eye level, on the upper third of the doorway. The mezuzah is hung at an angle, with the top facing in toward the house or room. Two simple blessings are said before hammering the nails.
Baruch ata Adonai Eloheynu Melech Ha-olam asher kid'shanu b'mitzvotav vitzivanu likboa mezuzah.
Blessed be the Eternal One, Source of Life, by Whose power we sanctify life with the mitzvah of affixing this mezuzah.
Baruch ata Adonai Eloheynu Melech Ha-olam shehecheyanu v'key'manu v'higianu lazman hazeh.
Blessed be the Eternal One, Source of Life, Who has given us life, helped us to grow, and enabled us to reach this moment.
* * *
Why do we affix the mezuzah to the doorposts of rooms within rooms? This is necessary so that no one should think that only in public must one avoid doing wrong.
ALSHEKH, 16TH CENTURY SAFED
* * *
Mezuzot are usually placed within 30 days of moving into a new house with a little ceremony called Hanukat Habayit, "dedication of the home." The blessing itself is the ceremony; however, you can add readings, songs, and prayers. One simple way to involve all your guests is to ask them to stand outside the door while you hang the mezuzah; then as each person enters, he or she gives a blessing for the new home.
Hanukat Habayit—Dedication of a Home ADAPTED BY RABBI BARBARA R. PENZNER
We face the Eternal every moment we live.
We stand before God in every action we take.
The presence of the Holy One fills the whole world.
There is no place in the heavens or the earth that is not touched by holiness.
If we but open our eyes we would recognize that the gateway to fulfillment is wherever we stand. It is to open our eyes to the holiness everywhere about us and within us that we perform the mitzvah of mezuzah.
We place the mezuzah on the gateway to our home, to remind us of the Holy when we enter and when we leave.
"Blessed shall you be in your comings and blessed shall you be in your goings."
Love Adonai with all your heart, with all your soul, with all your might. Take this teaching to heart. Transmit it to your children. Recite it at home and away, morning and night. Bind it upon your hands that your deeds be just. Keep it ever before your eyes that your vision be daring and true. Inscribe it upon the doorposts of your homes and upon your gates, that your going out and your coming in be for peace.2
(Challah is passed around.)
When the Temple in Jerusalem was destroyed twenty-five hundred years ago, the rabbis ordained that the Jewish home would replace the Temple. It would become a mikdash ma'at, a little sanctuary, and our table would be the altar, our bread and salt the sacrifice, and every meal a holy occasion.
Baruch ata Adonai Eloheynu Melech Ha-olam hamotzi lechem min ha'aretz.
Blessed be the Eternal One, Source of life, Who brings forth bread from the earth.3
(Holding the mezuzah, members of the household say:)
May our house be a place of holiness, by welcoming guests, hachnasat orchim, in the bonds of family, with deeds of loving-kindness, gifts of tzedakah, and words of Torah.
Baruch ata Adonai Eloheynu Melech Ha-olam asher kid'shanu b'mitzvotav vitzivanu likboa mezuzah.
Blessed be the Eternal One, Source of Life, by Whose power we sanctify life with the mitzvah of affixing this mezuzah.
Baruch ata Adonai Eloheynu Melech Ha-olam, shehecheyanu v'key'manu v'higianu lazman hazeh.
Blessed be the Eternal One, Source of Life, Who has given us life, helped us to grow, and enabled us to reach this moment.
(Affix mezuzah)
Bruchim Ha'baim
May all who enter be blessed.
## THE SABBATH
We all have moments when the perfection of the world is revealed to us. A walk on the beach. A spectacular sunset. Our lover's eyes. A sleeping child. Sometimes, these moments take us by surprise, like rainbows. Sometimes, we engineer them: we plan vacations in the mountains, or tiptoe into the baby's room.
Shabbat is the way Jews arrange their lives to stay in touch with what is perfect in the world on a regular basis. It is Judaism's essential insight, its backbone, its methodology.
Shabbat, the Hebrew word for Sabbath, has been described a thousand ways. It has been called shelter, palace, fortress, bride, and queen. Shabbat is the only day of the week with a Hebrew name at all; the others are merely numbered in relation to Shabbat: the first day, the second day, the third day. In Yiddish, it is pronounced Shabbes.
The apparently simple idea that one day out of seven should be devoted to rest and reflection has always been a radical concept. Its earliest practice challenged the ancient world, which despised labor as the lot of beasts and slaves, and reserved leisure as the privilege of the rich and powerful. Today, when the hum of the machine never stops, when everyone has too much to do and not enough time in which to finish, Shabbat continues to pose fundamental questions about values and the value of life. For 21st century Jews, the challenge of Shabbat is literally radical, taking us back to our roots, recalling the biblical story of creation:
The heaven and the earth were finished, and all their array. On the seventh day God finished the work and stopped. And God blessed the seventh day and made it holy, because on it God rested from all the work of creation.4
To the Talmudic rabbis who interpreted these words, the story does not mean that on the seventh day God rolled over, pulled up the covers and went back to sleep. On the seventh day, Shabbat came into being—and only then was the world completed, and perfect.
The Meaning of Shabbat
"The meaning of the Sabbath," wrote Rabbi Abraham Joshua Heschel, "is to celebrate time rather than space. Six days a week we live under the tyranny of things of space; on the Sabbath we try to become attuned to holiness in time. It is a day on which we are called upon to share in what is eternal in time, to turn from the results of creation to the mystery of creation; from the world of creation to the creation of the world."5
Millions of words have been written about the meaning of Shabbat in language ranging from legal to ecstatic. It has been associated with the great themes of Judaism: freedom, covenant, peace, and redemption. Sections of the Shabbat liturgy recall the time when the Jews were slaves in Egypt.6 And although Shabbat celebrates freedom, it is also a reminder of the contrast between slavery and freedom. The Jewish notion of freedom entails both political and personal responsibilities; the mandate to work for the liberation of all oppressed people and the task of remaining free from enslavement to false idols, such as wealth, power, and fame.
Shabbat is called a covenant between God and the Jews. Just as the relationship between a loving couple is represented by a token, such as a wedding ring, Shabbat is the token between God and the people of Israel. "I have given them my Sabbath to be a sign between Me and them, so they will know that I am the One that sanctifies them."7
The charge of this covenant is to create wholeness, in Hebrew, shalom. Shabbat is about making peace with everyone: business associates, strangers, and especially within families. The highest priority is given to reconciliation and loving-kindness. Intimacy and sex are among the blessings of Shabbat.
Finally, Shabbat embodies the Jewish vision of redemption. Observing Shabbat fully means behaving as if the world were redeemed—complete, safe, perfect—right now. Shabbat is the opportunity to focus on what is right with the world, and thus to be refreshed to do the work of redemption: of repairing the world (tikkun olam). Indeed, the Talmud says that if everyone on earth were to observe two consecutive Sabbaths, the world would be redeemed.8
History
The word Shabbat appears almost two hundred times in the Bible. ("Bible" refers to the Hebrew Bible, which consists of the Torah, or Pentateuch, the Writings, and Prophets. See "People of the Library" for a discussion of these terms.) The earliest mention of Sabbath rest is found in Exodus, when the Israelites who escaped from Egyptian slavery are told to gather a double portion of manna on the sixth day so they do not have to work on the seventh.9 By the time of the First Temple (the 10th century B.C.E.), Shabbat was associated with joy as well as rest. The prophet Isaiah said, "And you should call the Sabbath a delight."10
During the Second Temple period (the first century C.E.), the nature of Shabbat was the subject of an intense and passionate debate whose outcome has shaped Jewish practice ever since. Among the sect known as the Sadducees, Shabbat was given an extremely ascetic interpretation: virtually all movement and all indoor illumination were forbidden. However, the Pharisees (forerunners of the rabbis) permitted far more latitude, declaring Shabbat laws moot in cases of helping the sick or saving a life. The Pharisees also made the lighting of candles on Friday night a precept that developed into the most evocative of all Jewish rituals.11 After the destruction of the Second Temple by the Romans in 70 C.E., Shabbat observance came under the purview of rabbis, who have been interpreting and debating its meaning and practice ever since.
Although Shabbat has been a constant feature of Jewish life throughout history, its observance changed over time and varies among Jews living in different lands. For American Jews, most of whom have Eastern European roots, Shabbat associations—smells, tastes, sounds, and images—tend to have a Yiddish flavor mediated through American popular culture. Thus, Shabbat conjures up not only memories of chicken soup and braided challah, but also scenes from the musical comedy Fiddler on the Roof. Less familiar to most Americans are the customs of Mediterranean and Middle Eastern Jews, whose Shabbat was permeated by the aroma of lemons, food seasoned with fresh mint and garlic, and syncopated melodies.
Regardless of the particulars, however, Shabbat has always been experienced as different from the other days: it is the day for wearing new clothes, for inviting guests to share the best meal of the week, for singing at the table, for giving and receiving blessings. Jewish life and Jewish time are oriented around Shabbat, which takes precedence over almost everything else. Jewish weddings are not permitted on the Sabbath and neither are funerals because Shabbat is meant to be savored on its own, undiluted by other celebrations and unclouded, as much as possible, even by death.
Jews have often suffered for their loyalty to Shabbat. Antiochus Epiphanes, the villain of the Hannukah story, outlawed it and many Jews died defying his order. Marranos, Jews who publicly converted to Christianity during the Spanish Inquisition but practiced Judaism in secret, lit Shabbat candles in their cellars.12 And there are heart-wrenching stories of Sabbath observances in the darkness of Hitler's death camps.13
* * *
More than Israel has kept the Sabbath, the Sabbath has kept Israel.
AHAD HA-AM, MODERN HEBREW ESSAYIST
* * *
Choosing Shabbat
The first appearance of Shabbat in the Torah is as a verb, shavat. "And God ceased/rested/stopped."
Shabbat is re-created weekly as Jews make Shabbat. The first verb for most Jews today, however, is not "make" but "choose." And choosing Shabbat is not one decision, but many. Choosing Shabbat means making a commitment to a weekly period of rest and peace. It means making distinctions between activities that are Shabbat-like from those that are workweeklike. It means avoiding things that might violate a sense of peace and planning ways to enhance that feeling.
These choices vary from one household to the next. Many Jews let voice mail pick up all their calls during Shabbat, but some find telephone conversations with family members and friends are relaxing and appropriate. Though traditionally, money is not handled on Shabbat, some people make a distinction between a day at the mall and taking the kids out for ice cream.*
Because Shabbat is often defined in terms of prohibitions against certain kinds of activities, Sabbath observance has been seen as a series of restrictions, a weekly sentence of self-denial.14 But Shabbat is not an exercise in asceticism, and "making Shabbat" is not only a matter of refraining, but also of doing. The Talmud says "the affairs of heaven" are permitted on the Sabbath, which was specifically meant to include teaching children and arranging weddings.
Resting, eating, and praying are not only permitted, but mandated. There are other verbs appropriate to Shabbat, too; sleeping, reading, thinking, studying, talking, listening, meditating, visiting the sick, laughing, singing, welcoming guests, making love.
* * *
The real and the spiritual are one, like body and soul in a living man. It is for the law to clear the path; it is for the soul to sense the spirit.
RABBI ABRAHAM JOSHUA HESCHEL
* * *
Oddly, it turns out to be difficult, this choice to focus on peace and rest. All choices have consequences. If Friday night is going to be time at home, that means turning down invitations for dinner and a movie with friends or family. And for chronically overscheduled people, sitting still for an hour, much less an afternoon, can be a real challenge. However, these are precisely the reasons that many people view Shabbat as an opportunity to reorient a too-hectic life around the need for relaxation and time with family and friends.
This is not always an easy change. The decision to start making Shabbat requires planning and discussion, which may lead to some discomfort and disagreement. Although it is common for one member of a family to be the instigator and guiding force behind a commitment to making Shabbat, it is important to include as many family members as possible in the idea. This is rarely a problem with young children, who tend to enjoy the specialness of Shabbat for its own sake, and quickly come to look forward to the magic of Friday night. For older kids, however, beginning Shabbat observance may seem restrictive or just plain weird. Parents need to be secure in their own desire and enthusiasm for Shabbat, and ease the transition by emphasizing the playful and joyful aspects of the day, encouraging children's input as well as their participation.
It is essential for family members to talk not only about how to make Shabbat, but also why. Reasons can range from the practical to the mystical: Shabbat is something constructive and pleasant the family can do together; it is an opportunity to learn; it is something Jews have done for thousands of years and it can connect us to our heritage; it creates an opportunity to visit with friends and family we otherwise don't see; it is something beautiful and positive we want our family to share and remember; it is a way of finding and building community with other Jews.
Regardless of the whys or the ways, however, a commitment to consistency and regularity is important. Most important, always remember that Shabbat is not something you do for or to your family; it is something you make together.
Making Shabbat
While it would be difficult to overemphasize Shabbat's intellectual and theological significance, the Jewish Sabbath is not an abstraction or disembodied idea that can be attained through revelation or prayer. Shabbat must be understood in its uniquely Jewish form—as a mitzvah.
A mitzvah is a command from God, chosen and enacted by people. The mitzvah of Shabbat asks us to be human in the most humane context that we can imagine and create.
The rest of this chapter is a kind of cookbook for making Shabbat. Just as it would be self-defeating for a novice in the kitchen to attempt an elaborate, multicourse dinner, it is not a good idea to take on every aspect of Shabbat observance all at once. Most people begin with Friday night table rituals: lighting candles, eating challah, singing songs. It may take weeks before even simple acts feel natural, but after a few months of repetition, comfort and a sense of expertise will come.
And just as cooks learn through apprenticeship, the best way to learn how to make Shabbat is with and from others. Sharing Friday night meals, attending services at different synagogues, getting together with friends on Saturday afternoon, can provide you with ideas, models, and support for developing personal Shabbat observance. Some synagogues run Shabbat retreats, a weekend at a camp, inn, or estate, where people study, pray, relax, and practice the fine art of Sabbath rest and joy.
On the following pages, Shabbat observances are divided into four sections: The first is devoted to preparing for the seventh day. The second part describes Friday night, the eve of the Sabbath, (erev Shabbat), where the focus is around the dinner table. The next section describes Saturday morning, and the synagogue service and Torah reading. And the last section is about Shabbat afternoon, which begins with a special lunch and ends with havdalah, the ritual that separates Shabbat from the new week.
Preparation
Shabbat is a vacation from the demands of the week, an invitation to shift gears, to slow down. For some, preparing for Shabbat starts with avoiding late-afternoon appointments on Friday and trying to be home at a specified time.
Shabbat also creates a deadline for finishing up things like getting the house clean, making sure that essential errands have been run, and that challah, wine, and flowers have been purchased. A traditional analogy compares making Shabbat to inviting a queen to your home. If you knew that royalty would be having dinner at your house, you would surely run the vacuum, take out the good china, think about the menu, and familiarize yourself with the special protocols and conventions of the event.
Food. Although Jewish law calls for three "feasts" on Shabbat to ensure a sense of celebration, it also forbids the lighting of fires, which traditionally means "no cooking." Thus, the biggest job of preparing for Shabbat tends to be food preparation. But even if you do cook on Saturday, preparing some food in advance can create more time for rest, relaxation, and fun.
Historically, Friday night dinner has always been the gustatory highlight of the week for Jews, no matter what their financial circumstances. Making it special does not necessarily mean making it elaborate, nor does it mean conforming to the chicken-soup-and-brisket menus of Eastern Europe. Some people find that making the same special meal every Friday night has its advantages: not only is it easier for the cook, it also reinforces the soothing, repetitive ritual nature of the meal and establishes a family tradition.
Any menu can be made special with a tablecloth and flowers on the dining room table. Ritual objects such as an embroidered cloth for the challah, candlesticks, and special wine goblets will immediately identify this meal as an event. And remember, anything you reserve for Shabbat use only, can become an heirloom. An inexpensive bread knife that never cuts anything but challah on the Sabbath may someday be a priceless family treasure.
Slowing down. Shabbat brings a release from the usual patterns of doing and being and celebrates some of the sensual, creative aspects of ourselves that may be sacrificed during the workweek. Celebrating the sensual can mean lowering the lights, taking time to smell as well as taste food, making sure to hug and kiss the people you love. And for those who cannot be with you, a few phone calls to say "Shabbat Shalom" is a two-way blessing.
In the rush to prepare home and table for Shabbat, it is easy to forget the importance of readying yourself. Nothing accomplishes the major shifting of gears from work to rest better than a hot shower or a bath. If you can find the time, meditate, listen to music, or read something to help you "get in the mood." But even taking a few minutes to wash hands and face, shave, comb or brush hair, put on perfume or cologne, or change clothes can help. Some people get into the spirit of Shabbat by listening to Jewish music as they set the table.
Traditionally, best clothes and new clothes are worn on Shabbat. However, if dressing up feels too much like work, a change into casual clothes might better facilitate your shift into Shabbat mode. Some people put on a skullcap (kippah in Hebrew, yarmulke in Yiddish), before beginning Friday night rituals.
Children. Shabbat easily becomes a focal point of anticipation and fun for children. The celebration can begin with a baking session or trip to the bakery for challah and other goodies. Setting the Shabbat table with children can be both a game and a reward, with special jobs assigned to each child: candlesticks and candles for you, the kiddush cups for you because you're so grown up and responsible. Kids can also create Shabbat place cards for guests, and centerpieces of LEGOs, or paper flowers, or dandelions from the yard.
Shabbat can inspire all sorts of arts-and-crafts projects. Since most small children love wearing hats—kippot (the plural of kippah) can be part of the fun. Some kids collect them, and a "custom-made" kippah can be created with some felt, a little glue, and a plain satin yarmulke. To make a Sabbath plate or set of dishes, apply Jewish symbols and lots of imagination to a melamine kit available in many toy stores. (Special pens are provided, and the dishes are then sent to a factory where the child's design is permanently baked on.)
Finally, when everything and everyone is ready, remove your watches. Empty your pockets. Ignore the phone. You are going to a party. Shabbat is not a solemn occasion. Along with the candles, the wine, and the challah, smiles and laughter belong at the table.
Friday Night
The four core ritual elements of a home Shabbat evening (erev Shabbat) celebration are: (1) blessings over candles, (2) wine, (3) bread, and (4) the eating of the meal. Friday night rituals vary from one Jewish household to the next. In some, there are many songs; in others, there is no singing. Some families recite all the blessings in Hebrew only; in others, there are English translations. Some discuss the weekly Torah portion at dinner; others use the time to reflect upon the week past. Some eat earlier than usual in order to attend services; others eat after services, lingering at the table as the candles burn down.
The various elements of Friday night observance are a menu from which a personal Shabbat home ritual can be created. As with any menu, all sorts of combinations are possible. Once you find a comfortable way to proceed, it can be helpful to make a one-page guide to the rituals and blessings in English, transliterated, and/or in Hebrew. This summary of your "Shabbat seder" can be decorated, laminated, and given to guests.
Despite the fairly detailed explanations below, Shabbat cannot be understood by reading a book. The best way to learn it is to live it—by watching and participating with others.
Friday night rituals:
Giving tzedakah
Singing
Lighting candles
Blessing for spouses
Blessing for children
Blessing for wine (kiddush)
Blessing for hand washing
Blessing for challah
The meal
Blessings after the meal
More singing
Synagogue
Making love
Giving tzedakah. Giving money to the poor is associated with nearly all Jewish celebrations and festive occasions. In moments of great joy, tzedakah is a way both of sharing happiness and of recalling that the world requires our attention.
It is traditional to put aside money for tzedakah before candles are lit. Many people cherish childhood associations of Shabbat with little tin cans called pushkes, which represented different Jewish charitable organizations. Making a collection box by decorating a can or jar, or making a container out of clay or paper, is a great project and a wonderful way of introducing children to the concept of tzedakah. (See "Good Deeds.")
* * *
"We will sing," said Rabbi Nachman of Bratslav, "and God on high will understand us."
* * *
Singing. Beginning a meal with a song breaks the week's routine and inaugurates Shabbat. While almost any song will accomplish this, many Hebrew songs (z'mirot) are associated with the Shabbat table. One of the simplest and best known is "Shabbat Shalom," whose lyrics consist of those two words. Shabbat is a wonderful time for children to show off new songs they have learned.
But words are not really necessary. According to one tradition, a wordless melody, or niggun, is itself a prayer, and one of the purest forms of prayer at that. Niggunim (the plural) are usually fairly simple, repetitive, and easily taught.
One song most closely associated with Friday night is "Shalom Aleichem," which is an invocation of angels who are thought to hover close on Shabbat.
Shalom aleichem.
malachei hasharet
malachei elyon.
Mi melech malchei hamlachim
Hakadosh Baruch Hu.
Peace be yours, angels of peace
Angels of the most high
Angel of the King who is King of kings
The holy blessed One.
Candlelighting. In cultures throughout the world, fire is considered one of the basic elements, a universal symbol of power, mastery, and divinity. Friday night candle lighting dates back to the first century C.E., and the blessing is as old as the eighth or ninth century.15 For Jews, the lighting of candles is the act that formally ends the week and begins Shabbat.
Candlelighting is the most evocative of all Jewish rituals. Children who watched mothers and grandmothers bench licht (Yiddish for "blessing the light"), carry the image with them for the rest of their lives. Remembering her mother's Shabbat ritual at the turn of the 20th century, Bella Chagall wrote:
With a match in her hand she lights one candle after another. All the seven candles begin to quiver. The flames blaze into Mother's face. As though an enchantment were falling upon her, she lowers her eyes. Slowly, three times in succession, she encircles the candles with both her arms; she seems to be taking them into her heart. And with the candles her weekday worries seem to melt away.
She blesses the candles. She whispers quiet benedictions through her fingers and they add heat to the flames. Mother's hands over the candles shine like the tablets of the Decalogue over the holy ark.
I push closer to her. I want to get behind her blessing hands myself. I seek her face. I want to look into her eyes. They are concealed behind her spread-out fingers.16
According to Jewish law, candles are lit not at dark but at sunset—technically, no later than 18 minutes before sunset. Candlelighting times are listed on Jewish calendars and in Jewish newspapers. Among liberal Jews, the common practice is to light candles when the whole household is gathered at the table for dinner.
The candles are lit before the blessing is recited or sung. There is a custom of circling the candles with hands and arms after lighting them, and then covering the eyes during the blessing. This practice can feel awkward or artificial to people who have never tried or even seen it done. If these gestures make you too self-conscious to get into a Shabbat-like mood, they defeat the purpose. Some people simply take a moment to inhale and release a very deep breath before lighting candles and reciting the blessing.
Baruch ata Adonai Eloheynu Melech Ha-olam asher kid'shanu b'mitzvotav vitzivanu l'hadlik ner shel Shabbat.
Holy One of Blessing, Your Presence Fills Creation
Making us holy with Your commandments and calling us to light the lights of Shabbat.17
At least two candles are lit, symbolizing the great dualities of life: female and male, light and darkness. The rabbis declared that the two candles stand for the two forms of the commandment to "remember" and "observe" Shabbat.18 But while two is the minimum, there is no maximum. Bella Chagall's mother lit seven candles because she added a flame for each of her five children. Among some Sephardic Jews, candles are lit for family members who have died.19 If guests are present at candlelighting, they can be invited to light candles for their families as well. A great blaze of candles is always festive.
According to tradition, the mitzvah of lighting candles is assigned to women, though incumbent upon men in their absence. While some women prefer to reserve this custom to themselves, there is a wide range of practice on this count. In many homes, all women and girls light a pair of candles, though in some families, the honor rotates and includes everyone regardless of gender.
Candlelighting is a wonderful moment for children, and blowing out the Shabbat match is a special treat in liberal homes.20 A gift of small candlesticks on a birthday or Hannukah confers a new, more grown-up Jewish status on a child, and the first time he or she uses them can be a family event. Long fireplace matches are a good idea, and fun.
Generally, the candles are the short, white, kosher (no animal fat) tapers that are sold for Sabbath use in many supermarkets as well as Jewish food and specialty stores. Some people substitute colored or rainbow candles for a special occasion Shabbat, such as a child's birthday.
The only regulation regarding candlesticks or other ritual objects for Shabbat is the rabbinic principle of hiddur mitzvah, which states that when a physical object is needed to fulfill a commandment, it should be beautiful. Candlesticks handed down from one generation to the next are especially precious, but any object reserved for Shabbat use only quickly becomes a family treasure. Candlesticks with Jewish symbols may be purchased at Judaica shops, but for something that already has the patina of age and experience, a secondhand store or antique shop may yield an "instant" heirloom.
After the candles are lit, someone or everyone says "Shabbat Shalom" ("Sabbath peace") or "Gut Shabbes" (Yiddish for "a good Sabbath"). In some families, everyone exchanges kisses.
Blessings for a spouse. According to ancient custom, a husband reads or (chants) to his wife from the book of Proverbs (31:10–31). Eshet Chayil, "a woman of valor," is the phrase that begins this section, which lists her many virtues, including generosity, industry, business acumen, beauty, wisdom, cheerfulness, and loving-kindness. Verses from the Song of Songs can be substituted and read aloud.
In some households, this tradition is honored by spouses taking a moment to look into each other's eyes and say, "Eshet chayil" (to a woman) or "Ish chayil" (to a man). Others simply take a moment to kiss and say "I love you." Any such gesture makes it very difficult to allow leftover quarrels to compromise the peace and harmony of Shabbat.
Blessings for children. The Bible records several parental blessings, which are echoed in the custom of blessing children on Friday. There are three traditional blessings. The blessing for sons refers to Joseph's sons, Ephraim and Menashe, whose mother, Osenath, was an Egyptian-born noblewoman. The Midrash says that these two were singled out for praise because they held fast to their Jewish identity. The blessing for daughters names the matriarchs: Sarah, whose response to adversity was laughter; Rebecca, the model of hospitality; Rachel and Leah, who personify sisterhood in the most difficult circumstances. Last, there is the threefold benediction, also called the "priestly blessing" (birkat kohanim), so called because it is traditionally recited over the entire congregation by the members of the priestly caste, kohanim, or the rabbi.
Some parents add or substitute a more personal message for each child—praise for something that happened during the week, or just a whispered "I love you."
For boys:
Y'simcha Elohim k'Efrayim v'ch'M'nashe.
May God make you as Ephraim and Menasheh.
For girls:
Y'simeych Elohim k'Sara, Rivka, Rachel, v'Leah.
Make God make you as Sarah, Rebecca, Rachel, and Leah.
For either or both:
Y'varech-ch'cha Adonai v'yish-m'recha.
Ya'er Adonai panav eylecha vichuneka.
Yisa Adonai panav eylecha v'yasem l'cha shalom.
May Adonai bless you and keep you.
May Adonai shine the Countenance upon you and be gracious to you.
May Adonai favor you and grant you peace.
In her prayer book, The Book of Blessings, poet Marcia Falk rewrote the traditional blessings in language that speaks to the individuality of each child.
Blessing of the Children BY MARCIA FALK
To a girl:
_____ (her name)
Hayi asher tihyi—
vahayi b'rukhah
ba'asher tihyi.
_____ (her name)
Be who you are—
and may you be blessed
in all that you are.
To a boy:
_____ (his name)
Heyeyh asher tihyeh—
veheyeyh barukh
ba'asher tihyeh.
_____ (his name)
Be who you are—
and may you be blessed
in all that you are.21
Blessing for wine (kiddush). The word kiddush comes from the Hebrew kadosh, which means "holy." The term refers to all blessings made over wine, all of which contain this line:
Baruch ata Adonai Eloheynu Melech Ha-olam boray pree hagafen.
Holy One of Blessing, Your Presence fills Creation, forming the fruit of the vine.
On Friday night, this blessing is sandwiched between two longer passages. The first, from the Torah, recounts the creation of the world. The second sounds three of the great themes of Shabbat: Creation, the exodus from Egypt, and the sanctity of the Sabbath.
Vayehi erev vayehi voker yom hashishi. Vayechulu hashamayim veha'aretz vechol tzeva'am vayechal Elohim bayom hashevi'i melachto asher asa, vayushbot bayom hashevi'i mikol melachto asher asa. Vayevarech Elohim et yom hashevi'i vayekadesh oto, ki vo shavat mikol melachto asher bara Elohim la'asot.
There was evening and there was morning the sixth day. And the heavens and the earth and all that they contain were completed. And on the seventh day God completed the work that God had made. And God rested on the seventh day from all the work that God had made. And God blessed the seventh day and made it holy, because on it God rested from all the work that God created and made.22
Baruch ata Adonai Eloheynu Melech Ha-olam Boray pree hagafen.
Baruch ata Adonai Eloheynu Melech Ha-olam asher kid'shanu be-mitzvotav v'ratza vanu, veShabbat kodsho be'ahava uveratzon hinchilanu, zikaron lema'asei vereishit; ki hu yom techila lemikra'ei kodesh, zecher litziyat mitzrayim; ki vanu vacharta ve'otanu kidashta mikol ha'amim veShabbat kodshecha be'ahava uveratzon hinchaltanu. Baruch ata Adonai mekadesh haShabbat.
Holy One of Blessing, Your Presence fills Creation, forming the fruit of the vine.
Holy One of blessing, Your Presence fills Creation, You have made us holy with Your commandments and delighted in us. In love You have favored us with the gift of Your holy Shabbat, a heritage that recalls the work of creation. It is the first day among holy days, reminding us of our going out from Egypt. You gave us Your holy Shabbat as a treasure to grace all our generations. Holy One of Blessing, You make Shabbat holy.
There are many customs for how to give voice to kiddush. Some simply say the "boray pree hagafen" part of the prayer; others sing the entire kiddush aloud in Hebrew. In some families, it is the custom for everyone to stand, but in other households, everyone stays seated. Some make the blessing over a single cup, which is then passed or poured into other cups. Elsewhere, everyone drinks from his or her own glass.
It is also traditional to hold the cup so as to demonstrate that this cup of wine is not simply for drinking or even toasting. According to the Zohar, a medieval book of mystical Bible interpretation, the glass is held in the palm of the right hand, with the fingers facing upward and curled around the base to represent a five-petaled rose, an ancient symbol of perfection and of longing for God. Any glass can be used for kiddush, but again, it is considered preferable to use a special glass or goblet to fulfill the precept of hiddur mitzvah, or beautifying the commandment. Kiddush cups are common gifts for bar and bat mitzvah kids, but there is no reason to wait until a child is 12 or 13. Younger children treasure their own special Shabbat cups, as well.
Jewish law calls for kosher wine to be used whenever a blessing is recited. (For a full explanation of kosher wine and food, see "What Jews Eat.") For some, kiddush isn't kiddush unless the wine in the cup is the thick, sweet, red, and indisputably kosher liquid produced by companies like Mogen David and Manischewitz; however, there is a great selection of fine kosher vintages, produced in Israel, the United States, France, Italy, among others. Some parents substitute watered wine or grape juice reserved for Shabbat for children.
* * *
Rabbi Hanina wrote, He who prays on the eve of the Sabbath and recites the verses that begin, "...and the heaven and the earth were finished," the scriptures speak of him as though he been a partner in creation with the Holy One.
TALMUD: SHABBAT 119B
* * *
Hand washing: This ritual has nothing to do with hygiene, but is a symbolic reminder of the ceremonies in the ancient Temple, a gesture that reminds us that our tables are, in fact, altars. By saying a prayer over the washing of hands, we are prompted to discover the sacred within even the most mundane acts.
While any glass or cup can be used, two-handled cups or lavers are made especially for this purpose, some of which bear the accompanying blessing:
Baruch ata Adonai Eloheynu Melech Ha-olam asher kid'shanu b'mitzvotav vitzivanu al netilat yadayim.
Holy One of Blessing, Your Presence Fills Creation, making us holy with your commandments and calling us to wash our hands.
There is a custom of remaining silent after saying this blessing until reciting the blessing for challah, making a connection between the two rituals. Some people hum during this pause, which not only enhances the moment but also makes it easier (and more fun) to keep from speaking.
Blessing the challah. In many languages, the word "bread" is synonymous with "food." A blessing for bread is thus a blessing over food, sustenance, life. Jews make a blessing called motzi ("brings") over challah, a word that comes from a biblical reference to a sacrificial Temple offering of dough.23 According to tradition, challah is any bread prepared for the purpose of making a motzi, a process that requires breaking off and burning a small piece of dough and reciting a blessing. Today, challah generally refers to a braided egg-rich loaf with a soft, almost cakelike texture. It is available in Jewish bakeries, and happens to be one of the easiest yeast breads to bake at home. Good recipes abound, children love braiding the dough, and the aroma of fresh bread is certainly an example of heaven on earth.
Baruch ata Adonai Eloheynu Melech Ha-olam hamotzi lechem min ha-aretz.
Holy One of Blessing, Your Presence Fills Creation, bringing forth bread from the earth.
It is traditional to have two loaves on the table, recalling the double portion of manna the Israelites gathered on the sixth day so they would not have to collect food on Shabbat. The double portion of bread also symbolizes bounty, and some use a small challah roll to symbolize a second loaf. The bread is often covered with an embroidered or woven cloth, which, like special challah plates and knives, adds to the beauty of the Shabbat table.
There are many customs for saying the blessing. Some hold two loaves together; others invite everyone at the table to touch the bread or make a connection with someone else who has a hand on the challah. Some sprinkle the bread with salt, the traditional reminder of tears and of the destruction of the Temple. Because metal is considered a reminder of war, some people keep sharp knives off the table, which is why, in some households, no knife is put to the challah at all and it is ripped apart by hand instead.
* * *
When the world was created, God made everything a little bit incomplete. Rather than making bread grow right out of the earth, God made wheat grow so that we might bake it into bread. In this way, we could become partners in completing the work of creation.
MIDRASH
* * *
The meal. The very act of eating and sharing meals on Shabbat is considered a mitzvah, which is why there are so many rabbinic stories and folktales about the importance of feeding beggars and bringing strangers home on the Sabbath. Judaism has always been respectful of the fact that basic needs must be satisfied and that holiness and hunger are, in some fundamental sense, mutually exclusive. As the Talmud says, "Without flour [food] there is no Torah."24
The Shabbat table is considered a place to nourish mind and spirit, as well as the body. In the words of Pirke Avot, a much-quoted section of the Mishna, "If three have eaten at the table and speak words of Torah, it is as if they have eaten from the table of God."25
In some families, a real attempt is made to avoid "shop talk" or gossip. People might take turns talking about the important events of the previous week: good news, blessings, accomplishments, something newly learned. It is a mitzvah to host guests for Shabbat dinner, but the guests also do a mitzvah in that they enrich and enliven the conversation.
Blessings after the meal (birkat hamazon). The birkat hamazon (blessings for food) is a series of blessings and prayers filled with thanks and praise and set to a string of melodies. Praying the birkat hamazon is also called benching, from the Yiddish word for prayer, and is found in most daily prayerbooks, or siddurim. On Shabbat, birkat hamazon begins with Psalm 126, which begins with the joyful words, "When God brought Israel back to Zion/We were as in a dream/Our mouths were filled with laughter/Our tongues with joyous song."
The following paragraph of birkat hamazon is sometimes used as an abbreviated version of the longer blessing.
Holy One of Blessing, Your Presence fills creation, You nourish the world with goodness and sustain it with grace, loving-kindness, and mercy. You provide food for every living thing because You are merciful. Because of Your great goodness, the earth yields its fruit. For Your sake we pray that we shall always have enough to eat, for You sustain and strengthen all that lives and provide food for the life that You created. Holy One of Blessing, You nourish all that lives.26
After dinner, the candles create a kind of hearth for lingering or reading. Shabbat candles are lit not merely for decoration, but for use, so studying by their light is considered an added mitzvah. Relax. Listen to music. Go outside and watch the night sky. Read Shabbat stories aloud to your children. Read love poems to your beloved.
Synagogue. The cycle of formal Shabbat worship begins on Friday evening with a service known as Kabbalat Shabbat (welcoming or receiving the Sabbath), which was developed by a group of Jewish mystics who lived in the city of Safed in the 16th century. Although there are variations on the Friday evening service, virtually all of them contain some version of "L'cha Dodi," a poem from that community set to music. Today, in many congregations, when the final stanza is sung, everyone rises to face the door to symbolically welcome the Sabbath bride.
The Friday night service is held at different times in different synagogues; some just before sunset so people can get home to Shabbat dinner; others are scheduled to follow the evening meal. Some synagogues host Shabbat dinners on a regular or occasional basis.
Many liberal congregations include candle lighting and kiddush on Friday night and some share challah as well. When services are held later in the evening, they are followed by a gathering called Oneg Shabbat ("joy of the Sabbath"), a communal celebration of schmoozing (conversation) and noshing (eating).
Making love. The imagery of marriage abounds in Jewish texts; Shabbat is often described as a bride. God and the people Israel are like groom and bride, with the Torah as their ketubah, their marriage contract. The Kabbalists imagined God's unity to have been shattered by the expulsion of humanity from Eden. The feminine side of God—called Shechinah—would wander the earth in exile until the redemption of the world was complete. On Shabbat, however, God's two halves were reconciled and united in an act of love.
In Yiddish literature of the late 19th and early 20th century, there is a keen sense that on Friday night, husbands and wives looked at each other with different eyes. On a purely practical level, the men and women of the shtetl and ghetto looked their best. The quarrels and conflicts of the week were put aside as well since another reason for all the smiling was the rather public secret that Friday night was the time for sex. Indeed, Jewish folklore held that erev Shabbat was the most auspicious time for conceiving a child.
"Y'did Nefesh," a traditional song for Friday night, makes the connection between spiritual and physical union quite explicit.
Draw me to You with the breath of love,
Swiftly shall I come to stand within your radiance
That I may attain that sweetest of all intimacies.
My soul aches to receive your love.
Only by the tenderness of Your light can she be healed.
Engage my soul that she may taste your ecstasy.27
Shabbat Morning
With the morning, the focus shifts from family to community, from home to synagogue. For some, Saturday morning services are a weekly event, while others attend only rarely or, on special occasions, such as when invited to attend a bar or bat mitzvah (literally, "son or daughter of the commandment," a rite of passage for 13-year-old boys and girls). (See pages 225-233.)
For those unfamiliar with Hebrew and synagogue customs, Shabbat morning services can seem daunting. The best way to explore and enjoy them is to try to relax. No one in the synagogue is there to judge you. No one will know if it is your first time ever inside a temple, or the first time you have been to synagogue in decades. Some of the most important elements of Shabbat are available for newcomers as well as for regulars; voices raised in song, being part of a community gathered in peace, the opportunity to sit still and simply be. If you feel strange about just showing up at a temple, you can call the rabbi, introduce yourself, and tell him/her that you are planning to attend services. This is also a good way to gauge the warmth of a congregation.
What follows is a general outline of Sabbath worship services. While variety is one of the hallmarks of liberal observance, the essential elements that appear here are as close to "standard" as possible.
The Sabbath morning service (Shacharit). Commonly, there are five sections in the Shabbat morning service. The first two—morning blessings, and hymns and psalms—are introductory. Shacharit proper begins with a call to worship (Barchu), and continues with the Shema and its blessings, and the standing prayer (called Amida or Tefila). This is followed by the Torah reading.
The Torah, which is also called the Five Books of Moses and the Pentateuch, consists of the first five books of the Hebrew Bible: Genesis, Exodus, Leviticus, Numbers, and Deuteronomy. The Torah is divided into 54 sections, each of which is called a parasha or sedra, and which are read in an annual or, in many congregations, a triennial cycle.
Every portion is further divided into seven parts, each of which is called an aliyah, and on Shabbat morning all seven are read or chanted. (Only one aliyah is read during the Torah service on Monday and Thursday morning, and Saturday afternoon.) Special blessings are recited before and after each reading, and it is a special honor, also called an aliyah, to be called up to read from the Torah and/or to say these blessings.
The Torah is read from a scroll that contains no vowels or punctuation of any kind, so its reading requires training and skill. There are special books that contain the Torah text with vowels, punctuation, and cantillation (called trope)—markings that dictate the melody used for chanting. The designated Torah reader, called a Baal Kriyah (or Baal Korey), which means "master of the reading," prepares the reading in advance using such a book, which is called a Tikkun. A bar or bat mitzvah spends months learning to read a few verses, but even a skilled reader reviews the weekly portion before attempting it at services.
The Torah reading itself can vary from one congregation to the next. In some synagogues, the entire portion is chanted in Hebrew, while in others only a few sections are read. Some congregations do some or all of the Torah portion in English, and some have adopted the custom of a triennial or three-year cycle for Torah reading, so only a third of each parasha is read every week.
The Torah reading is the emotional and intellectual center of the service. The Torah is read as communal study and offered as an ever-renewing challenge to discover fresh meanings in its words, stories, characters, and ideas. Rabbis often base their sermons on the portion being read, and in some synagogues the rabbi or a congregant will lead a discussion of it. This kind of Torah reading can range far and wide, into politics and psychology as well as theology.
In most congregations, the Torah service includes a haftarah reading. Haftarah, which means "conclusion" or "completion," refers to selections from the biblical books of the Prophets, which are arranged in readings that thematically correspond to Torah portions. This part of the service probably dates from the second century B.C.E., when the Syrian Greeks prohibited reading from the Torah and Jews substituted selections from the Prophets that contained themes reminiscent of the forbidden parasha.
After the Torah portion has been read, there are concluding prayers and a familiar hymn. Some congregations have an additional service (Musaf ).
Children at services. Taking children to Shabbat morning services can be wonderful or awful, depending both on parental attitudes and synagogue policies. Some parents feel that attending services is an important part of their children's Jewish education; that just being in the synagogue, hearing the sounds of worship, and seeing adults engaged in prayer is vital. To keep very young children occupied, a Shabbat backpack is part of the morning, filled with quiet playthings (books, crayons, puzzles, etc.) for use in the synagogue.
Others believe that worship services are basically an adult activity and that forcing children to sit for hours will do nothing but make them hate Judaism. They either arrange for a sitter, or take turns coming to services.
Actually, both of these approaches can be accommodated by good synagogue programming for children. Such activities might include age-appropriate services for schoolchildren, Shabbat-centered arts-and-crafts projects and singing for little ones, and even child care for babies. Sometimes, children join their parents during the pageantry of the Torah service as the scrolls are paraded around the sanctuary with singing, and at the end of the service for a final song. Some synagogues plan family services that feature singing, movement, and even puppet shows to tell the story in the week's Torah portion. Most congregations are very supportive of parents who want to help organize such activities, if they don't already exist.
Shabbat Afternoon
The first order of business after services is lunch, the second official meal for Shabbat. (Traditionally, breakfast does not count as one of the three Sabbath meals.) The kiddush over wine at this meal is called "the great kiddush" (kiddush rabbah). According to legend, the fancy name was supposed to compensate for the longer, more impressive Friday night kiddush. The second loaf of challah from the Friday night meal is often eaten at lunch.
The "great kiddush" and the blessing for bread (motzi) are often said in the synagogue after services, with everyone gathered around a table of wine (or spirits) and challah. If there is a bar or bat mitzvah celebration, the blessings may precede and kick off the simcha, which literally means "joy," and is also the name for a Jewish party.
In general, however, most people have lunch at home, which is where they spend the remainder of Shabbat. Again, it is always a mitzvah to invite guests home on Shabbat, especially anyone who might not otherwise have a warm, friendly place to eat. Encouraging children to invite friends over to eat and play helps make Shabbat a joyful time, and gives them the chance to extend hospitality of their own.
While lunch is seldom as elaborate as Friday night's meal, the noon meal is often festive or in some way different from weekday lunches. The whole notion of Shabbat rest discourages fancy cooking in favor of leftovers, casseroles prepared in advance, or a selection of salads and sandwich fixings. But in some families, Saturday means lunch rabbah (the great lunch) because it always features chocolate pudding or soda or chips. Shabbat can be a day of rest from saying "No" to children's insatiable passion for otherwise-forbidden treats.
A whole culinary history could be written about Shabbat lunch. In order to fulfill the mitzvah of eating a full meal without lighting fires or doing any real cooking, hearty casseroles were kept warm either at the back of the family stove or in a community oven. In Eastern Europe, for example, lunch was cholent, a heavy meat stew. In Morocco, the midday Shabbat meal was dafina, a concoction of chickpeas, potatoes, wheat, and meat, warmed all night in Arab bakery ovens. In Iraq, lunch was tbeet, a pot filled with rice and stuffed chicken, on top of which eggs were baked for breakfast.
After lunch, the afternoon stretches lazily on. The goal for Shabbat afternoon is to achieve the same level of relaxation one feels on the last afternoon of a two-week vacation. However, since many people find it difficult to face hours of uninterrupted leisure—especially at a time when the rest of the world is busy doing errands and cleaning out the garage—it can be helpful to make specific plans.
* * *
a rest of love freely given
a rest of truth and sincerity
a rest in peace and tranquility, in quiet and safety
a perfect rest in which You find favor.
FROM THE SHABBAT MINCHA SERVICE
* * *
Traditional Shabbat afternoon activities include napping, visiting the sick, and walking without a particular destination in mind. Some people reserve these hours for activities and pastimes such as bicycle riding, swimming, writing letters, baking cookies, puttering in the garden, reading poetry, sitting still and really listening to music, and going for nature walks. Shabbat is a wonderful time for spouses to talk, and for parents and children to play. And the more any activity is saved only for Shabbat, the more Shabbat-like it becomes.
Perhaps the most time-honored Shabbat afternoon activity is study. Some people meet monthly with a group of friends to discuss a book or the week's Torah section, a project that truly requires no knowledge of Hebrew or academic background in Judaism. The first five books of the Bible have been studied for more than two thousand years, in part for the sheer pleasure of trying to comprehend their meanings. There are no correct or ultimate answers—just new levels of understanding.
One way to proceed is by reading the week's portion out loud. This not only lifts the activity out of the weekday practice of reading for information; it also means that no one will have failed to do the "homework."
Nor does a Shabbat study circle have to be limited to the Bible. Indeed, the phrase "studying Torah" is traditionally applied to all Jewish learning, which includes the Hebrew language, a Jewish novel, a book of history or commentary, even last Sunday's editorial about Israeli politics. The caveat is that sad topics are avoided to preserve the joy of Shabbat.
Shabbat ends: Havdalah. According to the Talmud, Shabbat ends when three stars are visible in the sky, or on overcast evenings, when a blue thread is indistinguishable from a white thread held at arm's length. In other words, it should be dark.
Even so, there is almost no limit to how late havdalah can begin. The ritual that ends the Sabbath, havdalah, which means "separation" or "division," dates back to Talmudic times. It is a brief, enchanting ceremony that recalls the intimate power of the Friday night home ritual, though it is far more melancholy because it marks Shabbat's passing. While some congregations hold havdalah services, this is, by and large, a home celebration. It consists of four blessings: over wine, over fragrant spices, over fire, and over distinctions between sacred and profane.
The lighting of a candle announces the end of the Sabbath, when making fire is no longer prohibited. The candle used for havdalah has at least two wicks, because the blessing refers to the "lights of the fire." Havdalah candles, which are available in Judaica shops and online, contain several braided wicks and are often elaborate, multicolored, and beautiful.
Although the candle is lit first, the first blessing does not mention light or fire; it is kiddush, although the wine is not drunk at that moment.
Baruch ata Adonai Eloheynu Melech Ha-olam boray pree hagafen.
Holy One of Blessing, Your Presence Fills Creation, forming the fruit of the vine.
Next comes a blessing over fragrant spices. The sense of smell has been put to religious use since ancient times; indeed, incense was part of the service in the Temple in Jerusalem. There are a number of imaginative explanations for the presence of spices at havdalah. The sweetness of the spices symbolizes both the sweetness of paradise and also the wish for a sweet week to come. And according to one legend, during Shabbat people are given an additional soul, and when the Sabbath ends and this soul departs, the spices revive us and keep us from fainting.
Baruch ata Adonai Eloheynu Melech Ha-olam boray minai v'samim.
Holy One of Blessing, Your Presence Fills Creation, making fragrant spices.
After this blessing, it is common to pass a spice box filled with cloves and spices. Flowers or freshly cut fruit can be used as well, but the spice box is a lovely ritual object. The oldest date from 16th century Germany, when they were made to resemble architecturally ornate towers or turrets. Today, spice boxes come in all shapes and sizes, made out of everything from tin to wood to porcelain, often as part of a havdalah set that includes a candleholder, kiddush cup, and tray.
Next comes the blessing over the fire of the candle, which has been burning during the blessings over wine and spices.
Baruch ata Adonai Eloheynu Melech Ha-olam boray m'orai ha'eysh.
Holy One of Blessing, Your Presence Fills Creation, forming the lights of fire.
Since all Jewish blessings require some form of action, it is traditional to hold the hands up in order to feel the warmth of the flame and to use the light to distinguish between the nails and fingers. This custom probably derives from folk beliefs that fingernails revealed omens of the future. However, since there was great rabbinic opposition to such forms of divination, the rabbis devised alternative interpretations. They reasoned that since God started the first week with light, it was fitting to begin every week with a prayer of thanks for light. Then there's the legend that Adam and Even were covered by a protective shell, like the fingernails, before their expulsion from Eden, so looking at the nails is a way to recall the perfection of paradise.
The final blessing thanks God for creation and for the distinctions (havdalah) that differentiate the universe into the place we inhabit and sanctify.
Baruch ata Adonai Eloheynu Melech Ha-olam hamavidil bayn kodesh l'chol, bayn l'hosheh or l'choshech, bayn Yisrael l'amim, bayn yom hashvi-i leshaishet y'may hama'aseh. Baruch ata Adonai hamavdil bayn kodesh l'hol.
Holy One of Blessing, Your Presence Fills Creation. You separate the holy from the not-yet-holy, light from darkness, Israel from the other peoples, Shabbat from the six other days.
Holy One of Blessing, You separate the holy from the ordinary.
The wine is drunk after this blessing, but only after a few drops are spilled into a plate or tray. This is a gesture of sadness and loss; as Shabbat ends, so ends its glimpse of redemption, of a world made whole. Havdalah expresses a longing for a never-ending Shabbat, which for Jews is embodied in the idea of moshiach, Messiah. Because the prophet Elijah (Eliyahu) is the legendary harbinger of Messiah and since Talmudic legend has it that Elijah will come after havdalah, it is traditional to sing a song about him at the end of havdalah.
Eliyahu Hanavi
Eliyahu Hatishbi
Eliyahu, Eliyahu
Eliyahu ha-Giladi
Bimheira v'yameinu
yavo eilenu
Im Maschiach ben David
Im Maschiach ben David.
Elijah the prophet
Elijah the Tishbite
Elijah from Gilad
Come to us soon
in our days
with Messiah
child of David.
For a dramatic flourish, the burning candle is lowered into the wine while singing "Eliyah HaNavi," timing it so that the light sizzles out with the very last word. Russian Jews, who used schnapps instead of wine for havdalah, would thus set fire to the liquor, and the smoke was thought to represent departing Sabbath angels. Hasidic Jews would dip their fingers into the wine and touch their pockets and foreheads as invocations for a successful, wise, and sweet week.
Havdalah is a treat for children as well as adults. The ceremony is short, dramatic, and full of ways for everyone to participate with all the senses. Children can be given most if not all the honors of touching, carrying, and passing the ritual objects. Indeed, it is traditional for a child to hold the candle up during the ceremony.
At the conclusion of havdalah, everyone says "Shavua tov. A good week." In some families, everyone kisses, or takes a moment to make a wish for the coming week. "Shavua Tov" is also the name of a simple, well-known song.
A good week
A week of peace
May gladness reign
And joy increase...
With havdalah over, a new week begins and a different spirit prevails almost immediately. Some people try to make the feeling last by making a little ritual of cleaning and setting aside their Shabbat candlesticks and other ritual objects until the next week, or planning whom to invite for the following Friday night Shabbat dinner.
Havdalah can segue into a party called a Melavah Malkah, literally "escorting the queen." This happens most often during the weekend of a major life-cycle event. So a Saturday evening party after a bar or bat mitzvah concludes a full day of celebration; Sunday wedding festivities may begin right after havdalah.
Shabbat in the Real World
Few recipes come out looking like the illustration in the cookbook. After all, those dishes were not only prepared by a professional chef; they were also arranged for the camera by a food stylist and perhaps even digitially enhanced. In real life, the same dish may taste great, but it invariably looks messier.
The same goes for Shabbat. Despite plans and good intentions, kids will balk about coming to the table on Friday night, and your spouse will be late or unable to get home at all. Or Friday night will be delightfully peaceful but Saturday will be filled with chores and errands and e-mails that can't wait; the kids will want to play soccer on Saturday morning along with the rest of their friends, Jews as well as non-Jews.
In the past, the world was divided into people who observed all the laws of Shabbat and those who observed none of them. The choice was either/or. Even today, the Shabbat-versus-work/errands/soccer question is rarely an issue if the entire family spends most of Saturday in synagogue, and shares lunch with others within a supportive community doing much the same. But for most American Jews, Shabbat is a work-in-progress, a goal. In other words, a "practice," in every sense of the word.
Almost everyone begins experimenting with Shabbat observance by trying on Friday night home rituals. For some, that remains the extent of their Shabbat observance. Others create a regular Saturday lunch group. Some try to avoid errands on Saturday but, when something important intrudes, put it off until the last minute to extend Shabbat as long as possible. And even on a Saturday filled with chores and soccer, some families try to have everyone regroup for havdalah so that Shabbat can at least end as peacefully as it began.
Starting any Shabbat observance may engender some family conflict, and it is true that many Jewish choices—including Shabbat—do impose limits that other kids do not face.
With older children, it is important to talk about your reasons for choosing to make Shabbat and to answer their questions: Why do we have to be home on Friday nights? Why do we go to synagogue? Why do we do this stuff when even Grandma thinks it's weird? Parents need to be able to answer honestly, even if that includes occasionally acknowledging your own doubts and fears and talking about what it means to make Jewish choices.
It is also important to let older children and especially teenagers decide about Shabbat observance for themselves—even if you disagree with their decisions. Later you can ask, "How did you feel about going to Jan's slumber party instead of staying home for Shabbat dinner?" For parents who want their children to grow up to identify as Jews and cherish their Judaism, one of the tasks of parenting is to give kids practice at making their own Jewish choices.
Of course, being a good parent also means making unpopular decisions about all sorts of things, from breakfast menus to bedtimes. Being a Jewish parent entails making Jewish parenting decisions. Say, for example, your son is invited to a friend's bar mitzvah on the morning of a very important soccer game. He tells you that he wants to play in the game and then go to the big party, after the bar mitzvah ceremony is over. If you give permission for him to go to the party and miss the religious service, you are letting him know that as far as you are concerned, Judaism is not as important as either soccer or ice cream and cake. Which probably does not further your goals as a Jewish parent.
But most of all, children learn from their parents' example. When adults make a heartfelt commitment to Shabbat, when Jewish family rituals seem as natural and dependable as the tides and the seasons, when the Jewish parts of family life are fun, arguments about soccer games and slumber parties take their place as minor disturbances in a broader context that has been defined in positive Jewish terms.
* This kind of decision-making is a prime example of liberal Jewish practice, which focuses as much upon the spirit of the law, or halachah, as on the letter of the law.
## GOOD DEEDS
When a Jewish baby is born, there is a traditional prayer that the child will grow into a life that includes Torah, huppah, and ma'asim tovim. Torah stands for learning, especially Jewish learning. Huppah, the wedding canopy, symbolizes love, commitment, and family. Ma'asim tovim means good deeds, because for Jews doing good is what defines a mensch—a human being.
Because one of Judaism's primary goals is the transformation of people into menschen (the plural of mensch), good deeds are not left to the regrettably unreliable human impulse to do good. Feeding the hungry, clothing the naked, housing the homeless; for Jews, these are not voluntary acts of charity, a word that derives from the Latin caritas, and means "Christian love." Jews are commanded to feed, clothe, and shelter those who lack the basic necessities through mitzvot.
The general concept of good deeds—ma'asim tovim—may be divided into three categories: tzedakah, gemilut hassadim, and tikkun olam. Tzedakah, the giving of money to the poor, is commonly explained as charity, although a more accurate translation is "righteous giving." Gemilut hassadim, "acts of loving-kindness," refers to the kinds of activities Americans tend to associate with voluntarism: donating time and energy to help those in need. Tzedakah and gemilut hassadim are ancient Jewish concepts, discussed in the Talmud and recognized by all Jews as fundamental to Jewish observance. Tikkun olam, "the repair of the world," is a 20th century notion (based on a 400-year-old mystical story) that elevates the biblical prophets' demands for social justice to the status of a mitzvah. Tikkun olam is the religious obligation to work for peace, freedom, and justice for all people.
These three categories are all expressions of ma'asim tovim. Tzedakah, tikkun olam and gemilut hassadim are described separately in this chapter not only for the sake of organization, but also to reflect the fact that people tend to "specialize" in one or another aspect of ma'asim tovim. The man who volunteers at a soup kitchen every Sunday is not always the person who collects vast sums for that operation. The woman who lobbies tirelessly on behalf of universal health care is not necessarily the person who visits nursing homes.
The obligation to do tzedakah, gemilut hassadim, and tikkun olam is, first and foremost, incumbent upon individuals and families. That said, no one is expected to repair the world by him or herself. The Jewish community as a whole is considered responsible for the performance of good deeds and is obligated to organize on behalf of the poor and the needy. "The Organizational World" contains information about communal organizations concerned with ma'asim tovim.
The Talmud states, "Though it is not your duty to complete the work, neither are you free to desist from it."28 This chapter contains many practical suggestions for ways of incorporating good deeds—ma'asim tovim—into everyday life.
Righteous Giving—Tzedakah
The word tzedakah is related to several other Hebrew words, including tzadik, "righteous person," and tzodek, "correct." In the Bible, the word generally denotes righteousness. The much-quoted passage from Deuteronomy, usually translated, "Justice, justice shall you pursue," actually calls for tzedek, tzedek.29 The Talmud is full of references, parables, and teachings on the mitzvah of tzedakah and goes so far as to say, "Tzedakah is as important as all the other commandments put together."30
Giving tzedakah is not viewed as an expression of individual goodness or goodwill, but as a response to an obligation based upon biblical imperatives and the belief that all needy humans deserve help. While it has always been considered preferable to give tzedakah cheerfully and willingly, the important thing is the gift itself, not the spirit in which it is given.
The story is told about two women on a fund-raising tour of a hospital's pediatric ward. At the end of the visit, one woman is in tears, deeply moved by the care and compassion of the place. She pulls out her checkbook and offers a check for $100. The other woman is visibly annoyed throughout the tour, and even complains about having her time wasted; why didn't they just send her a letter. As she walks out, she calls her attorney and asks him to direct $100,000 from her foundation to the hospital. For Jewish tradition, the tears are nice but essentially irrelevant.
Which is not to say that the rabbis did not recognize the intrinsic value of tzedakah to the donor as well as to the recipient. Tzedakah was never looked upon as a burden or a tax, but as a privilege: a way of expressing dignity, affirming self-respect, and participating in an activity that defines a mensch. Doing good feels good, which is partly why Jewish law requires that even the very poor give something to those less fortunate than themselves, even if their gift comes directly from someone else's tzedakah to them.31
* * *
Rabbi Chayim of Sanz said: "The merit of charity is so great that I am happy to give to one hundred beggars even if only one might actually be needy. Some people, however, act as if they are exempt from giving to one hundred beggars in the event that one might be a fraud."
DARKAI CHAYIM, 16TH CENTURY BOOK OF MORAL TEACHINGS
* * *
The most important commentary on tzedakah in Jewish history was written by Rabbi Moses Maimonides in the 12th century. Known as "Maimonides' Ladder of Tzedakah," it lists ways of giving in order of their worthiness, a ranking organized according to what would spare the poor embarrassment. The ladder's highest rung is reserved for that which is given anonymously and enables another to become self-sufficient. Maimonides was also quite specific about how much tzedakah is enough, and considered 10 percent of income an average and proper budget.
Maimonides' Ladder of Tzedakah
* 1. To help someone else to become self-sufficient
* 2. To give so that neither the person giving nor the receiver knows each other's identity
* 3. To give anonymously (donor knows the recipient, but the recipient doesn't know the donor)
* 4. To give without knowing who is receiving (recipient knows the donor, but the donor doesn't know the recipient)
* 5. To give without being asked to give
* 6. To give what is needed, but only after being asked
* 7. To give less than one should, but with compassion and in a friendly manner
* 8. To give grudgingly, reluctantly, or without wanting to give and not in a friendly manner
MISHNEH TORAH, MAT'NOT ANIYIM 10:7–14
Tzedakah does not just happen by accident. Although Jewish tradition supports spontaneous giving—such as responding to beggars on the street or neighbors asking for a donation to cancer research—taking on the mitzvah of tzedakah requires finding ways to incorporate it into the rhythm of daily life.
Many Jews make this happen through the time-honored tradition of making regular donations on Jewish holidays and personal milestones. Some put aside money for tzedakah before lighting Shabbat candles every week and on holidays. For small gifts like these, the pushke—a coin box reserved for tzedakah, a kind of Jewish piggy bank—is used. Pushkes range from works of art made of brass or silver, to blue-and-white aluminum cans. Making a family pushke is a favorite arts-and-crafts project and whether the result is a glazed clay masterpiece or an old coffee can covered with children's handprints, the result can become a family heirloom.
The custom of remembering the poor at moments of celebration is a way to add even more meaning to life's sweetest moments. In the small, tight-knit Jewish communities of the past, local beggars were invited to wedding feasts, and at Passover the community ensured that even the poorest family could afford a proper seder. In that spirit, many families, synagogues, and other Jewish organizations now regularly set aside a voluntary tzedakah gift of 3 percent of the food costs at weddings, b'nai mitzvah, and other banquets for an organization called MAZON, A Jewish Response to Hunger. MAZON allocates donations from the Jewish community to prevent and alleviate hunger among people of all faiths and backgrounds. For more information, go to www.mazon.org.
It is also traditional to give tzedakah in honor of a rite of passage. Indeed, some wedding invitations, bar and bat mitzvah invitations, and birth announcements request that donations be sent to a specified charity, sometimes in lieu of a gift. Indeed, tzedakah has become a focus for many synagogue bar and bat mitzvah programs; children may study and volunteer at a local agency, teach others about what they learned, and give some of their cash gifts to that organization. Twelve-and 13-year-old children are old enough to understand that the world is filled with inequities and tzedakah becomes a way for them to make a difference. Indeed, in Jewish schools of all kinds raising money and volunteering are part of the curriculum.
There are many ways to make tzedakah a family project. Putting coins into a pushke every Friday night is the simplest, and is also a way to begin talking to children about poverty and hunger, and how they can help. School-age children can help decide where the pushke money should go, and some parents talk candidly about the family's tzedakah budget, explaining how much money they give and to whom. Another easy way to add tzedakah to everyday life is at the supermarket. Let children pick out a can of food for donation to your synagogue or school food drive, and then volunteer for a family outing to help stock a local food pantry.
In some families, children are expected to designate some portion of their allowance for tzedakah. Parents and grandparents might want to open a tzedakah endowment fund for children, either at birth or on the occasion of a bar or bat mitzvah. Using the word tzedakah and linking your giving with Jewish settings and values reinforces the lesson.
Deciding where to give money is difficult because there are so many worthy causes. Traditionally, tzedakah was allocated in concentric circles, beginning with family and extending to the poor of the local community, and then to the poor who live at a distance, especially in Israel. Although Jews have always been enjoined to help the non-Jewish poor as well, the primary goal of tzedakah was seen as helping fellow Jews, who could not rely on others. This argument remains compelling. If Jews don't support services for the Jewish elderly, or Jewish educational and cultural institutions, there is no reason to expect non-Jews to do so. Many Jews also feel strongly that nondenominational organizations deserve their support as well, and divide their giving accordingly.
Much Jewish giving is done through federations, umbrella fund-raising organizations that allocate monies to local and national Jewish agencies and to Israel. Family foundations are an increasingly common conduit, and some individuals pool their resources in tzedakah collectives, leveraging individual giving by joining with others to research, discuss, and select beneficiaries.
* * *
As tiny scales join to form a strong coat of mail, so little donations combine to form a large total of good.
TALMUD: BABA BATHRA 9B
* * *
Deciding how much to give is another sort of challenge. Maimonides' questions still challenge us to consider "How much is enough?" One oft-cited rule of thumb is: If the total of all charitable contributions makes absolutely no dent in your lifestyle, if you don't have to give up so much as one dinner in a nice restaurant, you're probably not giving enough.
Acts of Loving-kindness
According to many Jewish sources, gemilut hassadim is the highest form of doing good in the world. Raising money and writing checks to Jewish institutions and other worthy causes is an essential mitzvah, but there is also a sense that money alone does not meet the biblical demand for righteousness. Especially in America, where it can be relatively easy to remain insulated from hunger, poverty, and pain, gemilut hassadim calls for face-to-face encounter with real needs.
Gemilut hassadim is not, strictly speaking, a mitzvah. Because it is a feeling, loving-kindness cannot be required or commanded. But like a mitzvah, loving-kindness is not only about feelings but about rolling up your sleeves, giving up an evening a week, and working for the benefit of strangers. For American Jews, this notion dovetails with the national tradition of voluntarism.
There are six traditional forms of gemilut hassadim: providing clothes for the naked, visiting the sick, comforting mourners, accompanying the dead to the grave, providing for brides, and offering hospitality to strangers. These acts are considered especially holy because, according to Midrash, God performed them for human beings: attending Eve at her wedding to Adam, comforting Isaac as he mourned for Abraham, his father, and burying Moses.32
In the Talmud, gemilut hassadim is described as more spiritually powerful than tzedakah in three ways. First, tzedakah involves only money, but gemilut hassadim requires personal involvement. Second, tzedakah is given only to the poor, but gemilut hassadim can be done for anyone, regardless of his or her station in life. And third, while tzedakah can only be given to the living, gemilut hassadim can even extend to the dead.
The definition of gemilut hassadim has been extended over time to include such activities as feeding the hungry, helping people find jobs, visiting the elderly, teaching people to read, providing shelter for the homeless, saving animals from suffering, planting trees, lifting the spirits of the depressed, caring for orphans, and perpetuating the memory of someone who has died.
Nearly one-third of all Americans do some kind of volunteer work on a weekly basis, the highest percentage among developed nations. Thus, urban synagogue soup kitchens and shelters are staffed by congregants, and Jewish religious schools require high school students to perform some kind of community service.
* * *
Rabbi Isaac said: "He who gives a coin to a poor man is rewarded with six blessings. But he who encourages him with friendly words is rewarded with eleven."
TALMUD: BABA BATHRA 9A
* * *
Families can participate in gemilut hassadim in a number of ways. Parents who are involved in volunteer work can explain exactly what they are doing and why to their children. And while it may not be appropriate to take children to a battered women's shelter or soup kitchen, there are other ways to involve kids, such as collecting outgrown and unused clothes and making a family trip to deliver them to a local shelter; baking Hannukah cookies and bringing them to a Jewish nursing home; or "adopting" an isolated Jewish elder and visiting him or her regularly.
Jewish organizations are always in need of volunteers. So are community hospitals, nursing homes, legal aid societies, and literacy programs. The list is endless, and so are opportunities for acts of loving-kindness.
Repairing the World
During the 16th century, in the town of Safed in the land of Israel, Isaac Luria33 described the creation of the world in terms that have captured the imaginations of Jews ever since.
Before creation, said Luria, there was nothing but God. God was in all time and space, and God's light filled the cosmos. In order to make room for creation, God had to make some space where there was no God. So God took a deep breath to make room for the universe.
In the space from which God had withdrawn, the heavens and the earth were formed. But that meant God was nowhere in creation. So God exhaled some of God's light into the world.
But this light was too strong, too bright, too much for the vessels that were meant to hold it, so they shattered. And the world was filled with tiny sparks of God's light.
The world is filled with these divine sparks. They are hidden, lost, everywhere, and it is the responsibility of each Jew to gather some of these sparks and to restore them to their place. By doing this, creation can be restored to its original, perfect state. The task of restoring or repairing the world is called tikkun olam.
According to Luria's intent and traditional interpretations, tikkun olam is accomplished by performing the mitzvot: from the commandments for keeping kosher and lighting Shabbat candles to those that mandate caring for the elderly or working for world peace. In modern times, Jews have come to understand tikkun olam in somewhat different and broader terms. The repair of the world is associated with tackling problems in macrocosmic rather than in interpersonal or even communal terms. Tikkun olam is identified with working for social justice, peace, freedom, equality, and the restoration of the environment.
This definition is not an exclusively modern formulation, however. Judaism has always blurred distinctions between religious duties and social obligations. Indeed, the Jewish notion of redemption is political in the sense that it calls not for the perfection of individual souls but for the liberation of the entire world. The prophets demanded an end to poverty, bigotry, and all forms of oppression. The words of Isaiah, which are repeated at services every Yom Kippur, have never been more powerful in their insistence upon action than they are today.
Behold on the day of your fast you pursue business as usual and oppress your workers. Behold you fast only to quarrel and fight, to deal wicked blows. Such fasting will not make your voice audible on high.
This is my chosen fast: to loosen all the bonds that bind men unfairly, to let the oppressed go free, to break every yoke. Share your bread with the hungry, take the homeless into your home. Clothe the naked when you see him, do not turn away from people in need...
If you remove from your midst the yoke of oppression, the finger of scorn, the tongue of malice, if you put yourself out for the hungry and relieve the wretched, then shall your light shine in the darkness, and your gloom shall be as noonday.34
Since the opening of the ghettos in the 19th century, Jews have been involved in virtually all attempts to improve human life. Sometimes, tikkun olam takes a specifically Jewish form, as in the search for a just and secure peace for Israel and her neighbors. However, a commitment to tikkun olam also requires, almost by definition, attention to many issues that are not strictly limited to Jewish interests, among them, the environment and ecology, nuclear disarmament and international peace, and equal protection for all, regardless of race, sex, sexual orientation, or national origin. Jews are prominent among the supporters, activists, and leaders in all of these causes.
Doing tikkun olam includes everything from writing letters to Congress about toxic waste, to attending rallies in support of funding for health care. Tikkun olam means supporting candidates and voting with a self-consciously Jewish perspective. Even recycling waste paper, bottles, and cans responds to the call to repair the world.
This formulation of tikkun olam claims political commitment as a specifically Jewish endeavor. And it helps blur the tendency to segregate Jewishness to those things that are done at home, or in a synagogue, or among other Jews. In a sense, tikkun olam demands that Jews act as Jews in every arena of life.
## THE PEOPLE OF THE LIBRARY
Jews are often called "the people of the book," and for good reason. The legacy of universal literacy—for women and men, for poor and rich—has set Jews apart from their neighbors throughout history.
It would be more accurate to refer to Jews as "the people of the library." First of all, "The Book," the Jewish Bible, is itself a library, a collection of books, and the foundation and cornerstone of a 3,000-year-old tradition of intellectual inquiry, writing, and publishing. But the basic texts of Judaism include much more than the Bible. Jewish literacy requires familiarity with some of the classical sources and genres as well: Torah, Talmud, Midrash, Kabbalah, siddur.
The presence of books, especially books dealing with Jewish subjects, is a hallmark of virtually all Jewish homes. Reading and study, discussion and writing, are part of the social as well as intellectual glue that has kept Judaism and the Jewish people alive. The secret ingredient of this glue, taught to children by their parents, is the pleasure of study for its own sake, in Hebrew, Torah lishma.
Jewish Texts: Some Definitions
Bible. There is no Hebrew word for "bible." The English word probably comes from the Greek biblia, meaning books and reflecting the fact that the Bible is itself an anthology. When Jews talk about the Bible, the reference is shorthand for "the Jewish Bible" or "the Hebrew Bible." (It is only the "Old Testament" to Christians, who believe that there is a "New Testament," which describes a new covenant between God and humanity that was announced by Jesus.)
The Hebrew term for the Bible is tanakh, which is an acronym for the three Hebrew letters that correspond to its three major divisions:
Torah—The five books of Moses, Pentateuch
Ne'vi'im—Prophets
Ketuvim—Writings
Arguments about the authorship of the Bible cut right to the heart of religious belief. Traditionalists attribute the writing of the Torah to Moses, Psalm 92 to Adam, and Song of Songs to King Solomon. Modern biblical scholars generally agree that the Bible, as we know it, was codified sometime during the first or second century C.E.
The Hebrew Bible—Tanakh
Torah:
Genesis—Beresheet
Exodus—Shemot
Leviticus—Vayikra
Numbers—Bemidbar
Deuteronomy—Devarim
Prophets: Nevi'im
Joshua—Yehoshua
Judges—Shoftim
I Samuel—Shmuel Alef
II Samuel—Shmuel Bet
I Kings—Melakhim Alef
II Kings—Melakhim Bet
Isaiah—Yishayahu
Jeremiah—Yirmiyahu
Ezekiel—Yekhezkel
The 12 Minor Prophets
Hosea—Hoshea
Joel—Yoel
Amos—Ahmos
Obadiah—Ovadya
Jonah—Yona
Micah—Meekhah
Nahum—Nakhum
Habakkuk—Khbakuk
Zephania—Tzafania
Haggai—Haggai
Zakariah—Zekharya
Malachi—Malakhi
Writings: Ketuvim
Psalms—Tehilim
Proverbs—Mishlei
Job—Eyov
Song of Songs—Shir Hashirim
Ruth—Root
Lamentations—Eikha
Ecclesiastes—Kohelet
Esther—Ester
Daniel—Daniel
Ezra—Ezra
Nehemiah—Nekhemya
I Chronicles—Divray Yamim Alef
II Chronicles—Divray Yamim Bet
Torah. A word with multiple meanings, the Torah is also called the Pentateuch and the five books of Moses. It consists of the first five volumes of the Bible: Genesis, Exodus, Leviticus, Numbers, and Deuteronomy. The Torah also refers to the scroll on which this part of the Bible is written.
But "Torah," without the definite article, refers to much larger concepts. "Torah" can be used to mean revelation—God's word as understood by human beings. To further complicate things, Torah also refers to all Jewish study, and all of Jewish literature.35
Talmud. The Talmud (Hebrew for "study") is an encyclopedia of commentaries on Jewish law, and of commentaries upon commentaries on Jewish law. Written in Hebrew and Aramaic, which was the lingua franca of the ancient Near East, the Talmud comprises two major sections called Mishna and Gemara.
According to tradition, Moses received two forms of revelation on Mount Sinai: written and oral. The written law, the Torah, was much shorter and less specific than the oral law, which was transmitted through the generations, first from Moses to Joshua, then to the elders of the Hebrew people, to the prophets, and on to successive leaders until it reached the men who were, in effect, the earliest rabbis. These scholars of the first and second century C.E. began putting the oral law into writing in what came to be called the Mishna.
The Mishna (Hebrew for "recitation" or "recapitulation") was completed by the third century C.E. in an attempt to put the commands contained in the written Torah into practical terms. Its authors sought to convey the idea that the laws found in the Bible did not apply just in their original context, but embraced all aspects of life throughout time. The six sections of the Mishna are called Orders, which are further divided into 63 smaller sections called tractates (literally, "webbings"). The Mishna deals with holiday observance, family life, agriculture, the rituals of the Temple, and much more.
The most famous section of the Mishna is the tractate known as Avot, or "fathers," which contains many famous proverbs, axioms, and sayings, such as, "If I am not for myself, who will be for me? If I am for myself alone, what am I? And if not now, when?"36 This tractate has long been published as a book of practical wisdom entitled Pirke Avot, usually translated as "Ethics of the Fathers."
* * *
Who is wise? One who learns from all men.
Who is wealthy? One who is happy with is portion.
Who is mighty? One who subdues his passions.
Who is honored? One who honors all creation.
PIRKE AVOT 4:1
* * *
Over succeeding generations, the study of Mishna inspired a literature of explanation and commentary, which became an object of study in its own right. This body of writing was called Gemara, Aramaic for "study." The Gemara, which is an unstructured, almost stream-of-consciousness transcript of discussions, arguments, and stories, examines a broad range of questions from daily life. Sometimes the sublime and the ridiculous share a single paragraph:
Who is to be considered truly wealthy?
In the opinion of Rabbi Meir: He who derives peace of mind from his wealth.
Rabbi Tarfon says: He who has a hundred vineyards, a hundred fields, and a hundred workers working in them.
Rabbi Akiva says: He who has a spouse who does exquisite deeds.
Rabbi Yossi says: He who has a bathroom near his dining room table.37
Midrash. Midrash, which means "search," or "investigation," refers not to a single book but to a genre of biblical commentary. Using every kind of imaginative and literary device, Midrash embroiders upon the biblical text. Explaining Midrash requires metaphoric language; it has been described as something "between commentary and fantasy...that sprouts up in the spaces between the consecrated words of Scripture."38 If the compressed images of the Bible are like photographs, a midrash is the story about what happened or what might have happened before and after the flash went off.
There are several collections of midrashim (plural of midrash), most them produced between 400 and 1200 C.E. One of the most famous of these is Midrash Rabbah, the "Great Midrash." Here is an example of how Midrash Rabbah explicates the line in Genesis that says, "And God said, Let us make man."
When the Holy One came to create the first man, the angels took sides. Mercy said, "Let him be created, for he will be merciful." But Truth said, "Do not let him be created because he will lie." Righteousness said, "Let him be created for he will do righteous deeds." But Peace said, "Do not let him be created because he is full of strife."
The Holy One took Truth and flung him to earth, and the angels argued with God, and asked God to raise truth up again from the earth.
While the angels were arguing, The Holy One created man. And then God said to the angels, "Why do you argue? Man is already made."39
Codes. The whole of Jewish law is called halachah, probably from the verb for "going," as in, the way one should go. Halachah is often used to refer to the laws and rules that govern and inform Jewish life. The Talmud is not a set of laws but a discussion of the law, and has been compared with the Congressional Record, which provides a verbatim account of what is said on the floor of the U.S. Congress; not only the formal speeches, but the jokes and side comments as well. To find out what the law says, people turn not to the Talmud but to the codes, which are practical, accessible guides to action based upon the debates in the Talmud.
The two classic codes are the Mishna Torah, written by Moses Maimonides, the great 12th century Mediterranean rabbi and philosopher, and the Shulchan Aruch ("The Prepared Table") by Joseph Karo, a 16th century rabbi who lived in the town of Safed, Palestine. Maimonides and Karo based their guides on careful reading of Talmud, consideration of contemporary rabbis' decisions (known as responsa literature), and the Jewish practice of their times. These books remain cornerstones of halachic discussion and debate, which continues unabated today.
Kabbalah. The rationalist tradition in Jewish thought has been dominant, but there has also been a long and illustrious history of Jewish mysticism, which is called Kabbalah. Like Midrash, Kabbalah is not a book but a way of looking at the world and understanding Jewish tradition. Kabbalistic literature includes several books of biblical commentary, including Sefer Yetzirah ("The Book of Creation") and the Bahir ("Brilliance"). The most influential of all mystical texts, however, is the Zohar ("The Book of Splendor"). Typified by evocative, lyrical language and concepts, the Zohar was a commentary on the Torah, probably written by the Spanish rabbi Moses de Leon (1230–1305).
The contemporary fad for Kabbalah, among non-Jews as well as Jews, minimizes the ways that this subject is rooted in Jewish tradition and law, stressing an esoteric mysticism divorced from mitzvot, halachah, and Jewish life.
Siddur. The daily book of prayer—used both in the synagogue and at home—is called the siddur, from the Hebrew root for "order." The prayer book used for festivals and the High Holidays is called the machzor, from the Hebrew root for "cycle."
Prayer books have been the most commonly owned of all Jewish books. Over time, the content and order of the prayer book has evolved and changed. Modern prayer books tend to contain readings that reflect Jewish history and theology from many periods, including our own.
Creating a Home Library
No two Jewish homes have identical Jewish libraries. People select books as idiosyncratically as they choose art for their walls and food for their tables. Books reflect the character, curiosity, and impulses of their owners. Jewish literature expands exponentially every few years with the publication of important new works in virtually every discipline, so that any listing is bound to be outdated almost before the ink dries. And of course the Internet will continue to enlarge the limits of the Jewish home library, with ever-growing connections to books, periodicals, institutions, blogs. What follows is a short list of classics, offered as a guide to assembling the foundation for a Jewish home library.
Bible
The Jewish Publication Society (www.jewishpub.org) produces an accurate, readable translation of the Bible, available in either one or three volumes.
The Jerusalem Bible, published by Koren Publishers of Jerusalem (www.judaism.com) contains very accurate Hebrew and English versions in a single volume, although the English is not as readable as the JPS version.
Torah
As a rule, Jews do not read the first five books of the Bible without some form of commentary. For close study of the Torah as it is read in its weekly portions during services, people use what is called a chumash. A chumash (from the Hebrew word for "five") includes both Hebrew and English versions of each week's portion, the weekly Haftarah section (readings from the Prophets), and English commentaries and notes. Two of the best known of these are: The Torah: A Modern Commentary, edited by Rabbi Gunther Plaut (www.ccarpress.org), and Etz Hayim: Torah and Commentary (www.uscj.org).
Siddurim / Prayer Books
Generally produced by the movements, prayer books offer more than just the rubric for synagogue services. Most provide essays and commentaries on prayer as well as sections covering home observances, such as the prayers for the Sabbath and holidays.
Conservative: Sim Shalom (www.uscj.org)
Reconstructionist: Kol Haneshamah (www.jrf.org)
Reform: Mishkan Tefila (www.ccarpress.org)
Talmud
The Essential Talmud by Adin Steinsaltz (Basic Books, 1984) is a brief and lucid introduction to Talmud.
The Talmud: The Steinsaltz Edition (Random House) gives unprecedented English access to the original text by one of the 20th century's most erudite and prolific Jewish scholars.
The Mishna is available in English in several editions of one or two volumes. The section of Mishna known as Pirke Avot is available in many versions, including some with explanatory notes and commentaries.
Also recommended are Back to the Sources by Barry Holtz (Summit Books, 1986), a single volume with eight essays about the major Jewish texts, including the Bible, Talmud, Midrash, Hasidic writings, and the prayer book; and The Zohar, Annotated and Explained by Daniel Chanan Matt (Skylight Paths Publishing, 2003), a good introduction to the classic book of Jewish mystical commentary.
General Reference
The Encyclopedia Judaica (Macmillan Library Reference, 2006). The "EJ," as it is known, is the Britannica of Judaism, and there is little it does not cover. The 18-volume set, newly updated, includes contributions by thousands of scholars. A CD version is available from www.jewishsoftware.com.
A Guide to Jewish Religious Practice by Isaac Klein (Ktav Publishing House, 1979) is the standard reference book of halachah published by the Conservative movement; this is where you go to look up the law on just about anything.
The New Joys of Yiddish by Leo Rosten and Lawrence Bush (Three Rivers Press, 2003). More than just a funny dictionary of English, Yiddish, and "Yinglish" words, this is a useful guide for exploring Yiddishkeit—"Jewishness."
Jewish Literacy: The Most Important Things to Know About the Jewish Religion, Its People and Its History by Rabbi Joseph Telushkin (William Morrow, 1991). An excellent overview.
History
A History of the Jewish People, edited by H. H. Ben-Sasson (Harvard University Press, 1985). A definitive volume of 1,000 pages that covers Jewish history to the modern period.
The Gifts of the Jews: How a Tribe of Desert Nomads Changed the Way Everyone Thinks and Feels by Thomas Cahill (Anchor, 1999). A light-handed, modern perspective.
American Judaism: A History, by Jonathan Sarna (Yale University Press, 2005). Concise and readable, it covers 350 years, from colonial beginnings in 1654.
Jewish People, Jewish Thought: The Jewish Experience in History by Robert M. Seltzer (Prentice-Hall, 2003). A survey of Jewish thought, beginning with the ancients and running through the 20th century.
Israel
The Zionist Idea, edited by Arthur Hertzberg (Jewish Publication Society, 1997). A collection of essays providing an intellectual history of Zionism, with brief biographies of the leaders of the early movement.
In the Land of Israel, by Amos Oz (Harvest Books, 1993). A series of interviews conducted by the well-known Israeli novelist.
One Palestine Complete: Jews and Arabs Under the British Mandate, by Tom Segev (Owl Books, 2003). An Israeli journalist and historian explores the early history of the state.
Philosophy
God in Search of Man: A Philosophy of Judaism, by Abraham Joshua Heschel (Farrar, Straus and Giroux, 1976), is a contemporary attempt to describe the relationship between human beings and God.
After Auschwitz, by Richard Rubenstein (The Johns Hopkins University Press, 1992), articulates a radical post-Holocaust Jewish theology.
A Maimonides Reader, by Isador Twersky (Behrman House, 1976), is an introduction to one of Judaism's great minds, written by a master.
Spirituality
The Way of Man According to the Teachings of Hasidism, by Martin Buber (Citadel Press, 1995). A modern interpretation of six Hasidic tales that explain some of Judaism's basic tenets.
The Sabbath, by Rabbi Abraham Joshua Heschel (Farrar, Straus and Giroux, 2005), is the classic text for understanding the theological and spiritual importance of Shabbat.
God Was in This Place and I, i Did Not Know: Finding Self, Spirituality and Ultimate Meaning, by Lawrence Kushner (Jewish Lights Publishing, 1993). A spiritual journey into a single biblical verse (Genesis 28:16).
Major Trends in Jewish Mysticism, by Gershom Scholem (Schocken Books, 1995). A historical consideration of the mystical "counterhistory" that includes Kabbalah and Hasidism.
Holocaust
The War Against the Jews: 1933–1945, by Lucy Dawidowicz (Bantam, 1986), is an exhaustively researched historical anthology of the Holocaust.
Fiction and memoir provide some of the most powerful commentaries on those years. A few of the best include Night by Elie Wiesel, Survival in Auschwitz by Primo Levi, and The Last of the Just by André Schwarz-Bart.
* * *
Holy One of Blessing, Your Presence Fills Creation, You make us holy with Your commandments and call us to occupy ourselves with words of Torah.
THE BLESSING RECITED BEFORE JEWISH STUDY
* * *
## WHAT JEWS EAT
The philosopher Martin Buber described Judaism as a system for living without distinctions between the secular and the spiritual. He wrote, "Basically the holy in our world is what is open to God, as the profane is what is closed off from Him...hallowing is the event of opening out..."40 Kashrut, the system of rules and laws regulating what Jews eat and how Jews prepare food, can be understood as a way of hallowing the very mundane act of eating, as a way of "opening out" to God with every meal.
For over two thousand years, kashrut has been a defining element of Jewish life, part of the cultural glue that kept Jewish communities interdependent and united, and also a constant affirmation of Jewish differentness in the most fundamental aspects of life. Because the laws of kashrut so clearly set Jews apart, food often became a focus of anti-Semitism. There are countless stories about Jews being forced to eat pork—or dying rather than comply.41
Although many Jews think of kashrut as an essential aspect of Jewish identity and observance, most American Jews do not "keep kosher." Nonetheless, there is increasing interest in the dietary laws among liberal Jews who are willing to learn from all aspects of tradition. And given that so many people are eating more self-consciously for reasons of health, fitness, and even in response to political and ecological concerns, Judaism's approach to spiritual eating takes on new possibilities for meaning. (Of course, Jews are not the only ones with religious dietary laws. Muslims share the stricture against pork and almost all of India—as many as 20 percent of the world's population—eat no meat whatsoever, and many do not touch eggs or milk either.)
What's Kosher, What's Trafe
The laws of kashrut divide all edibles into two categories: kosher and trafe. The word "kosher" means "fit" or "proper." Trafe, which comes from the Hebrew for "torn" or "damaged," designates things that are unfit or improper to eat.
Kashrut further divides all kosher foods into three categories: dairy (milchig), meat (flayshig), and neutral (pareve). Kashrut demands a complete separation of dairy and meat. Pareve foods, which include all fruits, vegetables, many fish, and eggs, can be prepared and eaten with either dairy or meat products.
The primary source for the dietary laws is the Torah, which lists the animals, birds, fish, and insects that may and may not be consumed by the people of Israel.42 However, the laws that regulate food preparation were laid out in the Talmud and subsequent codes of law. For example, the biblical injunction against boiling a kid in its mother's milk,43 was elaborated by the rabbis into the total separation of milk and meat, which then calls for different sets of dishes and utensils. Although the laws of kashrut are specific, food presents too many individual issues for any written code to address them all, which is why one of the major tasks assigned to rabbis throughout history has been to answer questions about kashrut. That said, here are the fundamentals:
Fruits and vegetables. Everything that grows is both kosher and neutral or pareve. Every kind of plant, herb, weed, grain, tree, shrub, moss, fungi, fern, and bush is kosher. Every fruit, flower, vegetable, seed, root, and nut is permitted.
Fish. Any fish that has both fins and scales is kosher. This encompasses a great many varieties, including (but not limited to): anchovies, bluefish, carp, flounder, grouper, halibut, lake trout, mackerel, perch, rainbow trout, salmon, tuna, whitefish, and yellowtail. Kosher fish are also pareve, and can be served with either dairy or meat.
Nonkosher fish include: shellfish (crustaceans such as crab, lobster, mussels, and shrimp), eels, porpoise, shark, whale, and all other sea mammals. Frog, turtle, and octopus are also trafe.
Meat. All animals that both chew their cud and have a split hoof are kosher. This includes: antelope, buffalo, cattle, deer, eland, hart, gazelle, goat, moose, sheep, and yak. Trafe animals include: camels, donkeys, pigs, horses, and rodents.
However, for meat to be considered kosher, the permitted animals must be ritually slaughtered according to the laws of sh'chitah by a butcher called a shochet, a person who is conversant with both the relevant religious teachings and has hands-on skills. Furthermore, since meat may have no trace of blood on it, after ritual slaughter and inspection, it is soaked in water, salted, and soaked again.
Fowl. Most domestic birds are kosher, including: chicken, turkey, duck, and geese. Domesticated pigeon, dove, and songbirds are also permitted. Fowl are considered meat, and must be slaughtered, inspected, and soaked and salted as described above.
Wild birds and birds of prey are forbidden. Trafe birds include: eagle, heron, ostrich, owl, pelican, swan, and vulture. Eggs from nonkosher birds are prohibited.
Eggs from kosher birds are kosher and pareve; however, a single spot of blood renders an egg trafe.
Dairy products. Generally, all dairy products are permitted.
Liquor and wine. All beers, and grain and fruit liquors, are kosher and pareve. Some cream liquors are dairy.
Because wine falls into the category of things used for sacramental purposes—specifically, for making kiddush—the Talmud outlawed the use of any wine made by non-Jews for fear it might have been used for idol worship. "Kosher wine" is a designation given to wine made under rabbinical supervision, with the intent of being used for kiddush.
There are many excellent kosher vintages and some people make a point of buying kosher wine from Israel as a way of supporting the nation and people.
High-tech trafe. BHT, MSG, mono-and diglycerides, food colorings, preservatives, growth hormones: while none of these things are technically trafe, some Jews treat them as such. Since Judaism places great value on protecting health, careful reading of labels and the avoidance of potentially harmful additives and ingredients can be seen as a religious act as well as prudent shopping.
The Meaning of Kashrut
The most common assumption about kashrut is that it was implemented to protect health and life. While rationales based on health have been offered for centuries, there is little evidence to support the argument that God wants Jews to forgo spaghetti carbonara because ham mixed with cream does bodily harm.44 Jews who keep strictly kosher have managed to clog their arteries with chicken fat while assiduously avoiding bacon grease.
Actually, the health argument has been widely dismissed since the time of the Talmud. Rabbis have always "explained" kashrut as something Jews do because God demands it in the Torah. The act of obeying the commandment—of performing the mitzvah—is its own reward. However, since rabbinic Judaism also encourages Jews to discern God's intent in the Torah and to find personal meaning and fulfillment in the laws, kashrut has been given many interpretations.
Perhaps the most compelling explanation is the idea, restated in modern times by Martin Buber, that kashrut hallows the everyday. The intent of kashrut is not to deny the body's needs or pleasures, but to turn a natural function into a holy act.
According to another ancient line of thought, kashrut has been interpreted as a way of instilling reverence for life, especially animal life. There is evidence that boiling a kid in its mother's milk was a pagan ritual the Hebrews rejected, perhaps simply as a way of distinguishing themselves from their neighbors. But the injunction against boiling or slaughtering a kid in front of its mother has long been interpreted as a way of preventing cruelty to animals. The biblical mandate not to "cause pain to any living creature," tsa'ar ba'alei chayim, has been cited as an explanation for the rules of ritual slaughter and as the justification for Jewish vegetarianism.
According to many interpreters, God's original plan did not include meat eating at all. The description of Eden includes a completely herbivorous and vegetarian world: "I give you every seed-bearing plant that is upon the earth, and every tree that has seed-bearing fruit, they shall be yours for food."45 It is only in the story of Noah that humanity was given permission to eat meat, and then as a concession to the post-Edenic state of the species. Later in the Bible, Isaiah's vision of a redeemed world is entirely vegetarian. "And the lion shall eat straw like the ox."46
To the rabbis who wrote the Talmud, it seemed clear that since only God could give life, only God was permitted to take it. While they were disturbed by any killing, even for food, the fact remained that people eat meat. Thus they instituted the elaborate laws regarding animal slaughter, which reinforced the idea that Jews kill only by divine sanction. Specific prayers were prescribed, and quick, relatively pain-free (for the era) methods were mandated. Jews were thus effectively prevented from hunting.
Choosing Kashrut
For people who grew up in kosher homes, there is nothing strange or difficult about using two sets of dishes, buying meat from kosher butchers, or forgoing cheeseburgers. Kashrut is as normal as apple pie; kosher food is comfort food. But for those who have no family or gustatory memories of special meals and special recipes, kashrut may seem daunting.
Jews take on the mitzvah of kashrut for a variety of reasons: as something that connects us to countless generations of Jews; as a daily reminder of our Jewishness; as part and parcel of the overall discipline of being Jewish that we choose to practice. But for many Jews who keep kosher, the decision does not lend itself to rational explanation; it just feels right.
While kashrut may be a system for cultivating a holier approach to life, it is not always easy. It entails a certain amount of self-denial that will be far more difficult for meat-and-potatoes people than folks who prefer fish and salad for dinner. Choosing to keep kosher can be a difficult decision on many levels. For one thing, it is not easy to explain to others. Keeping kosher means embracing a basically non-Western system of self-discipline that runs counter to a culture of consumerism and instant gratification. It means making a very fundamental distinction between yourself and others—and that includes not only non-Jews, but also Jews who do not keep kosher, and Jews who keep kosher differently than you do.
Besides, any major change in eating habits can be a deeply unsettling experience. Unlike animals, human beings do not eat simply to sustain life. For people, eating, like sex, is not simply a physical act. Eating is arguably life's first sensual pleasure and the table is an important setting for social as well as physical sustenance. Furthermore, food places us within historical, ethnic, and familial contexts, even as it expresses idiosyncrasies and individuality.
The following list describes some of the ways that contemporary Jews choose to keep kosher, arranged in levels of increasing complexity and challenge.
Biblical kosher. Basically, this means avoiding all animals and fish prohibited in the Torah. At a Chinese restaurant, it means passing up the spring rolls unless you determine they contain no shrimp or pork. Some people also read labels in order to avoid foods prepared with lard and other nonkosher meat products.
Biblical kosher plus separation of meat and milk. As above, plus not mixing meat and milk at the same meal. This means not cooking chicken breasts in butter and avoiding meats served with cream sauces at restaurants.
Kosher meat. This represents a quantum leap. Fresh meat is purchased only at a kosher butcher shop, and frozen meat must display a hechsher, a symbol of rabbinic supervision (explained below). Dining at nonkosher restaurants means vegetarian or pareve meals only.
Further separation of meat and milk. At home, this entails two separate sets of dishes, cutlery, and pots and pans. Some people institute a waiting period (one to six hours) after eating meat before dairy is served. Traditionally, there is no waiting period for serving meat after eating dairy products.
Rabbinic supervision. Eating prepared foods that have been produced under rabbinic supervision and bear a symbol (hechsher) attesting to their kashrut. This reflects concern not only about kosher ingredients, but also about the status of the utensils and environment in which food is prepared. In order to maintain this level of kashrut, dining out would be limited to kosher restaurants and to kosher homes. However, some people who require hechshers at home eat vegetarian meals elsewhere.
Vegetarian/Vegan diets. Vegetarianism certainly simplifies kashrut, since it does away with the need to find kosher meat and resolve issues around mixing meat and dairy. In addition to the biblical and religious justifications for this practice, there are also political, ecological, and ethical rationales for avoiding meat altogether. Given that meat is such a resource-intensive food and since so many other sources of high-quality protein are now available, a vegetarian lifestyle can be seen as a way of helping to repair the world.47
Dining out. Many Jews who keep kosher eat at nonkosher restaurants and in nonkosher homes—making selections that reflect their level of observance. Practice varies from individual to individual, from family to family. Some who are kosher at home will eat only vegetarian meals at other people's homes and in restaurants while others make a fairly complete separation between what goes on at home and what they do in public; there may be nothing but kosher meat in the freezer, but when at McDonald's, it's cheeseburgers all around. While this may seem like a double standard, practicing different levels of kashrut at home and on the road may be seen as a way of making a distinction between what goes on inside a Jewish home and what happens in the rest of the world.
Kashrut and children. The idea of turning into "kashrut cops" repels some people and discourages them from instituting any observance of Jewish dietary laws. However, children raised in kosher homes generally do not feel deprived. If home cooking is kosher cooking, the idea of drinking milk with a roast beef sandwich will seem as foreign and unappetizing as roasted bugs (which also happen to be trafe). Reading labels can be made into a game, and so can keeping meat and milk dishes separate.
It is, of course, far more difficult for an older child to understand a decision to suddenly outlaw cheeseburgers from the backyard grill if she's been eating them for as long as she can remember. Transitions should be slow, methodical, and fully explained. As in every other aspect of observance, if a parent's attitude is positive, and the approach flexible and open, children will learn by example.
A Kosher Home
Traditionally, a kosher home is one in which only kosher meat is prepared and eaten, where the separation of dairy and meat products includes separate dishes, cutlery, pots, pans, and cooking utensils. Some kosher households may have separate dish towels, dishrags, sponges, and cutting boards. Glassware is exempt from this division and may be used on all occasions.
However, since there are so many styles and levels of kashrut, everyday decisions about how to keep kosher vary. Some families that do not cook or eat meat and milk at the same meal use a single set of dishes and utensils. Others keep dishes and utensils strictly separated, but use the same cleanup gear for all meals. However it is defined, a kosher home is one in which family members respect, understand, and follow the same rules.
People who choose to keep kosher usually do it in a series of incremental steps rather than one leap. Kashering—making kosher—a home is a big step. Rabbis and friends who keep kosher are a good source of practical advice about the "how-tos" of setting up a kosher home.
No matter how kashrut is defined or observed, mistakes will happen: a dairy pot gets used for reheating chicken soup; halfway through the soup that the waitress promised was strictly vegetarian, you discover a big chunk of beef.
Ever realistic about human foibles, Jewish law is very explicit about how to correct errors. According to halachah, certain things that are "trafed" are boiled, others buried in the ground, and still others thrown away. Some Jews correct errors simply by washing the offending item, and trying not to make the same mistake again.
The bottom line on accidents is that they do not invalidate anything. It has been suggested that the way people handle mistakes says a great deal about their understanding of kashrut as a mitzvah. Screaming at a spouse or a child, or making a guest feel terrible, about mixing up the spoons seems way out of line with a discipline intended to keep you in touch with holiness. If mix-ups become an everyday occurrence and kashrut is the source of tension, it might be time to reexamine why and how you are keeping kosher, and to recall the old story about a great rabbi who arrived in a strange town, where he was invited to spend the night in the mayor's home. As the mayor escorted the sage to his house, he boasted, "Rabbi, you should know that we adhere to the highest standards of kashrut. No one has ever made a mistake in my house." To which the rabbi replied, "Well then, I couldn't possibly eat in your house."
Sopping kosher. Shopping for kosher food is not difficult. Regular supermarkets and specialty shops can supply virtually everything except perhaps meat, though some supermarkets do stock frozen kosher poultry. Cities of any size support at least one kosher butcher, and people living in smaller communities may commute to larger Jewish centers to buy meat. Kosher food is also available online.
Shopping kosher does require a fair amount of label reading, first to see that products are free of lard—animal fat that renders them nonkosher. Foods designated "kosher" are thus sought not only by Jews, but also by Muslims and vegetarians who want to avoid pork or meat products. Another reason for reading labels is to determine whether a product contains any milk products, which would make it incompatible with a kosher meat meal.
When buying packaged and prepared food, some people buy only foods that bear a symbol called a hechsher, which is a validation that the product is kosher and prepared under rabbinical supervision. Hechshers appear on a wide variety of products, from cheeses to cake mixes to canned fish. The FDA permits use of the K (for kosher) wherever there is rabbinic supervision. There are many hechshers, some granted by regional or local rabbinic boards. A few of the better-known symbols include:
THE UNION OF ORTHODOX JEWISH CONGREGATIONS (OU)
THE ORGANIZED KASHRUS LABORATORIES (OK)
KOSHER SUPERVISION
Jewish cooking. "Vesti da Turco e mangia da Ebreo." The ancient Italian adage advises, "Dress like a Turk and eat like a Jew."48 Jewish culinary tradition is rich and diverse, reflecting the fact that Jews have lived all over the world and absorbed the best of many cuisines.
Jewish cooking in America has been associated mostly with a limited number of gastronomic clichés: bagel, lox, and chicken soup. The tendency toward starchy, heavy food comes from Central and Eastern Europe, where German and Russian peasant foods were adapted to lives of heavy manual work in cold climates. However, American Jews have embraced other Jewish culinary traditions. Sephardic Jews cook with dates, raisins, leeks, plum sauces, and exotic spices. Israeli foods—falafel (fried chickpea patties), shwarma (roasted meat), and various fresh salads—are now staples for American Jews as well.49
Around the world and throughout history, Jewish cooks have found ways to prove the Talmudic dictum that every forbidden food, even ham, has an exact, kosher taste-equivalent.50 Today, there are hundreds of Jewish and kosher cookbooks that prove the point. While specifically kosher cookbooks are a good source for special holiday menus and recipes, most books (except maybe The Wonderful World of Pork) may be adapted to kosher cooking. Vegetarian cookbooks are an obvious choice, but cuisines based on oil rather than butter—Italian, Middle Eastern, and most Asian culinary traditions—are also a great resource. It is also easy to adapt and change nonkosher recipes. In many cases, using nondairy margarine instead of butter will not affect the flavor of a dish, and meat-based soups can become pareve with the substitution of vegetable stock for beef or chicken.
Kosher for Passover. Kashrut takes a new dimension during the holiday of Passover when, in memory of the exodus from Egypt, Jews eat no leavened foods. In order to be "kosher for Passover," all food must be absolutely free of any leavening agent, such as yeast. Thus all breads are forbidden, as is beer.
However, the prohibition against leaven extends not only to things made with yeast but any foodstuff likely to ferment, which includes anything made with flour, including pastas and most cereals. These restrictions are challenging, especially in baking, but potato starch and matzo meal are substituted for flour. Passover cookbooks are a big help in planning interesting leaven-free meals, and all kinds of prepared food may be purchased with a "Kosher for Passover" hechsher, which means the product was prepared in a leaven-free as well as a kosher environment. (See "Passover.")
As in all things, Jews observe Passover kashrut in a wide variety of ways. Keeping kosher for Passover traditionally requires an intensive housecleaning to free the house of even a trace of leavening, or hametz. Some people have a closet of special dishes, pots and pans, utensils, and cutlery that have never touched hametz and are used only at Passover. Other families, which do not keep kosher the rest of the year, simply clean the house of hametz and avoid bread and other foods made with flour.
Kosher etiquette. As dietary needs, allergies, and health-related restrictions have become more widespread, people tend to be vocal about what they can and cannot eat, which has made it easier to keep kosher. A kosher-observant guest invited to dinner in a nonkosher home should volunteer information about what he or she can and cannot eat. Likewise, kosher-observant hosts can help by tactfully explaining their practice to guests who offer to bring food or drink. At Passover in particular, a basket of fruit or a a box of "kosher for Passover" candy are among the safest edible "hostess gifts."
The most important rule of thumb is always "When in doubt, ask." If everyone is relaxed and tolerant, questions can lead to an interesting conversation about the hows and whys of kashrut.
## COMMUNITY
According to a Yiddish proverb, "The best synagogue is the heart." Many people have attributed Judaism's survival to its focus on the family. But there is a necessary counterpoint to Judaism's emphasis on hearth and home. "Do not separate yourself from the community," says the Talmud.1 In other words, Judaism's vitality does not reside solely within individuals, but also depends upon the energy and momentum generated by groups of people working together in all kinds of settings: synagogues, schools, charitable agencies, cultural activities, social clubs, political groups.
In a sense, the organized Jewish community exists to support individual Jews in their decision to live as Jews. Because the truth is, no one can be a Jew by him or herself. Lighting candles every Friday night, reading sophisticated Jewish books, celebrating the holidays at home with friends and family, and never eating shrimp again may all be deeply meaningful, but there is a limit to a totally insular, personal Judaism.
There is a limit to how much anyone can learn without teachers or other students to challenge their assumptions. There is a limit to how fully anyone can explore his or her Jewish commitment without exercising it in a public forum. Without a community, energy is bound to ebb and inspiration wane.
Another Yiddish proverb says, "Life is with people." Jewish life can only be fully experienced in the company of other Jews. Especially in the absence of extended family, which is the norm for many Americans, the Jewish community creates a larger context for all aspects of life, an indispensable source of identity, growth, recognition, and support, especially at times of transition. Births are greeted with resounding congratulations; illness and deaths are surrounded by healing concern.
The relationship between public and private, personal and communal, clearly benefits the individual, but it is also necessary for the survival of Judaism. Individuals do not educate rabbis, cantors, and Jewish teachers. Nor can individuals provide for the needs of all the Jewish elderly, or advocate for Jews who are persecuted or attacked. These functions, and many others, require work and financial support from everyone in a community that cares about the continuation of its culture, faith, ideas, and dreams.
Continuity is, in fact, one of Judaism's most compelling demands. The Talmud tells the tale of a man named Honi, who one day saw an old man planting a carob tree.
Honi asked, "How long will it take for that tree to bear fruit?"
"Seventy years," replied the old man.
"But you are already old; you will never live that long," said Honi.
"I know," said the man, "but my parents and grandparents planted fruit trees for me, so I am planting fruit trees for my children and my grandchildren."2
As long as there have been Jews, there have been Jewish communal groups. At first these were called tribes, and membership was all-inclusive, automatic, and permanent. Today, membership is largely voluntary. Becoming a part of the community requires filling out application forms and writing checks—in other words, making choices and connections with other Jews. Joining a synagogue, attending a lecture or a class, volunteering to serve on a committee or a board of directors, organizing a discussion group, even joining a virtual community for study and connection: any and all of these are opportunities to establish Jewish roots.
Of course, all human contact entails friction, and Jews are a notoriously contentious bunch. Fortunately, the American Jewish community is large and diverse, with countless places and ways to fit in. And, in the great Jewish tradition of dissent, if you do not like the institutions that you find, you can always start your own.
The doors to the Jewish community are wide open. Browsers are always welcome.
## SYNAGOGUES
A synagogue is a beit k'nesset, a house of gathering or assembly. A place to find lifelong friends, a place where teenagers forge Jewish identities over pizza, and where families go to laugh at the annual Purim play and to organize canned food drives for the hungry.
A synagogue is a beit midrash, a house of study, a house of stories. A place with a library and classrooms, with teachers and students of all ages. A place of argument and enlightenment.
A synagogue is a beit tefilah, a house of prayer. A place to say words of praise that are older than memory, a place to sing about the birth of a child, a place to sit in sorrow, a place to search for peace.
Judaism purposefully mixes and confuses these categories: community, prayer, and learning. Among Jews, prayer services require the presence of the community, represented by a quorum of 10 called a minyan. The study of Jewish texts is considered a form of prayer.
People go to synagogues for all kinds of reasons: human contact, intellectual stimulation, spiritual fulfillment. People rarely find precisely what they are looking for in any one synagogue, in part because their criteria are impossibly high, and in part because synagogues rarely live up to their own goals. Still, over the course of their lifetimes, most American Jews join and belong to synagogues in search of a communal and spiritual home.
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An individual who prays alone must hope that the time of prayer is an acceptable one; for the prayer of a congregation there is never an unpropitious time.
DEUTERONOMY RABBAH 2:12
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History
The first building associated with Jewish worship was built in Jerusalem by King Solomon during the 10th century B.C.E. The complicated rituals described in the book of Leviticus—including animal sacrifices, instrumental music, and burning incense—took place in this temple, The Temple. The ancient Israelites traveled from all over the land for the festivals and holidays celebrated there and only there.
This centralized form of worship, performed by the priestly castes of Kohanes and Levites, was interrupted in 586 B.C.E. when the Babylonians conquered Jerusalem and took the Jews into captivity. Scholars do not agree about the precise beginnings of what we would recognize as synagogues, but groups of Jews probably began meeting for the purpose of prayer and Torah study during the Babylonian captivity.
When the Babylonians were defeated by the Persians in the 586 B.C.E., the Jews were permitted to return to Jerusalem, which is when public readings of the Torah on Shabbat, Mondays, and Thursdays began. By the time of the destruction of the Second Temple by the Romans in 70 C.E., synagogues and regular patterns of worship were part of Jewish life, both in and outside of Israel.
By the second century of the Common Era, the synagogue was so much a fact of Jewish life that it was considered incumbent upon any community that could muster a minyan—10 adult Jewish men at the time—to build one. Synagogues were eventually built in every corner of the earth—Alexandria and Rome, Worms and Barcelona, Singapore and New Delhi—with architecture that reflected the styles of their time and host cultures. There are Byzantine, Romanesque, Gothic, Renaissance, Baroque, and Moorish synagogues. In Kai Feng, China, one was built after the pattern of the region's Taoist temples.
Actually, "synagogue" is not a Hebrew word. The term appeared in the Christian Bible as the Greek translation of the term beit k'nesset, "house of assembly." Until the 18th century, Jews used the word "temple" only to refer to the Temple of Jerusalem, which would, according to tradition, be rebuilt only by divine command. But the Reform movement (described below) rejected the notion of a rebuilt Temple and reclaimed the word as a synonym for synagogue. Shul, the Yiddish word for synagogue, comes from the German shule, or "school."
The Movements
Despite the universal tendency to romanticize the past as a period of unanimity and universal piety, sectarianism has permeated Jewish history from the ancient days of the Pharisees and the Sadducees until today. But the Enlightenment introduced a whole new dimension to the divisions within the Jewish world. The subsequent political emancipation, which unlocked the ghettos and opened the great universities of Europe, permitted Jews to step outside their communal identity and act as individuals. For the first time, Jews had the option of becoming citizens of the wider world without having to convert to Christianity.
In response to this revolutionary change, the precursors of the modern Jewish movements—Reform, Conservative, and Orthodox—made their debuts. Despite their differences, all three schools of thought faced the same challenge: reconciling the traditions and beliefs of Judaism with modern intellectual and political realities. Out of that dilemma, liberal Judaism—the process of reconsidering and wrestling with tradition, and then self-consciously choosing how to be Jewish—was born.
Liberal Judaism in America has three major denominations or movements: Reform, Conservative, and Reconstructionist, described below. Each of these has a central organization with which most individual congregations are affiliated, and all of them train educators and rabbis; publish books, magazines, and teaching materials; run summer camps and youth programs; and more.
Although the three movements differ in their approach to theology and practice, all ordain women as rabbis, engage in interfaith and inter-movement dialogues, and actively support the state of Israel. Although there are differences, these three also share the basic assumption that Jewish law, halachah, is an historical collection of human responses to the divine.
In addition to the movements, there are unaffiliated synagogues as well, some of which avoid all labels, or describe themselves as postdenominational or "renewal." The hallmark of American Judaism is its diversity. Because each congregation is autonomous, official movement statements or position papers do not necessarily describe the practice of each affiliated synagogue. And every synagogue changes over time, reflecting changes in membership and leadership. Indeed, movement affiliation may describe little more than the rabbi's alma mater and even that is not a given, since some congregations do hire rabbis trained in the seminaries of other movements.
Worship differs from one temple to the next in many ways—congregational singing versus formal cantorial singing, the amount of Hebrew in the service, the introduction of creative prayers and new services. Programmatically, congregations have unique strengths and weaknesses, sometimes based on a rabbi's interests, sometimes reflecting congregants' passions. Thus, some synagogues are known for their social action programs, while others focus more energy on worship and spirituality. You can learn about what's going inside any given shul by looking at its Web site and reading its membership materials and mailings. Ultimately, you have to walk through the doors and talk to the people.
Reform
The Reform movement (it's Reform, not Reformed) was the first organized attempt at a systematic liberal Jewish theory and practice. While it began in Germany, Reform matured and flourished in the United States. The early Reform movement was characterized by rationalist philosophy and a "light unto the nations" theology, which saw the Jews as special heirs to the biblical prophetic tradition of social justice. The movement also instituted many radical changes in synagogue observance, including the use of vernacular languages, musical instruments, and mixed seating for men and women. Reform leaders eased restrictions on Sabbath activities and rejected the dietary laws, in some measure as an effort to attract Jews who were abandoning Judaism altogether.
Classical Reform Judaism was often charged with being assimilationist, and more concerned with Christian approval than with Judaism's integrity. However, the Reform movement began an era of Jewish political and social activism that helped redefine Judaism's place in the world. Reform Judaism has changed a great deal since its beginnings, and continues to change, citing the truism "Reform is a verb." Practices, symbols, and rituals once dismissed by the movement—everything from prayer shawls and head coverings, to immersion in a mikveh—have been embraced by many in the movement.
Reform Judaism affirms the ability of every Jew to choose, on the basis of study and experimentation, the observances and rituals that bring him or her closer to God. Halachah, Jewish law, serves as a resource but does not determine these choices. For Reform Jews, the Talmud and its subsequent elaborations are part of Judaism's evolving insight as to how individuals and communities make God available in their lives. For more information about the Reform movement, see www.urj.org.
Conservative
Conservative Judaism, which also had its roots in early 19th century Germany, was formulated in the late 19th and early 20th century in the United States. It was conceived as a middle ground between Reform, which was viewed with alarm as having gone too far, and traditionalists, who were seen as unrealistic in their rejection of modern opportunities and insights.
While Conservative Judaism shares with Reform the idea that Jewish law is historical and therefore changing, it supports a commitment to the workings of the law. According to the Conservative view, while the law itself changes in every era in response to social, economic and political realities, individuals are nonetheless expected and encouraged to conform to certain classical behaviors, such as keeping kosher, Sabbath and holiday observance, and daily prayer. The authority of these behaviors and of the laws contained in the Torah and later commentaries derives from the belief that they were inspired by God.
While Conservative Judaism counts certain ritual behaviors as necessary and even mandatory, the range of practice among Conservative Jews is extremely varied. Indeed, the religious practice of many Conservative Jews does not differ from that of many Reform and Reconstructionist Jews; on the other hand, there are members of Conservative congregations who embrace a lifestyle essentially indistinguishable from that of many Orthodox Jews.
Conservative Judaism has always responded to important changes in modern life, as when the ban on Shabbat driving was modified to enable suburban Jews to get to their synagogues. The Jewish Theological Seminary began ordaining women in the mid-1980s in response to lay support for the change, and the tension of holding the middle ground continues to challenge the movement on theological and social issues. For more information about the Conservative movement, see www.uscj.org.
Reconstructionist
The Reconstructionist movement began as Mordecai Kaplan's vision of a new direction for Conservative Judaism. A longtime faculty member of the Conservative rabbinical seminary, Kaplan was eventually convinced by his students to lend his support to the founding of the Reconstructionist Rabbinical College in Philadelphia. The seminary, which opened in 1968, trains leaders for the synagogues and havurot (fellowships, described below) that were formed in response to Kaplan's teachings.
Kaplan conceived of Judaism not simply as a religion but as an evolving, changing civilization with a religious basis. Kaplan believed that Jews in every generation had an obligation to keep Judaism alive through the process of reconstructing it; reinterpreting ancient rituals and practices and discovering new meanings in them.
According to Reconstructionism, the rabbi is not an authority but a facilitator and resource who teaches and guides congregants in their own process of creating Jewish community. Kaplan's ideas have had an enormous impact on many Reform and Conservative Jews. For more information about Reconstructionist Judaism, see www.jrf.org.
Nondenominational Communities
In addition to the three formal branches of liberal Judaism, alternative Jewish institutions exist to fulfill the functions of synagogues for their members. Some unaffiliated congregations have rabbis, dues, boards of directors, and buildings with mortgages. Other groups meet in rented spaces or living rooms, and while some pay a teacher, rabbi, or "guide," others are entirely run by volunteers. Less-formal groups require more of a commitment of time and work from their members and usually do not offer the full range of synagogue "services," such as a religious school. However, they can provide a kind of intimate, hands-on Judaism—a fact that has led large congregations to foster small groups within their membership.
Havurot, usually translated as "fellowships," are autonomous groups that choose their own activities and set their own calendar of events, services, and meetings. Because they often concentrate on home-and family-based celebrations, members sometimes describe havurot as their extended families. A havurah might meet to break the Yom Kippur fast, build a communal sukkah and eat in it, enjoy a Hanukkah party, and celebrate a Passover seder together. Some havurot schedule regular book discussions, and some attend Jewish cultural events, such as plays and films, as a group. An annual summer institute, sponsored by the National Havurah Committee, gathers groups and individuals from around North America for study, worship, and community networking. For more information, see www.havurah.org.
Many synagogues now encourage members to form havurot as part of congregational life—a way to foster the warmth and intimacy of a small group within a larger institution. Synagogue-based havurot meet for study or family-centered holiday observance, and often function as extended families for their members.
A minyan is the name for the quorum of 10 adult Jews traditionally required for certain prayers to be said, and for a full worship service to be held. Although minyanim (the plural) run many of the same kind of family-and holiday-focused activities as havurot, they tend to be worship-focused. Many were formed as a way to permit women's full participation in otherwise traditional services and their members tend to be more observant of dietary and Sabbath laws. Some individual minyanim have Web sites.
The Jewish Renewal movement is a network of individuals, synagogues, and havurot, some of which have formal affiliations with ALEPH the Alliance for Jewish Renewal, which runs workshops and publishes books and other materials. Based in large measure upon the philosophy and teachings of Reb Zalman Schachter-Shalomi, Jewish Renewal combines an emphasis on Jewish mysticism and a commitment to tikkun olam, "the repair of the world." For more information search "Jewish Renewal" on the Web, and see www.aleph.org.
Joining a Synagogue
Although some Jews join a synagogue strictly on the basis of geography, becoming members of the closest and most convenient congregation, most people shop around before making such an important commitment. While it may seem a little crass to talk about "shopping" for a spiritual home, it is actually far less so than selecting a synagogue based on commuting time.
The criteria for what makes a "good" synagogue are very personal, which makes selecting a synagogue rarely a simple or straightforward process. Expectations may be vague or confused; past experiences may create anxiety.
To begin the process, ask people who already belong to a congregation what they like about their synagogue, and ask if you can go to services or a class with them.
In general, it is not a good idea to go synagogue shopping during the High Holidays. Rosh Hashanah and Yom Kippur services are not representative of what goes on the rest of the year, and the rabbi and staff will probably be extremely busy and not as free to chat or schedule meetings with prospective members.
A good first step is to attend a regular Shabbat service. Call the synagogue office and find out when services are held. The call can be anonymous, or you can say that you are thinking of joining the synagogue, in which case you may be referred to the rabbi or another staff member. A membership committee person may call you back, to tell you something about the congregation and to offer brochures, a copy of the temple newsletter, or membership materials. Some congregations hold regular open houses for prospective members, and in some temples, potential members are invited for Shabbat dinner.
On a first visit to any synagogue, it can be helpful to remember that few people feel altogether comfortable their first time anywhere. Customs vary from one congregation to the next, so newcomers always feel somewhat awkward, especially when everyone else seems to know all the words to all the songs. Try to relax. Hum along with the melodies. Look around you at the faces in the sanctuary. Is there a wide range of ages in the room? Are there single people? Are there children around and/or is there special programming for them? Do you see people you would like to meet?
Regarding the service, is the amount of Hebrew used intimidating or inadequate for you? Are supplemental readings meaningful? Who leads the service? Are laypeople helping or does the rabbi (and/or cantor) do it all? Are people smiling? Do they seem engrossed in the prayers or are they dozing?
Do you like the way music is used in the service? Does the cantor perform or do people sing along? If the rabbi gives a sermon, does it challenge or bore you? Does he or she seem to have a rapport with the congregants? As the service progressed, did you get more relaxed or more tense?
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If a house was built just as a house, and then afterward it was dedicated as a synagogue, it is considered a synagogue. However, it is not considered holy until people have prayed in it.
SHULCHAN ARUCH, ORACH CHAIM 153:8
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In addition to your reaction to the synagogue, consider the synagogue's reaction to you. Does anyone greet you or say "Shabbat Shalom"?
Unless your first impression is totally negative, go a second time, and a third. Are you starting to strike up conversations with people? Has the rabbi greeted you? If your first visit is on a Friday night, remember that the congregants who attend Saturday morning services may be an altogether different group of people. It might be worthwhile to attend a whole Shabbat's worth of services as well as a lecture or adult education class. Explore the range of programs the synagogue offers to see how and where you might fit in. Ask yourself whether this particular shul can meet your needs and those of your family, not only now but in five years or ten.
There are many things to consider when exploring a prospective congregation: Does the schedule of adult education classes or lectures appeal to you? Does the synagogue ever run retreats? How good is the religious school for children? (See "Education.") Is there a synagogue youth group? Does the synagogue stress family education and family programming? Are there special events on the holidays where children and parents participate together? Does the synagogue help organize and foster havurot, small groups that function as extended families within the larger community? Does the temple have special programs for empty-nesters and elders? Is there a nursery school? A women's group? A men's group? Does it provide a clear welcome to Jews of color, and to gay and lesbian Jews? Is the building accessible to the handicapped?
Does the congregation participate in local interfaith programs? Is there an active social action committee, and what are its priorities? How does the synagogue relate to its intermarried members and to the children of intermarried couples? If this question is relevant to you, it should be asked immediately. While many synagogues welcome non-Jews as full members of the congregation, some limit the participation of non-Jewish spouses and the children of non-Jewish mothers.
Although any temple is much more than the rabbi(s) on its staff, the personality and skills of the clergy do shape the congregation, and your response to him/her/them is worth taking into account. Rabbis' job descriptions are almost dizzying. Congregational rabbis are spiritual leaders who teach and preach. They also officiate at religious ceremonies and rituals, visit the sick, and provide family, marriage, and spiritual counseling. They act as representatives of the Jewish community at interfaith meetings and secular events, and some rabbis function as business administrators of their congregations and as principals of their religious schools.
Not surprisingly, few rabbis are good at all these tasks. A superb pastoral counselor may be a mediocre preacher; an inspired leader of prayer may be a terrible administrator. Despite the improbability of finding one human being who can excel at everything, most people bring impossible expectations to their relationship with the rabbi, who is also inevitably viewed as a symbolic parent.
In the past few decades, there has been slow movement away from the model of the authoritarian rabbi: the one with all the answers, the one who "does" Judaism on behalf of his or her congregation. In much the same way that the physician's role as the ultimate, unquestioned medical authority has been challenged by more sophisticated patient-consumers, laypeople are taking more responsibility for their own Jewish lives. This is actually less a break from tradition than an acknowledgment of the rabbi's true status: not priest, but teacher.
Despite the move toward greater lay participation, rabbis still shape their synagogues in fundamental ways. The rabbi generally sets the tone of worship services, leads in policy decisions regarding Sabbath observance within the synagogue, and provides leadership in his or her own areas of interest and strength.
Before joining a congregation, it is a good idea to schedule a private meeting with the rabbi—preferably not during the late summer or early autumn, when rabbis are preparing for the High Holidays and the beginning of the school year. In synagogues where there is a senior and a junior or associate rabbi, try to speak with both. While you may have more contact with the associate rabbi, the senior rabbi sets the tone for the congregation. Besides, junior rabbis often leave for their own pulpits after two or three years.
Go to the meeting with the rabbi prepared to answer a few questions. You might be asked about your Jewish background, and what you and your family want from the congregation. You should feel free to ask questions of your own, for example: What makes this congregation unique? What do you do best here? In the rabbi's opinion, what are the congregation's failings? What needs to be improved? What is expected from congregants and how important is lay participation?
Parents may have many questions about religious education at the temple, and rabbis should be able to talk about the school's philosophy and direct you to the educator or a teacher. But don't let your children's needs trump all others, and ask yourself, how can this synagogue help me grow as a Jew?
Finally, before meeting with a rabbi, it is also useful to examine your own feelings about the rabbinate. Interviewing a rabbi is not unlike a first meeting with a physician or a therapist, someone with whom you are going to have an intimate but professional relationship. It is best to try to leave expectations and grudges at home.
Concerning other staff, if the rabbi doesn't suggest it, feel free to ask for meetings with the synagogue's other professional staff: the cantor and, if applicable, the director of education or religious school principal.
The job of the cantor is to lead the congregation in prayer and song. The title of cantor (in Hebrew hazzan, hazzanit for female cantors) is given to people trained in liturgical music. The Reform and Conservative movements both run cantorial schools, which operate as graduate programs in Jewish liturgical music. Cantors frequently lead services and officiate at funerals in the absence of the rabbi, and are usually licensed by the state to perform weddings.
Cantors have very different approaches to their musical and congregational roles. Some perform and are listened to, while others invite the congregation to sing along. Some cantors lead services quite often, and in some synagogues they are in charge of bar and bat mitzvah preparation. There are congregations where the cantor teaches children and adults.
If the synagogue runs a religious school, the director of education or principal and school committee chair helps set educational policy. A meeting with them is in order if you plan to enroll a child in the congregational school. Like cantors, directors of education can be a major force in the congregation, shaping programs for adults as well as children, and generally contributing to the educational and spiritual life of the community.
Membership
There are as many ways to belong to a congregation as there are reasons to join. Some people see synagogue membership as a necessary evil, like life insurance. They pay their dues as a bet against future needs (for a bar or bat mitzvah, wedding, or funeral) or as a way of ensuring children's Jewish identity. Their monthly checks are the total extent of their commitment.
If, however, you join a synagogue with hopes of exploring your own spirituality, or of expanding your sense of community, or of delving into Jewish thought, signing the membership form is just the beginning. The next step is finding a niche. Attending services and classes, and volunteering on a committee or for a project, are among the best ways to explore possibilities and to begin feeling like someone who belongs.
Synagogues are complex organizations, and it is a good idea to know how they function. While there are enormous variations, most are governed by an elected volunteer board of directors. In some congregations, prestige is attached to officerholders, with positions of leadership going to people who support the institution with substantial financial gifts. Elsewhere, people rise through the ranks of committees, and become community leaders as a result of commitment and ability.
As with most nonprofit organizations, committees do much of the work. Joining a committee is one way to get immersed in synagogue life and lore, and its feuds and politics, too. Synagogue committees may include: membership, which recruits and meets with new members; finance, which may prepare budgets or raise money; ritual/worship, which helps plan religious services and works closely with the rabbi and cantor; adult education, which plans courses, lectures, and events such as weekend retreats; school, which oversees the religious school and may be broken down in various ways (preschool, high school, family education, youth group, etc.); social action, which advocates for justice, with social and political concerns ranging from helping resettle Jewish immigrants to running soup kitchens and shelters for the homeless. And caring community committees organize assistance for members who need help due to the birth of a new baby, illness, or death.
Obviously, all activities require financial support. Synagogues run like businesses, with fixed expenses for mortgage, staff, utilities, and movement dues, which support seminaries, youth programs, and summer camps. Synagogue expenses are met, in part, by annual membership dues. Some congregations have sliding scales; others charge a fixed amount, which may be reduced or waived by special arrangement. No synagogue turns people away because of an inability to pay dues, but each congregation handles financial need in its own way, some with more sensitivity than others. In addition to dues, there may be other financial expectations of members, such as pledges to a building fund, school fees, and charges for attending adult education courses and lectures.
Perhaps the oldest joke in the long history of Jewish humor is the one about the Jew who was stranded on a desert island. When a ship happens across him years later, his rescuers find three huts.
"Why three?" he is asked.
"I live in one," he says. "The other two are synagogues."
"Why on earth would you need two synagogues?" asks the rescue party.
"One I pray in. The other I wouldn't be caught dead in."
No two Jews can agree on much of anything, especially when it comes to religious practice. Many a large, venerable synagogue began as a renegade splinter group from another even more venerable congregation. If there is no synagogue that provides you with reasonable levels of comfort and fulfillment, you can always begin your own congregation or havurah.
Starting a synagogue or havurah means focusing religious and communal goals, usually in agreement with several other families. It also requires a huge investment of time, work, and money. Then again, creating an authentic communal spiritual home is its own priceless reward.
## THE ORGANIZATIONAL WORLD
Nothing demonstrates the vitality of Jewish life as well as its array of organizations, agencies, federations, committees, associations, and councils. The alphabet soup of the organized Jewish world represents every conceivable area of Jewish concern, and provides leadership and assistance at every level, from feeding the Jewish elderly in America, to supporting various strategies for peace in the Middle East.
For the first centuries of Jewish life in North America, communal groups focused strictly on the basic needs of newcomers and founding community institutions, including synagogues. But as each new wave of Jewish immigration expanded the needs of the community, the organizational mandate expanded as well.
For a time, many social and cultural needs were met by landsmanschaften, organized groups of people from the same town in the old country. These groups pooled their resources to provide such services as death benefits for widows and orphans. Hebrew Free Loan societies were established to make low-cost credit available to immigrants, and the traditional Jewish commitment to tzedakah, "righteous giving," supported thousands of small relief efforts and local projects. For example, Jews saw to it that poor members of their community could buy kosher food for Passover.
Religious Movements
Most American Jews belong to one of the three major liberal religious Jewish denominations—Conservative, Reconstructionist, and Reform—with a smaller number affiliated with Renewal or Havurah groups. Although expressly not religious, the Society for Humanistic Judaism and the Workmen's Circle provide members with the kind of fellowship and learning opportunities generally associated with synagogues. Traditional or Orthodox Judaism is not monolithic either: Hasidic sects and independent synagogues fall under this rubric; however, the Orthodox Union is the umbrella organization for what is called Modern Orthodoxy. For more information about the Orthodox Union, see www.ounetwork.org.
In addition to providing a wide array of services to their constituent congregations and havurot—everything from educational materials for adults and children to synagogue management consultation—the denominations ordain clergy, run youth programs and adult retreats, publish books and magazines, lobby Congress on issues of concern; the list goes on and on. You can learn more about each on their respective Web sites.
United Synagogue of Conservative Judaism—www.uscj.org
Reconstructionist Federation—www.jrf.org
Union for Reform Judaism—www.urj.org
The National Havurah Committee—www.havurah.org
Renewal—www.aleph.org
Federations
Communal efforts became larger and more sophisticated in the 19th century, when Jewish communities built hospitals and supported a growing social work network. As the Jewish community grew and diversified, the need for a more integrated, centralized way to raise and allocate funds became increasingly apparent. By the beginning of the 20th century, the "federations" became a force in American Jewish life.
Federations began as loose associations of community service groups and agencies that pooled fund-raising efforts to avoid competition and to enhance effectiveness. Today, Jewish federations (which have different names in different cities) support a vast array of programs, which can be divided into three broad categories: social service (Jewish Big Brother/Big Sister, family and children's agencies, services for the elderly, etc.), education (support for local schools, vocational counseling, etc.), and community relations (community relations councils, and the Anti-Defamation League). The federations provide significant support to Israeli agencies, and also contribute to secular and non-Jewish relief efforts.
* * *
The longest road in the world is the one that leads from your pocket.
YIDDISH PROVERB
* * *
Federations are the primary philanthropic and grant-making bodies for local Jewish communities. They raise funds, assess and plan for the needs of the community, setting programmatic goals and directions and channeling dollars accordingly. Federations work to develop leadership by running programs that include study, social action programs, Israel trips, and purely social gatherings. While they employ professional administrators, federations depend upon volunteers to do the hard work of fund-raising and staffing committees.
Volunteering in any Jewish organization—including your synagogue—is one of the surest and fastest routes to a sense of belonging. Opportunities to make a difference are virtually unlimited, from serving juice to children in synagogue preschool classrooms, to participating on the committees that make important decisions about the future of American Judaism. Every organization represents a doorway into Jewish communal life and to a sense of belonging and of making a difference. Local federation Web sites can direct you to a volunteer clearinghouse. For more information about federations and to locate the one in your community, see www.ujc.org.
Alphabet Soup
The national and international Jewish scene is fluid, ever-changing, and potentially confusing. Organizations are born, die, redefine their missions, or split in response to the times. The Jewish National Fund, for example, which began in 1901 to buy land for Jewish settlement in Palestine, now supports land development and the forestation of Israel. B'nai B'rith, which began as a fraternal and social group for German Jews, grew to become an international organization, and in 1989, B'nai B'rith's women's division split off to form an independent organization. The American Jewish World Service was incorporated in 1985 to provide a Jewish presence in the realm of international assistance.
New agencies and organizations open every year to meet the changing needs of the Jewish community. There are programs, support groups, and Web sites for every kind of Jew and any Jewish concern you can imagine. This makes it impossible to compile an up-to-date listing of Jewish organizations, agencies, and advocacy groups, which makes the Internet an invaluable tool for finding the resources you need: from camps for special needs children to trips to Israel for seniors, from local organizations that fight anti-Semitism to reviews of Jewish-themed films. One good portal for exploring the Jewish Web is www.shamash. org. The "Jewish Finder" listing on www.ujc.org also provides a current listing of organizations.
## EDUCATION
Study may be the only undisputed and shared value upon which all Jews, regardless of affiliation or belief, can agree. Study is seen as its own reward and is considered one of life's great pleasures.
Historically, Jewish learning was valued above wealth or fame, and community standing was based upon erudition. Having a scholar in the family was such a source of pride that, in the days of arranged marriages, promising students were preferred even over wealthy young men as matches for daughters. Knowledge of Torah and Talmud was considered a virtue second to none. Well, almost none. The Talmud says, "An animal is better than a sage who lacks sensitivity to people's feelings."3
The sweetness of learning is a common theme in traditional writings: "Anyone who teaches Torah in public and does not make the words as pleasant as honey from the honeycomb for those who are listening, it were better that he not teach the words at all."4 On the first day of school in some Eastern European communities, children were given sweet cakes in the shapes of the Hebrew letters.
But study is not considered a virtue for children only; education is considered a lifelong obligation and joy for Jews of every age and status. A common Yiddish greeting is "Sog mir ein possock," "Tell me a verse," or "Teach me something." In the Torah, the Israelites were challenged to become a "nation of priests." The Jews became a nation of students.
In the 20th century, the Jewish passion for learning was applied to secular studies with impressive results. The overwhelming majority of American Jews attend college, and although less than 3 percent of the population, account for more than 20 percent of students in elite college.
But while Jews were entering the arts and sciences, the quality of Jewish education languished. Today, many Jews recall their religious school as boring, or worse: a kind of unpleasant but necessary rite of passage meant as an inoculation against assimilation—momentarily painful but good for you in the long run. For most, it was over after bar or bat mitzvah, which is how it came to be that several generations of American Jews knew more about Milton and Newton than Maimonides.
Today, however, there is greater support and demand for excellence in Jewish education for people of all ages, from preschool through retirement. There has also been a broadening of the definition of Jewish education to include the informal learning that takes place outside of the classroom. While there are many ways to define excellence or success, the goal of a Jewish education is to impart the skills, concepts, vocabulary, curiosity, and commitment that will motivate a lifetime of Jewish study.
Day Care and Preschool
Although most Jewish learning for very young children happens at home (setting the table for Shabbat, preparing for holidays, listening to the grown-ups talk, reading bedtime stories), an early education program can help reinforce and supplement family lessons. The Jewish communal world provides a variety of options for the littlest Jews. Jewish community centers, YM/YWHAs, and synagogues offer everything from half-day nursery schools to full-time day care for infants and toddlers.
Jewish preschool is not a place where children sit at tables memorizing Hebrew letters. Most early-childhood specialists today feel that formal "study" is not appropriate for preschoolers at all. The guiding philosophy is that learning is a developmental process, which means that children are encouraged to learn through stimulating play.
In many ways, there is little difference between a day at a Jewish preschool and a day at a secular program. Children enrolled at Jewish preschools sing songs, do art projects, play outside, visit the fire station, take naps, eat snacks, and sit down to listen to stories during "circle time." What is different at Jewish early education programs is the content of the story, the names of the songs, and the subjects of the art projects.
Jewish programming varies a great deal from one preschool setting to the next, but generally, art projects will follow the Jewish calendar, making menorahs in December and Purim masks in March. The weekly cycle is also important, with Friday as a highlight, as children pour grape juice, eat challah, and sing Shabbat songs.
The primary consideration in choosing day care or a preschool is that children have a happy, safe, and warm experience. If their first memories of "school" are fond ones that include pleasant associations with things Jewish, they will have made a wonderful discovery. Apart from Jewish content, the same criteria that apply to all early education programs apply to Jewish day care and preschool: the operation should be licensed, clean, and cheerful; the ratio of staff to children should be low and at least in compliance with state law; parental visits should be welcome at all times.
Elementary Education
Most Jewish Americans enroll their children in some kind of formal program either in full-time private day schools or in a supplementary religious school, which is usually, though not always, part of a synagogue and held after school and/or on weekends. With parental support and participation, either choice can result in a successful Jewish education, which is to say one that instills a love of Judaism and a passion for lifelong Jewish commitment and learning.
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From what age should a parent begin to teach his child? From the moment he begins to speak.
SHULCHAN ARUCH
Whether you are considering day school or supplementary school, take the time to visit, attend classes, look at the art projects hanging on the walls, examine the textbooks and other materials in use, and talk to other parents and to the principal or director. It's important to think about the curriculum as more than just a listing of courses and books, too; consider the school's approach toward Judaism, its goals for students, and the role of parents. It's helpful to draw up a list of questions when considering a step as important as enrolling a child in school; that list can be used to pose questions or just to clarify your own values and goals. For example:
Are subject areas developed from year to year for continuity? Do teachers stress dialogue and discussion? Are lessons taught through lectures, worksheets, or games? Is there a regular music program or song-leader? How much time is devoted to the arts?
What is the body of Jewish knowledge that the school hopes to teach? What kind of Jew does the school hope to "produce"? Is religious observance expected of children, and how is that expectation expressed? Is prayer a part of the classroom experience? In the more advanced grades, is a single theology or approach to halachah (Jewish law) taught, or are different points of view presented?
How long do teachers tend to stay employed in this school? Are they offered in-service training? What is the student absentee and dropout rate? How many students continue their Jewish education through high school?
Supplementary school. The majority of Jewish parents choose a supplementary program for Jewish learning, offered after school or on weekends. Called Hebrew school, or religious school, these are usually run by synagogues, although there are some free standing, transdenominational programs as well. Also, the Workmen's Circle runs secular programs that stress Yiddish rather than Hebrew.
It is extremely difficult to generalize about religious schools since they vary in almost every way, beginning with their hours of instruction. Time requirements range from one to eight hours per week, with variations between grades. And despite published criteria and goals generated by the denominations, religious school faculties, administrations and curricula are dependent upon the culture and resources of each synagogue or school. In some synagogues, the rabbi or cantor runs the school; in others there is a paid school administrator or principal. The principal might hold a graduate degree in Jewish education, and teachers might be well trained and well paid. However, some schools are entirely run and taught by volunteers.
Paid or volunteer, teachers may be extremely knowledgeable and motivated. But because of the chronic shortage of Jewish teachers, professional standards are not always observed. College students often serve as religious school teachers, with varying results. Efforts to train and maintain talented teachers are ongoing, but the range of quality in religious school runs the gamut from excellent to abysmal.
Measuring the academic achievement in supplementary schools is difficult, in part because expectations are all over the map. Many parents expect religious schools to produce Jewish identity and Hebrew literacy in a few hours a week. Then again, others expect little, considering it merely "better than nothing."
The world is only maintained by the breath of schoolchildren.
MAIMONIDES, MISHNEH TORAH
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However, there are many excellent supplementary programs, proving that it is possible to devise demanding and reasonable goals for supplemental Jewish schooling. Some of these might include: a working Jewish vocabulary (mitzvot, tzedakah, Shabbat, kiddush, Torah, Maimonides, Herzl, Kristallnacht, Tel Aviv, etc.); the ability to read prayer book Hebrew; familiarity with the Jewish calendar of holidays and life-cycle rituals. It is also reasonable to expect children graduating from religious school to know more about the Torah and the Bible than a few stories. Most important, a religious school should nurture children's natural curiosity and enthusiasm for learning within a friendly, warm, and positive environment. While the formal curriculum is crucial, the way it feels to learn there—to be there—will ultimately determine whether religious school becomes a good or a bad memory.
Many religious schools now feature off-site programs that bolster children's sense of belonging. Shabbat retreat weekends can be a vital and invigorating teaching tool. These nights or weekends away from home with classmates and teachers are part summer camp, part spiritual retreat, part slumber party, and create an instant Jewish community and are often the high point of the school year. The presence of retreats for schoolchildren of various ages is a sign of a lively religious school.
People choose religious school programs for several reasons. Jewish parents, as a group, continue to support public education and feel that a supplementary education can provide what they want for their children in terms of developing a positive Jewish identity and community. Indeed, religious school can not only introduce the child to new friends but help integrate the entire family into congregational life. Cost is also a factor.
There are, however, some inherent problems with even the best supplemental Jewish education. Afternoon programs put tired, restless kids into classrooms precisely when they want and need to play. Also, religious school is invariably in competition with other after-school and weekend programs.
Another major dilemma for religious schools is the fact that many parents enroll their children for only a few years, in preparation for bar or bat mitzvah. Children attend classes, study with tutors, and then disappear after the big day. The bar/bat mitzvah "mill" approach offends many people, and religious schools and synagogues deal with this issue differently. Some congregations do not permit bar or bat mitzvah for students who have not been enrolled in the school for several years. Others will enroll students at any point, hoping that the experience at religious school will make children want to return for high school classes. One clue to the vitality of a religious school—and probably its best measure—is the number of students who stay past bar and bat mitzvah, get involved in the youth group, and/or graduate from the high school program.
However, one of the biggest problems for religious schools has less to do with students than with parents. If Mom permits virtually any other activity (skiing or shopping or cramming for a math test) to take precedence, if Dad never sets foot in the synagogue, if the adults do not even ask about what happened in religious school today—a child will start to treat the whole experience as the parents do: as an afterthought. But if parents make religious school a priority, if they volunteer for committees and fields trips, if they are taking classes at the temple, then religious school can be an important part of learning how to make Jewish choices for a lifetime.
Many communities support a local board of Jewish education as part of the local federation, which may provide an overview of the local community's resources for supplementary education, and indeed, all forms of Jewish learning.
Day school. A growing segment of the liberal Jewish community is choosing full-time day school education for their children. Once associated solely with Orthodox Jews, who still account for about 80 percent of all day school students, liberal day schools are proliferating across North America. The most established and numerous of these are sponsored by the Conservative movement, many of whose schools are named for Solomon Schechter, a founder of the Conservative movement. A smaller number of Reform-sponsored schools have opened, and there are also a number of community day schools, unaffiliated with any particular movement, that serve children from a wide range of Jewish backgrounds.
As with other private schools, Jewish day schools vary in curriculum and pedagogic approach, which can range from creative to traditional, from very competitive to noncompetitive. Every school has its strengths and weaknesses, and the principal or headmaster tends to set the tone and the agenda. Jewish day schools are typically run by people who hold advanced degrees in Jewish studies and/or education.
Some schools divide the day between Jewish studies (including Hebrew language and literature, classic Jewish texts, the Jewish calendar, Jewish history, Israel) and a full complement of secular studies (math, science, history, English language and literature). Many day schools emphasize Hebrew, which is not only taught but used as a language of instruction, which means graduates may become fluent or near-fluent Hebrew speakers and readers. Secular academics tend to be excellent in all Jewish day schools, which typically pride themselves on the success of their students after graduation.
Socially, day schools offer a totally integrated Jewish experience and a full-time immersion in unconflicted Jewish identity. Many schools begin the day with a morning prayer service. Cafeteria food is kosher. The school year is arranged around the Jewish calendar; obviously there are no Christmas carols and no Easter break. Nor is there any division between sports and Jewishness, or math and Jewishness. School friends will be Jewish friends, and while some members of the faculty may be non-Jews, the majority of adult role models will be knowledgeable, committed Jews.
An added advantage noted by many parents is the fact that attendance at a Jewish school means more free time for kids who might otherwise be enrolled in afternoon or weekend religious school. Day school can also provide a communal focus—a place where parents can meet other like-minded adults.
There are issues and drawbacks connected with day school, the chief problem being the expense; while most schools provide tuition assistance and scholarships, private education can be as costly as college. Other issues include a lack of racial, religious, and social diversity, and the fact that day school attendance can make commuting a constant fact of life for parents. With school friends scattered all over town, after-school and weekend play dates require more driving. Also, children with special needs are often at a disadvantage at day schools, which tend to have extremely high academic expectations and requirements and may not be able to provide the support staff needed.
If there is no private Jewish high school option for graduates from elementary day schools (after sixth grade or eighth grade), students must negotiate the transition to secular settings. Teachers and administrators help children and parents make the switch, which most take in stride. Principals and headmasters can put you in touch with families who have traveled this path before.
It is not a good idea to select a Jewish day school strictly on the basis of its reputation for secular academics and its success rates, or only because the public schools are not an option. Parents need to feel comfortable with a school's mission and goals, which should be clearly stated in its promotional materials.
Some organizations that can provide more information about day schools include:
PEJE Partnership for Excellence in Jewish Education; a national initiative to strengthen the quality of Jewish day school education in North America—www.peje.org
PARDES: Progressive Association of Reform Day Schools—www.pardesschool.org
RAVSAK: Reshet Batei Sefer Kehillatim, The Jewish Community Day School Network—www.ravsak.org
The Solomon Schechter Day School Association: Conservative movement—www.ssdsa.org
Special education. Jewish communities strive to provide special education programs for the physically and mentally challenged, and for those with learning disabilities. There are a variety of programs for children with special needs, including bar and bat mitzvah tutoring and camping opportunities, as well as in-class support for all kinds of education settings.
To find out what is available, check out the local Jewish family agency (Jewish Family and Children's Services) or the education department at your local federation. Rabbis, day school principals, and religious school principals will be aware of other resources as well.
Some of the organizations committed to providing access for all include:
The Association of Jewish Family and Children's Agencies—www.ajfca.org
The Jewish Braille Institute of America—www.jewishbraille.org
Tikvah: A camping program for children who are learning disabled or who are emotionally or mentally challenged, run by the Conservative movement's Ramah camps—www.campramah.org/tikvah
P'TACH: Parents for Torah for All Children; a resource for parents of children with learning disabilities—www.ptach.org
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The parent should teach the child on the level of the child's understanding.
TALMUD: PESAHIM 116A
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High School
The vast majority of Jewish children in America do not continue their Jewish education after bar or bat mitzvah. This is a great shame since, by high school, students are developmentally ready and eager for meaningful conversations about personal responsibility, ethics, God and spirituality, the problem of evil in the world, anti-Semitism, and the Holocaust. Hebrew high school programs can address these subjects, explore the real-world moral choices facing adolescents, and also engage teenagers' passions for social justice in Jewish settings.
Supplementary programs for teens are run by some synagogues, consortia of congregations, or nondenominational community organizations. Many programs meet weekly, others more often. Some stop after 8th grade while others go through 11th or 12th grade, ending with a confirmation or graduation ceremony.5
Teenagers are savvy consumers and they will reject programs that do not challenge and excite them. Given the distractions and competing interests of adolescence, a well-attended Hebrew high school indicates a good program and excellent teachers. Finally, the social aspects of Hebrew high schools are also important. Since they provide a place to meet other Jews of similar ages and interests, Jewish high school programs are a venue for young adults to start making Jewish choices of their own.
While Orthodox day schools generally continue through high school, in recent years, a growing number of liberal, nondenominational Jewish high schools have been founded. Some of these offer a dual-track program to accommodate students who did not attend an elementary Jewish day school.
Most of the information regarding elementary day schools above applies to Jewish high schools as well. On the whole, Jewish secondary schools are academically strong institutions with arts and sports programming to meet the needs of the students. Religious pluralism is generally addressed head-on, with opportunities for respectful discussion and debate unavailable elsewhere in the Jewish world. Graduates tend to be accepted by the colleges and universities of their choice. Socially, a Jewish high school tends to limit conflicts with parents about dating non-Jews, or participating in events on Shabbat or holidays.
Informal Jewish Education
Experiential or informal Jewish education is a category that includes the learning that takes place outside the classroom, in settings where young and not-so-young Jews learn how to make Jewish choices through a shared experience of Jewish living. Although not as structured as classroom learning, informal education doesn't "just happen." It involves a serious, planned effort to build a strong Jewish identity.
Settings for this kind of learning include Jewish summer camps, youth groups, family education, JCC cultural and sports events, Hillel events, and trips to Israel. For all their differences, these experiences teach through direct experience.
Jewish camping. American Jews have been sending their children to Jewish summer camps since the early 20th century. At its inception, camping was an extension of Jewish day school—a way to create a year-round Jewish learning experience while getting the kids away from the hot city. Over time, Jewish camps added the full complement of American camping experiences: softball, hiking, canoeing, swimming, arts and crafts, and the like.
Jewish camping has grown and diversified, and parents now choose Jewish camps for a wide variety of reasons. Some simply want their children to play with other Jews while others seek a total immersion in Jewish practice for their kids, complete with Hebrew study. Zionist camps focus on Israel in song, dance, language, and in just about every other imaginable way. There are camps for the religious and camps for secularists, camps for children of all ages, and specialized summer programs in Jewish arts, leadership, and social justice.
There are some camps where the only obviously Jewish element is the campers' last names; these tend to be privately owned for-profit camps. However, most Jewish camps are nonprofit programs run by large organizations, such as local federations or their agencies. The Conservative, Reform, and Reconstructionist movement all sponsor summer camps.
The best way to select any summer camp is to start a year early and, if possible, visit several, but there are other ways to explore what different camps have to offer. Synagogues and Jewish community centers run summer camp fairs, at which representatives set up booths and talk to prospective campers and their parents. Camp directors often spend the winter months on the road recruiting campers. Some questions to ask camp directors might include: What are your qualifications? How old are the counselors and on what basis are they hired? What is the staff-camper ratio? Most important, how many campers return from one summer to the next?
The best source of information about Jewish camping is word of mouth. Both parents and kids should do some research, and the child's opinion deserves serious consideration, since he or she is the one who literally lives with this decision.
Summer camp is expensive. But if money is keeping you from sending your child to a Jewish camp, be sure to ask whether scholarships are available. Local federations may provide financial aid, and some synagogues have automatic scholarships for kids going to camps run by their movement.
Many parents—especially those who remember their own Jewish camping experiences fondly—see summer camp as an educational and Jewish priority. Jewish camping allows a child to try on ideas and practices on his or her own. To spend time in a beautiful place where the rhythms of daily life are set according to a Jewish clock, where there are no distractions or competing pressures from the secular world. Camp is a place where being Jewish is easy and fun, and where peer pressure is generally on the side of doing more rather than less Jewish stuff. The staff—especially high-school-and college-age counselors—are very special role models. Perhaps most important of all, Jewish camp memories belong wholly to the child as an individual, not as a member of a family.
As children grow and discover their talents and passions, you might want to explore alternative Jewish summer programs, some of which are run by the denominations, some of which are held on college campuses.
To find a local Jewish day camp, check out your Jewish Community Center or YM / YWHA.
For more about overnight or resident camping, contact the following organizations.
The Foundation for Jewish Camping: A nondenominational agency and the central address for information about and advocacy for nonprofit Jewish overnight camps.—www.jewishcamping.org
Reform Camps—www.urjcamps.org
Conservative Camps—www.ramahcamps.org
Reconstructionist Camps—www.campjrf.org
JCC Resident Camps—www.jcca.org/find_camp
Youth groups. For many adolescents, youth groups provide an independent forum for developing a Jewish identity. A youth group creates a local community of friends who may attend different high schools and would not otherwise meet. Since youth groups are part of regional and national organizations, which run conferences, retreats, and summer camps, the chance to travel and meet Jewish kids from all over a city, a state, and the country, is both a great attraction and a wonderful informal Jewish learning experience. For those who get involved, the social events, religious services, conferences, first loves, and late-night bull sessions that are the mainstay of youth grouping, are the source of strong, positive, and entirely personal (rather than family-oriented) Jewish memories.
There are three large national youth organizations, which operate on regional, local, and chapter levels. NFTY, the North American Federation of Temple Youth, is the youth program of the Reform movement (www.nfty.org). USY, United Synagogue Youth, is run by the Conservative movement (www.usy.org). Unlike the NFTY and USY chapters, which are usually run by synagogues, BBYO, B'nai B'rith Youth Organization, is sponsored by local B'nai B'rith chapters (www. bbyo.org). No'ar Hadash is the Reconstructionist federation youth program (www.noarhadash.org). All of these organizations run a variety of programs, including summer camps, youth leadership training programs, social justice and tzedakah projects, and tours of Israel.
There are also Zionist youth organizations that promote interest in and support for Israel through summer camps, year-round youth group activities, and programs in Israel. These include: Hashomer Hatzair (www.hashomerhatzair.org), Habonim Dror (www.habonimdror.org), and Young Judea (www.youngjudea.org), which is run under the auspices of Hadassah.
Synagogues that sponsor youth groups provide an adult adviser, and the national organizations are run by professional staffs. However, youth grouping seeks to give kids a major say in decisions about programs, conferences, and social events. The structure of committees, officers, and boards of directors on chapter, regional and national levels, mirrors the world of adult Jewish organizations, which makes youth grouping a hands-on leadership training program. It is common for youth group machers (Yiddish for "big shots") to assume leadership roles in the adult Jewish community later in life.
Youth group programming varies a great deal and includes everything from dances to seminars with rabbis to leading Shabbat and holiday worship services to working in food pantries. While Zionist groups are focused on Israel, all Jewish youth organizations run tours that bring thousands of Jewish American teens to Israel every summer. (See "Israel trips," below.)
Family education. Synagogues and JCCs offer all kinds of programs that involve parents and children learning together. Some of these are part of religious school curricula, some are freestanding annual events. But they also respond to the fact that the most important Jewish learning takes place within the family. Activities are geared to interest children of various ages, and may include things like baking challah, creating a mural about Passover, learning Hebrew songs and dances, or building a sukkah. For families with older children, there may be fewer arts and crafts and more discussion and study.
Family education is not only for children but can be a relaxed way for adults to begin or renew their own Jewish education. Indeed, one of the goals of family education is to teach and empower parents to act as Jewish teachers to their children.
One of the most memorable kinds of family education experiences is family camp or a family retreat—time spent at a conference center or summer camp. Away from familiar contexts and removed from the usual chores and expectations, studying and playing in an entirely Jewish context, parents and children have the chance to be students together—a rare and precious opportunity. Similarly, a family trip to Israel—either as part of a group or on your own—is a way to share a powerful experience of cultural and religious connection, identity, and education.
Israel trips. There are all kinds of tours available for teens, for families, for young adults, and for professionals. Youth group tours offer various combinations of sightseeing with meeting Israeli teens, working on a kibbutz or at an archaeological site, or volunteering with the poor, the ill, and the elderly in Israel. Family trips seek to balance the needs of children for play and rest, with their parents' desire to tour and see the sights. (For more about Israel, see below.)
College
For some young adults, the college years are a time for putting distance between themselves and Jewish life; for others, it's a time of forging a new connection to their religious heritage. If you want your adolescent to choose a college or university where it is possible to make meaningful Jewish choices, it's important to introduce Jewish criteria to the selection and application process.
Opportunities for formal and informal Jewish learning abound on many campuses. Jewish learning in college has become increasingly easy as hundreds of private and public colleges and universities offer a variety of relevant courses. Jewish Studies departments have proliferated, but many schools that do not have an entire department frequently offer classes with Jewish content. A look at the course catalog may reveal, for example, Hebrew language courses, "The Literature of the Holocaust" (in the English department), and classes in Jewish philosophy.
For many, Jewish academics are less important than a Jewish social life on campus, which requires a critical mass of fellow Jews and a place for them to meet. While the denominations run programs for college students and some local federations sponsor events and services for students, most Jewish college programming is run under the auspices of Hillel: The Foundation for Jewish Life on Campus (www.hillel.org).6 Hillel is a national nondenominational organization with a presence on more than 500 campuses in North America. The Web site includes a "Guide to Jewish Life on Campus," with information about hundreds of colleges and universities, including the size of the Jewish population, Jewish studies, religious life, student interest groups, and kosher dining.
Every campus program provides a different combination of services, depending both on the student body and on the staff. Some Hillels have several full-time staff members, including one or more rabbis. Hillels also serve graduate students and faculty, and sometimes attract participation from the surrounding community.
Many Hillels run kosher kitchens and sponsor as many as five separate worship services every Shabbat, with different liturgies for Reform, Conservative, egalitarian-traditional, Reconstructionist, and Orthodox students. Some Hillels are renowned for lecture series and Israeli folk dance evenings, and most run social action or community service programs. Hillel offices can also help students arrange Israel trips.
Adult Education
On one level, all any adult Jewish student needs to continue his or her Jewish education is access to a good bookstore or a decent Jewish library, an Internet connection, and perhaps subscriptions to some Jewish magazines. However, Jewish tradition encourages communal learning in the strongest terms. In the Talmud, Rabbi Eliezer spoke of a student who studied silently, but after three years forgot all he had learned.7
The classroom is a cornerstone of the Jewish community, one of the raisons d'être of the synagogue. Torah study—examining the weekly portion—is a Shabbat tradition that fulfills both intellectual and communal needs. Indeed, studying with partners or in a hevrah—a circle of friends—is a time-honored Jewish tradition. And Judaism teaches that there is no greater honor or pleasure than studying with a great teacher. Taking a course is one of the best ways to transform feelings of Jewish inadequacy and illiteracy into a sense of engagement, empowerment, mastery, and even wonder.
The range of courses and lectures for the adult learner is virtually limitless, and in larger communities there is something for nearly everyone: lectures by visiting scholars, weekly conversations about the Torah, college courses with demanding reading lists, weekend Sabbath retreats, beginning prayer book Hebrew and advanced modern Hebrew conversation, classes in basic Judaism, close readings of mystical texts, introductions to the Torah service, Talmud study, workshops for intermarried couples, holiday cooking classes, film series, panel discussions on Israeli life and politics.
Adult education opportunities are provided by all sorts of organizations, including Jewish community centers, YM/YWHAs, and local chapters of national organizations such as Hadassah. Colleges and universities sometimes offer evening courses in Judaica for part-time students or auditors. Local Jewish newspapers invariably contain advertisements and listings for lectures and courses that are either free or low cost. Upon request, organizations that sponsor adult education programs will gladly add you to their regular mailing list.
Virtually all synagogues sponsor a panel of adult education programs. Usually, the rabbi(s), cantor, and director of education will teach some courses, with others offered by members of the religious school faculty, congregants, as well as guest teachers and lecturers.
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If you have studied with one teacher, do not say, "It is enough." Go study with another, too
AVOT DE RABBI NATAN A:3
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## ISRAEL
The relationship between the Jewish people and the land of Israel begins with the biblical promise that the children of Abraham would inherit the land and that it would be theirs forever. Jewish identification with and longing for the ancestral land in the Middle East has been a dream kept alive in literature and liturgy for centuries. In many ways, that dream of a homeland unified and sustained a wandering, homeless, often hunted people.
Although a small number of Jews have lived in the land of Israel from the Babylonian exile (which began in 586 B.C.E.) until 1948, when the modern state of Israel was established, the overwhelming majority lived in the Diaspora, in a self-described state of exile. Throughout those centuries, Jews have always faced toward Jerusalem in prayer, acknowledging the sacred geography of the Jewish imagination. This faithful orientation and a committed familiarity with the biblical names and places that define our earliest history and identity express a deep longing for home and everything that word means: rest, welcome, unconditional belonging.
Since 1948, this metaphysical and metaphorical relationship to the land of Israel (Eretz Yisrael) has coexisted with the new metaphors and realities of the modern nation-state of Israel (Medinat Yisrael). Although the state is officially secular, the very first law it passed—granting the right to citizenship for any Jew who wished to move there—honored the ancient, fundamental, and essentially religious centrality of this particular place as home. Whether or not Jews in Canada or Cancún chose to move to Israel, the "right of return" was tangible proof of their membership in a worldwide peoplehood.
Israel was founded in the shadow of the Holocaust, its acceptance and approval by the international community a response, in large measure, to its guilt over the genocide of six million Jews. From its birth, the state of Israel inspired pride in Jews around the world as it welcomed hundreds of thousands of immigrants that no other country wanted, and then quite literally, caused the desert to bloom through hard labor, ingenuity, and the support of worldwide Jewry.
The emotional impact of Israel's founding has faded somewhat for Jews living abroad; for most people alive today, the state has always been a fact on the ground. And while the overwhelming majority of Jews around the world continue to provide support to Israel, Diaspora Jews are no longer universally deferential when it comes to Israeli politics and policies on subjects ranging from the struggle over recognition and resources for liberal Jews in Israel, to the relationship between Israeli Arabs and Israeli Jews, to the questions surrounding Palestinian statehood.
But disagreements over such matters remain dinner-table debates, family differences that, however heated, cannot threaten the passionate and practical connections and commitments among Jews, wherever they live. North American Jews send vast sums of money to Israel, making choices about contributions that reflect their interests and concerns: environmental causes, peace fellowships for teens, support for people wounded by terror attacks, universities, the arts.
Visiting Israel is a milestone in Jewish life for those who make the trip.8 For a tiny country, no bigger than New Jersey, there are a staggering number of sights to see and experiences to savor. The countryside includes mountains, valleys, deserts, seashores, as well as countless historical sites sacred to the histories of Judaism, Christianity, and Islam. Of course, Israel is anything but a museum, with a vibrant contemporary arts scene flourishing in Tel Aviv, and the challenges of a nation still absorbing immigrants of all ages, races, and national backgrounds.
Although many individuals travel to Israel on their own, the majority of first-timers go on tours organized by local federations, synagogues, or youth groups. High school and college students can attend summer-long, semester-long, or yearlong programs for touring and study, which provide contact with young Israelis.
Trips to Israel can be exhausting, confusing, exalting, inspiring, and frustrating. There are too many sights to see, too many stories to hear. But for Jews, travel to Israel is different from a trip to Costa Rica or Corsica, or any other international adventure. As Rabbi Lawrence Hoffman has written, "Jews visit Israel not just as tourists but as pilgrims."9 Indeed, a great many people make the trip in groups called "missions."
"They pack tour guides but also Bibles and prayer books that they haven't looked at in years...They can't get enough [of Hebrew and] stare in awe at Coca-Cola written in Hebrew letters."10
Israel exerts a gravitational pull on Jewish hearts and minds. Some are so drawn to the integrity of living in a place where everything slows down on Shabbat, where the language of the marketplace and the Internet is Jewish, that they "make aliyah" (the word means "to go up") and move to Israel. But even for those who live elsewhere, Israel is one of the gifts of being a Jew in the 21st century, one of its challenges, one of its choices.
Here are a few of the hundreds of Web resources about Israel.
American Israel Public Affairs Committee: AIPAC is a registered lobby that meets with members of Congress on legislation affecting Israel—www.aipac.org
ARZA: The Association of Reform Zionists of America—www.rza.org
Israel Ministry of Tourism—www.goisrael.com
Hadassah: The Women's Zionist Organization of America, which sponsors Zionist youth programs and supports many social welfare and medical programs in Israel—www.hadassah.org
JNF: Jewish National Fund, which works for forestation, land reclamation, and environmental causes in Israel—www.jnf.org
MERCAZ: The Zionist organization of the Conservative movement—www.mercazusa.org
The New Israel Fund: Supports social justice projects in Israel, including women's rights and Arab-Jewish cooperation—www. nif.org
The World Zionist Organization: Promotes immigration to Israel—www.wizo.org.il
## TRAVELING JEWISH
If making Jewish choices happens only at home or in the synagogue, then traveling for pleasure or on business means leaving Judaism behind along with the cat and the television set. But if Jewishness is an authentic part of self and life, it does not get shelved when the newspaper delivery is suspended.
Traveling Jewish can be a special delight; a unique opportunity for learning about Judaism, and about the world and your place in it. Celebrating Shabbat in a hotel room can be a way of calming down and of finding peace and balance during an otherwise dreadful business trip. Attending services at an ancient European synagogue or in Anytown, USA, can transform your experience of the city and even your perception of an entire culture. Giving money to a begging child in a poverty-stricken land can move you to reconsider your budget for tzedakah.
Making Jewish choices on the road takes two forms, the first of which involves re-creating personal Jewish routines. Lighting candles and saying blessings in a vacation cottage by the sea or in a tent on a mountainside can become a treasured family memory. Packing and shopping for a vacation Shabbat focuses the trip in a particular way, and Judaica vendors sell traveling candleholders, kiddush cups, and hannukiot that fold up to easily packable proportions.
Jews who keep kosher find it relatively easy to maintain their practice on the road. Airplanes and ocean liners generally offer kosher as well as vegetarian alternatives for travelers. Kosher meals are available in the most unlikely places—such as the Air Lanka flight from Colombo, Sri Lanka, to Bangkok, Thailand.
While there are kosher cruises and kosher resorts—in the Caribbean and in Mexico as well as in Miami Beach—people have managed kosher trips in far less hospitable places simply by keeping to a vegetarian diet. All major airlines and cruise lines offer kosher food on request and do not charge extra for it. In cities and countries where there are Jewish communities, seeking out kosher restaurants can lead to very special travel experiences and a sense of belonging to a global family.
Traveling Jewish means seeking out new Jewish experiences: finding a Jewish neighborhood, eating in a kosher restaurant, or visiting the local Jewish museum. Once you have seen all the landmarks that every tourist visits, you have the opportunity to make a far more personal connection with a foreign culture. Attending a service in Rome or New Delhi can make you feel at home even in a place where you had felt like a complete stranger. If you find yourself very far from home during a Jewish holiday, consider exploring the local customs: imagine Hannukah in Hong Kong, Passover in Paris, or Sukkot in Singapore. But even on business trips in North America, attending services at a synagogue near the hotel can forever alter your feelings about trips to Cleveland, Houston, or Toronto.
Of course, not all Jews are hospitable or effusive, and it would be naive to expect to be treated like a long-lost sibling just because you are in what seems an exotically non-Jewish place. Nevertheless, there are countless stories about unexpectedly warm welcomes for total strangers simply because they identified themselves as Jews. Travelers have been invited to people's homes and given tours of the city.
For a worldwide synagogue directory see Maven Search (www.maven.co.il).
* * *
May it be your will, Adonai, God of our parents, to lead us in peace and guide our steps in safety, so that we arrive at our destination alive, happy, and in peace. Deliver us from enemies and danger along the way. May we find favor, kindness and compassion in your eyes and in the eyes of all we meet. Hear our prayers, for You are a God who listens to prayers. Holy One of blessings, hear our prayer.
THE TRAVELER'S PRAYER
* * *
## THE CYCLE OF THE YEAR
Rabbi Abraham Joshua Heschel wrote, "Jewish ritual may be characterized as the art of significant forms in time, as architecture of time."1 Heschel, one of the great teachers of the 20th century, thought of Shabbat as the essential expression of Judaism's "architecture of time," and referred to the Sabbaths as "our great cathedrals." Judaism provides other ritual structures, too, in the annual cycle of holidays and in the ceremonies that mark rites of passage.
There is another, more personal metaphor that may be applied to the Jewish cycles of observance. Tradition—made up of history and custom, memory and song—is like a mirror, a tool for considering life and self in the context of Judaism. Looking into it, every person calls forth something new. Not answers. Mirrors do not supply answers. Yet there is something special about a mirror that can change the way people see themselves. The source of the transforming power of this mirror is time. Possessing context, connection, and continuity, time is both why and how Jewish holidays and life cycle observances "work."
Time seems tender and almost palpable at the holidays because every celebration is a window on the past: when parents were children lighting their first Hannukah candles, when the light from the candles was the brightest light in the house, or when the Maccabees lit a lamp in a rededicated Temple. Every Hannukah distills the present, like a snapshot. Every Hannukah is a "first": the first year the baby is allowed to light the candles, the first year without Grandpa.
Every time a couple meets under the huppah, the Jewish wedding canopy, it is as if time collapses. The details of the day—the style of the bride's dress, the music, the menu—are forgotten. Suddenly and forever, it is the first wedding, when according to one legend, God braided Eve's hair. And it is the ultimate wedding, the culmination of four thousand years of Jewish weddings.
## JEWISH TIME
The holidays are islands in time where people can stop to reflect on the meaning of their days, to consider the distance between who they are and who they wish to be, the distance between today and the day when the world will be what we wish it to be. Like Shabbat, the holidays are about providing a glimpse into what life and time will be like when those wishes are realized. These islands in time are not abstract ideas but ritual structures built of customs, prayers, food, songs, family gatherings, and memories. They are embedded in the Jewish calendar, which expresses a particular understanding of time and eternity.
The calendar. For more than two thousand years, Jews have juggled two time zones, straddled two calendars. According to the secular calendar, the date changes at midnight, the week begins on Monday, and the year starts in the winter. According to the Jewish calendar, the day begins at sunset, the week begins on Saturday night, and the new year is celebrated in the autumn.
The secular or Gregorian calendar is a solar calendar, based on the fact that it takes 365.25 days for the earth to circle the sun.2 With only 365 days in a year, after four years an extra day is added to February and there is a leap year. The Jewish calendar is both solar and lunar. The months are lunar, made up of either 29 or 30 days, which add up to a 354-day year, 11.25 days short of a solar year. The discrepancy is corrected with the occasional addition of a leap month tucked between the spring months of Adar and Nisan.
The Jewish month begins with the new moon, when no moon is visible in the sky, so the moon is full on the 15th of every month whose names (starting with the autumn month when the year begins) are: Tishrei, Heshvan, Kislev, Tevet, Shvat, Adar (and seven times every 19 years Adar II), Nisan, Iyar, Sivan, Tammuz, Av, and Elul. The year changes on Rosh Hashanah, on the first day of Tishrei, when according to the traditional Jewish reckoning of time, the world was created.
The Gregorian and Jewish calendars are never quite in sync, thus the inevitable grumbling about how the Jewish holidays are never "on time"—somehow either too late or too early in relation to the secular date. But since their purposes are so different, the two calendars are rarely in conflict. The Gregorian calendar is the calendar of the workweek, the school year, and the mundane needs of daily life. The Jewish calendar has exclusively religious purposes: it is for keeping track of holidays, and is used for writing Jewish marriage contracts and for determining the anniversary of a death. The secular calendar is a tool for keeping track of time, for managing time, unlike the Jewish calendar, which is not used for civil purposes anywhere—not even in Israel.
The secular calendar stretches endlessly into the future. The Jewish calendar is a tool for cherishing time, and for sanctifying it. The Jewish calendar moves forward toward redemption in a dance with the past, choreographed by the holidays.
The Jewish holidays have two main sources: biblical and historical.3 The Torah established the observance of Rosh Hashanah, Yom Kippur, Sukkot, Shmini Atzeret, Pesach (Passover), and Shavuot. They are called "holy convocations," or "a Sabbath unto the Lord," and the Torah contains specific instructions for celebrating these days and for refraining from work on them.
The Torah also assigns reason and meaning to the holidays as well: Rosh Hashanah is for sounding the ram's horn and for the new year; Yom Kippur is the day for asking forgiveness; Sukkot is about the harvest; Passover is for remembering slavery and the exodus from Egypt; Shavuot is about the harvest of the first fruits.
The historical holidays developed in response to transforming events in the experience of the Jewish people: Purim reacts to the dangers of living in exile; the day of mourning called Tisha B'Av became part of the calendar after the destruction of the Temple in Jerusalem; in the second century B.C.E., after the Maccabees fought and won the right to Jewish self-rule in the land of Israel, Hannukah became an annual celebration of rededication. The historical development of the calendar continues in modern times with the addition of Yom HaAtzmaut and Yom Hashoah, respectively, Israeli Independence Day and Holocaust Remembrance Day.
The historical, evolutionary nature of the Jewish calendar is also demonstrated in the way certain festivals have waned and waxed in their observance. Shmini Atzeret, for example, with its unique prayer for autumn rain, may have made spiritual sense in the context of an agricultural and Temple-oriented society. However, as the Jews became a more urban and Torah-centered people, Simchat Torah, a post-biblical observance, came to overshadow and even preempt the older holiday. For modern Jews, the Holocaust and not the destruction of the Temple has become the focus of communal grief, thus Holocaust Remembrance Day has come to eclipse Tisha B'Av as an observance of public grief and mourning.
Perhaps the most confusing aspect of Jewish holiday observance is the discrepancy regarding celebrations on the second day of Rosh Hashanah, Sukkot, Passover, and Shavuot. For example, some Jews observe two seders and eat matzah for eight days, while others attend only one seder and eat bread again after seven days. The difference in practice dates back to sometime around the fourth century C.E. and is based on doubts as to the exact date of the new moon, which is invisible. Rather than risk celebrating on the wrong date, Jews living outside of the land of Israel began two-day observances of the holidays that required refraining from work and attending worship services. This division continues: Israeli Jews and many Reform Jews outside of Israel celebrate holidays based on the new moon for only a single day; however, many Diaspora Jews continue with two-day observances.4
Making yontif. Yontif is the Yiddish word for holiday. Literally, it means "good day" and is based in the Hebrew, yom tov. Hence the greeting, "Gut yontif." (The Hebrew word for holiday is chag. Chag sameach, means "happy holiday.")
As with Shabbat, the Jewish holidays only have meaning in the doing. The operant verb for holidays is not "celebrating" or "observing," but "making." Thus, making Jewish choices about the holidays is a matter of "making yontif."
Jews make yontif in many different ways; some are traditional, some brand-new, and the following chapters contain many examples of both. The richness of each holiday makes it impossible to do any of them justice in an introductory book. Books about the holidays are a mainstay of most Jewish home libraries because, in a sense, the holidays are the best curriculum for Jewish education since they encompass nearly every religious, cultural, and historical theme of Judaism.
Each holiday has its own mood, texture, and weight. (Yom Kippur is somber. Purim is hilarious.) While virtually every holiday has some synagogue observance connected with it, some holidays are primarily liturgical and synagogue-centered—Rosh Hashanah is a good example—whereas others like Hannukah are essentially home-based.
Various holidays also have different qualities and different importance in every Jewish household. For example, many people consider Purim primarily a children's holiday and focus on dress-up, plays, and pageants at synagogue or in school. But there are many adults for whom Purim is the occasion for both serious (and silly) study—not to mention the costume party of the year.
Furthermore, individual and family interest in particular holidays may wax and wane, and not only as a result of children's ages. Enthusiasm for a celebration can be sparked by any number of reasons: a good lecture, a book or movie that speaks to the themes of the holiday, an event in the past year. For people who have recently lost a loved one, for example, attending Yom Kippur services can feel like part of the mourning process.
The meaning and joy of the holidays is uncovered year by year in the process of making yontif. But perhaps the most important part of that process—the make-it-or-break-it element—is preparation, hachanah in Hebrew.
Hachanah includes everything from stocking up on matzah for Passover, to making paper chain decorations for Hannukah, from meditating on the unkind words you wish you hadn't said in preparation for Yom Kippur, to reading bedtime stories about Queen Esther during the week before Purim. Preparation is the difference between mechanical holidays and meaningful holidays, between enforced holidays and holidays that are genuinely fun.
Jewish tradition is replete with examples of the importance of preparing for the holidays. The entire forty days before Yom Kippur are considered a period of spiritual preparation. And then, as soon as Yom Kippur is over, even before breaking the fast, preparations for Sukkot begin with the hammering of the first nail in a sukkah, the hut in which Jews celebrate the harvest festival. According to the Hasidic view, these preparations are themselves holy; by orienting secular time toward the celebration to come, hachanah sanctifies the everyday.
Still, there is a crucial difference between preparing and celebrating, between hachanah and yontif. The point of getting ready is not merely to have delicious meals or a big party when the day finally arrives. Preparation is what enables us to bask in the present without worrying about what is left unfinished. This sense of celebration—this taste of redemption—is the goal of all Jewish ritual, of Shabbat, and of the Jewish holidays.
The menu that follows consists of ideas, strategies, projects, and approaches for making yontif. This is not a "to-do" list; there is more here than any one person or any one family can reasonably undertake. This is a "can-do" list—a catalog of the ways that people explore the Jewish holidays.
Getting oriented. One of the easiest ways to focus on the holiday cycle is by purchasing a beautiful Jewish calendar and hanging it prominently. Look for one with room for notes and scribbling, and flip through the months, making note of the week before every holiday as a reminder to start getting ready.
One way to focus on holiday celebrations is by picking a primary symbol for each, for instance the hannukiah (the eight-candle candelabra of Hannukah) or the Sukkot etrog (a citrus fruit imported from Israel). Learn as much as you can about it and feature it in centerpieces on the table, in conversation, in stories and art projects for children.
As markers in time, the Jewish holidays can be a way to organize all kinds of memories. Pictures of ten years' worth of Passover tables make for a moving collage of continuity and change. Or have a family portrait taken every year during the same holiday.
Continuity is good, but so is change. In observing the Jewish holidays, it's a good idea to try to reconcile this seeming contradiction by being flexible. The holidays acquire more and more meaning as they are repeated consistently. The same menus, the same guests, the same ritual objects taken out just once a year, all add to the evocative power of the day. But holidays can also be opportunities for growth. Just as individuals change from one year to the next, so can their holiday observance.
Some holidays may hold more meaning than others for you and your family. Some people "specialize" in certain observances and all their friends know that the So-and-Sos really "do" Hannukah with a big party complete with dancing, a royal feast, and gifts for everyone. As you explore the Jewish calendar from year to year, you'll discover favorites and create ways to make them your own
Family time. There are all kinds of families. And regardless of their size or composition, holidays create time and space for relaxing, sharing, listening, and enjoying one another. For families with children, the holidays are formative Jewish experiences redolent of both continuity and change.
There are many ways to enhance the holidays. Taking time to talk about them at the Friday night Shabbat table, for example, is one way to help children prepare and also to let them know that the grown-ups have begun getting ready. Reading stories and drawing pictures about the holiday in anticipation of the celebration is another way to prepare with kids.
In order to associate the holidays with pleasantness, some parents give gifts to their children on the major holidays. A trip to the bookstore or music store for a holiday-related book or CD, followed by an ice cream cone, heightens the anticipation and sweetness of a holiday. And since it is traditional to wear new clothes on holidays (and Shabbat), new clothes might be purchased with an eye to a first wearing on yontif.
Holidays are like chapter headings in a family history. The light of holiday candles can prompt the telling of "our" stories: of Sarah's first Hannukah, when she tried to eat the candles; of the time everyone went to Grandma's house and all the presents were forgotten at home; of the favorite gifts, and guests, and parties.
It is a good idea to try to strike a balance between activities for children and time for adults. Arts-and-crafts projects may be the perfect way for preschoolers to get acquainted with a holiday, but that's probably not entirely fulfilling for parents. Besides, if children see that their parents are really not involved, they will learn that making yontif is essentially kid stuff, that is, something to be outgrown.
Setting the mood. Decorating for the holiday—making tangible preparations—is a good way to enter into a spirit of celebration. This can include everything from buying fresh flowers for the table to making a centerpiece using holiday symbols. Children's artwork about the holiday can be featured on the refrigerator or on the front door.
One nice holiday project is to buy or create special place settings. Commercial place mats are available for Passover and Hannukah, but children can make their own by covering an original drawing or painting with clear Contact paper. Likewise, you can create "dinnerware" for holidays, either by purchasing a new set of plastic tableware, or by going the clear Contact paper route using a paper plate or by getting a "decorate a plate" kit, which is shipped off to the factory so the original design can be permanently baked on.
Another way to set the mood is with music. Recordings of traditional and modern holiday songs abound, as well as music that reflects the diversity of Jewish culture: everything from cantorial singing to Israeli rock and roll, from American Jewish bluegrass to modern classics, such as Leonard Bernstein's "Kaddish" and Steven Reich's "Tehillim." English/Hebrew CDs for children are a popular way to introduce Jewish vocabulary and Hebrew words to youngsters, and their parents.
Eating. The holidays are experienced with all the senses, and special dishes are associated with certain times of the year. It just isn't Rosh Hashanah without apples and honey. Potato pancakes (latkes) are Hannukah.
Families create traditions around holiday foods as well. Passover would be weird without Mom's matzah stuffing. Shavuot means Aunt Molly's cheesecake. It is easy to start this kind of family table tradition by finding a dish beloved by everyone in the household and more or less reserving it for the holiday. Holidays are also a good excuse for baked treats. Making cookies, cupcakes, and candy can be a great way to involve children in holiday preparations.
Cookbooks are a way to explore the holidays from a sensory perspective. Most Jewish cookbooks contain a special section on holiday food, and there are many titles devoted entirely to holiday recipes. For North American Jews, the vast majority of whom are of Eastern European descent, cookbooks devoted to the Jewish cuisines of Greece and Italy can be a revelation, and not just gastronomically. The fact that holiday traditions include such a breadth of flavors and aromas validates the diversity and variation in modern Jewish life.
Study. One way for adults to enter into the spirit of the holidays is to learn something new about each. Study can take many forms, from going to a lecture about the holiday, enrolling in a course about the holiday cycle, or simply reading a chapter about the upcoming festival. Many holidays also have Torah readings and other traditional texts associated with them.
Tzedakah. It has long been the Jewish custom to share holiday joy by making contributions to the poor. Convening the family to decide where to send money "this season" can be a way to focus on the meaning of the holiday; by sending money to relevant organizations. For example, environmental causes seem an apt choice on Tu B'Shvat, which celebrates trees and the natural world.
Synagogue attendance. The Jewish holidays are marked by special worship services. Many synagogues also offer other activities: from communal candlelighting and meals in the temple sukkah, to Purimshpiels (Purim plays or pageants), to late-night study sessions on Shavuot. Attending synagogue activities is a good way to participate in communal life and learn about the holidays at the same time.
Spiritual preparation. In the rush to run errands, cook, and get everything finished before a holiday begins, it is easy to forget about making oneself ready for yontif. For Jews, spiritual preparation has long been associated with mikveh, the ritual bath of purification. A physical manifestation of kavannah (intentionality) prior to a holiday, immersion in a mikveh, like no othe ritual, permits you to stop and take stock of things, to step outside of time, as it were.5
However, there are simple ways to slow down and get centered at home as well. Set aside time to take a solitary walk, to arrange flowers for the table, or to take a long bath; read a poem or prayer to shift mental gears from the everyday into holiday mode.
The Yontif Seder
The word seder, which means "order," is most closely associated with Passover. The Passover seder is made up by the order of the readings, blessings, and rituals that take place before, during, and after the ritual meal on the first and (for many) second nights of the holiday. People have also created seders for Tu B'Shvat, Hannukah, and Purim; ritual menus of songs, readings, blessings, and activities surrounding a meal.
The yontif seder is similar to the Shabbat seder, which is the order of blessings, customs, and songs surrounding the Friday night meal, described on pages 35–49. Most of the holidays described in the following chapters begin with a festival meal that includes four basic blessings: over candles, wine (kiddush), the season (shehechiyanu), and bread (motzi).
Candles. Festival candles mark the beginning of most holiday celebrations, just as Shabbat candles mark the beginning of the Sabbath. If a holiday begins on Friday night, the blessing for the candles concludes with the words shel Shabbat v'yom tov, "the lights of Shabbat and the holiday."
Baruch ata Adonai Eloheynu Melech Ha-olam asher kid'shanu b'mitzvotav vitzivanu l'hadlik ner shel (Shabbat v') yom tov.
You Abound in Blessings, Adonai Our Lord, You make us holy with commandments, and call us to light the lights of (Shabbat and of) the holiday.
Wine. The kiddush, or sanctification over wine, can be done in a number of ways. The full kiddush for holidays usually includes at least a phrase and as much as a paragraph about the specific festival, and is published in most daily prayer books, or siddurim. However, many people use the basic kiddush for any occasion.
Baruch ata Adonai Eloheynu Melech Ha-olam boray pree hagafen.
You Abound in Blessings, Adonai Our Lord, You make the fruit of the vine.
The season. Shehecheyanu is a blessing recited at many sorts of occasions, ceremonies, and rituals. At the holidays, it acknowledges the advent of a new time in the year, a new time in the life of the people gathered at the table.
Baruch ata Adonai Eloheynu Melech Ha-olam shehecheyanu v'kiamanu vihigianu lazman hazeh.
You Abound in Blessings, Adonai Our Lord, You have kept us alive. You have sustained us. You have brought us to this moment.
Bread. Called the motzi ("brings"), the blessing over bread represents all the food at the meal. The motzi acknowledges that human beings are, ultimately, dependent upon gifts from the earth.
Baruch ata Adonai Eloheynu Melech Ha-olam Ha motzi lechem min ha'aretz.
You Abound in Blessings, Adonai Our Lord, You bring forth bread from the earth.
Dinner is served.
## ROSH HASHANAH AND YOM KIPPUR
Picture people running around, sneaking up behind one another with a big ram's horn, giving it a blast, as if to say, "Wake up! It is upon us again." The liturgy of Rosh Hashanah is designed to get you to wake up and pay attention not only to who you are, but to who you have been and who you mean to be.
Yom Kippur is not eating, not drinking, not sleeping very much, not having sex, not dressing in fine clothes and looking in the mirror and seeing what you're going to look like after you've died. And the most joyous noise a Jew can hear is the sound of the shofar announcing the end of Yom Kippur, because it means that you have lived through the day of death and not died.
Rosh Hashanah is about reverence and gratitude for life, the mother lode of all religious insight. Yom Kippur is about telling the worst truth about yourself, and getting new life from that.
RABBI LAWRENCE KUSHNER6
Rosh Hashanah (the New Year) and Yom Kippur (the Day of Atonement) are the most liturgical of all the Jewish holidays. The Hebrew word for prayer is tefila, which is a reflexive form of the verb "to judge." For Jews, prayer—especially the prayers of these two holidays, known as the Days of Awe—are best understood as a form of reflection and self-judgment.
The two holidays that begin the Jewish year are unlike virtually every other. Neither one is based on an agricultural festival or historical event. And although Rosh Hashanah meals may be elaborate, neither of these holidays is associated with the kinds of symbols, foods, and home celebrations that make other Jewish holidays beloved of children.
The Days of Awe, Yamim Noraim, are synagogue-based and existential. They confront every Jew with the fact of his or her own mortality, and thus with an appreciation of life. While these holidays are not inherently "fun" the way that Sukkot, Hannukah, Purim, or Passover can be, they are deeply compelling.
Indeed, Rosh Hashanah and Yom Kippur are the only times when American synagogues are filled to the rafters. Jews who rarely or never attend worship services make a point of going to the longest, most formal services of the year. The reasons for this loyalty are complex. Childhood memories and nostalgia draw many people, and some rabbis have suggested that there is a magical element to High Holiday services that makes attendance seem like the renewal of an ancient Jewish life insurance policy, a hedge against death, or at least a repudiation of assimilation.
By and large, making yontif for the Days of Awe means attending worship services. There are many ways to prepare for these holidays and to mark their observance at home, but because of the importance of community worship, this chapter outlines the liturgy, including some of the religious themes and key Hebrew words found in Rosh Hashanah and Yom Kippur services. However, because individual congregations make so many choices about the content and form of services, this discussion represents only a fraction of the menu from which rabbis, cantors, and ritual committees make their selections.
Preparation
According to tradition, the entire Hebrew month that precedes Rosh Hashanah, Elul, is dedicated to preparing for the Days of Awe. Psalm 27 is added to the daily worship service and the shofar, a ram's horn, is sounded every weekday morning. Special penitential prayers called slichot, from the Hebrew for "excuse" or "to be sorry," are recited during Elul, and on the Saturday night preceding Rosh Hashanah, many congregations hold a late-night Slichot service. Some synagogues run adult education programs about the approaching Days of Awe during Elul.
The most common personal preparation for these holidays is the sending of New Year's cards. These greetings originated from the custom of signing letters during the month of Elul with the phrase "May you be inscribed [in the Book of Life] for a good year." Commercial cards are available, but some families make their own, featuring artwork by children.
Another way to get into the spirit of the holidays is to buy a shofar, the horn of a ram or other animal, available in Judaica stores. A shofar is not a sacred object but something both children and adults can play with. A shofar can even be used as the family alarm clock in preparation for the holidays to come.
It is also customary to wear new clothes for Rosh Hashanah, and to get a haircut in anticipation of the new year.
Since Rosh Hashanah is associated with both the creation of the first human beings and with the creation of the world, children enjoy decorating the table (or the refrigerator door) with birthday-related projects. They can also decorate the table and the house for the break-the-fast meal that follows the Yom Kippur fast.
Traditionally, the weeks before the Days of Awe are associated with mending relationships, apologizing, and asking for forgiveness for transgressions big and small. People call out-of-town relatives and friends. Some families make a point of resolving conflicts and clearing the air of arguments. It is also customary to visit the graves of family members and loved ones who have died.
Study
Of all the holidays, the Days of Awe seem the most intellectual. Since so much time is spent in services, it can be helpful to browse through the special holiday prayer book or machzor, Hebrew for "cycle," you will be using. Getting familiar with the structure and content of the prayers can make the services more accessible and meaningful.
Holiday prayer books contain the holiday Torah and Haftarah portions that are read out loud during services. The Rosh Hashanah Torah readings (Genesis 21 and 22) are among the most powerful and problematic in the Torah. The first includes the story of the birth of Isaac, the casting out of Hagar and Ishmael into the desert, and their subsequent deliverance. Genesis 22 contains the test of Abraham's faith, when he is asked to sacrifice his son Isaac. This story is referred to as "the binding of Isaac," or the akedah.
The Haftarah portions (prophetic readings) for both the morning and afternoon Torah services on Yom Kippur also provide complex texts for study and discussion. The morning passage from Isaiah rejects piety divorced from a commitment to social justice; "Behold, on the day of your fast you pursue business as usual, and oppress your workers...Such fasting will not make your voice audible on high."7 The Haftarah for the afternoon of Yom Kippur is the four-chapter Book of Jonah, which is available in illustrated versions for children.
Tzedakah
It is customary to give money to the poor during this season. Since Rosh Hashanah is a celebration of life, some make an annual blood donation before the holiday. Many make a contribution to a hunger-related charity for an amount equivalent to a day's worth of meals at Yom Kippur through Mazon: A Jewish Response to Hunger (www. mazon.org). During the memorial or yizkor service of Yom Kippur, one of the prayers pledges tzedakah in memory of loved ones who have died, which prompts donations to charities that were important to them.
Another way of performing a mitzvah, a holy act, during the Days of Awe is to go to a Jewish nursing home to visit the residents and/or to assist with or attend services with those who cannot get to a synagogue.
Children
Rosh Hashanah and Yom Kippur are days of intense prayer and reflection in the synagogue, clearly not an easy setting for children. Most liberal congregations provide some kind of special programming for little ones, with age-specific activities, including babysitting for toddlers, singing and organized play for preschoolers, and an abbreviated service for school-age children; however, not all temples are able to accommodate all ages. Some parents bring books and puzzles for school-age children, and encourage them to stay in the sanctuary to absorb the melodies and rhythms of the service. Others prefer to leave little ones with babysitters, both for the comfort of the children and fellow congregants, and also for their own prayers. Then again, many parents treasure their memories of spending some (or most) of the High Holidays in the temple foyer or playground, with other parents and children.
Making Rosh Hashanah
At Home
The evening meal that begins the holiday constitutes the high point of home celebration on Rosh Hashanah. Families tend to create their own holiday traditions around this dinner: menus and recipes, special table settings and decorations, guests who return every year. Since Rosh Hashanah is often referred to as the birthday of the world, parents of young children sometimes serve birthday cake or cupcakes, complete with candles, for dessert.
Dinner is preceded by the yontif seder that is discussed on pages 149–151, with lighting of candles, kiddush, and motzi. It is traditional to use a round challah on Rosh Hashanah, a symbol of the cycle of the year. Shehecheyanu is then recited, the blessing for all "firsts." And to begin the new year sweetly, it is customary to dip apple sections in a bowl of honey and to say:
Y'hi ratzon milfanecha Adonai Eloheynu vaylohay avotenu, she'te'chadesh aleynu shana tova u-metukah.
May it be your will, Adonai, God of our parents, to renew us for a good and sweet year.
After services, people generally have lunch with family and friends, go for walks, or search out a body of water for the informal ceremony called tashlich, from the Hebrew for "send off" or "cast away."
Tashlich is a symbolic casting off of sins by emptying pockets into running water, built around the words of the prophet Micah. "And you will cast all their sins into the depths of the sea."8 Short, informal ceremonies have been created for tashlich, which include songs about water and various readings.
Take a bag of stale bread and head for a duck pond—a favorite with children, especially on a day when they may be asked to sit still a great deal. Some families use this time to apologize to one another for the wrongs of the past year and promise to try to be more patient and kinder in the year ahead.
For those who observe a second day of Rosh Hashanah, it's customary, during the yontif seder, to taste a fruit that hasn't been eaten for several months, providing the occasion to recite Shehecheyanu, the prayer for firsts.
Synagogue Observance
The evening service for Rosh Hashanah is relatively short and, with a few exceptions, much like other evening services. However, a great emotional and spiritual transformation is wrought by the distinctive melodies of the Days of Awe, which are reprised again and again during both Rosh Hashanah and Yom Kippur services. For most Jews, it is the tunes that evoke the spirit and mood of these powerful holidays.
At the morning service for Rosh Hashanah, the themes of judgment and repentance are repeated. The recurrent image of God as a father-king is given voice in one of the most memorable prayers and melodies of all the Jewish holidays, "Avinu Malkenu," "Our Father, Our King."
One of the overarching metaphors of Rosh Hashanah and Yom Kippur is "the Book of Life." According to legend, on Rosh Hashanah, the first day of the year, the names of the righteous are written in this book, inscribed for another year of life. But those who are not entirely good or righteous, even the wicked, have the next ten days in which to turn away from their wrongs and repent before the book is closed and sealed on Yom Kippur.
* * *
Help us to break down the barriers which keep us from You: falsehood and faithlessness callousness and selfishness injustice and hard-heartedness
FROM THE ROSH HASHANAH SERVICE
* * *
The Torah scrolls are "dressed" in different coverings for the holidays; usually in white, to denote purity. And their readings are a high point of the service, and often the subject of one of the rabbi's sermons, which are highly crafted and much anticipated. One of the most dramatic parts of the Rosh Hashanah service is the blowing of the shofar.
The liturgy for the second day of Rosh Hashanah is largely a repetition of the first, with a different sermon, and often different Torah readers. If the first day of Rosh Hashanah falls on Shabbat, tashlich is performed on the second day, as is the sounding of the shofar.
The Ten Days
Rosh Hashanah and Yom Kippur begin and end a ten-day period of reflection and repentance, in Hebrew, teshuvah, which literally means "turning." The Sabbath between the two holidays is called Shabbat Shuvah, the "Sabbath of turning." In some synagogues, these ten days are observed with special services and/or with an ethical will–writing workshop. An ethical will, a form of moral literature that dates back to biblical times, is a personal statement of beliefs, hopes, and advice. A counterpart to a legal will that distributes material goods after a person's death, the ethical will is a way of communicating the values and insights of a lifetime to loved ones. After reading and discussing examples of ethical wills, participants at these workshops sit with pen and paper and write their own. People who have done this say it is a powerfully clarifying exercise, and wonderful preparation for Yom Kippur. Ethical wills are usually stored with legal wills and other important personal documents, and some congregations keep copies on file.
Making Yom Kippur
At Home
Yom Kippur is called Shabbat Shabbaton, or the "Sabbath of Sabbaths." The meal prior to the start of the daylong fast is not begun with blessings, although a motzi may be said before any meal. However, as with Rosh Hashanah, the meal that precedes Yom Kippur can become a family tradition by virtue of special menus and rituals, such as standing and drinking a glass of water together to end the meal.
After dinner, people who have lost family members light memorial or yahrzeit candles (see the chapter on "Death"). Finally, Yom Kippur candles are lit with the following blessing.
Baruch ata Adonai Eloheynu Melech Ha-olam asher kidshanu b'mitzvotav vitzivanu l'hadlik ner shel (Shabbat v'shel) Yom HaKippurim.
You Abound in Blessings, Adonai Our Lord, You make us holy with commandments and call us to kindle the light of (Shabbat and of) Yom Kippur.
After dinner, some people put a white tablecloth over the table that will remain empty until the following evening.
This is the last meal eaten before healthy adults undertake a complete fast from food and water, which ends the following sunset. Fasting is only the most obvious form of self-denial on the tenth day of the seventh month, which the Torah calls "a day for self-affliction."9 Life's daily pleasures are avoided in order to focus attention upon the task at hand, which is repentance.
Children under the age of 13 are not expected to fast during Yom Kippur, nor is anyone for whom a lack of food or water might cause physical harm. Pregnant and nursing women are forbidden to fast. People who cannot or do not fast, including children, often choose a modified fast, drinking water only, or eating very little. People who undertake a complete fast are often advised to cut back on caffeine consumption several days in advance, since caffeine withdrawal is a common cause of headaches, grouchiness, and other unpleasant symptoms.
Synagogue Observance
Kol Nidre is the evening service for Yom Kippur, named for its dramatic opening prayer. The Kol Nidre prayer is chanted while three people stand, acting as a ceremonial "court," for the text is legal in nature, declaring all unfulfilled vows and promises null and void. The full meaning of this prayer has been the subject of debate for generations, but it clearly addresses the power of words and vows, a recurrent theme in the Yom Kippur liturgy. At least one member of the "court" will hold a white-clad Torah scroll as the haunting melody fills the sanctuary.
The evening service then continues with the stately, somber melodies of the Yom Kippur liturgy and the penitential and confessional language of the Day of Atonement. The communal confession, repeated several times during the holiday, called the viddui, is an alphabetical listing of communal sin that begins, "We abuse, we betray, we are cruel. We destroy, we embitter, we falsify."
Kol Nidre is the only evening service at which people wear prayer shawls, and there are other distinctive customs regarding clothing as well. Some people dress in white, a sign of purity and some even don a bathrobelike white garment called a kittle, which is sometimes worn at the Passover seder or by a groom to his wedding. Some refrain from wearing leather shoes, an ancient symbol of luxury, and others remove their shoes during services and pray barefoot—a universal sign of humility.
In the morning, services continue and last all day long. Not all liberal congregations hold all of the services listed here, nor is the order or content described here universal. Still, this represents the outline of the Yom Kippur liturgy.
Shacharit, the morning service, traditionally includes a Torah reading from Leviticus, which describes the sacrificial rites for Yom Kippur in the Temple. Some congregations choose to substitute another Torah reading, Deuteronomy 29:9–30:20, which ends with the lines "I have put before you this day life and death, blessing and curse. Choose life..." The morning Haftarah reading is Isaiah's passionate sermon demanding justice of the Jewish people.
In some synagogues, musaf, the additional service, is part of Yom Kippur observance, and includes the recitation of the martyrology, a list of atrocities suffered by the Jewish people, beginning with the murders of Talmudic sages by the Romans and including stories from the Holocaust.
The memorial, or yizkor, service is a time for special prayers for the dead. Yizkor is scheduled at different times of the day, depending upon the synagogue's custom: at the end of the morning service, or immediately preceding or following afternoon prayers.
Mincha is the afternoon service, which traditionally includes a reading from the Torah that outlines the laws of incest,10 though this is often replaced with another Torah portion, Leviticus 19, called "the holiness code," which includes the injunction to "love your neighbor as yourself." The Haftarah reading is the Book of Jonah.
Ne'ilah, from the Hebrew "to lock," concludes the day. The name refers to the symbolic closing of heaven's gates and communicates the sense that time is running out. At ne'ilah, the liturgy changes in its references to the Book of Life, as "Write us in the Book of Life" becomes "Seal us in the Book of Life." Many people stand throughout this brief service, which ends with a final shofar blast. In some congregations, ne'ilah is followed by a short evening or ma'ariv service.
The final words of the day come from Havdalah, the ceremony that ends the Sabbath and holidays and which distinguishes between the holy and the profane. As the braided candle is extinguished in wine, a palpable sense of relief fills the room, which empties quickly as people leave to break the fast with family and friends.
A Few Words about Prayer
Prayer is both a discipline and a spontaneous activity. It requires preparation (hachanah) and also a kind of passive receptivity. Sometimes it works. Sometimes it does not. Prayer is not possible for every individual in every synagogue, which is why it is important to find a place where your prayer is a possibility. But even in the most hospitable setting, it can be difficult to sustain prayer for a long period of time. During the long services of Rosh Hashanah and Yom Kippur, there are times when individuals may feel the liturgy is downright hostile to prayer. Repeated references to a King-God, to judgment, and to sin can be offputting. But then, a sentence or a phrase from the prayer book may take your breath away. The challenge is to try to remain open to those flashes of insight, those moments of awe and turning, which are available during the Days of Awe as they are at no other time during the year.
The Hebrew word for prayer, tefila, which can be translated as "self-judging," contains the notion that prayer is not about getting God to do something for you, but is a way of affecting change in yourself, a process of meditation, reflection, and stock-taking.
The Hebrew word for sin is chayt, a term based in archery that means "missing the mark." A sin is thus a missed opportunity for kindness or righteousness. During Rosh Hashanah and especially Yom Kippur, the liturgy's insistence upon human sinfulness can become a reminder of times during the past year when a generous act was not undertaken, or when a kind word was not spoken. Indeed, the liturgy is replete with references to the ways that people hurt one another with words: through slander and insult, with words that embarrass, and words spoken in anger. During the Days of Awe, prayer can be understood as the process of judging one's own language or conduct with others.
Perhaps the best example of the reflexive nature of prayer and sin is the Jewish approach toward atonement. Prayers to God do not wipe away sins committed against other people. The only way to do that is by asking the person you wronged for forgiveness. It is not necessary for the other person to accept the apology—only that the request for forgiveness be offered sincerely. This is what is meant by "making teshuva," which means turning away from your own sin by taking action.
## SUKKOTAND SIMCHAT TORAH
Sukkot only makes sense in that it follows a narrow scrape with death and when it is experienced from inside a sukkah, the flimsy booth we make our literal home for a week. Sukkot is about the kind of happiness that comes from looking through a leafy roof at the sunshine or the starry night and thinking, "I am glad I am alive."
At the very moment we are about to conclude the reading of the Torah, a project that we have worked on relentlessly and religiously for the past year, we grab another Torah scroll and lay it down and, without so much as a pause, start again. Simchat Torah means that learning never stops, and it contains one of the fundamental insights of the Jews: "How can I be sad, how can I despair, if there is something more to learn, something more to know?"
RABBI LAWRENCE KUSHNER11
Where Rosh Hashanah and Yom Kippur are intellectual and reflective, Sukkot (literally, "huts" or "booths") and Simchat Torah ("joy of the Torah") are sensual and expansive. Five days after the austere Days of Awe comes a festival cycle that celebrates pleasures and the senses: the joy of being human.
Sukkot is a seven-day (for some, eight-day) festival described three separate times in the Torah.12 It celebrates the end of the growing season and the harvest. The primary symbol of Sukkot is the sukkah: a flimsy, temporary hut, reminiscent of the structures the ancient Israelites constructed near ripened crops during harvest time, and a symbol of life's fragility. In many ways, Sukkot is the autumnal mirror image of Passover. Not only are both week-long festivals that begin at the full moon and involve a great deal of preparation, but the huts of Sukkot are also reminders of the shelters used during the years of wandering in the wilderness after the exodus from Egypt.
As Sukkot ends, another holiday begins. Shmini Atzeret, the Eighth Day of Assembly, is also ordained by the Torah and celebrated with a special synagogue service that features a prayer for rain, reflecting agricultural needs in the land of Israel. In contemporary times, this observance is all but eclipsed by the holiday that falls on the very next day: Simchat Torah. When the Torah reading cycle was established during the 11th century, Simchat Torah became the ninth day of the autumn holiday cycle, celebrating both the completion and beginning of a year's Torah reading. Shmini Atzeret and Simchat Torah are combined and celebrated as one in Israel and by some liberal Jews. The official name for the combined holiday is Atzeret HaTorah, "the Assembly of the Torah," but is usually referred to as Simchat Torah.
Simchat Torah is celebrated with the kind of happiness and enthusiasm associated with Jewish weddings. The last of the autumn holidays—the end of three intense weeks—Simchat Torah closes the circle on a triumphant and joyful note.
Preparation
The biggest part of preparing for Sukkot is building a sukkah, the booth or hut in which Jews are supposed to live during the festival. According to tradition, the first nail is driven into the sukkah as soon as Yom Kippur ends, even before breaking the fast.
A sukkah is a temporary structure and can be made in any number of ways: as a kind of tent, as a lean-to built against the wall of a house, as a freestanding hut. Sukkot (the plural of sukkah) have been constructed out of all kinds of materials, including bamboo, Plexiglas, aluminum poles, and lumberyard two-by-fours. Walls can be filled in with colorful fabric, old doors, canvas, pieces of plywood paneling, or just about any other material. Kits and prefabricated models are widely available on the Internet (keywords: sukkah or sukkah kit).
The most important element of the sukkah is the roof, which is supposed to be dense enough to provide shade from the sun, but not solid enough to obscure starlight. The material called for in covering the sukkah is called s'khach, which is anything that once grew but has been cut, such as evergreen boughs, bamboo, palm branches, and cornstalks.
Inside the sukkah, it is customary to decorate with hanging fruits, dried gourds, leaves, and other harvest-type items, which are often hung from the rafters. Posters, paper chains, paper flowers, dolls, toys, and Rosh Hashanah cards may be used to festoon the walls.
If you are not able to construct a real sukkah, you can still get into the spirit of the holiday by buying and making special Sukkot decorations for the house and table. A sukkah-like canopy can even be raised over the dining room table for a week. Another way to celebrate the harvest is to go pick apples, pumpkins, gourds, and other fall fruits.
There are two other central symbols of Sukkot; the etrog, a lemonlike fruit, and the lulav, a green bouquet consisting of a palm frond and myrtle and willow branches. These are used in an ancient ritual performed inside the sukkah and also during synagogue Sukkot services, described below. Judaica shops stock etrogim and lulavim in advance of the holiday and many synagogues order them for their congregations. Shopping for the "best" lulav and the "perfect" etrog is an ancient obsession, and suggests a family outing.
Simchat Torah is much more a synagogue-based holiday than Sukkot, so there tends to be far less home preparation, though some families make flags and banners for the festive processions held in the synagogue. Another art project entails making a child-size Torah, using two dowels and a long sheet of paper, decorated with original renderings of various Bible stories.
To get ready for Simchat Torah, take a close look at a Torah, especially if you have never had the chance to see one. This is relatively easy to arrange by making an appointment with your synagogue's rabbi, cantor, religious school director, or just someone who is comfortable handling the scroll.
Study
In addition to the Torah readings prescribed for the holidays, the traditional text for study at this time of year is the Book of Ecclesiastes, best known for its poetic listing of the seasons of life: "A time to plant and a time to uproot, a time for tearing down and time for building up." As is often the case, the reason why this particular book of the Bible is studied at this season is unclear, which makes a good starting point for discussion. Since the Torah is the focus of Simchat Torah, studying a commentary about the Torah seems most appropriate.
Tzedakah
Sukkot celebrates the harvest of this season in anticipation of the day our harvest will feed everyone on earth; thus it is customary to send money to programs that feed the poor and hungry. Connections between Sukkot and current concerns about ecology, environment, and land use also suggest donations to projects that help foster agriculture in poor countries.
In honor of Simchat Torah, donations to literacy programs and libraries seem especially appropriate.
Making Sukkot
Building and decorating a sukkah is a big, engaging project, but the point of building one is to have fun in it. While tradition encourages living inside a sukkah, in practice the major activity that takes place inside these little huts is eating. The sukkah becomes an al fresco dining room—and more.
Sukkot begins with the yontif seder, inside a sukkah if possible. In addition to the candles, wine, bread, and the blessing for the new season, there is an additional blessing.
Baruch ata Adonai Eloheynu Melech Ha-olam asher kid'shanu b'mitzvotav vitzivanu leyshev ba-sukkah.
You Abound in Blessings, Adonai Our Lord, You make us holy with commandments and call us to dwell in the sukkah.
There is no one dish or menu associated with the Sukkot meal in Ashkenazi tradition, though harvest foods seem appropriate. It is a good holiday for beginning a family food tradition, and since it is a meal of thanksgiving, some people serve their first roast turkey or pumpkin pie of the autumn, and have their first taste of fresh apple cider in the sukkah.
* * *
Recall, O Israel, our wanderings,
When life was harsh and insecure.
When cold winds blew,
The stars our only comfort.
May our lives be as upright as the palm,
The coming year as the sweet scent of the etrog.
VETAHER LIBENU, PRAYER BOOK OF CONGREGATION
BETH OF THE SUDBURY RIVER VALLEY, MASS.
* * *
A sukkah is an opportunity and an excuse for a seven-day picnic. A week of family breakfasts, solitary lunches, and informal dinners out of doors is a wonderful way to enjoy the waning light of the autumn—something to share with family and friends.
Sukkot is a holiday that has always been associated with hospitality. According to a mystical story, the spirits of different biblical ancestors visit each day: Abraham and Sarah, Isaac and Rebecca, Jacob and Rachel, Joseph and Leah, Moses and Miriam, Aaron and Abigail, David and Esther. Sephardic Jews set aside a special chair for these guests. But the sukkah is a natural venue for gatherings of flesh-and-blood guests, too. You can host a party to help decorate the sukkah, to share the first-night festivities, and to celebrate Shabbat. Some families try to have guests for dinner every night, or hold an annual "open sukkah" on a weekend afternoon.
A sukkah is not only a place for eating, though. It is also a place to sit quietly with a book and a cup of tea, to read aloud and study with friends, to sing, to tell stories and stay up late talking, to set up cots and sleeping bags and look up at the stars. For children lucky enough to do it, sleeping in the sukkah becomes a wonderful memory.
Not everyone is able or wants to build a sukkah and there are other ways to enjoy its unique pleasures. One is to visit friends' sukkot; the other is to make use of your synagogue's sukkah. Most congregations build a communal sukkah and hold services and potluck meals in it; these may also be available for members who wish to have a family or havurah meal there.
If you and your children can't build your own sukkah outside, consider making one out of an empty appliance box and creating a miniature version for indoors. A tabletop sukkah (made out of a shoe box, for example) can be used as a centerpiece throughout the festival.
Synagogue Observance
Holiday services are held on the first (and in some congregations the second) days of Sukkot. There are a few changes in the liturgy, but most striking are the rituals involving the lulav and etrog. The bouquet of tree leaves and the citron are ancient symbols of the harvest, possibly associated with some agricultural fertility rite. Over the centuries they have been given many religious interpretations: symbols of the parts of the human body, elements of the Jewish people, the male and female parts of creation.13 As a blessing is said, everyone who owns a lulav and etrog holds them close together and then waves them in six directions demonstrating that God is everywhere: to the four points of the compass, skyward and earthward. Then, people—especially children—parade around the sanctuary, holding lulavim and etrogim aloft as they walk.
Making Simchat Torah
Simchat Torah begins at home with a yontif seder: candles, wine, bread, and a blessing for the season. During the Simchat Torah evening service, all the Torah scrolls are removed from the ark and paraded around the sanctuary in circles called hakafot. It is considered an honor to carry the Torah, and in some congregations virtually everyone gets the opportunity.
The Hasidic model of celebration for Simchat Torah has inspired spontaneous and joyful observances in many American congregations. Live music, champagne, dancing, and singing may be part of these celebrations, which sometimes even spill out into the street. In some temples, a Torah scroll is completely unfurled in a huge circle, enacting the full cycle of the year, from the final reading from Deuteronomy to the beginning of Genesis.
The mood of Simchat Torah resembles the joyful feeling at a wedding. Indeed, it is customary to call the person honored with reading the last portion of Deuteronomy "the bridegroom (or bride) of the Torah." The person who reads from Genesis is "the bride (or bridegroom) of the Beginning."
At morning services on Simchat Torah, some synagogues call the children up to the Torah, and sometimes a large prayer shawl is draped over their heads for a special blessing. Simchat Torah has also become the occasion for ceremonially welcoming children to religious school with a gift of a mini–prayer shawl, toy Torah, or prayer book.
* * *
Here where the end embraces the beginning, Like the eternal bride and bridegroom joined as one, Rejoice!
VETAHER LIBENU
* * *
## HANNUKAH
We watch the days grow shorter and shorter. We become frightened because it occurs to us that if this keeps up we will all freeze to death in the dark. We light candles in a transparently symbolic attempt to get somebody up there to notice and turn on the lights. We are literally whistling in the dark.
RABBI LAWRENCE KUSHNER14
Hannukah falls on the darkest phase of the moon in the darkest season of the year, the 25th day of Kislev. An intimate holiday, it is defined by the circle of light cast by little, colored candles arranged in rows that recalls two very different stories, one of which rests on a military victory, one which involves a miracle. But at its emotional core, Hannukah—like the other holidays of the season—celebrates the return of the light in the heart of winter darkness.
The historical basis for Hanukkah (from the Hebrew word for "dedication") is found in the Books of Maccabees, part of the Apocrypha, a collection of ancient writings not included in the Hebrew Bible. During the second century B.C.E., Antiochus Epiphanes of Syria and ruler of the land of Israel began a process of Hellenization that included persecutions of anyone who continued to practice Judaism. Antiochus ordered the desecration of the Temple in Jerusalem and the killing of those who opposed him. The Jewish guerrilla rebellion against this oppression was led by Mattathias Maccabee and his five sons, who defeated the Syrian forces and rededicated the Temple in 164 B.C.E. with an eight-day celebration.15
Although the rabbis who codified Jewish law and practice in the Talmud were disturbed by the prospect of a holiday that celebrated a military victory, it was clear that the people were not about to give up their midwinter celebration of lights and merrymaking. Thus, the story of the miracle of the oil became the preferred justification for the lighting of candles, a custom that was probably borrowed from pagan solstice celebrations.
According to this story, the Maccabees found a single jar of consecrated oil, which was used to keep the Eternal Flame alight in the Temple. There was only enough oil to last for one day, but lo and behold, the oil lasted for eight days. With the addition of this miracle, God became a central part of Hannukah's message of redemption.
Preparing
Hannukah celebration can be elaborate or simple, depending on your tastes and family constellation. It can entail little more than buying a box of candles and polishing your Hannukah menorah, or hannukiah. For many, Hannukah is a wonderful pretext for a midwinter celebration complete with home decorations, special meals and parties, and gift-giving. The eight-branched hannukiah is the primary symbol of the holiday. Judaica vendors carry a dizzying array of these, ranging from fine art to happy kitsch. Making hannukiot (the plural of hannukiah) is a favorite school and home art project for children.
Some people decorate for Hannukah by hanging banners, draydls, gold coins, and lights. A shopping trip for a box of Hannukah candles and some new draydls (Hannukah tops) is a great way to kick off the holiday.
Study
In addition to the Books of Maccabees, traditional study texts for this holiday include two more stories found in the Apocrypha, both rather bloody tales of heroic women: Judith, a widow who killed a general leading a siege against the land of Judah; and Hannah, the mother of seven sons who died with them rather than bow to a pagan idol. And every year, Hannukah inspires new Jewish children's books and songs. Jewish popular culture has also embraced the holiday with new music, humor, and parties at clubs as well as JCCs.
Tzedakah
At Hannukah, which celebrates a Jewish victory over religious persecution, some people make contributions to organizations that work for religious and political freedom for Jews and for all oppressed people.
Making Hannukah
Hannukah is one of the most home-based of the Jewish holidays. Anytime after sunset when family members and guests are assembled to light the hannukiah, you begin by lighting the shamash or helper candle, which is usually taller or set apart from the other lights; the shamash is then used to light the others. A hannukiah is filled from right to left, but lit left to right, so the newest candle is always kindled first.
Any number of hannukiot can be lit. In some households, everyone has his or her own hannukiah, and on nights when guests are invited they can be asked to bring menorahs and candles, too, so dozens of flames can be kindled. According to custom, the Hannukah lights are set in a prominent window, publicly announcing this is a house where Hannukah is celebrated, and making the night that much brighter.
On Shabbat, Hannukah candles are lit before the Sabbath lights.
Every night of the festival, two blessings are recited.
Baruch ata Adonai Eloheynu Melech Ha-olam asher kid'shanu be'mitzvotav vitzivanu l'hadlik ner shel Hannukah.
You Abound in Blessings, Adonai Our Lord, You make us holy with commandments and call us to light the Hannukah lights.
Baruch ata Adonai Eloheynu Melech Ha-olam sh'asa nissim laa'voteynu bayamim hahem bazman hazeh.
You Abound in Blessings, Adonai Our Lord, You performed miracles for our ancestors in days of old, at this season.
On the first night only, a third blessing, the shehecheyanu, is added.
Baruch ata Adonai Eloheynu Melech Ha-olam shehecheyanu v'kiamanu v'higianu lazman hazeh.
You Abound in Blessings, Adonai Our Lord, You have kept us alive, You have sustained us, You have brought us to this moment.
It is customary to sing "Maoz Tzur," "Rock of Ages," immediately after the blessings, and to add other Hannukah songs.
The custom of giving Hannukah gelt (Yiddish for money)—gold coins or chocolate coins wrapped in gold foil—dates back to 17th century Poland. As Jews came into closer contact with Christians and Christmas, since the 19th century, Hannukah has also meant gift-giving.
The extreme commercialization of Christmas and Hannukah drives many people of both faiths crazy. Because it is the business of America to raise every consumer's gift expectations to dizzying heights, many parents devise strategies to keep Hannukah from becoming an eight-day festival of greed, such as designating "book night," or "music night." Some households create a sort of rotating "designated gift-giver" routine, which can be modified to suit any number of people. For example: On night number one, Mom gives the gifts. On night number two, sister distributes presents. Night number three is for Dad. Four is for brother. Five is for gifts from maternal grandparents. Six for paternal grandparents. Seven is for throwing or attending a party, so no gifts are exchanged. And the last night is devoted to tzedakah, when everyone in the household puts aside some money and decides on an appropriate organization, agency, or cause with which to share the season's bounty.
Traditional Hannukah foods tend to recall the story of the miracle of the oil with an unswerving devotion to fried foods. For Ashkenazi Jews, Hannukah means potato pancakes, latkes, served with applesauce and sour cream. In Israel, jelly doughnuts, called sufganiot, are the official holiday treat.
Hannukah is celebrated with parties, which can be held on any and all of the eight nights. After candle lighting, there is singing, eating, and even gambling either with cards or with draydls (sivivon in Hebrew), four-sided tops. Although Jewish law is extremely hostile to gambling—the rabbis reasoned that a transfer of money in the absence of honest work was a form of theft—at Hanukkah, the ban is lifted and people are encouraged to enjoy themselves.
* * *
I have a little draydl
I make it out of clay
And when it's dry and ready
Then draydl I shall play.
HANNUKAH SONG
* * *
To play draydl, a game of dumb luck, each player antes up with nuts or chocolate coins, buttons or pennies. Each of the draydl's sides bears a Hebrew letter. If the draydl falls on (Nun), you get nothing; on (Hay), take half the pot, on (Shin), add something to the kitty, and on C (Gimel), the winner takes all. The letters are an acrostic for the words —Nes Gadol Haya Sham, "A great miracle happened there." (In Israel, the letters spell out —Nes Gadol Haya Po, "A great miracle happened here.") The truth is, playing draydl is only slightly less tedious than frying potato pancakes. But little kids just love it. To play the "human draydl" game, children spin till they drop and the last one standing wins a prize.
While Hannukah is by and large a home-centered holiday, it is also celebrated in synagogues with dinners, concerts, family parties, and the like.
About Christmas
The proximity of Hannukah and Christmas can raise questions and issues for Jewish and intermarried families, partly because Christmas makes many Jews extremely defensive. For one thing, it is the time of year when Jews most acutely feel their differentness in a Christian culture. It is also the season when children confront that sense of being different for the first time, and at successive developmental stages every year. Christmas is when children ask their parents to explain why they are not allowed to take part in the dazzling festival that apparently everyone else gets to enjoy.
Interfaith families may find themselves fighting a symbolic battle over the Christmas tree. To the non-Jewish partner of an intermarriage, the tree may be nothing but a secular symbol of the winter solstice. However, to the Jew, it is a symbol of Christianity, with nearly as much religious meaning as the cross itself. Synagogues run workshops at this season to help couples sort out their differences and learn from each other's choices.
Families deal with the Christmas–Hannukah conundrum in very different ways. For many, Christmas is simply a holiday celebrated in other people's homes—a holiday to enjoy with non-Jewish friends or at Grandma's house, but not in our Jewish home. At the other end of the spectrum, there are households where there is a tree "for Dad."
Some Jews feel the need to compensate for a lack of Christmas by making Hannukah its equal in expectations and gift-giving ("They have only one day of giving; we have eight!"). Others resent that tactic, and, citing the relative unimportance of Hannukah in the Jewish calendar of holidays, try to make as little fuss over it as possible. There is a middle ground.
Hannukah can be celebrated with candles, stories, tzedakah, gatherings of family and friends, crafts, and gifts, without collapsing under the strain of Christmas expectations. The Jewish calendar has often accommodated itself to historical change, and making Hannukah into a bigger party than it was in past centuries does not nullify its Jewishness.
However, for Hannukah to retain its integrity, it cannot stand alone. If Hannukah is the only Jewish celebration of a family's year, then it does become that strange creature, the "Jewish Christmas." The truth is, no matter how many candles are lit or expensive gifts are given, Hannukah will never be as big, flashy, and seductive as Christmas; however, if it is just one of many joyful Jewish celebrations, it has no need to compete. Perhaps the best explanation of the differences between the two winter holidays comes from the mouth of a three-year-old, who said, "Christine and Zack have Christmas. We have Hannukah and Shabbat."
## TU B'SHVAT
Two men who were fighting over a piece of land brought their dispute to a rabbi. After listening to each man's case, the rabbi put his ear to the ground. After a moment he stood up and said, "The land says that it belongs to neither of you. You both belong to the land."
TALMUD
Once a minor observance, Tu B'Shvat is in the process of becoming a more important Jewish celebration complete with its own seder, the most positive celebration word in the Jewish lexicon.
Tu B'Shvat, which means the 15th of Shvat, is not mentioned in the Torah (nor are Hanukkah, Purim, Tisha B'Av, or Simchat Torah). And while the Talmud describes it as "the New Year of the Trees," it mandates no rituals, no blessings, no synagogue observance. Tu B'Shvat may have been noted simply as a way of dating trees, so it would be possible to know when a fruit tree was old enough to be tithed—or when 10 percent of the fruit crop was due to the Temple priesthood. Historically, Tu B'Shvat was a way of maintaining a connection with the land of Israel, where, in the month of Shvat, the winter rains end and the first signs of spring begin. In that hot, arid climate, trees mean food, shade, water—indeed, life itself.
Among Ashkenazi Jews, Tu B'Shvat was observed by eating fruit, especially fruits grown in the land of Israel. Because it traveled well, carob (also known as bosker or St. John's bread) became the traditional food of the holiday. While it was never a major holiday for Sephardic Jews either, they celebrate Tu B'Shvat with more festivity, including readings from a book called The Fruit of the Goodly Tree, and with special fruit platter meals, songs, and games for children.16 After the founding of the state of Israel, Tu B'Shvat became a sort of international Jewish Arbor Day, a day for planting seeds in paper cups at religious school, and for raising money for the Jewish National Fund, which supports the reforestation of Israel.
The modern focus for Tu B'Shvat broadened to include the relationship between people and the natural world—the ecology of the planet upon which we depend for our lives. In Jewish tradition, the primary symbol of this relationship is the tree. The Torah itself is called a tree of life, and the rollers around which the scroll is wrapped are also called trees of life—atzay hayyim. The planting of trees was seen as a holy activity. According to Jochanan ben Zakkai, "If you have a seedling in your hand, and someone says to you, 'Look, here comes the Messiah!' go and plant the seedling first, and then come out to meet the Messiah."17 The Torah forbids the cutting down of an enemy's fruit trees in times of war, even if trees are needed for the siege of a city.18 The confluence of the traditional concern for trees and contemporary worries about the health of the earth's forests, fields, air, and seas created renewed interest in this midwinter holiday and the Tu B'Shvat seder. A once-arcane custom, celebrated by a group of mystics living in the town of Safed during the 16th century, it was modeled after the Passover talking-feast and its four cups of wine, but added the eating of four categories of fruit, which corresponded with the four "emanations" of God.19
Preparing
Hosting or participating in a Tu B'Shvat seder means shopping for fruit and wine and decorating with greens and flowers. There are all sorts of delightful arts-and-crafts projects for children, such as making a tzedakah box in the shape of a watering can, or creating a forest of trees out of recycled cardboard paper towel tubes, or decorating cups for planting parsley seeds to be harvested for use in the Passover seder.
To get into the spirit of the growing season, people peruse seed catalogs and select flowers for the coming spring. Other family activities might include visiting a botanical garden or even making a tour of your yard to see whether any of the trees need attention. Since Tu B'Shvat is called the New Year of the Trees, one rabbi even suggests blowing a shofar for your own trees.20
Study might include reading more about the holiday's history, and reading through a Tu B'Shvat seder or two. The ecological aspect of the holiday suggests study of environmental problems and solutions.
Tzedakah
The most common tzedakah custom for the holiday is to donate money to the Jewish National Fund, which not only plants trees in Israel, but also works to protect the environment there (www.jnf.org). There is also an old tradition of giving money for fruit, ma'ot perot, to the poor, so they could afford a taste of fruit from Israel on Tu B'Shvat. In that spirit, making a contribution to a food program seems appropriate. Some people make donations at this season to national and international organizations dedicated to protecting the environment. For more information about Jewish environmental activism in the United States, check out the Coalition on the Environment and Jewish Life (www.coejl.org).
Making Tu B'Shvat
Tu B'Shvat is a holiday in the making, so there are no formal or standard home or synagogue rituals associated with the holiday. The Tu B'Shvat seder takes many forms depending upon who is in charge. Synagogues, havurot, and individuals host them, and there are several haggadot (plural of haggadah, which means "the telling") for the holiday, including many photocopied collections of readings that are rewritten and updated annually. A few have been published by the denominations; check their Web sites.
Feel free to experiment with the Tu B'Shvat seder; there is no doing it "wrong." When it is built around a meal, the food is vegetarian with readings, poems, and songs built around two ritual acts: the drinking of four cups of wine and the eating of four kinds of fruits.
The four cups of wine can change in color, starting with white, proceeding to mixtures of white and red, and concluding with red wine. The same blessing is recited before each cup.
Baruch ata Adonai Eloheynu Melech Ha-olam boray pree hagafen.
You Abound in Blessings, Adonai Our Lord, You create the fruit of the vine.
For the fruit, set out festive platters with as many varieties as possible. One custom is to get 15 kinds of fruit to correspond with the 15th of Shvat; these are then divided into four categories, according to a metaphorical association with the elements, or seasons, or human characteristics. One level consists of fruits with a hard outside and soft inside—nuts, pineapple, pomegranate, and coconut—which may be associated with winter, with the earth, with the physical. The second level includes fruits with a soft outside and hard inner core: cherry, peach, and avocado, which may be associated with spring, with water, with the emotions. The third category comprises fruits that are totally edible: strawberry, fig, grape, raisin, which may be associated with summer, with the air, and with the cerebral. The fourth category is the most abstract and spiritual and is sometimes symbolized by inedible fruits, such as pinecones and acorns, or else it is given no physical representation at all.
The same blessing is recited before eating from each category of fruit.
Baruch ata Adonai Eloheynu Melech Ha-olam boray pree ha-aytz.
You Abound in Blessings, Adonai Our Lord, You create the fruit of the tree.
## PURIM
Purim elevates laughter to a religious category. It is the one day when taking oneself seriously is a sin. At Purim, we make fun of everything, especially what we consider to be most sacred and reverent. Because religion without humor is blasphemy.
RABBI LAWRENCE KUSHNER21
Purim is the Jewish equivalent of Mardi Gras, a giddy outburst of energy and excess. This holiday of the early spring (on the 14th of Adar, which falls near the vernal equinox), celebrates a narrow escape from a disaster that probably never happened and takes its name from the Hebrew word pur, which means "lot," as in lottery. In the Purim story, the villains cast lots to determine a date for the slaughter of the Jews. The biblical Book of Esther is bawdy and improbable, but its ironic and dark subtext has struck a chord for hundreds of generations among a people that has suffered and survived terrible persecutions and losses.
According to the Purim tale, a large and prosperous Jewish community once lived in the land of Persia. The Jews were so well integrated into the society that one of them, Mordechai, was a member of the court of the king, Ahasuerus. One day, this feckless king banishes his wife, Vashti, for refusing to obey a command to appear naked before his guests. To replace her, he holds a beauty contest, which is won by Esther, a Jewish woman who only just happens to be Mordechai's relative.
As this Cinderella tale unfolds, a new Grand Vizier is appointed, a dreadful anti-Semite by the name of Haman. Indeed, Haman is considered a prototype of evil, descended as he is, from the wicked Amalek, the archetypal enemy of the Jews described in the Torah.22 When Mordechai refuses to bow down before this wretched man, Haman decides to punish him by massacring all the Jews in the kingdom.
Mordechai and Esther conspire to foil this plot by having Esther invite King Ahasuerus to her chambers, where she wines and dines him, and then reveals that Haman, despite all his fawning, is actually plotting against his royal highness. She also reveals herself to be a Jew, and asks that he rescind Haman's decree against her and her people. The king has Haman hanged on the scaffold that had been built for Mordechai, who is named Grand Vizier in his place. And as the sun sets, Esther and the Jews of Persia live happily ever after.
The name of God does not appear anywhere in this melodrama, which is probably based on a Persian legend given the fact that the names of its heroes—Esther and Mordechai—are forms of two well-known local deities, fertile Ishtar and warlike Marduk. Furthermore, Purim celebrations—typified by masks, revelry, and drunkenness—recall ancient Persian customs for a springtime new year.
* * *
Why is it pointless to put Jews in jail?
They eat lox!
* * *
Purim observance has changed over time, and customs vary from nation to city to synagogue. Nevertheless, it is the universal Jewish holiday of release, springtime, laughter, and excess. On Purim, it is a religious obligation to poke fun at Jewish tradition, and piety takes the form of jokes, puns, drinking, cross-dressing, and outrageous behavior in general. According to the Talmud, Purim is the only holiday that will still be celebrated after the Messiah comes to redeem the world and restore peace and harmony. Evidently, even in paradise it will still be necessary to make fun of ourselves.
Preparing
Purim is celebrated in synagogues and schools, but since one of the customs of the holiday involves dress-up, adults as well as children spend time on costumes, which can be either beautiful, silly, or outrageous and may include masks, wigs, and makeup. If you're attending a megillah reading or Purimspeil (Purim play), you'll need a gragger, too—a noise-maker used to drown out the name of Haman. These are available for purchase in Judaica stores and online.
The tradition of giving gifts to friends and to the poor is mandated in the Book of Esther, which says, "the Jews...made the 14th day of the month of Adar a day of gladness and feasting, a holiday, and of sending portions to one another (mishloach manot)." Thus, some Jews deliver gifts of food to friends, a paper plate or bag filled with Hamantaschen (a three-cornered cookie), along with fruit, and candy made in Israel. Baking cookies and assembling and decorating plates or bags is a Purim custom in some congregations and families.
Tzedakah
Giving to the poor on Purim is a mitzvah called mattanot le-evyonim, and reflects the notion everyone should be able to celebrate. In some congregations, money is collected for tzedakah in the synagogue before the Purim story is read. Responding to the command in the Book of Esther that two portions be sent to the poor, some people make contributions to two charities.
Making Purim
The only home ritual associated with Purim is the Purim seudah, or Purim feast. Unlike all other holiday meals, which are eaten in the evening, this feast is generally a lunch that features merrymaking, nonsense, and silliness. Putting on a Purimspiel is often part of this celebration, the more foolish the better. However, since there is no obligation to refrain from work on Purim, this feast usually only happens on weekends.
Among Jews of Eastern European descent, the traditional food for Purim is a three-cornered pastry called Hamentaschen, "Haman's pockets," a delicacy that has been part of Purim celebration since at least the 12th century. Sephardic cooks make Purim ravioli and a deep-fried confection called Haman's ears.
Synagogue Observance
The only religious obligation is that everyone—adults and children—hear a reading of the Book of Esther, which is called the megillah, or "scroll." While there are four other scrolls or megillot in the Bible (Song of Songs, Lamentations, Ruth, and Ecclesiastes), the Book of Esther is known as the megillah.
After the evening service, the ten chapters of the megillah are chanted aloud, often in an abbreviated, hilarious performance. Sometimes the story is acted out by costumed players and audience participation is required; whenever the villain's name is mentioned, boos, hisses, catcalls, and the rude sound of noisemakers (whistles, drums and bells, as well as the traditional graggers) erupt as the audience does its duty and "stamps out" Haman's name.
"Purim Torah" is the name given to the sacred duty to make fun of all things sacred on this holiday. Rabbis dress up like furry blue monsters and deliver absurd Purim sermons, synagogue newsletters are full of ridiculous articles and advertisements, and even the evening service that precedes the reading of the megillah is fair game, as traditional prayers are sung to the melody of "Home on the Range," or "I Want to Hold Your Hand."
Synagogues celebrate Purim with costume parties, parades, dances, theatrical offerings (Purimspiels), carnivals, beauty contests, and fairs. Gambling, forbidden every other day except Hannukah, is permitted on Purim. Drinking is not only permitted, but encouraged to the extent that the Talmud says that Purim obliges every Jew to get so drunk that he or she cannot tell the difference between blessing Mordechai and cursing Haman.23 Which is mighty drunk. In Israel, Purim is marked by a raucous parade called the adloyada, a word based on the Hebrew for "not being able to tell the difference."
## PASSOVER
The liturgy of the seder meal is a way of responding to the question, "Why?" The answer to all of the questions asked at the Passover seder begin with the words, avadim hayinu, "because we were slaves." Through song, word, and symbol we not only remember that we were slaves but also reexperience ourselves as slaves. And we learn that our freedom, if it does not translate into making others free, is a sham.
RABBI LAWRENCE KUSHNER24
No holiday in the Jewish calendar is more complex or evocative than Passover. The spring holiday that celebrates the return of the sunlight and the first spring fruits on the table, also reflects upon the profound religious themes of the autumn festivals: awakening, life and death, rebirth, gratitude. Passover recalls the crucial event in the history of the Jewish people in which a group of slaves became a nation possessed of the dream called Torah.
No other holiday inspires the same kind of loyalty as Passover. No Jewish ritual word has more positive associations than seder, the Passover talking-feast. It is—according to some demographers—the most practiced of all Jewish observances, even more common than the lighting of Hannukah candles. Passover memories—the holiday table, the crunch of matzah, songs, phrases, aromas—have inspired a kind of collective unconscious that recognizes the seder as the Jewish celebration.
Passover can also be the most demanding of the Jewish holidays because it requires a drastic change of diet during its weeklong observance. The Bible forbids not only eating but even owning leavened foods, as a reminder of the time when the Jews were a hunted people who did not have even enough time to wait for dough to rise before baking it. The Talmud elaborated the biblical injunction against leavened food into an entire system for breaking from the normal eating routines of the year. Homes and habits are turned upside down in order to help reenact the essential religious insights of Judaism: that once we were slaves and now we are free; that political liberation and personal change are both necessary for the redemption of the world, a world in which all forms of slavery are forever abolished.25
Called the Festival of Spring, the Season of Our Liberation, the Holiday of Matzah, the name Pesach, or Passover, comes from the most dramatic story in Jewish history. On the night of the last plague that God unleashed upon the Egyptians to force Pharaoh to free the enslaved Israelites, the Jews were told to sacrifice a lamb and mark their homes by smearing their doorposts with its blood. According to the story, the angel of death stopped in all the unmarked houses, taking the firstborn of every family. But wherever Death saw the blood of the animal that the pagan Egyptians worshipped as a god, Death passed over—in Hebrew, pasach.
For this fragment to make sense, the rest of the story must be told, too: the history of how the Jews came to Egypt, the story of Moses, of the resistance of the midwives, and much more. This is both the method and the message of Passover: to tell the story so vividly that it becomes part of memory and consciousness from one generation to the next.26
Preparing
No other holiday requires more preparation than Passover, or more choices. Thus, no two households prepare for Passover in the same fashion, and no two seders are quite the same. The menu of Passover customs is endless and always changing, but regardless of specifics, preparations may be divided into two general areas: getting ready for the seder, and preparing for a week of doing without bread and other leavened foods.
Seder, literally "order," is the meal held on the first and (for some people) second night of Passover. Patterned on the Greek and Roman symposium, where an evening was spent discussing a particular topic over dinner, the Passover seder has been celebrated since the days of the Second Temple, though the seder that is celebrated by Jews today was essentially set by the 11th century C.E.
Planning for a seder begins sometime after Purim, when people draw up guest lists, look over cookbooks, and choose a haggadah. Haggadah, literally "a telling," is the name of the book that contains the rituals and readings of the Passover seder. Because the haggadah is the script that determines the content of the evening, selecting one that suits your needs is one of the most important aspects of the seder.
Scores of haggadot (the plural) are in use today, in English and Hebrew, with translations and transliterations. Some express contemporary political concerns; some are vividly illustrated; many are annotated, with long footnotes explaining every aspect of the seder. The denominations produce haggadot, as do many Jewish and secular publishers. There are haggadot that feature museum-quality illustrations, and coloring-book haggadot for children. Some people use a number of different haggadot at the seder, comparing and contrasting the variations among them, but most try to purchase or borrow enough copies of the same edition so everyone can follow along together.
A good place to start exploring the options is a synagogue library or other collection of Jewish books. Jewish bookstores usually offer a wide selection. Rabbis, other Jewish professionals, and friends can make helpful suggestions, and synagogues sometimes run a workshop about choosing and using haggadot. Of course, you can also put the word "haggadah" into your favorite search engine and see what you find.
When shopping for a haggadah, it is also important to remember that virtually everyone customizes or edits the seder. Few people read every word in the book, so planning requires deciding which readings to include, which to skip, what songs to sing, and how to encourage participation at the table. In families with children, the seder changes from year to year, reflecting the changing attention span of the little ones. Some people put together their own seders, cutting and pasting, collecting readings, poems, artwork, and songs from various sources to create their own haggadah.
Passover is, first and foremost, a teaching holiday, but it would be a mistake to think of it as a class. The best seders are informal and interactive; according to tradition, if no one asks a question at the seder table, the meal cannot be concluded. The goal is to provide experiential learning so that everyone, but especially children, will actually feel as though they had been liberated themselves. Parents tend to gear at least part of the seder to engage their children's participation, and it's not hard to make Passover an annual high point for the young. (See "Elaborations" below.)
Many haggadot provide basic information about the holiday and how to celebrate it. Some include explanations and brief histories of various readings and ritual items, as well as descriptions and instructions for setting the Passover table and for preparing a seder plate.
The holiday table is never more elaborate than at Passover. While the table is often made festive with spring flowers, the real centerpiece is the seder plate, which contains six ritual items: a shank bone (sometimes a roasted chicken or turkey bone) and a roasted egg, both symbolizing the ritual sacrifices of the Temple; bitter herbs (usually horseradish) and salt water to represent the bitterness of slavery; a green vegetable (parsley, celery, or lettuce) is symbolic of the new season; and haroset (a sweet paste of fruit, wine, and nuts) symbolizing mortar, a reminder of the heavy labor the Israelites were forced to do. In recent years, an orange has been added to the seder plate, as a symbol of the inclusion of once-invisible Jews—gays, lesbians, and women.27
Setting the table and making haroset are tasks children look forward to all year. Other seder plate projects might include harvesting parsley planted at Tu B'Shvat, roasting eggs, and grating fresh horseradish. Arts-and-crafts projects for the table might include making place cards, place mats, napkin rings, or a matzah cover, designing a comic-book haggadah, or creating a seder plate out of a decorated paper covered with clear Contact paper. If the seder includes a dramatization of part of the Exodus story, children can collect and create costumes, masks, or puppets.
Some people bake their own matzah—or at least a symbolic portion for the seder. According to Jewish law, in order to prevent fermentation the matzah must be baked precisely 18 minutes after water is added to flour. Since this is quite an elaborate production, some synagogues run a matzah-baking workshop, which can become a memorable game of "beat the clock."
In planning the seder meal, many cooks stick to family favorites. Roast chicken, turkey, and brisket are among the more popular traditional main courses for Ashkenazi Jews; Sephardic meals often feature roast lamb. Spring foods, such as asparagus and strawberries, recall the seasonal aspect of the holiday. There are many Passover cookbooks on the market, and most Jewish cookbooks have Passover recipes and menus as well. Vegetarian cookbooks are a good resource for planning meatless Passover meals—and there are even vegetarian haggadot.
Preparing for the fast from leavened food is the second major task of getting ready for Passover (the first being the removal of hametz, a term that designates foods that are not "kosher for Passover"). Hametz includes not only leavened foods, but also foods that can easily ferment, such as wheat, malt, and barley. Ashkenazi Jews also refrain from eating beans, peas, lentils, rice, corn, and legumes.
For some families, the days before Passover are taken up with a thorough housecleaning, putting away dishes and cookware, and unpacking china and pots that are used only during the holiday. Children tend to find this process exciting, and it is the source of many powerful memories for adults who grew up with the tradition. In other households, however, dishes and cookware stay the same, and Passover observance is limited to avoiding bread and other leavened foods. Likewise, although some people only buy packaged or processed foods that are specifically designated as "Kosher for Passover," which means they were prepared and packaged under rabbinical supervision, others simply read labels and avoid foods prepared with yeast and other leavening agents. (See also "What Jews Eat.")
Some people try to consume all their leavened foods during the month before Passover. Others put leftovers—including cereals, pasta, beer and other liquors, and prepared foods such as ketchup, many vinegars, and even confectionery sugar (it can contain cornstarch)—in a box or cupboard that is marked and taped or tied shut for the week. Because the Torah says that one should not even own any hametz during Passover, it is customary to ritually "sell" it to a non-Jew for the duration of the holiday. Some synagogues fulfill this mandate, complete with a signed contract, in a transaction that ultimately ends with a donation to charity.
The ritual conclusion of preparing a house for Passover is called Bidikat Hametz, the search for hametz. Pieces of bread may be hidden for a family hide-and-seek, which is traditionally conducted with a candle (it is more fun to do this in the dark) and a feather (for brushing the pieces onto a paper plate). The next morning, it is customary to burn what was found. The Hebrew blessings that precede and follow the search are printed in many haggadot.
On the day of the seder, it is customary to refrain from eating either bread or matzah between breakfast and the evening meal; the purpose of waiting is to sharpen the pleasure of the first taste of matzah.
Study
The primary study text for Passover is the haggadah, but perhaps the best way of putting the Passover story into context is to read the Book of Exodus, which tells the whole story of the departure from Egypt, the wandering in the desert, and the giving of the Torah. Many people also go back to the chapters in Genesis that tell the story of Joseph and explain how the Jews came to be in Egypt in the first place. It is also traditional to read Song of Songs, the biblical cycle of love poems, filled with images of nature and sexuality, and which addresses the agricultural elements of the holiday.
Books about the Jewish holidays can explicate the theological and historical background of the holiday, and in the weeks before Passover synagogues offer seminars or workshops on making a seder. All of which can be a great source of inspiration as well as of basic information.
Tzedakah
Feeding the hungry is a basic theme of the seder, which includes the clarion call "Let all who are hungry come and eat." Traditionally, Jewish communities saw to it that their poor could afford matzah and wine for the holiday. The American Jewish community continues to honor this tradition by giving special attention to the needs of the poor, the elderly, and recent immigrants. Individuals can participate directly in this mitzvah by making room at their seders for people who would otherwise have nowhere to celebrate the holiday, such as Jewish travelers, college students, and people in the military service stationed locally. Furthermore, synagogues often match members in need of an invitation with others who have plenty of room at their tables. It is also customary to give money to programs and agencies that feed the hungry at Passover. Many synagogues and other Jewish organizations collect canned goods and other packaged foods that contain hametz, which are then donated to local food pantries before Passover.
Making Passover
Three core elements of making Passover are: retelling the story, remembering that "we were slaves in Egypt," and not eating hametz. The table rituals, the housecleaning, the special foods, and the family gathering all enhance and celebrate these three elements.
Passover begins at the seder table. While synagogues often hold community seders, and some people attend them at hotels, resorts, or on cruise ships (and thus avoid the lengthy preparations), the Passover seder is one of the most home-identified of all Jewish observances. Family traditions include everything from buying new toothbrushes, to filling the house with daffodils, to closely guarded recipes for Passover cakes, cookies, and candies. The descriptions that follow only suggest the possibilities: they are by no means definitive.
The Seder Table
The Passover table is an altar, a classroom, and a theater as well as a place for eating. The tradition of placing cushions or special pillows on the chairs comes from ancient days; tokens of leisure, they demonstrated that the people at the table were free men and women.
In addition to the seder plate described above, there are a few other ritual objects on the table as well: a plate containing three matzot (plural of matzah) covered by a napkin or special matzah cover; Elijah's cup, a goblet filled with wine, a symbol of hope that the prophet Elijah, the harbinger of the Messiah, will come to announce the redemption of the world this very night; Miriam's cup, filled with water, a relatively new addition to the table, which honors Moses' sister, also a prophet, who leads the women in song after the people have crossed the sea on their way to freedom.
The Order
A classic Jewish contradiction in terms, variation is the rule when it comes to the order of the seder. Some people move things around; others delete some rituals and readings and add others. Some prepare questions to spark discussion; others add singing, dancing, and theatrics. The ceremony can last for twenty minutes, forty minutes, or several hours. Then after the meal, some people spend hours at the table for more readings and songs while others dispense with most or all of the postdinner readings and ritual.
Making a seder means making choices. The outline of the Passover seder that follows is not exhaustive; there are stories and songs not mentioned here that many people consider essential while others may omit elements. It is your table.
The yontif seder described on pages 149–151 is embedded in the Passover seder, but changed in many ways. Some scholars believe that some parts of the Passover ritual exist for the sole purpose of getting children to ask "Why?"
OUTLINE
PART I: INTRODUCTION
Lighting candles.
Kiddush is recited over the first cup of wine.
Shehecheyanu: the prayer for having reached this moment.
Ceremonial hand-washing, but without the traditional blessing.
Karpas: A blessing is recited over the green vegetable, which is then dipped into salt water and tasted by everyone.
Afikomen: This is the name given to the middle of the three matzot on the covered plate. The piece is broken, and the larger part of it is hidden and then ransomed by the children after the meal. Afikomen derives from the Greek word for dessert and the seder cannot end until everyone eats a piece of it.
PART II: TELLING THE STORY
The Maggid: The story. The Passover story begins with the line "This is the bread of slavery which our ancestors ate in Egypt when they were slaves. Let all who are hungry come and eat."
The Four Questions: Customarily asked by the youngest child capable of memorizing the words, the four questions are: Why do we eat matzah? Why do we eat bitter herbs? Why do we dip our vegetables? Why do we recline? (In other words, What are we doing here?)
The Four Sons/Children: A parable about the proper way to answer the Four Questions when asked by different kinds of children: wise, stubborn, simple, and those who do not know to enough ask.
The Ten Plagues: As each of the calamities that befell the Egyptians is recounted, a drop of wine is spilled from every glass. The most common explanation for this practice is that when any human life is lost or diminished, all people suffer, which means our cups of joy are diminished as well.
Dayenu: A song that lists the miracles God performed to free the Jewish people from slavery.
Kiddush: The blessing for the second cup of wine is recited and drunk.
PART III: PRELUDE TO THE MEAL
Ceremonial hand-washing, with the traditional blessing.
Motzi and the blessing over matzah.
Blessing over the bitter herbs.
Hillel sandwich. A mixture of bitter herbs and sweet haroset is prepared on matzah and everyone eats of the bittersweetness.
The meal is served.
PART IV: AFTER DINNER
The afikomen is "bought" back from children, and a piece is eaten by everyone.
Blessings after the meal, birkat hamazon, are sung.
Kiddush: Blessing for the third cup of wine.
The door is opened for the prophet Elijah.
Singing: Traditionally, psalms of praise called hallel.
Kiddush: for the fourth and final cup of wine.
Conclusion: The traditional phrase that ends the seder is L'shana haba-a b'Yerushalayim, "Next year in Jerusalem," a statement expressing the hope that next year all people will be free and none will be enslaved.
Elaborations
The Passover seder has always inspired creativity and innovation. Laughter, enchantment, silliness, and argument are all appropriate to a celebration of the freedom to be fully human. The haggadah says, "To elaborate on the story is praiseworthy." The following examples demonstrate how people elaborate on the story, the haggadah, and the seder. They are offered as inspiration to your own creativity.
The entire seder can be a "potluck" affair. Not only can food courses be assigned to participants, so can sections of the ritual, thus turning the proceedings into a series of surprises, which keeps everyone engaged and eager to find out what will happen next.
A nice way to begin—either before or immediately after candle-lighting—is to invite everyone to share a personal Passover memory, or to talk about what the holiday means to them, or discuss the meaning of "freedom."
To keep people from getting too hungry to enjoy the proceedings, serve a first course of raw and/or cooked vegetables right after the blessing for karpas (green vegetables).
There are many customs around the afikomen. Parents usually hide it, which leads to a children's treasure hunt later in the evening. In order to get the afikomen back, parents pay the winner in coins or treats or prizes. Alternately, older children can hide the afikomen, and make their parents search for it. In some households, pieces of matzah are hidden all over the house, one for each child who will be attending. When all the previously hidden bits of afikomen are found, all the children are given toys.
Giving gifts at Passover is another custom, either as a reward for finding the afikomen, or when the door is opened for Elijah. At that point, a bag of treats might be "discovered" on the doorstep. In some families, an adult dresses up like the prophet and brings in a sack of goodies when the door is flung open.
Elijah's cup is on the table as symbol of hope for redemption and a healed world. Some people put an empty cup in the center of the table and, at some point in the seder, pass it around so that each person can pour a little wine from their own glass into it, symbolizing how each person needs to help "bring Messiah," how everyone must work to bring about a world of peace. Elijah's cup can also be the subject of fun; some people rig the glass to mysteriously drain during the course of the evening, "proving" that he has been present.
The maggid, the telling of the story, offers limitless possibilities. The following suggestions are ways to encourage the sense of personally experiencing the redemption from Egypt:
* Prepare a skit, puppet show, pantomime, musical, or video to recount the story of the exodus from Egypt or some part of it. The story can be scripted and parts can be drawn from a hat (Miriam, Moses, frogs, God, Pharaoh, narrator, etc.). A costume box, masks, and hats heighten the drama.
* Some people have adopted the Sephardic custom of getting up and walking around the table at the point in the story when the Israelites leave Egypt. Similarly, one can play music and dance around the table when the story reaches the moment when the people rejoice at having reached the other side of the Sea of Reeds.
* The plagues have inspired a minor industry, with sacks filled with plastic frogs and bugs. You can make your own plagues with red food coloring (for blood), dolls (death of the firstborn), a burned-out lightbulb (darkness), etc.
* Some people sit in darkness to enact that plague for a few moments, during which everyone names a modern plague: nuclear weapons, AIDS, homelessness, poverty, cancer, racism, anti-Semitism, war.
* Song sheets can encourage everyone to sing. In addition to the traditional Hebrew songs that are printed in many haggadot, consider including folks songs and spirituals such as "If I Had a
* Hammer" and "Go Down, Moses," or any familiar popular songs relevant to the themes of the holiday.
* It's a good idea to aim for a balance between tradition and innovation. Seders should change as children grow more able to participate in grown-up conversation, but there's nothing like consistency to plant precious Passover memories; a beloved poem, a silly joke told at the same juncture in the meal, a favorite recipe served only once a year.
* If adults wish to have a longer, more intellectual seder than their children can sit still for, they can be excused during discussions and some readings from the haggadah. However, at every important "event" of the seder (another cup of wine, the Four Questions, the Hillel sandwich) someone can blow a whistle or bang a drum to summon the kids back.
* Where there are no young children or they have all fallen asleep, the seder can become an opportunity for intellectual and even esoteric discussion of the story and the other elements of the seder. These kinds of meals can go on until past midnight, until everyone is satisfied that they finally understand what it all "really" means—at least for this year.
* Not everyone has such stamina, and by the end of the meal and after four (or more) cups of wine, some people end their seders on a lighter note. One family tradition consists of a tipsy contest for the person with the fastest or funniest performance of the traditional song "Who Knows One?" ("Echad Mi Yodeah," included in most haggadot).
Many people attend two seders, on the first and second nights of Passover. To keep the experience fresh, it's a good idea to differentiate between them: for example, a big group one night, a more intimate gathering the next; emphasis on teaching and entertaining children one night, more grown-up conversation the next, which might mean hiring a sitter for the kids.
The Intermediate Days
The only home observance after the seder and before the final day of Passover is the eating of matzah and the avoidance of hametz. As with the practice of kashrut, the range of observance is broad. Some people simply do not eat bread or other leavened foods, but otherwise make no change in their kitchens and simply tailor their orders at restaurants. Others clean their homes of hametz for the week, with or without a changeover in dishes.
The challenge of cooking without leavening can get tedious as the week goes on, so some people try to plan potluck dinners with family and friends to share recipes and ease the potential monotony of Passover cooking.
Although it is traditional to say the havdalah prayer over wine at the end of Passover, for most people, the holiday tends to just peter out with a stop at a pizzeria or Chinese restaurant. However, Sephardic custom ends the holidays with a feast called Maimuna. Named to honor Maimon ben Joseph, father of the great 12th century rabbi Maimonides, Maimuna is still celebrated with festive, elaborate traditions in communities of Moroccan Jews and in the state of Israel. People wear their finest clothes and eat at tables decorated with flowers and wheat stalks. Traditional Maimuna feasts are meatless, featuring buttermilk, sweets, and special pancakes called muflita. Some individuals and synagogues have adopted the custom as a way to provide a sense of joyful closure to Passover.
Synagogue Observance
Home observance tends to overshadow all other aspects of Passover; however, holiday services are held on the first (and second) days, which the Torah denotes as days of rest; the same goes for the last day (or two). On the last day of Passover, a memorial service is held and the yizkor prayer is recited in memory of loved ones who have died. Some congregations hold a community seder on the first or second night. Extra community seders are often planned on the intermediate days, when members of the larger community are invited for interfaith and/or interracial teaching-and-sharing ceremonies.
## LAG B'OMER
Fifty days after Passover, the holiday of Shavuot marks the giving of the Torah to the Israelites. These observances of liberation and revelation are linked by the counting of those days, which is called the counting of the omer.
An omer was the measure of grain set apart for offerings to the Temple. On the second day of Passover, the first of 50 measures of barley was given, as an offering or gift to God; thereafter, one measure a day was given for the next 49 days. These 50 days eventually came to be associated with terrible persecutions of the Jews, so that certain mourning practices were observed. Some people still do not cut their hair and some rabbis will not officiate at weddings during the counting of the Omer, except on the 33rd day of the Omer, in Hebrew, Lag B'Omer.
Lag B'Omer is considered a semiholiday, and has long been associated with weddings and picnics. However, it was never widely celebrated and its origins and proper observance have been the subject of rabbinic debate. Since it falls in the spring, Lag B'Omer is mostly known today as the occasion for outdoor congregational and community events: family field days, picnics, softball games, and races. In Israel, the air is thick with the smell of outdoor grilling and picnics.
## HOLOCAUST REMEMBRANCE DAY AND ISRAEL INDEPENDENCE DAY
Nothing is so whole as a broken heart.
RABBI NACHMAN OF BRATSLAV
In one of its earliest sessions, the Israeli Knesset (parliament) declared that Israel Independence Day would be celebrated on the fifth of Iyar—the Hebrew date corresponding to May 15, 1948, when Israel became a sovereign nation. Three years later, the Knesset proclaimed Holocaust Remembrance Day on the 27th of Nisan, 14 days after the start of Passover and eight days before the celebration of Israel's birth.
The addition of these holidays to the Hebrew calendar reflect the profound impact of two historical events on the Jewish psyche. The world could never be the same after the Shoah, the Holocaust that killed one-third of the world's pre–World War II Jewish population. Nor could the future be the same after the realization of the dream of returning to the land of Israel. The relationship between the two holidays is undeniable, but not simple. The establishment of the state of Israel in no way compensates for the slaughter of European Jewry, but it is, undeniably, a response to that horror and an affirmation of life and Jewish continuity against the overwhelming evidence of death and destruction.28
Outside of Israel, Yom HaShoah and Yom HaAtzma'ut are celebrated in communal observances. It is difficult to create ritual responses to the raw emotion and the historical ramifications of the Holocaust and Israel are still unfolding.
Holocaust Remembrance Day
It seems almost blasphemous to attempt to make sense out of the senseless slaughter of six million Jewish men, women, and children. The photographs, film footage, diaries, and memoirs of survivors are excruciating. And yet, the responsibility to remember is absolute and, in some sense, sacred.
It is terrible to remember. It is worse to forget. These are the twin realities of Yom HaShoah and the tension between them is the source of their observance.
In America, commemorations of the Holocaust include a wide range of events including civic ceremonies attended by public officials and clergy of all faiths. There are classroom presentations about the Nazi horror tailored to the age and ability of students to understand what is incomprehensible. Some synagogues and Jewish community centers mark Yom HaShoah with displays of art, photographs, or books, and with seminars, lectures, and film series. Fasting has been suggested as an appropriate way to mark Yom HaShoah and some people abstain from eating sweet foods.
While liturgies have been published and used, many congregations create original services for Yom HaShoah from year to year. Readings from Lamentations and Psalms are often used, but the most common source for commemorations held in hushed and darkened sanctuaries is literature from the Holocaust—the testimony of victims, survivors, and witnesses. Six yellow tulips may be displayed on the bimah.
Thus far, the ritual gesture that seems to have taken root is the lighting of six memorial candles, one for each of the six million Jews who were killed. This is done both in synagogues and at home, and some light a seventh candle in memory of non-Jews who were killed in the Holocaust, or to honor the righteous non-Jews who risked their lives to help Jews. Candles and flowers recall the dead and affirm life and hope, even in the heart of the blackest night.
In Israel, on what is called "Holocaust and Resistance Remembrance Day," all public entertainments are closed. A three-minute siren blast is heard throughout the country, and everyone stands at attention.
Yom HaShoah is not associated with any home observances. The Holocaust is still too close, too awful, to bring to the table. However, since it is a time when schoolchildren may be introduced to or reminded of the events of the Holocaust at school, families sometimes use the opportunity to discuss the thoughts and feelings these lessons provoke. There are many good books and films about the Holocaust for all ages.
Donations to virtually any Jewish organization seem appropriate tzedakah at Yom HaShoah since the vitality of the Jewish community repudiates its attempted annihilation. Some earmark money at this time for projects devoted to keeping the memory of the Holocaust alive, or for the support of Righteous Gentiles—those who saved and aided Jews during the Shoah.
Israel Independence Day
After nearly two thousand years in exile, the formation of a Jewish state in the land of Israel transformed the self-image of Jews everywhere. Even Jews who have no relatives there or have not visited tend to feel a connection to, commitment to, and responsibility for her existence. While Israel Independence Day is, by and large, a secular event, it is impossible to forget its context in Jewish tradition. From the Torah, where God promises Abraham, "I give all the land that you see to you and your offspring forever,"29 to the annual Passover wish, "Next year in Jerusalem," the land of Israel has been a focal point of the Jewish hope for redemption. Thus, there is a sense that the modern state of Israel has a profound connection with God's purpose for the Jews. The challenge of living up to the prophetic call for justice while facing virtually constant mortal threats from her neighbors continues to test the spirit and will of Israelis and all Jews everywhere. The test is met with hope, tikvah, as in the national anthem of Israel, "HaTikvah," "The Hope."
In North America, Israel Independence Day is the occasion for public gatherings of all sorts, the Israel Day Parade in New York City being the largest. Local community centers and synagogues hold dances, concerts, film series, seminars, and lectures that feature Israeli culture and concerns. Religious schools and day schools usually schedule programs, parties, and pageants in conjunction with the holiday. In Israel, Yom HaAtzma'ut is celebrated with flags, bands, fireworks, picnics, parties, and dancing in the streets. Many American Jews try to schedule trips to Israel to coincide with this gala celebration.
Tzedakah for Israel Independence Day has come to mean supporting the state of Israel by purchasing Israel bonds, by making a contribution to any Israeli charity, and by buying Israeli goods and products.
Yom HaZikaron (Remembrance Day) is an Israeli holiday observed the day before Yom HaAtzma'ut, and honors the memory of those who died fighting for Israel's independence and continuing existence. Another Israeli observance, Yom Yerushalayim (Jerusalem Day), is celebrated three weeks after Israel Independence Day and commemorates the capture of Jerusalem during the Six Day War of 1967.
## SHAVUOT
Shavuot celebrates the moment when the Jewish people stood before God at Mount Sinai and received a scroll containing all the secrets of the universe as a memento of their encounter. The scroll was the Torah. She is called a tree of life.
RABBI LAWRENCE KUSHNER 30
Seven weeks after Passover—seven weeks after leaving Egypt—comes Shavuot, Hebrew for "weeks," and the holiday that celebrates the encounter between the Jewish people and God through the giving of the Torah at Mount Sinai. The Torah is sometimes called a ketubah, a marriage contract that describes the covenantal relationship between the people of Israel and God; Shavuot can be thought of as the celebration of this wedding anniversary.
The Bible, however, makes no connection between Shavuot and the Torah; references to Shavuot in Exodus, Leviticus, and Deuteronomy describe an agricultural pilgrimage holiday—a day when people came from all over the land of Israel to the Temple, bearing gifts from the first fruits of the wheat and fruit harvest as an offering to God.31 The agricultural and seasonal aspects of Shavuot are still reflected in its many names: the Day of the First Fruits, the Day of the Harvest, the Feast of the Flowers (in ancient Persia), and the Feast of the Roses (in Italy).
But after the destruction of the Second Temple in 70 C.E., the holiday was changed to celebrate the Torah, the new center of Judaism. The agricultural roots of the holiday are echoed in seasonal decorations and especially in Israeli celebrations that include public processions featuring singing and dancing. But for the most part, Shavuot is perhaps the most mystical of all the Jewish holidays—the day that celebrates revelation.
Much as Passover encourages every member of every generation to feel as though he or she had experienced slavery and liberation, Shavuot insists that revelation—receiving the Torah—is experienced by every Jew. Shavuot is celebrated with greens and flowers, with dairy meals, sweets, and reading the Book of Ruth, about a woman who was Jewish not by birth but by choice.
Preparing
In recognition of the late spring–early summer season of the holiday, it is customary to decorate with green plants and flowers. An old European craft associated with Shavuot is the paper cut. Called shavuoslech, raizelech, or shoshanta (the latter two words refer to roses), these were hung on windows so that light would filter through the floral designs.32 Baking bread for the yontif seder is another Shavuot custom. And some people go to the mikveh for a ritual of purification to get ready to receive the Torah.
Study
Study is the primary way of preparing for Shavuot. It is traditional to read Pirke Avot, "The Ethics of the Fathers," a very accessible section of the Talmud, during the weeks between Passover and Shavuot. In line with the custom of the tikkun (described below), some people try to read a little bit of each book of the Bible, with special attention to the Torah and Bible readings for Shavuot: Exodus 19–20 (the Ten Commandments), the Book of Ruth, and Ezekiel 3:12, the strange vision of "the wheel."
In terms of giving tzedakah, the themes of learning and agriculture suggest donations to organizations devoted to education, feeding the poor, and restoring the earth.
Making Shavuot
Shavuot begins with a festival meal, including all the blessings of the yontif seder: candles, a festival kiddush, shehecheyanu, and motzi. Since the Torah mentions the offering of two loaves of bread made from newly harvested wheat, it is customary to have two loaves on the table. Some people bake two loaves of challah side by side and connected, so that they resemble the popular image of the two tablets of the Ten Commandments.
Shavuot meals feature dairy foods, especially cheese. For Ashkenazi Jews, blintzes (sweet cheese wrapped in a thin pancake) are traditional. Eating outdoors is a nice way to welcome the summer season.
The custom of late-night Shavuot synagogue study sessions can be translated to the home. For children, it can be a special night for staying up late and reading stories about the Bible, or watching Bible movies on DVD.
Synagogue Observance
Synagogue observance of Shavuot begins in the evening with a holiday service that often starts later than usual. Afterward, many congregations run some kind of tikkun, or study session. This custom dates back to the 16th century mystics of Safed who stayed up all night long to read and study from the Bible and from the Zohar, a mystical book. Modern Shavuot study sessions take many forms: a series of seminars led by members of the congregation or invited scholars; discussion of modern as well as ancient Jewish texts; writing of modern midrashim—imaginative commentaries on a biblical passage. Some synagogues run study sessions until midnight or even till dawn, when the morning service is held and breakfast is served.
The Torah portion for the morning service includes the reading of the Ten Commandments. The Haftarah portion comes from Ezekiel, and includes the hallucinatory vision of the merkavah—God's chariot or throne, which is attended by marvelous strange creatures: angels, divine beings. The prophet's description of wheels within wheels has been given many interpretations, and remains always a stunning expression of religious imagination.
The Book of Ruth is a popular Shavuot text. Ruth, the archetypal Jew-by-choice, demonstrates that it is not birth or family identity but acceptance of the Torah that distinguishes Jews from the other peoples. Ruth's place as an ancestor of King David celebrates the importance of converts to the continuity of the Jewish people. Some congregations honor Jews-by-choice on Shavuot with panel discussions about people's Jewish journeys.
Many congregations hold confirmation or graduation ceremonies on Shavuot, which has long been associated with Jewish study.
## TISHA B'AV
Tisha B'Av, the ninth day in the month of Av, is a day of mourning for the destruction of the Temple in Jerusalem first in the year 586 B.C.E. by Nebuchadnezzar, King of Babylonia, and again seven centuries later in 70 C.E. by General Titus of the Roman Empire.
The destruction of the Temple was, quite literally, the end of the world to the Jews of those times. The end of the Temple meant the end of a way of life, of a religion of sacrifices and priesthoods, and of national identity for the Jewish people, who were dispersed and exiled in the aftermath of military defeat. The destruction of the Temple was also interpreted as a sign that God had withdrawn from the world and from intervening on behalf of the Jewish people. Over time, other sad events were associated with and commemorated on Tisha B'Av, among them: the end of Bar Kochba's revolt against the Romans (135 C.E.), the expulsion of Jews from England (1290 C.E.), from Spain (1492), and from Vienna (1670).
Tisha B'Av is a day of fasting observed with mourning customs, such as not shaving and sitting low to the ground. It also culminates a three-week period of semimourning when weddings and other celebrations are avoided. Those who observe Tisha B'Av light memorial candles and attend services, where there is no singing or chanting. The Torah may be draped with dark or black covers. The text for Tisha B'Av is the Book of Lamentations, a long poem that keens over the destruction of Jerusalem and the First Temple.
In America, Tisha B'Av is the least known of traditional Jewish holidays. In some part this is due to the fact that it falls during the middle of the summer, when many congregations are on summer schedule and many people are on vacation. Also, the destruction of the Temple does not evoke the emotions of grief and mourning called for by Tisha B'Av and in a sense, Holocaust Remembrance Day has taken its place as a communal day of grief and mourning. Because Tisha B'Av is a holiday mourning the exile of the Jews, the founding of the state of Israel seems to lighten the grief and suggest an element of hope, since there is a legend that the Messiah will be born on Tisha B'Av.
Because it is the only event on the Jewish calendar during the summer months, Jewish camps have made Tisha B'Av a focus for teaching and creative programming. Campers participate in dramatic reenactments and services in candle-lit recreation halls, original poetry-writing workshops, and discussion groups.
## THE LIFE CYCLE
Jewish ritual is the art of turning time into celebration. The ceremonies and customs that surround the great transitions of human life—birth, coming of age, marriage, death—provide wise pathways through the soul's uncharted territories; they give us perfect words when the heart is too full to speak. The Jewish life cycle is a venerable guide, but as in all things Jewish, it is also full of choices about how to celebrate, and what to observe, say, and sing. And indeed, the life cycle itself is changing, and adding new choices.
Adding a chapter about conversion and adoption to the list of Jewish life-cycle events acknowledges these changes and also stands as an expression of creative liberal Jewish piety. Although it is difficult to find reliable statistics about conversion and adoption, it is safe to say that there has been no other period in Jewish life to match the present in terms of the numbers entering Judaism through these ancient portals. But it is not merely a matter of numbers: the urge to sanctify life-changing transitions with rituals, prayers, songs, and celebration is part of the DNA of Judaism. Taking the time to honor a profound change of status is simply a Jewish thing to do.
The more that liberal Jews learn of their tradition, the greater their desire to give Jewish dimensions to passages that went unnoted in the past; this means reclaiming customs and mitzvot that earlier generations rejected, and inventing new ones. Thus, Jewish women have identified moments in their physical lives that call out for spiritual mindfulness and ritual, including menarche, menstruation, pregnancy, miscarriage, weaning, and menopause. Men and women, boys and girls, have identified other transformational events and passages: graduation from a course of study, becoming an adult bar/bat mitzvah, recovery from serious illness, becoming a grandparent. In some cases, the tradition already provides a meaningful response; the recitation of the gomel1 prayer after an illness or escaping injury, is making a return to synagogue liturgy, giving public voice to personal gratitude. Immersion in the ritual bath, the mikveh, has returned to the menu of choices for liberal Jews, both for traditional uses (i.e., sanctifying sexuality) and for an array of new purposes, such as those listed above. See www.mayyimhayyim.org.
Some contemporary situations seem to require entirely new prayers and gestures, or new combinations of the old and the new, as in the case of getting a driver's license or of coming out to one's family (www.ritualwell.org).
The repertoire of life-cycle rituals, which once seemed settled for eternity, has become flexible and fluid. This is not a rejection of the past but an embrace of its teaching that the Torah is a "tree of life." The nature of living things is to change and grow.
## BIRTH
The first mitzvah— the first "commandment"—in the Bible is "Be fruitful and multiply," from Genesis 1:28. For Jews, having children is both a religious obligation and the crown of human life, the source of the greatest happiness. The birth of Jewish babies is thus greeted with rituals that are both solemn and joyful.
All parents know that their baby is the center of the universe, a "fact" that is acknowledged by the Jewish view of time. Every Jewish baby is considered a link in the chain that extends back to the birth of Isaac, the first Jewish baby, and extends forward to the day when the world will be peaceful and whole. After all, any baby might grow up to be the Messiah, the person who will lead the world to redemption. The Jewish traditions and rituals described in this chapter give voice to the powerful feelings that surround the birth of every baby: gratitude, awe, fear, humility, continuity, and hope.
* * *
With each child, the world begins anew.
THE MIDRASH
* * *
Names
The choice of a name is the first Jewish decision parents are called upon to make, and for Jews, a name is a complicated gift because it bestows not only personal identity but also familial and religious connection. A baby named Daniel or Rebecca is often a living testament to a grandparent who has died, and a link to every Jewish Daniel and Rebecca back to the Bible.
Jewish tradition is very attentive to names and naming. HaShem, "The Name," is one way of referring to God, and the Torah contains several dramatic and important name changes. Once Abram and Sarai accepted the covenant with God, they became different people with different names: Abraham and Sarah, the parents of the Jewish people. Even more striking is the transformation of Jacob, "supplanter," into Israel, "wrestler with God." There is a story that the Jews enslaved in Egypt were saved from complete assimilation by keeping two identifying signs that set them apart: the custom of circumcision and their Hebrew names.
Biblical names have long been a source for parents, but of the 2,800 personal names in the Bible, fewer than 5 percent are used today. And throughout history, Jews have given their children names from many sources, reflecting the fashions and cultures of their times as well as tradition. For example, Esther, a quintessentially Jewish name, is Persian in origin and shares its root with Astarte, also known as Ishtar, the great fertility goddess of the ancient Middle East. The Eastern European custom of naming children after deceased relatives dates back to the Egyptian Jews of the sixth century B.C.E., who probably borrowed the idea from their non-Jewish neighbors.
The practice of giving a secular name for everyday use and a religious name for prayer and on Jewish legal documents developed during the Middle Ages in Eastern Europe.2 This custom is still very much alive in America, where the connection between the secular and Hebrew name is sometimes as tenuous as an initial sound; thus a baby girl named for her grandmother Shayna becomes Susan, and Max is named in memory of Uncle Moshe.
Since the founding of the state of Israel, the lexicon of Jewish names has expanded with the introduction of biblical names that had not been heard for generations, such as Amnon, Yoram, Avital, and Tamar. Israelis also translate names from Yiddish to Hebrew, so, for example, Gittel ("good one") becomes Tovah. Inspired by the land of Israel, children are named Kinereth (a sea), Arnon (a wadi), Barak (lightning), and Ora (light).
Today, Jewish American parents have embraced biblical names with a passion, and preschools are full of Samuels and Rachels, Benjamins and Sarahs. Modern Israeli names are also growing in popularity: Ariella, Levi, Noam, Shoshana. Increasingly, parents are choosing identifiably Jewish names (from Abigail to Zachariah) because they work well in three settings where American Jews are likely to find themselves: in secular life, in synagogues, and in Israel.
Covenant—Brit
A covenant is a contract—an agreement that acknowledges the participation and assent of various parties. Covenant is the term for the relationship of the people of Israel with God. With the birth of every Jewish child, that covenant is renewed again with ritual and celebration.
The ancient ceremony for bringing sons into the covenant of Israel is brit milah, a religious ceremony that includes circumcision as a physical sign of the bond between the Jewish people and God. For daughters, American Jews have created a ceremony, brit bat, "covenant for a daughter," to invoke the joys and responsibilities of entering the covenant of the people of Israel.
In many ways, the covenant of circumcision and the covenant for a daughter are as different as two ceremonies can be. Brit milah is the oldest continuous Jewish rite, celebrated with remarkable consistency throughout the world. Brit bat, which goes by many names, is a recent development in Jewish history, and no two are quite the same. What these two celebrations have in common, however, is the element of covenant, expressed with joy, gratitude, and wonder. Brit ceremonies give parents a way to express the complex feelings occasioned by the birth of a baby, a way to express new feelings of connection with a Jewish past and faith in the future.
The Covenant of Circumcision Brit Milah
In this ritual, the foreskin is removed within a religious ceremony, as a physical token signifying the unique relationship between each Jewish male and God. Brit milah is called the covenant of Abraham, because the biblical patriarch was the first to practice circumcision as a Jewish ritual. According to the biblical story, Abraham responded to God's command and circumcised himself (at the age of 99) and all the men of his household, including his 13-year-old son, Ishmael. Isaac, the firstborn of a circumcised Hebrew, underwent brit milah on the eighth day, which set the precedent for the ritual's timing ever since.
The importance of circumcision as a mark of peoplehood is a recurring theme in the Bible, and the covenant has been renewed in every generation. During periods of persecution, it singled Jewish men out for execution, and circumcision became an act of defiance and courage. In the 20th century, stories from the Holocaust and from the Soviet Union testify to the steadfastness of Jewish practice of brit milah—regardless of the consequences.
* * *
Such shall be the covenant between Me and you and your offspring to follow which you shall keep: every male among you shall be circumcised. You shall circumcise the flesh of your foreskin, and that shall be the sign of the covenant between Me and you.
GENESIS 17:10–11
* * *
The liturgy of brit milah was established before the first century C.E., and the laws that regulate and explain it are contained in the Talmud. Brit milah takes place on the eighth day of life,* even if that falls on Shabbat or holidays, including Yom Kippur.
However, illness or weakness of any kind requires that the rite be postponed until it is completely safe for the baby. A bris (as it is pronounced in Yiddish) may occur anytime before sundown, but it is customarily scheduled early in the day, responding to the tradition that says that one should be eager to perform a mitzvah. A bris may be held anywhere, but most take place at home.
A father is responsible for his son's brit milah, and technically he performs the circumcision; the mohel (the Yiddish pronunciation is moyl, the Hebrew, mo-hail), or ritual circumciser, acts as his representative. The only people who absolutely must be present at a bris are the baby, the mohel, and one honored assistant called the sandek; often a grandfather, who holds the baby. However, since a bris is considered a joyful event, it is customary to invite friends and family members.
Choosing Brit Milah
Nearly all Jewish parents fulfill this mitzvah, arguably the most difficult of all the commandments. It is a choice made even by Jews with little or no connection to community or congregation, by Jews with little or no understanding of the ritual or its meaning. Even so, brit milah does pose questions that deserve to be considered and answered: Is it safe? Will my baby suffer? What is the best way to have it done? Why should we continue this tradition at all?
As recently as the 1960s, approximately 98 percent of all boys born in the United States were circumcised for reasons of health and hygiene.3 For years, this custom excused many Jewish parents from the need to make a decision. But after an official announcement by pediatricians in 1985 that routine circumcision was not medically warranted, that figure quickly dropped to 59 percent.4 In the late 1980s, the medical debate again shifted somewhat back in favor of universal circumcision. But the fact is, Jews have always performed brit milah as a religious obligation, never as a health measure.
Jewish tradition, which is so concerned with the sanctity of life and health, would not require an act that might jeopardize either. Circumcision is a medically safe procedure—complications are extremely rare—and clearly, Jewish sons have survived the procedure for 3,500 years.5
Although brit milah was performed for centuries with no more anesthesia than a few drops of wine, today most physicians and mohelim (plural of mohel) numb the area with topical or injectible anesthetic and anyone who has attended more than one bris knows that babies are easily comforted after the procedure.
Some Jewish parents, feeling more confidence in medicine than ritual practice, decide to have their sons circumcised by a physician in the hospital before they take the baby home. (This is actually a false dichotomy in many communities; see the section below about the mohel.) Apart from the fact that a medical circumcision is not the same as a brit milah, which is a religious ritual performed on the eighth day with the deliberate intent of bringing a son into the covenant, there are other important differences between a hospital "circ" and a bris performed by a mohel.
In many hospitals, residents of varying experience perform the procedure. In order to immobilize the baby, his limbs are strapped onto a board where he may be held for as long as ten or fifteen minutes. After the procedure is over, there may be no one around to immediately comfort the baby. At a brit milah, the baby is held by loving hands throughout the procedure, which is performed by an expert at the operation. The baby is given some wine, which is thought to lessen the pain and may help him fall asleep afterward. When the ceremony is over, he is returned to his mother, who can nurse and comfort him.
As to the "why" of brit milah, the most compelling reasons are not always the easiest to explain. For many parents the answer to the question is: If we stop doing brit milah, we stop being Jews. Brit milah is a physical connection to the ancient Jewish past and to all subsequent generations to this day, and it is one of the few ritual practices upon which virtually all Jews still agree. Choosing not to circumcise a son may, in effect, cut him off from full membership in the Jewish community, or present him with the choice of undergoing a painful operation as an adult. The implications of the decision not to circumcise a Jewish baby are best discussed with a rabbi.
The mohel. Traditional mohelim learn their skills by apprenticeship to and supervision by an accomplished, established practitioner. The Reform and Conservative movements now train board-certified physicians as mohelim with a course on the theology, Jewish law, folklore, and liturgy of brit milah. Indeed, more and more mohelim of all denominations are doctors.
On the day of a brit milah, the mohel examines the baby, and if there is the slightest question about the child's health, Jewish law requires that the circumcision be postponed. The mohel will usually act as the "master of ceremonies" for the brit, leading prayers and explaining the ritual as well as performing the circumcision. Sometimes, a rabbi, cantor, the parents, or others will share the liturgical honors. After the ceremony, the mohel again examines the baby, gives instructions for caring for the circumcised penis, and then remains "on call" for questions about healing.
Word-of-mouth recommendation is the best way to find a mohel, and since rabbis and cantors go to many circumcisions, they are probably the best people to consult. Local denominational offices may also be able to provide a list of names, and some mohelim place advertisements in local Jewish newspapers.
The ceremony. The liturgy of brit milah is ancient and, as with most Jewish life-cycle rituals, the ceremony is very brief—no more than five or ten minutes long. A bris consists of three parts. The first is as normative and universal as any part of Jewish religious life: a blessing is recited, the circumcision is performed, and another blessing follows. The second part begins with kiddush, the blessing over wine, and includes a longer prayer that gives the baby his name. The third segment, required by Jewish law, is the seudat mitzvah, the ritual meal of celebration.
There are variations and many customs attached to this simple outline. The father may hand the circumcision knife to the mohel, demonstrating that he bears responsibility for the act; sometimes, the mother joins in this ritual gesture. Sephardic Jews follow the blessing over wine with the scent of fragrant spices—Moroccan Jews use dried rose petals—and recite the blessing over spices, familiar from the Sabbath havdalah service.
Parents can customize and personalize the ceremony with readings, prayers, or a short d'rash, or teaching, but additions to the liturgy tend to be brief, since the comfort of the baby is paramount. Sometimes, when the baby is brought into the room, he is passed from one generation to the next, from great-grandparents to grandparents to parents. If an older sibling is mature enough to participate, he or she might carry the baby into the room, or light a candle, or say a few words.
Most parents take the opportunity to talk about the baby's name. This is a time for remembering Uncle Jake, for whom little Jacob has been named, and to hope he will grow up to be as learned, as quick to laugh, and as devoted a friend and father as his namesake. After the naming or at the meal of celebration, guests can offer personal blessings for the new baby: "May he be blessed with long life," "May he grow up in a world free of want and fear," "May he inherit his mother's good looks and his father's appetite."
There is an old custom of distributing kibbudim, "honors," to family members and friends during the ceremony. The most important of these is the role of the sandek (the word derives from the Greek syndikos, or "patron"); the sandek assists the mohel by holding the baby during the circumcision. The other traditional ceremonial roles are that of kvatterin (godmother), who carries the baby from the mother to the room where the bris takes place, and kvatter (godfather), who in turn brings the baby to the chair of Elijah. (Kvatter and kvatterin are entirely ceremonial roles. There is no formal Jewish role analogous to that assumed by Christian godparents, who become responsible for the child in case of his parents' death. The Jewish community as a whole is responsible for the education and support of orphaned children.)
According to the ancient legend, the prophet Elijah, who is associated with the coming of the Messiah, attends every bris. The special chair set aside for the prophet is a symbol of hope that this baby will bring peace and redemption to the world.
Covenant for a Daughter—Brit Bat
Although not as universally familiar as brit milah, ceremonies for baby girls are hardly a new invention. Sephardic tradition is rich in rituals and customs to celebrate a daughter's birth, including a ceremony called Seder zeved habat, "celebration for the gift of a daughter." The Jews of Spain held a special party at home after the mother's recovery called las fadas, a celebration that welcomed good fairies and was probably adapted from non-Jewish folk beliefs.6
American Jews have adopted this tradition with enthusiasm and variety, replacing the simple Ashkenazi custom of announcing a baby girl's name at services with new rituals, liturgies, and customs. Many rabbis officiate at "baby namings" in their synagogues, introducing the little girl and announcing her Hebrew name. Her parent(s) and grandparent(s) are invited up to the bimah (the raised platform, usually in front of the ark where the Torah scrolls are kept), usually during Shabbat services, with songs and words of welcome.
But many brit bat ceremonies take place in the home. Of the many new ceremonies being written and celebrated in America today, it may be that a single, standard liturgy for daughters will eventually become as normative as the words associated with brit milah. However, it is possible that this ceremony will continue to be given many interpretations like the Passover seder, which retains its identity even as it is interpreted anew every year.
Where and when. There are no rules for brit bat, but current practice offers a menu of choices. As noted above, the ceremony can take place at home or in the synagogue; although a sanctuary or social hall encourages a larger community celebration, some people prefer the intimacy of home. When brit bat takes place at home, the baby's parents usually lead the ceremony, sometimes with a rabbi's or cantor's assistance. When it is held in a synagogue, the rabbi tends to officiate, sometimes with parental participation. In general, grandparents tend to be given the most important kibbudim or honors, sometimes using the honorary roles and titles of brit milah: for example, the sandek (or if a woman, sandeket) holds the baby during part of the ceremony, and the kvatterin and kvatter may carry her to and from the room.
Generally, parents schedule brit bat for a time when the mother is sufficiently recovered to enjoy the event, and when it will be possible for out-of-town family members to attend. Various intervals are used and justified on traditional grounds. For example, holding the ceremony on the eighth day mirrors the ancient customs of brit milah. However, since mothers often do not feel ready for a party so soon after giving birth, this is a relatively infrequent choice and thirty days after birth is a popular choice, which has a basis in tradition, since the rabbis of the Talmud believed children were viable only after thirty days.
Elements of the ceremony. There are countless brit bat ceremonies in circulation. Some are short and simple, others are long and elaborate. Some incorporate music, some use a lot of Hebrew, and others use very little. It is difficult to generalize about these ceremonies, but despite the variety, there are some nearly universal elements.
1. The introductory section begins with the greeting "Blessed is she who enters," B'rucha haba'a. Songs may be sung, and candles are sometimes lit. There are usually prayers or readings by the parents, rabbi, and/or cantor. Kiddush, the blessing for wine that is part of all Jewish rituals marking significant events or times, is recited.
2. The second part of the ceremony is about covenant. Using blessings and symbolic actions, a baby daughter is entered into the people of Israel. While daughters are most commonly entered into the covenant simply by saying a blessing, many parents add a symbolic gesture as well as words. Washing the baby, or sometimes just her feet or hands, is an earthy yet gentle physical act that recalls the water imagery of the Torah, much of it associated with women: Rebecca and Rachel make their first appearances at wells, and Miriam the prophetess is associated with a well of living water that sustained the Israelites in the wilderness.
Generally, the covenant is followed by some version of the threefold wish recited at brit milah: "As she has entered the covenant, so may she enter a life devoted to Torah, huppah, and the accomplishment of good deeds."
3. In the third section, the baby's name is announced and her namesake(s) recalled. Anything said about how a name was chosen can be very moving, especially since most American Jews name children to honor the memory of a family member who has died. The Hebrew or biblical meaning of a name can also suggest ways for parents to talk about their hopes and dreams for a daughter.
Other kinds of readings, prayers, poems, and songs are added here and family and friends may be invited to offer spontaneous prayers and wishes for the new baby: "May she live to be 120," "May she sleep through the night soon." If the group is small and the baby placid enough, she might even be passed from person to person as they speak.
4. The end of the ceremony is signaled by one, some, or all of the following three prayers: Shehecheyanu, which is the generic prayer of thanks for anything new, and may be the most common element of all brit bat ceremonies; the traditional blessing for a daughter, which is recited on Friday night, part of the Shabbat seder; the threefold or priestly benediction, which concludes many Jewish rituals and services, and which some parents include in the Shabbat blessing of their children. (Check the index for references to these blessings.)
5. Brit bat concludes with the seudat mitzvah, a celebratory meal. The Jewish term for this kind of party is simcha, a word that means both joy and its celebration.
Celebrating
According to Jewish law, all major life-cycle events are marked, concluded, and celebrated with a seudat mitzvah, the "meal of the mitzvah." The celebrations to honor the birth of a new baby boy or girl range from catered dinners to potluck buffet brunches. However plain or fancy, large or small, these meals traditionally begin with the blessing over challah (motzi).
The meal can also be an informal continuation of the brit ceremony, a time for guests to offer their blessings and wishes for the baby and family. Messages from people who could not be present might be read aloud, or older siblings can be given a chance to shine during a day in which they are eclipsed.
Tzedakah
Traditionally, Jews mark happy occasions like births with contributions of tzedakah, righteous giving or charity. Giving tzedakah is a way of both sharing the joy of the occasion and of acknowledging that personal happiness is incomplete in a world so badly in need of repair. A donation to honor the birth of a child is a kind of investment in a more just world for all children.
In ancient Israel, it was customary to plant a cedar sapling at the birth of boy, a cypress when a baby girl was born. The cedar symbolized strength and stature, the cypress gentleness and sweetness, and eventually, branches were cut down from each tree to hold up a wedding canopy. Some parents have revived this custom, planting a sapling in the yard when a baby is born. And many people have a tree planted in Israel's Children's Forest in honor of a birth (www.jnf.org).
* * *
God commands us to perform countless acts of love.
How can we begin to obey such a difficult commandment? It is not such a mystery really.
Every lullaby, every diaper change, every smile, every sleepless night, every wordless prayer of thanks for this perfect baby—in these and the unending ways we care for and teach and protect our children, we perform countless acts of love.
And the world is made holier. And so are we.
ADAPTED FROM THE MIDRASH
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*According to the Jewish calendar, a day begins with the preceding nightfall, so if a boy is born on Monday night, his bris would be on the following Tuesday.
## BAR AND BAT MITZVAH
May you live to see your world fulfilled,
May your destiny be for worlds still to come,
And may you trust in generations past and yet to be.
May your heart be filled with intuition and your words be filled with insight.
May songs of praise ever be upon your tongue and your vision be on a straight path before you.
May your eyes shine with the light of holy words and your face reflect the brightness of the heavens.
May your lips ever speak wisdom and your fulfillment be in righteousness even as you ever yearn to hear the words of the Holy Ancient One of Old.
PARENTS' BLESSING 7
According to the rules of Hebrew grammar, no one is ever bar mitzvah ed. One becomes a bar mitzvah, "son of the commandment," or bat mitzvah, "daughter of the commandment." There is more to this distinction than grammar. The ceremonies called bar and bat mitzvah—the preparation and study, the public recognition, the celebration—do not confer the status of bar or bat mitzvah. At the age of 13, Jews automatically become bar or bat mitzvah, full-fledged members of the community.
Nevertheless, the ceremony associated with this change of status has become one of Judaism's most potent rites of passage. Bar and bat mitzvah mark and celebrate a fundamental and irrevocable life change: the end of childhood. While no one treats a 12-year-old or 13-year-old as an adult, the beginning of adolescence is a momentous transition, one that many human cultures mark with ritual and ceremony.
Traditionally, bar/bat mitzvah is understood as a ceremony that welcomes a young Jew into the formal, adult prayer life of the community. In a religious culture that stresses communal rather than individual action and prayer, it is a unique moment and the only ceremony that features one Jew acting upon his or her own behalf solely. In celebrating the transition from childhood to puberty, bar/bat mitzvah ceremonies are also family rituals of transformation, marking the beginning of major changes for everyone, including parents.
Looking in the mirror, parents suddenly see people who are old enough to have a child of bar/bat mitzvah age—a child who is maturing sexually, a child who suddenly has strong opinions about everything under the sun. Watching a son or daughter stand, Torah in arms, in front of a crowded sanctuary, can be a revelation. As this poised and somehow mature child begins a new stage of their development, parents need to change, too.
History. Bar mitzvah does not appear in the Bible, which gives the age of 20 as the time when adult obligations begin.8 However, by the first century C.E., adulthood was universally held to begin at 13 for boys and 12 for girls, a view codified in the Talmud, which states, "At age 13, one becomes subject to the commandments."9 The earliest reference to any ceremony to mark this change dates from the Second Temple period, when a special blessing was recited for 13-year-old boys who had completed their first Yom Kippur fast.10 But in fact, until the Middle Ages, the religious distinction between a 10-year-old and a 13-year-old was strictly theoretical. Children were regularly counted for the purposes of creating a minyan, the quorum of ten needed for certain prayers, so that reaching the age of 13 was not associated with any particular rituals or celebrations.11
That approach to ritual maturity changed drastically sometime between the 14th and 16th century in Germany and Poland, where minors were no longer permitted to read from the Torah or to be counted in a minyan. From that point in history, bar mitzvah became an important life-cycle event throughout the Jewish world. Boys were called to the Torah to symbolize the attainment of adult status in the prayer life of the community.
The central act of the ceremony was receiving the honor of an aliyah—of being called to bless and/or read from the Torah. However, other elements were soon added to the ceremony. As early as the 16th century, a bar mitzvah boy was expected to deliver a d'rash, a discourse on the Torah portion he had read. In the 17th and 18th century, some synagogues permitted accomplished students to lead part of the service as well. As with every joyful occasion, or simcha, bar mitzvah carried with it the obligation of a seudat mitzvah, a commanded meal of celebration.
Bat mitzvah. Because girls' coming-of-age was not connected with the performance of public religious rites, the notion of a parallel synagogue ceremony for girls was basically unthinkable before the modern era. In some German communities, families would hold a seudah, or party, on the occasion of a daughter's 12th birthday, and while a girl might deliver a speech and her father recite a blessing, this was not a religious celebration.
Bat mitzvah was invented in the 20th century. Although the Reform movement officially instituted equality between the sexes in the late 19th century, the first recorded bat mitzvah did not occur until 1922, and was celebrated by Judith Kaplan (Eisenstein), the eldest daughter of Mordecai Kaplan, the founder of the Reconstructionist movement. The practice did not become commonplace until the 1950s, first in Reform congregations and then in Conservative synagogues.
For many years, bar and bat mitzvah were distinctly different. Boys were usually expected to read or chant a Torah and/or Haftarah portion on Saturday morning while girls were limited to a Friday night reading of the Haftarah. The differences between bar and bat mitzvah have been steadily diminishing to the point that today, in most congregations, they are virtually indistinguishable.
Current practice. The custom of bar/bat mitzvah has become a focal point of Jewish identity. For many parents, the prospect of a child's turning 13 is the impetus for the first contact with the organized Jewish community since their wedding. Indeed, bar and bat mitzvah are the main reason many American Jews send their children to religious school, or even affiliate with a synagogue.
Synagogues prepare students for bar/bat mitzvah. In addition to regular religious school classes, there may be smaller and/or individual tutorial sessions with teachers and/or the rabbi or cantor. These sessions focus on the text the student will read or chant: a portion of Torah (the first five books of the Bible) and/or a reading of the Haftarah, selections from the Prophets associated with each week's Torah portion, and some kind of speech or d'rash.
To offset the tendency to stress a one time performance over the process of Jewish learning, most congregations have instituted special programs for children studying for bar/bat mitzvah. The content of Torah portions might be explored in depth, and guest teachers may be invited to the classroom to talk about more "grown-up issues," everything from sexual ethics to Israeli politics. Rabbis may schedule private meetings with each child. There are often mitzvah requirements, such as doing volunteer work, and/or collecting money for a charity. Many congregations have enriched the bar/bat mitzvah year curriculum to include weekend retreats, special one-on-one sessions with the clergy, field trips, and parent-child classes.
In theory, bar/bat mitzvah can take place at any service where the Torah is read. Although most take place on Shabbat, some families opt for a Sunday (if it coincides with Rosh Hodesh) or Monday of a holiday weekend, for a variety of reasons. In Conservative synagogues where there is a ban on music and photography on the Sabbath, those prohibitions do not apply, and for families with Shabbat-observant relatives, the complications and expense are fewer on a weekday. Children are commonly assigned a date more than a year in advance. Some people try to schedule the occasion for the first Shabbat after the 13th birthday, though in large congregations with many students and a limited number of dates, the results can be rather random and there may even be "double headers."
Bar/bat mitzvah ceremonies vary enormously from one congregation to the next. In some synagogues, the bat mitzvah leads part of the service, reading prayers in Hebrew and English, and leading songs and responsive readings. In other congregations, participation is limited to reading a Torah portion and making a speech. In some congregations, the liturgical participation for bar/bat mitzvah is always the same, but in others, more accomplished students are given more to do.
Synagogues tend to have a more or less standard format for bar/bat mitzvah ceremonies, but some rabbis and congregations are flexible and open to creative changes in the service. Special-needs children who wish to become bar/bat mitzvah are almost always accommodated with sensitivity and respect.
It is customary in some synagogues for the parents to "dress" their son/daughter in a tallit (perhaps for the very first time) before the ceremony, in private, and then to address their child publicly during the service, talking about their thoughts, feelings, and wishes on this occasion. Another lovely custom is for the Torah scroll to be passed from grandparents to parents to the bar/bat mitzvah, in a symbolic passing of the tradition from one generation to the next.
Despite the great variety in how a bar/bat mitzvah is conducted, there are three elements that are virtually universal: the aliyah, the speech, and the celebration.
The aliyah. Receiving an aliyah means being called up to the raised platform in the front of the synagogue, the bimah, to recite the blessings for the Torah reading and/or to read from the scroll. A bar/bat mitzvah may read or chant as little as three verses or as much the entire weekly Torah portion. In some congregations, s/he will only read a Haftarah, and in others both a Haftarah portion and from the Torah.
On the day of a bar or bat mitzvah, it is also customary to honor the young person's relatives with aliyot (the plural of aliyah). Parents, grandparents, siblings, uncles, aunts, and cousins may be called up to recite the Torah blessings, open the ark where the Torah is stored, and lift or "dress" the Torah.
The speech or d'rash. At some point in the service, the bat or bat mitzvah usually delivers a speech of some kind. While these are very personal and tend to include a "thank you" to parents, siblings, and teachers, the real purpose of this presentation is to demonstrate the young person's understanding of the text s/he has read in Hebrew. The d'rash, sometimes written as part of a religious school class or in consultation with the rabbi, cantor, and/or parents, may focus on the content of the portion for the week, or just start from there. Many teachers see the d'rash as an opportunity for a young person to make an important statement about who s/he is and what s/he believes in. There is also almost always a second speech delivered by the rabbi. Often called the rabbi's "charge," this tends to be a kind of personal sermon addressed to the bar/bat mitzvah.
The celebration. Important rites of passage are always celebrated with a festive meal. While tradition dictates a seudat mitzvah to mark the occasion of a bar/bat mitzvah, there are no Jewish laws that regulate the nature of that celebration; local and congregational custom and children's peer groups tend to dictate what these events look like.
Many families put enormous amounts of energy and money into the celebration of bar/bat mitzvah, largely in response to social pressure. If everyone in the congregation puts on a lavish party, it seems shoddy not to do the same. Likewise, hiring clowns, offering a children's menu, and buying expensive party favors may seem mandatory if your child has been so entertained. Unfortunately, some parents use the bar/bat mitzvah reception as a way to repay social and business obligations.
Many people have ridiculed and bemoaned the commercialization of bar/bat mitzvah, and unfortunately there are many accounts of bad taste: huge ice sculptures in the shape of the bar mitzvah boy, a caped superhero character called "Captain Bar Mitzvah," even monkeys wearing yarmulkes.
The problem of conspicuous consumption is not new. During the Middle Ages, rabbis promulgated laws limiting the number of guests who could be invited to bar mitzvah celebrations, and even regulated what kinds of finery could be worn. In part, sumptuary laws were an attempt to stave off anti-Semitic sentiments about Jewish wealth and ostentation; however, the rabbis were also concerned about unseemly excess that could overwhelm the religious significance of the day.
In reaction to modern excesses and to help keep the focus on the ritual rather than social aspects of the day, some families plan more intimate parties, less formal receptions. While there is still great pressure to conform, there is a growing desire to personalize the celebration. From this perspective, "personalize" means more than engraved match-book covers or yarmulkes with the bar/bat mitzvah's name inside. Making a celebration that genuinely reflects a family's beliefs and tastes can start with designing an invitation that features the bar/bat mitzvah's own artwork or poetry, or contains a request that guests bring a can of food for distribution at a local shelter.
Increasingly, tzedakah is becoming a focus of bar/bat mitzvah preparations and celebrations. In small, close-knit Jewish communities of the past, beggars were invited to wedding and bar mitzvah feasts. Today, many families symbolically invite the poor to their celebratory meals by setting aside a voluntary tax of 3 percent of the money spent for food to MAZON, A Jewish Response to Hunger, which funds soup kitchens, food pantries, and other feeding programs in the United States and around the world (www.mazon.org). Likewise, leftover food may be donated to local shelters for the homeless.
There are many other ways to make tzedakah an important part of the bar/bat mitzvah experience. In some families, a percentage of all money spent on the event is donated to charity, or a portion of cash gifts is earmarked for tzedakah. If parents know that a particular relative plans to give money as a gift, they may request that donations be made to a charitable endowment instead; the bar/bat mitzvah then becomes trustee for this fund and decides which charities should receive interest payments. If there are floral centerpieces at the simcha, the bar/bat mitzvah and his/her family can deliver them to a local nursing home after the party. Alternately, money that might have been spent on flowers may be donated to some worthy cause, with a note on each table explaining that decision.
It is, however, important to remember that children have social pressures of their own to contend with. Young adolescents want their parties to be just like their friends' parties, and ignoring or dismissing the strong emotions of kids at this age can be counterproductive. It makes sense to listen to their concerns and even compromise on details that seem especially crucial to your 13-year-old. For example, if the local custom "demands" a candle-lighting cake ceremony at the reception (a practice that, as far as anyone can tell, probably originated with Long Island caterers interested in selling big cakes), there's little to be gained by making a stand on that essentially minor matter.
Nevertheless, parents of 13-year-olds should be making most of the decisions that affect their children's lives, and setting limits is as much a part of planning a bar/bat mitzvah party as deciding on the menu. Besides, virtually every decision parents make about the bar/bat mitzvah celebration becomes a lesson in making Jewish choices. If parents pay more attention to the color scheme than to the Torah portion, the child learns that the religious ceremony is secondary to putting on a pretty show.
Alternatives. While the overwhelming majority of families choose to hold bar/bat mitzvahs in a synagogue, they have also been celebrated in living rooms, function halls, and backyards. Do-it-yourself bar/bat mitzvahs tend to be small, intimate, and modest, and tend to be made by families who are part of or active in a havurah or minyan, small, self-directed groups of Jews who meet for study, community, and worship. As Jewish religious services do not absolutely require the presence of a rabbi, the proceedings may be led by a learned family member or friend, or by the bar/bat mitzvah him/herself. Some people consult with a teacher or rabbi for advice and assistance, or hire someone to run the service.
The most common alternative to the synagogue bar/bat mitzvah, however, is to take the ceremony to Israel. Families can hold the ceremony at the Western Wall in Jerusalem (for boys only, as Orthodox rulings restrict public and communal observances and services for women at the Wall), at the historical ruins of Masada (for both boys and girls), and at other sites, both sacred and secular.
This kind of trip has had a very powerful impact on many families, who consider it a turning point in their Jewish lives. Tour companies that specialize in bar/bat mitzvah trips to Israel make all necessary arrangements, and even provide the Torah. Some families celebrate a bar/bat mitzvah twice; once at their synagogue and again in Israel.
Afterward. Traditionally, bar/bat mitzvah marks the beginning of adult Jewish commitment. In terms of Jewish law, a bar/bat mitzvah can be counted in a minyan, the quorum needed for prayer, and may act as a witness in a legal proceeding. Bar/bat mitzvah also signals the start of more mature learning, and certainly few people are ready to tackle the moral, ethical, and theological questions of Jewish tradition before the age of 13.
In practice, however, many parents permit bar/bat mitzvah to be a "graduation" from Jewish learning and, indeed, from Jewish life. If parents permit their children to quit religious school, and if they themselves give up synagogue membership after their last child's "big day," young adults will understand that Jewishness is hardly a priority. On the other hand, parents who remain active in synagogue life, and who insist that religious school confirmation is no more optional than high school graduation, send the message that Jewishness is essential, and an ongoing choice for adults—a powerful lesson.
## MARRIAGE
To the Jewish imagination, the wedding is a prototypical act of creation and thus the premier life-cycle event. The Zohar, the great book of Jewish mysticism, states, "God creates new worlds constantly. In what way? By causing marriages to take place."12 Although the core of the Jewish wedding ritual is simplicity itself, the customs, symbols, and rituals associated with marriage spill over into more than a year's worth of celebration and joy.
Reb Nachman of Bratslav, a 17th century Hasidic master, is credited with a wonderful story about keeping the focus of a wedding on what's really important:
A group of people who have been to a wedding are walking home when one says, "That was a beautiful wedding. The food was out of this world." One of her companions says, "It was a great wedding. The band was terrific." A third friend chimes in, "I never had more fun at a wedding. I got to talk to people I hadn't seen in years."
But Reb Nachman, who overhears this conversation, says, "Those people weren't really at a wedding."
Then a fourth person joins the group and says, "Isn't it wonderful that those two people found each other!" At that Reb Nachman says, "Now that person was at a wedding!"
At their best, Jewish weddings are simultaneously reverent and hilarious, delicious and schmaltzy, intimate and communal, mysterious, romantic, and revealing. And everyone who has been there feels like they witnessed some sort of miracle.
Symbols, Laws, and Customs
The season of preparation and celebration that surrounds Jewish weddings includes parties and rituals, customs and symbols, documents and gifts that take the happy couple and their families from the first announcement of an engagement to the wedding day, and beyond. The following discussion of laws and customs includes only selections from the much longer wedding menu.
The huppah. Jewish marriage ceremonies take place beneath a huppah—a canopy supported by four poles. Although there are customs and conventions about the most appropriate location for a wedding, a huppah can be raised anywhere, reflecting the Jewish notion that almost any place can be made a holy place by human action and intention.
The huppah is a multifaceted symbol: of home, garment, bedcovering, and a reminder of the tents of the ancient Hebrews. During the 16th century, the vogue was for a portable canopy held aloft by four friends, a custom that remains popular to this day.
Some couples* have embraced the old custom of using a prayer shawl, or tallit, as a canopy, a symbol that affirms a commitment to creating a Jewish home. People also commission or make beautiful canopies using batik, silk screen, weaving, quilting and embroidery. These become instant heirlooms and are often displayed in the couple's home, on a wall, or even suspended as a canopy over the bed. Some couples raise their huppah again, over a child's brit ceremony (see "Birth").
Timing. While a huppah can be raised almost anywhere, Jewish law is far more prescriptive about the timing of weddings. Marriages do not take place on the Sabbath, nor on the major holidays and festivals, including Rosh Hashanah, Yom Kippur, Passover, Shavuot, and Sukkot, nor, traditionally, during the days between Passover and Shavuot. Weddings are forbidden on Shabbat not only because the work and travel involved could violate the Sabbath spirit of rest, but also because of the injunction against mixing one simcha—or joy—with another. The combining of two kinds of happiness risks that one or both of them will not be given their full due, which is why double weddings are discouraged.
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From every human being there rises a light that reaches straight to heaven. And when two souls that are destined to be together find each other, their streams of light flow together, and a single brighter light goes forth from their united being.
THE BAAL SHEM TOV
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The ketubah. The Jewish marriage contract is one of the oldest elements of Jewish weddings. It is also one of the least romantic. In its traditional form, the ketubah—a word derived from the Hebrew for "to write"—does not mention love, trust, the establishment of a Jewish home, or God. The ketubah is a legal contract, plain and simple, written in Aramaic, the technical language of Talmudic law, not the poetic biblical Hebrew of Song of Songs.13
When it came into use during the first century C.E., the ketubah was considered a great advance for its time, in part because it provided women with legal status and rights in marriage. Over the centuries, it has changed very little, and indeed, a contemporary traditional ketubah is very much like a marriage contract from over a thousand years ago, complete with phrases such as:
And I here present you with the marriage gift of virgins, two hundred silver zuzim, which belongs to you, according to the law of Moses and Israel; and I will also give you your food, clothing and necessities, and live with you as husband and wife according to the universal custom. And this maiden consented and became his wife. The trousseau that she brought to him from her father's house in silver, gold, valuables, clothing, furniture and bedclothes, all this the bridegroom accepted in the sum of one hundred silver pieces.
Clearly, these terms are archaic, at best, in describing relationships between women and men today. In order to sign a marriage contract in good faith (and also to reflect the realities of same-sex couples) rabbis and calligraphers, brides and grooms, and loving partners have written many new ketubah texts to reflect the realities of contemporary marriage and partnership. Contemporary documents not only express mutual and egalitarian obligations and commitments, they can also be a way for couples to give voice to their feelings for each other and hopes for their marriage. Some ketubot use the traditional text with additions, but many are wholly original. In general, modern ketubot are written both in English and Hebrew, and are signed by the bride and groom, as well as witnesses and the rabbi, cantor, or other officiant.
Beautifully calligraphed, illustrated, and illuminated, there are a wide variety of ketubot available for sale. Individuals may also commission unique works by artists. (Search "ketubah" on the Internet for a huge selection.)
Here is an example of a modern ketubah text:
On the first day toward Shabbat, the _____ day of _______, in the year five thousand ________ since the creation of the world according to our accustomed reckoning in __________, ___________ (bride's name) and __________ (groom's name), in the presence of beloved family and friends entered into this covenant with each other.
We promise to consecrate ourselves, one to the other as husband and wife, according to the tradition of Moses and Israel; to love, honor and cherish each other; to work together to create a home faithful to the teachings of Torah, reverent of the Divine, and committed to deeds of loving-kindness. We promise to try always to bring out in ourselves and in each other qualities of forgiveness, compassion, and integrity. All this we take upon ourselves to uphold to the best of our abilities.
Rabbis and witnesses. In a Jewish wedding, the bridal couple actually marry each other through their own words and actions. However, it is customary to have an officiant, a person called a mesader kiddushin, "one who leads [literally, orders or arranges] the sanctification." Although any knowledgeable Jew can recite the necessary blessings at a wedding, cantors and rabbis almost always perform this honor. Most clergy also meet with the couple in advance of the wedding to discuss marriage and the establishment of a Jewish home, as well as plans for the ceremony.
Two impartial witnesses are required to make a Jewish wedding "kosher," or proper. Neither of the witnesses may be related to either the bride or groom, so they can have no emotional, social, or economic stake in the marriage. Because they are such important participants, it has been suggested that witnesses assume a special kind of responsibility for the marriage, especially in times of trouble.
The wedding. The essence of the Jewish wedding ceremony can be summed up in a few words: the bride accepts an object worth more than a dime from the groom, and the groom recites a ritual formula of consecration. If these two actions are witnessed by at least two other people, a wedding has taken place.
Over the centuries, some of the customs and traditions that surround this simple ceremony have taken on almost equal authority and importance. They are described here, in brief.
The processional. In a standard Hollywood wedding, the father escorts his daughter down the aisle and gives her away. The Jewish custom is very different. Both parents lead their children—sons as well as daughters—to the huppah and to marriage. No one is "given away." Indeed, the Jewish processional demonstrates how a marriage is a union of families, not just individuals.
In some communities, it is customary for a handheld huppah, carried on long poles, to precede the couple, and for members of the processional to light the way with candles. Perhaps the most common way of welcoming the bride and groom to the huppah is with music. In ancient times, the sounds of flutes greeted the bride and groom, and Yemenite brides are sometimes preceded by a group of singing women. In America, string quartets, organs, choirs, soloists, or the guests themselves perform this customary honor.
Under the huppah. Before the 11th century, the Jewish wedding was composed of two distinct rituals separated by as much as a year. The first of these was betrothal or kiddushin, from the same root as the word kadosh, or holy. After betrothal, the bride and groom were considered legally wed, and a formal bill of divorce was necessary to dissolve the marriage. Even so, the marriage was not consummated until after the next ceremony, the nuptials or nissuin, a word derived from the verb nasa, which means to carry or lift, and may refer to the days when a bride was carried through the streets to her new home. The nuptials are not accomplished by words, but in a symbolic act of intimacy called yichud. Betrothal designates the bride and groom for each other only; nuptials give them to one another.
It has been nearly ten centuries since these two ceremonies were made into one, but Jewish weddings still show the seam where the two rituals were joined. The presence of two cups of wine, one for each ceremony, is a reminder of the time when two separate ceremonies were begun with kiddush, the prayer of sanctification recited over wine.
Circling. Just before the ceremony begins, it is customary for the bride to circle the groom, either three times or seven times, according to various customs. Circling is a magical means of protection, so the bride builds a wall against evil spirits by walking around the groom. The bride's circle has also been interpreted as a gesture that binds the groom to her.
A custom once abandoned because of its magical connotations and the implied subservience of the bride, the gesture has been reclaimed by many couples. In some ceremonies, both partners circle each other in turn, or simultaneously, holding hands.
Betrothal (Kiddushin). Most Jewish weddings begin with two introductions. The first one is addressed to the people gathered—especially the bride and groom.
B'ruchim haba'im b'Shem Adonai.
Welcome in the name of Adonai.
The second, a prayer asking for God's presence at and blessing of the marriage, is called the "Mi Adir."
Splendor is upon everything.
Blessing is upon everything.
May the One Who is full of this abundance
Bless this groom and bride.
TRANSLATION BY DEBRA CASH14
Next comes the recitation of kiddush over wine, which begins virtually all Jewish observances and celebrations. The betrothal blessing, which follows, was once recited a full year before the nuptials and includes a specific warning that betrothed couples are not sexually permitted to one another until after the next ritual takes place. Today, it is often translated loosely. For example:
"Praised are you Adonai, Ruler of the universe, who has made us holy through Your commandments and has commanded us concerning marriages that are forbidden and those that are permitted when carried out under the canopy and with the sacred wedding ceremonies."
The wine is drunk after this blessing is recited. In some communities the first cup of wine is shared with members of the immediate family.
The core of the ceremony follows, with the groom's giving and the bride's acceptance of a ring. As he gives her the ring, the groom recites the words that literally marry them. This part of the ceremony is called the Haray aht (from the first two words), and because it is essential that both people understand the meaning of these words, the phrase is recited both in Hebrew and English, or whatever language the couple knows best.
Haray aht m'kudeshet li b'taba'at zo k'dat Moshe v'Yisrael
By this ring you are consecrated to me in accordance with the traditions/laws of Moses and Israel.
The bride is not legally required to say or do anything when she receives the ring. However, in many ceremonies today, the bride replies, either with a line from Songs of Songs ("I am my beloved's and my beloved is mine") or with the same words the groom addressed to her (adapted for gender), which in effect, equalizes the wedding ritual.
Haray ata m'kudash li b'taba'at zo k'dat Moshe v'Yisrael.
By this ring you are consecrated to me in accordance with the traditions/laws of Moses and Israel.
The Jewish wedding liturgy contains no wedding vows or "I do's." However, since an expression of intention is such a powerful image in American culture, and since couples often feel a need to say "yes" during the ceremony, many rabbis and couples add vows either just prior to or immediately following the ring ceremony. Most rabbis and cantors avoid the "To have and to hold, to honor and obey" formulas common to secular and Christian wedding ceremonies. Instead, vows or promises can be personal and specific. Sometimes they are taken from the ketubah, or are written by the bride and groom themselves.
The ring ceremony completes betrothal/kiddushin. At this juncture it has been customary, almost since the beginning of the combined betrothal-and-nuptials wedding in the 12th century, to make a clear separation, traditionally done by reading the ketubah or part of it; generally, this is also the time when the rabbi makes a short speech.
Sometimes, there are personal additions to the ceremony as well: songs, poems, or personal prayers by family members and friends.
Nuptials (nissuin). This ceremony consists of two elements: the seven wedding blessings, sheva b'rachot, and the seclusion of the bridal couple, called yichud.
While a wedding requires only two witnesses to be valid, a minyan—ten adult Jews—must be present for the seven blessings to be recited. Generally, the rabbi or cantor chants the wedding blessings, but there is also a long tradition of honoring special guests by asking them to read or chant one or more of them. In one Sephardic tradition, parents cover the bride and groom with a prayer shawl before the seven wedding blessings are recited.
Although the seven blessings constitute the longest part of the wedding liturgy, only the last two have anything to say about weddings or brides and grooms. Read as a whole, however, they situate the bride and groom within the entire span of Jewish time. The seven blessings mention the beginning of time in Eden when life was perfect, and the end of days when that perfection, or wholeness, will be restored. A fulcrum between the first and the last, every wedding becomes the embodiment of union. And since Judaism has no concept of individual redemption, the huppah provides the whole community with a glimpse into an unbroken, healed reality.
The Seven Blessings
You abound in blessings, Adonai our God, who creates the fruit of the vine.
You abound in Blessings, Adonai our God, You created all things for Your glory.
You abound in Blessings, Adonai our God, You created humanity.
You abound in Blessings, Adonai our God, You made humankind in Your image, after Your likeness, and You prepared for us a perpetual relationship. You abound in Blessings, Adonai our God, You created humanity.
May she who was barren rejoice when her children are united in her midst in joy. You abound in Blessings, Adonai our God, who makes Zion rejoice with her children.
You make these beloved companions greatly rejoice even as You rejoice in Your creation in the Garden of Eden as of old. You abound in Blessings, Adonai our God, who makes the bridegroom and bride to rejoice.
You abound in Blessings, Adonai our God, who created joy and gladness, bridegroom and bride, mirth and exultation, pleasure and delight, love, fellowship, peace and friendship. Soon may there be heard in the cities of Judah and in the streets of Jerusalem, the voice of joy and gladness, the voice of the bridegroom and the voice of the bride, the jubilant voice of bridegrooms from their canopies and of youths from their feasts of song. You abound in Blessings, Adonai, our God, You make the bridegroom rejoice with the bride.
The seven blessings conclude the marriage service. Some rabbis give the wedding sermon at this point, and others end with the official secular pronouncement, "By the power vested in me by the state of..." Most cantors and rabbis conclude with a benediction.
The broken glass. The shattering of a glass to mark the end of the wedding is a practice that dates back to the writing of the Talmud and has become one of the most kaleidoscopic of all Jewish wedding symbols. The broken glass is a joyous conclusion that encourages merriment and rejoicing at the meal to follow. The wedding ritual can become rather solemn, and the shattering gives permission for levity to break out. There is an irony in this since, according to one explanation, the glass-breaking may have originated at one particularly raucous wedding party, as a way of calming things down.15
By the 14th century, the broken glass was generally interpreted as a reminder of the destruction of the Temple in Jerusalem, and of the fact that even at moments of personal joy, Jews remember that terrible loss. This remains the dominant interpretation, although it is generally broadened to include all of the losses suffered by the Jewish people, and also the need for the repair and redemption of the whole world. The breaking is not only a reminder of sorrow, but also an expression of hope for a future free from all violence.
There are other interpretations as well. A broken glass cannot be mended, likewise marriage is irrevocable, a transforming experience that leaves individuals forever changed. The fragility of glass also suggests the frailty of human relationships; even the strongest love is subject to disintegration. In this context, the glass is broken to "protect" the marriage with the wish that, "As this glass shatters, so may our marriage never break."
Loud noises are also an ageless method for frightening and appeasing demons, who, it was widely believed, were attracted to the beautiful and the fortunate—people like brides and grooms. In a more general way, the breaking glass hints at the intensity and release of sexual union (the classic Freudian interpretation of this custom is that it represents the breaking of the hymen), which is not only allowed married couples but required of them.
The sound of breaking glass signals the end of the ceremony. The silence that surrounded the huppah ends with an explosion. People exhale, shout "Mazal tov!" clap their hands, embrace, talk, and sing the traditional wedding song, "Siman Tov u Mazal Tov" ("a good sign and good luck" or "a good omen and a good star") as the couple departs.
Yichud. After they leave the huppah, bride and groom traditionally spend ten or fifteen minutes alone together. Yichud, or seclusion, is a custom that dates from ancient days when a groom would carry the bride off to his tent to consummate the marriage. Although consummation has not immediately followed the wedding ceremony for many centuries, these moments of private time have remained as a demonstration of the couple's new level of intimacy.
Yichud is a precious pause in a hectic day, an island of privacy and peace before the public celebration begins. It is a time for bride and groom to hold each other, to face each other, to let it all sink in. And since it is customary for a bride and groom to fast on the day of their wedding, Yichud also permits the couple to break the fast as husband and wife.
Celebrating. "Reception" is too formal a word for the celebration of a wedding. Simcha is more accurate; it means joy as well as the celebration of a joyous event, and the purpose of Jewish wedding parties is to increase the joy of the bride and groom. The Talmud says that anyone who enjoys a wedding feast but does nothing to rejoice the hearts of the bride and groom has transgressed against the "five voices": the voice of joy, the voice of gladness, the voice of the bridegroom, the voice of the bride, and the voice that praises God.
The meal that follows a Jewish wedding is a seudat mitzvah, a meal that fulfills a religious commandment to rejoice. At a wedding, everything that increases happiness—words of Torah, blessings, songs, dances, toasts, riddles, jokes, parodies, indeed anything that makes the bride and groom laugh—is considered a religious act, a way of praising God.
In order to ensure the mitzvah of entertaining the bride and groom, it is customary to have someone play the role of badchan, or "jester." The badchan's job is to act as master of ceremonies for the celebration by making toasts, telling jokes, and organizing and eliciting performances from other guests. Sentiment as well as foolishness play a part in this assignment, thus a badchan may start by reading a love poem, then lead the guests in a song or cheer, crown the "royal" couples with paper crowns, and lead the dancing.
One of the best known of all Jewish wedding customs is the moment at which the bride and groom are raised up on chairs and whirled around each other holding either end of a handkerchief. The custom may have originated as a way for the bride and groom to catch a glimpse of each other over the physical barrier that separates the rejoicing of the women from the men. But it may also be an echo of the privileges of royalty, who have been carried in chairs and on litters from earliest times.
The first year. Since biblical times, a couple is referred to as "bride and groom" for their entire first year together. That year begins with a week of parties. According to one tradition, a minyan of friends gather with the couple each night for a week, for a meal, blessings, and songs; this practice is also called sheva brachot for the "seven blessings" recited nightly in their honor.
The yearlong public recognition of the special status of brides and grooms is a way for the couple and the community to savor the joy and gladness of the wedding. The designations "husband" and "wife" only apply after the first anniversary.
Intermarriage. A fact of life for more than 50 percent of couples in North America, intermarriage is perceived by the Jewish community as a threat to the continuation of the Jewish people. It may be difficult to find a rabbi to officiate (or co-officiate) at a wedding where one of the partners is not a Jew, and it is difficult not to feel personally rejected by this rejection.
It is important to remember that a Jewish wedding has legal (halachic) standing when two witnesses see the bride accept a ring from the groom and hear him say, "With this ring you are consecrated to me according to the laws of Moses and Israel." A rabbi does not marry a bride and groom; they marry each other with these words and gestures. Thus, if one of the parties is not bound "by the laws of Moses and Israel," the marriage has no standing.
Another reason for rabbis' reluctance to participate in intermarriage ceremonies is that the major function of Jewish weddings is to establish Jewish homes and families. According to Jewish law, children born to non-Jewish mothers are not considered Jews. Demographic evidence seems to show that few children of mixed-faith marriages identify as Jews as adults.
The ongoing debate and hair-pulling over intermarriage tends to overwhelm and ignore the dilemmas facing many intermarrying couples. However, there are individuals in most cities and towns—among them counselors at Jewish agencies, rabbis, cantors, and marriage counselors—who are willing to listen to and discuss the ways intermarrying couples can affirm their connection to Judaism, beginning with the wedding. Many rabbis suggest that couples seek out a judge or justice of the peace to perform a ceremony that includes Jewish references and symbols.
Some rabbis and cantors will officiate at weddings between Jews and non-Jews, not as a matter of course but on a case-by-case basis. Such rabbis agree to officiate when the non-Jew has no religious affiliation and both people express a willingness to create a Jewish home. These interfaith weddings, which may not include all the liturgical elements of a traditional Jewish wedding, are seen as a way of encouraging couples to become members of the Jewish community, and to raise Jewish children. Alternately, Jewish tradition can be incorporated into a wedding ceremony by a justice of the peace.
Divorce. Divorce has always been a fact of Jewish life, which means that there has always been a body of law attached to this transition as well. While Jewish law permits a few instances where a wife can dissolve a marriage, it is by and large a male prerogative. According to traditional practice, a husband commissions a religious divorce decree called a get, which is formally delivered to his wife. If she accepts it, the divorce is then certified by a court of three rabbis, a bet din.
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When a marriage ends, the altar sheds tears.
TALMUD
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In fact, only a small fraction of divorced American Jews seek a Jewish divorce, and since between one-third and half of all Jewish marriages end in divorce, it seems clear that most people consider civil divorce sufficient, valid, and final. However, as rabbis have been called upon to do more family and marriage counseling, many people have expressed the need for a formal Jewish conclusion to a relationship that began with Jewish blessings. Thus, some liberal rabbis offer a Jewish divorce ritual to help give the parties a sense of resolution and closure.
Liberal gittin (the plural of get) and accompanying divorce rituals are egalitarian, reciprocal agreements, which can be initiated by either partner. The get may be written either in English or Hebrew, or in both languages. It may include specific clauses relevant to the couple that is divorcing, but the core of the document is a formal statement of dissolution. For example:
I, _______________, son/daughter of ______________ and _________________, of my own free will grant you this bill of divorce. I release you from the contract which established our marriage. From this day onward you are not my husband/wife and I am not your wife/husband. You belong to yourself and are free to marry another.16
Such a document can be executed in a rabbi's study or any place agreeable to the parties involved, and is usually signed by the couple, the rabbi, and, in some cases, by witnesses. In order to physically enact the dissolution of the marriage covenant, a corner of the document might be cut or ripped.
This form of divorce differs substantially from a traditional Jewish divorce and may not be recognized as legitimate by Orthodox Jews. Since divorce is one of the most divisive issues in the community, affecting remarriage and the Jewish status of children, this is an issue to discuss fully with a rabbi.
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For everything there is a season and
a time for every purpose under heaven
a time to be born and a time to die
a time to plant and a time to uproot...
a time for tearing down and a time for building up
a time for weeping a time for laughing a time for embracing and
a time to refrain from embracing.
ECCLESIASTES
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*Many liberal rabbis and congregations welcome same-sex couples under the huppah, both in places where their union will have secular legal sanction, and in those where "gay marriage" is illegal. This introduction to the Jewish wedding, while it occasionally employs the terms "bride" and "groom," applies in all particulars to gay and lesbian couples as well.
## CONVERSION AND ADOPTION
The Jewish community is changing. More people are choosing to become Jews than at any point since the beginning of the Common Era, and more Jews are creating and enlarging their families through adoption.
Of course, conversion and adoption are not new to Judaism. Both are honored in the biblical stories of Ruth and Moses, and the Talmud speaks of converts with admiration. "The convert is dearer to God than Israel. When the nation assembled at the foot of Mount Sinai, Israel would not have accepted the Torah without seeing the thunders and the lightning and the quaking mountains and hearing the sound of the shofar. Whereas the proselyte, without a single miracle, consecrated himself to the Holy One, praised be God, and puts upon himself the yoke of the kingdom of heaven. Can anyone be deemed more worthy of God's love?"17
For centuries, conversion was discouraged because it posed a danger to the Jewish community. Renouncing Christianity for Judaism was a capital offense, which extended to the Jews who welcomed any convert. Jewish attitudes toward converts and conversion was slow to change, and the tradition that required rabbis to rebuff people interested in converting three times is still in effect in some parts of the community.
However, for the most part, the door is wide open to those who choose Judaism. Where conversion for the purpose of marriage was once treated as suspect, today rabbis and Jewish organizations welcome and even solicit interest from non-Jews planning to marry or already married to Jewish spouses.
In large part, this change is a response to the fact that as many as half of all American Jews marry non-Jews, but it also reflects a recognition that, in the marketplace of ideas and in a world of seekers, Judaism is an intrinsically fulfilling way of life that appeals to people for many different reasons.
Whatever the circumstances, choosing Judaism is a profound and momentous decision, and one who takes this path with a full heart is called a ger tzedek, "righteous proselyte," from the same root as tzadik, which means a righteous or pious person.
For those interested in finding out whether Judaism is right for them, the liberal movements offer a variety of introduction-to-Judaism courses. These programs vary both in content and form, but they generally cover a broad range of subjects, including history, theology, Sabbath and holiday observance, Israel, the Holocaust, an introduction to the Hebrew alphabet, and some basic prayers. Students are also encouraged to practice making some Jewish choices, by attending worship services and trying out home observances.
Although classwork is important in these courses, the primary experience of study is done one-on-one with a rabbi. The content and duration of meetings with the rabbi depend upon his/her requirements and the student's level of interest and diligence. When a rabbi determines that a student is ready, s/he will explain and schedule the ritual elements of conversion.
Not all liberal rabbis require their students to undertake all of these rituals, but according to tradition, conversion requires mikveh (ritual immersion) for men and women, and circumcision or ritual circumcision (drawing one drop of blood from an already circumcised foreskin) for men. Converts also meet with a bet din, literally, "house of law," a Jewish court that usually consists of three rabbis, who examine the candidate about his/her her knowledge of Judaism, and, perhaps even more important, try to discern the sincerity and motivation for making this extraordinary choice. A public ceremony of acknowledgment is part of the process in some, though not all, congregations.
Mikveh entails immersion in a ritual bath (also called a mikveh), and the recitation of two short prayers. Like virtually all religious traditions, Judaism treats water as a symbol of rebirth and renewal; the mikveh represents the source of human life, the waters of the womb, and according to one legend, the "living water" of mikveh flows from the mystical source of all water and all life, the river whose source is in Eden.18 Of all the rituals associated with conversion, mikveh is often counted the most powerful. For a tradition that is so intellectual, the pure physicality of being completely nude in a body of warm water is a revelatory and radical enactment of changing one's status from not-Jewish to Jewish.
The importance of brit milah, the covenant of circumcision, is discussed in the chapter on "Birth" and is best discussed with one's rabbi.
People get very nervous at the prospect of meeting with a bet din; however, it is best not to think of this as a pass-fail test for which you need to cram. Although it is not a pro forma meeting, rabbis will not bring unqualified candidates before a panel of their peers. As a rule, batei din tend to be far less concerned with dates and Hebrew fluency than they are with learning about a candidate's motivation for conversion and his/her commitment to basic Jewish concepts and practices.
Historically, conversion to Judaism was a strictly private event; indeed, focusing public attention on the process was seen as an abrogation of respect. Since a Jew-by-choice is a Jew, period, there was a sense that reminding people of the distinction was somewhat denigrating. Now that conversion is more common and widely seen as a source of strength and pride, the reluctance to go public has faded. Indeed, understanding conversion as a Jewish life-cycle event means that, like birth or marriage, it has an impact beyond the individual; every time a person becomes Jewish, s/he transforms at least one and usually two families. Furthermore, every new Jew changes the entire Jewish community forever.
With this in mind, celebrating conversion seems not only appropriate but necessary. Some people bring close friends or family members to the mikveh or to the meeting with the bet din for support, and then go to celebrate afterward, with gifts, a meal, or even an excursion to shop for a tallit, or a kiddush cup, or a mezuzah.
In some congregations, new Jews are acknowledged at a worship service, where they might be called up to the Torah for a blessing. Some Jews-by-choice address a speech or d'rash to the congregation and then sponsor a festive meal afterward—a seudat mitzvah.
Conversion raises complex issues within the Jewish world about "who is a Jew" and the authenticity of liberal Jewish life. The Orthodox community and the state of Israel recognize only conversions performed under Orthodox auspices, a position that may have ramifications for the children of Jews converted by Reform, Reconstructionist, and Conservative rabbis. Becoming Jewish means taking part in this and many other contentious debates; it is essential to begin this discussion with a rabbi you know and trust.
Adoption
As adoption has become more common, it has become the source for public joy, celebration, and nachas—a word that conveys the intense pleasure parents take in their children. All kinds of Jews now complete their families through adoption, including single people who wish to become parents, gay and lesbian couples, and those who have difficulty conceiving. For people who struggled for a biological child, adoption may be a difficult choice, and experts stress the need to grieve for that loss before moving on. However an adoptive child arrives, his/her arrival always brings gratitude and awe at the fulfillment of a cherished dream.
Although there is little about adoption in the Bible or Talmud, Jewish law assumes that foster or adoptive parents bear all the responsibilities of biological parents, and the rabbis tended to favor "nurture" over "nature." "Those who raise a child are called its parents, and not the ones who conceived it."19
During the Second Commonwealth (538 B.C.E.–70 C.E.), Jews were known to rescue gentile children who were orphaned or outcast, and reared them as Jews.20 But that was before Christian and Muslim laws made converting to Judaism a capital crime, and since then, Judaism has concerned itself, for the most part, with the needs of orphans born to Jewish parents. Nevertheless, the adoption of non-Jewish children happened often enough that Jewish law made the conversion of minors provisional until a child reached maturity. Thus, when a child reared as a Jew but born to a non-Jewish mother reached the age of 13, he or she was given the right to affirm or renounce his or her Jewishness.21 In this way, Judaism always mandated full disclosure of children's adoptive status, an openness supported by psychologists and adoption experts today, when nearly all children adopted by Jews are born to non-Jewish parents.
Although adoption has become far more normative and accepted than ever before, Jewish adoptive parents do face challenges as they begin the process and as they navigate their family's unique path. However, there is no need to go it alone. Virtually every congregation includes some adoptive families who can provide guidance and support, as can staff at the local Jewish Family and Children's Services.
Stars of David, a nonprofit, national support network for Jewish adoptive parents, creates links to other families and professionals through local support groups; its members include Jews of all affiliations and beliefs, and it welcomes intermarried couples, single parents, gay and lesbian families, prospective parents, interracial couples with biological children, and grandparents (www.starsofdavid.org). Another support group is the Jewish Multiracial Network, which connects Jews of color and multiracial Jewish families for mutual education and advocacy (www.isabellafreedman.org/jmn/jmn_intro.shtml).
According to Jewish law, the adoption of a baby born to a non-Jewish mother requires a formal conversion, which entails ritual immersion, mikveh, for both girls and boys, and circumcision, brit milah, for boys. Mikveh is the only ritual requirement for the conversion of girls. Baby girls are named either immediately following immersion or sometime later in a synagogue or at home in a brit bat ceremony. An uncircumcised adopted male newborn is given a brit milah on the eighth day after birth, or as soon as possible. For a baby adopted at four months or older, circumcisions are generally done under anesthesia in a hospital, with both a physician and a mohel (ritual circumciser) in attendance. If a boy was circumcised without religious ceremony, a ritual is performed in which a mohel draws a drop of blood from the site of the circumcision and recites the appropriate blessings. (See "Birth" for more about ceremonies for both girls and boys.)
Liberal rabbis interpret Jewish law in different ways. The Reform and Reconstructionist movements recognize the Jewishness of children not born of a Jewish mother who are given a Jewish upbringing both in religious school and at home, who celebrate Jewish holidays, and who publicly identify with the Jewish people. Parents who are in the process of adopting the child of a non-Jewish mother are advised to discuss these issues with a rabbi.
For some parents, the special feelings of joy, gratitude, and awe inspired by adoption call out for an additional ritual, and have created Jewish ceremonies that speak to this need. Since there is no precedent for these rituals, their timing, location, and content are entirely determined by the parents, often with assistance from a member of the clergy.
## DEATH AND MOURNING
The primary principle underlying every Jewish law, ritual, and custom having to do with death and mourning is kavod, a word that means "honor" and "respect." The Jewish approach to bereavement is also based on respect for the powerful emotions of loss.
Unlike the widespread American practice of encouraging mourners to hide or repress their grief and get back to work within a matter of days, Jewish law and custom create time for grief and provide a methodology for grieving. The specific laws regarding the mechanics of burial—even to selecting a coffin—give mourners guidance during a time when making necessary decisions is so difficult. And after the funeral, mourners are given a structure to encourage feeling their loss, and thus heal.
While this chapter provides an introduction to Jewish burial and mourning practices, when a death occurs it is crucial to seek out assistance and support from members of the Jewish community: rabbis, Jewish funeral home personnel, members of your synagogue or the deceased's congregation. It is relatively easy to find such help, even for people who are unfamiliar with Jewish burial and mourning practices. For those coping with a loss in a strange city, hospital chaplains—of all denominations—can direct you to local Jewish resources.
Burial
From the moment of death until a body is buried, Jewish law and custom are entirely focused upon honoring the deceased. Symbolic gestures of respect include closing the eyes and mouth, lighting a candle, and opening a window for the soul's release.
The traditional prayer said upon witnessing or hearing of a death is a statement of total acceptance.
Baruch Ata Adonai Eloheynu Melech Ha-olam Dayan Haemet.
Holy One of Blessing Your presence fills creation, You are the
True Judge.
Jewish tradition stresses that the body should not be left alone from the time of death until burial, which takes place as quickly as possible. The custom is to have someone read Psalms beside the body, a duty that can be performed by family members, friends, or by synagogue members. Upon request, Jewish funeral homes will provide a ritual guardian, or shomer, for this purpose.
If a death occurs in a hospital, family members should inform the staff of their wishes regarding respectful treatment for the body. Autopsies are not automatically approved because they are seen as a desecration of the body and thus an abrogation of respect. However, since the rabbinic principle that saving a life takes precedence over nearly every other law, autopsies, organ donation, and donation of the body for medical research may be authorized with this mitzvah in mind. These issues are best discussed on a case-by-case basis with a rabbi.
While some people make their own burial and funeral arrangements in advance of their own deaths, family members are often left to make the decisions surrounding burial. Jewish tradition is quite specific in this regard: embalming, viewing the body, and holding a wake are considered disrespectful to the body and to the memory of the deceased.
Mahogany caskets with silver hardware may be purchased from a Jewish funeral home for the price of a luxury car, but according to Jewish tradition, respect for the dead is expressed not by "burying money," but by contributing to tzedakah—especially to charities and causes that were important to the deceased. A plain wooden coffin is seen not as a sign of cheapness or disrespect, but as a way to promote the natural processes of death and decomposition, a way of returning to the earth, to the source of life.
A desire for simplicity can be expressed to representatives of a Jewish funeral home with a request for "the least expensive kosher casket available." In this context, "kosher" means "in conformance with Jewish law," in other words, made of plain wood by Jews for the purpose of burying a Jew.
According to Jewish tradition, the body is prepared for the grave with the utmost simplicity. No attempt is made to preserve or prettify the body, which is washed and cleaned according to specific regulations. All people, male and female, rich and poor, are buried alike, wearing nothing but plain, white shrouds, without pockets. Jews are sometimes buried wearing a tallit; however, the fringes on the prayer shawl will be cut, since they are reminders of the mitzvot or obligations that are binding only in this world.
These practices are known to Jewish funeral home personnel, however, it may be necessary to ask for them to be performed.
* * *
A baby enters the world with closed hands. A person leaves the world with open hands. The first says, "The world is mine." The second says, "I can take nothing with me."
ECCLESIASTES RABBAH
* * *
Cremation
Jewish law prohibits cremation, based on a belief that the natural process of the decomposition of the flesh shows respect for the body. Jewish burial methods stress a return of the body to its source, unadulterated, reuniting one part of creation with the rest. Cremation is seen not only as a repudiation of the natural pace of "dust to dust," but as the desecration of that which was created in God's own image. In modern times, the Holocaust has cast cremation into an especially problematic light. The very word conjures up images of ovens, chimneys, and the charred remains of thousands of Jewish bodies that were never laid to rest.
In the past, someone who chose cremation was treated as one who had cut him or herself off from the Jewish community. In traditional circles, official forms of mourning are not permitted for one who has been cremated and survivors may not be permitted to say Kaddish or sit shiva; the response is rarely so drastic in liberal circles.
Despite the legal, historical, and emotional arguments against it, some Jews express wishes and even make arrangements for their own cremation, often with the intention of sparing their families the trauma and expense of a funeral. A loved one's wish to be cremated can create an emotional dilemma for family members who would prefer to follow a more traditional Jewish path. The son or daughter of a parent who wishes to be cremated is asked to choose between not obeying Mom or Dad's last wishes, and doing something that violates a belief or need as mourners. For many people, having a grave to visit is an important part of healing after a loss.
While it is difficult to speak about these matters with a healthy parent, sibling, or spouse, this is a conversation worth having. The counsel of a sympathetic rabbi can also be extremely helpful.
The Funeral
Jewish funerals take place as soon as possible following death, although they may be postponed until relatives and friends can arrive, as a way to honor the dead. Burials are not permitted on Shabbat and most holidays.
Funeral services usually take place at a funeral chapel or in a synagogue, though they may also be conducted at a home or at the cemetery. While anyone knowledgeable about Jewish burial customs may conduct a funeral, it is a function performed almost exclusively by rabbis and cantors. The decision about whether or how much family members want to participate in the funeral service, reading a eulogy or prayers, for example, is entirely personal and should be made in consultation with the officiating clergy member. Many families leave the service entirely up to him or her.
Compared with the specific rules and requirements for treatment of the body and burial, there are few liturgical requirements for a funeral service. Psalm 23, "The Lord is my shepherd," is nearly universal and certain prayers are traditional, especially the El Maley Rachamim, "God Filled with Compassion":
God who is full of compassion, dwelling on high
Grant perfect peace to the soul of ______________.
May s/he rest under the wings of Your Presence
Holy and Pure, Who shines bright as the sky.
And may his/her place of rest be as Eden
We pledge tzedakah for the sake of her/his memory.
We pray that You comfort her/his soul in eternal life, under the protection of your wings.
Adonai, You are our heritage.
May s/he rest in peace.
Amen.
The single most important element of the funeral is the eulogy, or hesped, which honors the dead by speaking of him/her in personal terms. Typically, eulogies are delivered by rabbis, who meet with mourners in advance of the funeral to talk about the one who has died and to solicit stories and suggestions for his or her remarks. Sometimes members of the family write the eulogy or parts of it for the rabbi. In some cases, a relative or close friend will deliver the hesped him/herself.
The tearing of a mourner's garments, called k'riah, is an ancient, physical enactment of the feeling that the world has been torn apart. K'riah is often done just prior to the funeral service, although it can take place at the graveside or when someone first hears of the death. For men, the tear is usually made on the lapel of a sport coat or jacket. Women will tear a sweater, dress, or blouse. It is also common to substitute a torn black ribbon, which is then worn on the lapel for the next seven days.
At the Cemetery
It is considered both an honor and duty to help bury the dead.22 Carrying a loved one to his or her grave is seen as a way of paying loving tribute, which explains the custom of having those present participate in the burial by lifting a shovel of earth, a process usually initiated by close family members. Inviting participation in the physical act of burial makes it extremely difficult to deny the reality of death, which in turn makes it possible for grief and healing to begin. Those in attendance generally do not leave the grave until the body is placed into the earth and the coffin is covered with earth, although this, too, is a choice left to family members in consultation with clergy.
Even if there was a chapel or synagogue service, a brief service is also held at the graveside, consisting of Psalms and the recitation of the Kaddish. Kaddish, from the word kadosh, or "holy," is a familiar and much-recited prayer, which has several forms and purposes. Written in Aramaic, the Mourner's Kaddish does not mention death at all, but praises God for the gift of life. Sometime during the Middle Ages, this prayer became associated with mourning and today its recitation evokes the pain of loss and the consolation of remembrance for Jews everywhere. There is a legend that angels brought Kaddish to earth. The 20th century writer S. Y. Agnon imagined that the prayer was first recited by a human mourner to comfort God, Who is said to grieve over the deaths of men and women.23
The recitation of the Kaddish at the graveside begins the mourner's obligation to repeat this prayer during the formal period of mourning, and again at appropriate occasions, such as during a synagogue service.
Mourner's Kaddish
Exalted and hallowed be God's greatness
In this world of Your creation.
May Your will be fulfilled
And Your sovereignty revealed
In the days of our lifetime
And the life of the whole house of Israel
Speedily and soon.
And say, Amen.
May You be blessed forever,
Even to all eternity.
May You, most Holy One, be blessed,
Praised and honored, extolled and glorified,
Adored and exalted above all else.
Blessed are You,
Beyond all blessings and hymns, praises and consolations
That may be uttered in this world,
And say, Amen.
May peace abundant descend from heaven
With life for us and for all Israel,
And say Amen.
May God, Who makes peace on high,
Bring peace to all and to all Israel,
And say, Amen.24
Mourning
The Talmud says, "Do not comfort the bereaved with their dead still before them."25 In other words, it is considered inappropriate to offer words of condolence to mourners until after the funeral. But from the moment the mourners turn away from the grave, the focus shifts from honoring the deceased to comforting the bereaved.
Jewish tradition designates official mourners very narrowly to include people who have one of seven relationships with the deceased: father, mother, son, daughter, sister, brother, spouse. The laws and customs regarding mourning apply only to this small and intimate circle. This does not mean that cousins, grandchildren, and friends are not bereaved or should not express their grief. However, limiting this circle also limits the time one must spend on the official acts of mourning, which call for some withdrawal from the world and from joyful activities.
Jewish mourning practices are arranged in a series of concentric circles that reflect and respond to the diminishing intensity of grief and concurrently reintroduce mourners to the world of the living.
Aninut, the period between death and burial, is a time filled with shock and even denial. Mourners essentially do nothing but prepare for the burial, funeral, and the mourning period to follow. They make necessary phone calls, meet with the rabbi, and spend time with only their closest friends. This is generally not a time when visitors call. Aninut ends with the sound of earth being thrown onto a coffin.
Shiva, from the Hebrew word for seven, refers to the seven days that include and follow the funeral.
This is the most intense period of formal mourning. People often refer to this period as "sitting shiva," because of the custom of sitting on or near the floor, an ancient gesture of being struck low by grief. Funeral homes sometimes provide shiva benches or low stools. Some people remove cushions from couches and chairs and simply sit lower to the ground. Only mourners, not guests, sit on or near the ground.
Shiva usually begins as soon as the mourners return from the cemetery. Since Shabbat and certain holidays affect the counting of these seven days, a rabbi can help determine when this period begins and ends. There are circumstances where shiva is postponed or even canceled, and some people choose to observe shiva for fewer than seven days.
When the family returns from the grave, hands may be washed at the door—a symbolic acknowledgment of the sad duty just completed at the grave and an act of symbolical purification after contact with death. A seven-day candle, usually provided by the funeral home, is lit. Then, a meal is served. This seudat havra'ah, "meal of consolation," is a graphic reminder of the fact that life must go on, even for those with the taste of death in their mouths. It is considered a great act of kindness, a mitzvah, for friends to provide and serve this meal to mourners. Eggs and other round foods, such as lentils, are often served as a symbol of the continuing cycle of life, but this not a festive meal. It is eaten quietly.
During shiva, mourners refrain from business and pleasure. They do not go to work, or watch television, or even leave the house. Mirrors are covered to discourage vanity. Mourners often do not shave, wear new clothing, or have sex. Some Jews do not wear leather shoes, which were a sign of luxury in the ancient world.
The purpose of shiva is not to make mourners feel better or to cheer them up, but to encourage them to grieve. Shiva means taking time to remember and cry, to feel anger, loss, sorrow, panic—whatever feelings are present—fully and without distraction. For seven days, mourners speak of the life that is over; they tell and retell stories, weeping over their loss and also laughing at happy memories. Some families read and discuss books about Jewish mourning customs and books about death and dying during shiva.
If mourners are observing the custom of not going out during shiva, a daily minyan is held in the home so that the bereaved can say Kaddish. The task of organizing a minyan is often done by a synagogue committee set up for that purpose.
Paying a shiva call. Visiting a house of mourning is considered a mitzvah, a good and holy thing to do. Many rules of etiquette are suspended where people are sitting shiva. First of all, one enters without ringing the bell or knocking; mourners are not hosts, nor are guests emissaries of good cheer. People come not to console the mourner so much as to share his or her grief. There is very little that can be said at times like this, but words are not as important as the presence of friends. It is enough that people just come, in the words of the prophet Ezekiel, to "sigh in silence."26
Generally, it is inappropriate to send or bring flowers to a Jewish house of mourning. A donation to charity in the name of the deceased is considered a far more meaningful tribute. Gifts of food are traditional, but rather than bringing the sixth plate of brownies, it may be more helpful to call whoever is taking responsibility for food in the house to find out what is most needed: a dinner casserole, a trip to the grocery store, a few hours of babysitting for small children, or someone to take out-of-town relatives to the airport. These sorts of arrangements, among others, may be performed by a group of friends or a synagogue committee.
Shiva ends on the morning of the seventh day. The memorial candle is blown out in silence, and sometimes mourners go for a walk around the block, as a way of taking a first step back into the real world.
* * *
People used to bring food to a house of mourning. The wealthy brought it in baskets of silver and gold, the poor in baskets of willow twigs, and the poor felt ashamed. Therefore our sages taught that everyone should use baskets of willow twigs out of deference to the poor and in hopes of fostering unity.
TALMUD: MO'ED KATAN 27A–B
* * *
Shloshim refers to the 30 days following burial and includes the seven days of shiva. During shloshim—but after shiva—many of the prohibitions against work and pleasure are lifted. Mourners return to their jobs, sit on real chairs again, go out of their homes, wear perfume, have sex. However, some restrictions still apply, and some people will not attend parties or other social functions, or go to movies or listen to music. Some Jews go to services every day to say Kaddish; others attend services every Shabbat with the same intention. On the 30th day, all outward signs of mourning are suspended, except for those who have lost a parent, who may continue to abstain from attending joyful events and continue to say Kaddish regularly.
Avelut, literally "mourning," is the 12-month period observed only by people who have lost a parent. It is counted from the day of death and ends after 12 Hebrew months. Jewish law requires that mourners recite Kaddish daily for 11 months, which means attending a prayer service where a minyan will be present. Some liberal Jews observe avelut by saying Kaddish at Shabbat services every week for a year.
The year of mourning also mandates refraining from "joyous" activities, so some people do not go to movies or parties. This practice is a way of reminding oneself, "I am not finished mourning. I am not entirely ready to be soothed." As with many practices, the transformative power of accepting such restrictions becomes clear only in retrospect. If one, for example, chooses not to listen to music as a way of mourning a parent, the first notes one hears after such a year are extraordinarily powerful.
Another way to observe the year of remembering a loved one is with gifts to charities that were especially important to the deceased. Similarly, some people volunteer and work for a social service or religious organization, in memory of a parent.
Unveiling. The dedication of a gravestone takes place anytime between the end of shloshim and the anniversary of the death. A cloth or veil is removed from the grave marker in the presence of the immediate family and perhaps a few close friends. An unveiling is not a second funeral, and while rabbis sometimes officiate, it is common for family members to gather on their own to read Psalms or prayers, or just reminisce. There is no set ceremony for an unveiling.
Simplicity tends to be the rule regarding Jewish gravestones. As the Talmud puts it, "We need not make monuments for the righteous—their words serve as their memorial."27 Generally, the marker includes the full Hebrew and secular name of the deceased, the Hebrew date of death, the secular calendar dates of birth and death. There are usually a few Hebrew letters on the stone, which stand for, "Here is buried," or "May his/her soul be bound up in the bonds of life." Jewish symbols, such as the six-pointed star of David, are commonly inscribed, as are quotes from scripture, or personal notes.
The custom of leaving pebbles on a gravestone may date back to biblical days when people were buried under piles of stones. Today, pebbles are usually left as tokens that people have been there to visit and remember.
Yarzeit and yizkor. Yarzeit, from the Yiddish for "a year's time," is the anniversary of a death. A special, 24-hour memorial candle is lit on the eve of the day of the death, and also on the eve of Yom Kippur. It is also traditional to light these candles at the end of the festivals of Sukkot, Passover, and Shavuot. No special prayer is associated with this act of remembrance. Sometimes, silence is the most eloquent tribute.
Yizkor, which means "remember," is the name of a prayer and also the name of the short memorial service that takes place four times every year: on Yom Kippur and at the end of Sukkot, Passover, and Shavuot. The prayer consists of a series of paragraphs that all begin with the words "Yizkor Elohim," "May God remember." It is recited by anyone who has ever lost a parent, a child, a sibling, or a spouse. The Memorial Service also includes paragraphs for those mourning other relatives and friends.
As in all aspects of Jewish life, the traditions surrounding death present mourners with choices. One of the most common alterations in mourning practices among liberal Jews is the choice to attend a weekly rather than a daily minyan during the month of shloshim and the year of avelut. Liberal Jews also reinterpret shiva restrictions in ways that respect the spirit, if not the letter, of the law; for example, while the tradition is not to leave the house during shiva or listen to music, some people make long, meditative walks a regular part of those seven days, or spend time listening to music that was especially beloved by the deceased.
Traditional Jewish burial and mourning customs respond to two fundamental needs, practical and psychological. During the emotional crisis that follows a death, it is comforting to have a set of clear directions to follow. Equally compelling is the way that Jewish burial and mourning customs reflect modern insights into the healing processes of grief. The image of Jewish tradition as a mirror, a tool of reflection, seems particularly apt for mourners. During the week of shiva, the mirrors in a mourner's house are draped to encourage people to look within and also to seek answers from those gathered around them in sympathy. Recovering from the death of a loved one is never easy or speedy, and there is much evidence that people who do not fully explore the depth of their feelings immediately following a death, tend to suffer more depression and disorientation years later. The "schedule" of Jewish mourning customs insists both that people take time to fully grieve, and that they reenter the world of the living, step-by-step.
* * *
The memory of the righteous is a blessing.
PROVERBS 10:7
* * *
## GLOSSARY
Afikomen From the Greek for "dessert." In the passover seder, the afikomen is the middle of three pieces of matzah, which is usually hidden and ransomed.
Akeda "Binding." The name given to the story of the binding of Isaac in Genesis 22.
Aleph-Bet Name of the Hebrew alphabet; also, its first two letters.
Aliyah "To go up." Receiving an aliyah means being called to the torah, usually to recite a blessing or to read. "Making aliyah" refers to moving to the land of Israel.
Aninut The name of the period between death and burial.
Apochrypha Fourteen writings, including the Books of Maccabees, not included in the final redaction of the Bible, but which are, nevertheless, important Jewish texts.
Aramaic An ancient Semitic language closely related to Hebrew. Aramaic was the lingua franca of the Middle East, and is the language spoken by Jesus. The gemara, the later part of the talmud, was written in Aramaic.
Ashkenazi Jews and Jewish culture of Eastern and Central Europe.
Aufruf The honor given to a couple called up to the torah on the shabbat before their wedding.
Avelut "Mourning"; an avel is a mourner. Avelut refers to the yearlong (or 11-month) observances for the death of a parent.
B.C.E. Before the Common Era. Jews avoid the Christian designation B.C., referring to Christ.
Baal Shem Tov "Master of the Good Name." Israel ben Eliezer, the founder of hasidism, the 18th-century mystical revival movement.
Baruch ata Adonai Words that begin Hebrew blessings, most commonly rendered in English as "Blessed art Thou, Lord our God, King of the Universe." This book contains many alternatives to that translation.
Bat Daughter, or "daughter of," as in bat mitzvah, which means "daughter of the commandment."
Bench, also Benching Yiddish for "to bless"/blessing.
Bible The Hebrew Bible, in Hebrew called tanach, which includes the torah, Prophets, and Writings.
Bimah Raised platform in the synagogue from which the worship service is led.
Brit Covenant; also covenant ceremony. (Bris is the Yiddish form.)
Brit Bat Covenant of the daughter—a term applied to ceremonies that welcome baby girls into the covenant of the Jewish people.
Brit Milah The covenant of circumcision.
Cantor A Jewish professional trained in liturgical music who leads services or co-officiates with a rabbi.
Challah Braided loaf of egg bread, traditional for shabbat and holidays.
Cholent A hearty meat stew served for lunch on shabbat by Eastern European Jews.
Conservative A modern religious movement, developed in the United States during the 20th century as a more traditional response to modernity than offered by the Reform movement.
Day School Jewish parochial school.
D'rash Religious insight, often based on a text from the torah.
D'var Torah "Words of Torah"; an explication of a portion of the torah. (Plural: divrei Torah).
Daven (Yiddish) Pray.
Diaspora Exile. The dwelling of Jews outside the land of Israel.
Draydl (Yiddish) A spinning top used for playing a game of chance during the festival of hannukah; in Hebrew, sivivon.
Erev Eve. "The evening of," especially a holiday. "Erev Shabbat" is Friday evening.
Etrog Citron. A lemonlike fruit, used in observance of the holiday of sukkot.
Flayshig (Yiddish) Meat food, which according to kashrut, may not be mixed with dairy products.
Gemara An expansive commentary on the mishna, completed around the fifth century C.E. The Gemara and the Mishna together are called the talmud.
Gemilut Hassadim Acts of loving-kindness.
Get A Jewish divorce document.
Haggadah The book containing the liturgy of the passover seder.
Haimish (Yiddish) Homelike; giving one a sense of belonging.
Halachah Probably from the Hebrew for "to go"; the umbrella term for Jewish law.
Hametz Food prepared with leavening, which is not eaten during passover.
Hannukah The eight-day winter festival of lights.
Hannukiah A candelabra with nine branches used during the festival of Hannukah.
Haroset A mixture of apple, nuts, and wine used as a part of the passover seder.
Hasidism Eighteenth-century mystical revival movement that infused the traditional ritual and liturgy with song, dance, and joy.
Havdalah Hebrew for separation. The Saturday evening ceremony that separates shabbat from the rest of the week.
Havurah "Fellowship." Small, participatory groups that meet for prayer, study, and celebration.
Hazzan Hebrew term for cantor.
Hazzanit Hebrew term for female cantor.
Hechsher A symbol on food packaging that means its contents are kosher and prepared under rabbinical supervision.
Hesped Eulogy.
Hiddur Mitzvah The beautification of a mitzvah and the rabbinic precept of adorning or decorating something used for religious purposes.
Holocaust Remembrance Day Established in 1951 as a memorial to those who died in the Holocaust. Held on the 27th of the Hebrew month of Nissan—a week after passover.
Huppah Wedding canopy.
Israel Independence Day Spring celebration that corresponds to the fifth of Iyar in the Hebrew calendar marking the creation of the state of Israel in 1948.
K'riah The mourning custom of tearing a garment as a sign of grief.
Kaballah From the Hebrew for "receive" or "tradition." The tradition of Jewish mysticism.
Kaddish A prayer recognizing the supreme nature of God, which appears in many forms, written in Aramaic. Often appears in liturgy to separate parts of the service; the best-known form is associated with mourning.
Kallah Bride. Also, a name for shabbat.
Karpas A green vegetable used as a part of the passover seder.
Kashrut System of laws that govern what and how Jews eat.
Ketubah A Jewish marriage contract.
Kibbudim Ceremonial honors.
Kibbutz Israeli collective farm.
Kiddush Sanctification; the blessing over wine recited on shabbat, festivals, and other occasions.
Kohane/Kohen One who traces his/her line to the ancient priesthood.
Kosher Fit and proper; foods deemed fit for consumption according to the laws of kashrut.
Kvatter, Kvatterin Godfather, godmother.
Lulav A bouquet consisting of palm, willow, and myrtle branches, used during the holiday of sukkot.
Ma'asim Tovim Good deeds, righteous actions.
Magid From the Hebrew for "telling"; the telling of the story of passover at the seder.
Maimonides Rabbi Moshe ben Maimon, also known as the Rambam, lived from 1135 to 1204 in Spain and North Africa. One of the great scholars and philosophers in Jewish history, he is best known for two books: the Mishneh Torah and The Guide for the Perplexed.
Martin Buber An Austrian-Jewish philosopher, educator, and theologian (1878–1965), who wrote about religious consciousness, interpersonal relations, and community.
Maven (Yiddish) An expert.
Mazel Tov "Good luck." In daily use, it means "Congratulations."
Menorah A candelabra. The term is often used to refer to the hannukah menorah, the hannukiah.
Mensch Person; an honorable, decent person. Menschen is the plural. Menschlichkeit means "person-ness," the quality of being a mensch.
Mesader Kiddushin One who "orders" or leads a wedding ceremony.
Mezuzah A small, decorative container, affixed to the doorways of and inside Jewish homes, which holds a handwritten parchment scroll of the first two paragraphs of the shema.
Midrash A body of literature consisting of imaginative exposition of and stories based on the bible.
Mikdash Ma'at A little sanctuary; a Jewish home.
Mikveh Ritual bath.
Milah Circumcision; brit milah is the covenant of circumcision.
Milchig (Yiddish) Dairy foods, which, according to the laws of kashrut, may not be mixed with meat products.
Minhag Custom (plural: minhagim).
Minyan A prayer quorum of ten adult Jews needed for certain worship services and rituals.
Mishna The first part of the talmud, composed of six "orders" of debate and law regarding everything from agriculture to marriage.
Mitzvah A commanded deed. A fundamental Jewish concept about the obligation of the individual to perform commandments put forth in the torah and elaborated by Jewish law. (Plural: mitzvot).
Mohel One who is trained in the rituals and procedures of brit milah, circumcision.
Motzi Blessing over bread recited before meals.
Nachas (Yiddish) Special joy derived from the achievements of one's children.
Niggun A wordless prayerlike melody.
Oneg Shabbat "Joy of the Sabbath." The informal gathering for conversation and community after Friday night Sabbath services.
Orthodox The modern Orthodox movement developed in the 19th century in response to the Enlightenment and Reform Judaism.
Parasha The weekly torah portion or reading.
Pareve Neutral foods, including all fruits and vegetables, which can be eaten with either dairy or meat meals.
Passover The spring holiday recalling the exodus from Egypt. In Hebrew, pesach.
Pesach passover.
Pharisees Jews who lived during the period of the Second Temple (536 B.C.E.–70 C.E.), and the progenitors of what is known as rabbinic or traditional Judaism.
Purim A late winter holiday based on the Book of Esther.
Pushke A coin box used to collect money for tzedakah or charity.
Rabbi Teacher. Today, "rabbi" refers to an ordained member of the clergy. "The rabbis" refers to the men who codified the talmud.
Reconstructionist Religious movement, begun in the United States in the 20th century by Mordecai Kaplan. It views Judaism as an evolving religious civilization, which is constantly being "reconstructed."
Reform A movement, begun in 19th century Germany, that sought to reconcile Jewish tradition with modernity.
Responsa An ongoing body of rabbinic legal literature containing decisions and opinion about contemporary questions.
Rosh Hodesh First day of every lunar month; the New Month, a semiholiday.
Rosh Hashanah The New Year—the head of the Jewish year when the shofar is sounded.
Safed A town in northern Israel (pronounced S'fat in Hebrew) associated with Jewish mysticism.
Sandek Godfather; the one who holds the baby during the circumcision. Sandeket, godmother, is the feminine form.
Seder Hebrew for "order"; usually refers to the talking-feast of passover.
Seudat Mitzvah A commanded meal; the festive celebration of a milestone.
Shalom Peace; also a term of greeting.
Shalom Bayit Peace of the home.
Sh'chitah Laws governing the kosher slaughter of animals.
Shabbat Sabbath. In Yiddish, Shabbos or Shabbes.
Shamash Usually refers to the "helper" candle used to light the other eight candles on the hannukiah.
Shavuot A holiday that takes place seven weeks after passover and celebrates the harvest of first fruits and the giving of the torah on Mount Sinai.
Shechinah God's feminine attributes, sometimes referred to metaphorically as a separate entity.
Shehecheyanu A common prayer of thanksgiving for new blessings.
Shloshim The month following the burial of a loved one—a period during which mourners attend services and refrain from joyful activities.
Shema The most-often-recited Jewish prayer that declares God's unity.
Sheva B'rachot Seven marriage blessings.
Shiva From the Hebrew word for "seven", the seven-day mourning period that begins on the day of a funeral.
Shmooz (Yiddish) To chat.
Shochet A person who is familiar with the laws of sh'chitah and performs ritual kosher slaughter.
Shofar A ram's horn, an instrument blown at rosh hashanah.
Shtetl Small town, especially one inhabited by ashkenazi Jews before the Holocaust.
Shul Synagogue.
Siddur Daily and shabbat prayer book.
Simcha Joy; a celebration of joy or party.
Simchat Torah The joyful holiday at the end of sukkot, marking the end and beginning of the annual torah reading cycle.
Siman Tov u'Mazal Tov "A good sign and good luck"; a song of good wishes sung at celebrations.
Sukkah A temporary hut or booth erected for the holiday of sukkot.
Sukkot The fall harvest festival.
Tallis/Tallit Prayer shawl.
Talmud Collection of rabbinic thought and laws, codified between 200 B.C.E. and 500 C.E.
The Temple The first building associated with Jewish worship is referred to as "the Temple." Built in Jerusalem by King Solomon beginning in 868 B.C.E., the rituals of animal sacrifice described in the book of Leviticus took place there. In ancient times, Israelites traveled from all over the land for festivals and holidays celebrated there.
Tikkun Olam Repairing the world; taking responsibility for correcting the damage done by people to one another and to the planet.
Tisha B'Av The ninth day of the Hebrew month of Av, a day of mourning and fasting recalling the destruction of the Temples in Jerusalem and other tragedies that have befallen the Jewish people.
Torah First five books of the Hebrew bible, portions of which are read every shabbat. Also, Jewish learning in general.
Trafe The opposite of kosher. Literally, "torn."
Tu B'Shvat The 15th of the Hebrew month of Shvat, the new year for trees.
Tzedakah Righteous giving, charity.
Ulpan An intensive course in conversational Hebrew.
Yahrzeit Yiddish for "a year's time." The anniversary of a death.
Yeshiva An academy of Jewish learning.
Yichus (Yiddish) Family status; also pride in family members' achievements.
Yiddish Language spoken by ashkenazi Jews, a combination of early German and Hebrew.
Yizkor A memorial service recited on yom kippur, sukkot, pesach, and shavuot.
YMHA/YWCA Young Men's Hebrew Association/Young Women's Hebrew Association; the Jewish versions of the YM/YWCA.
Yom Kippur Day of Atonement, the holiest of the High Holidays.
Zohar A mystical commentary on the torah and several other biblical books.
## TIMELINE
These dates are provided to give historical context to places, events, and names that appear in Living a Jewish Life.
Secular Calendar
| |
Hebrew Calendar
---|---|---
|
Before Common Era
| |
3761 | Creation of Adam, the sixth day of Creation | 1
2704 | Birth of Noah | 56
2104 | The Flood | 1656
1812 | Birth of Abraham | 1948
1764 | Tower of Babel | 1996
1742 | Covenant between God and Abraham | 2018
1712 | Birth of Isaac | 2048
1675 | Binding of Isaac | 2085
1652 | Births of Jacob and Esau | 2108
1589 | Isaac blesses Jacob 2171
|
1568 | Jacob marries Rachel and Leah | 2192
1544 | Joseph sold by his brothers | 2216
1522 | Jacob and his family move to Egypt | 2238
1505 | Death of Jacob | 2255
1451 | Death of Joseph | 2309
1428 | Beginning of slavery in Egypt | 2332
1392 | Birth of Moses | 2368
1312 | Exodus from Egypt, giving of the Torah | 2448
1272 | Death of Moses | 2488
1106 | The story of Deborah | 2654
1000 | First Temple completed | 2648
950 | The story of Samson | 2810
879 | Samuel anoints Saul as king of Israel | 2881
877 | Samuel anoints David as king of Israel | 2883
836 | King Solomon begins his rule | 2924
796 | Split of the kingdom of Israel | 2964
586 | First Temple destroyed, Babylonian exile begins | 3174
356 | The story of Purim | 3404
352 | Construction of the Second Temple | 3408
312 | Alexander the Great conquers Persia, beginning of Greek rule | 3448
139 | Miracle of Hannukah, kingdom of the Hasmoneans begins | 3622
36 | Hasmonean dynasty ends, Herod begins his rule | 3724
32 | Leadership of Rabbi Hillel begins | 3728
18 | Herod begins Temple reconstruction | 3748
|
Common Era
|
68 | Second Temple destroyed by the Romans | 3828
73 | Fall of Masada | 3833
80 | Leadership of Rabbi Akiva begins | 3840
93 | Josephus completes Jewish Antiquities | 3853
120 | Rebellion of Bar Kochba | 3880
219 | Mishna compiled | 3979
306 | Constantine makes Christianity the state religion of the Roman Empire | 4066
325 | Council of Nicea, Christians begin to celebrate Sabbath on Sunday | 4075
358 | The permanent Jewish calendar is instituted | 4118
368 | Jerusalem Talmud compiled | 4128
476 | Fall of Rome, beginning of Byzantine rule over Israel | 4236
500 | Babylonian Talmud completed | 4260
622 | Hegira—Muhammad flees from Mecca to Medina | 4382
638 | Islamic conquest of Jerusalem | 4398
814 | Death of Charlemagne
| 4574
1040 | Birth of Rashi, biblical and Talmudic commentator | 4800
1096 | First Crusade | 4856
1131 | Birth of Maimonides, Rambam | 4891
1144 | First Blood Libel against the Jews in England | 4904
1215 | Magna Carta | 4975
1290 | Expulsion of the Jews from England | 5050
1305 | Death of Rav Moshe DeLeon, author of the Zohar | 5065
1337 | Beginning of the Hundred Years War | 5097
1348 | The Black Death | 5108
1394 | Expulsion of the Jews from France | 5155
1480 | Inquisition established in Spain | 5240
1492 | Expulsion of the Jews from Spain; Columbus discovers America | 5252
1516 | Ottoman Turks conquer Palestine | 5276
1544 | Martin Luther, Protestant Reformation | 5304
1569 | Rav Isaac Luria comes to Safed to teach Jewish Mysticism (Kaballah) | 5329
1582 | Gregorian Calendar established | 5342
1620 | Mayflower arrives at Plymouth Rock | 5380
1648 | Chmelnitzki massacres in Poland; end of Thirty Years War | 5408
1654 | First Jewish settlement in North America (New Amsterdam) | 5414
1760 | Death of Baal Shem Tov, the founder of Hasidism | 5520
1776 | American Revolution | 5536
1789 | Beginning of the French Revolution | 5549
1791 | French National Assembly grants full civil rights to Jews Pale of Settlement established in Russia | 5551
1804 | Napoléon crowned Emperor | 5564
1806 | End of Holy Roman Empire | 5566
1815 | German Jewish immigration to America begins; Waterloo | 5575
1844 | First meeting of German Reform leaders | 5604
1861 | American Civil War | 5612
1881 | Czar Alexander II is assassinated; Pogroms against the Jews | 5641
1882 | Mass immigration of Russian Jews to America begins | 5642
1885 | Pittsburgh Platform (Statement by American Reform Movement) | 5645
1894 | Dreyfus trial (France) | 5654
1897 | First Zionist Congress (Basel) | 5657
1902 | Conservative Movement emerges in U.S. | 5662
1914 | World War I begins | 5674
1917 | British defeat Turks, capture Jerusalem; Balfour Declaration | 5677
1920 | England receives Mandate over Palestine | 5680
1933 | Hitler comes to power | 5693
1938 | Kristallnacht riot against Jews in Germany | 5698
1939 | World War II begins | 5699
1947 | Dead Sea Scrolls first discovered | 5707
1948 | State of Israel is declared | 570
1967 | Six Day War. Reunification of Jerusalem | 5727
1972 | First woman rabbi ordained by Reform Movement | 5732
1976 | Entebbe Rescue | 5736
1978 | Camp David Peace Accord | 5738
1979 | Israeli-Egyptian Peace Treaty | 5739
1984 | Operation Moses, rescue of Ethiopian Jews | 5744
1987 | Intifada, Arab uprising in Israel begins | 5748
1988 | Elie Wiesel receives Nobel Peace Prize | 5749
1989 | Berlin Wall comes down | 5750
1991 | Operation Solomon: Rescue of remainder of Ethiopian Jews in massive 24-hour airlift | 5751
1993 | Israel and PLO sign Oslo Accords | 5753
1994 | Israel and Jordan sign peace treaty; Arafat, Rabin, and Peres share Nobel Peace Prize | 5754
1995 | Israeli Prime Minister Rabin assassinated | 5755
2000 | Israel withdraws from Lebanon; second Intifada begins | 5760
2001 | Terrorist attacks on the United States | 5761
2005 | Israel withdraws military personnel and settlers from Gaza Strip | 5765
Sources: Encyclopedia Judaica; Seder Hadorot by Rabbi Yechiel Heilpern; Toldot Am Olam by Rabbi Shlomo Rottenberg, as compiled by Tzvi Black.
## FURTHER READING
SHABBAT
Heschel, Rabbi Abraham Joshua. The Sabbath: Its Meaning for Modern Man. Shambhala, 2003.
For children
Schwartz, Amy. Mrs. Moskowitz and the Sabbath Candlesticks. Jewish Publication Society, 1991.
Hirch, Marilyn. Joseph Who Loved the Sabbath. VikingPenguin Puffin Books, 1988.
Schwartz, Howard. The Sabbath Lion: A Jewish Folktale from Algeria. HarperTrophy, 1996.
TZEDAKAH
Heschel, Rabbi A. J. The Prophets. Harper Perennial Classics, 2001. Siegel, Danny. Books for adults and children including, Gym Shoes and Irises: Personalized Tzedakah. 1987. Munbaz II and Other Mitzvah Heroes. 1988. http://www.ziv.org/danny_sbooks.html.
For children
Zellman, Sella, and Brigitte Evans. The Man with Many Telephones. United Synagogue Book Service, 1987.
KASHRUT
Dresner, Samuel H. The Jewish Dietary Laws. United Synagogue Book Service, 1980.
Greenberg, Blu. How to Run a Traditional Jewish Household. Jason Aronson, 1997.
Schwarts, Richard H. Judaism and Vegetarianism. Lantern Books,
2001.
COMMUNITY
Borowitz, Eugene, and Naomi Patz. Explaining Reform Judaism. Behrman House, 1985.
Kaplan, Dana Evan. American Reform Judaism. Rutgers University Press, 2003.
Dorff, Elliot. Conservative Judaism: Our Ancestors to Our Descenders. United Synagogue of America, 1977.
Alpert, Rebecca, and Jacob Staub. Exploring Judaism: A Reconstructionist Approach. Reconstructionist Press, 2000.
ISRAEL AND TRAVEL
Hoffman, Rabbi Lawrence A. Israel: A Spiritual Travel Guide: A Companion for the Modern Jewish Pilgrim. Jewish Lights Publishing, 2005.
Tigay, Alan M., ed. The Jewish Traveler. Jason Aronson, 1994. The Jewish Travel Guide 2006: International Edition. Vallentine Mitchell, 2006.
For children
Burstein, Chaya. A Kid's Catalog of Israel. Jewish Publication Society,
1998. School-age.
Carmi, Giora. And Shira Imagined. Jewish Publication Society, 1988. Preschool–2.
Sofer, Barbara. Kids Love Israel, Israel Loves Kids. Kar-Ben, 1995. For families.
THE HOLIDAY CYCLE
Greenberg, Irving. The Jewish Way: Living The Jewish Holidays. Jason Aronson, 1998.
Nathan, Joan. The Jewish Holiday Kitchen: 250 Recipes from Around the World to Make Your Celebrations Special. Schocken Books, 1998.
Strassfeld, Michael. Jewish Holidays. Collins, 1993.
Waskow, Arthur. Seasons of Our Joy. Beacon Press, 1991.
For children
Sofer, Barbara. The Holiday Adventures of Achbar. Kar-Ben Copies, Inc., 1983. For young readers.
Cashman, Greer Fay. Jewish Days and Holidays. Adama Books, 1988. Grade 4 and up.
ROSH HASHANAH AND YOM KIPPUR
Agnon, S. Y. Days of Awe. Schocken Books, 1995.
Reimer, Gail Twersky, and Judith Kates. Beginning Anew: A Woman's Companion to the High Holy Days. Touchstone, 1997.
Speigel, Shalom. The Last Trial: On the Legends and Lore of the Command to Abraham to Offer Isaac as a Sacrifice: The Akedah 1899–
1984. Jewish Lights Publishing, 1993.
For children
Singer, Marilyn. Minnie's Yom Kippur Birthday. HarperCollins Children's Books, 1989.
Weilerstein, Sadie Rose. K'Tonton's Yom Kippur Kitten. Jewish Publication Society, 1995.
HANNUKAH
Singer, Isaac Bashevis. The Power of Light. Farrar, Straus and Giroux/
Sunburst Edition, 1990.
For children
Chaiken, Miriam. Alexandra's Scroll: The Story of the First Hanukkah. Henry Holt and Co., 2002.
Erlich, Amy. The Story of Hannukah. Dial, 1989.
Hirsh, Marilyn. Potato Pancakes All Around. Jewish Publication Society, 1982.
Koons, Jon. A Confused Hanukkah: An Original Story of Chelm. Dutton Juvenile, 2004.
Rouss, Sylvia. Sammy Spider's First Hanukkah. Kar-Ben Publishing, 1993.
TU B'SHVAT
Appelman, Harlene Winnick. A Seder for Tu B'Shevat. Kar-Ben Copies, 1984. For families with children.
Fisher, Adam. Seder Tu BiShevat; The Festival of the Trees. Central Conference of American Rabbis, 1989.
Waskow, Arthur. Trees, Earth, and Torah: A Tu B'Shvat Anthology. Jewish Publication Society, 1999.
PURIM
Novak, William, and Moshe Waldoks. The Big Book of Jewish Humor. Harper & Row, 1981.
For children
Feder, Harriet K. It Happened in ShuShan. Kar-Ben Copies, 1988. Rouss, Sylvia. Sammy Spider's First Purim. Kar-Ben Publishing, 2000. Simpson, Lesley. The Purim Surprise. Kar-Ben Publishing, 2004.
PASSOVER
Haggadot
Passover Haggadah; The Feast of Freedom. United Synagogue Book Service, 1982. Conservative movement publication.
Levitt, Joy, and Michael Strassfeld. A Night of Questions: A Passover Haggadah. Reconstructionist Press, 2000.
A Passover Haggadah. Central Conference of American Rabbis, 1994. Reform movement publication.
Stern, Chaim. Gates of Freedom, A Passover Haggadah. Behrman House Publishing, 1998.
The Shalom Seders: Three Haggadahs. Compiled by New Jewish Agenda. Adama Books, 1984.
Kalechofsky, Roberta. Haggadah for the Liberated Lamb. Micah Press, 1988. Vegetarian Passover handbook.
A Sephardic Passover Haggadah. Prepared by Rabbi Marc D. Angel. Ktav Publishing, 1988.
Silberman, Shoshana. A Family Haggadah II. Kar-Ben Publishing, 1997.
Books
Arnow, David. Creating Lively Passover Seders: An Interactive Source-book of Tales, Texts and Activities. Jewish Lights Publishing, 2004.
Sarna, Nahum. Exploring Exodus: The Origins of Biblical Israel. Schocken Books, 1996.
Walzer, Michael. Exodus and Revolution. Basic Books, 1986.
For children
Cohen, Barbara. The Carp in the Bathtub. Kar-Ben, 1987.
Miller, Deborah Uchill. Only Nine Chairs: A Tall Tale for Passover. Kar-Ben, 1982.
Rouss, Sylvia. Sammy Spider's First Passover. Kar-Ben, 1995.
Schwartz, Lynn Sharon. The Four Questions. Puffin, 1994.
BIRTH
Cohen, Debra Nussbaum. Celebrating Your New Jewish Daughter: Creating Jewish Ways to Welcome Baby Girls into the Covenant. Jewish Lights Publishing, 2001.
Diamant, Anita. The New Jewish Baby Book. Jewish Lights Publishing, 2005.
Kolatch, Alfred, J. The Comprehensive Dictionary of English and Hebrew First Names. Jonathan David Publishers, 2004. Kunin, Samuel A., M.D. Circumcision: Its Place in Judaism, Past and Present. Isaac Nathan Publishing, 1998.
BAR/BAT MITZVAH
Davis, Judith. Whose Bar/Bat Mitzvah Is This, Anyway?: A Guide for Parents through a Family Rite of Passage. St. Martin's Press, 1998.
Salkin, Rabbi Jeffrey K. Putting God on the Guest List: How to Reclaim the Spiritual Meaning of Your Child's Bar/Bat Mitzvah. Jewish Lights Publishing, 2005.
Siegel, Danny. The Bar and Bat Mitzvah Book: A Practical Guide for Changing the World through Your Simcha. http://www.ziv.org/ danny_sbooks.html.
MARRIAGE
Diamant, Anita. The New Jewish Wedding. Simon & Schuster, 2001.
CONVERSION/ADOPTION/NEW TRADITIONS
Diamant, Anita. Choosing a Jewish Life: A Handbook for People Converting to Judaism and for Their Families and Friends. Schocken Books, 1997.
Orenstein, Rabbi Deborah. Lifecycles: Jewish Women on Life Passages and Personal Milestones. Jewish Lights Publishing, 1998.
DEATH AND MOURNING
Diamant, Anita. Saying Kaddish: How to Care for the Dying, Bury the Dead, and Mourn as a Jew. Schocken Books, 1998.
Grollman, Earl A. Talking about Death: A Dialogue between Parent and Child. Beacon Press, 1991.
Reimer, Rabbi Jack, and Nathaniel Stampfer. So That Your Values Live On: Ethical Wills and How to Prepare Them. Jewish Lights Publishing, 1994.
JEWISH PARENTING
Abramowitz, Yosef, and Susan Silverman. Jewish Family and Life: Traditions, Holidays, and Values for Today's Parents and Children. St. Martin's Press, 1997.
Diamant, Anita, with Karen Kushner. How to Be a Jewish Parent: A Practical Handbook for Family Life. Schocken Books, 2000.
Fuchs-Kreimer, Rabbi Nancy. Parenting as a Spiritual Journey: Deepening Ordinary and Extraordinary Events into Sacred Occasions. Jewish Lights Publishing, 1998.
Friedland, Ronnie, and Edmund Case. The Guide to Jewish Interfaith Family Life: An Interfaithfamily.com Handbook. Jewish Lights Publishing, 2001.
Mogul, Wendy. The Blessing of a Skinned Knee: Using Jewish Teachings to Raise Self-Reliant Children. Penguin Compass, 2001.
## ACKNOWLEDGMENTS
This book is a collaboration between a writer and a teacher; it began in an adult education class taught at Congregation Beth El of the Sudbury River Valley, in Sudbury, Massachusetts. Howard Cooper, then director of education, was teaching a course titled "Making a Jewish Home Now That You Have a Family of Your Own," which offered people the opportunity to peruse the menu of Jewish practice: "prior knowledge or experience not necessary." Howard, who holds an undergraduate degree in Judaic Studies and a master's degree in education, is the kind of teacher who inspires students with his obvious love of his subject. A silly sense of humor doesn't hurt either. His approach to Jewish tradition, which I share, suggested this collaboration and this book.
The process of creating Living a Jewish Life began with and regularly returned to long conversations between us, many of them held at an ice cream shop halfway between our respective homes. Over endless cups of watery coffee and a few sundaes, we hammered out the contents of each chapter, discussed philosophy and vocabulary, and worried about what to leave out.
Howard collected source material from a variety of Jewish texts, as well as anecdotes and bibliographies, which became the backbone of my own research. He also drew heavily upon his own personal experience. Some of the original material in this book came from a questionnaire we sent to people around the country, asking about their holiday and Shabbat observance. More information and ideas came from conversations with colleagues, teachers, friends, and acquaintances. We polled many rabbis, but also listened carefully to the voices of laypeople—the people we imagined as readers, people with varied levels of Jewish knowledge, who are interested in making more meaningful Jewish choices.
Three people, extraordinarily generous with their time, read every chapter: Rabbi Neil Cooper (Howard's brother) was our "on call" rabbi. Leslie Tuttle, a student of Judaism who was raising two Jewish children, pointed out places that needed better definition or further amplification. Rabbi Barbara Penzner's contributions were practical, creative, spiritual, learned, loving, and always on target.
Many others read, criticized, and suggested changes in one or more chapters, including: Fran Addison and Rob Gogan, Marsha Feder, Rabbi Lawrence Kushner, Joan Kaye, Billy Mencow, Rabbi Nehemia Polen, Jenique Radin, Brian Rosman, Danny Siegel, Larry Sternberg, Rabbi Gerald Teller, Moshe Waldoks, and Jonathan Woocher.
The following people answered our questionnaire, made comments on specific chapters, engaged in helpful conversations, or provided other kinds of support during the research and writing of this book, for which we are most grateful: Velda Adams, Rabbi Herman Blumberg, Rabbi Lester Bronstein, Debra Cash, Betsy Cohen, Rabbi Richard Israel (whose memory is a blessing), Sherry Israel, Jay Fialkov, Lev Friedman, Rabbi Janice Garfunkel, Ora Gladstone, Mitchell Silver, Rabbi Devorah Jacobson, Rabbi Stuart Weinberg Gershon, Karen Kushner, Maddy and Peter Langmann, Jeff Liberman and Joni Levy Liberman, Cantor Riki Lippitz, Rabbi Norman Mendel, Joel Rosenberg, Marion Ross, Arthur Samuelson, Rabbi John Schechter, Ella Taylor, Craig Taubman, Scott Tepper, Betsy Platkin-Teutsch, William Whalen, Susan and Marty Wieskoff, and the office staff at Temple Emmanuel in Worcester, Massachusetts.
Howard Cooper also wishes to thank Rabbi Gerald Teller, a lifelong teacher and mentor. He also acknowledges the support of his family: siblings par excellence, Marsha and Bob Feder, and Neil and Lori Cooper; wonderful stepchildren, Hanan and Gavriella; daughter, Hannah Evy, in whose eyes I see the bright light of the future, and the warm glow of the past; and his wife, best friend, and lover, Ellen, who made me whole, keeps me laughing, and helped me become a mensch.
I would also like to thank my family and friends for their support and patience during the writing of this project, especially my husband, the one and only Jim Ball.
Finally, Rabbi Lawrence Kushner has had the most profound influence on both Howard and me—as Jews and as people. His imagination and his erudition continue to inspire us to learn and to teach. He is the godfather of this book. And we thank him with love.
Anita Diamant
## NOTES
INTRODUCTIONS AND DEFINITIONS
1. The phrase came from the 1866 poem "Awake My People," by Judah Leib-Gordon, a Russian-Hebrew poet of the Haskalah, the Jewish enlightenment. The exact line is, "Be a man abroad and a Jew in your tent." The early-nineteenth-century Jewish Enlightenment poet Judah Leib Gordon coined the slogan (in Hebrew) for Jews: "Be a Jew in your tent and a human being when you go out of it."
2. However, the opportunity to perform some of them, for example, the commandments related to the rituals of the Temple in Jerusalem, is not available.
3. William Novak and Moshe Waldoks, The Big Book of Jewish Humor (New York: Harper & Row, 1981), p. 288.
4. "The Divine Authority of the Mitzvah," in Herman E. Schaalman, Gates of Mitzvah, ed. Simeon J. Maslin (New York: Central Conference of American Rabbis), p. 103.
5. Schaalman, p. 103.
6. Hasidism was a mystical revival of the 18th century. This idea is attributed to Rabbi Yehudah Aryeh-Leib of Ger, in S'fas Emes, a five-volume classic of Hasidic spiritual insights, and was suggested to the authors by Rabbi Nehemia Polen.
7. Exodus 24:7
HOME
1. Deuteronomy 6:4–9, 11:13–21. Translation from Vetaher Libeynu, Purify Our Hearts, the prayer book (siddur) of Congregation Beth El of the Sudbury River Valley, Sudbury, Massachusetts, p. 35.
2. This translation/adaptation, taken from the verse written on the mezuzah parchment is by Rabbi Rami Shapiro.
3. Baruch ata Adonai Eloheynu Melech Ha-olam are the words that introduce many blessings. The most familiar English translation for the Hebrew is "Blessed art Thou, Lord our God, King of the Universe." Alternatives to this translation are found throughout this book, none of which refer to God as a male monarch.
4. Genesis 2.
5. Abraham Joshua Heschel, The Sabbath (New York: Farrar, Straus and Giroux, 2005) p. 110.
6. Deuteronomy 5:15.
7. Ezekiel 20:12.
8. Talmud: Shabbat 118b.
9. Exodus 16.
10. Isaiah 58:13.
11. Hayyim Schauss, The Jewish Festivals (New York: Schocken Books, 1962), pp. 11–12.
12. Samuel H. Dresner, The Sabbath (New York: The Burning Bush Press, 1970), p. 66.
13. Hasidic Tales of the Holocaust, by Yaffa Eliach (New York: Avon Books, 1982).
14. The kinds of work that are forbidden on Shabbat are based on a list of 39 specific jobs listed in the Mishna, which is part of the Talmud. The rabbis theorized that these tasks, which are largely agricultural in nature, were derived from the work of constructing the portable Tabernacle in the wilderness. Rabbis have based other restrictions—including the modern prohibition against using electricity—both on the Mishna and on subsequent codes of Jewish law.
15. Schauss, p. 33.
16. Bella Chagall, Chagall: Burning Lights (New York: Schocken Books, 1969; reprint of 1946 edition, reissued in March 1988), p. 48–49. This volume is described as a "double portrait of the warm world of Russian Jewry." The text is by Bella Chagall, and the book is illustrated by 36 line drawings by her husband, the artist Marc Chagall.
17. This translation and others in this chapter come from Vetaher Libeynu, op. cit.
18. Exodus 20, Deuteronomy 5.
19. Herbert C. Dobrinski, A Treasury of Sephardic Laws and Customs (Hoboken, N.J.: Ktav, 1986), p. 231.
20. Actually, since Shabbat begins at the very moment the candle is lit, actively extinguishing a flame is forbidden by Jewish law.
21. Used by permission. © Marcia Falk, The Book of Blessings (HarperSanFrancisco, 1996), pp. 124–25. www.marciafalk.com.
22. Genesis 1:31; 2:1–3.
23. Numbers 15:17–21.
24. Pirke Avot 3:17.
25. Ibid., 3:4.
26. Translation from Vetaher Libeynu.
27. "Y'did Nefesh" was written by Rabbi Eleazar Azikri, who lived in Palestine during the 16th century. Translation from Vetaher Libeynu.
28. Pirke Avot 2:21.
29. Deuteronomy 16:20.
30. Talmud: Baba Bathra 9a.
31. Danny Siegel, Gymshoes and Irises (Spring Valley, N.Y.: Town Mill Press, 1982), pp. 120–24.
32. Sota 14a, quoted in ibid., p. 126.
33. Isaac Luria's book, Sefer Yetzirah, is one the basic books of Jewish mysticism, called Kabbalah.
34. Isaiah 57:14–58:14.
35. See Barry Holtz, Back to the Sources (New York: Summit Books, 1984), p. 13.
36. Pirke Avot 1:14.
37. Talmud: Shabbat 25b.
38. Rabbi Lawrence Kushner, River of Light (Woodstock, NY: Jewish Lights Publishing, 2000), p. xii.
39. Genesis Rabbah, VIII, 5
40. Quoted in Samuel H. Dresner, The Jewish Dietary Laws (New York: The Burning Bush Press, 1970), pp. 15–16.
41. Rabbi Hayim Halevy Donin, To Be a Jew (New York: Basic Books, 1972), pp. 98–99.
42. Leviticus 11.
43. The rule is repeated three times in the Torah: Exodus 23:19 and 34:26; Deuteronomy 14:21.
44. Rabbi Seymour E. Freedman, The Book of Kashruth (New York: Bloch Publishing Company, 1970), p. 3.
45. Genesis 1:29–30.
46. Isaiah 11:7
47. Sheila Weinberg, "Kashrut: How Do We Eat?" in The Jewish Family Book, ed. Sharon Strassfeld and Kathy Green (New York: Bantam Books, 1981), p. 85.
48. Edda Servi Machlin, Classic Cuisine of the Italian Jews (New York: Dodd, Mead & Co., 1981), p. 11.
49. Josephine Levy Bacon, Jewish Cooking from Around the World (Woodbury, N.Y.: Barron's, 1986), p. 2.
50. Blu Greenberg, How to Run a Traditional Jewish Household (New York: Simon & Schuster, 1983), p. 109.
COMMUNITY
1. Pirke Avot 2:5.
2. Ta'anit 22b.
3. Midrash Sefer Eliahu Rabba 7.
4. Midrash Rabba 4:11, Song of Songs.
5. Jewish confirmation ceremonies were begun in the 19th century by the Reform movement as a substitute for bar mitzvah in response to the consensus that 13-year-olds were too young to be admitted as adult members of the community. Today, however, confirmation is a collective ceremony that occurs somes year later than and in addition to bar/bat mitzvah.
6. Hillel: The Foundation for Jewish Life on Campus is named for one of Judaism's most beloved teachers. Hillel the Elder, who lived toward the end of the first century B.C.E., engaged in a lifelong debate with another great teacher, the brilliant but impatient Shammai. Hillel was known for his benevolence, gentleness, and humility and is credited with many famous aphorisms. Perhaps the most famous story about him involves the impatient student who asks him to explain all of Judaism while standing on one foot. Hillel answered, "Love your neighbor as yourself. The rest is commentary. Go and study" (Shabbat 31a).
7. Talmud: Eruvin 54a.
8. According to the Policy Planning Institute of the Jewish Agency in Israel, Only about 35 percent of American Jews have actually visited Israel (2005).
9. Rabbi Lawrence A. Hoffman, The Journey Home: Discovering the Deep Spiritual Wisdom of Jewish Tradition (Boston: Beacon Press, 2002), p. 110.10. Ibid., p. 111.
THE CYCLE OF THE YEAR
1. Heschel, p. 8.
2. The Gregorian calendar was brought into use by Pope Gregory XIII during the 16th century.
3. There are also agricultural and pagan sources.
4. For an excellent treatment of this subject, see Arthur Waskow, "The Second Day of Festivals," in Seasons of Our Joy (New York: Bantam Books, 1982), pp. 226–27.
5. For more information about this use of mikveh, see www.mayyimhayyim.org.
6. From an interview with the author.
7. Isaiah 57:14–58:14.
8. Micah 7:20.
9. Leviticus 23:26–32:3.
10. Leviticus 18.
11. From an interview with the author.
12. Exodus 23:16–16, Leviticus 23:33–44, Deuteronomy 16:13–17.
13. For further discussion of these interpretations, see Michael Strassfeld, The Jewish Holidays (New York: Harper & Row, 1985), and Philip Goodman, The Sukkot/Simchat Torah Anthology (Philadelphia: Jewish Publication Society, 1973).
14. From an interview with the author.
15. According to the revisionist version of the "official" Hannukah story, the war was, in fact, a civil conflict between the devout masses in the countryside and the assimilated city-folk who had adopted Greek ways. Years after the Maccabee victory, they, too, became Hellenized.
16. Dobrinski, pp. 376–80.
17. Avot de Rabbi Natan 31b.
18. Deuteronomy 20:19
19. For a good description of the Tu B'Shvat seder of the mystics of Safed, see Waskow, pp. 108–9.
20. Rabbi Zalman Schachter-Shalomi, in Strassfeld, The Jewish Holidays, p. 183.
21. From an interview with the author.
22. Deuteronomy 25:17.
23. Talmud: Megilot 7B.
24. From an interview with the author.
25. This description of Passover as the essential Jewish holiday owes a great deal to Rabbi Irving Greenberg's views, expressed in The Jewish Way: Living the Holidays (New York: Summit Books, 1988).
26. Actually, most of the story is not told at the seder table. Passover sets in motion a season of study.
27. See Anita Diamant, "The Orange on the Seder Plate," in Pitching My Tent: On Marriage, Motherhood, Friendship and Other Leaps of Faith (New York: Scribner, 2003), p. 148.
28. Greenberg, p. 339.
29. Genesis 17.
30. From an interview with the author.
31. Exodus 23:16, Leviticus 23:17, Deuteronomy 16:10–12.
32. Waskow, p. 202.
THE LIFE CYCLE
1. The gomel blessing may be recited by one who has recovered from illness, escaped danger, returned from a perilous journey, or been released from prison or captivity. It is typically said in conjunction with an aliyah to the Torah. From the Reconstructionist prayer book: "Blessed are You, Abundant One, our God, the sovereign of all worlds, Who bestows good things on one in debt to you, and who has granted me all good." Kol Haneshamah (Wyncote, Penn.: The Reconstructionist Press, 1996), p. 400.
2. Alfred Kolatch, The Name Dictionary (Middle Village, N.Y.: Jonathan David Publishers, 1967), p. xi.
3. Lawrence K. Altman, M.D., "Pediatricians Find Medical Benefit in Circumcision," New York Times, March 6, 1989.
4. Betsy A. Lehman, "The Age-old Question of Circumcision," Boston Globe, June 22, 1987.
5. Rabbi Lawrence Kushner, "Save This Article," Bulletin of the Congregation Beth El of the Sudbury River Valley, Sudbury, Mass., Vol. VIII, No. 6., Sivan/Tammuz 5742, p. 3.
6. Toby Fishbein Reifman with Ezrat Nashim, Blessing the Birth of a Daughter: Jewish Naming Ceremonies for Girls (Englewood, N.J.: Ezrat Nashim, 1978). Quoting an unpublished paper by Rabbi Marc Angel of the Spanish and Portuguese Synagogue in New York, p. 27.
7. Adapted from the Talmud, Berachot 17a, translation by Rabbi Lawrence Kushner.
8. Exodus 30:14; Leviticus 27:3–5; Numbers 1:3, 20.
9. Pirke Avot 5:21.
10. Encyclopedia Judaica, Vol. 4 (Jerusalem: Keter Publishing House, 1972), p. 243.
11. Sukkah 42a, Megilla 23a, as cited in Strassfeld and Strassfeld, eds. The Second Jewish Catalog (Jewish Publication Society, 1976), p. 62.
12. Zohar 1:89a.
13. Rabbi Maurice Lamm, The Jewish Way in Love and Marriage (San Francisco: Harper & Row, 1980), p. 198.
14. Adapted from a translation by Debra Cash.
15. Philip and Hanna Goodman, The Jewish Marriage Anthology (Philadelphia: Jewish Publication Society, 1977), p. 28.
16. From a get written by Rabbi Lawrence Kushner and Rabbi Henry Zoob.
17. Tanchuma Buber, Lech Lecha 6, 32a. Although there are some negative comments about converts in the Talmud, they are far outnumbered by the positive.
18. Rabbi Aryeh Kaplan, Waters of Eden: The Mystery of the Mikvah (New York: National Conference of Synagogue Youth/Union of Orthodox Jewish Congregations, 1976), p. 35.
19. Sanhedrin, 19b.
20. Lawrence Jeffrey Epstein, The Theory and Practice of Welcoming Converts to Judaism (Lewiston, N.Y.: Edwin Mellen Press, 1992), p. 66.
21. This tends to be an automatic "choice," as a person who knows but makes no reference to her origin has accepted the decision, and the conversion is final. Today, the ceremony of bar or bat mitzvah is seen as a formal affirmation of Jewish identity.
22. According to tradition, Jews are buried only in Jewish cemeteries or in portions of cemeteries designated for Jews only. Thus, whenever Jews settle in a new place, one of their first communal acts is the purchase of land for a cemetery.
23. Rabbi Rami M. Shapiro, Open Hands: a Jewish Guide on Dying, Death and Bereavement (Miami: Temple Beth Or), p. 15.
24. Translation from Vetaher Libeynu, p. 119.
25. Pirke Avot 4:23a.
26. Ezekiel 24:17.
27. Talmud: Shekalim 2:5.
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## About the Author
ANITA DIAMANT a Boston-based writer and lecturer, is the author of six books about contemporary Jewish life, including The New Jewish Wedding, The New Jewish Baby Book, and How to Be a Jewish Parent, as well as the best-selling novel The Red Tent.
Visit www.AuthorTracker.com for exclusive information on your favorite HarperCollins author.
## Also by Anita Diamant
NONFICTION
The New Jewish Wedding
The New Jewish Baby Book
Choosing a Jewish Life: A Handbook for People Converting to Judaism
Saying Kaddish
How to be a Jewish Parent
Bible Baby Names
FICTION
The Red Tent
Good Harbor
The Last Days of Dogtown
ESSAYS
Pitching My Tent: On Marriage, Motherhood, Friendship and Other
Leaps of Faith
## Credits
Cover design by Leah Lococo
## Copyright
LIVING A JEWISH LIFE, UPDATED AND REVISED EDITION. Copyright © 2007 by Anita Diamant and Howard Cooper. All rights reserved under International and Pan-American Copyright Conventions. By payment of the required fees, you have been granted the non-exclusive, non-transferable right to access and read the text of this e-book on-screen. No part of this text may be reproduced, transmitted, down-loaded, decompiled, reverse engineered, or stored in or introduced into any information storage and retrieval system, in any form or by any means, whether electronic or mechanical, now known or hereinafter invented, without the express written permission of HarperCollins e-books.
ePub edition August 2007 ISBN 9780061748516
10 9 8 7 6 5 4 3 2 1
## About the Publisher
Australia
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HarperCollins Publishers Inc.
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http://www.harpercollinsebooks.com
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Q: Does Android Application.getInstance always exist? For example: If I start some Service and create a separate thread on this Service, And the service is killed by system and other Android components (services/activities,e.t.c.) are killed too. But the thread and the app's process are still alive. Can I access Application.getInstance in this case? And when the app object is destroyed?
A:
And the service is killed by system and other Android components (services/activities,e.t.c.) are killed too. But the thread and the app's process are still alive.
That combination does not exist.
Android terminates processes to free up system RAM. That's it. The only reason why components will be "killed" — with the process "still alive" — is if something destroys them (e.g., finish(), stopService(), stopSelf()). In general, the system does not do this on its own.
Can I access Application.getInstance in this case?
If your process is around, the Application instance is around.
And when the app object is destroyed?
Never. It goes away when the process does.
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package main
// round returns size rounded up to the next multiple of align;
// align must be a power of two.
func round(size, align Addr) Addr {
return (size + align - 1) &^ (align - 1)
}
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{"url":"http:\/\/www.physicsforums.com\/showthread.php?t=671626","text":"# Bragg reflection at the BZ\n\nby hokhani\nTags: bragg, reflection\n P: 238 As far as I know, Bragg diffraction happens for incident particles which are free; for example free electrons or X-ray are Bragg-reflected under the special conditions. Why the Bragg diffraction happens for electrons which are not free in a crystal?\nP: 67\n Quote by hokhani As far as I know, Bragg diffraction happens for incident particles which are free; for example free electrons or X-ray are Bragg-reflected under the special conditions. Why the Bragg diffraction happens for electrons which are not free in a crystal?\nBragg diffraction happens for WAVES.\nWaves can be of any nature and spread in any medium. Electron wave in ion's lattice is a WAVE with ions as diffracting screen.\n P: 238 If we consider the diffraction classically, incident waves are in direction of $k$ and reflected waves are in direction of $k^\\prime$ and $G=k-k^\\prime$. But for electrons in crystals direction of motion is not direction of wave vector.\nP: 67\n\n## Bragg reflection at the BZ\n\n Quote by hokhani If we consider the diffraction classically, incident waves are in direction of $k$ and reflected waves are in direction of $k^\\prime$ and $G=k-k^\\prime$. But for electrons in crystals direction of motion is not direction of wave vector.\n If we consider the diffraction classically\nIn classical physics electrons are not WAVES, so you could not bragg diffract electrons.\n\n Related Discussions Atomic, Solid State, Comp. Physics 3 Advanced Physics Homework 3 Advanced Physics Homework 1 Advanced Physics Homework 0 Advanced Physics Homework 0","date":"2014-03-10 04:10:55","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.24726420640945435, \"perplexity\": 1132.6193693177606}, \"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-2014-10\/segments\/1394010623118\/warc\/CC-MAIN-20140305091023-00050-ip-10-183-142-35.ec2.internal.warc.gz\"}"} | null | null |
#ifndef __ROUTER_PLUGIN_H
#define __ROUTER_PLUGIN_H
class RakPeerInterface;
#include "RakNetTypes.h"
#include "PluginInterface.h"
#include "DS_OrderedList.h"
#include "DS_WeightedGraph.h"
#include "PacketPriority.h"
#include "SystemAddressList.h"
#include "RouterInterface.h"
#include "Export.h"
#include "ConnectionGraph.h"
/// \defgroup ROUTER_GROUP Router
/// \ingroup PLUGINS_GROUP
/// \ingroup ROUTER_GROUP
/// \brief Used to route messages between peers
class RAK_DLL_EXPORT Router : public PluginInterface , public RouterInterface
{
public:
Router();
virtual ~Router();
// --------------------------------------------------------------------------------------------
// User functions
// --------------------------------------------------------------------------------------------
/// We can restrict what kind of messages are routed by this plugin.
/// This is useful for security, since you usually want to restrict what kind of messages you have to worry about from (as an example) other
/// clients in a client / server system
/// \param[in] restrict True to restrict what messages will be routed. False to not do so (default).
void SetRestrictRoutingByType(bool restrict__);
/// If types are restricted, this adds an allowed message type to be routed
/// \param[in] messageId The type to not allow routing of.
void AddAllowedType(unsigned char messageId);
/// Removes a restricted type previously added with AddRestrictedType
/// \param[in] messageId The type to no longer restrict routing of.
void RemoveAllowedType(unsigned char messageId);
/// Set the connection graph, which is a weighted graph of the topology of the network. You can easily get this from the
/// ConnectionGraph plugin. See the 'router' sample for usage.
/// This is necessary if you want to send (not necessary just to route).
/// \param[in] connectionGraph A weighted graph representing the topology of the network.
void SetConnectionGraph(DataStructures::WeightedGraph<ConnectionGraph::SystemAddressAndGroupId, unsigned short, false> *connectionGraph);
/// Sends a bitstream to one or more systems. If multiple systems are specified, the message will be multicasted using a minimum spanning tree
/// \pre You just have called SetConnectionGraph with a valid graph representing the network topology
/// \note Single target sends from RakPeer with this plugin installed will also be routed. Sends from other plugins will also be routed as long as this plugin is attached first.
/// \param[in] data The data to send
/// \param[in] bitLength How many bits long data is
/// \param[in] priority What priority level to send on.
/// \param[in] reliability How reliability to send this data
/// \param[in] orderingChannel When using ordered or sequenced packets, what channel to order these on.- Packets are only ordered relative to other packets on the same stream
/// \param[in] recipients A list of recipients to send to. To send to one recipient, just pass a SystemAddress
/// \return True on success, false mostly if the connection graph cannot find the destination.
bool Send( char *data, BitSize_t bitLength, PacketPriority priority, PacketReliability reliability, char orderingChannel, SystemAddressList *recipients );
bool Send( const char *data, BitSize_t bitLength, PacketPriority priority, PacketReliability reliability, char orderingChannel, SystemAddress systemAddress );
// --------------------------------------------------------------------------------------------
// Packet handling functions
// --------------------------------------------------------------------------------------------
virtual void OnAttach(RakPeerInterface *peer);
virtual void OnDetach(RakPeerInterface *peer);
virtual void OnShutdown(RakPeerInterface *peer);
virtual void Update(RakPeerInterface *peer);
virtual PluginReceiveResult OnReceive(RakPeerInterface *peer, Packet *packet);
virtual void OnCloseConnection(RakPeerInterface *peer, SystemAddress systemAddress);
protected:
void SendTree(PacketPriority priority, PacketReliability reliability, char orderingChannel, DataStructures::Tree<ConnectionGraph::SystemAddressAndGroupId> *tree, const char *data, BitSize_t bitLength, RakNet::BitStream *out, SystemAddressList *recipients);
void SerializePreorder(DataStructures::Tree<ConnectionGraph::SystemAddressAndGroupId> *tree, RakNet::BitStream *out, SystemAddressList *recipients) const;
DataStructures::WeightedGraph<ConnectionGraph::SystemAddressAndGroupId, unsigned short, false> *graph;
bool restrictByType;
DataStructures::OrderedList<unsigned char,unsigned char> allowedTypes;
RakPeerInterface *rakPeer;
};
#endif
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,453 |
package com.danymany.minerutils.proxy;
public abstract class CommonProxy implements IProxy
{
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,764 |
package io.dmitryivanov.tcpfrontman
import io.dmitryivanov.tcpfrontman.config.{ ServerConfig, DefaultConfigs, CliArgParser }
import io.netty.bootstrap.ServerBootstrap
import io.netty.channel.ChannelOption
import io.netty.channel.nio.NioEventLoopGroup
import io.netty.channel.socket.nio.NioServerSocketChannel
import io.netty.handler.logging.{ LogLevel, LoggingHandler }
object Boot extends App with CliArgParser with DefaultConfigs {
// TODO get it from application.conf
val DefaultBindPort = 8080
val DefaultRemoteHost = "localhost"
val DefaultRemotePort = 80
parse(args) match {
case Some(config) => startServer(config)
case None =>
// error msg will be displayed automatically
// but we want to send a non-zero exit code to be shell-friendly
System.exit(-1)
}
private def startServer(config: ServerConfig): Unit = {
val bossGroup = new NioEventLoopGroup(1)
val workerGroup = new NioEventLoopGroup()
try {
val bootstrap = new ServerBootstrap()
bootstrap.group(bossGroup, workerGroup)
.channel(classOf[NioServerSocketChannel])
.handler(new LoggingHandler(LogLevel.INFO))
.childHandler(new TcpProxyInitializer(config.remoteHost, config.remotePort))
.childOption[java.lang.Boolean](ChannelOption.AUTO_READ, false)
.bind(config.bindPort).sync().channel().closeFuture().sync()
} finally {
bossGroup.shutdownGracefully()
workerGroup.shutdownGracefully()
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,785 |
Schools Closed In Delhi Due To Air Pollution: Environment Minister
Image credit: Shutterstock
Due to the city's present air pollution levels, all schools in Delhi will be closed starting tomorrow till further notice, according to Environment Minister Gopal Rai. Following the Supreme Court's condemnation of the Delhi government's decision to reopen schools, the minister made the declaration. The Supreme Court today handed the federal government, Delhi, and other neighbouring states a 24-hour deadline to take action to reduce pollution in the National Capital Region."We had reopened schools considering the forecast that air quality would improve. However, the air pollution levels have increased again and we have decided to shut schools from Friday till further orders," Mr Rai said.
Delhi's air quality started deteriorating after Diwali. On November 13, Chief Minister Arvind Kejriwal announced that schools will be closed for a week so that students can be kept away from breathing the polluted air. The closure was extended beyond one week as the air quality in the city did not improve significantly.
On November 24, despite recording 'very poor' air quality, schools were allowed to reopen for physical classes. Parents had mixed reactions to the decision of the national capital government.
The Supreme Court of India on December 2 expressed dissatisfaction with the measures taken by the Delhi government to control air pollution. Pollution levels has increased in Delhi despite the state government claims, the top court said.
"We feel that nothing is happening and the pollution keeps increasing... only time is being wasted," Chief Justice NV Ramana said during the hearing.
The Supreme Court criticised the Delhi government's decision to reopen schools and said that "three-year-olds and four-year-olds are going to schools but adults are working from home". "We will appoint somebody to administer your government." | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 4,382 |
{"url":"https:\/\/tex.stackexchange.com\/questions\/329939\/section-item-numbering-right-to-left","text":"# section\/item numbering right to left\n\nSince upgrading MiKTeX I have a problem with bilingual documents English\/Arabic: All header numberings, the numbers of an enumerated list (in English) and any number in regular English text which is immediately followed by a period is typeset right to left.\n\nHere is an example:\n\n%!TEX TS-program = xelatex\nchapterprefix=off]{scrbook}\n\n\\usepackage{amsmath}\n\\usepackage{array}\n\\usepackage{amsthm}\n\\usepackage{enumitem}\n\\usepackage{multicol}\n\\usepackage{fontspec}\n\\usepackage{polyglossia}\n\\setmainlanguage{english}\n\\setotherlanguage{arabic}\n\\newcommand\\rl{\\textarabic}\n\n\\begin{document}\n\\chapter[Chapter One]{XXXXX}\n\\section{YYYYY}\nEnumerated lists, first in Arabic\n\n\\begin{Arabic}\n\\begin{enumerate}\n\\item \u0627\u0644\u0643\u062a\u0627\u0628 \u062c\u062f\u064a\u062f.\n\\item \u0627\u0644\u0637\u0627\u0644\u0628 \u062c\u0645\u064a\u0644.\n\\end{enumerate}\n\\end{Arabic}\n\neverything is OK. But in English .....\n\n\\begin{enumerate}\n\\item An item in an English environment\n\\item Just a second one\n\\end{enumerate}\n\n\\section{ZZZZZ}\nNow normal text in English. But when a number is followed by a period, we run into the same problem, like\n\"This happened in 1999.\"\n\nIf I change this to \"This happened in 1999 .\", just adding a space before the period, it works OK, only I don't want that space there.\n\n\\section{Exercises}\n\\begin{Arabic}\n\\begin{multicols}{2}\n\\begin{enumerate}\n\\item \u0627\u0644\u0637\u0627\u0644\u0628 \u0641\u064a \u0645\u0643\u062a\u0628.\n\\item \u0627\u0644\u0645\u062f\u064a\u0631 \u0641\u064a \u0627\u0644\u0645\u0643\u062a\u0628.\n\\item \u0627\u0644\u0645\u0643\u062a\u0628\u0629 \u0628\u0639\u064a\u062f\u0629 \u0639\u0646 \u0627\u0644\u062c\u0627\u0645\u0639\u0629.\n\\item \u0627\u0644\u0645\u0643\u062a\u0628\u0629 \u0642\u0631\u064a\u0628\u0629 \u0645\u0646 \u0627\u0644\u062c\u0627\u0645\u0639\u0629.\n\\item \u0627\u0646\u0627 \u0637\u0627\u0644\u0628\u0629 \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062c\u0627\u0645\u0639\u0629.\n\\item \u0627\u0646\u0627 \u0627\u0644\u0645\u062f\u064a\u0631 \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0645\u0643\u062a\u0628.\n\\end{enumerate}\n\\end{multicols}\n\\end{Arabic}\n\\end{document}\n\n\u2022 Welcome to TeX.SX! Please provide a small LaTeX document showing the problem you encounter, such that it becomes possible to copy the code and run it on our installations. Use the edit button at the bottom of your post to add the code. \u2013\u00a0gernot Sep 16 '16 at 21:52\n\u2022 I actually supplied a small document which produces these errors, but I can't see it anymore. I must have done it wrong. Additionally I am temporarily banned from any more edits - no idea why. So I would happily supply it again with a little guidance. \u2013\u00a0user81292 Sep 17 '16 at 15:44\n\u2022 I have no control over this platform. But if you give me the link to your document as a comment, I can add it to the question for you. \u2013\u00a0gernot Sep 17 '16 at 18:18\n\u2022 I have put the sample into my dropbox. The link to it is: dropbox.com\/sh\/r7y4tyipbzsbexx\/AACwegHvBBPHfS-2Zh54SYDQa?dl=0 \u2013\u00a0user81292 Sep 18 '16 at 8:00\n\u2022 This must be a problem specific to MiKTeX, or to this particular version of MiKTeX. I just compiled your document on Linux with TeXLive 2016, and it looks fine. \u2013\u00a0gernot Sep 18 '16 at 15:59","date":"2019-09-16 02:35:10","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 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\": 0.7233301997184753, \"perplexity\": 2787.5174554812825}, \"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-2019-39\/segments\/1568514572471.35\/warc\/CC-MAIN-20190916015552-20190916041552-00082.warc.gz\"}"} | null | null |
package com.streamsets.pipeline.lib.dirspooler;
import com.streamsets.pipeline.api.FileRef;
import com.streamsets.pipeline.api.el.ELEval;
import com.streamsets.pipeline.api.el.ELEvalException;
import com.streamsets.pipeline.api.el.ELVars;
import com.streamsets.pipeline.config.DataFormat;
import com.streamsets.pipeline.lib.io.fileref.FileRefUtil;
import com.streamsets.pipeline.lib.parser.DataParser;
import com.streamsets.pipeline.lib.parser.DataParserException;
import com.streamsets.pipeline.lib.parser.DataParserFactory;
import org.slf4j.Logger;
import org.slf4j.LoggerFactory;
import java.io.IOException;
import java.util.Arrays;
import java.util.List;
public class SpoolDirUtil {
private SpoolDirUtil() {}
private final static Logger LOG = LoggerFactory.getLogger(SpoolDirUtil.class);
private static final String SLASH = "/";
private static final String ASTERISK = "*";
private static final String ESCAPED_ASTERISK = "\\*";
/**
* True if f1 is "newer" than f2.
*/
public static boolean compareFiles(WrappedFileSystem fs, WrappedFile f1, WrappedFile f2) {
if (!fs.exists(f2)) {
return true;
}
try {
long mtime1 = fs.getLastModifiedTime(f1);
long mtime2 = fs.getLastModifiedTime(f2);
long ctime1 = fs.getChangedTime(f1);
long ctime2 = fs.getChangedTime(f2);
long time1 = Math.max(mtime1, ctime1);
long time2 = Math.max(mtime2, ctime2);
int compares = Long.compare(time1, time2);
if (compares != 0) {
return compares > 0;
}
} catch (IOException ex) {
LOG.error("Failed to get ctime: '{}'", f1.getFileName(), ex);
return false;
}
return f1.getAbsolutePath().compareTo(f2.getAbsolutePath()) > 0;
}
/*
* Returns the {@code DataParser} of the file, could be local file and hdfs file
*
* @return the {@code DataParser} of the file
*/
public static DataParser getParser(
WrappedFileSystem fs,
WrappedFile file,
DataFormat dataFormat,
DataParserFactory parserFactory,
String offset,
int wholeFileMaxObjectLen,
ELEval rateLimitElEval,
ELVars rateLimitElVars,
String rateLimit
) throws DataParserException, ELEvalException, IOException {
DataParser parser;
switch (dataFormat) {
case WHOLE_FILE:
FileRef fileRef = fs.getFileRefBuilder()
.filePath(file.getAbsolutePath())
.bufferSize(wholeFileMaxObjectLen)
.rateLimit(FileRefUtil.evaluateAndGetRateLimit(rateLimitElEval, rateLimitElVars, rateLimit))
.createMetrics(true)
.totalSizeInBytes(file.getSize())
.build();
parser = parserFactory.getParser(file.getFileName(), file.getFileMetadata(), fileRef);
break;
default:
parser = parserFactory.getParser(file.getFileName(), file.getInputStream(), offset);
}
return parser;
}
/**
* Returns true if the directory string contains *
*
* @param directory String containing the path to the directory
* @return true if the directory contains *
*/
public static boolean isGlobPattern(String directory) {
return directory.contains(ASTERISK);
}
/**
* Returns the absolute path from the root to the last base directory
* Meaning the path until the last / before the first *
*
* @param directory String containing the path to the directory
* @return the path truncated to the las complete directory
*/
public static String truncateGlobPatternDirectory(String directory) {
String[] absolutePath = directory.split(ESCAPED_ASTERISK);
String truncatedString = absolutePath[0];
if (lastCharacterIsAsterisk(truncatedString) != SLASH.toCharArray()[0]) {
List<String> subDirectories = Arrays.asList(truncatedString.split(SLASH));
StringBuffer stringBuffer = new StringBuffer();
stringBuffer.append(String.join(SLASH, subDirectories.subList(0, subDirectories.size() - 1))).append(SLASH);
truncatedString = stringBuffer.toString();
}
LOG.debug(String.format("Checking existence of path: %s", truncatedString));
return truncatedString;
}
private static char lastCharacterIsAsterisk(String truncatedString) {
char[] charArray = truncatedString.toCharArray();
return charArray[charArray.length - 1];
}
} | {
"redpajama_set_name": "RedPajamaGithub"
} | 9,308 |
Q: Saving changes made with Google Developer Tools I'm trying to access page(s) on a website. The pages are loaded via a ribbon navigation across the top of the page (which is always present), which then loads the data in a div container below.
The ribbon/navigation bar SHOULD allow me to scroll left and right - to access other links, and thus other pages - but the scroll button isn't appearing. I can overcome this problem by using Developer Tools and making the navigation bar much wider (editing the width attribute), thus revealing the links that otherwise remain hidden.
Problem: when I change the CSS to allow access to the 'hidden pages', and then click to load a new page (or new set of data, rather), the new page is loaded, and the navigation bar reverts to its shorter, original state.
Is there any way of preserving my change to the page's CSS?
This is NOT my website. I have contacted the owners, but they have not answered yet.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,843 |
Београдска операција представља низ повезаних борби вођених за ослобођење Београда и његове околине у Другом светском рату, октобра 1944. године. Операцију су извеле јединице Прве армијске групе НОВ и ПОЈ и Трећег украјинског фронта Црвене армије наневши тежак пораз немачкој Групи армија "Србија".
Операција је трајала од 10. до 23. октобра 1944. и одвијала се у три фазе:
припремне борбе од 10. до 14. октобра — у овој фази партизанске и совјетске снаге сломиле су немачку спољну линију одбране која се протезала од Обреновца, преко Јајинаца, Кумодража, Авале и Бањице до Смедерева.
борбе за непосредно ослобођење Београда од 14. до 20. октобра — ова фаза представља борбе вођене у самом граду, из улице у улицу, из куће у кућу, али и на спољним прилазима граду против немачких јединица, које су у току операције продирале с југа и дошле до Великог и Малог Мокрог Луга, Болеча и Авале из правца Смедерева.
завршне борбе од 20. до 23. октобра — у овој фази партизанске и совјетске снаге наставиле су са одбацивањем непријатеља и ослободиле Земун, Сурчин и околна места. Сусретом партизанско-совјетских јединица, које су прешле преко Савског моста и ослободиле Земун и јединица 12. војвођанског корпуса, које су форсирале Саву и ослободиле Сурчин и околна села, 23. октобра код Нове Пазове завршена је Београдска операција и отпочело гоњење непријатељских снага кроз Срем.
Припремне борбе
9. октобар
У току ноћи 9/10. октобра јединице 12. војвођанског корпуса — 11. крајишка и 16. војвођанска дивизија извршиле напад на Обреновац. Напад је извршен са свих страна — 11. дивизија је нападала с истока и југа, 16. дивизија са запада и северозапада, Пета крајишка бригада са југа из правца Мислођина, а 12. крајишка бригада са истока из правца села Барича. Услед одлучне одбране немачких снага, којима је у току борбе стигло појачање из правца Београда, напад је одбијен. Партизанске снаге успеле су да заузму Мислођин и Барич, али су у свитање 10. октобра биле принуђене на повлачење на почетне положаје. У овим борбама партизанске снаге имале су губитке од 40 мртвих и 76 рањених бораца.
У току ноћи 9/10. октобра Прва крајишка бригада извршила напад на немачки гарнизон у Тополи, али је због јаке одбране и дејства непријатељских тенкова, морала да се повуче ка Наталинцима. У току исте ноћи, један батаљон Четврте крајишке бригаде порушио је железничку пругу и железничку станицу у Ковачевцу и ликвидирао непријатељску посаду на станици. Непријатељске снаге претрпеле су губитке од 11 мртвих и 4 заробљена, док су партизанске снаге имале 11 рањених бораца.
10. октобар
Код Ковачевца и Кусадка, код Младеновца, јединице из састава Пете крајишке дивизије (Прва, Четврта и Седма крајишка бригада) разбиле колону од око 300 немачких војника, наневши јој губитке од око 80 мртвих и 40 заробљених. Овом приликом уништено је једно оклопно возило, седам камиона и мотоцикл, а заплењена су два топа и већа количина наоружања и муниције. Партизанске снаге имале су једног погинулог и шест рањених бораца.
У Мељаку, код Умке Трећа личка ударна бригада, из састава Шесте личке дивизије, сломила отпор немачких војника, наневши им губитке од 20 мртвих и више рањених и запленивши два камиона, мотоцикл и већу количину наоружања и друге војне опреме. Бригада је имала 5 мртвих и 10 рањених бораца.
Два батаљона Четврте крајишке бригаде извршила напад на немачке снаге у Младеновцу, али су се после краће борбе повукли из града, јер је непријатељу стигло појачање из Београда. Немачка моторизована колона је следећег јутра продужила ка Тополи, одбацивши делове Прве пролетерске дивизије са пута Младеновац—Топола.
Након неуспелог напада на Обреновац, Штаб 12. војвођанског корпуса донео је одлуку да се напад обнови у току ноћи 10/11. октобар додатним ангажовањем делова 36. војвођанске дивизије. Непријатељске снаге су после првог напада, скратиле линију одбране и повукле се на упоришта — Обреновац, Барич и Умка. Услед одлучне непријатељске одбране из бетонских бункера, напад није успео па су се партизанске снаге у зору 11. октобра повукле на почетне положаје. У овим борбама 36. дивизија је имала 17 мртвих и 36 рањених бораца, међу којима је била Вера Мишчевић (1925—1944), референт санитета Трећег батаљона Треће војвођанске бригаде, која је страдала у селу Звечка. Посмртно је проглашена за народног хероја.
У току ноћи 10/11. октобра Пета крајишка бригада извршила неуспели напад на Мислођин, код Обреновца. Бригада је имала 6 мртвих и 11 рањених.
11. октобар
У ослобођеној Смедеревској Паланци дошло до првог сусрета јединица из састава Прве армијске групе НОВ и ПОЈ и јединица Трећег украјинског фронта Црвене армије. У раним јутарњим часовима борци Првог батаљона Прве крајишке бригаде спојили су се са предњим деловима совјетске 236. стрељачке дивизије. Истог дана извршено је пребацивање Четвртог механизованог корпуса, под командом генерал-лајтнанта Владимира Жданова на леву обалу Велике Мораве, код Велике Плане.
Након два неуспела напада на Обреновац, Штаб 12. војвођанског корпуса донео одлуку да делом снага блокира Обреновац, а делом крене у даље наступање ка Београду. За блокаду је одређена 36. војвођанска дивизија, ојачана 32. српском бригадом из састава 11. крајишке дивизије. Главнина корпуса — 11. крајишка, 16. војвођанска и 28. славонска дивизија прешле су Колубару, пресекле железничку пругу Београд—Обреновац и наставиле наступање ка Београду, заузимајући насеља између десне обале Саве и Лазаревачког друма.
Jединице 11. крајишке и 16. војвођанске дивизије, уз садејство Друге личке бригаде, из састава Шесте личке дивизије, савладале тежак отпор немачких снага и снага Српског добровољачког корпуса и Српске државне страже и овладале линијом Јасенак—Велика Моштаница—Сремчица. У борбама за ослобођење Сремчице погинуло је 15 и заробљено 10 немачких војника.
Јединице Седамнаесте источнобосанске дивизије (Друга крајишка и Петнаеста мајевичка бригада) на комуникацији Крагујевац—Топола напале немачку моторизовану колону, уништиле два камиона и један путнички аутомобил и нанеле непријатељу велике губитке. Партизанске снаге имале су 2 рањена борца.
У току ноћи 11/12. октобра јединице Прве пролетерске ударне бригаде, из састава Прве пролетерске дивизије, заузеле железничку станицу у близини села Ђуринци, код Сопота. Том приликом уништена су два оклопна возила, два камиона и једна локомотива.
У току ноћи 11/12. октобра Прва војвођанска бригада, после једнодневне борбе, заузела Малу Моштаницу, код Умке. Том приликом немачким снагама су нанети губици од 14 мртвих и више рањених бораца, док је бригада имала четири погинула и 28 рањених бораца.
12. октобар
У близини Рипња, код Београда јединице Друге личке ударне бригаде, из састава Шесте личке дивизије, водиле тешке борбе против немачких снага, заузеле железничку станицу Клење, порушиле железничку пругу Рипањ—Ресник и оштетиле три железничке композиције. Том приликом страдало је седам непријатељских војника, док је бригада имала два рањена борца.
Наступајући из правца Мале Моштанице, коју су ослободиле у току ноћи, јединице Прве војвођанске бригаде, након краће борбе против немачких снага ослободиле Умку и Остружницу.
Након дводневних борби против немачких снага, јединице Тринаесте пролетерске ударне бригаде Раде Кончар, из Прве пролетерске дивизије, јединице Друге крајишке ударне бригаде, из састава 17. источнобосанске дивизије и три батаљона из Десете крајишке ударне бригаде, из састава Пете крајишке дивизије, уз садејство 36. тенковске бригаде из састава Четвртог гардијског механизованог корпуса Црвене армије, ослободиле Тополу. Била је ово прва заједничка борба југословенских и совјетских бораца у склопу Београдске операције.
Код Белосаваца, на друму Топола—Младеновац, Други батаљон Тринаесте пролетерске бригаде Раде Кончар из заседе убио 22 и ранио 25 немачких војника, а уништио камион и запленио минобацач и неколико пушака.
Јединице из састава Прве пролетерске и Пете крајишке дивизије, уз садејство једног моторизованог пука и једног стрељачког батаљона из састава јединица Трећег украјинског фронта, након вишечасовне борбе ослободиле Младеновац. У борбама за Младеновац од 10. до 12. октобра погинуло је 120, а заробљена су 54 немачка војника.
13. октобар
Јединице 32. српске (мачванске) бригаде из састава Једанаесте крајишке дивизије напале и заузеле немачка упоришта у Звечкој и Белом Пољу, код Обреновца.
Јединице Прве пролетерске ударне бригаде, из састава Прве пролетерске дивизије, уз садејство 36. тенковске бригаде, из састава Четвртог механизованог корпуса, ослободиле Раљу, код Сопота. Они су сломили отпор непријатеља, који се под заштитом авијације повукао према Авали.
Код Шупљег камена, испод Авале дошло до првог сусрета команданта Прве армијске групе НОВ и ПОЈ генерал-лајтнанта Пеке Дапчевића и команданта Четвртог гардијског механизованог корпуса генерал-лајтнанта Владимира Жданова.
Јединице 15. гардијске механизоване бригаде, наступајући из правца Велике Плане и водећи борбе са непријатељским снагама код Лугавчине, Вранова и Раље избиле на Дунав у рејону Смедерева чиме је пресечена комуникација Смедерево—Београд и одсечена немачка групација укупне јачине око 20.000 војника са целокупном борбеном техником и наоружањем.
У вечерњим часовима 13. октобра јединице Треће личке ударне бригаде, у садејству са деловима Друге личке ударне бригаде, заузеле Рушањ и Ресник. Истовремено, остатак Друге личке ударне бригада је уз мање сукобе са немачким снагама заузео простор између Барајева и Авале. Истог дана на Авалском друму, северно од Раље, дошло је до сусрета бораца Другог батаљона Друге личке бригаде са борцима Црвене армије — био је ово први сусрет јединица из састава Шесте личке пролетерске ударне дивизије Никола Тесла са борцима совјетске Црвене армије.
У току ноћи 13/14. октобра јединице Прве армијске групе НОВ и ПОЈ и Четвртог механизованог корпуса отпочеле напад на немачку спољну линију одбране Београда, која се протезала линијом Гроцка—Врчин—Авала—Пиносава—Железник—Остружница. У току исте ноћи, делови Прве пролетерске и Пете крајишке дивизије и совјетске 14. гардијске механизоване бригаде сломили су отпор немачких снага и заузели Авалу, а потом ослободили Јајинце и Кумодраж. У тешким борбама, вођеним у Јајинцима, од стране немачке авијације, која је грешком тукла своје положаје, тешко је рањен немачки генерал-пуковник Вили Шнекенбургер (1891—1944), командант одбране Београда, чији се Штаб налазио у овом месту. Од последица рањавања Шнекенбургер је преминуо сутрадан.
Борбе за Београд
14. октобар
У Јајинцима одржан састанак команданта Прве армијске групе НОВ и ПОЈ генерал-лајтнанта Пеке Дапчевића и команданта Четвртог гардијског механизованог корпуса генерал-лајтнанта Владимира Жданова, на коме је разрађен план непосредног напада на Београд, који је предвиђао да се главни удар нанесе правцем: Бањица—Аутокоманда—Славија—Савски мост, а као помоћни правци су одређени: Чукарица—Мостар, Топчидерско брдо—Мостар и Цветкова механа—Вуков споменик—Панчевачки мост. Снаге НОВ и ПОЈ биле су распоређене у четири групе и наступале су према одређеним правцима:
12. војвођански корпус: Жарково—Баново брдо—Чукарица—Топчидер—Главна Железничка станица—Савски мост;
Шеста личка пролетерска дивизија: Ресник—Топчидер—Теразије—Калемегдан;
Прва пролетерска дивизија: Бањица—Дедиње—Аутокоманда—Славија—Калемегдан
Пета крајишка дивизија: Врчин—Лештане—Велики и Мали Мокри Луг—Улица краља Александра.
Након састанака, око поднева 14. октобра у рејону Шупљег камена, испод Авале извршена је снажна артиљеријска припрема из преко 300 оруђа (више од 300 топова и минобацача и 24 "каћуше"), а част да повуче обарач првог топа имао је генерал Дапчевић. Снажна артиљеријска ватра трајала је 30 минута након чега је настављен општи напад на Београд.
Правац напада Првог пролетерског корпуса (централни правац):
Јединице Друге и Треће личке ударне бригаде, из састава Шесте личке дивизије, након сламања јаког немачког отпора ослободиле Ресник, Кијево и Кнежевац, а потом су у садејству једног пешадијског батаљона и мањих артиљеријских снага Црвене армије сломиле немачки отпор на Миљаковцу и потиснуле га ка Кошутњаку и Топчидеру, заузевши железничку станицу Топчидер. У овим борбама бригаде су имале губитке од 4 мртва и 15 рањених бораца. Истовремено са овим нападом, Осма црногорска бригада, из састава Прве пролетерске дивизије је сломивши немачки отпор код Пиносаве, наступала преко Ресника и заузела Раковицу, овладавајући непријатељским упориштем на јужној ивици града, као и фабриком авионских мотора.
После вишечасовне борбе јединице Прве пролетерске дивизије и 36. гардијске тенковске бригаде су у вечерњим часовима 14. октобра ослободиле Бањицу и Дедиње, а у току ноћи наставиле наступање према граду – Прва пролетерска дивизија кретала се преко Аутокоманде ка Славији, а 13. гардијска механизована бригада у правцу хиподрома.
Правац напада Дванаестог војвођанског корпуса (бочни леви правац):
Након тешких борби против немачких јединица три батаљона Треће војвођанске ударне бригаде, из састава 36. војвођанске дивизије, ослободила Обреновац и Забрежје, а непријатеља одбацили преко реке Саве у Срем. Непријатељ је имао 23 погинула, око 30 рањених и 21 заробљеног, док је бригада имала 4 мртва и 8 рањених бораца.
Након што су ослободиле Макиш, Прва и Друга војвођанска бригада, из састава 16. војвођанске дивизије, у вечерњим часовима 14. октобра извршиле напад на Чукарицу, док су Пета крајишка бригада и Седамнаеста славонска бригада напале непријатељске положаје у Жаркову, на југозападним прилазима Београду.
Правац напада Пете крајишке дивизије (бочни десни правац):
У току ноћи 14/15. октобра Четврта крајишка ударна бригада, из састава Пете крајишке дивизије, избила пред село Мали Мокри Луг и пре поноћи прешла у напад на немачке положаје на Коњарнику и Великом Врачару (Звездара). И поред огорченог отпора непријатеља, који је имао утврђену одбрану, са рововима и митраљеским заклонима, бригада је успела да продре у град. Јаке непријатељске снаге прешле су против напад и одбациле бригаду на почетне положаје, у рејону Малог Мокрог Луга. Овде су се бригади прикључили други делови Пете крајишке дивизије — 10. крајишка и 21. српска бригада, са којима је напад обновљен у току наредног дана.
15. октобар
Правац напада Првог пролетерског корпуса (централни правац):
Након што су у току ноћи 14/15. октобра овладале Топчидерским брдом, јединице Шесте личке пролетерске дивизије (Друга и Трећа личка ударна бригада) избиле на трг код Мостара, одакле су продужиле напад Улицом кнеза Милоша и Сарајевском улицом према блоку зграда министарстава у Немањиној улици. Прва личка ударна бригада је након заузимања Топчидера упућена на Чукарицу, да пружи подршку јединицама Дванаестог војвођанског корпуса.
У току преподнева Други батаљон 214. стрељачког пука 73. гардијске стрељачке дивизије, уз подршку тенкова и артиљерије, покушао да овлада тргом Славија, али је одбијен јаком артиљеријском и митраљеском ватром, јер су немачке снаге пружале јак отпор. Потом су совјетски самоходни јуришни топови заузели положаје на угловима улица, а противтенковски топови и тенкови гађали отворе у немачким бункерима. Уз ватрену подршку, јуриш на немачке положаје извршио је Први црногорски батаљон Прве пролетерске ударне бригаде, чији су борци успели да заузму положаје на ободу трга и у правцу према Београдској улици, борећи се за сваку зграду на угловима улица Светог Саве и Цара Николе. У овим борбама, поред зграде хотела "Славија", погинуо је капетан Душан Милутиновић (1920—1944), заменик команданта Првог батаљона, који је посмртно 1953. проглашен за народног хероја.
У току дана, Прва пролетерска бригада, уз подршку совјетских тенкова, наставила продирање према Улици краља Александра и избила пред зграде Народне скупштине и Главне поште. На десном крилу напада Прве пролетерске дивизије налазила се Трећа пролетерска санџачка бригада која је у тешким борбама успела да овлада Ташмајданом и зароби чету Немаца. Истовремено, Осма црногорска бригада је наступајући заједно са јединицама Црвене армије кроз Улицу краља Милана избила до Новог двора, надомак Теразија.
Правац напада Дванаестог војвођанског корпуса (бочни леви правац):
После вишечасовне борбе против јаких немачких снага јединице Пете крајишке козарске ударне бригаде и један батаљон Дванаесте крајишке ударне бригаде, из састава Једанаесте крајишке дивизије, ослободиле Жарково. У овим борбама непријатељ је имао 30 мртвих, 40 рањених и 55 заробљених војника, док су партизански губици износили 24 погинула и 32 рањена борца. У току наредне ноћи, Петра крајишка бригада је након тешких борби, пробила одбрану немачког батаљона на Бановом брду и заузела важан одбрамбени положај непријатеља. У овој борби непријатељ је имао 30 мртвих и 55 заробљених војника, а заплењена је већа количина наоружања и ратне опреме.
Правац напада Пете крајишке дивизије (бочни десни правац):
У току преподнева 15. октобра јединице из састава Пете крајишке дивизије (Четврта и Десета крајишка и 21. српска бригада) обновиле напад на немачке положаје на Коњарнику и Великом Врачару (Звездара). Напредујући Улицом краља Александра, ове снаге су код Цветкове механе успоставиле везу са јединицама 14. гардијске механизоване бригаде Црвене армије, након чега су заједно избиле код зграде Техничког факултета. У близини Вуковог споменика уништена је колона немачке технике (аутомобили, топови, тенкови), а у току дана је сломљена непријатељска одбрана на Великом Врачару, чиме је уништен један од најјачих чворова немачке одбране у Београду.
Борбе против немачке групе "Штетнер"
Одступајући из источне Србије, немачка корпусна група "Штетнер" све се више примицала Београду. Њене предње јединице су се у току преподнева 15. октобра приближиле источном делу Београда, где су у рејону Малог Мокрог Луга нападнуте од јединица Прве крајишке бригаде, из Пете крајишке дивизије, и скоро потпуно уништене. Неколико немачких аутомобила успело је да се повуче у Гроцку. Гонећи немачке снаге у одступању, један батаљон Прве крајишке бригаде продро је у Гроцку, одбацио слабије немачке снаге и овладао овим местом. У току ноћи 15/16. октобра, Прва крајишка бригада, ојачана совјетским тенковима и артиљеријом, извршила је јуриш на немачку колону на друму између Гроцке и Брестовика, наневши јој знатне губитке, након чега је била принуђена да се повуче у рејон села Пударци.
У новонасталој ситуацији, Штаб Прве армијске групе НОВ и ПОЈ је наредио 21. српској дивизији, која се налазила у резерви у рејону Авале, да хитно образује јак заслон на Смедеревском друму и не дозволи пробијање непријатељских снага у Београд. Извршавајући постављени задатак, јединице 21. дивизије су заузеле следеће положаје: Четврта српска бригада на узвишицама Шугавцу и Липовици на левој обали Болечице и у дубини на линији Ерино брдо—Смрдан—Мали Мокри Луг—Велики Мокри Луг, где се до тада налазила 15. гардијска механизована бригада Црвене армије; Пета српска бригада на линији Голо брдо—Лештане—Забран, са задатком да делује у бок немачким снагама које одступају Смедеревским друмом.
У току ноћи 15/16. октобар немачке снаге извеле су напад на јединице 5. крајишке и 21. српске дивизије. Током тешких борби, које су трајале читаве ноћи и у којима су трпели велике губитке (само у борби код Малог Мокрог Луга имали су око 360 мртвих), Немци су упорно настојали да се пробију у град, што су успели делом снага, које су продрле на правцу Коњарника, Цветкове механе и Великог Врачара (Звездара), али нису успеле да се споје са својим јединицама у центру.
16. октобар
Јединице 75. стрељачког корпуса Црвене армије ослободиле Смедерево, а немачку Прву брдску дивизију, под командом генерал-лајтнанта Валтера Штетнера, одбациле према Београду.
Након два дана борби, Прва армијска група НОВ и ПОЈ и Црвена армија ликвидирале су најважније непријатељске отпорне тачке на јужној и источној ивици града: Жарково—Баново брдо—Топчидер—Дедиње—Бањички вис—Вождовац—Коњарник—Велики Врачар (Звездара), чиме је већи део града ослобођен. Непријатељ се држао само у северозападном делу града, на линији железничка станица "Дунав" (Вилине воде)—Ботаничка башта—зграда Народне скупштине—Теразије—блок зграда министарства (угао Немањине и Кнеза Милоша)—Главна железничка станица, као и на Чукарици, где су немачке јединице биле одсечене од оних у граду.
Борбе против немачке групе "Штетнер"
У рејону Великог Мокрог Луга, немачке јединице напале положаје 14. гардијске механизоване бригаде Црвене армије, с циљем да подрже своје снаге, које су, нападајући у захвату Смедеревског друма, продрле у источно предграђе Београда. Немачки војници су узастопно јуришали, али су совјетски војници одржали своје положаје. Услед великих губитака, немачке снаге су биле приморане да одустану од даљих напада на том делу фронта и да своје снаге усмере у рејоне, где су већ успеле да продру у град.
Након пробоја у источно предграђе Београда, немачке снаге покушале да се споје са својим снагама у центру. Ове снаге је у Улици краља Александра напао један батаљон Друге пролетерске бригаде и одбацио у рејон основне школе "Војислав Илић" (данас Архитектонска техничка школа), где их је у садејству са 36. гардијском тенковском бригадом окружио и уништио.
У току дана разбијена је и већим делом уништена група Немаца, која се пробила ка Коњарнику, а најјачи отпор пружила је група која се пробила у рејон Великог Врачара (Звездара). Концентричним ударом 14. гардијске механизоване бригаде и јединица Пете крајишке дивизије ова група је разбијена и уништена, чиме је пропао други немачки покушај да обезбеде пробој својих главних снага у Београд из правца Смедерева.
17. октобар
18. октобар
У ослобођеном делу Београда отпочео рад Команде града Београда, која је организовала прву војно-цивилну власт у граду. Командант града био је генерал-мајор Љубодраг Ђурић, а поред њега у Команди су се налазили — Ђоко Савићевић задужен за снабдевање; Митар Ковачевић за обавештајни рад; Бранко Вучинић секретар Команде града и секретар партијске организације. Одмах по функционисању, Команда је упутила Проглас грађанима позивајући их да свим снагама помогну Народноослободилачку борбу. Команда града је функционисала до 26. октобра 1944. када је на седници Главног Народноослободилачког одбора Србије именован Народноослободилачки одбор града Београда, на челу са Михаилом Ратковићем.
19. октобар
20. октобар
Завршне борбе
21. октобар
22. октобар
23. октобар
Командни састав јединица
НОВ и ПОЈ
Црвена армија
Напомене
Фотогалерија
<div style="text-align:center;font-size:85%;">
Референце
Литература
Београд у Народноослободилачкој борби
Хронологија Народноослободилачке борбе 1944. | {
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"Why'd I put my heart on every cursive letter?"
- Melanie Martinez
Album of the day (#3123): Graceland by Paul Simon
Forum Index -> Best Ever Albums -> Music
Neil Young as a butternut squash
I probably don't understand the history and strategy of the boycotts enough, so if someone could help me understand, that would be great. If a) the boycott was intended to make Apartheid economically untenable for white South Africans to continue and b) Paul Simon's actions resulted in black South Africans making money but not white South Africans, what is the mechanism by which Paul Simon caused harm to the anti-Apartheid movement?
Surely it's not about the ripple effects of those black artists' increased buying power. That would be a grotesque argument.
Is it the fact that he was not respectful enough to those organizing the boycott in South Africa and around the world? Is it about a precedent or a moral hazard? Is there a less abstracted reason I'm missing?
P.S. Putting Ronstadt on the album was a very bad move and he deserves every bit of criticism for that.
Add me on RYM
birdman_handrub.gif
baystateoftheart wrote:
Good questions. This post is a placeholder for a (hopefully) thoughtful answer that I don't have time to provide right now.
2019 in full effect. Come drop me some recs.
Skinny wrote:
Seth, nobody is suggesting either you or Paul Simon is racist. The "I've got a black friend" analogy refers to the misguided logic which suggests a person's offences towards a community or common cause can be written off because they have the support of one person, or a small number of people, within that community. Ergo, Hugh Masakela arguing in support of Paul Simon doesn't make his decision any less naïve, patronising, or pigheaded, just as Elton John performing with Eminem doesn't absolve the latter of his overt, targeted homophobia.
As I've said previously, I think Paul Simon was well-intentioned. But I think it takes a special kind of arrogance to believe that your good intentions outweigh carefully planned, internationally agreed protocol aimed at damaging an oppressive regime. You're right in saying that there's no evidence that Paul Simon's work in South Africa did anything to extend Apartheid, though the opposite is also true - such is the case with hypotheticals. But Paul Simon knowingly threatened to undermine the protest movement in order to record an album, because he thought he knew better than thousands, if not millions, of academics, performers, politicians, and activists. Just because some good came of it for some people doesn't make it the right decision.
Thank you for this clarification. Somehow I got a different vibe from your previous posts. All is well.
I think in the end you gotta decide whether you hate scabs or realize they are just trying to feed their family too. I realize that's a poor analogy to this issue, but it kind of feels like that's the essence of the conversation. Sometimes it's the single act and not the context that's considered and I just wanted to discuss the context a little more. If that single fact is a deal break or not I suppose is clearly still a "debated"/often written about topic on the internet. In the end I can see where you are coming from and while I wouldn't necessarily 100% agree with it (if indeed I'm reading it right that it's dude disobeyed the resolution and for that sing reason, dude's a douche). Your arguments totally have merit though - I suppose depending on the situation I don't know Paul personally, so maybe his heart wasn't in the right place. I just imagine an African guitarist wouldn't work with him for 30 years if that's the case. Maybe I'm wrong.
I'm also intrigued to be enlightened a little more of your point of view from BayState's questions.
Also my mom had a black friend once, so she witnessed in person the I Have A Dream speech by Dr. King. ( I'm half kidding... but not about the part that she was there and took part with the civil rights movement throughout her 20s). She ended up getting a masters in multi-culturalism.
Last edited by RoundTheBend on 07/10/2019 03:29; edited 4 times in total
I'm curious about that as well. Where is there hard evidence Paul Simon undermined the movement and prolonged Apartheid? Granted, at the time, it was controversial, and potentially damaging, but has history proved it so? Either way, it was over 30 years ago, and Apartheid is long over now.
It's hard living in a world without Chris Cornell.
I think Skinny answered that already?
You're right in saying that there's no evidence that Paul Simon's work in South Africa did anything to extend Apartheid, though the opposite is also true - such is the case with hypotheticals.
It's the whole evidence of God argument. Well you can't prove "he" is or isn't there.
I think the point is Simon knowingly (although to what extent I'm not clear) went against the UN resolution. And that alone has consequences.
The counterpoint I was making is does that really make him a douche? Sometimes "good ideas" have good/bad consequences... sometimes "breaking the law" is the right thing to do... it's not so black and white. But maybe I don't know what I'm talking about.
If you're gonna hold a grudge against a man (Simon), for something he did 1/3 of a century ago (broke UN sanctions against South Africa), that could have been damaging at the time, but there doesn't seem to be evidence that it was damaging, and then it became a moot point (fall of Apartheid)...just seems like an unnecessary grudge at this point. I would like to hear more from that perspective.
rkm
#27 | Posted: 3 days ago | Post subject:
He wouldn't be the first artist to have that level of arrogance, or a perverse sense of reality. You could even argue that this level of arrogance is a necessary precursor to making great art. Artists of all kinds need this kind of sense of grandiosity, or at least a sense of individualism that causes them to see themselves outside of the accepted norm (perhaps even a U.N. boycott), in order to create something new that hasn't previously existed.
I have greater trouble with artists who have shown themselves to be assholes in their personal relationships, who are misogynistic and/or violent towards women, than I do with someone who "breaks the law but operates within the spirit of it".
Album of the day (#981): Graceland by... albummaster Music 13 07/26/2013 00:11
Album of the day (#1802): Graceland b... albummaster Music 30 11/07/2015 05:34
Album of the day (#2775): Paul Simon ... albummaster Music 15 07/22/2018 18:33
[ Poll ] Bob Dylan vs Paul Simon or Van Morrison RoundTheBend Music 91 03/10/2013 03:17 | {
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Q: setText function does not change the TextView the app runs the way I want I can see that in the Logcat
but the text view is not changing and keeps the default value
i also tried to change button enable status programmatically but stayed in the same , nothing get changed !!
I tried in the setText method both
String.valueof(int)
and
Integer.toString(int)
java
@Override
protected void onCreate(Bundle savedInstanceState) {
super.onCreate(savedInstanceState);
setContentView(R.layout.activity_main);
play =(Button) findViewById(R.id.button4);
Pause =(Button) findViewById(R.id.button5);
hourstext =(TextView) findViewById(R.id.textView1);
mintext =(TextView) findViewById(R.id.textView2);
sectext =(TextView) findViewById(R.id.textView3);
}
void playb(View v) {
while (!ispause) {
sec = 0 ;
while (sec < 60) {
SystemClock.sleep(1000);
sec++;
sectext.setText(Integer.toString(sec));
Log.d("this", "sec value=" + sec);
}
sec = 0;
min++;
Log.d("this","min value ="+min);
mintext.setText(String.valueOf(min));
}
}
XML
<?xml version="1.0" encoding="utf-8"?>
<android.support.constraint.ConstraintLayout xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
xmlns:tools="http://schemas.android.com/tools"
android:layout_width="match_parent"
android:layout_height="match_parent"
tools:context=".MainActivity">
<TextView
android:id="@+id/textView3"
android:layout_width="114dp"
android:layout_height="94dp"
android:layout_marginTop="159dp"
android:layout_marginEnd="16dp"
android:layout_x="274dp"
android:layout_y="120dp"
android:gravity="center|center_horizontal"
android:text="00"
android:textSize="40sp"
app:layout_constraintEnd_toEndOf="parent"
app:layout_constraintTop_toTopOf="parent" />
<Button
android:id="@+id/pauseButton"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_marginStart="72dp"
android:layout_marginTop="116dp"
android:layout_marginEnd="93dp"
android:layout_x="217dp"
android:layout_y="296dp"
android:enabled="false"
android:onClick="playb"
android:text="Pause"
app:layout_constraintEnd_toEndOf="parent"
app:layout_constraintStart_toEndOf="@+id/playbutton"
app:layout_constraintTop_toBottomOf="@+id/textView3" />
<Button
android:id="@+id/playbutton"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_marginStart="70dp"
android:layout_marginTop="116dp"
android:layout_x="63dp"
android:layout_y="293dp"
android:onClick="playb"
android:text="playb"
app:layout_constraintStart_toStartOf="parent"
app:layout_constraintTop_toBottomOf="@+id/textView2" />
<TextView
android:id="@+id/textView2"
android:layout_width="120dp"
android:layout_height="97dp"
android:layout_marginTop="156dp"
android:layout_marginEnd="17dp"
android:layout_x="139dp"
android:layout_y="117dp"
android:gravity="center|center_horizontal"
android:text="00"
android:textSize="40sp"
app:layout_constraintEnd_toStartOf="@+id/textView3"
app:layout_constraintTop_toTopOf="parent" />
<TextView
android:id="@+id/textView1"
android:layout_width="103dp"
android:layout_height="94dp"
android:layout_marginStart="16dp"
android:layout_marginTop="159dp"
android:layout_x="11dp"
android:layout_y="117dp"
android:gravity="center_horizontal|center_vertical"
android:text="00"
android:textSize="40sp"
app:layout_constraintStart_toStartOf="parent"
app:layout_constraintTop_toTopOf="parent" />
</android.support.constraint.ConstraintLayout>
i get no error message ! the app keeps working but no updated textView
i've included my XML Code
A: It's likely to do with running everything on the main thread. You should never call sleep on the main thread or you will block the UI.
When the button is clicked you should start the counter on a background thread. You will then need to update the TextView on the main thread.
It can be achieved quite easily with RxJava:
private Disposable disposable;
disposable = Observable.interval(1, 1, TimeUnit.SECONDS)
.subscribeOn(Schedulers.io())
.observeOn(AndroidSchedulers.mainThread())
.subscribe(value -> {
// Update UI
});
To stop the counter:
disposable.dispose();
A: If you want make counter up for 60 sec you can use this code
long time=60;
new CountDownTimer(time*1000, 1000)
{
public void onTick(long millisUntilFinished) {
mTextField.setText("seconds : " + (time-millisUntilFinished /1000));
}
public void onFinish() {
mTextField.setText("done!");
}
}.start();
A: Before trying to fix this problem, let first understand why it happens
CAUSE
When you call View.setText(), Android doesn't actually set the text immediately. It pushes all of these set-text works to a queue on main thread to do LATER whenever it has free time.
Let's try to run this block, you will notice that until this while loop finish, View.setText() will not be done.
void playb(View v) {
min = 0
while (min < 1000000) {
min++
Log.d("this", "min value =$min")
mintext.setText(String.valueOf(min))
}
}
So in your situtation, actually the TextView will still be set, but you will not see the change until the while loop finishes.
SOLUTION
You should move this while loop to another thread, you can simply use an AsyncTask or a HandlerThread for that
Ex. Use a HandlerThread:
void playb() {
// Start a new background thread
HandlerThread thread = new HandlerThread("");
thread.start();
// Obtain the handler of new background thread
Handler handler = new Handler(thread.getLooper());
// Obtain the handler of main thread (UI Thread)
final Handler mainHandler = new Handler(this.getMainLooper());
// Create a runnable and send it to background thread to execute
handler.post(new Runnable() {
public final void run() {
// Do the job
int min = 0;
while(true) {
int sec = 0;
while(sec < 60) {
SystemClock.sleep(1000L);
sec ++;
final int currentSec = sec;
// Send the update-text job to main thread to execute
mainHandler.post(new Runnable() {
public final void run() {
secText.setText(currentSec);
}
});
}
sec = 0;
min++;
final int currentMin = min;
// Send the update-text job to main thread to execute
mainHandler.post(new Runnable() {
public final void run() {
minText.setText(currentMin);
}
});
}
}
});
}
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\section{Introduction}
Since the first detection of gravitational waves (GWs) by the LIGO-Virgo collaboration in 2015 \cite{Abbott2016a}, {a big effort has been devoted to {exploring} how much this new probe will help us to understand the universe in various fields, such as astrophysics, cosmology and gravitation} \cite{Bailes2021}. {Particularly the} GW events that are followed by electromagnetic counterparts, such as gamma ray bursts, stand out as important for cosmology, since they provide measurements of both the redshift of the source and its luminosity distance, as first remarked in \cite{Schutz1986}. These so-called standard sirens constitute, therefore, a new class of sources that allows the reconstruction of the distance-redshift relation, complementary to type Ia supernovae surveys but without the need of tricky calibrations. In fact, the detection of multimessenger events has already yielded a measurement of the Hubble constant \cite{Abbott2021} which, even if not yet competitive in accuracy with the current best measurements, illustrates that these observations provide a powerful additional independent test of the concordance $\Lambda$-cold-dark matter ($\Lambda$CDM) model.
Joint events of GWs and electromagnetic (EM) signals are also powerful to measure deviations of General Relativity (GR), as demonstrated by the first detection of this kind, GW170817 \cite{LIGOGW170817, LIGO2017, LIGO2019}. That detection alone put a stringent bound on the speed of propagation of GWs at low redshifts, allowing for a relative difference to the speed of light of just one part in $10^{15}$. {Apart from UV cutoff arguments \cite{deRham2018},} this information highly disfavored, if one wants to avoid fine-tuning issues, a {significant fraction} of the gravity theories within the Horndeski family \cite{Horndeski:1974wa, Deffayet2011, Kobayashi:2011nu}, one of the most general Lagrangians that give rise to second order field equations with a single scalar field.
However, there is still a wide range of models not yet ruled out by observations, within and beyond Horndeski, that feature modifications in the propagation of GWs through cosmological distances even with a speed equal to the speed of light \cite{Baker2017, Creminelli2017, Ezquiaga2017, Sakstein2017}. In particular, they change the friction rate at which the tensor modes propagate, an effect that can be encoded as a modification on what has been called recently the GW distance \cite{Lombriser2016, Amendola2018, Belgacem2018G}. Since the GW signals exhibit a radiative behavior far from the sources, i.e. their amplitude is inversely proportional to the distance, this GW distance can be inferred from the detected waveform at ground or space-based interferometers, especially when the inclination of the binary source orbital plane is also relatively well determined. Such information might be more precisely obtained in the future with the advent of a network of third generation detectors \cite{Maggiore2020, Amaro-Seoane2017, Reitze2019, Zhao2018}, covering a large range of frequencies and types of sources, that will also be sensitive to other signatures of modified gravity (MG), such as the existence of extra polarization modes \cite{Takeda2019}.
In this work we will focus on the Einstein Telescope (ET), a proposed underground cryogenic third generation GW observatory \cite{Maggiore2020, Sathyaprakash2010}. ET is particularly interesting for testing GR because, among other kinds of signals from sources up to redshift of order 20, those emitted by binary neutron stars (BNS) {fall into} its sensitivity frequency band ($\sim 1 - 10^4$ Hz). ET is expected to see, within a decade of running, several hundred multimessenger events emitted by BNS, up to redshift $z = 2$. Several works such as \cite{Matos2021,DAgostino2019,Belgacem2019b,Zhao2011,Nunes2019,Bachega2020} have recently investigated the ability of ET to constrain gravity and cosmology, finding, for instance, that bright standard sirens will give a percent level measurement of the Hubble constant. Concerning MG, its effect on the GW distance is however highly degenerate with the cosmological background and for some particular models, even in the best scenarios, the results can be much weaker than current constraints (for example in $f(R)$, GWs will give $|f_{R0}| < 10^{-2}$ at best \cite{Matos2021}).
The degeneracy between MG and cosmology in the GW measurements requires combining them in the future with other powerful tests, such as observations of the large-scale structure of the universe. A common way of currently testing gravity in the scalar sector is by measuring the gravitational slip, i.e. a difference between the two gravitational potentials $\Phi$ and $\Psi$, that is in general non-vanishing whenever we are in MG (see for instance \cite{Amendola2013,Amendola2014, Pinho2018, Blanco2021}). Indeed, measuring the slip by looking at the clustering of matter from the distribution of galaxies and the cosmic shear generated by weak lensing is one of the targets of galaxy surveys such as the upcoming \textit{Euclid}~satellite \cite{Amendola2018b}.
The fundamental fact that will be explored in this work is that, in many MG theories such as the Horndeski models, the very same function that modifies the GW friction, which is the running of the Planck mass, also affects the scalar perturbations, generating slip. When aiming for model-independent, {phenomenological} tests of gravity, this relation is usually tuned out and the two observables are considered independently. The goal of this work is, on the contrary, to take advantage of {this} connection and to compare the constraining power of the scalar and tensor sectors of the cosmological perturbations on MG through measurements of, respectively, the slip and the GW distance, as first proposed in \cite{Saltas2014}.
The structure of the paper is the following. In Section \ref{sec:theory} we briefly introduce our theoretical framework of a linearly perturbed FLRW metric in MG theories, define our main observables (the GW distance and the slip) and the gravity models we studied. In Section \ref{sec:data}, we describe the analysed data sets: forecasts for a \textit{Euclid}-like survey with both weak lensing and galaxy clustering contributions, cosmic microwave background (CMB) data from \textit{Planck} and simulations of GWs emitted by BNS detected by the Einstein Telescope. Finally, in Section \ref{sec:results} we present our results: first, a naive comparison between the constraining power of data from the tensor and scalar sectors on the Planck mass running rate; then the constraints on the cosmological parameters and our MG model from all data sets and their combinations. In Section \ref{sec:conclusion} we discuss these results and conclude.
\section{Theory}
\label{sec:theory}
Our cosmology is defined by a perturbed spatially flat FLRW metric,
\begin{equation}
ds^2 = a(\tau)^2\left[ -(1 + 2\Psi)d\tau^2 + (1 - 2\Phi)(\delta_{ij} + h_{ij})dx^idx^j\right]\,,
\end{equation}
where $a$ is the scale factor, $\tau$ is the conformal time, $\Phi$ and $\Psi$ are the scalar potentials and $h_{ij}$ is the transverse traceless tensor perturbation, that can be decomposed into $h_+$ and $h_{\times}$ polarizations.
In the context of cosmology, it has been shown \cite{Gubitosi:2012hu,Bellini2014,Gleyzes:2014qga} that the information content of a broad class of DE/MG theories can be described at background and linear perturbation levels by only five functions of time,
\begin{equation}
\left({\mathcal H}, \alpha_M, \alpha_T, \alpha_K, \alpha_B\right)\,,
\end{equation}
where ${\mathcal H}:=a'/a$ is the conformal Hubble parameter $(a' := da/d\tau)$ and the $\alpha_i$'s are property functions that govern the evolution of both scalar and tensor perturbations. This setting encompasses one of the most general theories that give rise to second order field equations of motion with a single scalar field $\phi$, the Horndeski theory \cite{Horndeski:1974wa, Deffayet2011, Kobayashi:2011nu}, which includes families of models such as $f(R)$ \cite{Carrol2004, DeFelice2010} and quintessence \cite{Ratra1988, Wetterich1988}. The property functions $\alpha_i$ can be either inferred from a first-principled approach based on a particular Lagrangian or modeled with a suitable phenomenological parametrization;\footnote{See \cite{Bellini2014} for an in-depth discussion of their properties.} in both cases they encode possible deviations from the standard GR concordance cosmological model.
As first pointed out in \cite{Saltas2014}, two of these functions affect simultaneously the difference between the scalar potentials and the propagation of GWs through cosmological distances: the Planck mass run rate
\begin{equation}
\alpha_M := \frac{d(\ln M_{\ast}^2)}{d\ln a}
\end{equation}
and the tensor speed excess $\alpha_T$. More precisely, the GW polarization modes evolve in such theories according to
\begin{equation}
h_P'' + (2 + \alpha_M){\mathcal H}h'_P + (1 + \alpha_T)k^2h_P = \Pi_P\,, \label{GW}
\end{equation}
with $P = +, \times$, and where $\Pi_P$ is the tensor part of the anisotropic stress of matter, which is affected only by radiation and neutrinos and can be neglected at late times. The propagation equations show that, besides a non-luminal speed of propagation whenever $\alpha_T \neq 0$, the friction rate at which the modes are damped is modified by $\alpha_M$, changing the amplitude of the GW detected by local interferometers. This gives rise to a new cosmological distance that is inferred from the detected GW waveform, the gravitational wave distance $D^{\text{gw}}$\cite{Belgacem2018, Amendola2018}. Its ratio to the standard electromagnetic luminosity distance in a given theory is given by
\begin{equation}
\Xi(z) := \frac{D^{\text{gw}}(z)}{D^{\text{em}}_L(z)} = \exp\left\{\frac{1}{2}\int_0^z \frac{\alpha_M(\tilde{z})}{1 + \tilde{z}}d\tilde{z}\right\} = \sqrt{\frac{M_{\ast}^2(0)}{M_{\ast}^2(z)}}\,. \label{gw_distance}
\end{equation}
For the scalar sector, on the other hand, among the equations that govern the evolution of the metric and matter perturbations, it is interesting to look at the one that gives the difference between the scalar potentials, which vanishes in GR when the scalar anisotropic stress of matter, $\Pi$, is negligible, which is normally the case at late times and on sub-horizon scales,
\begin{equation}
\Psi - (1 + \alpha_T)\Phi + (\alpha_M - \alpha_T){\mathcal H}\frac{\delta \phi}{{\phi}'} = \Pi\,, \label{phi_minus_psi}
\end{equation}
where $\delta \phi$ is the perturbation of the scalar field in the Newtonian gauge. Remarkably, as shown in \cite{Amendola2014}, it is possible to obtain in an operational way from observations, the slip parameter, defined as
\begin{equation}
\eta := \frac{\Phi}{\Psi}\,,
\end{equation}
constituting an important variable in tests of MG \cite{Motta2013}.
The crucial fact that we will explore in this work is that in a given theory of modified gravity or dark energy, the deviation of the GW propagation and the gravitational slip from the GR values are generally linked, since both are described by equations that come from the spatial part of the Einstein field equations. We can see this explicitly in the example of Horndeski-type theories that we study here, where the same property functions affect GW propagation and gravitational slip.
Therefore, this motivates investigating whether measurements of the GW distance and the slip might be complementary (or not) to the inference of $\alpha_M$ and $\alpha_T$.
On the GW side, the link between $\alpha_M$ and the observable is given by Eq.\ \eqref{gw_distance} and is relatively simple. The connection between the gravitational slip and the $\alpha_i$'s is more complex as it depends on the evolution of the scalar field. In the quasi-static limit for $\alpha_T=0$ and assuming a $\Lambda$CDM background, following the notation of \cite{Bellini2014}, the slip is given by
\begin{equation}
\eta = 1 - \frac{2\alpha_M(\alpha_B + 2\alpha_M)}{4(\alpha_B + 2\alpha_M) -2\alpha_B(1 + w_m)\tilde{\rho}_{\textrm{m}}/H^2 + 4\alpha_B'/\mathcal{H}} \, . \label{slip}
\end{equation}
We notice that for $\alpha_M = 0$ the slip vanishes, but in general it is a function of not only $\alpha_M$ but also $\alpha_B$. In the quasi-static limit the slip also vanishes for $\alpha_B = -2\alpha_M$, a case that is called the `no-slip' scenario \cite{Linder2018}.
In general it is not clear which parameter, $\alpha_M$ or $\alpha_B$, is more strongly constrained by a measurement of the slip. Only if the braiding parameter varies slowly it is possible to conclude that, in a DE dominated era, $\eta \approx 1-\alpha_M/2$ and that the slip is mostly constraining $\alpha_M$. This also illustrates that in general we would need to measure both the slip and the GW distance to disentangle the two parameters.
Another useful way to phenomenologically describe deviations from GR for linear scalar perturbations consists in modifying the Poisson and lensing potential equations \cite{Kunz:2012aw},
\begin{align}
k^2\Psi &= - \mu(a, k) 4\pi Ga^2\rho \Delta\,, \\
k^2(\Phi + \Psi) &= - \Sigma(a, k) 8\pi Ga^2 \rho \Delta\,, \label{lensing}
\end{align}
where $\Delta$ is the gauge invariant density contrast as defined in \cite{Zucca2019}. The functions $\mu$ and $\Sigma$ are sometimes called $G_\textrm{matter}$ and $G_\textrm{light}$ \cite{Linder2018} and probe modifications in, respectively, the growth of structure and the lensing potential. Although it is straightforward to obtain the slip from these functions, in the approach where they are independently parametrized, one loses the connection with GW propagation. This is why here we chose to parametrize the property functions instead, allowing us to track MG effects on the slip and the GW distance in a unified way.
\subsection{Base gravity model} \label{subsec:base_model}
We now define the base gravity model of our main analysis. First, as discussed before, in order to have a GW speed equal to unity we will set $\alpha_T = 0$. Second, we will use the relation $\alpha_B = - \alpha_M$, which corresponds to imposing a conformal coupling and that can be equivalently stated in terms of the Horndeski Lagrangian or the EFT base functions, as detailed in Appendix \ref{app:horndeski}.
The last property function $\alpha_K$ is then chosen such that the speed of sound of the scalar field, in the quasi-static limit, equals 1. This last choice should not impact our results strongly since, firstly, both the GWs and the slip in the quasi-static limit do not depend on $\alpha_K$, and secondly Refs.\ \cite{Bellini:2015xja,Gleyzes:2015rua,Alonso:2016suf} claim that $\alpha_K$ is hardly measurable. We end up with a model which is completely specified by a single free property function $\alpha_M$ (or, equivalently, the Planck mass) and the background evolution $H(\tau)$, which will be set to that of $\Lambda$CDM, since we are interested in the perturbations. We then parametrize the evolution of the Planck mass as a power law of the scale factor, so that the modifications of gravity kick in at late times, i.e.
\begin{equation}
M_{\ast}^2 = 1 + \Omega_0 a^{\beta_0}\, , \label{parametrization}
\end{equation}
where $\Omega_0$ is a free amplitude parameter.
We now briefly comment on the impact of such modifications of gravity on cosmological observables. Concerning the tensor sector, the above parametrization implies the ratio between the GW and electromagnetic luminosity distances in Eq.\ (\ref{gw_distance}) to be given by
\begin{equation}
\Xi(z) = \sqrt{\frac{1 + \Omega_0}{1 + \Omega_0 a^{\beta_0}}}\,. \label{xi}
\end{equation}
When the deviation from GR is small, i.e. $|\Omega_0| \ll 1$, it reduces to the parametrization proposed in \cite{Belgacem2018},
\begin{equation}
\Xi(z) = \Xi_0 + \frac{1 - \Xi_0}{(1 + z)^n}\,,
\end{equation}
with $n = \beta_0$ and $\Xi_0 = 1 + \Omega_0/2$. The functional form in Eq.\ (\ref{xi}), which is depicted in Figure \ref{fig:xi}, mimics the typical behavior of $\Xi$ in $f(R)$ but also in several other MG theories. Its value at high redshifts depends only on $\Omega_0$ and so we fix $\beta_0 = 1$. Therefore, the models considered here feature only one additional degree of freedom $\Omega_0$, changing simultaneously the scalar and tensor sectors via the slip and the GW distance.
\begin{figure}
\centering
\includegraphics[scale=0.49]{figures/xi.pdf}
\includegraphics[scale=0.49]{figures/slip_late_times.pdf}
\caption{Left panel: The ratio between the GW and the luminosity distances that follows from the parametrization of the EFT base functions. The blue curve corresponds to our fiducial model, reaching a maximum 5\% deviation from the GR value of unity at the highest redshifts. On the right, the slip as a function of redshift for our fiducial model at different scales.}
\label{fig:xi}
\end{figure}
Regarding the scalar perturbations, such models differ from $\Lambda$CDM in the low-multipole temperature power spectrum $C_{\ell}^{TT}$ of the CMB and in its lensing potential power spectrum, which is roughly amplified by a global factor, as we will discuss in section \ref{sec:results} (cf. Figure \ref{fig:lensing_cls}). Also the matter power spectrum today in the linear regime, for sub-horizon scales, is simply multiplied by a constant factor, an effect which is degenerate with the galaxy bias (and also $\sigma_8$ or $A_s$). Finally, the slip parameter as a function of redshift is shown in the right panel of Figure \ref{fig:xi}. For our fiducial model, its value today is increased by about 7\%. We remark that for the GWs the maximum effect of the modification of gravity occurs at the highest redshifts, until it saturates, while the slip peaks today. However, this behavior of $\eta$, as compared to $\Xi$, is more sensitive to the exact parametrization assumed for $\alpha_M$, since they have roughly a proportionality relation, while the GW distance is an integrated effect.
Finally, for the initial conditions at high redshift, we consider purely adiabatic scalar primordial perturbations with a power-law spectrum. We fix the primordial spectral index $n_s$, the baryon energy density $\omega_b$ and the reionization optical depth $\tau$ to the values shown in Table \ref{tab:fiducial_model}, corresponding to the best fit of the \textit{Planck} primary spectra from \cite{Planck2018}. We assume three neutrino species with only one massive state with mass $m_{\nu} = 0.06$ eV. The free parameters characterizing our models are, then,
\begin{equation}
(\omega_c, A_s, h, \Omega_0)\,,
\end{equation}
which stand for, respectively, the cold dark matter density, the amplitude of the initial curvature perturbations at $k = 0.05 \; \mathrm{Mpc}^{-1}$, the dimensionless Hubble constant and the proportionality constant related to the Planck mass.
\subsection{No slip gravity} \label{subsec:no_slip}
Additionally, we investigate the no-slip model proposed in \cite{Linder2018}. These models have $\alpha_B = -2\alpha_M \neq 0$ but still no modification of the GW speed ($\alpha_T = 1$). They are interesting theories to compare our main analysis with because here only the propagation of GWs is modified in the quasi-static limit, since inside the horizon at late times
\begin{equation}
\mu = \Sigma = \frac{1}{M_{\ast}^2}\,,
\end{equation}
resulting in $\eta = 1$, as can be seen from Eq.\ \eqref{slip}.
In this model, we adopt the following parametrization for the Planck mass and the corresponding running rate:
\begin{align}
M_{\ast}^2 &= \textrm{e}^{(2A/r)(1 + \tanh{[(r/2)\ln(a/a_t)]})}\,,\\
\alpha_M &= \frac{4A(a/a_t)^r}{[(a/a_t)^r + 1]^2}\,.
\end{align}
In terms of $\alpha_M$, this parametrization implies a `hill-like' behavior for the GW friction $\alpha_M$, as the viability conditions for this model ($c_s^2 \geq 0$ and no ghosts) demand that $\alpha_M \rightarrow 0$ both in the asymptotic past and future, while the modification reaches a peak value of $A$ at $a=a_t$. On the Planck mass side, $M_{\ast}^2$ starts with the value of unity at high redshifts up to the transition point $a = a_t$ after which it goes asymptotically to $\textrm{e}^{4A/r}$, with rapidity $r$. As compared to our base model, this behavior of the Planck mass in no-slip gravity gives an opposite deviation for the ratio between the GW and luminosity distances, i.e. it increases with redshift, as illustrated in Figure \ref{fig:xi_no_slip}
\begin{figure}
\centering
\includegraphics[scale=0.49]{figures/xi_no_slip.pdf}
\caption{The ratio between the GW and luminosity distances as a function of redshift for the no-slip model with $a_t = 0.5$ and $r = 3/2$. The model with $A = 0.005$ is the fiducial model in our simulations while the one with $A = 0.03$ is discussed in \cite{Linder2018} and plotted here for comparison.}
\label{fig:xi_no_slip}
\end{figure}
As discussed in \cite{Linder2018}, such a model with $A = 0.03$, $\tau = 1.5$ and $a_t = 0.5$ is compatible with measurements of the growth of structure observable $f\sigma_8$ when assuming a $\Lambda$CDM background. Therefore, we will systematically fix $\tau$ and $a_t$ to these values and explore the amplitude of the deviation from GR, which is encoded in the parameter $A$. By also setting $c_s^2 = 1$ we effectively have once again a one-parameter family of MG models.
\begin{table}[t]
\centering
\setlength{\extrarowheight}{5pt}
\begin{tabularx}{0.5\textwidth}{>{\centering\arraybackslash}X >{\centering\arraybackslash}X | >{\centering\arraybackslash}X >{\centering\arraybackslash}X}
\hhline{= = = =}
\multicolumn{2}{c}{Free} & \multicolumn{2}{c}{Fixed} \\ \hline
$\omega_{c}$ & 0.1202 & $\omega_b$ & 0.02236 \\
$10^9 A_s$ & 2.101 & $\tau_{\text{reio}}$ & 0.0544 \\
$h$ & 0.6727 & $n_s$ & 0.963 \\
$\Omega_0$ & $-0.1$ & $\sum m_{\nu}$ & 0.06 eV \\[2mm]
\hline
\end{tabularx}
\caption{Parameter values of the fiducial model corresponding to those in Table 2 of \cite{Planck2018} (TT,TE,EE+lowE column), with the addition of the modified gravity related parameter $\Omega_0$.}
\label{tab:fiducial_model}
\end{table}
\section{Data}
\label{sec:data}
\subsection{Gravitational waves}
We now briefly describe the procedure to simulate the GW mock data for the Einstein Telescope, as was done in \cite{Matos2021}.
We consider the waveform emitted at redshift $z$ by a BNS inspiral up to the 3rd post-Newtonian (PN) correction \cite{Blanchet2014}. It is given by:
\begin{eqnarray}
& \tilde{h}(f) = \mathcal{A} \sqrt{F_+^2 (1 + \cos^2\iota)^2 + 4F_{\times}^2\cos^2\iota} (f^{-7/6})e^{i\Phi(f)}\,, \\
& \mathcal{A} \coloneqq \sqrt{\dfrac{5}{96}}\dfrac{M_{c}^{5/6}}{\pi^{2/3}D^{\textrm{gw}}}\sum\limits_{j = 0}^{6}A_j \left(\pi Mf\right)^{\frac{j}{3}}\,,
\end{eqnarray}
where $M_c := (1 + z)M\left( \frac{\sqrt{m_1m_2}}{M}\right)^{3/5}$ is the redshifted chirp mass with $M = m_1 + m_2$ and
\begin{eqnarray}
F_+ \coloneqq \frac{\sqrt{3}}{2}\bigg[\frac{1}{2}(1 + \cos^2\theta) \cos(2\phi)\cos(2\psi) - \cos\theta \sin(2\phi)\sin(2\psi)\bigg]\,, & \nonumber \\
F_{\times} \coloneqq \frac{\sqrt{3}}{2}\bigg[\frac{1}{2}(1 + \cos^2\theta) \cos(2\phi) \sin(2\psi) + \cos\theta \sin(2\phi)\cos(2\psi)\bigg]\,, &
\end{eqnarray}
are the antenna pattern functions \cite{Zhao2011} when the angle between the arms {of the interferometer} equals $\pi/3$. Here, the parameters of the source $\bm{s} = (m_1, m_2, \iota, \theta, \phi, \psi)$ appearing in the above expressions stand for, respectively: the masses of the binary components, the angle of orbital inclination, the direction of the line of sight and the GW polarization angle. We assume, for simplicity, the spins of each one of the binary components to vanish in the coefficients $A_j$ of the PN expansion, whose expressions can be found in \cite{DAgostino2019}. The specific form of the phase function $\Phi$ does not affect our further calculations (cf. Eq.\ \eqref{SNR}).
The inference of the parameters encoded in the waveform, up to some degeneracies, can be made by a matched filtering procedure, where one compares several templates for $\tilde{h}$ with the observed signal considering a given noise spectrum \cite{Maggiore2007}. For high signal to noise ratio (SNR) events, one can work in the Fisher matrix approximation, where the instrumental error in the GW distance ends up depending only on the SNR evaluated at the most likely $\tilde{h}$, given by
\begin{equation}
\text{SNR}^2 = 4 \int_{f_{\text{low}}}^{f_{\text{up}}} \frac{\left|\tilde{h}(f)\right|^2}{S_n(f)}df\,. \label{SNR}
\end{equation}
Here $S_n$ is the noise power spectral density of the detector, which for ET we assume the ET-B model \cite{Zhao2011}, and $(f_{\text{low}}, f_{\text{up}}) = (1\textrm{ Hz}, 10^4\textrm{ Hz})$ are the limits of {ET's sensitivity band. However, the distance and the orbital angle of the source are degenerate, effect that can be roughly taken into account by adding a factor 2 to the error \cite{DAgostino2019}, which becomes}
\begin{equation}
\sigma_{\text{ins}} = \frac{2 D^{\textrm{gw}}}{\text{SNR}}\,. \label{sigma_ins}
\end{equation}
We assume that we can use the geometrical optics limit for the GWs of interest to us, so that they propagate on null geodesics and are affected by gravitational lensing. This contributes an additional scatter to the GW distance that needs to be added in quadrature to the instrumental error, similarly to the treatment of supernova distance measurements. We use the approximation \cite{Sathyaprakash2009, Martinelli2022}
\begin{equation}
\sigma_{\text{lens}} = 0.05 z D^{\textrm{gw}}\,, \label{sigma_lens}
\end{equation}
giving a total error in each of the $N_{\text{obs}}$ estimated GW distances equal to
\begin{equation}
\sigma_i = \sqrt{\sigma_{\text{ins}}(z_i, \bm{s}_i)^2 + \sigma_{\text{lens}}(z_i)^2}\,, \label{sigma}
\end{equation}
for $ i = 1, ..., N_{\text{obs}}$. Here the errors will always be evaluated at the fiducial model employed in the simulations.
Given a fiducial gravitational and cosmological model, we draw the redshift of the i-th binary source from the distribution
\begin{equation}
\rho (z_i) = N_{z} \frac{4\pi [D_c(z_i)]^2}{(1 + z_i)^2 \mathcal{H}(z_i)} r(z_i)\,, \label{z_pdf}
\end{equation}
where $D_c(z) = \int_0^z dz/H(z)$ is the fiducial comoving distance, $r(z)$ is the rate of BNS mergers evolution and $N_z$ is a normalization factor. For the parameters $\bm{s}$, the distributions $\rho(\bm{s})$ assumed in this work are the following. The masses were uniformly sampled from [1, 2]$M_{\odot}$; $\iota$ was sampled from [\ang{0}, \ang{20}] to be consistent with the detection of a gamma ray burst \cite{Zhao2011}; for $(\theta, \phi)$ we made a uniform sampling in the sky and $\psi$ was drawn from [0, 2$\pi$].
Finally, the GW distance $D^{\textrm{gw}}_i$ of the $i$-th event is drawn from a Gaussian distribution, with standard deviation given by Eq.\ (\ref{sigma}), centered in its theoretical value $D^{\textrm{gw}}(z_i, \bm{\Theta})$, where $\bm{\Theta}$ are the cosmological and gravitational parameters defining the model assumed in Eq.\ \eqref{gw_distance}. One may obtain, then, the posterior probability for the parameters of interest, given the simulated data. That is
\begin{equation}
\rho(\bm{\Theta}| \bm{D}^{\,gw} ) \propto \rho (\bm{\Theta}) \exp \Bigg\{-\sum_{i = 1}^{N_{\text{obs}}} \frac{\left[D^{\,gw}_{i} - D^{\,gw}(z_i, \bm{\Theta})\right]^2}{2\sigma_i^2}\Bigg\}\,. \label{final_posterior}
\end{equation}
We consider reliable only those events with SNR $>$ 8 and discard the others as in \cite{Matos2021, DAgostino2019}, which deforms the ultimate probability density of redshifts, as expected. Errors in the inference of the redshifts from the EM signals, expected to be subdominant, were not included in our analysis, neither selection effects that depend on the network of telescopes that will be operating at the same time as ET. Also, other sources of uncertainty were neglected in this work, such as overdensities near emission and peculiar velocities. The latter should be important only at low redshifts, where the population of mergers is of little relevance.
In our analysis, no dependency on the redshift distribution of the binaries was added to the above likelihood. This distribution depends in general on the star formation rate and it is sensitive to the cosmological background $\mathcal{H}(\tau)$, affecting the constraints on the cosmological parameters and the dark energy equation of state, particularly when doing forecasts where also the total amount of events is an unknown variable. However, here our main interest is on the constraining power of standard sirens on the modifications of gravity described in Section \ref{sec:theory}, which are encoded in the distance-redshift relation. Thus, we instead compute only the probability density of $\bm{\Theta}$ given the fact that, for a binary source at redshift $z_i$, precisely obtained via its EM counterpart, one measures a distance $D^{gw}_i$ from the GW signal, regardless of how the sources of such signals are distributed in the sky.
\subsection{Planck}
Another data set included in our analysis consists of the temperature and polarization maps of the CMB measured by the \textit{Planck} mission in 2018. Each Planck likelihood is described in detail in \cite{Planck2018V, Planck2018VIII}, and so here we simply summarize our notation:
\begin{itemize}
\item \textit{Planck} TT,TE,EE is the product of two likelihoods: the combination of the high-multipole ($\ell \geq 30$) $\mathtt{Plik}$ likelihoods from temperature (TT), E-mode polarization (EE), and temperature-polarization (TE) power spectra, including their correlations; and the low-multipole ($2 \leq \ell < 30$) $\mathtt{Commander}$ likelihood for the temperature-only power spectrum;
\item \textit{Planck} lowE is the $\mathtt{SimAll}$ likelihood from the low-multipole ($2 \leq \ell < 30$) E-mode power spectrum;
\item \textit{Planck} lensing is the likelihood from the CMB lensing power spectrum.
\end{itemize}
We refer for brevity to the joint likelihoods from the temperature and polarization power spectra, i.e. \textit{Planck} TT,TE,EE + lowE, as ``CMB" and its combination with {\it Planck} lensing as ``CMB+lens".
\subsection{Large-scale structure likelihoods}
Large-scale structure surveys, particularly the combination of galaxy number counts and weak lensing surveys, are well suited to constrain the gravitational slip \cite{Daniel2008}.
Here we use as a particular example a 15'000 square degree survey that will measure number counts and galaxy shapes out to a redshift of about 2, modeled on the Euclid specifications. Specifically, we use the likelihoods from \cite{Sprenger2019}. These likelihoods are in turn based on an older version described in \cite{Audren2013}. We briefly describe them below.
The \textit{Euclid-like weak lensing} likelihood (called WL in the rest of this paper) is based on measurements of cosmic shear, that is, the alignment of galaxies generated by weak gravitational lensing due to the structure present in the light path between the galaxy and the observer. The correlations between such alignments are computed at 10 different redshift bins, each with 30 galaxies per square-arcmin. The resulting shear power spectrum coefficients $C^{ij}_{\ell}$ $(i,j = 1, \dots, 10)$ can be related to the matter power spectrum $P(k,z)$ via
\begin{equation}
C^{ij}_{\ell} = \frac{9}{16}\Omega_{m0}H_0^4\int_0^{\infty}\frac{dr}{r^2}g_i(r)g_j(r)\Sigma\big(\ell/r, z(r)\big)^2P\big(\ell/r,z(r)\big)\,,
\end{equation}
where $g_i$ is a function of the distribution of galaxies in the i-th redshift bin. A systematic error due to intrinsic alignments is then added to $C^{ij}_{\ell}$. We highlight that in addition to the effect of the modification of gravity inside $P(k,z)$, we have to account explicitly for the extra $\Sigma^2$ factor in view of eq. (\ref{lensing}).
The \textit{Euclid-like P(k)} likelihood (GC) quantifies the probability of the cosmological model given the distribution of galaxies in the sky in redshift space. The relation between the observable and the theoretical isotropic matter power spectrum is computed considering the Alcock-Paczy\'nski effect, the limited resolution of the instruments and redshift-space distortions. The RSD modelling includes both the Kaiser formula, concerning the large scales, and the distortions in the small scales due to the peculiar velocities of galaxies. Furthermore, a linear and scale-independent galaxy bias is assumed. Contrary to the weak lensing \textit{Euclid}-like likelihood, where we inserted the $\Sigma^2$ correction, for \textit{Euclid}-like $P(k)$ no modification in the likelihood already implemented in \texttt{MontePython} is necessary.
\section{Results}
\label{sec:results}
In this section we present the results of the parameter estimation from our Monte Carlo Markov Chains (MCMCs). They were generated using version 3.5.0 of the $\mathtt{MontePython}$ code \cite{Audren2012wb, Brinckmann2018cvx}, with the help of $\mathtt{hi\_class}$ \cite{Zumalacarregui2017, Bellini2020}, a modification of the Einstein-Boltzmann solver $\mathtt{CLASS}$ \cite{Blas2011} that computes cosmological observables in the wider context of the Horndeski family of gravity models.
\subsection{Slip \textit{versus} GWs} \label{subsec:slip_vs_gws}
We are interested to investigate first to which precision one can infer $\Omega_0$ whenever the slip is measured at a certain accuracy level. For this purpose, we assume a Gaussian likelihood for $\eta$ at a certain redshift $z$ and scale $k$ with standard deviation of 1\% around the $\Lambda$CDM value of 1 and fix all the cosmological parameters to the values in Table \ref{tab:fiducial_model}. Notice that Eq.\ \eqref{phi_minus_psi} is scale dependent being subject to horizon effects, and so in practice we have to specify a scale. By assuming that the slip is measured today ($z=0$) at either $k = 0.1 \; \text{Mpc}^{-1}$ or $k = 0.01 \; \text{Mpc}^{-1}$, the 68\% CL found for $\Omega_0$ was
\begin{align}
\Delta \Omega_0 = 0.015
\end{align}
for both scales.
Since the error does not depend on the choice of scale for the two cases considered, as expected from the weak $k$-dependence of the slip inside the horizon (cf. figure \ref{fig:xi}), we will only consider the larger scale from now on.
In our baseline model, the Planck constant changes linearly with the scale factor, so that the gravitational slip is largest at late times (cf.\ Fig.\ \ref{fig:xi}). It is then no surprise that measuring the slip with the same precision at higher redshift, $z=1.1$, results in a significantly larger uncertainty,
\begin{align}
\Delta \Omega_0 = 0.07
\end{align}
(for $k=0.01 \; \text{Mpc}^{-1}$).
We then considered a more realistic scenario in which the slip is assumed to be measured at $k = 0.01 \; \text{Mpc}^{-1}$ in three redshift bins, according to the quite model-independent forecasts in Table X of \cite{Amendola2014}: at $z = 0.7$, $\Delta \eta = 3.1\%$, at $z = 1.1$, $\Delta \eta = 3.7\%$ and at $z = 1.5$, $\Delta \eta = 3.2\%$. The result is
\begin{align}
\Delta \Omega_0 = 0.12\,.
\end{align}
Furthermore, we also simulated a data set of GW events detected by the Einstein Telescope with electromagnetic counterpart. Again, by fixing all other parameters, we get the following 68\% CL on $\Omega_0$ for two scenarios:
\begin{align}
\Delta \Omega_0 =
\begin{cases}
0.08\,, \quad \,\,\, \text{100 GWs}\\
0.035\,, \quad \text{500 GWs}.
\end{cases}
\end{align}
The improvement in the error when increasing the number of GW events is consistent with the expected $\sqrt{N}$ scaling.
The case with 500 GW events described above provides a measurement of the deviation from GR at the percent level of accuracy. This is our best-case scenario though still realistic, once we consider that the cosmological parameters present in the GW likelihood, $h$ and $\omega_{c}$, are independently measured with high precision by other probes. On the other hand, the less informative case occurs when letting the cosmological parameters also free still only with GW mock data. The resulting contours in this case are shown in Figure \ref{fig:gw_500_3d}.
\begin{figure}
\centering
\includegraphics[scale=0.5]{figures/gw_500_3d_3_triangle.pdf}
\caption{Constraints from five hundred multimessenger gravitational wave events as forecasted for the Einstein Telescope.}
\label{fig:gw_500_3d}
\end{figure}
As a summary, Figure \ref{fig:fake_slip_gws} shows a comparison between these constraints. We point out that, from these first simple estimates, depending on the modelling of the slip measurement and the exact number of observed multimessenger GW events, one or the other might be a better probe of the deviations from GR that we study here. This justifies performing the more robust analysis with actual forecasts on the slip side that follows next. The values of the marginalized one dimensional 68\% CLs for the main cases studied are summarized in Table \ref{tab:results}.
\begin{figure}
\centering
\includegraphics[scale=0.6, trim = 1.1cm 0 0 0]{figures/fake_slip_gws.pdf}
\caption{Comparison between the 68\% CLs for $\Omega_0$ from hypothetical measurements of the slip parameter or GW detections.}
\label{fig:fake_slip_gws}
\end{figure}
\begin{table*}[t]
\centering
\setlength{\extrarowheight}{10pt}
\begin{tabularx}{\textwidth} {
>{\raggedright\arraybackslash}X
>{\centering\arraybackslash}X
>{\centering\arraybackslash}X >{\centering\arraybackslash}X >{\centering\arraybackslash}X }
\hhline{= = = = =}
Parameter & WL+GC & CMB+lens & GW & All data\\ \hline
$\omega_{c}$ \dotfill & $\pm 0.0006$ & $\pm 0.0009$ & $^{+0.13}_{-0.27}$ & $\pm 0.0003$\\
$10^9 A_s$ \dotfill & $\pm 0.035$ & $\pm 0.012$ & $-$ & $\pm 0.01$\\
$h$ \dotfill & $\pm 0.0023$ & $\pm 0.0033$ & $^{+0.017}_{-0.013}$ & $\pm 0.001$\\
$\Omega_0$ \dotfill & $\pm 0.01$ & $\pm 0.026$ & $^{+0.7}_{-0.5}$ & $\pm 0.006$ \\[2mm] \hline
\end{tabularx}
\caption{Marginalized one-dimensional 68\% CL errors on the cosmological parameters and $\Omega_0$ for the analysed data sets and their combination. The last column shows the results of the combination of all datasets considered, i.e. CMB+lens + WL+GC + GW.}
\label{tab:results}
\end{table*}
\subsection{Planck}
We now present the results from current CMB data and its combination with GWs. Figure \ref{fig:planck_results} shows the two-dimensional marginalized 68\% CLs in the parameter space of our base model for three different cases: \textit{Planck} TT,TE,EE+lowE, its combination with \textit{Planck} lensing and their further combination with five hundred GWs from the Einstein Telescope. The main result to be stressed here is that, in all cases, we get a percent level accuracy on $\Omega_0$, which is in agreement with a similar analysis performed in \cite{Planck2018} for a different parametrization of $\alpha_M$ and all cosmological parameters free.
\begin{figure*}
\centering
\includegraphics[scale=0.4]{figures/planckTTTEEElowE_final_smooth-vs-planckTTTEEElowElens_smooth-vs-gw_planckTTTEEElowElens_smooth2_triangle.pdf}
\caption{Constraints from Planck TT,TE,EE+lowE (red), its combination with Planck lensing and the further combination with the forecasted five hundred GWs from the Einstein Telescope.}
\label{fig:planck_results}
\end{figure*}
We also point out that \textit{Planck} favours MG models with a decreasing Planck mass (in time) and, furthermore, that \textit{Planck} TT,TE,EE+lowE alone recovers the $\Lambda$CDM value $\Omega_0 = 0$ only at $2\sigma$ from the best fit model ($\Omega_0 = -0.1)$. This was already noticed and discussed in, for instance, \cite{Planck2015DE} (see Figure 17) and \cite{Planck2015CP} (subsection 5.1), where the authors attribute this feature to a degeneracy between $(\mu, \Sigma)$ and the lensing amplitude calibration $A_L$. In fact, Figure \ref{fig:lensing_cls} shows that adding a small variation to the Planck mass has the same effect in the lensing potential power spectrum as allowing for an overall amplitude slightly different from 1; we checked that when letting $A_L$ free the error in $\Omega_0$ is roughly multiplied by a factor 3. When adding the \textit{Planck} lensing likelihood, as we see again in Figure \ref{fig:planck_results}, the contours are pushed towards GR $\Lambda$CDM (dashed grey line). We comment that, on the other hand, more updated CMB analysis alleviate or even do not show this preference for larger values of $A_L$ \cite{Aiola2020} and therefore one should check the consistency of the bounds on $\Omega_0$ across different CMB likelihoods.
\begin{figure}
\centering
\includegraphics[scale=0.55, trim= 0 0 0 0]{figures/CMB_lensing_cl.pdf}
\caption{Comparison between the lensing potential power spectrum coefficients for the following models: MG with $\Omega_0 = -0.1$ and $A_L = 1$, $\Lambda$CDM with $A_L = 1.15$ and $\Lambda$CDM with $A_L = 1$. All other cosmological parameters have the same values.}
\label{fig:lensing_cls}
\end{figure}
Regarding the combination of CMB and GWs, by also looking at Figure \ref{fig:gw_500_3d} we note that CMB helps setting the matter density parameter $\omega_{c}$ that is poorly inferred from GWs, while the addition of data in the tensor sector improves the measurement of $\Omega_0$ reducing its error by 40\%. While this is a significant improvement, we stress that the more important aspect of testing the distance-redshift relation with future GW data comes from its ability to probe one of the MG property functions ($\alpha_M$) alone, while CMB and LSS in general are sensitive to combinations of all the $\alpha$'s. This advantage cannot be illustrated with our simple base model, since it summarizes all the deviations from GR in only one degree of freedom.
\begin{table*}[t]
\centering
\setlength{\extrarowheight}{10pt}
\newcolumntype{s}{>{\hsize=.6\hsize \centering\arraybackslash}X}
\newcolumntype{l}{>{\hsize=\hsize \centering\arraybackslash}X}
\begin{tabularx}{\textwidth} {
>{\hsize=.6\hsize\raggedright\arraybackslash}X
ssllslls }
\hhline{= = = = = = = = =}
& GW & WL & WL+GC & WL+GC + GW & CMB & CMB+lens & CMB+lens + GW & All data \\ \hline
$\Delta\Omega_0$ & $^{+0.7}_{-0.5}$ & $\pm 0.1$ & $\pm 0.01$ & $\pm 0.01$ & $\pm 0.042$ & $\pm 0.026$ & $\pm 0.02$ & $\pm 0.006$ \\[2mm] \hline
\end{tabularx}
\caption{Marginalized one-dimensional 68\% CL errors on $\Omega_0$ for all the analysed data sets and their combinations. The last column shows the results of the combination of all datasets considered, i.e. CMB+lens +WL+GC + GW.}
\label{tab:results_Omega_0}
\end{table*}
\subsection{Large-scale structure data} \label{subsec:euclid}
We now present the results from \textit{Euclid}-like forecasts. Figure \ref{fig:euclid_results} shows the two dimensional marginalized 68\% and 95\% CLs on the parameter space of our models for, in red, weak lensing with uniform priors, in blue, galaxy clustering and their combination. Here we also show the result for the derived parameter $\eta_0$ which is the value of the gravitational slip today at $k=0.01 \; \textrm{Mpc}^{-1}$. We remind that our fiducial model features a 10\% deviation from 1 on the Planck mass and that it coincides with the bestfit model of the \textit{Planck} primary spectrum. We conclude that such model would be easily distinguished from GR's $\Lambda$CDM by a near-future \textit{Euclid}-like large scale structure survey alone in $\sim 10 \sigma$, through measurements of both $\eta_0$ and $\Omega_0$ with 1\% of accuracy.
\begin{figure}
\centering
\includegraphics[scale=0.35]{figures/euclid_lens_Sigma_plane2-vs-euclid_pk_final2_smooth-vs-euclid_lens_pk_Sigma_smooth_triangle.pdf}
\caption{Forecasted constraints from weak lensing (red), galaxy clustering (blue) and their combination (green) for a \textit{Euclid}-like survey. The further combination with five hundred multimessenger GW detections by the Einstein Telescope was omitted since it generates similar contours as the green ones.}
\label{fig:euclid_results}
\end{figure}
We comment that, in the approach where the functions $\mu$ and $\Sigma$ are independently parametrized, it is expected that weak lensing and galaxy clustering data would be complementary to infer the slip, since each of them probe different combinations of the scalar potentials. However, in our analysis we find that WL provides much weaker constraints than GC, even though it is still relevant for constraining the MG deviations, as we can see in figure \ref{fig:euclid_results}.
This is due to the fact that, again, the models here considered have only one extra degree of freedom $\alpha_M$, which is exactly what allows us to connect GW and slip measurements without further assumptions. This creates a relation between the derived $\mu$ and $\Sigma$, depending on the cosmological parameters, as illustrated in figure \ref{fig:mu_Sigma}, by noticing how their values (at a certain scale and redshift) are correlated for the different analysed data sets.
\begin{figure}
\centering
\includegraphics[scale=0.4]{figures/mu_Sigma.pdf}
\caption{Constraints from large-scale structure on the derived parameter space ($\mu$, $\Sigma$), where the sub-index 0 stands for evaluation today and $k = 0.01$/Mpc.}
\label{fig:mu_Sigma}
\end{figure}
Finally, we find that the addition of five hundred GWs from the Einstein Telescope alone, despite constituting an independent test, does not significantly improve the results from our large-scale structure likelihood. We leave the comparison between the outcome of such tests in the scalar and tensor sectors for the next subsection.
\subsection{Combination of data sets}
We finally compare the constraining power of our different data sets, as summarized in figure \ref{fig:combined_results}. First, by comparing the green and red 68\% and 95\% contours, we see that a \textit{Euclid}-like survey and \textit{Planck} give complementary information on the cosmological parameters. The former, however, provides a measurement of the MG parameter $\Omega_0$ twice more accurate than that of current CMB data (see also table \ref{tab:results}).
As mentioned in the last subsection, we obtain that a \textit{Euclid}-like large-scale structure survey alone will measure the slip with 1\% error. Then, one might wish to compare its corresponding bound on $\Omega_0$ (of also 1\%, see Table \ref{tab:results_Omega_0}) with the results of our rough estimation in subsection \ref{subsec:slip_vs_gws}, where we fixed all cosmological parameters and assumed a hypothetical 1\% accuracy for the slip. Since GWs alone do not constrain the cosmological parameters due to large degeneracies, we can use \textit{Planck} TT,TE,EE+lowE to fix them, obtaining the blue contours in figure \ref{fig:combined_results}; one gets then a 3\% error in $\Omega_0$. From these we conclude that future measurements of the slip from \textit{Euclid}-like surveys, for the simple gravity models here studied, will reach slightly higher accuracy levels in measurements of deviations of GR via $\alpha_M$, as compared to future GW data from the Einstein Telescope, when additional data (like from the CMB) constrains the other cosmological parameters sufficiently.
\begin{figure*}
\centering
\includegraphics[scale=0.4]{figures/planckTTTEEElowElens_smooth-vs-gw_planckTTTEEElowE_final_smooth-vs-euclid_lens_pk_Sigma_smooth-vs-gw_planck_euclid_Sigma_smooth3_triangle.pdf}
\caption{Comparison between the constraints from \textit{Planck} TT,TE,EE+lowE+lensing; five hundred GWs from the Einstein Telescope combined with \textit{Planck} primary spectra; from weak lensing and galaxy clustering; and the final combination of all data sets.}\label{fig:combined_results}
\end{figure*}
Futhermore, the addition of future data on both sectors, here data from large-scale structure and multimessenger GW events, will substantially improve the current results of \textit{Planck}, as we notice by comparing the yellow and red contours in Figure \ref{fig:combined_results}. More precisely, by looking at Table \ref{tab:results}, we see that the errors in the background cosmological parameters $\omega_c$ and $h$ and the MG parameter $\Omega_0$ are decreased in around 67\%, 70\% and 77\%, respectively.
{Finally, we obtain that the bounds on the derived parameters $\mu_0$ and $\Sigma_0$ from the combination CMB+lens+WL+GC+GW will reach the sub-percent level, as well as the slip, with $\Delta\eta_0 = 0.5\%$. However, we remind that since our MG models have only one extra degree of freedom and $\mu$ and $\Sigma$ are related, they end up being more strongly constrained than in a scenario where they are independently parametrized, and thus these strong bounds are actually driven by the choice of model.}
\subsection{No-slip model}
We also studied the constraints from the three data sets, \textit{Planck}, standard sirens and large-scale structure, on the no-slip model described in subsection \ref{subsec:no_slip}. In the analysis of \cite{Linder2018}, a no-slip model with $A = 0.03$ is compatible with measurements of the growth rate $f\sigma_8$. Here, however, even if it generates deviations in the CMB spectra, when compared to $\Lambda$CDM, of the same order as our base model, it turns out to be completely excluded by Planck data. This is because \textit{Planck}\ favors models with decreasing Planck mass, as discussed before, and so it constrains the viable no-slip models better than our base-models with negative $\Omega_0$, since they have increasing Planck mass.
In the \textit{Euclid}-like and Einstein Telescope forecasts we used for the fiducial model the values of the cosmological parameters given in Table \ref{tab:fiducial_model} and $A = 0.005$, which is compatible with \textit{Planck} data at 1$\sigma$. We also imposed the prior $A>0$ in order to avoid instability issues as discussed previously. Figure \ref{fig:no_slip_results} shows the constraints from GWs, CMB, LSS and their combinations assuming the universe is well described by a no-slip model as far as possible from $\Lambda$CDM while still being compatible with CMB data.
\begin{figure*}
\centering
\includegraphics[scale=0.35]{figures/no_slip_gw_prior_triangle.pdf}
\includegraphics[scale=0.35]{figures/no_slip_planck_prior_smooth-vs-no_slip_euclid_lens_pk_Sigma4_smooth3-vs-no_slip_gw_planck_euclid_Sigma_smooth2_triangle.pdf}
\caption{Results for viable no-slip models marginalized in $A_s$. On the left, 68\% and 95\% CLs. from five hundred standard sirens with the Einstein Telescope and, on the right, Planck TT,TE,EE+lowE+lensing, galaxy clustering and weak lensing, and their combination with five hundred GWs.} \label{fig:no_slip_results}
\end{figure*}
Table \ref{tab:results_no_slip} shows the 1-dimensional bounds on the cosmological parameters and $A$. We comment that $\Lambda$CDM ($A = 0$) is compatible within $1\sigma$ with all data sets and their combinations. {We also notice in Fig.\ \ref{fig:no_slip_results} that $A$ and $\omega_c$ are highly degenerate, which prevents GW data alone from putting strong bounds on the deviation from GR, as discussed in \cite{Mitra2021}, where they use a parametrization for $\Xi$ that does not consider the viability conditions of no-slip gravity.}
Remarkably, these models have vanishing slip at late times, and thus purely (model-independent) slip measurements in principle would not be able to constrain them. However, here we conclude that LSS still gives better bounds on the deviation of the Planck mass for the analysed no-slip models, and this is because both weak lensing and galaxy clustering are separately modified.
\begin{table*}[t]
\centering
\setlength{\extrarowheight}{10pt}
\begin{tabularx}{\textwidth} {
>{\raggedright\arraybackslash}X
>{\centering\arraybackslash}X
>{\centering\arraybackslash}X >{\centering\arraybackslash}X >{\centering\arraybackslash}X }
\hhline{= = = = =}
Parameter & WL+GC & CMB+lens & GW & All data\\ \hline
$\omega_{c}$ \dotfill & $\pm 0.0006$ & $\pm 0.0008$ & $^{+0.03}_{-0.10}$ & $^{+0.0002}_{-0.0003}$\\
$10^9 A_s$ \dotfill & $\pm 0.03$ & $\pm 0.011$ & $-$ & $\pm 0.01$\\
$h$ \dotfill & $\pm 0.002$ & $\pm 0.003$ & $^{+0.018}_{-0.013}$ & $\pm 0.001$\\
$A$ \dotfill & $< 0.005 \; (0.006)$ & $< 0.005 \; (0.006)$ & $< 0.36 \; (0.44)$ & $< 0.004 \; (0.006)$ \\[2mm] \hline
\end{tabularx}
\caption{Marginalized one-dimensional 68\% CL errors on the parameters of the no-slip model for the analysed data sets and their combination (CMB+lens + WL+GC + GW). The last row shows the 68\% (95\%) upper bounds on $A$, the deviation of $\Lambda$CDM.}
\label{tab:results_no_slip}
\end{table*}
\section{Conclusion}
\label{sec:conclusion}
The starting point of our investigation was the question how measurements of the gravitational slip from large-scale structure and of GW distances compare when the goal is to constrain an underlying MG theory. Often, the GW side and the LSS side are considered separately. This is particularly the case when using so-called `phenomenological modified gravity' parameters like $\mu$, $\Sigma$ and $\Xi$. However, for a given action-based model, those parameters are generally linked to the fundamental model parameters and so are not independent. Here we illustrate this with the help of Horndeski-type models, where a running of the Planck mass affects both the GW friction and the gravitational slip simultaneously.
As a first step, we use an order-of-magnitude estimate for the gravitational slip constraints, and compare the corresponding limits on the non-minimal coupling parameter $\Omega_0$ with those from predictions for the Einstein Telescope. Fig.\ \ref{fig:fake_slip_gws} shows that, depending on the redshift at which we infer the slip or the exact amount of GW events, one data set might be better than the other, so it makes sense to perform a more precise investigation.
Comparing CMB observations from the {\it Planck} satellite and galaxy clustering as well as weak lensing data from a survey like the upcoming \textit{Euclid}\ satellite with GW distances from the Einstein Telescope, we find that generally the large-scale structure data constrains the Planck mass run rate more strongly, see Fig.~\ref{fig:combined_results} {and Table \ref{tab:results_Omega_0}}. We conclude that we get stronger bounds on the Planck mass from the scalar sector than from the tensor sector for the particular class of models featuring only this extra degree of freedom, described in Subsection \ref{subsec:base_model}. However, it is important to emphasize a few points: Firstly, in models where many parameters are varying (rather than a single one as in our investigation) we will need multiple observations to constrain all the parameters {simultaneously}. In this case the inclusion of standard sirens might be crucial since they remain sensitive to only $\alpha_M$ (and this is why our results from the tensor sector are less model-dependent). Secondly, GW and LSS data do measure fundamentally different observables, and they can only be compared within the context of a particular model. Clearly, both types of observations are fundamentally important to understand the nature of the dark sector. Finally, multiple observations also allow to test for consistency and systematic effects.
{As mentioned in Subsection \ref{subsec:euclid}, the impact of the addition of standard sirens from the Einstein Telescope to the LSS data of a \textit{Euclid}-like survey was found to be very modest for the models here studied. This is, however, not necessarily true for more general models, as discussed above, and particularly for other planned interferometers. As shown in \cite{Baker2021}, LISA could improve the bound on the Planck mass running rate in Horndeski theories from CMB+BAO+RSD by a factor 5. Therefore, a natural next step would be to compare measurements of the GW friction from the network of current and future GW detectors with slip measurements from LSS, for more general viable models, for example relaxing the condition $\alpha_M = - \alpha_B$.}
{In this work, we also analysed the constraints from LSS and GWs on the no-slip model, an interesting case of MG that produces modifications in the GW friction but does not generate gravitational slip, being a blind spot in tests of gravity through measurements of the latter. Assuming the universe is well described by a no-slip model as far as possible
from $\Lambda$CDM but compatible with CMB data, we found that LSS also provides stronger bounds in this case.}
Here, the cosmological background was fixed to that of $\Lambda$CDM in all cases. A second analysis could be made, then, parametrizing the dark energy equation of state $w_{\textrm{DE}}$ in order to include background effects. On the GW side, however, our simplification is reasonable since, despite the likelihood dependency on the EM luminosity distance, it has been shown \cite{Zhao2011,Belgacem2018,Matos2021} that this test provides only a weak constraint on $w_{\textrm{DE}}$, as compared to the one on the friction $\Xi$.
We comment that Eq.\ \eqref{gw_distance} shows that, in the end, the effect of Horndeski modifications of gravity in the GW distance depends only on the values of the Planck mass at the emission and detection events. This fact is also valid in a more general context of an arbitrary background metric \cite{Dalang2020}, and thus it naturally raises the question on whether standard sirens would only be sensitive to the local value of the Planck mass \cite{Lagos2020, Baker2021}. The deviations from GR on the local values of $M_{\ast}^2$ are usually suppressed by most of the known screening mechanisms, that were not considered here, and they are strongly constrained by local tests of gravity such as lunar laser ranging \cite{Williams2004, Tsujikawa2019}. Of course there are other gravity theories in which $\Xi$ is modified not simply because of the variation of the Planck mass, such as the non-local models \cite{Belgacem2018}, which by itself justifies testing gravity with the redshift-GW-distance relation. Regardless of the exact outcome of this discussion in the literature, we point out that the simultaneous MG effect on the propagation of GWs and on the anisotropic stress is a general feature that goes beyond the Horndeski theories, and thus here we use these models as prototypes to compare the constraining power of the two observables.
Finally, it is possible to show that our base model with $\Omega_0 < 0$ has ghost instabilities. However, since Planck prefers negative values of $\Omega_0$ we did not impose priors to avoid ghosts. Again, our goal is not to investigate these particular models, that sometimes have physical problems, but rather to use them as an example for the combination of slip and GW distance measurements.
\acknowledgments
It is a pleasure to thank Luca Amendola, Charles Dalang, Pierre Fleury, Michele Mancarella, Miguel Quartin, Matteo Biagetti, and Ioav Waga and for useful discussions. I.S.M.~thanks the Department of Theoretical Physics of the University of Geneva and its members for hospitality during the PhD scholarship funded by both Brazilian agency CAPES (No 88887.569351/2020-00) and the department. I.S.M. also thanks Brazilian funding agency CNPq for PhD scholarship GD 140324/2018-6. E.B.~has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 754496. M.K.\ acknowledges funding from the Swiss National Science Foundation.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,084 |
"""Main module."""
from typing import Dict, Optional, Tuple, Union
import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
from torch.distributions import Normal
from torch.distributions import kl_divergence as kl
from scvi._compat import Literal
from scvi.core.distributions import (
NegativeBinomial,
NegativeBinomialMixture,
ZeroInflatedNegativeBinomial,
)
from ._base import DecoderTOTALVI, EncoderTOTALVI
from .utils import one_hot
torch.backends.cudnn.benchmark = True
# VAE model
class TOTALVAE(nn.Module):
"""
Total variational inference for CITE-seq data.
Implements the totalVI model of [GayosoSteier20]_.
Parameters
----------
n_input_genes
Number of input genes
n_input_proteins
Number of input proteins
n_batch
Number of batches
n_labels
Number of labels
n_hidden
Number of nodes per hidden layer for encoder and decoder
n_latent
Dimensionality of the latent space
n_layers
Number of hidden layers used for encoder and decoder NNs
dropout_rate
Dropout rate for neural networks
gene_dispersion
One of the following
* ``'gene'`` - genes_dispersion parameter of NB is constant per gene across cells
* ``'gene-batch'`` - genes_dispersion can differ between different batches
* ``'gene-label'`` - genes_dispersion can differ between different labels
protein_dispersion
One of the following
* ``'protein'`` - protein_dispersion parameter is constant per protein across cells
* ``'protein-batch'`` - protein_dispersion can differ between different batches NOT TESTED
* ``'protein-label'`` - protein_dispersion can differ between different labels NOT TESTED
log_variational
Log(data+1) prior to encoding for numerical stability. Not normalization.
gene_likelihood
One of
* ``'nb'`` - Negative binomial distribution
* ``'zinb'`` - Zero-inflated negative binomial distribution
latent_distribution
One of
* ``'normal'`` - Isotropic normal
* ``'ln'`` - Logistic normal with normal params N(0, 1)
protein_batch_mask
Dictionary where each key is a batch code, and value is for each protein, whether it was observed or not.
encode_covariates
Whether to concatenate covariates to expression in encoder
protein_background_prior_mean
Array of proteins by batches, the prior initialization for the protein background mean (log scale)
protein_background_prior_scale
Array of proteins by batches, the prior initialization for the protein background scale (log scale)
use_observed_lib_size
Use observed library size for RNA as scaling factor in mean of conditional distribution
"""
def __init__(
self,
n_input_genes: int,
n_input_proteins: int,
n_batch: int = 0,
n_labels: int = 0,
n_hidden: int = 256,
n_latent: int = 20,
n_layers_encoder: int = 2,
n_layers_decoder: int = 1,
dropout_rate_decoder: float = 0.2,
dropout_rate_encoder: float = 0.2,
gene_dispersion: str = "gene",
protein_dispersion: str = "protein",
log_variational: bool = True,
gene_likelihood: str = "nb",
latent_distribution: str = "normal",
protein_batch_mask: Dict[Union[str, int], np.ndarray] = None,
encode_covariates: bool = True,
protein_background_prior_mean: Optional[np.ndarray] = None,
protein_background_prior_scale: Optional[np.ndarray] = None,
use_observed_lib_size: bool = True,
use_batch_norm: Literal["encoder", "decoder", "none", "both"] = "both",
use_layer_norm: Literal["encoder", "decoder", "none", "both"] = "none",
):
super().__init__()
self.gene_dispersion = gene_dispersion
self.n_latent = n_latent
self.log_variational = log_variational
self.gene_likelihood = gene_likelihood
self.n_batch = n_batch
self.n_labels = n_labels
self.n_input_genes = n_input_genes
self.n_input_proteins = n_input_proteins
self.protein_dispersion = protein_dispersion
self.latent_distribution = latent_distribution
self.protein_batch_mask = protein_batch_mask
self.use_observed_lib_size = use_observed_lib_size
# parameters for prior on rate_back (background protein mean)
if protein_background_prior_mean is None:
if n_batch > 0:
self.background_pro_alpha = torch.nn.Parameter(
torch.randn(n_input_proteins, n_batch)
)
self.background_pro_log_beta = torch.nn.Parameter(
torch.clamp(torch.randn(n_input_proteins, n_batch), -10, 1)
)
else:
self.background_pro_alpha = torch.nn.Parameter(
torch.randn(n_input_proteins)
)
self.background_pro_log_beta = torch.nn.Parameter(
torch.clamp(torch.randn(n_input_proteins), -10, 1)
)
else:
if protein_background_prior_mean.shape[1] == 1 and n_batch != 1:
init_mean = protein_background_prior_mean.ravel()
init_scale = protein_background_prior_scale.ravel()
else:
init_mean = protein_background_prior_mean
init_scale = protein_background_prior_scale
self.background_pro_alpha = torch.nn.Parameter(
torch.from_numpy(init_mean.astype(np.float32))
)
self.background_pro_log_beta = torch.nn.Parameter(
torch.log(torch.from_numpy(init_scale.astype(np.float32)))
)
if self.gene_dispersion == "gene":
self.px_r = torch.nn.Parameter(torch.randn(n_input_genes))
elif self.gene_dispersion == "gene-batch":
self.px_r = torch.nn.Parameter(torch.randn(n_input_genes, n_batch))
elif self.gene_dispersion == "gene-label":
self.px_r = torch.nn.Parameter(torch.randn(n_input_genes, n_labels))
else: # gene-cell
pass
if self.protein_dispersion == "protein":
self.py_r = torch.nn.Parameter(2 * torch.rand(self.n_input_proteins))
elif self.protein_dispersion == "protein-batch":
self.py_r = torch.nn.Parameter(
2 * torch.rand(self.n_input_proteins, n_batch)
)
elif self.protein_dispersion == "protein-label":
self.py_r = torch.nn.Parameter(
2 * torch.rand(self.n_input_proteins, n_labels)
)
else: # protein-cell
pass
use_batch_norm_encoder = use_batch_norm == "encoder" or use_batch_norm == "both"
use_batch_norm_decoder = use_batch_norm == "decoder" or use_batch_norm == "both"
use_layer_norm_encoder = use_layer_norm == "encoder" or use_layer_norm == "both"
use_layer_norm_decoder = use_layer_norm == "decoder" or use_layer_norm == "both"
# z encoder goes from the n_input-dimensional data to an n_latent-d
# latent space representation
self.encoder = EncoderTOTALVI(
n_input_genes + self.n_input_proteins,
n_latent,
n_layers=n_layers_encoder,
n_cat_list=[n_batch] if encode_covariates else None,
n_hidden=n_hidden,
dropout_rate=dropout_rate_encoder,
distribution=latent_distribution,
use_batch_norm=use_batch_norm_encoder,
use_layer_norm=use_layer_norm_encoder,
)
self.decoder = DecoderTOTALVI(
n_latent,
n_input_genes,
self.n_input_proteins,
n_layers=n_layers_decoder,
n_cat_list=[n_batch],
n_hidden=n_hidden,
dropout_rate=dropout_rate_decoder,
use_batch_norm=use_batch_norm_decoder,
use_layer_norm=use_layer_norm_decoder,
)
def sample_from_posterior_z(
self,
x: torch.Tensor,
y: torch.Tensor,
batch_index: Optional[torch.Tensor] = None,
give_mean: bool = False,
n_samples: int = 5000,
) -> torch.Tensor:
"""
Access the tensor of latent values from the posterior.
Parameters
----------
x
tensor of values with shape ``(batch_size, n_input_genes)``
y
tensor of values with shape ``(batch_size, n_input_proteins)``
batch_index
tensor of batch indices
give_mean
Whether to sample, or give mean of distribution
n_samples
Number of samples for monte carlo estimation
Returns
-------
type
tensor of shape ``(batch_size, n_latent)``
"""
if self.log_variational:
x = torch.log(1 + x)
y = torch.log(1 + y)
qz_m, qz_v, _, _, latent, _ = self.encoder(
torch.cat((x, y), dim=-1), batch_index
)
z = latent["z"]
if give_mean:
if self.latent_distribution == "ln":
samples = Normal(qz_m, qz_v.sqrt()).sample([n_samples])
z = self.encoder.z_transformation(samples)
z = z.mean(dim=0)
else:
z = qz_m
return z
def sample_from_posterior_l(
self,
x: torch.Tensor,
y: torch.Tensor,
batch_index: Optional[torch.Tensor] = None,
give_mean: bool = True,
) -> torch.Tensor:
"""
Provides the tensor of library size from the posterior.
Parameters
----------
x
tensor of values with shape ``(batch_size, n_input_genes)``
y
tensor of values with shape ``(batch_size, n_input_proteins)``
batch_index
tensor of values with shape ``(batch_size, 1)``
give_mean
return mean of l or sample from it
Returns
-------
type
tensor of shape ``(batch_size, 1)``
"""
if self.log_variational:
x = torch.log(1 + x)
y = torch.log(1 + y)
_, _, ql_m, ql_v, latent, _ = self.encoder(
torch.cat((x, y), dim=-1), batch_index
)
library_gene = latent["l"]
if give_mean is True:
return torch.exp(ql_m + 0.5 * ql_v)
else:
return library_gene
def get_sample_dispersion(
self,
x: torch.Tensor,
y: torch.Tensor,
batch_index: Optional[torch.Tensor] = None,
label: Optional[torch.Tensor] = None,
n_samples: int = 1,
) -> Tuple[torch.Tensor, torch.Tensor]:
"""
Returns the tensors of dispersions for genes and proteins.
Parameters
----------
x
tensor of values with shape ``(batch_size, n_input_genes)``
y
tensor of values with shape ``(batch_size, n_input_proteins)``
batch_index
array that indicates which batch the cells belong to with shape ``batch_size``
label
tensor of cell-types labels with shape ``(batch_size, n_labels)``
n_samples
number of samples
Returns
-------
type
tensors of dispersions of the negative binomial distribution
"""
outputs = self.inference(
x, y, batch_index=batch_index, label=label, n_samples=n_samples
)
px_r = outputs["px_"]["r"]
py_r = outputs["py_"]["r"]
return px_r, py_r
def get_reconstruction_loss(
self,
x: torch.Tensor,
y: torch.Tensor,
px_dict: Dict[str, torch.Tensor],
py_dict: Dict[str, torch.Tensor],
pro_batch_mask_minibatch: Optional[torch.Tensor] = None,
) -> Tuple[torch.Tensor, torch.Tensor]:
"""Compute reconstruction loss."""
px_ = px_dict
py_ = py_dict
# Reconstruction Loss
if self.gene_likelihood == "zinb":
reconst_loss_gene = (
-ZeroInflatedNegativeBinomial(
mu=px_["rate"], theta=px_["r"], zi_logits=px_["dropout"]
)
.log_prob(x)
.sum(dim=-1)
)
else:
reconst_loss_gene = (
-NegativeBinomial(mu=px_["rate"], theta=px_["r"])
.log_prob(x)
.sum(dim=-1)
)
py_conditional = NegativeBinomialMixture(
mu1=py_["rate_back"],
mu2=py_["rate_fore"],
theta1=py_["r"],
mixture_logits=py_["mixing"],
)
reconst_loss_protein_full = -py_conditional.log_prob(y)
if pro_batch_mask_minibatch is not None:
temp_pro_loss_full = torch.zeros_like(reconst_loss_protein_full)
temp_pro_loss_full.masked_scatter_(
pro_batch_mask_minibatch.bool(), reconst_loss_protein_full
)
reconst_loss_protein = temp_pro_loss_full.sum(dim=-1)
else:
reconst_loss_protein = reconst_loss_protein_full.sum(dim=-1)
return reconst_loss_gene, reconst_loss_protein
def inference(
self,
x: torch.Tensor,
y: torch.Tensor,
batch_index: Optional[torch.Tensor] = None,
label: Optional[torch.Tensor] = None,
n_samples=1,
transform_batch: Optional[int] = None,
) -> Dict[str, Union[torch.Tensor, Dict[str, torch.Tensor]]]:
"""
Internal helper function to compute necessary inference quantities.
We use the dictionary ``px_`` to contain the parameters of the ZINB/NB for genes.
The rate refers to the mean of the NB, dropout refers to Bernoulli mixing parameters.
`scale` refers to the quanity upon which differential expression is performed. For genes,
this can be viewed as the mean of the underlying gamma distribution.
We use the dictionary ``py_`` to contain the parameters of the Mixture NB distribution for proteins.
`rate_fore` refers to foreground mean, while `rate_back` refers to background mean. ``scale`` refers to
foreground mean adjusted for background probability and scaled to reside in simplex.
``back_alpha`` and ``back_beta`` are the posterior parameters for ``rate_back``. ``fore_scale`` is the scaling
factor that enforces `rate_fore` > `rate_back`.
``px_["r"]`` and ``py_["r"]`` are the inverse dispersion parameters for genes and protein, respectively.
"""
x_ = x
y_ = y
if self.use_observed_lib_size:
library_gene = x.sum(1).unsqueeze(1)
if self.log_variational:
x_ = torch.log(1 + x_)
y_ = torch.log(1 + y_)
# Sampling - Encoder gets concatenated genes + proteins
qz_m, qz_v, ql_m, ql_v, latent, untran_latent = self.encoder(
torch.cat((x_, y_), dim=-1), batch_index
)
z = latent["z"]
untran_z = untran_latent["z"]
untran_l = untran_latent["l"]
if not self.use_observed_lib_size:
library_gene = latent["l"]
if n_samples > 1:
qz_m = qz_m.unsqueeze(0).expand((n_samples, qz_m.size(0), qz_m.size(1)))
qz_v = qz_v.unsqueeze(0).expand((n_samples, qz_v.size(0), qz_v.size(1)))
untran_z = Normal(qz_m, qz_v.sqrt()).sample()
z = self.encoder.z_transformation(untran_z)
ql_m = ql_m.unsqueeze(0).expand((n_samples, ql_m.size(0), ql_m.size(1)))
ql_v = ql_v.unsqueeze(0).expand((n_samples, ql_v.size(0), ql_v.size(1)))
untran_l = Normal(ql_m, ql_v.sqrt()).sample()
if self.use_observed_lib_size:
library_gene = library_gene.unsqueeze(0).expand(
(n_samples, library_gene.size(0), library_gene.size(1))
)
else:
library_gene = self.encoder.l_transformation(untran_l)
if self.gene_dispersion == "gene-label":
# px_r gets transposed - last dimension is nb genes
px_r = F.linear(one_hot(label, self.n_labels), self.px_r)
elif self.gene_dispersion == "gene-batch":
px_r = F.linear(one_hot(batch_index, self.n_batch), self.px_r)
elif self.gene_dispersion == "gene":
px_r = self.px_r
px_r = torch.exp(px_r)
if self.protein_dispersion == "protein-label":
# py_r gets transposed - last dimension is n_proteins
py_r = F.linear(one_hot(label, self.n_labels), self.py_r)
elif self.protein_dispersion == "protein-batch":
py_r = F.linear(one_hot(batch_index, self.n_batch), self.py_r)
elif self.protein_dispersion == "protein":
py_r = self.py_r
py_r = torch.exp(py_r)
# Background regularization
if self.n_batch > 0:
py_back_alpha_prior = F.linear(
one_hot(batch_index, self.n_batch), self.background_pro_alpha
)
py_back_beta_prior = F.linear(
one_hot(batch_index, self.n_batch),
torch.exp(self.background_pro_log_beta),
)
else:
py_back_alpha_prior = self.background_pro_alpha
py_back_beta_prior = torch.exp(self.background_pro_log_beta)
self.back_mean_prior = Normal(py_back_alpha_prior, py_back_beta_prior)
if transform_batch is not None:
batch_index = torch.ones_like(batch_index) * transform_batch
px_, py_, log_pro_back_mean = self.decoder(z, library_gene, batch_index, label)
px_["r"] = px_r
py_["r"] = py_r
return dict(
px_=px_,
py_=py_,
qz_m=qz_m,
qz_v=qz_v,
z=z,
untran_z=untran_z,
ql_m=ql_m,
ql_v=ql_v,
library_gene=library_gene,
untran_l=untran_l,
log_pro_back_mean=log_pro_back_mean,
)
def forward(
self,
x: torch.Tensor,
y: torch.Tensor,
local_l_mean_gene: torch.Tensor,
local_l_var_gene: torch.Tensor,
batch_index: Optional[torch.Tensor] = None,
label: Optional[torch.Tensor] = None,
) -> Tuple[
torch.FloatTensor, torch.FloatTensor, torch.FloatTensor, torch.FloatTensor
]:
"""
Returns the reconstruction loss and the Kullback divergences.
Parameters
----------
x
tensor of values with shape ``(batch_size, n_input_genes)``
y
tensor of values with shape ``(batch_size, n_input_proteins)``
local_l_mean_gene
tensor of means of the prior distribution of latent variable l
with shape ``(batch_size, 1)````
local_l_var_gene
tensor of variancess of the prior distribution of latent variable l
with shape ``(batch_size, 1)``
batch_index
array that indicates which batch the cells belong to with shape ``batch_size``
label
tensor of cell-types labels with shape (batch_size, n_labels)
Returns
-------
type
the reconstruction loss and the Kullback divergences
"""
# Parameters for z latent distribution
outputs = self.inference(x, y, batch_index, label)
qz_m = outputs["qz_m"]
qz_v = outputs["qz_v"]
ql_m = outputs["ql_m"]
ql_v = outputs["ql_v"]
px_ = outputs["px_"]
py_ = outputs["py_"]
if self.protein_batch_mask is not None:
pro_batch_mask_minibatch = torch.zeros_like(y)
for b in torch.unique(batch_index):
b_indices = (batch_index == b).reshape(-1)
pro_batch_mask_minibatch[b_indices] = torch.tensor(
self.protein_batch_mask[b.item()].astype(np.float32),
device=y.device,
)
else:
pro_batch_mask_minibatch = None
reconst_loss_gene, reconst_loss_protein = self.get_reconstruction_loss(
x, y, px_, py_, pro_batch_mask_minibatch
)
# KL Divergence
kl_div_z = kl(Normal(qz_m, torch.sqrt(qz_v)), Normal(0, 1)).sum(dim=1)
if not self.use_observed_lib_size:
kl_div_l_gene = kl(
Normal(ql_m, torch.sqrt(ql_v)),
Normal(local_l_mean_gene, torch.sqrt(local_l_var_gene)),
).sum(dim=1)
else:
kl_div_l_gene = 0.0
kl_div_back_pro_full = kl(
Normal(py_["back_alpha"], py_["back_beta"]), self.back_mean_prior
)
if pro_batch_mask_minibatch is not None:
kl_div_back_pro = (pro_batch_mask_minibatch * kl_div_back_pro_full).sum(
dim=1
)
else:
kl_div_back_pro = kl_div_back_pro_full.sum(dim=1)
return (
reconst_loss_gene,
reconst_loss_protein,
kl_div_z,
kl_div_l_gene,
kl_div_back_pro,
)
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,523 |
Ruby for Good is an annual event based out of the DC-metro area where Ruby programmers from all over the globe get together for a long weekend to build projects that help our communities. In 2019 the event will take place in Washington DC at George Mason University. Participants stay in on-site dorms; hacking and socializing takes place in communal areas. Join us this year just for the fun of giving back! Questions? Drop us a note.
Projects in 2019 will be focused on issues with mental illness. We have some great projects lined up but we need more! We need YOU to help us find other great projects - suggest a project below! Project details, including available teams to join, will be announced to attendees around the beginning of May. Team leads will get information on projects at the start of June.
Get the latest updates, early notice for event registrations, and other Ruby for Good news!
Bring yourself, your laptop, and whatever you plan on wearing. Lodging consists of non-shared dorm rooms complete with linens, pillows, blankets and towels. We'll also be supplying food, drinks, and fun atmosphere. For a more in-depth run down of the weekend, check out our attendee information page. More questions? Drop us a note.
$250 all-inclusive. Registration includes room, linens, pillows, towels, swag, and three all-you-can-eat meals a day. We are a break-even operation; all funds go toward paying for the event!
Loves bringing people together through technology and food—and making music with others.
Loves building cool things, the community, helping folks learn—and silly projects with kids.
Ruby For Good is providing scholarship tickets to allow more people the opportunity to participate. The deadline to apply for a scholarship is April 19th and everyone who applies will be notified after the 1st of June. Click the link below to submit your request! | {
"redpajama_set_name": "RedPajamaC4"
} | 2,614 |
Q: Is this QQ convex or concave? With my data I got this exponential QQplot :
is this QQplot convex or concave ?
Thanks in advance
A:
Con-cave = Looks like a cave
This is a simple way to remember the difference: concave looks like a cave, and by process of elimination, convex is the other one. Your plot of blue dots look roughly (but not exactly) concave. The strict definition for concavity of a series of points would require each of the points to be above the line intersecting any surrounding points.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,452 |
Esta é uma lista dos títulos oficiais conquistados pelos clubes soviéticos que participaram nas competições desse país de futebol até a época de 1991/1992 quando houve a dissolução da URSS. Esta lista inclui as competições nacionais organizadas pela Federação de Futebol da União Soviética, essas competições eram: O Campeonato Soviético, a Taça da União Soviética, a Supertaça da União Soviética e a Taça da Federação de Futebol da União Soviética. A lista também inclui as competições internacionais vencidas pelos clubes da URSS reconhecidas pela UEFA que são: A UEFA Cup Winners' Cup e a UEFA Supercup.
Lista
Ver também
Lista de títulos oficiais dos clubes russos de futebol
Federação de Futebol da União Soviética
Lista de títulos dos clubes da Alemanha Oriental de futebol
Listas de títulos no futebol | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,622 |
{"url":"https:\/\/www.mathwords.com\/l\/l%27hopitals_rule.htm","text":"index: click on a letter A B C D E F G H I J K L M N O P Q R S T U V W X Y Z A to Z index index: subject areas numbers & symbols sets, logic, proofs geometry algebra trigonometry advanced algebra & pre-calculus calculus advanced topics probability & statistics real world applications multimedia entries\n\nL'H\u00f4pital's Rule\nL'Hospital's Rule\n\nA technique used to evaluate limits of fractions that evaluate to the indeterminate expressions and . This is done by finding the limit of the derivatives of the numerator and denominator.\n\nNote: Most limits involving other indeterminate expressions can be manipulated into fraction form so that l'H\u00f4pital's rule can be used.\n\n L'H\u00f4pital's Rule: If f and g are differentiable on an open interval containing a such that g(x)\u00a0\u2260\u00a00 for all x\u00a0\u2260\u00a0a in the interval, and if either and or and then Example:","date":"2021-12-09 00:45:24","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8684070110321045, \"perplexity\": 323.08218870333025}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-49\/segments\/1637964363641.20\/warc\/CC-MAIN-20211209000407-20211209030407-00567.warc.gz\"}"} | null | null |
\section{Introduction} \label{sec:intro}
The solar corona dynamically expands into interplanetary space in the form of the continuous solar wind \citep{Parker1958,Coleman1966}, the birth and the acceleration mechanism of which are still not well understood \citep{Tu2005,He2007,Cranmer2019}. The solar wind flowing into interplanetary space carries information about its source region, and on the other hand, involves diversified nonlinear physical processes \citep{Tu1995,Bruno2013}. It is essential to investigate the nature of near-sun fluctuations in order to analyze and understand these nonlinear physical processes as well as the heating and acceleration mechanisms of solar wind.
The statistical properties of the solar wind generally vary with speed, location and type of source region and heliocentric distance \citep{Bavassano1982,Tu1989,He2013,Matteini2014,Stansby2018,Horbury2018,Wang2019,Perrone2019,Bandyopadhyay2020,Chen2020,Chhiber2020,Duan2020,Qudsi2020}. \citet{Tu1989} contrast the properties of MHD turbulence between high speed and low speed solar wind at 0.3AU using the spectra of Els\"asser variables, cross helicity, residual energy, Alfv\'en ratio and Els\"asser ratio. They consider that, compared to the high speed wind, the turbulence evolves in an advanced state in slow wind, due to the longer expansion time. The $z^+$ and $z^-$ are close to a balanced state with an approximate -1.67 spectral index. The mode composition therein is dominated by the Alfv\'en mode and slow mode in the limit of incompressibility \citep{Dobrowolny1980}. \citet{Bavassano1982} study the variation of the nature of the fluctuations with heliocentric distance and scale in the trailing edge of a stream interaction region. The anisotropy defined with respect to the direction corresponding to the minimum eigenvalue decreases as the heliocentric distance increases and the scale decreases. The magnetic field closer to the sun is more compressed. However, \citet{Chen2020} report the evolution of solar wind turbulence from 0.17AU to 1AU, recently, and find at 0.17AU that: (1) the spectra of magnetic field, velocity and Els\"asser variables present a -3/2 slope at MHD scales; (2) the magnetic field is less compressed and (3) the outward propagating Alfv\'en waves are more dominant than at 1AU. Fast solar wind is characterised by highly Alfv\'enic fluctuations, although a new type of Alfv\'enic slow solar wind, possibly coming from quiet-Sun regions or coronal-hole boundaries, has been reported at distances from 0.3 AU to 1 AU. \citep{D'Amicis2015,Wang2019,Perrone2020,Parashar2020}. It is of interest to study this kind of solar wind, on account of its distinct properties, which differ from the classical slow solar wind.
Even if we relax the assumption of a pure superposition of linear waves, nonlinear turbulent fluctuations still retain certain polarization and correlation properties of linear modes \citep{Tu1995}. When we use the term 'wave', we refer to the mode composition of the fluctuations within this wave-turbulence paradigm. The composition of wave modes in the solar wind near 1 AU has been extensively studied and controversially discussed. There are many means to diagnose the wave modes: correlation analysis between velocity and magnetic field fluctuations \citep{Wang2012,Safrankova2019}, cross helicity analysis \citep{Roberts1987}, comparison of the MHD dispersion relations derived from measurements with theory predictions \citep{Shi2015}, and mode recognition methods \citep{Glassmeier1995,Narita2015,Chaston2020}. According to these studies, non-compressive outward Alfv\'en modes dominate the fluctuations in the solar wind especially in fast streams \citep{Bruno2013}. Compressive waves likely suffer strong Landau damping \citep{Barnes1966}, resulting in their suppression in the overall fluctuations. Correlations among variables (e.g. magnetic pressure, thermal pressure, density and temperature), show that the compressive component simultaneously exists of magnetosonic waves and pressure balanced structures (PBSs) \citep{Kellogg2005,Yao2011,Yang2017}. The majority of the compressive fluctuations is slow-mode-like rather than fast-mode-like in polarization \citep{Howes2012,He2015,Shi2015}. In situ observations show that the Alfv\'enicity decreases with heliocentric distance, which might be caused by the increased contribution of inward propagating Alfv\'en waves or the compressive fluctuations \citep{Bruno1993}.
To further comprehend the underlying multi-scale nature and evolution of near-sun turbulence, we systematically study the variation of the fluctuations' properties with scale and heliocentric distance within 0.3AU. The properties include the propagation direction of the wave, the mode composition, and the characteristic of anisotropy on average. In Section \ref{sec:data}, we briefly introduce the data sets we use. In Section \ref{sec:result}, we present our methods and analysis results, and give our summary and conclusions in Section \ref{sec:sum}. Our observations can provide observational evidence for the verification of existing theoretical models at closer heliocentric distances, and also impose constraints on the improvement of existing theoretical models and the proposal of new models.
\section{ Data Sets and Data Deduction} \label{sec:data}
We conduct our analysis using the data obtained from {\em Parker Solar Probe} (PSP), which is the closest human-built satellite to the sun up to now \citep{Fox2016}. We use the Level-2 magnetic field data supplied by the Flux-gate Magnetometer (MAG; \cite{Bale2016}) and the Level-3i proton data provided by the Solar Probe Cup (SPC; \cite{Kasper2016}). The time interval investigated spans from UTC2018-10-31/20:00:00 to UTC2018-11-10/15:00:00 in which period PSP cruised between 0.166AU (35.78 solar radii)and 0.243AU (56.37 solar radii). The interval we choose is shorter than the high-cadence interval around the first perihelion, because there are several sampling gaps longer than 30 minutes in the other intervals from which the SPC data are unavailable. We analyze time periods of the fluctuations in the range from 10s to 1000s, corresponding to MHD scales in the plasma frame. We do not exclude the so-called `switchback' patterns that exist among various scales (see \cite{Bale2019,Kasper2019,Dudokdewit2020}).
For the analysis of propagation direction and fluctuation anisotropy, we use the Singular Value Decomposition (SVD) method to resolve the frequencies and wavevectors of the waves based on Faraday's law. We estimate the three singular values of the spectral matrix (Eq.(8) of \citet{Santolik2003}), based on the principle of divergence-free magnetic field. We estimate the electric field at MHD scales for our SVD analysis as $E=-V_i\times B$ \citep{Shi2015}, where $V_i$ is the proton bulk velocity obtained from SWEAP/SPC. Note that only one wavevector is solved for every specific frequency with the SVD method. Therefore, the resolved frequency and wavevector can be regarded as the frequency and wavevector of the major wave mode. In reality, it is possible that multiple wave modes exist in the turbulence at the same time and scale. For the mode composition analysis, we use the method suggested by \citet{Glassmeier1995}, and get the contributions of the six MHD modes (parallel and anti-parallel propagating Alfv\'en mode, fast mode and slow mode) to the fluctuations. We estimate the spectral energy density of each mode as $e_i^TS(f_{sc},t)e_i$, where $S(f_{sc},t)$ is the spectral density matrix as defined by \citet{Glassmeier1995} and $e_i$ is the eigenvector of the corresponding mode.
\begin{figure}
\centerline{\includegraphics[width=20cm, clip=]{Figure1.eps}}
\caption{Time sequences overview of magnetic and plasma measurements during PSP's first encounter. Panel (a): magnetic field strength ($|B|$) and proton density ($N_{\rm p}$). Panel (b\&c\&d): magnetic fields ($B_{\rm R}, B_{\rm T}, B_{\rm N}$) and proton bulk velocities ($V_{\rm R,p}, V_{\rm T,p}, V_{\rm N,p}$) in RTN coordinates. Panel (e): proton density ($N_{\rm p}$) and thermal velocity ($W_{\rm p}$). Panel (f): plasma beta ($\beta$) and heliocentric distance ($R$) of spacecraft's position.
\label{fig:fig1}}
\end{figure}
\section{Analysis Results} \label{sec:result}
We present an overview of the observed magnetic field and plasma measurements in Figure \ref{fig:fig1}. To highlight the correlated fluctuations of the variables over such a long duration of about 10 days, we smooth all the measurements with a running window of 30 min. Figure 1(a) shows that the proton density ($N_{\rm p}$) and the magnetic field strength ($|B|$) decrease with increasing heliocentric distance. The three components of the magnetic field ($B_{\rm R}, B_{\rm T}, B_{\rm N}$) and the proton velocity ($V_{\rm R,p}, V_{\rm T,p}, V_{\rm N,p}$) in the RTN coordinates are positively correlated, respectively, which suggests that the large-scale outward-propagating Alfv\'enic fluctuations are dominant during this encounter. The proton thermal velocity ($W_{\rm p}$) varies between 50 km/s and 100 km/s and there is no global correlation between the proton density and the thermal velocity. The plasma beta ($\beta_{\rm p}$) is around 2, which does not exhibit a significant variation with heliocentric distance ($R$).
We solve the wavevector, $\bm{k}(\tau, R(t))$, at different heliocentric distances ($R(t)$) and periods ($\tau$), where $R$ is a function of time ($t$). The local background magnetic field, $\bm{B_0}(\tau, R(t))$, is acquired by Gaussian-weighting of the magnetic-field time series at time $t$, where the width of the Gaussian profile is defined by the period $\tau$ \citep{Podesta2009}. We then calculate the angles between $\bm{k}$ and $\bm{B_0}$, $\theta_{{\rm k,B_0}}(\tau, R(t))$. Figure \ref{fig:fig2} (a1), (b1) and (c1) show the probability distribution functions (PDFs) of wavevectors in three distance ranges. For $kd_{\rm i}>0.02$, the wavevectors cluster around the quasi-perpendicular direction. For $kd_{\rm i}<0.02$, the most probable wavevectors are quasi-parallel, relative to the local background magnetic field. Figure \ref{fig:fig2} (a2), (b2) and (c2) show the PDFs of $\theta_{\rm k,B_0}$ depending on $kd_{\rm i}$, in three different distance ranges. The propagation angles are close to $160^{\circ}$ for $kd_{\rm i}<0.02$, and close to $90^{\circ}$ for $kd_{\rm i}<0.02$. This indicates that the propagation angles are scale-dependent and turn from quasi-parallel at large scales to quasi-perpendicular at small scales.
\begin{figure}
\centerline{\includegraphics[width=20cm, clip=]{Figure2.eps}}
\caption{Panel (a1\&b1\&c1): Probability distribution functions of the wavevector in $|k_{\parallel}d_{\rm i}|-|k_{\perp}d_{\rm i}|$ space in the range of 0.180AU-0.185AU, 0.209AU-0.214AU, and 0.238AU-0.243AU, respectively. The white solid lines represent the relation between $k_{\parallel}$ and $k_{\perp}$ as predicted from the phenomenology of critical balance, $k_{\parallel}\sim k_{\perp}^{\frac{2}{3}}k_0^{\frac{1}{3}}$, where $k_0$ is the wavenumber of the outer scale. Panel(a2\&b2\&c2): PDFs of the propagation angle ($\theta_{{\rm k,B_0}}$) at differing scales ($kd_{\rm i}$), in the corresponding distance ranges.
\label{fig:fig2}}
\end{figure}
We carry out a mode composition diagnosis \citep{Glassmeier1995} and directly obtain the fractions of the six MHD wave modes, at different heliocentric distances and periods. According to the radial component of the local background magnetic field, $B_{0r}=\bm{B_0}\cdot\bm{\hat{e}_r}$, we transform the parallel and anti-parallel modes into outward/anti-sunward modes when $\bm{k}\cdot\bm{B_0}>0$, and inward/sunward modes when $\bm{k}\cdot\bm{B_0}<0$, respectively. The variation results of the averaged fractions of the transformed MHD modes are shown in Figure \ref{fig:fig3}. The upper three panels show the variation of the fractions of the MHD modes with period averaged over the distance ranges of 0.180AU-0.185AU, 0.209AU-0.214AU and 0.238AU-0.243AU, respectively. The wave mode occupying the highest spectral proportion is the outward Alfv\'en mode at most scales in these three $R$-intervals. The outward fast mode, the inward Alfv\'en mode and the outward slow mode represent the modes with the lowest fractional proportions throughout the whole MHD range at these distances. The fractional proportions of these three modes slightly increase with increasing distance. On average, from 0.180AU to 0.185AU, the inward fast mode is the second-most abundant mode, while the inward slow mode is in third place. From 0.209AU to 0.214AU, the inward slow mode and the inward fast mode have approximately equivalent proportions. From 0.238AU to 0.243AU, the inward slow mode is in second place, followed by the inward fast mode. We also find this change of mode composition with distance in the radial variation of the period-averaged fraction of mode compositions (see lower panel of Figure \ref{fig:fig3}). The outward Alfv\'en mode dominates throughout the whole near-Sun region under investigation. The fractional contribution of the fast mode decreases with increasing distance, while the contribution from inward slow modes increase with distance.
\begin{figure}
\plotone{Figure3.eps}
\caption{(Top) The period-depending variation of the spectral fractions of the six MHD modes i.e., outward/anti-sunward ({\it solid line}) and inward/sunward ({\it dashed line}) propagating Alfv\'en modes ({\it green}), fast modes ({\it blue}) and slow modes ({\it red}), as averaged over different distance ranges: 0.180AU-0.185AU ({\it Left}), 0.209AU-0.214AU ({\it Middle}) and 0.238AU-0.243AU ({\it Right}), respectively. (Bottom) The heliocentric distance variation of the spectral fractions of the six MHD modes as averaged over the time scale (period) from 10 to 1000s. The lime shadow sections correspond to the distance ranges used for the averaging of the intervals in the upper three panels.
\label{fig:fig3}}
\end{figure}
To further verify this composition diagnosis results, we reconstruct the dispersion relations of Alfv\'en waves and slow waves, as shown in Figure \ref{fig:fig4}. We first demonstrate a benchmark test to verify the ability of the SVD method to resolve the MHD dispersion relations. The preset basic parameters are: bulk velocity, $V_0=400{\rm km/s}$, background magnetic field, $B_0=90{\rm nT}$, proton number density, $n_p=300{\rm cm^{-3}}$, proton thermal velocity, $60{\rm km/s}$, $\theta_{{\rm k,B_0}}=20^{\circ}$. Based on the polarization relations of the Alfv\'en mode and slow mode, we set up the corresponding magnetic field and velocity disturbances of the two modes respectively, and use these disturbances as an artificial data input of the SVD method. In order to test the robustness of the SVD method, we also add 0.1\% level of noise for each wave at all scales to the virtual data input. As a result, we obtain a solution in terms of the wavevector ($kd_{\rm i}$) at every frequency ($\omega/\omega_{\rm ci}$) and during every local time interval, and $\omega_{{\rm ci}}$ is the ion cyclotron frequency. Furthermore, we construct the PDF($kd_{\rm i}$, $\omega/\omega_{\rm ci}$) statistically based on the information of $kd_{\rm i}$($\omega/\omega_{\rm ci}$, $t$). The PDFs($kd_{\rm i}$, $\omega/\omega_{\rm ci}$) for the benchmark tests of the Alfv\'en mode and slow mode are illustrated in Figure \ref{fig:fig4}(a) and \ref{fig:fig4}(b). The dispersion relations as indicated by the ridges with high PDF values are fully consistent with the theoretical dispersion relations, which means that the SVD method is well able to resolve the MHD dispersion relations from our observations. Thereafter, we apply the SVD method to the observational measurements to examine whether the dispersion relations of Alfv\'en waves and slow waves prevail. The results are shown in Figure \ref{fig:fig4}(c) and Figure \ref{fig:fig4}(d). The green patches corresponding to high levels of PDF concentrate on and around the theoretical dispersion relations of MHD Alfv\'en and slow modes. These results further confirm the existence of incompressible Alfv\'en waves (the most prevalent component) and compressible slow waves (the sub-dominat component).
\begin{figure}
\plotone{Figure4.eps}
\caption{Panel (a)\&(b): The PDFs of the normalized wavenumbers, $kd_{\rm i}$, for Alfv\'en waves and slow waves, at each normalized angular frequency, $\omega/\omega_{{\rm ci}}$ in the plasma frame, resolved by a benchmark test of the SVD method, with MHD Alfv\'en-mode and MHD slow-mode fluctuations. The theoretical MHD dispersion relations of Alfv\`en mode, fast mode and slow mode are plotted in black, blue and red solid lines, respectively. Panel(c)\&(d): The PDFs of $kd_{\rm i}$ for Alfv\'en waves and slow waves, at each $\omega/\omega_{{\rm ci}}$, obtained from application of the SVD method to the magnetic and velocity measurements from PSP in [20:00, 21:00] UT on 2018-11-05 (panel c) and [18:20, 18:25] UT on 2018-11-04 (panel d), consistent with the dispersion relations of Alfv\'en and slow modes, respectively. Unlike in panels (a) and (b), we use the averaged plasma parameters over the corresponding time intervals in panels (c) and (d).
\label{fig:fig4}}
\end{figure}
Lastly, we investigate the variation of the fluctuation anisotropy with period and distance in Figure \ref{fig:fig5}. The ratio of the middle and maximum singular values of the spectral matrix (Eq.(8) of \citet{Santolik2003}), $\lambda_{{\rm mid}}/\lambda_{{\rm max}}$, is adopted to represent the anisotropy of the magnetic field fluctuations in the plane perpendicular to the propagation direction, which we take to be oriented along the direction with the minimum singular value $\lambda_{{\rm min}}$. $\lambda_{{\rm mid}}/\lambda_{{\rm max}}$ is also known as the ellipticity. The ratio increases from around 0.3 to over 0.37 as the wave period increases, throughout the distance range under investigation. According to the above analysis, the dominant Alfv\'en mode increases in its degree of circular or arc polarization with increasing period.
\begin{figure}
\plotone{Figure5.eps}
\caption{(a) The distance profiles of the ratio between the middle and maximum singular values of the magnetic spectral matrix ($\lambda_{{\rm mid}}/\lambda_{{\rm max}}$) for the magnetic fluctuations at different periods from 10 to 1000 s. (b) The variations of $\lambda_{{\rm mid}}/\lambda_{{\rm max}}$ with period for the magnetic fluctuations at different distances from 0.17 to 0.24 AU.
\label{fig:fig5}}
\end{figure}
\section{Conclusion}\label{sec:sum}
The diversity, complexity and evolution of solar wind turbulence have always been important research topics in heliospheric physics. Hence, we statistically study mode propagation, mode composition, and fluctuation anisotropy of the solar wind MHD turbulence as measured by PSP. We find that:
(1) At 0.166AU$<$R$<$0.243AU: The propagation angles ($\theta_{{\rm k,B_0}}$) of wave-like turbulent fluctuations for $kd_{\rm i}<0.02$ are greater than $135^{\circ}$, mainly concentrating around $160^{\circ}$, while the distribution gradually shifts its center to $\theta_{{\rm k,B_0}}\sim90^{\circ}$ for $0.02<kd_{\rm i}<0.1$.
(2) The distance variations of the scale-averaged fractions of the MHD modes show that: (a) the outward/anti-sunward propagating Alfv\'en mode dominates the mode composition throughout the whole investigated range of distances, while the outward slow mode, the inward/sunward Alfv\'en mode and the outward fast mode represent the three smallest proportions; (b) the fraction of the inward fast mode decreases with distance, whereas the fraction of the inward slow mode increases with distance; (c) at 0.166AU$<$R$<$0.215AU, the inward fast mode takes the second place and the inward slow mode is in third place; at 0.215AU$<$R$<$0.243AU, the inward slow mode is in third place followed by the inward fast mode.
(3) The ellipticity increases with spacecraft-frame period in the heliocentric distance range studied.
According to the critical balance hypothesis \citep{Goldreich1995,Horbury2008}, the anisotropy of the power spectrum follows from the condition that the nonlinear time and the propagation time are approximately equal ($k_{\parallel}V_A\sim k_{\perp}\delta v$) in strong MHD turbulence with balanced Els\"asser fluxes. However, in solar wind turbulence with imbalanced fluxes dominated by outward Alfv\'en waves, our probability distribution function of wave propagation in $k_{\parallel}-k_{\perp}$ space (see color maps in Figure \ref{fig:fig2})) is inconsistent with this prediction of critical balance theory (see white solid lines in Figure \ref{fig:fig2}). For $kd_{\rm i}<0.02$, the most probable wavevector is more parallel, while for $kd_{\rm i}>0.02$, the most probable wavevector is closer to the quasi-perpendicular direction. This observational result will help to enlighten and promote the theory of turbulence anisotropy characterized by a transition of propagation direction from quasi-parallel to quasi-perpendicular with a large angular jump at a certain scale. After integrating the ideas of both "slab+2D" and "critical balance" scenarios, an upgraded turbulence phenomenology in Fourier space was proposed to involve "quasi-parallel wavelike fluctuations" and "quasi-2D fluctuations" as well as energy transfer between them and within themselves \citep{Oughton2015}. The observed transition from quasi-parallel to quasi-perpendicular propagation with increasing wavenumber shows a way how to improve the turbulence model in the future.
The transition of the dominant outward Alfv\'en mode from $\theta_{{\rm k,B_0}}\sim160^{\circ}$ to $\theta_{{\rm k,B_0}}\sim90^{\circ}$, as the period decreases from 1000s to 10s, may also indicates the geometry of the Alfv\'en waves at kinetic scales in the near-sun solar wind. Quasi-perpendicular Alfv\'en waves are more likely to dominate at scales closer to ion scale. Accordingly, quasi-perpendicular modes (e.g. kinetic Alfv\'en waves) may participate in the turbulent cascade and further dissipation, energizing and shaping the non-thermal ion distributions, which may develop temperature anisotropic and feed back to excite the ion-cyclotron waves reported during this interval \citep{Bowen2020}. In the future, we will study such chain of energy conversion process: damping of quasi-perpendicular kinetic waves $\longrightarrow$ energization of particles $\longrightarrow$ growth of quasi-parallel waves.
In some respect, our mode composition diagnosis results differ from the results of \citet{Chaston2020}. They study the spectral energy density fractions of six MHD modes inside and outside the field reversal regions, separately. They report that the three outward (anti-sunward) modes are dominant at MHD scales on average. This difference may lie in the calculation of the propagation angle, which is an input parameter of the mode-recognition method \citep{Glassmeier1995}. \citet{Chaston2020} obtained the propagation direction using the spectral matrix of the magnetic field only as suggested by \citet{Samson1980}, while we use both the magnetic and the electric field based on the Faraday's law \citep{Santolik2003}. This aspect may lead to the different results of mode composition.
The ellipticity serves here as an indicator to distinguish if the polarization is circular ($\lambda_{{\rm mid}}/\lambda_{{\rm max}}\sim1$), arc ($0<\lambda_{{\rm mid}}/\lambda_{{\rm max}}<1$), or linear ($\lambda_{{\rm mid}}/\lambda_{{\rm max}}\sim0$). The ellipticity increases with the period of the fluctuations from 0.3 to 0.37, which indicates that the magnetic fluctuations tend to be more and more circular-polarized as the period increases. Based on Figure \ref{fig:fig2}, the waves are also quasi-parallel propagating at larger periods. This observation is consistent with the prediction that the Alfv\'en branch of the MHD solutions is circular-polarized when $\theta_{{\rm k,B_0}}\sim0^{\circ}$.
\section{Acknowledgements}
This work at Peking University (PKU) is supported by NSFC under contracts 41574168, 41674171, 41874200, and 41421003. The team from PKU is also supported by CNSA under contract Nos. D020301 and D020302. D.V. is supported by the STFC Ernest
Rutherford Fellowship ST/P003826/1 and STFC Consolidated Grant ST/S000240/1. S.D.B. acknowledges the
support of the Leverhulme Trust Visiting Professorship program. The authors acknowledge the contributions of the Parker Solar Probe mission operations and spacecraft engineering teams at the Johns Hopkins University Applied Physics Laboratory as well as the FIELDS and SWEAP teams for use of the data. PSP data is available on SPDF (https://cdaweb.sci.gsfc.nasa.gov/index.html/).
\section{Introduction} \label{sec:intro}
\latex\ \footnote{\url{http://www.latex-project.org/}} is a document markup
language that is particularly well suited for the publication of
mathematical and scientific articles \citep{lamport94}. \latex\ was written
in 1985 by Leslie Lamport who based it on the \TeX\ typesetting language
which itself was created by Donald E. Knuth in 1978. In 1988 a suite of
\latex\ macros were developed to investigate electronic submission and
publication of AAS Journal articles \citep{1989BAAS...21..780H}. Shortly
afterwards, Chris Biemesdefer merged these macros and more into a \latex\
2.08 style file called \aastex. These early \aastex\ versions introduced
many common commands and practices that authors take for granted today.
Substantial revisions
were made by Lee Brotzman and Pierre Landau when the package was updated to
v4.0. AASTeX v5.0, written in 1995 by Arthur Ogawa, upgraded to \latex\ 2e
which uses the document class in lieu of a style file. Other improvements
to version 5 included hypertext support, landscape deluxetables and
improved figure support to facilitate electronic submission.
\aastex\ v5.2 was released in 2005 and introduced additional graphics
support plus new mark up to identifier astronomical objects, datasets and
facilities.
In 1996 Maxim Markevitch modified the AAS preprint style file, aaspp4.sty,
to closely emulate the very tight, two column style of a typeset
Astrophysical Journal article. The result was emulateapj.sty. A year
later Alexey Vikhlinin took over development and maintenance. In 2001 he
converted emulateapj into a class file in \latex\ 2e and in 2003 Vikhlinin
completely rewrote emulateapj based on the APS Journal's RevTEX class.
During this time emulateapj gained growing acceptance in the astronomical
community as it filled an author need to obtain an approximate number of
manuscript pages prior to submission for cost and length estimates. The
tighter typeset also had the added advantage of saving paper when printing
out hard copies.
Even though author publication charges are no longer based on print pages
\footnote{see Section \ref{sec:pubcharge} in the Appendix for more details
about how current article costs are calculated.} the emulateapj class file
has proven to be extremely popular with AAS Journal authors. An
analysis of submitted \latex\ manuscripts in 2015 revealed that $\sim$65\%
either called emulateapj or have a commented emulateapj classfile call
indicating it was used at some stage of the manuscript construction.
Clearly authors want to have access to a tightly typeset version of the
article when corresponding with co-authors and for preprint submissions.
When planning the next \aastex\ release the popularity of emulateapj played
an important roll in the decision to drop the old base code and adopt and
modify emulateapj for \aastex\ v6.+ instead. The change brings \aastex\
inline with what the majority of authors are already using while still
delivering new and improved features. \aastex\ v6.0 through v6.3 were
written by Amy Hendrickson. The release dates were January 2016 (v6.0),
October 2016 (v6.1), January 2018 (v6.2), and June 2019 (v6.3),
respectively.
The new features in the recent releases includes:
\begin{itemize}
\item{v6.0}
\begin{enumerate}
\item line numbering and watermarking,
\item improved citations for third party data repositories and software,
\item easier construction of matrix figures consisting of multiple
encapsulated postscript (EPS) or portable document format (PDF) files,
\item figure set mark up for large collections of similar figures,
\item color mark up to easily enable/disable revised text highlighting,
\item improved url support, and
\item numerous table options such as the ability to hide columns, column decimal alignment, automatic column math mode and numbering, plus splitting of wide tables (see Section \ref{subsec:tables} for details).
\end{enumerate}
\item{v6.1}
\begin{enumerate}
\item ORCID support for preprints,
\item improved author, affiliation and collaboration mark up,
\item reintroduced the old AASTeX v5.2 {\tt\string\received}, {\tt\string\revised}, {\tt\string\accepted}, and {\tt\string\published} commands plus added the new {\tt\string\submitjournal} command to document which AAS Journal the manuscript was submitted to, plus
\item new typeset style options including {\tt\string modern}.
\end{enumerate}
\item{v6.2}
\begin{enumerate}
\item A new RNAAS style option for Research Note manuscripts,
\item Titles no longer put in all caps,
\item No page skip between the title page and article body,
\item re-introduce RevTeX's widetext environment for long lines in two column style formats, and
\item upgrade to the {\tt\string\doi} command.
\end{enumerate}
\item{v6.3}
\begin{enumerate}
\item New {\tt\string interactive} environment to highlight interactive figures (see Section \ref{animation}),
\item Improved collaboration commands,
\item New {\tt\string anonymous} style to keep the authors, affiliations and acknowledgments from showing in the compiled pdf for dual anonymous review, and
\item Adoptions of IAU approved syntax for nominal units, see Section \ref{nominal}.
\end{enumerate}
\end{itemize}
The rest of this article provides information and examples on how to create
your own AAS Journal manuscript with v6.3. Special emphasis is placed on
how to use the full potential of \aastex\ v6+. The next section describes
the different manuscript styles available and how they differ from past
releases. Section \ref{sec:floats} describes table and figure placement.
Specific examples of tables, Section
\ref{subsec:tables}, and figures, Section \ref{subsec:figures}, are also
provided. A special emphasis is placed on interactive figures.
Section \ref{sec:displaymath} discusses how to display math and
incorporate equations in a manuscript while Section \ref{sec:highlight}
discuss how to use different ways to highlight revisions. The last section,
\ref{sec:cite}, shows how recognize software and external data as first
class references in the manuscript bibliography. An appendix is included
to show how to construct one and provide some information on how article
charges are calculated. Additional information is available both embedded
in the comments of this \latex\ file and in the online documentation at
\url{http://journals.aas.org/authors/aastex.html}.
\section{Manuscript styles} \label{sec:style}
The default style in \aastex\ v6.3 is a tight single column style, e.g. 10
point font, single spaced. The single column style is very useful for
article with wide equations. It is also the easiest to style to work with
since figures and tables, see Section \ref{sec:floats}, will span the
entire page, reducing the need for address float sizing.
To invoke a two column style similar to the what is produced in
the published PDF copy use \\
\noindent {\tt\string\documentclass[twocolumn]\{aastex63\}}. \\
\noindent Note that in the two column style figures and tables will only
span one column unless specifically ordered across both with the ``*'' flag,
e.g. \\
\noindent{\tt\string\begin\{figure*\}} ... {\tt\string\end\{figure*\}}, \\
\noindent{\tt\string\begin\{table*\}} ... {\tt\string\end\{table*\}}, and \\
\noindent{\tt\string\begin\{deluxetable*\}} ... {\tt\string\end\{deluxetable*\}}. \\
\noindent This option is ignored in the onecolumn style.
Some other style options are outlined in the commented sections of this
article. Any combination of style options can be used.
Two style options that are needed to fully use the new revision tracking
feature, see Section \ref{sec:highlight}, are {\tt\string linenumbers} which
uses the lineno style file to number each article line in the left margin and
{\tt\string trackchanges} which controls the revision and commenting highlight
output.
There is also a new {\tt\string modern} option that uses a Daniel
Foreman-Mackey and David Hogg design to produce stylish, single column
output that has wider left and right margins. It is designed to have fewer
words per line to improve reader retention. It also looks better on devices
with smaller displays such as smart phones.
For a Research Note use the {\tt\string RNAAS} option. This will produce a
manuscript with no abstract and in the {\tt\string modern} style.
The {\tt\string anonymous} option will prevent the author and affiliations
from being shown in the compiled pdf copy. This option allows the author
to keep this critical information in the latex file but prevent the reviewer
from seeing it during peer review if dual anonymous review is requested.
Likewise, acknowledgments can also be hidden if placed after the
{\tt\string\acknowledgments} command.
\section{Floats} \label{sec:floats}
Floats are non-text items that generally can not be split over a page.
They also have captions and can be numbered for reference. Primarily these
are figures and tables but authors can define their own. \latex\ tries to
place a float where indicated in the manuscript but will move it later if
there is not enough room at that location, hence the term ``float''.
Authors are encouraged to embed their tables and figures within the text as
they are mentioned. Please do not place the figures and text at the end of
the article as was the old practice. Editors and the vast majority of
referees find it much easier to read a manuscript with embedded figures and
tables.
Depending on the number of floats and the particular amount of text and
equations present in a manuscript the ultimate location of any specific
float can be hard to predict prior to compilation. It is recommended that
authors textbf{not} spend significant time trying to get float placement
perfect for peer review. The AAS Journal's publisher has sophisticated
typesetting software that will produce the optimal layout during
production.
Note that authors of Research Notes are only allowed one float, either one
table or one figure.
For authors that do want to take the time to optimize the locations of
their floats there are some techniques that can be used. The simplest
solution is to placing a float earlier in the text to get the position
right but this option will break down if the manuscript is altered.
A better method is to force \latex\ to place a
float in a general area with the use of the optional {\tt\string [placement
specifier]} parameter for figures and tables. This parameter goes after
{\tt\string \begin\{figure\}}, {\tt\string \begin\{table\}}, and
{\tt\string \begin\{deluxetable\}}. The main arguments the specifier takes
are ``h'', ``t'', ``b'', and ``!''. These tell \latex\ to place the float
\underline{h}ere (or as close as possible to this location as possible), at
the \underline{t}op of the page, and at the \underline{b}ottom of the page.
The last argument, ``!'', tells \latex\ to override its internal method of
calculating the float position. A sequence of rules can be created by
using multiple arguments. For example, {\tt\string \begin\{figure\}[htb!]}
tells \latex\ to try the current location first, then the top of the page
and finally the bottom of the page without regard to what it thinks the
proper position should be. Many of the tables and figures in this article
use a placement specifier to set their positions.
Note that the \latex\ {\tt\string tabular} environment is not a float. Only
when a {\tt\string tabular} is surrounded by {\tt\string\begin\{table\}} ...
{\tt\string\end\{table\}} is it a true float and the rules and suggestions
above apply.
In AASTeX v6.3 all deluxetables are float tables and thus if they are
longer than a page will spill off the bottom. Long deluxetables should
begin with the {\tt\string\startlongtable} command. This initiates a
longtable environment. Authors might have to use {\tt\string\clearpage} to
isolate a long table or optimally place it within the surrounding text.
\subsection{Tables} \label{subsec:tables}
Tables can be constructed with \latex's standard table environment or the
\aastex's deluxetable environment. The deluxetable construct handles long
tables better but has a larger overhead due to the greater amount of
defined mark up used set up and manipulate the table structure. The choice
of which to use is up to the author. Examples of both environments are
used in this manuscript.
Tables longer than 200 data lines and complex tables should only have a
short example table with the full data set available in the machine
readable format. The machine readable table will be available in the HTML
version of the article with just a short example in the PDF. Authors are
required to indicate in the table comments that the data in machine
readable format in the full article.
Authors are encouraged to create their own machine
readable tables using the online tool at
\url{http://authortools.aas.org/MRT/upload.html}.
\aastex\ v6 introduced five new table features that were designed to make
table construction easier and the resulting display better for AAS Journal
authors. The items are:
\begin{enumerate}
\item Declaring math mode in specific columns,
\item Column decimal alignment,
\item Automatic column header numbering,
\item Hiding columns, and
\item Splitting wide tables into two or three parts.
\end{enumerate}
Full details on how to create each type are given in the following
sections. Additional details are available in the AASTeX
guidelines at \url{http://journals.aas.org/authors/aastex.html}
\subsubsection{Column math mode}
Both the \latex\ tabular and \aastex\ deluxetable require an argument to
define the alignment and number of columns. The most common values are
``c'', ``l'' and ``r'' for \underline{c}enter, \underline{l}eft, and
\underline{r}ight justification. If these values are capitalized, e.g.
``C'', ``L'', or ``R'', then that specific column will automatically be in math
mode meaning that \$s are not required. Note that having embedded dollar
signs in the table does not affect the output.
\subsubsection{Decimal alignment}
Aligning a column by the decimal point can be difficult with only center,
left, and right justification options. It is possible to use phantom calls
in the data, e.g. {\tt\string\phn}, to align columns by hand but this can
be tedious in long or complex tables. To address this \aastex\ introduces
the {\tt\string\decimals} command and a new column justification option,
``D'', to align data in that column on the decimal. In deluxetable the
{\tt\string\decimals} command is invoked before the {\tt\string\startdata}
call but can be anywhere in \latex's tabular environment.
Two other important thing to note when using decimal alignment is that each
decimal column \textit{must end with a space before the ampersand}, e.g.
``\&\&'' is not allowed. Empty decimal columns are indicated with a decimal,
e.g. ``.''. Do not use deluxetable's {\tt\string\nodata} command.
The ``D'' alignment token works by splitting the column into two parts on the
decimal. While this is invisible to the user one must be aware of how it
works so that the headers are accounted for correctly. All decimal column
headers need to span two columns to get the alignment correct. This can be
done with a multicolumn call, e.g {\tt\string\multicolumn2c\{\}} or
{\tt\string\multicolumn\{2\}\{c\}\{\}}, or use the new
{\tt\string\twocolhead\{\}} command in deluxetable. Since \latex\ is
splitting these columns into two it is important to get the table width
right so that they appear joined on the page. You may have to run the
\latex\ compiler twice to get it right.
\subsubsection{Automatic column header numbering} \label{subsubsec:autonumber}
The command {\tt\string\colnumbers} can be included to automatically number
each column as the last row in the header. Per the AAS Journal table format
standards, each column index numbers will be surrounded by parentheses. In
a \latex\ tabular environment the {\tt\string\colnumbers} should be invoked
at the location where the author wants the numbers to appear, e.g. after
the last line of specified table header rows. In deluxetable this command
has to come before {\tt\string\startdata}. {\tt\string\colnumbers} will
not increment for columns hidden by the ``h'' command, see Section
\ref{subsubsec:hide}.
Note that when using decimal alignment in a table the command
{\tt\string\decimalcolnumbers} must be used instead of
{\tt\string\colnumbers} and {\tt\string\decimals}.
\subsubsection{Hiding columns} \label{subsubsec:hide}
Entire columns can be \underline{h}idden from display simply by changing
the specified column identifier to ``h''. In the \latex\ tabular environment
this column identifier conceals the entire column including the header
columns. In \aastex's deluxetables the header row is specifically
declared with the {\tt\string\tablehead} call and each header column is
marked with {\tt\string\colhead} call. In order to make a specific header
disappear with the ``h'' column identifier in deluxetable use
{\tt\string\nocolhead} instead to suppress that particular column header.
Authors can use this option in many different ways. Since column data can
be easily suppressed authors can include extra information and hid it
based on the comments of co-authors or referees. For wide tables that will
have a machine readable version, authors could put all the information in
the \latex\ table but use this option to hid as many columns as needed until
it fits on a page. This concealed column table would serve as the
example table for the full machine readable version. Regardless of how
columns are obscured, authors are responsible for removing any unneeded
column data or alerting the editorial office about how to treat these
columns during production for the final typeset article.
Table \ref{tab:messier} provides some basic information about the first ten
Messier Objects and illustrates how many of these new features can be used
together. It has automatic column numbering, decimal alignment of the
distances, and one concealed column. The Common name column
is the third in the \latex\ deluxetable but does not appear when the article
is compiled. This hidden column can be shown simply by changing the ``h'' in
the column identifier preamble to another valid value. This table also
uses {\tt\string\tablenum} to renumber the table because a \latex\ tabular
table was inserted before it.
\begin{deluxetable*}{cchlDlc}
\tablenum{1}
\tablecaption{Fun facts about the first 10 messier objects\label{tab:messier}}
\tablewidth{0pt}
\tablehead{
\colhead{Messier} & \colhead{NGC/IC} & \nocolhead{Common} & \colhead{Object} &
\multicolumn2c{Distance} & \colhead{} & \colhead{V} \\
\colhead{Number} & \colhead{Number} & \nocolhead{Name} & \colhead{Type} &
\multicolumn2c{(kpc)} & \colhead{Constellation} & \colhead{(mag)}
}
\decimalcolnumbers
\startdata
M1 & NGC 1952 & Crab Nebula & Supernova remnant & 2 & Taurus & 8.4 \\
M2 & NGC 7089 & Messier 2 & Cluster, globular & 11.5 & Aquarius & 6.3 \\
M3 & NGC 5272 & Messier 3 & Cluster, globular & 10.4 & Canes Venatici & 6.2 \\
M4 & NGC 6121 & Messier 4 & Cluster, globular & 2.2 & Scorpius & 5.9 \\
M5 & NGC 5904 & Messier 5 & Cluster, globular & 24.5 & Serpens & 5.9 \\
M6 & NGC 6405 & Butterfly Cluster & Cluster, open & 0.31 & Scorpius & 4.2 \\
M7 & NGC 6475 & Ptolemy Cluster & Cluster, open & 0.3 & Scorpius & 3.3 \\
M8 & NGC 6523 & Lagoon Nebula & Nebula with cluster & 1.25 & Sagittarius & 6.0 \\
M9 & NGC 6333 & Messier 9 & Cluster, globular & 7.91 & Ophiuchus & 8.4 \\
M10 & NGC 6254 & Messier 10 & Cluster, globular & 4.42 & Ophiuchus & 6.4 \\
\enddata
\tablecomments{This table ``hides'' the third column in the \latex\ when compiled.
The Distance is also centered on the decimals. Note that when using decimal
alignment you need to include the {\tt\string\decimals} command before
{\tt\string\startdata} and all of the values in that column have to have a
space before the next ampersand.}
\end{deluxetable*}
\subsubsection{Splitting a table into multiple horizontal components}
Since the AAS Journals are now all electronic with no print version there is
no reason why tables can not be as wide as authors need them to be.
However, there are some artificial limitations based on the width of a
print page. The old way around this limitation was to rotate into
landscape mode and use the smallest available table font
sizes, e.g. {\tt\string\tablewidth}, to get the table to fit.
Unfortunately, this was not always enough but now along with the hide column
option outlined in Section \ref{subsubsec:hide} there is a new way to break
a table into two or three components so that it flows down a page by
invoking a new table type, splittabular or splitdeluxetable. Within these
tables a new ``B'' column separator is introduced. Much like the vertical
bar option, ``$\vert$'', that produces a vertical table lines
the new ``B'' separator indicates where to \underline{B}reak
a table. Up to two ``B''s may be included.
Table 2
shows how to split a wide deluxetable into three parts with
the {\tt\string\splitdeluxetable} command. The {\tt\string\colnumbers}
option is on to show how the automatic column numbering carries through the
second table component, see Section \ref{subsubsec:autonumber}.
\begin{splitdeluxetable*}{lccccBcccccBcccc}
\tabletypesize{\scriptsize}
\tablewidth{0pt}
\tablenum{5}
\tablecaption{Measurements of Emission Lines: two breaks \label{tab:deluxesplit}}
\tablehead{
\colhead{Model} & \colhead{Component}& \colhead{Shift} & \colhead{FWHM} &
\multicolumn{10}{c}{Flux} \\
\colhead{} & \colhead{} & \colhead{($\rm
km~s^{-1}$)}& \colhead{($\rm km~s^{-1}$)} & \multicolumn{10}{c}{($\rm
10^{-17}~erg~s^{-1}~cm^{-2}$)} \\
\cline{5-14}
\colhead{} & \colhead{} &
\colhead{} & \colhead{} & \colhead{Ly$\alpha$} & \colhead{N\,{\footnotesize
V}} & \colhead{Si\,{\footnotesize IV}} & \colhead{C\,{\footnotesize IV}} &
\colhead{Mg\,{\footnotesize II}} & \colhead{H$\gamma$} & \colhead{H$\beta$}
& \colhead{H$\alpha$} & \colhead{He\,{\footnotesize I}} &
\colhead{Pa$\gamma$}
}
\colnumbers
\startdata
{ }& BELs& -97.13 & 9117$\pm 38$& 1033$\pm 33$&$< 35$&$< 166$& 637$\pm 31$& 1951$\pm 26$& 991$\pm 30$& 3502$\pm 42$& 20285$\pm 80$& 2025$\pm 116$& 1289$\pm 107$\\
{Model 1}& IELs& -4049.123 & 1974$\pm 22$& 2495$\pm 30$&$< 42$&$< 109$& 995$\pm 186$& 83$\pm 30$& 75$\pm 23$& 130$\pm 25$& 357$\pm 94$& 194$\pm 64$& 36$\pm 23$\\
{ }& NELs& \nodata & 641$\pm 4$& 449$\pm 23$&$< 6$&$< 9$& -- & 275$\pm 18$& 150$\pm 11$& 313$\pm 12$& 958$\pm 43$& 318$\pm 34$& 151$\pm 17$\\
\hline
{ }& BELs& -85 & 8991$\pm 41$& 988$\pm 29$&$< 24$&$< 173$& 623$\pm 28$& 1945$\pm 29$& 989$\pm 27$& 3498$\pm 37$& 20288$\pm 73$& 2047$\pm 143$& 1376$\pm 167$\\
{Model 2}& IELs& -51000 & 2025$\pm 26$& 2494$\pm 32$&$< 37$&$< 124$& 1005$\pm 190$& 72$\pm 28$& 72$\pm 21$& 113$\pm 18$& 271$\pm 85$& 205$\pm 72$& 34$\pm 21$\\
{ }& NELs& 52 & 637$\pm 10$& 477$\pm 17$&$< 4$&$< 8$& -- & 278$\pm 17$& 153$\pm 10$& 317$\pm 15$& 969$\pm 40$& 325$\pm 37$&
147$\pm 22$\\
\enddata
\tablecomments{This is an example of how to split a deluxetable. You can
split any table with this command into two or three parts. The location of
the split is given by the author based on the placement of the ``B''
indicators in the column identifier preamble. For more information please
look at the new \aastex\ instructions.}
\end{splitdeluxetable*}
\subsection{Figures\label{subsec:figures}}
\begin{figure}[ht!]
\plotone{cost.pdf}
\caption{The subscription (squares) and author publication (asterisks)
costs from 1991 to 2013. Subscription cost are on the left Y axis while
the author costs are on the right Y axis. All numbers in US dollars and
adjusted for inflation. The author charges also account for the change
from page charges to digital quanta in April 2011. \label{fig:general}}
\end{figure}
Authors can include a wide number of different graphics with their articles
but encapsulated postscript (EPS) or portable document format (PDF) are
encouraged. These range from general figures all authors are familiar with
to new enhanced graphics that can only be fully experienced in HTML. The
later include figure sets, animations and interactive figures. All
enhanced graphics require a static two dimensional representation in the
manuscript to serve as the example for the reader. All figures should
include detailed and descriptive captions. These captions are absolutely
critical for readers for whom the enhanced figure is inaccessible either
due to a disability or offline access. This portion of the article
provides examples for setting up all these types in with the latest version
of \aastex.
\subsection{General figures\label{subsec:general}}
\aastex\ has a {\tt\string\plotone} command to display a figure consisting
of one EPS/PDF file. Figure \ref{fig:general} is an example which shows
the approximate changes in the subscription costs and author publication
charges from 1991 to 2013 in the AAS Journals. For a general figure
consisting of two EPS/PDF files the {\tt\string\plottwo} command can be
used to position the two image files side by side.
Both {\tt\string\plotone} and {\tt\string\plottwo} take a
{\tt\string\caption} and an optional {\tt\string\figurenum} command to
specify the figure number\footnote{It is better to not use
{\tt\string\figurenum} and let LaTeX auto-increment all the figures. If you
do use this command you need to mark all of them accordingly.}. Each is
based on the {\tt\string graphicx} package command,
{\tt\string\includegraphics}. Authors are welcome to use
{\tt\string\includegraphics} along with its optional arguments that control
the height, width, scale, and position angle of a file within the figure.
More information on the full usage of {\tt\string\includegraphics} can be
found at \break
\url{https://en.wikibooks.org/wiki/LaTeX/Importing\_Graphics\#Including\_graphics}.
\subsection{Grid figures}
Including more than two EPS/PDF files in a single figure call can be tricky to
easily format. To make the process easier for authors \aastex\ v6 offers
{\tt\string\gridline} which allows any number of individual EPS/PDF file
calls within a single figure. Each file cited in a {\tt\string\gridline}
will be displayed in a row. By adding more {\tt\string\gridline} calls an
author can easily construct a matrix X by Y individual files as a
single general figure.
For each {\tt\string\gridline} command a EPS/PDF file is called by one of
four different commands. These are {\tt\string\fig},
{\tt\string\rightfig}, {\tt\string\leftfig}, and {\tt\string\boxedfig}.
The first file call specifies no image position justification while the
next two will right and left justify the image, respectively. The
{\tt\string\boxedfig} is similar to {\tt\string\fig} except that a box is
drawn around the figure file when displayed. Each of these commands takes
three arguments. The first is the file name. The second is the width that
file should be displayed at. While any natural \latex\ unit is allowed, it
is recommended that author use fractional units with the
{\tt\string\textwidth}. The last argument is text for a subcaption.
Figure \ref{fig:pyramid} shows an inverted pyramid of individual
figure constructed with six individual EPS files using the
{\tt\string\gridline} option.
\begin{figure*}
\gridline{\fig{V2491_Cyg.pdf}{0.3\textwidth}{(a)}
\fig{HV_Cet.pdf}{0.3\textwidth}{(b)}
\fig{LMC_2009.pdf}{0.3\textwidth}{(c)}
}
\gridline{\fig{RS_Oph.pdf}{0.3\textwidth}{(d)}
\fig{U_Sco.pdf}{0.3\textwidth}{(e)}
}
\gridline{\fig{KT_Eri.pdf}{0.3\textwidth}{(f)}}
\caption{Inverted pyramid figure of six individual files. The nova are
(a) V2491 Cyg, (b) HV Cet, (c) LMC 2009, (d) RS Oph, (e) U Sco, and (f)
KT Eri. These individual figures are taken from \citet{2011ApJS..197...31S}.
\label{fig:pyramid}}
\end{figure*}
\subsection{Enhanced graphics}
Enhanced graphics have an example figure to serve as an example for the
reader and the full graphical item available in the published HTML article.
This includes Figure sets, animations, and interactive figures. The
Astronomy Image Explorer (\url{http://www.astroexplorer.org/}) provides
access to all the figures published in the AAS Journals since they offered
an electronic version which was in the mid 1990s. You can filter image
searches by specific terms, year, journal, or type. The type filter is
particularly useful for finding all published enhanced graphics. As of
June 2019 there are over 3000 videos, 1000 figure sets, and 65 interactive
figures. The next sections describe how to include these types of graphics
in your own manuscripts.
\subsubsection{Figure sets}
The grid commands given above works great for a limited set of individual
figure files but what do you do if you have many 10s or 100s or even 1000s of
individual figure files? Figure sets represents a virtual flip book of a
large group of similar style figures. The derived PDF article will only
shows an example figure while the enhanced content is available in the
figure set in the HTML edition. The advantage of a figure set gives the
reader the ability to easily sort through a large collection to find
individual component figures. The advantage to the author is that grouping
similar figures into a figure set can result in significant cost savings in
terms of reduced publication charges, see Appendix B. All of the figure set
components, along with their html framework, are also available to the reader
for download in a single .tar.gz package.
Special \latex\ mark up is required to create a figure set. Prior to
\aastex\ v6 the underlying mark up commands had to be inserted by hand
but is now included. Note that when an article with figure set is compiled
in \latex\ none of the component figures are shown and a floating Figure
Set caption will appear in the resulting PDF.
\figsetstart
\figsetnum{4}
\figsettitle{Swift X-ray light curves}
\figsetgrpstart
\figsetgrpnum{1.1}
\figsetgrptitle{KT Eri}
\figsetplot{KT_Eri.pdf}
\figsetgrpnote{The Swift/XRT X-ray light curve for the first year after
outburst of KT Eri.}
\figsetgrpend
\figsetgrpstart
\figsetgrpnum{1.2}
\figsetgrptitle{RS Oph}
\figsetplot{RS_Oph.pdf}
\figsetgrpnote{The Swift/XRT X-ray light curve for the first year after
outburst of RS Oph.}
\figsetgrpend
\figsetgrpstart
\figsetgrpnum{1.3}
\figsetgrptitle{U Sco}
\figsetplot{U_Sco.pdf}
\figsetgrpnote{The Swift/XRT X-ray light curve for the first year after
outburst of U Sco.}
\figsetgrpend
\figsetgrpstart
\figsetgrpnum{1.4}
\figsetgrptitle{V2491 Cyg}
\figsetplot{V2491_Cyg.pdf}
\figsetgrpnote{The Swift/XRT X-ray light curve for the first year after
outburst of V2491 Cyg.}
\figsetgrpend
\figsetgrpstart
\figsetgrpnum{1.5}
\figsetgrptitle{Nova LMC 2009}
\figsetplot{LMC_2009.pdf}
\figsetgrpnote{The Swift/XRT X-ray light curve for the first year after
outburst of nova LMC 2009.}
\figsetgrpend
\figsetgrpstart
\figsetgrpnum{1.6}
\figsetgrptitle{HV Cet}
\figsetplot{HV_Cet.pdf}
\figsetgrpnote{The Swift/XRT X-ray light curve for the first year after
outburst of HV Cet.}
\figsetgrpend
\figsetend
\begin{figure}
\plotone{KT_Eri.pdf}
\caption{The Swift/XRT X-ray light curve for the first year after
outburst of the suspected recurrent nova KT Eri. At a maximum count rate of
328 ct/s, KT Eri was the brightest nova in X-rays observed to date. All
the component figures (6) are available in the Figure Set. Note that
these components that are {\bf not} shown in the compiled pdf. The figure
set consists of the same figures as shown in Figure \ref{fig:pyramid}.
The example figure shown for figure sets can be one component or many.
\label{fig:fig4}}
\end{figure}
Authors are encouraged to use an online tool at
\url{http://authortools.aas.org/FIGSETS/make-figset.html} to generate their
own specific figure set mark up to incorporate into their \latex\ articles.
\subsubsection{Animations \label{animation}}
Authors may, and are in fact encouraged, to include animations in their
manuscripts. The video will stream inline with the published article and
also be available for download. When writing the manuscript, a stand alone
figure is necessary to serve as an example for the reader. Ideally, this
is a single still frame from the animation but in some case the animation
may only represent a small portion of the example figure, say one many
panels as shown in Figure \ref{fig:video}. Regardless, it is very
important that the author provide descriptive text in the figure caption
including start and stop times and the video duration. Authors should
review the AAS animation guidelines in the graphics guide at
\url{https://journals.aas.org/graphics-guide/#animations}.
\begin{figure}
\begin{interactive}{animation}{movie.mp4}
\plotone{f4.pdf}
\end{interactive}
\caption{Figure 1 from \citet{2018ApJ...868L..33L}. AIA 171\AA (a,b),
AIA 131\AA (c), and AIA 304\AA images are shown. The red rectangle
in (a) shows the field of view of the other panels. An animation of
panels (b-d) is available. It covers 8 hours of observing beginning
at 01:00 UT on 2012 January 19. The video duration is 20 seconds.
\label{fig:video}}
\end{figure}
Animations and interactive figures (Section \ref{sec:interactive}) should
use the {\tt\string\begin{interactive}} environment in the figure call. This
environment
places a blue border around the figure to indicate that the figure is
enhanced in the published HTML article. The
command also serves to alert the publisher what files are used to generate
the dynamic HTML content. {\tt\string\interactive} takes two arguments. The
first details the type and currently only three are allowed. The types are
{\tt\string js} for generic javascript interactive figures,
{\tt\string animation} for inline videos, and
{\tt\string timeseries} for interactive light curves produced
by astropy \citet{2013A&A...558A..33A}\footnote{To be release in the
summer of 2019}. If these types are not provide the compiler will issue an
error and quit. The second argument is the file that produces the enhanced
feature in the HTML article.
\subsubsection{Interactive figures \label{sec:interactive}}
Interactive figures give the reader the ability to manipulate the
information contained in an image which can add clarity or help further the
author's narrative. These figures consist of two parts, a static
representative figure for the manuscript and the dynamic javascript plus
HTML framework that allows for interactive control.
An example of an interactive figure is a 3D model.
The underlying figure is a X3D file while x3dom.js is the javascript driver
that displays it. An author created interface is added via a html wrapper.
The first 3D model published by the AAS Journals using this technique was
\citet{2014ApJ...793..127V}.
Figure \ref{fig:interactive} provides an interactive example which can be
run locally to demonstrate how a simple javascript plus html interface
allows a reader to switch between figures. The necessary files for this
particular interactive figure are in the {\tt\string interactive.tar.gz}
file included with this package. Unpack the file and point the browser to
the local html file. In this case, the javascript that runs the interactive
buttons is embedded in the html file but it could just as easily be calls
to external javascript libraries. Ideally, the javascript should be
included with the submitted package of interactive files to minimize
external dependencies within the published article.
\begin{figure}
\begin{interactive}{js}{interactive.tar.gz}
\plotone{f5.pdf}
\end{interactive}
\caption{Figure 4 from \citet{2018AJ....156...82C}. \emph{Upper panel}: the
cumulative median observing time to measure the $3\sigma$ RV masses of TESS
planets as a function of host star spectral type and up to $10^3$ hours.
The \emph{dashed blue curves} represent the results from the optical
spectrograph whereas the \emph{solid red curves} represent the near-IR
spectrograph. \emph{Lower panel}: the time derivative of the cumulative
observing time curves used to indicate the RV planet detection efficiency.
The \emph{horizontal dashed line} highlights the value of the detection
efficiency at 20 hours per detection. Note that unlike the lower panels,
the upper panels do not share a common ordinate due to the differing number
of planet detections around stars in each spectral type bin. The
interactive version has two buttons that allows one to turn the optical and
NIR layers. \label{fig:interactive}}
\end{figure}
Authors should consult the online tutorials at
\url{https://journals.aas.org/graphics-guide/#interactive_figures}
for more information on what is currently supported and links to
tutorials and examples.
\section{Displaying mathematics} \label{sec:displaymath}
The most common mathematical symbols and formulas are in the amsmath
package. \aastex\ requires this package so there is no need to
specifically call for it in the document preamble. Most modern \latex\
distributions already contain this package. If you do not have this
package or the other required packages, revtex4-1, latexsym, graphicx,
amssymb, longtable, and epsf, they can be obtained from
\url{http://www.ctan.org}
Mathematics can be displayed either within the text, e.g. $E = mc^2$, or
separate from in an equation. In order to be properly rendered, all inline
math text has to be declared by surrounding the math by dollar signs (\$).
A complex equation example with inline math as part of the explanation
follows.
\begin{equation}
\bar v(p_2,\sigma_2)P_{-\tau}\hat a_1\hat a_2\cdots
\hat a_nu(p_1,\sigma_1) ,
\end{equation}
where $p$ and $\sigma$ label the initial $e^{\pm}$ four-momenta
and helicities $(\sigma = \pm 1)$, $\hat a_i=a^\mu_i\gamma_\nu$
and $P_\tau=\frac{1}{2}(1+\tau\gamma_5)$ is a chirality projection
operator $(\tau = \pm1)$. This produces a single line formula. \latex\ will
auto-number this and any subsequent equations. If no number is desired then
the {\tt\string equation} call should be replaced with {\tt\string displaymath}.
\latex\ can also handle a a multi-line equation. Use {\tt\string eqnarray}
for more than one line and end each line with a
\textbackslash\textbackslash. Each line will be numbered unless the
\textbackslash\textbackslash\ is preceded by a {\tt\string\nonumber}
command. Alignment points can be added with ampersands (\&). There should be
two ampersands per line. In the examples they are centered on the equal
symbol.
\begin{eqnarray}
\gamma^\mu & = &
\left(
\begin{array}{cc}
0 & \sigma^\mu_+ \\
\sigma^\mu_- & 0
\end{array} \right) ,
\gamma^5= \left(
\begin{array}{cc}
-1 & 0\\
0 & 1
\end{array} \right) , \\
\sigma^\mu_{\pm} & = & ({\bf 1} ,\pm \sigma) ,
\end{eqnarray}
\begin{eqnarray}
\hat a & = & \left(
\begin{array}{cc}
0 & (\hat a)_+\\
(\hat a)_- & 0
\end{array}\right), \nonumber \\
(\hat a)_\pm & = & a_\mu\sigma^\mu_\pm
\end{eqnarray}
\section{Revision tracking and color highlighting} \label{sec:highlight}
Authors sometimes use color to highlight changes to their manuscript in
response to editor and referee comments. In \aastex\ new commands
have been introduced to make this easier and formalize the process.
The first method is through a new set of editing mark up commands that
specifically identify what has been changed. These commands are
{\tt\string\added\{<text>\}}, {\tt\string\deleted\{<text>\}}, and
{\tt\string\replaced\{<old text>\}\{<replaced text>\}}. To activate these
commands the {\tt\string trackchanges} option must be used in the
{\tt\string\documentclass} call. When compiled this will produce the
marked text in red. The {\tt\string\explain\{<text>\}} can be used to add
text to provide information to the reader describing the change. Its
output is purple italic font. To see how {\tt\string\added\{<important
added info>\}}, {\tt\string\deleted\{<this can be deleted text>\}},
{\tt\string\replaced\{<old data>\}\{<replaced data>\}}, and \break
{\tt\string\explain\{<text explaining the change>\}} commands will produce
\added{important added information}\deleted{, deleted text, and }
\replaced{old data}{and replaced data,} toggle between versions compiled with
and without the {\tt\string trackchanges} option.\explain{text explaining
the change}
A summary list of all these tracking commands can be produced at the end of
the article by adding the {\tt\string\listofchanges} just before the
{\tt\string\end\{document\}} call. The page number for each change will be
provided. If the {\tt\string linenumbers} option is also included in the
documentclass call then not only will all the lines in the article be
numbered for handy reference but the summary list will also include the
line number for each change.
The second method does not have the ability to highlight the specific
nature of the changes but does allow the author to document changes over
multiple revisions. The commands are {\tt\string\edit1\{<text>\}},
{\tt\string\edit2\{<text>\}} and {\tt\string\edit3\{<text>\}} and they
produce {\tt\string<text>} that is highlighted in bold red, italic blue and
underlined purple, respectively. Authors should use the first command to
\edit1{indicated which text has been changed from the first revision.} The
second command is to highlight \edit2{new or modified text from a second
revision}. If a third revision is needed then the last command should be used
\edit3{to show this changed text}. Since over 90\% of all manuscripts are
accepted after the 3rd revision these commands make it easy to identify
what text has been added and when. Once the article is accepted all the
highlight color can be turned off simply by adding the
{\tt\string\turnoffediting} command in the preamble. Likewise, the new commands
{\tt\string\turnoffeditone}, {\tt\string\turnoffedittwo}, and
{\tt\string\turnoffeditthree} can be used to only turn off the
{\tt\string\edit1\{<text>\}}, {\tt\string\edit2\{<text>\}} and
{\tt\string\edit3\{<text>\}}, respectively.
Similar to marking editing changes with the {\tt\string\edit} options there
are also the {\tt\string\authorcomments1\{<text>\}},
{\tt\string\authorcomments2\{<text>\}} and
{\tt\string\authorcomments3\{<text>\}} commands. These produce the same
bold red, italic blue and underlined purple text but when the
{\tt\string\turnoffediting} command is present the {\tt\string<text>}
material does not appear in the manuscript. Authors can use these commands
to mark up text that they are not sure should appear in the final
manuscript or as a way to communicate comments between co-authors when
writing the article.
\section{Software and third party data repository citations} \label{sec:cite}
The AAS Journals would like to encourage authors to change software and
third party data repository references from the current standard of a
footnote to a first class citation in the bibliography. As a bibliographic
citation these important references will be more easily captured and credit
will be given to the appropriate people.
The first step to making this happen is to have the data or software in
a long term repository that has made these items available via a persistent
identifier like a Digital Object Identifier (DOI). A list of repositories
that satisfy this criteria plus each one's pros and cons are given at \break
\url{https://github.com/AASJournals/Tutorials/tree/master/Repositories}.
In the bibliography the format for data or code follows this format: \\
\noindent author year, title, version, publisher, prefix:identifier\\
\citet{2015ApJ...805...23C} provides a example of how the citation in the
article references the external code at
\doi{10.5281/zenodo.15991}. Unfortunately, bibtex does
not have specific bibtex entries for these types of references so the
``@misc'' type should be used. The Repository tutorial explains how to
code the ``@misc'' type correctly. The most recent aasjournal.bst file,
available with \aastex\ v6, will output bibtex ``@misc'' type properly.
\acknowledgments
We thank all the people that have made this AASTeX what it is today. This
includes but not limited to Bob Hanisch, Chris Biemesderfer, Lee Brotzman,
Pierre Landau, Arthur Ogawa, Maxim Markevitch, Alexey Vikhlinin and Amy
Hendrickson. Also special thanks to David Hogg and Daniel Foreman-Mackey
for the new "modern" style design. Considerable help was provided via bug
reports and hacks from numerous people including Patricio Cubillos, Alex
Drlica-Wagner, Sean Lake, Michele Bannister, Peter Williams, and Jonathan
Gagne.
\vspace{5mm}
\facilities{HST(STIS), Swift(XRT and UVOT), AAVSO, CTIO:1.3m,
CTIO:1.5m,CXO}
\software{astropy \citep{2013A&A...558A..33A},
Cloudy \citep{2013RMxAA..49..137F},
SExtractor \citep{1996A&AS..117..393B}
}
\subsubsection*{#1}}
\pagestyle{headings}
\markright{Reference sheet: \texttt{natbib}}
\usepackage{shortvrb}
\MakeShortVerb{\|}
\begin{document}
\thispagestyle{plain}
\newcommand{\textsc{Bib}\TeX}{\textsc{Bib}\TeX}
\newcommand{\texttt{#1}\def\filedate{#2}\def\fileversion{#3}}}{\texttt{#1}\def\filedate{#2}\def\fileversion{#3}}}
\begin{center}{\bfseries\Large
Reference sheet for \texttt{#1}\def\filedate{#2}\def\fileversion{#3}}\ usage}\\
\large(Describing version \fileversion\ from \filedate)
\end{center}
\begin{quote}\slshape
For a more detailed description of the \texttt{#1}\def\filedate{#2}\def\fileversion{#3}}\ package, \LaTeX\ the
source file \texttt{#1}\def\filedate{#2}\def\fileversion{#3}}\texttt{.dtx}.
\end{quote}
\head{Overview}
The \texttt{#1}\def\filedate{#2}\def\fileversion{#3}}\ package is a reimplementation of the \LaTeX\ |\cite| command,
to work with both author--year and numerical citations. It is compatible with
the standard bibliographic style files, such as \texttt{plain.bst}, as well as
with those for \texttt{harvard}, \texttt{apalike}, \texttt{chicago},
\texttt{astron}, \texttt{authordate}, and of course \texttt{#1}\def\filedate{#2}\def\fileversion{#3}}.
\head{Loading}
Load with |\usepackage[|\emph{options}|]{|\texttt{#1}\def\filedate{#2}\def\fileversion{#3}}|}|. See list of
\emph{options} at the end.
\head{Replacement bibliography styles}
I provide three new \texttt{.bst} files to replace the standard \LaTeX\
numerical ones:
\begin{quote}\ttfamily
plainnat.bst \qquad abbrvnat.bst \qquad unsrtnat.bst
\end{quote}
\head{Basic commands}
The \texttt{#1}\def\filedate{#2}\def\fileversion{#3}}\ package has two basic citation commands, |\citet| and
|\citep| for \emph{textual} and \emph{parenthetical} citations, respectively.
There also exist the starred versions |\citet*| and |\citep*| that print
the full author list, and not just the abbreviated one.
All of these may take one or two optional arguments to add some text before
and after the citation.
\begin{quote}
\begin{tabular}{l@{\quad$\Rightarrow$\quad}l}
|\citet{jon90}| & Jones et al. (1990)\\
|\citet[chap.~2]{jon90}| & Jones et al. (1990, chap.~2)\\[0.5ex]
|\citep{jon90}| & (Jones et al., 1990)\\
|\citep[chap.~2]{jon90}| & (Jones et al., 1990, chap.~2)\\
|\citep[see][]{jon90}| & (see Jones et al., 1990)\\
|\citep[see][chap.~2]{jon90}| & (see Jones et al., 1990, chap.~2)\\[0.5ex]
|\citet*{jon90}| & Jones, Baker, and Williams (1990)\\
|\citep*{jon90}| & (Jones, Baker, and Williams, 1990)
\end{tabular}
\end{quote}
\head{Multiple citations}
Multiple citations may be made by including more than one
citation key in the |\cite| command argument.
\begin{quote}
\begin{tabular}{l@{\quad$\Rightarrow$\quad}l}
|\citet{jon90,jam91}| & Jones et al. (1990); James et al. (1991)\\
|\citep{jon90,jam91}| & (Jones et al., 1990; James et al. 1991)\\
|\citep{jon90,jon91}| & (Jones et al., 1990, 1991)\\
|\citep{jon90a,jon90b}| & (Jones et al., 1990a,b)
\end{tabular}
\end{quote}
\head{Numerical mode}
These examples are for author--year citation mode. In numerical mode, the
results are different.
\begin{quote}
\begin{tabular}{l@{\quad$\Rightarrow$\quad}l}
|\citet{jon90}| & Jones et al. [21]\\
|\citet[chap.~2]{jon90}| & Jones et al. [21, chap.~2]\\[0.5ex]
|\citep{jon90}| & [21]\\
|\citep[chap.~2]{jon90}| & [21, chap.~2]\\
|\citep[see][]{jon90}| & [see 21]\\
|\citep[see][chap.~2]{jon90}| & [see 21, chap.~2]\\[0.5ex]
|\citep{jon90a,jon90b}| & [21, 32]
\end{tabular}
\end{quote}
\head{Suppressed parentheses}
As an alternative form of citation, |\citealt| is the same as |\citet| but
\emph{without parentheses}. Similarly, |\citealp| is |\citep| without
parentheses. Multiple references, notes, and the starred variants
also exist.
\begin{quote}
\begin{tabular}{l@{\quad$\Rightarrow$\quad}l}
|\citealt{jon90}| & Jones et al.\ 1990\\
|\citealt*{jon90}| & Jones, Baker, and Williams 1990\\
|\citealp{jon90}| & Jones et al., 1990\\
|\citealp*{jon90}| & Jones, Baker, and Williams, 1990\\
|\citealp{jon90,jam91}| & Jones et al., 1990; James et al., 1991\\
|\citealp[pg.~32]{jon90}| & Jones et al., 1990, pg.~32\\
|\citetext{priv.\ comm.}| & (priv.\ comm.)
\end{tabular}
\end{quote}
The |\citetext| command
allows arbitrary text to be placed in the current citation parentheses.
This may be used in combination with |\citealp|.
\head{Partial citations}
In author--year schemes, it is sometimes desirable to be able to refer to
the authors without the year, or vice versa. This is provided with the
extra commands
\begin{quote}
\begin{tabular}{l@{\quad$\Rightarrow$\quad}l}
|\citeauthor{jon90}| & Jones et al.\\
|\citeauthor*{jon90}| & Jones, Baker, and Williams\\
|\citeyear{jon90}| & 1990\\
|\citeyearpar{jon90}| & (1990)
\end{tabular}
\end{quote}
\head{Forcing upper cased names}
If the first author's name contains a \textsl{von} part, such as ``della
Robbia'', then |\citet{dRob98}| produces ``della Robbia (1998)'', even at the
beginning of a sentence. One can force the first letter to be in upper case
with the command |\Citet| instead. Other upper case commands also exist.
\begin{quote}
\begin{tabular}{rl@{\quad$\Rightarrow$\quad}l}
when & |\citet{dRob98}| & della Robbia (1998) \\
then & |\Citet{dRob98}| & Della Robbia (1998) \\
& |\Citep{dRob98}| & (Della Robbia, 1998) \\
& |\Citealt{dRob98}| & Della Robbia 1998 \\
& |\Citealp{dRob98}| & Della Robbia, 1998 \\
& |\Citeauthor{dRob98}| & Della Robbia
\end{tabular}
\end{quote}
These commands also exist in starred versions for full author names.
\head{Citation aliasing}
Sometimes one wants to refer to a reference with a special designation,
rather than by the authors, i.e. as Paper~I, Paper~II. Such aliases can be
defined and used, textual and/or parenthetical with:
\begin{quote}
\begin{tabular}{lcl}
|\defcitealias{jon90}{Paper~I}|\\
|\citetalias{jon90}| & $\Rightarrow$ & Paper~I\\
|\citepalias{jon90}| & $\Rightarrow$ & (Paper~I)
\end{tabular}
\end{quote}
These citation commands function much like |\citet| and |\citep|: they may
take multiple keys in the argument, may contain notes, and are marked as
hyperlinks.
\head{Selecting citation style and punctuation}
Use the command |\bibpunct| with one optional and 6 mandatory arguments:
\begin{enumerate}
\item the opening bracket symbol, default = (
\item the closing bracket symbol, default = )
\item the punctuation between multiple citations, default = ;
\item the letter `n' for numerical style, or `s' for numerical superscript
style, any other letter for
author--year, default = author--year;
\item the punctuation that comes between the author names and the year
\item the punctuation that comes between years or numbers when common author
lists are suppressed (default = ,);
\end{enumerate}
The optional argument is the character preceding a post-note, default is a
comma plus space. In redefining this character, one must include a space if
one is wanted.
Example~1, |\bibpunct{[}{]}{,}{a}{}{;}| changes the output of
\begin{quote}
|\citep{jon90,jon91,jam92}|
\end{quote}
into [Jones et al. 1990; 1991, James et al. 1992].
Example~2, |\bibpunct[; ]{(}{)}{,}{a}{}{;}| changes the output of
\begin{quote}
|\citep[and references therein]{jon90}|
\end{quote}
into (Jones et al. 1990; and references therein).
\head{Other formatting options}
Redefine |\bibsection| to the desired sectioning command for introducing
the list of references. This is normally |\section*| or |\chapter*|.
Define |\bibpreamble| to be any text that is to be printed after the heading but
before the actual list of references.
Define |\bibfont| to be a font declaration, e.g.\ |\small| to apply to
the list of references.
Define |\citenumfont| to be a font declaration or command like |\itshape|
or |\textit|.
Redefine |\bibnumfmt| as a command with an argument to format the numbers in
the list of references. The default definition is |[#1]|.
The indentation after the first line of each reference is given by
|\bibhang|; change this with the |\setlength| command.
The vertical spacing between references is set by |\bibsep|; change this with
the |\setlength| command.
\head{Automatic indexing of citations}
If one wishes to have the citations entered in the \texttt{.idx} indexing
file, it is only necessary to issue |\citeindextrue| at any point in the
document. All following |\cite| commands, of all variations, then insert
the corresponding entry to that file. With |\citeindexfalse|, these
entries will no longer be made.
\head{Use with \texttt{chapterbib} package}
The \texttt{#1}\def\filedate{#2}\def\fileversion{#3}}\ package is compatible with the \texttt{chapterbib} package
which makes it possible to have several bibliographies in one document.
The package makes use of the |\include| command, and each |\include|d file
has its own bibliography.
The order in which the \texttt{chapterbib} and \texttt{#1}\def\filedate{#2}\def\fileversion{#3}}\ packages are loaded
is unimportant.
The \texttt{chapterbib} package provides an option \texttt{sectionbib}
that puts the bibliography in a |\section*| instead of |\chapter*|,
something that makes sense if there is a bibliography in each chapter.
This option will not work when \texttt{#1}\def\filedate{#2}\def\fileversion{#3}}\ is also loaded; instead, add
the option to \texttt{#1}\def\filedate{#2}\def\fileversion{#3}}.
Every |\include|d file must contain its own
|\bibliography| command where the bibliography is to appear. The database
files listed as arguments to this command can be different in each file,
of course. However, what is not so obvious, is that each file must also
contain a |\bibliographystyle| command, \emph{preferably with the same
style argument}.
\head{Sorting and compressing citations}
Do not use the \texttt{cite} package with \texttt{#1}\def\filedate{#2}\def\fileversion{#3}}; rather use one of the
options \texttt{sort} or \texttt{sort\&compress}.
These also work with author--year citations, making multiple citations appear
in their order in the reference list.
\head{Long author list on first citation}
Use option \texttt{longnamesfirst} to have first citation automatically give
the full list of authors.
Suppress this for certain citations with |\shortcites{|\emph{key-list}|}|,
given before the first citation.
\head{Local configuration}
Any local recoding or definitions can be put in \texttt{#1}\def\filedate{#2}\def\fileversion{#3}}\texttt{.cfg} which
is read in after the main package file.
\head{Options that can be added to \texttt{\char`\\ usepackage}}
\begin{description}
\item[\ttfamily round] (default) for round parentheses;
\item[\ttfamily square] for square brackets;
\item[\ttfamily curly] for curly braces;
\item[\ttfamily angle] for angle brackets;
\item[\ttfamily colon] (default) to separate multiple citations with
colons;
\item[\ttfamily comma] to use commas as separaters;
\item[\ttfamily authoryear] (default) for author--year citations;
\item[\ttfamily numbers] for numerical citations;
\item[\ttfamily super] for superscripted numerical citations, as in
\textsl{Nature};
\item[\ttfamily sort] orders multiple citations into the sequence in
which they appear in the list of references;
\item[\ttfamily sort\&compress] as \texttt{sort} but in addition multiple
numerical citations are compressed if possible (as 3--6, 15);
\item[\ttfamily longnamesfirst] makes the first citation of any reference
the equivalent of the starred variant (full author list) and subsequent
citations normal (abbreviated list);
\item[\ttfamily sectionbib] redefines |\thebibliography| to issue
|\section*| instead of |\chapter*|; valid only for classes with a
|\chapter| command; to be used with the \texttt{chapterbib} package;
\item[\ttfamily nonamebreak] keeps all the authors' names in a citation on
one line; causes overfull hboxes but helps with some \texttt{hyperref}
problems.
\end{description}
\end{document}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,219 |
{"url":"https:\/\/www.physicsforums.com\/threads\/damped-oscillator-equation-energy.657731\/","text":"Damped Oscillator equation - Energy\n\n1. Dec 8, 2012\n\nthe damped oscillator equation:\n\n(m)y''(t) + (v)y'(t) +(k)y(t)=0\n\nShow that the energy of the system given by\n\nE=(1\/2)mx'\u00b2 + (1\/2)kx\u00b2\n\nsatisfies:\n\ndE\/dt = -mvx'\n\ni have gone through this several time simply differentiating the expression for E wrt and i end up with\n\ndE\/dt = x'(-vx')\n\nim at a brick wall. Am i doing something wrong? Any help is much appreciated! Thanks\n\n2. Dec 8, 2012\n\nDick\n\nThere is some sort of problem with the equation you have been asked to prove. A damped oscillator is always losing energy. Your solution shows that is true. The given solution would say the oscillator is sometimes gaining energy if the sign of x' is correct. I don't think that's correct.\n\n3. Dec 9, 2012\n\nrude man\n\nYou can't just differentiate E the way you did and prove the theorem. You need to incorporate the basic diff eq representing a damped spring-mass system. The expression for E represents ANY spring-mass system, damped or not, linear or not, etc.\n\nThe only thing I can think of is to solve the diff eq (it's a simple 2nd order one with constant coeff). Apply an initial condition to x = x0. Derive the solution x(t) and then substitute in E, take dE\/dt and there you are.\n\n(BTW why is y used in the diff eq and x in E?)\n\nDick's comment is well taken! Not only his, but I noticed the dimensions don't make sense. dE\/dt has dimensions of FLT-1 whereas -mvx' has dimensions of MF where\nM = mass\nF = force = MLT-2\nL = length\nT = time.\n\nThus -mvx' has the wrong dimensions to be dE\/dt.\n\nLast edited: Dec 9, 2012\n4. Dec 9, 2012\n\nDick\n\nPaddyod1509 did substitute the differential equation into dE\/dt to get his answer. The given answer can't be right. -vx'^2 has the correct units of J\/s. -mvx' doesn't.\n\n5. Dec 9, 2012\n\nrude man\n\nOK, I was misled by his wording.\n\n6. Dec 9, 2012\n\nDick\n\nWell, he didn't actually say that that's what he did. But once you form dE\/dt it's the obvious way to get to -vx'^2.\n\n7. Dec 9, 2012\n\nrude man\n\nSo did he solve the d.e. for x(t) and then substitute in E, or what?\n\n8. Dec 9, 2012\n\nDick\n\nNo. He found dE\/dt=mx'x''+kxx'=x'(mx''+kx). The DE then tells you mx''+kx=(-vx'). You don't need to actually solve the DE.\n\n9. Dec 9, 2012\n\nrude man\n\nThanks. Good job.","date":"2018-02-24 20:58:03","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8246358036994934, \"perplexity\": 1772.6352776519568}, \"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-2018-09\/segments\/1518891815934.81\/warc\/CC-MAIN-20180224191934-20180224211934-00798.warc.gz\"}"} | null | null |
\section{introduction}
In this paper, we study the regularizing effect of the gain part of the collision operator of the relativistic Boltzmann equation:
\begin{eqnarray*}\label{RBE}
\partial_tf+\hat{p}\cdot\nabla_xf =Q(f,f).
\end{eqnarray*}
Here the momentum four vector $p^{\mu}$ is defined by $p^{\mu}=(p^0,p)$ where $p^0=\sqrt{1+|p|^2}$ and $p=(p_1,p_2,p_3)\in\mathbb{R}^3$ denote the energy and the momentum of a particle respectively. Here we have set the speed of light $c=1$ and the particle mass $m=1$. The normalized velocity $\hat{p}$ is given by $\hat{p}= p/p^0=p/\sqrt{1+|p|^2}$. The velocity distribution function $f(x,p,t)$
represents the number density of the particle system on the phase point $(x,p)\in\mathbb{R}^3_x\times \mathbb{R}^3_p$ at time $t\in R_+$.
The collision operator $Q$ is given by
\begin{eqnarray*}
Q(f,h)(p)=Q^+(f,h)(p)-Q^-(f,h)(p).
\end{eqnarray*}
In the \textit{center-of-momentum} frame, the gain term $Q^+$ and the loss term $Q^-$ are written as \cite{DeGroot,Strain},
\begin{eqnarray*}
\displaystyle Q^+(f,h)=\int_{\mathbb{R}^3\times \mathbb{S}^2} v_{\o}\sigma(g,\theta)f(p^{\prime})h(q^{\prime})d\omega dq,\quad
\displaystyle Q^-(f,h)=\int_{\mathbb{R}^3\times \mathbb{S}^2} v_{\o}\sigma(g,\theta)f(p)h(q)d\omega dq,
\end{eqnarray*}
where $\sigma(g,\theta)$ is the scattering kernel, and the M{\o}ller velocity $v_{\o}$ is given by
\begin{eqnarray*}
v_{\o}=v_{\o}(p,q)=\sqrt{\left|\frac{p}{p_0}-\frac{q}{q_0}\right|^2-\left|\frac{p}{p_0}\times\frac{q}{q_0}\right|^2}
=\frac{g\sqrt{s}}{p_0q_0}.
\end{eqnarray*}
Here $s$ represents the square of the energy in the \textit{center-of-momentum} frame, $p+q=0$:
\begin{eqnarray*}
s=-(p^{\mu}+q^{\mu})(p_{\mu}+q_{\mu})
=2(p^0q^0-p\cdot q+1)\geq 0,
\end{eqnarray*}
and $g$ denotes the relative momentum
\begin{eqnarray*}
g=\sqrt{(p^{\mu}-q^{\mu})(p_{\mu}-q_{\mu})}=\sqrt{2(p^0q^0-p\cdot q-1)}.
\end{eqnarray*}
Note that $s=g^2+4$.
The pre-collisional momentum pair $(p,q)$ and the post-collisional momentum pair $(p^{\prime},q^{\prime})$ are related by
\begin{equation}\label{p'}
\begin{split}
p^{\prime}=&\frac{p+q}{2}+\frac{g}{2}\left(\omega+(\gamma-1)(p+q)\frac{(p+q)\cdot\omega}{|p+q|^2}\right),\\
q^{\prime}=&\frac{p+q}{2}-\frac{g}{2}\left(\omega+(\gamma-1)(p+q)\frac{(p+q)\cdot\omega}{|p+q|^2}\right),
\end{split}\end{equation}
where $\gamma=(p^0+q^0)/\sqrt{s}$. The microscopic energy is given by
\begin{eqnarray*}
p^{\prime}_0=\frac{p_0+q_0}{2}-\frac{g}{2\sqrt{s}}\omega\cdot(p+q),\quad q^{\prime}_0=\frac{p_0+q_0}{2}-\frac{g}{2\sqrt{s}}\omega\cdot(p+q).
\end{eqnarray*}
The collision operator $Q$ satisfies
\begin{eqnarray}\label{symmetry}
\int_{\mathbb{R}^3}Q(g,g)(p)\left(1, p, p^0\right)dp=0,\quad \int_{\mathbb{R}^3}Q(g,g)(p)\ln f dp\leq 0,
\end{eqnarray}
which respectively leads to the conservation of mass, momentum and energy, and the celebrated H-theorem.
\subsection{Main results} We start with our main hypothesis on the collision kernel.\newline
\noindent{\bf $\bullet$ Hypothesis on $\sigma$}
The relativistic Boltzmann collision kernel $\sigma(g,\theta)$ is a non-negative function which depends only on the relative velocity $g$ and the scattering angle $\theta$. We assume that $\sigma$ satisfies
\begin{equation}
\label{hypothesis}\sigma(g,\theta)\lesssim g^a \sigma_0(\theta), \qquad(a>-3)
\end{equation}
where the angular kernel $\sigma_0(\theta)$ is nonnegative and bounded.
This hypothesis includes the full-range of generic hard- ($a\geq 0$) and soft-potential ($a< 0$) collisional kernels; for example, \eqref{hypothesis} with $a\geq 0$ includes the relativistic analogue of the hard-ball case with $a=1$ and the (elastic) neutrino gas with $a=2$, and \eqref{hypothesis} with $a<0$ includes the interactions of Israel particles with $a=-1$.
We now state our main result. In the following, $||\cdot||_{L^m_\nu}$ with $\nu\in \mathbb{R}$ denotes
$$||f||_{L^m_\nu(\mathbb{R}^3)}\equiv\left( \int_{\mathbb{R}^3} |f(p)|^m(p^0)^{\nu}dp\right)^{\frac{1}{m}},$$ where we abbreviate $f(x,p,t)$ by $f(p)$ for fixed $t$ and $x$.
\begin{theorem}\label{regularitymain}$[L^1\times L^2\rightarrow \dot{H^1}]$
$($\textit{Hard potentials}$)$ Assume that the scattering kernel $\sigma$ satisfies \eqref{hypothesis} with $a\geq 0$. Also, suppose that $f\in L^m_{\frac{m}{2}(a-1)}$ and $h\in L^n_{\frac{n}{2}(a-1)}$ with $\frac{1}{m}+\frac{1}{n}=\frac{3}{2}.$ Then the gain term $Q^+$ has the following regularizing property:
$$\|\nabla_p Q^{+}(f,h)\|_{L^2}\lesssim \|f\|_{L^m_{\frac{m}{2}(a-1)}}\|h\|_{L^n_{\frac{n}{2}(a-1)}}.$$
Note that, by choosing $m=1$ and $n=2$, we have
$$\|\nabla_p Q^{+}(f,h)\|_{L^2}\lesssim \|f\|_{L^1_{\frac{a-1}{2}}}\|h\|_{L^2_{a-1}}.$$
\end{theorem}
\begin{theorem} \label{regularitymain2}
$(1)$ $[L^2\times L^2\rightarrow \dot{H^1}]$ $($\textit{Hard potentials}$)$
Assume that the scattering kernel $\sigma$ satisfies \eqref{hypothesis} with $a\geq 0$. Suppose that $f,h\in L^2_{a+2+\varepsilon}$ for some $\varepsilon>0$. Then the gain term $Q^+$ has the following regularizing property:
$$\|\nabla_p Q^{+}(f,h)\|_{L^2}\lesssim \|f\|_{L^2_{a+2+\varepsilon}}\|h\|_{L^2_{a+2+\varepsilon}}.$$
\noindent $(2)$ $[L^m\times L^n\rightarrow \dot{H^1}]$ $($\textit{Soft potentials}$)$ Assume that the scattering kernel $\sigma$ satisfies \eqref{hypothesis} with $-3<a<0$. Suppose that $f\in L^{m}_{\left(\frac{|a|}{2}+1+\varepsilon\right)m}$ and
$h\in L^{n}_{\left(\frac{|a|}{2}+1+\varepsilon\right)n}$ with $\frac{1}{m}+\frac{1}{n}=1+\frac{a}{3}$
for some $\varepsilon>0$. Then the gain term $Q^+$ has the following regularizing property:
\begin{align*}
\|\nabla_p Q^{+}(f,h)\|_{L^2}\lesssim \|f\|_{L^{m}_{\left(\frac{|a|}{2}+1+\varepsilon\right)m}}\|h\|_{L^{n}_{\left(\frac{|a|}{2}+1+\varepsilon\right)n}}.
\end{align*}
\end{theorem}
\begin{remark} The notation $\nabla_p$ above stands for the momentum derivatives with respect to $p\in\mathbb{R}^3$ only.\end{remark}\begin{remark}
Theorem \ref{regularitymain} holds only for the hard potential case with $a\geq0$, but it holds even if one of $f$ and $h$ lies in $L^1$ as in \cite{Andreasson,Lions,M-V,Wennberg2}.
In Theorem \ref{regularitymain2}, none of $f$ and $h$ can be a $L^1$ function, but the full-range of generic collision kernels with angular cut-off is covered.
\end{remark}
The smoothing estimate of the gain part of the collision operator was proved for the first time for regularized collision kernel by Lions in \cite{Lions},
who observed the Radon transform structure in the collision operator.
Wennberg \cite{Wennberg2} then provided a proof which covers the physical collision kernel using the Carlemann representation of $Q^+$.
A much simplified proof using only the Fourier transform, at the cost of confining the function space into $L^2$, was obtained in \cite{B-D,Lu}.
Mouhot and Villani generalized the estimates of \cite{B-D,Lu,Wennberg2} to weighted Sobolev spaces in \cite{M-V}.
Various restrictions on the collision kernel were further relaxed by Jiang in \cite{Jiang}. Lions' proof was generalized to the relativistic case by Andreasson in \cite{Andreasson}. Wennberg obtained a unified proof of such regularizing effects
for both classical and relativistic cases in \cite{Wennberg1} by showing that both can be deduced from the smoothing estimates of the generalized Radon transform.
In this paper, we provide a simplified proof of the regularizing estimate of the $Q^+$ operator from the relativistic Boltzmann equation in the spirit of \cite{B-D,Lu}.
Unlike \cite{B-D,Lu}, however, our proof gives the regularizing effect for the operator even when one of the functions lies in $L^1$ in the case of the full-range of the hard potentials $a\geq 0$ (Theorem \ref{regularitymain}) and shows the smoothing estimate for the full-range of generic hard and soft potentials
(Theorem \ref{regularitymain2}).
\section{Proof of Theorem 1.1}
We initially record the following pointwise estimates (see \cite{GS}, Lemma 3.1):
\begin{equation}
\label{pointwise g}
\frac{|p-q|}{\sqrt{p^0q^0}}\leq g\leq |p-q| \ \text{and}\ g\leq 2\sqrt{p^0q^0}.
\end{equation} Note that their definition of $``g"$ in \cite{GS} is actually a half of our $``g"$. Then we also have $s=4+g^2\lesssim p^0q^0$.
By the pre-post collisional change of variables $(p,q)\mapsto (p',q')$, we have
\begin{align}\label{1}
\begin{split}
\int_{\mathbb{R}^3}Q^+(f,h)e^{-ik\cdot p}dp&=\int_{\mathbb{R}^6\times\mathbb{S}^2}v_{\o}\sigma(g,\theta)f(p^{\prime})h(q^{\prime})e^{-ik\cdot p}d\omega dpdq\cr
&=\int_{\mathbb{R}^6\times \mathbb{S}^2}v_{\o}\sigma(g,\theta)f(p)h(q)e^{-ik\cdot p^{\prime}}d\omega dp^{\prime}dq^{\prime}\cr
&\equiv\int_{\mathbb{R}^6}v_{\o}\sigma(g,\theta)f(p)h(q)I(p,q,k) dp^{\prime}dq^{\prime},
\end{split}
\end{align}
where we define
$$I(p,q,k)\equiv \int_{\mathbb{S}^2}
e^{-ik\cdot \left\{\frac{p+q}{2}+\frac{g}{2}\left(\omega+(\gamma-1)(p+q)\frac{(p+q)\cdot\omega}{|p+q|^2}\right)\right\}}
d\omega .$$
Then $I(p,q,k)$ further satisfies that
\begin{align}\label{2}
\begin{split}
&=e^{-\frac{1}{2}i(p+q)\cdot k}
\int_{\mathbb{S}^2}e^{-i\frac{g}{2}\left\{\omega\cdot k+(\gamma-1)(p+q)\cdot k\frac{(p+q)\cdot\omega}{|p+q|^2}\right\}}d\omega\cr
&=e^{-\frac{1}{2}i(p+q)\cdot k}
\int_{\mathbb{S}^2}e^{-i\frac{g}{2}\left\{k+(\gamma-1)(p+q)\cdot k\frac{(p+q)}{|p+q|^2}\right\}\cdot\omega}d\omega\cr
&\equiv e^{-\frac{1}{2}i(p+q)\cdot k} II(p,q,k),
\end{split}
\end{align}
where $$ II(p,q,k)\equiv\int_{\mathbb{S}^2}e^{-i\frac{g}{2}\left\{k+(\gamma-1)(p+q)\cdot k\frac{(p+q)}{|p+q|^2}\right\}\cdot\omega}d\omega.$$
We then define $$A\equiv \frac{g}{2}\left\{k+(\gamma-1)(p+q)\cdot k\frac{(p+q)}{|p+q|^2}\right\},$$
and compute using the polar coordinate as
\begin{align*}
II&=\int_{\mathbb{S}^2}e^{-iA\cdot\omega}d\omega=\int_0^{2\pi}\left( \int_{0}^{\pi}\ e^{-i|A|\cos\psi}\sin\psi d\psi\right)d\vartheta\\
&=2\pi\int_{-1}^{1}e^{-i|A|s}ds=\frac{2\pi}{i|A|}(e^{i|A|}-e^{-i|A|})\\
&=4\pi\frac{\sin\left(\left|\frac{g}{2}\left\{k+(\gamma-1)(p+q)\cdot k\frac{(p+q)}{|p+q|^2}\right\}\right|\right)}{\left|\frac{g}{2}\left\{k+(\gamma-1)(p+q)\cdot k\frac{(p+q)}{|p+q|^2}\right\}\right|}.
\end{align*}
Since $|\sin(|A|)|\leq 1$, this gives
\begin{align}\label{3}
|II|\leq\frac{8\pi}{g\left|k+(\gamma-1)(p+q)\cdot k\frac{(p+q)}{|p+q|^2}\right|}.
\end{align}
Combining (\ref{1}), (\ref{2}) and (\ref{3}), we arrive at
\begin{align}\label{4}
\bigg|\int_{\mathbb{R}^3}Q^+(f,h)e^{-ik\cdot p}dp\bigg|\leq C\left|\int_{\mathbb{R}^6}v_{\o}\sigma(g,\theta)g^{-1}
\frac{e^{-\frac{1}{2}i k\cdot(p+q)}f(p)h(q) }{\left|k+(\gamma-1)(p+q)\cdot k\frac{(p+q)}{|p+q|^2}\right|}dpdq\right|.
\end{align}
We then observe from $\displaystyle|x|=\max_{|y|=1}|y^{\top}x|$ that
\begin{align*}
\left|k+(\gamma-1)(p+q)\cdot k\frac{(p+q)}{|p+q|^2}\right|&=\big|\left(I+(\gamma-1)A\otimes A\right)k\big|\cr
&=\max_{|y|=1}\big|y^{\top}\left(I+(\gamma-1)A\otimes A\right)k\big|\cr
&\geq\left|\left(\frac{k}{|k|}\right)^{\top}\left(I+(\gamma-1)A\otimes A\right)k\right|\cr
&=\frac{1}{|k|}\left(|k|^2+(\gamma-1)\left\{A\cdot k\right\}^2\right)\cr
&\geq |k|,
\end{align*}
where $A=\frac{p+q}{|p+q|}$. The last inequality holds because $$\gamma-1=\frac{p^0+q^0-\sqrt{s}}{\sqrt{s}}=\frac{|p+q|^2}{\sqrt{s}(p^0+q^0+\sqrt{s})}>0.$$
Therefore we obtain from (\ref{4}) that
\begin{align}\label{ineq1}
\left|\int_{\mathbb{R}^3}Q^+(f,h)e^{-ik\cdot p}dp\right|\leq\frac{C}{|k|}\bigg|\int_{\mathbb{R}^6}v_{\o}\sigma(g,\theta)g^{-1}e^{-\frac{1}{2}i k\cdot(p+q)}f(p)h(q) dpdq\bigg|.
\end{align}
Note that
$g\lesssim \sqrt{p^0q^0}$ and $s\lesssim p^0q^0$. Since $\sigma_0$ is bounded, we then have
\begin{equation}\label{vphi1}
v_{\o}\sigma(g,\theta)g^{-1}\lesssim \frac{g\sqrt{s}}{p^0q^0}g^{a-1}\approx g^a\frac{\sqrt{s}}{p^0q^0}\lesssim (p^0q^0)^{\frac{a}{2}}\frac{1}{\sqrt{p^0q^0}},
\end{equation}
because of the pointwise estimates \eqref{pointwise g} and that $a\geq 0$.
Therefore,
\begin{align*}\
\displaystyle|k|\left|\widehat{Q^{+}(f,h)}(k)\right|\lesssim\left|\int_{\mathbb{R}^6}e^{-\frac{1}{2}ik\cdot(p+q)}(p^0q^0)^{\frac{a-1}{2}}f(p)h(q)dpdq\right|\approx\left|\widehat{f_a}\left(\frac{k}{2}\right)\right|\left|\widehat{h_a}\left(\frac{k}{2}\right)\right|,\notag
\end{align*}
where $f_a(p)\equiv (p^0)^{\frac{a-1}{2}}f(p)$ and $h_a(q)\equiv (q^0)^{\frac{a-1}{2}}h(q)$. On the other hand, Plancherel's identity gives
$$
||\nabla_p Q^+||^2_{L^2}=\left|\left|\widehat{\nabla_p Q^+}\right|\right|^2_{L^2}=\left|\left||k|\widehat{Q^+}\right|\right|^2_{L^2}.
$$
Altogether, we obtain that
\begin{align*}
||\nabla_p Q^+(f,h)||^2_{L^2
\lesssim\int_{\mathbb{R}^3} \left|\widehat{f_a}\left(\frac{k}{2}\right)\widehat{h_a}\left(\frac{k}{2}\right)\right|^2dk
\approx \int_{\mathbb{R}^3}\left|\widehat{f_a*h_a}\left(\frac{k}{2}\right)\right|^2dk
\approx \|\widehat{f_a*h_a}\|^2_{L^2}\approx\|f_a*h_a\|^2_{L^2},
\end{align*}
where we use the convolution formula for the Fourier transform and Plancherel's identity. Then, by Young's convolution inequality, we finally have
$$
||\nabla_p Q^+(f,h)||^2_{L^2}\lesssim \|f_a\|^2_{L^m}\|h_a\|^2_{L^n},\quad\quad \left(\frac{1}{m}+\frac{1}{n}=\frac{3}{2}\right).
$$
That is,
$$
||\nabla_p Q^+(f,h)||_{L^2}\lesssim \|f\|_{L^m_{\frac{m}{2}(a-1)}}\|h\|_{L^n_{\frac{n}{2}(a-1)}}.$$
This completes the proof for Theorem \ref{regularitymain}.
\section{Proof of Theorem 1.2} \subsection{Hard potential case $(a\geq 0)$:}
We start with \eqref{ineq1} and \eqref{vphi1}.
By taking the $L^2$ norm of the left-hand side of \eqref{ineq1} and using Plancherel's identity and \eqref{vphi1}, we have
$$\|\nabla_p Q^{+}(f,h)\|^2_{L^2}\lesssim \int_{\mathbb{R}^3}\left|\int_{\mathbb{R}^6}e^{-\frac{1}{2}ik\cdot(p+q)}(p^0q^0)^{\frac
{a-1}{2}}f(p)h(q)dpdq\right|^2dk.$$
Then we take the following change of variables:
\begin{align}\label{CV}
x=\frac{p+q}{2},\quad y=p-q,
\end{align}
and denote
\[
H_y(x)=f\left(x+\frac{y}{2}\right)h\left(x-\frac{y}{2}\right)\left(1+\left|x+\frac{y}{2}\right|^2\right)^{\frac
{a-1}{4}}\left(1+\left|x-\frac{y}{2}\right|^2\right)^{\frac
{a-1}{4}}
\]
to derive
\begin{align*}
\|\nabla_p Q^{+}\|^2_{L^2}\lesssi
\int_{\mathbb{R}^3}\left|\int_{\mathbb{R}^3}\left\{\int_{\mathbb{R}^3}e^{-ik\cdot x}H_y(x)dx\right\}dy\right|^2dk=\int_{\mathbb{R}^3}\left|\int_{\mathbb{R}^3}\widehat{H_y}(k)dy\right|^2dk.
\end{align*}
Then by Cauchy-Schwarz inequality,
\begin{align*}
\|\nabla_p Q^{+}\|^2_{L^2}&\lesssim\int_{\mathbb{R}^3}\left(\int_{\mathbb{R}^3}|\widehat{H_y}(k)|(1+|y|^2)^{\frac{3+\varepsilon}{4}}(1+|y|^2)^{-\frac{3+\varepsilon}{4}}dy\right)^2dk\cr
&\lesssim\int_{\mathbb{R}^3}\left\{\int_{\mathbb{R}^3}|\widehat{H_y}(k)|^2(1+|y|^2)^{\frac{3+\varepsilon}{2}}dy\int_{\mathbb{R}^3}(1+|y|^2)^{-\frac{3+\varepsilon}{2}}dy\right\}dk\cr
&=C_{\varepsilon}\int_{\mathbb{R}^3}\left\{\int_{\mathbb{R}^3}|\widehat{H_y}(k)|^2(1+|y|^2)^{\frac{3+\varepsilon}{2}}dy\right\}dk,
\end{align*}
and by Fubini's theorem and Plancherel's identity, we have
\begin{align*}
\|\nabla_p Q^{+}\|^2_{L^2
&\lesssim \int_{\mathbb{R}^3}\left\{\int_{\mathbb{R}^3}|H_y(x)|^2dx\right\}(1+|y|^2)^{\frac{3+\varepsilon}{2}}dy\cr
&\approx\int_{\mathbb{R}^6}(p^0q^0)^{
a-1}|f(p)|^2|h(q)|^2(1+|p-q|^2)^{\frac{3+\varepsilon}{2}}dpdq\cr
&\lesssim \int_{\mathbb{R}^6}(p^0q^0)^{a-1+3+\varepsilon}|f(p)|^2|h(q)|^2dpdq\cr
&\lesssim\|f\|^2_{L^2_{a+2+\varepsilon}}\|h\|^2_{L^2_{a+2+\varepsilon}},
\end{align*}
where we used
\begin{align}\label{p-q}
1+|p-q|^2\lesssim (p^0q^0)^2.
\end{align}
This completes the proof for the hard-potential case with $a\geq 0$.
\subsection{Soft potential case $(a<0)$:} Again, we start from \eqref{ineq1}.
In this case, the scattering kernel becomes more singular in $g$, and we use the following sharp inequality instead of \eqref{vphi1}:
$$v_{\o}\sigma(g,\theta)g^{-1}\lesssim \frac{g\sqrt{s}}{p^0q^0} g^{a-1}\lesssim \left(\frac{|p-q|}{\sqrt{p^0q^0}}\right)^{a}\frac{1}{\sqrt{p^0q^0}},$$ where we used $v_{\o}=\frac{g\sqrt{s}}{p^0q^0}$, $a<0$, $g\gtrsim \frac{|p-q|}{\sqrt{p^0q^0}}$, and $s\lesssim p^0q^0$ from the pointwise estimates \eqref{pointwise g}. By taking the $L^2$ norm of the left-hand side of \eqref{ineq1} and using Plancherel's identity, we have
$$\|\nabla_p Q^{+}\|^2_{L^2}\lesssim \int_{\mathbb{R}^3}\left|\int_{\mathbb{R}^6}e^{-\frac{1}{2}ik\cdot(p+q)}\left(\frac{|p-q|}{\sqrt{p^0q^0}}\right)^{a}\frac{1}{\sqrt{p^0q^0}}f(p)h(q)dpdq\right|^2dk.$$
Then we take the same change of variables as in (\ref{CV})
and define
\[
S_y(x)=|y|^{a}f\left(x+\frac{y}{2}\right)h\left(x-\frac{y}{2}\right)\left\{\left(1+\left|x+\frac{y}{2}\right|^2\right)\left(1+\left|x-\frac{y}{2}\right|^2\right)\right\}^{-\frac{a+1}{4}},
\]
to obtain
\begin{align*}
\|\nabla_p Q^{+}\|^2_{L^2
=\int_{\mathbb{R}^3}\left|\int_{\mathbb{R}^3}\left\{\int_{\mathbb{R}^3}e^{-ik\cdot x}S_y(x)dx\right\}dy\right|^2dk
=\int_{\mathbb{R}^3}\left|\int_{\mathbb{R}^3}\widehat{S_y}(k)dy\right|^2dk.
\end{align*}
Then by Cauchy-Schwarz inequality, we have
\begin{align*}
\|\nabla_p Q^{+}\|^2_{L^2}&\lesssim\int_{\mathbb{R}^3}\left(\int_{\mathbb{R}^3}|\widehat{S_y}(k)|(1+|y|^2)^{\frac{3+\delta}{4}}(1+|y|^2)^{-\frac{3+\delta}{4}}dy\right)^2dk\cr
&\lesssim\int_{\mathbb{R}^3}\left\{\int_{\mathbb{R}^3}|\widehat{S_y}(k)|^2(1+|y|^2)^{\frac{3+\delta}{2}}dy\int_{\mathbb{R}^3}(1+|y|^2)^{-\frac{3+\delta}{2}}dy\right\}dk\cr
&=C_{\delta}\int_{\mathbb{R}^3}\left\{\int_{\mathbb{R}^3}|\widehat{S_y}(k)|^2(1+|y|^2)^{\frac{3+\delta}{2}}dy\right\}dk.
\end{align*}
Applying Fubini's theorem and Plancherel's identity, we obtain
\begin{align*}
\|\nabla_p Q^{+}(f,h)\|^2_{L^2
&\lesssim \int_{\mathbb{R}^3}\left\{\int_{\mathbb{R}^3}|S_y(x)|^2dx\right\}(1+|y|^2)^{\frac{3+\delta}{2}}dy\cr
&\approx\int_{\mathbb{R}^6}\left(\frac{|p-q|}{\sqrt{p^0q^0}}\right)^{2a}\frac{1}{p^0q^0}|f(p)|^2|h(q)|^2(1+|p-q|^2)^{\frac{3+\delta}{2}}dpdq\cr
&\lesssim\int_{\mathbb{R}^6}\frac{|f(p)|^2|h(q)|^2}{|p-q|^{2|a|}}(p^0q^0)^{|a|-1+3+\delta}dpdq\cr
&\approx\int_{\mathbb{R}^6}\frac{|f(p)|^2|h(q)|^2}{|p-q|^{2|a|}}(p^0q^0)^{|a|+2+\delta}dpdq.
\end{align*}
We then recall the Hardy-Littlewood-Sobolev inequality:
\begin{align*}
\|\nabla_p Q^{+}(f,h)\|^2_{L^2}&\lesssim \big\||f(p)|^2(p^0)^{|a|+2+\delta}\big\|_{L^{m'}}\big\||h(p)|^2(p^0)^{|a|+2+\delta}\big\|_{L^{n'}}
\quad \left(\frac{1}{m'}+\frac{1}{n'}=2-\frac{2|a|}{3}\right)\cr
&\approx\|f\|^2_{L^{2m'}_{\left(|a|+2+\delta\right)m'}}\|h\|^2_{L^{2n'}_{\left(|a|+2+\delta\right)n'}}.
\end{align*}
Finally, we rewrite $2m'=m$, $2n'=n$ and $\frac{\delta}{2}=\varepsilon$ to complete the proof.
\section{Acknowledgement}J. W. Jang was supported by
the Korean IBS project IBS-R003-D1. S.-B. Yun was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1B03935955).
\bibliographystyle{amsplain}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,606 |
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