text:
// Copyright 2014 The Bazel Authors. All rights reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//    http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
package com.google.devtools.build.docgen;

import com.google.common.collect.ImmutableList;
import com.google.common.collect.ImmutableMap;
import com.google.common.io.ByteStreams;
import com.google.common.io.Files;
import java.io.IOException;
import java.io.InputStream;
import java.nio.charset.StandardCharsets;

/**
 * A class to contain the base definition of common BUILD rule attributes.
 */
public class PredefinedAttributes {

  /**
   * List of documentation for common attributes of *_test rules, relative to {@link
   * com.google.devtools.build.docgen}.
   */
  public static final ImmutableList<String> TEST_ATTRIBUTES_DOCFILES =
      ImmutableList.of(
          "templates/attributes/test/args.html",
          "templates/attributes/test/env.html",
          "templates/attributes/test/env_inherit.html",
          "templates/attributes/test/size.html",
          "templates/attributes/test/timeout.html",
          "templates/attributes/test/flaky.html",
          "templates/attributes/test/shard_count.html",
          "templates/attributes/test/local.html");

  /**
   * List of common attributes documentation, relative to {@link com.google.devtools.build.docgen}.
   */
  public static final ImmutableList<String> COMMON_ATTRIBUTES_DOCFILES =
      ImmutableList.of(
          "templates/attributes/common/compatible_with.html",
          "templates/attributes/common/data.html",
          "templates/attributes/common/deprecation.html",
          "templates/attributes/common/deps.html",
          "templates/attributes/common/distribs.html",
          "templates/attributes/common/exec_compatible_with.html",
          "templates/attributes/common/exec_properties.html",
          "templates/attributes/common/features.html",
          "templates/attributes/common/licenses.html",
          "templates/attributes/common/restricted_to.html",
          "templates/attributes/common/tags.html",
          "templates/attributes/common/target_compatible_with.html",
          "templates/attributes/common/testonly.html",
          "templates/attributes/common/toolchains.html",
          "templates/attributes/common/visibility.html");

  /**
   * List of documentation for common attributes of *_binary rules, relative to {@link
   * com.google.devtools.build.docgen}.
   */
  public static final ImmutableList<String> BINARY_ATTRIBUTES_DOCFILES =
      ImmutableList.of(
          "templates/attributes/binary/args.html",
          "templates/attributes/binary/env.html",
          "templates/attributes/binary/output_licenses.html");

  private static ImmutableMap<String, RuleDocumentationAttribute> generateAttributeMap(
      String commonType, ImmutableList<String> filenames) {
    ImmutableMap.Builder<String, RuleDocumentationAttribute> builder =
        ImmutableMap.<String, RuleDocumentationAttribute>builder();
    for (String filename : filenames) {
      String name = Files.getNameWithoutExtension(filename);
      try {
        InputStream stream = PredefinedAttributes.class.getResourceAsStream(filename);
        if (stream == null) {
          throw new IllegalStateException("Resource " + filename + " not found");
        }
        String content = new String(ByteStreams.toByteArray(stream), StandardCharsets.UTF_8);
        builder.put(name, RuleDocumentationAttribute.create(name, commonType, content));
      } catch (IOException e) {
        throw new IllegalStateException("Exception while reading " + filename, e);
      }
    }
    return builder.build();
  }

  public static final ImmutableMap<String, RuleDocumentationAttribute> COMMON_ATTRIBUTES =
      generateAttributeMap(DocgenConsts.COMMON_ATTRIBUTES, COMMON_ATTRIBUTES_DOCFILES);

  public static final ImmutableMap<String, RuleDocumentationAttribute> BINARY_ATTRIBUTES =
      generateAttributeMap(DocgenConsts.BINARY_ATTRIBUTES, BINARY_ATTRIBUTES_DOCFILES);

  public static final ImmutableMap<String, RuleDocumentationAttribute> TEST_ATTRIBUTES =
      generateAttributeMap(DocgenConsts.TEST_ATTRIBUTES, TEST_ATTRIBUTES_DOCFILES);
}


Give your bedroom a stylish makeover with the Little Seeds Jax Reversible Comforter Set. Decked out in a stylish geometric pattern in teal, navy, yellow, grey and white hues, the unique bedding is a fun addition to your child's bed.
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Dumpling dough: Boil the water with the colouring. When it reaches boiling point, pour onto the starch. Knead well until smooth and elastic.
Dumpling filling: Fry together the garlic, onion, shallot and celery. When soft, add the tomato and continue to fry. Add the wine and reduce. Add the juniper berries, galangal root and lemon grass. Brown the duck breasts, thighs and wings and add. Cover the mixture with water and simmer for 5-6 hours. When the duck is cooked, remove and break up the meat. Strain the sauce and reduce to the desired texture. Mix the duck with the reduced sauce and add salt to taste.
Carrot purée: Peel and cut the carrots, then steam. When cooked, place in the robot with the butter and beat to make a thin, creamy purée. Season with salt.
Carrot air: Peel the carrots and liquidise. Use an electric beater to make a carrot air with body.
Tree tomato and wine ketchup: Reduce the red wine to 100 ml then add to the tree tomatoes. Place in a vacuum pack and chill for two days. Blend in the robot together with the other ingredients. Season with salt and correct the texture.
Duck tongues: Trim the tongues then completely cover with the oil. Confit in the oven at 99ºC for 3 hours. Then fry in very hot oil to brown.
Spicy sauce: Mix the ingredients, forming a sauce with the desired flavour and texture.
Mini carrots: Peel and wash the carrots, then cook carefully in the butter.
Roll out the dough, add the filling and form into dumplings. Steam for 7 minutes. Arrange on pieces of Brik pastry and brown on a flat-top grill.
Serve on a plate the tree tomato and wine ketchup, the hot carrot purée, the baby carrots, the powdered smoked tea and the posticker dumpling.
Finish with the carrot air and a brochette of spicy tongues. (Serve the spicy sauce over the tongues – see photo).


text:
Author/Poet Robert Morgan To Be Featured At Barton College Friends Of Hackney Library Fall Dinner
Posted September 17, 2010 · Add Comment
WILSON, N.C. – Author and poet Robert Morgan, Kappa Alpha Professor of English at Cornell University, will be the featured speaker at the Barton College Friends of Hackney Library fall dinner scheduled for Tuesday, Oct. 5. The evening's festivities, to be held in Hardy Alumni Hall, will begin with a book signing and wine reception at 6 p.m., followed by dinner and the program at 7 p.m.
Tickets for the dinner event are $35 per person, with reservations accepted through Sept. 28. Members of the Barton College Friends of Hackney Library may reserve tickets for $30 per person. Table reservations must be for a total of eight persons. Please contact Cynthia Collins at 399-6503 or fohl@barton.edu for reservations or additional information.
A native of Hendersonville, Morgan received a Bachelor of Arts degree in English from the University of North Carolina at Chapel Hill, a Master of Fine Arts degree from the University of North Carolina at Greensboro, and an Honorary Doctor of Letters degree from the University of North Carolina at Chapel Hill.
Morgan began teaching at Cornell University in 1971, and he has served as the Kappa Alpha Professor of English since 1992. He has held a variety of visiting writer and professorship appointments throughout his professional career, including appointments at Appalachian State University, East Carolina University, Duke University, Furman University, and Davidson College.
Although his earliest publications were short stories, Morgan's work covers a variety of genres. He published his first poetry collection, "Zirconia Poems," in 1969. Three more books of poetry followed over the next decade, including "Land Diving," "Trunk & Thicket," and "Groundwork." In 1980, Morgan returned to fiction and published his first book of short stories, "The Blue Valleys," which was nominated for the First Fiction Award by the American Academy of Arts and Letters. Morgan's novel "The Truest Pleasure" garnered several honors including a "New York Times" Notable Book, listing by "Publishers Weekly" as one of the outstanding books of the year, and first runner-up for The Southern Book Critics Circle Award. Morgan's novel "Gap Creek," earned additional recognition, including the 2000 Southern Book Critics Circle Award, "New York Times" Notable Book, "New York Times" best seller, January 2000 Oprah's Book Club selection, and 2000 Book of the Year by the Association of Appalachian Writers. His 2007 "Boone: A Biography" was named a finalist for the Los Angeles Book Award.
Among Morgan's story and poetry collections is "The Balm of Gilead Tree and Other Stories." The title story from this collection was included in the 1997 O. Henry Awards anthology and the 2004 "The Strange Attractor: New and Selected Poems." His latest collection of poetry, "October Crossing," was published in September 2009, and hailed by Michael Chitwood of the "News & Observer" as displaying "the rich, grounded work that he does so well…There's music aplenty in Morgan's work, and his portraits not only capture the daily lives of the people of the North Carolina mountains but always manage to get at an even larger canvas, to find the common human story that we all share, no matter our particular location."
Morgan's numerous honors and awards include NEA grants in 1974, 1981, and 1987. He was awarded a Guggenheim Fellowship and a Rockefeller Foundation Fellowship in 1988. Honored again in 1991, he received the James G. Hanes Poetry Prize by the Fellowship of Southern Writers and the North Carolina Literature Award.
Morgan and his wife make their home in Ithaca, N.Y.
Questions? Contact Kathy Daughety, director of public relations, at 252-399-6529 or email: kdaughety@barton.edu.

redpajama_set_name: RedPajamaCommonCrawl


text:
Biografia

Dopo aver studiato canto al conservatorio Umberto Giordano di Foggia si trasferì a Torino, per perfezionarsi con il grande basso torinese Tancredi Pasero.

Nel 1952 vinse un concorso della Rai come cantante e da questa vittoria iniziò la sua carriera sia in radio sia come cantante jazz, inizialmente usando lo pseudonimo Cesare May e formando il complesso Danyl's Boy (in alcune incisioni riportato come i Danil o i Danil's), formato da Danilo Pomini al sax tenore, al violino e ai cori, Egidio Galvani alla tromba e ai cori, Uliano Sesoldi alla tromba, al flauto, alle percussioni e ai cori, Tullio Beber al pianoforte, alla fisarmonica e agli arrangiamenti, Elvio Lazzeri alla batteria (poi sostituito da Gianni Tortorelli), Stelvio Salvi al contrabbasso (poi sostituito da Sergio Petronio), Lino Croce alla chitarra e ai cori.

Nella seconda metà degli anni cinquanta ottenne un contratto con la Hollywood, casa discografica di proprietà della Meazzi specializzata in jazz (per cui, nello stesso periodo, incise i primi dischi Jimmy Fontana); con quest'etichetta pubblicò 12 45 giri, alcuni EP ed un album.

Nel decennio successivo cantò con i gruppi di molti grandi nomi del jazz italiano, tra cui Franco Cerri, Gianni Basso, Franco D'Andrea, Sante Palumbo, esibendosi in molti spettacoli televisivi e radiofonici sia in Italia che all'estero.

Partecipò inoltre come cantante alla realizzazione di alcune colonne sonore come Le ragazze di San Frediano (del 1955, regia di Valerio Zurlini), La diga sul Pacifico (realizzata da Nino Rota nel 1958 per il film di René Clément) o Brucia ragazzo, brucia nel 1969 (regia di Fernando Di Leo) o

Pur esibendosi in giro per il mondo, continuò ad essere legato a Foggia, effettuando spesso delle session nel principale jazz club della sua città, la Taverna del Gufo, e formando, nel 1985, una sua orchestra chiamata appunto La Nuova Orchestra La Taverna del Gufo in onore del locale, con cui si esibirà fino a poco tempo prima della scomparsa proponendo evergreen di Duke Ellington, Irving Berlin, Cole Porter, Count Basie, Woody Herman e molti altri grandi del jazz.

Pur essendo lontano dal suo stile musicale, fu molto legato al cantautore folk pugliese Matteo Salvatore, esibendosi spesso con lui ed aiutandolo anche (nel periodo finale della sua vita, quando era già malato) nell'adempimento delle pratiche burocratiche per il riconoscimento dei suoi diritti previdenziali ed assistenziali.

Ha l'occasione di collaborare anche con nomi della musica leggera come Lucio Dalla e Pino Daniele: quest'ultimo affermerà che la voce di Ninni Maina era paragonabile a quella di Frank Sinatra e dello spettacolo in genere come Renzo Arbore ed Arnaldo Santoro.

Negli anni novanta si esibì anche come voce della Jazz Studio Orchestra di Paolo Lepore, e collaborò con Gegè Telesforo.

A causa di una malattia scomparve nel marzo 2008, assistito dalla moglie, la signora Rosa D'Agostino e dai figli Marco e Luca.

La ventinovesima edizione dello storico Foggia Jazz Festival lo ha ricordato dedicandogli il concerto di apertura, in cui si è esibita anche la Ninni Maina Big Band, così denominata in suo onore.

La Nuova Orchestra La Taverna del Gufo - Formazione

Ninni Maina: voce solista
Gino Sannoner: sax contralto (dal 1985 al 2001)
Salvatore Papa: sax contralto
Nunzio Prencipe: sax tenore
Alberto Mione: sax tenore
Giacinto Barbone: sax baritono
Potito Porrari: tromba, flicorno
Mimmo Marasco: tromba, flicorno
Matteo Mangiacotti: tromba, flicorno
Riccardo Di Corato: tromba(dal 1985 al 1996)
Dino Marasco: trombone
Orlando Rignanese: trombone
Vincenzo Albore: trombone
Michele Mango: trombone (dal 1985 al 1992)
Roberto Rubino: pianoforte
Vincenzo Ciffo: basso
Nicola Jocola: batteria (dal 1985 al 1987)
Lorenzo Sannoner: batteria (dal 1987 in poi)

Discografia parziale

LP

 1989: Classic with swing (Gaja Record); con: Ettore Righello (Piano), Sergio Fanni (Tromba), Marco  Ratti (Contrabbasso), Giancarlo Pillot (Batteria)

CD

 2002: Ninni Maina & La Nuova Orchestra La Taverna del Gufo  (Bravo Records - Alabianca Group)

EP

 1960: At the Moulin Rouge in Geneva (Hollywood, HE 3000; come Cesar May with the Danyl's Boys)

45 giri

 1961: Piscatore 'e Pusilleco/E' bersagliere (Hollywood, H 1065; come I Danil e Cesare Maina)
 1961: Vieni al sodo/Il pullover (Hollywood, H 1066; come I Danil con Cesar Maina)
 1969: Poi ho conosciuto te/T'amo lo stesso (Brio Records, BRN NP 35009; come Cesare Maina)

Note

Bibliografia

 Adriano Mazzoletti - Il jazz in Italia - Ed. EDT, Torino, 2004
 Matteo Salvatore - La luna aggira il mondo e voi dormite. Autobiografia raccontata ad Angelo Cavallo - Stampa Alternativa, 2002
 Maurizio Maiotti - 1944-1963. I complessi musicali italiani. La loro storia attraverso le immagini - Maiotti editore, Milano, 2010
 La Taverna del Gufo con il vocalist Maina, pubblicato su la Repubblica del 24 febbraio 2002 pag. 12
 Il jazz fedele alle origini Usa e le voci della Studio Orchestra, di Alice Viola, pubblicato su la Repubblica del 19 febbraio 2004 pag. 15
 Da Gershwin a Ellington e Miller Lepore rievoca i grandi del jazz, pubblicato su la Repubblica del 14 settembre 2005 pag. 10
 Ciao Ninni, voce del jazz made in Foggia, di Sabrina Palumbo, pubblicato sul numero 3 del 2008 di Gema, pag. 6

Gruppi e musicisti della Puglia

redpajama_set_name: RedPajamaWikipedia


(1) The near-sediment/sea water interface intrusion of a dolerite sill into Santonian strata around 80 Ma in early Campanian times (Well 219/28-2).
(2) A major episode of explosive volcanic eruptions depositing many primary basic ashfall tuffs in the basal early Eocene (both wells).
(3) Minor further volcanic activity continuing throughout most of the early Eocene (both wells) with two slightly more significant eruptions in the late early Eocene and early mid-Eocene respectively.
(4) The intrusion of a dolerite sill into Campanian strata close to 50 Ma in mid-Eocene times (Well 219/28-2).


text:
In case you missed it,
Guest Editorial by Evelyn Pyburn-Originally published in the Yellowstone County News print edition
So if you have missed it, there's more "to-do" about Gov. Steve Bullock's misuse of the state plane than what hits the accounting books. His most regular travel companion is what is raising eyebrows, and who that is dovetails with rumors that have been flying around Helena since before Lt. Gov. Angela McLean resigned.
If travel with the governor to all corners of the country and beyond are any measure, then commerce in Montana should be in very fine shape, because Montana Department of Commerce Director Meg O'Leary has traveled more with the governor than any other member of his department.
O'Leary traveled with Bullock on the state plane 56 times – two and a half times more often than the next frequent flyer, Jason Smith, who flew 20 times with the governor. (All but a paltry $1,500 was at taxpayer expense, of course.)
The Paul McCartney concert in Missoula is one of those joint trips made by the governor and O'Leary, which must have raised as many eyebrows then as it has since. The blatancy of it singles it out as most interesting. While issues of prudent use of taxpayers' dollars abound about flying to such a nearby destination, and about whether the trip was for business (which the governor says it was, even though the time frame would hardly have allowed for a business meeting), but the thing is, O'Leary was not invited. Montana's first lady Lisa Bullock was, according to research conducted by Matthew Monforton, an attorney, former judge and legislator.
Since the governor was allowed a guest (with the expectation of it being Mrs. Bullock), O'Leary was welcomed, but she is the only member of the governor's cabinet who attended. Others, like O'Leary, received no invitation to an event that had no business items on its agenda.
But, who knows, maybe Lisa Bullock is no fan of Paul McCartney.
This was not the only time that O'Leary was the governor's travel companion when one might have expected to see his wife, instead. O'Leary is said to have traveled to Puerto Rico with the governor, and she attended the Kentucky Derby with him (pictures of which are posted on the Internet).
All are situations which add to a rumor that began circulating the halls of the Capital months before the former lieutenant governor resigned. And, as one media person recently said, it is "common knowledge" in Helena, that what was termed as a "poor relationship" between the governor and the former lieutenant governor was rooted in her knowledge of his extramarital affair.
There's lots of grumbling about the lack of media attention to the matter, but the fact is there is no evidence to support the theory of an affair except for the indirect evidence of travel records. The former lieutenant governor is not talking, and except for flying rumors, nor is anyone else.
Some media do seem to be attempting to flush out the story. Of course, one has to suspect that if the governor were of a different political persuasion, the accuracy of the rumor wouldn't be quite so troublesome.
But in all fairness, the media did go after the governor's emails. The ones that they got revealed little, and left unexplained the reason why the lieutenant governor was so abruptly dismissed from the governor's inner circle. That there is no answer to that question adds to the rumor mill.
And also, it was media who asked both candidates during the second debate, this week, if either had had any affairs. That's not a typical debate question, and raising it was certainly an effort of media to tip public awareness to the issue.
And, it is media that is now pushing for more emails, only to learn that the governor destroyed all his emails as Attorney General. Again, why would a forthright person serving in a forthright manner, as a public servant, feel compelled to destroy emails?
If that's not enough grist for the mill, it is certainly true that Lisa Bullock hasn't been on the campaign trail – but then, neither has Meg O'Leary.
Tags: Billings Gov Steve Bullock Greg Gianforte Montana Governor Debate
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text:
Credit: Chris Kitchen/Cornell University
Filmmaker and professor Jeffrey Palmer, center, speaks about his film, "N. Scott Momaday: Words From a Bear," during the College of Arts and Sciences' Arts Unplugged event Oct. 17 in the Schwartz Center for the Performing Arts. Also pictured are Eric Cheyfitz, left, the Ernest I. White Professor of American Studies and Humane Letters in the Department of English; and Gus Palmer Jr., Jeffrey Palmer's father.
PMA professor Jeffrey Palmer releases two short films
By Amaris Janel Henderson |
Jeffrey Palmer, assistant professor in the Department of Performing and Media Arts, has released two new short films that continue his mission to capture untold stories.
"Sounds of Life" follows the story of a Native American teenage girl; "Disqualified Warriors" highlights the impact of the Native warrior tradition on Palmer's father, Gus Palmer Jr. Both works were commissioned over the summer by PBS and The Healthy US Collaborative.
The release comes after the success of Palmer's first full-length film, "N. Scott Momaday: Words From a Bear," which premiered at the 2019 Sundance Film Festival and aired Nov. 18 on PBS' American Masters series.
These new short documentaries provided the filmmaker with a distinct set of challenges and opportunities.
"Both short stories are from the perspectives of everyday people," Palmer said. "N. Scott Momaday is a celebrity in the Native community and a celebrity within the celebrity community. Telling ['Words From a Bear'] in feature form or long form was easier than the short form of these two examples and, furthermore, no one knows who these subjects are. They do now, and that is the aim."
It was important for Palmer that "Sounds of Life" be told from the perspective of a young girl.
"I think we seldom hear stories from women of color in America. KhaLoni had a wonderful story of perseverance and leadership in this community at such a young age," he said. "I hope that through the style of documentary that I made, we provided her with the agency to tell this story through her lens."
"Sounds of Life" had a considerable budget and full film crew, which included cinematographer Shana Hagan and producer Becky Korman, Palmer said. The team traveled to Minnesota to document KhaLoni's journey.
"We all flew into Minneapolis, to the Phillips neighborhood, which is called the American Indian Cultural Corridor," Palmer said. "This is the poorest neighborhood but had so much life and culture."
Palmer realized his father happened to be the perfect subject for "Disqualified Warriors," which focuses on the celebrated Native American tradition of service in the armed forces.
"It is a rite of passage for many Native men and women in the armed forces today," Palmer said, "but there is a certain level of expectation that comes along with this honor, and there is pressure felt by those who decide not to serve or those who have been disqualified due to an illness or other reasons. I wanted to tell a story that illuminated these pressures."
The production of "Disqualified Warriors" was more intimate than that of "Sounds of Life."
"It was a small shoot, with me and my wife, Youngsun, who is also an amazing cinematographer," he said. "We kept the locations small and tight, literally to my father's house in Norman, Oklahoma."
Although the films differed in their production processes, Palmer cites them both as "living examples of Native people in contemporary society."
Amaris Janel Henderson is a communications assistant for the College of Arts and Sciences.
Gillian Smith
gillian.smith@cornell.edu
Podcast describes efforts to 'decolonize the screen'
New Cayuga language class focuses on nature, culture


GeoSonix is a graphical music sequencer and music composition application.
Drum machine and step sequencer that allows you to easily create amazing music loops.
GeoSonix is a graphical music production app for Linux.


Catholic Charities/Catholic Social Services seeks to improve the quality of life for persons of all faiths and cultures by serving their social, emotional, intellectual, physical and spiritual needs. Catholic Charities has been making a difference in the lives of Albertans for over 40 years.
We are an equal opportunity employer serving and employing people of all faiths and cultures since 1961.


A medium duty booster pump, the 550 series are appropriate for applications that include drawing water from a holding tank or shallow water source and pressurizing household plumbing; as well as moving water from one location, over distance or uphill, to another location.
A booster pump is intended to be placed near the water source with a maximum draw on the intake side of 13 feet of lift(derate by 1' for every 1000' above sea level). Despite this capability, Backwoods always recommends a foot valve on the intake pipe when drawing water up from a source, to help keep the intake primed. An optimum configuration would be to supply gravity fed water from an elevated holding tank or cistern to the pump's intake to drive household's pressure tank and plumbing.
Backwoods features a model that includes a standard 5 chamber diaphragm pump head, a permanent magnet motor, quick disconnect inlet/outlet ports, and a built-in pressure switch(cut-in at ~45 psi, shut-off at 60 psi). We include 1/2" barbed intake and outlet port fittings, which are ideal for connection to flexible hose to act as a shock absorber for pump vibrations. Order our P-EZ kit separately if desired. The built-in pressure switch is NOT adjustable. Backwoods has an external Square D pressure switch that can be used instead, to operate the pump at lower, adjustable pressure settings for lower power consumption.
The 550 is a higher volume booster pump, capable of 5.15 gallons per minute at no head/pressure; and a maximum pressure capability of 70 psi(the equivalent of 161' of lift) with a delivery of 3.1 gallons per minute. At half power, the pumps can run for extended periods of at least a couple of hours with no heat concerns; BUT running at higher pressures than ~25 psi should be limited to runs of 25 minutes at a time to avoid overheating. This is a possible issue to consider with very large pressure tanks that take a long time to fill, but easily avoided with a small to medium pressure tank that can be charged to full in 10 minutes or less.
Power draw at no head is 3.0 amps, up to 8.5 amps at 70 psi.
The diaphragm pump head does have parts that will wear out over time and are field serviceable. Backwoods stocks the most commonly needed Lower Housing Assembly that includes the diaphragm and "wobble" bearing, and the Valve Housing Assembly that has the actual valve manifold. Typical service life for these parts are 2 to 5 years. Reduced GPM volumes over time indicate that the diaphragm and valves are suffering wear. This pump is capable of being run dry.


text:
\section{Introduction}\label{sec:1}
In heavy-ion collisions, centrality is an important concept for characterizing the size of the produced fireball. The centrality of an event is often represented by the number of particle production sources $V$ (for example participating nucleons or constituent quarks) in the initial state. These sources are then used to define other important geometry quantities, such as the nuclear overlap function~\cite{Eskola:1988yh,dEnterria:2003xac} for jet quenching studies~\cite{Qin:2015srf,Connors:2017ptx} and eccentricities~\cite{Teaney:2010vd,Alver:2008zza} for collective flow studies.~\cite{Luzum:2013yya,Jia:2014ysa} Since the sources in an event are not directly measurable, a Glauber model is used to calculate $V$ and relate it to the final observed particle multiplicity $N$, with $N=\sum_{i=1}^{V} n_i$ calculated as a sum of the multiplicity for each source $n_i$ sampled independently from a common distribution $p(n)$~\cite{Abelev:2013qoq,Miller:2007ri,Adler:2013aqf}. Due to fluctuations in the particle production, events selected with the same $V$ can have different values of $N$ and vice versa. The fluctuation of sources at fixed multiplicity, often referred to as the ``volume fluctuations'', is an irreducible ``centrality fluctuations'' (CF) or centrality resolution~\cite{Jeon:2003gk,Skokov:2012ds,Luo:2013bmi,Zhou:2018fxx}. The main issue concerning centrality is to understand how the final-state $p(N)$ is related to the source distribution $p(V)$ and particle production for each source $p(n)$.

The centrality or volume of an event is often assumed to be a global concept, long-range in pseudorapidity ($\eta$): a central event should be a central event independent of $\eta$. This assumption can be checked by studying the the correlation of multiplicities between two different $\eta$ windows, also referred to as forward-backward (FB) multiplicity correlation~\cite{Back:2006id,Abelev:2009ag,Bialas:2010zb,Bzdak:2012tp,Jia:2015jga}. In experimental analysis, the observed centrality is usually defined as the particle multiplicity $N_{{a}}$ in a forward pseudorapidity window A, and the measurement is performed using particles with total multiplicity $N_{{b}}$ in a different pseudorapidity window B, usually around mid-rapidity. If the system is boost invariant and same sources are responsible for particles in both subevents (see Fig~\ref{fig:1}(a)), the particle multiplicity distribution in subevent B for fixed $N_{{a}}$ can be expressed as,
\begin{align}\label{eq:1}
p(N_{{b}})_{N_{{a}}}= \sum_{V} p(N_{{b}})_{V}p(V)_{N_{{a}}}.
\end{align}
The distribution $p(V)_{N_{{a}}}$, reflecting the extent of the CF, is controlled by the smearing from $p(n)$ in subevent A. Narrow $p(V)_{N_{{a}}}$ distribution would imply poor centrality resolution in subevent A and vice versa. Eq.~\eqref{eq:1} shows that the CF arising from subevent A directly influences the multiplicity fluctuations in subevent B, and this is the picture assumed by most previous analyses~\cite{Miller:2007ri,Abelev:2013qoq,Adler:2013aqf}.

\begin{figure}[h!]
\begin{center}
\includegraphics[width=1\linewidth]{fig_01.pdf}
\end{center}
\vspace*{-0.5cm}\caption{\label{fig:1} Schematic illustration of the relation between sources (large circles) and final-state particles (small circles) produced in subevent A for centrality determination and subevent B for measurements for two cases: 1) same sources, wounded nucleons $N_{\mathrm{part}}$, for both subevents (panel a), and 2) different sources, forward-going and backward-going wound nucleons $N_{\mathrm{part}}^{\mathrm{F}}$ and $N_{\mathrm{part}}^{\mathrm{B}}$, for the two subevents (panel b). The second scenario is particularly relavent for fixed-target experiments, which often use the forward multiplicity for centrality and mid- or backward rapidity for multiplicity measurements.}\vspace*{-0.3cm}
\end{figure}

Recently, several studies also consider the possibility that the number of sources and their transverse distributions may fluctuate along $\eta$ in a single event. This is because the number of forward-going and backward-going participating nucleons, i.e. $N_{\mathrm{part}}^{\mathrm{F}}$ and $N_{\mathrm{part}}^{\mathrm{B}}$, are not the same in a given event~\cite{Jia:2015jga,Jia:2014ysa}, and they contribute differently in the forward (backward) rapidity.  This forward-backward asymmetry is realized in one of the two ways in dynamical models: 1) In string picture~\cite{Bozek:2015bna,Pang:2015zrq,Shen:2017bsr}, each string originates from a participant nucleon and extends to the opposite direction. Therefore, the number of strings, their lengths and end-points fluctuate in rapidity. 2) In a gluon saturation picture, the sub-nucleonic degree-of-freedoms evolve with rapidity~\cite{Schenke:2016ksl}. In the forward rapidity, the projectile nucleons are dominated by a few large-$x$ partons, while the target nucleons are expected to contribute mainly low-$x$ partons. In this case, the Eq.~\eqref{eq:1} can be revised as,
\begin{align}\label{eq:2}
p(N_{{b}})_{N_{{a}}}= \sum_{V_{{a}},V_{{b}}} p(N_{{b}})_{V_{{b}}}p(V_{{b}})_{V_{{a}}}p(V_{{a}})_{N_{{a}}}.
\end{align}
The fluctuation between the number of sources in the two subevents, denoted by $p(V_{{b}})_{V_{{a}}}$, can weaken the centrality correlation between different rapidities (see Fig~\ref{fig:1}(b)). Such ``centrality decorrelations'' effects is expected to have a strong influence on the correlation of multiplicities between two different $\eta$ windows.

Eqs.~\eqref{eq:1} and \eqref{eq:2} show that information about centrality fluctuations and particle productions is encoded in a set of one-dimensional distributions, which are customarily analyzed via multiplicity cumulants of $p(x)$ ($x=N$, $n$ or $V$): mean $\bar{x}\equiv\lr{x}$, variance $\lr{(x-\bar{x})^2}$,  skewness $\lr{(x-\bar{x})^3}$,... In this paper, we use the reduced form to scale out the overall system size:
\begin{align}\label{eq:3}
k_1\{p(x)\}=\bar{x}, k_2\{p(x)\}=\lr{(x-\bar{x})^2}/\bar{x}, k_3\{p(x)\}=\lr{(x-\bar{x})^3}/\bar{x},....
\end{align}
Previous studies mainly focused on the scaling behavior of the mean multiplicity per source, $N/\lr{V}$~\cite{Adler:2013aqf,Lacey:2016hqy,Loizides:2016djv,Bozek:2016kpf,Acharya:2018hhy,Rohrmoser:2019xis}. Our paper extends these studies to higher-order moments/cumulants of $p(N)$ and $p(V)$, and their dependences on particle production $p(n)$. These cumulants reveal detailed structures of the two-dimensional correlation between $N_{{b}}$ and $N_{{a}}$, and provide constraints on $p(n)$, $p(V_{{a}})$ and $p(V_{{b}})_{V_{{a}}}$.

A good understanding of CF is also important for other areas of heavy-ion physics: for any physics observable $x$ that varies with $V$, its fluctuation $p(x)$ should be sensitive to $p(V)$~\cite{Zhou:2018fxx}. The CF is one of the main background sources in the ongoing search for the critical end point in the QCD phase diagram based on the fluctuations of conserved quantities~\cite{Luo:2017faz,Li:2017via}. The CF also strongly affects the fluctuations of harmonic flow~\cite{Zhou:2018fxx}, and is responsible for the observed sign-change behavior in ultra-central A+A collisions (UCC)~\cite{Aaboud:2019sma}. Understanding the longitudinal fluctuations of sources and the resulting centrality decorrelation effects can also help to describe previous measurements of harmonic flow decorrelations in $\eta$~\cite{Pang:2015zrq,Khachatryan:2015oea,Aaboud:2017tql,Aad:2020gfz}.

In this paper, we study the influence of centrality smearing from particle production (Fig~\ref{fig:1}a)) and centrality decorrelations from the initial sources (Fig~\ref{fig:1}b)) on the event-by-event forward-backward multiplicity fluctuations. The study is based on an independent source Glauber model with particle production tuned to reproduce the ATLAS data~\cite{Aaboud:2019sma}, and the initial number of sources is chosen to be the $V=N_{\mathrm{part}}$ for the scenario shown in Fig~\ref{fig:1}a) and $V_{{a}}\equivN_{\mathrm{part}}^{\mathrm{F}}$ and $V_{{b}}\equivN_{\mathrm{part}}^{\mathrm{B}}$ for the scenario shown in Fig~\ref{fig:1}b). We found that the fluctuations in the UCC region are very sensitive to the source distribution $p(V)$ and particle production $p(n)$, due to the steeply falling distributions (upper boundary effect)~\cite{Skokov:2012ds,Xu:2016qzd,Bzdak:2016jxo}. We also found that the multiplicity dependence of the mean and variance of $p(V)$ have a very simple interpretation in terms of the two types of centrality fluctuations, and they can constrain the longitudinal structure of initial sources and particle production mechanism via comparison between data and model. The structure of the paper is the following. Section~\ref{sec:2} and \ref{sec:3} discuss the expected general behavior of the CF in the presence of multiplicity smearing and centrality decorrelations, respectively. After a brief description of the Glauber model setup in Section~\ref{sec:4}, the results for the two types of CF are given in Section~\ref{sec:5} and \ref{sec:6}, respectively. The summary of the results are given in Section~\ref{sec:7}. The Appendix~\ref{sec:app1} gives a derivation of the formulas used in this paper, and some additional results are given in Appendix~\ref{sec:app2}.

\section{centrality fluctuations due to multiplicity smearing}\label{sec:2}
The CF arising from multiplicity smearing effects (Fig.~\ref{fig:1}a)) is considered in an independent source model framework, by assuming that the total particle multiplicity is a sum of particles from each source $N \equiv \sum_{i=1}^{V} n_i$ sampled from $p(n)$. In this case, one can show that cumulants of $p(N_{{b}})_{V}$ in Eq.~\eqref{eq:1} is related to $p(n)$ by a factor $V$~\cite{Skokov:2012ds}, i.e. $\lr{N_{{b}}}_{V} = V \lr{n}\;, \lr{\delta N_{{b}}^2}_{V} = V \lr{\delta n^2}\;, \lr{\delta N_{{b}}^3}_{V} = V \lr{\delta n^3}\;,....$, and that
\begin{align}\label{eq:4}
k_m\{p(N_{{b}})_{V}\} = k_m\{p(n)\}, m=2,3,4.....
\end{align}
From this, Skokov et al.~\cite{Skokov:2012ds} find the following relations connecting the cumulants for the three distributions in Eq.~\eqref{eq:1}:
\begin{align}\nonumber
\bar{N_{{b}}} &= \barb{n}\lr{V}_{N_{{a}}}\;, ( \bar{N_{{b}}} \equiv  \Kn{1}{b}\;, \barb{n} \equiv  \kn{1}{b} \;, \lr{V}_{N_{{a}}} \equiv  \kn{1}{V|N_{{a}}})\\\nonumber
K_{2,\mathrm{b}} &= k_{2,\mathrm{b}}+\barb{n}k_{2,V|N_{{a}}}\;,\\\nonumber
K_{3,\mathrm{b}} &= k_{3,\mathrm{b}}+3k_{2,\mathrm{b}}\barb{n}k_{2,V|N_{{a}}}+\barb{n}^2k_{3,V|N_{{a}}},\\\label{eq:5}
K_{4,\mathrm{b}} &= k_{4,\mathrm{b}}+(4k_{3,\mathrm{b}}+3k_{2,\mathrm{b}}^2)\barb{n}k_{2,V|N_{{a}}}+6k_{2,\mathrm{b}}\barb{n}^2k_{3,V|N_{{a}}}+\barb{n}^3k_{4,V|N_{{a}}},
\end{align}
where we have used a simpler notation, $k_n\{p(N)\}\rightarrow K_n$, $k_n\{p(N)_{V}\}\rightarrow k_n$ and $k_n\{p(V)\}\rightarrow k_{n,V}$.

The behavior of centrality cumulants $k_{n,V|N_{{a}}}$ for $p(V)_{N_{{a}}}$ in Eq.~\eqref{eq:1} can be understood qualitatively from the correlation between $V$ and $N_{{a}}$ in Fig.~\ref{fig:2}. In the absence of smearing from particle production, i.e. by setting $p(n_{{a}})=\delta(n_{{a}}-\bara{n})$, $V$ and $N_{{a}}$ are related by a linear function $N_{{a}}=V \bara{n}$ (thick solid line). In the presence of smearing, $p(n_{{a}})$ broadens the correlation along the $x$-axis (shaded area). As a result, the $\lr{V}_{N_{{a}}}$ deviates from the linear relation in the UCC region (thick dashed line). This deviation arises because the distribution $p(V)_{N_{{a}}}$ is bounded above by $V^{\mathrm{max}}$ (twice of the atomic number for $N_{\mathrm{part}}$), leading to an asymmetric shape in the UCC region as illustrated by the middle and right insert panels. For even larger $N_{{a}}$ values, the $p(V)_{N_{{a}}}$ becomes narrower and more asymmetric, and eventually converges to $V^{\mathrm{max}}$. For this reason, the cumulants of $p(V)$ as a function of $N_{{a}}$ are strongly modified in the UCC collisions: in addition to the departure of the mean from the linear relation, the variance of $p(V)_{N_{{a}}}$ is expected to approach zero, the skewness of $p(V)_{N_{{a}}}$ becomes negative and then approaches zero, and the kurtosis of $p(V)_{N_{{a}}}$ oscillates from negative to positive then approaches zero. Outside the UCC region, where $p(V)_{N_{{a}}}$ is not constrained by the upper boundary effect (left insert panel), the $\lr{V}_{N_{{a}}}$ is expected to overlap with the solid line, and the higher-order cumulants of $p(V)_{N_{{a}}}$ are determined mainly by $p(n_{{a}})$. In this paper, we focus on the first four cumulants of CF, as their importance can be clearly identified from the shape of $p(V)_{N_{{a}}}$.
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.7\linewidth]{fig_02.pdf}
\end{center}
\caption{\label{fig:2} Schematic illustration of correlation between $V$ and $N_{{a}}$ before (solid line) and after multiplicity smearing (shaded average) which broadens the $N_{{a}}$ distribution at fixed $V$. The average $V$ for fixed $N_{{a}}$, $\lr{V}_{N_{{a}}}$ (red dashed line), deviates from a linear relation in ultra-central collisions. The insert distributions show the $V$ distribution for fixed $N_{{a}}$ in mid-central collisions (left panel), central collisions (middle panel) and ultra-central collisions (right panel).}
\end{figure}

The origin of CF and the behavior of centrality cumulants $k_{n,V|N_{{a}}}$ for $n=2$--4 were studied in detail in Ref.~\cite{Zhou:2018fxx}. In the UCC region, the moments of CF (and therefore $k_{n,V|N_{{a}}}$) are driven mainly by the shape of $p(V)$,
\begin{eqnarray}
\label{eq:6}
\lr{(\deltaV)^k}_{N_{{a}}}\approx \int (\deltaV)^k\frac{1}{\sqrt{2\pi\hat{\sigma}^2V}}  \mathrm{exp}({-\frac{(V-\lr{V}_{\scriptscriptstyle{N_{{a}}}})^2}{2\hat{\sigma}^2V}}) p(V) dV\;.
\end{eqnarray}
where we assume $p(N_{{a}})_{V} \approx \frac{1}{\sqrt{2\pi \hat{\sigma}^2 V}} e^{-\left.(N_{{a}}-\bara{n}V)^2\right/2\hat{\sigma}^2V}$ via the central-limit theorem for large $V$, and $\hat{\sigma}^2=\lr{(\delta n_{{a}})^2}/\bara{n}^2$ is the relative width for $p(n_{{a}})$. In the mid-central region where $p(V)$ is slowly changing, $k_{n,V|N_{{a}}}$ are found to be approximately constant, and the scaled variance of the multiplicity fluctuation in subevent B is sensitive to both $p(n_{{a}})$ and $p(n_{{b}})$,
\begin{align}
\label{eq:7}
\frac{\lr{(\deltaN_{{b}})}^2}{\barb{N}^2} = \frac{1}{\lr{V}_{N_{{a}}}}\left(\frac{\lr{(\deltan_{{b}})^2}}{\barb{n}^2}+\frac{\lr{(\deltan_{{a}})^2}}{\bara{n}^2}\right).
\end{align}
This relation implies that for mid-central collisions and within the independence source picture, the variance of the measured multiplicity fluctuations has the same functional dependence on $p(n_{{a}})$ and $p(n_{{b}})$ in the two subevents.

\section{Centrality decorrelations due to longitudinal fluctuations}\label{sec:3}
Next we consider the CF due to centrality decorrelations as illustrated by Fig.~\ref{fig:1}b). Equation~\eqref{eq:2} can be decomposed into two equations
\begin{align}\label{eq:2a}
p(N_{{b}})_{N_{{a}}}&= \sum_{V_{{b}}} p(N_{{b}})_{V_{{b}}}p(V_{{b}})_{N_{{a}}}\\\label{eq:2b}
p(V_{{b}})_{N_{{a}}}&= \sum_{V_{{a}}} p(V_{{b}})_{V_{{a}}}p(V_{{a}})_{N_{{a}}}.
\end{align}
The cumulants for the first equation are given by Eq.~\eqref{eq:5}. The second equation contains the effects of centrality decorrelations from $p(V_{{b}})_{V_{{a}}}$, which, unlike the $p(N_{{b}})_{V_{{b}}}$, is not described by the independent source picture (i.e $V_{{b}}$ is not an independent sum of $V_{{a}}$ number of sources via some common distribution). Indeed, we find that the cumulants of $p(V_{{b}})_{V_{{a}}}$ are not strictly proportional to $V_{{a}}$. However, by assuming the departure from such proportionality is small, we have derived the relations including the first-order correction (see Appendix~\ref{sec:app1}):
\begin{align}\nonumber
&\bar{V}_{b} = \kn{1}{ab} \lr{V_{{a}}}_{N_{{a}}}\;, \\\nonumber
&k_{2,V_{{b}}} = k_{2,ab}+\frac{k_{1,ab}'^2}{k_{1,ab}} k_{2,V_{{a}}|N_{{a}}}\;, \\\nonumber
&k_{3,V_{{b}}} = k_{3,ab}+3k_{2,ab}'k_{1,ab}'k_{2,V_{{a}}|N_{{a}}}+\frac{k_{1,ab}'^3}{k_{1,ab}}k_{3,V_{{a}}|N_{{a}}}\;,\\\label{eq:8}
&k_{4,V_{{b}}} = k_{4,ab}+(4k_{3,ab}'k_{1,ab}'+3k_{2,ab}'^2k_{1,ab})k_{2,V_{{a}}|N_{{a}}}+6k_{2,ab}'k_{1,ab}'^2k_{3,V_{{a}}|N_{{a}}}+\frac{k_{1,ab}'^4}{k_{1,ab}}k_{4,V_{{a}}|N_{{a}}}\;.
\end{align}
The $k_{n,ab}$ are the reduced cumulants for $p(V_{{b}})_{V_{{a}}}$, while $k_{n,ab}'$ also include the leading-order correction,
\begin{align}\nonumber
&k_{1,ab}' = \frac{\partial (k_{1,ab} V_{{a}})}{\partial V_{{a}} } =  k_{1,ab}+V_{{a}} \frac{\partial k_{1,ab}}{\partial V_{{a}} }\;,\\\label{eq:9}
&k_{n,ab}' = \frac{\partial (k_{1,ab}k_{n,ab} V_{{a}})}{k_{1,ab}\partial V_{{a}} } =  k_{n,ab}+V_{{a}} \frac{\partial (k_{1,ab}k_{n,ab})}{k_{1,ab} \partial V_{{a}} }\;, n\geq 2
\end{align}

The total multiplicity cumulants in subevent B, $\Kn{n}{b}$, can be obtained by replacing the $k_{n,V|N_{{a}}}$ in Eq.~\eqref{eq:5} by Eq.~\eqref{eq:8}. If the centrality resolution of subevent A is very good, $k_{n,V_{{a}}|N_{{a}}}\approx 0$ and $k_{n,V_{{b}}} \approx k_{n,ab}$ for $n>1$, and we recovers the Eq.~\eqref{eq:5}. In this case, the behavior of $\Kn{n}{b}$ is dictated by the FB fluctuations.

\section{Glauber model setup}\label{sec:4}
For quantitative study of the effects of multiplicity smearing and the longitudinal centrality decorrelations, we follow the implementation of our previous work~\cite{Zhou:2018fxx}, which is described briefly here. The number of sources in subevent A and B are chosen to be $N_{\mathrm{part}}^{\mathrm{F}}$ and $N_{\mathrm{part}}^{\mathrm{B}}$ calculated for each event in a standard Glauber model framework~\cite{Miller:2007ri}. The nucleons are assumed to have a hard-core of 0.3 fm in radii, their transverse positions are generated according to the Woods-Saxon distribution as provided by Ref.~\cite{Loizides:2014vua}. A nucleon-nucleon cross-section of $\sigma=68$~mb is used to simulate the collisions at $\mbox{$\sqrt{s_{\mathrm{NN}}}$}=5.02$ TeV. Since the $p(V)$ distribution as well as the correlation between $N_{\mathrm{part}}^{\mathrm{F}}$ and $N_{\mathrm{part}}^{\mathrm{B}}$ change with system size, we studied several nuclei covering a broad range of the $V$: Xe+Xe, Cu+Cu, S+S and O+O collisions, with total number of nucleons $2A=$ 258, 126, 64, 32 respectively.

The particle productions for each source are chosen to follow the negative binomial distribution (NBD):
\begin{eqnarray}
\label{eq:10}
p(n) = \frac{(n+m-1)!}{(m-1)!n!} p^n(1-p)^m,\; p = \frac{\bar{n}}{\bar{n}+m}
\end{eqnarray}
where $\bar{n}$ is the average number of particles in a given subevent. One important quantity is the relative width $\hat{\sigma}$: $\hat{\sigma}^2 \equiv \left.\lr{(\delta n)^2}\right/\bar{n}^2$, which controls the strength of fluctuations for each source.

Table~\ref{tab:1} lists the three NBD parameter sets used to produce particles in subevents A and B, taken directly from Ref.~\cite{Zhou:2018fxx}. The Par0 and Par1 are adjusted to approximately describe the shapes of the experimental distributions of $\mbox{$N_{\mathrm{ch}}^{\mathrm{rec}}$}$ ($|\eta|<2.5$) and $\Sigma E_{\textrm T}$ ($3.2<|\eta|<4.9$) from the ATLAS Collaboration~\cite{Aaboud:2019sma}, while the Par2 corresponds to a case with much larger fluctuations.
\begin{table}[!h]
\centering
\caption{The three parameters sets for the NBD (Eq.~\eqref{eq:10}) used for modeling the particle production in the wounded nucleon model from Ref.~\cite{Zhou:2018fxx}. The corresponding values of reduced cumulants $k_2$, $k_3$ and $k_4$ are also listed.}
\label{tab:1}
\begin{tabular}{|c|c|c|c|c|c|c|c|}\hline
         &   $p$ &   $m$ & mean $k_1=\bar{n}$& RMS/mean $\hat{\sigma}$ & $k_2$ & $k_3$ & $k_4$ \\\hline
Par0     & 0.688 & 3.45  &      7.6     & 0.65 & 3.2   & 17.3 & 139\\\hline
Par1     & 0.831 & 1.55  &      7.6     & 0.88 & 5.9   & 63.8 & 1031\\\hline
Par2     & 0.928 & 0.593 &      7.6     & 1.35 & 13.8  & 368  & 14692\\\hline
\end{tabular}
\end{table}

The calculation of cumulants follows the standard procedure. Each A+A event has two subevents: subevent A for centrality selection and subevent B for the calculation of multiplicity cumulants. The particle multiplicities in these two subevents, $N_{{a}}$ and $N_{{b}}$, are generated independently from 1) the same sources $V_{{a}}=V_{{b}}=N_{\mathrm{part}}$ for the study of multiplicity smearing effect or 2) $V_{{a}}=N_{\mathrm{part}}^{\mathrm{F}}$ and $V_{{b}}=N_{\mathrm{part}}^{\mathrm{B}}$ for the study of longitudinal centrality decorrelations. The generated events are divided into classes according to $N_{{a}}$. The cumulants are first calculated from $V$ and $N_{{b}}$ distributions for events with the same $N_{{a}}$, which are then combined into broader $N_{{a}}$ ranges to reduce the statistical uncertainty. In the following, we first discuss the behavior of cumulants by assuming $V_{{a}}=V_{{b}}=N_{\mathrm{part}}$, we then show results for cumulants calculated by assuming $V_{{a}}=N_{\mathrm{part}}^{\mathrm{F}}$ and $V_{{b}}=N_{\mathrm{part}}^{\mathrm{B}}$.

\section{Results on centrality fluctuations from particle production}\label{sec:5}
We first consider the case when participant nucleons are used as common sources for subevents A and B, $V_{{a}}=V_{{b}}=N_{\mathrm{part}}\equivV$. Figure~\ref{fig:3} illustrates the behavior of the centrality fluctuations by selecting events with fixed $N_{{a}}$ in Pb+Pb collisions. The top three panels show the correlation between $V$ and $N_{{a}}$ generated with Par0, Par1 and Par2 in Table~\ref{tab:1}. The centrality cumulants $k_{n,V}$ for distribution $p(V)_{N_{{a}}}$ are calculated and shown in the bottom panels.
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.72\linewidth]{csmear_t0_s0_p3.pdf}\\
\vspace*{-0.2cm}\includegraphics[width=1\linewidth]{paper_ccum_t0_s0_p3.pdf}
\end{center}
\vspace*{-0.4cm}\caption{\label{fig:3} Top row: the correlation between $V\equivN_{\mathrm{part}}$ and $N_{{a}}$ in Pb+Pb collisions generated with Par0 (left), Par1 (middle) and Par2 (right) parameter sets from Table~\ref{tab:1}. Bottom row: the corresponding cumulants of $V$, $\kn{n}{V}$, calculated for the three parameter sets, with  $n=1$, 2, 3, and 4 from left to right panels. The insert panel shows the ratio of $N_{{a}}/(\bar{n}\lr{V})$, to quantify the deviation of particle per source from $\bar{n}$ (or from the linear relation).}
\end{figure}

The behavior of these cumulants follows the naive expectation of Fig.~\ref{fig:2}. The $k_{1,V}=\lr{V}$ is proportional to $N_{{a}}$, except in UCC region where it turns over. For larger $\hat{\sigma}$ value, this turn-over starts earlier and extends to larger $N_{{a}}$ range, as expected from a poorer centrality resolution. The insert panel shows the ratio $N_{{a}}/(\bar{n}\lr{V})$, to quantify the deviation of particle per source from $\bar{n}$. This ratio should be unity in the absence of centrality smearing effects. The ratio exhibits a suppression in the peripheral region and an enhancement in the central region, as expected from the boundary effects. We notice that in the central region, the ratios for different parameter sets are nearly parallel to each other. We found that the slopes of the ratios are mainly controlled by the shape of the $p(N_{\mathrm{part}})$ distributions for the UCC events. The larger $\hat{\sigma}$ value only shifts the turn-over point to a smaller $N_{{a}}$ value and extends the suppression region to a larger $N_{{a}}$ value, but has little impact on the slope.

The behavior of higher-order centrality cumulants follows what was observed before in Ref.~\cite{Zhou:2018fxx}.  The $k_{n,V}$ are flat in mid-central collisions but show strong variations in central region: the $k_{2,V}$ decreases to 0,  the $k_{3,V}$ decreases to negative minimum values and then approaches 0 from below, while the $k_{4,V}$ decreases to a negative minimum, increases to reach a positive maximum and then decreases to approach 0. The larger smearing associated with Par2 further enhances the magnitudes of $k_{n,V}$ and their oscillating behaviors in the ultra-central region.

The source distributions for events with fixed $N_{{a}}$, $p(V)_{N_{{a}}}$, is then used to produce the distribution of $N_{{b}}$ according to a common distribution $p(n_{{b}})$ for each source. The top panels of Fig.~\ref{fig:4} shows the correlation between $N_{{b}}$ and $N_{{a}}$, obtained by smearing the 2D distributions in Fig.~\ref{fig:3} along the $y$-axis using the Par1 for $p(n_{{b}})$. The cumulants of $p(N_{{b}})_{N_{{a}}}$, $\Kn{n}{b}$, are calculated and shown in the bottom panels. According to Eq.~\eqref{eq:5}, they are expressed as a linear combination of $k_{n,V}$,
\begin{align}\nonumber
\bar{N_{{b}}} &= 7.6\lr{V}\;\\\nonumber
K_{2,\mathrm{b}} &= 5.9+7.6\kn{2}{V}\;,\\\nonumber
K_{3,\mathrm{b}} &= 63.8 +135 \kn{2}{V}+57.8 \kn{3}{V},\\\label{eq:11}
K_{4,\mathrm{b}} &= 1031+2733 \kn{2}{V}+2045\kn{3}{V}+439\kn{4}{V},
\end{align}
\begin{figure}[h!]
\begin{center}
\vspace*{-0.4cm}\includegraphics[width=0.72\linewidth]{csmear_t0_s0_p1.pdf}\\
\includegraphics[width=1\linewidth]{paper_ccum_t0_s0_p1.pdf}
\end{center}
\caption{\label{fig:4} Top row: the correlation between $N_{{b}}$ generated with Par1 and $N_{{a}}$ generated with Par0 (left), Par1 (middle) and Par2 (right) in Pb+Pb collisions. Bottom row: the corresponding cumulants of $N_{{b}}$, i.e. $\Kn{n}{N_{{b}}}$, calculated from the three distributions in the top row, with $n=1$, 2, 3, and 4 from left to right panels. The insert panel show the ratio of $N_{{a}}/\lr{N_{{b}}}$, to quantify the deviation of $N_{{a}}$ dependence of $\lr{N_{{b}}}$ from the linear relation.}
\end{figure}
where the coefficients are determined from the $k_{n}$ for Par1 in Table~\ref{tab:1}. Eq.~\eqref{eq:11} shows that the $\lr{N_{{b}}}$ is related to $\lr{V}$ in Fig.~\ref{fig:3} by a constant scale factor. The $\Kn{2}{b}$ is related to $k_{2,V}$ by a constant offset and a constant scale factor, etc. In general, one could isolate the $\kn{n}{V}$ iteratively order-by-order: $\kn{2}{V}$ can be extracted from $K_{2,\mathrm{b}}$ by identifying and subtracting a constant, which then can be subtracted from $K_{3,\mathrm{b}}$ to isolate the $\kn{3}{V}$, etc. Note that this is only true in the independent source model framework and considering only multiplicity smearing effects.

\begin{figure}[h!]
\begin{center}
\includegraphics[width=1\linewidth]{paper_csys_t0_p1_p3_a.pdf}\\
\includegraphics[width=1\linewidth]{paper_csys_t0_p1_p3_ascal.pdf}
\end{center}
\vspace*{-0.4cm}\caption{\label{fig:5} The distribution of sources $p(V)$ (left panel), its $\lr{V}$ vs $N_{{a}}$ (2nd panel), ratio $N_{{a}}/(\bar{n} \lr{V})$ vs $N_{{a}}$ (3rd panel) and  ratio $N_{{a}}/(\bar{n} \lr{V})$ vs $\lr{V}$ (right panel) for different collision systems. The bottom panels show the same distributions but normalized by the knee, defined as $2A$ for left and right panels, and $2A\bar{n}$ for the middle two panels. The $N_{{a}}$ is generated with Par1 parameter set in Table~\ref{tab:1}.}
\end{figure}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.8\linewidth]{paper_csys_t0_p1_p3_b.pdf}\\
\includegraphics[width=0.8\linewidth]{paper_csys_t0_p1_p3_bscal.pdf}
\end{center}
\vspace*{-0.4cm}\caption{\label{fig:6} The centrality cumulants, $\kn{2}{V}$ (left panel), $\kn{3}{V}$ (middle panel),  and $\kn{4}{V}$ (right panel) as a function $N_{{a}}$ (top row) or as a function of $N_{{a}}/N_{knee}$ (bottom row) for various collision systems. The $N_{{a}}$ is generated with Par1 parameter set in Table~\ref{tab:1}.}
\end{figure}
The centrality fluctuations are sensitive to the shape of $p(V\equivN_{\mathrm{part}})$, which changes with the size of the collision system. The top-left panel of Fig.~\ref{fig:5} shows the distribution $p(V)$ from five collision systems in central collision region. The same distribution is replotted in the bottom-left panel, but the $x$-axes have been rescaled by $V^{\mathrm{max}}=2A$. The smaller system shows a broader tail in the $V$ distributions.  For system-size dependence studies, the centrality cumulants $k_{n,V}$ are calculated with Par1 from Table~\ref{tab:1}. The results are presented both as a function of $N_{{a}}$ and as a function of $N_{{a}}/N_{\textrm{knee}}$, where the knee is defined as the average multiplicity for maximum $V=2A$ nucleons, $N_{\textrm{knee}}=2A\bar{n}$. The 2nd column of Fig.~\ref{fig:5} show the $k_{1,V}=\lr{V}$ as a function of $N_{{a}}$ and $N_{{a}}/N_{\textrm{knee}}$. The $\lr{V}$ increases almost linearly with $N_{{a}}$, and flattens out close to $N_{\textrm{knee}}$. To quantify the non-linear behavior in the UCC region, we calculate the ratios $N_{{a}}/(\bara{n}\lr{V})$ and present them in the third column. In the very small $N_{{a}}$ region,  the ratios are below unity and agree with each other, reflecting the fact that the $p(V)$ distributions have very similar shape in the small $V$ region. Towards the large $N_{{a}}$ region, the ratios separate from each other and increase to above unity with the smaller system showing a larger deviation from unity. The third bottom panel shows the ratios as a function of $N_{{a}}/N_{\textrm{knee}}$, where the increase in UCC is linear for all systems. For a smaller system, the rate of increase is smaller but over a broader range in $N_{{a}}/N_{\textrm{knee}}$, consistent with the smoother fall-off for smaller system in the central region shown of the bottom-left panel.

Previous studies on the particle production often focused on the scaling behavior of the particle production per source, i.e. $N/\lr{V}$, with $V$ defined as $N_{\mathrm{part}}$ or the number of quark participants. They found that the sources based on the quark participant number has a better scaling behavior than that based on the nucleon participant number from $pp$, $\mbox{$p$+A}$ to A+A systems~\cite{Adler:2013aqf,Lacey:2016hqy,Loizides:2016djv,Bozek:2016kpf,Acharya:2018hhy}. However, a detailed study by ALICE Collaboration showed that both types sources show a sharp increase of $N/\lr{V}$ vs $\lr{V}$ in the UCC region~\cite{Acharya:2018hhy}. To perform a similar check, the right column of Fig.~\ref{fig:5} shows $N_{{a}}/(\bara{n}\lr{V})$ as a function of $\lr{V}$ and $\lr{V}/2A$, where $\lr{V}$ is obtained by mapping from $N_{{a}}$ using the data in the top panel in the second column. The linear increase in the third column now appears as a sharp increase in the UCC region, similar to the data. The increase is stronger and affects most of the centrality range in a small system, consistent with the experimental observation.

On the other hand, the experimental observable is defined as $N_{{b}}/\lr{V}$ as appose to $N_{{a}}/\lr{V}$ in our study. In the independent source model framework, $N_{{b}}/\lr{V}$ would always equal to $\bar{n}$ by construction. Therefore, one natural explanation would be that there are strong correlations between the particle production in subevents A and B, i.e. $n_{{a}}$ and $n_{{b}}$ are strongly correlated. In an extreme case of $n_{{a}}=n_{{b}}$, the $N_{{b}}=N_{{a}}$ would be valid for each event, and $N_{{b}}/\lr{V}$ would also show an increase in the UCC region, we leave this point to a future investigation.

Figure~\ref{fig:6} shows higher-order $k_{n,V}$ as a function of $N_{{a}}$ (top row) or $N_{{a}}/N_{\textrm{knee}}$ (bottom row). The $k_{n,V}$ have the same constant values in mid-central collisions, but deviates from each other towards more peripheral or more central region where the lower and upper boundary effects from the $p(V)$ distribution are important. Such deviation appears over a larger fraction of the $N_{{a}}$ range for smaller collision systems. In the central region, the magnitudes of the $k_{3,V}$ and $k_{4,V}$ are smaller for smaller collision systems. At the same time, the widths of the maxima region are larger in terms of $N_{{a}}/N_{\textrm{knee}}$, implying that the centrality fluctuations influences a larger fraction of the centrality region. This can be understood from the bottom-left panel in Fig.~\ref{fig:5} , which shows that the decrease in the central region is smoother in smaller collision systems.

\section{Results on forward-backward centrality decorrelations}\label{sec:6}

To study the effects of centrality decorrelations, we consider $V_{a}=N_{\mathrm{part}}^{\mathrm{F}}$ and $V_{b}=N_{\mathrm{part}}^{\mathrm{B}}$ as the sources for particles in subevent A and B, respectively. According to Eq.~\eqref{eq:8}, the cumulants of $p(V_b)$ are expressed in terms of cumulants $k_{n,ab}$ and $k_{n,ab}'$ describing $p(V_{{b}})_{V_{{a}}}$, as well as $k_{n,V_{{a}}}$ describing the fluctuation of $V_{a}$. In the following, we first discuss the behaviors of $k_{n,V_{{a}}}$, $k_{n,ab}$ and $k_{n,ab}'$ and then show quantitatively how well $k_{n,V_{{b}}}$ are described by Eq.~\eqref{eq:8}.

Figure~\ref{fig:7} shows the centrality cumulants $k_{n,V_{{a}}}$ for Pb+Pb and O+O collisions. The magnitudes of $k_{n,V_{{a}}}$ depend on the centrality resolution of subevent A, and are calculated with Par0--Par2 as a function of $N_{{a}}$. The results for Pb+Pb are similar to those presented in the bottom row of Fig.~\ref{fig:3}. The only difference is that the $N_{\mathrm{part}}^{\mathrm{F}}$ instead of $N_{\mathrm{part}}$ is used as sources in this figure, therefore the maximum range of $N_{{a}}$ reaches only about half of that in Fig.~\ref{fig:3}. The results for O+O are much more affected by the boundary effects, such that no plateau is observed for the second- and higher-order cumulants.

\begin{figure}[h!]
\begin{center}
\includegraphics[width=1\linewidth]{paper_ccum_t2_s0_p3.pdf}\\
\includegraphics[width=1\linewidth]{paper_ccum_t2_s4_p3.pdf}
\end{center}
\vspace*{-0.5cm}\caption{\label{fig:7} The centrality cumulants for $p(V_{{a}})$ with $V_{{a}}\equivN_{\mathrm{part}}^{\mathrm{F}}$, $k_{1,V_{{a}}}=\lr{V_{{a}}}$ (left column),  $k_{2,V_{{a}}}$ (2nd column),  $k_{3,V_{{a}}}$ (3rd column), $k_{4,V_{{a}}}$ (right column) as a function of $N_{{a}}$ from Pb+Pb system (top row) and O+O system (bottom row). The insert panels show the ratios $N_{{a}}/(\bar{n} \lr{V_{{a}}})$ to quantify the deviation of $N_{{a}}$ dependence of $\lr{V_{{a}}}$ from the linear relations.}
\end{figure}

Next we discuss the behavior of $k_{n,ab}$ and $k_{n,ab}'$ describing $p(V_{{b}})_{V_{{a}}}$. The latter is rather spread out as shown in the left panels of Fig.~\ref{fig:8} for Pb+Pb and O+O collisions. In principle, $p(V_{{b}})_{V_{{a}}}$ is not necessarily described by independent source picture, i.e. the value of $V_{{b}}$ can not be treated as a sum of independent contributions from $V_{{a}}$ number of sources. In practice, the deviation from the independent source picture is small and the cumulants of $p(V_{{b}})_{V_{{a}}}$ are approximately proportional to $V_{{a}}$.  Nevertheless, we need to use Eq.~\eqref{eq:9} to calculate $k_{n,ab}'$, which includes the first-order correction to account for the residual dependence of $k_{n,ab}$ on $V_{{a}}$. Such corrections can be quite important if the centrality resolution of subevent A is poor (i.e. $\kn{n}{V_{{a}}}$ are large).

The right panels of Fig.~\ref{fig:8} show $k_{n,ab}$ and $k_{n,ab}'$ as a function of $V_{{a}}$. The first-order cumulants $k_{1,ab}$ and $k_{1,ab}'$ are close to unity in mid-central collisions, where $\lr{V_{{b}}}_{V_{{a}}}\approx V_{{a}}$. The rather sharp decrease of $k_{n,ab}'$ in central region is due to $V_{{a}} \frac{\partial k_{1,ab}}{\partial V_{{a}} }$ in Eq.~\eqref{eq:9}, which are quite large in the central region. Overall the influence of $k_{1,ab}$ and $k_{1,ab}'$ to the higher-order $\kn{n}{V_{{b}}}$ should be small except in the very central and peripheral collisions.

\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.9\linewidth]{paper_cfb_s0.pdf}\\
\includegraphics[width=0.9\linewidth]{paper_cfb_s4.pdf}
\end{center}
\vspace*{-0.5cm}\caption{\label{fig:8} The 2D correlation between $V_{{a}}=N_{\mathrm{part}}^{\mathrm{F}}$ and $V_{{b}}=N_{\mathrm{part}}^{\mathrm{B}}$ (left column) and corresponding $k_{n,ab}$ and $k_{n,ab}'$ for $n=1$ (2nd column), $n=2$ (3rd column),$n=3$ (4th column) and $n=4$ (right column) in Pb+Pb system (top row) and O+O system (bottom row).}
\end{figure}

The third column of Fig.~\ref{fig:8} shows that the scaled variance $k_{2,ab}$ increases sharply and then decreases gradually for the remaining $V_{{a}}$ range. This behavior can be understood from the leaf-like shape of the 2D correlation between $V_{{b}}$ and $V_{{a}}$: although the variance of $V_{{b}}$ is small towards small and large $V_{{a}}$ region, the scaled variance of $V_{{b}}$ (i.e. normalized by $\lr{V_{{b}}}$) is large in small $V_{{a}}$ region and decreases to nearly zero at largest $V_{{a}}$. The higher-order cumulants $k_{3,ab}$ and  $k_{4,ab}$ have more complex behaviors. In the small $V_{{a}}$ region,  $k_{n,ab}$ are  positive since $V_{{b}}>0$. At large $V_{{a}}$, the fluctuations of $V_{{b}}$ is bounded by $V_{{b}}\leq A$, leading to a negative $k_{n,ab}$. Note that the sign-change of cumulants occurs in mid-central region, around $V_{{a}}\approx 110$ for $k_{3,ab}$ and $V_{{a}}\approx 60$ for $k_{4,ab}$ for Pb+Pb. This behavior is very different from the influence of pure multiplicity fluctuations in Section~\ref{sec:5}, where the sign-change happens only in the UCC region. For higher-order cumulants, we note that the value of $k_{n,ab}'$ are very different from $k_{n,ab}$ over the full range of $V_{{a}}$ due to $V_{{a}} \frac{\partial (k_{1,ab}k_{n,ab})}{k_{1,ab} \partial V_{{a}} }$ in Eq.~\eqref{eq:9}. This implies that the deviation from the independent source assumption has a stronger impact for the third and higher-order cumulants.

In the smaller O+O system, even the $k_{1,ab}$ and $k_{1,ab}'$ already show a quite sizable deviation from unity. In general, the higher-order cumulants $k_{n,ab}$ and $k_{n,ab}'$ have smoother variations but over a much broader $V_{{a}}$ range.

From $k_{n,V_{{a}}}$ in Fig.~\ref{fig:7} and $k_{n,ab}$ and $k_{n,ab}'$ in Fig.~\ref{fig:8}, we calculate the $k_{n,V_{{b}}}$ via Eq.~\eqref{eq:8} and compare with the results from full calculation. This comparison is shown in Fig.~\ref{fig:9} for Pb+Pb and O+O collisions, together with the breakdown of the contributions from its individual components. The behavior of cumulants and the comparison can be summarized as follows:
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.8\linewidth]{ccumfb_s0_p1A.pdf}\\
\includegraphics[width=0.8\linewidth]{ccumfb_s4_p1A.pdf}
\end{center}
\vspace*{-0.5cm}
\caption{\label{fig:9} The centrality cumulants $k_{n,V_{{b}}}$ in subevent B as a function of $N_{{a}}$, obtained from full calculation (thick solid line) or calculation via Eq.\eqref{eq:11} (thick dashed lines) and its various components (thin solid lines) for $n=1$ (the first column), $n=2$ (2nd column), $n=3$ (3rd column) and $n=4$ (right column) in the Pb+Pb system (top row) and the O+O system (bottom row).}
\end{figure}

\begin{enumerate}
\item The $\lr{V_{{b}}}_{V_{{a}}}$ in the left panels agrees very well with Eq.~\eqref{eq:8}. In Pb+Pb collisions, the $\lr{V_{{b}}}_{V_{{a}}}$ is nearly identical to $\lr{V_{{a}}}$, but significant deviation is observed in O+O collisions, which can be fully explained by the behavior of $k_{1,ab}$ shown in Fig.~\ref{fig:8}. The flattening behavior of $\lr{V_{{b}}}_{V_{{a}}}$ in central collisions is expected to be dominated by pure multiplicity smearing effects in subevent A, and the centrality decorrelations is important only for small collision systems.

\item The results of $k_{2,V_{{b}}}$ are shown in the second column. The $N_{{a}}$ dependence of $k_{2,V_{{b}}}$ in Pb+Pb collisions is described nearly perfectly by Eq.~\eqref{eq:8}, while a small deviation is observed in O+O collisions around the maximum of $k_{2,V_{{b}}}$. In Pb+Pb collisions, the decrease of $k_{2,V_{{b}}}$ as a function of $N_{{a}}$ is mainly driven by $\kn{2}{ab}$, while $k_{2,V_{{a}}}$ mainly contributes an offset in mid-central region and a sharp decrease in the UCC region. In O+O collisions, these two components have more similar shapes, although the $\kn{2}{ab}$ term dominates in the central region and the most peripheral region.

\item The results of $k_{3,V_{{b}}}$ are shown in the third column. In Pb+Pb collisions, the description by Eq.~\eqref{eq:8} is also very good, except that it slightly underestimates the magnitude in the most central collisions. In O+O collisions, Eq.~\eqref{eq:8} underestimates the magnitude of $k_{3,V_{{b}}}$ in the central region, and around its maximum in the peripheral region. Looking at the three individual components of Eq.~\eqref{eq:8}, the genuine FB decorrelation term $\kn{3}{ab}$ dominates only in the peripheral region, but its contribution is not as important as the second term associated with $k_{2,V_{{a}}|N_{{a}}}$. The last term associated with $k_{3,V_{{a}}|N_{{a}}}$ is nearly a constant, and it has little influence on the shape of $k_{3,V_{{b}}}$, except in central collisions. These behaviors also imply that $\kn{3}{ab}$ can only be reliably extracted if $k_{3,V_{{a}}|N_{{a}}}$ are small; otherwise, one has to first measure $\kn{2}{ab}'$ and $\kn{1}{ab}'$ using the information in the first two columns.

\item The behavior of $k_{4,V_{{b}}}$ shown in the right column are much more complex. In Pb+Pb collisions, the description of $k_{4,V_{{b}}}$ by Eq.~\eqref{eq:8} is only good in peripheral and the most central collisions. In O+O collisions, Eq.~\eqref{eq:8} has poor description over most of the region for the Par1 parameter set. When the Par0 parameter set is used, the agreement is much better in Pb+Pb collisions, but is still relatively poor in O+O collisions. Looking at the contributions of individual terms, the intrinsic kurtosis term $k_{4,ab}$ from FB fluctuations is important only in the very peripheral and central regions. The mixing terms between lower-order $k_{n,ab}$ and $k_{n,V_{{a}}}$ dominate in the mid-central collisions and are also important in the other centrality range.
\end{enumerate}

Figure~\ref{fig:10} summarizes the results in the five collision systems for Par1 parameter set. The results of $k_{n,V_{{b}}}$ in the bottom row are related to $k_{n,V_{{a}}}$ in the top row and $k_{n,ab}$ and $k_{n,ab}'$ in the middle row via Eq.~\eqref{eq:8}. For the first-order cumulants shown in the left column, the behavior of $\lr{V_{{b}}}_{V_{{a}}}$ largely resembles those of $\lr{V_{{a}}}$, except for very small systems where the $k_{1,ab}$ show a significant deviation from one. For all higher-order cumulants, the values of $k_{n,V_{{a}}}$ are much smaller than $k_{n,ab}$.  In fact, in the absence of the centrality resolution effect in subevent A, $k_{n,V_{{a}}}$ vanish and $k_{n,V_{{b}}}$ approach $k_{n,ab}$. We find that if Par2 is chosen for multiplicity smearing in subevent A, the $k_{n,V_{{a}}}$ are much larger and dominate the behavior of $k_{n,V_{{b}}}$. The shapes of $k_{n,ab}$ and $k_{n,ab}'$ are similar between different collision systems, but the magnitudes are smaller for smaller collision systems. This leads to a similar system-size ordering for the values of $k_{n,V_{{b}}}$.
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.8\linewidth]{paper_csys_t2_p1_p3.pdf}\\
\includegraphics[width=0.8\linewidth]{paper_csysvol_t1_comb.pdf}\\
\includegraphics[width=0.8\linewidth]{paper_csys_t1_p1_p3.pdf}
\end{center}
\vspace*{-0.5cm}
\caption{\label{fig:10}  The centrality cumulants in subevent A $k_{n,V_{{a}}}$ as a function of $N_{{a}}$ (top row), the cumulants for forward-backward source correlation, $k_{n,ab}$ and  $k_{n,ab}'$, as a function of $V_{{a}}$ (middle row), and the centrality cumulants in subevent B $k_{n,V_{{b}}}$ as a function of $N_{{a}}$ (bottom row) for various collision systems, for $n=1$ (first column), $n=2$ (2nd column), $n=3$ (3rd column) and $n=4$ (right column).}
\end{figure}

Given the fact that $k_{1,ab}$ and $k_{1,ab}'$ are close to one, the features of $k_{2,V_{{b}}}$ can be used to separate $k_{2,ab}$ and $k_{2,V_{{a}}}$ via Eq.~\eqref{eq:8}: the increase and decrease from peripheral to mid-central collisions mainly reflects the contribution of $k_{2,ab}$, while the sharp decrease and flattening out behavior in central region are dominated by the $k_{2,V_{{a}}}$. In contrast, we find that $k_{3,V_{{b}}}$ and $k_{4,V_{{b}}}$ are much more sensitive to mixing terms between $k_{n,ab}$, $k_{n,ab}'$ and $k_{n,V_{{a}}}$, especially in mid-central and central regions, similar to Fig.~\ref{fig:9}. Separate these different components would be a rather challenging task.

In the final step, the centrality cumulants $k_{n,V_{{b}}}$ shown in Figs.~\ref{fig:9} and ~\ref{fig:10} are used to obtain the full results of multiplicity cumulants including the smearing effects in subevent B via Eq.~\eqref{eq:5} or Eq.~\eqref{eq:11} for Par1.  Examples can be found in Sec.~\ref{sec:app2}.

\section{Summary and discussion}\label{sec:7}
In heavy ion collisions, the centrality or the volume of the fireball, characterized by the number of sources $V$ in the initial state geometry, is not fixed but fluctuates for events with the same final-state particle multiplicity $N$. This so-called centrality or volume fluctuations (CF) can arise from either 1) fluctuations in the particle production process which smears the mapping between $N$ and $V$ or 2) longitudinal fluctuations of $V$ within the same event which decorrelates the $N$ between different $\eta$ ranges. In this paper, we propose to study CF using the correlation of multiplicities $N_{{b}}$ and $N_{{a}}$ in two subevents separated in pseudorapidity. This two-dimensional correlation are analyzed via cumulants of the conditional probability distribution $p(N_{{b}})_{N_{{a}}}$ as a function of $N_{{a}}$. The contributions from the two types of CFs can be identified from features in the $N_{{a}}$ dependence of these cumulants.

For a quantitative study of the CF, a standard Glauber model based on an independent source picture is used: the Glauber model is used to produce the $V$ for each event, and the final-state particle multiplicity in each event is then calculated as a sum of particles from each source $N=\sum_{i=1}^{V} n_i$ with $n_i$ sampled independently from a common $p(n)$. For the study on the effects of multiplicity smearings, the sources for subevents A and B are chosen as $V_{{a}}=V_{{b}}=N_{\mathrm{part}}$. For the study on the effects of centrality decorrelations, they are chosen as $V_{{a}}=N_{\mathrm{part}}^{\mathrm{F}}$ and $V_{{b}}=N_{\mathrm{part}}^{\mathrm{B}}$. The centrality selection is based on $N_{{a}}$ for both cases, i.e. cumulants are calculated upto fourth-order:  mean $\lr{V}$, scaled variance $k_{2,V}=\lr{(\deltaV)^2}/\lr{V}$, skewness $k_{3,V}=\lr{(\deltaV)^3}/\lr{V}$ and kurtosis $k_{4,V}=(\lr{(\deltaV^4)}-3\lr{(\deltaV^2)}^{_2})/\lr{V}$.

The $\lr{V}$ is observed to be linearly proportional to $N_{{a}}$, except in ultra-central collisions (UCC) where the increase slows down as $N_{{a}}$ approaches the upper bound. This means that $N_{{a}}/\lr{V}$ exhibits a sharp increase in the UCC region similar to what is observed in the experimental data~\cite{Acharya:2018hhy,Aaboud:2019sma}. We also verified that (not shown) this linearity is not affected much by the centrality decorrelations considered in this paper, except in smaller systems where the correlation between $V_{{a}}$ and $V_{{b}}$ has significant deviations from diagonal. Such behavior in the UCC is very sensitive to the properties of $p(V)$ and $p(n)$.

When including only effects of multiplicity smearings, the scaled variance $k_{2,V}$ is nearly constant in mid-central collisions, but decreases to zero in UCC events as $N_{{a}}$ approaches the upper bound. In the presence of centrality decorrelations, the $k_{2,V}$ also exhibits a linear decrease in the mid-central collisions. The rate of decrease should be a robust measure of the extent of longitudinal fluctuations in the particle production sources.

The $N_{{a}}$ dependence of higher-order centrality cumulants are more complex. In the presence of centrality decorrelations, they receive significant contributions from several mixing terms related to the lower-order cumulants, which are also much larger in smaller systems. Furthermore, additional correction terms need to be included to account for the fact that the cumulants for $p(V_{{b}})_{V_{{a}}}$ is not proportional to $V_{{a}}$ except for the first order. Due to these reasons, the $\lr{V}$ and $k_{2,V}$ are considered most valuable observables to probe the nature of $p(V)$ and $p(n)$.

From the centrality cumulants $k_{n,V}$, we calculated the cumulants for final-state multiplicity $N_{{b}}$ in subevent B, $K_{n,\mathrm{b}}$ via Eq.~\eqref{eq:5}. We find that the flattening behavior of $\lr{N_{{b}}}$ as a function of $N_{{a}}$ in UCC remains. Experimentally, one can calculate both $\lr{N_{{b}}} (N_{{a}})$ and $\lr{N_{{a}}} (N_{{b}})$ from $p(N_{{b}},N_{{a}})$ to quantify the relative centrality resolution of the two subevents. If $\lr{N_{{b}}} (N_{{a}})$ is more diagonal than $\lr{N_{{a}}} (N_{{b}})$, it would imply that $N_{{a}}$ has a better centrality resolution on $V$ than $N_{{b}}$ (a similar conclusion was reached from ATLAS data~\cite{Aaboud:2019sma}). For the scaled variance $K_{2,\mathrm{b}}$, we find that most of the features of $k_{2,V}$ has been preserved, therefore experimentally measured scaled variance in subevent B for events selected in subevent A can also be used to extract information about the centrality decorrelations.

The centrality decorrelations considered in this paper is rather simplistic. This can be improved by considering the partonic degree of freedom in the nucleons and assuming the quark participant number $n_{qp}$ to be a number that vary with $\eta$. In addition, one should consider situation used by most collider experiments, where the subevent A for centrality is defined in both forward and backward rapidity, and subevent B is defined at mid-rapidity. In this case, although $V_{{a}}$ and $V_{{b}}$ are largely correlated with $N_{\mathrm{part}}$, they should still be decorrelated due to difference in $n_{qp}$. We leave this to future investigations.

In summary, we have studied the centrality fluctuations in terms of the number of initial sources $V$ using the correlation of the final-state multiplicity between two subevents $N_{{a}}$ and $N_{{b}}$. The sources and final multiplicity are generated with a Glauber model within an independent source picture. This correlation is analyzed in terms of cumulants for multiplicity distribution in one subevent ($N_{{b}}$) for events selected in another subevent with a fixed multiplicity ($N_{{a}}$). The $N_{{a}}$ dependence of the cumulants are affected by both pure multiplicity smearing in the particle production as well as the decorrelation between the sources in the two subevents. We find that the behavior of cumulants in ultra-central collisions are very sensitive to the particle production for each source $p(n)$ and $p(V)$ due to the steeply falling $p(V)$ distribution. The FB centrality decorrelations have very little impact on the mean multiplicity but leads to an decrease of scaled variance $\lr{(\deltaV_{{b}})^2}/\lr{V_{{b}}}$ and $\lr{(\deltaN_{{b}})^2}/\lr{N_{{b}}}$ as a function of $N_{{a}}$. These features can be used to constrain the particle production mechanism as well as the longitudinal fluctuations of the initial-state sources.

This research is supported by National Science Foundation under grant number PHY-1613294 and PHY-1913138, and the National Natural Science Foundation of China under grant number 11922514.

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Loose Leaf for General, Organic, and Biochemistry
Kim Woodrum, Katherine Denniston, Robert Caret, Joseph Topping - 2013 - 1824 pages
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The eighth edition of General, Organic, and Biochemistry is designed to help undergraduate health-related majors, and students of all other majors, understand key concepts and appreciate the significant connections between chemistry, health, disease, and the treatment of disease. This text continues... to strike a balance between theoretical and practical chemistry, while emphasizing material that is unique to health-related studies. The text has been written at a level intended for students whose professional goals do not include a mastery of chemistry, but for whom an understanding of the principles and practice of chemistry is a necessity. Designed for the one- or two-semester course, this text has an easy-to-follow problem-solving pedagogy, vivid illustrations, and engaging applications.
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Buying your first synth: What to consider and where to get...
Make Music I by Scott Wilson I 04.02.17
Buying your first synth: What to consider and where to get the best deals
Looking for a first synth to compose music or just make some noise? Scott Wilson tells you everything you need to know and picks seven of the best models for novice synthesists.
There's never been a better time to buy a first synth. Synthesizers are smaller, more affordable and more inviting to beginners than ever before, and whether you want to build your own or phase out Ableton Live's software instruments, it's possible to buy a synth that you can make music with for not a lot of money.
However, if you're just starting out, it's easy to be confused. Some synths for beginners don't even look like synths in the traditional sense, while others may have more features than you need, especially if you've already experimented with apps or software. The most important consideration for novice synthesists: cheap doesn't necessarily mean easy to use.
Don't pay anything over $200 if you're a total novice
It's tempting to blow all your money on a high-end synth in the hopes you won't ever have to buy another one, but this could turn out to be a false economy. The more expensive the synth, the more functions it's likely to have, and if you're a complete beginner you'll probably find yourself spending hours browsing menus instead of making music. Choose a cheap, simple synth in the $50 to $200 bracket to learn with and you'll have a better idea of where to go next.
If you're already experienced with software synths but want to start working outside the box, there's still not much point in paying more than $500. Roland, Korg and Arturia have made huge inroads creating affordable gear over the past few years, and a lot of it is stuff you'll be happy to keep around, even if you upgrade to a more expensive model.
Consider buying a synth with a sequencer
If you're buying a first synthesizer, it's possible that your keyboard ability will be limited to non-existent. If this is the case, you're going to want to make sure your synth has a built-in sequencer of some kind. This will allow you to write a melody or a bassline, note by note, into the on-board memory, leaving your hands free to tweak stuff like cutoff and resonance (vital if you want to create an acid-like sound) or add effects while your pattern loops in the background.
Make sure it's not too big
Gigantic synths look cool, but if you don't have easy access to it then it'll probably get forgotten about. If you're starting out you're likely to have very limited studio space: buy a compact synth, and you can have it sitting on a desk and ready to use all the time, rather than having to set it up and pack it away. If it's small enough to throw in a bag, you'll be more likely to make music outside your home as well.
Consider buying a model with a built-in speaker
If you're just curious abut synths and want something to noodle on, you probably won't have a mixer, soundcard or monitors to route your synth's audio through. If this is the case, consider buying a synth with its own speaker. It won't sound great, but it's more liberating than using headphones. Just make sure to use headphones if you're in public though – nobody wants to hear your techno bassline on the train.
Analog or digital?
Some people believe analog synths sound "warmer" than digital, and some can't tell the difference. For a first synth, the way the synth sounds isn't that important. However, choosing between analog and digital is still an important consideration, because the type of synthesis employed by the instrument might have a bearing on whether you make your own sounds with it or you just stick with the presets.
If you're starting out, subtractive synthesis – the type commonly associated with analog synths – is arguably the easiest and most logical type to learn. Digital FM synthesis on the other hand, is often confusing for even the most experienced of musicians. It's also possible to get digital synths with analog modelling technology, but the same advice applies: buy a subtractive synth that has clear controls and labels for the oscillators, envelopes and filters and you'll pick up the basics of synthesis in no time.
7 of the best synths for beginners
Best for learning synthesis: Korg littleBits
Korg's littleBits synth kit is the synth to go for if you're fascinated by all the knobs and switches and want to know more. Spawned out of littleBits' home science lab for kids and grown-ups, the company's music-focused collaboration with Korg consists of a box of tiny modules that cover all the components of a basic synthesizer: oscillators, envelope, sequencer, keyboard, filter, delay, mixer and speaker.
Unlike most DIY synth kits, which require soldering, Korg and littleBits' team-up snaps together with magnets. It also comes with a comprehensive instruction booklet that explains how each part of the synth works and how to get it to make a sound. If you're starting at the very beginning, this kit will tell you everything you need to know. With some light modification, the packaging even doubles up as a rack for your modules.
Best price in the US: Amazon ($116.00)
Best price in the UK: Juno (£99.00)
Best for having fun: Teenage Engineering PO-20 Arcade
If you want your first synth to be fun, Teenage Engineering's PO-20 Arcade is like making music with a Game Boy. One of seven pocket-sized instruments with their own personalities, the PO-20 is a chiptune for creating 8-bit beats and melodies with an LCD screen that displays your actions as a cute, animated arcade scene. It sounds as lo-fi as you'd expect a synth on a tiny circuit board to sound, but it's got a lot of character.
The PO-20 has a lot of features for its size: the sequencer, 16 effects and space for 16 patterns is enough to create simple but detailed loops, which you can record into software such as Ableton Live or sync with the other Pocket Operators in the range. If retro video game music isn't your thing, put together a PO-12 drum machine, PO-14 bass synth and PO-16 lead synth for a hardware techno rig that's less than $150.
Best price in the US: Sweetwater ($59.00)
Best price in the UK: Gear4Music (£48.00)
Best for building a whole track: Novation Circuit
Novation's Circuit isn't just a synth – it's a drum machine, sampler and sequencer as well. It's the ideal first synth for someone that wants to make more than just a melody, but doesn't like the distraction of making music with a laptop. It's equally as good for someone that's an Ableton expert that wants a hands-on tool for sketching ideas outside software.
The Circuit is also quite powerful for its price and size. It's not analog, but it includes two digital polyphonic synths that can do basslines, ambient pads or lead sounds, lots of built-in effects and software that allows you to upload your own samples to the four drum tracks. It doesn't offer the deep controls for shaping sound as some synths, but if you're happy with modifying presets Circuit is ideal.
Best price in the US: Sweetwater ($329.99)
Best price in the UK: DJ Superstore (£237.00)
Best for making noise: Arturia MicroBrute
Some people just want a synth to make a lot of loud, weird noises, and there's no shame in that. If that's you, Arturia's MicroBrute is perfect. It's got all the real analog grunt of a much larger synthesizer in a very small body, with just enough hands-on controls to teach you all the basics of synthesis. Its sequencer can store eight patterns of 64 steps each, a huge amount compared to the 16 steps offered by some manufacturers.
The MicroBrute has lots of other features that make it louder and wilder than other synths: an "ultra saw" wave for extra jagged sounds, a "metalizer" for weird harmonics and a "modulation matrix," which lets you patch cables like a modular synth and do things like have the LFO (low frequency oscillator) modulate the filter. If you want something hands on but the littleBits is too much like a toy, the MicroBrute is perfect.
Best price in the US: Turntable Lab ($299.99)
Best price in the UK: Music Matter (£225.00)
Best for dance music: Roland TB-03
There's a reason why Roland's classic TB-303 is so popular: it's got a genuinely distinctive sound, and though it's a little overused, it always gets people moving in the club. Vintage units are tricky to come by, but Roland's TB-03 reissue offers the same simple-to-program experience as the original model. It's not a real analog reissue, but it sounds so close to the original it'll make no difference to anyone but the most staunch acid purists.
Roland's reissue even adds a few features not seen on the TB-303: LCD display for more precise editing, MIDI connection, USB port, overdrive and delay effects, and a shuffle function for adding variation to patterns. However, it's the ease of use that makes this such a great first synth. Writing a bassline on the TB-03 is almost foolproof; just add a drum machine and you can make your own club music.
Best price in the UK: West End DJ (£329.00)
Most versatile: Korg Minilogue
Not everyone wants their first synth to be small and simple. If you're already an experienced user of Ableton Live and want to move from Operator to a real synth, Korg's Minilogue is one of the best synths you can buy. At $499.99 it won't break the bank, but it's real analog, polyphonic (which means it can play full chords) and has all the hands-on controls you need to use without having to dive into menus.
Like a lot of synths in its price range, the Minilogue has reduced-size mini keys, but if you're mainly using it for sequencing then that probably won't matter. If you already own Korg's Volca gear, it can connect via the company's proprietary sync connector, meaning you can even add a Volca drum machine for beats. The Minilogue isn't completely future-proof, but it's a fine all-rounder while you save up for something more expensive.
Best price in the UK: Red Dog Music (£424.10)
Best for budding modular musicians: Moog Mother-32
Moog make the kind of synths that can convince people to part with their money whether they want to make music or not. Until recently, you would have to part with a small fortune to buy one, but the Mother-32 offers the legendary Moog sound for under $600, which is enough to be considered affordable, especially for a company that charges over $3,000 for its flagship model.
The Mother-32 is semi-modular, which means it can work as a standalone unit or as part of a larger modular synth. It's a little too advanced for complete beginners, but it's perfect for anyone wanting to build their own Eurorack modular system: it's got everything you need to get started, including a sequencer, meaning you easily expand it with a case and a few other modules.
Best price in the US: Control ($599.00)
Best price in the UK: Kazbar Systems (£519.00)
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Read next: The 5 best drum machines to turn you into a master beat-maker
Tags: ArturiaKorgNovationRoland
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Refuting a tired pro-abortion ad hominem argument.
In response to Heather Hill (4/16), I propose we immediately close MCCSC and Indiana University. After all, a man "can't possibly know much about" abortion, since he has no personal experience with it. If the only true knowledge comes from personal experience, why are we spending billions upon billions to educate children and young adults? Hill's argument is absurd.
It's interesting that a man's opinion on abortion is only irrelevant if he opposes killing babies by dismemberment in the womb. Somehow, I do not think abortion rights advocates would be supportive of an anti-abortion woman arguing that a man has no right to advocate for abortion rights. Oh, and you people protesting the war in Iraq? Unless you have served in Iraq, your arguments against the war have no merit. I am opposed to the Iraq war, by the way.
City government has given Planned Parenthood a handout from our pockets for ten consecutive years, a total of over $28,000. That needs to stop, especially since a "nurse" at Planned Parenthood was caught on videotape trying to cover up what she believed to be sexual abuse of a 13 year old girl by a 31 year old man.