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Inside 'The Walking Dead,' 'Invincible' Owner Skybound Entertainment's $75 Million Public Equity Campaign
Rob Salkowitz
Jan 23, 2023, 08:00am EST |
'Invincible' on Amazon Prime is one of the big media properties developed by Skybound Entertainment.
Skybound Entertainment
Skybound Entertainment is the company behind some of the most popular original IP of the past 20 years, including The Walking Dead, Invincible (both from the mind of cofounder Robert Kirkman) and the upcoming movie Renfield. Like many companies that got started in comics publishing, Skybound is looking to assert more control over the production and distribution of its material across the media landscape by increasing its internal capabilities. But unlike others who have sought institutional investment or overseas financing, the privately-held Skybound LLC is going directly to its fans with an unusual investment offering.
Today the company is announcing a new Regulation A+ campaign on the Republic platform to raise up to $75 million in new capital direct from the public, including $11 million raised in a quiet-period round that just ended. [prospective investors, be sure to examine the company's Form 1-A]
On Friday, I spoke with Skybound CEO Dave Alpert and co-Chairman Jon Goldman about the company's strategy, the terms of the offering, and what Skybound is trying to accomplish with the new infusion of cash. Our conversation has been edited for length and clarity.
Rob Salkowitz, FORBES Contributor: Can you briefly summarize what Skybound is up to with this announcement?
Skybound Entertainment CEO David Alpert
Courtesy of Skybound Entertainment
Dave Alpert, CEO, Skybound. At Skybound we talk about "the Wheel of Awesome," where we help creators commercialize their ideas in any medium they want to, from digital to TV to comics to games. The purpose of this Reg. A raise is to bring the fans into our ecosystem, have them be inside the company, make our success their success and be that connective tissue.
It looks like you are offering 150,000 "units" at $500 each, is that correct?
Jon Goldman, co-Chairman, Skybound: The headline raise is $50 million and you're allowed to extend to $75 million, so we'll see where it goes.
Does that include the $11 million already raised during the quiet period?
Goldman: Yes.
I note that in the Prospectus, it says the price of the units bears no relationship to the company's asset value, worth or earnings. On what basis are you pricing the units then?
Skybound co-Chair Jon Goldman
Goldman: I think that's probably legalese. We arrived at a fair market valuation in consultation with the platform Republic as well as some research groups that looked at the stock for us. We had priced an institutional round at $330 million post money, and that was before we had a second [post-The Walking Dead] hit, Invincible, which is a legitimate global hit. I think that given the growth trajectory, and the fact that we are probably the second largest independent library of IP not owned by a major conglomerate, there's value there. And when you consider the multiples in the videogame industry, which is a large part of our business, we feel that we priced it sensibly.
So, ballpark, what percentage of equity does this offering represent?
Alpert: We're based at $500 million pre-money, so it'll be a little less than 10% post-money [based on the baseline $50M target, not the extended goal of $75M].
How will the new capital be used?
Alpert: If I may give you a little narrative context first… For the first 9 years of the company were entirely bootstrap. We put all the money we were making back into the company. We started out touching the consumer directly in comics, but in the in television we still had to go AMC and studios and networks to get our shows out to market. In gaming, it was purely a licensing business.
As we continued to recycle our profits and our cash flow, we ended up building up more capacity to option and develop and pay for scripts in the film ans TV space. We expanded our comic book business. On the videogame side, we had some in-house talent that would help supervise the production.
As the company continued to grow, we realized we were making a tremendous amount of money for third parties, and not necessarily as much for ourselves or our creators. We saw that there was both a market opportunity and an obligation to take a little bit more of that in house. Then, in 2012, we had a situation where we needed to come up with several million dollars on short notice to salvage a videogame project when our partner went bankrupt. That was tough without access to outside capital.
In the past, it's taken us a long time to get outside partners to see the value of our IP. Now we'll be able to accelerate that, by bringing more of that capacity in house and not relying on third parties to make things happen for us.
'The Walking Dead' was Skybound Entertainment's breakout hit.
You mentioned that part of your goal is to build this partnership between fans, creators and the company. Are any shares being set aside for creators? Are they participating?
Alpert: We're offering creators the ability to buy in; in lieu of cash, right? [The offering] is about a cash raise, so people want to participate in that way, we're absolutely willing to do that, and we're encouraging people to do that.
Are the units being offered through the Reg A sale common stock with voting rights and rights to distributions, or are they a special class?
Skybound founder Robert Kirkman
Goldman: They have the same rights as common stock, same as Dave and Robert [Kirkman] and I have. As minority shareholders, they can't force the direction of the company, although they often say smart things, and as we've seen on the campaign page, they are not shy about expressing their ideas, and that's fine.
Are these units liquid? Is there a secondary market for them where people can sell them?
[At this point, the Skybound PR rep joined in to clarify some points for the principals]
Goldman: It's not liquid the way a public company is, although there are now investment banks that deal in secondary markets for private companies, especially in large blocks. The limit on this offering is that one individual can buy up to $2 million, so I imagine if we have any big players like that, they'll have opportunities for secondary sales in the future. It will probably be harder to move single units.
Some might see this public campaign and think you're trying to raise money by appealing to people's fandom rather than their investment sense, because people have such an emotional stake in the properties. What do you say to them?
Goldman: If you looked at it that way, we're incredible undervalued and Tesla is incredibly overvalued (laughs). If you did a traditional comp analysis of global IP holding companies – for example, the ones that sold to Disney – I think it's easy to draw the conclusion that there are many multiples of the pricing that our investors can earn on exit. You know, we can't guarantee it; no business can. But the types of things we do are valued far more highly than $500 million at some potential exit point.
Alpert: We had, and still have, plenty of opportunity to take more institutional money, and at some point may end up doing so. The goal here was twofold: one to raise additional capital for our strategic initiatives across media, but also the opportunity to partner with the fan really is something that we think is transformational in the sense that a lot of traditional media companies, and even some of the disruptive ones, like Netflix NFLX , are still organized around that one form of distribution, and we can switch the focus. We think we're the first media company organized around, not just an individual channel distribution, but on connecting you to that in a 360-degree way.
Given this grand strategy that you're proposing in terms of media integration and direct access to customers, are you concerned about the headwinds we're seeing in the streaming, entertainment and tech industries right now?
Goldman: No. Everybody is adhering to that traditional strategy, but the idea of putting together our own stuff is in not having to sell it to a streamer immediately. To be able to sell that show that we talked about in Africa, individually by territories, I think, is going to end up being a very smart strategy. And, by the way, both of us have been through up and down markets, and it turns out that people spend more on entertainment in a downturn, because some people have more time on their hands, and they spend more money.
One thing we've seen in the past year with investments and acquisitions in the comics space is that the investors are getting much less patient, and companies find themselves having to make hard choices with layoffs and strategy. By going directly to the public for this kind of capital, to people who are not in a position to play so rough with you guys, do you think you'll have a little more space to pursue your strategy?
Alpert: It's about not being dependent on those outside forces. The whole point of this Reg A for us is, if you buy a share of stock in Skybound, we're on the same team. You're following us. We're following you. That is a real thing: nobody, not Facebook, Netflix, Amazon AMZN , or Apple AAPL , can take that away. And that is why this is such a powerful thing for us.
Follow me on Twitter. Check out my website.


CDVCA's Annual Conference is the premier training and networking event for impact investors providing startup and growth capital to sustainable businesses that make a measurable difference in people's lives. Those who attend will get a chance to speak with industry leaders and government officials about issues that are currently affecting our industry. Our goal is to ensure that participants walk away with a better idea of how to achieve tangible results for their own organizations and communities.
The 2018 CDVCA Annual Conference will be held on March 22-23, 2018 at Washington Plaza Hotel, Washington, D.C.
An Introductory Workshop precedes the Conference on Wednesday, March 21, 2018. This full-day workshop provides an overview of the industry and practice of impact investing. Attending this event offers an in-depth look at leading funds and best practices in the industry, and serves as the ideal entry point to the Conference and the industry.


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#include <aws/globalaccelerator/model/DeleteCustomRoutingListenerRequest.h>
#include <aws/core/utils/json/JsonSerializer.h>

#include <utility>

using namespace Aws::GlobalAccelerator::Model;
using namespace Aws::Utils::Json;
using namespace Aws::Utils;

DeleteCustomRoutingListenerRequest::DeleteCustomRoutingListenerRequest() :
    m_listenerArnHasBeenSet(false)
{
}

Aws::String DeleteCustomRoutingListenerRequest::SerializePayload() const
{
  JsonValue payload;

  if(m_listenerArnHasBeenSet)
  {
   payload.WithString("ListenerArn", m_listenerArn);

  }

  return payload.View().WriteReadable();
}

Aws::Http::HeaderValueCollection DeleteCustomRoutingListenerRequest::GetRequestSpecificHeaders() const
{
  Aws::Http::HeaderValueCollection headers;
  headers.insert(Aws::Http::HeaderValuePair("X-Amz-Target", "GlobalAccelerator_V20180706.DeleteCustomRoutingListener"));
  return headers;

}

redpajama_set_name: RedPajamaGithub


Marisa Rader Huston works for the Ann Arbor District Library and is the former finance and communications director for the Anil Kumar U.S. Congressional campaign. This is her first bid for elected office.
Previously, Huston worked as a graduate intern with the Peace Education Initiative at the University of Toledo, and as an intern with the Michigan Young Democrats. She also has served as a lead organizer with the Washtenaw County Workers' Center, which focused on issues affecting low-wage and immigrant workers.
In 2015, Huston earned a master's degree in peace education from the University for Peace. She graduated from Beloit College in 2010 with a bachelor's degree in anthropology and religious studies. She lives on Ann Arbor's west side. Her mother, Rosemary Rader, is a retired WCC chemistry and science instructor.


Help us meet everyday needs by making an in-kind donation from our immediate needs list today. WCCS accepts new in-kind items throughout the year. If you have questions regarding your non-monetary gift/in-kind donation or need to schedule a drop off appointment, please call our Administrative Office at (562) 945-3937.


I am currently an HBA1 student from Burlington, Ontario. I have worked in the customer service industry for six years now at Glen Abbey Golf Club, where I have occupied multiple leadership positions. Outside of school and work, I love to snowboard and play golf.
I enjoy exploring new experiences that are outside my comfort zone. This spring I am participating in the African Service Learning Course in Ghana, and next year I am going on exchange to Switzerland. I find the strongest learning happens when you challenge yourself in new environments.
Whether it be for profit or environmental decisions, it is easy to be short-term oriented. Sustainability involves looking past short-term gains to pursue long-term interests that are mutually beneficial to all stakeholders involved and the environment. Sustainability is often seen as an individual, narrow concept. However, it is something that should be taken into consideration for all business decisions. Sustainability is not about maintaining the status quo for the future: it is about re-defining the meaning of the status quo to make a better future.
During my second year at Western, my roommate and I started Western Spread the Net. Spread the Net is a student challenge for high schools and universities in Canada that is run by Rick Mercer each year. Proceeds raised are used to buy bed nets, which are sent to Africa to protect families from Malaria. The charity did not have a group from Western registered, and we took the initiative to form a team of like-minded, driven students to participate. As a result of our fundraising efforts, 23 bed nets were sent to Africa.
For my Business 2257 Feasibility project last year at Western, my group pursued a topic related to sustainability. We proposed a venture, called SunCents, which involved leasing solar panels to homeowners. The energy produced was sold back to the government through the Ontario MicroFIT program. This venture provided value for our business, the residents of Ontario, and the environment.
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All flyers and signs require approval from the Building Manager (unless noted otherwise) in each building across campus.
All signs must be attached to bulletin boards or other designated areas and are not to be hung on walls.
Signs displayed on all campus bulletin boards are restricted to a maximum size of 17"x 23". Signs may not be displayed on the outside of any buildings.
The KUB Main Desk coordinator must approve signs displayed in the Kehr Union. Signs posted on bulletin boards in residence halls are subject to the approval of the area coordinator.
Digital signage is available in various locations throughout campus.
BU branded templates are available at https://drive.google.com/file/d/1pLhnspQIjLk8rsQwN3ANIpP9c1c_Enma/view - all may be used for digital signage messaging.
Click the download button to open the templates in PowerPoint.


This introductory course covers the concepts and techniques concerning exploratory data analysis, descriptive statistics, probability distributions, sampling and sampling distributions, statistical inference methods including confidence interval and hypothesis testing, and an introduction of categorical data analysis. Students will learn how these topics apply to and can be used in business, using both manual computations and statistical software. Prerequisite(s): A minimum grade of "C" in CISM 2530, and MATH 1232 or MATH 1441 or MATH 1112 or MATH 1113 or a minimum grade of "B" in MATH 1111 and Sophomore standing.


text:
Current Issue: Winter 2023
MQR Prizes
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Meet Our Contributors, MQR 57:4
Meet Our Contributors, MQR News
By MQR Staff
Purchase MQR 57:4 (Fall 2018) — our special issue on Caregiving — in print or as a downloadable PDF.
Ahmad Almallah | poetry | "House/Cleaning"
Ahmad Almallah received the 2018 Edith Goldberg Paulson Memorial Prize for Creative Writing and the 2017 Blanche Colton Williams Fellowship from Hunter College, where he obtained his MFA. His poems have appeared in various journals, and his book of poems, Bitter English, is forthcoming in the Phoenix Poets Series from the University of Chicago Press.
Idris Anderson | poetry | "A Shuffle In the Woods"
Idris Anderson's second collection of poems, Doubtful Harbor, was selected by Sherod Santos for the Hollis Summers Prize of Ohio UP and was published in 2018. Her first collection of poems, Mrs. Ramsay's Knee, was selected by Harold Bloom for the May Swenson Poetry Award and published by Utah State UP. She has held a number of grants from the National Endowment for the Humanities to study lyric poetry with Helen Vendler at Harvard, Greek tragedy at Stanford, and Virginia Woolf in London.
Elizabeth Aquino | poetry | "Three Meditations on Caregiving"
Elizabeth Aquino is a writer living in Los Angeles with her three children. Published in several literary anthologies, The Los Angeles Times, and online at Slow Trains and quaartsiluni, among others, she is currently working on a memoir about her life with her severely disabled young adult daughter. Her blog, a moon worn as if it had been a shell, is a place where disability, poetry, parenting, and politics intersect. She is passionate about telling the stories of caregivers in a new project, a podcast called Who Lives Like This?!, that airs each Tuesday.
Amy Beeder | poetry | "Leviathan"
Amy Beeder's third book, And So Wax Was Made & Also Honey, is forthcoming from Tupelo Press. A receipt of a "Discovery"/ The Nation Award and an NEA Fellowship, her work has appeared in Poetry, Kenyon Review, Ploughshares, AGNI and other journals. She serves as Editor-at-large for Plume.
Chloë Boxer | fiction | "Dog Days"
Chloë Boxer is a writer of fiction and true crime television pursuing an MFA in fiction at Arizona State University.
Karen Brennan | poetry | "Everyone Sad" & "When Rachel Sings"
Karen Brennan is the author of seven books, the most recent of which is a hybrid short fiction collection, Monsters. Professor Emerita at the University of Utah, she is on the faculty of the Warren Wilson MFA Program for Writers.
Marc Brenman | poetry | "Family Archaeology"
Marc Brenman is a semi-retired bureaucrat who lives in suburban Washington, DC, and in San Francisco. He publishes mostly on civil and human rights issues, including the books The Right to Transportation and Planning as if People Matter: Governing for Social Equity.
Jeff Camhi | essay | "Words Unspoken"
Jeff Camhi is a seventy-seven-year-old new writer of creative nonfiction. He is also a retired professor of neurobiology; founding director of a university museum; and, for the past seven years, a devoted student of creative nonfiction writing. "Words Unspoken" is modified from a chapter of his memoir-in-progress, now coming to a conclusion, about "surviving" his wife's Alzheimer's.
Rafael Campo | poetry | "Gastroenterology" & "Immunology"
Rafael Campo teaches and practices internal medicine at Harvard Medical School, where he is Director of Literature and Writing Programs in the Art and Humanities Initiative. His work has appeared recently or is forthcoming in American Poetry Review, Image, The Hudson Review, The New Criterion, Poetry, The Poetry Review (UK), The Threepenny Review, and elsewhere. Duke University Press will publish his new and selected poems, Comfort Measure Only, in the fall of 2018.
Victoria Chang | poetry | "Obit"
Victoria Chang's most recent book is Barbie Chang, published by Copper Canyon Press in 2017. Other books are The Boss, Salvinia Molesta, and Circle. She was awarded a Guggenheim Fellowship and a Sustainable Arts Foundation Fellowship in 2017. In 2018, she was awarded the Poetry Society of America's Alice Fay Di Castagnola Award for her manuscript-in-progress, OBIT. She lives in Los Angeles and teaches within Antioch's low-residency MFA Program. Find out more at victoriachangpoet.com, or follow her on Twitter @VChangPoet.
Maryah Converse | essay | "Bringing Umm Saleh Home"
Maryah Converse was a Peace Corps educator in Jordan, 2004–2006, and was studying in Cairo during the 2011 Arab Spring. She has written for such publications as From Sac, New Madrid Journal, BLYNKT, Silk Road Review, Newfound, and The Matador Review. Gulf Stream Literary Magazine nominated her work for the 2017 "Best of the Net" collection. Maryah holds a Masters in Near Eastern Languages, teaches Arabic and English as foreign languages in the New York area, and blogs intermittently at bymaryah.wordpress.com. Follow her on Twitter @MaryahRC.
Desiree Cooper | essay | "When Persephone Goes Away"
Desiree Cooper is a 2015 Kresge Artist Fellow, former attorney, and Pulitzer Prize-nominated journalist. Her debut collection of flash fiction, Know the Mother, is a 2017 Michigan Notable Book and a 2017 Next Generation Indie Book Award winner. Cooper's fiction, poetry, and essays have appeared in The Best Small Fictions 2018, Callaloo, Hypertext Review, and Best African American Fiction 2010, among other online and print publications. Cooper was a founding board member of Cave Canem, a national residency for emerging black poets. Follow her on Twitter @descooper.
Barbara Crooker | poetry | "Mirror" & "Linguistics"
Barbara Crooker is a poetry editor for Italian-Americana, and author of eight full-length books and twelve chapbooks of poetry. Her awards include the WB Yeats Society of New York Award, the Thomas Merton Poetry of the Sacred Award, and three Pennsylvania Council on the Arts Creative Writing Fellowships. She is the mother of a thirty-three-year-old son with autism. Find out more at barbaracrooker.com, or follow her on Twitter @barbaracrooker.
Vicki Derderian | fiction | "Tango"
Vicki Derderian is a writer living in North Carolina. She is working on a collection of short stories.
Chard de Niord | poetry | "I Couldn't Grieve" & "Like a Cicada"
Chard de Niord is the poet laureate of Vermont and author of six books of poetry, most recently Interstate, (The University of Pittsburgh Press, 2015) and The Double Truth (University of Pittsburgh Press, 2011). He is also the author of a new book of interviews with nine American poets (Galway Kinnell, Jane Hirshfield, Carolyn Forche, Martin Esppada, Stephen Kuusisto, Ed Ochester, Peter Everwine, Stephen Sandy, Ntasha Trethewey) and James Wright's widow, Anne Wright titled I Would Lie To You If I Could. He is a professor of English and Creative Writing at Providence College, where he has taught since 1998 and trustee of the Ruth Stone Trust. He lives in Westminster West, Vermont with his wife, Liz.
Suzanne Edison | poetry | "When My Child Fell Ill"
Suzanne Edison MA, MFA, writes most often about the intersection of illness, healing, medicine and art. She has a child living with Juvenile Myositis. Her chapbook, The Moth Eaten World, was published by Finishing Line Press. Poetry can be found in CMAJ, HEAL, Isacoustic, Persimmon Tree, JAMA, SWWIM, What Rough Beast, Bombay Gin, The Naugatuck River Review, The Ekphrastic Review, and in several anthologies, including, The Healing Art of Writing, Volume One. Find out more at seedison.com, or keep up with Edison's work on Facebook.
Margaret Gibson | poetry | "Washing the Body"
Margaret Gibson is the author of twelve books of poems, all from LSU Press, most recently Not Hearing the Wood Thrush in 2018. A poem from that collection, "Passage," was included in The Best American Poetry, 2017. The title poem from her previous collection, Broken Cup (2014), won a Pushcart Prize for 2016. The Vigil was a Finalist for the National Book Award in Poetry in 1993. She has also written a memoir, The Prodigal Daughter (University of Missouri Press, 2008). Gibson is Professor Emerita, University of Connecticut, and lives in Preston, CT.
Jeremy Gregersen | poetry | "Sistine Notebooks: The Delphic Sybil"
Jeremy Gregersen is a graduate of the MFA program at the University of Michigan, where he won the Meader Family Award for Poetry. His work has appeared in a wide variety of publications, including Poet Lore, The Maine Review, and Cortland Review. He lives in Las Vegas, Nevada with his wife and son, where he works as Head of School at The Meadows School.
Karen Heuler | fiction | "The Year of His Father"
Karen Heuler's stories have appeared in over a hundred literary and speculative magazines and anthologies, from Alaska Quarterly Review to Confrontation to Weird Tales, as well as a number of Best Of anthologies. She has published four novels, three collections, and a novella, and has received a number of awards. This is her third appearance in MQR. Find out more at karenheuler.com, or follow her Twitter @KarenHeuler.
J.D. Ho | essay | "We Will Return After These Messages"
J.D. Ho received an MFA from the Michener Center at the University of Texas in Austin, and has work in Ninth Letter, Georgia Review, and other journals.
Tom C. Hunley | poetry | "Prayer Asking for Mercy"
Tom C. Hunley is a professor in the MFA/BA Creative Writing programs at Western Kentucky University and a father of four. His latest collection of poems is Here Lies (Stephen F. Austin State University Press, 2018). He recently signed a contract with McFarland for an expanded second edition of his textbook, The Poetry Gymasium.
Joshua Kryah | poetry | "Children of the Middle Ages" & "Survival by Children"
Joshua Kryah is the author of two collections of poetry, Glean and We Are Starved. He lives in St. Louis. Find out more at joshuakryah.com.
Heather Kirn Lanier | poetry | "The Baby Is"
Heather Kirn Lanier's poems most recently appear (or are forthcoming) in Image, Barrow Street, Rogue Agent, and Rhino. She's the author of the nonfiction book Teaching in the Terrordome, along with two award-winning poetry chapbooks. Her memoir about raising a daughter with a rare chromosomal syndrome is forthcoming from Penguin Press. Find out more at heatherkirnlanier.com, or follow her on Twitter @heatherklanier.
Amy Lemmon | poetry | "Sea-Bands™"
Amy Lemmon is the author of five poetry collections, most recently The Miracles (C&R Press, 2019). She is Professor and Chairperson of English and Communication Studies at the Fashion Institute of Technology, and co-editor (with Sarah Freligh) of The CDC Poetry Project. Find out more at saint-nobody.blogspot.com, follow her on Facebook @amy.lemmon.16, on Twitter @thatAmyLemmon, or on Instagram @thatamylemmon.
Elisabeth Lewis Corley | poetry | "What Belongs to Us"
Elisabeth Lewis Corley's poems have appeared in Southern Poetry Review, Hyperion, Carolina Quarterly, Feminist Studies, BigCityLit, MahMag, New Haven Review, Cold Mountain Review, Consequence, and other magazines. She holds an MFA in poetry from the Warren Wilson Program for Writers and a BA with Highest Honors in Poetry from the University of North Carolina at Chapel Hill, where she sometimes teaches poetry in performance and screenwriting.
J. Estanislao Lopez | poetry | "Aubade on the 8th Floor of St. Luke's" & "The Figurative"
J. Estanislao Lopez lives and teaches in Houston, TX. His work has appeared in Harvard Review, Ploughshares, The New Yorker, and elsewhere. He is currently an MFA candidate at Warren Wilson College. Find him on Twitter @EstanislaoPoet.
Ed Madden | poetry | "What Time is Made Of," "Never," & "Imminent"
Ed Madden is the author of four books of poetry, most recently Ark, a memoir in verse about his father's last months with cancer. His poetry has been published in Prairie Schooner, Crazyhorse, Poetry Ireland Review, and other journals, as well as in Best New Poets 2007 and Hard Lines: Rough South Poetry. He is a professor of English and director of Women's & Gender Studies at the University of South Carolina. In 2015, he was named the poet laureate for the City of Columbia, SC.
Kai Maristed | fiction | "Mrs. Trefoil's Parlor"
Kai Maristed is a writer, translator, playwright, and engaged ecolo-gist. Her books include Broken Ground: a Berlin novel, and the story collection Belong to Me. Short work has appeared or is forthcoming in the Kenyon Review, Zoetrope, The American Scholar, the Southwest Review, StoryQuarterly, Agni, the Iowa Review, and other publications. Find out more at kaimaristed.net.
Michael Mark | poetry | "It's all in your head, Estelle," "The year we're living in," & "In the handicap stall"
Michael Mark is a hospice volunteer and author of two books of stories, Toba and At the Hands of a Thief (Atheneum). His poetry has appeared or is forthcoming in Alaska Quarterly Review, Cimarron Review, Columbia Poetry Review, Pleiades, Rattle, River Styx, Spillway, Sugar House Review, The New York Times, The Sun, Verse Daily and The Poetry Foundation's American Life in Poetry. His poetry has been nominated for three Pushcart Prizes and the Best of the Net. Find out more at michaeljmark.com, or follow him on Twitter @Michaelgrow.
Nancy McCabe | essay | "The Inmost Cave"
Nancy McCabe is the author of the novel Following Disasters and four books of creative nonfiction, most recently From Little Houses to Little Women: Revisiting a Literary Childhood. Her work has appeared in many magazines and anthologies, won a Pushcart, and made notable lists in Best American anthologies six times. She directs the writing program at the University of Pittsburgh at Bradford and teaches in the low residency MFA program in writing at Spalding University.
Heather McHugh | introduction | "Emit and Edit"
Heather McHugh spent her working life in college classrooms with some gifted writers. At seventy she is having the time of her life exploring bays and islands with a kindly and gifted sailor. Her first new poetry collection in ten years will be published by Copper Canyon in 2019, as will a chapbook from Sarabande.
Gregory Leon Miller | fiction | "Something Else"
Gregory Leon Miller's book reviews regularly appear in the San Francisco Chronicle. "Something Else" is his first published work of fiction. He teaches at the University of California, Davis and received his MFA in 2018 from Warren Wilson College.
Carol Tell Morse | essay | "There Must Be More to Life"
Carol Tell Morse teaches writing at the University of Michigan and directs the Lloyd Hall Scholars Program, an undergraduate program for writing and the arts. She has her PhD in Irish poetry from the University College, Dublin.
Sara Parrott | poetry | "At the Pillow of the Sick"
Sara Parrott's work has appeared in Nine Mile Magazine, Ghost City Review, and the Syracuse Poster Project. She holds an MA from Binghamton University and is a former Bookspan Creative Director. She currently is a member of the Downtown Writers Center in Syracuse, NY, and the UK Poetry School.
Irma Pineda (translated by Wendy call) | poetry | "Cándida"
Irma Pineda is an author, editor, translator, and educator who lives in Juchitán, Oaxaca, Mexico. Her seventh book of bilingual Spanish-Isthmus Zapotec poetry, Naxiña' Rului'ladxe' – Rojo Deseo (Red Desire) (Pluralia Ediciones, 2018), has earned national awards and significant media attention in Mexico. Pineda is the only woman to have been president of Mexico's national Association of Writers in Indigenous Languages (ELIAC). She was a 2013-2015 member of Mexico's Sistema Nacional de Creadores de Arte, the equivalent of the National Endowment for the Arts. She serves on the faculty of the National Teachers' University in Ixtepec, Oaxaca and travels widely to perform her poetry.
Wendy Call is an author, editor, translator, and educator who lives in Seattle. Her book No Word for Welcome (Nebraska, 2011) won the Grub Street National Book Prize for Nonfiction. An essay from her book-in-progress, Grief Ephemera(l), won the StoryQuarterly Nonfiction Prize and was named a "Notable Essay of 2017" by Best American Essays. Call's translations of Irma Pineda's poetry have appeared in two dozen publications. She was a 2015 National Endowment for the Arts Fellow and is a 2018 Fulbright Core Scholar to Colombia. She serves on the faculty of Pacific Lutheran University (PLU) in Tacoma, Washington and currently directs PLU's Spanish immersion program in Oaxaca, Mexico. Find out more at wendycall.com.
Christa Romanosky | fiction | "The Hard Burn of Traveling Light"
Christa Romanoksy is a native of northern Appalachia. She was a 2017–2018 fiction fellow at the Provincetown Fine Arts Work Center, and a 2018 Writer-in-Residence at the James Merrill House. Her work has appeared in Glimmer Train, the Kenyon Review Online, The Massachusetts Review, the Missouri Review, and elsewhere. She currently teaches creative writing and STEM workshops to elementary students through various programs.
Robin Rosen Chang | poetry | "Black Bubbles" & "Physical Exam"
Robin Rosen Chang's poetry has appeared or is forthcoming in Zone 3, Paterson Literary Review, Yemassee Journal, Vinyl Poetry and Prose, and other journals and anthologies. She is currently completing her first full-length manuscript. She has an MFA in poetry from The Program for Writers at Warren Wilson College. An educator and resident of New Jersey, Robin has lived in different parts of the U.S. and overseas. Follow her on Twitter @chang_rosen.
Tina Schumann | poetry | "Interlude"
Tina Schumann is the author of three poetry collections: As If (Parlor City Press, 2010), winner of the Stephen Dunn Poetry Prize; Requiem: A Patrimony of Fugues (Diode Editions, 2017), winner of the Diode Editions Chapbook Contest; and Praising the Paradox (Red Hen Press, 2019.) She is editor of the anthology Two Countries: U.S. Daughters and Sons of Immigrant Parents (Red Hen Press, 2017.)
Betsy Sholl | poetry | "Knot"
Betsy Sholl's eighth collection of poetry is Otherwise Unseeable. In 2019 the University of Wisconsin Press will publish House of Sparrows: New & Selected Poems. She teaches in the MFA Program of Vermont College of Fine Arts.
Kate Osana Simonian | fiction | "Transference"
Kate Osana Simonian is an Armenian-Australian hailing from Sydney, but she's currently a PhD candidate at Texas Tech. Her work centers on moral dilemmas, especially those concerning sex and feminism. Her work has been published by, or is forthcoming in, Colorado Review, Shenandoah, Chicago Tribune, and Best Australian Stories. Recent honors include the Nelson Algren Award, a Tennessee Williams Scholarship to Sewanee Writers' Conference, and a position as the Hemingway-Pfeiffer Writer-in-Residence. Find her at katesimonian.com or follow her on Twitter @kate_o_simonian.
Shirley Stephenson | poetry | "Hand Carriage"
Shirley Stephenson works as a Nurse Practitioner on Chicago's west side. She is a recipient of an Illinois Arts Council Artist Fellowship and her poems have appeared in The Gettybsburg Review, Blackbird, The Southern Review, and other journals.
Connie Voisine | poetry | "All is Well, Safely Rest, God Is Nigh"
Connie Voisine is the author of the forthcoming chapbook And God Created Women and the forthcoming book The Bower. Find out more at connievoisine.com, or follow her on Twitter @CLVoisine.
Kim Wyatt | essay | "Terroir"
Kim Wyatt's work has been published in Creative Nonfiction and The Best American Travel Writing 2017, as well as in dozens of newspapers and regional magazines. She holds an MFA from the University of Alaska, Anchorage, and a Bachelor of Science in Nursing. She lives in South Lake Tahoe.
MQR contributor Jaimy Gordon wins National Book Award
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Selections from the Upcoming Great Lakes Issue
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Hong Kong and the Hope of Cosmopolitanism: Reading Xu Xi's Monkey in Residence & Other Speculations December 16, 2022
A Review of Arji Manuelpillai's Improvised Explosive Device October 24, 2022
Hunger and Home: A Review of Dur e Aziz Amna's American Fever July 15, 2022
Prayers and Incantations July 11, 2022
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In April 2010, I visited Haiti and saw the destruction wreaked upon the people of this already desperately poor nation by the earthquake. I was deeply saddened to see how much the Haitian people had lost and was extremely concerned about the amount of effort it would take to rebuild what was left of the country. In late June of this year, 14 months later, I returned and was astonished by the progress that I saw.
There remains a monumental amount of work to do on the road to recovery and to rebuilding a country that is better than the one ravaged by the earthquake. But it is important to understand that despite all the oft-reported problems, the contrast between now and three months after the earthquake is night and day.
I bring a thirty-year perspective on Haiti. I first came to know Haiti as a Foreign Service Officer from 1981 - 83. I returned in 2007 and saw the economic decline that had taken place in the intervening decades of disorder. Through my association with CHF International, I knew about the gradual, but very real improvement in the years just prior to the earthquake. The vast amount that has been achieved since the destruction of January 2010 -- and the best of it achieved in cooperation with the Haitian people -- is deeply impressive.
One of the first contrasts that one notices is in the roads. In April 2010, they were gridlocked with the SUVs of virtually every known, and many unknown, relief agencies and military supply vehicles which responded to the earthquake's aftermath. Along the sides of the roads and spilling into the streets was tons of debris from buildings shaken to disintegration by the brutal seconds of the quake. Now, while the roads are as congested as one might expect for a busy, densely populated city, the number of aid agencies and the military presence is much reduced. Rubble removal has also been effective: where there were pancaked buildings and homes that had become ruins, now many of these lots have been cleared, or transitional shelters built in their stead.
The visible signs of economic activity are everywhere: everything on sale at the side of the road, from vegetables and meats to flip-flops and art work, to shampoo and cell phones. In some areas, traffic congestion has been alleviated by new markets that have been built to give merchants better conditions to sell their wares away from oncoming traffic. The small stores that represent hair salons, the lottery, electronics and more are brightly colored and busy -- all signs that one would hope and expect to see in a bustling city of 3 million people.
There are still many displaced people in camps -- the so-called "tent cities" -- but they are not as prevalent as they once were. Some that I had seen on my previous trip had completely disappeared, others had been decongested. Complementing this were the many transitional shelters in neighborhoods to where the camp residents have returned, far safer and more conducive to family hygiene.
While one still sees medical workers, the military and tents, they are noticeably fewer, being replaced by dump trucks removing debris, concrete trucks rebuilding roads and dwellings and by shelters built to withstand future tropical storms. The economic activity is palpable, lending to a sense of a return -- or at least the beginning of a return -- to normalcy.
, a program designed to reverse the decline in the Haiti garment sector by providing training for workers in the garment industry from sewing machine operators to high level executives -- the jobs needed across the whole sector.
These are all very positive signs. But these signs do not contradict reports of failures and frustrations -- they complement them and provide reason for optimism. Advances have been and must continue to be made. The donors, who have promised so much to Haiti, must not lose interest or allow bureaucratic delay to suffocate the momentum of progress. It took bold action to make a difference after the earthquake and it will take continued bold action to work in partnership with the people of Haiti to create a better future. The headlines have faded and public attention has shifted elsewhere, but Haiti must not be forgotten and the pledges and commitments must be honored.


text:
VIDEO: Bill Gates Claims We Have to Endure Economic Collapse to Fight COVID-19
Less than one month ago, Bill Gates said the world must endure a borderline economic collapse to fight the virus.
by Archive
in Coronavirus
Last Updated on May 5, 2020
In a sparsely reported interview from last month, Microsoft co-founder and self-appointed vaccine expert Bill Gates told the Financial Times that the world had no choice but to enter the worst global depression in modern history to fight the spread of coronavirus.
Gates told the interviewer that the global economy is going to shrink, causing economic devastation that could be as bad, or worse, than the Great Depression or the Panic of 1873, but that wreaking havoc on the economy was the only solution to combating the virus.
"[The economy] won't to go to zero, but it will shrink," said Gates. "Global GDP is going to take, you know, probably the biggest hit ever. Maybe the depression was worst, or 1873, I don't know, but in my lifetime this will be the greatest economic hit."
"But you don't have a choice. People act like you have a choice, people don't feel like going to the stadium when they might get infected. It's not the government who's saying, 'Okay, just ignore this disease and you know,' people are deeply affected by seeing these deaths, by knowing they could be part of the transmission chain," Gates continued.
Gates cautioned that only rich countries may be able to "open up" over the next "few months," but warned that the world will only return to something approximating normal when a significant part of the global population has been vaccinated against coronavirus.
"But, for the world at large, normalcy only returns when we've largely vaccinated the entire global population," said Gates. "Trying to achieve that ambitious goal, which has never been done, for the vaccine, that rises to the top of the list."
While most of the West did shut down through March and April in response to supposed experts like Gates, some large, developed, Western countries chose not to, and appear to be virtually no worse for their efforts.
Though President Donald Trump has derided Sweden for its decision not to enter a lockdown and crush its economy, the country's decision to have vulnerable populations stay at home and allow the wider population to mingle in order to reach herd immunity seems to be working.
Throughout April and the first few days of May, Sweden's healthcare system has not been crippled by an overwhelming number of cases, the reason why the United States shut down to "slow the spread," and top science publications are now wondering if herd immunity may be the only solution for the coronavirus crisis.
According to an article in Discover Magazine:
As the rest of the world has hunkered down to weather the COVID-19 pandemic, Sweden has remained remarkably open. The government has taken steps like issuing guidelines for Swedes to stay home, banning gatherings of more than 50 people and closing museums. Yet restaurants, schools and parks remain open. Consequently, Sweden's ambassador to the U.S., Karin Ulrika Olofsdotter, said the country's capital, Stockholm, could reach herd immunity sometime this month.
Herd immunity is how a society collectively fights off infections to keep the transmission of disease low. The Swedish approach may sound appealing in countries like the U.S., where lockdown measures have crippled the economy. But remaining open has had costs, with elderly people making up 86 percent of Sweden's more than 2,000 deaths so far. And scientists are still unsure whether individuals who have recovered from the novel coronavirus are immune to further infection — much less whether entire populations can keep the disease from reaching their most vulnerable members.
Additionally, when lockdowns were first initiated, it was believed that the virus would very frequently require hospitalization, and would be extremely fatal in those it infects. This has, according to the latest data, seemingly been proven untrue, as as many as one in five New Yorkers may have already come into contact with the virus and recovered, presenting either no symptoms or mild symptoms.
Similar data presents itself on the country's opposite coast, where in Los Angeles, nearly 500,000 may have already encountered the virus.
Those who have already encountered the virus may have antibodies that would prevent future illness from exposure to coronavirus, creating herd immunity as the virus would have less new hosts to infect. Some have pointed out that, with most of the world locked down, there is no way for herd immunity to be reached without a vaccine, as there is no mingling of population.
National File has also pointed out that most of the country's experts, who are unified in pushing for lockdowns and waiting patiently for experts to develop a vaccine, are financially tied to Gates.
Senior Reporter Patrick Howley reported:
Gates has a lot of pull in the medical world, he has a multi-million dollar relationship with Dr. Fauci, and Fauci originally took the Gates line supporting vaccines and casting doubt on Chloroquine. Coronavirus response team member Dr. Deborah Birx, appointed by former president Obama to serve as United States Global AIDS Coordinator, also sits on the board of a group that has received billions from Gates' foundation, and Birx reportedly used a disputed Bill Gates-funded model for the White Houses' Coronavirus effort.
Gates is a big proponent for a population lockdown scenario for the Coronavirus outbreak.
As the United States begins to reopen in some areas, it is worth noting that Gates and other apparent experts were claiming that we would need months of shutdown and there would be no return to normal until vaccines were widely distributed.
Tags: Bill GatesCoronavirus


The Role of Big Data Analysis.
Since technology has really changed in this recent days, a number of data centres have been put in place to guarantee the data security. Big data is among the major things that have contributed to the development of systems that have artificial intelligence. Before making any important decisions in your company, it is advisable that you contact a reputable data analysis company. Going through the business analytic process will enable you learn various thing done by the business analyst such as prediction and how to inform business decisions. During the data visualization process, you manage to teach people how to understand the patterns, trends and also the insights when you convert the big data into visual content. Pie charts, line and column graphs are some of the ways visual data can be represented. Since businesses are faced with big data, and the changes in technology, artificial intelligence is being used in businesses. Data analysis has been taken by storm through the introduction of metadata-driven integration.
The dream for any business is to see their big data analyzed and thus should use metadata driven integration. You will be able to maintain a gap with your competitors when you use metadata driven integration into your business data analysis. For you to be innovative as you process your products, it is important that you use the data that would be generated by internet of everything (IoT). For this process, it is crucial that you have the insights. Businesses using data analytics will always enjoy several benefits as opposed to that business that does not really on the data analysis. For you to measure the level of your mission accomplishment, it is crucial that you use data analysis skills. It important to use the data business analysis which will enable you be pro-active and also be able to determine the customer's needs.
Regardless of the big data involved, you will be able to make the right decisions for you customers. Data analytics in your organization will help you mitigate the risks as well as the fraud. In order to get the best security and fraud protection level, it is important that you use data analysis skills. For effective field operations as well as productivity, it is important that you use advanced analytical skills. For you to provide your customers with the right and relevant products, it is crucial that you use the right and relevant data analysis skill. You will be able to transform your data into visual content after it has been extracted from the big data. Lastly, it is through data analysis that you will be able to remain updated and also relevant in the market throughout.
What Has Changed Recently With Analysis?


text:
\section{Introduction}

In many multi-agent applications, the underlying problem can be reduced to solving a system of linear equations\cite{mou2015distributed}.
Because the autonomous networked agents are usually discretely deployed, each agent only has the access to communicate with direct neighbors. Moreover, in certain scenarios, each agent only desires its own state. Such characteristics consequently give rise to distributed solvers for linear systems.  Different from the centralized solvers, distributed solvers usually adopt iterative manners. The key feature of iterative approaches is \emph{linear iterations}, where each agent receives states of direct neighbors; updates and sends its own state. The barycentric linear localization algorithm\cite{ECHO}, is a typical iteration-based method.

The convergence speed is a crucial factor of the iteration-based distributed algorithms, which determines whether the distributed algorithm can be used when the application requires a fast response.
However, the convergence rate of many iterative methods, e.g., Jacobi iteration, Gauss-Seidel iteration, and Richardson iteration\cite{Wolfgang2016}, are characterized by the spectral radius of the iteration matrix. However, the spectral radius is determined by the network topology and is difficult to be pre-tuned. Thus the convergence speed is highly uncertain and may be very slow in some network states.

\begin{figure}
	\centering
	\subfigure[The Richardson Iteration]{
		\begin{minipage}[T]{0.46\linewidth}
			\centering
			\includegraphics[width=1\textwidth]{trace_richardson_2d}
			\label{fig:trace_richardson_2d}
		\end{minipage}
	}
	\vspace{-0.2cm}
	\subfigure[DCG]{
		\begin{minipage}[T]{0.46\linewidth}
			\centering
			\includegraphics[width=1\textwidth]{trace_dcg_2d}
			\label{fig:trace_dcg_2d}
		\end{minipage}
	}
	\caption{The convergence trails in $\mathbb{R}^2$. The marker `+' represents the start a trail. The marker `$*$' and `$\circ$' represent the converged estimation $\mathbf{\hat{x}}_i$ and the ground truth  $\mathbf{x}_i$, respectively. }
	\label{fig:show_iter_2d}
\end{figure}

\begin{figure}
	\centering
	\includegraphics[width=.99\linewidth]{effectiveness_dcg_2d}
	\caption{The mean square error w.r.t. iteration rounds.}
	\label{fig:effectiveness_dcg_2d}
\end{figure}

To guarantee fast convergence of distributed algorithms in solving linear equations, this study explores  the idea of  Conjugate Gradient (CG)\cite{aggarwal2020linear}. CG has two desired properties for solving the linear systems: 1) CG converges to the exact solution after a finite number of iterations, which is not larger than the size of the system	matrix; 2)  CG is suited for solving linear systems with large and sparse system matrices.
But CG is essentially a centralized solver. In pursuit of distributed implementation, we design an efficient protocol to synchronize the necessary vectors to update the residual. Our distributed CG, i.e., DCG remarkably speeds up convergence by paying limited neighborhood communication costs.

The rest of the paper is organized as follows. We formulate the problem and present related algorithms in Section~\ref{sect:preliminaries}. DCG is proposed in Section~\ref{sect:dcg}.  Applications of DCG are discussed in Section~\ref{sect:applications}. DCG is evaluated in Section~\ref{sect:evaluation}. The paper is concluded with further discussions in Section~\ref{sect:conclusion}.

\noindent \textbf{Notations:} Throughout the paper, let $\mathbf{AX=b}$ denote a system of linear equations, where $\mathbf{A}\in\mathbb{R}^{n\times n}$ is the \emph{coefficient matrix}, $\mathbf{b}\in\mathbb{R}^{n\times d}$ is the \emph{right-hand side} vector, and  $\mathbf{X}\in\mathbb{R}^{n\times d}$ is the vector of unknowns.  $n$ is the number of variables and $d$ is the spatial dimension of a vector, $d\in\{2,3\}$. The vector $\mathbf{A}_{i,:} = [A_{i1} \cdots A_{in}]$ denotes the $i$th row of $\mathbf{A}$, $i\in\{1\cdots n\}$.

\section{Preliminaries}
\label{sect:preliminaries}
\subsection{Problem Formulation}

Consider a network of $n$ agents $\mathcal{V} = \{v_1,\cdots, v_n\}$,  each agent $v_i$ is capable of communicating with the agents within its reception range $R$. Let $\mathcal{E}$ be the set of edges and $(i,j)\in \mathcal{E}$ if the distance between $v_i$ and $v_j$ is not larger than $R$. Then the multi-agent network can be represented as a graph $\mathcal{G=(V,E)}$. The neighbors of $v_i$ is denoted by $\mathcal{N}_i$, $j\in\mathcal{N}_i$ if $(i,j)\in\mathcal{E}$.

\noindent \textbf{Problem:} Assume that $\mathbf{A}$ is non-singular. Let $\mathbf{X}^{*}$ denote the unique solution satisfying $\mathbf{AX=b}$. Suppose each agent $v_i$ holds a state vector $\mathbf{\hat x}_i\in\mathbb{R}^d$. Initially, $v_i$ knows $\mathbf{\mathbf{A}}_{i,:}$ and $\mathbf{\mathbf{b}}_{i,:}$. The problem is to devise a local rule for each agent to update its state $\mathbf{\hat x}_i$ leveraging the local communication with agents in $\mathcal{N}_i$ so that $\mathbf{\hat x}_i(t)$ converges to $\mathbf{x}^{*}_i$ within finite $t$.

\subsection{Related Work}
The basic idea of the iterative methods is as follows. Given an initialization $\mathbf{\hat x}(0)$, generate an iteration sequence  $\{\mathbf{\hat x}(t)\}_{t=0}^{\infty}$ in a certain manner, so that:

\begin{equation}
	\label{equ:iteration_sequence}
	\lim\limits_{t \to\infty}\mathbf{\hat x}(t) = \mathbf{x}^{*}\triangleq\mathbf{A}^{-1}\mathbf{b}.
\end{equation}

Generally, the state update of an iterative method can be represented as:
\begin{equation}
	\mathbf{\hat x}(t+1) = \phi_k(\mathbf{\hat x}(t),\mathbf{\hat x}(t-1)\cdots,\mathbf{\hat x}(0),\mathbf{A},\mathbf{b}),
\end{equation}
where $\mathbf{\hat x}(0)=\phi_0(\mathbf{A},\mathbf{b)}$ or $\mathbf{\hat x}(0)$ is selected manually. $\phi_k$ is called the \emph{iteration function}. The specific design of iterative functions are based on the \emph{matrix splitting}.
\begin{definition}[Matrix Splitting]
	Suppose a  non-singular matrix  $\mathbf{A}\in\mathbb{R}^{n\times n}$, a split of matrix $\mathbf{A}$ is defined  as $\mathbf{A} = \mathbf{M} - \mathbf{N}$, where $\mathbf{M}$ is also non-singular.
\end{definition}

Consider a general linear system:
\begin{equation}
	\label{equ:linear_system}
	\mathbf{AX=b},
\end{equation}
where $\mathbf{A}$ is non-singular. (\ref{equ:linear_system}) can be transformed as follows through matrix splitting $\mathbf{A} =\mathbf{M} - \mathbf{N}$.
\begin{equation}
	\label{equ:linear_split}
	\mathbf{M{X}=N{X}+b}.
\end{equation}
Then, we can construct an iteration function as:
\begin{equation}
	\label{equ:iteration_function}
	\mathbf{M\hat{X}}(t+1)=\mathbf{N\hat{X}}(t)+\mathbf{b},
\end{equation}
which is equivalent to:
\begin{equation}
	\label{equ:iteration_function_transform}
	\mathbf{\hat{X}}(t+1)=\mathbf{M}^{-1}\mathbf{N\hat{X}}(t)+\mathbf{M}^{-1}\mathbf{b} \triangleq \mathbf{G\hat{X}}(t) + \mathbf{g}.
\end{equation}
$\mathbf{G}=\mathbf{M}^{-1}\mathbf{b}$ is called the \emph{iteration matrix}.
It is straightforward that different iterative methods can be constructed by varying $\mathbf{M}$.

In Jacobi iteration, $\mathbf{A}$ is splitted as:

\begin{equation}
	\mathbf{A=D-L-U}.
\end{equation}
$\mathbf{D}$ is the diagonal component of $\mathbf{A}$. $-\mathbf{L}$ and $-\mathbf{U}$ are the upper triangle component and the lower triangle component of $\mathbf{A}$, respectively. Then, the Jacobi iteration is  specified as:

\begin{equation}
	\mathbf{\hat{X}}(t+1) = \mathbf{D}^{-1}(\mathbf{L}+\mathbf{U})\mathbf{\hat{X}}(t) + \mathbf{D}^{-1}\mathbf{b}.
\end{equation}

From the local behavior of an individual agent $v_i$, the state update is:

\begin{equation}
	\mathbf{\hat x}_i(t+1) = \frac{1}{A_{ii}}\left(\mathbf{b}_i-\sum\limits_{j=1,j\neq i}^n A_{ij}\mathbf{\hat x}_j(t)\right)
\end{equation}

In Gauss-Seidel iteration, the iteration function is designed as:

\begin{equation}
	\mathbf{\hat X}(t+1) = (\mathbf{D-L})^{-1}\mathbf{U}\mathbf{\hat X}(t) + (\mathbf{D-L})^{-1}\mathbf{b}.
\end{equation}

The local update of agent $v_i$'s state is:
\begin{equation}
	\mathbf{\hat x}_i(t+1) = \frac{1}{A_{ii}}\left(\mathbf{b}_i-\sum\limits_{j=1}^{i-1} A_{ij}\mathbf{\hat x}_j(t+1) - \sum\limits_{j=i+1}^{n}A_{ij}\mathbf{\hat x}_j(t) \right)
\end{equation}

Another brief iteration method is the Richardson iteration when $\mathbf{A}$ is symmetric positive definite. The iteration function is:

\begin{equation}
	\mathbf{\hat X}(t+1) = \mathbf{\hat X}(t)+ \omega(\mathbf{b}-\mathbf{A}\mathbf{\hat X}(t)).
\end{equation}

The state of agent $v_i$ is updated as:

\begin{equation}
	\mathbf{\hat x}_i(t+1) = \mathbf{\hat x}_i(t)+ \omega\left(\mathbf{b}_i- \sum\limits_{j=1}^{n}\mathbf{A}_{ij}\mathbf{\hat x}_j(t)\right),
\end{equation}
where $\omega$ is  a non-negative scalar and is suggested to be $\frac{2}{\lambda_{max}+\lambda_{min}}$.	Similar methods include the Successive Over-Relaxation (SOR) iteration, the Symmetric SOR (SSOR) iteration, the Accelerated OR (AOR) iteration, the Symmetric AOR (SAOR) etc \cite{barrett1994templates}.

\subsection{Convergence and Convergence Rate}
Since the aforementioned methods are iterative, a  crucial issue is to guarantee iteration convergence. For a general iteration function as in (\ref{equ:iteration_function_transform}), its convergence is guaranteed by the following theorem.

\begin{theorem}
	\label{theorem:correct_convergence}
	The iterates formulated by $\mathbf{\hat X}(t+1)=\mathbf{G}\mathbf{\hat X}(t)+\mathbf{b}$ converges for any $\mathbf{\hat X}(0)$, if and only if $\rho(\mathbf{G})<1$\cite{saad2003iterative}.
\end{theorem}
$\rho(\mathbf{G})$ is the spectral radius of the iteration matrix $\mathbf{G}$. See Theorem 4.1 of \cite{saad2003iterative} for the proof.

Apart from knowing when the iteration converges, it is also desirable to explore how fast it converges. Saad \cite{saad2003iterative} presented that the convergence rate $\tau$ is the natural logarithm of the inverse of the spectral radius:

\begin{equation}
	\tau=\ln\frac{1}{\rho(\mathbf{G})} = -\ln\rho(\mathbf{G}).
\end{equation}

It can be seen that these iterative methods converge slowly when $\mathbf{G}$ has unstable eigenvalues.

\section{DCG: A General Distributed Conjugate Gradient Implementation}
\label{sect:dcg}
The most attractive feature of CG is that it converges within a fixed round of iterations. But CG is essentially a centralized gradient-based solver for linear equations. See Section 6 of \cite{saad2003iterative} for the original CG algorithm.
Although parallel or distributed CG algorithms have been reported for allocating computational loads in cloud computing\cite{ismail2013implementation} and estimating spectrum in sensor networks\cite{xu2016distributed}, the general distributed CG has not been well touched.

The key difficulty in implementing Distributed CG (DCG) is that the state $\widehat{X}_i$ is updated based on several vectors, however, $v_i$ only knows the $i$th element of these vectors. Specifically,
$\widehat{X}_i(t)=\widehat{X}_i(t-1)+\alpha_i(t){d}_i(t)$.
$\alpha_i(t)$ and $d_i(t)$ are calculated using the direction vector $\mathbf{d}(t)$ and the residual vector $\mathbf{r}(t)$. But $v_i$ only knows $d_i$ and $r_i$.
\subsection{Vector Synchronization}

To supplement the necessary information, we design the \emph{Synchronize\_Vector}($z_i$) protocol, through which $v_i$ can gather any complete vector $\mathbf{z}$ by constantly exchanging respective elements with neighbors (Line~\ref{dcg:syn_ini}-\ref{dcg:syn_ret} of Algorithm~\ref{alg:DCG}). $H$ is the largest number of hops throughout the network. So the synchronization can be finished in $H$ rounds. $H$ can be set to $n$ if it is not given at network deployment. The operation `\emph{merge}' (Line~\ref{dcg:syn_merge}) means selecting all non-zero elements of the input vectors and stacking them as a new vector while maintaining their original indexes.

\subsection{Distributed Conjugate Gradient}
\label{sect:general_DCG}
DCG is detailed as \textbf{Function DCG} (Line~\ref{dcg:ini}-\ref{dcg:ret} of Algorithm~\ref{alg:DCG}). At initialization (Line~\ref{dcg:ini}), the state $\widehat{X}_i(0)$ is set to 0. The direction vector component ${d}_i$ and the residual vector component ${r}_i$ are set to 0 and $-{b}_i$, respectively. At each iteration $t$, the local behavior of a node $v_i$ is as follows:
\begin{itemize}
	\item \textbf{Update Residual} (Line \ref{dcg:residual}).
	The residual ${r}_i$ is updated by	${r}_i(t)=(\mathbf{\mathbf{A}\widehat{X}})_i(t-1)-{b}_i$, which is realized  by ${r}_i(t) = -b_i+\sum\nolimits_{j\in\mathcal{N}_i}\mathbf{A}_{ij}\widehat{X}_j(t-1)$. $\mathbf{\mathbf{A}}_{(i,:)}$ and $b_i$ are known to $v_i$ at the begining. $\widehat{X}_j(t-1)$ is the state of neighbor $v_j$ obtained by local communication.
	\item \textbf{Check Residual} (Line \ref{dcg:terminate}).
	CG theoretically completes after $n$ iterations \cite{Wolfgang2016}. However, due to the accumulated floating point rounding off errors, the residual and the direction gradually lose accuracy. Thus, DCG terminates by checking whether $\mathbf{r}(t)^T\mathbf{r}(t)<\varepsilon$. The threshold $\varepsilon$ is an empirical value based on accuracy requirement. 	$\mathbf{r}(t)$ is obtained by: $\mathbf{r}(t)=$  \emph{Synchronize\_Vector}($r_i(t)$). After knowing the synchronized $\mathbf{r}$, the squared residual is calculated as $\mathbf{r}(t)^T\mathbf{r}(t)=\sum_{i=1}^{n}r_i(t)^2$.

	\item \textbf{Update Direction} (Line \ref{dcg:direction}).
	$d_i$ needs another vector $\mathbf{r}(t-1)$ to be updated. It is  obtained by \emph{Synchronize\_Vector}($r_i(t-1)$). Then, $\mathbf{r}(t-1)^T\mathbf{r}(t-1)=\sum_{i=1}^{n}r_i(t-1)^2$ and $d_i$ can be calculated locally.
	\item \textbf{Update Step Size} (Line \ref{dcg:step}).

	Represent the numerator and denominator of $\alpha_i$ as  $numer=\mathbf{d}(t)^T\mathbf{r}(t)$ and $denom=\mathbf{d}(t)^{T}\mathbf{\mathbf{A}}\mathbf{d}(t)$, respectively.
	The direction vector $\mathbf{d}(t)$ is obtained by \emph{Synchronize\_Vector}($d_i(t)$). So the numerator can be known as $numer=\sum_{i=1}^{n}d_i(t)r_i(t)$.

	An intermediate vector $\mathbf{T}(t)=[T_1(t)\cdots T_n(t)]^T$ is introduced to calculate $denom$. By communicating with neighbors, $v_i$ calculates ${T}_i(t)= \sum\nolimits_{j\in\mathcal{N}_i}\mathbf{A}_{ij}{d}_{j}(t)$. The complete $\mathbf{T}(t)$ is obtained by \emph{Synchronize\_Vector}($T_i(t)$). So $denom=\sum\nolimits_{i=1}^{n}d_i(t)T_i(t)$. Then $\alpha_i=-numer/denom$.

	\item \textbf{Update State}  (Line \ref{dcg:estimation}).
	The state $\widehat{X}_i(t)$ updates a step $\alpha_i(t){d}_i(t)$ along its last state.
\end{itemize}
Overall, all of the above DCG procedures are completely distributed and implemented through neighborhood message passing.

	\begin{algorithm}[h]
		\caption{\textbf{Distributed Conjugate Gradient (DCG) of $v_i$}}
		\label{alg:DCG}
		\KwIn{$\mathbf{\Omega}_{(i,:)}$; $b_i$\;}
		\KwOut{$\mathbf{\hat x}_i$\;}

		{

			\lnl{dcg:ini} $\widehat{X}_i(0)\gets 0$; ${d}_i(0)\gets 0$;
			${r}_i(0)\gets -b_i$ \tcp{\small{Initialize}}
			\tcc{\small{Update $\widehat{X}_i$ as in Section~\ref{sect:general_DCG}}}
			\nl \For{iterations $t\in\{1,\cdots,t_{max}\}$}
			{
				\lnl{dcg:residual} ${r}_i(t)=(\mathbf{\Omega \widehat{X}}(t-1))_i-{b}_i$; \tcp{\small{residual}}
				\lnl{dcg:terminate} \If{$\mathbf{r}(t)^T\mathbf{r}(t)<\varepsilon$}
				{
					\nl\textbf{break} \tcp{\small{meets accuracy requirement}}
				}
				\lnl{dcg:direction} ${d}_i(t)$=$-{r}_i(t)$+$\frac{\mathbf{r}(t)^{T}\mathbf{r}(t)}{\mathbf{r}(t-1)^{T}\mathbf{r}(t-1)}$${d}_i(t-1)$
				$//$\texttt{\small{direction}}\\
				\lnl{dcg:step} $\alpha_i(t)=-\frac{\mathbf{d}(t)^{T}\mathbf{r}(t)}{\mathbf{d}(t)^{T}\mathbf{\Omega}\mathbf{d}(t)}$; \tcp{\small{step size}}
				\lnl{dcg:estimation} $\widehat{X}_i(t)=\widehat{X}_i(t-1)+\alpha_i(t){d}_i(t)$; \tcp{\small{state}}
			}
		}
		\lnl{dcg:ret}\KwRet{$\widehat{X}_i(t)$.}
		\vspace{5pt}\\
		\textbf{Function Synchronize$\_$Vector}($z_i$)\\
		{

			\lnl{dcg:syn_ini} initialize $\mathbf{z}_i(0)$ $\gets$ $[\boldsymbol{0}_{(i-1)\times 1}~z_i~\boldsymbol{0}_{(n-i)\times 1}]$\;
			\nl \For {iterations $k\in\{0,\cdots,H\}$}
			{
				\nl exchange $\mathbf{z}_i(k)$ with $\mathcal{N}_i$\;
				\nl \For{each $v_j\in\mathcal{N}_i$}
				{
					\lnl{dcg:syn_merge} $\mathbf{z}_i(k+1)$  $\gets$ \textbf{merge}($\mathbf{z}_i(k)$, $\mathbf{z}_{j}(k)$)\;
				}
			}
			\lnl{dcg:syn_ret}\KwRet{$\mathbf{z}_i$}.
		}

	\end{algorithm}

\subsection{Analysis of DCG}

In each round, four vectors are obtained by synchronization, so it converges within $4Hn$ rounds when $\mathbf{A}$ is non-singular. In actual applications, there may exist measurement noise so that $\mathbf{A}$ and $\mathbf{b}$ are influenced and the constructed linear system may be unsolvable\cite{Xie2020}. Let $\overline{\mathbf{A}}$ and $\overline{\mathbf{b}}$ denote the noisy matrices as:
\begin{equation}
	\label{equ:noise}
	\overline{\mathbf{A}} = \mathbf{A}+\Delta\mathbf{A}, \overline{\mathbf{b}} = \mathbf{b}+\Delta\mathbf{b},
\end{equation}
where $\Delta\mathbf{A}$ and $\Delta\mathbf{b}$ are error matrices implying the noise. If the noisy matrix $\overline{\mathbf{A}}$ is still non-singular, DCG still converges to the neighborhood of $\mathbf{X}^*$.
\begin{lemma}
	For a noisy linear system $\overline{\mathbf{A}}\mathbf{X}=\mathbf{b}$, DCG converges if the error matrix satisfies:
	\begin{equation}
		\label{equ:noise_converge}
		||\Delta\mathbf{A}||<\lambda_{min}(\mathbf{A}).
	\end{equation}
\end{lemma}
\begin{proof}
	From (\ref{equ:noise}), we can obtain:
	\begin{equation}
		\overline{\mathbf{A}} = \mathbf{A}(I+\mathbf{A}^{-1}\Delta\mathbf{A}).
	\end{equation}
	Since $||\mathbf{A}^{-1}\Delta\mathbf{A}||\leq||\mathbf{A}^{-1}||~||\Delta\mathbf{A}||=\frac{||\Delta\mathbf{A}||}{\lambda_{min}(\mathbf{A})}$, the matrix $\overline{\mathbf{A}}$ must be non-singular if (\ref{equ:noise_converge}) holds. Thus DCG can converge to the neighborhood of $\mathbf{X}^*$ shown as: $\mathbf{\overline X}^*=\overline{\mathbf{A}}^{-1}\overline{\mathbf{b}}$.
\end{proof}
\section{Applications of DCG}
\label{sect:applications}
In this section, we investigate applying DCG to two actual scenarios.

\subsection{The Least Square Problem}
Linear equations arising from the era of engineering are usually over-determined. A typical scenario is distributed parameter estimation, where the observation equations are as:

\begin{equation}
	A_i x_i = b_i+\delta_i,
\end{equation}
where $x_i$ is the desired parameter to be calculated and $\delta_i$ is the component implying the measurement noise of $b_i$. Due to the measurement noise, such linear equations usually do not have a solution that exactly meets the constraints. This problem can be formulated as follows. Suppose there is no solution to the linear system $\mathbf{AX=b}$ and $\mathbf{AA}^{T}$ is non-singular. Each agent $v_i$ only knows the $i$th row of $\mathbf{A}$ and $\mathbf{b}$, which are denoted by  $\mathbf{A}_{i,:}$ and $\mathbf{b}_{i,:}$, respectively. Design a distributed rule for each agent to update its state $\mathbf{x}_i$ so that $\mathbf{x}_i(t)$ converges to the unique solution of:
\begin{equation}
	\label{equ:least_square}
	\mathbf{A}^{T}\mathbf{AX}=\mathbf{A}^{T}\mathbf{b}.
\end{equation}

Let $\boldsymbol{\Omega} =\mathbf{A}^{T}\mathbf{A}$ and $\boldsymbol{\beta} =\mathbf{A}^{T}\mathbf{b}$.
To solve the least square problem as in (\ref{equ:least_square}), each agent should be aware of the $i$th row of $\boldsymbol{\Omega}$ and $\boldsymbol{\beta}$ using $\mathbf{A}_{i,:}$ and $\mathbf{b}_{i,:}$.

Initially, $v_i$ maintains $\mathbf{A}_{i,:}$
Then, $v_i$ transmits ${A}_{i,j}$ to $\mathcal{N}_i$ and receives ${A}_{j,i}$ from $\mathcal{N}_i$, then  it also knows the nonzero elements of the $i$th column $\mathbf{A}_{:,i}$, i.e., $\mathbf{A}^T_{i,:}$. Thus the nonzero elements of $\boldsymbol{\Omega}_{i,:}$ are calculated distributively as:
\begin{equation}
	\label{equ:ini_omega}
	{\Omega}_{ij}=\sum\nolimits_{k=1}^{n} {A}^T_{ik}A_{kj},\forall v_j\in\mathcal{N}_i.
\end{equation}

Similarly, $\boldsymbol{\beta}_{i,:}$ can be calculated as:
\begin{equation}
	\label{equ:ini_beta}
	{\beta}_{ij}=\sum\nolimits_{k=1}^{n} {A}^T_{ik}b_{kj},  j\in\{1,\cdots,d\}.
\end{equation}

Finally, the problem can be solved as $\mathbf{x}_i=DCG(\boldsymbol{\Omega}_{i,:}, \boldsymbol{\beta}_{i,:})$. Therefore $\mathbf{x}$ solves the least squares problem in (\ref{equ:least_square}).

\subsection{The Network Localization Problem}
The geographical locations of nodes are fundamental information for many multi-agent applications\cite{Nguyen2020,Sun2018,Wang2018}. Network localization techniques are usually adopted for calculating node locations in infrastructure-less scenarios\cite{Ping2020,PingHGO}, which are formulated as follows.
For a network of $m+n$ agents in $\mathbb{R}^d$, let $\mathcal{V}=\mathcal{A}\cup\mathcal{F}$ denote the entire node set.   Nodes in $\mathcal{A}=\{v_1,\cdots,v_m\}$ are called \emph{anchor agents}, whose locations $\mathbf{P}_{\mathcal{A}} = \{\mathbf{p}_1,\cdots,\mathbf{p}_m\}$ are known.  Nodes in $\mathcal{F}= \{v_{m+1},\cdots,v_{m+n}\}$ are called \emph{free agents}, whose locations $\mathbf{P}_{\mathcal{F}} = \{\mathbf{p}_{m+1},\cdots,\mathbf{p}_{m+n}\}$ are unknown. Each agent $v_i$ can only sense the relative distance $d_{ij}$ between $v_i$ and any neighbor $v_j\in\mathcal{N}_i$. Each agent can exchange its estimated location  $\hat{\mathbf{p}}_i$ and distance measurements with neighbors. The network localization problem is to design a distributed protocol for each agent to update its location $\hat{\mathbf{p}}_i$ so that it converges to $\mathbf{p}_i$.

To solve the network localization problem, we transform it to a linear system. First, each location $\mathbf{p}_i$ is represented as a linear combination of locations of neighbors:
\begin{equation}
	\label{equ:cal_bary}
	\mathbf{p}_i = \sum_{v_j\in\mathcal{N}_i} a_{ij}\mathbf{p}_j,
\end{equation}
where $a_{ij}$ are called \emph{barycentric coordinates}. The calculation of barycentric coordinates involve only local distance measurements and the specific process is introduced by Diao et al. \cite{ECHO} in $\mathbb{R}^2$ and by Han et al. \cite{Han2017} in $\mathbb{R}^3$. Then after calculating the barycentric coordinates for each node, the agent locations can form a linear system:
\begin{equation}
	\label{equ:linear_representation}
	\left[ {\begin{array}{*{20}{c}}
			{{{\mathbf{P}}_{\mathcal{A}}}} \\
			{{{{\mathbf{ P}}}_{\mathcal{F}}}}
	\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
			{\mathbf{I}}&{\mathbf{0}} \\
			{\mathbf{B}}&{\mathbf{C}}
	\end{array}} \right]\left[ {\begin{array}{*{20}{c}}
			{{{\mathbf{P}}_{\mathcal{A}}}} \\
			{{{{\mathbf{P}}}_{\mathcal{F}}}}
	\end{array}} \right].
\end{equation}
$\mathbf{A}=\left[ {\begin{array}{*{20}{c}}
		{\mathbf{I}}&{\mathbf{0}} \\
		{\mathbf{B}}&{\mathbf{C}}
\end{array}} \right] \in\mathbb{R}^{(m+n)\times(m+n)}$ is constructed with barycentric coordinates, i.e., the $i$th row of $\mathbf{A}$  is the barycentric coordinate of $v_i$ w.r.t. its neighbors $\mathcal{N}_i$. Then, the localization problem can be transformed into  solving the following linear system:
\begin{equation}
	\label{equ:bll_problem}
	(\mathbf{I}-\mathbf{C})\mathbf{P}_{\mathcal{F}} = \mathbf{B}\mathbf{P}_{\mathcal{A}}.
\end{equation}
Writing $\mathbf{I}-\mathbf{C}$ as $\mathbf{M}$, (\ref{equ:bll_problem})  can be reformulated as:
\begin{equation}
	\label{equ:gbll_problem_reformulate}

	\mathbf{M}\mathbf{P}_{\mathcal{F}} = \mathbf{B}\mathbf{P}_{\mathcal{A}}.
\end{equation}
Considering that CG is used when the system matrix is positive definite \cite{Wolfgang2016}. Thus, we multiply $\mathbf{M}^{T}$ to both sides of (\ref{equ:gbll_problem_reformulate}):
\begin{equation}
	\label{equ:gbll_problem_positive}
	\mathbf{M}^{T}\mathbf{M}\mathbf{P}_{\mathcal{F}} = \mathbf{M}^{T}\mathbf{B}\mathbf{P}_{\mathcal{A}}.
\end{equation}
Then, $\mathbf{M}^{T}\mathbf{M}$ is positive definite.
To apply DCG to distributed localization, the  localization model in (\ref{equ:gbll_problem_positive}) is reformulated to $\boldsymbol{\Omega}\mathbf{P}_{\mathcal{F}}=\boldsymbol{\beta}$, where $\boldsymbol{\Omega}$ = $\mathbf{M}^{T}\mathbf{M}\in\mathbb{R}^{n\times n}$ and $\boldsymbol{\beta}$ = $\mathbf{M}^{T}\mathbf{B}\mathbf{P}_{\mathcal{A}}\in\mathbb{R}^{n\times d}$.

Algorithm~\ref{alg:DCG_Loc} shows the routine of DCG-Loc. For initialization, $v_i$ needs to know the $i$th row of $\boldsymbol{\Omega}$ and $\boldsymbol{\beta}$ to invoke the general DCG.
After constructing the local linear model by (\ref{equ:cal_bary}), $v_i$ maintains $\mathbf{A}_{i,:}$, so it knows the nonzero elements of the $i$th row $\mathbf{M}_{i,:}$ by ${M}_{i,j}=-A_{i,j}$ if $v_j\in\mathcal{N}_i$.
Then, $v_i$ transmits ${M}_{ij}$ to $\mathcal{N}_i$ and receives ${M}_{ji}$ from $\mathcal{N}_i$ (Line~\ref{dcg:send_M}-\ref{dcg:receive_M}), so it also knows the nonzero elements of the $i$th column $\mathbf{M}_{:,i}$, i.e., $\mathbf{M}^T_{i,:}$. Thus the nonzero elements of $\boldsymbol{\Omega}_{i,:}$ are calculated distributively as:
\begin{equation}
	\label{equ:dcg_ini_omega}
	\boldsymbol{\Omega}_{ij}=\sum\nolimits_{k=1}^{n} {M}^T_{ik}M_{kj},\forall v_j\in\mathcal{N}_i.
\end{equation}
To calculate $\boldsymbol{\beta}_{(i,:)}$, an intermediate vector $\boldsymbol{\mu}\in\mathbb{R}^{n\times d}$ implying $\mathbf{B}\mathbf{P}_{\mathcal{A}}$ is introduced. $v_i$ locally calculates the $i$th row of $\boldsymbol{\mu}$:
\begin{equation}
	\label{equ:dcg_ini_mu}
	\boldsymbol{\mu}_{i,:}=\sum\nolimits_{v_a\in \mathcal{N}_i\cap\mathcal{A}} A_{ia}\mathbf{p}_a,
\end{equation}
where $\mathcal{N}_i\cap\mathcal{A}$ represents neighboring anchors.
$\boldsymbol{\mu}_{i,:}$ = $[0,0]$ if no anchor is found in $\mathcal{N}_i$. Then, $v_i$ sends $\boldsymbol{\mu}_{i,:}$ to $\mathcal{N}_i$ and receives $\boldsymbol{\mu}_{j,:}$  of each $v_j\in\mathcal{N}_i^*$ (Line~\ref{dcg:send_M}-\ref{dcg:receive_M}). Thus, $\boldsymbol{\beta}_{i,:}$ is calculated as:

\begin{equation}
	\label{equ:dcg_ini_beta}
	\boldsymbol{\beta}_{i,:} = \sum\nolimits_{v_j\in \mathcal{N}_i\cap\mathcal{F}}M^T_{i,j}\boldsymbol{\mu}^{}_{j,:},
\end{equation}
where $\mathcal{N}_i\cap\mathcal{F}$ means the non-anchor barycentric neighbors.
For convenience, each location $\mathbf{\hat{p}}_i\in\mathbb{R}^{d\times 1}$ is decomposed to $[\hat{p}^{1}_i,\cdots,\hat{p}^{d}_i]$.  $\boldsymbol{\beta}_{(i,:)}$ is decomposed to $[\beta_i^{1},\cdots,\beta_i^{d}]$. The element $\hat{p}^j_i$ is calculated by \textbf{DCG}($\boldsymbol{\mathbf{A}}_{i,:}$, $\beta_i^j$) (Line~\ref{dcg:ret_loc}). Therefore, from the GBLL model in (\ref{equ:gbll_problem_positive}), $\mathbf{\hat{p}}_i$ is calculated leveraging DCG-Loc, where communications only involve message passing with neighbors.

	\begin{algorithm}[h]
		\caption{\textbf{Distributed Conjugate Gradient Localization (DCG-Loc) of $v_i$}}

		\label{alg:DCG_Loc}
		\KwIn{neighbors: $\mathcal{N}_i$;  barycentric coordinates: $\mathbf{A}_{i,:}$\;}
		\KwOut{location: $\mathbf{\hat p}_i$\;}

		\lnl{dcg:init_M} $M_{ij}\gets-A_{ij}$; calculate $\boldsymbol{\mu}_{i,:}$ as (\ref{equ:dcg_ini_mu})\;
		\lnl{dcg:send_M} transmit $M_{ij}$ and $\boldsymbol{\mu}_{i,:}$ to $v_j\in\mathcal{N}_i$\;
		\lnl{dcg:receive_M} receive $M_{ji}$ and $\boldsymbol{\mu}_{j,:}$ from $v_j\in\mathcal{N}_i$\;

		\lnl{dcg:init_omega} calculate $\boldsymbol{\Omega}_{i,:}$ as (\ref{equ:dcg_ini_omega}), calculate $\boldsymbol{\beta}_{i,:}$ as (\ref{equ:dcg_ini_beta})\;
		\lnl{dcg:ret_loc}\KwRet $\mathbf{\hat{p}}_i\gets$ [\textbf{DCG}($\boldsymbol{\Omega}_{i,:}$, $\beta_i^1$),$\cdots$, \textbf{DCG}($\boldsymbol{\Omega}_{i,:}$, $\beta_i^d$)].

	\end{algorithm}

\section{Evaluation}
\label{sect:evaluation}

In this section, we evaluate the convergence speed between our proposed DCG algorithm and the representative Richardson iteration by counting the iteration rounds. Simulations are conducted using MATLAB R2020b in both $\mathbb{R}^2$ and $\mathbb{R}^3$. A network denoted by $\mathcal{G=\{V,E\}}$ is deployed. The number of anchors is set to $d+1$, which is the minimum number of anchors required to uniquely localize a network in $\mathbb{R}^d$.

Fig. \ref{fig:show_iter_2d} and Fig. \ref{fig:effectiveness_dcg_2d} shows the results in $\mathbb{R}^2$. DCG  and Richardson iteration are adopted to solve the linear
localization problem modeled by the network in Fig. \ref{fig:show_iter_2d}. It is shown that both DCG  and Richardson successfully converge to the ground truth within finite rounds of iterations. However, Fig. \ref{fig:effectiveness_dcg_2d} shows that the Richardson iteration consumes $5\times10^{5}$ rounds while DCG only needs 550 rounds.
From Fig. \ref{fig:show_iter_3d} and Fig. \ref{fig:effectiveness_dcg_3d}, similar results can be obtained in $\mathbb{R}^3$. Overall, DCG-Loc is shown to be faster than Richardson iteration
about 1,000 times.

\begin{figure}
	\centering
	\subfigure[The Richardson Iteration]{
		\begin{minipage}[t]{0.46\linewidth}
			\centering
			\includegraphics[width=1\textwidth]{trace_richardson_3d}
			\label{fig:trace_richardson_3d}
		\end{minipage}
	}
	\vspace{-0.2cm}
	\subfigure[DCG]{
		\begin{minipage}[t]{0.46\linewidth}
			\centering
			\includegraphics[width=1\textwidth]{trace_dcg_3d}
			\label{fig:trace_dcg_3d}
		\end{minipage}
	}
	\caption{The convergence trails in $\mathbb{R}^3$.
	\label{fig:show_iter_3d}
\end{figure}

\begin{figure}
	\centering
	\includegraphics[width=.99\linewidth]{effectiveness_dcg_3d}
	\caption{The mean square error w.r.t. iteration rounds.}
	\label{fig:effectiveness_dcg_3d}
\end{figure}

\section{Conclusion}
\label{sect:conclusion}
In this paper, we proposed DCG to enable a network of $n$ agents to solve linear equations like $\mathbf{AX=b}$ in fixed rounds of iterations. The DCG algorithm is presented with property analysis and two applications. Compared with traditional Richardson iteration, DCG shows 3 magnitudes faster convergence speed. In future work, we will consider reducing the communication burden that DCG requires.

\bibliographystyle{unsrt}

redpajama_set_name: RedPajamaArXiv


text:
Man banned from contacting his own parents for three years after attacking them during vodka binge
Andrew Graham attacked his elderly parents after drinking vodka in his room all day
Mark Naylor
Andrew Graham has been banned from contacting his parents for three years (Image: Grimsby & Scunthorpe Newspapers)
A nightmare son who made the lives of his elderly parents a misery viciously attacked them both after drinking vodka in his room all day.
His mother had been "treading on egg shells" trying not to upset him but he has now been banned by a court from contacting them for three years.
Andrew Graham, 50, who has been living at Harbour Place, Grimsby, admitted assaulting his mother and father on December 21.
Kate Fairburn, prosecuting, told Grimsby magistrates that a restraining order had previously been made against Graham concerning his parents but he breached it.
He later lived with them for about eight months because he had nowhere else to stay.
Police were alerted just before 8pm after he went downstairs to where they were watching TV.
He had been drinking vodka all day in his room.
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Graham went over to his father and attacked him with both hands, punching him to the head at least six times, leaving him with a cut to his ear and a bruise near his eye.
Graham's mother telephoned 999 but he pulled her by her hair and punched her on her arm, near her shoulder.
He later told police that his relationship with his parents had always been bad and that he did not get on with his father and "could not stand him".
He branded him a "horrible man" and claimed the house in Cleethorpes, was not fit to live in.
He claimed he argued with his parents all the time, especially his father.
Graham's elderly mother later said in a statement that her son's behaviour made her feel very nervous.
She felt intimidated by him and said: "I have been treading on egg shells trying to live with him and appease him.
"I am afraid of what he might do."
Barney Murphy, mitigating, told the court that Graham might suffer from mental health problems but had not been in trouble since March 2014, when he appeared in court for breaching a restraining order.
£11k disappears from pensioner's bank account in four months - 'setting off alarm bells'
Shockingly low conviction rate for domestic abuse in region
"Clearly, alcohol is one of the problems he faces," said Mr Murphy.
"He had been drinking vodka all day in his room. He had probably drunk more than normally."
Graham had admitted: "I can't even remember what happened."
He felt remorse but had difficulty showing it.
Unemployed Graham was given a 12-week suspended prison sentence, six months' alcohol treatment, six days' rehabilitation and a three-year restraining order, banning him from contacting his parents or entering their street.
He was ordered to pay £100 compensation and £85 costs.
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text:
You are here: Home › Corpora › Corpus of Oz Early English › 1-201 (Text)
1-201 (Text)
addressee author,male,Broadside,un
1-201 (Raw), Raw 1-201 (Text), Text 1-201 (Original), Original
Newspapers & Broadsides
Ingleton, 1988
1-201-plain.txt
1-201#Text
1-201-plain.txt — 3 KB
Whereas, on Saturday Night last, the 15th Instant, between 9 & 10 O'clock, at the South End of Prince-street, Mr. Robert Howe was most barbarously and cruelly stabbed with an old Rusty Bayonet, by some Ruffian, with an evident Intent to murder him: - The above Reward of Fifty Pounds will be paid at the GAZETTE OFFICE to any Person or Persons, who will give such Evidence as shall lead to a Conviction of the Perpetrator of this bloody Deed.
GAZETTE OFFICE, SYDNEY, June 16, 1822.
Few transactions are recorded in the annals of human guilt that are stamped with so deep and horrid an atrocity, or so destitute of every circumstance that could soften and mitigate the crime, as that which it is now our painful task to relate.
On the evening of Saturday last, the 15th instant, a little after 9 o'clock, as Mr Robert Howe, the printer and publisher of the SYDNEY GAZETTE, was walking from the Mission-house, in Prince-street, he observed a suspicious man crossing the street, opposite the chapel; but, apprehending nothing serious, he proceeded along the foot-path, and the man continued to walk before him, at the distance of six or seven yards; till on coming to an abrupt curvature in the street, the villain suddenly turned back, rushed on Mr Howe, plunged a bayonet into his breast, and instantly disappeared.
The dreadful cry of "Murder!" alarmed the whole neighbourhood - multitudes hurried into the street - but it was too late to overtake the cowardly assassin, who, concealed by the dark mantle of night, but too well eluded pursuit.
Mr Howe ran as far as Mr Scott's door, where, exhausted by the effort, he fell into the arms of his dismayed friends, and was carried into the house, weltering in his blood, and apparently in the agonies of death. Surgical aid being immediately called in, it was ascertained to be a ragged triangular punctured wound, about two inches from the left breast externally, perforating into the cavity of the thorax. The lung appeared, very fortunately to have escaped Unwounded; a circumstance perhaps solely attributed to the point of the instrument having been broken off. Had the wound perforated the viscus, there is too much reason to dread, from its proximity to the larger blood vessels, that its effects would have been instantly fatal.
The weapon with which the foul deed was perpetrated was found in the street, at a short distance from Mr Howe's hat; and it was truly the most horrid kind of instrument which could be thrust into the human body. It was an old bayonet, fastened to the end of a poll about four feet long; the blade thickly encrusted with rust, about an inch of the point broken off, and the edges hacked like the teeth of a saw. When picked up it was stained with blood about four inches deep; which shews with what desperate force the stab must have been given, and how narrow was the escape from instant death.
But from what motives could this deed of horror have been perpetrated? It is obvious that the cold-blooded assassin sought only his defenceless victim's life; for no sooner had he given the deadly thrust, than he uttered a shout of exultation, threw down the weapon, and, without the least attempt at robbery, hurried from the spot.
His only motive must have been - REVENGE. But Mr Howe's character was too just and inoffensive to have given any reasonable cause for so diabolic a passion. The infatuated man must have long brooded over some fancied injury, till his passions were wrought into a frenzy, fit for the most ruthless deeds.
Though the night was too dark for the ruffian's person to be distinctly recognized, Mr Howe had an instant suspicion of one of two individuals, both of whom were immediately lodged in custody; but one has since been liberated, being able to prove that he was in his own house at the time the attack was made. The other remains, under suspicion, for futher examination.
http://ns.ausnc.org.au/corpora/cooee/source/1-201#Text


Web content synchronization Web content, including HTML pages that define the application itself, is synchronized through M-Business Anywhere.
Data synchronization The UltraLite database is synchronized with a MobiLink server.
Although these two kinds of synchronization are distinct, you can initiate them together in a technique called one-button synchronization. One-button synchronization is the recommended model for most applications, but as there may be cases where it is necessary to keep synchronization of data and web content entirely separate, that technique is discussed below.


text:
namespace Poco {
namespace Net {

HTTPServer::HTTPServer(HTTPRequestHandlerFactory::Ptr pFactory, const ServerSocket& socket, HTTPServerParams::Ptr pParams):
	TCPServer(new HTTPServerConnectionFactory(pParams, pFactory), socket, pParams),
	_pFactory(pFactory)
{
}

HTTPServer::HTTPServer(HTTPRequestHandlerFactory::Ptr pFactory, Poco::ThreadPool& threadPool, const ServerSocket& socket, HTTPServerParams::Ptr pParams):
	TCPServer(new HTTPServerConnectionFactory(pParams, pFactory), threadPool, socket, pParams),
	_pFactory(pFactory)
{
}

HTTPServer::~HTTPServer()
{
}

void HTTPServer::stopAll(bool abortCurrent)
{
	_pFactory->serverStopped(this, abortCurrent);
	stop();
}

} } // namespace Poco::Net