text:
The 8 Best Jam-Centric Albums Ever
Warren Haynes knows exactly what appeals about a jam session.
"It's momentary composition," says the prolific Gov't Mule singer and guitarist, who also tripled up as a member of the Allman Brothers Band and the Grateful Dead's post-Jerry Garcia incarnation, The Dead. "You're composing on the spot. And for a solo instrumentalist, that's probably the most gratification you can get. When you're improvising, it's totally on the fly. There is no second chance."
Haynes should know. The man voted the 23rd greatest guitarist of all time by Rolling Stone magazine is a performer prone to cross-pollinating all kinds of everything, from blues to jazz, rock to country. And as for that old cliché of jam bands playing toke'd-up, heads-down variants of 12-bar boogie, Haynes says the purest examples are anything but.
"I've always felt the jam scene should include more jazz, blues, reggae, bluegrass, whatever," he offers. "Anybody who makes improvisation their lifeblood should feel like that, because what makes it work is the open-mindedness."
Jam-centric live albums are legion, but their studio counterparts are an altogether rarer beast. Here, then, is Warren Haynes's choice spread of both..
John Coltrane - Blue Train (Blue Note, 1957)
When I was growing up, it felt like somewhere between the blues and Coltrane's jazz records was the source of inspiration for rock 'n' roll bands who would play long solos. I loved it when Coltrane pushed the boundaries, but I particularly loved the records he made prior to that. Blue Train is my favorite of those.
Some critics thought he was just trying too hard to create something strange; then he'd turn around and make a record that was absolutely beautiful.
Sly & The Family Stone - Stand! (Epic, 1969)
All the music I grew up listening to was soul music: Otis Redding, Wilson Pickett, Sam & Dave, James Brown. Eventually, when my eldest brother got Stand!, that started building a bridge to rock 'n' roll for me.
When I got a guitar in 1972, I would spend hours listening to records like this, trying to figure out what they were playing. I think that's a phase all guitar players go through.
BB King - Indianola Mississippi Seeds (ABC, 1970)
When the blues guys I loved started making more contemporary records, ones that were combining modern soul music with blues, they kind of got into jam territory. Freddie King did it with Burglar [1974] and Albert King did it with Born Under A Bad Sign [1967].
B.B. King did it on this album. All of a sudden there were wah-wah pedals and rock musicians accompanying blues players side by side, improvising.
The Allman Brothers Band - At Fillmore East (Capricorn, 1971)
All the musicians I was hanging out with at the time were big fans of this album. One of us had an eight-track cassette of it and we'd play it over and over. It sounds incredible, even to this day.
Sonically, it's so beautiful and fresh, with some of the greatest guitar sounds I've ever heard. And there's a great chemistry. It's a perfect indication of a band that can't be captured the same way in the studio as they can be live.
Steely Dan - The Royal Scam (ABC, 1976)
I went to see Steely Dan perform The Royal Scam in Chicago, with Larry Carlton playing guitar. There was something about that record that really appealed to me.
It had so many great guitar solos and the music was so complex compared to most rock 'n' roll records we were listening to at that time. This was a record I studied a lot as well.
Little Feat - Waiting for Columbus (Warner Brothers, 1978)
It way surpasses any of their studio recordings. One of the odd things about this album is that the tempos are slower than they are on the studio records.
They found their groove by slowing the music down, whereas it tends to be the opposite with most bands in live performance. Little Feat somehow figured out that doing that would make them groove harder. I think it's Lowell George's most amazing performance, but the entire band are on fire.
Medeski, Martin & Wood - Notes From the Underground (Gramavision Records, 1992)
When I grew up, you'd hear Sly & The Family Stone on FM radio, then right after that there'd be The Byrds or Bob Dylan. The only things that made those acts similar were the intent and the open-mindedness.
I kind of hark back to that in my own tastes. There are bands like Medeski, Martin & Wood that I love a lot. They get attention in the jam band scene and they are always interesting.
Widespread Panic - Light Fuse, Get Away (Capricorn, 1998)
We went out with The Allman Brothers and Widespread Panic. Those two combined bring in a lot of people from the jam community. Widespread Panic are an example of a band who are somehow in the jam band category, but create their own thing. And that's important.
Phish are creating something similar. The Derek Trucks Band were another one. He's really exceptional at improvising, but isn't afraid of the song either. There needs to be a balance between songwriting and improvisation. One offsets the other.
This article was written by Warren Haynes from Louder Sound and was legally licensed through the Industry Dive publisher network. Please direct all licensing questions to legal@industrydive.com.
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From the very beginning, I wanted the name of my coaching practice to honor the memory of my beautiful mother who dedicated her life to serving others. On Good Friday in March 2013, she passed on to a higher purpose after enduring 14 months of treatment for multiple myeloma cancer. Her passing brought me to my knees and also served as my greatest catalyst to follow my dreams of making a life, making a living, and making a difference by doing what I love, with whomever I love, from wherever I love.
Blossom of Snow is a lyric from the song "Edelweiss" in The Sound of Music, which my mother sang to me as a lullaby. It beautifully integrates the ideas of growing ("blossom") and hibernating ("snow"). Most of us have been taught to take outward action to grow and succeed. While there's a time and a place for that, it is not at the beginning. The most critical and effective first step to accomplishing anything is to slow down and turn inward -- to connect with our heart, our soul, and the Divine. I describe this approach as working from the inside-out, and it's the foundation of my coaching style.
Blossom of Snow also speaks to being unique. I believe our best success strategy for life, relationships, career and business is to be authentically ourselves -- to create a life around our unique set of natural strengths + passions, and collaborate with others who complement us.
My "why" for being a professional coach is to be an instrument of hope, peace, joy and love in the world ... and, to have lots of fun along the way.
Success at Blossom of Snow is defined in a single word: Love. Every day, we do our best to give and receive love with ourselves, God and others.
I believe our dreams -- the desires of our hearts -- are our Callings. Our dreams are the path to experiencing our greatest joy and being of greatest service. I'm on a mission to help one million women dream without limits and co-create their most impossible dreams.
My coaching clients are my heroes; for their courage, vulnerability and unlimited resourcefulness.
I'm often described as short and tough.
I prefer deep conversation over social chit-chat.
I have a strong right brain. I like pictures more than spreadsheets, and prefer art over math.
I was raised Catholic and still practice Catholicism. I also have an interfaith marriage, and appreciate and practice beautiful aspects from a variety of faith traditions.
My curiously strong curiosity is my greatest natural strength. My husband says coaching is my calling because I get to ask questions for a living.
I used to think there was something wrong with me for not knowing what I wanted to be when I grew up. Now I know I'm just a multi-passionate. Besides coaching, I also love traveling, photography, event planning, interior design, cooking, entertaining, and integrating my multiple passions with coaching.
I don't have a favorite season. I love them all for different reasons, as well as the interplay between nature and our human lives.
My idea of a perfect evening is a long, leisurely, al fresco, candlelit dinner with beautiful people, beautiful food, beautiful music, and a beautiful view.
One of my wildest dreams is to travel the world with my husband. (Our motto for our marriage is "How 'bout an adventure?") We're off to a good start -- living and working remotely, domestically and abroad, throughout the year.
Bonnie Utley is the founder-owner of Blossom of Snow, creator of The Dream Retreat and Soul Leadership Artistry, and a certified coach specializing in personal and professional leadership development. She describes her calling as a personal trainer for the mind, body and spirit, who loves using an "inside-out" approach and mind-body techniques.
Bonnie's expertise and passion is supporting people in dreaming without limits for their lives and co-creating their most impossible dreams. She believes that our dreams -- the desires of our hearts -- are how we are each being called to experience our greatest joy and be of greatest service. Bonnie's approach to this work is completely custom. She is committed to creating personalized and transformative experiences with every client, in every coaching session.
The big dreamers, lovers and creators who are up to inspiring things in the world are Bonnie's clients. They range from business leaders and owners, to stay-at-home moms who want to make big impacts. She loves laughing with her clients and they love laughing with her, because laughter is often a precursor to the greatest epiphanies.
Bonnie brings to coaching an innate sense of wonder and curiously strong curiosity, along with 24 years of creative and leadership experience with The Walt Disney Company, plus a combination of backgrounds in the corporate, nonprofit and entrepreneurial worlds. She graduated from Chapman University with a Bachelor's degree in Communications and completed professional coaching training and certification through Martha Beck, Inc. Bonnie lives a life of love, laughter and adventure with her husband Chris from their home in Southern California, or wherever their frequent travels take them.


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Enter the value that you want to convert miles per hour to meters per second or meters per second to miles per hour.
A mile per hour is measuring unit of speed in both the imperial and United States customary systems. It is denoted as mph or mi/h. One mph is equal to 0.44704 meters/second.
A meter per second is a measuring unit of both speed and velocity in the International System of a unit SI. It is denoted as m/s. One m/s is equal to 2.2369362921 mile/hour.
It is a free online mile per hour to meters per second (mph to m/s ) speed converter. A mile per hour is measuring unit of speed in both the imperial and United States customary systems. It is denoted as mph or mi/h. One mph is equal to 0.44704 meters/second. A meter per second is a measuring unit of both speed and velocity in the International System of a unit SI. It is denoted as m/s. One m/s is equal to 2.2369362921 mile/hour.
Mile/hour to Meter/second Metric Conversion Table.
How to convert miles per hour to meters per second (mph to m/s )?
For converting mph to m/s we go with an example.
Convert 10 mph to meters per second?
We know 1 mph = 0.44704 m/s ; 1 m/s = 2.2369362921 mph.


text:
Q: Check for file existance and read permissions I am trying to check if my file specified by file_path exists and is readable. This is my code:
if (stat(file_path,&fileStat) > 0 && (fileStat.st_mode & S_IRUSR))
{
    puts("SUCCESS");
    create_message(OK);
}

Can you detect a problem with the given code? Is the part (fileStat.st_mode & S_IRUSR)  correct?

A: You don't want stat() for this, you want access().
if (access(filename, R_OK)) {
    // code to handle missing or unreadable file
} else {
    // code to handle readable file
}

Your code would work if you changed the test on the return value of stat() as Jonathan Leffler points out, but Unix provides a system call to do precisely what you want, so you might as well use it.
But as other commenters have pointed out, if you are going to read this file, you would be better served to just open it for reading and let the open failure inform you of the problem.

redpajama_set_name: RedPajamaStackExchange


text:
Confronting the Classics (Ebook)
Traditions, Adventures and Innovations
Mary Beard takes us on an exhilarating journey through the extraordinary riches of the classical heritage, and why it still matters.
Mary Beard is one of the world's best-known classicists - a brilliant academic, with a rare gift for communicating with a wide audience both though her TV presenting and her books.
In a series of sparkling essays, she explores our rich classical heritage - from Greek drama to Roman jokes, introducing some larger-than-life characters of classical history, such as Alexander the Great, Nero and Boudicca. She invites you into the places where Greeks and Romans lived and died, from the palace at Knossos to Cleopatra's Alexandria - and reveals the often hidden world of slaves. She takes a fresh look at both scholarly controversies and popular interpretations of the ancient world, from The Golden Bough to Asterix.
The fruit of over thirty years in the world of classical scholarship, Confronting the Classics captures the world of antiquity and its modern significance with wit, verve and scholarly expertise.
Confronting the Classics (Paperback)
Reviews for Confronting the Classics
'With such a champion as Beard to debunk and popularise, the future of the study of classics is assured'
'She's pulled off that rare trick of becoming a don with a high media profile who hasn't sold out, who is absolutely respected by the academy for her scholarship ... what she says is always powerful and interesting'
'witty, erudite collection...To Beard, the classical past is alive and kicking - and she has the great gift of being able to show just why classics is still a subject worth arguing about'
'an irrepressible enthusiast with a refreshing disregard for convention'
'She stands in the great tradition of myth-puncturing Latin classicists'
'Beard is the best...communicator of Classics we have'
Independent on Sunday
'highly engaging'
'sparkling'
'so engaging, and at times so very funny'
Edith Hall Times
'this is the perfect introduction to classical studies, and deserves to become something of a standard work in the future'
Mary Beard is one of the most original and best-known classicists working today. She is Professor of Classics at Newnham College, Cambridge, and the Classics editor of the TLS. She is a fellow of the British Academy and a member of the American Academy of Arts and Sciences. Her books include the Wolfson Prize-winning Pompeii: The Life of a Roman Town (2008) and the best-selling SPQR: A History of Ancient Rome (2015). Her popular TLS blog has been collected in the books It's a Don's Life and All in a Don's Day. Her latest book is Women & Power: A Manifesto (2017).
'A classic in every sense of the word' John Julius Norwich Revised and updated to include the story of the New Acropolis Museum, the controver…
Civilisations: How Do We Look / The Eye of Faith
Companion to the BBC series CIVILISATIONS
Mary Beard on Ancient Rome: Britain's favourite classicist lifts the lid on the Roman Empire. A major new BBC TV series presented by the author st…
How to Manage Your Slaves by Marcus Sidonius Falx
Jerry Toner
An entertaining and amazingly informative guide to the realities of slavery in ancient Rome, with an introduction by Mary Beard
All in a Don's Day
Mary Beard's famous blog 'A Don's Life' has been running on the TLS website for nearly five years. Through it she made her name as a w…
Keith Hopkins
Award winning classicist, Mary Beard with Keith Hopkins, tell the story of Rome's greatest arena
It's a Don's Life
Britain's best known classicist speaks her mind on the ancient, and modern, worlds. A wide-ranging selection from her 'best hit' blog.
'Much of what you think you know about Pompeii may turn out, on reading this eye-opening book, to be wrong. The town was not full of brothels (Bea…

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: Android proxy using sockets I'm trying to create a proxy in Android and I have to use sockets . I've read many tutorials and came up with following code. Unfortunately browser doesn't seem to get any data and after some time it displays standard web page saying that web page is not available. What might be the cause? Thanks for your help.
        ServerSocket serverSocket = null;
            try {
                serverSocket = new ServerSocket(9902, 0, InetAddress.getByName("localhost"));
            } catch (Exception e) {
                e.printStackTrace();
            }
    if (serverSocket != null) {
                while (!Thread.currentThread().isInterrupted()) {
                    try {
                        Socket socket = serverSocket.accept();
                        new Thread(new RunnableToReadSocketData(socket)).start();
                    } catch (Exception e) {
                        e.printStackTrace();
                    }
                }
            }

private class RunnableToReadSocketData implements Runnable {
        private final Socket clientSocket;

        public RunnableToReadSocketData(Socket socket) {
            this.clientSocket = socket;
        }

        @Override
        public void run() {
            Socket serverSocket = null;
            try {
                InputStream streamFromClient = clientSocket.getInputStream();
                PrintWriter streamToClient = new PrintWriter(clientSocket.getOutputStream());

                StringWriter writer = new StringWriter();
                IOUtils.copy(streamFromClient, writer);
                String requestString = writer.toString();

                int firstSpace = requestString.indexOf(" ");
                int secondSpace = requestString.indexOf(" ", ++firstSpace);

                String url = requestString.substring(firstSpace, secondSpace);
                Uri uri = Uri.parse(url);
                String urlWithoutProtocol = uri.getHost();

                System.out.println("==============Reading Socket==============\n" + clientSocket.toString() + "\n" + requestString);

                serverSocket = new Socket(urlWithoutProtocol, 80);

                PrintWriter streamToServer = new PrintWriter(serverSocket.getOutputStream(), true);
                streamToServer.write(requestString);
                streamToServer.flush();

                InputStream streamFromServer = serverSocket.getInputStream();
                StringWriter writerResponse = new StringWriter();
                IOUtils.copy(streamFromServer, writerResponse);
                String responseString = writerResponse.toString();

                System.out.println("==============RECEIVED==============\n" + serverSocket.toString() + "\n" + responseString);

                streamToClient.write(responseString);
                streamToClient.flush();

                streamToClient.close();
            } catch (Exception e) {
                e.printStackTrace();
            } finally {
                try {
                    if (serverSocket != null) {
                        serverSocket.close();
                    }

                    if (clientSocket != null) {
                        clientSocket.close();
                    }
                } catch (Exception e) {
                    e.printStackTrace();
                }
            }
        }
    }

A: You're doing this wrong. After you process the CONNECT command you need to start two threads to copy bytes over the connection, one in each direction. Don't attempt to read the entire request before you send anything; ditto the response. Just copy bytes as you receive them.
When you read EOS on one socket, shutdown the other socket for output and exit that thread. If you've already shutdown the socket you read the EOS from, close both and exit the thread. You need this in case either end does a shutdown, to propagate it properly.

A: I agree with previous.
The general principle is:

*

*Client connects

*Start reading thread

*Receive request

*Parse destination

*Open socket to destination

*Forward request

*For every Read on the destination socket, do a write on the client socket

*For every Read on client socket, do a write on destination socket

*If either socket closes (errors), close the other

So, two InputStream's, two OutputStreams, and just ferry data across them.


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text:
package org.jabref.gui.desktop.os;

import java.awt.Desktop;
import java.io.File;
import java.io.IOException;
import java.nio.file.Path;
import java.util.List;

import org.slf4j.Logger;
import org.slf4j.LoggerFactory;

public class DefaultDesktop implements NativeDesktop {
    private static final Logger LOGGER = LoggerFactory.getLogger(NativeDesktop.class);

    @Override
    public void openFile(String filePath, String fileType) throws IOException {
        Desktop.getDesktop().open(new File(filePath));
    }

    @Override
    public void openFileWithApplication(String filePath, String application) throws IOException {
        Desktop.getDesktop().open(new File(filePath));
    }

    @Override
    public void openFolderAndSelectFile(Path filePath) throws IOException {
        File file = filePath.toAbsolutePath().getParent().toFile();
        Desktop.getDesktop().open(file);
    }

    @Override
    public void openConsole(String absolutePath) throws IOException {
        LOGGER.error("This feature is not supported by your Operating System.");
    }

    @Override
    public void openPdfWithParameters(String filePath, List<String> parameters) throws IOException {
        //TODO imlement default
    }

    @Override
    public String detectProgramPath(String programName, String directoryName) {
        return programName;
    }

    @Override
    public Path getApplicationDirectory() {
        return getUserDirectory();
    }
}

redpajama_set_name: RedPajamaGithub


text:
\section*{Acknowledgements}
The authors would like to thank the LHCb computing and simulation teams for their support and for producing the simulated LHCb samples used in the paper. We also would like to thank the LHCb RTA team for supporting this publication and reviewing the work.
M. De Cian acknowledges support from the Swiss National Science Foundation grant ``Probing right-handed currents in quark flavour physics", PZ00P2\_174016.
\section{Conclusion}
\label{sec:Conclusion}
We presented an alternative implementation of a Kalman filter for the LHCb experiment. Based on simple parametrizations of material effects and the extrapolation through the magnetic field of the detector, this algorithm achieves a significant speedup with respect to the current implementation, while retaining comparable quality of the track parameters. In the future, further improvements of the parametrizations might allow an even better estimate of the track parameters and a subsequent speedup. Ideas currently under discussion include for example an analytic parametrization of the $x$ and $y$ dependence of the parameters employed in the extrapolation from the UT to the SciFi detector and a better account for the limited acceptance of low momentum particles.
The version presented in this document or a future implementation might therefore be well suited for the usage in the \mbox{LHCb}\xspace software trigger system for Run 3 of the \mbox{LHC}\xspace.
\section{Detector and simulation}
\label{sec:Detector}

The \mbox{LHCb}\xspace detector~\cite{LHCb-DP-2008-001} is a single-arm forward
spectrometer covering the \mbox{pseudorapidity} range $2<\eta <5$.
Its Run 3 configuration includes a high-precision tracking system
consisting of a silicon-pixel vertex detector surrounding the $pp$
interaction region~\cite{LHCb-TDR-013} (VELO), a large-area silicon-strip detector (Upstream Tracker (UT))~\cite{LHCb-TDR-015} located
upstream of a dipole magnet with a bending power of about
$4{\mathrm{\,Tm}}$~\cite{LHCb-TDR-001}, and three stations of scintillating-fibre detectors (SciFi)~\cite{LHCb-TDR-015}
placed downstream of the magnet. Different types of charged hadrons are distinguished using information
from two ring-imaging Cherenkov detectors~\cite{LHCb-TDR-003,LHCb-TDR-014}.
Photons, electrons and hadrons are identified by a calorimeter system consisting of an electromagnetic
and a hadronic calorimeter~\cite{LHCb-TDR-002,LHCb-TDR-014}. Muons are identified by a
system composed of alternating layers of iron and multiwire proportional chambers~\cite{LHCb-TDR-004,LHCb-TDR-014}.

Given the lack of collision data at this point for Run 3, simulation is required to model the effects of the detector response, the detector acceptance and the imposed selection requirements. In the simulation, $pp$ collisions are generated using \mbox{\textsc{Pythia}}\xspace~\cite{Sjostrand:2007gs,*Sjostrand:2006za} with a specific \mbox{LHCb}\xspace configuration~\cite{LHCb-PROC-2010-056}.  Decays of unstable particles are described by \mbox{\textsc{EvtGen}}\xspace~\cite{Lange:2001uf}, in which final-state radiation is generated using \mbox{\textsc{Photos}}\xspace~\cite{Golonka:2005pn}. The interaction of the generated particles with the detector, and its response, are implemented using the \mbox{\textsc{Geant4}}\xspace toolkit~\cite{Allison:2006ve, *Agostinelli:2002hh} as described in Ref.~\cite{LHCb-PROC-2011-006}.

\section{Introduction}
\label{sec:Introduction}

The \mbox{LHCb}\xspace experiment is a dedicated heavy flavour physics experiment at the \mbox{LHC}\xspace focusing on the study of hadrons containing {\ensuremath{\Pb}}\xspace and {\ensuremath{\Pc}}\xspace quarks~\cite{LHCb-DP-2008-001}. Due to the high luminosity at the \mbox{LHC}\xspace and the high proton-proton interaction cross section, a sophisticated trigger system is needed to reduce the rate of collisions saved for offline analysis. During Runs 1 and 2 of the \mbox{LHC}\xspace, this trigger system consisted of a hardware stage, reducing the rate from $40\ensuremath{\aunit{MHz}}\xspace$ to $1\ensuremath{\aunit{MHz}}\xspace$, followed by a two-stage software trigger. In the latter, the full tracking system was read out and a partial (first stage) and full (second stage) event reconstruction were performed~\cite{LHCb-DP-2019-001}.
Both software stages included a fit of selected track candidates using a Kalman filter to extract their parameters and to reject fake tracks. In addition, the software trigger allowed an online calibration and alignment of the detector~\cite{BORGHI2017560}.

During Run 3 of the \mbox{LHC}\xspace, \mbox{LHCb}\xspace will be provided with a factor five higher luminosity compared to Run 2. In this scope, most of the subdetectors are currently being replaced or upgraded\cite{LHCb-TDR-012,LHCb-TDR-013,LHCb-TDR-014,LHCb-TDR-015} and a new trigger strategy has been developed \cite{LHCb-TDR-016}.
The hardware trigger will be removed and a two-stage, fully software-based trigger will process the full $30\ensuremath{\aunit{MHz}}\xspace$\footnote{The nominal bunch-crossing frequency of the \mbox{LHC}\xspace is 40\ensuremath{\aunit{MHz}}\xspace, however empty and non-colliding bunches reduce this to a collision frequency of 30\ensuremath{\aunit{MHz}}\xspace at \mbox{LHCb}\xspace.} of bunch-crossing rate. In the first stage, tracks with a high transverse momentum (\ensuremath{p_{\mathrm{T}}}\xspace) and primary vertices will be reconstructed. These objects are used to select events with displaced topologies typical for {\ensuremath{\Pb}}\xspace-hadron and {\ensuremath{\Pc}}\xspace-hadron decays, and to select high-\ensuremath{p_{\mathrm{T}}}\xspace objects from decays of heavy vector bosons.
In the second stage, a full event reconstruction will be performed, without any requirement on the \ensuremath{p_{\mathrm{T}}}\xspace and including particle identification.
A large number of exclusive and several universal event selections based on the decay topology will be applied.

In \mbox{LHCb}\xspace, track reconstruction is split into a \textit{pattern recognition} and a \textit{Kalman filtering}\cite{Kalman1960, FRUHWIRTH1987444} stage.
During pattern recognition, sets in each subdetector are constructed from signals that potentially result from the passage of a single charged particle. Simple parametrizations are used throughout this procedure as it is only concerned with finding the right sets of signals and not to provide the best estimate of the track parameters. During the filtering stage, an estimate for the track parameters is calculated, and fake tracks are rejected. Given that the output of the filtering stage is used for physics selections the best possible precision needs to be achieved, hence an (extended) Kalman filter is used for track fitting.
Ideally, Kalman filtering of the track candidates is already performed during the first trigger stage. However, the Kalman filter which was used during Run 1 and 2 in \mbox{LHCb}\xspace, in the following called \textit{default Kalman}, is significantly too slow. It relies on lookup tables for the magnetic field and the material distribution of the detector\cite{Bos:1070314}, so-called \textit{maps}. In addition it uses Runge-Kutta methods to solve the differential equations necessary to propagate the particle through the regions with an inhomogeneous magnetic field. Accessing the values in the lookup table and solving the differential equations are time consuming and prohibit the usage of the current Kalman filter in the first stage of the upgraded trigger system. This conclusion is independent of the choice of computing architecture (CPU or GPU) which is used for the first trigger stage.

In this paper, a fully parametrized version of the Kalman filter in \mbox{LHCb}\xspace, called \textit{parametrized Kalman}, is presented. It obtains precise values of track parameters and track quality variables,
while relying on neither computationally costly extrapolation methods nor material or magnetic field maps.

\section{Parametrizations}
\label{sec:Parametrizations}
Depending on the strength of the magnetic field and the typical distance between detector layers, different empirical analytical functions for the extrapolation are used.

Inside the VELO\xspace, where the magnetic field is very weak, these functions and the noise matrix are given by:
\begin{align}
\renewcommand*{\arraystretch}{1.2}
\boldsymbol{f}(\boldsymbol{x}) =
\begin{pmatrix}f^x(\boldsymbol{x}) \\
  f^y(\boldsymbol{x}) \\
  f^{t_x}(\boldsymbol{x}) \\
  f^{t_y}(\boldsymbol{x}) \\
  f^{\frac{q}{p}}(\boldsymbol{x})
\end{pmatrix}
 =
\begin{pmatrix}
  x+0.5[t_x+f^{t_x}(\boldsymbol{x})]\Delta z\ \\
  y+t_y\Delta z\\
  t_x+p^{\text{V}}_0\frac{q}{p}(z_0+p^{\text{V}}_1)\Delta z\\
  t_y\\
  \frac{q}{p}
\end{pmatrix}
\end{align}
and
\begin{align}
\boldsymbol{Q} =
\begin{pmatrix}
  \left(\tilde{p}^{\text{V}}_1\Delta z\right)^2Q^{t_xt_x} & 0 & \tilde{p}^{\text{V}}_2\sqrt{Q^{xx}Q^{t_xt_x}} & 0 & 0\\
  0 & \left(\tilde{p}^{\text{V}}_1\Delta z\right)^2Q^{t_yt_y} & 0 & \tilde{p}^{\text{V}}_3\sqrt{Q^{yy}Q^{t_yt_y}} & 0\\
  \tilde{p}^{\text{V}}_2\sqrt{Q^{xx}Q^{t_xt_x}} & 0 & \left(\tilde{p}^{\text{V}}_0\left|\frac{q}{p}\right|\right)^2 & 0 & 0\\
  0 & \tilde{p}^{\text{V}}_3\sqrt{Q^{yy}Q^{t_yt_y}} & 0 & \left(\tilde{p}^{\text{V}}_0\left|\frac{q}{p}\right|\right)^2 & 0\\
  0 & 0 & 0 & 0 & 0\\
\end{pmatrix},\label{eq:noisematrix}
\end{align}
where $\Delta z$ is the extrapolation distance along the $z$-direction and $z_0$ the initial or final $z$ coordinate for a downstream or upstream extrapolation, respectively. The parameters $p^{\text{V}}_0$, $p^{\text{V}}_1$ and $\tilde{p}^{\text{V}}_0$ to $\tilde{p}^{\text{V}}_3$ are the same for all upstream and downstream extrapolations inside the VELO\xspace.
They are determined using simulated \decay{{\ensuremath{\B^0_\squark}}\xspace}{\phi\phi} decays within the \mbox{LHCb}\xspace software framework, where \decay{\phi}{{\ensuremath{\kaon^+}}\xspace{\ensuremath{\kaon^-}}\xspace}. This simulated sample allows to create a dataset $D$, containing pairs of states representing two consecutive measurements of one track inside the VELO\xspace. In addition to the true state parameters obtained from the simulation, also an extrapolation of each state to the $z$ position of the respective other state is included in the dataset. Such extrapolation is based on the default extrapolation algorithm in \mbox{LHCb}\xspace~\cite{Bos:1070314}.
This dataset allows tuning the parameters employing a minimization of the following likelihood-inspired function:
\begin{align}
\prod_{D}\left[\mathcal{G}\left(f^s(\boldsymbol{x_1})-\boldsymbol{x_2}^s,\sqrt{Q^{ss}}\right)+ c\right].
\end{align}
Here, $\mathcal{G}(x,\sigma_x)$ is a normalized Gaussian distribution centered around $0$ with width $\sigma_x$. The two states of each dataset entry are represented by $\boldsymbol{x}_1$ and $\boldsymbol{x}_2$, and the variable $s$ is one of the state variables, $s\in\{x,t_x,y,t_y\}$. The positive empirical constant $c$ is chosen to be small with respect to the amplitude of the Gaussian function and softens the impact of outliers.

In a first step, the extrapolation functions $f^x$ to $f^{t_x}$ are tuned individually, taking into account that $f^x$ depends on the previously determined parameters for $f^{t_x}$. These tuning minimizations employ the state vector $\boldsymbol{x}_2$ that is obtained by the extrapolation of the state vector $\boldsymbol{x}_1$. This choice improves the precision of the parametrized extrapolation, by removing the effect of multiple scattering that would be present if instead the true state was chosen for $\boldsymbol{x}_2$.

In a second step, the parameters of the extrapolation functions are fixed, and a minimization of the following function is performed:
\begin{align}
\prod_{D}\left[\mathcal{G}_2\left(
f^d(\boldsymbol{x_1})-\boldsymbol{x_2}^d,
f^{t_d}(\boldsymbol{x_1})-\boldsymbol{x_2}^{t_d},
\sqrt{Q^{dd}},
\sqrt{Q^{t_dt_d}},
Q^{dt_d}/\sqrt{Q^{dd}Q^{t_dt_d}}\right)+ c\right].
\end{align}
Here, $\mathcal{G}_2(x,y,\sigma_y,\sigma_y,\rho)$ is a normalized two-dimensional Gaussian distribution centered around $0$ with widths $\sigma_x$ and $\sigma_y$ and a correlation factor $\rho$. The variable $d$ is either $x$ or $y$. In this minimization, the true state vector $\boldsymbol{x}_2$ is used in order to get the correct estimate of the parameters for the respective elements of the noise matrix $\boldsymbol{Q}$.

Inside the UT and the SciFi detector stations, the magnetic field is significantly stronger than inside the VELO\xspace and higher order terms are needed for the extrapolation functions:
\begin{align}
\boldsymbol{f}(\boldsymbol{x}) =
 \renewcommand*{\arraystretch}{1.4}
 \begin{pmatrix}
 x+\left[p^{\text{T}}_3t_x+(1-p^{\text{T}}_3)f^{t_x}(\boldsymbol{x})\right]\Delta z\\
 y+\left[p^{\text{T}}_5t_y + (1-p^{\text{T}}_5)f^{t_y}(\boldsymbol{x})\right]\Delta z\\
 t_x+\left[p^{\text{T}}_0\frac{q}{p} + p^{\text{T}}_1(\frac{q}{p})^3 + p^{\text{T}}_2y^2\frac{q}{p}\right]\Delta z\\
 t_y + p^{\text{T}}_4\frac{q}{p}t_x\frac{y}{|y|}\\
 \frac{q}{p}
 \end{pmatrix}.
\end{align}
The noise matrix is given in full analogy to Equation \ref{eq:noisematrix} with the parameters $\tilde{p}^{\text{T}}_0$ to $\tilde{p}^{\text{T}}_3$, where T either stands for the UT or the SciFi detector. These parameters and the parameters $p^{\text{T}}_0$ to $p^{\text{T}}_4$ are individually determined on simulation for every step from one detector layer to the next and for the upstream and downstream extrapolation separately. The same strategy as for the tuning of the parameters related to the extrapolation inside the VELO\xspace is followed.

For the long extrapolations between the different tracking subdetectors, more sophisticated parametrizations are necessary. In the case of the step between the VELO\xspace and the UT, where the magnetic field is still weak, the extrapolation is based on two equations. The first describes the change in momentum along the $x$-direction of the particle:
\begin{align}
\Delta p_x
= p\left(\frac{t_{x,\text{UT}}}{\sqrt{1+t^2_{x,\text{UT}}+t^2_{y,\text{UT}}}}-\frac{t_{x,\text{V}}}{\sqrt{1+t^2_{x,\text{V}}+t^2_{y,\text{V}}}}\right)
= q\int \left( \text{d}\boldsymbol{l}\times \boldsymbol{B} \right)_{x},\label{eq:delta_px}
\end{align}
where $t_{x/y,\text{UT}}$ and $t_{x/y,\text{V}}$ are the state variables at the first UT detector layer and the last measurement inside the VELO\xspace, respectively. The right hand side of the equation consists of an integral of the magnetic field along the trajectory of the particle. Note that the integral expression is simply a parameter which was fitted for on the dataset.
The second ingredient for the extrapolation is to model the effect of the magnetic field as a single kink of the trajectory at a certain $z$-position $z_{\text{mag}}$ between the VELO\xspace and the UT:
\begin{align}
x_{\text{UT}} = x_{\text{V}} + (z_{\text{mag}}-z_{\text{V}})t_{x,\text{V}} + (z_{\text{UT}}-z_{\text{mag}})t_{x,\text{UT}},\label{eq:kink}
\end{align}
where $z_{\text{V}}$ and $z_{\text{UT}}$ are the positions of the states inside the VELO\xspace and the UT, respectively.

Equation \ref{eq:delta_px} can be solved for $t_{x,\text{UT}}$ and Equation \ref{eq:kink} is then employed to get an expression for $x_{\text{UT}}$. The unknowns in these expressions are parametrized as a function of the state variables inside the VELO\xspace:
\begin{align}
t_{y,\text{UT}} &= t_{y,\text{V}} + p^{\text{S}}_0\frac{q}{p}t_{x,\text{V}}\frac{y_{\text{V}}}{|y_{\text{V}}|}\\
\int \left( \text{d}\boldsymbol{l}\times \boldsymbol{B} \right)_{x} &= p^{\text{S}}_1 + p^{\text{S}}_2z_{\text{V}} + p^{\text{S}}_3 t^2_{y,\text{V}} \\
z_{\text{mag}} &= p^{\text{S}}_4 + p^{\text{S}}_5 z_{\text{V}} + p^{\text{S}}_6z^2_{\text{V}} + p^{\text{S}}_7 t^2_{y,\text{V}}.
\end{align}
In addition, the $y$-position of the extrapolated state is given by:
\begin{align}
y_{\text{UT}} = y_{\text{V}}+\left[p^{\text{S}}_8t_{y,\text{V}} + (1-p^{\text{S}}_8)t_{y,\text{UT}}\right]\Delta z,
\end{align}
where $\Delta z$ is defined as the difference between $z_{\text{UT}}$ and $z_{\text{V}}$. The noise matrix is defined in analogy to Equation \ref{eq:noisematrix} with the parameters $\tilde{p}^{\text{S}}_0$ to $\tilde{p}^{\text{S}}_3$. These parameters and the parameters $p^{\text{S}}_0$ to $p^{\text{S}}_8$ are individually determined for the upstream and downstream extrapolation.
The same strategy as for the tuning of the parameters related to the extrapolation inside the VELO\xspace is followed.

The extrapolation from the UT to the SciFi detector is more delicate
because it is done over a distance of more than 5 meters through
a strong magnetic field. Moreover, this field is far from uniform -
in particular, it varies rapidly in the upper and lower regions,
close to the magnet yoke. To ensure a good quality of the global
track fit, the error on the extrapolation should be well
below the other sources of error, mainly multiple
scattering. The chosen solution is an expansion of the magnetic
deviation in powers of $q/p$. The parametrization aims at giving good precision for charged particles
used in physics analyses, that is for trajectories which roughly come from
the origin.

To do so, the \textit{ideal} direction $(t_x^0,t_y^0)$ as the one of a
particle of charge $q$, momentum $p$, starting from the origin and
hitting the UT detector layer in a given point $(x,y)$ is defined. As a good approximation, we can take $t_x^0 = x/z+{\cal B}q/p$, $t_y^0 = y/z$, where $\cal{B}$ is proportional to the integrated field between the origin and the UT. The deviations from the ideal direction, $\delta t_x=t_x-t_x^0$, $\delta t_y=t_y-t_y^0$, are small, so only a first order expansion in  $\delta t_x,\delta t_y$ is considered. Corrections of higher order would be negligible compared to multiple scattering errors.

Finally, a polynomial expansion in $q/p$ for the ideal direction is built, and a correction
in $\delta t_x,\delta t_y$ with coefficients which are themselves polynomials of $q/p$ is added:
\begin{align}
 f^x(\boldsymbol{x}) = x+t_x\Delta z+ \sum_{k=1}^{K_1} A^x_k(x,y)\left(\frac{q}{p}\right)^k
 +\sum_{k=1}^{K_2} \left(B^x_k(x,y)\,\delta t_x+C^x_k(x,y)\,\delta t_y\right)\left(\frac{q}{p}\right)^k,
 \end{align}
where the first two terms are the straight line extrapolation, and the
next ones the curvature correction. Similar expressions are used for
the other state parameters $f^y(\boldsymbol{x})$,
$f^{t_x}(\boldsymbol{x})$, $f^{t_y}(\boldsymbol{x})$. The
degrees of expansion $K_1$ and $K_2$ are tuned for each parameter to
obtain the required precision. In practice $K_1=9$, $K_2=7$
for $f^x$ and $f ^{t_x}$ and  $K_1=7$, $K_2=5$
for $f^y$ and $f ^{t_y}$ are used.

The dependence on $x,y$ of the coefficients $A^u_k$, $B^u_k$,
$C^u_k$, with $u=x,y,t_x,t_y$, is described through a tabulation on a grid of 50$\times$50
points regularly spaced on the rectangle defined by $|x/z|\leq 0.25$,
$|y/z|\leq 0.25$, by steps $\Delta X$, $\Delta Y$. In order to avoid a systematic convexity bias of a
bilinear interpolation, the values at $x,y$ are computed by a quadratic
interpolation between the tabulated values at the six closest points on
the grid: if $(X,Y)$ is the closest one, these values are: $F_{00}=(X,Y)$, $F_{+0}=F(X+\Delta X,Y)$, $F_{-0}=F(X-\Delta X,Y)$,
$F_{0+}=F(X,Y+\Delta Y)$, $F_{0-}=F(X,Y-\Delta Y)$,
and $F_{\varepsilon_x \varepsilon_y}=F(X+\varepsilon_x\Delta X,Y+\varepsilon_y\Delta Y)$,
 where $\varepsilon_x$ and $\varepsilon_y$ are the signs of $\xi=(x-X)/\Delta X$
and $\psi=(y-Y)/\Delta Y$, respectively. With these notations the
interpolation formula for a quantity $F$ is given by :
\begin{align}
F(x,y) = F_{00} +F_d\,\xi\psi + \big(&(F_{+0}-F_{-0})\,\xi +  (F_{0+}-F_{0-})\,\psi \nonumber \\
 &+ (F_{+0}+F_{-0}-2F_{00})\,\xi^2 +(F_{0+}+F_{0-}-2F_{00})\,\psi^2\big)/2\\
\text{with}\;\;\; F_d = &\varepsilon_x\varepsilon_y (F_{00}+F_{\varepsilon_x\varepsilon_y}-F_{\varepsilon_x 0}-F_{0 \varepsilon_y} ).
\end{align}
The tabulated values are obtained using the standard Runge-Kutta method of order 4,
with 20
values of $q/p$ in the range ($-1/p_{min},1/p_{min}$), with
$p_{min}=3000 \ensuremath{\aunit{Me\kern -0.1em V\!/}c}\xspace$ and a polynomial fit in $q/p$. As a consequence,
they do not give a reliable result for momenta below
$p_{min}$. Another limitation is the larger errors on the edges of the
acceptance, especially for $|t_y|\simeq 0.25$, where the field has
strong spatial variations.

\section{Performance}
\label{sec:Performance}
A sample of simulated proton-proton collisions that include a $B^0_s\rightarrow\phi\phi$, \decay{\phi}{{\ensuremath{\kaon^+}}\xspace{\ensuremath{\kaon^-}}\xspace} decay
is used to compare the reconstruction quality of the parametrized and the default Kalman filter. The extrapolation of the most upstream state estimate to the beam line is the same in both filters and is based on a simplified material map of the detector \cite{Bos:1070314}. Therefore, not the state near the beam line, but the state at the most upstream measurement is employed for the comparison of the two Kalman filters. Although only tracks with measurements in each of the subdetectors are considered for this study,
this is in principle not a requirement for operating the parameterized Kalman filter

Figure \ref{fig:Resolution} compares the resolution of the momentum, the $x$-position and the slope $t_x$ as a function of the true momentum of a particle.
\begin{figure}
\begin{center}
\includegraphics[width=.49\textwidth]{figs/QopRes_PRMS.pdf}
\includegraphics[width=.49\textwidth]{figs/XRes_PRMS.pdf}\\
\includegraphics[width=.49\textwidth]{figs/TXRes_PRMS.pdf}
\end{center}
\caption{\label{fig:Resolution}Comparison of the resolution in simulation in (top left) momentum, (top right) $x$-position and (bottom) slope $t_x$ between the default and parametrized Kalman filter. The resolution is represented by the root mean square of the residual distribution when comparing to the true value.}
\end{figure}
Since the position and slope are nearly exclusively determined by the measurements in the VELO, where only a very weak magnetic field is present, the parametrizations of the parametrized Kalman filter are sufficient to obtain
results comparable to the default Kalman filter in these variables. In contrast, the momentum estimate strongly depends on the extrapolations in regions with strong magnetic field. There, especially at momenta below 10\ensuremath{\aunit{Ge\kern -0.1em V\!/}c}\xspace, an up to $20\%$ worse resolution is observed for the parametrized Kalman filter.

The Kalman filter does not only provide an estimate of the state parameters, but also a corresponding covariance matrix. In Figure \ref{fig:Pull} the pull distributions of the estimated momentum, $x$-position and slope $t_x$ for the parametrized Kalman filter are shown.
\begin{figure}
\begin{center}
\includegraphics[width=.49\textwidth]{figs/pull_Two_qop.pdf}
\includegraphics[width=.49\textwidth]{figs/pull_Two_x.pdf}\\
\includegraphics[width=.49\textwidth]{figs/pull_Two_tx.pdf}
\end{center}
\caption{\label{fig:Pull}Pull distributions of the momentum, $x$-position and slope $t_x$ estimates of the parametrized Kalman filter at the most upstream measurement. The given values correspond to the mean, width and root mean square of a Gaussian function that is fitted to the distribution.}
\end{figure}
In all three cases, good uncertainty estimates are visible. However, in analogy to the observations made for the resolution, the pull distribution of the momentum features slightly more pronounced tails.

Besides the estimate of the state near the beam line, which is used for the reconstruction of charged particles, an important output of the Kalman filter is the fit quality described by the $\chi^2_{\text{track}}$ per degrees of freedom $N_{\text{dof}}$. In Figure \ref{fig:Chi2}, this quantity is shown for the parametrized Kalman filter for real tracks coming from a particle and fake tracks consisting of random combinations of clusters. In addition, the real track efficiencies and fake track rejection rates are shown for both Kalman filter versions when applying upper bounds on this quantity.
\begin{figure}
\includegraphics[width=0.5\textwidth]{figs/Chi2_Two_.pdf}
\includegraphics[width=0.5\textwidth]{figs/ROC_Chi2_.pdf}
\caption{\label{fig:Chi2}Track quality estimate, $\chi^2_{\text{track}}/N_{\text{dof}}$, in simulation for the parametrized filter (left). Fake tracks are shown in red and real tracks in black. Real track efficiency and fake track rejection for the parametrized and default Kalman filter (right).}
\end{figure}
The parametrized Kalman filter shows a slightly worse but overall comparable performance in separating the two track classes.

The fitted tracks are combined to reconstruct $B^0_s\rightarrow\phi\phi$ candidates. Figure \ref{fig:mass} shows the invariant mass distribution of candidates based on the two Kalman filter versions.
\begin{figure}
\includegraphics[width=0.5\textwidth]{figs/MassPlot_Default.pdf}
\includegraphics[width=0.5\textwidth]{figs/MassPlot_Param.pdf}
\caption{\label{fig:mass}Reconstructed $B^0_s$ mass in simulated $B^0_s\rightarrow\phi\phi$ decays for the parametrized and the default Kalman filter. Fit projections are overlaid.}
\end{figure}
A single Gaussian distribution and a first order polynomial are employed to model the signal peak and the combinatorial background, respectively.
This yields nearly identical estimated mass resolutions of $12.8\ensuremath{\aunit{Me\kern -0.1em V\!/}c^2}\xspace$ and $12.9\ensuremath{\aunit{Me\kern -0.1em V\!/}c^2}\xspace$ for the default and the parametrized Kalman filter, respectively.

In order to compare the timing performance of the parametrized Kalman filter and the default Kalman filter, throughput studies on a machine with two Intel(R) Xeon(R) Silver 4214 processors were performed. Simulated proton-proton collisions
were used in order to mimic the situation of real data taking. Depending on the configuration of the outlier removal strategy, an overall speedup factor between 4 and 5.5 with respect to the default Kalman filter was achieved. The largest speedup is achieved when no iterations for the outlier removal are performed. Singling out the calculation steps of the Kalman filter, \mbox{\itshape i.e.}\xspace neglecting the part of the algorithms where the measurement information is constructed, the speedup factor is even larger and ranges from 5.7 to 10.

In the case of the parametrized Kalman filter, and singling out again the calculation step of the Kalman filter, $50\%$ of the time is spent extrapolating the states between the detector layers. Here, the extrapolation between the UT and the SciFi constitutes the biggest component with a relative fraction of $40\%$.
The remaining Kalman filter steps, consisting of updating the states with the cluster information and the combination of upstream and downstream filtered states, are responsible for  $16\%$ and $14\%$ of the time spent, respectively. The extrapolation to the beam line, which is based on the default LHCb extrapolation algorithm, is responsible for the remaining $20\%$ of the time budget.

\section{Principles}
\label{sec:Principles}
In the following, the Kalman filter formalism and its application in the \mbox{LHCb}\xspace track reconstruction is outlined. During Kalman filtering, the information from measurements at detector planes is successively combined to obtain optimal estimates of the track parameters.
The track is represented as a set of states at fixed $z$-positions\footnote{The detector coordinate system is chosen such that the $z$-axis is parallel to the beam line and charged particles are deflected in the direction of the $x$-axis.}, which are typically detector layers. Each of these states is given by $\boldsymbol{x}=(x,y,t_x,t_y,\frac{q}{p})$ and the corresponding covariance matrix $\boldsymbol{P}$, where $t_x$ and $t_y$ are the slopes with respect to the $z$ axis, $q$ the charge of the particle in units of the electron charge and \ensuremath{p}\xspace its absolute momentum.

The Kalman filter procedure needs an estimate of a state as a starting point. Filtering is then a repeated application of two steps. Firstly, the current state is extrapolated to the next detector layer, and secondly, the extrapolated state is updated using the measurement in this layer. If the track has no associated measurement in this layer, the update step is omitted.
These steps can be formalized as follows: given the state {($\boldsymbol{x}_{k-1|k-1}$}, $\boldsymbol{P}_{k-1|k-1}$) at position $z_{k-1}$, the extrapolated state ($\boldsymbol{x}_{k|k-1}$, $\boldsymbol{P}_{k|k-1}$) at position $z_{k}$ is given by
\begin{align}
\boldsymbol{x}_{k|k-1} &= \boldsymbol{f}_k(\boldsymbol{x}_{k-1|k-1}),\\
\boldsymbol{P}_{k|k-1} &= \boldsymbol{F}_k\boldsymbol{P}_{k-1|k-1}\boldsymbol{F}_k^T+\boldsymbol{Q}_k,
\end{align}
where the extrapolation function $\boldsymbol{f}_k(\boldsymbol{x})$ is given by five individual mappings $\boldsymbol{f}_k=(f_k^x,f_k^y,f_k^{t_x},f_k^{t_y},f_k^{\frac{q}{p}})$. This leads to the transport matrix $\boldsymbol{F}_k$ as
\begin{align}
F_k^{ij} = \frac{\partial f_k^i}{\partial x_j}.\label{eq:transp_matrix}
\end{align}
The noise matrix $\boldsymbol{Q}_k$ accounts for uncertainties of the extrapolation, \mbox{\itshape e.g.}\xspace due to scattering at the material of the detector layers or the material in between.

The extrapolated state is then combined with the measurement $\boldsymbol{m}_{k}$ in the respective detector layer to obtain the new state estimate at the position $\boldsymbol{z}_{k}$, $\boldsymbol{x}_{k|k}$ and $\boldsymbol{P}_{k|k}$, using the following steps:
\begin{align}
\boldsymbol{r}_k &= \boldsymbol{m}_k-\boldsymbol{H}_k\boldsymbol{x}_{k|k-1}, \\
\boldsymbol{S}_k &= \boldsymbol{H}_k\boldsymbol{P}_{k|k-1}\boldsymbol{H}_k^T + \boldsymbol{R}_k, \\
\boldsymbol{K}_k &= \boldsymbol{P}_{k|k-1}\boldsymbol{H}_k^T\boldsymbol{S}_k^{-1},\\
\boldsymbol{x}_{k|k} &= \boldsymbol{x}_{k|k-1} + \boldsymbol{K}_k \boldsymbol{r}_k,\\
\boldsymbol{P}_{k|k} &= (\boldsymbol{1}-\boldsymbol{K}_k\boldsymbol{H}_k)\boldsymbol{P}_{k|k-1}.
\end{align}
Here $\boldsymbol{H}_k$ projects the estimated state vector to the measurement space in order to allow a calculation of the residual $\boldsymbol{r}_k$. The covariance matrix of this residual is given by $\boldsymbol{S}_k$ and is combined with the covariance matrix of the state to obtain the Kalman gain $\boldsymbol{K}_k$. The latter defines then how the estimated state is modified by the residual. The variance of the residual is given by $\boldsymbol{R}_k$.

Starting at the most upstream measurement, the measurements are successively added and the track parameters updated until the last detector layer is reached.
The same procedure is repeated starting at the most downstream measurement and successively including more upstream measurements. This yields two sets of states at every measurement position, which can be combined to obtain the respective optimal state.

The quality of a track can be estimated by its $\chi^2_{\text{track}}$ value. The value at each measurement is given by:
\begin{align}
\chi^{2}_{k} &= \chi^2_{k-1} + \boldsymbol{r}_{k}^{T} \boldsymbol{P}_{k|k}^{-1} \boldsymbol{r}_{k},
\end{align}
and $\chi^2_{\text{track}}$ is then simply $\chi^{2}_{k}$ after all measurements have been added using the combined, optimal states.

The optimal state estimates and the measurement information can also be used to remove measurements that show a large separation from the fitted trajectory by having a large contribution to the $\chi^2_{\text{track}}$ value. They are therefore likely to be wrongly associated to the respective track, and are so-called \textit{outliers}. Once an outlier is removed, all Kalman filter steps are performed again. This procedure can be repeated until the maximum allowed number of outliers are removed, or no more outliers are present.

The above formalism is also the basis of the Kalman filter that is currently used for track fitting in the \mbox{LHCb}\xspace experiment.
The extrapolation functions $\boldsymbol{f}_k$ are based on maps of the magnetic field along the trajectory and numerical models for the extrapolations. Their complexities range up to a fifth-order Runge-Kutta method. The noise matrices $\boldsymbol{Q_k}$ are obtained by a dedicated model for the multiple scattering and a map of the material traversed by the particle.

In the parametrized Kalman filter presented in this paper, these two costly steps are replaced by simple parametrizations. The extrapolation functions $\boldsymbol{f}_k$ are given by analytic expressions that allow a fast evaluation and calculation of the derivatives in Equation \ref{eq:transp_matrix}.
The noise matrices $\boldsymbol{Q}_k$ depend on the momentum of the particle and are parametrized by a few parameters per extrapolation step.

An important difference with respect to the default Kalman filter is the treatment of energy loss due to the interaction with the detector material. While the multiple scattering is taken directly into account, the energy loss is not part of the extrapolation functions $\boldsymbol{f}_k$, \mbox{\itshape i.e.}\xspace $f_k^{\frac{q}{p}}$ is the unity transformation. This shortcoming is compensated by choosing the momentum of the state vectors to represent the momentum at the moment of production of the particle. Thereby, the extrapolation functions also take this initial momentum as input and thus indirectly take into account all energy loss that happened on average up to the respective detector layer. The only caveat being that $\frac{q}{p}$ after the filtering is only the best representation of the true value at the production point of the particle.

\section{References}
\label{sec:References}

References should be made using Bib\TeX~\cite{BibTeX}. A special style
\texttt{LHCb.bst} has been created to achieve a uniform
style. Independent of the journal the paper is submitted to, the
preprint should be created using this style. Where arXiv numbers
exist, these should be added even for published articles. In the PDF
file, hyperlinks will be created to both the arXiv and the published
version, using the {\tt doi} for the latter.

Results from other experiments should be cited even if not yet published.

\begin{enumerate}

\item Citations are marked using square brackets, and the
  corresponding references should be typeset using Bib\TeX\ and the
  official \mbox{LHCb}\xspace Bib\TeX\ style. An example is in
  Ref.~\cite{Sjostrand:2006za}.

\item For references with four or less authors all of the authors'
  names are listed~\cite{Lee:1967iu}, otherwise the first author
  is given, followed by \mbox{\itshape et al.}\xspace. The \mbox{LHCb}\xspace Bib\TeX\ style will
  take care of this. The limit of four names can be changed by changing the number 4 in
  ``{\tt \#4 'max.num.names.before.forced.et.al :=}''
  in {\tt LHCb.bst}, as was done in Ref.~\cite{LHCb-PAPER-2017-038}.

\item The order of references should be sequential when reading the
  document. This is automatic when using Bib\TeX.

\item The titles of papers should in general be included. To remove
  them, change \texttt{\textbackslash
    setboolean\{articletitles\}\{false\}} to \texttt{true} at the top
  of this template.

\item Whenever possible, use references from the supplied files
\verb!main.bib!, \verb!LHCb-PAPER.bib!, \verb!LHCb-CONF.bib!, and \verb!LHCB-DP.bib!.
These are kept up-to-date by the EB. If you see a mistake, do not edit these files,
but let the EB know. This way, for every update of the paper, you save
yourself the work of updating the references. Instead, you can just copy or
check in the latest versions of the \verb!.bib! files from the repository.
{\bf Do not take these references from \texttt{inspirehep} instead} (``{\tt Aaaij:20XXxyz}''), as \texttt{inspirehep} sometimes adds mistakes, does not handle errata properly and does not use LHCb-specific macros.

\item For those references not provided by the EB, the best
  is to copy the Bib\TeX\ entry directly from
  \href{http://inspirehep.net}{inspirehep}.
    Often these need to be edited to get the
  correct title, author names and formatting. The warning about special UTF8 characters should never be ignored. It usually signals a accentuated character in an author name.
  For authors with multiple initials, add a space between them (change \texttt{R.G.C.} to \texttt{R. G. C.}),
  otherwise only the first initial will be taken.
  Also, make sure to eliminate unnecessary capitalisation.
  Apart from that, the title should be respected as much as possible
  (\mbox{\itshape e.g.}\xspace do not change particle names to PDG convention nor introduce/remove factors of $c$, but do change Greek capital letters to use our slanted font.).
  Check that both the arXiv and the journal index are clickable
  and point to the right article.

\item The \texttt{mciteplus}~\cite{mciteplus} package is used
  to enable multiple references to show up as a single item in the
  reference list. As an example \texttt{\textbackslash
    cite\{Cabibbo:1963yz,*Kobayashi:1973fv\}} where the \texttt{*}
  indicates that the reference should be merged with the previous
  one. The result of this can be seen in
  Ref.~\cite{Cabibbo:1963yz,*Kobayashi:1973fv}. Be aware that the
  \texttt{mciteplus} package should be included as the very last item
  before the \texttt{\textbackslash begin\{document\}} to work
  correctly.

\item It should be avoided to make references to public notes and
  conference reports in public documents. Exceptions can be discussed
  on a case-by-case basis with the review committee for the
  analysis. In internal reports they are of course welcome and can be
  referenced as seen in Ref.~\cite{LHCb-CONF-2012-013} using the
  \texttt{lhcbreport} category. For conference reports, omit the
  author field completely in the Bib\TeX\ record.

\item To get the typesetting and hyperlinks correct for \mbox{LHCb}\xspace reports,
  the category \texttt{lhcbreport} should be used in the Bib\TeX\
  file. See Refs.~\cite{LHCb-INT-2011-047, *LHCb-ANA-2011-078,
    *CERN-THESIS-2014-057, *LHCb-PROC-2014-017, *LHCb-TALK-2014-257}
  for some examples. It can be used for \mbox{LHCb}\xspace documents in the series
  \texttt{CONF}, \texttt{PAPER}, \texttt{PROC}, \texttt{THESIS},
  \texttt{LHCC}, \texttt{TDR} and internal \mbox{LHCb}\xspace reports. Papers sent
  for publication, but not published yet, should be referred with
  their \texttt{arXiv} number, so the \texttt{PAPER} category should
  only be used in the rare case of a forward reference to a paper.

\item Proceedings can be used for references to items such as the
  \mbox{LHCb}\xspace simulation~\cite{LHCb-PROC-2011-006}, where we do not yet have
  a published paper.

\end{enumerate}

There is a set of standard references to be used in \mbox{LHCb}\xspace that are
listed in Appendix~\ref{sec:StandardReferences}.

redpajama_set_name: RedPajamaArXiv


text:
Wildly Ordinary
tea and conversation with the wildly ordinary women who raised me
Mully
Mully: Women's Work
December 15, 2013 MullyEliza
Read Mully's story from the beginning
Mully: I had already made the preschool program for Cere in Berkeley, now I wanted to make a program for Oliver. Skip decided he was going to get a job because now he had two children. So he became a real estate agent and we bought this repossessed place that had three acres but the plumping was non-functional. The yard was full of old cars, there was a hole in the wall where a fire had been and, there was this old funky chicken coop that was perfect for a preschool!
So our friend, Blake, who lived across the street, rented a sander and we sanded off all the chicken shit. We put a stove in and insulated the walls and put in sheet rock. I built a loft. We found this outhouse in the woods across the street from my house and I said " Well we need a bathroom for the kids." So we moved it across the street and dug the holes, and that was our bathroom.
Meanwhile, I am doing all the plumbing in our house. I apparently am a worker. I like to roll up my sleeves. I love chopping wood, all the physical things, going out and chain sawing whatever it is. That was what we did a lot of in those days. There were a ton of women around here doing the same thing. One group of women formed a team and they would go to each others' houses and help garden or paint.
This wasn't a new thing on the island. Women got the right to vote in 1910 in Washington, which was ten years before the United States gave all white women the right to vote. There was an all women's administration complete with the mayor and city council in our town here in 1919.
Front row, L-R: Grace English, Helen Coe (mayor), Emma Monson.Back row, L-R: Clara Brown, Lillian Wylie, Maggie McLeod, all-woman city government
Because we live on an island, and its only resources were trees and seafood, the area drew pioneers. People who had the kind of energy to make something out of nothing, and that was still true when we came in the 70s, and it is still that way today.We were this collection of entrepreneurs and visionaries with all of this initiatory energy to make things happen. We liked taking care of business.
I was definitely "all systems go". There were no social services here so we all helped to start an alternative health clinic called Wellspring. I taught childbirth education and served on the board of directors for a number of years. I had my preschool. Oliver called it the Yellow Cabin Pre-School. It was to die for!
Square from the fund raising quilt for Wellspring Health Clinic
We started a record store with Country Joe for a while when he first moved here. But his record company made him move back to California so we let that go. I was in a women's choir, writing women's music. I performed in Bob's acting group, The Fools …What else was I doing?
Oh! Hanging out with Shanti and exploring all the women's spirituality and you know, mushrooms and whatever else. I was a total full moon goddess devotee. I had realized I could never be a communist because they don't believe in spirituality so I was done with communism and into the Goddess instead! laughs.
But, I could never go on the women's canoe trips that they took out on the Nootka Sound because I was the only one in my peer group of women with two children, and Skip wouldn't take care of them. All these women and lesbians were a threat to him. The last thing he wanted me to do was associate with "these people" that were going to take me even further out of "reality" than I already was. So I never got to go.
By then, Oliver was ready to start Kindergarten and Cere was in 5th grade, I decided to give all my pre-school equipment away to this fledgling childcare program that was starting up at the Senior Center. I was going to take a short break and figure out what I wanted to do next. Little did I know that in a few months I would begin my "alternative service " as a woman running a gas station.
← Mully: Homebirth	Mully: Rainbow Shell →
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Hi does anyone know best app to download for Samsung s4 watch to show gps positioning and mapping and also show speed. Tried map my run but no good.
I use Dawn Patrol App on iPhone, it's excellent, but don't know if it's on Sammy.
Otherwise also see is "Surf Track" works. I use this on iPhone. Has advantages over DP, but doesn't have Apple Watch access.
Alternatively, as I just worked out, use GoPro's GPS. Surprisingly good!


My name is Timothy Frappier and this is my blog. I've been following world events for the last eight years and have decided it is time to help inform the public on what is about to occur.
Born and raised in the good state of Minnesota, USA. With my Creator's good grace I was raised in a middle-class family with the privilege to have access to many of the resources and knowledge that others lack.
In 2010 I experienced a personal awakening. This happened very abruptly and has led me down a path of self-discovery. I started to research many of the things that most people consider to be taboo, other-worldly and esoteric. My curiosity though, was too far intrigued to be fully subdued by the old programming. I had my fair share of struggles, but I've come to embrace them. Because without them, I wouldn't be the person I am today.
The driving motivation in my life is to make this world a better place. I wish to contribute to humanity in whatever capacity my Creator deems necessary. I strive to see the whole world thrive and imagine a society that defies all current models. A society that embodies peace within and without. Where we live in harmony with our environment. Where violence is non-existent and crime ceases to exists. Like John Lennon said "You may say that I'm a dreamer, but I'm not the only One." How true these words ring even to this day.
My personal spiritual experiences have given me proof that there is more to this existence then we've been led to believe. This is a place where all are welcomed and accepted. You're not alone, that's what I've been told by great teacher and friend. I went through the phase of being ridiculed and judged, but it made me stronger. If your in the same situation, I send my light and love and welcome you to my blog. I'm here for you all, just as I know you're here for me.
This blog will have a variety of topics discussed upon and I hope you're able to gain something from this website. The main themes to most of my posts will be in regards to spirituality, extraterrestrials, future visions and The Event.
Thank you very much for visiting and I send my Love to all you beautiful light beings!
Lovely. I hope we meet in person someday. You sound like an awesome person, someone I'd enjoy getting to know better.
Greetings. I'm originally from MN, and still spent time there. I share your interests and outlook. Thanks for your work.
It's a pleasure to meet you. We Minnesotans need to stick together :P. Thank you so much for your kind words and many blessings to you.
You are a very smart man. I am so proud of you. I have always been amazed with all the knowledge you have. Keep up the great work. May God bless you on your journey threw life.


With textile fibre attached to the walls the pattern of the existing architecture got imprinted. I numbered the many pieces to be able to reconstruct the space. This textile skin - now left behind - is meant to remind the viewers of the history of this building and the lives of its former residents.


Each of you should make some preparation just in case a major earthquake, tornado or hurricane does strike your area.
It is very important to not overreact following such a major disaster!
There have been dozens of harebrained suggestions from various well meaning groups put forward. We wish to offer you some simple, common sense emergency procedures and reasonable preparations which everyone living should make.
On the top of our list is at least one a legal size clip board with paper and pen or pencil (attached by a string). A red, permanent ink, felt tipped marking pen attached by a string is also necessary for your clipboard. (Carbon paper recommended) and a can of international orange spray paint! The spray paint is used to paint a large arrow on the side of the building/residence that points to the location of the clipboard so that rescuers can find it.
Additional Notes and Instructions: (sample use follows) Timmy, we are all right. I am at the High School Shelter and Mom is at the hospital with a broken leg. She is doing well. Come to the school. Dad Aug., 12, 1993 - 10:32 a.m. - Building verified and cleared by VUHR Cliff Henry, VUHR Team etc.
It provides any rescuer with pertinent information on the occupants, their condition and where about.
It allows rescue teams to pass information to other rescuers so that the dwelling is not searched a second or third time thus wasting valuable search efforts.
It provides information to friends and relatives who may have joined in the search for you.
By using carbon paper it provides authorities with a removable record which may be taken to the Disaster Command Center and added to a database.
Can you think of any more purposes this form would serve?
The red marker will allow a rescuer to place a check mark on the paper to show the dwelling has been cleared.
For one thing, you won't need a flashlight or radio inside a basic disaster (earthquake, tornado or hurricane) survival kit. One radio for 200 persons is plenty. A century ago there were zero radios. News will travel from person to person. Radios and a flashlights both need batteries, which run out quickly, have a short shelf life, etc. And don't forget, there probably won't be any stores open that can sell you more new batteries after a major disaster!
If you end up at the refugee center they will probably have an emergency power source such as a small portable generator. If not, why not just sit in the dark to talk in the evenings. If you feel that must have a light source we would recommend chemical light sticks. They are cheap, light weight, readily available and have a long shelf life. One half dozen six inch light sticks! Each will burn for 12 hours (actually, they provide light for a much longer period of time). At least one should be r ed! You will use the red stick if you are trapped or pinned inside and can see outside. Once you have activated the red light stick a rescuer will see that there is someone in need of assistance.
There's an excellent chance, after a major disaster, that martial law will have been declared and you won't be going out at night. In this eventuality most activities requiring light will be done during the day when the sun was out. You prepare for night ahead of time. Depending on how you look at it, and having a positive outlook is very important during such trying times, losing electricity for a few days could actually be a blessing in disguise.
One of the kits and you should have at least one per household member, should be just inside the front door or near a window in your bedroom. A chemical light stick should be near your bed and readily accessible, not buried down inside your long term survival kit. A good location might be to place one or two between the box spring and mattress on each side of the bed.
A major disaster can happen anytime, day or night. So you have a 50% chance that a disaster hits it will happen during darkness. And if you sleep 8 hours a night then there is a 33.3% chance that you'll be sleeping. 66.7% chance that you'll be awake. How many hours a day are you at work or school? You should have one of our recommended disaster kits there as well. You probably won't be killed or maimed in a major disaster! Look at the statistics. It's kind of like flying. Some people are afraid of flying , but statistically speaking - flying is the safest way to travel. So let's make a reasonable level of general preparation, then we can go about our lives.
In any major disaster people may be killed immediately. But many more will die in the confusion of the aftermath possibly due to occurrences such as fires. Disorganization, lack of communication, no water, screaming people trapped in building rubble will all add to this confusion. People will rush to the large parks, where the authorities said they should go.
Disasters are horrible! People will die. Rumors start. Looting can begin with the breakdown of law enforcement. When regular authority breaks down people believe rumors according to their prejudices. Consequently ethnic people might be killed by insane mobs trying to stop the looting. International rescue teams have been accused of being looters in efforts to prevent their saving lives or to cover up government corruption and mistakes. In a major disaster, the world as you know it, will cease to exist and you must be prepared both mentally and with personal survival kits.
If you live or are in a big city when a major disaster, such as an earthquake, occurs try to get some personal identification like your passport, some money, clothes, etc., and walk out, if it appears possible to do so. A person can walk pretty far in one day with relatively level terrain, roads to follow, etc. No problem. At 4 miles/hour an uninjured person could walk a fair distance in a day or two.
There are several reasons to try to leave the quake area - and to help others do the same. In the Kobe quake we saw the almost total lack of personal initiative on the part of average Japanese citizens. Why should the locals need to be told what makes sense? Tourists driving in, blocking roads so that relief vehicles couldn't get through. Lack of coordination in food delivery. Little effort to search for trapped persons until a couple of days had passed... Unbelievable! A whistle on your pajamas? A pick ax and hydraulic jack would be more appropriate. What is the most reasonable level of preparation? That's our focus. We can't stop the quakes from happening. But we can respond quickly and help others to escape the danger. An important note is in order: the Japanese government wants everyone to go to the large city parks. But if law & order breaks down (followed by lack of sanitation), remember what has happened in history. -Incredibly, just following the Kobe Quake some Japanese news reports said that "foreigners" were looting. In fact, one story told that some foreigners were coming into the area to steal. That's just what "pre-judging" people need to hear! Actually I don't doubt the validity. But the consequences could be disastrous for us minority foreigners. Guilty until proven innocent.... This writer's advice is to make a few newfound friends and walk out to less congested areas, if possible.
The ARTI recommended Quake Kit is cheap, flexible and long lasting. Let the department stores sell their expensive wares. We're going down to the neighborhood shops for our kits. The main part of this kit should cost you a few dollars! That's all. For that amount of "insurance" you are reasonably prepared for most quake-related danger. But if a large cabinet crushes your leg or a chunk of concrete lands on your head then even the most expensive kit in the world wouldn't do you a bit of good, would it?
and 1 package of dry biscuits or crackers.
Heavy winter clothes? Depends on your climate, but maybe a sweater and plastic poncho are a good ideas as well.
These items are put together, wrapped inside 2 T-shirts, then wrapped in a waterproof plastic bag or 4-5 plastic shopping bags. All of this is minimum. And except for the cash and T-shirts it should cost you very little to put this all together.
The idea is to be able to survive the first day or so without too much discomfort given the overall situation. You must make 2 kits. One for home and the other for your primary work or school location. Earthquake preparation kits should be kept: Kit #1 - in trunk of car; Kit #2 - in a plastic sealed garbage can in a hole in backyard filled with sand and covered by a couple of inches of sand on top. Statistically speaking, this would be pretty good preparation. A compact, durable kit which will last for several years.
Think about this - the San Francisco quake happened at 5 p.m. Most people weren't home. So their elaborate kits at home were buried or at least inaccessible. We remember seeing people returning home a few days later - to retrieve (among other things) their emergency kits. You just can't completely prepare for the Big One.
In an emergency situation you must be innovative. This is paramount! Russian author Alexander Solzhenitsyn once wrote an entire book (while in prison) on onion skins. What can you do with a whole roll of toilet paper? You could write on it, make temporary flags, clean a wound, wrap food for later, blow your nose, twist tightly when wet, then dry, to make a crude wick, etc. And if there's no water you can't flush the toilets or wash your hands. How will you keep clean? Add a large container of `pre ned towelettes' to your survival kit. Sealed, they keep for years. Believe me, there is nothing like wiping your face with one when you've been coated in dust and grime for hours or even days at a time.
This is important - a million people, with limited sanitation! In 3-4 days diseases will begin spreading. Keep as clean as possible.
There is a possibility of heavy smoke from fires. Tie one of the T-shirts around your mouth and nose. If possible, a wet T-shirt. Your 2 T-shirts double as towels or they could be torn into strips for either a tunicate (to stop the blood from a gaping wound) or a splint. With toppled buildings nearby wood for splints should be readily available.
A broken arm or dislocated shoulder? Use those safety pins (or even heavy staples, glue, etc.) to make one T-shirt into a temporary sling. Affix the hem to the neckline. Put the T-shirt on and slip the arm into the "sling" made by the material.
And you really should add a few more things. But at least have the water, biscuits and a few other things on hand. To make 2 kits the cost is negligible. And it's all useable, long lasting stuff. Your school/office based kit should have extra prescription medication, contact lens cleaner, sanitary napkins, etc. Imagine that you can't go home and no stores will be open for a few days.
Part of your kit might include a few cans of cola. It has a long shelf life and carbohydrates. Chocolate though won't last through one August. As we stated earlier you want nothing that needs batteries. But then a deck of cards or flask of whiskey would be useful. Whiskey is a pain killer, friend maker, and crude sterilizer. How about one of those paperback books that you've been planning to read someday. Do you smoke? Unless you plan to quit for a few tense days you may want to add a few packs to your k it.
Without a change of clothes and probably no razor you won't win any beauty contests, but then who wants to carry extra baggage either. Realistically ... you'll probably be aiding the injured in some relief center rather than just saving your own skin. You'll help with foraging, traffic control, caring for the injured, etc. Don't plan to be alone nor completely outside. But this depends largely on where you live.
For disaster planning bureaucrats in many countries think they have it down pat. A lot of wisdom goes into their decision making. But when the unexpected happens it seems that no one knows what to do unless they're told. If and when a tragedy does strike ... let's help our neighbors and show them how to make quick decisions - that save lives.


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A hell-cursed Templar on an epic quest! Brian De Bois Guilbert, villain in Sir Walter Scott's Ivanhoe, returns as the doomed hero in this thrilling sequel to the classic work. After a brutal death at the hands of Sir Ivanhoe, Brian is reborn as Ravenskull, undead walker of the Shadow World, cursed by an impossible love. To save himself and the woman he loves, he must embark on a perilous journey to the East, facing all manners of monsters, black magic and evil assassins!


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Q: Non-negative polynomials on $[0,1]$ with small integral Let $P_n$ be the set of degree $n$ polynomials that pass through $(0,1)$ and $(1,1)$ and are non-negative on the interval $[0,1]$ (but may be negative elsewhere).
Let $a_n = \min_{p\in P_n} \int_0^1 p(x)\,\mathrm{d}x$ and let $p_n$ be the polynomial that attains this minimum.
Are $a_n$ or $p_n$ known sequences?  Is there some clever way to rephrase this question in terms of linear algebra and a known basis of polynomials?

A: Following Robert Israel's answer, we also scale everything to $[-1,1]$ (thus multiplying the result by 2). As he mentions, the optimal polynomial is always a square of some other polynomial, $p_{2n}=p_{2n+1}=q_n^2$, and $q_n$ is either even or odd (see Lemma below). So we are left to find the minimal $L_2[-1,1]$-norm of an odd/even polynomial $q_n$ such that $\deg q_n\leq n$ and $q_n(\pm1)=(\pm1)^n$. In other words (recall the division by 2 in the first line!), $a_{2n}=a_{2n+1}=d_n^2/2$, where $d_n$ is the distance from $0$ to the hyperplane  defined by $q(1)=1$ in the space of all odd/even polynomials of degree at most $n$ with $L_2[-1,1]$-norm.
Now, this hyperplane is the affine hull of the Legendre polynomials $ P_i(x)=\frac1{2^ii!}\frac{d^i}{dx^i}(x^2-1)^i$, where $i$ has the same parity as $n$ (since we know that $ P_i(1)=1$ and $P_i(-1)=(-1)^i$). Next, by $\| P_i\|^2=\frac{2}{2i+1}$, our distance is
$$
  \left(\sum_{j\leq n/2}\| P_{n-2j}\|^{-2}\right)^{-1/2}
  =\left(\sum_{j\leq n/2}\frac{2(n-2j)+1}{2}\right)^{-1/2}=\sqrt{\frac4{(n+1)(n+2)}},
$$
attained at
$$
  q_n(x)=\left(\sum_{i\leq n/2}\frac{2}{2(n-2i)+1}\right)^{-1}
    \sum_{i\leq n/2}\frac{2P_{n-2i}(x)}{2(n-2i)+1}.
$$
Thus the answer for the initial question is $a_{2n}=a_{2n+1}=\frac2{(n+1)(n+2)}$ and $p_{2n}=p_{2n+1}=q_n^2$.
Lemma. For every $n$, one of optimal polynomials on $[-1,1]$ is a square of an odd or even polynomial.
Proof. Let $r(x)$ be any polynomial.which is nonnegative on $[-1,1]$ with $r(\pm 1)=1$. We will replace it by some other polynomial which has the required form, has the same (or less) degree and the same values at $\pm 1$, is also nonnegative on $[-1,1]$, and is not worse in the integral sense. Due to the compactness argument, this yields the required result.
Firstly, replacing $r(x)$ by $\frac12(r(x)+r(-x))$, we may assume that $r$ is even (and thus has an even degree $2n$).  Let $\pm c_1,\dots,\pm c_{n}$ be all complex roots of $r$ (regarding multiplicities); then
$$
  r(x)=\prod_{j=1}^n\frac{x^2-c_j^2}{1-c_j^2},
$$
due to $r(\pm 1)=1$.
Now, for all $c_j\notin[-1,1]$ we simultaneously perform the following procedure.
(a) If $c_j$ is real, then we replace $\pm c_j$ by $\pm x_j=0$. Notice that
$$
  \frac{|x^2-c_j^2|}{|1-c_j^2|}\geq 1\geq \frac{|x^2-0^2|}{|1-0^2|}.
$$
for all $x\in[-1,1]$.
(b) If $c_j$ is non-real, then we choose $x_j\in[-1,1]$ such that $\frac{|c_j-1|}{|c_j+1|}=\frac{|x_j-1|}{|x_j+1|}$. Notice that all complex $z$ with $\frac{|c_j-z|}{|x_j-z|}=\frac{|c_j-1|}{|x_j-1|}$ form a circle passing through $-1$ and $1$, and the segment $[-1,1]$ is inside this circle. Therefore, for every $x\in[-1,1]$ we have
$$
  \frac{|c_j-x|}{|x_j-x|}\geq\frac{|c_j-1|}{|x_j-1|},
$$
thus
$$
  \frac{|x^2-c_j^2|}{|1-c_j^2|}
  =\frac{|c_j-x|}{|c_j-1|}\cdot\frac{|c_j+x|}{|c_j+1|}
  \geq \frac{|x_j-x|}{|x_j-1|}\cdot\frac{|x_j+x|}{|x_j+1|}
  =\frac{|x^2-x_j^2|}{|1-x_j^2|}.
$$
So, we replace $\pm c_j$ and $\pm\bar c_j$ by $\pm x_j$ and $\pm x_j$ (or simply $\pm c_j$ by $\pm x_j$ if $c_j$ is purely imaginary).
After this procedure has been applied, we obtain a new polynomial whose roots are in $[-1,1]$ and have even multiplicities, and its values at $\pm1$ are equal to $1$. So it is a square of some polynomial which is even/odd (since the roots are still split into pairs of opposite numbers). On the other hand, its values at every $x\in[-1,1]$ do not exceed the values of $r$ at the same points, as was showed above. So the obtained polynomial is not worse in the integral sense, as required. The lemma is proved.

A: For better symmetry, let me change the boundary points to $(-1,1)$ and $(1,1)$.
Then it is clear that we may assume $p_n$ is an even function (and thus you really want $P_n$ to be polynomials of degree at most $n$, otherwise you'll be likely to have an infimum rather than an actual minimum): $p_{2k+1} = p_{2k}$.  I get
$$ \eqalign{p_0(x) = 1, & a_0 =  2\cr
           p_2(x) = x^2, & a_2 = \dfrac{2}{3}\cr
           p_4(x) = \dfrac{(5 x^2 - 1)^2}{16},& a_4 = \dfrac{1}{3}\cr
           p_6(x) = \dfrac{x^2}{16} (7 x^2 - 3)^2,& a_6 =  \dfrac{1}{5}\cr
           p_8(x) = \dfrac{1}{64} (21 x^4 - 14 x^2 + 1)^2, & a_8 = \dfrac{2}{15}\cr
p_{10}(x) = \dfrac{x^2}{64} (33 x^4 - 30 x^2 + 5)^2, & a_{10} = \dfrac{2}{21}\cr
p_{12}(x) = \dfrac{1}{4096} (429 x^6 - 495 x^4 + 135 x^2 - 5)^2, & a_{12} = \dfrac{1}{14}}$$
Well, so far it looks like $a_{2n} = \dfrac{4}{(n+1)(n+2)}$