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The Riverside Biographical Series
NUMBER 7
JOHN MARSHALL
BY
JAMES BRADLEY THAYER
[Illustration: portrait of J Marshall]
JOHN MARSHALL
BY
JAMES BRADLEY THAYER
BOSTON AND NEW YORK
HOUGHTON, MIFFLIN AND COMPANY
The Riverside Press, Cambridge
1901
COPYRIGHT, 1901, BY JAMES BRADLEY THAYER
ALL RIGHTS RESERVED
PREFATORY NOTE
The writer has drawn with entire freedom from an address delivered by
him at Cambridge on February 4, 1901, before the Harvard Law School and
the Bar Association of the City of Boston, and from an article on John
Marshall in the Atlantic Monthly for March, 1901.
J. B. T.
CAMBRIDGE, March 30, 1901.
CONTENTS
CHAP. PAGE
I. HIS LIFE BEFORE BECOMING CHIEF JUSTICE;
HIS PERSONAL CHARACTERISTICS 1
II. ARGUMENTS AND SPEECHES; LIFE OF
WASHINGTON; RELATIONS WITH JEFFERSON 39
III. THE BEGINNINGS OF THE CHIEF JUSTICE'S
CAREER; AMERICAN CONSTITUTIONAL
LAW; MARBURY V. MADISON 54
IV. MARSHALL'S CONSTITUTIONAL OPINIONS 82
V. THE WORKING OF OUR SYSTEM OF CONSTITUTIONAL
LAW 102
VI. LETTERS OF MARSHALL 111
VII. MARSHALL AS A CITIZEN AND A NEIGHBOR 123
VIII. HIS LAST DAYS 147
_The portrait is from a miniature by St. Mémin._
JOHN MARSHALL
CHAPTER I
HIS LIFE BEFORE BECOMING CHIEF JUSTICE; HIS PERSONAL CHARACTERISTICS
In beginning his "Life of Washington," Chief Justice Marshall states
that Washington was born in 1732, "near the banks of the Potowmac," in
Westmoreland County, Virginia; mentions his employment by Lord Fairfax,
the proprietor of the Northern Neck, as surveyor of his estates in the
western part of that region; and adds that, in the performance of these
duties, "he acquired that information respecting vacant lands, and
formed those opinions concerning their future value, which afterwards
contributed greatly to the increase of his private fortune."
Thomas Marshall, the father of the Chief Justice, two years older than
Washington, was also born in Westmoreland County, was a schoolmate of
Washington, served with him both as surveyor of the Fairfax estates, and
soon afterwards, as an officer in the French and Indian wars; and he,
too, as time passed, found like advantage from his experience as a
surveyor.
In 1753, Thomas Marshall was made agent of Lord Fairfax in the
management of his estates. In the next year, he married Mary Isham
Keith, daughter of a Scotch clergyman, whose wife was a descendant of
William Randolph, of Turkey Island, the ancestor of the famous Virginia
family of that name. Their son, John Marshall, the oldest of fifteen
children, was born on September 24, 1755, in what was afterwards
Fauquier County, at a little settlement then known as Germantown,--now
Midland, on the Southern Railroad, a few miles south of Manassas. That
was the year of Braddock's defeat, and Thomas Marshall, like Washington,
was in the service, as an officer.
In Marshall's early childhood, his father's household, situated in a
frontier county, must have been agitated with the dreadful rumors,
anxieties, and terrors of the troubles with the French and Indians. "So
late," he tells us in the "Life of Washington," "as the year 1756, the
Blue Ridge was the northwestern frontier; and [Virginia] found immense
difficulty in completing a single regiment to protect the inhabitants
from the horrors of the scalping-knife, and the still greater horrors of
being led into captivity by savages who added terrors to death by the
manner of inflicting it." It was not until two years later that the
capture of Fort Duquesne relieved Virginia from the frightful ravages
that laid waste the region just west of the Blue Ridge.
When John Marshall was ten years old or more, his father left the level
country and poor soil of eastern Fauquier, for the higher and more
fertile region in the western part of the county, just under the Blue
Ridge. At Midland all they can show you now, relating to Marshall, is a
small, rude heap of bricks and rubbish,--what is left of the house
where he was born; and children on the farm reach out to you a handful
of the bullets with which that sacred spot and the whole region were
thickly sown, before a generation had passed, after his death.
Marshall's education was got from his father, from such teachers as the
neighborhood furnished, and, for about a year, at a school in
Westmoreland County, where his father and George Washington had
attended, and where James Monroe was his own schoolmate. But most he
owed to his father,--a man of good stock, of enterprise, experience,
strong character and sense, himself of no mean education,--who,
personally, took great pains with the training of his children. Marshall
admired his father, and declared him to be a far abler man than any of
his sons. From him and the teachers provided for him his son got a good
knowledge of English history, literature, and poetry, and a fair
acquaintance with the classics.
All Marshall's later youth was passed in the mountain region of
Fauquier County, under the Blue Ridge. Judge Story declared that it was
to the hardy, athletic habits of his youth among the mountains,
operating, we may well conjecture, upon a happy physical inheritance,
"that he probably owed that robust and vigorous constitution which
carried him almost to the close of his life with the freshness and
firmness of manhood."
The house that Marshall's father built at Oakhill is still standing, an
unpretending, small, frame building, having connected with it now, as a
part of it, another house built by Marshall's son Thomas. At one time
the farm comprised an estate of six thousand acres.[1] Since 1865 it has
passed out of the hands of the family. It is beautifully placed on high,
rolling ground, looking over a great stretch of fertile country, and
along the chain of the Blue Ridge, close by. To this region, where his
children and kindred lived, about a hundred miles from Richmond,
Marshall delighted to resort in the summer, all his life long. In the
autumn of 1807, after the Burr trial, he writes to a friend, "The day
after the commitment of Colonel Burr for a misdemeanor, I galloped to
the mountains." "I am on the wing," he tells Judge Story in 1828, "for
my friends in the upper country, where I shall find rest and dear
friends, occupied more with their farms than with party politics."
When Marshall was about eighteen years old he began to study Blackstone;
but he quickly dropped it, for the troubles with Great Britain
thickened, and, like his neighbors, he prepared for fighting.
He seems to have found a copy of Blackstone in his father's house, as he
had found there much other sterling English literature. It was then a
new book, but already famous. Published in England in 1765-69, a
thousand copies had been taken in this country;[2] and just now the
first American edition was out (Philadelphia, 1771-72), in which the
list of subscribers, headed by the name of "John Adams, barrister at
law, Boston," had also that of "Captain Thomas Marshall, Clerk of
Dunmore County." Dunmore County, now Shenandoah, was then a very new
county, just over the Blue Ridge from Fauquier; and it is believed that
there was but one Captain Thomas Marshall in those parts.
The earliest personal description of Marshall that we have belongs to
this period. It is preserved in Horace Binney's admirable address at
Philadelphia, after Marshall's death. He gives it from the pen of an
eyewitness, a "venerable kinsman" of Marshall. News had come, in May,
1775, of the fighting at Concord and Lexington. The account shows us the
youth, as lieutenant, drilling a company of soldiers in Fauquier
County:--
"He was about six feet high, straight, and rather slender, of dark
complexion, showing little if any rosy red, yet good health, the outline
of the face nearly a circle, and within that, eyes dark to
blackness,[3] strong and penetrating, beaming with intelligence and good
nature; an upright forehead, rather low, was terminated in a horizontal
line by a mass of raven-black hair, of unusual thickness and strength.
The features of the face were in harmony with this outline, and the
temples fully developed. The result of this combination was interesting
and very agreeable. The body and limbs indicated agility rather than
strength, in which, however, he was by no means deficient. He wore a
purple or pale blue hunting-shirt, and trousers of the same material
fringed with white. A round black hat, mounted with the buck's tail for
a cockade, crowned the figure and the man. He went through the manual
exercise by word and motion, deliberately pronounced and performed in
the presence of the company, before he required the men to imitate him;
and then proceeded to exercise them with the most perfect temper....
"After a few lessons the company were dismissed, and informed that if
they wished to hear more about the war, and would form a circle about
him, he would tell them what he understood about it. The circle was
formed, and he addressed the company for something like an hour. He then
challenged an acquaintance to a game of quoits, and they closed the day
with foot-races and other athletic exercises, at which there was no
betting."
"This," adds Mr. Binney, "is a portrait, to which in simplicity, gayety
of heart, and manliness of spirit, in everything but the symbols of the
youthful soldier, and one or two of those lineaments which the hand of
time, however gentle, changes and perhaps improves, he never lost his
resemblance."
Marshall accompanied his father to the war as a lieutenant, and in a
year or two became a captain. In leaving the father here, it may be said
that three of his sons were with him in the war, and that he himself
served with gallantry and distinction as a colonel. In 1780, he was at
the South with General Lincoln, and being included in the surrender of
that officer and on parole, visited Kentucky, not yet a State. After a
few years he removed there with the younger part of his family, leaving
Oakhill, as it seems, in the hands of his son John. He died in Kentucky
in 1806, having survived to witness the successive honors of his son
culminate in his becoming Chief Justice of the United States.[4]
It was in the autumn of 1775 that Marshall, as lieutenant in a regiment
of minutemen, of which his father was major, marched down through the
country to the seaboard to resist Lord Dunmore's aggressions. They were
clothed, we are told, in green home-spun hunting-shirts, having the
words "Liberty or Death" in large letters on the breast, with bucks'
tails in their hats, and tomahawks and scalping-knives in their belts.
The enemy at Norfolk feared, it is said, for their scalps, but they lost
none.[5]
He was thus in the first fighting in Virginia, in the fall of 1775, at
Norfolk; afterwards he served in New Jersey, Pennsylvania, and New York;
and again in Virginia toward the end of the war. He was at Valley Forge,
in the fighting at the Brandywine, Germantown, Monmouth, Stony Point,
and Paulus Hook, between 1776 and 1779. He served often as judge
advocate, and in this way was brought into personal relations with
Washington and Hamilton. A fellow officer and messmate describes him,
during the dreadful winter at Valley Forge, as neither discouraged nor
disturbed by anything, content with whatever turned up, and cheering
everybody by his exuberance of spirits and "his inexhaustible fund of
anecdote." He was "idolized by the soldiers and his brother officers."
President Quincy gives us a glimpse of him at this period, as he heard
him described at a dinner with John Randolph and a large company of
Virginians and other Southern gentlemen. They were talking of Marshall's
early life and his athletic powers. "It was said in them that he
surpassed any man in the army; that when the soldiers were idle at their
quarters, it was usual for the officers to engage in matches of quoits,
or in jumping and racing; that he would throw a quoit farther, and beat
at a race any other; that he was the only man who, with a running jump,
could clear a stick laid on the heads of two men as tall as himself. On
one occasion he ran in his stocking feet with a comrade. His mother, in
knitting his stockings, had the legs of blue yarn and the heels of
white. This circumstance, combined with his uniform success in the race,
led the soldiers, who were always present at these races, to give him
the sobriquet of 'Silver-Heels,' the name by which he was generally
known among them."
Toward the end of 1779, owing to the disbanding of Virginia troops at
the end of their term of service, he was left without a command, and
went to Virginia to await the action of the legislature as to raising
new troops. It was a fortunate visit; for at Yorktown he met the young
girl who, two or three years later, was to become his wife; and he was
also able to improve his leisure by attending, for a few months in the
early part of 1780, two courses of lectures at the college, on law and
natural philosophy. This was all of college or university that he ever
saw; but later, from several of them, he received their highest honors.
In 1802 the college of New Jersey (Princeton, where his oldest son,
Thomas, was to graduate in 1803), in 1806, Harvard, and in 1815, the
University of Pennsylvania, made him doctor of laws.[6] Marshall's
opportunity for studying law, under George Wythe, at William and Mary
College, seems to have been owing to a change in the curriculum, made,
just at that time, at the instance of Jefferson, governor of the State,
and, in that capacity, visitor of the college. The chair of divinity had
just been abolished, and one of law and police, and another of medicine,
were substituted. On December 29, 1779, the faculty voted that, "for the
encouragement of science, a student, on paying annually 1000 pounds of
tobacco, shall be entitled to attend any school of the following
professors, viz.: of Law and Police; of Natural Philosophy and
Mathematics," etc. Marshall chose the two courses above named; he must
have been one of the very first to avail himself of this new privilege.
He remained only one term. In view of what was to happen by and by, it
is interesting to observe that this opportunity for education in law
came through the agency of Thomas Jefferson.
The records of the Phi Beta Kappa Society at William and Mary College,
where that now famous society had originated less than a year and a half
before, show that on the 18th of May, 1780, "Captain John Marshall,
being recommended as a gentleman who would make a worthy member of the
society, was balloted for and received;" and three days later he was
appointed, with others, "to declaim the question whether any form of
government is more favorable to public virtue than a Commonwealth."
Bushrod Washington and other well-known names are found among his
associates in this chapter, which has been well called "an admirable
nursery of patriots and statesmen."
It was in the summer of 1780 that Marshall was licensed to practice law.
During this visit to Virginia, as I have said, he met the beautiful
little lady, fourteen years old, who became his wife at the age of
sixteen, was to be the mother of his ten children,[7] and was to receive
from him the most entire devotion until the day of her death in 1831.
Some letters of her older sister, Mrs. Carrington, written to another
sister, have lately been printed, which give us a glimpse of Captain
Marshall in his twenty-fifth year. These ladies were the daughters of
Jaquelin Ambler, formerly collector of customs at Yorktown, and then
treasurer of the colony, and living in that town, next door to the
family of Colonel Marshall. Their mother was that Rebecca Burwell, for
whom, under the name of "Belinda," Jefferson had languished, in his
youthful correspondence of some twenty years before. The girls had often
heard the captain's letters to his family, and had the highest
expectations when they learned that he was coming home from the war.
They were to meet him first at a ball, and were contending for the prize
beforehand. Mary, the youngest, carried it off. "At the first
introduction," writes her sister, who was but one year older, "he
became devoted to her." "For my own part," she adds, "I felt not the
smallest wish to contest the prize with her.... She, with a glance,
divined his character, ... while I, expecting an Adonis, lost all desire
of becoming agreeable in his eyes when I beheld his awkward, unpolished
manner and total negligence of person." "How trivial now seem all such
objections!" she exclaims, writing in 1810, and going on to speak with
the utmost admiration of his relations to herself and all her family,
and above all, to his wife. "His exemplary tenderness to our unfortunate
sister is without parallel. With a delicacy of frame and feeling that
baffles all description, she became, early after her marriage, a prey to
extreme nervous affection, which, more or less, has embittered her
comfort through her whole life; but this has only seemed to increase his
care and tenderness, and he is, as you know, as entirely devoted as at
the moment of their first being married. Always and under every
circumstance an enthusiast in love, I have very lately heard him
declare that he looked with astonishment at the present race of lovers,
so totally unlike what he had been himself. His never-failing
cheerfulness and good humor are a perpetual source of delight to all
connected with him, and, I have not a doubt, have been the means of
prolonging the life of her he is so tenderly devoted to."
"He was her devoted lover to the very end of her life," another member
of his family connection has said. And Judge Story, in speaking of him
after his wife's death, described him as "the most extraordinary man I
ever saw for the depth and tenderness of his feelings."
A little touch of his manner to his wife is seen in a letter, which is
in print, written to her from the city of Washington, on February 23,
1825, in his seventieth year. He had received an injury to his knee,
about which Mrs. Marshall was anxious. "I shall be out," he writes, "in
a few days. All the ladies of the secretaries have been to see me, some
more than once, and have brought me more jelly than I could eat, and
many other things. I thank them, and stick to my barley broth. Still I
have lots of time on my hands. How do you think I beguile it? I am
almost tempted to leave you to guess, until I write again. You must know
that I begin with the ball at York, our splendid assembly at the Palace
in Williamsburg, my visit to Richmond for a fortnight, my return to the
field, and the very welcome reception you gave me on my arrival at
Dover, our little tiffs and makings-up, my feelings when Major Dick[8]
was courting you, my trip to the Cottage [the Ambler home in Hanover
County, where the marriage took place],[9]--the thousand little
incidents, deeply affecting, in turn."
This "ball at York" was the one of which Mrs. Carrington wrote; and of
the "assembly at the Palace" she also gave an account, remarking that
"Marshall was devoted to my sister."
Miss Martineau, who saw him the year before he died, speaks with great
emphasis of what she calls his "reverence" and his affectionate respect
for women. There were many signs of this all through his life. Even in
the grave and too monotonous course of his "Life of Washington," one
comes now and then upon a little gleam of this sort, that lights up the
page; as when he speaks of Washington's engagement to Mrs. Custis, a
lady "who to a large fortune and a fine person added those amiable
accomplishments which ... fill with silent but unceasing felicity the
quiet scenes of private life." When he is returning from France, in
1798, he writes gayly back from Bordeaux to the Secretary of Legation at
Paris: "Present me to my friends in Paris; and have the goodness to say
to Madame Vilette, in my name and in the handsomest manner, everything
which respectful friendship can dictate. When you have done that, you
will have rendered not quite half justice to my sentiments." "He was a
man," said Judge Story, "of deep sensibility and tenderness; ...
whatever may be his fame in the eyes of the world, that which, in a just
sense, was his brightest glory was the purity, affectionateness,
liberality, and devotedness of his domestic life."
Marshall left the army in 1781, when most of the fighting in Virginia
was over; and began practice in Fauquier County when the courts were
opened, after Cornwallis's surrender, in October of that year.
Among his neighbors he was always a favorite. In the spring of 1782 he
was elected to the Assembly, and in the autumn to the important office
of member of the "Privy Council, or Council of State," consisting of
eight persons chosen by joint ballot of the two houses of the Assembly.
"Young Mr. Marshall," wrote Edmund Pendleton, presiding judge of the
Court of Appeals, to Madison, in November of that year, "is elected a
councilor.... He is clever, but I think too young for that department,
which he should rather have earned, as a retirement and reward, by ten
or twelve years of hard service." But, whether young or old, the people
were forever forcing him into public life. Eight times he was sent to
the Assembly; in 1788 to the Federal Convention of Virginia, and in 1798
to Congress.
Unwelcome as it was to him, almost always, to have his brilliant and
congenial place and prospects at the bar thus interfered with, we can
see now what an admirable preparation all this was for the great
station, which, a little later, to the endless benefit of his country,
he was destined to fill. What drove him into office so often was, in a
great degree, that delightful and remarkable combination of qualities
which made everybody love and trust him, even his political adversaries,
so that he could be chosen when no one else of his party was available.
In this way, happily for his country, he was led to consider, early and
deeply, those difficult problems of government that distressed the
country in the dark period after the close of the war, and during the
first dozen years of the Federal Constitution.
As regards the effect of his earlier experience in enlarging the circle
of a patriot's thoughts and affections, he himself has said: "I am
disposed to ascribe my devotion to the Union, and to a government
competent to its preservation, at least as much to casual circumstances
as to judgment. I had grown up at a time ... when the maxim, 'United we
stand, divided we fall,' was the maxim of every orthodox American; and I
had imbibed these sentiments so thoroughly that they constituted a part
of my being. I carried them with me into the army, where I found myself
associated with brave men from different States who were risking life
and everything valuable in a common cause; ... and where I was confirmed
in the habit of considering America as my country and Congress as my
government." It was this confirmed "habit of considering America as my
country," communicated by him to his countrymen, which enabled them to
carry through the great struggle of forty years ago, and to save for us
all, North and South, the inestimable treasure of the Union.
After Marshall's marriage, in January, 1783, he made Richmond his home
for the rest of his life. It was still a little town, but it had lately
become the capital of the State, and the strongest men at the bar
gradually gathered there. Marshall met them all. One has only to look at
the law reports of Call and Washington to see the place that he won. He
is found in most of the important cases. In his time no man's name
occurs oftener, probably none so often.
The earliest case in which the printed reports show his name is that of
Hite _v._ Fairfax (4 Call's Reports, 42), in May, 1786, and his argument
seems to be fully reported. It was a very important case, and Marshall
represented tenants of Lord Fairfax. There were conflicting grants on
the famous "Northern Neck" of Virginia, an extensive region given by the
crown to Lord Fairfax's ancestor, whose boundaries had been in dispute.
It comprised the land between the Potomac and the Rappahannock, "within
the heads of the rivers ... the courses of the said rivers, as they are
commonly called or known by the inhabitants and descriptions of those
parts, and Chesapeake Bay, together with the rivers themselves and all
the islands within the banks of the rivers." This description was
finally admitted by the crown (in 1745) to include all the land between
the head springs of the Potomac and those of the south branch of the
Rappahannock. Bishop Meade[10] describes it as the region which,
beginning on the Chesapeake Bay, lies between the Potomac and
Rappahannock rivers, and crossing the Blue Ridge, or passing through it
with the Potomac at Harper's Ferry, extends with that river to the heads
thereof in the Alleghany Mountains, and thence by a straight line
crosses the North Mountain and Blue Ridge at the headwaters of the
Rappahannock, ... "the most fertile part of Virginia."
Marshall had now to meet a total denial of Lord Fairfax's title. His
argument of ten or twelve pages shows already the characteristics, the
cogency, clear method, and neat precision of thought and speech, by
which his later work was marked. "I had conceived," he says, "that it
was not more certain that there was such a tract of country as the
Northern Neck than that Lord Fairfax was the proprietor of it....
Gentlemen cannot suppose that a grant made by the crown to the ancestor
for services rendered or even for affection can be invalidated in the
hands of an heir because these services and affections are forgotten, or
because the thing granted has, from causes which must have been
foreseen, become more valuable than when it was given. And if it could
not be invalidated in the hands of the heir, much less can it be in the
hands of the purchaser." As regards the construction of the grant:
"Whether Lord Fairfax's grant extended originally beyond the forks of
the rivers or not, will no more admit of argument than it ever could
have admitted of a doubt. But whether it should be bounded by the north
or south fork of the Rappahannock was a question involved in more
uncertainty.... It is, however, no longer a question, for it has been
decided.... That decision did not create or extend Lord Fairfax's
right, but determined what the right originally was. The bounds of many
patents are doubtful; the extent of many titles uncertain: but when a
decision is once made on them, it removes the doubt and ascertains what
the original boundaries were." In reference to a personal appeal in
behalf of certain settlers, he says, "Those who explore and settle new
countries are generally bold, hardy, and adventurous men, whose minds as
well as bodies are fitted to encounter danger and fatigue; their object
is the acquisition of property, and they generally succeed. None will
say that the complainants have failed; and if their hardships and
dangers have any weight in the court, the defendants share in them, and
have equal claim to countenance; for they, too, with humbler views and
less extensive prospects, have explored, bled for, and settled a till
then uncultivated desert."
Compare with this the like simple felicity and exactness of expression
in his last reported utterance in court, when he was closing his great
career as Chief Justice of the United States, forty-nine years later.
He is refusing a motion for delay: "The court has taken into its serious
and anxious consideration the motion made on the part of the government
to continue the cause of Mitchel _v._ The United States to the next
term. Though the hope of deciding causes to the mutual satisfaction of
parties would be chimerical, that of convincing them that the case has
been fully and fairly considered, that due attention has been given to
the arguments of counsel, and that the best judgment of the court has
been exercised on the case, may be sometimes indulged. Even this is not
always attainable. In the excitement produced by ardent controversy,
gentlemen view the same object through such different media that minds
not unfrequently receive therefrom precisely opposite impressions. The
court, however, must see with its own eyes, and exercise its own
judgment guided by its own reason.... The opinion of the court will be
delivered."[11]
At first, he had brought from the army, and from his home on the
frontier, simple and rustic ways which surprised some persons at
Richmond, whose conception of greatness was associated with very
different models of dress and behavior. "He was one morning strolling,"
we are told, "through the streets of Richmond, attired in a plain linen
roundabout and shorts, with his hat under his arm, from which he was
eating cherries, when he stopped in the porch of the Eagle Hotel,
indulged in a little pleasantry with the landlord, and then passed on."
A gentleman from the country was present, who had a case coming on
before the Court of Appeals, and was referred by the landlord to
Marshall as the best lawyer to employ. But "the careless, languid air"
of Marshall had so prejudiced the man that he refused to employ him. The
clerk, when this client entered the court-room, also recommended
Marshall, but the other would have none of him. A venerable-looking
lawyer, with powdered wig and in black cloth, soon entered, and the
gentleman engaged him. In the first case that came up, this man and
Marshall spoke on opposite sides. The gentleman listened, saw his
mistake, and secured Marshall: at once; frankly telling him the whole
story, and adding that while he had come with one hundred dollars to pay
his lawyer, he had but five dollars left. Marshall good-naturedly took
this, and helped in the case. In the Virginia Federal Convention of
1788, at the age of thirty-three, he is described, rising after Monroe
had spoken, as "a tall young man, slovenly dressed in loose summer
apparel.... His manners, like those of Monroe, were in strange contrast
with those of Edmund Randolph or of Grayson."
In such stories as these, one is reminded, as he is often reminded, of a
resemblance between Marshall and Lincoln. Very different men they were,
but both thorough Americans, with unborrowed character and manners, and
a lifelong flavor derived from no other soil.
At the height of Marshall's reputation, in 1797, a French writer, who
had visited Richmond lately, in speaking of Edmund Randolph, says, "He
has a great practice, and stands, in that respect, nearly on a par with
Mr. J. Marshall, the most esteemed and celebrated counselor of this
town." He mentions Marshall's annual income as being four or five
thousand dollars. "Even by his friends," it is added, "he is taxed with
some little propensity to indolence, but he nevertheless displays great
superiority when he applies his mind to business." Another contemporary,
who praises his force and eloquence in speaking, yet says: "It is
difficult to rouse his faculties. He begins with reluctance, hesitation,
and vacancy of eye.... He reminds one of some great bird, which
flounders on the earth for a while before it acquires impetus to sustain
its soaring flight." And finally, William Wirt, who was seventeen years
Marshall's junior, and came to the bar in 1792, when Marshall was nearly
at the head of it, writing anonymously in 1804, describes him as one,
"who, without the advantage of person, voice, attitude, gesture, or any
of the ornaments of an orator, deserves to be considered as one of the
most eloquent men in the world." He attributes to him "one original and
almost supernatural faculty, ... of developing a subject by a single
glance of his mind.... His eyes do not fly over a landscape and take in
its various objects with more promptitude and facility than his mind
embraces and analyzes the most complex subject.... All his eloquence
consists in the apparently deep self-conviction and the emphatic
earnestness and energy of his style, the close and logical connection of
his thoughts, and the easy gradations by which he opens his lights on
the attentive minds of his hearers."
In 1789 he declined the office of District Attorney of the United States
at Richmond,[12] in 1795 that of Attorney-General of the United States,
and in 1796 that of Minister to France, all offered him by Washington.
When President Adams persuaded him, in 1797, to go, with Pinckney and
Gerry, as envoy to France, he wrote to Gerry of "General Marshall" (as
he was then called, from his rank of brigadier general, since 1793, in
the Virginia militia), "He is a plain man, very sensible, cautious,
guarded, and learned in the law of nations." The extraordinary details
of that unsuccessful six months' attempt to come to terms with France
are found in Marshall's very able dispatches and in the diary which he
kept;[13] for, with the instinct of a man of affairs, he failed not to
remember, with Thomas Gray, that "a note is worth a cartload of
recollections." His own part in the business was marked by great
moderation and ability; and on his return, in 1798, he was received at
Philadelphia with remarkable demonstrations and the utmost enthusiasm. A
correspondent of Rufus King, writing from New York in July of that year,
says, "No two men can be more beloved and honored than Pinckney and
Marshall;" and again in November: "Saving General Washington, I believe
the President, Pinckney, and Marshall are the most popular characters
now in our country. There is a certain something in the correspondence
of Pinckney and Marshall ... that has united all heads and hearts in
their eulogy." It is understood that the American side of this
correspondence was by Marshall. Gerry had allowed himself in a measure
to be detached by the Directory from his associates, to their great
displeasure. With them, in important respects, he disagreed.
Among those who paid their respects to Marshall, on his return from
France, was Thomas Jefferson, the Vice-President, whose correspondence
shows him at the time expressing the most unflattering opinion of the
envoys. Jefferson wrote to Marshall the following note: "In after
years," says Mrs. Hardy, one of Marshall's descendants,[14] "the Chief
Justice frequently laughed over it, saying, 'Mr. Jefferson came very
near telling me the truth; the added _un_ to _lucky_, policy alone
demanded.'" The note ran thus: "Thos. Jefferson presents his
compliments to General Marshall. He had the honor of calling at his
lodgings twice this morning, but was so {un}^lucky as to find that he
was out on both occasions. He wished to have expressed in person his
regret that a pre-engagement for to-day, which could not be dispensed
with, would prevent him the satisfaction of dining in company with
Genl-Marshall, and, therefore, begs leave to place here the expressions
of that respect which in company with his fellow-citizens he bears him.
"Genl. Marshall,
at Oeller's Hotel, June 23d, 1798."
In 1798 Adams offered to Marshall the seat on the Supreme Bench, made
vacant by the death of James Wilson. He declined it; and it went to his
old associate at William and Mary College, Bushrod Washington. Marshall
did yield, however, to General Washington's urgent request to stand for
Congress that year. He held out long against Washington's arguments, and
only yielded, at last, when that venerated man called attention to his
own recent sacrifice in accepting the unwelcome place of
lieutenant-general of the army. When that went into the scale it was
too much. Marshall was then on a visit to Mount Vernon, whither he had
been invited in August or September, in company with Washington's
nephew, the coming judge.
On their way to Mount Vernon, the two travelers met with a misadventure
which gave great amusement to Washington, and of which he enjoyed
telling his friends. They came on horseback, and carried but one pair of
saddlebags, each using one side. Arriving thoroughly drenched by rain,
they were shown to a chamber to change their garments. One opened his
side of the bags and drew forth a black bottle of whiskey. He insisted
that he had opened his companion's repository. Unlocking the other side,
they found a big twist of tobacco, some corn bread, and the equipment of
a pack-saddle. They had exchanged saddlebags with some traveler, and now
had to appear in a ludicrous misfit of borrowed clothes.[15]
The election of Marshall to Congress excited great interest.[16]
Washington heartily rejoiced in it. Jefferson, on the other hand,
remarked that while Marshall might trouble the Republicans somewhat, yet
he would now be unmasked. He had been popular with the mass of the
people, Jefferson said, from his "lax, lounging manners," and with wiser
men through a "profound hypocrisy." But now his British principles would
stand revealed.
The New England Federalists were very curious about him; they had been
alarmed and outraged, during the campaign, by his expressing opposition
to the alien and sedition laws; but they were much impressed by him.
Theodore Sedgwick wrote to Rufus King that he had "great powers, and
much dexterity in the application of them.... We can do nothing without
him." But Sedgwick wished that "his education had been on the other side
of the Delaware." George Cabot wrote to King: "General Marshall is a
leader.... But you see in him the faults of a Virginian.... He thinks
too much of that State, and he expects that the world will be governed
by rules of logic." But Cabot hopes to see him improve, and adds, "He
seems calculated to act a great part." In the end, the Northern
Federalists were disappointed in finding him too moderate. He held the
place of leader of the House, and passed into the cabinet in May, 1800.
On January 31, 1801, he was commissioned as Chief Justice.
Chapter II
ARGUMENTS AND SPEECHES; LIFE OF WASHINGTON; RELATIONS WITH JEFFERSON
There is little room for quotations from Marshall's speeches or
dispatches.
Some reference has already been made to his earliest reported argument
in court, in 1786. In the Virginia Federal Convention, in 1788,
Marshall's principal speeches related to the subjects of taxation, the
militia, and the judiciary. These, so far as preserved, are found in the
third volume of Elliot's Debates, and in Dr. Grigsby's very interesting
History of that Convention, in the tenth volume of the "Virginia
Historical Collections." Nothing remains of a famous speech in support
of Jay's treaty, at a public meeting in Richmond in 1795. A summary of
his strong but unsuccessful argument in 1796, in the case of Ware _v_.
Hylton (3 Dallas 199), as to the claims of British creditors, his only
case before the Supreme Court of the United States, is preserved in the
volume of reports. This argument attracted much attention among the
statesmen at Philadelphia. "I then became acquainted," he wrote to a
friend, "with Mr. Cabot, Mr. Ames, Mr. Dexter, and Mr. Sedgwick of
Massachusetts, Mr. Wadsworth of Connecticut, and Mr. King of New
York.... I was particularly intimate with Mr. Ames."
After Washington's death in 1799, Marshall, in a short and well-known
speech, moved the resolution of the House of Representatives.
A little afterwards he made a great and admirably thorough address in a
matter which then deeply affected the public mind; from this, his
greatest public speech,[17] a quotation is given below. It was made
March 4, 1800, in defense of the President's action in the case of
Thomas Nash, _alias_ Jonathan Robbins. This person, a British subject,
but claiming to be an American citizen, and to have been impressed into
the British navy, was charged with piracy and murder on board a British
ship of war in 1791. Being found in Charleston, S. C., he was arrested
in 1799, at the instance of the British consul, and held to await an
application for his extradition under article 27 of the treaty with
Great Britain of 1795. That article bound the two countries reciprocally
to deliver up, on request of the other, persons charged with murder
committed within the jurisdiction of that other. Evidence of criminality
was first to be furnished, such as would justify commitment for trial on
the same charge in the country where the accused was found.
An application for extradition was made to the federal authorities in
Charleston, but at their suggestion this was transferred to the
President, through the Secretary of State. The Secretary informed Bee,
the United States District Judge, of the President's "advice and
request" that Nash should be delivered up, at the same time referring to
the clause in the treaty as to the necessary evidence of
criminality.[18] The judge on July 1, 1799, informed the Secretary that
he had notified the British consul that on the production of such
evidence, the prisoner would be delivered up when the consul was ready
to receive him. The delivery was made; and on September 9 of the same
year, the British admiral was able to inform the British Minister that
Nash "has been tried at a court martial, and sentenced to suffer death,
and afterwards hung in chains; which sentence has been put into
execution."
These events were used with great effect by the political opponents of
the administration. When Congress met, the President was called upon by
the House of Representatives for the papers relating to them; and when
they were sent in, Edward Livingston, of New York, submitted resolutions
condemning the action of the executive, on the ground that the
determination of the questions involved in the case "are all matters
exclusively for judicial inquiry;" that the acts of the President "are a
dangerous interference of the executive with judicial decisions;" and
that the compliance of the district judge "is a sacrifice of the
constitutional independence of the judicial power." After a full debate,
these resolutions were negatived by a decided vote. Marshall's very able
argument vindicated the action taken, and laid down principles which
have ever since governed the course of the government in such cases.
The following passages will afford a specimen of the style and method of
this address, a style and method which were characteristic of all
Marshall's work:--
"The same argument applies to the observations on the seventh article of
the amendment to the Constitution. That article relates only to trials
in the courts of the United States, and not to the performance of a
contract for the delivery of a murderer not triable in those courts.
"In this part of the argument, the gentleman from New York [Mr.
Livingston] has presented a dilemma, of a very wonderful structure
indeed. He says that the offense of Thomas Nash was either a crime or
not a crime. If it was a crime, the constitutional mode of punishment
ought to have been observed; if it was not a crime, he ought not to have
been delivered up to a foreign government, where his punishment was
inevitable.
"It has escaped the observation of that gentleman that if the murder
committed by Thomas Nash was a crime, yet it was not a crime provided
for by the Constitution or triable in the courts of the United States;
and that if it was not a crime, yet it is the precise case in which his
surrender was stipulated by treaty. Of this extraordinary dilemma, the
gentleman from New York is himself perfectly at liberty to retain either
form.
"He has chosen to consider it as a crime, and says it has been made a
crime by treaty, and is punished by sending the offender out of the
country. The gentleman is incorrect in every part of his statement.
Murder on board a British frigate is not a crime created by treaty. It
would have been a crime of precisely the same magnitude had the treaty
never been formed. It is not punished by sending the offender out of the
United States. The experience of the unfortunate criminal, who was hung
and gibbeted, evinced to him that the punishment of his crime was of a
much more serious nature than mere banishment from the United States.
"The gentleman from Pennsylvania [Mr. Gallatin] and the gentleman from
Virginia [Mr. Nicholas] have both contended that this was a case proper
for the decision of the courts, because points of law occurred, and
points of law must have been decided in its determination. The points of
law which must have been decided are stated by the gentleman from
Pennsylvania to be, first, a question whether the offense was committed
within the British jurisdiction; and, secondly, whether the crime
charged was comprehended within the treaty.
"It is true, sir, these points of law must have occurred, and must have
been decided, but it by no means follows that they could only have been
decided in court. A variety of legal questions must present themselves
in the performance of every executive duty, but these questions are not
therefore to be decided in court. Whether a patent for land shall issue
or not is always a question of law, but not a question which must
necessarily be carried into court. The gentleman from Pennsylvania seems
to have permitted himself to have been misled by the misrepresentations
of the Constitution made in the resolutions of the gentleman from New
York; and, in consequence of being so misled, his observations have the
appearance of endeavoring to fit the Constitution to his arguments,
instead of adapting his arguments to the Constitution.
"When the gentleman has proved that these are questions of law, and that
they must have been decided by the President, he has not advanced a
single step towards proving that they were improper for executive
decision. The question whether vessels captured within three miles of
the American coast, or by privateers fitted out in the American ports,
were legally captured or not, and whether the American government is
bound to restore them, if in its power, were questions of law, but they
were questions of political law, proper to be decided, and they were
decided by the executive, and not by the courts. The _casus fœderis_ of
the guaranty was a question of law, but no man could have hazarded the
opinion that such a question must be carried into court, and can only be
there decided. So the _casus fœderis_, under the twenty-seventh article
of the treaty with Britain, is a question of law, but of political law.
The question to be decided is, whether the particular case proposed be
one in which the nation has bound itself to act, and this is a question
depending on principles never submitted to courts. If murder should be
committed within the United States, and the murderer should seek an
asylum in Britain, the question whether the _casus fœderis_, of the
twenty-seventh article had occurred, so that his delivery ought to be
demanded, would be a question of law, but no man would say it was a
question which ought to be decided in the courts.
"When, therefore, the gentleman from Pennsylvania has established that,
in delivering up Thomas Nash, points of law were decided by the
President, he has established a position which in no degree whatever
aids his argument. The case is in its nature a national demand, made
upon the nation. The parties are the two nations. They cannot come into
court to litigate their claims, nor can a court decide on them. Of
consequence, the demand is not a case for judicial cognizance. The
President is the sole organ of the nation in its external relations, and
its sole representative with foreign nations. Of consequence, the demand
of a foreign nation can only be made on him....
"The treaty, which is a law, enjoins the performance of a particular
object. The person who is to perform this object is marked out by the
Constitution, since the person is named who conducts the foreign
intercourse and is to take care that the laws be faithfully executed.
The means by which it is to be performed, the force of the nation, are
in the hands of this person. Ought not this person to perform the
object, although the particular mode of using the means has not been
prescribed? Congress, unquestionably, may prescribe the mode, and
Congress may devolve on others the whole execution of the contract; but,
till this is done, it seems the duty of the executive department to
execute the contract by any means it possesses.
"The gentleman from Pennsylvania contends that, although this should be
properly an executive duty, yet it cannot be performed until Congress
shall direct the mode of performance.... The treaty stipulating that a
murderer shall be delivered up to justice is as obligatory as an act of
Congress making the same declaration. If, then, there was an act of
Congress in the words of the treaty, declaring that a person who had
committed murder within the jurisdiction of Britain, and sought an
asylum within the territory of the United States, should be delivered up
by the United States, on the demand of his Britannic Majesty and such
evidence of his criminality as would have justified his commitment for
trial, had the offense been committed here; could the President, who is
bound to execute the laws, have justified the refusal to deliver up the
criminal by saying that the legislature had totally omitted to provide
for the case?
"The executive is not only the constitutional department, but seems to
be the proper department to which the power in question may most wisely
and most safely be confided.... If, at any time, policy may temper the
strict execution of the contract, where may that political discretion be
placed so safely as in the department whose duty it is to understand
precisely the state of the political intercourse and connection between
the United States and foreign nations, to understand the manner in
which the particular stipulation is explained and performed by foreign
nations, and to understand completely the state of the Union?"
This clear, strong, convincing speech, of which I have quoted but a
small portion, settled the question then in dispute, and the principles
here laid down have controlled the action of the government ever since.
* * * * *
Very soon after entering upon his duties as Chief Justice, Marshall
undertook to write the "Life of Washington." This gave him a great deal
of trouble and mortification. It proved to be an immense labor; the
publishers were importunate, and he was driven into print before he was
ready. The result was a work in five volumes, appearing from 1802 to
1804, full of the most valuable and authentic material, well repaying
perusal, yet put together with singular lack of literary skill, and in
many ways a great disappointment.[19] In the later years of his life,
he revised it, corrected some errors, shortened it, and published it in
three volumes: one of them, in 1824, as a separate preliminary history
of the colonial period, and the other two, in 1834, as the "Life of
Washington." This work, in its original form, gave great offense to
Jefferson, written, as it was, from the point of view of a constant
admirer and supporter of the policy of Washington; a "five volume
libel," Jefferson called it.
Jefferson had ludicrous misconceptions as to Marshall's real character.
It is said that after Burr's trial, in 1807, all personal intercourse
between them ceased.[20] Referring in 1810 to the "batture" case, in
which Edward Livingston sued him, and which was to come before Marshall,
Jefferson says that he is certain what the result of the case should be,
but nobody can tell what it will be; for "the Judge's mind [is] of that
gloomy malignity which will never let him forego the opportunity of
satiating it upon a victim.... And to whom is my appeal? From the judge
in Burr's case to himself and his associate justices in Marbury v.
Madison. Not exactly, however. I observe old Cushing is dead. [Judge
Cushing had died a fortnight before.] At length, then, we have a chance
of getting a Republican majority in the Supreme Judiciary." And he goes
on to express his confidence in the "appointment of a decided
Republican, with nothing equivocal about him."
Who was this decided and unequivocal Republican to be? Jefferson was
anxious about it, and wrote to Madison, suggesting Judge Tyler, of
Virginia, as a candidate, and reminding the President of Marshall's
"rancorous hostility to his country." Who was it, in fact, that was
appointed? Who but Joseph Story!--a Republican, indeed, but one whom
Jefferson, in this very year, was designating as a "pseudo-Republican,"
and who soon became Marshall's warmest admirer and most faithful
supporter.
CHAPTER III
THE BEGINNINGS OF THE CHIEF JUSTICE'S CAREER; AMERICAN CONSTITUTIONAL
LAW; MARBURY _v_. MADISON.
Marshall's accession to the bench was marked by an impressive
circumstance. For ten years or more, he alone gave all the opinions of
the court to which any name was attached, except where the case came up
from his own circuit, or, for any reason, he did not sit. In the very
few cases where opinions were given by the other justices, it was in the
old way, _seriatim_,--the method followed before Marshall came in, as it
was also the method of contemporary English courts.
Whatever may have been the purpose of the Chief Justice in introducing
this usage, there can be no doubt as to the impression it was calculated
to produce. It seemed, all of a sudden, to give to the judicial
department a unity like that of the executive, to concentrate the whole
force of that department in its chief, and to reduce the side-justices
to a sort of cabinet advisers. In the very few early cases where there
was expressed dissent, it lost much of its impressiveness, when
announced, as it sometimes was, by the mouth that gave the opinion of
the court.
In 1812, when a change took place, the court had been for a year without
a quorum. Moreover, Judge Story had just come to the bench, a man of
quite too exuberant an intellect and temperament to work well as a
silent side-judge. We remark, also, at the beginning of that term, that
the Chief Justice was not in attendance, having, as the reporter tells
us, "received an injury by the oversetting of the stage-coach on his
journey from Richmond." And it may be added that just at this time the
anxious prayer of Jefferson was answered, and a majority of the judges
were Republicans. From whatever cause, henceforward there was a change;
and without returning to the old habit of _seriatim_ opinions, the
side-judges had their turn, as they do now.
In most of Marshall's opinions, one observes the style and special touch
of a thoughtful and original mind; in some of them the powers of a great
mind, in full activity. His cases relating to international law, as I am
assured by those competent to judge, rank with the best there are in the
books. As regards most of the more familiar titles of the law, it would
be too much to claim for him the very first rank. In that region he is,
in many respects, equaled or surpassed by men more deeply versed in the
learning and technicalities of the law, in what constitutes that
"artificial perfection of reason" which Coke used to glorify as far
transcending any man's natural reason,--men such as Story, Kent, or
Shaw, or even the reformer, Mansfield, whom he greatly admired, Eldon,
or Blackburn. But in the field of constitutional law, a region not open
to an English lawyer,--and especially in one department of it, that
relating to the nature and scope of the National Constitution, he was
preëminent,--first, with no one second. It is hardly possible, as
regards this part of the law, to say too much of the service he rendered
to his country. Sitting in the highest judicial place for more than a
generation; familiar, from the beginning, with the Federal Constitution,
with the purposes of its framers, and with all the objections of its
critics; accustomed to meet these objections from the time he had served
in the Virginia Convention of 1788; convinced of the purpose and
capacity of this instrument to create a strong nation, competent to make
itself respected at home and abroad, and able to speak with the voice
and strike with the strength of all; assured that this was the paramount
necessity of the country, and that the great source of danger was in the
jealousies and adverse interests of the States,--Marshall acted on his
convictions. He determined to give full effect to all the affirmative
contributions of power that went to make up a great and efficient
national government; and fully, also, to enforce the national
restraints and prohibitions upon the States. In both cases he included
not only the powers expressed in the Constitution, but those also which
should be found, as time unfolded, to be fairly and clearly implied in
the objects for which the federal government was established. In that
long judicial life, with which Providence blessed him, and blessed his
country, he was able to lay down, in a succession of cases, the
fundamental considerations which fix and govern the relative functions
of the nation and the States, so plainly, with such fullness, with such
simplicity and strength of argument, such a candid allowance for all
that was to be said upon the other side, in a tone so removed from
controversial bitterness, so natural and fit for a great man addressing
the "serene reason" of mankind, as to commend these things to the minds
of his countrymen, and firmly to fix them in the jurisprudence of the
nation; so that "when the rain descended and the floods came, and the
winds blew and beat upon that house, it fell not, because it was founded
upon a rock." It was Marshall's strong constitutional doctrine,
explained in detail, elaborated, powerfully argued, over and over again,
with unsurpassable earnestness and force, placed permanently in our
judicial records, holding its own during the long emergence of a feebler
political theory, and showing itself in all its majesty when war and
civil dissension came,--it was largely this that saved the country from
succumbing, in the great struggle of forty years ago, and kept our
political fabric from going to pieces.
I do not forget our own Webster, or others, in saying that to Marshall
(if we may use his own phrase about Washington), "more than to any other
individual, and as much as to one individual was possible," do we owe
that prevalence of sound constitutional opinion and doctrine at the
North that held the Union together; to that combination in him, of a
great statesman's sagacity, a great lawyer's lucid exposition and
persuasive reasoning, a great man's candor and breadth of view, and that
judicial authority on the bench, allowed naturally and as of right, to
a large, sweet nature, which all men loved and trusted, capable of
harmonizing differences and securing the largest possible amount of
coöperation among discordant associates. In a very great degree, it was
Marshall, and these things in him, that have wrought out for us a strong
and great nation, one which men can love and die for; that "mother of a
mighty race," that stirred the soul of Bryant half a century ago, as he
dreamed how--
"The thronging years in glory rise,
And as they fleet,
Drop strength and riches at thy feet;"
the nation whose image flamed in the heart of Lowell, a generation
since, as he greeted her coming up out of the Valley of the Shadow of
Death:--
"Oh Beautiful, my country, ours once more!...
Among the nations bright beyond compare!...
What were our lives without thee?
What all our lives to save thee?
We reck not what we gave thee,
We will not dare to doubt thee,
But ask whatever else, and we will dare!"
It was early in Marshall's day that the Supreme Court first took the
grave step of disregarding an act of Congress,--a coördinate
department,--which conflicted with the National Constitution. The right
to deal thus with their legislatures had already been asserted in the
States, and once or twice it had really been exercised. Had the question
related to a conflict between that Constitution and the enactment of a
State, it would have been a simpler matter. These two questions, under
European written constitutions, are regarded as different ones. It is
almost necessary to the working of a federal system that the general
government, and each of its departments, should be free to disregard
acts of any department of the local states which may be inconsistent
with the federal constitution. And so in Switzerland and Germany the
federal courts thus treat local enactments. But there is not under any
written constitution in Europe a country where a court deals in this way
with the act of its coördinate legislature. In Germany, at one time,
this was done, under the influence of a study of our law, but it was
soon abandoned.[21]
In the colonial period, while we were dependencies of Great Britain, our
legislation was subject to the terms of the royal charters. Enactments
were often disallowed by the English Privy Council, sometimes acting as
mere revisers of the colonial legislation, and sometimes as appellate
judicial tribunals. Our people were, in this way, familiar with the
theory of a dependent legislature, one whose action was subject to
reversal by judicial authority, as contrary to the terms of a written
charter of government.
When, therefore, after the war of independence, our new sovereign,
namely, ourselves, the people, came to substitute for the old royal
charters the people's charters, what we call our "constitutions,"--it
was natural to expect some legal restraint upon legislation. It was not
always found in terms; indeed, it was at first hardly ever, if at all,
found set down in words. But it was a natural and just interpretation
of these instruments, made in regions with such a history as ours and
growing out of the midst of such ideas and such an experience, to think
that courts, in the regular exercise of their functions, that is to say,
in dealing with litigated cases, could treat the constitutions as law to
be applied by them in determining the validity of legislation.
But this, although, as we may well think, a sound conclusion, was not a
necessary one; and it was long denied by able statesmen, judges, and
lawyers. An elaborate and powerful dissenting opinion by Chief Justice
Gibson, of Pennsylvania, containing the most searching argument on the
subject with which I am acquainted, given in 1825,[22] reaches the
result that under no constitution where the power to set aside
legislative enactments is not expressly given, does it exist. But it is
recognized that in the Federal Constitution the power is given, as
regards legislation of the States inconsistent with the Federal
Constitution and laws.
It is not always noticed that in making our Federal Constitution, there
was an avoidance of any explicit declaration of such a power as touching
federal legislation, while it was carefully provided for as regards the
States. In the Federal Convention, there was great anxiety to control
the States, in certain particulars; and various plans were put forward,
such as that Congress should have a negative on state laws, and that
governors of the States should be appointed by the federal authority,
with power to negative state acts.
But all these, at last, were rejected, and the matter took the shape of
a provision that the Constitution and the constitutional laws and
treaties of the United States should be the supreme law of _the
respective States_; and the judges of _the several States_ should be
bound thereby, anything in the constitution or laws of any State to the
contrary notwithstanding. Later, the Committee on Style changed the
phrase "law of the respective States" to "law of the land." But the
language, as to binding the judges, was still limited to the judges of
the several States. Observe, then, the scope of this provision: it was
to secure the authority of the federal system within the States.
As to any method of protecting the federal system within its own
household, that is to say, as against Congress, it was proposed in the
convention, for one thing, that each House of Congress might call upon
the judges for opinions; and, again, it was urged, and that repeatedly
and with great persistence, that the judges should be joined with the
executive in passing on the approval or disapproval of legislative
acts,--in what we call the veto power. It was explicitly said, in
objecting to this, that the judges would have the right to disregard
unconstitutional laws anyway,--an opinion put forward by some of the
weightiest members. Yet some denied it. And we observe that the power
was not expressly given. When we find such a power expressly denied, and
yet not expressly given; and when we observe, for example, that leading
public men, _e.g._, so conspicuous a member of the convention as
Charles Pinckney of South Carolina, afterwards a senator from that
State, wholly denied the power ten years later;[23] it being also true
that he and others of his way of thinking urged the express restraints
on state legislation,--we may justly reach the conclusion that this
question, while not overlooked, was intentionally left untouched. Like
the question of the bank and various others, presumably it was so left
in order not to stir up enemies to the new instrument; left to be
settled by the silent determinations of time, or by later discussion.
Turning now to the actual practice under the government of the United
States, we find that the judges of the Supreme Court had hardly taken
their seats, at the beginning of the government, when Chief Justice Jay
and several other judges, in 1790, communicated to the President
objections to the Judiciary Act, as violating the Constitution, in
naming the judges of the Supreme Court to be judges also of the circuit
courts.[24] These judges, however, did not refuse to act under this
unconstitutional statute; and the question did not come judicially
before the court until Marshall's time, in 1803,[25] when it was held
that the question must now be regarded as settled in favor of the
statute, by reason of acquiescence since the beginning of the
government.[26]
In observing, historically, the earlier conceptions of the judges of the
Supreme Court as to the method of dealing with unconstitutional
legislation, one or two other transactions should be looked at. In 1792
(1 U. S. Statutes, 243) a statute was enacted which required the circuit
court, partly composed, as we have seen, of the judges of the Supreme
Court, to pass on the claims of certain soldiers and others demanding
pensions, and to report to the Secretary of War; who was, in turn, to
revise these returns and report to Congress. The judges found great
difficulty in acting under this statute, because it imposed on them
duties not judicial in their nature; and they expressed their views in
various ways.
In one circuit, the judges thinking it improper to act under this
statute in their judicial capacity, for the reason above-named,
consented from charitable motives to serve as "commissioners."[27]
In the Pennsylvania circuit, the three judges wrote, in a letter to the
President, that "on a late painful occasion" they had held the law
invalid; and they now stated the matter to him, as being the person
charged with the duty of "taking care that the laws be faithfully
executed." They assured him that while this judicial action of
disregarding an act of Congress had been necessary, it was far from
pleasant.
The judges of another circuit, before which no case had come, wrote a
similar letter to the President, declaring their reasons for thinking
the law invalid.
In this same year, 1792, the Pennsylvania case came regularly up to the
Supreme Court, and was argued there.[28] This might have produced a
decision, but none was ever given; and in the next year a change in the
statute provided relief for the pension claimants in another way.
It is to be remarked, then, that this matter resulted in no decision by
the Supreme Court of the United States on the question of the
constitutionality of the pension act; it produced only a decision at one
of the circuits, and informal expressions of opinion from most of the
judges.
These non-judicial communications of opinion to the President seem, as
has been said, to have proceeded on the theory of furnishing information
to one whose official duty it was to see that the fundamental law was
faithfully carried out; just as "Councils of Revision," established by
the constitutions of Pennsylvania and Vermont, were to report
periodically as to infractions of the constitution.
It was, perhaps, these practices of private communication between the
President and the judges that led very soon to another interesting
matter,--a formal request by the President, in 1793, for an opinion from
the judges on twenty-nine questions relating to the treaties with
France. This request accorded with a colonial practice of asking such
opinions from judges; a usage centuries old in England, and preserved
to-day in the constitutions of a few States in this country. The judges,
however, declined answering these questions, "considering themselves,"
says Marshall, in his "Life of Washington," "merely as constituting a
legal tribunal for the decision of controversies brought before them in
legal form."[29] Although this seems to have been obviously the right
course, since the proposition to give power to put questions to the
judges in this way had been considered in the Federal Convention and not
allowed, yet we may remark how convenient such a power would often have
proved. If it be admitted, as it always has been in England, and is,
almost universally, here, that such opinions are merely learned advice
and bind nobody, not even the judges, they would often afford the
executive and Congress much needed and early help upon constitutional
questions in serious emergencies; such, for example, as have lately
presented themselves in our own history.
After this, there was an occasional allusion in the opinions of the
Supreme Court to the question of the power of that court to pass on the
constitutionality of Federal enactments as being an undecided and more
or less doubtful question. But not until 1803, early in Marshall's time,
was the point judicially presented to the Supreme Court. It came up in
the case of Marbury _v._ Madison,[30] the first case at the third term
after any opinions of Marshall were reported. In that case, an act of
Congress was declared unconstitutional.
It was more than half a century before that happened again.
Marbury _v._ Madison was a remarkable case. It was connected intimately
with certain executive action for which Marshall as Secretary of State
was partly responsible. For various reasons the case must have excited
peculiar interest in his mind. Within three weeks before the end of
Adams's administration, on February 13, 1801, while Marshall was both
Chief Justice and Secretary of State,[31] an act of Congress had
abolished the old system of circuit and district courts, and established
a new one. This gave to the President, Adams, the appointment of many
new judges, and kept him and his secretary busy, during the last hours
of the administration, in choosing and commissioning the new officials.
And another thing. The Supreme Court had consisted heretofore of six
judges. This same act provided that after the next vacancy there should
be five judges only. Such arrangements as these, made by a party just
going out of power, were not ill calculated to create, in the mind of
the party coming in, the impression of an intention to keep control of
the judiciary as long as possible.
There were, to be sure, other reasons for some of this action. Several
judges of the Supreme Court, as we have seen, had signified to
Washington, in 1790, the opinion that the judiciary act of the previous
year was unconstitutional in making the judges of that court judges also
of the circuit court. The new statute corrected this fault. Yet, in
regard to the time chosen for this very proper action, it was observable
that ten years and more had been allowed to pass before the mischief so
promptly pointed out by the early judges was corrected.
Again, in approaching the case of Marbury _v._ Madison, it is to be
observed that another matter relating to the Supreme Court had been
dealt with. This act of February 13, 1801, provided that the two terms
of the court, instead of being held, as hitherto, in February and
August, should thereafter be held in June and December. Accordingly, the
court sat in December, 1801. It adjourned, as it imagined, to June,
1802. But, on March 8 of that year, Congress, under the new
administration, repealed the law of 1801, unseated all the new judges,
and reinstated the old system, with its August and February terms. And
then, a little later in the year, the August term of the court was
abolished, leaving only one term a year, to begin on the first Monday in
February. Thus, since the June term was abolished, and February had then
passed, and there was no longer an August or a December term, the court
found itself in effect adjourned by Congress from December, 1801, to
February, 1803; and so it had no session during the whole of the year
1802.
If the legislation of 1801 was calculated to show the importance
attached by an outgoing political party to control over the judiciary,
that of 1802 might indicate how entirely the incoming party agreed with
them, and how well inclined they were to profit by their own
opportunities.
How was it, meantime, with the judiciary itself? Unfortunately, the
Supreme Court had already been drawn into the quarrel. For, at the
single December term, in 1801, held under the statute of that year, an
application had been made to the court by four persons in the District
of Columbia for a rule upon James Madison, Secretary of State, to show
cause why a writ of mandamus should not issue requiring him to issue to
these persons certain commissions as justice of the peace, which had
been left in Marshall's office undelivered at the time when he ceased to
add to his present functions those of Secretary of State. They had been
made out, sealed, and signed, and were supposed to have been found by
Madison when he came into office, and to be now withheld by him. This
motion was pending when the court adjourned, in December, 1801. Of
course, a motion for a mandamus to the head of the cabinet, upon a
matter of burning interest, must have attracted no little attention on
the part of the new administration. Abolishing the August term served to
postpone any opportunity for early action by the court, and to remind
the judiciary of the limits of its power.
At last the court came together, in February, 1803, and found the
mandamus case awaiting its action. It is the first one reported at that
term. Since Marshall had taken his seat, there had as yet been only
five reported cases. All the opinions had been given by him, unless a
few lines "by the court" may be an exception; and according to the new
usage by which the Chief Justice became, wherever it was possible, the
sole organ of the court, Marshall now gave the opinion in Marbury _v._
Madison. It may reasonably be wondered that the Chief Justice should
have been willing to give the opinion in such a case, and especially
that he should have handled the case as he did. But he was sometimes
curiously regardless of conventions.
If it be asked what was decided in Marbury _v._ Madison, the answer is
that this, and only this, was decided, namely, that the court had no
jurisdiction to do what they were asked to do in that case (_i. e._ to
grant a writ of mandamus, in the exercise of their original
jurisdiction), because the Constitution allowed to the court no such
power; and, although an act of Congress had undertaken to confer this
jurisdiction on them, Congress had no power to do it, and therefore the
act was void, and must be disregarded by the court.[32] It is the
decision upon this point that makes the case famous; and undoubtedly it
was reached in the legitimate exercise of the court's power. To this
important part of the case attention will be called in the next chapter.
Unfortunately, instead of proceeding as courts usually do, the opinion
began by passing upon all the points which the denial of its own
jurisdiction took from it the right to treat. It was elaborately laid
down, in about twenty pages, out of the total twenty-seven which
comprise the opinion, that Madison had no right to detain the
commissions; and that mandamus would be the proper remedy in any court
which had jurisdiction to grant it.
And thus, as the court, by its decision in this case, was sharply
reminding the legislature of its limitations, so by its _dicta_, and in
this irregular method, it intimated to the President, also, that his
department was not exempt from judicial control. In this way two birds
were neatly reached with the same stone.
Marshall made a very noticeable remark in his opinion, seeming to point
to the chief executive himself, and not merely to his secretary, when he
said, "It is not the office of the person to whom the writ is directed,
but the nature of the thing to be done, by which the propriety or
impropriety of issuing the mandamus is to be determined;"--a hint that,
on an appropriate occasion, the judiciary might issue orders personally
to him. This remark got illustration a few years later, in 1807, when
the Chief Justice, at the trial of Aaron Burr in Richmond, ordered a
subpœna to the same President, Thomas Jefferson, directing him to bring
thither certain documents. It was a strange conception of the relations
of the different departments of the government to each other, to imagine
that a subpœna, that is to say an order accompanied with a threat of
punishment, was a legitimate judicial mode of communicating with the
chief executive. On Jefferson's part, this order was received with the
utmost discontent; and justly. He had a serious apprehension of a
purpose to arrest him by force, and was prepared to protect himself.[33]
Meantime he sent to the United States Attorney at Richmond the papers
called for, but explained, with dignity, that while the executive was
willing to testify in Washington, it could not allow itself to be
"withdrawn from its station by any coördinate authority."
It was partly to the tendency on Marshall's part, just mentioned, to
give little thought, often, to ordinary conventions, and partly to his
kindness of heart, that we should attribute another singular
occurrence,--the fact that he attended a dinner at the house of an old
friend, one of Burr's counsel, when he knew that Burr was to be present,
and when that individual, having previously been brought to Richmond
under arrest, examined by Marshall, and admitted to bail, was still
awaiting the action of the grand jury with reference to further
judicial proceedings before Marshall himself. He accepted the
invitation before he knew that Burr was to be of the company. I have
heard from one of his descendants that his wife advised him not to go;
but he thought it best not to seem too fastidious, or to appear to
censure his old friend, the host, by staying away. He sat, we are told,
at the opposite end of the table from Burr, had no communication with
him, and went away early. But we must still wonder at an act which he
himself afterwards much regretted.
CHAPTER IV
MARSHALL'S CONSTITUTIONAL OPINIONS
This is not the place for any detailed consideration of Marshall's
decisions. But it would be a strange omission to leave out all
consideration of what played so great a part in his life. I must draw,
therefore, upon the patience of the reader, while some points are
mentioned relating to that class of his opinions which is at once the
most important and of the widest interest, viz., those given in
constitutional cases. If these matters seem to any reader dull or
unintelligible, he must be allowed full liberty to pass them by; but I
cannot wholly omit them.
The keynote to Marshall's leading constitutional opinions is that of
giving free scope to the power of the national government. These leading
opinions may be divided into three classes: _First_, such as discuss the
nature and reach of the Federal Constitution, and the general relation
of the federal government to the States. Of this class, McCulloch _v._
Maryland, probably his greatest opinion, is the chief illustration.
_Second_, those cases which are concerned with the specific restraints
and limitations upon the States. To this class may be assigned Fletcher
_v._ Peck, the bankruptcy cases of Sturgis _v._ Crowninshield and Ogden
_v._ Saunders, and Dartmouth College _v._ Woodward. _Third_, such as
deal with the general theory and principles of constitutional law. There
is little of this sort; except as it is incidentally touched, perhaps
the only case is Marbury _v._ Madison.
If we look at these great cases merely with reference to their effect
upon the history and development of the country, they are of the very
first importance. When one names Marbury _v._ Madison, the first case
where the Supreme Court held an act of Congress invalid, and the only
one in Marshall's time; Fletcher _v._ Peck and Dartmouth College _v._
Woodward, where legislative grants and an act of incorporation are held
to be contracts, protected by the United States Constitution against
state legislation impairing their obligation; and New Jersey _v._
Wilson, holding that a legislative exemption from taxation is also a
contract protected in the same way;--one sees the tremendous importance
of the decisions.
Of coarse we are not to confound this powerful effect of a judgment, or
the moral approbation with which we may be inclined to view it, with the
intrinsic merit of the reasoning or the legal soundness of the
conclusions. It is not uncommon to speak of the reasoning in Marbury
_v._ Madison and Dartmouth College _v._ Woodward with the greatest
praise. But neither of these opinions is entitled to rank with
Marshall's greatest work. The very common view to which I have alluded
is partly referable to the fallacy which Wordsworth once remarked upon
when a friend mentioned "The Happy Warrior" as being the greatest of his
poems. "No," said the poet, "you are mistaken; your judgment is affected
by your moral approval of the lines."
If we regard at once the greatness of the questions at issue in the
particular case, the influence of the opinion, and the large method and
clear and skillful manner in which it is worked out, there is nothing so
fine as the opinion in McCulloch _v._ Maryland, given at the February
term, 1819. The questions were, first, whether the United States could
constitutionally incorporate a bank; and, second, if it could, whether a
State might tax the operations of the bank; as, in this instance, by
requiring it to use stamped paper for its notes. The bank was sustained
and the tax condemned.
In working this out, it was laid down that while the United States is
merely a government of enumerated powers, and these do not in terms
include the granting of an incorporation, yet it is a government whose
powers, though limited in number, are in general supreme, and also
adequate to the great national purposes for which they are given; that
these great purposes carry with them the power of adopting such means,
not prohibited by the Constitution, as are fairly conducive to the end;
and that incorporating a bank is not forbidden, and is useful for
several ends. Further, the paramount relation of the national
government, whose valid laws the Constitution makes the supreme law of
the land, forbids the States to tax, or to "<DW44>, impede, burden, or
in any way control" the operations of the government in any of its
instrumentalities.
This was the opinion of a unanimous court, in which five out of the
seven judges had been nominated by a Republican President. But it caused
great excitement at the South. On March 24, 1819, Marshall wrote from
Richmond to Judge Story: "Our opinion in the bank case has roused the
sleeping spirit of Virginia, if indeed it ever sleeps. It will, I
understand, be attacked in the papers with some asperity, and as those
who favor it never write for the public it will remain undefended, and
of course be considered as _damnably heretical_." Again, two months
later, "The opinion in the bank case continues to be denounced by the
Democracy of Virginia.... If the principles which have been advanced on
this occasion were to prevail the Constitution would be converted into
the old Confederation."
Another great opinion, of the same class, and also bitterly attacked,
was given in the case of Cohens _v._ Virginia, in 1821. This case came
up on a writ of error from a local court at Norfolk. Cohens had been
convicted of selling lottery tickets there, contrary to the statute of
Virginia. He had set up as a defense an act of Congress providing for
drawing lotteries in the city of Washington, and insisted that this
authorized his selling tickets in Virginia. When the case reached the
Supreme Court of the United States, the counsel for the State first
denied the jurisdiction of that court, on the ground, among others, that
the Constitution allowed no such appeal from a state court, and that the
Judiciary Act of 1789 was unconstitutional in purporting to authorize
it. In an elaborate opinion by Marshall, one of his greatest efforts,
these contentions were negatived. When afterwards, the case came to be
argued on the merits, the decision below was sustained, on the ground
that the act of Congress did not purport to authorize the sale of
tickets in any State which forbade the sale of them.
Here again the court was unanimous; and it was composed of the same
judges who decided McCulloch _v._ Maryland. But the reception of Cohens
_v._ Virginia at the South was even worse than that accorded the other
case. Judge Roane, of the Court of Appeals in Virginia, attacked the
opinion anonymously in the newspapers, with what Marshall called
"coarseness and malignity." Jefferson, also, bitterly objected to it.
Of two other cases belonging in the same class of Marshall's opinions,
viz., Gibbons _v._ Ogden, in 1824, and Brown _v._ Maryland, in 1827, it
is enough here to say that they deal with one of the most difficult and
perplexed topics of constitutional law, namely, the coördination of the
functions of the national and state governments, in regard to the power
granted to Congress to regulate foreign and interstate commerce, a
subject of great importance and difficulty, on which the decisions of
the Supreme Court are now and long have been involved in much confusion
and uncertainty. Gibbons _v._ Ogden brought into question the
constitutionality of a law of New York granting to Fulton, the inventor,
the sole right of navigating the waters of New York by steam. The grant
had been sustained by Chancellor Kent and by the New York Court of
Appeals; but these decisions were now overruled in a famous and powerful
opinion. In two other cases on this subject, also of great importance,
Marshall gave leading opinions. It may fairly be thought that his
treatment of the general question involved in these cases, instructive
as it was, was yet less fruitful and less far-seeing than in most of his
other great cases.
He was now in a region pretty closely connected with the second class of
cases, above named; a set of cases, where even so great a man as
Marshall erred sometimes, from interpreting too literally and too
narrowly the restraints upon the States. It was natural, in giving full
scope to the authority of the general government, that he should be
inclined to apply, with their fullest force and operation, these clauses
of restraint and prohibition. His great service to the country and his
own generation was that of planting the national government on the
broadest and strongest foundations. That, as he rightly conceived, was
the one chief necessity of his time. In doing this, when it came to
considering the reach that must also be allowed to the States, and just
how the coördination of the two systems should be worked out, probably
no one man, no one court, no human wisdom was adequate, then, to mapping
it all out. Time alone, and a long succession of men, after some ages of
experience, might suffice for that. The wisdom of those who made the
Constitution, as it has lately been said, was mainly shown "in the
shortness and generality of its provisions, in its silence, and its
abstinence from petty limitations." But, as time went on, definitions
and specifications had to be made and applied; silence, abstinence,
generality, were no longer adequate. And in the class of cases, now
referred to, great and far-reaching as were the results of Marshall's
labor, and unqualifiedly as they are often praised, one may perceive, as
I venture to think, a less comprehensive and statesmanlike grasp of the
problems and their essential conditions than are found in some other
parts of his work.
And so, when the Chief Justice, in 1812, held, without argument, that a
grant of land by a State, with a privilege of exemption from taxation,
contained a contract against future taxation, protected, even in the
hands of subsequent holders, by the constitutional provisions against
impairing the obligation of contracts, something was done which would
probably not be done to-day, if the question came up for the first time.
Certainly the soundness of the doctrine has been frequently denied by
judges of the Supreme court, and it has only survived through the device
of construing all grants in the narrowest manner. "Yielding," says the
Court in a recent case, "to the doctrine that immunity from taxation
may be granted, that point being already adjudged, it must be considered
as a personal privilege, not extending beyond the immediate grantee,
unless otherwise so declared in express terms." And again the court has
recently remarked on the "well-settled rule that exemptions from
taxation are ... not to be extended beyond the exact and express
language used, construed _strictissimi juris_."
Again, in Dartmouth College _v._ Woodward, in 1819, when it was held
that a legislative grant of incorporation was a contract protected by
the same clause of the Constitution, something was done from which the
court was subsequently obliged to recede in an important degree. Acts of
incorporation for the manufacture of beer, for carrying on
slaughter-houses, for dealing in offal, and for conducting a lottery,--a
reputable business in 1819, when the Dartmouth College case was
decided,--such acts as these have been treated by the Supreme Court as
not being thus protected. It is held that no legislative body can
contract to part with the full power to provide for the health, morals,
and safety of the community. Such things, it is said, are not the proper
subject-matter of legislative contract,--a doctrine which it has been
widely thought should, originally, have been applied to all acts of
incorporation. "The State," says a distinguished judge, and writer on
constitutional law, in speaking of the Dartmouth College doctrine and
its development, "was stripped, under this interpretation, of
prerogatives that are commonly regarded as inseparable from sovereignty,
and might have stood, like Lear, destitute before her offspring, had not
the police power been dexterously declared paramount, and used as a
means of rescinding improvident grants."[34]
In the great bankruptcy cases of Sturgis _v._ Crowninshield and Ogden
_v._ Saunders, where it was held, in 1819 and 1827, that the
constitutional provision as to impairing the obligation of contracts
forbade the State to enact an insolvency law which should discharge a
person from liability on a contract made before the law; and then again
that it did not forbid the same thing as touching a contract made after
the law, Marshall, who gave the opinion in the first case, put it on a
ground equally applicable to the second; and so, in the second case,
gave a dissenting opinion. The obligation of the contract, he said,
comes from the agreement of the party; it does not arise from the law of
the State at the time it was made, entering into or operating on the
contract. But this doctrine and this reasoning were justly disallowed.
Finally, in 1830, in Craig _v._ Missouri, Marshall gave the opinion that
certain certificates issued by a State in return for deposits, and
intended to circulate as money, were bills of credit; and as such
forbidden by the Constitution. There were three dissenting opinions; and
soon after Marshall's death, a different doctrine was established by the
court,--wisely it would seem,--and has ever since been maintained.[35]
Coming now to the third class of cases mentioned above, that which
deals with the fundamental conceptions and theory of our American
doctrine of constitutional law, Marbury _v._ Madison is the chief case.
In speaking of that case I have purposely delayed until this point any
reference to this aspect of it. While, historically, this part of it is
what gives the case its chief importance, yet it occupies only about a
quarter of the opinion.
In outline, the argument there presented is as follows: The question is
whether a court can give effect to an unconstitutional act of the
legislature. This question is answered, as having little difficulty, by
referring to a few "principles long and well established." (1) The
people, in establishing a written constitution and limiting the powers
of the legislature, intend to control it; else the legislature could
change the constitution by an ordinary act. (2) If a superior law is not
thus changeable, then an unconstitutional act is not law. This theory,
it is added, is essentially attached to a written constitution. (3) If
the act is void, it cannot bind the court. The court has to say what
the law is, and in saying this must judge between the Constitution and
the act. Otherwise, a void act would be obligatory; and this would be
saying that constitutional limits upon legislation may be transgressed
by the legislature at pleasure, and thus these limits would be reduced
to nothing. (4) The language of the Federal instrument gives judicial
power in "cases arising under the Constitution." Judges are thus in
terms referred to the Constitution. They are sworn to support it and
cannot violate it. And so, it is said, in conclusion, the peculiar
phraseology of the instrument confirms what is supposed to be essential
to all written constitutions, that a law repugnant to it is void, and
that the courts, as well as other departments, are bound by the
constitution.
The reasoning is mainly that of Hamilton, in his short essay of a few
years before in the "Federalist." The short and dry treatment of the
subject, as being one of no real difficulty, is in sharp contrast with
the protracted reasoning of McCulloch _v._ Maryland, Cohens _v._
Virginia, and other great cases; and this treatment is much to be
regretted. Absolutely settled as the general doctrine is to-day,
and sound as it is, when regarded as a doctrine for the
descendants of British colonists, there are grave and far-reaching
considerations--such, too, as affect to-day the proper administration of
this extremely important power--which are not touched by Marshall, and
which must have commanded his attention if the subject had been deeply
considered and fully expounded according to his later method. His
reasoning does not answer the difficulties that troubled Swift,
afterwards chief justice of Connecticut, and Gibson, afterwards chief
justice of Pennsylvania, and many other strong, learned, and thoughtful
men; not to mention Jefferson's familiar and often ill-digested
objections.
It assumes as an essential feature of a written constitution what does
not exist in any one of the written constitutions of Europe. It does not
remark the grave distinction between the power of disregarding the act
of a coördinate department, and the action of a federal court in dealing
thus with the legislation of the local States; a distinction important
in itself, and observed under the written constitutions of Europe,
which, as I have said, allow this power in the last sort of case, while
denying it in the other.
Had Marshall dealt with this subject after the fashion of his greatest
opinions he must also have considered and passed upon certain serious
suggestions arising out of the arrangements of our own constitutions and
the exigencies of the different departments. All the departments, and
not merely the judges, are sworn to support the Constitution. All are
bound to decide for themselves, in the first instance, what this
instrument requires of them. None can have help from the courts unless,
in course of time, some litigated case should arise; and of some
questions it is true that they never can arise in the way of litigation.
What was Andrew Johnson to do when the Reconstruction Acts of 1867 had
been passed over his veto by the constitutional majority, while his veto
had gone on the express ground, still held by him, that they were
unconstitutional? He had sworn to support the Constitution. Should he
execute an enactment which was contrary to the Constitution, and so
void? Or should he say, as he did say to the court, through his
Attorney-General, that "from the moment [these laws] were passed over
his veto, there was but one duty, in his estimation, resting upon him,
and that was faithfully to carry out and execute these laws"?[36] And
why is he to say this?
Again, what is the House of Representatives to do when a treaty, duly
made and ratified by the constitutional authority, namely, the President
and Senate, comes before it for an appropriation of money to carry it
out? Has the House, under these circumstances, anything to do with the
question of constitutionality? If it thinks the treaty unconstitutional,
and so void, can it vote to carry it out? If it can, how is this
justified?
Is the situation necessarily different when a court is asked to enforce
a legislative act? The courts are not strangers to the case of political
questions, where they must refuse to interfere with the acts of the
other departments,--as in the case relating to Andrew Johnson just
referred to; and in dealing with what are construed to be merely
directory provisions of the Constitution; and with the cases, well
approved in the Supreme Court of the United States, where courts refuse
to consider whether provisions of a constitution have been complied
with, which require certain formalities in passing laws,--accepting as
final the certificate of the officers of the political departments. A
question, passed upon by those departments, is thus refused any
discussion in the judicial forum, on the ground, to quote the language
of the Supreme Court, that "the respect due to coequal and independent
departments requires the judicial department to act upon this
assurance."
So far as any necessary conclusion is concerned, it might fairly have
been said, with us, as it is said in Europe, that the real question in
all these cases is not whether the act is constitutional, but whether
its constitutionality can properly be brought in question before a given
tribunal. Could Marshall have had to deal with this great question, in
answer to Chief Justice Gibson's powerful opinion in Eakin _v._ Raub, in
1825,[37] instead of deciding it without being helped or hindered by any
adverse argument at all, as he did, we should have had a far higher
exhibition of his powers than the case now affords.[38]
CHAPTER V
THE WORKING OF OUR SYSTEM OF CONSTITUTIONAL LAW
I have drawn attention to the immense service that Chief Justice
Marshall rendered to his country in the field of constitutional law, and
have considered a few of the cases. Since his time not twice the length
of his term of thirty-four years has gone by, but more than five times
the number of volumes that sufficed for the opinions of the Supreme
Court during his period is required for those of his successors on the
bench. Nor does even that proportion indicate the increase in the
quantity of the court's business which is referable to this particular
part of the law. It has enormously increased. When one reflects upon the
multitude, variety, and complexity of the questions relating to the
regulation of interstate commerce, upon the portentous and ever
increasing flood of litigation to which the Fourteenth Amendment has
given rise; upon the new problems in business, government, and police
which have come in with steam and electricity, and their ten thousand
applications; upon the growth of corporations and of wealth, the changes
of opinion on social questions, such as the relation of capital and
labor, and upon the recent expansions of our control over great and
distant islands,--we seem to be living in a different world from
Marshall's.
Under these new circumstances, what is happening in the region of
constitutional law? Very serious things, indeed.
The people of the States, when making new constitutions, have long been
adding more and more prohibitions and restraints upon their
legislatures. The courts, meantime, in many places, enter into the
harvest thus provided for them with a light heart, and too promptly and
easily proceed to set aside legislative acts. The legislatures are
growing accustomed to this distrust, and more and more readily incline
to justify it, and to shed the consideration of constitutional
restraints,--certainly as concerning the exact extent of these
restrictions,--turning that subject over to the courts; and, what is
worse, they insensibly fall into a habit of assuming that whatever they
can constitutionally do they may do,--as if honor and fair dealing and
common honesty were not relevant to their inquiries.
The people, all this while, become careless as to whom they send to the
legislature; too often they cheerfully vote for men whom they would not
trust with an important private affair, and when these unfit persons are
found to pass foolish and bad laws, and the courts step in and disregard
them, the people are glad that these few wiser gentlemen on the bench
are so ready to protect them against their more immediate
representatives.
From these causes there has developed a vast and growing increase of
judicial interference with legislation. This is a very different state
of things from what our fathers contemplated, a century and more ago,
in framing the new system. Seldom, indeed, as they imagined, under our
system, would this great, novel, tremendous power of the courts be
exerted,--would this sacred ark of the covenant be taken from within the
veil. Marshall himself expressed truly one aspect of the matter, when he
said in one of the later years of his life: "No questions can be brought
before a judicial tribunal of greater delicacy than those which involve
the constitutionality of legislative acts. If they become indispensably
necessary to the case, the court must meet and decide them; but if the
case may be determined on other grounds, a just respect for the
legislature requires that the obligation of its laws should not be
unnecessarily and wantonly assailed." And again, a little earlier than
this, he laid down the one true rule of duty for the courts. When he
went to Philadelphia at the end of September, in 1831, on that painful
errand of which I have spoken, in answering a cordial tribute from the
bar of that city he remarked that if he might be permitted to claim for
himself and his associates any part of the kind things they had said,
it would be this, that they had "never sought to enlarge the judicial
power beyond its proper bounds, nor feared to carry it to the fullest
extent that duty required."
That is the safe twofold rule; nor is the first part of it any whit less
important than the second; nay, more; to-day it is the part which most
requires to be emphasized. For just here comes in a consideration of
very great weight. Great and, indeed, inestimable as are the advantages
in a popular government of this conservative influence,--the power of
the judiciary to disregard unconstitutional legislation,--it should be
remembered that the exercise of it, even when unavoidable, is always
attended with a serious evil, namely, that the correction of legislative
mistakes comes from the outside, and the people thus lose the political
experience, and the moral education and stimulus that come from fighting
the question out in the ordinary way, and correcting their own errors.
If the decision in Munn _v._ Illinois and the "Granger Cases,"
twenty-five years ago, and in the "Legal Tender Cases," nearly thirty
years ago, had been different; and the legislation there in question,
thought by many to be unconstitutional and by many more to be
ill-advised, had been set aside, we should have been saved some trouble
and some harm. But I venture to think that the good which came to the
country and its people from the vigorous thinking that had to be done in
the political debates that followed, from the infiltration through every
part of the population of sound ideas and sentiments, from the rousing
into activity of opposite elements, the enlargement of ideas, the
strengthening of moral fibre, and the growth of political experience
that came out of it all,--that all this far more than outweighed any
evil which ever flowed from the refusal of the court to interfere with
the work of the legislature.
The tendency of a common and easy resort to this great function, now
lamentably too common, is to dwarf the political capacity of the people,
and to deaden its sense of moral responsibility. It is no light thing to
do that.
What can be done? It is the courts that can do most to cure the evil;
and the opportunity is a very great one. Let them resolutely adhere to
first principles. Let them consider how narrow is the function which the
constitutions have conferred on them,--the office merely of deciding
litigated cases; how large, therefore, is the duty intrusted to others,
and above all to the legislature. It is that body which is charged,
primarily, with the duty of judging of the constitutionality of its
work. The constitutions generally give them no authority to call upon a
court for advice; they must decide for themselves, and the courts may
never be able to say a word. Such a body, charged, in every State, with
almost all the legislative power of the people, is entitled to the most
entire and real respect; is entitled, as among all rationally
permissible opinions as to what the constitution allows, to its own
choice. Courts, as has often been said, are not to think of the
legislators, but of the legislature,--the great, continuous body itself,
abstracted from all the transitory individuals who may happen to hold
its power. It is this majestic representative of the people whose action
is in question, a coördinate department of the government, charged with
the greatest functions, and invested, in contemplation of law, with
whatsoever wisdom, virtue, and knowledge the exercise of such functions
requires.
To set aside the acts of such a body, representing in its own field,
which is the very highest of all, the ultimate sovereign, should be a
solemn, unusual, and painful act. Something is wrong when it can ever be
other than that. And if it be true that the holders of legislative power
are careless or evil, yet the constitutional duty of the court remains
untouched; it cannot rightly attempt to protect the people, by
undertaking a function not its own. On the other hand, by adhering
rigidly to its own duty, the court will help, as nothing else can, to
fix the spot where responsibility lies, and to bring down on that
precise locality the thunderbolt of popular condemnation. The judiciary,
to-day, in dealing with the acts of their coördinate legislators, owe
to the country no greater or clearer duty than that of keeping their
hands off these acts wherever it is possible to do it. For that
course--the true course of judicial duty always--will powerfully help to
bring the people and their representatives to a sense of their own
responsibility. There will still remain to the judiciary an ample field
for the determinations of this remarkable jurisdiction, of which our
American law has so much reason to be proud; a jurisdiction which has
had some of its chief illustrations and its greatest triumphs, as in
Marshall's time, so in ours, while the courts were refusing to exercise
it.
CHAPTER VI
LETTERS OF MARSHALL
No systematic attempt seems ever to have been made to collect Marshall's
letters. It should be done. Only a few of his family letters have yet
found their way into print. One of them, to his wife, is quoted in a
previous page. In another to her, written on March 9, 1825, referring to
the inauguration of President John Quincy Adams, he says: "I
administered the oath to the President in the presence of an immense
concourse of people, in my new suit of domestic manufacture. He, too,
was dressed in the same manner, though his clothes were made at a
different establishment. The cloth is very fine and smooth."
In a letter of December 7, 1834,[39] to his grandson, "Mr. John
Marshall, jr.," he gives the boy some advice about writing which is a
good commentary on the extraordinary neatness and felicity, the close
fit, of his own clear, compact, and simple style:--
"The man who by seeking embellishment hazards confusion is greatly
mistaken in what constitutes good writing. The meaning ought never to be
mistaken. Indeed, the readers should never be obliged to search for it.
The writer should always express himself so clearly as to make it
impossible to misunderstand him. He should be comprehended without an
effort. The first step towards writing and speaking clearly is to think
clearly. Let the subject be perfectly understood, and a man will soon
find words to convey his meaning to others."
A letter to James Monroe, dated Richmond, December 2, 1784, was written
while Marshall was a member of the House of Delegates. He writes: "Not a
bill of public importance, in which an individual was not particularly
interested, has passed. The exclusive privilege given to Rumsey and his
assigns to build and navigate his new invented boats is of as much,
perhaps more, consequence than any other bill we have passed. We have
rejected some which, in my conception, would have been advantageous to
this country. Among these I rank the bill for encouraging intermarriage
with the Indians. Our prejudices, however, oppose themselves to our
interests, and operate too powerfully for them....
"I shewed my father [then, probably, living in Kentucky] that part of
your letter which respects the western country. He says he will render
you every service of the kind you mention which is within his power with
a great deal of pleasure. He says, though, that Mr. Humphrey Marshall, a
cousin and brother of mine,[40] is better acquainted with the lands and
would be better enabled to choose for your advantage than he would. If,
however, you wish rather to depend on my father I presume he may avail
himself of the knowledge of his son-in-law. I do not know what to say to
your scheme of selling out. If you can execute it you will have made a
very capital sum; if you can retain your lands you will be poor during
life unless you remove to the western country, but you will have secured
for posterity an immense fortune. I should prefer the selling business,
and if you adopt it I think you have fixed on a very proper price.
"Adieu. May you be very happy is the wish of your
J. MARSHALL."
* * * * *
In another letter to Monroe, while the latter was Madison's Secretary of
State, dated Richmond, June 25, 1812, just as the war was beginning, he
says:--
"On my return to-day from my farm, where I pass a considerable portion
of my time in _laborious relaxation_, I found a copy of the message of
the President, of the 1st inst., accompanied by the report of the
Committee of Foreign Relations and the declaration of war against
Britain, under cover from you.
"Permit me to subjoin to my thanks for this mark of your attention my
fervent wish that this momentous measure may, in its operation on the
interest and honor of our country, disappoint only its enemies.
"Whether my prayer be heard or not, I shall remain with respectful
esteem,
"Your obedient servant,
"J. MARSHALL."
* * * * *
When Marshall went to France as envoy in 1797, he wrote several long and
interesting letters to Washington, acquainting him with whatever foreign
intelligence might interest him.[41] The following passages from the
first letter, a very long one, will show the interest of these papers,
and the exactness of the information they convey:--
"THE HAGUE, 15th Sept., 1797.
"DEAR SIR,--The flattering evidences I have received of your favorable
opinion, which have made on my mind an impression only to wear out with
my being, added to a conviction that you must feel a deep interest in
all that concerns a country to whose service you have devoted so large
a portion of your life, induce me to offer you such occasional
communications as, while in Europe, I may be enabled to make, and induce
a hope that the offer will not be deemed an unacceptable or unwelcome
intrusion.
"Until our arrival in Holland we saw only British and neutral vessels.
This added to the blockade of the Dutch fleet in the Texel, of the
French fleet in Brest, and of the Spanish fleet in Cadiz, manifests the
entire dominion which one nation at present possesses over the seas. By
the ships of war which met us we were three times visited, and the
conduct of those who came on board was such as would proceed from
general orders to pursue a system calculated to conciliate America.
Whether this be occasioned by a sense of justice and the obligations of
good faith, or solely by the hope that the perfect contrast which it
exhibits to the conduct of France may excite keener sensations at that
conduct, its effects on our commerce are the same.
"The situation of Holland is truly interesting. Though the face of the
country still exhibits a degree of wealth and population still unequaled
in any part of Europe, its decline is visible. The great city of
Amsterdam is in a state of blockade. More than two thirds of its
shipping lie unemployed in port. Other seaports suffer, though not in so
great a degree. In the mean time the requisitions made upon them are
enormous. They have just completed the payment of the 100,000,000 of
florins (equal to 40,000,000 of dollars) stipulated by treaty; they have
sunk, on the first entrance of the French, a very considerable sum in
assignats; they made large contributions in specifics, and they pay,
feed, and clothe an army estimated, as I am informed, at near three
times its real number. It is supposed that France has by various means
drawn from Holland about 60,000,000 of dollars. This has been paid, in
addition to the natural expenditures, by a population of less than
2,000,000. Nor, should the war continue, can the contributions of
Holland stop here. The increasing exigencies of France must inevitably
increase her demands on those within her reach.
* * * * *
"The political opinions which have produced the rejection of the
Constitution, and which, as it would seem, can only be entertained by
intemperate and ill-informed minds, unaccustomed to a union of theory
and practice of liberty, must be associated with a general system which
if brought into action will produce the same excesses here which have
been so justly deplored in France. The same materials exist, though not
in so great a degree. They have their clubs, they have a numerous poor,
and they have enormous wealth in the hands of a minority of the nation.
On my remarking this to a very rich and intelligent merchant of
Amsterdam, and observing that if one class of men withdrew itself from
public duties and offices it would be immediately succeeded by another,
which would acquire a degree of power and influence that might be
exercised to the destruction of those who had retired from society, he
replied that the remark was just, but that they relied on France for a
protection from those evils which she had herself experienced. That
France would continue to require great supplies from Holland, and knew
its situation too well to permit it to become the prey of anarchy. That
Holland was an artificial country acquired by persevering industry, and
which could only be preserved by wealth and order. That confusion and
anarchy would banish a large portion of that wealth, would dry up its
sources, and would entirely disable them from giving France that
pecuniary aid she so much needed. That under this impression many who,
though friendly to the revolution, saw with infinite mortification
French troops garrison the towns of Holland, would now see their
departure with equal regret. Thus they willingly relinquished national
independence for individual safety. What a lesson to those who would
admit foreign influence into the United States!"...
The condition of affairs in Paris at that time is illustrated by the
fact that Marshall's later letters, written from there, were not
signed; and that they allude to the action of himself and his associates
in the third person. Thus, writing from Paris, October 24, 1797, in the
character of an anonymous private American to an unnamed correspondent,
he says:--
"Causes which I am persuaded you have anticipated forbid me to allow
that free range of thought and expression which could alone apologize
for the intrusive character my letters bear. Having, however, offered
what I cannot furnish, I go on to substitute something else perhaps not
worth receiving....
"Our ministers have not yet, nor do they seem to think it certain that
they will be received. Indeed they make arrangements which denote an
expectation of returning to America immediately. The captures of our
vessels seem to be only limited by the ability to capture. That ability
is increasing, as the government has let out to hardy adventurers the
national frigates. Among those who plunder us, who are most active in
this infamous business, and most loud in vociferating criminations
equally absurd and untrue, are some unprincipled apostates who were born
in America. The sea rovers by a variety of means seem to have acquired
great influence in the government. This influence will be exerted to
prevent an accommodation between the United States and France, and to
prevent any regulations which may intercept the passage of the spoils
they have made on our commerce, to their pockets. The government, I
believe, is but too well disposed to promote their views."
In a letter to Judge Peters, of Philadelphia, dated November 23, 1807,
just after the Burr trial, after thanking his correspondent for a volume
of "Admiralty Reports," he has something to say of that case:--
"I have as yet been able only to peep into the book, not to read many of
the cases. I received it while fatigued, and occupied with the most
unpleasant case which has ever been brought before a judge in this or,
perhaps, in any other country which affected to be governed by laws;
since the decision of which I have been entirely from home. The day
after the commitment of Colonel Burr for a misdemeanor I galloped to the
mountains, whence I only returned in time to perform my North Carolina
circuit, which terminates just soon enough to enable me to be here to
open the court for the ancient dominion. Thus you perceive I have
sufficient bodily employment to prevent my mind from perplexing itself
about the attentions paid me in Baltimore and elsewhere. I wish I could
have had as fair an opportunity to let the business go off as a jest
here as you seem to have had in Philadelphia; but it was most deplorably
serious, and I could not give the subject a different aspect by treating
it in any manner which was in my power. I might, perhaps, have made it
less serious to myself by obeying the public will, instead of the public
law, and throwing a little more of the sombre upon others."
CHAPTER VII
MARSHALL AS A CITIZEN AND A NEIGHBOR
There is more to be said of Marshall's private and personal life. After
he went on the bench, his principal non-judicial work, in the nature of
public service, seems to have been writing the "Life of Washington,"
with the later revision and reconstruction of that work, and his
activity in a few matters of not too partisan a sort, such as were
likely to engage the attention of a public-spirited citizen.
In 1813, at a meeting of the citizens of Richmond, he was appointed
member of a Committee of Vigilance, to aid in defending the city against
attack from the British. On June 28 he made a report, for a
sub-committee, that it was inexpedient to undertake to fortify the city.
After stating the topographical and other reasons for such an opinion,
the report goes on thus: "Your committee are too conscious of their
destitution of professional skill to advance with any confidence the
opinion they have formed; but the resolution under which they act having
made it their duty to give an opinion, they say, though with much
diffidence, that they do not think any attempt to fortify the city
advisable. It is to be saved by operations in the open field, by facing
the enemy with a force which may deter him from any attempt to penetrate
the interior of our country, and which may impress him with the danger
of separating himself from his ships. If this protection cannot be
afforded, Richmond must share the fate of other places which are in
similar circumstances. Throughout the world, open towns belong to the
army which is master of the country.... If the militia be put into the
best condition for service, if the light artillery be well manned and
supplied with horses, so as to move with celerity to any point where its
services may be required; if the cavalry be kept entire and in active
service; if the precaution of supplying in sufficient quantity all the
implements of war be taken, your committee hope and believe that this
town will have no reason to fear the invading foe."[42]
In those efforts on the part of some of the leaders of Virginia and the
South, early in the century, to rid themselves of slavery, to which we
at the North have never done sufficient justice, Marshall took an active
part.
The American Colonization Society was organized in 1816 or 1817, with
Bushrod Washington for president. In 1823 an auxiliary society was
organized at Richmond, of which Marshall was president, an office which
he held nearly or quite up to the time of his death. It is interesting
to observe that one of the plans for colonization was to have worked out
the abolition of slavery in Virginia in the year 1901. Of slavery
Marshall wrote to a friend, in 1826: "I concur with you in thinking that
nothing portends more calamity and mischief to the Southern States than
their slave population. Yet they seem to cherish the evil, and to view
with immovable prejudice and dislike everything which may tend to
diminish it. I do not wonder that they should resist any attempt, should
one be made, to interfere with the rights of property, but they have a
feverish jealousy of measures which may do good without the hazard of
harm, that, I think, very unwise."
In 1828, Marshall presided, in Virginia, over a convention to promote
internal improvements. On this subject he held and freely expressed
views, such as are now generally entertained, as to the power of the
general government, and the expediency of exerting them.[43]
In 1829, he allowed himself to be elected to the Virginia convention for
revising the state constitution, and took an active part in the debates.
"Tall, in a long surtout of blue, with a face of genius and an eye of
fire," is the description that is given of him in the convention. On
several questions he influenced greatly the course of the convention,
especially in continuing, for a score of years to come, the judicial
tenure of office during good behavior.
Marshall's membership of the society of Free Masons is sometimes spoken
of. It should be said that he lived to condemn that organization. During
the political excitement which followed the abduction of Morgan, he was
asked for information as to some praise of Freemasonry which had been
publicly attributed to him, and replied, in October, 1833, that he was
not particularly interested in the anti-masonic excitement. "The
agitations which convulse the North did not pass the Potomac.
Consequently ... I felt no inclination to volunteer in a distant
conflict, in which the wounds that might be received would not be
soothed by the consoling reflection that he suffered in the performance
of a necessary duty." And he added that he had "never affirmed that
there was any positive good or ill in the institution itself." This
cautious letter is illustrated by an earlier one, in July, 1833, in
which, writing confidentially to Edward Everett, he says that he became
a Mason soon after he entered the army, and afterwards continued in the
society because his neighbors did. "I followed the crowd for a time,
without attaching the least importance to its object or giving myself
the trouble to inquire why others did. It soon lost its attraction, and
though there are several lodges in the city of Richmond, I have not been
in one of them for more than forty years, except on an invitation to
accompany General Lafayette, nor have I been a member of one of them for
more than thirty. It was impossible not to perceive the useless
pageantry of the whole exhibition." And he adds that he has become
convinced "that the institution ought to be abandoned, as one capable of
producing much evil and incapable of producing any good which might not
be effected by safe and open means."[44]
As to Marshall's religious affiliations, he was a regular and devoted
attendant, all his life, of the Episcopal Church, in which he was
brought up; taking an active part in the services and the responses, and
kneeling in prayer, we are told, even when the pews were so narrow that
his tall form had to be accommodated by the projection of his feet into
the aisle. His friend, Bishop Meade, the Episcopal bishop of Virginia,
states that he was never a communicant in that church; and he quotes a
letter from an Episcopal clergyman who often visited Mrs. Harvie,
Marshall's only daughter, in her last illness, and who reports from her
the statement that, during the last months of his life, he told her
"that the reason why he never communed was that he was a Unitarian in
opinion, though he never joined their society." It is added, however, in
the same letter, that Mrs. Harvie, a person "of the strictest probity,
the most humble piety, and the most clear and discriminating mind," also
said that, during these last months, Marshall read Keith on Prophecy,
and was convinced by that work, and the fuller investigation to which it
led, of the supreme divinity of Jesus, and wished to commune, but
thought it his duty to do it publicly; and while waiting for the
opportunity, died.
The reader of such a statement seems to perceive or to conjecture an
anxiety to relieve the memory of the Chief Justice of an opprobrium.
Whatever the exact fact may be about this late change in opinion, there
is little occasion to be surprised that Marshall shared, during his
active life, the opinions of his friend Judge Story. The genuineness and
the simplicity of Marshall's lifelong piety are indicated by another
statement reported from Mrs. Harvie: "Her father told her that he never
went to bed without concluding his prayer with those which his mother
taught him when a child, viz. the Lord's prayer and the prayer
beginning, 'Now I lay me down to sleep.'"
Marshall was a man of vigorous physique. "He was always," says a
descendant,[45] "devoted to walking, but more especially before
breakfast in the early morning. A venerable professor I met in
Washington told me that, when he was a boy, regularly every morning at
seven o'clock, when he was on his way to school, he met the Chief
Justice returning from a long walk. He walked rapidly always. Hon.
Horace Binney says: 'After doing my best one morning to overtake Chief
Justice Marshall, in his quick march to the Capitol, when he was nearer
to eighty than seventy, I asked him to what cause in particular he
attributed that strong and quick step, and he replied that he thought it
was most due to his commission in the army of the Revolution, in which
he had been a regular foot practitioner for six years.'"
We often hear of the Chief Justice at his "Quoit Club." He was a famous
player at quoits. A club had been formed by some of the early Scotch
settlers of Richmond, and it came to include among its members leading
men of the city, such as Marshall, Wirt, Nicholas, Call, Munford, and
others. Chester Harding, the artist who painted the full-length portrait
of Marshall that hangs in the Boston Athenæum, tells us of seeing him at
the Quoit Club. Fortunately, language does not, like paint, limit the
artist to a single moment of time. He gives us the Chief Justice in
action. Marshall was then attending the Virginia Constitutional
Convention, which sat from October, 1829, to January, 1830. The Quoit
Club used to meet every week in a beautiful grove, about a mile from the
city. Harding went early. "I watched," he says, "for the coming of the
old chief. He soon approached, with his coat on his arm and his hat in
his hand, which he was using as a fan. He walked directly up to a large
bowl of mint julep, which had been prepared, and drank off a tumblerful
of the liquid, smacking his lips, and then turned to the company with a
cheerful 'How are you, gentlemen?' He was looked upon as the best
pitcher of the party, and could throw heavier quoits than any other
member of the club. The game began with great animation. There were
several ties; and before long I saw the great Chief Justice of the
United States down on his knees, measuring the contested distance with a
straw, with as much earnestness as if it had been a point of law; and if
he proved to be in the right, the woods would ring with his triumphant
shout."[46]
An entertaining account has been preserved[47] of a meeting of the club,
held, apparently, while Marshall was still at the bar, at which he and
Wickham--a leading Virginia lawyer, one of the counsel of Aaron
Burr--were the caterers. At the table Marshall announced that at the
last meeting two members had introduced politics, a forbidden subject,
and had been fined a basket of champagne, and that this was now
produced, as a warning to evil-doers; as the club seldom drank this
article, they had no champagne glasses, and must drink it in tumblers.
Those who played quoits retired, after a while, for a game. Most of the
members had smooth, highly polished brass quoits. But Marshall's were
large, rough, heavy, and of iron, such as few of the members could throw
well from hub to hub. Marshall himself threw them with great success and
accuracy, and often "rang the meg." On this occasion Marshall and the
Rev. Mr. Blair led the two parties of players. Marshall played first,
and rang the meg. Parson Blair did the same, and his quoit came down
plumply on top of Marshall's. There was uproarious applause, which drew
out all the others from the dinner; and then came an animated
controversy as to what should be the effect of this exploit. They all
returned to the table, had another bottle of champagne, and listened to
arguments, one from Marshall, _pro se_, and one from Wickham for Parson
Blair. The company decided against Marshall. His argument is a humorous
companion piece to any one of his elaborate judicial opinions. He began
by formulating the question, "Who is winner when the adversary quoits
are on the meg at the same time?" He then stated the facts, and remarked
that the question was one of the true construction and application of
the rules of the game. The one first ringing the meg has the advantage.
No other can succeed who does not begin by displacing this first one.
The parson, he willingly allowed, deserves to rise higher and higher in
everybody's esteem; but then he mustn't do it by getting on another's
back in this fashion. That is more like leapfrog than quoits. Then,
again, the legal maxim is, _Cujus est solum_, _ejus est usque ad
cœlum_,--his own right as first occupant extends to the vault of heaven;
no opponent can gain any advantage by squatting on his back. He must
either bring a writ of ejectment, or drive him out _vi et armis_. And
then, after further argument of the same sort, he asked judgment, and
sat down amidst great applause.
Mr. Wickham then rose, and made an argument of a similar pattern. No
rule, he said, requires an impossibility. Mr. Marshall's quoit is twice
as large as any other; and yet it flies from his arm like the iron ball
at the Grecian games from the arm of Ajax. It is an iron quoit,
unpolished, jagged, and of enormous weight. It is impossible for an
ordinary quoit to move it. With much more of the same sort, he contended
that it was a drawn game. After very animated voting, designed to keep
up the uncertainty as long as possible, it was so decided. Another trial
was had, and Marshall clearly won.
All his life he played this game. There is an account of a country
barbecue in the mountain region, where a casual guest saw him, then an
old man, emerge from a thicket which bordered a brook, carrying a pile
of flat stones as large as he could hold between his right arm and his
chin. He stepped briskly up to the company and threw them down. "There!
Here are quoits enough for us all."
Of Marshall's simple habits, remarkable modesty, and engaging simplicity
of conduct and demeanor, every one who knew him speaks. These things
were in the grain, and outlasted all the wear and tear of life. "What
was it in him which most impressed you?" asked one of his descendants,
now a distinguished judge,[48] of an older relative who had known him.
"His humility," was her answer. "With Marshall," wrote President Quincy,
"I had considerable acquaintance during the eight years I was member of
Congress, from 1805 to 1813, played chess with him, and never failed to
be impressed with the frank, cordial, childlike simplicity and
unpretending manner of the man, of whose strength and breadth of
intellectual power I was ... well apprised."
"Nothing was more usual," we are told, as regards his life in Richmond,
"than to see him returning from market, at sunrise, with poultry in one
hand and a basket of vegetables in the other." And, again, some one
speaks of meeting him on horseback, at sunrise, with a bag of seeds
before him, on his way to his farm, three or four miles out of town. It
was of this farm that he wrote to James Monroe, his old friend and
schoolmate, about passing so much time in "_laborious relaxation_." The
italics are his own.
In speaking of Marshall's personal qualities and ways, I must quote from
those exquisite passages in Judge Story's address, delivered in the fall
of 1835, to the Suffolk bar, in which his own true affection found
expression: "Upon a first introduction he would be thought to be cold
and reserved; but he was neither the one nor the other. It was simply a
habit of easy taciturnity, watching, as it were, his own turn to follow
the line of conversation, and not to presume to lead it.... Meet him in
a stage-coach as a stranger, and travel with him a whole day, and you
would only be struck with his readiness to administer to the
accommodation of others, and his anxiety to appropriate least to
himself. Be with him the unknown guest at an inn, and he seemed adjusted
to the very scene; partaking of the warm welcome of its comforts,
whenever found; and if not found, resigning himself without complaint to
its meanest arrangements.... He had great simplicity of character,
manners, dress, and deportment, and yet with a natural dignity that
suppressed impertinence and silenced rudeness. His simplicity ... had an
exquisite naïveté, which charmed every one, and gave a sweetness to his
familiar conversation approaching to fascination. The first impression
of a stranger, upon his introduction to him, was generally that of
disappointment. It seemed hardly credible that such simplicity should be
the accompaniment of such acknowledged greatness. The consciousness of
power was not there; the air of office was not there; there was no play
of the lights or shades of rank, no study of effect in tone or bearing."
Add to this what Judge Story said from the bench, in receiving the
resolutions of the Bar of the Supreme Court after Marshall's death:
"But, above all, he was the ornament of human nature itself, in the
beautiful illustrations which his life constantly presented, of its most
attractive graces, and its most elevated attributes."[49]
Of Marshall's appearance on the bench we have a picture in one of
Story's letters from Washington, while he was at the bar. He is writing
in 1808, the year after the Burr trial. "Marshall," he says, "is of a
tall, slender figure, not graceful or imposing, but erect and steady.
His hair is black, his eyes small and twinkling, his forehead rather
low, but his features are in general harmonious. His manners are plain,
yet dignified; and an unaffected modesty diffuses itself through all
his actions. His dress is very simple, yet neat; his language chaste,
but hardly elegant; it does not flow rapidly, but it seldom wants
precision. In conversation he is quite familiar, but is occasionally
embarrassed by a hesitancy and drawling.... I love his laugh,--it is too
hearty for an intriguer,--and his good temper and unwearied patience are
equally agreeable on the bench and in the study."
Daniel Webster, in 1814, while he was a member of Congress from New
Hampshire, wrote to his brother: "There is no man in the court that
strikes me like Marshall. He is a plain man, looking very much like
Colonel Adams, and about three inches taller. I have never seen a man of
whose intellect I had a higher opinion."
In the year 1808, when Judge Story wrote what has just been quoted,
Marshall was sketched in chalk by St. Mémin. It is a beautiful portrait,
which its present owner, Mr. Thomas Marshall Smith, of Baltimore, John
Marshall's great-grandson, has now generously allowed to be copied for
the use of the public.
It was in 1830 that Chester Harding painted for the Boston Athenæum the
full-length portrait, of which, a little later, he made the replica,
afterwards purchased, by subscription, for the Harvard Law School. "I
consider it," says Harding, "a good picture.[50] I had great pleasure in
painting _the whole_ of such a man.... When I was ready to draw the
figure into his picture, I asked him, in order to save time, to come to
my room in the evening.... An evening was appointed; but he could not
come until after the 'consultation,' which lasts until about eight
o'clock." It will be remembered that the judges, at that time, used to
lodge together, in one house. "It was a warm evening," continues
Harding, "and I was standing on my steps waiting for him, when he soon
made his appearance, but, to my surprise, without a hat. I showed him
into my studio, and stepped back to fasten the front door, when I
encountered [several gentlemen] who knew the judge very well. They had
seen him passing by their hotel in his hatless condition, and with long
strides, as if in great haste, and had followed, curious to know the
cause of such a strange appearance.... He said that the consultation
lasted longer than he expected, and he hurried off as quickly as
possible to keep his appointment with me." He declined the offer of a
hat on his return: "Oh no, it is a warm night; I shall not need one."
A good many artists tried their hands on the Chief Justice, and with
every sort of result. Some depicted a dull and wooden person, some a
worthy but feeble one. Other portraits, commended for their likeness to
the original, differ much in what they represent.[51]
In the written descriptions of him, also, one needs to compare several
before he can feel much assurance of the true image. In an anonymous
account of him, preserved in Van Santvoord's "Lives of the Chief
Justices,"[52] the reader seems to perceive the humorous exaggerations
of an entertaining and practiced writer, but, taken with due allowance,
the description may well be preserved.
"As to face and figure," says this account, "nature had been equally
little at pains to stamp, with any princely effigy of what pleases, the
virgin gold of which she had composed his head and heart. Except that
his countenance was thoughtful and benignant, it had nothing about it
that would have commanded a second look. Separately his features were
but indifferent, jointly they were no more than commonplace. Then as to
stature, shape, and carriage, there was nothing in him that was not the
opposite of commanding or prepossessing; he was tall, yet his height was
without the look of either strength or lightness, and gave neither
dignity nor grace. His body seemed as ill as his mind well compacted; he
not only was without proportion, but of members singularly knit, that
dangled from each other and looked half dislocated. Habitually he
dressed very carelessly; in the garb, I should not dare to say in the
mode, of the last century. You would have thought he had on the old
clothes of a former generation, not made for him by even some
superannuated tailor of the period, but gotten from the wardrobe of some
antiquated slop-shop of second-hand raiment. Shapeless as he was, he
would probably have defied all fitting, by whatever skill of the shears;
judge then how the vestments of an age when, apparently, coats and
breeches were cut for nobody in particular, and waistcoats were almost
dressing gowns, sat upon him."
Such a statement should be supplemented by what one of his family said
of him: "The descriptions of his dress are greatly exaggerated; he was
regardless of style and fashion, but all those who knew him best
testified to the extreme neatness of his attire."[53]
CHAPTER VIII
HIS LAST DAYS
The year 1831 was a sad one for Marshall. The greatest apprehensions
were felt for his health. "Wirt," says John Quincy Adams in his diary,
on February 13, 1831, "spoke to me, also, in deep concern and alarm at
the state of Chief Justice Marshall's health." In the autumn he went to
Philadelphia to undergo the torture of the operation of lithotomy,
before the days of ether. It was the last operation performed by the
distinguished surgeon, Dr. Physick. Another eminent surgeon, who
assisted him, Dr. Randall, has given an account of this occasion, in
which he says:--
"It will be readily admitted that, in consequence of Judge Marshall's
very advanced age, the hazard attending the operation, however
skillfully performed, was considerably increased. I consider it but an
act of justice, due to the memory of that great and good man, to state
that, in my opinion, his recovery was in a great degree owing to his
extraordinary self-possession, and to the calm and philosophical views
which he took of his case, and the various circumstances attending it.
"It fell to my lot to make the necessary preparations. In the discharge
of this duty I visited him on the morning of the day fixed on for the
operation, two hours previously to that at which it was to be performed.
Upon entering his room I found him engaged in eating his breakfast. He
received me with a pleasant smile upon his countenance, and said: 'Well,
doctor, you find me taking breakfast, and I assure you I have had a good
one. I thought it very probable that this might be my last chance, and
therefore I determined to enjoy it and eat heartily.' I expressed the
great pleasure which I felt at seeing him so cheerful, and said that I
hoped all would soon be happily over. He replied to this that he did not
feel the least anxiety or uneasiness respecting the operation or its
results. He said that he had not the slightest desire to live, laboring
under the sufferings to which he was then subjected; that he was
perfectly ready to take all the chances of an operation, and he knew
there were many against him; and that if he could be relieved by it he
was willing to live out his appointed time, but if not, would rather die
than hold existence accompanied with the pain and misery which he then
endured.
"After he finished his breakfast I administered to him some medicine; he
then inquired at what hour the operation would be performed. I mentioned
the hour of eleven. He said, 'Very well, do you wish me now for any
other purpose, or may I lie down and go to sleep?' I was a good deal
surprised at this question, but told him that if he could sleep it would
be very desirable. He immediately placed himself upon the bed, and fell
into a profound sleep, and continued so until I was obliged to rouse him
in order to undergo the operation. He exhibited the same fortitude,
scarcely uttering a murmur, throughout the whole procedure, which, from
the peculiar nature of his complaint, was necessarily tedious."
From the patient over a thousand calculi were taken. He had a perfect
recovery; nor did the disorder ever return.[54]
On Christmas Day of that year, as I have said, his wife died, the object
of his tenderest affection ever since he had first seen her, more than
fifty years before. The day before she died, she hung about his neck a
locket with some of her hair. He wore it always, night and day; and, by
his order, it was the last thing removed from his body when he died.[55]
It was at this period, in 1831 and 1832, that Inman's fine portrait of
him, now hanging in the rooms of the Law Association of Philadelphia,
was painted, for the bar of that city. A replica which Marshall himself
bought for his daughter, is on the walls of the state library in
Richmond. This portrait is regarded as the best of those painted in his
later life. Certainly it best answers the description of him by an
English traveler, who, seeing him often in the spring of 1835, remarked
that "the venerable dignity of his appearance would not suffer in
comparison with that of the most respected and distinguished-looking
peer in the British House of Lords."[56]
After his recovery, in 1831, Marshall seems to have been in good health
down to the early part of 1835. Then, we are told, he suffered "severe
contusions" in the stage-coach in returning from Washington.[57] His
health now rapidly declined. He went again for relief to Philadelphia,
and died there on July 6, 1835, of a serious disorder of the liver. He
had missed from his bedside his oldest son, Thomas, for whom he had been
asking. Upon the gravestone of that son, behind the old house at
Oakhill, you may read the pathetic tragedy, withheld from his father,
that accounts for this absence. While hastening to Philadelphia, at the
end of June, he was passing through the streets of Baltimore, in the
midst of a tempest, and was killed by the falling of a chimney in the
storm.
The great Chief Justice was carried home with every demonstration of
respect and reverence. He was buried by the side of his wife, in the
Shockoe Hill Cemetery in Richmond. There, upon horizontal tablets, are
two inscriptions of affecting simplicity, both written by himself. The
first runs thus: "John Marshall, Son of Thomas and Mary Marshall, was
born the 24th of September, 1755. Intermarried with Mary Willis Ambler,
the 3d of January, 1783. Departed this life the [6th] day of July,
1835." The second, thus: "Sacred to the memory of Mrs. Mary Willis
Marshall, Consort of John Marshall, Born the 13th of March, 1766.
Departed this life the 25th of December, 1831. This stone is devoted to
her memory by him who best knew her worth, And most deplores her loss."
* * * * *
Among the tributes to Chief Justice Marshall which were made in the
months that followed his death, and in later times, nothing finer has
been said than the heartfelt expression of the bar of his own circuit,
at Richmond, in November, 1835. The resolutions of Mr. B. Watkins Leigh,
unanimously adopted, recalled "the memory of the venerable judge" who
had presided there for more than thirty-four years "with such remarkable
diligence in office, that until he was disabled by the disease which
removed him from life, he was never known to be absent from the bench,
during term time, even for a day,--with such indulgence to counsel and
suitors that everybody's convenience was consulted but his own,--with a
dignity, sustained without effort, and apparently without care to
sustain it, to which all men were solicitous to pay due respect,--with
such profound sagacity, such quick penetration, such acuteness,
clearness, strength, and comprehension of mind, that in his hands the
most complicated causes were plain, the weightiest and most difficult,
easy and light,--with such striking impartiality and justice, and a
judgment so sure, as to inspire universal confidence, so that few
appeals were ever taken from his decisions, during his long
administration of justice in this court, and those only in cases where
he himself expressed doubt,--with such modesty that he seemed wholly
unconscious of his own gigantic powers,--with such equanimity, such
benignity of temper, such amenity of manners, that not only none of the
judges who sat with him on the bench, but no member of the bar, no
officer of the court, no juror, no witness, no suitor, in a single
instance, ever found or imagined, in anything said or done, or omitted
by him, the slightest cause of offense.
"His private life was worthy of the exalted character he sustained in
public station. The unaffected simplicity of his manners; the spotless
purity of his morals; his social, gentle, cheerful disposition; his
habitual self-denial, and boundless generosity towards others; the
strength and constancy of his attachments, his kindness to his friends
and neighbors; his exemplary conduct in the relations of son, brother,
husband, father; his numerous charities; his benevolence toward all men,
and his ever active beneficence; these amiable qualities shone so
conspicuously in him, throughout his life, that highly as he was
respected, he had the rare happiness to be yet more beloved. He was,
indeed, a bright example of the true wisdom which consists in the union
of the greatest ability and the greatest virtue."
* * * * *
On the west side of the Capitol at Washington, midway between the
staircases that ascend from the garden to the great building, and a
little in advance, there is a colossal bronze figure of Marshall by the
sculptor Story, the son of the great man's colleague and friend,--placed
there in 1884. It is a very noble work of art, worthy of the subject and
the place. The Chief Justice is sitting, clothed in his judicial robe,
in the easy attitude of one engaged in expounding a subject of which he
is master. The figure is leaning back in the chair with the head
slightly inclining forward; the right arm rests on the arm of the chair,
with the hand open and extended; the left hand, holding a scroll, lies
easily on the other arm of the chair. The crossed legs are covered by
the gown, while low shoes and buckles, and hair gathered in a queue,
speak of lifelong habits. The solid and beautiful head, and the grave
and collected dignity of the features and the whole composition are very
noble, satisfactory, and ideally true.
The figure, standing, would be ten feet high. It sits seven feet high,
and is raised upon a suitable pedestal, decorated with marble
bas-reliefs of classical designs. These, if the truth were told, might
well be spared, but the statue itself will fitly commemorate for many
ages one of the greatest, noblest and most engaging characters in
American history.
The Riverside Press
_Electrotyped and printed by H. O. Houghton & Co._
_Cambridge, Mass., U.S.A._
FOOTNOTES:
[1] The Chief Justice seems to have inherited and accumulated a
considerable estate. By his will he gave to each of his grandsons
named John a thousand acres of land. _The Green Bag_, viii. 4. He also
had been a surveyor. _Ib._ 480.
[2] Hammond's Blackstone, vol. i., pp. viii. xxv.
[3] Marshall's eyes are often spoken of as black. In fact, they were
brown.
[4] It may be added that Thomas Marshall, father of the Chief Justice,
was the son of John Marshall, called "of the Forest," from the name
of his place in Westmoreland County. Of this John it is said, in a
little autobiography of the Chief Justice of some five hundred words,
preserved in Mr. Justice Gray's valuable oration at Richmond, on
February 4, 1901, that his "parents migrated from Wales and settled in
the county of Westmoreland in Virginia." The will of "Thomas Marshall
carpenter," proved May 31, 1704, describing himself as of Westmoreland
County, is printed in the _Virginia Magazine of History_, ii. 343,
344; and it is there stated in a note that this Thomas "was the
first of his race in America." On the other hand, we are told by an
intelligent writer in Appleton's _Cyclopædia of American Biography_,
and elsewhere, that the father of "John of the Forest" was Thomas,
born in Virginia in 1655, who died in 1704; and that it was his
father, John, a captain of cavalry in the service of Charles I., who
emigrated to Virginia about 1650.
[5] Flanders, _Lives of the Chief Justices_, ii. 291.
[6] His youngest son, Edward Carrington Marshall, graduated at Harvard
in 1826.
[7] Only six of his children grew to full age. See his touching letter
to Judge Story of June 26, 1831: "You ask me if Mrs. Marshall and
myself have ever lost a child. We have lost four," etc.--_Proceedings
of the Mass. Hist. Soc._ (2d series) xiii. 345.
[8] Richard Anderson, father of Robert Anderson, the hero of Fort
Sumter. See Marion Harland's _Old Colonial Homesteads_, 97.
[9] But see Mrs. Hardy, in _The Green Bag_, viii. 482.
[10] _Old Churches and Families of Virginia_, ii. 105.
[11] It was given by another judge.
[12] Mr. Justice Gray preserves this fact in his address on Marshall.
His commission bore the same date with that of Chief Justice Jay,
September 26, 1789,--two days after the approval of the Judiciary Act.
[13] See Wait's _State Papers_, iii. 165-304.
[14] _The Green Bag_, viii. 482.
[15] Paulding's _Life of Washington_, ii. 191; _Lippincott's
Magazine_, ii. 624, 625.
[16] In an amusing account of this election (Munford's _The Two
Parsons_), we are told that the sheriff presided, with the two
candidates, Marshall and John Clopton, seated on the justice's
bench. The voter, being asked for whom he voted, gave the name of
his candidate; and the latter thanked him; _e.g._, "Your vote is
appreciated, sir," said Marshall to his friend Parson Blair. For an
account of the same method of conducting elections in Virginia at a
later period, see John S. Wise's _The End of an Era_.
[17] "The masterly and conclusive argument of John Marshall in the
House of Representatives. 8 Stat. 129; Wharton's State Trials, 392;
Bee [Reports], 286; 5 Wheat. appendix 3."--Gray, J., speaking for
the Supreme Court of the United States, in Fong Yue Ting _v._ U. S.,
149 U. S. 698, 714. This speech is also found in Moore's _American
Eloquence_, ii. 7.
[18] The President had written to the Secretary of State from Quincy,
May 21, 1799: "How far the President of the United States would be
justified in directing the judge to deliver up the offender is not
clear. I have no objection to advise, and request him to do so."
Wharton's State Trials, 418.
[19] The short "autobiography" before referred to (_ante_, p. 10, n.)
ends thus: "I have written no book except the 'Life of Washington,'
which was executed with so much precipitation as to require much
correction."
[20] Van Santvoord, _Lives of the Chief Justices_, 343, n.
[21] Coxe, _Jud. Power_, 95-102; Thayer's _Cases on Constitutional
Law_, i. 146-149.
[22] Eakin _v._ Raub, 12 Sergeant & Rawle, 330.
[23] What Pinckney said in 1799 was this: "Upon no subject am I
more convinced than that it is an unsafe and dangerous doctrine in
a republic ever to suppose that a judge ought to possess the right
of questioning or deciding upon the constitutionality of treaties,
laws, or any act of the legislature. It is placing the opinion of
an individual, or of two or three, above that of both branches of
Congress, a doctrine which is not warranted by the Constitution, and
will not, I hope, long have many advocates in this country." Wharton,
_State Trials_, 412.
[24] 4 Amer. Jurist, 293; Story, Const. § 1579, n.
[25] Stuart _v._ Laird, 1 Cranch, 299.
[26] Marshall, when the act of 1802 restored the old system, stated
to his associates his deliberate agreement with the opinion expressed
by his predecessors above referred to, and proposed to refuse to sit
in the circuit court. All his brethren agreed with his view on the
constitutional point, but thought the question should be regarded
as at rest, by reason of the earlier practice of the court, up to
1801. This view prevailed, and was soon afterwards, as above stated,
judicially adopted by the court. This statement is made by Chancellor
Kent in 3 N. Y. Review, 347 (1838).
For the knowledge of the authorship of this valuable article and of
another related one in 2 _ib._ 372, I am indebted to the courtesy of
Dr. J. S. Billings, the Director of the New York Public Library, and
the investigations of Mr. V. H. Paltsits, one of the librarians in
that institution.
[27] This construction, that the statute purported to authorize their
acting in that capacity was afterwards, in 1794, held by the Supreme
Court to be wrong. Yale Todd's Case, 13 Howard, 52.
[28] Hayburn's Case, 2 Dallas, 409.
[29] Volume v., p. 444 (Philadelphia edition, 1807).
[30] 1 Cranch, 137.
[31] In like manner, Jay, commissioned Chief Justice on September
26, 1789, continued, at Washington's request, to act also as foreign
secretary until Jefferson's return from Europe. Jefferson did not
reach New York until March 21, 1790.
[32] And so the careful headnote of Judge Curtis in 1 Curtis's
_Decisions of the Supreme Court_, 368.
[33] See Ford's _Jefferson_, ix. 62; draft of a letter to District
Attorney Hay.
[34] Hare, Am. Const. Law, i. 607.
[35] See, however, Chancellor Kent in 2 N. Y. Rev. 372.
[36] Mississippi _v._ Johnson, 4 Wallace, 475, 492 (1866).
[37] 12 Serg. & Rawle, 330; s. c. 1 Thayer's Const. Cases, 133.
[38] As to this general subject see "Origin and Scope of the American
Doctrine of Constitutional Law," 7 _Harvard Law Review_, 129. Compare
the remark of Lord John Russell: "Every political constitution, in
which different bodies share the supreme power, is only enabled
to exist by the forbearance of those among whom this power is
distributed." I quote this from the motto of Woodrow Wilson's fifth
chapter in his _Congressional Government_.
[39] _The Nation_, February 7, 1901.
[40] He married John Marshall's sister.
[41] These letters were printed in 1897 in the _American Hist.
Review_, ii. 294. I was not aware of their ever having been printed,
until after these pages were in type.
[42] _The Virginia Magazine of History_, vii. 233.
[43] Chancellor Kent in _New York Review_, 348, 349.
[44] _Anti-masonic Pamphlets_, Harvard College Library, No. 12, p. 18;
_ib._ No. 9.
[45] Mrs. Hardy, 8 _Green Bag_, 487.
[46] In speaking of this same Club, Mr. G. W. Munford says: "We have
seen Mr. Marshall, in later times, when he was Chief Justice of the
United States, on his hands and knees, with a straw and a penknife,
the blade of the knife stuck through the straw, holding it between
the edge of the quoit and the hub; and when it was a very doubtful
question, pinching or biting off the ends of the straw, until it would
fit to a hair."
James K. Paulding has preserved an entertaining account of a game,
in 1820, when Jarvis, the artist, was present, playing, apparently
on the same side with the Chief Justice. "I remember," he says, "in
the course of the game, and when the parties were nearly at a tie,
that some dispute arose as to the quoit nearest the meg. The Chief
Justice was chosen umpire between the quoit belonging to Jarvis and
that of Billy Haxall. The judge bent down on one knee, and with a
straw essayed the decision of this important question on which the
fate of the game in a great measure depended. After nicely measuring,
and frequently biting off the end of the straw, 'Gentlemen,' said
he, 'you will perceive this quoit would have it, but the rule of
the game is to measure from the visible iron. Now that clod of dirt
hides almost half an inch. But, then he has a right to the nearest
part of the meg; and here, as you will perceive, is a splinter, which
belongs to and is part of the meg, as much as the State of Virginia
is a part of the Union. This is giving Mr. Haxall a great advantage;
but, notwithstanding, in my opinion, Jarvis has it by at least the
sixteenth part of an inch, and so I decide, like a just judge, in my
own favor.'"*
* _Lippincott's Magazine_, 623, 626. It is said that he was often
appointed thus to be judge in his own case.
[47] See _The Two Parsons_, by G. W. Munford.
[48] Mr. Justice Keith, now President of the Virginia Court of Appeals.
[49] 10 Peters's Reports, vii.
[50] The half-length, sitting portrait of Marshall, in the dining-hall
at Cambridge, was painted by Harding, in 1828, for the Chief Justice
himself; and by him given to Judge Story, "to be preserved, when
I shall sleep with my fathers, as a testimonial of sincere and
affectionate friendship." Story bequeathed it to the college.
[51] See an interesting' article by Mr. Justice Bradley, of the
Supreme Court of the United States, on portraits of Marshall, in
the _Century Magazine_ for September, 1889, (vol. 38, page 778.) A
portrait by Jarvis, valued as a work of art and as a good likeness,
is in the possession of Mr. Justice Gray. Mr. Justice Bradley appears
to be wrong in saying that there is a full-length of Marshall at
Washington and Lee University. There are two portraits of him there,
but, as I am assured, no full-length.
[52] P. 363, n.
[53] Mrs. Hardy, quoting her grandmother, in 8 _Green Bag_, 484.
[54] My friend Dr. Horace Howard Furness, of Philadelphia, writes
(and allows me to quote): "I remember hearing my father say that Dr.
Physick told him, just after that operation of lithotomy, that he had
'washed the judge out as clean as a plate,' and that he went on to
say that after the operation the strictest quiet was enjoined, not
a muscle was to be moved; but what was his alarm on his next visit
to see Judge Marshall sitting up in bed with paper and pencil on his
knees, writing to his wife!"
[55] Marion Harland, _Old Colonial Homesteads_, 98.
[56] _Travels in North America_, by Hon. Charles Augustus
Murray,--"the late Sir Charles Murray, at one time Master of the
Household to the Queen, who, as a young man, was attached to the
British Legation at Washington."--_The Spectator_, February 9, 1901,
p. 199.
[57] Many a "severe contusion" must he have suffered in those
primitive days, from upsets and joltings, in driving every year
between Richmond and Washington, some 120 miles each way; from
Richmond to Raleigh and back, in attending his North Carolina circuit,
about 175 miles each way; and between Richmond and Oakhill, his
country place, every summer, about 100 miles each way. For instance,
in 1812, Cranch, the reporter, remarks that Marshall was not present
at the beginning of the term, as he "received an injury by the
oversetting of the stage-coach on his journey from Richmond."
End of the Project Gutenberg EBook of John Marshall, by James Bradley Thayer
*** | {
"redpajama_set_name": "RedPajamaBook"
} | 9,184 |
This is the last blog before we move back to the South Hams of South Devon. We shall be sad to leave as we have loved living in such a remote and quiet place – and we shall be sorry to leave the wild life that we have attracted into the gardens. We can but pray that the next people to live here will want to nurture them or, at the very least, leave the wild bits around the ponds as untidy as they are at present. This is a state of affairs that would shock any self-respecting gardener but would appeal greatly to anyone who is as nutty about the natural world as I am.
Having said that we are sorry to leave, I should add that we are excited to be going back to the area which we both think of as home. I suppose the centre of our lives will once again be the lovely town of Totnes which, and this is becoming quite important, has a railway station. No doubt we shall be looking in at places such as Salago and Effings (both mentioned in the books) as well as some of the hostelries where we shall be meeting old friends for coffee or a drink. At the bottom of Fore Street is the Seven Stars where Marcia and her family stayed. They always sat at the big round table in the dining room and, there being two parents and five girls, they became know as "the seven stars". Quite right, too.
Totnes is connected to Dartmouth by the river. This river has been important throughout my life and for much of Marcia's, I learned to swim in the boat float at Dartmouth (would you be allowed to do that now?) and to row and handle a sailing boat on the river itself. Marcia and I have owned three boats which we kept on the river which we have thoroughly explored from outside the mouth right up to the weir just up the river from Totnes. Hattie's Mill owed much to these jaunts.
Apart from the fact that we lived on Dartmouth for a while shortly after we were married, we have both known it for ever. My mother was born there (in what is now the hotel associated with Dartmouth Marina) and my father arrived when his father became the Borough Engineer for the town just after the first world war. It was in the Royal Castle overlooking the boat float that I enjoyed the last drink I had with my father shortly before he died.
A rather odd thing happened the other day. I was sorting through things (as you would expect) when I came across a membership card for the South Hams Society. It told me that I became a life member about forty years ago. I had completely forgotten this. It was formed to protect and enhance the natural beauty and heritage of the South Hams – which is something I agreed with then and still do. In those days the society was busy planting hundreds of primroses along the lanes. Now these are well established and we are able to reap the benefits of all that hard work. They are even more active now: tomorrow they are organising an event to clean up the West Charleton beach and the have another eight events planned during the next few months. Reading the list of the present committee members I have to confess that I recognise not one – and I am sure they have forgotten all about me, too. I might pop along to one of their meetings just to repair that connection.
Now I must return to the packing while Marcia, who will be at Chagford Library this afternoon (an event planned long ago), is getting ready to meet some of her readers. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,374 |
Q: How to auto refresh table content in sql from .txt when .txt changed? I have a table in Database like dbo.foo and have stored procedure which one reads data to dbo.foo from foo.txt. Until this point everything is working fine. Now, I need an automatism, which starts stored procedure when foo.txt has changed (saved).
foo.txt is coming from a client in the network with 'robocopy'. This works as well. I created a .bat file in server with SQLCMD for 'exec' the stored procedure. It also works on server, but I cannot run it from client.
The SQLCMD is just a possible way, not necessary to follow this path. The greatest solution would be a 'trigger' or something in MsSql server based on foo.txt changing.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,357 |
/*
* Do not modify this file. This file is generated from the apigateway-2015-07-09.normal.json service model.
*/
using System;
using System.Collections.Generic;
using System.Xml.Serialization;
using System.Text;
using System.IO;
using Amazon.Runtime;
using Amazon.Runtime.Internal;
namespace Amazon.APIGateway.Model
{
/// <summary>
/// Container for the parameters to the GetIntegration operation.
/// Represents a get integration.
/// </summary>
public partial class GetIntegrationRequest : AmazonAPIGatewayRequest
{
private string _httpMethod;
private string _resourceId;
private string _restApiId;
/// <summary>
/// Gets and sets the property HttpMethod.
/// <para>
/// Specifies a get integration request's HTTP method.
/// </para>
/// </summary>
public string HttpMethod
{
get { return this._httpMethod; }
set { this._httpMethod = value; }
}
// Check to see if HttpMethod property is set
internal bool IsSetHttpMethod()
{
return this._httpMethod != null;
}
/// <summary>
/// Gets and sets the property ResourceId.
/// <para>
/// Specifies a get integration request's resource identifier
/// </para>
/// </summary>
public string ResourceId
{
get { return this._resourceId; }
set { this._resourceId = value; }
}
// Check to see if ResourceId property is set
internal bool IsSetResourceId()
{
return this._resourceId != null;
}
/// <summary>
/// Gets and sets the property RestApiId.
/// <para>
/// Specifies a get integration request's API identifier.
/// </para>
/// </summary>
public string RestApiId
{
get { return this._restApiId; }
set { this._restApiId = value; }
}
// Check to see if RestApiId property is set
internal bool IsSetRestApiId()
{
return this._restApiId != null;
}
}
} | {
"redpajama_set_name": "RedPajamaGithub"
} | 9,588 |
package com.yahoo.aptutils.writer.parameters;
import com.yahoo.aptutils.model.DeclaredTypeName;
import com.yahoo.aptutils.model.TypeName;
import com.yahoo.aptutils.utils.AptUtils;
import javax.lang.model.element.Modifier;
import java.util.List;
/**
* An object for containing the information needed to begin a method declaration. Required by
* {@link com.yahoo.aptutils.writer.JavaFileWriter#beginMethodDefinition(MethodDeclarationParameters)}
*
* An instance of this class can be constructed by calling the no-arg constructor and then chaining method calls:
*
* new MethodDeclarationParameters().setMethodName("methodName").setReturnType(returnType) etc.
*/
public class MethodDeclarationParameters {
private DeclaredTypeName constructorName;
private String methodName;
private TypeName returnType;
private List<Modifier> modifiers;
private List<? extends TypeName> methodGenerics;
private List<? extends TypeName> argumentTypes;
private List<String> argumentNames;
private List<? extends TypeName> throwsTypes;
public boolean isConstructor() {
return getConstructorName() != null;
}
public DeclaredTypeName getConstructorName() {
return constructorName;
}
public MethodDeclarationParameters setConstructorName(DeclaredTypeName constructorName) {
this.constructorName = constructorName;
return this;
}
public String getMethodName() {
return methodName;
}
public MethodDeclarationParameters setMethodName(String methodName) {
this.methodName = methodName;
return this;
}
public TypeName getReturnType() {
return returnType;
}
public MethodDeclarationParameters setReturnType(TypeName returnType) {
this.returnType = returnType;
return this;
}
public List<Modifier> getModifiers() {
return modifiers;
}
public MethodDeclarationParameters setModifiers(Modifier... modifiers) {
this.modifiers = AptUtils.asList(modifiers);
return this;
}
public MethodDeclarationParameters setModifiers(List<Modifier> modifiers) {
this.modifiers = modifiers;
return this;
}
public List<? extends TypeName> getMethodGenerics() {
return methodGenerics;
}
public MethodDeclarationParameters setMethodGenerics(List<? extends TypeName> methodGenerics) {
this.methodGenerics = methodGenerics;
return this;
}
public List<? extends TypeName> getArgumentTypes() {
return argumentTypes;
}
public MethodDeclarationParameters setArgumentTypes(TypeName... argumentTypes) {
this.argumentTypes = AptUtils.asList(argumentTypes);
return this;
}
public MethodDeclarationParameters setArgumentTypes(List<? extends TypeName> argumentTypes) {
this.argumentTypes = argumentTypes;
return this;
}
public List<String> getArgumentNames() {
return argumentNames;
}
public MethodDeclarationParameters setArgumentNames(String... arguments) {
this.argumentNames = AptUtils.asList(arguments);
return this;
}
public MethodDeclarationParameters setArgumentNames(List<String> arguments) {
this.argumentNames = arguments;
return this;
}
public List<? extends TypeName> getThrowsTypes() {
return throwsTypes;
}
public MethodDeclarationParameters setThrowsTypes(List<? extends TypeName> throwsTypes) {
this.throwsTypes = throwsTypes;
return this;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,071 |
package org.barracuda.horvik.context.session;
import java.lang.annotation.ElementType;
import java.lang.annotation.Retention;
import java.lang.annotation.RetentionPolicy;
import java.lang.annotation.Target;
import org.barracuda.horvik.context.Scope;
@Scope
@Target({ ElementType.TYPE })
@Retention(RetentionPolicy.RUNTIME)
public @interface SessionScoped { }
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,208 |
using System.Reflection;
using System.Runtime.CompilerServices;
using System.Runtime.InteropServices;
// General Information about an assembly is controlled through the following
// set of attributes. Change these attribute values to modify the information
// associated with an assembly.
[assembly: AssemblyTitle("Arenaii.AIGames.FourInARow")]
[assembly: AssemblyDescription("")]
[assembly: AssemblyConfiguration("")]
[assembly: AssemblyCompany("")]
[assembly: AssemblyProduct("Arenaii.AIGames.FourInARow")]
[assembly: AssemblyCopyright("Copyright © 2016")]
[assembly: AssemblyTrademark("")]
[assembly: AssemblyCulture("")]
// Setting ComVisible to false makes the types in this assembly not visible
// to COM components. If you need to access a type in this assembly from
// COM, set the ComVisible attribute to true on that type.
[assembly: ComVisible(false)]
// The following GUID is for the ID of the typelib if this project is exposed to COM
[assembly: Guid("cc77abee-1cb8-4381-b9b6-dcdb152639d1")]
// Version information for an assembly consists of the following four values:
//
// Major Version
// Minor Version
// Build Number
// Revision
//
// You can specify all the values or you can default the Build and Revision Numbers
// by using the '*' as shown below:
// [assembly: AssemblyVersion("1.0.*")]
[assembly: AssemblyVersion("1.0.0.0")]
[assembly: AssemblyFileVersion("1.0.0.0")]
| {
"redpajama_set_name": "RedPajamaGithub"
} | 952 |
Difficult mattresses are too firm, they do not have bounce and comfort, there is nothing gentle about the surface area and there is no comfort. Some individuals like the firmness however end up with persistent pain. Shoulder discomfort, pain in the back and numerous other musculoskeletal discomforts are very common when you sleep on a hard bed mattress. Soft bed mattress is not a better option if it cannot evenly distribute the weight and doesn't offer appropriate back or lumbar assistance. Many soft bed mattress tend to lose their firmness, regardless of how firm they were initially. There is no pressure relief at strategic points of the body. In a short span of time, the soft mattress completely gives up. Medium quality bed mattresses do not use any reprieve as they integrate the shortcomings of difficult and soft bed mattress. They are simply as bad for persistent discomfort like hard bed mattress as they can facilitate arthritis like soft mattresses.
Purple has as many as fifteen patents going into simply one bed mattress. Some of the patents take care of press releasing comfort while some address the assistance, some attend to toughness while some address no feel motion transfer. Purple mattress will not cave in, it will not develop any indentation or impression of the body, it will not lose its firmness or softness, the upper layer or the base layer will not lose their main qualities, the bed mattress will be flexible adequate to hold up against pressure thus providing relief at tactical points whenever needed. It is much better to be like turf than a tree. Lawn can withstand a storm whereas a tree gets uprooted. Buckling of the surface is not a bad thing when one needs even circulation of weight or pressure. Purple bed mattress is nontoxic and allergen resistant or hypoallergenic. It is made from recyclable products. The mattress is CertiPUR-US ® licensed.
You may or might not have viewed the advertisement video called the Purple bed mattress egg test. In the video, a sleep expert utilizes four eggs at 4 various places, pasted onto a glass frame that she drops from a height on numerous mattresses. The simple objective is to view if the eggs break or they remain undamaged. The expectation is that if a mattress can equally distribute weight and can absorb the weight of an individual or any load then there will be no specific force exerted onto any part of the object or person sleeping on the mattress. All specific pressure points will have equal relief as the weight gets dispersed equally throughout the bed mattress. Hence, if a mattress is ideal then the eggs will not break. As one would anticipate, the eggs do break when they are enabled to fall from a height being pasted to a glass frame onto the majority of mattresses with the exception of Purple mattress.
Now, there has actually been criticism of the advertisement since Purple bed mattress has a grid life formation on its upper layer so the eggs can suit those grids or box like structures without getting blasted due to the pressure of the glass frame onto the upper surface of the mattress. To be fair to Purple, it has the right to demonstrate its product's superiority. It also has videos showing a side sleeper test, back sleeper test and pressure mapping test. You can enjoy them on the main website.
You can purchase Purple bed mattress on Amazon or on the main website. You can use a Purple mattress discount coupon to obtain a discount. But you would possibly consider Purple Mattress Vs Casper or Purple Mattress Vs GhostBed prior to you make a final decision. You need to also consider Nectar bed mattress, which transcends to Purple, Casper and GhostBed to name a few. Let us quickly explore why.
Casper has four foam layers, GhostBed has three and Purple has three. Nectar has four. Casper and Purple are thinner than Nectar. Casper, GhostBed and Purple have firmness rating of six to 7, 6 and a half to seven and six to 6 and a half from ten respectively. Nectar has a lower firmness score, thus offering more comfort without jeopardizing on stability and assistance. Nectar has the least motion transfer among the four. It is also the least expensive. Queen Casper costs $950, Queen GhostBed costs $795 and Queen Purple costs $999. Queen Nectar mattress is tagged at $795 but you would get a $125 discount rate so you pay $670. Nectar has lifetime guarantee. Casper and Purple have 10 years. GhostBed has twenty years. Casper and Purple have a hundred nights trial while GhostBed has a hundred and one nights. Nectar has three hundred and sixty 5 nights of threat totally free trial. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,664 |
{"url":"https:\/\/people.maths.bris.ac.uk\/~matyd\/GroupNames\/97\/C3xC3sDic3.html","text":"Copied to\nclipboard\n\n## G\u00a0=\u00a0C3\u00d7C3\u22caDic3order 108 = 22\u00b733\n\n### Direct product of C3 and C3\u22caDic3\n\nAliases: C3\u00d7C3\u22caDic3, C334C4, C325C12, C324Dic3, C3\u22ca(C3\u00d7Dic3), C6.7(C3\u00d7S3), (C3\u00d7C6).9S3, (C3\u00d7C6).8C6, C6.6(C3\u22caS3), (C32\u00d7C6).2C2, C2.(C3\u00d7C3\u22caS3), SmallGroup(108,33)\n\nSeries: Derived Chief Lower central Upper central\n\n Derived series C1 \u2014 C32 \u2014 C3\u00d7C3\u22caDic3\n Chief series C1 \u2014 C3 \u2014 C32 \u2014 C3\u00d7C6 \u2014 C32\u00d7C6 \u2014 C3\u00d7C3\u22caDic3\n Lower central C32 \u2014 C3\u00d7C3\u22caDic3\n Upper central C1 \u2014 C6\n\nGenerators and relations for C3\u00d7C3\u22caDic3\nG = < a,b,c,d | a3=b3=c6=1, d2=c3, ab=ba, ac=ca, ad=da, bc=cb, dbd-1=b-1, dcd-1=c-1 >\n\nSubgroups: 100 in 52 conjugacy classes, 26 normal (10 characteristic)\nC1, C2, C3, C3, C3, C4, C6, C6, C6, C32, C32, C32, Dic3, C12, C3\u00d7C6, C3\u00d7C6, C3\u00d7C6, C33, C3\u00d7Dic3, C3\u22caDic3, C32\u00d7C6, C3\u00d7C3\u22caDic3\nQuotients: C1, C2, C3, C4, S3, C6, Dic3, C12, C3\u00d7S3, C3\u22caS3, C3\u00d7Dic3, C3\u22caDic3, C3\u00d7C3\u22caS3, C3\u00d7C3\u22caDic3\n\nSmallest permutation representation of C3\u00d7C3\u22caDic3\nOn 36 points\nGenerators in S36\n(1 25 24)(2 26 19)(3 27 20)(4 28 21)(5 29 22)(6 30 23)(7 35 16)(8 36 17)(9 31 18)(10 32 13)(11 33 14)(12 34 15)\n(1 20 29)(2 21 30)(3 22 25)(4 23 26)(5 24 27)(6 19 28)(7 31 14)(8 32 15)(9 33 16)(10 34 17)(11 35 18)(12 36 13)\n(1 2 3 4 5 6)(7 8 9 10 11 12)(13 14 15 16 17 18)(19 20 21 22 23 24)(25 26 27 28 29 30)(31 32 33 34 35 36)\n(1 7 4 10)(2 12 5 9)(3 11 6 8)(13 24 16 21)(14 23 17 20)(15 22 18 19)(25 35 28 32)(26 34 29 31)(27 33 30 36)\n\nG:=sub<Sym(36)| (1,25,24)(2,26,19)(3,27,20)(4,28,21)(5,29,22)(6,30,23)(7,35,16)(8,36,17)(9,31,18)(10,32,13)(11,33,14)(12,34,15), (1,20,29)(2,21,30)(3,22,25)(4,23,26)(5,24,27)(6,19,28)(7,31,14)(8,32,15)(9,33,16)(10,34,17)(11,35,18)(12,36,13), (1,2,3,4,5,6)(7,8,9,10,11,12)(13,14,15,16,17,18)(19,20,21,22,23,24)(25,26,27,28,29,30)(31,32,33,34,35,36), (1,7,4,10)(2,12,5,9)(3,11,6,8)(13,24,16,21)(14,23,17,20)(15,22,18,19)(25,35,28,32)(26,34,29,31)(27,33,30,36)>;\n\nG:=Group( (1,25,24)(2,26,19)(3,27,20)(4,28,21)(5,29,22)(6,30,23)(7,35,16)(8,36,17)(9,31,18)(10,32,13)(11,33,14)(12,34,15), (1,20,29)(2,21,30)(3,22,25)(4,23,26)(5,24,27)(6,19,28)(7,31,14)(8,32,15)(9,33,16)(10,34,17)(11,35,18)(12,36,13), (1,2,3,4,5,6)(7,8,9,10,11,12)(13,14,15,16,17,18)(19,20,21,22,23,24)(25,26,27,28,29,30)(31,32,33,34,35,36), (1,7,4,10)(2,12,5,9)(3,11,6,8)(13,24,16,21)(14,23,17,20)(15,22,18,19)(25,35,28,32)(26,34,29,31)(27,33,30,36) );\n\nG=PermutationGroup([[(1,25,24),(2,26,19),(3,27,20),(4,28,21),(5,29,22),(6,30,23),(7,35,16),(8,36,17),(9,31,18),(10,32,13),(11,33,14),(12,34,15)], [(1,20,29),(2,21,30),(3,22,25),(4,23,26),(5,24,27),(6,19,28),(7,31,14),(8,32,15),(9,33,16),(10,34,17),(11,35,18),(12,36,13)], [(1,2,3,4,5,6),(7,8,9,10,11,12),(13,14,15,16,17,18),(19,20,21,22,23,24),(25,26,27,28,29,30),(31,32,33,34,35,36)], [(1,7,4,10),(2,12,5,9),(3,11,6,8),(13,24,16,21),(14,23,17,20),(15,22,18,19),(25,35,28,32),(26,34,29,31),(27,33,30,36)]])\n\nC3\u00d7C3\u22caDic3 is a maximal subgroup of\nC334C8\u00a0 C3\u00d7S3\u00d7Dic3\u00a0 C338(C2\u00d7C4)\u00a0 C337D4\u00a0 C334Q8\u00a0 C339(C2\u00d7C4)\u00a0 C339D4\u00a0 C335Q8\u00a0 C12\u00d7C3\u22caS3\u00a0 C32\u22caC36\u00a0 C32\u22caDic9\u00a0 C322Dic9\u00a0 C33\u22caDic3\u00a0 C334C12\u00a0 C33.Dic3\u00a0 He36Dic3\u00a0 C3\u22caDic3.2A4\nC3\u00d7C3\u22caDic3 is a maximal quotient of\nC334C12\u00a0 C33.Dic3\u00a0 He3.4Dic3\u00a0 He3.5C12\n\n36 conjugacy classes\n\n class 1 2 3A 3B 3C \u00b7\u00b7\u00b7 3N 4A 4B 6A 6B 6C \u00b7\u00b7\u00b7 6N 12A 12B 12C 12D order 1 2 3 3 3 \u00b7\u00b7\u00b7 3 4 4 6 6 6 \u00b7\u00b7\u00b7 6 12 12 12 12 size 1 1 1 1 2 \u00b7\u00b7\u00b7 2 9 9 1 1 2 \u00b7\u00b7\u00b7 2 9 9 9 9\n\n36 irreducible representations\n\n dim 1 1 1 1 1 1 2 2 2 2 type + + + - image C1 C2 C3 C4 C6 C12 S3 Dic3 C3\u00d7S3 C3\u00d7Dic3 kernel C3\u00d7C3\u22caDic3 C32\u00d7C6 C3\u22caDic3 C33 C3\u00d7C6 C32 C3\u00d7C6 C32 C6 C3 # reps 1 1 2 2 2 4 4 4 8 8\n\nMatrix representation of C3\u00d7C3\u22caDic3 in GL4(\ud835\udd3d13) generated by\n\n 9 0 0 0 0 9 0 0 0 0 3 0 0 0 0 3\n,\n 1 0 0 0 0 1 0 0 0 0 9 0 0 0 0 3\n,\n 10 0 0 0 2 4 0 0 0 0 1 0 0 0 0 1\n,\n 8 2 0 0 0 5 0 0 0 0 0 1 0 0 1 0\nG:=sub<GL(4,GF(13))| [9,0,0,0,0,9,0,0,0,0,3,0,0,0,0,3],[1,0,0,0,0,1,0,0,0,0,9,0,0,0,0,3],[10,2,0,0,0,4,0,0,0,0,1,0,0,0,0,1],[8,0,0,0,2,5,0,0,0,0,0,1,0,0,1,0] >;\n\nC3\u00d7C3\u22caDic3 in GAP, Magma, Sage, TeX\n\nC_3\\times C_3\\rtimes {\\rm Dic}_3\n% in TeX\n\nG:=Group(\"C3xC3:Dic3\");\n\/\/ GroupNames label\n\nG:=SmallGroup(108,33);\n\/\/ by ID\n\nG=gap.SmallGroup(108,33);\n# by ID\n\nG:=PCGroup([5,-2,-3,-2,-3,-3,30,483,1804]);\n\/\/ Polycyclic\n\nG:=Group<a,b,c,d|a^3=b^3=c^6=1,d^2=c^3,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d^-1=b^-1,d*c*d^-1=c^-1>;\n\/\/ generators\/relations\n\n\u05ff\n\u00d7\n\ud835\udd3d","date":"2021-10-28 07:29:23","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9619408249855042, \"perplexity\": 6816.666347426791}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-43\/segments\/1634323588282.80\/warc\/CC-MAIN-20211028065732-20211028095732-00555.warc.gz\"}"} | null | null |
Cold But Super
By using superconductors — wires cooled to extremely low temperatures — SuperPower creates electric power devices that promise huge energy savings and improvements in electrical transmission networks
After exiting I-890 in Schenectady, New York, I drive through working class neighborhoods on my way to visit SuperPower. Then, just past a church and convent, the plant comes into sight. The small company operates in a building dating back to 1875, originally built as a knitting mill but refurbished to give it a modern corporate appearance.
Even with the facelift, though, these are not the trappings you'd expect for SuperPower, a company engaged in the cutting-edge science of superconductivity. A bevy of technical people there undertake the daunting challenge of developing superconductors, materials that have no resistance to the flow of electricity when cooled to a very low temperature. SuperPower builds electric power components such as underground transmission cables, transformers, motors, generators, and fault current limiters incorporating superconductors. Why? Superconductors act as perfect conductors of electricity because they dissipate no energy by resistive heating; therefore, they hold tremendous promise for saving energy and improving the performance of these devices and, in turn, our nation's electrical grid.
Superconductivity ranks as one of the last frontiers of scientific discovery, as we have not reached its limits, and scientists haven't fully explained the theories behind it. Although it seems high-tech, superconductivity was actually first observed in 1911 when a researcher cooled mercury to the boiling point of helium, four degrees Kelvin (-452F, -269C). (You remember from high school science class that Kelvin represents a temperature scale with zero meaning absolute zero and equating to -456F).
The first major commercial application of superconductivity came with magnetic resonance imaging (MRI), commonly used today for clinical diagnosis. With this, a strong superconductor-driven magnetic field permeates the body, and hydrogen atoms in water and fat molecules accept energy from the magnetic field. They release this at a frequency detected and displayed graphically by a computer, generating an image of the injured area.
Meanwhile, two researchers at the IBM Research Laboratory in Switzerland opened the possibility of applying the technology to electric power devices in 1986 when they discovered ceramic-based high-temperature superconductors (HTS). Superconductors come in two flavors, low-temperature (LTS) and high-temperature, denoting the level to which a material must be cooled to become superconducting. In this game, "high-temperature" is relative, of course. LTS requires liquid helium for cooling, while HTS can get by with liquid nitrogen, which has a boiling point of a balmy 77K (-379F). This has great significance because nitrogen is cheaper than helium and requires less than a tenth the energy to cool it to its boiling point.
SuperPower traces its origins to Intermagnetics General Corporation (IGC), a manufacturer of superconducting products started in 1971 as a spinoff from General Electric. IGC makes magnets for MRI machines, which use LTS, and in 1988, the company formed a group to develop applications for HTS. In 2000, SuperPower became a separate company with the mission of commercializing electric power devices incorporating HTS technology. Some 20 people from IGC formed the company, and today, SuperPower numbers 56 people, 80 percent of them technical, including Ph.D.s and mechanical, electrical, and chemical engineers — President Phil Pelligrino is a electrical engineer.
Chuck Weber, project manager, describes SuperPower's mission from an engineer's point of view: "It's very exciting. I get to work on something that very few people in the world are doing, basically in my back yard. I never would've dreamed it was possible to do something to help change the way this country and the world delivers power, more efficiently and environmentally-friendly. I hope to see that come to pass in my lifetime." Weber hails from the area and has a B.S. in mechanical engineering from Union College in Schenectady and an MBA from Rensselaer Polytechnic Institute in nearby Troy, New York.
Reducing Transmission Losses Another major application of superconductivity, and the first for HTS, will come in the form of cable used to transmit electrical power. Up to ten percent of the electricity generated in the U.S. is lost because of the resistance inherent in conventional copper cables. The U.S. Department of Energy estimates using HTS could eliminate half this, reducing the use of fossil fuels, pollutants such as greenhouse gases, and subsequent global warming.
Drew Hazelton, principal engineer, says it goes even further. "The other main advantage with the HTS cables is the power density. With the same cross-sectional area, you can carry three to five times the amount of power. So in an urban area like New York City, you can pull out your old copper cable, put in HTS cable in the same ducts, and put three to five times the power through that." Hazelton also comes from the area and has a B.S. in materials engineering from RPI and an M.S. in mechanical engineering from Union College.
The challenge lies in producing the necessary lengths of cable and cooling them with cryogenics. As Weber tells it, "In this industry, we're bringing together cryogenic engineering expertise along with electrical utility environments. Putting those together is an extremely challenging task. There are very few people in the world that have experience with trying to do something at high voltage at those temperatures."
At the start, a first generation of superconductors (1G HTS) evolved using bismuth-based materials, and these demonstrated a variety of HTS power devices. Unfortunately, their high silver content and labor-intensive manufacturing process make 1G HTS too expensive for commercial applications.
Enter a second-generation conductor (2G HTS), which uses a new material consisting of yttrium, barium, and copper oxide (YBCO). This yields more than 10 times greater current density than 1G HTS, and because it uses nickel instead of silver, it cuts the production cost up to 80 percent. SuperPower has signed an agreement with Los Alamos National Laboratories to transfer technology for producing second-generation superconductors.
Their brittleness makes ceramic materials nearly impossible to form into conventional round wire, so they take a flat shape. While manufacturing 1G HTS wire involved a slow batch process, 2G HTS superconductors are produced in a continuous process using inexpensive metal alloy tape as a base substrate. Noel Rutter, thin film process engineer, reveals, "That's one of the major challenges, getting a ceramic material onto a flexible tape. The answer is to make it thin enough." Weber adds, "If you can imagine a semiconductor deposition process and now trying to do that on a moving tape for kilometers. You're making a very thin and long wafer."
The tape has five layers, the middle one being the ceramic layer, a tenth as thick as a human hair. Resulting 2G HTS tape measures 100 microns thick and typically a centimeter wide, with the process depositing a buffer, superconductor, and protective layers. SuperPower has multiple pieces of equipment for this, so they can run production on one line and conduct research on another.
Ready for Manufacture Reflecting on the fabrication process, Rutter says, "There's still research to be done, but we're at a stage where we can produce significantly long lengths." From England, Rutter has an academic background with a material science specialty. He did undergraduate and doctoral work at Cambridge University and then spent two years at Oak Ridge National Laboratory in Tennessee working on coating superconducting tapes, after which he returned to Cambridge as a post doc researcher.
Stepping into the manufacturing area for a tour, we first come to an aluminum ion deposition machine, the first in a line of machines for making tape. Wound on reels, tape feeds through the machines, with most processes done in a vacuum. Ken Lenseth, engineering project manager , joins us. With a B.S. in electrical engineering and a specialty in microelectronics from Rochester Institute of Technology, he came to SuperPower with expertise from the semiconductor industry.
Next we come to a machine for applying the YBCO ceramic conductor layer to the tape. Lenseth and Rutter throw around a big acronym, MOCVD, and tell me it stands for "metal organic chemical vapor deposition" system. Lenseth states, "That's the most important step." In applying the layers, they pump fluid through what he calls "a shower head," actually a nozzle.
Back in a conference room, I peruse a diagram of a superconductor cable with Weber. Many strands of tape form a helix around a copper core known as a former, which looks like a copper cable. Besides providing mechanical strength, the former protects the superconductor when a fault current occurs.
Weber then proceeds to give me a lesson in how cryogenics integrates with the cables. "All three electrical phases are contained in one pipe, and down that pipe, you flow liquid nitrogen, and it's pumped just like any other fluid. The trick is to keep the nitrogen at the proper temperature throughout the cable. Nitrogen is benign to the environment, but it does have some engineering headaches you have to overcome." If so-called warm spots occur, the nitrogen will go into the gaseous phase and expand very rapidly, as it has a gas-to-liquid volume ratio of 700 to one at room temperature, so tremendous pressure can build up inside the pipe. As the ultimate justification of superconductors, however, Weber adds that the energy required for cooling HTS cables is far less than the energy saved by having zero resistance in them.
The three wire assemblies fit within a cryostat, actually two coaxial corrugated stainless steel pipes with a vacuum space between them. The liquid nitrogen floods the space within the inner pipe and reaches the superconducting cable. "If you get a tremendous amount of current flowing through the center, you can create heat and vaporize that nitrogen. So you have to design for those kinds of upsets in the system," Weber explains. "Basically, you've got a 400-degree temperature differential across the space. Maintaining a good vacuum between the two pipes is the key." Standard electrical insulation covers the outside of the pipe assembly.
Sumitomo Electric Industries, one of Superpower's partners in the industry, has just developed a joint to splice sections of cable, enabling long lengths. Informal studies say you can pump liquid nitrogen about one kilometer to cool cable. For longer lengths, you place cryocooling units at required increments along the cable.
New Project on the Horizon To date, a handful of demonstration projects have been built to test superconducting cables. SuperPower began a four-year project in 2003 in partnership with the BOC Group, a refrigeration manufacturer; Sumitomo; and National Grid (formerly Niagara Mohawk Power Corporation). They're installing an underground power cable between two Niagara Mohawk substations in Albany, New York, with funding coming from the New York State Energy Research & Development Authority and the U.S. Department of Energy. The 350-meter-long installation will fit in a standard utility right-of-way with a test splice joint in the cable. The cryogenic refrigeration unit lies at one end and pumps to the other, after which liquid nitrogen circulates back through a separate return pipe in a continuous loop.
You can feel the excitement building for the Albany Cable Project at SuperPower as they enter the final months of installing equipment. They expect to have it complete and the cable energized by early this summer. Weber relates, "It's very exciting because you see all the hardware being installed." He acknowledges the risk that it won't work as they envision when they flip the switch, and it will become what he dubs "a four-year learning experience." This epitomizes working in the fledgling superconductor business. "You can have tremendous highs and lows. Hopefully, the highs are more frequent than the lows."
With all the potential superconductivity offers in transmission cables, its greatest impact may come with electric motors and generators. Initial applications will be in large AC induction motors over 1000 horsepower, typically used for continuous-duty pump and fan drives found in utilities and industries. They will eventually see use in motors as small as 300 HP. Motors consume roughly 64 percent of electrical energy generated in the U.S., and units greater than 1000 HP account for half of that.
HTS motors will be much more efficient than conventional types, saving significant energy. For example, a 5000-HP, 1800-rpm motor made with HTS would have an efficiency of 98.6 percent compared with 96.8 percent for a conventional type. That may not seem like much, but it reduces losses by as much as 50 percent. And HTS motors will be half as large as conventional ones.
In the construction of a motor or generator, the superconducting tape is woven into the windings of the rotor and stator. Liquid nitrogen is brought into the rotor through the center of the shaft to cool the windings there, using a rotating coupling. Somewhat complex, yes, but the cost of cryogenics pales in comparison to the cost of windings in large motors.
Transformers comprise another opportunity for superconductors. These convert voltage from generation level to transmission level, reducing the amount of energy lost in the transmission of power over long distances. HTS transformers operate at greater efficiency and don't require cooling oil like conventional types, eliminating the possibility of oil fires and environmental hazards. About a third the size of conventional transformers, they can be sited safely in urban areas or inside buildings.
One product SuperPower would make themselves completely is a fault current limiter. In today's high-voltage transmission network, the introduction of new generating facilities and network upgrades can result in fault-current overages on existing protective equipment. Installed in substations, SuperPower's HTS Matrix Fault Current Limiter reduces the fault current to a lower, safer level, so existing circuit breakers can still protect the electrical grid.
So where do superconducting devices stand on their way to commercialization? Weber reports, "Even at this early stage, there are a few niche applications where it would make sense for a utility to consider an HTS cable. As energy prices rise, that becomes more and more in our favor. The same for copper prices rising. We're coming down, while everything else is going up. Wherever that crossover occurs, whoever gets that right makes a lot of money." Weber realizes it will require a long-term selling job on the utility industry. "It's a very slow changing industry. Utilities aren't used to dealing with cryogenics. It's a big step for them to adopt this new technology."
But SuperPower is slowly making strides with superconductors, conquering one of the final frontiers of science in the process. Tremendous energy savings, an improved electrical grid, and a reduced occurrence of blackouts will result from their efforts. And who knows, someday they'll probably occupy a much bigger building than a former knitting mill next to a convent.
For more information on SuperPower, visit
www.igc-superpower.com
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Award-worthy Oscar party themes
By save | 12 February 2019
The 91st Academy Awards airs on February 24, 2019, and as always, it will be a star-studded event — with some surprises and delights, no doubt. While it's fine to watch alone, with a bag of chips in one hand and the remote in the other, it can also be fun to throw a soiree to celebrate Hollywood's biggest night.
Whether you're a movie buff or a celebrity gossip junkie — or both — it's fun to choose an appropriate party theme to suit your personal esthetic or a notable film from this year's nominees. Stumped on your Oscar party theme? Try one of these.
Golden Age of Hollywood
This theme is all about glam! Whether you send out paper or email invitations, they must be opulent and elegant. Make your dress code formal — it gives your friends a chance to dust off those old prom and bridesmaid dresses, as well as suits and tuxedos for the gents. Encourage creativity and think outside the box … maybe some of the gals want to rock a suit … so long as it's glam, anything goes!
Transform your living room into a ballroom and serve delicate hors d'oeuvres, such as a variety of canapés, on a silver platter. Champagne (or some sort of sparking wine or non-alcoholic beverage) must be served in fluted glasses.
Throughout the night give away awards for best dressed and so on. Make it a night to remember.
This theme hearkens back to a time when films were in black and white only. The dress code is simple — everyone must come dressed in black and white … and the fancier and more creative, the better! Ladies could wear black and white polka-dot or striped dresses. For men, a suit with a crisp white shirt and a black tie never goes out of style.
Use only black and white decor — from the tablecloths and napkins to the plates and cutlery. You can even get creative with the food, trying your best to keep it as on-theme as possible. Serve white pizza, black olives, dark chocolate cake with white frosting, popcorn, blackberries in glasses of sparkling white wine, and so on.
Give away prizes for the most creative costumes, and do a classic movie trivia quiz during commercial breaks.
PJ party
If you were planning on watching the Oscars in your pyjamas anyway, why not invite your friends to do it along with you? The dress code is comfy PJs and slippers. Pretty simple.
The decor should include blankets, pillows and stuffed animals galore. The menu can include pizza, buttered popcorn, hot chocolate, and cookies and milk (serve the milk in champagne flutes, if you want to be classy).
Print out some award prediction sheets, and give out prizes to those who get the most correct.
The best part is that when the show runs late, as it inevitably does, you are already dressed for bed.
Red carpet mania
Transform your living room into the red carpet and ask your guests to come dressed as a nominee or celebrity attendee. Use a fake microphone to interview guests as they arrive, and be sure to have a photographer to capture everyone's good side.
Create a photobooth-style background so that you can get those glamorous shots of your friends. And don't forget the swag bags! Yes, we all know Oscar attendees are given some pretty luxurious items. You could include small bottles of sparkling wine, gourmet chocolates and other silly items within your budget.
You can give away prizes for guessing which celebrity each guest is, and rate the real celebrity outfits as well.
So, there you have it: some Oscar party themes that will be sure to win over your friends. They will be talking about your party long after the shock and awe over the actual awards wears off.
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USS Bagley (FF-1069) was a of the United States Navy. She was the 18th ship of the Knox class, built as a destroyer escort (DE) and redesignated as a frigate (FF) in the 1975 USN ship reclassification. Bagley was the fourth ship of the USN named for Ensign Worth Bagley, the only US Navy officer killed in action during the Spanish–American War.
Construction and career
Bagley was laid down on 5 October 1970 at Seattle, Washington, by the Lockheed Shipbuilding and Construction Company. The ship was launched on 17 April 1971, sponsored by Mrs. Marie Louise H. Bagley, widow of Admiral David Worth Bagley and posthumous sister-in-law of Ensign Worth Bagley. The vessel was commissioned on 6 May 1972 at the Puget Sound Naval Shipyard.
1972–1979
The escort ship conducted acceptance trials along the coasts of Washington and British Columbia and then headed south for her new home port at San Diego, California, where she arrived on 25 July 1972. The warship began a restricted availability from 31 July to 9 September. She departed San Diego on 16 September, bound for Pearl Harbor and her shakedown cruise. Bagley arrived in Pearl Harbor on 22 September and operated in Hawaiian waters into October. On the 3d of that month, she stood out of Pearl Harbor and headed for San Diego. The warship reached that port on 9 October. Over the next month, she conducted exercises out of San Diego. On 15 November, Bagley entered the Long Beach Naval Shipyard and began an extended post-shakedown availability during which her main propulsion plant was converted to use Navy distillate fuel.
The warship completed repairs and modifications on 4 May 1973 and returned to San Diego that same day. She began training operations along the California coast three days later and continued those evolutions through most of the summer. She stood out of San Diego on 11 September and headed for the western Pacific. She conducted training operations in the Hawaiian Islands 17 September–26 and then resumed her westward voyage. She arrived in Yokosuka, Japan, on 5 October. A week later, the escort ship shaped a course for the Philippines. Bagley arrived in Subic Bay on 17 October for two days of upkeep and liberty. On the 19th, she weighed anchor and headed for a patrol station in the Gulf of Tonkin.
Ten days later, she received orders to accompany the aircraft carrier to the Indian Ocean. That contingency force went to the western portion of the Indian Ocean in response to hostilities that had broken out between Israel and her neighbors, Egypt and Syria (the Yom Kippur War). Bagley spent the next seven weeks on patrol in the Indian Ocean as an indication of American resolve to end the fighting in the Middle East and as a deterrent to keep Soviet forces from intervening in the conflict. During that time, she and the guided missile destroyer entered the Red Sea and docked at the port of Masawa, Ethiopia for a few days.
On 17 December 1973, Bagley reentered Subic Bay for an extended leave and upkeep period. For the remainder of the deployment, the warship participated in the usual 7th Fleet exercises punctuated by port visits to Hong Kong; Keelung, Taiwan; Buckner Bay, Okinawa; Pusan, Korea; and Yokosuka, Japan. On 20 February 1974, she departed Yokosuka and began the voyage home. The warship stopped at Midway Island and Pearl Harbor before arriving in San Diego on 8 March.
For the rest of 1974 and the first six months of 1975, she operated out of San Diego conducting a series of exercises, inspections, and qualifications. On 30 June 1975, Bagley was redesignated a frigate, FF-1069. The warship spent the month of July 1975 preparing for her second deployment to the Far East. She stood out of San Diego on 1 August. Following stops at Pearl Harbor and Guam, the frigate arrived in Subic Bay on 13 September. For the next five months, Bagley conducted normal operations—training evolutions and port visits—with ships of the 7th Fleet. She departed Subic Bay on 12 February 1976 to return to the United States. She stopped at Pearl Harbor from 26 February to 3 March before continuing on to San Diego where she arrived on 1 April. She resumed normal operations out of San Diego, and continued that duty into 1977.
On 17 February 1977, she shaped a course for Hawaiian waters where she joined ships of the American, Australian, Canadian, and New Zealand navies in Exercise RIMPAC 77. The frigate returned to San Diego on 12 March and, two days later, was drydocked in the Long Beach Naval Shipyard for hull repairs. She came out of drydock on 2 April and returned to San Diego on the 6th.
Bagley weighed anchor again 12 April 1977 and set course for the Orient. She made the usual stopover at Pearl Harbor and arrived in Subic Bay on 6 May. During this six months in the Far East, the frigate visited most of the usual liberty ports and participated in a number of training exercises with other ships of the 7th Fleet. On 6 November, she departed Yokosuka for an uninterrupted voyage to San Diego. The warship reentered her home port on 21 November and remained there through the end of the year.
The frigate conducted normal operations out of San Diego during the first six weeks of 1978. On 14 February 1978, she entered the Long Beach Naval Shipyard for an overhaul that occupied the rest of 1978. She completed post-overhaul trials and tests in January 1979 and resumed operations out of San Diego early in February. Exercises, qualifications, and tests in the southern California operating area occupied her throughout 1979 and for most of the first two months of 1980. The warship departed San Diego on 25 February, bound ultimately for the Far East. En route to the western Pacific, however, she participated in the multinational Exercise RIMPAC 80 conducted in the Hawaiian Islands. She resumed her voyage west on 19 March and entered Subic Bay on 8 April.
1980–1989
After conducting training operations—notably gunfire support drills and ASROC firings—in the Subic Bay operating area, Bagley departed the Philippines late in April in company with a task force built around the aircraft carrier . The task force constituted a part of the increased American military presence in the western Indian Ocean deemed necessary after radical Iranian students occupied the American embassy in Tehran and took the American diplomatic staff hostage. The continuing hostage crisis and hostilities between Iran and Iraq kept a large number of Navy ships on patrol in nearby waters. Bagleys task force remained in the vicinity until 29 July when it headed back to the Pacific. En route to the Philippines, she stopped at Singapore and at Pattaya, Thailand. She reentered Subic Bay on 20 August with 36 Vietnamese refugees whom she had rescued on the passage from Thailand. Bagley voyaged to Pusan, Korea, for a goodwill port call in mid-September and returned to Subic Bay on 23 September. On 1 October, the frigate got underway to return to the United States. After the customary pause at Pearl Harbor, Bagley arrived back in San Diego on 15 October. Except for a brief period underway on 20 November, the frigate remained in port at San Diego for the remainder of 1980.
She continued the inport period through the first seven weeks of 1981. On 18 February, Bagley resumed normal operations in the southern California operating area. Fleet exercises and single ship drills occupied her until 20 October 1981 when she again headed for the Far East. She stopped at Pearl Harbor 31 October – 2 November and then resumed her voyage west. Bagley arrived in Subic Bay on 22 November. She operated out of Subic Bay until early when she headed for the Indian Ocean. En route to Indian Ocean contingency operations, the warship encountered Vietnamese refugees adrift in a boat in the South China Sea. She took the boat's 37 occupants on board, sank the boat as a potential hazard to navigation, and proceeded to Singapore where she disembarked the refugees. The frigate resumed her voyage to the Indian Ocean on 12 December and arrived at Al Masirah, Oman, on the last day of 1981.
The year 1982, opened with Bagley operating in the western Indian Ocean and in the Arabian Sea. That deployment lasted until late January when she made a port visit to Mombasa, Kenya, before heading back to the Far East. On that journey, she took a very circuitous route, visiting the Australian port of Geraldton, Diego Garcia Island, and Penang in Malaysia, before returning to Subic Bay in mid-April. Late in April and early in May, Bagley took part in readiness exercises carried out near Guam in company with Constellation, and . At the conclusion of those evolutions on 8 May, the frigate set a course, via Hawaii, to the west coast and reentered San Diego on 23 May. After the customary month of post-deployment leave and upkeep, Bagley resumed normal training duty in California waters and remained so occupied for the rest of the year.
Local operations out of San Diego kept the frigate busy well into 1983. She did not set out for another overseas assignment until 9 June when she put to sea, once again bound for the western Pacific. Along the way, Bagley and her travelling companions , , , and spent a week in the Hawaiian Islands in mid-June before resuming the voyage west on the 17th. The warships "INCHOPped" (changed operational control) to the Commander, 7th Fleet, on 27 June and reached the Philippines at Manila on Independence Day 1983. Over the next five months, the frigate took part in a number of exercises at sea, most often with a task group built around Midway, and visited a series of Far Eastern ports. Late in July, she visited Singapore and Thailand before heading for a set of exercises in Korean waters carried out at the end of July and during the first part of August. After a call at Guam in late August and early September, Bagley steamed to Sasebo, Japan, whence she operated until the first week in November when she returned to the Philippines at Subic Bay. The warship made one more stop at a Japanese port, Yokosuka, and then headed back to the United States on 1 December. She called briefly at Pearl Harbor before arriving back in San Diego on 13 December 1983.
Post-deployment leave and upkeep kept Bagley immobile at San Diego for the rest of the year and during the first half of January 1984. In fact, despite a short two-day period underway between 17 and 19 January, she did not resume normal west coast operations until the second week in February when she put to sea for READIEX 84-2 and a cruise to the Pacific coast of Central America. Bagley returned to San Diego from those missions on 9 March and remained there until 22 March. At that time, the warship headed north to Esquimalt, British Columbia, where she took part in CNO Project 371, tests on new submarine torpedo designs. She completed her part in the tests on 30 March and, after visits to Vancouver, British Columbia, and to San Francisco, returned to San Diego on 11 April. Just over a month after her return, Bagley began an eight-month regular overhaul at the naval station.
Bagley completed the overhaul on 19 January 1985 and embarked upon more than four months of post-overhaul checks, qualifications, and certifications. These she carried out in a long series of short underway periods in nearby waters. Late in May, the frigate participated in Exercise EASTPAC 85-5 conducted in late May and early June. At the conclusion of the evolution, Bagley called at Portland, Oregon, for that city's Rose Festival and then moved on to Concord, California, to load ammunition. "Bagley" then visited San Francisco before returning to San Diego on 22 June. Except for another visit to CFB Esquimalt in September, followed by Bagleys arrival in San Francisco, on 12 October 1985, for the start of Navy Fleet Week '85 activities. Bagley operated locally out of San Diego for the remaining months of the year.
Her west coast employment came to an end early in 1986. On 15 January, the warship set out on her first overseas deployment in two years as part of a task group built around the aircraft carrier . After reaching Pearl Harbor on 21 January, she spent the rest of January in Hawaii taking part in a series of exercises and then resumed her voyage to the Far East on 2 February. Bagley arrived in Subic Bay on 17 February and made a port of call in Olongapo City. Bagley operated locally in the waters off of the coast of the Republic of the Philippines for the rest of the month. Early in March, the frigate's task group visited Singapore on the way to duty in the eastern Indian Ocean, the Arabian Sea, and the Mediterranean Sea. While operating in the "I.O." Bagley briefly anchored off of the coast of Mombasa, Kenya, however the crew was denied liberty there, due to concerns over the AIDS epidemic there. After months in the Indian Ocean, Bagley participated in joint exercises with units of the Pakistani Navy. Then, she stopped off at Karachi, Pakistan, between 15 and 17 March before dropping anchor at Masirah Island, Oman, on the 18th. On 9 April, Bagley set out for Diego Garcia Island at which place she called briefly on the 12th before shaping a course for the Suez Canal.
The Enterprise battle group, "Battle Group Foxtrot," transited the canal on 28 and 29 April 1986 and arrived in the Mediterranean to reinforce American forces there which were already engaged in "Operation El Dorado Canyon," a series of retaliatory actions against the provocations and terrorist activities of Libya's Colonel Muammar al-Gaddafi. Bagley and her battle group spent the next two months cruising the Mediterranean in support of American foreign policy, and patrolling along the "Line of death", While operating in the Mediterranean Sea, Bagley made ports of call in Monte Carlo, the Principality of Monaco, Gaeta, Italy and Catania, on the island of Sicily. On 28 June, she left Catania, Italy, steamed through the Suez Canal, crossed the Indian Ocean, and arrived in Subic Bay on 17 July. She returned to sea with the task group on the 22nd bound for home. After the customary port of call at Oahu, where Bagley picked up family members of the crew, for the "Tiger Cruise" portion of the deployment, back to home port, the warship reentered San Diego on 11 August. Bagley earned the Meritorious Unit Commendation Ribbon and the Navy Expeditionary Medal for its outstanding service during operations while on deployment, as well as another Sea Service Ribbon. Bagley returned from its extended deployment, having conducted operations in three of the U.S. Navy's four active fleets, and began an extended post-deployment standdown period soon after! In fact, the left port only briefly on four occasions in October; the rest of the year she spent in San Diego.
Another series of four brief underway periods in January 1987 punctuated a month otherwise spent largely in upkeep. In February, she traveled to Concord where she unloaded ammunition before beginning a restricted availability at San Diego on the 16th. The repair period lasted until early summer and included a seven-week drydocking in that occupied most of April and all of May. Late in June 1987, Bagley resumed normal operations out of San Diego; and, except for operations in the Bering Sea that took up most of November, she remained active in the immediate vicinity of San Diego for the rest of the year.
As 1987 waned and 1988 began, however, Bagley anticipated imminent departure for overseas duty. She stood out of San Diego on 4 January 1988 in company once more with the Enterprise task group. The warships made an unusual nonstop, but leisurely, Pacific crossing during which they carried out a five-day readiness exercise in the Hawaiian operating area. The frigate and her colleagues reached Subic Bay in the Philippines on 1 February and remained in that port until the 6th. On that day she and the other warships in the group got underway for a tour of duty in the Arabian Sea, returning once more to a region of chronic political convulsions spawned by a decade of Iranian provocations. En route to the Arabian Sea, Bagley participated in a series of exercises with units of the Indonesian Navy. She and her units reached their destination at mid-month and relieved the Midway task group as contingency force on station. For about two months, Bagley patrolled the waters of the northern Arabian Sea with her task group with the only untoward event being the loss of her helicopter which ditched because of a material casualty.
During Operation Earnest Will, struck an Iranian mine and suffered severe damage on 14 April 1988. Bagley was one of the warships selected to retaliate on the Iranians in Operation Praying Mantis. Accordingly, she joined and on 18 April, and the three warships steered for the Sirri Island oil platform which they then put out of operation with gunfire. Soon after destroying the oil platform, the trio engaged the Iranian patrol boat with surface-to-surface missiles and finished her off with gunfire. When a Marine Corps AH-1 Cobra helicopter operating from Wainwright failed to return after the actions of the 18th, Bagley spent the next two days engaged in a futile search for the missing aircraft and its crew. It became apparent that the helicopter went down during the operation when the bodies of the crew, Marine Corps Captains Stephen C. Leslie and Kenneth W. Hill were recovered almost a month later about southeast of Abu Musa Island.
Late in April 1988, Bagley and escorted and through the Strait of Hormuz into the Arabian Sea. The warship then resumed operations in the northern reaches of that sea. That employment lasted until 15 May when Bagley parted company with the task unit and joined in setting a generally easterly course. After exercises with units of the Indonesian and Malaysian navies and a series of port calls in the Philippines and along the coast of the Asian continent, the warship set out from Pusan, Korea, on 17 June to return to the United States. She stopped off at Seattle to embark a group of male relatives and friends of her crewmen for the last leg of the voyage home and completed this "Tiger" portion of the journey at San Diego on 2 July.
After more than a month of post-deployment standdown at San Diego, Bagley resumed normal duty training in waters along the west coast. Exercises, drills, and inspections—the normal fare of west coast operations—occupied the warship for the remainder of 1988 and the first two months of 1989. She entered drydock in Steadfast at San Diego at the end of February 1989 and remained docked for the entire month of March. Exiting the drydock on 4 April, she continued repairs and the installation of new equipment until mid-May. At that time she resumed her schedule of west-coast training missions and continued so engaged through the summer.
On 18 September 1989, Bagley embarked once again on the long voyage to the Far East and another several months of service there and in the Arabian Sea. This particular passage to the Orient, however, played out differently than most because the frigate and her task group remained at sea for more than a month before entering port in the Far East. Bagleys unit rendezvoused with two other units—one built around the aircraft carrier and the other around Constellation—and sailed north to conduct the exercise Operation PACEX 89 in the vicinity of the Aleutian Islands during the period between 20 September and 30. In October, the warship took part in Operation ANNUALEX 89 with the Carl Vinson group augmented by the battleships and USS New Jersey. That exercise ranged westward across the northern Pacific and then north into the Sea of Japan. At one point in the massive operation, elements of the Japanese Maritime Self-Defense Force joined American warships and planes in carrying out bilateral training in the waters surrounding Okinawa. The crossing, prolonged by the exercise, ended with Operation Valiant Blitz carried out with units of the South Korean Navy in the Sea of Japan.
On 31 October 1989, Bagley and her colleagues made their first port of call since leaving North America in mid-September when they arrived in Hong Kong. After nearly a week of liberty, the warship returned to sea with the task group on 6 November for the voyage to the Philippines and arrived in Subic Bay on the 11th. She spent the next four weeks either in port at Subic Bay or operating in nearby waters. On 10 December, she set out for a tour of duty with the contingency forces operating in the Arabian Sea. Along the way, she made a liberty call at Pattaya Beach, Thailand, another at Singapore, and a resupply stop a Diego Garcia Island before arriving on station in the Arabian Sea in mid-January 1990. Her stay in the troubled region proved a brief one, however, for she called only once at a local port, Muscat in Oman between the 20th and the 22d, and cleared the region entirely early in February 1990. After visits to Penang, Malaysia, and Subic Bay, Bagley set out on the voyage home on 23 February. She stopped along the way at Pearl Harbor in Hawaii and reentered San Diego on 16 March 1990.
Decommissioning
Following the customary post-deployment standdown, the frigate put to sea on 27 April to take up normal west coast training missions once again. For almost 10 months, she carried out the usual schedule of drills, exercises, and inspections punctuated with visits to variety of ports in the United States and Canada. She continued so occupied through 1990 and into the early months of 1991. In February 1991, however, Bagley embarked upon a brief, but novel, phase of her career when she left San Diego on the 15th bound for the coast of Central America for two months of drug interdiction duty. During that period, she cruised the Pacific coasts of Guatemala, El Salvador, Panama and Costa Rica stopping and inspecting fishing boats and other small craft and carrying out air tracking operations. The warship concluded the assignment on 3 April and headed back to San Diego where she arrived on the 9th. Over the last five months of her active service, the warship spent a lot of time in port at San Diego. She did put to sea occasionally both to prepare for her final material inspection or to visit ports farther up the coast. She returned to San Diego from her last underway period on 8 July 1991 and secured fires for the last time. After almost 12 weeks of final preparations, Bagley was decommissioned at San Diego on 26 September 1991. Her name was stricken from the Naval Vessel Register on 11 January 1995 and later sold for scrapping. Bagley was cut up and recycled by the end of September 2000.
References
External links
Navysite.de Photos
NavSource images
NDAWS Awards Navy Military
Ships built by Lockheed Shipbuilding and Construction Company
Knox-class frigates
1971 ships
Cold War frigates and destroyer escorts of the United States | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 2,611 |
Q: jQuery hide IE mess up Could anyone let me know why the hide and show boxes are playing up when you click contact?
They only do this in IE. I cannot seem to fix the problem.
This is the website: http://molossi.psm2.co.uk/
Thanks :)
EDIT: Here is a picture of on of the issues on IE.This is taken after I have clicked Contact then Cancel. I have zoomed out to 75% to capture more.
A: It is working fine for me when I tested the link in IE...I think this css is causing the problem:
/*Win IE browsers - hide from Mac IE\*/
* html #main-nav { margin-top:20px; }
* html #main-nav li { display:inline; float:left; }
/*End hide*/
When you click on contact it shows a div below the navigation-bar and when you cancel it loads a separate div outside of navigation-bar div. So in your browser somehow the switching among nav-bar and outside div is not happening as it should be.
Try to concentrate on main-nav property of the css. Maybe line-height or margin-top or height is causing this.
A: You need to add a doctype in order to use Standards Mode and you should validate your HTML and CSS:
http://validator.w3.org/check?verbose=1&uri=http%3A%2F%2Fmolossi.psm2.co.uk%2F
http://jigsaw.w3.org/css-validator/validator?profile=css21&warning=0&uri=http%3A%2F%2Fmolossi.psm2.co.uk%2F
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,884 |
Regencós – gmina w Hiszpanii, w prowincji Girona, w Katalonii, o powierzchni 6,29 km². W 2011 roku gmina liczyła 295 mieszkańców.
Przypisy
Gminy w Katalonii | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,140 |
The SCCA's US series was initially for 3-litre FA plus classes for FB and FC. These classes had started in 1965 but with only appeared at the Road Race of Champions for the first time in 1966. The 5-litre cars joined in for the 1968 season with the smaller classes being separated off at the end of that year. The SCCA decided to replace F5000 with a new Single-Seat Can-Am for 1977. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,226 |
Q: Race Condition inside Parallel.Foreach with List I need help on how to resolve this race condition. Below is the code:
Task.Factory.StartNew(Sub()
' Do something...
dim newPeople as new List(Of Person)
dim myNames as ConcurrentBag(Of String) = GetNames()
Parallel.ForEach(myNames, Sub(name)
Dim person as new Person
person.Name = name
person.Gender = "MALE"
newPeople.Add(person)
GridView.BeginInvoke(Sub()
GridView.DataSource = newPeople
End Sub)
' Do something...
dim index as Integer = newPeople.FindIndex(Function(p) p.Name = name) ' Race condition error
newPeople(index).Gender = "FEMALE"
GridView.Invoke(Sub()
GridView.DataSource = newPeople
End Sub)
End Sub)
End Sub, param ,TaskCreationOptions.None)
What this code basically does is this:
*
*Set the name and gender of the person in the object
*Add this person object in the person list
*Display in grid view (to display the before and after)
*After do something, change the gender of person
*Display in gridview after the person element has been updated.
End Result: The gridview will automatically change the status during the execution of the tasks.
I'm running out of ideas on how to get past this. Could you suggest anything to resolve this?
A: I think I found the answer. It is by changing List(Of T) to ConcurrentBag(Of T) resolved the issue. According to the this link
The ConcurrentBag<T> collection, in the System.Collections.Concurrent
namespace, provides a multiset that is thread-safe. The collection
allows you to add and remove items freely from multiple threads
without having to worry about thread synchronisation. The fact that
the bag has no ordering allows it to be particularly efficient when
you have multiple threads or parallel tasks where each both adds and
removes items.
| {
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} | 2,286 |
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<title>RemoteSyslogAppender.ActivateOptions Method</title>
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<h1 class="dtH1">RemoteSyslogAppender.ActivateOptions Method </h1>
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<p> Initialize the options for this appender </p>
<div class="syntax">
<span class="lang">[Visual Basic]</span>
<br />Overrides Public Sub ActivateOptions() _<div> Implements <a href="log4net.Core.IOptionHandler.ActivateOptions.html">IOptionHandler.ActivateOptions</a></div></div>
<div class="syntax">
<span class="lang">[C#]</span>
<br />public override <a href="http://msdn.microsoft.com/library/default.asp?url=/library/en-us/cpref/html/frlrfSystemVoidClassTopic.asp">void</a> ActivateOptions();</div>
<h4 class="dtH4">Implements</h4>
<p>
<a href="log4net.Core.IOptionHandler.ActivateOptions.html">IOptionHandler.ActivateOptions</a>
</p>
<h4 class="dtH4">Remarks</h4>
<p> Initialize the level to syslog severity mappings set on this appender. </p>
<h4 class="dtH4">See Also</h4><p><a href="log4net.Appender.RemoteSyslogAppender.html">RemoteSyslogAppender Class</a> | <a href="log4net.Appender.html">log4net.Appender Namespace</a></p><hr /><div id="footer"><p><a href="http://logging.apache.org/log4net">Copyright 2001-2006 The Apache Software Foundation.</a></p><p>Generated from assembly log4net [1.2.10.0]</p></div></div>
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"redpajama_set_name": "RedPajamaGithub"
} | 5,377 |
{"url":"https:\/\/statsandr.com\/blog\/paper-epilps-a-fast-and-flexible-bayesian-tool-for-estimation-of-the-time-varying-reproduction-number\/","text":"# Introduction\n\nA colleague (and friend) of mine recently published a research paper entitled \u201cEpiLPS: A fast and flexible Bayesian tool for estimation of the time-varying reproduction number\u201d in PLoS Computational Biology.\n\nI am not in the habit of sharing research paper to which I did not contribute. Nevertheless, I would like to make an exception with this one because I strongly believe that the method developed in the paper deserves to be known, especially for anyone working in epidemiology.\n\nBelow is the motivation behind the article, as well as an illustration on simulated and real data (US hospitalization data). More information can be found in the paper and on the accompanying website.\n\n# Motivation\n\nEpiLPS is a methodology for flexible Bayesian inference of the time-varying reproduction number $$\\mathcal{R}_t$$; the average number of secondary cases generated by an infected agent at time $$t$$. This is a key epidemiological parameter that informs about the transmission potential of an infectious disease and can be used by public health authorities to gauge the effectiveness of interventions and propose an orientation for future control strategies.\n\nThis metric has gained in popularity during the SARS-CoV-2 pandemic with wide media coverage as its meaning is easily and intuitively grasped. Put simply, when $$\\mathcal{R} < 1$$, the signal is encouraging as the epidemic is under control and will eventually vanish. On the contrary, a value of $$\\mathcal{R} > 1$$ means that the disease keeps spreading and infections are witnessing an expansionary impact. Having a robust and reliable tool to compute the reproduction number from infectious disease data is therefore crucial.\n\nA group of researchers in the EpiPose team from Hasselt University (Belgium), Leiden University (The Netherlands), and the University of Bern (Switzerland) have recently developed a new methodology for estimating the instantaneous reproduction number from incidence time series data for a given serial interval distribution (the time elapsed between the onset of symptoms in an infector and the onset of symptoms of secondary cases).\n\nThey termed their approach EpiLPS for \u201cEpidemiological modeling with Laplacian-P-Splines\u201d as Laplace approximations and P-splines smoothers are key ingredients that form the backbone of the proposed methodology.\n\nThe EpiLPS model assumes that the observed reported cases (by reporting date or date of symptom onset) are governed by a negative binomial distribution. As such, it allows to take the feature of overdispersion into account, contrary to a Poisson model. The epidemic curve is smoothed with P-splines (where posterior estimates of latent variables are computed via Laplace approximations) in a first step and a renewal equation model is used in a second step as a bridge between the reproduction number and the estimated spline coefficients through a \u201cplug-in\u201d method.\n\nThe authors also explain the main difference between EpiLPS and EpiEstim, a well established approached for estimating $$\\mathcal{R}_t$$ in real-time developed by Cori et al. (2013) and make extensive comparisons between the two approaches under different epidemic scenarios.\n\nAn interesting feature of EpiLPS is that the user can choose between a fully \u201csampling-free\u201d path, where model hyperparameters are fixed at their maximum a posteriori (LPSMAP) or a fully stochastic path (LPSMALA) based on a Metropolis-adjusted Langevin algorithm (LPSMALA). Talking about efficiency, routines for Laplace approximations and B-splines evaluations have been coded in C++ and integrated in R via the Rcpp package, so that the underlying algorithm can be executed in negligible time.\n\nBelow, we provide a short example of how to use the EpiLPS routines to estimate $$\\mathcal{R}_t$$.\n\n# Getting started\n\nThe EpiLPS package is available from CRAN (see https:\/\/cran.r-project.org\/web\/packages\/EpiLPS\/index.html) and can be installed from the R console by typing:\n\ninstall.packages(\"EpiLPS\")\n\nThe package can then be loaded as follows:\n\nlibrary(\"EpiLPS\")\n\nThe EpiLPS package structure is fairly simple as it consists in a few routines:\n\n\u2022 The function epilps() is the core routine for fitting the reproduction number.\n\u2022 With plot.epilps(), the user can plot the estimated epidemic curve and $$\\mathcal{R}_t$$.\n\u2022 Finally, two ancillary routines, episim() and perfcheck() have been developed to essentially reproduce the simulation results of the associated paper.\n\n# A simulated example\n\nA set of epidemic data can be simulated with the episim() routine by specifying a serial interval distribution and by choosing among a set of available patterns for the true reproduction number curve (here we choose pattern number 5 corresponding to a rather wiggly curve).\n\nThe simulated outbreak is for a duration of 40 days as specified in the endepi option. By setting the option plotsim = TRUE, the routine returns a figure summarizing the incidence time series, a bar plot for the specified serial interval distribution and the true underlying reproduction number curve.\n\nset.seed(1234)\n\nSI <- c(0.344, 0.316, 0.168, 0.104, 0.068)\nsimepidemic <- episim(\nserial_interval = SI,\nRpattern = 5,\nplotsim = TRUE,\nverbose = TRUE,\nendepi = 40\n)\n## Chosen scenario: 5 'Wiggly then stable Rt'.\n## Incidence of cases generated from a Poisson distribution.\n## Total number of days of epidemic: 40.\n\nIf you want to have an overview of the generated incidence time series, just type:\n\nsimepidemic$y ## [1] 10 6 15 24 37 43 54 46 47 28 20 8 10 10 3 5 3 4 6 ## [20] 6 15 21 44 75 135 217 329 409 453 487 457 443 297 290 255 246 246 339 ## [39] 395 573 ## Smoothing the epidemic curve and estimating $$\\mathcal{R}_t$$ Let us now use the epilps() routine to smooth the epidemic curve and estimate the reproduction number. We will do this through LPSMAP (a fully sampling-free approach) and via LPSMALA (a fully stochastic approach relying on a MCMC algorithm with Langevin dynamics), where we specify a chain of length 10000 and a burn-in of size 4000. LPSMAP_fit <- epilps( incidence = simepidemic$y,\nserial_interval = SI,\ntictoc = TRUE\n)\n## Inference method chosen: LPSMAP.\n## CI for LPSMAP computed via lognormal posterior approx. of Rt.Total number of days: 40.\n## Mean Rt discarding first 7 days: 1.327.\n## Mean 95% CI of Rt discarding first 7 days: (1.164,1.527)\n## Elapsed real time (wall clock time): 0.261 seconds.\nLPSMALA_fit <- epilps(\nincidence = simepidemic$y, serial_interval = SI, method = \"LPSMALA\", chain_length = 10000, burn = 4000 ) ## Inference method chosen: LPSMALA with chain length 10000 and warmup 4000. ## MCMC acceptance rate: 56.41%. ## Geweke z-score < 2.33 for: 32 \/ 33 variables. ## Total number of days: 40. ## Mean Rt discarding first 7 days: 1.326. ## Mean 95% CI of Rt discarding first 7 days: (1.117,1.555). ## Timing of routine not requested. After execution, each routine prints in the console a brief summary of the method that has been requested by the user. For LPSMALA, it summarizes the chain length, the acceptance rate (should be around 56%) and other basic information. As can be seen from the printed output, the mean reproduction number for the simulated epidemic is around 1.33. We can now use, say, the LPSMALA_fit object together with the plot() routine to obtain the smoothed epidemic curve and the estimated reproduction number (by default the credible interval is at a 5% level of significance but this can be changed by the user). days <- seq(8, 40) #--- Smoothed epidemic curve gridExtra::grid.arrange( plot(LPSMALA_fit, plotout = \"epicurve\", incibars = TRUE, themetype = \"light\", epicol = \"darkgreen\", cicol = rgb(0.3, 0.73, 0.3, 0.2), epititle = \"Smoothed epidemic curve\", titlesize = 13, barwidth = 0.25 ), #--- Estimated reproduction number plot(LPSMALA_fit, plotout = \"rt\", theme = \"light\", rtcol = \"black\", titlesize = 13, Rtitle = \"Estimated R (LPSMALA)\" ), nrow = 1, ncol = 2 ) The figure can be customized in various ways: \u2022 Users can specify the theme under themetype. Available options are gray (the default), classic, light and dark. \u2022 Other choices, such as whether or not to show the incidence bars, the color of the credible interval envelope, the color of the smoothed epidemic curve and the estimated reproduction number are also available. The figure above was generated within the ggplot2 package, but there is also another way of extracting information directly from the LPSMAP_fit and LPSMALA_fit objects. In fact, the estimated reproduction number values and their associated credible interval for each day can be extracted and plotted. Below, we make the exercise and plot the estimated $$\\mathcal{R}_t$$ obtained with LPSMAP and LPSMALA, respectively and compare it with the true underlying reproduction number curve. The fit is quite good. par(mfrow = c(1, 2)) #--- LPSMAP vs target R plot(days, sapply(days, simepidemic$Rtrue),\ntype = \"l\", lwd = 2, ylim = c(0, 4),\nylab = \"Estimated R\", xlab = \"Time\"\n)\npolygon(\nx = c(days, rev(days)), y = c(\nLPSMAP_fit$epifit$R95CI_low[8:40],\nrev(LPSMAP_fit$epifit$R95CI_up[8:40])\n),\ncol = rgb(0.23, 0.54, 1, 0.3), border = NA\n)\nlines(days, LPSMAP_fit$epifit$R_estim[8:40], type = \"l\", col = \"cornflowerblue\", lwd = 2)\nlines(days, sapply(days, simepidemic$Rtrue), type = \"l\", lwd = 2) grid(nx = 10, ny = 10) legend(\"topright\", lty = c(1, 1), lwd = c(2, 2), col = c(\"black\", \"blue\", rgb(0.23, 0.54, 1, 0.3)), c(\"Target R\", \"LPSMAP\", \"LPSMAP 95% CI\"), bty = \"n\", cex = 0.9 ) #--- LPSMALA vs target R plot(days, sapply(days, simepidemic$Rtrue),\ntype = \"l\", lwd = 2, ylim = c(0, 4),\nylab = \"Estimated R\", xlab = \"Time\"\n)\npolygon(\nx = c(days, rev(days)), y = c(\nLPSMALA_fit$epifit$R95CI_low[8:40],\nrev(LPSMALA_fit$epifit$R95CI_up[8:40])\n),\ncol = rgb(1, 0.23, 0.31, 0.3), border = NA\n)\nlines(days, LPSMALA_fit$epifit$R_estim[8:40], type = \"l\", col = \"red\", lwd = 2)\nlines(days, sapply(days, simepidemic$Rtrue), type = \"l\", lwd = 2) grid(nx = 10, ny = 10) legend(\"topright\", lty = c(1, 1), lwd = c(2, 2), col = c(\"black\", \"red\", rgb(1, 0.23, 0.31, 0.3)), c(\"Target R\", \"LPSMALA\", \"LPSMALA 95% CI\"), bty = \"n\", cex = 0.9 ) You can access, say, the results of the last week of the epidemic by typing: # Estimated R of the last week (with LPSMAP) round(tail(LPSMAP_fit$epifit[, 1:4], 7), 3)\n## Date R_estim R95CI_low R95CI_up\n## 34 34 0.708 0.663 0.756\n## 35 35 0.724 0.676 0.775\n## 36 36 0.809 0.755 0.868\n## 37 37 0.971 0.908 1.039\n## 38 38 1.205 1.135 1.279\n## 39 39 1.461 1.384 1.541\n## 40 40 1.671 1.557 1.794\n# Estimated mean number of cases of the last week (with LPSMAP)\nround(tail(LPSMAP_fit$epifit[, 5:7], 7)) ## mu_estim mu95CI_low mu95CI_up ## 34 284 225 357 ## 35 254 202 319 ## 36 248 196 312 ## 37 267 211 338 ## 38 319 253 404 ## 39 411 325 520 ## 40 552 394 774 # USA hospitalization data To illustrate EpiLPS on real data, we download hospitalization data from the COVID19 package for the USA in the period ranging from 2021-09-01 to 2022-09-01 and apply the epilps() routine to estimate the reproduction number. install.packages(\"COVID19\") library(\"COVID19\") # Get data and specify serial interval distribution USADat <- COVID19::covid19( country = \"US\", level = 1, start = \"2021-09-01\", end = \"2022-09-01\", verbose = FALSE ) si <- c(0.344, 0.316, 0.168, 0.104, 0.068) inciUSA <- USADat$hosp\ndateUSA <- USADat\\$date\n\nWe use the epilps() routine with method LPSMAP (default) and plot the smoothed epidemic curve and the estimated reproduction number with a 95% credible interval.\n\nepifit <- epilps(incidence = inciUSA, serial_interval = si, K = 20)\n## Inference method chosen: LPSMAP.\n## CI for LPSMAP computed via lognormal posterior approx. of Rt.Total number of days: 366.\n## Mean Rt discarding first 7 days: 0.994.\n## Mean 95% CI of Rt discarding first 7 days: (0.983,1.005)\n## Timing of routine not requested.\ngridExtra::grid.arrange(\nplot(epifit,\ndates = dateUSA, datelab = \"3m\",\nplotout = \"epicurve\", incibars = FALSE, themetype = \"light\",\nepicol = \"darkgreen\", cicol = rgb(0.3, 0.73, 0.3, 0.2),\nepititle = \"USA smoothed epidemic curve\", titlesize = 13\n),\nplot(epifit,\ndates = dateUSA, datelab = \"3m\",\nplotout = \"rt\", theme = \"light\", rtcol = \"black\",\ntitlesize = 13, Rtitle = \"USA Estimated R\"\n),\nnrow = 1, ncol = 2\n)\n\n# Conclusion\n\nI hope you will find the method developed in the paper as useful as I do. Feel free to reach out to me and to the authors if you happen to use it for your own research.\n\nAs always, if you have a question or a suggestion related to the topic covered in this article, please add it as a comment so other readers can benefit from the discussion.\n\n# References\n\nCori, Anne, Neil M Ferguson, Christophe Fraser, and Simon Cauchemez. 2013. \u201cA New Framework and Software to Estimate Time-Varying Reproduction Numbers During Epidemics.\u201d American Journal of Epidemiology 178 (9): 1505\u201312.\nGressani, Oswaldo, Jacco Wallinga, Christian L Althaus, Niel Hens, and Christel Faes. 2022. \u201cEpiLPS: A Fast and Flexible Bayesian Tool for Estimation of the Time-Varying Reproduction Number.\u201d PLoS Computational Biology 18 (10): e1010618. https:\/\/doi.org\/10.1371\/journal.pcbi.1010618.\n\n### Liked this post?\n\n\u2022 Get updates every time a new article is published (no spam and unsubscribe anytime):\n\n\u2022 Support the blog\n\u2022 Share on:","date":"2023-03-27 01:12:16","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.498064786195755, \"perplexity\": 3694.043215001231}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-14\/segments\/1679296946584.94\/warc\/CC-MAIN-20230326235016-20230327025016-00177.warc.gz\"}"} | null | null |
Lycalopex culpaeus reissii, comúnmente llamado lobo del páramo, lobo de la sierra, zorro culpeo ecuatoriano, o zorro colorado ecuatoriano, es una de las subespecies en que se divide la especie Lycalopex culpaeus, un cánido que habita en el oeste y sur de América del Sur.
Descripción
Esta subespecie tiene el aspecto de un zorro robusto, de cabeza y patas rojizas, vientre, cuello y boca blancos y lomo gris rayado de negro. La cola está muy poblada de pelos grises que se vuelven negros en su punta.
Hábitat
Habita en montañas, praderas, estepas arbustivas, desiertos,páramos y bosques.
Distribución
Se distribuye especialmente a lo largo de la Cordillera de los Andes, desde el departamento de Nariño en el sudoeste de Colombia, hasta Ecuador. Posiblemente también habite en el extremo norte del Perú.
Alimentación
Se alimenta de roedores, conejos, aves y lagartos, y en menor medida de plantas y carroña. En algunas zonas muy antropizadas ataca a los rebaños de ovejas, razón por la cual ha sido perseguido duramente por los ganaderos, que le disparan o envenenan carroñas. Como consecuencia de esto, se ha vuelto muy raro en algunas zonas y en otras se ha extinguido. En Colombia su mejor población estaría en el Santuario de fauna y flora Galeras.
Referencias
Enlaces externos
Cánidos (Canidae) no amenazados
Carnívoros de América del Sur
reissii | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,100 |
\section{Introduction}
\label{sec:Intro}
Recent advances in convolutional neural networks (CNNs) have led to far-reaching improvements in computer vision tasks \cite{he2016deep,lecun2015deep}.
However, vulnerability of CNNs to image variations, including image corruptions \cite{goodfellow2014explaining} and adversarial samples \cite{dong2020benchmarking}, has not been well resolved yet. Researchers are thus exploring various ways to improve the network robustness against these variations.
\begin{figure}
\centering
\includegraphics[width=.47\textwidth]{task_remake_11.pdf}
\caption{Some solutions to improve the robustness of CNN. Unlike with the regular training (a), adversarial training (b) widely utilizes adversarial samples to train a robust CNN. Data augmentation and regularization based method (c) improves the robustness performance by filling up new samples surrounding the decision boundary. The proposed regularization method (d) enables network to increase the representation space (e.g. red auxiliary axis in \textit{d1}) of the features learned by the CNN,
and achieves better robustness against corrupted and adversarial samples, with various projections on new planes (e.g. \textit{d2} and \textit{d3}). Best viewed in color.
}
\label{fig:task}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=.38\textwidth]{problem_4.pdf}
\caption{The heatmap visualization of feature maps encoded with ResNet-50, based on Grad-CAM \cite{zhou2016learning,selvaraju2017grad} with or without the proposed method.
Our method locates more diverse discriminative regions (in red boxes) for both single-instance (a) and multiple-instance (b) samples.
}
\label{fig:problem}
\end{figure}
Adversarial training \cite{goodfellow2014explaining,zheng2020efficient,xie2019feature} is a typical solution to improve the robustness of CNNs, which includes the attacked samples into the training data, as shown in Fig. \ref{fig:task} (b).
Since adversarial training may impair the generalization performance,
there is often an inherent trade-off between classification accuracy and adversarial robustness \cite{xie2019feature, xie2020adversarial}.
In order to improve the robustness and generalization simultaneously, data augmentation and regularization methods (e.g. Random Erasing \cite{zhong2020random}, Augmix \cite{hendrycks2019augmix}, Cutout\cite{devries2017improved}, Dropout \cite{hinton2012improving} and DeepAugmentation\cite{hendrycks2020many}) are proposed. As shown in Fig. \ref{fig:task} (c), these algorithms address data augmentation by randomly generating new samples obeying the same distribution as the training data. Generally, data regularization methods are state-agnostic, which can not be dynamically adjusted during CNN training.
Thus, these regularization techniques of CNNs
\cite{choe2019attention,wang2020self,hou2018self,wei2017object} failed to learn features with sufficient diversity.
As shown in the first row of Fig. \ref{fig:problem}, CNNs can locate the most discriminative regions \cite{zhou2016learning} for both single-instance and multi-instance samples with the regularization method, while neglecting other auxiliary features that are critical for the recognition.
The lack of auxiliary features may lead to insufficient feature diversity, which consequently results in a feature space
with low-dimension for classification and limits the robustness.
Meanwhile, current adversarial training and regularization methods concentrate on the global image information by expanding the training set, while the independence of local features is not fully explored.
These limitations motivate us to improve the diversity of extracted features by CNNs and devise a non-image-wise regularization strategy to enhance network robustness.
In this paper, we propose a group-wise inhibition based regularization method for improving feature diversity and network robustness, denoted as TENET Training.
Fig.\ref{fig:task} (d1), (d2) and (d3) show the motivation of the proposed method, where the increase of feature dimension and diversity is beneficial for classification robustness against input variations and adversarial attacks.
To increase feature representation space, group-wise feature regularization is proposed to leverage the independence among group-wise features. To improve feature diversity, the proposed algorithm regularizes group-wise features dynamically in each training step.
Specifically, based on the grouping of feature maps and their importance evaluation, the group-wise reversed map is proposed to suppress the activation values corresponding to the most significant discriminative regions, and
guide the network to learn more auxiliary information in less significant regions.
As shown in the second row of Fig. \ref{fig:problem}, the suppression of most significant discriminative regions is beneficial for exploring more diverse features in CNNs.
Experimental results show that the proposed method can improve the top-1 error rate of adversarial training from 36.37\% to 31.75\%, and outperforms regularization methods significantly in terms of classification accuracy based on small sample. In summary,
\begin{itemize}
\item A group-wise inhibition based regularization method is proposed to explore auxiliary features and promote feature diversity.
\item Feature maps with different activation distribution are processed separately to learn richer discriminative features hierarchically to better represent images.
\item Our proposed method achieves competitive performances in terms of adversarial robustness and generalization compared with related variants and the state of the arts.
\end{itemize}
\section{Related Work}
\label{sec:RelatedWork}
\subsection{Robustness against Corruption and Adversarial Attack}
The human vision system is robust in ways that CNN based computer vision systems are not \cite{hendrycks2019benchmarking}.
Particularly, a large mount of studies \cite{dong2020benchmarking,jefferson2020robust,hendrycks2019benchmarking,goodfellow2014explaining} show that CNNs can be easily fooled by small variations in query images, including common corruption \cite{hendrycks2019benchmarking} and adversarial perturbation \cite{goodfellow2014explaining}.
In order to improve the robustness against these variations, studies have been proposed based on various strategies, such as structure modification, adversarial training and regularization.
Xie et al. \cite{xie2019feature} proposed a non-local feature denoising block to suppress the disturbation caused by the malicious perturbation. A Discrete Wavelet Transform (DWT) layer is proposed by Li et al. \cite{li2020wavelet}, which disentangles the low- and high-frequency components to yield the noise-robust classification. Different from structure based methods, adversarial training and regularization methods can improve the robustness without the modification of network structure. Adversarial training proposed by Goodfellow et al. \cite{goodfellow2014explaining}, in which a network is trained on adversarial examples, is reported to be able to withstand strong attacks \cite{shafahi2019adversarial}.
However, there is a trade-off between classification accuracy (generalization) and adversarial robustness.
Hence, more and more studies are resorted to the regularization solutions \cite{zhong2020random,hendrycks2019augmix,devries2017improved,hinton2012improving} to simultaneously improve generalization and robustness against variations, i.e. common corruption and adversarial attack.
\subsection{Regularization for CNNs}
Regularization \cite{zhong2020random,hendrycks2019augmix,devries2017improved,hendrycks2020many,hinton2012improving,Tompson_2015_CVPR,hou2018self,wei2017object} has been widely employed in the training of CNNs, where image-wise and feature-wise regularization methods were proposed to improve generalization or robustness.
Data augmentation is a typical image-wise solution to regularize the data distribution \cite{zhong2020random,hendrycks2019augmix,devries2017improved,hendrycks2020many}.
Devries et al. \cite{devries2017improved} proposed a regularization technique to randomly mask out square regions of input during training. Random Erasing proposed by Zhong et al. \cite{zhong2020random} randomizes the values of pixels in a random rectangle region.
Hendrycks et al. \cite{hendrycks2019augmix} proposed Augmix to coordinate simple augmentation operations with a consistency loss.
In a nutshell, these image-wise regularization solutions generate images by random operations (e.g. cutout, erasing and mixing), which concentrate on the global information without fully exploring the independence of local features. Meanwhile, the random operations are not dynamically adapted during the training, which limit the feature diversity. These studies motivate us to enhance the feature diversity to improve network robustness and generalization performances.
To explore local information during regularization, feature-wise regularization techniques, including attention based dropout \cite{choe2019attention}, self-erasing \cite{hou2018self,wei2017object} and group orthogonal training \cite{chen2017training}, are proposed.
Attention based dropout proposed by Choe et al. \cite{choe2019attention} utilizes the self-attention mechanism to regularize the feature maps.
Self-erasing \cite{hou2018self,wei2017object} is an extension method of popular class activation map (CAM) \cite{zhou2016learning,selvaraju2017grad}, which erases the most discriminative part of CAM, and guides the CNNs to learn classification features from auxiliary regions and activations \cite{wang2020self}.
However, these methods are proposed for semantic segmentation rather than the classification task. Meanwhile, the steep gradients introduced by the binary mask limit the performances of dropout and erasing operation for classification task. From another aspect, the erasing operation and dropout are global regularizers, which do not fully explore the independence of feature semantics, i.e. different feature groups contain different semantics and should be processed specifically.
Group orthogonal training proposed by Chen et al. \cite{chen2017training} provides a solution for this problem, which guides CNNs to learn discriminative features from foreground and background separately. Although this group orthogonalization strategy brings improvement of classification performance by enhancing feature diversity, the relied large annotation limits its applicability for general tasks.
In this paper, a regularization method based on group-wise inhibition, namely TENET Training, is proposed to improve network robustness and generalization, which is free of extra annotations. Particularly, a Channel-wise Feature Grouping (CFG) module is proposed to model the channel-wise features in groups. Subsequently, the features in different groups are processed specifically by Group-wise Map Weighting (GMW) module to quantify the importance of each group. Meanwhile, in order to avoid the steep gradients caused by binary mask, a Rectified Reverse Function (RRF) is proposed to smooth group-wise reversed maps. Finally, these reversed maps are used to suppress the activation values to regularize the learned features. Extensive experiments clearly show the significant improvements in terms of robustness and generalization performances.
\section{Proposed Method}
\label{sec:method}
The overview of the proposed TENET Training is shown in Fig. \ref{fig:pipeline}., where CNN is dynamically regularized according to the training step, and significant activation values are suppressed to guide network to explore different features hierarchically.
Since the feature maps with the similar activation distribution are prone to contain redundant information, we firstly group the channel-wise feature maps using the proposed CFG module in Section \ref{sec:CFG}.
In order to further quantify the contribution of each group, the GMW module is introduced in Section \ref{sec:GMW} to evaluate the group importance.
Considering the feature groups with negative importance score should contribute less to the classification performance, Rectified Reverse Function (RRF) is proposed to smooth the reversed map of the filtered groups. Following RRF, the group-wise inhibition is devised to suppress the most significant features and explores the less significant auxiliary features, which is introduced in Section \ref{sec:RRF}. Finally, we conclude the pipeline of the proposed TENET Training together with the loss design in Section \ref{sec:LD}.
\begin{figure*}
\centering
\includegraphics[width=.95\textwidth]{TENET_pipline_border_new_3.pdf}
\caption{
The pipeline of the proposed regularization method (TENET Training). Notice that CNNs consist of the feature extraction module $F(\cdot)$ and the classifier $D(\cdot)$. In the first inference, feature maps $A$ encoded with $F(\cdot)$ are divided into $N_G$ groups by the $CFG$ module, and loss $\mathcal{L}_{d}$ is calculated based on $D(\cdot)$. Reversed maps $RM$ are then derived using $GMW$ module and $RRF$. In the second inference, the Hadamard Product of $A$ (with $IDS$) and $RM$ is fed to $D(\cdot)$ to calculate the loss $\mathcal{L}_{total}$.
}
\label{fig:pipeline}
\end{figure*}
\subsection{Channel-wise Feature Grouping Module}
\label{sec:CFG}
According to the pipeline shown in Fig. \ref{fig:pipeline}, a feature extraction module $F(\cdot)$ is firstly applied to encode the features set $A = \{ a_1, ..., a_j, ... , a_{N_c} \}$ of the input sample $x$, where $a_j$ is the $j$th feature map. Since $A$ is prone to contain redundant features, a Channel-wise Feature Grouping module, denoted as CFG module, is introduced to group $A$ to reduce the complexity of feature-wise operation. Given $N_c$ features as input, the corresponding $N_G$ centers are obtained to form the set $A_c$, which are initialized as a random subset of $A$. The distance from each feature map of $A$ to the corresponding center is calculated as follows
\begin{align}
\label{eq:1}
Dist(a_j,A_c[l]) = \frac{1}{H_a \times W_a} \sum_{H_a} \sum_{W_a} (a_j-A_c[l])^2
\end{align}
where $l \in [1,N_G]$ is the index of the center and ($H_a$, $W_a$) is the size of $a_j$. Based on Eq. (\ref{eq:1}), the centers are updated as similar as k-means clustering. $N_G$ groups are then obtained by grouping the feature maps to the corresponding center. In order to alleviate the influence caused by the random selection, the center searching process is carried out repeatedly in the CFG module. Based on the grouping procedure, the centers are updated according to Center Point Search Function, i.e. CF($\cdot$) as follows
\begin{align}
\label{eq:2}
\text{CF}(I\!D\!S) \!=\! \{ \mathop{\arg\min}\limits_{a_j\in A} dist(a_j,\!\frac{1}{n_l}\!\sum_{ID_i=l}\! a_i\! ) \Big| l\! \in\! [1,\!N_G] \}
\end{align}
where the set $IDS = \{ ID_1, ..., ID_j, ..., ID_{N_c}\}$ stands for the set of feature map indices corresponding to each group. $ID_j$ refers to the group index of $a_j$. $n_l$ is the number of feature maps in the $l$th group. Based on Eq. (\ref{eq:2}), $A_c$ can be refined iteratively until CF($\cdot$) is stable.
\subsection{Group-wise Map Weighting Module}
\label{sec:GMW}
Following feature grouping module, the feature maps are processed in the group-wise mode. To differ the contribution of each group, a Group-wise Map Weighting module, namely GMW module, is proposed to calculate the weight $w_j$ of each $a_j$ as follows
\begin{align}
\label{eq:w}
\begin{split}
w_j &= \frac{1}{H_a \times W_a}\sum_{H_a}\sum_{W_a}\frac{\partial \mathcal{L}_d(A) }{\partial a_j} \\
\mathcal{L}_d(A) &= D(A) \times \text{One-Hot}(D(A))
\end{split}
\end{align}
where $D(\cdot)$ is a classifier, which maps $A$ to the class score. $\mathcal{L}_d(A)$ is the product of prediction and the corresponding one-hot vector of $D(A)$. Since $\frac{\partial \mathcal{L}_d(A)}{\partial a_j}$ is applied to quantify the importance of $a_j$ to the prediction, the group-wise importance scores, i.e. $IS = \{ I_1, ..., I_l,..., I_{N_G}\}$ can be obtained by averaging $w_j$ of each group ($ID_j$=$l$) as follows
\begin{align}
\label{eq:l}
I_l = \frac{1}{N_l}\sum_{ID_j = l} w_j
\end{align}
Similar to $IS$, the group-wise feature maps, i.e. $M = \{ m_1, ..., m_l, ..., m_{N_G} \}$ can be obtained by averaging the weighted feature maps as follows
\begin{align}
\label{eq:m}
m_l = \frac{1}{N_l}\sum_{ID_j = l} w_j \times a_j
\end{align}
\subsection{Group-wise Inhibition using Rectified Reverse Function}
\label{sec:RRF}
Based on the importance scores, group-wise feature maps are applied to obtain the reversed map set, i.e. $RM = \{ rm_1, ..., rm_l,...,rm_{N_G} \}$. Since the steep gradients introduced by the binary mask may limit the classification performance, the reversed maps are further smoothed. Meanwhile, considering the feature groups with negative importance scores should contribute less to the update of the reversed mask, we therefore propose a Rectified Reverse Function, i.e. RRF($\cdot$), to obtain the reversed maps as follows
\begin{align}
\label{eq:rrf}
rm_l = \text{RRF}(m_l,I_l) = sgn(I_l>0) \times \frac{1}{1+e^{m_l}}
\end{align}
where $sgn(\cdot)$ is the sign function.
Due to the negative correlation between $m_l$ and $rm_l$, the computation of $RM$ is deemed as a reversed map. Based on $RM$, the group-wise inhibition is formulated as follows
\begin{align}
\label{eq:y}
\hat{y} = D(RM \otimes A)
\end{align}
where $D(\cdot)$ is a classifier with the input of $A$ and $\hat{y}$ refers to the predicted label of the group-wise inhibition. $\otimes$ refers to the group-wise Hadamard product.
\subsection{Loss Design of TENET Training}
\label{sec:LD}
While $\hat{y}$ is obtained by group-wise inhibition, $F(\cdot)$ and $D(\cdot)$ can be directly learned based on the loss $\mathcal{L}_c(y,\hat{y})$, i.e. the cross entropy for single-label classification or binary cross entropy for multi-label classification. The group-wise inhibition reduces the variation between groups, while it may introduce invalid activation units in $F(\cdot)$ or $D(\cdot)$. To regularize these activation units, an orthogonal loss $\mathcal{L}_o(A)$ is adopted, which is formulated as follows
\begin{align}
\label{eq:or}
\mathcal{L}_o(A) = \prod \limits_{l=1}^{N_g}(\sum_{j=1}^{N_c}(sgn(ID_j = l) \times a_j))
\end{align}
From another aspect, by mapping $rm_l$ into the region of [0, 1], the magnitude of back-propagation gradients is suppressed for $F(\cdot)$ and $D(\cdot)$. To alleviate vanishing gradient problem, a general classification loss, i.e. $\mathcal{L}_c(y_i, D(A))$, is employed. Finally, the total loss is formulated as follows
\begin{align}
\mathcal{L}_{total} = \mathcal{L}_c(y_i, D(A))+ \alpha \mathcal{L}_c(y_i,\hat{y}) + \mu \mathcal{L}_o(A)
\label{eq:total}
\end{align}
where $\alpha$ and $\mu$ are the hyper parameters. For clarity, TENET Training is summarized in Algo. 1
\begin{algorithm}[!htb]
\label{algo:1}
\caption{TENET Training}
\begin{algorithmic}
\Require\\
Training Sample: $x$ \\
Initialization of $F(\cdot)$ and $D(\cdot)$
\Ensure \State Trained CNNs: $F(\cdot)$ and $D(\cdot)$
\end{algorithmic}
\begin{algorithmic}[1]
\For {all training steps}
\State Extract $A$ from $F(x)$;
\State Obtain $IDS$ of $A$ using CFG Module according to Eqs. (\ref{eq:1}) and (\ref{eq:2});
\State Derive $(IS,M)$ with GMW Module according to Eqs. (\ref{eq:w}), (\ref{eq:l}) and (\ref{eq:m});
\State Employ RRF to obtain $RM$ according to Eq. (\ref{eq:rrf});
\State Obtain $\hat{y}$ according to Eq. (\ref{eq:y});
\State Calculate $\mathcal{L}_{total}$ according to Eqs. (\ref{eq:or}) and (\ref{eq:total});
\State Update $F(\cdot)$ based on $\frac{\partial \mathcal{L}_{total}}{\partial F}$ and update $D(\cdot)$ based on $\frac{\partial \mathcal{L}_{total}}{\partial D}$;
\EndFor
\State Return $F(\cdot)$ and $D(\cdot)$.
\end{algorithmic}
\end{algorithm}
\section{Experimental Results and Analysis}
\label{sec:experiment}
\begin{table}[!htbp]
\centering
\caption{Summary of Experiment Configurations and TENET Training Gains.}
\Huge
\resizebox{.48\textwidth}{14.6mm}{
\begin{threeparttable}
\begin{tabular}{c|ccc}
\toprule
Task-[protocol] & Dataset & Previous SOTA & Gain\\
\midrule
\textbf{Standard Classification}-\cite{chen2017training}& \tabincell{c}{PASCAL \\ VOC 2012\cite{everingham2010pascal}} & \tabincell{c}{Group Orthogonal \\ Training \cite{chen2017training}}& \textbf{2.9\%} \\
\midrule
\textbf{Robustness} against & \multirow{2}{*}{CIFAR-10/100 \cite{krizhevsky2009learning}} & A. T. \cite{shafahi2019adversarial} & \textbf{5.75\%}\\
Adversarial Attack-\cite{shafahi2019adversarial,dong2020benchmarking} & & Augmix\cite{hendrycks2019augmix} & \textbf{15.56\%}$^*$\\
\midrule
\textbf{Robustness} against & CIFAR-10/100-C \cite{hendrycks2019benchmarking} & \multirow{2}{*}{Augmix\cite{hendrycks2019augmix}} & \textbf{1.77\%}\\
Common Corruption-\cite{hendrycks2019benchmarking,hendrycks2019augmix,li2020wavelet} & ImageNet-C \cite{hendrycks2019benchmarking} & & \textbf{2.8\%}$\dag$\\
\midrule
\textbf{Generalization}-\cite{azuri2020learning} & CUB-200 \cite{wah2011caltech} & GLICO \cite{azuri2020learning} & \textbf{2.75\%}\\
\bottomrule
\end{tabular}
\begin{tablenotes}
\huge
\item $^*$ The gain is obtained in CIFAR-10 against FGSM (8/255).
\item $^\dag$ The gain is obtained by following 90-epoch Protocol \cite{li2020wavelet}.
\end{tablenotes}
\end{threeparttable}
}
\label{tab:summary}
\end{table}
As listed in Table \ref{tab:summary}, to evaluate the performance of the proposed method, extensive experiments are carried on publicly-available data sets, including PASCAL VOC 2012 \cite{everingham2010pascal}, CIFAR-10/100 \cite{krizhevsky2009learning}, ImageNet-C \cite{hendrycks2019benchmarking} and CUB-200 \cite{wah2011caltech}. We firstly introduce the employed data sets and the corresponding implementation details. The performance of the proposed method on standard image classification task is evaluated, and the encoded feature maps are visualized for the algorithm analysis. Finally, both the robustness and generalization performances of the proposed method are evaluated based on the comparison with the state-of-the-art methods.
\begin{table*}[!htbp]
\centering
\caption{The Ablation Study of the Proposed Method on the Validation Dataset of Pascal VOC 2012 in terms of Average Precision (\%).}
\Huge
\resizebox{.99\textwidth}{11.2mm}{
\begin{tabular}{cccc|cccccccccccccccccccc|c}
\toprule
Baseline&\tabincell{c}{Channel-wise \\ Inhibition} & \tabincell{c}{Group-wise \\ Inhibition} & $L_o$ & areo & bike & bird & boat & bottle & bus & car & cat & chair & cow & table & dog & horse & mbk & prsn & plant & sheep & sofa & train & tv & \textbf{mean}\\
\midrule
$\surd$&$\times$ & $\times$ & $\times$ & 94.8 & 83.8 & 91.5 & 79.4 & 56.6 & 88.2 & 78.9 & 90.8 & 64.8 & 61.5 & 57.9 & 90.9 & 73.7 & 83.8 & 96.0 & 51.6 & 77.1 & 58.2 & 89.8 & 77.1 & 77.1\\
$\surd$&$\surd$ & $\times$ & $\times$ & 94.2 & 82.8 & \textbf{92.9} & 83.3 & 62.2 & 90.8 & 81.0 & \textbf{92.8} & 71.1 & 74.1 & 63.0 & 88.2 & 83.9 & 88.5 & 93.5 & \textbf{58.4} & \textbf{85.2} & 64.7 & 93.1 & 80.6 & 81.2\\
$\surd$&$\times$ & $\surd$ & $\times$ & 93.9 & 81.7 & 92.5 & \textbf{83.7} & \textbf{63.8} & 90.9 & 82.7 & 91.5 & 69.5 & 76.4 & 64.6 & 89.6 & \textbf{85.9} & \textbf{89.3} & \textbf{96.5} & 58.1 & 84.6 & 64.5 & 93.2 & \textbf{83.7} & 81.8\\
$\surd$&$\times$ & $\surd$ & $\surd$ & \textbf{95.6} & \textbf{84.3} & 91.1 & 83.1 & 61.3 & \textbf{91.4} & \textbf{83.2} & 91.6 & \textbf{72.8} & \textbf{77.4} & \textbf{65.9} & \textbf{91.3} & 84.4 & 89.2 & 96.3 & 57.4 & 83.9 & \textbf{67.6} & \textbf{94.5} & 83.1 & \textbf{82.3}\\
\bottomrule
\end{tabular}
}
\label{tab:ABPASCAL}
\end{table*}
\subsection{Data Sets and Implementation Details}
We evaluate the performance of TENET Training from three aspects, i.e. standard classification, robustness and generalization (see Table \ref{tab:summary}).
\textbf{Standard Classification. }
In this case, ResNet-18 \cite{he2016deep} is selected as the backbone in our TENET Training. PASCAL VOC 2012 \cite{everingham2010pascal} is used for the evaluation, while 5,717 and 5,823 images are used for the training and validation, respectively. The protocol in \cite{chen2017training} is adopted. The CNNs for evaluation are pretrained on the ImageNet \cite{deng2009imagenet}, and fine-tuned on PASCAL VOC 2012 training set. In the training stage, the shorter side of image is resized to a random value within [256,480] for the scale augmentation. The resized image is then randomly cropped to the size of $224 \times 224$ for the training based on the batch size of 256. In the testing stage, ten-crop testing is used to evaluate the performance.
\textbf{Robustness. }
In this case, the robustness of the proposed algorithm against both adversarial attack and image corruption is evaluated on CIFAR 10/100 \cite{krizhevsky2009learning}, CIFAR 10/100-C \cite{hendrycks2020many} and ImageNet-C \cite{hendrycks2020many}. ResNeXt-29 \cite{xie2017aggregated} and ResNet-50 \cite{he2016deep} are chosen as the backbones.
To test the robustness of the proposed method against adversarial attacks, two popular attacks, FGSM \cite{goodfellow2014explaining} and PGD \cite{athalye2018obfuscated}, are employed. The performance is then evaluated according to the protocol in \cite{dong2020benchmarking}. The perturbation budget ($\epsilon$) is set to $8/255$ or $4/255$ under $l_{\infty }$ norm distance for the two attacks. PGD-K stands for K-step attack with a step size of $2/255$.
Meanwhile, adversarial training is used to defense powerful iterative attacks of PGD. To make the results more convincing, an efficient adversarial training method (free-AT) \cite{shafahi2019adversarial} is adopted, where the \textit{hop step} of free-AT, i.e. $m$, is set to $4$.
Against image corruption, 15 different kinds of corruptions, such as noise, blur, weather and digital corruptions, are performed on CIFAR 10/100-C and ImageNet-C for the evaluation, and each kind of corrupted data has five different severity levels \cite{hendrycks2020many}. We follow the training protocols and evaluation metrics used in Augmix \cite{hendrycks2019augmix} and WResNet50 \cite{li2020wavelet}.
The \textit{Clean Error} is the regular classification error on the original (uncorrupted) test or validation dataset, and
\textit{mCE (Mean Corruption Error)} for CIFAR-10/100-C is the mean over all 15 corruptions. Meanwhile, the \textit{mCE} for ImageNet-C is normalized by the corruption error of AlexNet \cite{krizhevsky2012imagenet}.
Due to the computational efficiency, Augmix without Jensen-Shannon divergence (JSD) loss is implemented.
\textbf{Generalization. }
Since CUB-200 \cite{wah2011caltech} contains only 30 images for each of the 200 species of birds, it is used as a popular benchmark to test the generalization of CNNs.
We follow the protocol in \cite{azuri2020learning}, and evaluate the generalization with three numbers of samples per class (SPC) for training, i.e. 10, 20 and 30.
For a fair comparison, the same ResNet-50 \cite{he2016deep} in the protocol \cite{azuri2020learning} is adopted as the backbone.
To train the CNNs, the smaller side of the images from CUB-200 is resized to 256, the scaled images are then randomly cropped to the size of $224 \times 224$. In the testing stage, the prediction is based on the center cropping with the size of $224 \times 224$.
\begin{table*}[!htbp]
\centering
\caption{Performance Comparison between the Proposed Method and the State of the Arts on the Validation Dataset of Pascal VOC 2012 in terms of Average Precision (\%).}
\Huge
\resizebox{.99\textwidth}{14.0mm}{
\begin{tabular}{c|cccccccccccccccccccc|c}
\toprule
Model & areo & bike & bird & boat & bottle & bus & car & cat & chair & cow & table & dog & horse & mbk & prsn & plant & sheep & sofa & train & tv & \textbf{mean}\\
\midrule
ResNet18\cite{he2016deep} reported in \cite{chen2017training} & 95.2 & 79.3 & 90.2 & 82.8 & 52.6 & 90.9 & 78.5 & 90.2 & 62.3 & 64.9 & 64.5 & 84.2 & 81.1 & 82.0 & 91.4 & 50.0 & 78.0 & 61.1 & 92.7 & 77.5 & 77.5\\
ResNet18 trained in this paper & 94.8 & 83.8 & 91.5 & 79.4 & 56.6 & 88.2 & 78.9 & 90.8 & 64.8 & 61.5 & 57.9 & 90.9 & 73.7 & 83.8 & 96.0 & 51.6 & 77.1 & 58.2 & 89.8 & 77.1 & 77.1\\
\midrule
GoCNN \cite{chen2017training} & \textbf{96.1} & 81.0 & 90.8 & \textbf{85.3} & 56.0 & \textbf{92.8} & 78.9 & 91.5 & 63.6 & 69.7 & 65.1 & 84.8 & 84.0 & 83.9 & 92.3 & 52.0 & 83.9 & 64.2 & 93.8 & 78.6 & 79.4\\
\midrule
TENET (Binary Mask) & 93.2 & 83.8 & 91.3 & 83.2 & 59.8 & 91.6 & 79.6 & 90.6 & 66.3 & 75.2 & 62.1 & 89.7 & 84.7 & 88.4 & 96.3 & \textbf{58.0} & \textbf{87.0} & 65.2 & 93.1 & 82.1 & 81.1 \\
TENET (Instance-wise Inhibition) & 93.1 & 82.7 & \textbf{92.6} & 82.9 & 61.1 & 90.9 & 81.8 & \textbf{91.6} & 70.6 & 73.7 & 63.3 & \textbf{91.5} & \textbf{85.6} & 88.5 & \textbf{96.4} & 56.8 & 85.1 & 61.8 & 93.2 & 82.3 & 81.3 \\
TENET & 95.6 & \textbf{84.3} & 91.1 & 83.1 & \textbf{61.3} & 91.4 & \textbf{83.2} & \textbf{91.6} & \textbf{72.8} & \textbf{77.4} & \textbf{65.9} & 91.3 & 84.4 & \textbf{89.2} & 96.3 & 57.4 & 83.9 & \textbf{67.6} & \textbf{94.5} & \textbf{83.1} & \textbf{82.3}\\
\bottomrule
\end{tabular}
}
\label{tab:VOC}
\end{table*}
\textbf{TENET Training.}
For the hyper parameter setting, the cluster number $N_G$ is set to 6, while $\alpha$ and $\mu$ are set as 0.1 and 0.1, respectively.
The public platform pytorch \cite{paszke2017automatic} is used for the implementation of all the experiments on a work station with CPU of 2.8GHz, RAM of 512GB and GPU of NVIDIA Tesla V100.
\begin{figure}[!htb]
\centering
\includegraphics[width=.38\textwidth]{visualization_small_colorful_4.pdf}
\caption{
The visualization of the discriminative regions for image classification of CUB-200 using Grad-CAM \cite{zhou2016learning,selvaraju2017grad}.
The 1st-3rd rows show the input samples, the discriminative regions extracted by ResNet-50 and the results based on TENET Training.
}
\label{fig:visual_feature}
\end{figure}
\begin{table*}[t]
\centering
\caption{Top-1 error rates (\%) on ImageNet and Top-1 mCE rates (\%) on ImageNet-C with ResNet-50. Aug. stands for Augmix.}
\begin{threeparttable}
\Huge
\resizebox{.98 \textwidth}{17.6mm}{
\begin{tabular}{c|c|c|ccc|cccc|cccc|cccc|c}
\hline
\multicolumn{1}{l|}{} & \multirow{2}{*}{Protocol} & Clean & \multicolumn{3}{c|}{Noise} & \multicolumn{4}{c|}{Blur} & \multicolumn{4}{c|}{Weather} & \multicolumn{4}{c|}{Digital} & \multicolumn{1}{l}{} \\ \cline{4-19}
\multicolumn{1}{l|}{} & & Error & Gauss. & Shot & Impulse & Defocus & Glass & Motion & Zoom & Snow & Frost & Fog & Bright & Contrast & Elastic & Pixel & JPEG & \textbf{mCE} \\ \hline
\multicolumn{2}{c|}{\tabincell{c}{Baseline \cite{he2016deep} reported in \cite{hendrycks2019augmix}}} & 23.8 & 79 & 80 & 82 & 82 & 90 & 84 & 80 & 86 & 81 & 75 & 65 & 79 & 91 & 77 & 80 & 80.6 \\ \hline
Cutout \cite{devries2017improved} & \multirow{5}{*}{\tabincell{c}{90-epoch \\ Protocol\cite{li2020wavelet}}} & 23.2 & 79 & 81 & 80 & 77 & 90 & 80 & 81 & 80 & 78 & 70 & 61 & 74 & 87 & 74 & 75 & 77.7 \\
WResNet50 (Haar) \cite{li2020wavelet} & & 23.1 & 77 & 79 & 79 & 71 & 86 & 77 & 77 & 80 & 75 & 66 & 57 & 71 & 84 & 75 & 77 & 75.3 \\
Augmix \cite{hendrycks2019augmix} & & 23.0 & 71 & 71 & 71 & 72 & 88 & 72 & 72 & 78 & 78 & 67 & 60 & 72 & 86 & 75 & 76 & 73.9 \\
TENET & & 23.1 & 73 & 78 & 75 & 74 & 87 & 76 & 80 & 79 & 78 & 67 & 63 & 73 & 84 & 72 & 71 & 75.3 \\
TENET (Aug.) & & 22.8 & 69 & 69 & 69 & \textbf{69} & 87 & 69 & 70 & 76 & 75 & \textbf{64} & \textbf{56} & 69 & 82 & 72 & 73 & 71.1 \\ \hline
Augmix \cite{hendrycks2019augmix} & \multirow{2}{*}{\tabincell{c}{180-epoch \\ Protocol\cite{hendrycks2019augmix}}} & 22.5 & \textbf{68} & 69 & 70 & 73 & \textbf{81} & 69 & \textbf{67} & 75 & \textbf{73} & 67 & 61 & 61 & \textbf{80} & 71 & 72 & 70.5 \\
TENET (Aug.) & & \textbf{22.4} & 69 & \textbf{67} & \textbf{68} & 72 & \textbf{81} & \textbf{66} & 69 & \textbf{74} & 74 & 65 & 59 & \textbf{60} & 82 & \textbf{69} & \textbf{70} & \textbf{69.6} \\ \hline
\end{tabular}
}
\end{threeparttable}
\label{tab:image}
\end{table*}
\subsection{Effectiveness Analysis of the Proposed Method}
\begin{figure}[!htb]
\centering
\includegraphics[width=.47\textwidth]{group_vis-05.pdf}
\caption{
The visualization and quantification of the feature maps extracted by the 3rd residual block of ResNet-50 using TENET Training.
(a) An input image with the label of European Goldfinch. (b) The activation distribution, the corresponding importance and confidence scores of each group clustered by CFG module.
(c) The example feature maps selected from the 3rd and 4th groups.
}
\label{fig:visual_group}
\end{figure}
\textbf{Ablation Study.}
To quantify the contribution of each module in TENET Training, we test the discriminative performance of the variant with or without this module. Table \ref{tab:ABPASCAL} shows the results carried out for standard classification. Since GMW is based on CFG module, these two modules denoted as Channel-wise Inhibition and Group-wise Inhibition are evaluated integratedly.
Table \ref{tab:ABPASCAL} shows
that the performance of the baseline in the first row can be improved by both channel-wise inhibition and group-wise inhibition.
Specifically, an improvement of 4.1\% in terms of mAP is achieved by channel-wise inhibition. To study the performance of GMW and CFG modules, Table \ref{tab:ABPASCAL} shows that the group-wise inhibition further improves the performance using $\mathcal{L}_o(A)$. The most significant improvement of TENET Training happens when all the proposed modules are employed, i.e. the proposed method achieves a mAP of 82.3\%, which largely outperforms the baseline with a mAP of 77.1\%.
\textbf{Visualization of TENET Training.}
To study the diversity of the learned features with the proposed TENET Training, we visualize the discriminative regions of the input samples from CUB-200 using Grad-CAM \cite{zhou2016learning,selvaraju2017grad} in Fig. \ref{fig:visual_feature}. Compared with the baseline, the CNN using TENET Training derives more discriminative regions, such as wings, heads and tails, for classification.
To study the distribution of the extracted features, we further visualize the group-wise maps with different importance scores of the input image in Fig. \ref{fig:visual_group}, where feature maps are clustered into six groups.
The confidence score of each group corresponds to the variant with or without the selected group. Fig. \ref{fig:visual_group} (b) shows that, the importance score (orange line) calculated by GMW module is similar with confidence score (green line) in tendency, which illustrates the effectiveness of the GMW module.
Meanwhile, Fig. \ref{fig:visual_group} (b) also shows the large variations among the activation distributions of the group-wise features, which indicates the reasonability of group-independent processing. As a contrast, the instance-wise operation involved in traditional methods can not regularize the most important features but only the features with the largest group size ( i.e. group-1 in Fig. \ref{fig:visual_group}), based on the average of activation maps or annotations. Thus, the proposed group-independent processing can facilitate our TENET training to achieve better performance than other regularization methods.
Fig. \ref{fig:visual_group} (c) shows that group-3 and group-4 out of six groups are the most important for CNN, which can improve the confidence score output by the CNN from 0 to 99.8\%.
Group-1 is relatively less important than group-3 and group-4 but can increase confidence score, while the impacts of group-2, 5 and 6 on the classification performance is very limited. More precisely, when these three groups are not used, the confidence score has dropped by only 0.09\%.
This observation indicates that the inhibition of the important groups can help improve the efficiency without losing accuracy.
Hence, in the proposed method, we only regularize the groups with higher importance scores.
\subsection{Comparison with Related Methods}
\textbf{Comparison in Standard Classification.}
To study the classification performance of the proposed method, we compare it with the group orthogonal training \cite{chen2017training} denoted as GoCNN in Table \ref{tab:VOC}. In additional, we include TENET (Binary Mask) and TENET (Instance-wise Inhibition) for the comparison. TENET (Binary Mask) refers to the proposed method that suppresses the activation value using binary masks rather than the smoothed reversed maps. In TENET (Instance-wise Inhibition), CFG module and GMW module are replaced by Grad-CAM \cite{zhou2016learning,selvaraju2017grad}, which process features by instance-wise operation.
Table \ref{tab:VOC} shows that TENET Training outperforms the competing methods significantly. The proposed method achieves a mAP of 82.3\%, exceeding group orthogonal training by 2.9\% absolutely. This indicates group-wise inhibition using the smoothed reversed maps is suitable for classification.
Meanwhile, the proposed method uses less information than group orthogonal training, i.e. large-scale dense annotations, e.g. segmentation or localization labels, are not demanded.
While state-agnostic inhibition used in group orthogonal training regularizes features in a coarse way,
it limits both the accuracy and efficiency.
However, based on the proposed group-wise inhibition, our method can consistently improve the classification performance, and does not demand any extra annotations.
\begin{table}[!htbp]
\centering
\caption{Top-1 error rates (\%) on CIFAR-10 and Top-1 mCE rates (\%) on CIFAR-10-C trained with various methods based on ResNeXt-29. A.T. stands for Adversarial Training. The brackets following the adversarial attack method show the perturbation budget ($\epsilon$). }
\resizebox{.45\textwidth}{23.1mm}{
\begin{tabular}{c|c|c|ccc}
\toprule
& Clean & mCE & \begin{tabular}[c]{@{}c@{}}FGSM\\ (8/255)\end{tabular} & \begin{tabular}[c]{@{}c@{}}PGD-7\\ (4/255)\end{tabular} & \begin{tabular}[c]{@{}c@{}}PGD-100\\ (8/255)\end{tabular} \\
\midrule
Baseline \cite{xie2017aggregated} & 5.72 & 29.88 & 72.81 & 94.15 & - \\
Cutout \cite{devries2017improved} & 3.97 & 29.20 & 71.07 & 97.19 & - \\
Augmix \cite{hendrycks2019augmix} & 3.95 & 13.32 & 76.03 & 93.67 & - \\
TENET & 3.89 & 26.46 & 61.05 & 91.28 & - \\ \hline
\begin{tabular}[c]{@{}c@{}}TENET\\ (Aug.)\end{tabular} & \textbf{3.50} & \textbf{12.31} & 60.47 & 90.45 & - \\
\toprule
A.T. \cite{shafahi2019adversarial} & - & - & 36.37 & 22.61 & 42.82 \\ \hline
\begin{tabular}[c]{@{}c@{}}TENET\\ (A.T.)\end{tabular} & - & - & \textbf{31.75} & \textbf{20.07} & \textbf{37.07} \\
\bottomrule
\end{tabular}
}
\label{tab:Cifar10}
\end{table}
\textbf{Comparison in Robustness.}
We compare the proposed method with two state-of-the-art regularization methods \cite{devries2017improved,hendrycks2019augmix}, a wavelet integrated method \cite{li2020wavelet} and an adversarial training one \cite{shafahi2019adversarial}, for robustness evaluation against image corruption and adversarial attacks in Tables \ref{tab:image}, \ref{tab:Cifar10} and \ref{tab:Cifar100}. One can observe that TENET Training outperforms the competing methods in each case. For the recognition against image corruption, the best performance is achieved with the combination of TENET Training and Augmix (denoted as TENET(Aug.)), which achieves 69.6\%, 12.31\% and 35.73\% error rates on ImageNet-C, CIFAR-10-C and CIFAR-100-C, respectively.
Augmix \cite{hendrycks2019augmix} with JSD loss can achieve a mCE of 68.4\% on ImageNet-C, while it requires three times the GPU memory and runtime cost compared with the proposed method.
For robustness against adversarial attacks, two attack paradigms, namely FGSM and PGD, are employed to test the trained CNNs with different regularization methods. Tables \ref{tab:Cifar10} and \ref{tab:Cifar100} show that the CNNs using the proposed method outperform those with other regularization methods by a large margin. When FGSM is considered, our method can achieve an error rate of 60.47\%, exceeding other regularization methods by around 10\% absolutely. Meanwhile, our method is complementary to the Adversarial Training (denoted as A.T.). Typically, the proposed method achieves the error rates of 37.07\% and 63.13\% against PGD-100 on CIFAR-10/100, which outperforms Adversarial Training clearly, i.e. 37.07\% vs. 42.82\% and 63.13\% vs. 65.17\%.
\begin{table}[!htbp]
\centering
\caption{Top-1 error rates (\%) on CIFAR-100 and Top-1 mCE rates (\%) on CIFAR-100-C trained with various methods based on ResNeXt-29.}
\resizebox{.45\textwidth}{23.0mm}{
\begin{tabular}{c|c|c|ccc}
\toprule
& Clean & mCE & \begin{tabular}[c]{@{}c@{}}FGSM\\ (8/255)\end{tabular} & \begin{tabular}[c]{@{}c@{}}PGD-7\\ (4/255)\end{tabular} & \begin{tabular}[c]{@{}c@{}}PGD-100\\ (8/255)\end{tabular} \\
\midrule
Baseline \cite{xie2017aggregated} & 23.33 & 53.40 & 85.93 & 95.96 & - \\
Cutout \cite{devries2017improved} & 20.73 & 54.60 & 87.03 & 98.13 & - \\
Augmix \cite{hendrycks2019augmix} & 21.83 & 37.50 & 84.65 & 95.32 & - \\
TENET & 20.56 & 51.21 & 78.71 & 94.62 & - \\ \hline
\begin{tabular}[c]{@{}c@{}}TENET\\ (Aug.)\end{tabular} & \textbf{19.46} & \textbf{35.73} & 75.28 & 93.54 & - \\
\toprule
A.T. \cite{shafahi2019adversarial} & - & - & 60.13 & 47.99 & 65.17 \\ \hline
\begin{tabular}[c]{@{}c@{}}TENET\\ (A.T.)\end{tabular} & - & - & \textbf{58.60} & \textbf{46.17} & \textbf{63.13} \\
\bottomrule
\end{tabular}
}
\label{tab:Cifar100}
\end{table}
\begin{table}[!htbp]
\centering
\caption{Comparison of TOP-1 Accuracy (\%) for CUB-200 based on ResNet-50 with Different Numbers of Training Samples Per Class (SPC). }
\resizebox{.42\textwidth}{18.4mm}{
\begin{tabular}{cccc}
\toprule
Methods & SPC = 10 & SPC = 20 & SPC = 30 \\
\midrule
MixMatch \cite{berthelot2019mixmatch} & 36.02 & 60.57 & 70.41 \\
Random Erase \cite{zhong2020random} & 63.72 & 66.14 & 73.74 \\
Cutout \cite{devries2017improved} & 64.33 & 68.47 & 74.97 \\
\midrule
GLICO \cite{azuri2020learning} & 65.13 & 74.16 & 77.75 \\
\midrule
A.T. \cite{shafahi2019adversarial} & 44.53 & 57.91 & 63.67 \\
\midrule
TENET & \textbf{66.07} & \textbf{76.91} & \textbf{80.34}\\
\bottomrule
\end{tabular}
}
\label{tab:generation}
\end{table}
\textbf{Comparison in Generalization.}
To further study the generalization performance achieved by TENET Training, we compare the proposed method with regularization methods \cite{berthelot2019mixmatch,zhong2020random,devries2017improved}, data augmentation method \cite{azuri2020learning} and adversarial training \cite{shafahi2019adversarial} in Table \ref{tab:generation}.
Table \ref{tab:generation} shows the evident improvements of TENET Training over other methods in every case.
Typically, when 20 samples per class are used for training, the proposed method can achieve 76.91\% in terms of Top-1 accuracy. As a comparison, adversarial training \cite{shafahi2019adversarial} achieves the Top-1 accuracy of only 57.91\% in this case. It seems that adversarial training can improve the robustness, while it may also largely impair the generalization performance. Hence, Table \ref{tab:generation} illustrates that the proposed method can better maintain the generalization performance compared with other methods.
\section{Conclusion}
\label{sec:conclusion}
In this paper, we proposed a group-wise inhibition based feature regularization method to improve the robustness and generalization of CNNs.
In the proposed algorithm, CNN is regularized dynamically when learning, where the most discriminative regions with significant activation values are suppressed to enable the network to explore more diverse features.
Richer features then help to better represent images even with malicious variations.
The effectiveness of the proposed method was verified in terms of standard classification, adversarial robustness and generalization performance based on small number of training samples.
\section*{Acknowledgment}
The work is partially supported by the National Natural Science Foundation of China under grants no. 62076163, 91959108, 61602315 and U1713214,the Science and Technology Project of Guangdong Province under grant no. 2020A1515010707, the Shenzhen Fundamental Research fund JCYJ20190808163401646, JCYJ20180305125822769 and JCYJ20190808165203670, and Tencent "Rhinoceros Birds"-Scientific Research Foundation for Young Teachers of Shenzhen University.
{\small
\bibliographystyle{ieee_fullname}
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\section{Approach Overview}
\label{sec:overview}
BootKeeper is an offline analysis approach leveraging state-of-the-art binary analysis techniques to evaluate the validity and correctness of boot firmware images.
\subsection{Threat Model}
\label{sec:threat_model}
Our approach targets systems that implement measured boot protection mechanisms by using Trusted Computing technology.
From a high-level perspective, an attacker may attempt to tamper with a system's firmware in two ways:
\begin{itemize}
\item By exploiting weaknesses of the \gls{SCRTM}, \eg a buggy or incorrect \gls{SCRTM} may only perform partial measurements. In this case, an attacker may be able to inject code within the vendor's firmware image in the non-measured portions of the memory.
\item By directly injecting a malicious \gls{SCRTM}, the attacker may spoof the vendor's golden measurement values to pretend that the legitimate firmware is in place, while executing a malicious version of it.
\end{itemize}
By successfully circumventing the measurement process, an attacker may not only compromise the integrity of the system
while tricking the attestation procedure into reporting a legitimate software platform, but it may also leak secret
information from the \gls{TPM} such as cryptographic keys used for full disk encryption (as used by
Microsoft Windows's BitLocker, among other software products relying on this mechanism).
In the remainder of this paper, we assume the following attacker model:
\label{sec:attacker_model}
\begin{enumerate}
\item The attacker does not have physical access to the system.
\item The attacker does not have any form of privileged access to the system (neither local or remote, \ie no control over the \gls{OS}).
\item The system itself has not been infected prior to the attack and is non-malicious (\ie the \gls{SCRTM} is invoked from a non-malicious environment).
\item The \gls{SCRTM}'s code does not implement user input mechanisms (but such mechanisms may be implemented as part of later stages of the EFI boot process).
\item The attacker has the ability and sufficient knowledge about the target platform to craft malicious firmware images, \ie access to the vendors' official firmware images, and knowledge about the platform's golden values (\ie correct measurement values), or the ability to obtain those by reverse engineering.
\item The attacker may spread malicious images online (\eg by compromising the vendor's website or through third party websites such as user forums).
\item Optionally, the attacker may remotely interfere with the automated firmware update process that comes with some systems by compromising the download site, or by mounting a man in the middle attack when applicable (\eg if this process does not check the validity of SSL certificates), to trick the remote system into applying a firmware update using an attacker-chosen malicious image.
\end{enumerate}
\subsubsection{Signature Verification}
In order to successfully install a malicious firmware image in the target system, an attacker needs to bypass eventual signature verification mechanisms in place. While this aspect is outside of the scope of this paper, we briefly demonstrate the practicality of this assumption as follows.
A good practice when releasing software updates is to rely on cryptographic signatures in order to guarantee the integrity of the new software image before or during the installation process.
Unfortunately, this process is often imperfect, as several vendors do not implement proper signature verification mechanisms, leaving gaps for an attacker to use a forged firmware image.
In other situations, attackers may use a stolen certificate~\cite{kim2017} to sign malicious firmware images, or may remotely exploit a vulnerability in the firmware update routine, to bypass the signature checks. In the remainder of this paper, we assume that the signature verification mechanism is either absent, or vulnerable.
\subsection{Analysis Steps}
Our analysis approach relies on the verification of a set of key properties, which we describe in more detail the remainder of this section.
\subsubsection{Code Integrity Properties (CIP)}
\label{sec:cip}
The \gls{SCRTM} code is always implemented
with two main fundamental operations: (1) an operation of fingerprinting, which scans the code regions in memory (\eg using SHA-1) and (2) a \gls{TPM} write operation, storing the computed fingerprints in the \gls{TPM}.
We define these two operations as the building blocks of any \gls{SCRTM} measurement process performed on the platform.
In order to elude the measurement process, an attacker may act at two different
levels.
\begin{itemize}
\item Firstly, as illustrated in~\autoref{fig:forgery}, the attacker may modify the fingerprint
function (\eg code or parameters) to generate spoofed measurement values which
correspond to valid golden values (\ie values corresponding to correct measurements on the
vendor's firmware) even though the original firmware code is modified.
\item Secondly, the attacker may modify the results of the fingerprint function just before
these are written to the \gls{TPM}.
\end{itemize}
The \textit{tick} and the \textit{flea} attacks, described by \citet{butterworth2013bios},
are concrete examples of such attacks.
\begin{figure}[h]
\centering
\resizebox{\columnwidth}{!}{
\input{tikz/forgery.tex}
}
\Description{A figure describing a measurement-spoofing attack where the malicious BIOS sends a forged fingerprint to the TPM. The BIOS contains three blocks: a malicious SCRTM, a legitimate hash function, and a legitimate firmware. The malicious SCRTM calls the hash function with forged parameters to only measure the legitimate firmware which is not executed. Then, the malicious SCRTM sends the forged fingerprint to the TPM.}
\caption{Example of a measurement-spoofing attack where an attacker sends a legitimate fingerprint of non-executed firmware.}
\label{fig:forgery}
\end{figure}
In order to prevent these attacks,
our system verifies the three following properties:
\begin{enumerate}
\item {\it The authenticity of cryptographic hash functions}. Regardless of any potential implementation variants,
our system must be able to verify the authenticity of the code used as part of the fingerprinting measurement
process.
BootKeeper leverages binary analysis techniques to verify that the correct hash function is indeed used
as part of the firmware's fingerprinting code.
\item {\it The atomicity of the measurement process}. A correct \gls{SCRTM} implementation should also guarantee
the atomicity of its measurement process, \ie that the fingerprinting and \gls{TPM} write operations are invoked
sequentially in the correct order, and that the integrity of the measurement values if preserved between these two
operations.
In order to verify this property, BootKeeper constructs a \gls{CFG} of the \gls{SCRTM}, and detects eventual
operations modifying the measurement results before those are written to
the \gls{TPM}.\footnote{In practice, such operations may either correspond to malicious code attempting to forge measurement values, or to benign buggy code reporting erroneous measurements.}
\end{enumerate}
These two properties ensure the correctness of the \gls{SCRTM}'s code measurements process.
In addition to these, BootKeeper also ensures that the firmware under analysis does not present risks of certain classes of runtime attacks, as described below.
\subsubsection{Code Execution Integrity Property (CEIP)}
\label{sec:ceip}
Even if properties (1) and (2) are guaranteed, an attacker may attempt to alter the control-flow of the \gls{SCRTM} by redirecting the execution to malicious code hidden in the binary firmware image.
Fortunately, UEFI firmware runs in an execution environment protected by Data Execution Prevention (DEP). In other words, an attacker cannot trivially execute code injected in arbitrary sections of the binary image.
\textit{In the execution context of the \gls{SCRTM}, an attacker does not have the ability to inject code at runtime} since the SCRTM's code does not implement user input mechanisms and the \gls{SCRTM} code is invoked from a non-malicious environment (see rules 3 and 4 of our attacker model in~\autoref{sec:attacker_model}).
However, it remains possible for the attackers to hide code within the binary firmware image, and to attempt to trigger its execution at runtime.
\begin{figure}[h]
\centering
\resizebox{0.7\columnwidth}{!}{
\input{tikz/measurement_completeness.tex}
}
\Description{A figure with five basic blocks: four benign and one malicious. All are reachable, all the benign ones are measured, while the malicious one is reachable but not measured.}
\caption{Example of an incomplete measurement of the firmware where reachable (malicious) code is not measured.}
\label{fig:cfg}
\end{figure}
BootKeeper addresses this family of attacks as well by relying on an additional property:
\begin{enumerate}[resume]
\item {\it Completeness of the measurements}.
The \acrshort{SCRTM} must guarantee the completeness of the measurements of the firmware code memory regions.
More in detail, every memory region belonging to the \gls{CFG} of the \gls{SCRTM} must be measured and
reported to the \gls{TPM} component.
By doing so, attempts to hide malicious code within non-measured memory regions is detected, as
represented in~\autoref{fig:cfg}, showing benign (B) and malicious (M) basic blocks forming a \gls{CFG}.
\end{enumerate}
We emphasize that BootKeeper does not rely on a-priori knowledge of the legitimate \gls{CFG} of firmware images.
Instead, the goal of BootKeeper is to ensure that \emph{all reachable code} will be \emph{correctly} measured and
reported to the \gls{TPM} at runtime.
As such, the detection of malicious code is a two-stage process: a static part (BootKeeper) which ensures that the
verification code is correctly implemented, and a dynamic part (the measured boot process), which relies on
those mechanisms.
Recall the attacker model presented in~\autoref{sec:threat_model}: (3) the \gls{SCRTM} executes in a non-malicious environment (\ie the initial state of the system is non-malicious, only firmware images are) and (4) it does not implement I/O mechanisms. As a consequence, dynamic code injection attacks are specifically excluded.
\section{Background}
In this section, we introduce the background technology needed to
understand our approach.
We first describe the principles of the \gls{TPM}, then we describe the UEFI specifications and some of the
software/hardware components involved in the boot measurement process.
\subsection{Trusted Platform Module (TPM)}
The \gls{TPM} specification defines a co-processor offering
cryptographic features (\eg SHA-1, RSA, random number generator, or
HMAC), and tamper-resistant storage for cryptographic
keys~\cite{trusted2007tpm}.
The \gls{TPM} provides a minimum of 16 \gls{PCR} which are
160-bit wide registers used to store the measurements done by the
\gls{SCRTM} (usually SHA-1 hashes). The design of these registers
allows an unlimited amount of measurements and prevents an attacker from
overwriting them with arbitrary values. In order to do this, the only
possible operation is \textit{extend}:
\[
PCR_i = H(PCR_i\ ||\ m)
\]
Where $PCR_i$ is the $i$th \gls{PCR} register, $H$ is the hash function and $m$ the new measurement.
The \gls{TPM} \emph{concatenates} each new measurement sent with the previous value of the register, then it hashes the
result, which becomes the new value of the register.
This mechanism is crucial to establishing a chain of trust, since the only way to obtain a given measurement value
from a \gls{PCR} is to reproduce the same series of measurements in the same order.
The measured boot process relies on this mechanism to guarantee that a given software platform is valid and has not
been tampered with.
The \gls{TPM} also relies on these measurements to provide specific features
(\eg secure storage or remote attestation).
For instance, with the sealing operation, the \gls{TPM} offers the
ability to encrypt data, with a key only known to the \gls{TPM},
and it binds the decryption to the \glspl{PCR} values.
During the decryption (\ie unsealing),
the \gls{TPM} only decrypts the data if the \glspl{PCR}
values match the ones used during the encryption.
One common use case for the sealing operation is to store
the disk encryption key.
It ensures that the disk is decrypted only if the platform
has booted with the expected hardware and software,
and if no attacker tampered with the boot process
(\eg an evil maid attack).
\subsection{Static Core Root of Trust for Measurement}
The \gls{SCRTM} is responsible for the first measurement sent to
the \gls{TPM} in the PCR0 register and it is considered trusted by default
on the system.
Since the default
values of the \gls{PCR}s are known (either \verb~0x00...0x00~ or
\verb~0xFF...0xFF~), the entire trust in the \gls{SRTM} relies on the
\gls{SCRTM}. If it is possible for an attacker to modify the \gls{SCRTM}, then it is also possible for the attacker to forge the first measurement, and the next one, etc.
Therefore, the \gls{TCG} PC client specific
implementation~\cite{tcg2005client} states that the \gls{SCRTM}
must be an immutable portion of the firmware. The specification
defines immutability such that only an approved agent and method can
modify the \gls{SCRTM}. Most firmware fulfill this
requirement by using signed updates, because the \gls{SCRTM}
can only be modified if the update is coming from the vendor.
Recent firmware fulfill the requirement using an immutable
hardware protected \gls{SCRTM}~\cite{intelBootGuard, hpSureStart}.
Unfortunately, legacy platforms do not provide signed updates, or do
not require them. Furthermore, \citet{kallenberg2013defeating}, and \citet{wojtczuk2009attacking} have successfully exploited
multiple vulnerabilities in the implementation of signed firmware
updates by vendors, allowing an attacker to update the firmware with
a malicious one. Finally, if the private key of the vendor is
compromised, the platform is vulnerable.
\subsection{Unified Extensible Firmware Interface}
In 2005, 11 industry leading technology companies created the
\gls{UEFI} forum which defines specifications for interfaces~\cite{uefi2017}
used by the \gls{OS} to communicate with the
firmware~\cite{zimmer2010beyond} and \gls{PI}
specifications~\cite{uefi2015PI} which define the required interfaces
for the components in the firmware, allowing multiple providers to
create different parts.
\gls{UEFI} specifications are about the interfaces, while
\gls{UEFI} \gls{PI} specifications are about building \gls{UEFI}-compliant firmware.
Manufacturers are now providing, as boot
firmware replacing the \gls{BIOS}, \gls{UEFI}-compliant
firmware images.
\gls{UEFI} and \gls{PI} specifications define seven phases,
as illustrated in~\autoref{fig:uefi_phases}, which describe the boot
process of a platform:
\begin{enumerate}
\item The \gls{SEC} is the initial code running, it switches from real
mode to protected mode, initializes the memory space to run stack-based
C code, and discovers, verifies and executes the next phase.
\item The \gls{PEI} initializes permanent memory, handles the different
states of the system (\eg recovery after suspending), executes the next phase.
\item The \gls{DXE} discovers and executes drivers which initialize
platform components.
\item The \gls{BDS} chooses the boot loader to execute.
\item The \gls{TLS} handles special applications or executes the boot loader from
the \gls{OS}.
\item The \gls{RT} is when the \gls{OS} executing, but
there are still runtime services of firmware available to communicate with
the \gls{OS}.
\item The \gls{AL} takes control back over the \gls{OS} when it has
shutdown.
\end{enumerate}
\begin{figure}[ht]
\centering
\scalebox{0.75}{
\input{tikz/uefi_phases.tex}
}
\Description{A figure describing the several UEFI PI phases where the SCRTM encapsulates the SEC
and PEI phases, while the SRTM encapsulates the SEC, PEI, DXE, and BDS phases.}
\caption{\gls{UEFI} \gls{PI} phases with the ones corresponding to the \gls{SCRTM} and \gls{SRTM}}
\label{fig:uefi_phases}
\end{figure}
The \gls{TCG} specifies requirements for the measurement of \gls{UEFI}-compliant
firmware in \gls{TPM} \gls{PCR}s~\cite{tcg2014EFI}.
The \gls{SCRTM} in UEFI-compliant firmware is generally formed by the SEC
and PEI phases~\cite{zimmer2010beyond}, although no strict
requirements about its location are specified in the \gls{TCG} specification
as it can also be the entire BIOS~\cite{tcg2005client}.
Moreover, in recent platforms, the \gls{SCRTM} is a hardware-protected component,
outside of the BIOS, that performs measurements on the BIOS before its
execution~\cite{intelBootGuard, hpSureStart}.
In our work, however, we only consider a non-hardware protected \gls{SCRTM}.
\section{Conclusion}
In this paper, we introduce BootKeeper, a binary analysis approach to validate the measurement process of a boot firmware.
Our system uses static analysis and symbolic execution to validate a set of software properties on the measurement process implemented as part of the UEFI \emph{measured boot} specification.
BootKeeper detects incorrect implementations of UEFI firmware which do not exhaustively or correctly implement the measured boot process, as well as malicious images crafted with the intention of bypassing the measured boot process. More specifically, BootKeeper focuses on the \gls{SCRTM}, which is the most critical component in the verification chain.
An incomplete \gls{SCRTM} implementation leaves room for an attacker to hide code in subsequent parts of the firmware, whereas a malicious \gls{SCRTM} voluntarily ignores specific regions where malicious payloads are hidden, or attempts to forge measurements in order to match the measured values of a legitimate vendor firmware (\ie golden values), among other possible attacks.
This approach
can greatly improve trust in boot firmware update procedures. We evaluate BootKeeper against real-world firmware used in the industry as well as custom malicious firmware images, and show that our system is able to detect multiple variants of a variety of attacks from the state-of-the-art in the literature.
\section{Discussion}
\label{sec:discussion}
BootKeeper is a purely static approach relying on advanced binary
program techniques to analyze firmware images. As any static approach,
it comes with some challenges. In this section, we describe in more
detail the nature of these challenges, and how BootKeeper addresses
those. Finally, we point to some practical limits of our approach and
propose alternative research directions of interest.
\subsection{Theoretical Limitations}
In order to detect violations of the properties introduced in
Section~\ref{sec:overview}, BootKeeper relies on a combination of
state-of-the-art static analysis techniques, which together provide
the basis for implementing the verification algorithms presented in
Section~\ref{sec:approach}. These techniques, however, are subject to
theoretical limits, which prevents our approach from reasoning about
certain classes of properties in all possible situations.
BootKeeper relies in particular on:
\begin{itemize}
\item Static \gls{CFG} recovery to determine the set of possible execution paths of a firmware image.
The \gls{CFG} obtained from binary analysis is neither sound nor complete (the general problem of deciding if
an arbitrary path in a program is executable is undecidable~\cite{ramalingam1994undecidability}).
\item Symbolic execution and constraint solving, to reason about the possible concrete values of memory
and registers at arbitrary points of the execution.
Symbolic execution is subject to the well-known state explosion problem due to its exponential growing
nature, and the general problem of constraint (SMT) solving is NP complete.
\item Data-flow analysis, to isolate program paths involving measurement values, to generate program
slices in order to isolate the instructions affecting these values, and more generally, to detect faulty
operations.
Reasoning about data-flow at the binary level requires accurate models of data structure recovery,
and is subject to the pointer aliasing problem~\cite{ramalingam1994undecidability}.
\end{itemize}
Our approach inherits from these general limitations.
We discuss the practical impact of these theoretical limitations in~\autoref{sec:practical} below.
\subsection{Practical Impact}
\label{sec:practical}
The following is a discussion of the practical impact of the aforementioned limitations in our approach.
\subsubsection{False Positives}
In the case where the \gls{CFG} is too conservative and includes an overestimate of possible code paths in the graph,
BootKeeper will accordingly operate conservatively during the verification of property 3, \ie the completeness
of measurements.
While this may lead to false positives in certain circumstances, we stress that the \gls{CFG} we obtain from a binary has
a basic-block level granularity.
In comparison, vendors typically scan entire memory regions corresponding to sections from the firmware binary.
\textit{Why not just measure entire sections then?}
Our approach is more fine-grained, and aims to ensure that the vendor conforms to at least a defined minimal code
coverage corresponding to (an estimation) of the possible execution paths.
In the case of an incomplete \gls{CFG} between the return value of the hash function used in the measurements and the
subsequent \gls{TPM} write operation,
BootKeeper will not be able to compute a backward slice and therefore will not be able to validate property 2,
\ie the atomicity of the measurement process.
In this case, \emph{it will flag the image as malicious}, thus generating a false positive.
\subsubsection{False Negatives}
Similarly, the \gls{CFG} may miss edges in the graph corresponding, such as indirect jumps caused by complex instances
of runtime binding which cannot be resolved even with symbolic execution.
This may happen, among other possible cases, when external information (\ie external to the program) is required to compute the jump target.
The presence of such obfuscated or evasive code in early stages of firmware execution is, by itself, an excellent indicator of maliciousness which our approach could be extended with.
When such constructs are benign and part of the official vendor's firmware, an attacker may
succeed in hiding a payload $P$ if: 1) the \gls{SCRTM} omits one portion of executable memory $M_1$ during the measurements, 2) BootKeeper is missing a part of the \gls{CFG} corresponding to a set of basic blocks mapped in memory during runtime as $M_2$ (in practice, $M_2$ may not be contiguous), and the following holds true:
$$M1 \cap M2 \neq \emptyset \wedge |M_1 \cap M_2| \geq sizeof(P)$$
Without ruling out the possibility of strong attacker specifically challenging state-of-the-art static analysis techniques, we estimate that BootKeeper significantly raises the bar for an attacker to circumvent the measurement process, and we consider our approach practical in the context of a large span of possible attacks.
The presented limitations are intrinsic to any static approach, and cannot trivially be addressed without additional knowledge of the runtime environment. In the next section, we discuss possible alternatives to overcome these limitations.
\subsection{Alternative Solutions}
In order to analyze the program paths involved in firmware during execution in
a dynamic setting, an emulation of all the hardware components involved during
the platform initialization process would be necessary. Implementing such a
system is a cumbersome engineering task, especially if numerous targets need to
be supported. An alternative approach is to directly instrument the hardware
to dump the state of registers and memory as the firmware executes, the
knowledge of which would ease offline analysis. Similar to this is the Avatar
approach~\cite{avatar} which selectively switches between different execution
models, in a setup which is backed by the physical hardware.
While relevant to this discussion, neither of these approaches fits
within the scope of this paper. In comparison, BootKeeper requires no
hardware nor custom hardware models.
\subsection{Obfuscation}
Static binary program analysis techniques are vulnerable to the presence of obfuscation, and it is possible that a malicious firmware author could attempt to attack BootKeeper in this manner.
For instance, \citet{sharifimpeding} obfuscate conditional code by using the result of a hash function as a condition replacement. Since cryptographic hash functions have the pre-image resistance property, it is impossible for constraints solvers to solve all the constraints generated by the operations of the hash function.
These weaknesses are inherent to any tool relying on static program analysis~\cite{shoshitaishvili2015firmalice,chipounov2012s2e,yadegari2015symbolic}.
In the context of boot firmware, the problem related to obfuscation is two-fold. First, genuine vendors could use obfuscation techniques to protect their code against reverse engineering. Secondly, by relying on obfuscation techniques, an attacker could attempt to defend against automated program analysis. While the former would affect BootKeeper, the latter may be used as an indicator malice.
\section{Experimental Evaluation}
\label{sec:evaluation}
This section presents our experimental results.
Our evaluation metrics cover multiple attack vectors representing a large span of the attack surface against
the \gls{SCRTM}.
These include the ability of our prototype to identify and recover the location of \gls{TPM} write instructions,
the effectiveness of our approach to detect the presence of forged \gls{TPM} measurements, and to detect possible hidden
code areas which are left unmeasured.
In addition to this, we also evaluate the robustness of our analysis against various compiler optimization settings.
\subsection{Experimental Setup}
We evaluate BootKeeper on two real-world implementations of boot firmware used in the industry, as well as a
custom-crafted malicious firmware implementing state-of-the-art attacks.
\begin{enumerate}
\item SeaBIOS~\cite{seabios}, a native x86 BIOS implementation with \gls{TPM} support.
It also supports standard BIOS features and calling interfaces that are implemented by a typical proprietary
x86 BIOS implementations.
This project is meant to provide an improved and more easily extendable implementation in comparison to the
proprietary counterparts which come as stock firmware on standard x86 hardware,
and can be deployed as replacement firmware on a variety of motherboards.
\item EDK~II~\cite{edk2}, a modern, cross-platform firmware platform supported by a number of real Intel and
ARM hardware platforms.
It is a component of Intel's TianoCore (Intel's reference implementation of \gls{UEFI}).
Major vendors (\eg Apple, ARM, or HP) contribute to its development, and it serves as a basis for a number
of proprietary UEFI-compliant firmware implementations.
\item A custom-crafted malicious firmware image which we implemented to reproduce
multiple variants of the state-of-the-art attacks introduced by \citet{butterworth2013bios}.
\end{enumerate}
For validating cryptographic
functions, we are using firmware (EDK~II) that implements the SHA-1
function of the OpenSSL~\cite{openssl} libraries and \verb~gcc~ as a compiler.
\subsection{TPM Write Access Detection}
We evaluated BootKeeper against SeaBIOS, EDK~II, and our custom firmware.
Our hypothesis is that complex firmware implementations, like SeaBIOS{} and EDK~II,
use abstraction layers which tend to obfuscate \gls{TPM} write instructions,
\ie these do not exhibit such instructions in the form of a fixed address corresponding to the specification
(\eg \verb~mov 0xfed40024, al~).
Additionally, these abstraction layers may invoke several functions to initialize data structures,
perform hardware tests, use loop structures or handle
different types of errors, thus creating many paths, potentially leading our analysis to path explosion during its symbolic execution phase.
In order to test the resiliency of our approach against the aforementioned intricacies, but also against compiler optimizations, we evaluated BootKeeper in the context of multiple compiler optimization settings. For each firmware implementation, we produced 5 variants using different optimization flags: \verb~-O1~ to \verb~-O3~ which optimize for speed, \verb~-Os~ which optimizes for size, and \verb~-O0~ for no optimization. This process generates 15 firmware variants.
We present the results in~\autoref{tbl:accuracy_find_writes}.
\begin{table}
\centering
\caption{Detection of the function writing the measurements}
\label{tbl:accuracy_find_writes}
\begin{tabular}{cccc}
\toprule
\specialcell{Optimization\\flags} &
\specialcell{Custom\\firmware} &
EDK~II &
SeaBIOS \\
\midrule
\verb|-O0| & \tikzcircle{2.5pt} & \tikzcircle[black, fill=white]{2.5pt} & \ding{55} \\
\verb|-O1| & \tikzcircle{2.5pt} & \tikzcircle[black, fill=white]{2.5pt} & \tikzcircle{2.5pt} \\
\verb|-O2| & \tikzcircle{2.5pt} & \tikzcircle{2.5pt} & \tikzcircle{2.5pt} \\
\verb|-O3| & \tikzcircle{2.5pt} & \tikzcircle{2.5pt} & \tikzcircle{2.5pt} \\
\verb|-Os| & \tikzcircle{2.5pt} & \tikzcircle{2.5pt} & \tikzcircle{2.5pt} \\
\bottomrule
\end{tabular}
\vspace{1em}
\tikzcircle{2.5pt}~:~detected~\tikzcircle[black, fill=white]{2.5pt}~:~not~detected~\ding{55}~:~error
\end{table}
BootKeeper can successfully detect the \gls{TPM} write access in 80\% of all cases (12 out of 15).
During this evaluation phase, we set an analysis timeout threshold of 10 minutes.
It is worth noting that BootKeeper found all the write access instructions within all the tested variants,
with the notable exception of \textit{unoptimized} EDK~II{} images.
We explain this observation by the fact that a lesser optimization level means more instructions to execute,
more loops and therefore more likelihood of path explosion during symbolic analysis.
While extending the analysis timeout threshold would be a viable option, we argue that vendors typically compile their
code with size optimizations (using \verb~-Os~) when releasing firmware for production use,
to reduce memory footprint,
in which case our approach succeeds under the 10 minutes threshold.
In the case of SeaBIOS, the analysis results are missing in the situation where no optimization is used (\verb~-O0~).
Unfortunately, a bug in SeaBIOS{} prevented the code from compiling with this optimization level at the time of our
evaluation, hence we could not test it.
Nonetheless, BootKeeper can successfully detect \gls{TPM} write operations in SeaBIOS{} in all other optimization
settings.
In summary, these experiments demonstrate that our approach can correctly detect the \gls{TPM} write operations even
in intricate cases, in real-world firmware implementations, from legacy \gls{BIOS} to recent \gls{UEFI}-compliant firmware.
\subsection{Forged TPM Measurements Detection}
\label{sec:sub:forged-tpm-measurements-detection}
In order to evaluate the effectiveness of our approach against state-of-the-art attacks, we reproduced multiple variants of the \textit{tick} attack, described by \citet{butterworth2013bios}.
Each developed attack variant attempts to forge the measurements sent to the
\gls{TPM} by relying on several techniques: (1) attacking the SHA-1
function, (2) leaving out non-measured code, (3) modifying the \gls{TPM} parameters.
We now describe how BootKeeper performs against these attacks.
\paragraph{Hash Function Validation}
A first attack attempts to subvert the hash function results. In order to
test this attack, we create two firmware versions: one without a SHA-1
function, and another with a modified version of SHA-1 which
returns a tampered hash value. In either case, BootKeeper reports no
match when generating signatures for the function defined inside the instruction
traces (compared against a generated database of common cryptographic implementations from Crypto++ and libOpenSSL) and reports a violation of the property ``valid hash function''.
\paragraph{Completeness of the Measurement}
We evaluate this property by implementing an attack that can
modify the firmware's code
by including
new code to the \gls{CFG} of the program. More specifically, we add new malicious
functions to a non-measured code area that is invoked before returning from the \gls{SCRTM} code.
Since this code is not included in any measurement performed by the hash function,
BootKeeper can detect it by ensuring that every part of the \gls{CFG} is correctly measured
(as described previously in~\autoref{sec:coverage}).
\paragraph{Atomicity Property}
In order to validate the atomicity property, we define a scenario
where an attacker properly measures the firmware with the correct SHA-1
function, but then tampers with the results by overwriting the measurements with other values before sending those to the \gls{TPM}, thus violating the atomicity property of the measurement operations.
During the analysis, BootKeeper can fetch the parameters of the hash function, and more importantly the
address of the pointer where the hash is stored.
Then, by performing the symbolic execution step described in~\autoref{sec:atomic}, it can detect the malicious instruction responsible for overwriting the measurements.
In order to fully reflect practical analysis challenges, we also consider the
case where an attacker attempts to trick the analysis by incorporating a real measurement using the correct hash function, and later writing the measured value somewhere else before sending a forged value to the \gls{TPM}. We reproduce this attack scenario to evaluate the resilience of our analysis step presented in Section~\ref{sec:atomic} against the presence of false positives involved by the backward slicing algorithm.
In our evaluation, false positives indeed occur, but these are effectively filtered by the following step of forward reaching definition analysis (as expected).
In this situation again, BootKeeper can detect the attack, and report the malicious instruction responsible for overwriting the measurements.
\subsection{Performance}
While performance is not critical in the context of an offline analysis setting, we demonstrate the practicality of BootKeeper in terms of analysis time and memory usage.
In the following, we use a valid firmware for evaluation, and measure the required amount of time BootKeeper takes to proceed, while monitoring the peak of RAM usage. In this experiment, we use a single-thread on an Intel Xeon E312 with 64GB of RAM. The results presented in~\autoref{tbl:performance} were obtained by running this experiment 100 times, and represent the mean, minimum, maximum values and the standard deviation of both the runtime (in milliseconds) and the RAM usage (in
megabytes).
\begin{table}
\centering
\caption{Time and RAM usage for firmware analysis}
\label{tbl:performance}
\begin{tabular}{llllll}
\toprule
Type & & Minimum & Maximum & Mean & \specialcell{Standard\\deviation} \\
\midrule
Time & (ms) & 103 950 & 108 760 & 105 704 & 849 \\
RAM & (MB) & 522.3 & 522.8 & 522.7 & 0.1 \\
\bottomrule
\end{tabular}
\end{table}
Executing the entire analysis (\ie validating the firmware) takes on average 1 minute and 48 seconds. The memory usage peaks at 522 megabytes.
\section{System Design and Implementation}
\label{sec:approach}
In this section, we present the algorithmic properties of our analysis components.
\subsection{Code Integrity Properties (CIP) Validation}
The process of validating the Code Integrity Properties presented in~\autoref{sec:cip} relies on four analysis steps:
(1) Detecting \gls{TPM} write operations inside the firmware code,
(2) Detecting hash functions inside the firmware code,
(3) Validating the authenticity of hash functions,
(4) Validating the atomicity of the measurement process.
We now describe how the system achieves each step of the analysis.
\subsubsection{TPM Write Operation Detection}
The first step of our analysis is to identify the \gls{TPM} write
operations inside the firmware code. Such operations can be identified
by searching for standard API prototypes. According to the \gls{TPM}
specification version 1.2~\cite{tcg2005TIS, tcg2005client}, such
functions must use a fixed address (\verb~0xFED40000~ is the default),
along with an offset used for distinguishing among different
operations (\eg read and write) on the \gls{TPM} registers.
Unfortunately, we cannot predict how the compiler organizes the
instructions or how the code of the firmware performs the write
accesses. Developers tend to create abstraction layers (\eg to avoid
redundancy or to have a modular code), and may use different
optimization flags for the compilation of the firmware.
As a result of this, \gls{TPM} read and write operations do not straightforwardly appear as an offset from the specified constant address value in the
binary executable version of the firmware. Therefore, in order to tackle this problem and find a state of
the program where a write access to the \gls{TPM} known
address happens, we leverage symbolic execution, starting at
the entry point of the firmware, and record every instruction writing at the specified address
(\verb~0xFED40024~ in our case). This step of symbolic execution allows BootKeeper to resolve computed addresses for which it would be extremely difficult to reason about in a purely static setup.
We leverage the angr~\cite{angr} platform to perform symbolic execution.
During symbolic execution, the system tracks the state of registers and memory throughout program execution along with the constraints on those variables. Whenever a conditional branch is reached, the execution follows both paths while applying constraints to the program state to reflect whether the condition evaluates to True or False.
At the end of this analysis step, BootKeeper has obtained a list of addresses in the firmware corresponding to the
\gls{TPM} write operations, if any such operation is present.
If the system does not find any \gls{TPM} write operation, it flags the firmware image as non-valid.
\subsubsection{Detecting Hash Functions}
\label{subsec:slicing}
The second step of our analysis is to identify hash functions
among the functions used by the firmware image to elaborate the measurement values.
We apply the following algorithm. The analyzer starts from the
\gls{TPM} write operations and works iteratively on the
instructions flow in reverse order. To this end, we leverage a static backward approach~\cite{kiss2003interprocedural}.
where for each identified \gls{TPM} write operation, our analyzer computes a backward slice starting from the
sensitive data. Sensitive data are the parameters of the
\gls{TPM} write operations, in our case the measurements value of
the hash function stored in a particular memory region. The aim of this
backward slicing analysis step is to identify modifications on
sensitive data, and to find all the data sources from which the modified
data is derived.
The backward slice technique allows us to focus our analysis only on
the instructions that lead to a single \gls{TPM} write access,
which is important for two reasons. First, for performance reasons,
focusing on a subset of the program greatly improves the time needed to
perform further analyses. Second, and more importantly, it
ensures that the \gls{TPM} write access is connected to a
measurement computed earlier in the execution (\ie not inserted in an ad-hoc manner).
Hence, given a set of instructions related to the \gls{TPM} write
access, BootKeeper detects if an actual measurement is present.
The output of this analysis step is a set of traces corresponding to instructions correlated with the \gls{TPM} write
operations parameters.
Such traces could also be leveraged to locate the hash function code as well.
However, it is worth noting that the backward slicing algorithm returns an over-approximation of the instructions
leading to the program point where the \gls{TPM}
measurements are sent, and therefore, it might include unrelated instructions.
For example, functions which simply move computed hash values from one
memory structure to another may also be whitelisted by this analysis.
For this reason, we cannot simply rely on this technique to accurately locate the hash functions themselves,
and we leverage a different approach to precisely locate those, as presented in the following paragraph.
\subsubsection{Validating the Authenticity of Hash Functions}
\label{sec:hash}
\label{sec:sub:sub:discovery_sha1}
After BootKeeper has identified the set of instructions related to a particular
\gls{TPM} operation, it extracts the corresponding blocks and attempts to recognize one of the possible valid hash function (\eg SHA-1).
In order to automatically identify cryptographic functions within binary code, we leverage the approach presented by \citet{lestringant2015automated} which relies on \gls{DFG} isomorphism. From a high-level perspective, this approach compares the code structure of known functions with the code structure of unknown functions, to determine if these implement the same algorithm.
This approach first employs a normalization step (based on a code rewrite mechanism), which is designed to increase the detection capability by erasing the peculiarities of each
instance of an algorithm. Then, by relying on a sub-graph isomorphism algorithm, the normalized \gls{DFG} is compared to that of known reference functions. We chose this approach to recognize functions of well-known libraries which are used in real-world boot firmware images (including Crypto++ and OpenSSL~\cite{openssl}).
BootKeeper leverages this technique starting from the instruction traces highlighted in the previous analysis step. From there, it creates a \gls{DFG} for each corresponding function of the firmware image involved in the trace, and attempts to match the signature of a standard hash function, such as the SHA-1 implementation of libOpenSSL.
The output of this analysis step is the set of basic blocks belonging to the identified hash function. If no known hash function is found, then \emph{BootKeeper flags the firmware image as non-valid.}
\subsubsection{Validating the Atomicity Property}
\label{sec:atomic}
\label{sec:sub:sub:operations-atomicity}
The final step involved in validating code integrity is to ensure
that no modification of the computed measurements occurs before those are written to the \gls{TPM}.
From the instruction traces obtained during the backward slicing step (\autoref{subsec:slicing}),
BootKeeper executes the corresponding code paths symbolically,
from the hash function's return instruction to the \gls{TPM} write operation, and rules out the presence of
instructions modifying the computed hash value.
In order to detect such instructions, BootKeeper performs a last step of forward reaching definition analysis on each
identified code path to ensure that the value stored in the \gls{TPM} indeed corresponds to the return value
of the correct hash function.
If any instruction on a given path modifies the measurement value, the atomicity property is violated.
In this case, the firmware image is reported as invalid, and BootKeeper reports the faulty instruction and program path.
\subsection{Code Execution Integrity Validation}
Recall that, in addition to verifying the correctness of the measurement process, BootKeeper also evaluates the risks of runtime attacks through a Code Execution Integrity Property (CEIP) described earlier in Section~\ref{sec:ceip}, which consists in the completeness of measurements.
Conceptually, if the measurement process is incomplete, \ie leaving out portions of the code section, it becomes possible for an attacker to ``hide'' malicious code in the non-fingerprinted areas, hence the importance of this property.
\subsubsection{Completeness of the Measurements}
\label{sec:coverage}
BootKeeper ensures that every function in the \gls{CFG} of the \gls{SCRTM} is measured. The acute reader may wonder what becomes of basic blocks of code which is deemed non-reachable by the control-flow recovery analysis: this point is discussed in~\autoref{sec:discussion}.
The \gls{CFG} is computed by a recursive algorithm which disassembles and analyzes each
basic block, identifies its possible exits (\ie successors) and adds them to the
graph. It repeats this analysis recursively until no new exits are
identified.
\gls{CFG} recovery has one fundamental challenge: indirect
jumps. Indirect jumps occur when the code transfers control flow to
a target represented by a value in a register or a memory location
(\eg \verb|jmp
classes: (1) Computed, an example could be an application that uses
values in a register or memory to determine an index into a jump table
stored in memory; (2) Runtime binding, \ie function pointers
which jump targets are determined at runtime.
BootKeeper leverages state-of-the-art analysis techniques for control-flow recovery, as available in the
\verb|angr| framework~\cite{angr}.
This process leverages a combination of forced execution, backwards slicing, and symbolic execution to recover,
to the extent possible, all jump targets of each indirect jump.
While it may not always be possible to recover all jump targets in complex software projects,
it is practical in the context of a boot firmware's \gls{SCRTM} due to the minimal aspect of such a code base.
A more detailed discussion of this point and the practical limitations that it may involve
is provided in~\autoref{sec:discussion}.
Once BootKeeper has obtained a \gls{CFG} of the \gls{SCRTM},
it proceeds to verify the coverage of the \gls{SCRTM} in terms of code fingerprinting.
In order to do so, BootKeeper analyses all input values passed to the fingerprinting functions
(\ie hash function identified in~\autoref{sec:hash}) to determine the address and size of the memory areas used to compute the measurements.
At this point, BootKeeper has statically identified the addresses and sizes of the memory regions that will be
fingerprinted by the \gls{SCRTM} at runtime. Its next step is to ensure that all reachable code in the SCRTM's
\gls{CFG} does indeed fall within the measured memory regions.
In order to do so, BootKeeper verifies that the address of each basic block belonging to the \gls{CFG} falls within that range.
If it is not the case, it means that a part of the firmware's code will not be measured correctly, and \emph{flags the firmware image as non-valid.}
By ensuring that all the reachable code in the \gls{CFG} is indeed measured by the \gls{SCRTM}, BootKeeper prevents firmware modification attacks. where malicious code is inserted within the executable paths of the firmware's code.
\section{Introduction}
One of the most critical components of every computer is the boot
firmware (\eg BIOS or UEFI-compliant firmware), which is in charge of
initializing and testing the various hardware components, and then
transfer execution to the \gls{OS}. As a result of its early
execution, the boot firmware is a highly privileged program. Any
malicious alteration of its behavior can have critical consequences on
the entire system. An attacker that can control the firmware can
control any parts of the software and undermine the security of the
entire \gls{OS}. Without any protection of the integrity of the boot
firmware, we cannot assure any security properties of the software
executing on the system.
To guarantee the software integrity of the machine, the \gls{TCG}, an
industry coalition formed to implement trusted computing concepts
across personal computers, designed a new set of hardware components,
the aim of which is to solve various hardware-level trust issues. In
their specification, they define the \gls{TPM}, which is composed of a
co-processor that offers cryptographic functions (\eg SHA-1, RSA,
random number generator, or HMAC) and a tamper-resistant non-volatile
memory used for storing cryptographic keys~\cite{trusted2007tpm}. The
\gls{TPM} along with other software components together form a root of
trust, which is leveraged as part of several security mechanisms,
including the \emph{measured boot} process. With measured boot,
platforms with a \gls{TPM} can be configured to measure every
component of the boot process, including the firmware, boot loader,
and kernel. Such measurement process is also called the \gls{SRTM}.
The core of trust of the entire process is established based on the
integrity of the first piece of code inside the boot firmware which is
doing the first measurements, also called the
\gls{SCRTM}~\cite{zimmer2009trusted}. In the event where a malicious modification
of the \gls{SCRTM} successfully hides from the self-measurement
technique, the whole chain of trust and, consequently, the
integrity of the entire system may be broken.
In this direction, \citet{butterworth2013bios}
described different examples of attacks against the \gls{SCRTM}
component.
In particular, the authors show how a novel ``tick'' malware, a
51-byte patch to the \gls{SCRTM}, can replay a forged measurement to the \gls{TPM},
falsely indicating that the BIOS is genuine.
These attacks take
advantage of the fact that some vendors do not measure the
\gls{SCRTM} code, thus allowing an attacker to modify it and to forge
measurements without being detected.
Recent platforms incorporate an immutable, hardware protected
\gls{SCRTM}~\cite{intelBootGuard,hpSureStart}.
Intel Boot Guard and HP Sure
Start are immutable \glspl{SCRTM} which measure and verify, at boot time, the integrity of the BIOS image before executing it.
Such technologies are not directly vulnerable to the aforementioned attacks,
since their code cannot be modified by an attacker.\footnote{Nonetheless, Intel Boot Guard has been shown to be vulnerable to some attacks as well~\cite{alex}.}
Both technologies, however, are only available in recent Intel and HP platforms,
\emph{leaving previous hardware implementations, or devices of other vendors,
vulnerable against forged measurements}.
In such implementations, since the \gls{SCRTM} is not hardware protected, \emph{it is usually attached to the firmware image itself during the firmware update process}.
Even when the firmware image is signed, attacks may compromise this process~\cite{kim2017}, and consequently allow an attacker to modify both the firmware code and the \gls{SCRTM}.
In order to solve these challenges in validating the \gls{SCRTM} code, we design a self-contained approach based on static analysis at the binary level, which is able, starting from a boot firmware image, to validate the correctness of the measurement process.
Our system verifies software properties on the \gls{SCRTM} code embedded in firmware images, including: (1) the completeness of firmware code measurements in terms of fingerprinted
memory regions, (2) the correctness of cryptographic functions
implemented\footnote{Vendors typically implement the cryptographic functionalities used as part of the measurement process in software.} inside the \gls{SCRTM} (\eg SHA-1), and (3) the
correctness of the \gls{SCRTM}'s control flow.
More in detail, the first property ensures that the code of the entire firmware is measured correctly by the \gls{SCRTM}, \ie that none of the instructions to be executed at runtime will be missed by the measurement process. The second property ensures that the implementation of cryptographic functions inside the \gls{SCRTM} is correct. The third property validates the correctness of the measurement operations performed by the \gls{SCRTM} in terms of execution order. It also guarantees the atomicity of operations occurring between memory fingerprinting and write operations performed on the \gls{TPM} component (\ie ensuring that what is measured is what is written to the TPM).
Altogether, this set of properties can prevent attacks aiming to elude the measurement process,
and it guarantees that the integrity of a firmware image is properly verified during the \emph{measured boot} process.
We implement a prototype of our system, dubbed BootKeeper, based on the angr program analysis
framework~\cite{angr,shoshitaishvili2016state}.
We evaluate our system on different open source boot firmware images,
and we implement different attacks against the firmware to
show the efficacy of our approach.
Our paper makes the following contributions:
\begin{itemize}
\item We devise a set of software properties that can be used for validating the measurement process
and mitigate firmware attacks aimed to subvert the entire system.
\item We design and implement BootKeeper, a binary analysis approach to detect and prevent measurement boot
firmware attacks in different attack scenarios.
\item We perform experimental evaluation against different attacks and several boot firmware implementations
to demonstrate the effectiveness of our approach.
\end{itemize}
\section{Related Work}
To the best of our knowledge, John Heasman developed the first public
\gls{BIOS} rootkit by modifying \gls{ACPI} tables stored in
the \gls{BIOS}~\cite{heasman2006implementingACPI}, and he also
showed how to make a persistent rootkit by re-flashing the expansion
\gls{ROM} of a \gls{PCI}
device~\cite{heasman2007implementingPCI}. Other attacks have been
performed since then, Anibal Sacco and Alfredo Ortega discussed how to
inject malicious code in Phoenix Award
\gls{BIOS}~\cite{sacco2009persistent} and Jonathan Brossard
showed the practicability of infecting different kinds of
firmware~\cite{brossard2012hardware}. In addition to papers and proof
of concepts of attacks, some malware is also taking advantage of the
lack of security of the boot firmware. For example, the Chernobyl
virus~\cite{cih}, which appeared in 1999, tried to overwrite the
\gls{BIOS} to make it unbootable. In 2011, the malware
called Mebromi~\cite{mebromi} re-flashed the \gls{BIOS} of its
victims to later write a malicious \gls{MBR} which infected the
\gls{OS} even when it was re-installed
from scratch.
All these attacks can be detected if the vendor is trustworthy, a
\gls{TPM} device is present and used correctly.
Several misconfiguration and design issues, however, show that the \gls{TPM} can be
attacked as well.
In this direction, \citet{butterworth2013bios}
demonstrated a replay-attack that forges the
measurement sent to the \gls{TPM} to fake an uncorrupted
\gls{BIOS} in case of non-respect of the specifications and
recommendations.
\citet{bruschi2005replay} also showed a replay-attack in an
authorization protocol of the \gls{TPM}.
\citet{sadeghi2006tcg} and \citet{butterworth2013bios} revealed that some \gls{TPM}
implementations do not meet the \gls{TCG} specifications which
may have critical security implications.
\citet{kauer2007oslo} also
demonstrated a \gls{TPM} reset attack which
allows an attacker to forge the \gls{PCR} values.
Several approaches have been proposed
to improve the \gls{TPM} technology and the boot firmware integrity techniques.
For example, Bernhard Kauer proposed a counter
measure~\cite{kauer2007oslo} to the reset attack on the \gls{TPM}
by using a \gls{DRTM}. In the direction of firmware security,
dynamic analysis using symbolic execution has been extensively used to
find vulnerabilities in
firmware~\cite{davidson2013fie,bazhaniuk2015symbolic,shoshitaishvili2015firmalice,zaddach2014avatar,kuznetsov2010testing}.
More related to our work, \citet{bazhaniuk2015symbolic}
used an approach to detect vulnerabilities in boot firmware. Our work
is orthogonal to such approach and focuses on boot firmware phases
where vulnerabilities are not detected or fixed by the vendor and they
can be used by an attacker to tamper with the boot process (\eg
to forge \glspl{PCR} values).
\citet{butterworth2013bios} designed a timing-based attestation at the
\gls{BIOS} level as an alternative to
the hashing of the firmware. Such a technique provides a reliable way
to attest the integrity of a platform even if the attacker has the
same privilege level as the \gls{SCRTM}. The idea, adapted from
previous work on timing-based
attestation~\cite{schellekens2008remote}, is that in the absence of an
attacker the time required to perform a checksum of the firmware will
be constant. When an attacker tries to fake the checksum, she requires
additional instructions that increase the execution time, hence it
can be detected by the system.
While this work greatly improves the trust in the remote attestation,
and fixes the vulnerabilities discovered in their paper, it requires a
complicated architecture for being deployed. In fact, it needs to set
up a remote server for the attestation phase and to modify the interrupt
signal handling in the \gls{OS} to obtain a precise measurement of
the code execution.
On the contrary, our approach works without having an attestation
architecture and it only performs static checks on the firmware boot
image.
Recent platforms incorporate immutable, hardware protected \glspl{SCRTM},
called Intel Boot Guard~\cite{intelBootGuard} and HP Sure
Start~\cite{hpSureStart}. They are immutable \glspl{SCRTM} that measure and
verify at boot time the BIOS before its execution, thus providing firmware
integrity and a trusted boot chain with a Root-of-Trust locked into
hardware. Such technologies ensure that the first measurement cannot
be forged, since the attacker cannot modify their code. Both
technologies, however, are only available in recent Intel and HP platforms.
In addition, Intel Boot Guard has been showed to be vulnerable to a certain
class of attacks~\cite{alex}.
The advantage of our approach with
respect to those new technologies is twofold. First, it can be used to
protect architectures that are not equipped with such hardware
features. Second, our approach is orthogonal to such hardware
protections, since BootKeeper can be used as a standalone analyzer from
the vendor side for validating the \gls{SCRTM} code as the last step of the
deployment process. The main contribution of BootKeeper is related to
the software properties that we devise for validating the measurement
process. When BootKeeper is used by the vendor, our analyzer can
perform the same analysis (\eg enforcing software properties) at the
source code level, and verify that no one tampers with the measurement
task during the developing process.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 2,751 |
Countless opportunities are present with this large home boasting many rooms plus the added bonus of a huge multi-purpose building all situated on a sizable allotment of 657sqm approx.
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"redpajama_set_name": "RedPajamaC4"
} | 9,195 |
Le 2-mercaptobenzimidazole est un composé organique de la famille des benzimidazoles de formule C7H6N2S. Il est utilisé comme , en particulier pour les caoutchoucs résistant aux vibrations et à la chaleur.
Propriétés
Le 2-mercaptobenzimidazole se présente sous la forme d'une poudre jaune inodore. Il existe sous la forme d'un équilibre tautomérique entre une forme « thione » (1H-Benzo[d]imidazol-2(3H)-thione), et une forme « thiol » (1H-Benzo[d]imidazol-2-thiol) :
Synthèse
Le 2-mercaptobenzimidazole peut être produit par réaction entre l'orthophénylènediamine et l'éthylxanthate de potassium ou le disulfure de carbone.
Notes et références
Voir aussi
2-Mercaptobenzothiazole
2-Mercaptobenzoxazole
Benzimidazole
Thiocarbamide | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 586 |
\section{Introduction}
\label{sec:intro}
The launch of the \textsl{Solar and Heliospheric Observatory} \citep[SOHO;][]{Domingo1995} and the subsequent \textsl{Large Angle and Spectrometric Coronagraph} \citep[LASCO;][]{Brueckner1995} C2 and C3 white-light data ushered in an entirely new era of detailed observations of the structure and dynamics of the coronal streamers and the helmet streamer belt. \citet{Sheeley1997} analyzed the continual, intermittent outflow of density enhancements known as streamer blobs and the improved spatial and temporal resolution enabled the characterization of inflows in the wake of coronal mass ejections (CMEs) and streamer disconnection events \citep[e.g.,][]{WangYM1999a,WangYM1999b,WangYM2000}. Hundreds of coronal inflow events were observed and cataloged by \citet{Sheeley2002} and a new class of inflows in which an outward and inward component are clearly identified became known as in/out pairs \citep{Sheeley2007}. Coherent, small-scale flux rope structures were also being found in the in-situ observations from IMP~8 and \textsl{Wind} \citep{Moldwin2000} and were shown to have magnetic fields that could be fairly well-described by the same linear force-free cylinder model often used for larger interplanetary CME (ICME) flux rope structures \citep{Cartwright2008,Yu2014}. \citet{Crooker2004} analyzed in-situ observations of high-beta regions (heliospheric plasma sheets) in the \textsl{Wind} data that strengthened their interpretation of intertwined flux tubes, likely caused by interchange reconnection at the cusp of the helmet streamer belt \citep{Crooker1996hps,Crooker1996hfds}.
The multispacecraft remote-sensing and in-situ observations provided by the \textsl{Solar Terrestrial Relations Observatory} \citep[STEREO;][]{Kaiser2008} spacecraft meant that \citet{Sheeley2009} were able to analyze the 3D structure of streamer blobs and under favorable spacecraft positions, the small flux ropes observed in the heliosphere were able to be directly traced back to their coronal source regions \citep[e.g.,][]{Kilpua2009b, Rouillard2010a, Rouillard2010b, Rouillard2011}. Advanced image processing enabled \citet{DeForest2012} to observe signatures of flux disconnection in the heliospheric imager field of view and \citet{HowardT2012}, \citet{SanchezDiaz2017b}, and others to better track and compile statistics of the kinematic evolution of both small-scale and large-scale transient outflows.
Recently, \citet{Hess2017inflows} have examined inflows in the inner white-light corona representing the closing down of magnetic flux beneath CME eruptions, \citet{WangYM2018blobs} have shown that gradual streamer expansion is often a precursor to streamer blob pinch-off at the cusp and whether an inflow is observed depends on the radial distance the reconnection occurs, which is in turn a function of field strength/flux content under the streamer belt, and \citet{SanchezDiaz2017a} have used STEREO data to argue that coronal inflows and streamer blob outflows are always associated, and in a follow up study, investigated the correspondence between small flux ropes, high density regions, and heliospheric current sheet (HCS) crossings in \textsl{Wind}, STEREO, and \textsl{Helios} data \citep{SanchezDiaz2019}.
Data from the first several perihelia of \textsl{Parker Solar Probe} \citep[PSP;][]{Fox2016} already represent a treasure trove of new remote-sensing and in-situ observations: \citet{Wood2020} analyzed a streamer blob/disconnection event in the \textsl{Wide-field Imager for Parker Solar Pobe} \citep[WISPR;][]{Vourlidas2016} imaging data; \citet{Rouillard2020} have tracked helmet streamer outflow and its fluctuations in STEREO coronagraph and heliospheric imager data all the way to their in-situ measurement by PSP; and \citet{ZhaoLL2020} have shown the first PSP flyby contained multiple flux rope structures ranging in duration from 8--300~minutes. In addition, \citet{MurphyA2020} have recently analyzed small flux ropes in the solar wind seen with the MESSENGER spacecraft over a range of radial distances in preparation for better understanding current and future PSP and \textsl{Solar Orbiter} \citep[SolO;][]{Mueller2020} observations.
The underlying physics of streamer blob formation, inflows, and in/out pairs is more-or-less agreed upon, i.e.\ each of these signatures reflect coronal plasma dynamics resulting from magnetic reconnection associated with the open--closed field boundaries of coronal streamers, their evolution, and their intrinsic variability. However, the details of these reconnection processes, and our understanding of their role in creating the structured variability of the slow solar wind, remain an active area of research \citep[see reviews by][]{Abbo2016, Viall2020}.
{
Early attempts to model at least the outward moving part of these streamer disconnection/slow CME events were reasonably successful in 2.5D magnetohydrodynamic (MHD) simulations \citep[e.g.,][]{Linker1992} and confirmed that the dynamics associated with magnetic reconnection were, at least qualitatively, in agreement with the observations. \citet{Suess1996} examined the role of coronal heating and heat conduction on the structure of the streamer belt, showing that the pointed, cusp-like feature was a result of the continual shedding of flux. \citet{Einaudi1999, Einaudi2001} and \citet{Rappazzo2005} modeled magnetic island formation in the wake--neutral sheet configuration of the streamer cusp--HCS system and \citet{Endeve2003, Endeve2004} characterized the lack of a stable equilibrium for the dipole streamer where the heating periodically accumulates enough gas pressure at the streamer cusp to overcome the magnetic tension forces causing the outermost layers to expand/open into the plasma sheet and solar wind. This expansion/opening facilitates magnetic reconnection in the equatorial current sheet that acts to closes magnetic flux back down, allowing the cycle to repeat. \citet{ChenY2009} showed with a sufficient density gradient and velocity shear across the streamer boundary, a Kelvin--Helmholtz instability can develop and act as the gas pressure/mass density perturbation that drives magnetic reconnection at the cusp. Recently, \citet{Allred2015} have examined the force balance within 2.5D streamer blob plasmoids and shown their ejection periodicity can be controlled with the coronal heating factor.
}
\citet{Higginson2018} presented the first 3D MHD simulation of streamer blob formation at the cusp of the streamer belt and within the HCS in the extended corona for an idealized, solar minimum-like global field configuration. This paper continues the work of \citet{Higginson2018} through a detailed examination of the near-Sun consequences of magnetic reconnection occurring at the open--closed field interfaces of the coronal streamer belt in a more complex, solar maximum-like global field. The simulation results herein reproduce favorably many of the observed characteristics of coronal inflows, in/out pairs, and streamer blob flux rope formation, consistent with the \citet{Sheeley2002, Sheeley2007} and \citet{SanchezDiaz2017a} interpretations that all these phenomena result from the same magnetic reconnection processes occurring in the corona.
The paper is organized as follows. Section~\ref{sec:arms} presents a brief overview of the MHD model and the implementation of the initial magnetic field and solar wind boundary conditions. Section~\ref{sec:inflow} presents the simulation results including: (\ref{sec:inflow:wl}) the different types of coronal inflow morphologies in synthetic white-light emission; (\ref{sec:inflow:ht}) the analysis of the height--time and velocity profiles of the inward and outward moving transients; and an examination of the global (\ref{sec:inflow:mag}) and local (\ref{sec:inflow:mag2}) coronal magnetic field structure associated with these transient flows and their evolution.
{
Section~\ref{sec:disc} discusses the applicability and extension of our simulation results to: (\ref{sec:disc:sads}) the low coronal supra-arcade downflows; (\ref{sec:disc:ps}) pseudostreamer outflows and reconnection dynamics; (\ref{sec:disc:ylm}) the relationship between inflows and the underlying magnetic field distribution; and (\ref{sec:disc:turb}) the structure of turbulence in the heliospheric plasma sheet. The summary and conclusions are presented in Section~\ref{sec:summary}.
}\vskip 0.10in
\begin{figure*}[!htb]
\centering
\includegraphics[width=0.95\textwidth]{fig1.pdf}
\caption{Magnetic field lines at $t=160$~hr after relaxing to a steady-state isothermal wind outflow. Panel (a): Approximately the LASCO C2 field of view with central meridian $\phi=60^{\circ}$ in Carrington longitude in CR2165. Positive (negative) polarity open fields are shown in green (red). The helmet streamer belt field lines are shown in the shades of blue. Panel (b): A closer-up view of the northwest quadrant to highlight the streamer belt structure near limb. The axis units are solar radii.
}
\label{fig:swfls}
\end{figure*}
\section{Quasi-steady State Solar Wind}
\label{sec:arms}
The numerical simulation was performed with the Adaptively Refined MHD Solver \citep[ARMS;][]{DeVore2008} code. ARMS calculates solutions to the 3D nonlinear, time-dependent ideal MHD equations using a finite volume, multi-dimensional flux-corrected transport algorithm \citep{DeVore1991}. ARMS uses the PARAMESH framework \citep{MacNeice2000} for dynamic, solution-adaptive grid refinement and efficient multi-processor parallelization.
The spherical computational domain uses logarithmic grid spacing in $r$ and uniform grid spacing in $\theta, \phi$. The domain extends from $r \in [1\,R_\odot, 30\,R_\odot]$, $\theta \in [11.25^{\circ}, 168.75^{\circ}]$ ($\pm78.75^{\circ}$ in latitude), and $\phi \in [0^{\circ}, 360^{\circ}]$ (longitude). The initial grid consists of $7 \times 7 \times 15$ blocks with $8^3$ grid cells per block. There are 3 additional levels of static grid refinement and the level 3 refinement extends from $r \in [1\,R_\odot , 6.984\,R_\odot ]$ for all $\theta, \phi$. The level-4 grid refinement is centered on a southern hemisphere polarity inversion line for a separate study on the activation and eruption of a high-latitude filament.
The initial magnetic field configuration is constructed with a relatively low-degree ($\ell_{\rm max} = 14$) potential field source surface \citep[PFSS;][]{WangYM1992} extrapolation from the NSO/GONG \citep{Harvey1996} zero-point corrected, daily-updated $B_r$ synoptic map for Carrington Rotation 2165, taken on 2015 July~10 at 00:14UT.
A basic, quasi-steady state outflow is obtained via an isothermal \citet{parker1958} solar wind corresponding to a uniform temperature of $T_0 = 1.4 \times 10^{6}$~K \citep[e.g.,][]{Masson2013,Lynch2016b,Higginson2017a}. The base density is $n_0=3.62 \times 10^{8}$~cm$^{-3}$ at $1\,R_\odot$ and the initial radial velocity at the outer boundary is $v_{sw}(30\,R_\odot) \simeq 410$~km~s$^{-1}$. The magnetic field and outflow conditions adjust and eventually equilibriate creating the quasi-steady state open and closed flux distributions with a slow solar wind for $t > 100$~hr. The definition of `quasi-steady state' used here includes the small-scale, time-dependent dynamics of streamer evolution but maintains the stable, large-scale distribution of magnetic flux and resulting 3D solar wind structure in an average sense, along with essentially constant global energy measures (e.g. magnetic, kinetic, gravitaitonal, internal) in time.
Figure~\ref{fig:swfls}(a) shows the global coronal magnetic field during the quasi-steady state outflow at $t=160$~hr. Figure~\ref{fig:swfls}(b) plots a closer-up view of the northwest quandrant of panel (a) where we observe the simulation's coronal inflows. The axis ranges are normalized to solar radii. The same field lines are plotted in each panel: the open field lines are shown in green (red) for positive (negative) polarity; the closed field regions of the helmet streamer belt are illustrated with the blue field lines; and the set of dark cyan, cyan, and blue streamer arcade field lines are traced from points along the $B_r=0$ contour at heights $r=2.0R_{\odot}$, $2.5R_{\odot}$, and $5.0R_{\odot}$, respectively. Additional blue field lines are plotted above the streamer belt at each limb (i.e. in the plane of the sky) to indicate the global orientation in the extended corona. The east limb is at $\phi = -30^{\circ}$ and the west limb at $\phi = 150^{\circ}$ longitude. The spatial dimensions of Figure~\ref{fig:swfls}(b) correspond to the exact axis ranges for the panels in Figures~\ref{fig:wl} and \ref{fig:wl2}, and further analysis of the helmet streamer magnetic structure is presented in $\S\S$\ref{sec:inflow:mag}, \ref{sec:inflow:mag2}.
\section{Inflows and In/Out Pairs}
\label{sec:inflow}
\begin{figure*}
\centering
\includegraphics[width=1.0\textwidth]{fig2.pdf}
\caption{Representative examples of `sinking column' inflows along the PA 293$^\circ$ radial cut (dotted yellow line). Panels (a)--(c) show synthetic white-light coronagraph imagery from the MHD simulation. Panels (d)--(f) show the corresponding times in running-difference processing. Arrows indicate the leading edge of density depletion inflows.
\\
(An animation of this figure is available.)
}
\label{fig:wl}
\end{figure*}
\subsection{Morphology in Synthetic White-light Images}
\label{sec:inflow:wl}
\citet{Sheeley2002} described the morphology of the most common type of coronal inflow in coronagraph images as a `sinking column' in which a weak localized density enhancement appears between 3—$5\,R_\odot$ and accelerates towards the sun (and then decelerates) while leaving a dark, collimated, and extended channel structure in its wake, corresponding to a 10--30\% intensity depletion. These inflows are sometimes referred to as `raining inflows.' Figure~\ref{fig:wl} plots the synthetic Thomson scattered white-light intensity from the 3D MHD data cube of number density assuming $n_p = n_e$ \citep[as in, e.g.,][]{Lynch2004,Lynch2016b,Vourlidas2013}. The top row, panels (a)--(c), show the ratio $I(t)/I_0$ at times 171.33~hr, 172.33~hr, and 174.33~hr, where $I_0$ is obtained from the $t=0$~hr spherically symmetric density profile. The bottom row, panels (d)--(f), show the running-difference processing of the synthetic white-light images above, defined as $\Delta I = \left( I(t) - I(t-\Delta t) \right)/I_0$ with $\Delta t = 20$~min.
\begin{figure*}
\centering
\includegraphics[width=1.0\textwidth]{fig3.pdf}
\caption{Representative examples of `shrinking loop' inflows along the PA 310$^\circ$ radial cut (dotted purple line) in the same format as Figure~\ref{fig:wl}(d)--(f). Arrows indicate the darker leading loop and brighter training cusp.
}
\label{fig:wl2}
\end{figure*}
The arrows in Figure~\ref{fig:wl}(a)--(c) show the location of the leading edge of the dark `sinking columns' characteristic of coronal inflow observations. The same arrows are also in Figure~\ref{fig:wl}(d)--(f) as pointing to the clear bipolar intensity signals of the coronal inflows above. The morphology of these simulation features is essentially identical to that of observed inflows (e.g., cf. Figure~3 in \citealt{WangYM1999a}; Figure~9 in \citealt{WangYM2000}; Figures~1, 4, and 7 in \citealt{Sheeley2002}; Figures~7 and 8 in \citealt{Sheeley2004}). The animated version of Figure~\ref{fig:wl} highlights the dynamical evolution of the synthetic white-light and running-difference features.
The second type of inflow has a morphology described as a `shrinking loop' corresponding to the downward motion of a dark, arched loop structure, often accompanied by a trailing brighter cusp shape in the running-difference processing. In the standard background-subtracted white-light intensity images, these types of inflows are much harder to see, i.e. often there is just a slight downward motion/contraction of a semi-circular contour of streamer brightness. Figure~\ref{fig:wl2} shows three representative examples of shrinking loop inflows (indicated by the arrows) in the same format as the Figure~\ref{fig:wl} running-difference panels. The morphology of these simulation features is again, essentially identical to this type of observed inflow as well (e.g., cf. Figure 7 in \citealt{WangYM1998}; Figure 9 in \citealt{Sheeley2007}; Figures 1, 4, and 10 in \citealt{Hess2017inflows}; Figures 1 and 3 in \citealt{WangYM2018blobs}).
Figures \ref{fig:wl}(d)--(f) and \ref{fig:wl2} also have radial cuts indicated at position angles (PAs) 310$^\circ$ (purple dotted line) and 293$^\circ$ (yellow dotted line) corresponding to latitudes of +40$^\circ$ and +23$^\circ$, respectively. These radial cuts are used to construct the height--time evolution of the outflow and inflow running-difference intensity features in the next section. It is also worth noting that the sinking-column inflows are located at the PA 293$^\circ$ while the shrinking-loop inflows appear at PA 310$^\circ$. Section~\ref{sec:inflow:mag} will show these PAs correspond to viewing the helmet streamer belt edge-on (PA 310$^\circ$) and face-on (PA 293$^\circ$).
\begin{figure*}
\centering
\includegraphics[width=1.0\textwidth]{fig4.pdf}
\caption{height--time plots for the two radial cuts in Figures~\ref{fig:wl}, \ref{fig:wl2} and their resulting velocity profiles. Panel (a): PA 310$^{\circ}$ samples an edge-on portion of the helmet streamer belt. Panel (b): PA 293$^{\circ}$ samples a face-on portion of the helmet streamer belt. Panel (c): Each of the $v_r(r)$ profiles derived from the quadratic fits to the height--time data in (a), (b). The inflow (outflow) tracks are shown in the green-cyan-blue (yellow-orange-red) color gradient.
}
\label{fig:jmap}
\end{figure*}
\subsection{Height--time and Velocity Profiles}
\label{sec:inflow:ht}
To quantify the apparent motion of the inwards and outwards moving features in the synthetic white-light running difference movie, height--time plots (`J-maps') are constructed at the two position angles indicated in Figures~\ref{fig:wl} and \ref{fig:wl2}. Figures~\ref{fig:jmap}(a) and \ref{fig:jmap}(b) show the running difference height--time plots from PAs 310$^{\circ}$, 293$^{\circ}$, respectively. A set of height--time tracks are traced via the point-and-click method and shown as yellow-orange-red data points for the outflows and green-cyan-blue for the inflows. The height--time data are fit using the IDL {\tt curvefit} procedure to the standard quadratic profile \citep[as in][]{Sheeley1997} given by
$r(t) = r_0 + v_0 t + \onehalf a_0 t^2$
resulting in a velocity profile of $v^2(r) = 2 a_0 ( r - r_1 )$ where $r_1 = r_0 - v_0^2/(2a_0)$.
Figure~\ref{fig:jmap}(c) plots the $v_r(r)$ profiles from each of the quadratric fits to the height--time data in panels (a) and (b) in the same color scheme. For the most part, the set of inflow velocity profiles and the set of outflow velocity profiles are each relatively consistent---there is some variation between tracks with the occasional outlier, but overall, each set is essentially clustered together within a $\pm$100~km~s$^{-1}$ envelope. The inflow tracks originating at the greatest radial distances start with an initial negative velocity between $-200$ and $-350$~km~s$^{-1}$ for $r > 3\,R_\odot$ and rapidly decrease in velocity as they approach the Sun; e.g. for $r < 2\,R_\odot$, most of the inflow velocities are slower than $-100$~km~s$^{-1}$ and many of the analytic fits overshoot the $v_r = 0$ threshold by the last few height--time points. The outflow tracks show a broader distribution in their initial $v_r$ at lower radial distances ($r < 3\,R_\odot$) but they tend to narrow with distance until the upper boundary of the height--time plots; $v_r(7\,R_\odot) \sim 325\pm75$~km~s$^{-1}$.
The simulation inflow and outflow velocity magnitudes and their radial dependence are reasonably consistent with the observed profiles. Typical inflow velocities are observed to reach a maximum speed of approximately $-100$~km~s$^{-1}$ (e.g., cf. Figure~5 in \citealt{WangYM1999a}; Figure~2 in \citealt{WangYM1999b}). The observed streamer blob outflow velocity profiles are usually clustered around the ambient slow solar wind profile and at $r=7\,R_\odot$ these are in the $200\pm100$~km~s$^{-1}$ range (e.g., cf. Figure~6 in \citealt{Sheeley1997}; Figure~7 in \citealt{WangYM2000}; Figure~5 in \citealt{Song2009}). The simulation inflow velocity profiles tend to start a bit larger than the initial velocity magnitudes in the observations, but they rapidly decelerate to radial velocity magnitudes comparable to observed coronal inflows close to the sun (e.g. for $ r \lesssim 2\,R_\odot$). Likewise, the streamer blob/density enhancement outflows tend to start and remain a bit faster than the 400~km~s$^{-1}$ isothermal slow solar wind profile. Given that the inflow tracks and most of the outflow tracks originate in reconnection exhaust, it is not surprising the simulation and observed velocity profiles are not an exact match.
\subsection{Global Magnetic Field Structure and Dynamics}
\label{sec:inflow:mag}
Some of the first statistical results from coronal inflow observations was their occurance frequency followed the solar activity cycle \citep{WangYM1999a,Sheeley2002} and they almost always appeared in regions of the corona associated with sector boundaries \citep{Sheeley2002,Sheeley2007}, i.e. the transition from one open field polarity to the other across the helmet streamer belt and HCS. The orientation of the HCS changes drastically with the solar cycle, and solar maximum magnetic field configurations often have large latitudinal excursions of the helmet streamer belt. Since the coronal inflows are best observed in these highly distorted/vertical sections of the helmet streamer belt (i.e. when the HCS is parallel to the plane of the sky), then the relationship between observed inflow occurance to solar activity is straightforward.
\begin{figure}
\centering \includegraphics[width=0.46\textwidth]{fig5.pdf}
\caption{Panel (a): The initial $t=0$~hr PFSS magnetic field derived from NSO/GONG synoptic map for Carrington Rotation 2165. The positive (negative) open field regions are indicated in red (green), the HCS neutral line is shown as the black contour and the helmet streamer belt field lines are shown in blue. Panel (b): The $t=160$~hr global magnetic field associated with the quasi-steady state solar wind outflow in the same format as above. Panel (c): Synthetic line-of-sight integrated white-light emission at $5\,R_\odot$ as a synoptic map. The central meridian (CM) and west limb (WL) for Figure~\ref{fig:wl} are shown as the vertical dashed lines in each panel. The purple and yellow `+' signs indicate the WL position angles of the radial cuts used for the height--time plots in Figure~\ref{fig:jmap}.
}
\label{fig:mag1}
\end{figure}
To investigate the global coronal context for the various simulation inflows, Figure~\ref{fig:mag1} shows the large-scale magnetic field and streamer belt configuration in Carrington rotation coordinates. Figure~\ref{fig:mag1}(a) is PFSS reconstruction from the NSO/GONG radial field synoptic map in the style of the GONG data products: Positive open field regions are green, negative open field regions are red, the boundary of the helmet streamer belt is in blue, and the black $B_r=0$ neutral line at $r=2.5\,R_\odot$ indicates the base of the HCS. Figure~\ref{fig:mag1}(b) shows the MHD version of the panel (a) figure at $t=160$~hr. Overall, the large-scale coronal structure in the presence of the isothermal solar wind maintains an excellent qualitative agreement to the PFSS extrapolation. Figure~\ref{fig:mag1}(c) plots the synoptic map of white-light intensity in Carrington coordinates. The synoptic map was created by generating 90 synthetic coronagraph images in 2$^{\circ}$ increments from the $t=160$~hr data cube and then sampling each one along the $r = 5\,R_\odot$ circle and assigning each limb to their corresponding Carrington longitudes. The $B_r=0$ neutral line is also overplotted. The white-light Carrington map is a standard procedure employed in the analysis of coronagraph data \citep[e.g.,][]{WangYM1999b} and has been used recently by \citet{Rouillard2020} in linking streamer outflows to PSP in-situ observations.
The west limb (plane of the sky in Figure~\ref{fig:wl}) is indicated as `WL' at Carrington longitude $\phi=150^{\circ}$ and the central meridian is labeled `CM' at $\phi=60^{\circ}$. The latitude and longitude position of the radial cuts in Figures~\ref{fig:wl}, \ref{fig:wl2} are shown in Figure~\ref{fig:mag1}(b) and \ref{fig:mag1}(c) as the purple and yellow `+' symbols. The streamer belt/HCS is highly inclined and in a face-on orientation 10--15$^{\circ}$ in front of the plane-of-they-sky (at $\phi \sim 140^{\circ}$). The streamer belt then wraps around above the radial sampling points to become edge-on at high latitude (HCS in the $r$--$\phi$ plane at $\theta \sim 40^{\circ}$) and comes back down on the other side of the negative polarity coronal hole extension---this time 30--40$^{\circ}$ behind the plane-of-the-sky (longitude $\phi \sim 190^{\circ}$).
The large-scale, global context provided by Figure~\ref{fig:mag1} is especially important when trying to unravel the contributions of different coronal structures to the line-of-sight integration. For example, the upper radial sample (purple `+') occurs in the dense streamer stalk outflow and has approximately $\pm25^{\circ}$ of streamer outflow material along the line of sight at $r=5\,R_\odot$ centered on the plane of the sky. Conversely, the lower radial sample (yellow `+') is above the extension of the negative polarity coronal hole which cannot contribute much to the white-light intensity because of the low density on open field lines, despite the favorable scattering geometry. Rather, the significantly more dense helmet streamer arcade and HCS extension only 10--15$^{\circ}$ east from the plane of the sky is largely responsible for the observed inflow and outflow dynamics.
\begin{figure*}
\centering
\includegraphics[width=1.0\textwidth]{fig6.pdf}
\caption{Visualization of the magnetic field structure and density distribution during the inflow events of Figure~\ref{fig:wl}. Panels (a)--(c): 3D perspective of representative magnetic field lines of the streamer belt and the base of the HCS. The semi-transparent meridional plane bisecting the streamer arcade at $\phi=135^{\circ}$ shows $v_r(r,\theta)$ in red/blue for the $\pm{\hat{r}}$ directions. Panels (d)--(f): The density distribution $n(r,\phi)$ in a semi-transparent latitudinal plane at $\theta=+23^{\circ}$ viewed from the solar north pole. The dashed white lines show the lines of sight at the positions of the `sinking column' inflows in Figure~\ref{fig:wl} and the white arrows indicate their intersection with the collimated density-depleted legs of newly reconnected loops retracting back down. The black arrows indicate magnetic island plasmoids formed by reconnection at the streamer cusp/HCS base. \\
(An animation of this figure is available.)
}
\label{fig:mag2}
\end{figure*}
\subsection{Local Magnetic Field Structure and Dynamics}
\label{sec:inflow:mag2}
Figure~\ref{fig:mag2} shows the magnetic field and plasma evolution at the vertical/warped portion of the helmet streamer belt near the west limb. Panels \ref{fig:mag2}(a)--(c) show a 3D perspective of a transparent meridional plane of radial velocity at Carrington longitude $\phi=135^\circ$ at the three times shown in Figure~\ref{fig:wl} ($t=171.33$, 172.33, and 174.33~hrs). A set of magnetic field lines are traced from starting points in the $\phi=135^{\circ}$ plane at latitudes $+18^\circ$ (green), $+23^\circ$ (blue), and $+30^\circ$ (yellow) over a range of radial distances to make up three representative arcades in the vicinity of the PA 293$^\circ$ (23$^\circ$ latitude) radial cut used to generate up the height--time plot in Figure~\ref{fig:jmap}(b). The blue--white--red gradient in radial velocity above the streamer arcade is indicative of the outflows caused by localized reconnection at the extended cusp of the streamer and base of the HCS. Here the negative radial velocities (blue) show the reconnection exhaust flowing back towards the sun. The animation of Figure~\ref{fig:mag2} makes clear the transient nature of the reconnection in this region---it moves around, the outflow velocities increase and decrease in intensity, and in general, the reconnection sets in after sufficient accumulation of material and stretching of the arcade field lines into the HCS region. The reconnection at the streamer cusp/HCS base forms 3D plasmoid flux ropes that are either ejected into the dense neutral sheet surrounding the HCS or are ejected back into the streamer arcade flux system. The black arrows in panels \ref{fig:mag2}(a) and \ref{fig:mag2}(c) point to two of these reconnection flux ropes; the first one is clearly in the downflow and rejoins/reconnects back into the streamer arcade while the second one is in the upflow and becomes part of the dense plasma sheet outflow.
Figure \ref{fig:mag2}(d)--(f) shows the number density on a transparent plane at latitude $\theta = 23{^\circ}$ (again, corresponding to the yellow radial cut in Figures~\ref{fig:wl}, \ref{fig:wl2}). The vertical dashed lines show the position along the $x$-axis corresponding to the location of the arrows in Figure~\ref{fig:wl}. The white arrows in panels \ref{fig:mag2}(d)--(f) indicate the narrow, newly-reconnected, evacuated outer layer of the helmet streamer. In the Figure~\ref{fig:mag2} animation, these low-density columns are seen moving towards the sun, tracing both edges of the helmet streamer along the magnetic field structure. These tenuous downflows at the flanks of the streamer arcade when viewed edge-on originate in the reconnection exhaust downflows incident at the streamer cusp shown above that then flow down the legs of the arcade loops. The same magnetic island plasmoid flux ropes from \ref{fig:mag2}(a) and \ref{fig:mag2}(c) are highlighted with black arrows in \ref{fig:mag2}(d) and \ref{fig:mag2}(f). The magnetic island plasmoid flux ropes are always associated with a localized density enhancement in the current sheet \citep[see also][]{Lynch2016a}. The sunward-moving plasmoids are inflowing density enhancements that reconnect with and rejoin the coronal arcade while the outflowing plasmoids correspond to the classic streamer blob density enhancements with a 3D magnetic flux rope structure.
The animation of Figure~\ref{fig:mag2} shows both of the physical processes proposed by \citet{WangYM2000} for inflows: contraction of loops after reconnection---a non-energetic, large-scale version of the geometry of flare reconnection and post-eruption arcade formation from a tiny pinch-off flux rope high in the corona, and the retraction of stretched/distended loops via magnetic tension and gravity.
The expansion--reconnection--contraction--expansion cycle results from the interplay between the gas pressure and magnetic field tension in the streamer cusp region \citep[e.g.,][]{Endeve2004,ChenY2009,Allred2015}. One of the reasons the cusp of the helmet streamer belt is so ``unsteady'' is the difference in the response to small perturbations between an X-point null and a Y-point null. Reconnection at an X-point null driven by a short-duration, external transient can cause oscillatory reconnection \citep[e.g.,][]{McLaughlin2009,Murray2009} that will damp out because the different flux systems can transfer flux back and forth via reconnection until the magnetic stresses have dissipated, whereas the Y-point null (line) at the streamer belt cusp and base of the HCS is less stable. The plasma sheet region has a significantly lower magnetic pressure than the open field on either side (and $B \sim 0$ in the current sheet itself). Thus, any pressure fluctuations from the streamer large enough to overcome the magnetic tension of the outer flux surfaces will just move the Y-point, effectively causing the streamer flux system to expand. Once reconnection has set in at the over-expanded cusp, the streamer flux system is reconfigured so quickly that it overshoots the force-balance equilibrium and the cycle can begin again. The animation of Figure~\ref{fig:mag2} illustrates exactly this process.
\section{Discussion}
\label{sec:disc}
\subsection{Extension to Supra-Arcade Downflows}
\label{sec:disc:sads}
Once coronal inflows had been identified and characterized in the coronagraph observations, there was an considerable effort to figure out if the same physical processes and evolution of the magnetic field were responsible for the phenomena known as supra-arcade downflows \citep[SADs;][]{McKenzie2000, McKenzie2009, Savage2010, Savage2011, Savage2012}. SADs are observed much lower in the corona in EUV and X-ray measurements of the hot plasma surrounding the reconnecting current sheet above post-eruption arcades in the aftermath of CME eruptions. SADs are almost identical to the `sinking column' coronal inflows in their shape, radial and transverse motions, and in the trailing dark lanes in their wake \citep[e.g.,][]{Sheeley2004}. \citet{Savage2010} showed that the deprojected SADs in the current sheet from $r \le 1.42\,R_\odot$ had initial velocities between $0$ and $-200$~km~s$^{-1}$. We note that, with one exception, all of the Figure~\ref{fig:jmap} inflow tracks have radial velocities below $-200$~km~s$^{-1}$ for $r < 2\,R_\odot$. SADs are most often seen when the flare arcade is oriented such that the current sheet above the arcade loops appears face-on. This is an equivalent viewing orientation as when the helmet streamer belt/HCS is significantly warped with a large latitudinal extent, i.e. at the sector boundaries (such as the streamer orientation in Figure~\ref{fig:mag2}).
\citet{Cassak2013} performed numerical simulations to examine the relationship between SADs and flare reconnection outflows. Their model was based on (1) a realistic density stratification so the less-dense reconnection jet outflow creates a depletion, (2) the reconnection being steady enough and of sufficient duration to keep plasma from filling this depletion in, and (3) localization of the reconnection site with respect to the length of the current sheet for the jet outflow to remain collimated. This was in contrast to the intermittent, patchy reconnection models proposed earlier \citep[e.g.,][]{Linton2006, Longcope2010} which were also able to reproduce some qualitative agreement with properties of observed SADs, such as the height--time profile and trailing density voids \citep{Linton2009,Guidoni2011}.
The results presented herein are, in some sense, a mix of the \citet{Cassak2013} and \citet{Linton2009} scenarios. The global corona modeled here has both gravitational stratification as well as a significant density variation between the open and closed flux systems, meaning the open field lines being swept into the HCS dissipation region to form newly-closed loops that retract back down, have a much lower (open-field) mass density than the rest of the underlying (closed-field) streamer system. However, the reconnection at the streamer cusp/HCS base is also fairly ``patchy.'' The formation and ejection of magnetic island plasmoids that transfer the mass and magnetic flux into the streamer arcade take the form of time-dependent, bursty reconnection jet outflows rather than a continuous smooth and stable outflow profile. Consequently, the trailing dark tails seen in the face-on PA~293$^{\circ}$ location are relatively short-lived in these simulation results.
A similar effect was seen by \citet{Edmondson2017} during their investigation of the density fluctuations in plasmoid-unstable current sheets with varying guide field strengths. In those simulations, the reconnection outflow into the denser, closed-flux region produced density voids with the same `tadpole-like' morphology of a `sinking column' with a dark, sinuous wake (see the mass density panels in Figures 6--8 of \citealt{Edmondson2017}). The most visible (darkest) and collimated reconnection jet outflows were in the zero guide field case, they were a little broader and still visible at 10\% guide field, and they were significantly wider and less visible in the 50\% guide field case (i.e. less contrast with respect to background density). When viewing the current sheet face-on, the spatial width of these intermittent low-density reconnection jet outflows appears to increase in proportion to the strength of the guide field component. The \citet{Edmondson2017} results provide an intuitive explanation for why SADs are more visible in flare arcade plasma sheets during the gradual or decay phase of long-duration events \citep{McKenzie2000}. During the impulsive phase of a flare there is a strong guide field component in the reconnection region from the highly sheared and twisted fields of the erupting structure. Therefore, the density-depleted outflows are more spread out (less collimated) parallel to the current sheet. By the late gradual/decay phase of the flare, there is not much guide field left to reconnect in the wake of a CME \citep[e.g. Figure 11 in][]{Lynch2016a}. At this stage the post-eruption arcade flare loops are reforming with significantly less shear \citep{Aulanier2012} and the density-depleted outflows are more aligned (collimated) perpendicular to the post-eruption arcade current sheet.
While it is relatively well accepted that inflows in white-light coronagraph data, especially in the wake of CMEs, are just larger versions of SADs \citep[e.g.,][]{Sheeley2004}, the simulation results presented herein also highlight the importance of the viewing perspective in determining the apparent structure and morphology of the inflows. For the common `raining' or `sinking column' inflows at sector boundaries, the line-of-sight integration is likely to intersect both legs of the density-depleted, retracting loop if the streamer belt (or flare arcade) is oriented such that the HCS (flare current sheet) is parallel to plane of sky and has a negligible guide field component---exactly the case as in Figure~\ref{fig:mag2}(d)--(f). If there is still a large-scale shear component or the arcade is oriented at a significant angle with respect to the plane of the sky, then the smaller contribution to the line-of-sight integral will result in less visible inflow signatures. The `shrinking loop' inflows seen in the edge-on streamer at PA 310$^{\circ}$ result from the same retraction of a density-depleted loop process as depicted in the viewpoint of Figure~\ref{fig:mag2}(d)--(f). Here the perspective from the solar north pole views the vertical, warped portion of the streamer belt (at $\phi=135^{\circ}$) as edge-on and perpendicular to the line of sight for Figures~\ref{fig:wl}, \ref{fig:wl2}.
\subsection{{Extension to Pseudostreamer Outflows and Reconnection Dynamics}}
\label{sec:disc:ps}
{
The magnetic topology of coronal pseudostreamers has been discussed in detail \citep[e.g.,][]{WangYM2007a, WangYM2012, Titov2012, Panasenco2013, Rachmeler2014, Scott2018} along with observations and modeling of their slow solar wind outflow \citep{Crooker2012a, Riley2012, WangYM2012, Owens2014}. Pseudostreamers differ from helmet streamers in that they are surrounded by a single open field polarity rather than separating positive and negative polarity open fields which creates a HCS and sector boundary. The network of pseudostreamer connectivity in the heliosphere and its relation to the main helmet streamer belt has been named the Separatrix Web \citep[S-Web;][]{Antiochos2011,Antiochos2013} and is a favorable location for interchange reconnection \citep[e.g.,][]{Higginson2017a}.
}
{
\citet{Masson2014} examined gradual reconnection in a slowly stressed, 3D separatrix fan-spine configuration showing a smooth, continuous outflow of material along the external spine line. \citet{Lynch2013} showed that pseudostreamer interchange reconnection, in the form of pre-eruption breakout reconnection, could result in bursty but quasi-steady signatures in density along the external spine and coronal dimming signatures near the stressed null point and current sheet \citep[e.g.,][]{KumarP2020}. In that simulation the sunward portion of the interchange reconnection outflow became downflows in the adjacent flux system loops, similar to the dynamics in Figure~\ref{fig:mag2}. Another type of downflow is `coronal rain' which is also observed at null points in multipolar systems \citep[e.g.,][]{Mason2019}. This type of downflow is primarily a result of plasma thermodynamics (thermal nonequilibrium condensation of cooler, dense material observed in EUV, e.g. SDO/AIA 304~{\AA}), although interchange reconnection may also play some role in its subsequent transport.
}
{
Streamer blobs originating from pseudostreamers are far less common and/or visible in white-light coronagraph observations \citep[e.g.,][]{WangYM2007a,WangYM2012}. However, there are some in-situ observations of bidirectional electron signatures that are suggestive of closed-field structures with coronal connections at both foot points and a subset of these interplanetary small-scale flux ropes appear to originate from coronal pseudostreamers, i.e. far from the HCS and its plasma sheet \citep[e.g.,][]{Feng2015b}. Future numerical simulations will be required to characterize pseudostreamer wind variability and its comparison with helmet streamer slow wind.}
\subsection{Relating Inflow Occurrence to the Underlying Magnetic Field Distribution}
\label{sec:disc:ylm}
{
As discussed above, the interplay between gas dynamics and the magnetic field at the Y-type null line at the cusp of helmet streamers is ultimately responsible for the ``unsteady'' character of the quasi-steady state outflows. Any change in the relative balance of forces will cause a similar cycle of expansion, reconnection and over-correction followed by another period of expansion in response to the over-correction. For example, an increase in the magnetic pressure of the closed flux system through the addition of new flux (through photospheric emergence) or the addition of magnetic stresses through coherent surface motions (large-scale shearing, or other global flow patterns such as differential rotation) or incoherent surface motions (convective turbulence/granulation and/or the accumulation of large-scale twist via helicity condensation) could result in a similar disruption.
}
{
As the streamer flux system responds to evolving surface fields, the streamer swells in width and expands radially. \citet{WangYM2018blobs} have examined this process in detail and shown the occurrence of coronal inflows are well-correlated with the total polarized brightness ($pB$ radiance) in the LASCO C2 field of view on the timescale of Carrington rotations. On a global scale, the increase in the number of sector boundaries---the vertical, highly warped portions of the helmet streamer belt---occurring in the ecliptic plane can also be represented by the power (coefficient magnitude) in the nonaxisymmetric components of the PFSS spherical harmonic expansion ($Y_{l,|m|}$). In particular, the equatorial dipole ($Y_{1,1}$) and equatorial quadrupole ($Y_{2,2}$) components are known to vary with the solar activity cycle \citep{WangYM1997} and thus, also show good correlation with the observed inflow rates \citep[e.g.,][]{Sheeley2014}.
}
{
\citet{WangYM2018blobs} showed that the highest inflow rate and C2 $pB$ radiance levels in cycle 24 were recorded during 2014 October--December, above NOAA 12192 and its remnants. During this period, the helmet streamer overlying active region 12192 appears to have expanded well beyond its ``normal'' position. This sunspot grouping was extremely active, generating many strong flares (6 X- and $\sim$18 M-class flares) that, surprisingly, only resulted in a single CME eruption during the period October 18--28 \citep[e.g.,][]{SunX2015}. This (confined) flaring activity would certainly produce an abundance of significant fluctuations in both the plasma and magnetic field structure in the overlying helmet streamer belt. Additionally, regions of the streamer belt/HCS that are highly inclined with respect to the ecliptic are, in general, likely experiencing continual interchange reconnection to preserve the rigid rotation of coronal holes and their low-latitude extensions \citep{WangYM2004, Lionello2005}.
}
\subsection{{Intermittent Streamer Blob Outflow as a Source of Heliospheric Turbulence}}
\label{sec:disc:turb}
{
Direct, in-situ magnetic field and plasma measurements by \textsl{Ulysses}, ISEE~3, and other spacecraft of small flux rope structures and the structured variability in density and other solar wind properties in the plasma sheet region surrounding the HCS led \citet{Crooker1996hps,Crooker1996hfds,Crooker2004} to interpret this region as being essentially filled with tangled, slow solar wind flux rope or flux tube transients. Heavy ion elemental and ionic composition measurements are consistent with this scenario, showing statistical properties of time series with lots of discontinuities \citep[e.g.,][]{Zurbuchen2002} and coincident boundaries in magnetic field, bulk plasma, and composition quantities \citep[e.g.,][and references therein]{Kepko2016,Viall2020}.
}
{
As discussed by \citet{Higginson2018}, a major implication of the heliospheric plasma sheet region being essentially filled with tangled and possibly interacting small flux ropes, is the role they play in the development of solar wind turbulence \citep[e.g.,][]{Zheng2018,ZhaoLL2020}. Future work on this aspect of the slow solar wind's structured variability could include: (1) investigating the evolutionary processes that streamer blob/plasmoid flux ropes and other reconnection-generated outflows experience during their heliospheric transit \citep[e.g.,][]{Borovsky2012, Janvier2014a, MurphyA2020}; (2) studying how this variability interacts with stream interaction regions or coronal/heliospheric transients such as CMEs or CME-driven shocks and sheath regions \citep[e.g.,][]{Borovsky2006, Malandraki2019, Good2020}; (3) determining the contribution of magnetic island turbulence to particle energization processes in and around coronal streamers, the slow solar wind, and/or the HCS and plasma sheet \citep[e.g.,][]{Drake2006b, Dahlin2014, Guidoni2016, Khabarova2016}; and (4) whether this variabilty is sufficient to generate the seed population necessary for the most intense shock-accelerated SEP profiles \citep[e.g.,][]{Dahlin2015, Dahlin2016, Khabarova2015, Khabarova2016}.
}
\section{Summary and Conclusions}
\label{sec:summary}
This work presents an analysis of coronal inflows, generated as a consequence of intermittent reconnection at the cusp of helmet streamer belt and base of the HCS, in a time-dependent MHD simulation of a quasi-steady state solar wind in the moderately complex global magnetic field configuration of CR 2165 in July 2015. The simulation results confirm that the different viewpoints/orientations of the line-of-sight integration of Thomson-scattered white light give rise to different inflow morphologies. The dark, collimated `sinking column'/`tadpole-like' inflows are seen at sector boundaries when the HCS is face-on with respect to the observer. The semi-circular `shrinking loop' inflows are seen when the streamer belt arcade is oriented edge-on. Significantly, these two different types of inflows are indistinguishable from their height--time or velocity profiles alone, strongly suggesting the same underlying physical mechanisms---consistent with the prevailing interpretation of a common reconnection process.
While the \citet{Higginson2018} analysis was concentrated on the magnetic field and plasma signatures of the streamer blob flux ropes generated in an idealized equatorial HCS configuration, this paper focused on the low-corona signatures of the same magnetic reconnection processes. Taken together, these MHD simulations of dynamic, time-dependent coronal streamer evolution in a quasi-steady state slow solar wind represent a significant step forward in terms of begining to capture some of the intrinsic variability of the slow solar wind with numerical models. Understanding the origin and evolution the magnetic field and plasma signatures associated with streamer blob flux ropes, coronal downflows, in/out pairs, and streamer detachments will be an increasingly necessary component of the interpretation and analysis of current and future PSP and SolO observations. These data are expected make a significant contribution to the ability to observe and model the direct connection between heliospheric in-situ measurements and their origin in the solar corona.
\acknowledgments
B.J.L. acknowledges support from the NASA HGI and HSR programs 80NSSC18K0645, 80NSSC18K1553, and 80NSSC20K1448. This work utilizes GONG data from NSO, which is operated by AURA under a cooperative agreement with NSF and with additional financial support from NOAA, NASA, and USAF. The computational resources for this work were provided by the NASA High-End Computing Program through the NASA Center for Climate Simulation at Goddard Space Flight Center.
| {
"redpajama_set_name": "RedPajamaArXiv"
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Q: Ajax call freezes the page when downloading video stream (mp4) I am attemping an AJAX call where I get an MP4 and set the source of an hmtl5 <video> tag.
//...other promises that are successful...
// get mp4
downloadurl.done(function(data) {
console.log('Starting the ajax call for Stream')
var stream = $.ajax({
type: "GET",
url: data.data,
beforeSend : function(xhr) {
xhr.setRequestHeader("Authorization", "JWT " + access_token);
},
contentType: 'application/json',
mimeType : "video/mp4",
success: function(response){
$('video-source').attr('src', "data:video/mp4;base64," + response)
},
error:function(jqXHR, textStatus, errorThrown) {
console.log("request for secure stream failed: ", textStatus, errorThrown, jqXHR);
},
});
stream.fail(function(){
console.log("Stream Failed")
})
When I run this final ajax promise, the page freezes. The file is not very large, so I believe my ajax call is incorrectly handling the download of the video.
I am not getting any errors, but as you can see the file.mp4 is downloading into browser memory:
What am I doing wrong?
A: Base64 is the worst response you can get back. It's ~3x larger. This ajax method is bad cuz you have to download the hole movie before you can look at anything
Best solution would be if you can download chunks and append it to the video
https://developers.google.com/web/updates/2011/11/Stream-video-using-the-MediaSource-API?hl=en
Even better if you can add the token header via service worker fetchEvent.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 286 |
ACCEPTED
#### According to
Integrated Taxonomic Information System
#### Published in
Fl. N. Amer. 2:346. 1842
#### Original name
null
### Remarks
null | {
"redpajama_set_name": "RedPajamaGithub"
} | 2,478 |
Speakers and Events
Sand Volleyball
Daily Trojan Editorial Board
Newcomers impress as Trojans wrap up spring ball
By TAJWAR KHANDAKER
April 14, 2019 in Football, Sports
Early-enrollee quarterback Kedon Slovis played surprisingly well at spring practice. (Ling Luo/Daily Trojan)
Now that spring football practice has come to an end, the Trojans won't take the field again to prepare for the 2019 season for two months. There's no shortage of questions surrounding the team; the way it bounces back from last year's disappointing season may define the program for years to come.
Though little more than a month of spring football doesn't make the answers to those questions much clearer, it does give a better idea of what to expect from some of the younger team members.
Throughout spring ball, a number of early-enrollee incoming freshmen on both sides of the ball made strong cases for playing time in the fall. With the loss of so many veterans to the draft, the freshmen's ability to step up and contribute will be perhaps the most critical factor in the coming season.
Defensive back Briton Allen, a late flip from Georgia Tech, found his way into plenty of reps this spring as a result of the numerous injuries hampering the secondary. Allen performed impressively when thrust into the fire at cornerback in the early practices — a departure from his usual safety position. Though his technique and footwork in coverage have a ways to go, Allen's raw football instincts and aggressiveness showed up regularly.
Allen continued to play well once he was moved back to safety, a position where the Trojans sorely lack depth. With the loss of so many veteran players in the secondary and the injury woes of many that remain, Allen's versatility could make him a crucial player in the fall.
Outside linebacker and defensive end Drake Jackson was perhaps the biggest shining star of spring ball. Jackson already looks the part of a Division I edge rusher, standing at 6-foot-4 and 260 pounds and having been compared to USC legend Leonard Williams by head coach Clay Helton. Jackson carries that frame with tremendous athleticism, showing a rare burst off the line of scrimmage along with a special quickness in moving off of blocks.
Jackson showcased his raw physical ability during the spring showcase, where he made a ridiculous one-handed interception at the line of scrimmage and proceeded to run it back for a touchdown. Jackson has been one of the most disruptive players on the Trojan front seven throughout the spring, and seems likely to have a big role to play come fall.
On the other side of the ball, quarterback Kedon Slovis has been a pleasant surprise for the Trojans. The Arizona native came into the spring with few expectations other than to be the fourth-string quarterback, yet his strong play has caught the attention of everyone in attendance.
Slovis showcases a natural understanding of the timing necessary for throws in offensive coordinator Graham Harrell's system, as well as refined touch on his passes. He doesn't have the strongest arm, and his mobility is limited. However, his ability to quickly make reads and put the ball where and when it needs to be makes him worthy of notice at the position. Although it's highly unlikely he wins the starting job, his ability to run the offense smoothly provides the Trojans with more security at signal caller — something a team always needs.
Fellow offensive newcomer wide receiver John Jackson III has been one of the most fun players to watch throughout the spring. From the first week of practice, Jackson has looked like he's played in this offense for years. His route running is smooth and sudden, with exceptionally clean breaks that allow him to create separation with ease. His natural athleticism, sound hands and route-running ability made him a favorite target throughout spring ball, regularly making plays against the first team defense.
Though the receiver room is crowded with an incredible amount of talent, Jackson's performance so far should earn him the opportunity to fight for a bigger role in fall camp. It wouldn't be a surprise to see him on the field regularly once the season begins.
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"redpajama_set_name": "RedPajamaCommonCrawl"
} | 9,351 |
<?php
/**
* Created by PhpStorm.
* User: Malgin
* Date: 23.01.15
* Time: 17:52
*/
/**
* Add plugin menu item in admin panel
*/
function dwr_add_options_page()
{
add_options_page(
__('dwr_plugin_page', DWR_PLUGIN_NAME),
__('dwr_plugin_menu_title', DWR_PLUGIN_NAME),
'manage_options',
DWR_PLUGIN_NAME,
'dwr_display_plugin_options_page'
);
add_options_page(
__('dwr_plugin_statistics_page', DWR_PLUGIN_NAME),
__('dwr_plugin_statistics_menu_title', DWR_PLUGIN_NAME),
'manage_options',
DWR_PLUGIN_NAME . '-statistics',
'dwr_display_plugin_statistics_page'
);
}
/**
* Display the admin options page
*/
function dwr_display_plugin_options_page()
{
echo "<div>";
echo "<h2>" . __('dwr_plugin_page_title', DWR_PLUGIN_NAME) . "</h2>";
echo '<form action="options.php" method="POST">';
settings_fields('dwr_plugin_options');
do_settings_sections(DWR_PLUGIN_NAME);
$dwr_result_url = get_option('dwr_result_url');
$dwr_result_url_method = get_option('dwr_result_url_method');
$dwr_merchant_login = get_option('dwr_merchant_login');
$dwr_merchant_pass_one = get_option('dwr_merchant_pass_one');
$dwr_merchant_pass_two = get_option('dwr_merchant_pass_two');
$dwr_default_donation_amount = get_option('dwr_default_donation_amount');
$dwr_operation_description = get_option('dwr_operation_description');
$dwr_force_delete_tables = (int)get_option('dwr_force_delete_tables');
echo "<table><tr>";
echo " <td>" . __('result_url', DWR_PLUGIN_NAME) . " <span class='dwr_required'>*</span></td><td><input name='dwr_result_url' size='40' type='text' value='" . $dwr_result_url . "' /></td>";
echo "</tr><tr>";
echo " <td>" . __('result_url_method', DWR_PLUGIN_NAME) . " <span class='dwr_required'>*</span></td><td>";
echo "<select name='dwr_result_url_method'>";
echo " <option value='POST' " . selected($dwr_result_url_method, 'POST', false) . ">POST</option>";
echo " <option value='GET' " . selected($dwr_result_url_method, 'GET', false) . ">GET</option>";
echo "</select>";
echo "</td></tr><tr>";
echo "<td> </td><td> </td>";
echo "</tr><tr>";
echo " <td>" . __('merchant_login', DWR_PLUGIN_NAME) . " <span class='dwr_required'>*</span></td><td><input name='dwr_merchant_login' size='40' type='text' value='" . $dwr_merchant_login . "' /></td>";
echo "</tr><tr>";
echo " <td>" . __('merchant_pass_one', DWR_PLUGIN_NAME) . " <span class='dwr_required'>*</span></td><td><input name='dwr_merchant_pass_one' size='40' type='password' value='" . $dwr_merchant_pass_one . "' /></td>";
echo "</tr><tr>";
echo " <td>" . __('merchant_pass_two', DWR_PLUGIN_NAME) . " <span class='dwr_required'>*</span></td><td><input name='dwr_merchant_pass_two' size='40' type='password' value='" . $dwr_merchant_pass_two . "' /></td>";
echo "</tr><tr>";
echo "<td> </td><td> </td>";
echo "</tr><tr>";
echo " <td>" . __('default_donation_amount', DWR_PLUGIN_NAME) . " <span class='dwr_required'>*</span></td><td><input name='dwr_default_donation_amount' size='40' type='text' value='" . $dwr_default_donation_amount . "' /></td>";
echo "</tr><tr>";
echo " <td>" . __('operation_description', DWR_PLUGIN_NAME) . " <span class='dwr_required'>*</span></td><td><input name='dwr_operation_description' size='40' type='text' value='" . $dwr_operation_description . "' /></td>";
echo "</tr><tr>";
echo "<td> </td><td> </td>";
echo "</tr><tr>";
echo " <td>" . __('force_delete_tables', DWR_PLUGIN_NAME) . "</td><td><input name='dwr_force_delete_tables' type='checkbox' value='1' " . checked(1 === $dwr_force_delete_tables) . " /></td>";
echo "</tr></table>";
submit_button();
echo '</form></div>';
}
/**
* Display the admin options page
*/
function dwr_display_plugin_statistics_page() {
global $wpdb;
$table_donations = $wpdb->prefix . DWR_DONATIONS_TABLE_NAME;
$total_transactions = $wpdb->get_var("SELECT COUNT(*) FROM $table_donations");
echo "<div>";
echo "<h1>" . __('dwr_plugin_statistics_page_title', DWR_PLUGIN_NAME) . "</h1>";
if ($total_transactions > 0) {
echo "<h2>" . __("general_statistics", DWR_PLUGIN_NAME) . "</h2>";
// transactions and total donations amount today
$transactions_today = $wpdb->get_var("SELECT COUNT(*) FROM $table_donations WHERE DATE(donation_date) = DATE(NOW())");
$amount_today = $wpdb->get_var("SELECT SUM(amount) FROM $table_donations WHERE DATE(donation_date) = DATE(NOW())");
echo "<div class='dwr_statistics_entry'>";
echo __("transactions_today", DWR_PLUGIN_NAME) . ": $transactions_today";
echo "<br />";
echo __("total_donation_amount_today", DWR_PLUGIN_NAME) . ": " . number_format($amount_today, 2);
echo "</div>";
// transactions and total donations amount for this 7 days
$transactions_this_week = $wpdb->get_var("SELECT COUNT(*) FROM $table_donations WHERE WEEKOFYEAR(donation_date) = WEEKOFYEAR(NOW())");
$amount_this_week = $wpdb->get_var("SELECT SUM(amount) FROM $table_donations WHERE WEEKOFYEAR(donation_date) = WEEKOFYEAR(NOW())");
echo "<div class='dwr_statistics_entry'>";
echo __("transactions_this_week", DWR_PLUGIN_NAME) . ": $transactions_this_week";
echo "<br />";
echo __("total_donation_amount_this_week", DWR_PLUGIN_NAME) . ": " . number_format($amount_this_week, 2);
echo "</div>";
// transactions and total donations amount for this month
$transactions_this_month = $wpdb->get_var("SELECT COUNT(*) FROM $table_donations WHERE MONTH(donation_date) = MONTH(NOW())");
$amount_this_month = $wpdb->get_var("SELECT SUM(amount) FROM $table_donations WHERE MONTH(donation_date) = MONTH(NOW())");
echo "<div class='dwr_statistics_entry'>";
echo __("transactions_this_month", DWR_PLUGIN_NAME) . ": $transactions_this_month";
echo "<br />";
echo __("total_donation_amount_this_month", DWR_PLUGIN_NAME) . ": " . number_format($amount_this_month, 2);
echo "</div>";
// transactions and total donations amount for this year
$transactions_this_year = $wpdb->get_var("SELECT COUNT(*) FROM $table_donations WHERE YEAR(donation_date) = YEAR(NOW())");
$amount_this_year = $wpdb->get_var("SELECT SUM(amount) FROM $table_donations WHERE YEAR(donation_date) = YEAR(NOW())");
echo "<div class='dwr_statistics_entry'>";
echo __("transactions_this_year", DWR_PLUGIN_NAME) . ": $transactions_this_year";
echo "<br />";
echo __("total_donation_amount_this_year", DWR_PLUGIN_NAME) . ": " . number_format($amount_this_year, 2);
echo "</div>";
$total_amount = $wpdb->get_var("SELECT SUM(amount) FROM $table_donations");
echo "<div class='dwr_statistics_entry'>";
echo __("transactions_total", DWR_PLUGIN_NAME) . ": $total_transactions";
echo "<br />";
echo __("total_donation_amount", DWR_PLUGIN_NAME) . ": " . number_format($total_amount, 2);
echo "</div>";
$last100transactions = $wpdb->get_results("SELECT * FROM `" . $table_donations . "` ORDER BY donation_date DESC LIMIT 100");
echo "<h2>" . __("last_hundred_transactions_detailed", DWR_PLUGIN_NAME) . "</h2>";
echo "<table class='dwr_transactions_table'>";
echo "<tr>";
echo "<th class='dwr_id_col'>" . __("transaction_id", DWR_PLUGIN_NAME) . "</th><th class='dwr_robokassa_id_col'>" . __("robokassa_id", DWR_PLUGIN_NAME) . "</th><th class='dwr_sum_col'>" . __("donation_sum", DWR_PLUGIN_NAME) . "</th><th class='dwr_date_col'>" . __("transaction_date", DWR_PLUGIN_NAME) . "</th>";
echo "</tr>";
foreach ($last100transactions as $transaction) {
echo "<tr>";
echo "<td class='dwr_id_col'>{$transaction->id}</td><td class='dwr_robokassa_id_col'>{$transaction->robokassa_id}</td><td class='dwr_sum_col'>{$transaction->amount}</td><td class='dwr_date_col'>" . date('F j, Y, g:i a', strtotime($transaction->donation_date)) . "</td>";
echo "</tr>";
}
echo "</table>";
} else {
_e("no_transactions_yet_been_performed", DWR_PLUGIN_NAME);
}
echo "</div>";
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 135 |
Cruise Specialists hosts Steve and Wendy Bodenheimer are taking us along on another amazing journey. We hope this series shows you what you can expect on a Holland America Grand Voyage. Here are previous peeks: Grand voyage send off, what to expect at sea, Polynesia, New Zealand, Western Australia, Singapore and Thailand.
Reunion is a good example of a place where you cannot judge the island by the port area. We were berthed in the middle of the container port, at La Possession and if it weren't for the beautiful mountain peaks and cliffs visible from the ship, it wouldn't be very appealing. It was a 25 minute bus ride from the ship north to Saint-Denis, the island's main city.
Although it is an international destination, very little English is spoken here.
It's all French – French cafes, French Colonial buildings, and chic French shops. We enjoyed an easy walk around the town; down the main boulevard with historical markers and plaques; past sculptures, parks and manicured public buildings; stately old hotels; and up to the big Cathedral with bright colors showing its African and Creole influences.
We also heard from some independent travelers that there were good biking and hiking trails not far away. So much to do, so little time.
Returning to the ship, guests were already gathering out on the Lido deck for the first of the President week events – a complimentary sail away.
It's called President's Week because Holland America's President, Orlando Ashford and his family are on board and hosting a number of special events.
The following day, we were invited to a luncheon for the highest level Mariners – those with over 900 sailing days on Holland America. It was a group of about 75 at tables hosted by Senior Staff.
The following day was a long presentation and Q & A by Orlando to a standing room only audience. The questions were mostly relevant and reasonable and he answered them candidly.
He also announced the itinerary for the 2020 World Voyage. It is quite a departure and was very well received. For the first time in many years, the World Voyage will cover much of South America, including Antarctica and will return to Africa as well.
He said these two places were by far the most requested and so they were combined in one longer than usual (126 days) trip. It will likely be very popular and probably will sell out.
Our next port was Maputo, the capital of Mozambique. It was there that 160 people left the ship for a variety of Overland Tours and Safaris.
Our fellow host Tom Mullen took a group of 32 to Kruger National Park for three days of game drives and animal viewing. Each morning they boarded an open-air vehicle for perfect ride to explore a private game reserve. The afternoon brought a second game drive deep into the bush, where you may encounter South Africa's top predators: cheetahs, hyenas, and lions.
Wendy took 14 Guests for a 5 day adventure in Zambia, Zimbabwe, and Botswana (more on this to come!).
Steve stayed on the ship to watch over the rest of our Guests. He had a chance to venture out into Maputo for a look around, it's a pretty raw looking place as you might expect from a third world country.
The ship was berthed near the famous Central Railway station with the bronze dome built in 1910. Much of the city was destroyed during the 30 years of war which ended in 1992. Reconstruction has been slow and it is hard not to notice the piles of garbage everywhere. City tours offered visits to Independence Square, the Central Market, the railway station, Maputo Fort, City Hall, and the Natural History Museum. Overall, it was an interesting but not very exciting port.
Stay tuned for the next stop and Wendy's incredible overland tour! | {
"redpajama_set_name": "RedPajamaC4"
} | 8,260 |
\section{Background} \label{sec:bkgd}
\subsection{Symbiotics} \label{sec:symbiotics}
Symbiotic binary systems, also known as symbiotics, are a type of cataclysmic variable star (CV) that consist of an interacting cool giant star and a hot compact object, most commonly a white dwarf (WD). Interaction between the cool and hot component results from an outflow of matter from the cool component that accretes onto the hot component. Matter outflow can be due to stellar wind off of the cool component or the cool component overfilling its Roche-lobe. In many cases, the rate of mass loss off of the cool component can be sufficient to fuel hydrogen burning in a thermonuclear shell around the hot component \citep[][and references therein]{Sokoloski_2006}. As a result of mass outflow, symbiotics often exist inside of a gas cloud that can be fully or partially ionized by the hot component \citep{1986syst.book.....K}.
Symbiotics undergo periods of quiescence and activity, driven by the state of equilibrium between mass outflow, accretion, and ionization of the gas cloud. In quiescence, symbiotics emit energy at a constant average rate. During an active phase where this equilibrium is disturbed, symbiotics can be observed to undergo outbursts that feature an optical brightening of the system by 2--3 magnitudes with amplitude decreasing at longer wavelengths \citep{2003ASPC..303..249S}. This classical symbiotic outburst (or classical novae) is the most common type of outburst and commonly recurs on timescales of a decade \citep{1986syst.book.....K}. The driving mechanism behind a classical symbiotic outburst is the shedding of material off of the cool component onto the hot component as it overfills its Roche lobe, triggering thermonuclear runaway in a shell on the surface of the hot component. Another common type of outburst observed in CV systems containing red dwarfs (as opposed to giants) is the dwarf nova, which is driven by instability in accretion disks surrounding the WD that cause an increase in mass flow through the disk, resulting in temporary heating and brightening. These types of outbursts necessarily have smaller peak magnitudes and timescales than those observed in classical symbiotic outbursts.
Though these mechanisms are reasonable explanations of some outbursts observed in symbiotics, there are many outbursts that have been observed that, due to their the scales and recurrence times, cannot be explained by these mechanisms alone \citep{1986syst.book.....K,1995AJ....109.1289M,1979ApJ...230..832S}. To this end, \citet{Sokoloski_2006} proposed a \emph{combination nova} model to describe outbursts in symbiotics that exhibit qualities of both classical symbiotic outbursts and dwarf novae. This model suggests that outbursts in symbiotics are due to enhanced thermonuclear burning with disk instability as a trigger event. This model can account for the peak luminosities and short recurrence times of outbursts seen in many symbiotics, particularly for Z~Andromedae as described in \citet{Sokoloski_2006}.
On a larger scale, studying symbiotics is important in the context of their being a possible progenitor of Type Ia supernovae. As such, we would like to understand the true nature of these outbursts in order to predict their activity patterns. For most symbiotics, we have not been able to observe state transitions from quiescence to activity due to their irregular outburst behavior. An interesting exception is the system known as AG~Draconis (AG~Dra). This symbiotic has cyclical activity patterns, making it possible to predict and observe its state transitions.
\subsection{AG~Draconis} \label{sec:agdra}
AG~Dra is one of the best-studied symbiotics, with observations spanning the last century. Like most symbiotics, AG~Dra has been observed to alternate between phases of quiescence and activity, undergoing a series of outbursts during its active phases. According to \citet{GR1999}, such outbursts can be of both hot and cool type. Cool outbursts are caused by the expansion of the hot component's pseudo-atmosphere and a subsequent drop in WD temperature, which can be seen as an anticorrelation between optical/UV and X–ray emission. Hot outbursts occur when the WD's radius remains fixed and its temperature increases or remains the same. Outbursts of this nature show consistencies with disk instability-driven dwarf novae outbursts, as well as with the \citet{Sokoloski_2006} combination nova model where the thermonuclear burning pseudo-atmosphere of the WD expands after exceeding a threshold accretion rate triggered by disk instabilities. Evidence of the existence of an accretion disk surrounding the WD has recently been provided in a study done by \citet{2019MNRAS.487.2166L}. Over the course of its observation, certain periods have been discovered that characterize the system's orbital motion and outburst behavior. With its semi-regular state transitions, AG~Dra is a useful subject to study in order to characterize the mechanisms of symbiotic outbursts that are generally unclear.
The system consists of a K3 III red giant \citep{1987AJ.....93..938K} and white dwarf that are 1.5~$M_\odot$ and 0.4--0.6~$M_\odot$ \citep{1995AJ....109.1289M}, respectively. The hot component has a luminosity of $\sim10^3~L_\odot$ and a temperature of $\sim80-150\times10^3~K$ \citep{1995AJ....109.1289M}. The components have been observed to be at an orbital separation of 400~$R_\odot$ \citep{1986AJ.....91.1400G} and are enveloped in a partially ionized circumbinary nebula \citep{1995AJ....109.1289M}. \citet{2019MNRAS.487.2166L} showed that the upper limit in accretion disk size is $0.3~\textrm{au}$ or $\sim65~R_\odot$. Radio observations of emission from the circumbinary nebula give a rate of mass loss of $10^{-7}~M_\odot \textrm{yr}^{-1}$ \citep{1995AJ....109.1289M}. There is also evidence of thermonuclear shell burning on the WD's surface at a rate of $3.2\times10^{-8}~M_\odot \textrm{yr}^{-1}$ \citep{GR1999}. From a study of the historical UBV light curve of AG~Dra done by \citet{Hric2014}, the time between active periods has been observed to be anywhere from 12--16~yr. Additionally, two periods for the system have been clearly established; an orbital period of $\sim$550~d and a period of $\sim$355~d thought to be a result of pulsations of the cool component \citep{Galis1999}. AG~Dra's orbital period becomes prominent at shorter wavelengths, showing itself most clearly in the U-band during quiescence. Its pulsation period can be seen during both quiescent and active phases and is most visible in B and V-bands \citep{Galis2016}.
In its observed active phases, AG~Dra exhibits outbursts with consistent peak magnitudes, but irregular multitudes and shapes. They are spaced anywhere from 359--375~d \citep{2015OEJV..169....4G}. Normally, after an extended period of quiescence at $\textrm{V}=9.8$~mag, AG~Dra begins its active phases with a major cool outburst with peak magnitude of about $\textrm{B}=8.8$~mag and $\textrm{V}=8.4$~mag \citep{Galis2017} followed by a series of minor hot outbursts. It has not been confirmed, but the combination nova outburst model seems like a promising explanation of the underlying mechanism for a number of these outbursts. However, in May of 2015 AG~Dra exhibited very unusual behavior as it entered its most recent active phase. The activity began with a minor outburst with peak magnitude of $\textrm{V}=9.6$~mag, followed (at the usual cadence of $\sim$360~d) by two more minor outbursts with peak magnitude of $\textrm{B}=9.1$~mag and $\textrm{V}=9.6$~mag \citep{Galis2017}. This study showed that during these minor outbursts the system exhibited signs of both hot and cool type outbursts by examining the equivalent widths of certain emission lines and observing the disappearance of the Raman scattered O VI lines, respectively. In early April of 2018, AG~Dra began its fourth minor outburst of its 2015--2018 active phase. The Survey of Transiting Extrasolar Planets at the University of Pittsburgh (STEPUP) has monitored this outburst by conducting R-band photometric observations to examine an understudied band-pass of the system's outbursts. With these measurements, we seek to characterize the nature of AG~Dra's most recent outburst.
\begin{table*}[t]
\centering
\caption{ Sample first ten data points of SIA output for STEPUP AG~Dra observations.}
\begin{tabular}{ccccccccc}
\hline
\hline
Date & Date & ExpTime & Target R & Uncertainty & Filter & Check Label & Check R & Airmass \\
& [JD] & [s] & [mag] & [mag] & & & [mag] \\
\hline
2018-04-30 & 2458239.611990740 & 30 & 8.5960 & 0.0008672 & R & 345 & 11.8312 & 1.3478 \\
2018-04-30 & 2458239.616747690 & 30 & 8.5818 & 0.0008344 & R & 345 & 11.6420 & 1.3338 \\
2018-04-30 & 2458239.623541670 & 30 & 8.5725 & 0.0008411 & R & 345 & 11.6270 & 1.3148 \\
2018-04-30 & 2458239.624884260 & 30 & 8.5966 & 0.0008593 & R & 345 & 11.6529 & 1.3111 \\
2018-04-30 & 2458239.625578700 & 30 & 8.5749 & 0.0008360 & R & 345 & 11.6265 & 1.3093 \\
2018-04-30 & 2458239.626250000 & 30 & 8.5678 & 0.0008362 & R & 345 & 11.6211 & 1.3075 \\
2018-04-30 & 2458239.627615740 & 30 & 8.5854 & 0.0008440 & R & 345 & 11.6348 & 1.3038 \\
2018-04-30 & 2458239.628287040 & 30 & 8.5789 & 0.0008348 & R & 345 & 11.6345 & 1.3020 \\
2018-04-30 & 2458239.629641200 & 30 & 8.5690 & 0.0008288 & R & 345 & 11.6299 & 1.2985 \\
2018-04-30 & 2458239.630324070 & 30 & 8.5812 & 0.0008463 & R & 345 & 11.6208 & 1.2968 \\
... & ... & ... & ... & ... & ... & ... & ... & ... \\
\\
\hline
\end{tabular}
\label{tab:siatable}
\tablecomments{First ten data points from STEPUP's observations of AG Dra's2018 outburst. The full table is available through the AAVSO ftp site at
\href{ftp://ftp.aavso.org/public/datasets/richie481-sia-agdra-output.txt}{ftp://ftp.aavso.org/public/datasets/richie481-sia-agdra-output.txt} (if necessary, copy and paste link into browser).}
\end{table*}
\section{STEPUP} \label{sec:stepup}
STEPUP\footnote{\href{http://pitt.edu/~stepup/}{www.pitt.edu/$\sim$stepup}} has used the Meade Instruments f/8, 16'' RCX400 Keeler Telescope at the Allegheny Observatory in Pittsburgh, Pennsylvania, USA to conduct photometric observations of a variety of objects since its inception in 2009 \citep{pittir9073}. The main camera is a Santa Barbara Instruments Group (SBIG) STL-6303e and the field of view is 29.2 arcminutes by 19.5 arcminutes. Founded by Melanie Good, STEPUP's original mission was to discover and study new transiting exoplanets and has recently expanded its reach to observing variable stars. STEPUP records their data and processes it with an image analysis program, STEPUP Image Analysis (SIA)\footnote{\href{https://github.com/mwvgroup/STEPUP_image_analysis}{www.github.com/mwvgroup/STEPUP\_image\_analysis}}, written in the Python programing language by lead undergraduate, Helena Richie. SIA is responsible for removing instrument signatures from STEPUP's data, generating WCS information for each file, and performing differential aperture photometry to generate a light curve of the target object. SIA uses the AstroPy Python package \citep{astropy:2018} throughout the routine as well as the WCSTools \citep{1997ASPC..125..249M} software package and Astrometry.net \citep{2010AJ....139.1782L} in the process of plate-solving the images. STEPUP has contributed to several publications \citep{Shporer2010, Fleming_2012} on exoplanet transit timing variations and discovery.
\begin{figure*}
\centering
\textbf{STEPUP Observations of AG~Draconis 2018 Outburst}\par\medskip
\plotone{{figures/stepupLC.pdf}}
\caption{STEPUP observations of AG~Draconis 2018 outburst. Figures are shown on a $0.13183~\textrm{d}=3.1639~\textrm{h}$ timescale. These observations show no obvious variation in brightness and thus put a lower limit on the brightening timescale of AG~Dra during outburst. \label{fig:brightening}}
\end{figure*}
\section{Observations} \label{sec:obs}
To monitor AG~Dra's outburst behavior, STEPUP began conducting observations of the system in late 2018 April and continued through 2018 July using the Cousins R filter. Observations were made using a variety of exposure times ranging from 5--30~s. We removed saturated data points using a square aperture centered around each target, check, and comparison star to ensure that no pixels had met or exceeded the expected saturation level. If a pixel in the aperture met or exceeded this level, the data point corresponding to the image containing the object was removed from analysis. Subsequent observations had shortened exposure times (15~s and 5~s) to avoid saturation. All data was recorded in the FITS file format \citep{1981A&AS...44..363W} and processed by SIA. These results can be seen in Table~\ref{tab:siatable}. In addition to our own photometric measurements, we included observations from the AAVSO International Database (\href{https://www.aavso.org/aavso-international-database}{AID}; \citet{kafka_2020}) in our analysis.
\section{Image Processing} \label{sec:improc}
We used our STEPUP Image Analysis code to process the photometric data taken by STEPUP of the 2018 outburst of AG~Dra. SIA works in three main steps: (1) instrument signature removal (ISR); (2) astrometric calibration (ASTROM); and (3) differential photometry (PHOT). As input, SIA takes raw science images in the FITS file format, three types of calibration images, a plate-solved science image \citep[generated by Astrometry.net][]{2010AJ....139.1782L}, and an input file that includes coordinates of the target, check, and comparison stars and the magnitudes of the comparison stars. We list the comparison stars used for AG~Dra's analysis in Table~\ref{tab:compstars} given by the \emph{AAVSO Variable Star Plotter} tool. All three steps of SIA were performed to process the AG~Dra data and are summarized as follows.
\par
For ISR, SIA writes a data set of files that have been corrected for dead pixel columns, uneven CCD illumination, and thermal noise using flat, bias, and dark calibration images. To generate master calibration files, SIA takes the median across the image set of each pixel for the dark and bias. For the master flat, the array is normalized with respect to the center region of the image that is evenly illuminated. The raw science images have the master bias and dark subtracted from them and are divided by the flat. The result is an instrument-signature-removed data set.
\par
\begin{deluxetable}{lrrrr}
\tablecaption{Comparison stars used to process AG~Dra data. \label{tab:compstars}}
\tablehead{
\colhead{AUID} & \colhead{Label} & \colhead{R.A.} & \colhead{Dec.} & \colhead{R} \\
& & \colhead{[HH:MM:SS]} & \colhead{[DD:MM:SS]} & \colhead{[mag]}
}
\startdata
000-BCY-347 & 129 & 16:00:08.77 & 66:49:20.0 & 12.555 \\
000-BCY-346 & 123 & 16:00:24.08 & 66:49:29.6 & 11.980 \\
000-BJS-730 & 111 & 16:02:54.40 & 66:41:33.9 & 10.708 \\
000-BCY-344 & 119 & 16:00:11.22 & 66:39:14.2 & 11.575 \\
000-BCY-348 & 132 & 16:01:08.41 & 66:55:21.4 & 12.900 \\
\enddata
\tablecomments{Comparison stars used for photometric analysis of AG~Dra data. These stars were given by the \emph{AAVSO Variable Star Plotter} Photometry Table with VSP code {\bf X24880AIL}.}
\end{deluxetable}
In the next step, ASTROM, SIA takes the instrument signature removed files generated by ISR and a plate-solved image generated by Astrometry.net to write a set of files with the WCS FITS header keywords of the plate-solved image to the headers of the rest of the dataset. Then, SIA uses the WCSTools software package \citep{1997ASPC..125..249M} to adjust this information to accurately represent the coordinates of each pixel in each individual file. The result is a dataset with instrument signature-removed, plate-solved images.
\par
The final step of SIA is to perform differential aperture photometry. This places apertures at the positions of the target, check, and several comparison stars to get the sum of counts in the aperture for each object in every image of the dataset. A background rate per square pixel ($s_\textrm{bkgd}$) for the region of the image is determined by placing an annulus around the aperture and dividing its count sum by its area. The aperture and annulus sizes are as follows: $r_\textrm{aper}=4$\arcsec, $r_\textrm{in}=25$\arcsec, and $r_\textrm{out}=27$\arcsec. Subtracting the product of $s_\textrm{bkgd}$ and the area of the aperture ($A_\textrm{aper}$) from the aperture sum gives the net counts of the object. A 2D-Gaussian fit is applied for aperture centroiding. This process is used to get the net counts for all objects of interest in each image. The uncertainty in net counts for an object is given by
\begin{equation}
N=\sqrt{S_*+s_\textrm{bkgd}A_\textrm{aper}}\label{eq:err}
\end{equation}
where $S_*$ is the net count value in the aperture around the object.
\par
The net count values are then calibrated to magnitudes using the relation,
\begin{equation}
m_*=m_c-2.5\log_{10}\left(\frac{S_*}{S_c}\right), \label{eq:mag}
\end{equation}
where $m_*$ and $S_*$ are the magnitude and counts of the target star, respectively and for the comparison star the same values given by $m_c$ and $S_c$. SIA outputs a light curve of the target and check star as well as output files giving magnitude values and net count values for both objects as well as unscaled light curves of comparison stars and a summary of aperture position corrections.
\par
\begin{figure*}
\centering
\plotone{{figures/outbursteph.pdf}}
\caption{(Top) 2018 outburst of AG~Draconis shown by AAVSO and STEPUP R-band measurements. The system has an orbital period of $T_\textrm{orbit}=549.73~d$ and the cool component has a pulsation period of $T_\textrm{pulse}=355.27~\textrm{d}$ \citep{Galis1999}, which are visible during quiescence. (Bottom) Light curve of check star 000-BCY-345. \label{fig:lceph}}
\end{figure*}
\begin{figure*}
\centering
\plotone{{figures/colorlc.pdf}}
\caption{Color evolution of AG~Dra's 2018 outburst. The system's behavior exhibits chromaticity of amplitude $\textrm{V}-\textrm{R}=0.112 \pm 0.015~\textrm{mag}$. A slight increase in temperature can be seen leading up to the outburst's peak followed by a larger reddening as the system returns to quiescence. \label{fig:colorlc}}
\end{figure*}
\begin{figure*}
\centering
\plotone{{figures/outburstRV.pdf}}
\caption{2018 outburst of AG~Draconis shown by STEPUP R-band and AAVSO R and V-band measurements. This shows all measurements available in the AID, instead of the median 1-d binned data as used in the analysis described in Section \ref{sec:analy}. The R-band amplitude of the outburst was observed to be $\Delta\textrm{R}=0.518\pm0.011~\textrm{mag}$ and the V-band amplitude was observed to be $\Delta\textrm{V}=0.781\pm0.003~\textrm{mag}$. Below this is the $\textrm{V}-\textrm{R}$ light curve over the course of the outburst, showing an amplitude of 0.100~mag as the system returns to quiescence. The vertical dashed line marks the peak of the outburst, which occurred on JD~2458247.448. \label{fig:lc}}
\end{figure*}
\section{Analysis} \label{sec:analy}
We used data collected by STEPUP as well as R-band and V-band observations available from the AID to analyze AG~Draconis's 2018 outburst behavior. SIA was used to analyze each night of STEPUP data on the outburst and, assuming a Gaussian distribution, the median of observed magnitudes was taken to be the system's magnitude for a given night. The measurements for all eight nights of observation can be seen in Table~\ref{tab:obsresults} and a plot of STEPUP's measurements in Figure~\ref{fig:brightening}. We took the uncertainty in each night's magnitude, $\sigma_i$ to be the standard error of the data set,
\begin{equation}
\sigma_i = \frac{\sigma}{\sqrt{n}},
\end{equation}
where $\sigma$ is the sample standard deviation from the median, and $n$ is the total number of data points. The light curve of the outburst including AAVSO and STEPUP data can be seen in Figure~\ref{fig:lceph}.
\par
We included AAVSO data to analyze the outburst depth and start and end date. The AID points used in our analysis are the median of all R-band observations in bins of 1~d. We took the quiescence value of AG~Draconis to be the median of these resulting magnitudes, giving a value of $\textrm{R}=8.853$~mag. Using this value as a threshold to distinguish between in-outburst and out-of-outburst data points, the outburst start and end dates are JD~2458190 and JD~2458351, respectively, giving an outburst duration of 161~d. Taking the difference of the minimum and maximum magnitude values during this period, we found an outburst depth of $\Delta\textrm{R}=0.518 \pm 0.011~\textrm{mag}$. Figure~\ref{fig:lc} presents the full outburst with AAVSO V and R observations as well as STEPUP R observations.
\par
\begin{deluxetable}{crrr}
\tablecaption{Observations of AG~Dra by STEPUP \label{tab:obsresults}}
\tablehead{
\colhead{Date} & \colhead{ExpTime} & \colhead{R} & \colhead{Uncertainty} \\
& \colhead{[s]} & \colhead{[mag]} & \colhead{[mag]}
}
\centering
\startdata
2018-04-30 & 30 & 8.5762 & 0.0008 \\
2018-05-01 & 30 & 8.4682 & 0.0008 \\
2018-05-23 & 30 & 8.7039 & 0.0009 \\
2018-05-24 & 15 & 8.7393 & 0.0018 \\
2018-06-14 & 15 & 8.7904 & 0.0013 \\
2018-06-28 & 5 & 8.8538 & 0.0023 \\
2018-07-08 & 10 & 8.7884 & 0.0015 \\
2018-07-12 & 10 & 8.8002 & 0.0016 \\
\enddata
\tablecomments{Median magnitudes of AG~Dra for each night of observation by STEPUP. An outburst depth of $\Delta\textrm{R}=0.518 \pm 0.011~\textrm{mag}$ was observed using STEPUP and AAVSO measurements over a period of 161~d.}
\end{deluxetable}
To determine the nature of the outburst, we next performed a color analysis of AG~Dra's 2018 outburst. All STEPUP R and AAVSO V and R observations were used to give $\textrm{V}-\textrm{R}$ color during the outburst period. To get a higher-resolution light curve, instead of using 1-d bins as was used in the R-band analysis, we divided the light curves into intervals of 0.3~d ($\sim7.2~\textrm{h}$) where the median of all points in each interval was taken to be the value of that interval's magnitude. Each value's associated uncertainty was propagated to give the uncertainty in each interval's magnitude. Then, the color light curve and its uncertainty values were determined by subtracting the values in each band for each interval and propagating their uncertainties. To determine the amplitude of the color light curve all points in the outburst interval with $\textrm{SNR}>20$ were considered. By taking the difference in the median of the pre-outburst values and the post-outburst values we found a color of $\textrm{V}-\textrm{R}=0.112 \pm 0.015~\textrm{mag}$. This result can be seen in Figure~\ref{fig:colorlc}.
\section{Results} \label{sec:res}
The AG~Draconis system was observed by STEPUP and AAVSO observers to outburst by $\Delta\textrm{R}=0.518$~mag over the course of 161~d, lasting from JD~2458190 until JD~2458351. The outburst peaked in the R-band on JD~2458242.749 and in the V-band on JD~2458247.448. This outburst exhibited color change of $\textrm{V}-\textrm{R}=0.112$~mag. This color change coincided with the V-band outburst's peak, so we will take JD~2458247.448 to be the date of the outburst's peak. The V-band depth of this outburst is similar to that of previous minor outbursts of AG~Dra, such as the system's 2016 outburst that peaked at around $\textrm{V}=9.1$~mag. \citet{Galis2017} studied this outburst by examining the system's equivalent widths of certain emission lines and the disappearance of the Raman scattered O VI lines. This study shows evidence of the outburst being of both hot and cool type. Our analysis of AG~Dra's 2018 outburst may suggest a similar temperature evolution, with the primary feature being a large reddening (and potentially a drop in temperature) following the outburst's peak, as shown in Figure~\ref{fig:lc}. Additionally, before AG~Dra began descending back to quiescence, a slightly bluer $\textrm{V}-\textrm{R}$ color can be seen as the system approaches its peak outburst value.
\par
There are three main pieces of evidence that suggest that this outburst was a disk instability: (1) the sharp increase in brightness followed by a longer descent to quiescence, (2) the scale of the outburst, and (3) the color evolution of the event. The system rose to outburst in 55.1~d. After a small amount of brightening for the first $\sim20$ days of the outburst, the system began to rapidly brighten, with its magnitude increasing linearly at a rate of $\textrm{V}=-0.018$~mag per day. A constraint on the timescale of this brightening can be seen in Figure~\ref{fig:brightening}, which shows no change in magnitude on the order of $\sim1.5$~hr. Following the outburst's peak, the system's brightness dropped off rapidly at first, declining at a rate of $\textrm{V}=0.033$~mag per day for the first $\sim15$~d, followed by a slower rate of decline for the duration of the system's return to quiescence. This exponential fall in brightness provides evidence against outbursts that typically have linear rates of decline, such as classical novae \citep{Hachisu_2015}. The system took $\sim105.9$~d to completely return to quiescence. It is quite typical of disk instability-driven dwarf novae to have brightening times that are shorter than the the timescale of their decline, as is seen in this outburst. This model would suggest that the system's brightness declines due to the propagation of a cooling wave inward through the disk at the local sound speed. \citet{2019MNRAS.487.2166L} provides an upper limit on the size of the WD's accretion disk of 65~$R_\odot$. For a rate of propagation of 0.7~$R_\odot$ per 7--10~d \citep{Sokoloski_2006}, this is reasonable, though it would suggest a much smaller disk size than the provided upper limit.
\par
Furthermore, the amplitudes of $\Delta\textrm{R}=0.518~\textrm{mag}$ and $\Delta \textrm{V}=0.781~\textrm{mag}$ are too small to be caused by the thermonuclear runaways that drive classical symbiotic outbursts. Viewing the color evolution of the system, we see that the system became slightly bluer as the peak of the outburst occurred, followed by sizable reddening corresponding to the $\textrm{V}-\textrm{R}=0.112$~mag amplitude of the light curve after the outburst's peak. This provides evidence against classical novae since these types of outbursts usually show a negative color (i.e. $\textrm{B}-\textrm{V}$ color $< 0~\textrm{mag}$ and $\textrm{U}-\textrm{B}$ color $< 0~\textrm{mag}$, according to \citet{Hachisu_2015}) following the peak of the event. Given our unresolved photometric data of the entire system, it is impossible to know which component of AG~Dra was responsible for this increase in temperature. In the disk instability-type outburst, we see a rise in accretion disk temperature that triggers a change in the disk's viscosity as it reaches a critical temperature. This change in viscosity causes an increase in mass flow through the disk and subsequent heating and brightening, which could be responsible for the behavior of the color light curve as the outburst reaches its peak. Then, as the event ends, the system cools until its normal temperature is restored by the lower rate of mass flow supplied by the cool component's mass loss, which could in theory be responsible for the increase in $\textrm{V}-\textrm{R}$ color seen in Figure \ref{fig:colorlc}. If it were confirmed that this temperature change corresponds to a change in the disk temperature, then this would provide further evidence for the disk instability nature of this outburst.
\par
Another model that is less suited to describe this event is the combination nova outburst. The combination nova outburst is also triggered by disk instabilities, but is followed by a large decrease in temperature and increase in brightness as the white dwarf expels a surrounding shell of material after enhanced thermonuclear burning has commenced. This seems less likely to have caused this event, as the peak luminosity caused by enhanced shell burning would be much higher than that observed in AG~Dra's outburst. Also, a combination nova type outburst would most probably not have a linear rise to peak luminosity, as is seen in this event. While the available evidence favors the disk instability model, further data would be useful to distinguish between the temperatures of the disk, hot component, and cool component. In the case of a disk instability outburst, we would expect an increase in temperature and luminosity of the accretion disk, while the other components remain fixed in these parameters. While the shape and timescales of this 2018 event are generally consistent with those of typical dwarf novae, the expected linear decline corresponding to the propagation of a cooling wave through the disk is not visible. The system's R-band and V-band brightness both fall off exponentially, indicating that there may be further activity involved in the system's cooling and decline in brightness. Additionally, if the size of the disk is as large as the upper limit provided by \citet{2019MNRAS.487.2166L}'s study, this cooling time would not be consistent with the cooling rate described by \citet{Sokoloski_2006}. Further data that resolves the activity of individual components of the system may be illuminating in consideration of this cooling mechanism.
\section{Discussion} \label{sec:future}
Since the conclusion of this event, AG~Dra has not exhibited any further outbursts, with a notable lack of activity in 2019 May during the time when the next outburst of AG~Dra was expected. This suggests that the 2015-2018 active phase of the system has concluded. Though this active stage's outburst frequency has remained consistent with previous active stages, continuous UBVR photometric monitoring of the system is still necessary to determine if AG~Dra has truly returned to quiescence or if it will continue to exhibit abnormal outburst behavior. In particular, monitoring the temperature evolution of the hot component and accretion disk individually would be especially helpful in looking for signs of combination nova-type outbursts.
\par
Though this event was probably triggered by disk instabilities, it remains unclear what caused the discrepancy between this outburst's exponential fall-off and the typical dwarf novae's linear decline. For the typical major outbursts exhibited by AG~Dra in its active phase the combination nova model shows strong potential of explaining the underlying mechanism for at least some of the outbursts, though it has not been confirmed as conclusively as in \citet{Sokoloski_2006}'s study of Z~And. What remains unclear about the system is the connection between the minor outbursts exhibited by AG~Dra in its 2015--2018 active phase and its typical behavior during major outbursts. Whether or not there is a connection between this activity and previous outbursts has yet to be determined. Knowing the temperature and individual luminosities of each component would clarify whether this is indicative of a different outburst mechanism (e.g., a combination nova-type outburst) or if this behavior is due to system properties of AG~Dra, such as having a small disk size or interference of thermal pulsations by the cool component, allowing us to connect this activity into the grand scheme of AG~Dra's outburst behavior.
\acknowledgments
We acknowledge with thanks the variable star observations from the AAVSO International Database contributed by observers worldwide and used in this research. We also would like to thank both Scott Kenyon and the anonymous referee for their helpful comments that improved this paper.
This research was funded by the NASA Pennsylvania Space Grant Consortium Research Scholarship Award and the University of Pittsburgh Department of Physics \& Astronomy.
\citestyle{aasjournal}
\section{Background} \label{sec:bkgd}
\subsection{Symbiotics} \label{sec:symbiotics}
Symbiotic binary systems, also known as symbiotics, are a type of cataclysmic variable star (CV) that consist of an interacting cool giant star and a hot compact object, most commonly a white dwarf (WD). Interaction between the cool and hot component results from an outflow of matter from the cool component that accretes onto the hot component. Matter outflow can be due to stellar wind off of the cool component or the cool component overfilling its Roche-lobe. In many cases, the rate of mass loss off of the cool component can be sufficient to fuel hydrogen burning in a thermonuclear shell around the hot component \citep[][and references therein]{Sokoloski_2006}. As a result of mass outflow, symbiotics often exist inside of a gas cloud that can be fully or partially ionized by the hot component \citep{1986syst.book.....K}.
Symbiotics undergo periods of quiescence and activity, driven by the state of equilibrium between mass outflow, accretion, and ionization of the gas cloud. In quiescence, symbiotics emit energy at a constant average rate. During an active phase where this equilibrium is disturbed, symbiotics can be observed to undergo outbursts that feature an optical brightening of the system by 2--3 magnitudes with amplitude decreasing at longer wavelengths \citep{2003ASPC..303..249S}. This classical symbiotic outburst (or classical novae) is the most common type of outburst and commonly recurs on timescales of a decade \citep{1986syst.book.....K}. The driving mechanism behind a classical symbiotic outburst is the shedding of material off of the cool component onto the hot component as it overfills its Roche lobe, triggering thermonuclear runaway in a shell on the surface of the hot component. Another common type of outburst observed in CV systems containing red dwarfs (as opposed to giants) is the dwarf nova, which is driven by instability in accretion disks surrounding the WD that cause an increase in mass flow through the disk, resulting in temporary heating and brightening. These types of outbursts necessarily have smaller peak magnitudes and timescales than those observed in classical symbiotic outbursts.
Though these mechanisms are reasonable explanations of some outbursts observed in symbiotics, there are many outbursts that have been observed that, due to their the scales and recurrence times, cannot be explained by these mechanisms alone \citep{1986syst.book.....K,1995AJ....109.1289M,1979ApJ...230..832S}. To this end, \citet{Sokoloski_2006} proposed a \emph{combination nova} model to describe outbursts in symbiotics that exhibit qualities of both classical symbiotic outbursts and dwarf novae. This model suggests that outbursts in symbiotics are due to enhanced thermonuclear burning with disk instability as a trigger event. This model can account for the peak luminosities and short recurrence times of outbursts seen in many symbiotics, particularly for Z~Andromedae as described in \citet{Sokoloski_2006}.
On a larger scale, studying symbiotics is important in the context of their being a possible progenitor of Type Ia supernovae. As such, we would like to understand the true nature of these outbursts in order to predict their activity patterns. For most symbiotics, we have not been able to observe state transitions from quiescence to activity due to their irregular outburst behavior. An interesting exception is the system known as AG~Draconis (AG~Dra). This symbiotic has cyclical activity patterns, making it possible to predict and observe its state transitions.
\subsection{AG~Draconis} \label{sec:agdra}
AG~Dra is one of the best-studied symbiotics, with observations spanning the last century. Like most symbiotics, AG~Dra has been observed to alternate between phases of quiescence and activity, undergoing a series of outbursts during its active phases. According to \citet{GR1999}, such outbursts can be of both hot and cool type. Cool outbursts are caused by the expansion of the hot component's pseudo-atmosphere and a subsequent drop in WD temperature, which can be seen as an anticorrelation between optical/UV and X–ray emission. Hot outbursts occur when the WD's radius remains fixed and its temperature increases or remains the same. Outbursts of this nature show consistencies with disk instability-driven dwarf novae outbursts, as well as with the \citet{Sokoloski_2006} combination nova model where the thermonuclear burning pseudo-atmosphere of the WD expands after exceeding a threshold accretion rate triggered by disk instabilities. Evidence of the existence of an accretion disk surrounding the WD has recently been provided in a study done by \citet{2019MNRAS.487.2166L}. Over the course of its observation, certain periods have been discovered that characterize the system's orbital motion and outburst behavior. With its semi-regular state transitions, AG~Dra is a useful subject to study in order to characterize the mechanisms of symbiotic outbursts that are generally unclear.
The system consists of a K3 III red giant \citep{1987AJ.....93..938K} and white dwarf that are 1.5~$M_\odot$ and 0.4--0.6~$M_\odot$ \citep{1995AJ....109.1289M}, respectively. The hot component has a luminosity of $\sim10^3~L_\odot$ and a temperature of $\sim80-150\times10^3~K$ \citep{1995AJ....109.1289M}. The components have been observed to be at an orbital separation of 400~$R_\odot$ \citep{1986AJ.....91.1400G} and are enveloped in a partially ionized circumbinary nebula \citep{1995AJ....109.1289M}. \citet{2019MNRAS.487.2166L} showed that the upper limit in accretion disk size is $0.3~\textrm{au}$ or $\sim65~R_\odot$. Radio observations of emission from the circumbinary nebula give a rate of mass loss of $10^{-7}~M_\odot \textrm{yr}^{-1}$ \citep{1995AJ....109.1289M}. There is also evidence of thermonuclear shell burning on the WD's surface at a rate of $3.2\times10^{-8}~M_\odot \textrm{yr}^{-1}$ \citep{GR1999}. From a study of the historical UBV light curve of AG~Dra done by \citet{Hric2014}, the time between active periods has been observed to be anywhere from 12--16~yr. Additionally, two periods for the system have been clearly established; an orbital period of $\sim$550~d and a period of $\sim$355~d thought to be a result of pulsations of the cool component \citep{Galis1999}. AG~Dra's orbital period becomes prominent at shorter wavelengths, showing itself most clearly in the U-band during quiescence. Its pulsation period can be seen during both quiescent and active phases and is most visible in B and V-bands \citep{Galis2016}.
In its observed active phases, AG~Dra exhibits outbursts with consistent peak magnitudes, but irregular multitudes and shapes. They are spaced anywhere from 359--375~d \citep{2015OEJV..169....4G}. Normally, after an extended period of quiescence at $\textrm{V}=9.8$~mag, AG~Dra begins its active phases with a major cool outburst with peak magnitude of about $\textrm{B}=8.8$~mag and $\textrm{V}=8.4$~mag \citep{Galis2017} followed by a series of minor hot outbursts. It has not been confirmed, but the combination nova outburst model seems like a promising explanation of the underlying mechanism for a number of these outbursts. However, in May of 2015 AG~Dra exhibited very unusual behavior as it entered its most recent active phase. The activity began with a minor outburst with peak magnitude of $\textrm{V}=9.6$~mag, followed (at the usual cadence of $\sim$360~d) by two more minor outbursts with peak magnitude of $\textrm{B}=9.1$~mag and $\textrm{V}=9.6$~mag \citep{Galis2017}. This study showed that during these minor outbursts the system exhibited signs of both hot and cool type outbursts by examining the equivalent widths of certain emission lines and observing the disappearance of the Raman scattered O VI lines, respectively. In early April of 2018, AG~Dra began its fourth minor outburst of its 2015--2018 active phase. The Survey of Transiting Extrasolar Planets at the University of Pittsburgh (STEPUP) has monitored this outburst by conducting R-band photometric observations to examine an understudied band-pass of the system's outbursts. With these measurements, we seek to characterize the nature of AG~Dra's most recent outburst.
\begin{table*}[t]
\centering
\caption{ Sample first ten data points of SIA output for STEPUP AG~Dra observations.}
\begin{tabular}{ccccccccc}
\hline
\hline
Date & Date & ExpTime & Target R & Uncertainty & Filter & Check Label & Check R & Airmass \\
& [JD] & [s] & [mag] & [mag] & & & [mag] \\
\hline
2018-04-30 & 2458239.611990740 & 30 & 8.5960 & 0.0008672 & R & 345 & 11.8312 & 1.3478 \\
2018-04-30 & 2458239.616747690 & 30 & 8.5818 & 0.0008344 & R & 345 & 11.6420 & 1.3338 \\
2018-04-30 & 2458239.623541670 & 30 & 8.5725 & 0.0008411 & R & 345 & 11.6270 & 1.3148 \\
2018-04-30 & 2458239.624884260 & 30 & 8.5966 & 0.0008593 & R & 345 & 11.6529 & 1.3111 \\
2018-04-30 & 2458239.625578700 & 30 & 8.5749 & 0.0008360 & R & 345 & 11.6265 & 1.3093 \\
2018-04-30 & 2458239.626250000 & 30 & 8.5678 & 0.0008362 & R & 345 & 11.6211 & 1.3075 \\
2018-04-30 & 2458239.627615740 & 30 & 8.5854 & 0.0008440 & R & 345 & 11.6348 & 1.3038 \\
2018-04-30 & 2458239.628287040 & 30 & 8.5789 & 0.0008348 & R & 345 & 11.6345 & 1.3020 \\
2018-04-30 & 2458239.629641200 & 30 & 8.5690 & 0.0008288 & R & 345 & 11.6299 & 1.2985 \\
2018-04-30 & 2458239.630324070 & 30 & 8.5812 & 0.0008463 & R & 345 & 11.6208 & 1.2968 \\
... & ... & ... & ... & ... & ... & ... & ... & ... \\
\\
\hline
\end{tabular}
\label{tab:siatable}
\tablecomments{First ten data points from STEPUP's observations of AG Dra's2018 outburst. The full table is available through the AAVSO ftp site at
\href{ftp://ftp.aavso.org/public/datasets/richie481-sia-agdra-output.txt}{ftp://ftp.aavso.org/public/datasets/richie481-sia-agdra-output.txt} (if necessary, copy and paste link into browser).}
\end{table*}
\section{STEPUP} \label{sec:stepup}
STEPUP\footnote{\href{http://pitt.edu/~stepup/}{www.pitt.edu/$\sim$stepup}} has used the Meade Instruments f/8, 16'' RCX400 Keeler Telescope at the Allegheny Observatory in Pittsburgh, Pennsylvania, USA to conduct photometric observations of a variety of objects since its inception in 2009 \citep{pittir9073}. The main camera is a Santa Barbara Instruments Group (SBIG) STL-6303e and the field of view is 29.2 arcminutes by 19.5 arcminutes. Founded by Melanie Good, STEPUP's original mission was to discover and study new transiting exoplanets and has recently expanded its reach to observing variable stars. STEPUP records their data and processes it with an image analysis program, STEPUP Image Analysis (SIA)\footnote{\href{https://github.com/mwvgroup/STEPUP_image_analysis}{www.github.com/mwvgroup/STEPUP\_image\_analysis}}, written in the Python programing language by lead undergraduate, Helena Richie. SIA is responsible for removing instrument signatures from STEPUP's data, generating WCS information for each file, and performing differential aperture photometry to generate a light curve of the target object. SIA uses the AstroPy Python package \citep{astropy:2018} throughout the routine as well as the WCSTools \citep{1997ASPC..125..249M} software package and Astrometry.net \citep{2010AJ....139.1782L} in the process of plate-solving the images. STEPUP has contributed to several publications \citep{Shporer2010, Fleming_2012} on exoplanet transit timing variations and discovery.
\begin{figure*}
\centering
\textbf{STEPUP Observations of AG~Draconis 2018 Outburst}\par\medskip
\plotone{{figures/stepupLC.pdf}}
\caption{STEPUP observations of AG~Draconis 2018 outburst. Figures are shown on a $0.13183~\textrm{d}=3.1639~\textrm{h}$ timescale. These observations show no obvious variation in brightness and thus put a lower limit on the brightening timescale of AG~Dra during outburst. \label{fig:brightening}}
\end{figure*}
\section{Observations} \label{sec:obs}
To monitor AG~Dra's outburst behavior, STEPUP began conducting observations of the system in late 2018 April and continued through 2018 July using the Cousins R filter. Observations were made using a variety of exposure times ranging from 5--30~s. We removed saturated data points using a square aperture centered around each target, check, and comparison star to ensure that no pixels had met or exceeded the expected saturation level. If a pixel in the aperture met or exceeded this level, the data point corresponding to the image containing the object was removed from analysis. Subsequent observations had shortened exposure times (15~s and 5~s) to avoid saturation. All data was recorded in the FITS file format \citep{1981A&AS...44..363W} and processed by SIA. These results can be seen in Table~\ref{tab:siatable}. In addition to our own photometric measurements, we included observations from the AAVSO International Database (\href{https://www.aavso.org/aavso-international-database}{AID}; \citet{kafka_2020}) in our analysis.
\section{Image Processing} \label{sec:improc}
We used our STEPUP Image Analysis code to process the photometric data taken by STEPUP of the 2018 outburst of AG~Dra. SIA works in three main steps: (1) instrument signature removal (ISR); (2) astrometric calibration (ASTROM); and (3) differential photometry (PHOT). As input, SIA takes raw science images in the FITS file format, three types of calibration images, a plate-solved science image \citep[generated by Astrometry.net][]{2010AJ....139.1782L}, and an input file that includes coordinates of the target, check, and comparison stars and the magnitudes of the comparison stars. We list the comparison stars used for AG~Dra's analysis in Table~\ref{tab:compstars} given by the \emph{AAVSO Variable Star Plotter} tool. All three steps of SIA were performed to process the AG~Dra data and are summarized as follows.
\par
For ISR, SIA writes a data set of files that have been corrected for dead pixel columns, uneven CCD illumination, and thermal noise using flat, bias, and dark calibration images. To generate master calibration files, SIA takes the median across the image set of each pixel for the dark and bias. For the master flat, the array is normalized with respect to the center region of the image that is evenly illuminated. The raw science images have the master bias and dark subtracted from them and are divided by the flat. The result is an instrument-signature-removed data set.
\par
\begin{deluxetable}{lrrrr}
\tablecaption{Comparison stars used to process AG~Dra data. \label{tab:compstars}}
\tablehead{
\colhead{AUID} & \colhead{Label} & \colhead{R.A.} & \colhead{Dec.} & \colhead{R} \\
& & \colhead{[HH:MM:SS]} & \colhead{[DD:MM:SS]} & \colhead{[mag]}
}
\startdata
000-BCY-347 & 129 & 16:00:08.77 & 66:49:20.0 & 12.555 \\
000-BCY-346 & 123 & 16:00:24.08 & 66:49:29.6 & 11.980 \\
000-BJS-730 & 111 & 16:02:54.40 & 66:41:33.9 & 10.708 \\
000-BCY-344 & 119 & 16:00:11.22 & 66:39:14.2 & 11.575 \\
000-BCY-348 & 132 & 16:01:08.41 & 66:55:21.4 & 12.900 \\
\enddata
\tablecomments{Comparison stars used for photometric analysis of AG~Dra data. These stars were given by the \emph{AAVSO Variable Star Plotter} Photometry Table with VSP code {\bf X24880AIL}.}
\end{deluxetable}
In the next step, ASTROM, SIA takes the instrument signature removed files generated by ISR and a plate-solved image generated by Astrometry.net to write a set of files with the WCS FITS header keywords of the plate-solved image to the headers of the rest of the dataset. Then, SIA uses the WCSTools software package \citep{1997ASPC..125..249M} to adjust this information to accurately represent the coordinates of each pixel in each individual file. The result is a dataset with instrument signature-removed, plate-solved images.
\par
The final step of SIA is to perform differential aperture photometry. This places apertures at the positions of the target, check, and several comparison stars to get the sum of counts in the aperture for each object in every image of the dataset. A background rate per square pixel ($s_\textrm{bkgd}$) for the region of the image is determined by placing an annulus around the aperture and dividing its count sum by its area. The aperture and annulus sizes are as follows: $r_\textrm{aper}=4$\arcsec, $r_\textrm{in}=25$\arcsec, and $r_\textrm{out}=27$\arcsec. Subtracting the product of $s_\textrm{bkgd}$ and the area of the aperture ($A_\textrm{aper}$) from the aperture sum gives the net counts of the object. A 2D-Gaussian fit is applied for aperture centroiding. This process is used to get the net counts for all objects of interest in each image. The uncertainty in net counts for an object is given by
\begin{equation}
N=\sqrt{S_*+s_\textrm{bkgd}A_\textrm{aper}}\label{eq:err}
\end{equation}
where $S_*$ is the net count value in the aperture around the object.
\par
The net count values are then calibrated to magnitudes using the relation,
\begin{equation}
m_*=m_c-2.5\log_{10}\left(\frac{S_*}{S_c}\right), \label{eq:mag}
\end{equation}
where $m_*$ and $S_*$ are the magnitude and counts of the target star, respectively and for the comparison star the same values given by $m_c$ and $S_c$. SIA outputs a light curve of the target and check star as well as output files giving magnitude values and net count values for both objects as well as unscaled light curves of comparison stars and a summary of aperture position corrections.
\par
\begin{figure*}
\centering
\plotone{{figures/outbursteph.pdf}}
\caption{(Top) 2018 outburst of AG~Draconis shown by AAVSO and STEPUP R-band measurements. The system has an orbital period of $T_\textrm{orbit}=549.73~d$ and the cool component has a pulsation period of $T_\textrm{pulse}=355.27~\textrm{d}$ \citep{Galis1999}, which are visible during quiescence. (Bottom) Light curve of check star 000-BCY-345. \label{fig:lceph}}
\end{figure*}
\begin{figure*}
\centering
\plotone{{figures/colorlc.pdf}}
\caption{Color evolution of AG~Dra's 2018 outburst. The system's behavior exhibits chromaticity of amplitude $\textrm{V}-\textrm{R}=0.112 \pm 0.015~\textrm{mag}$. A slight increase in temperature can be seen leading up to the outburst's peak followed by a larger reddening as the system returns to quiescence. \label{fig:colorlc}}
\end{figure*}
\begin{figure*}
\centering
\plotone{{figures/outburstRV.pdf}}
\caption{2018 outburst of AG~Draconis shown by STEPUP R-band and AAVSO R and V-band measurements. This shows all measurements available in the AID, instead of the median 1-d binned data as used in the analysis described in Section \ref{sec:analy}. The R-band amplitude of the outburst was observed to be $\Delta\textrm{R}=0.518\pm0.011~\textrm{mag}$ and the V-band amplitude was observed to be $\Delta\textrm{V}=0.781\pm0.003~\textrm{mag}$. Below this is the $\textrm{V}-\textrm{R}$ light curve over the course of the outburst, showing an amplitude of 0.100~mag as the system returns to quiescence. The vertical dashed line marks the peak of the outburst, which occurred on JD~2458247.448. \label{fig:lc}}
\end{figure*}
\section{Analysis} \label{sec:analy}
We used data collected by STEPUP as well as R-band and V-band observations available from the AID to analyze AG~Draconis's 2018 outburst behavior. SIA was used to analyze each night of STEPUP data on the outburst and, assuming a Gaussian distribution, the median of observed magnitudes was taken to be the system's magnitude for a given night. The measurements for all eight nights of observation can be seen in Table~\ref{tab:obsresults} and a plot of STEPUP's measurements in Figure~\ref{fig:brightening}. We took the uncertainty in each night's magnitude, $\sigma_i$ to be the standard error of the data set,
\begin{equation}
\sigma_i = \frac{\sigma}{\sqrt{n}},
\end{equation}
where $\sigma$ is the sample standard deviation from the median, and $n$ is the total number of data points. The light curve of the outburst including AAVSO and STEPUP data can be seen in Figure~\ref{fig:lceph}.
\par
We included AAVSO data to analyze the outburst depth and start and end date. The AID points used in our analysis are the median of all R-band observations in bins of 1~d. We took the quiescence value of AG~Draconis to be the median of these resulting magnitudes, giving a value of $\textrm{R}=8.853$~mag. Using this value as a threshold to distinguish between in-outburst and out-of-outburst data points, the outburst start and end dates are JD~2458190 and JD~2458351, respectively, giving an outburst duration of 161~d. Taking the difference of the minimum and maximum magnitude values during this period, we found an outburst depth of $\Delta\textrm{R}=0.518 \pm 0.011~\textrm{mag}$. Figure~\ref{fig:lc} presents the full outburst with AAVSO V and R observations as well as STEPUP R observations.
\par
\begin{deluxetable}{crrr}
\tablecaption{Observations of AG~Dra by STEPUP \label{tab:obsresults}}
\tablehead{
\colhead{Date} & \colhead{ExpTime} & \colhead{R} & \colhead{Uncertainty} \\
& \colhead{[s]} & \colhead{[mag]} & \colhead{[mag]}
}
\centering
\startdata
2018-04-30 & 30 & 8.5762 & 0.0008 \\
2018-05-01 & 30 & 8.4682 & 0.0008 \\
2018-05-23 & 30 & 8.7039 & 0.0009 \\
2018-05-24 & 15 & 8.7393 & 0.0018 \\
2018-06-14 & 15 & 8.7904 & 0.0013 \\
2018-06-28 & 5 & 8.8538 & 0.0023 \\
2018-07-08 & 10 & 8.7884 & 0.0015 \\
2018-07-12 & 10 & 8.8002 & 0.0016 \\
\enddata
\tablecomments{Median magnitudes of AG~Dra for each night of observation by STEPUP. An outburst depth of $\Delta\textrm{R}=0.518 \pm 0.011~\textrm{mag}$ was observed using STEPUP and AAVSO measurements over a period of 161~d.}
\end{deluxetable}
To determine the nature of the outburst, we next performed a color analysis of AG~Dra's 2018 outburst. All STEPUP R and AAVSO V and R observations were used to give $\textrm{V}-\textrm{R}$ color during the outburst period. To get a higher-resolution light curve, instead of using 1-d bins as was used in the R-band analysis, we divided the light curves into intervals of 0.3~d ($\sim7.2~\textrm{h}$) where the median of all points in each interval was taken to be the value of that interval's magnitude. Each value's associated uncertainty was propagated to give the uncertainty in each interval's magnitude. Then, the color light curve and its uncertainty values were determined by subtracting the values in each band for each interval and propagating their uncertainties. To determine the amplitude of the color light curve all points in the outburst interval with $\textrm{SNR}>20$ were considered. By taking the difference in the median of the pre-outburst values and the post-outburst values we found a color of $\textrm{V}-\textrm{R}=0.112 \pm 0.015~\textrm{mag}$. This result can be seen in Figure~\ref{fig:colorlc}.
\section{Results} \label{sec:res}
The AG~Draconis system was observed by STEPUP and AAVSO observers to outburst by $\Delta\textrm{R}=0.518$~mag over the course of 161~d, lasting from JD~2458190 until JD~2458351. The outburst peaked in the R-band on JD~2458242.749 and in the V-band on JD~2458247.448. This outburst exhibited color change of $\textrm{V}-\textrm{R}=0.112$~mag. This color change coincided with the V-band outburst's peak, so we will take JD~2458247.448 to be the date of the outburst's peak. The V-band depth of this outburst is similar to that of previous minor outbursts of AG~Dra, such as the system's 2016 outburst that peaked at around $\textrm{V}=9.1$~mag. \citet{Galis2017} studied this outburst by examining the system's equivalent widths of certain emission lines and the disappearance of the Raman scattered O VI lines. This study shows evidence of the outburst being of both hot and cool type. Our analysis of AG~Dra's 2018 outburst may suggest a similar temperature evolution, with the primary feature being a large reddening (and potentially a drop in temperature) following the outburst's peak, as shown in Figure~\ref{fig:lc}. Additionally, before AG~Dra began descending back to quiescence, a slightly bluer $\textrm{V}-\textrm{R}$ color can be seen as the system approaches its peak outburst value.
\par
There are three main pieces of evidence that suggest that this outburst was a disk instability: (1) the sharp increase in brightness followed by a longer descent to quiescence, (2) the scale of the outburst, and (3) the color evolution of the event. The system rose to outburst in 55.1~d. After a small amount of brightening for the first $\sim20$ days of the outburst, the system began to rapidly brighten, with its magnitude increasing linearly at a rate of $\textrm{V}=-0.018$~mag per day. A constraint on the timescale of this brightening can be seen in Figure~\ref{fig:brightening}, which shows no change in magnitude on the order of $\sim1.5$~hr. Following the outburst's peak, the system's brightness dropped off rapidly at first, declining at a rate of $\textrm{V}=0.033$~mag per day for the first $\sim15$~d, followed by a slower rate of decline for the duration of the system's return to quiescence. This exponential fall in brightness provides evidence against outbursts that typically have linear rates of decline, such as classical novae \citep{Hachisu_2015}. The system took $\sim105.9$~d to completely return to quiescence. It is quite typical of disk instability-driven dwarf novae to have brightening times that are shorter than the the timescale of their decline, as is seen in this outburst. This model would suggest that the system's brightness declines due to the propagation of a cooling wave inward through the disk at the local sound speed. \citet{2019MNRAS.487.2166L} provides an upper limit on the size of the WD's accretion disk of 65~$R_\odot$. For a rate of propagation of 0.7~$R_\odot$ per 7--10~d \citep{Sokoloski_2006}, this is reasonable, though it would suggest a much smaller disk size than the provided upper limit.
\par
Furthermore, the amplitudes of $\Delta\textrm{R}=0.518~\textrm{mag}$ and $\Delta \textrm{V}=0.781~\textrm{mag}$ are too small to be caused by the thermonuclear runaways that drive classical symbiotic outbursts. Viewing the color evolution of the system, we see that the system became slightly bluer as the peak of the outburst occurred, followed by sizable reddening corresponding to the $\textrm{V}-\textrm{R}=0.112$~mag amplitude of the light curve after the outburst's peak. This provides evidence against classical novae since these types of outbursts usually show a negative color (i.e. $\textrm{B}-\textrm{V}$ color $< 0~\textrm{mag}$ and $\textrm{U}-\textrm{B}$ color $< 0~\textrm{mag}$, according to \citet{Hachisu_2015}) following the peak of the event. Given our unresolved photometric data of the entire system, it is impossible to know which component of AG~Dra was responsible for this increase in temperature. In the disk instability-type outburst, we see a rise in accretion disk temperature that triggers a change in the disk's viscosity as it reaches a critical temperature. This change in viscosity causes an increase in mass flow through the disk and subsequent heating and brightening, which could be responsible for the behavior of the color light curve as the outburst reaches its peak. Then, as the event ends, the system cools until its normal temperature is restored by the lower rate of mass flow supplied by the cool component's mass loss, which could in theory be responsible for the increase in $\textrm{V}-\textrm{R}$ color seen in Figure \ref{fig:colorlc}. If it were confirmed that this temperature change corresponds to a change in the disk temperature, then this would provide further evidence for the disk instability nature of this outburst.
\par
Another model that is less suited to describe this event is the combination nova outburst. The combination nova outburst is also triggered by disk instabilities, but is followed by a large decrease in temperature and increase in brightness as the white dwarf expels a surrounding shell of material after enhanced thermonuclear burning has commenced. This seems less likely to have caused this event, as the peak luminosity caused by enhanced shell burning would be much higher than that observed in AG~Dra's outburst. Also, a combination nova type outburst would most probably not have a linear rise to peak luminosity, as is seen in this event. While the available evidence favors the disk instability model, further data would be useful to distinguish between the temperatures of the disk, hot component, and cool component. In the case of a disk instability outburst, we would expect an increase in temperature and luminosity of the accretion disk, while the other components remain fixed in these parameters. While the shape and timescales of this 2018 event are generally consistent with those of typical dwarf novae, the expected linear decline corresponding to the propagation of a cooling wave through the disk is not visible. The system's R-band and V-band brightness both fall off exponentially, indicating that there may be further activity involved in the system's cooling and decline in brightness. Additionally, if the size of the disk is as large as the upper limit provided by \citet{2019MNRAS.487.2166L}'s study, this cooling time would not be consistent with the cooling rate described by \citet{Sokoloski_2006}. Further data that resolves the activity of individual components of the system may be illuminating in consideration of this cooling mechanism.
\section{Discussion} \label{sec:future}
Since the conclusion of this event, AG~Dra has not exhibited any further outbursts, with a notable lack of activity in 2019 May during the time when the next outburst of AG~Dra was expected. This suggests that the 2015-2018 active phase of the system has concluded. Though this active stage's outburst frequency has remained consistent with previous active stages, continuous UBVR photometric monitoring of the system is still necessary to determine if AG~Dra has truly returned to quiescence or if it will continue to exhibit abnormal outburst behavior. In particular, monitoring the temperature evolution of the hot component and accretion disk individually would be especially helpful in looking for signs of combination nova-type outbursts.
\par
Though this event was probably triggered by disk instabilities, it remains unclear what caused the discrepancy between this outburst's exponential fall-off and the typical dwarf novae's linear decline. For the typical major outbursts exhibited by AG~Dra in its active phase the combination nova model shows strong potential of explaining the underlying mechanism for at least some of the outbursts, though it has not been confirmed as conclusively as in \citet{Sokoloski_2006}'s study of Z~And. What remains unclear about the system is the connection between the minor outbursts exhibited by AG~Dra in its 2015--2018 active phase and its typical behavior during major outbursts. Whether or not there is a connection between this activity and previous outbursts has yet to be determined. Knowing the temperature and individual luminosities of each component would clarify whether this is indicative of a different outburst mechanism (e.g., a combination nova-type outburst) or if this behavior is due to system properties of AG~Dra, such as having a small disk size or interference of thermal pulsations by the cool component, allowing us to connect this activity into the grand scheme of AG~Dra's outburst behavior.
\acknowledgments
We acknowledge with thanks the variable star observations from the AAVSO International Database contributed by observers worldwide and used in this research. We also would like to thank both Scott Kenyon and the anonymous referee for their helpful comments that improved this paper.
This research was funded by the NASA Pennsylvania Space Grant Consortium Research Scholarship Award and the University of Pittsburgh Department of Physics \& Astronomy.
\citestyle{aasjournal}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,601 |
NBA 2K Playgrounds 2
129,00 zl
In-game purchases optional
DUALSHOCK 4 vibration
NBA arcade action is back with NBA 2K Playgrounds 2! The sequel to the original smash hit takes street balling to the next level with a massive roster of current and retired NBA players, improved online matchmaking with dedicated servers, four-player online matches, three-point contests, new playgrounds, custom matches, and more! Pick your team, get ready to jam, and Ball Without Limits!
Chinese (Simplified), Chinese (Traditional), English, French (France), German, Italian, Japanese, Korean, Portuguese (Brazil), Russian, Spanish
To play this game on PS5, your system may need to be updated to the latest system software. Although this game is playable on PS5, some features available on PS4 may be absent. See PlayStation.com/bc for more details.
One-time licence fee to download to multiple PS4 systems. Sign in to PlayStation Network is not required to use this on your primary PS4, but is required for use on other PS4 systems.
© 2005-2018 Take-Two Interactive Software, Inc. and its subsidiaries. 2K, the 2K logo, and Take-Two Interactive Software are all trademarks and/or registered trademarks of Take-Two Interactive Software, Inc. The NBA and NBA member team identifications are the intellectual property of NBA Properties, Inc. and the respective NBA member teams. © 2018 NBA Properties, Inc. All Rights Reserved. Officially licensed product of the National Basketball Players Association. All other trademarks are property of their respective owners.
2K Privacy Policy & EULA
Country / Region: Poland | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,264 |
Q: Select radio button from external URL How do you select a radio button using external link such as /page.html#item1 or /page.html?item1 so that when the page loads it's already selected
<input type="radio" name="price" id="item-1">
<input type="radio" name="price" id="item-2">
<input type="radio" name="price" id="item-3">
Any method will do, javascript or jquery
A: Simple way to check radio button on window load.
Consider your url to be of form -
scheme://example.com/myproject/abc.php?id=2
After running below code snippet you will encounter an error so try it on your site it requires url inorder to work.
$(window).on('load', function() {
let prepend = 'item-';
let elem = 'input[type=radio]';
let url = window.location.href;
let keyVal = '1';
if (url.indexOf('?') !== -1)
keyVal = url.split('?')[1].split('=')[1];
let id = prepend + keyVal;
$(elem).each(function(i) {
if ($(this).prop('id') === id)
$(this).prop('checked', true);
});
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<input type="radio" name="price" id="item-1">
<input type="radio" name="price" id="item-2">
<input type="radio" name="price" id="item-3">
<input type="radio" name="price" id="item-4">
<input type="radio" name="price" id="item-5">
Hope, this works for you..!! :) :)
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,974 |
Q: member function obtains copy of shared pointer to class instance I am moving to using C++11 shared pointers.
I need to write member functions that adds pointers to the instance of their class to containers ( i.e. registers ( adds ) their presence in some collection )
Using plain old pointers, I can do this
class myClass {
public:
void Register( std::vector< myClass* >& v_registrants )
{
v_registrants.push_back( this );
}
};
But how to do the same when the collection holds shared pointers? Somehow the member function must obtain a copy of the shared pointer that owns the instance.
I cannot simply create a new shared pointer from this because:
If two shared_ptr are constructed (or made) from the same (non-shared_ptr) pointer, they will both be owning the pointer without sharing it, causing potential access problems when one of them releases it (deleting its managed object) and leaving the other pointing to an invalid location. ( reference )
So, what to do to implement the following class?
class myClass_safe {
public:
void Register( std::vector< std::shared_ptr<myClass_safe > >& v_registrants )
{
//v_registrants.push_back( this ); // compiler freaks out
}
};
As a workaround, I am doing this:
class myClass_safe {
public:
void Register(
std::shared_ptr<myClass_safe >& my_shared_ptr,
std::vector< std::shared_ptr<myClass_safe > >& v_registrants )
{
v_registrants.push_back( my_shared_ptr );
}
};
Which results in this rather strange code
// register the object
object->Register( object, v_registrants );
Is there not something better than this?
A: I believe this is exactly what std::enable_shared_from_this is intended for.
Inheriting from std::enable_shared_from_this<classname> provides your class with a member function called shared_from_this, that enables you to safely obtain a std::shared_ptr that shares ownership with the original owner.
So to use it, in your case, you would have to change your class definition like this:
class myClass_safe : public std::enable_shared_from_this<myClass_safe> {
public:
void Register( std::vector< std::shared_ptr<myClass_safe > >& v_registrants )
{
v_registrants.push_back( shared_from_this() );
}
};
Note also, that the object must be owned by a shared pointer prior to calling shared_from_this.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,045 |
JoJo Siwa Says She Wasn't Invited to 2022 Nickelodeon Kids' Choice Awards
April 10, 2022 by DonnaEast 0 Comments
Was JoJo Siwa snubbed from the 2022 Nickelodeon Children' Alternative Awards?
The ceremony happened in Santa Monica, Calif. on Saturday, April 9. The longtime Nickelodeon star was nominated for Favourite Social Music Star and didn't attend the present. That night time, Siwa took to Instagram to supply her followers a proof.
"Lots of you've been asking me why I am not on the Nickelodeon Children' Alternative Awards tonight and the reply may be very easy: I wasn't invited," she mentioned in a video. "I am undecided why, however I simply did not get an invitation."
E! Information has reached out to Nickelodeon for remark and has not heard again.
In September 2021, Siwa took to Twitter to voice frustration about Nickelodeon's JoJo Siwa D.R.E.A.M. The Tour. "My film musical [The J Team] was simply launched (with 6 new unique songs)," she wrote. "Nickelodeon instructed me at present that I am not allowed to carry out/add any of the songs from the movie into my present. These are MY songs, MY voice, MY writing. Does this appear honest???"
She added, "There is no such thing as a cause that this music shouldn't be included. Working for an organization as an actual human being handled as solely a model is enjoyable till it isn't."
E! Information reached out to Nickelodeon for remark concerning Siwa's Twitter remarks after they have been posted and didn't hear again. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,535 |
Q: mouse click using sendMessage issue after working like 3 hours I finally managed to make a code to make a mouse click inside a window without moving the cursor, or having the window active using sendMessage. Here is some of my code:
Private Sub Button1_Click(sender As Object, e As EventArgs) Handles Button1.Click
Dim x As Integer = Integer.Parse(TextBox1.Text)
Dim y As Integer = Integer.Parse(TextBox2.Text)
If (hw) Then
SendMessage(hw, WM_LBUTTONDOWN, 0, MAKELONG(x, y))
SendMessage(hw, WM_LBUTTONUP, 0, MAKELONG(x, y))
End If
End Sub
I tried it in notepad and it works great. However, I am trying to do it inside a game, but for some reason the x,y is not working, the click happens at my last mouse position inside the game. Any ideas how I can fix this issue?
A: Try sending the mousemove event to the window first like e.g.:
Public Const WM_MOUSEMOVE = &H200
SendMessage(MainWindow, WM_MOUSEMOVE, 0, MakeDWord(P.X, P.Y))
If this doesn't work, try adding Threading.Thread.Sleep(100) after the mouse move event is send to the window.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,480 |
<?php
require_once __DIR__ . '/Common.php';
use OSS\OssClient;
use OSS\Core\OssException;
use OSS\Model\TaggingConfig;
use OSS\Model\Tag;
$ossClient = Common::getOssClient();
if (is_null($ossClient)) exit(1);
$bucket = Common::getBucketName();
//******************************* Simple Usage****************************************************************
// Set bucket tag
$config = new TaggingConfig();
$config->addTag(new Tag("key1", "value1"));
$config->addTag(new Tag("key2", "value2"));
$ossClient->putBucketTags($bucket, $config);
// Get bucket tags
$config = $ossClient->getBucketTags($bucket);
Common::println("bucket $bucket tags: ".$config->serializeToXml());
// Delete bucket tags
// Delete the specified tag of the bucket.
$tags = array();
$tags[] = new Tag("key1", "value1");
$tags[] = new Tag("key2", "value2");
$ossClient->deleteBucketTags($bucket, $tags);
// Delete all tags in the bucket.
$ossClient->deleteBucketTags($bucket);
//******************************* For complete usage, see the following functions ****************************************************
putBucketTags($ossClient, $bucket);
getBucketTags($ossClient, $bucket);
deleteBucketTags($ossClient, $bucket);
/**
* Create bucket tag
* @param OssClient $ossClient OssClient instance
* @param string $bucket Name of the bucket to create
* @return null
*/
function putBucketTags($ossClient, $bucket)
{
try {
// 设置Bucket标签。
$config = new TaggingConfig();
$config->addTag(new Tag("key1", "value1"));
$config->addTag(new Tag("key2", "value2"));
$ossClient->putBucketTags($bucket, $config);
} catch (OssException $e) {
printf(__FUNCTION__ . ": FAILED\n");
printf($e->getMessage() . "\n");
return;
}
print(__FUNCTION__ . ": OK" . "\n");
}
/**
* get bucket tag
* @param OssClient $ossClient OssClient instance
* @param string $bucket Name of the bucket to create
* @return null
*/
function getBucketTags($ossClient, $bucket)
{
try {
$config = $ossClient->getBucketTags($bucket);
print_r($config->getTags());
} catch (OssException $e) {
printf(__FUNCTION__ . ": FAILED\n");
printf($e->getMessage() . "\n");
return;
}
print(__FUNCTION__ . ": OK" . "\n");
}
/**
* delete bucket tag
* @param OssClient $ossClient OssClient instance
* @param string $bucket Name of the bucket to create
* @return null
*/
function deleteBucketTags($ossClient, $bucket)
{
try {
// Delete the specified tag of the bucket.
$tags = array();
$tags[] = new Tag("key1", "value1");
$tags[] = new Tag("key2", "value2");
$ossClient->deleteBucketTags($bucket, $tags);
// Delete all tags in the bucket.
//$ossClient->deleteBucketTags($bucket);
} catch (OssException $e) {
printf(__FUNCTION__ . ": FAILED\n");
printf($e->getMessage() . "\n");
return;
}
print(__FUNCTION__ . ": OK" . "\n");
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,618 |
«The Perfect Boy» es el cuadragésimo primer sencillo de la banda británica The Cure, el cuarto en ser extraído de su álbum 4:13 Dream de 2008. Fue también el último de una serie de sencillos editados el día 13 de cada mes. «The Perfect Boy» se editó el 13 de julio de 2008, aunque en el territorio norteamericano se editó con un día de adelanto, el 12 de agosto de 2008.
Lista de canciones
Canciones escritas por: Jason Cooper, Simon Gallup, Robert Smith y Porl Thompson.
Posición en listas
Músicos
Robert Smith — Guitarra, voz
Simon Gallup — Bajo
Jason Cooper — Batería
Porl Thompson — Guitarra
Referencias
Sencillos de 2008
Sencillos de The Cure
Canciones de The Cure
Canciones en inglés
Canciones de rock | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,924 |
4. Working with the bundle
==========================
i. Simple example
-----------------
Here an example of how to use the bundle. Let's use the following entity:
```php
<?php
// MyEntity.php
namespace Project\Bundle\SuperBundle\Entity;
use Doctrine\ORM\Mapping as ORM;
use Symfony\Component\Validator\Constraints as Assert;
/**
* @ORM\Entity
*/
class MyEntity
{
/**
* @ORM\Id
* @ORM\Column(type="integer")
* @ORM\GeneratedValue(strategy="AUTO")
*/
protected $id;
/**
* @ORM\Column(type="string")
*/
protected $name;
/**
* @ORM\Column(type="integer")
*/
protected $rank;
}
```
Create a type extended from AbstractType, add `name` and `rank` and use the filter_xxxx types.
```php
<?php
// ItemFilterType.php
namespace Project\Bundle\SuperBundle\Filter;
use Symfony\Component\Form\AbstractType;
use Symfony\Component\Form\FormBuilderInterface;
use Symfony\Component\OptionsResolver\OptionsResolverInterface;
class ItemFilterType extends AbstractType
{
public function buildForm(FormBuilderInterface $builder, array $options)
{
$builder->add('name', 'filter_text');
$builder->add('rank', 'filter_number');
}
public function getName()
{
return 'item_filter';
}
public function setDefaultOptions(OptionsResolverInterface $resolver)
{
$resolver->setDefaults(array(
'csrf_protection' => false,
'validation_groups' => array('filtering') // avoid NotBlank() constraint-related message
));
}
}
```
Then in an action, create a form object from the ItemFilterType. Let's say we filter when the form is submitted with a GET method.
```php
<?php
// DefaultController.php
namespace Project\Bundle\SuperBundle\Controller;
use Symfony\Bundle\FrameworkBundle\Controller\Controller;
use Symfony\Component\HttpFoundation\Request;
use Project\Bundle\SuperBundle\Filter\ItemFilterType;
class DefaultController extends Controller
{
public function testFilterAction(Request $request)
{
$form = $this->get('form.factory')->create(new ItemFilterType());
if ($request->query->has($form->getName())) {
// manually bind values from the request
$form->submit($request->query->get($form->getName()));
// initialize a query builder
$filterBuilder = $this->get('doctrine.orm.entity_manager')
->getRepository('ProjectSuperBundle:MyEntity')
->createQueryBuilder('e');
// build the query from the given form object
$this->get('lexik_form_filter.query_builder_updater')->addFilterConditions($form, $filterBuilder);
// now look at the DQL =)
var_dump($filterBuilder->getDql());
}
return $this->render('ProjectSuperBundle:Default:testFilter.html.twig', array(
'form' => $form->createView(),
));
}
}
```
Basic template
```html
<!-- testFilter.html.twig -->
<form method="get" action=".">
{{ form_rest(form) }}
<input type="submit" name="submit-filter" value="filter" />
</form>
```
ii. Inner workings
------------------
A filter is applied by using events. Basically the `lexik_form_filter.query_builder_updater` service will trigger a default event named according to the form type to get the condition for a given filter.
Then once all condition have been gotten another event will be triggered to add these conditions to the (doctrine) query builder.
We provide a event/listener that supports Doctrine ORM and DBAL.
The default event name pattern is `lexik_form_filter.apply.<query_builder_type>.<form_type_name>`.
For example, let's say I use a form type with a name field:
```php
public function buildForm(FormBuilder $builder, array $options)
{
$builder->add('name', 'filter_text');
}
```
The event name that will be triggered to get conditions to apply will be:
* `lexik_form_filter.apply.orm.filter_text` if you provide a `Doctrine\ORM\QueryBuilder`
* `lexik_form_filter.apply.dbal.filter_text` if you provide a `Doctrine\DBAL\Query\QueryBuilder`
Then another event will be triggered to add all the conditions to the (doctrine) query builder instance:
* `lexik_filter.apply_filters.orm` if you provide a `Doctrine\ORM\QueryBuilder`
* `lexik_filter.apply_filters.dbal` if you provide a `Doctrine\DBAL\Query\QueryBuilder`
iii. Customize condition operator
---------------------------------
By default the `lexik_form_filter.query_builder_updater` service will add conditions by using AND.
But you can customize the operator (and/or) to use between conditions when its added to the (doctrine) query builder.
To do so you will have to use the `filter_condition_builder` option in your main type class.
Here a simple example, the main type `ItemFilterType` is composed of 2 simple fields and a sub type (RelatedOptionsType).
The `filter_condition_builder` option is expected to be a closuse that will be used to set operators to use between conditions.
```php
<?php
namespace Project\Bundle\SuperBundle\Filter;
use Symfony\Component\Form\AbstractType;
use Symfony\Component\Form\FormBuilder;
class RelatedOptionsType extends AbstractType
{
public function buildForm(FormBuilder $builder, array $options)
{
$builder->add('label', 'filter_text');
$builder->add('rank', 'filter_number');
}
public function getName()
{
return 'related_options';
}
}
```
```php
<?php
namespace Project\Bundle\SuperBundle\Filter;
use Symfony\Component\Form\AbstractType;
use Symfony\Component\Form\FormBuilder;
use Symfony\Component\OptionsResolver\ConditionBuilderInterface;
use Lexik\Bundle\FormFilterBundle\Filter\Condition\ConditionBuilderInterface;
class ItemFilterType extends AbstractType
{
public function buildForm(FormBuilder $builder, array $options)
{
$builder->add('name', 'filter_text');
$builder->add('date', 'filter_date');
$builder->add('options', new RelatedOptionsType());
}
public function setDefaultOptions(OptionsResolverInterface $resolver)
{
$resolver->setDefaults(array(
'filter_condition_builder' => function (ConditionBuilderInterface $builder) {
$builder
->root('or')
->field('options.label')
->andX()
->field('options.rank')
->field('name')
->end()
->field('date')
->end()
;
}
));
}
public function getName()
{
return 'item_filter';
}
}
```
With the above condition builder the complete where clause pattern will be: `WHERE <options.label> OR <date> OR (<options.rank> AND <name>)`.
Here another example of condition builder:
```php
$resolver->setDefaults(array(
'filter_condition_builder' => function (ConditionBuilderInterface $builder) {
$builder
->root('and')
->orX()
->field('options.label')
->field('name')
->end()
->orX()
->field('options.rank')
->field('date')
->end()
->end()
;
}
));
```
The generated where clause will be: `WHERE (<options.label> OR <name>) AND (<options.rank> OR <date>)`.
iv. Filter customization
-------------------------
#### A. With the `apply_filter` option:
All filter types have an `apply_filter` option which is a closure.
If this option is defined the `QueryBuilderUpdater` won't trigger any event, but if will call the given closure instead.
The closure takes 3 parameters:
* an object that implements `Lexik\Bundle\FormFilterBundle\Filter\Query\QueryInterface` from which you can get the query builder and the expression class.
* the field name.
* an array of values containing the field value and some other data.
```php
<?php
// ItemFilterType.php
namespace Project\Bundle\SuperBundle\Filter;
use Symfony\Component\Form\AbstractType;
use Symfony\Component\Form\FormBuilder;
use Doctrine\ORM\QueryBuilder;
use Lexik\Bundle\FormFilterBundle\Filter\Query\QueryInterface;
class ItemFilterType extends AbstractType
{
public function buildForm(FormBuilder $builder, array $options)
{
$builder->add('name', 'filter_text', array(
'apply_filter' => function (QueryInterface $filterQuery, $field, $values) {
if (empty($values['value'])) {
return null;
}
$paramName = sprintf('p_%s', str_replace('.', '_', $field));
// expression that represent the condition
$expression = $filterQuery->getExpr()->eq($field, ':'.$paramName);
// expression parameters
$parameters = array($paramName => $values['value']); // [ name => value ]
// or if you need to define the parameter's type
// $parameters = array($paramName => array($values['value'], \PDO::PARAM_STR)); // [ name => [value, type] ]
return $filterQuery->createCondition($expression, $parameters);
},
));
}
public function getName()
{
return 'item_filter';
}
}
```
#### B. By listening an event
Another way to override the default way to apply the filter is to listen a custom event name.
This event name is composed of the form type name plus the form type's parent names, so the custom event name is like:
`lexik_form_filter.apply.<query_builder_type>.<parents_field_name>.<field_name>`
For example, if I use the following form type:
```php
<?php
// ItemFilterType.php
namespace Project\Bundle\SuperBundle\Filter;
use Symfony\Component\Form\AbstractType;
use Symfony\Component\Form\FormBuilder;
use Doctrine\ORM\QueryBuilder;
use Lexik\Bundle\FormFilterBundle\Filter\Query\QueryInterface;
class ItemFilterType extends AbstractType
{
public function buildForm(FormBuilder $builder, array $options)
{
$builder->add('position', 'filter_number');
}
public function getName()
{
return 'item_filter';
}
}
```
The custom event name will be:
`lexik_form_filter.apply.orm.item_filter.position`
The correspondig listener could looks like:
```php
namespace MyBundle\EventListener;
use Lexik\Bundle\FormFilterBundle\Event\GetFilterConditionEvent;
class ItemPositionFilterConditionListener
{
public function onGetFilterCondition(GetFilterConditionEvent $event)
{
$expr = $event->getFilterQuery()->getExpr();
$values = $event->getValues();
if (!empty($values['value'])) {
// create a parameter name from the field
$paramName = sprintf('p_%s', str_replace('.', '_', $field));
// Set the condition on the given event
$event->setCondition(
$expr->eq($event->getField(), ':' . $paramName),
array($paramName => $values['value'])
);
}
}
}
```
```xml
<service id="my_bundle.listener.get_item_position_filter" class="MyBundle\EventListener\ItemPositionFilterConditionListener">
<tag name="kernel.event_listener" event="lexik_form_filter.apply.orm.item_filter.position" method="onGetFilterCondition" />
</service>
```
Note that before triggering the default event name, the `lexik_form_filter.query_builder_updater` service checks if this custom event has some listeners, in which case this event will be triggered instead of the default one.
#### C. Disable filtering for one field
For any reason if you need to don't apply some filter condition for a given field, you can set the `apply_filter` option to `false`.
This will make the bundle skip the field, so no condition will be added for this field.
```php
<?php
// ItemFilterType.php
namespace Project\Bundle\SuperBundle\Filter;
use Symfony\Component\Form\AbstractType;
use Symfony\Component\Form\FormBuilder;
class ItemFilterType extends AbstractType
{
public function buildForm(FormBuilder $builder, array $options)
{
$builder->add('name', 'filter_text', array(
'apply_filter' => false, // disable filter
));
}
public function getName()
{
return 'item_filter';
}
}
```
v. Working with entity associations and embeddeding filters
-----------------------------------------------------------
You can embed a filter inside another one. It could be a way to filter elements associated to the "root" one.
In the two following sections (A and B), I suppose we have 2 entities Item and Options.
And Item has a collection of Option and and Option has one Item.
#### A. Collection
Let's say the entity we filter with the `ItemFilterType` filter is related to a collection of options, and an option has 2 fields: label and color.
We can filter entities by their option's label and color by creating and using a `OptionsFilterType` inside `ItemFilterType`:
The `OptionsFilterType` class is a standard form, and would looks like:
```php
<?php
namespace Project\Bundle\SuperBundle\Filter;
use Symfony\Component\Form\AbstractType;
use Symfony\Component\Form\FormBuilderInterface;
use Doctrine\ORM\QueryBuilder;
/**
* Embed filter type.
*/
class OptionsFilterType extends AbstractType
{
public function buildForm(FormBuilderInterface $builder, array $options)
{
$builder->add('label', 'filter_text');
$builder->add('color', 'filter_text');
}
public function getName()
{
return 'options_filter';
}
}
```
Then we can use it in our `ItemFilterType` type. But we will embed it by using a `filter_collection_adapter` type.
This type will allow us to use the `add_shared` option to add joins (or other stuff) we needed to apply conditions on fields from the embedded type (`OptionsFilterType` here).
```php
<?php
namespace Project\Bundle\SuperBundle\Filter;
use Symfony\Component\Form\AbstractType;
use Symfony\Component\Form\FormBuilder;
use Doctrine\ORM\Query\Expr;
use Doctrine\ORM\QueryBuilder;
use Lexik\Bundle\FormFilterBundle\Filter\FilterBuilderExecuterInterface;
class ItemFilterType extends AbstractType
{
public function buildForm(FormBuilder $builder, array $options)
{
$builder->add('name', 'filter_text');
$builder->add('rank', 'filter_number');
$builder->add('options', 'filter_collection_adapter', array(
'type' => new OptionsFilterType(),
'add_shared' => function (FilterBuilderExecuterInterface $qbe) {
$closure = function (QueryBuilder $filterBuilder, $alias, $joinAlias, Expr $expr) {
// add the join clause to the doctrine query builder
// the where clause for the label and color fields will be added automatically with the right alias later by the Lexik\Filter\QueryBuilderUpdater
$filterBuilder->leftJoin($alias . '.options', $joinAlias);
};
// then use the query builder executor to define the join, the join's alias and things to do on the doctrine query builder.
$qbe->addOnce($qbe->getAlias().'.options', 'opt', $closure);
},
));
}
public function getName()
{
return 'item_filter';
}
}
```
#### B. Single object
So let's say we need to filter some Option by their related Item's name.
We can create a `OptionsFilterType` type and add the item field which will be a `ItemFilterType` and not a `filter_entity` as we need to filter on field that belong to Item.
Let's start with the `ItemFilterType`, the only thing we have to do is to change the default parent type of our by using the `getParent()` method.
This will allow us to use the `add_shared` option as in the `filter_collection_adapter` type (by default this option is not available on a type).
```php
namespace Project\Bundle\SuperBundle\Filter;
use Symfony\Component\Form\AbstractType;
use Symfony\Component\Form\FormBuilderInterface;
class ItemFilterType extends AbstractType
{
public function buildForm(FormBuilderInterface $builder, array $options)
{
$builder->add('name', 'filter_text');
}
public function getParent()
{
return 'filter_sharedable'; // this allow us to use the "add_shared" option
}
public function getName()
{
return 'filter_item';
}
}
```
Then we can use our `ItemFilterType` inside `OptionsFilterType` and add the joins we need through the `add_shared` option.
```php
namespace Project\Bundle\SuperBundle\Filter;
use Doctrine\ORM\Query\Expr;
use Doctrine\ORM\QueryBuilder;
use Lexik\Bundle\FormFilterBundle\Filter\FilterBuilderExecuterInterface;
use Symfony\Component\Form\AbstractType;
use Symfony\Component\Form\FormBuilderInterface;
class OptionsFilterType extends AbstractType
{
public function buildForm(FormBuilderInterface $builder, array $options)
{
$builder->add('item', new ItemFilterType(), array(
'add_shared' => function (FilterBuilderExecuterInterface $qbe) {
$closure = function (QueryBuilder $filterBuilder, $alias, $joinAlias, Expr $expr) {
$filterBuilder->leftJoin($alias . '.item', $joinAlias);
};
$qbe->addOnce($qbe->getAlias().'.item', 'i', $closure);
}
));
}
public function getName()
{
return 'filter_options';
}
}
```
#### C. Use existing join alias defined on the query builder (ORM).
So as explained above you can add some joins dynamically.
But in case you've already set some joins on the query builder and you want to use them, you can use the `setParts()` method from the `lexik_form_filter.query_builder_updater` service.
This method allow you to pre-set aliases to use for each relation (join).
```php
$form = /* your form filter instance */;
$queryBuilder = $container
->getDoctrine()
->getManager()
->getRepository('Entity\Namespace')
->createQueryBuilder('e');
$queryBuilder
->select('e, u, a')
->leftJoin('e.user', 'u')
->innerJoin('u.addresses', 'a');
$qbUpdater = $container->get('lexik_form_filter.query_builder_updater');
// set the joins
$qbUpdater->setParts(array(
'e.user' => 'u',
'u.addresses' => 'a',
));
// then add filter conditions
$qbUpdater->addFilterConditions($form, $queryBuilder);
```
vi. Doctrine embeddables
------------------------
Here an example about how to create embedded filter types with Doctrine2 embeddables objects.
In the following code we suppose we use entities defined in the [doctrine tutorial](http://doctrine-orm.readthedocs.org/en/latest/tutorials/embeddables.html).
The `UserFilterType` is a standard type and simply embeds the `AddressFilterType`.
```php
namespace Project\Bundle\SuperBundle\Filter;
use Symfony\Component\Form\AbstractType;
use Symfony\Component\Form\FormBuilderInterface;
class UserFilterType extends AbstractType
{
public function buildForm(FormBuilderInterface $builder, array $options)
{
// ...
$builder->add('address', new AddressFilterType());
// ...
}
}
```
Then in the `AddressFilterType` we will have to implement the `EmbeddedFilterTypeInterface`.
This interface does not define any methods, it's just used by the `lexik_form_filter.query_builder_updater` service to differentiate it from an embedded type with relations.
```php
namespace Project\Bundle\SuperBundle\Filter;
use Symfony\Component\Form\AbstractType;
use Symfony\Component\Form\FormBuilderInterface;
use Lexik\Bundle\FormFilterBundle\Filter\Form\Type\EmbeddedFilterTypeInterface;
class AddressFilterType extends AbstractType implements EmbeddedFilterTypeInterface
{
public function buildForm(FormBuilderInterface $builder, array $options)
{
$builder->add('street', 'filter_text');
$builder->add('postalCode', 'filter_text');
// ...
}
}
```
vii. Create your own filter type
--------------------------------
Let's see that through a simple example, we suppose I want to create a `LocaleFilterType` class to filter fields which contain a locale as value.
A filter type is basicaly a standard form type and Symfony provide a LocaleType that display a combox of locales.
So we can start by creating a form type, with the `locale` type as parent. We will also define a default value for the `data_extraction_method`, this options will define how the `lexik_form_filter.query_builder_updater` service will get infos from the form before the filter is applied.
So the `LocaleFilterType` class would look like:
```php
namespace Super\Namespace\Type;
use Symfony\Component\Form\AbstractType;
use Symfony\Component\OptionsResolver\OptionsResolverInterface;
class LocaleFilterType extends AbstractType
{
/**
* {@inheritdoc}
*/
public function setDefaultOptions(OptionsResolverInterface $resolver)
{
$resolver
->setDefaults(array(
'data_extraction_method' => 'default',
))
->setAllowedValues(array(
'data_extraction_method' => array('default'),
))
;
}
/**
* {@inheritdoc}
*/
public function getParent()
{
return 'locale';
}
/**
* {@inheritdoc}
*/
public function getName()
{
return 'filter_locale';
}
}
```
Then defined the `LocaleFilterType` as a service and don't forget to add the `form.type` tag:
```xml
<service id="something.type.filter_locale" class="Super\Namespace\Type\LocaleFilterType">
<tag name="form.type" alias="filter_locale" />
</service>
```
Now we can use the `filter_locale` type, but no filter will be applied. To apply a filter we need to listen some event, so let's create a subscriber:
```php
namespace Super\Namespace\Listener;
use Symfony\Component\EventDispatcher\EventSubscriberInterface;
use Lexik\Bundle\FormFilterBundle\Event\GetFilterConditionEvent;
class FilterSubscriber implements EventSubscriberInterface
{
/**
* {@inheritDoc}
*/
public static function getSubscribedEvents()
{
return array(
// if a Doctrine\ORM\QueryBuilder is passed to the lexik_form_filter.query_builder_updater service
'lexik_form_filter.apply.orm.filter_locale' => array('filterLocale'),
// if a Doctrine\DBAL\Query\QueryBuilder is passed to the lexik_form_filter.query_builder_updater service
'lexik_form_filter.apply.dbal.filter_locale' => array('filterLocale'),
);
}
/**
* Apply a filter for a filter_locale type.
*
* This method should work whih both ORM and DBAL query builder.
*/
public function filterLocale(GetFilterConditionEvent $event)
{
$expr = $event->getFilterQuery()->getExpr();
$values = $event->getValues();
if ('' !== $values['value'] && null !== $values['value']) {
$paramName = str_replace('.', '_', $event->getField());
$event->setCondition(
$expr->eq($event->getField(), ':'.$paramName),
array($paramName => $values['value'])
);
}
}
}
```
Don't forget to defined the subscriber as a service.
```xml
<service id="lexik_form_filter.doctrine_subscriber" class="Super\Namespace\Listener\FilterSubscriber">
<tag name="kernel.event_subscriber" />
</service>
```
Now the `lexik_form_filter.query_builder_updater` service is able to add filter condition for a locale field.
__Tip__: As you can see the `LocaleFilterType` class is very simple, we use the `default` data extraction method and we don't add any additional field to the form builder, we only use the parent form. In this case we could only create the listener and listen to `lexik_form_filter.apply.xxx.locale` instead of `lexik_form_filter.apply.xxx.filter_locale` and use the provided `locale` type:
```php
[...]
class FilterSubscriber implements EventSubscriberInterface
{
/**
* {@inheritDoc}
*/
public static function getSubscribedEvents()
{
return array(
'lexik_form_filter.apply.orm.locale' => array('filterLocale'),
'lexik_form_filter.apply.dbal.locale' => array('filterLocale'),
);
}
[...]
}
```
viii. Enable FilterType form validation
---------------------------------------
By default most `FilterForms` are submitted using `GET`, and are defined in class instead of via a formBuilder in the controller. When you injected the data in the `FilterForm` yourself via the `$form->submit($data)` method, all was fine. In order to let the `validator` service function properly, we need to tell the form it does use the `GET` method:
```php
public function setDefaultOptions(OptionsResolverInterface $resolver)
{
parent::setDefaultOptions($resolver);
$resolver->setDefaults(array(
'error_bubbling' => true,
'csrf_protection' => false,
'validation_groups' => array('filtering'), // avoid NotBlank() constraint-related message
'method' => 'get',
));
}
```
In order to automatically validate your requests, you have to make use of Symfony its built-in `$form->handleRequest()` function. In your controller, you can create your forms in a different way:
```php
// Handle the filtering
$filterForm = $this->createForm(new OrderFilterType());
$filterForm->handleRequest($request);
if ($filterForm->isValid()) {
$filterBuilder = $this->get('lexik_form_filter.query_builder_updater')->addFilterConditions($filterForm, $filterBuilder);
}
```
Now the Symfony `requestHandler` will take over and won't `addFilterConditions` to the builder in case the form isn't valid.
***
Next: [5. The FilterTypeExtension](filtertypeextension.md)
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,245 |
Oct 9, 2019 SOURCE: BusinessWire
The Intersection of Technology, Innovation and India's Energy Sector Will Be Among Key Areas of Focus at India Energy Forum by CERAWeek, October 13-15 in New Delhi
Technology and innovation's role in shaping the energy future will be in focus at the third annual India Energy Forum by CERAWeek, October 13-15 in New Delhi. The event, presented by IHS Markit (NYSE: INFO), a world leader in critical information, analytics and solutions, brings together delegates from Indian and regional energy companies, institutions and governments, as well as a number of international speakers.
This year's conference will mark the debut of the Innovation Agora, a program discussing insights on innovation within the energy industry, emerging technologies and solutions and will include sessions dedicated to digital transformation, electrification, sustainability and advanced fuels.
The Agora will also bring together 10 energy startups from India, chosen in cooperation with Invest India, Start-Up India and Accelerating Growth of New India's Innovations (AGNIi). The participants were selected based on the novelty and innovative nature of the solutions that they offer to business challenges in areas such as biofuels, solar power, artificial intelligence, battery storage, grid management and machine learning, among others. The companies selected to participate are:
Amol Carbons Pvt. Ltd.
Amperehour Solar Technology Pvt. Ltd.
DD Bio Solution Technology Pvt. Ltd.
Energos Technologies Pvt. Ltd.
Flutura Business Solutions Pvt. ltd.
h2e Power Systems Pvt. Ltd.
Indian School of Innovation in Sustainability
Indisolar Products Private Limited
Ossus Biorenewables Pvt. Ltd.
Red Ginger Technologies Pvt. Ltd.
"The addition of the Innovation Agora program at India Energy Forum by CERAWeek reflects the pivotal role that technology and innovation have to play in India's new energy future," said Atul Arya, senior vice president and chief energy strategist, IHS Markit. "The featured startups, chosen out of a field of more than 50 applicants, reflect India's ever-growing role as a robust and dynamic center for new thinking and innovation across the energy spectrum."
The startups will be provided with time to present their company and innovation story to delegates, as well as attendance of the full program at India Energy Forum by CERAWeek.
Visit https://indiaenergy.ceraweek.com for a complete list of speakers and the most up-to-date program information. Session times, topics and speakers are subject to change.
Registration for members of the news media:
Media registration is open for members of the news media that wish to cover India Energy Forum by CERAWeek.
All members of the media are required to apply for accreditation. Registrations are not transferrable.
Applications for media credentials can be submitted at the following link: https://bit.ly/2nEzt1i
Registered journalists will be able to attend the main conference program that begins Monday, October 14.
A designated work room for credentialed news media will be provided on site.
For media inquiries related to the India Energy Forum by CERAWeek, contact Jeff Marn, jeff.marn@ihsmarkit.com or Katherine Smith, katherine.smith@ihsmarkit.com.
Background Information about IHS Markit in India:
IHS Markit started its first center in India in 2005, and currently has more than 3,000 employees across Delhi's National Capital Region, Bengaluru, Hyderabad and Mumbai. India represents the firm's largest employee base outside of the United States and the United Kingdom.
IHS Markit works closely with governments and organizations in the Indian subcontinent across core sectors of energy & natural resources; automotive; financial markets, maritime & trade; and engineering & product design.
About IHS Markit (www.ihsmarkit.com)
IHS Markit (NYSE: INFO) is a world leader in critical information, analytics and solutions for the major industries and markets that drive economies worldwide. The company delivers next-generation information, analytics and solutions to customers in business, finance and government, improving their operational efficiency and providing deep insights that lead to well-informed, confident decisions. IHS Markit has more than 50,000 business and government customers, including 80 percent of the Fortune Global 500 and the world's leading financial institutions. Headquartered in London, IHS Markit is committed to sustainable, profitable growth.
IHS Markit is a registered trademark of IHS Markit Ltd. and/or its affiliates. All other company and product names may be trademarks of their respective owners © 2019 IHS Markit Ltd. All rights reserved.
OTHER ENERGY
CERAWEEK
Global Energy Leaders to Convene at India Energy Forum by CERAWeek in New Delhi
Emerson Provides Roadmap to Digital Transformation, Envisions Tomorrow's Energy Jobs at CERAWeek by IHS Markit 2019
U.S. Secretary of Energy Rick Perry Will Deliver Keynote Remarks at CERAWeek by IHS Markit 2018
U.S. Secretary of Energy Rick Perry Will Deliver Remarks at CERAWeek by IHS Markit 2019
IEA Executive Director and OPEC Secretary General to Deliver Remarks at CERAWeek by IHS Markit 2018
U.S. Senator Daniel Sullivan to Speak at CERAWeek 2018 by IHS Markit
U.S. Senators John Cornyn and Lisa Murkowski Join Program of Speakers at CERAWeek by IHS Markit 2018
CERAWeek by IHS Markit to Showcase the 2018 Class of Energy Innovation Pioneers
EIB - Construction of a metro depot
Deadline: Mar 2, 2020
ENI - Provision of Technical Assistance to Private Enterprises to Become Environmentally Compliant and Business Advisory Services to SMEs along the Litani River Basin (Previously: Technical Assistance and Business Advisory Services to SMEs)
Deadline: Feb 7, 2020
Supply and Delivery of Agriculture Research Supplies under Kulima Programme
MalaysiaLangkawi Island
CYDES 2020, 24-26 March, Mahsuri International Exhibition Centre, Langkawi Island, Malaysia
The Integrated Cyber Defence, Cyber Security & Future Technology For The Global National Security Landscape...
K and D Communication Ltd.
Peekay Steel Castings Pvt. Ltd.
MKU Pvt. Ltd. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,931 |
\section{Introduction}
Since the discovery of the accelerated expansion of the Universe from the observations
of supernovae Ia~\cite{Perlmutter1999,Riess1998,Amanullah2010} and its interpretation using the $\Lambda$CDM model of
standard cosmology, a large amount of investigations have been devoted to explain the
same phenomenon but using dark energy substances different from the cosmological constant $\Lambda$.
One can rank the dark energy models from the most ``conservative'' to the most
``radical'' ones. Among the former we can mention those which do not
introduce new fields or modifications to general relativity but which consider that
inhomogeneities in the Universe could be enough to account for the observations~\cite{inhomogeneous}.
There are also the models that introduce new fields and perfect fluids with exotic
equations of state within the framework of general relativity (GR) in order to avoid the
``problems'' associated with $\Lambda$~\cite{Sahni2000,Carroll2001,Martin2012,Bianchi2010}.
For instance, {\it quintessence}, {\it $k$--essence}, and Chaplygin gas are some of the most
popular models of this kind. The most radical attempts to explain the accelerated expansion are perhaps those
which propose to modify GR while keeping the hypothesis of homogeneity and isotropy as a first approximation.
Many alternate theories of gravity have been proposed to explain this phenomenon
as well as those related with the dark matter (e.g. rotation curves of galaxies).
The modified $f(R)$ metric gravity is just one of such theories and
maybe the most analyzed one in the last ten years, where the geometry takes care of mimicking the dark energy.
This alternative is certainly radical since GR
has been thoroughly tested for almost one hundred years and it has not only supported all
the tests but in addition most of its predictions have been confirmed as well.
Thus, the challenge of modified gravity is both to be consistent with GR tests and also to explain the phenomena they
were called for. This is a no trivial
task and many $f(R)$ models have failed in the attempt. The story concerning dark substances does not end
with the accelerated expansion. The measurements of the angular distribution of cosmic background
radiation anisotropies in the sky can also be explained by the $\Lambda$CDM model, and therefore,
the task for the alternative models, theories or dark energy substances is even more demanding.
As we mentioned, $f(R)$ theories have been studied in detail in a recent past and it is out of the scope
of the present article to discuss all the properties, problems and features
associated with some of the specific models proposed before
(see Refs. ~\cite{Nojiri2011,deFelice2010,Sotiriou2010,Capozziello2011,Clifton2011} for a review).
Our aim is to report the results of a potentially viable candidate, termed {\it exponential
gravity}, as a model for the accelerated expansion, but using an approach that has been
proposed recently by us~\cite{Jaime2012} and which avoids the identification with the scalar--tensor
theories. The reason to follow this ``unorthodox'' method is because in some cases the
scalar--tensor (ST) method can lead to ill-defined potentials, and moreover because we want to
circumvent any possible discussion concerning the use of {\it frames}
(Einstein vs Jordan). Debates of this sort plague the subject, some of which have only led to
create confusion instead of shedding light.
With our technique we propose to treat the Ricci scalar itself as a degree of freedom,
instead of using $\phi=f_R$ as in the ST method (hereafter a subindex $R$ indicates $\partial/\partial_R$).
Our approach also spare us of inverting all the quantities depending on $R$ for treating them as functions of $\phi$.
Moreover, we have found that in several specific applications the field equations can be recasted
in a rather friendly way that allows us to treat them numerically or even analytically~\cite{Jaime2011,Jaime2012}.
In the next section we present our method and apply it to the
Friedmann-Roberson-Walker (FRW) spacetime within the scope of analyzing the cosmological evolution
using the {\it exponential gravity} model. The analysis of other viable $f(R)$ models
using the current approach can be seen in~\cite{Jaime2012} and in references therein
using other techniques.
\section{$f(R)$ theories, the Ricci scalar approach}
\label{fR}
The action in $f(R)$ gravity is given by:
\begin{equation}
\label{f(R)}
S[g_{ab},{\mbox{\boldmath{$\psi$}}}] =
\!\! \int \!\! \frac{f(R)}{2\kappa} \sqrt{-g} \: d^4 x
+ S_{\rm matt}[g_{ab}, {\mbox{\boldmath{$\psi$}}}] \; ,
\end{equation}
where $\kappa \equiv 8\pi G_0$ (we use units where $c=1$), $f(R)$ is a sufficiently
differentiable but otherwise {\it a priori} arbitrary function of
the Ricci scalar $R$, and ${\mbox{\boldmath{$\psi$}}}$ represents schematically the matter
fields. The field equation obtained from Eq.~(\ref{f(R)}) is:
\begin{equation}
\label{fieldeq1}
f_R R_{ab} -\frac{1}{2}fg_{ab} -
\left(\nabla_a \nabla_b - g_{ab}\Box\right)f_R= \kappa T_{ab}\,\,,
\end{equation}
where $f_R$ indicates $\partial_R f$, $\Box= g^{ab}\nabla_a\nabla_b$ is the covariant
D'Alambertian and $T_{ab}$ is the energy-momentum tensor (EMT) of matter
associated with the ${\mbox{\boldmath{$\psi$}}}$ fields. From this equation it is
straightforward to obtain the following equation and its trace~\cite{Jaime2011,Jaime2012}
\begin{equation}
\label{fieldeq3}
G_{ab} =
\frac{1}{f_R}\Bigl{[} f_{RR} \nabla_a \nabla_b R + f_{RRR} (\nabla_aR)(\nabla_b R)
- \frac{g_{ab}}{6}\Big{(} Rf_R+ f + 2\kappa T \Big{)} + \kappa T_{ab} \Bigl{]} \; ,
\end{equation}
\begin{equation}
\label{traceR}
\Box R= \frac{1}{3 f_{RR}}\Big{[}
\kappa T - 3 f_{RRR} (\nabla R)^2 + 2f- Rf_R
\Big{]} \; ,
\end{equation}
where $(\nabla R)^2:= g^{ab}(\nabla_aR)(\nabla_b R)$ and $T:= T^a_{\,\,a}$.
The idea is then to solve simultaneously Eqs.~(\ref{fieldeq3}) and (\ref{traceR}) for the metric $g_{ab}$ and $R$ as
a system of coupled partial differential equations.
It is important to mention that the field equations imply that the EMT of matter alone is conserved, i.e., it satisfies
$\nabla_a T^{ab}=0$.
In this contribution we shall focus on the model $f(R)= R_*[{\tilde R} - \lambda (1- e^{-{\tilde R}})]$, referred to as
{\it exponential gravity}, where
${\tilde R}= R/R_*$, $\lambda$ is a positive dimensionless constant and $R_*>0$ is also a constant that fixes the built-in scale
and which is of the order of the current Hubble parameter $H_0^2$. This kind of exponential models have been analyzed in the past by
several authors using a different technique~\cite{Elizalde2008,Linder2009,Yang2010,Bamba2010,Elizalde2011a,Elizalde2011b}.
Other variants of this model have also been analyzed~\cite{Zhang2006}.
The scalar $f_R= 1- \lambda e^{-{\tilde R}}$ is positive provided $R> R_* {\rm ln} \lambda$ and this condition
ensures $G_{\rm eff}:= G_0/f_R>0$. This latter is always satisfied in the cosmological solutions given below.
The possible de Sitter points correspond to trivial solutions $R=R_1=const.$ of Eq.~(\ref{traceR})
in vacuum ($T=0$) and give rise to an effective cosmological constant $\Lambda_{\rm eff}= R_1/4$ in Eq.~(\ref{fieldeq3})
($G_{ab}= - g_{ab} \Lambda_{\rm eff}$ in vacuum). Here $R_1>0$ is a critical point of
the ``potential'' $V(R)$ such that $V_R(R_1)=0$ with
$V_R:=(2f-Rf_R)/3= R_*[{\tilde R}(1+\lambda e^{-{\tilde R}}) - 2\lambda (1- e^{-{\tilde R}})]/3$, and $V_{RR}= 1- \lambda(1+{\tilde R})e^{-{\tilde R}}$.
The ``potential'' is given by $V(R)= R_*^2[ {\tilde R}({\tilde R} - 4 \lambda) - 2\lambda({\tilde R} + 3) e^{-{\tilde R}}) ]/6$.
For $0<\lambda \leq 1$ one can easily see that $V(R)$ has just one critical point at $R=0$ which
is not a de Sitter point as in this case $\Lambda_{\rm eff}\equiv 0$. The point is
a global minimum (c.f. $V_{RR}(0)=1-\lambda$). For $\lambda > 1$ there is a local maximum at $R=0$ and a global minimum at
$R=R_1>0$ which corresponds to the actual de Sitter point that the cosmological
solution reaches asymptotically in the future. There is also a local minimum at $R= R_2<0$, but it is an anti de Sitter point
which is never reached as the cosmological solutions take place only in the domain $R>0$.
The potential $V(R)$ is depicted in Figure~\ref{fig:f(R)} (right panel) where one can appreciate the critical points just described.
In the high curvature regime ${\tilde R}\gg 1$, we have $f(R)\approx R- \lambda R_*$, and thus the model acquires
an effective cosmological constant $\Lambda_{\rm eff}^{\infty}:= \lambda R_*/2$ (c.f. left panel of Fig.~\ref{fig:f(R)}).
From the figure we see that for $\lambda$ sufficiently high, the de Sitter point verifies ${\tilde R}_1\gg 1$, and thus
$R_1 \approx 2 \lambda R_*$ as it turns out from $V_R(R_1)= 0$. Therefore $\Lambda_{\rm eff}\approx \Lambda_{\rm eff}^{\infty}$.
Finally, we stress that $f_{RR}= \lambda e^{-{\tilde R}}/R_* >0$ which ensures that no singularities are found in the equations due to
this scalar and moreover it guarantees that given $V_{RR}(R_1)>0$ the effective mass
$m^2:= V_{RR}/f_{RR}=(f_R-Rf_{RR})/(3f_{RR})|_{R_1}$ of the scalar mode is positive.
\begin{figure*}
\includegraphics[width= 5.6cm]{fR-B.eps}
\includegraphics[width= 5.6cm]{V-B.eps}
\vskip -.2cm
\caption{(color online) $f(R)$ exponential gravity (left panel) and the potential $V(R)$ (right panel) for several values of $\lambda$.}
\label{fig:f(R)}
\end{figure*}
\section{Cosmology in $f(R)$}
We assume the spatially flat FRW metric given by:
\begin{equation}
\label{FRWmetric}
ds^2 = - dt^2 + a^2(t) \left[ dr^2 + r^2 \left(d\theta^2 + \sin^2\theta d\varphi^2\right)\right]\,\,\,.
\end{equation}
From Eqs.~(\ref{fieldeq3}) and ~(\ref{traceR}) we have,
\begin{eqnarray}
\label{traceRt}
&& \ddot R = -3H \dot R - \frac{1}{3 f_{RR}}\left[3f_{RRR} \dot R^2 + 2f- f_R R + \kappa T \right]\,\,\,,\\
\label{Hgen}
&& H^2 = \frac{\kappa}{3}\left(\rule{0mm}{0.3cm} \rho +\rho_{X}\right) \,\,\,,\\
\label{Hdotgen}
&& \dot{H}= -H^2 -\frac{\kappa}{6}\left\{\rule{0mm}{0.4cm} \rho +\rho_{X}+3\left(p_{\rm rad}+ p_{X}\right) \right\} \,\,\,.
\end{eqnarray}
where a dot stands for $d/dt$ and $H= \dot a/a$, is the Hubble expansion. In the above equations we have included the energy
density $\rho$ associated with matter (baryons, dark matter and radiation) as well as the GDE density $\rho_{X}$ and pressure
$p_{X}$ given respectively by~\cite{Jaime2012}
\begin{equation}
\label{rhoX}
\rho_{X}=\frac{1}{\kappa f_{R}}\left\{\rule{0mm}{0.5cm} \frac{1}{2}\left( f_{R}R-f\right) -3f_{RR}H\dot{R} +
\kappa \rho\left(1- f_{R}\right)\right\},
\end{equation}
\begin{equation}
\label{pressX}
p_{X}=-\frac{1}{3\kappa f_{R}}\left\lbrace \frac{1}{2}\left(f_{R}R+f \right) + 3f_{RR}H\dot{R}-\kappa\left(\rho -3 p_{\rm rad} f_R \right)
\right\rbrace \,\,\,.
\end{equation}
Another differential equation that can be used to solve for $H$ instead of Eq.~(\ref{Hdotgen}) is given by
$R= 6(\dot H + 2 H^2)$. This latter is no other than the Ricci scalar computed directly from the metric~(\ref{FRWmetric}).
Equation (\ref{Hgen}) amounts to the modified Hamiltonian constraint which we use to set the
initial data and also to monitor the accuracy of the numerical solutions at every integration step. At this regard, we stress that
we shall not use the cosmic time $t$ but instead $\alpha= {\rm ln}(a/a_0)$ as ``time'' parameter (see Ref.~\cite{Jaime2012}),
where $a_0$ is the present value of $a$. Notice that at the de Sitter point $R\rightarrow R_1=const.$ where $2f(R_1)= R_1 f_R(R_1)$ and
with $\rho\rightarrow 0$, $p_{\rm rad}\rightarrow 0$ Eqs.~(\ref{rhoX}) and (\ref{pressX}), lead to $\rho_X\rightarrow \Lambda_{\rm eff}/\kappa$ and
$p_X\rightarrow -\Lambda_{\rm eff}/\kappa$, respectively, and from Eqs.~(\ref{Hgen}) and ~(\ref{Hdotgen}),
$H^2\rightarrow H^2_{\rm vac}= \Lambda_{\rm eff}/3= R_1/12$, and $q=-\ddot a/(aH^2)\rightarrow q_{\rm vac}= -1$.
So the main idea behind all $f(R)$ models is that as the Universe evolves, $R\rightarrow R_1$, and thus the GDE dominates and
mimics an effective cosmological constant that allows to explain the accelerated expansion required to account for the observations.
The matter variables obey the conservation equation $\dot \rho_i= -3 H \left(\rho_i + p_i\right)$ for each fluid component
(with $p_{\rm bar,DM}=0$ and $p_{\rm rad}= \rho_{\rm rad}/3$) which integrates straightforwardly and gives rise to the usual expression for
the energy density of matter plus radiation:
$\rho= (\rho_{\rm bar}^0 + \rho_{\rm DM}^0)(a/a_0)^{-3} + \rho_{\rm rad}^0 (a/a_0)^{-4}$,
where the knotted quantities indicate their values today. The $X$--fluid variables ~(\ref{rhoX}) and (\ref{pressX}) also
satisfy a conservation equation similar to the one above, but with an EOS $\omega_X:= p_X/\rho_X$ that evolves in cosmic time.
Other possible inequivalent definitions of $\rho_X$, $p_X$ and $\omega_X$ have been adopted in the past, but they suffer of several
drawbacks (see~\cite{Jaime2012} for a detailed discussion).
\begin{figure*}[t!
\includegraphics[width= 5.6cm]{R-B.eps}
\includegraphics[width= 5.6cm]{H-B.eps}
\vskip -.2cm
\caption{(color online) Ricci scalar (left panel) and the Hubble expansion (right panel)
for several values of $\lambda$ and $R_*$ (given in units of $H_0^2$). }
\label{fig:H-Rn}
\end{figure*}
\begin{figure*}[t]
\includegraphics[width=5.6cm]{Ome-L1-R4.eps}
\includegraphics[width=5.6cm]{Ome-L25-R2.eps}
\vskip -.4cm
\caption{(color online) Evolution of $\Omega_{\rm matt}$ (red solid line) and
$\Omega_X$ (blue solid line) for $\lambda= 1$ and $R_*= 4H_0^2$ (left panel) and $\lambda= 2.5$ and $R_*= 2H_0^2$
(right panel). For reference the corresponding quantities of the $\Lambda$CDM model are included
in each panel (dashed lines).}
\label{fig:Omegas}
\end{figure*}
The total EOS is defined by $\omega_{\rm tot} = (p_{\rm rad}+p_{X})/(\rho +\rho_{X})$ which using Eqs.~(\ref{rhoX}) and (\ref{pressX}) yields
\begin{equation}
\label{EOSTOT}
\omega_{\rm tot} = -\frac{1}{3}\left[ \frac{\frac{1}{2}\left(f_{R}R+f \right) + 3f_{RR}H\dot{R}-\kappa\rho}
{\frac{1}{2}\left( f_{R}R-f\right) -3f_{RR}H\dot{R} + \kappa \rho}\right] \,\,\,.
\end{equation}
This EOS allows us to track the epochs where the Universe is expanding in a decelerating or accelerating fashion. If
$\omega_{\rm tot} < -1/3$ then $\ddot a > 0$, while $\ddot a < 0$ if $\omega_{\rm tot} > -1/3$.
\begin{figure*}[t!
\includegraphics[width= 5.6cm]{wX-B.eps}
\includegraphics[width= 5.6cm]{w-total-B.eps}
\vskip -.2cm
\caption{(color online) The EOS $\omega_X$ (left panel) and the total EOS $\omega_{\rm tot}$ (right panel).}
\label{fig:EOS}
\end{figure*}
\section{Numerical Results and Discussion}
We integrate the differential equations forward, from past to future, starting from a given $z= a_0/a -1$, where matter
dominates, to $z\rightarrow -1$ where the GDE prevails. The initial conditions are fixed
as in~\cite{Jaime2012}. Figure~\ref{fig:H-Rn} shows the Hubble expansion and the Ricci scalar for several values of
$\lambda$. In all the cases where $\lambda >1$, $R$ reaches the de Sitter point at the global minimum of $V(R)$.
For $\lambda=1$ because the potential is very flat around the global minimum at $R=0$, and also due to the friction term,
$R$ varies very slowly as it approaches the minimum. This explains why in this case the model also mimics
a cosmological constant. Figure~\ref{fig:Omegas} depicts the fraction of dimensionless densities
$\Omega_i= \kappa \rho_i/(3H^2)$ which satisfy the constraint $\Omega_{\rm rad} + \Omega_{\rm matt} + \Omega_X =1$ where
$\Omega_{\rm matt}:= \Omega_{\rm bar}+ \Omega_{\rm DM}$. The radiation contribution, although taken into account, is very small
and cannot be appreciated from the plots. The current abundances at $z=0$ (today) match reasonably well the predicted values of the $\Lambda$CDM model
and the exponential models show an adequate matter domination era. The EOS of GDE is plotted in Figure~\ref{fig:EOS}
(left panel), and like in other $f(R)$ models~\cite{Jaime2012}, it oscillates around the phantom divide value $\omega_\Lambda= -1$ before reaching
its asymptotic value as $z\rightarrow -1$.
The total EOS depicted in Figure~\ref{fig:EOS} (right panel) shows that at higher $z$ the Universe is dominated by matter
with $\omega_{\rm tot} \sim 0$, and then interpolates to the value $\omega_{\rm tot}= -1$ in the far future. At
$z=0$, $\omega_{\rm tot}$ is similar to the value $\omega_{\rm tot}\sim 0.75$ predicted by the $\Lambda$CDM model. Figure~\ref{fig:Lum-q} (left panel)
shows the (modulus) luminous distance computed as in~\cite{Jaime2012} and the deceleration parameter (right panel).
In these exponential models it is technically difficult to integrate far in the past since $f_{RR}\rightarrow 0$ exponentially.
Since this quantity appears in the denominator of Eq.~(\ref{traceRt}), it produces large variations that affects
the precision during the numerical integration. This is something that we had encountered in other $f(R)$ models~\cite{Jaime2012}.
The exponential model seems to be consistent with the cosmological observations and also with the Solar System~\cite{Linder2009}.
Nevertheless, like other $f(R)$ models that look viable as well, a closer examination is required in all possible scenarios
before considering $f(R)$ theories as a serious threat to general relativity.
\begin{figure*}[t]
\includegraphics[width=5.6cm]{m-M-todas.eps}
\includegraphics[width=5.6cm]{q-B.eps}
\vskip -.3cm
\caption{(color online) Luminous distance (left panel) compared with the Union 2 data~\cite{Amanullah2010}. Deceleration parameter
(right panel).}
\label{fig:Lum-q}
\end{figure*}
\section*{References}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 742 |
Cooperative Wholesale Society war ein britischer Hersteller von Automobilen.
Unternehmensgeschichte
Das Unternehmen aus Manchester übernahm 1919 Bell Brothers aus Ravensthorpe. Die Produktion derer Kraftfahrzeugmodelle wurde fortgesetzt. Der Markenname lautete Bell für Personenkraftwagen und CWS-Bell für Nutzfahrzeuge. 1922 stand ein Kleinwagen als CWS im Angebot. Das Unternehmen existierte bis mindestens 1937.
Fahrzeuge
Das einzige Modell war ein Dreirad. Ein V2-Motor von J.A.P. mit 8 PS Leistung trieb über eine Kette das einzelne Hinterrad an. Das Dreiganggetriebe kam von Juckes. Der Neupreis lag mit 150 Pfund sehr hoch.
Literatur
George Nick Georgano (Chefredakteur): The Beaulieu Encyclopedia of the Automobile. Volume 1: A–F. Fitzroy Dearborn Publishers, Chicago 2001, ISBN 1-57958-293-1. (englisch)
Weblinks
Allcarindex (englisch, abgerufen am 2. Februar 2014)
Einzelnachweise
Ehemaliger Pkw-Hersteller (England)
Ehemaliges Unternehmen (Manchester) | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 259 |
Dan Powell is a Brooklyn-based sound designer and audio engineer specializing in podcasting, radio and other narrative media.
He is currently a staff audio engineer at Marketplace.
Co-creation and sound design for popular horror podcast Archive 81.
You can get in touch with me here. Thanks for stopping by! | {
"redpajama_set_name": "RedPajamaC4"
} | 381 |
Le championnat de France de football de Division 4 1979-1980 est la du Championnat de France de football de Division 4.
Classement
Groupe A
|}
Groupe B
|}
Groupe C
|}
Groupe D
|}
Groupe E
|}
Groupe F
|}
Groupe G
|}
Groupe H
|}
Voir aussi
Articles connexes
Championnat de France de football de Division 4
Coupe de France de football 1979-1980
Championnat de France de football 1979-1980
Liens externes
Le CFA 2 sur fff.fr
Championnat de France de football de quatrième division
France
Championnat de France en 1979
France
Championnat de France en 1980 | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,767 |
<!-- Start annyang.js -->
# Quick Tutorial, Intro and Demos
The quickest way to get started is to visit the [annyang homepage](https://www.talater.com/annyang/).
For a more in-depth look at annyang, read on.
# API Reference
## init(commands, [resetCommands=true])
Initialize annyang with a list of commands to recognize.
#### Examples:
````javascript
var commands = {'hello :name': helloFunction};
var commands2 = {'hi': helloFunction};
// initialize annyang, overwriting any previously added commands
annyang.init(commands, true);
// adds an additional command without removing the previous commands
annyang.init(commands2, false);
````
As of v1.1.0 it is no longer required to call init(). Just start() listening whenever you want, and addCommands() whenever, and as often as you like.
**Deprecated**
See: [Commands Object](#commands-object)
### Params:
* **Object** *commands* - Commands that annyang should listen to
* **boolean** *[resetCommands=true]* - Remove all commands before initializing?
## start([options])
Start listening.
It's a good idea to call this after adding some commands first, but not mandatory.
Receives an optional options object which supports the following options:
- `autoRestart` (boolean, default: true) Should annyang restart itself if it is closed indirectly, because of silence or window conflicts?
- `continuous` (boolean) Allow forcing continuous mode on or off. Annyang is pretty smart about this, so only set this if you know what you're doing.
- `paused` (boolean, default: true) Start annyang in paused mode.
#### Examples:
````javascript
// Start listening, don't restart automatically
annyang.start({ autoRestart: false });
// Start listening, don't restart automatically, stop recognition after first phrase recognized
annyang.start({ autoRestart: false, continuous: false });
````
### Params:
* **Object** *[options]* - Optional options.
## abort()
Stop listening, and turn off mic.
Alternatively, to only temporarily pause annyang responding to commands without stopping the SpeechRecognition engine or closing the mic, use pause() instead.
See: [pause()](#pause)
## pause()
Pause listening. annyang will stop responding to commands (until the resume or start methods are called), without turning off the browser's SpeechRecognition engine or the mic.
Alternatively, to stop the SpeechRecognition engine and close the mic, use abort() instead.
See: [abort()](#abort)
## resume()
Resumes listening and restores command callback execution when a result matches.
If SpeechRecognition was aborted (stopped), start it.
## debug([newState=true])
Turn on output of debug messages to the console. Ugly, but super-handy!
### Params:
* **boolean** *[newState=true]* - Turn on/off debug messages
## setLanguage(language)
Set the language the user will speak in. If this method is not called, defaults to 'en-US'.
See: [Languages](https://github.com/TalAter/annyang/blob/master/docs/FAQ.md#what-languages-are-supported)
### Params:
* **String** *language* - The language (locale)
## addCommands(commands)
Add commands that annyang will respond to. Similar in syntax to init(), but doesn't remove existing commands.
#### Examples:
````javascript
var commands = {'hello :name': helloFunction, 'howdy': helloFunction};
var commands2 = {'hi': helloFunction};
annyang.addCommands(commands);
annyang.addCommands(commands2);
// annyang will now listen to all three commands
````
See: [Commands Object](#commands-object)
### Params:
* **Object** *commands* - Commands that annyang should listen to
## removeCommands([commandsToRemove])
Remove existing commands. Called with a single phrase, array of phrases, or methodically. Pass no params to remove all commands.
#### Examples:
````javascript
var commands = {'hello': helloFunction, 'howdy': helloFunction, 'hi': helloFunction};
// Remove all existing commands
annyang.removeCommands();
// Add some commands
annyang.addCommands(commands);
// Don't respond to hello
annyang.removeCommands('hello');
// Don't respond to howdy or hi
annyang.removeCommands(['howdy', 'hi']);
````
### Params:
* **String|Array|Undefined** *[commandsToRemove]* - Commands to remove
## addCallback(type, callback, [context])
Add a callback function to be called in case one of the following events happens:
* `start` - Fired as soon as the browser's Speech Recognition engine starts listening
* `error` - Fired when the browser's Speech Recogntion engine returns an error, this generic error callback will be followed by more accurate error callbacks (both will fire if both are defined)
Callback function will be called with the error event as the first argument
* `errorNetwork` - Fired when Speech Recognition fails because of a network error
Callback function will be called with the error event as the first argument
* `errorPermissionBlocked` - Fired when the browser blocks the permission request to use Speech Recognition.
Callback function will be called with the error event as the first argument
* `errorPermissionDenied` - Fired when the user blocks the permission request to use Speech Recognition.
Callback function will be called with the error event as the first argument
* `end` - Fired when the browser's Speech Recognition engine stops
* `result` - Fired as soon as some speech was identified. This generic callback will be followed by either the `resultMatch` or `resultNoMatch` callbacks.
Callback functions for to this event will be called with an array of possible phrases the user said as the first argument
* `resultMatch` - Fired when annyang was able to match between what the user said and a registered command
Callback functions for this event will be called with three arguments in the following order:
* The phrase the user said that matched a command
* The command that was matched
* An array of possible alternative phrases the user might have said
* `resultNoMatch` - Fired when what the user said didn't match any of the registered commands.
Callback functions for this event will be called with an array of possible phrases the user might've said as the first argument
#### Examples:
````javascript
annyang.addCallback('error', function() {
$('.myErrorText').text('There was an error!');
});
annyang.addCallback('resultMatch', function(userSaid, commandText, phrases) {
console.log(userSaid); // sample output: 'hello'
console.log(commandText); // sample output: 'hello (there)'
console.log(phrases); // sample output: ['hello', 'halo', 'yellow', 'polo', 'hello kitty']
});
// pass local context to a global function called notConnected
annyang.addCallback('errorNetwork', notConnected, this);
````
### Params:
* **String** *type* - Name of event that will trigger this callback
* **Function** *callback* - The function to call when event is triggered
* **Object** *[context]* - Optional context for the callback function
## removeCallback(type, callback)
Remove callbacks from events.
- Pass an event name and a callback command to remove that callback command from that event type.
- Pass just an event name to remove all callback commands from that event type.
- Pass undefined as event name and a callback command to remove that callback command from all event types.
- Pass no params to remove all callback commands from all event types.
#### Examples:
````javascript
annyang.addCallback('start', myFunction1);
annyang.addCallback('start', myFunction2);
annyang.addCallback('end', myFunction1);
annyang.addCallback('end', myFunction2);
// Remove all callbacks from all events:
annyang.removeCallback();
// Remove all callbacks attached to end event:
annyang.removeCallback('end');
// Remove myFunction2 from being called on start:
annyang.removeCallback('start', myFunction2);
// Remove myFunction1 from being called on all events:
annyang.removeCallback(undefined, myFunction1);
````
### Params:
* *type* Name of event type to remove callback from
* *callback* The callback function to remove
### Return:
* undefined
## isListening()
Returns true if speech recognition is currently on.
Returns false if speech recognition is off or annyang is paused.
### Return:
* boolean true = SpeechRecognition is on and annyang is listening
## getSpeechRecognizer()
Returns the instance of the browser's SpeechRecognition object used by annyang.
Useful in case you want direct access to the browser's Speech Recognition engine.
### Return:
* SpeechRecognition The browser's Speech Recognizer currently used by annyang
## trigger(string|array)
Simulate speech being recognized. This will trigger the same events and behavior as when the Speech Recognition
detects speech.
Can accept either a string containing a single sentence, or an array containing multiple sentences to be checked
in order until one of them matches a command (similar to the way Speech Recognition Alternatives are parsed)
#### Examples:
````javascript
annyang.trigger('Time for some thrilling heroics');
annyang.trigger(
['Time for some thrilling heroics', 'Time for some thrilling aerobics']
);
````
### Params:
* *string|array* sentences A sentence as a string or an array of strings of possible sentences
### Return:
* undefined
# Good to Know
## Commands Object
Both the [init()]() and addCommands() methods receive a `commands` object.
annyang understands commands with `named variables`, `splats`, and `optional words`.
* Use `named variables` for one word arguments in your command.
* Use `splats` to capture multi-word text at the end of your command (greedy).
* Use `optional words` or phrases to define a part of the command as optional.
#### Examples:
````html
<script>
var commands = {
// annyang will capture anything after a splat (*) and pass it to the function.
// e.g. saying "Show me Batman and Robin" will call showFlickr('Batman and Robin');
'show me *tag': showFlickr,
// A named variable is a one word variable, that can fit anywhere in your command.
// e.g. saying "calculate October stats" will call calculateStats('October');
'calculate :month stats': calculateStats,
// By defining a part of the following command as optional, annyang will respond
// to both: "say hello to my little friend" as well as "say hello friend"
'say hello (to my little) friend': greeting
};
var showFlickr = function(tag) {
var url = 'http://api.flickr.com/services/rest/?tags='+tag;
$.getJSON(url);
}
var calculateStats = function(month) {
$('#stats').text('Statistics for '+month);
}
var greeting = function() {
$('#greeting').text('Hello!');
}
</script>
````
### Using Regular Expressions in commands
For advanced commands, you can pass a regular expression object, instead of
a simple string command.
This is done by passing an object containing two properties: `regexp`, and
`callback` instead of the function.
#### Examples:
````javascript
var calculateFunction = function(month) { console.log(month); }
var commands = {
// This example will accept any word as the "month"
'calculate :month stats': calculateFunction,
// This example will only accept months which are at the start of a quarter
'calculate :quarter stats': {'regexp': /^calculate (January|April|July|October) stats$/, 'callback': calculateFunction}
}
````
<!-- End annyang.js -->
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,383 |
A Vauriella a madarak osztályának verébalakúak (Passeriformes) rendjébe és a légykapófélék (Muscicapidae) családjába tartozó nem. Egyes szervezetek a Rhinomyias nembe sorolják ezeket a fajokat is.
Rendszerezésük
A nemet Hans Edmund Wolters német ornitológus írta le 1980-ban, az alábbi fajok tartoznak ide:
Vauriella gularis vagy Rhinomyias gularis
Vauriella insignis vagy Rhinomyias insignis
Vauriella albigularis vagy Rhinomyias albigularis
Vauriella goodfellowi vagy Rhinomyias goodfellowi
Előfordulásuk
Borneó és a Fülöp-szigetek területén honosak. Természetes élőhelyei a szubtrópusi vagy trópusi esőerdők, valamint másodlagos erdők. Állandó, nem vonuló fajok.
Megjelenésük
Testhosszuk 15-19 centiméter körüli.
Jegyzetek
Madárnemek | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,392 |
How did they make THIS mistake in "The Match" promo poster?
The organizers of "The Match" may want to allocate some of the $9 million purse to hiring someone to proof their ads.
Take a look at this Western-style poster Tiger Woods tweeted.
Notice anything? Take a closer look at Tiger's TaylorMade M3.
That's right, folks. Or rather, it's wrong. Whoever designed the poster is either a non-golfer or superb prankster, because that's a left-handed driver.
Phil Mickelson was quick to spot it.
What does this have to do with DJ's new putter?
The mistake? Putting it on in the first place never mind PPV. I'm sure I'll have laundry to do that day.
Ben, the poster is not the only thing that needs proofing. It's 'whomever' not 'whoever'.
Tiger has to play with Phil's sticks, thought everybody knew that. Seriously, the whole idea is kind of a joke so just for fun, they should have to play one hole out of each other's bag. I'd tune in for that.
Tiger this Tiger that. If you missed it watch golf channel he's on there 24-7 .thats in case you forgot who he is.
Pay for View? Seriously if all you want to see is 24/7 Tiger, watch the Golf Channel, he is all they show…..
This thing is a farce. I wonder why some comments are not posted. Is someone at WRX offended?
Big deal, I wish they were playing with their own money. Now really don't think much of the match.
Probably a photo from when he played Nike clubs, and somebody (badly)photoshopped in the TM.
You'll see the same goofy mistakes in any area you inspect; eg, people in ads and movies talking into the wrong part of a microphone (and often not plugged in)… You'll find tons of reversed images everywhere in advertising.
Maybe never in competititon. But NEVER?
Dude, he's literally wearing a blue shirt today in the northern trust.. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,145 |
{"url":"https:\/\/blog.splayx.com:10443\/?p=418","text":"# HDU 6039 Gear Up \u5e76\u67e5\u96c6 dfs\u5e8f \u7ebf\u6bb5\u6811\n\nhttp:\/\/acm.hdu.edu.cn\/showproblem.php?pid=6039\n\n# Gear Up\n\nTime Limit: 8000\/4000 MS (Java\/Others)\u00a0\u00a0\u00a0\u00a0Memory Limit: 131072\/131072 K (Java\/Others)\n\n### Problem Description\n\nconstroy has some gears, each with a radius. Two gears are considered adjacent if they meet one of the following conditions:\n1. They share a common edge (i.e. they have equal linear velocity).\n2. They share a common shaft (i.e. they have equal angular velocity).\nIt is guaranteed that no pair of gears meets both of the above conditions.\nA series of continuous adjacent gears constitutes a gear path. There is at most one gear path between each two gears.\nNow constroy assigns an angular velocity to one of these gears and then asks you to determine the largest angular velocity among them.\nsd0061 thinks this problem is too easy, so he replaces some gears and then asks you the question again.\n\n### Input\n\nThere are multiple test cases (about $30$).\nFor each test case:\nThe first line contains three integers $n, m, q$, the number of gears, the number of adjacent pairs and the number of operations. $(0 \\leq m < n \\leq 10^5, 0 \\leq q \\leq 10^5)$\nThe second line contains $n$ integers, of which the $i$-th integer represents $r_i$, the radius of the $i$-th gear. $(r_i \\in \\{2^\\lambda \\mid 0 \\leq \\lambda \\leq 30\\})$\nEach of the next $m$ lines contains three integers $a, x, y$, the $x$-th gear and the $y$-th gear are adjacent in the $a$-th condition. $(a \\in \\{1, 2\\}, 1 \\leq x, y \\leq n, x \\neq y)$\nEach of the next $q$ line contains three integers $a, x, y$, an operation ruled in the following: $(a \\in \\{1, 2\\}, 1 \\leq x \\leq n, y \\in \\{2^\\lambda \\mid 0 \\leq \\lambda \\leq 30\\})$\n$a = 1$ means to replace the $x$-th gear with another one of radius $y$.\n$a = 2$ means to assign angular velocity $y$ to the $x$-th gear and then determine the maximum angular velocity.\n\n### Output\n\nFor each test case, firstly output \"Case #$x$:\" in one line (without quotes), where $x$ indicates the case number starting from $1$, and then for each operation of $a = 2$, output in one line a real number, the natural logarithm of the maximum angular velocity, with the precision of $3$ digits.","date":"2018-10-23 20:05:06","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8772657513618469, \"perplexity\": 942.6641754080849}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-43\/segments\/1539583517376.96\/warc\/CC-MAIN-20181023195531-20181023221031-00164.warc.gz\"}"} | null | null |
Der Heimatverband Eutin war ein in Eutin im Kreis Ostholstein in Schleswig-Holstein ansässiger heimatkundlicher Verein.
Der Verband wurde am 29. Oktober 1966 in Eutin (damals Kreis Eutin) als "Verband zur Pflege und Förderung der Heimatkunde im Kreis Eutin e.V." gegründet. Nach Zusammenlegung der Kreise Eutin und Oldenburg 1970 zum Kreis Ostholstein benannte sich der Verein in Verband zur Pflege und Förderung der Heimatkunde im Eutinischen e.V. um. Er löste sich zum 31. Dezember 2016 auf.
Wirkungskreis
Der Verband konzentrierte sich in seinem Wirken insbesondere auf den südlichen Teil des Kreises Ostholstein und dessen Vorgänger:
Fürstbistum Lübeck
Fürstentum Lübeck
Kreis Eutin
Ur- und Frühgeschichte des Gebietes.
Der Grund für diesen Fokus war die bis 1937 in weiten Teilen Holsteins beziehungsweise Schleswig-Holsteins getrennt verlaufende historische und politische Entwicklung des südlichen Kreisgebietes.
Aufgaben und Tätigkeit
Die Aufgabe des Vereins umfasste die Förderung und Pflege der Heimatkunde für die Einwohner des Kreises Ostholstein – insbesondere im südlichen Teil – u. a. durch Unterstützung bei Schutz und Erhaltung von Denkmälern, Durchführung von Vorträgen, Ausflügen, Unterstützung von Museen sowie der Veröffentlichung von heimatkundlichen Schriften.
Der Verein engagierte sich für die Beschilderung von archäologischer Denkmälern (z. B. Informationstafel an der Katzburg) und Gebäuden, die Instandsetzung von Kulturgütern (z. B. Kruzifix der Kirche St. Laurentius (Süsel), Altar der Kirche St.-Michaelis-Kirche (Eutin)), vergab Zuschüsse für Veröffentlichungen und Projekte und rief zu Spendensammlungen auf.
Mitgliedschaften
Mitglied im Schleswig-Holsteinischen Heimatbund.
Es bestanden seit 2000/2001 wechselseitige Mitgliedschaften mit dem Verein Oldenburgische Landschaft und dem Verein für Heimatkunde im Landkreis Birkenfeld e.V.
Der Heimatverband Eutin war Gesellschafter der Eutiner Festspiele.
Veröffentlichungen
Jahrbücher:
1967–1971: Jahrbuch des Kreises Eutin (4 Bände)
Ab 1972: Jahrbuch für Heimatkunde – Eutin (bis 2015 44 Bände)
Blätter für Heimatkunde – erschienen bis 1998 alle zwei Wochen im Ostholsteiner Anzeiger (aus denen wurde das Jahrbuch zusammengestellt)
Erich Zander: Die Geschichte des Armenwesens in der Stadt Eutin vom Mittelalter bis zum 1. Weltkrieg. Eutin 1982
Frank Petzold: Kriegsende 1945 in Eutin. Eutin 1986
Sechs Urkunden zur Geschichte der Stadt Eutin. 1982 (zusammen mit dem Landesarchiv Schleswig-Holstein)
Bekannte Mitglieder
Max Steen (1898–1997; Gründungsmitglied)
Quellen
Klaus-Dieter Hahn: 40 Jahre Heimatverband Eutin. In: Jahrbuch für Heimatkunde. Eutin 2006, S. 27–38; Online: PDF
Zur Vergabe von Förderungen und Spendenaufrufen:
Otto Rönnpag: 30 Jahre Heimatverband Eutin. In: Jahrbuch für Heimatkunde. Eutin 1996, S. 175–178
Einzelnachweise
Kultur (Eutin)
Organisation (Eutin)
Eutin
Gegründet 1966
Aufgelöst 2016
Ehemaliger Verein (Schleswig-Holstein)
Geschichte (Kreis Ostholstein) | {
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} | 9,226 |
\section{Introduction}
Weak gravitational lensing is one of the most promising cosmological probes in studying the nature of dark matter, dark energy, and gravity \citep{Refregier2003,Mandelbaum2018}. The combination between different probes can be even more powerful, due to more constraining power and breaking the degeneracy between the parameters \citep{Planck2018I,DESY3cosmo}. However, possibly due to residual systematics or new physics beyond the standard $\Lambda$CDM model, the tension between CMB (cosmic microwave background) at redshift $z\sim1100$ and the late-time galaxy surveys at $z<\sim1$ {troubles us when using their synergy} \citep{Hildebrandt2017,HSC_Hamana2019,HSC_Hikage2019,Asgari2021,Heymans2021,DESY3cosmo,DESY3model,DESY3data,Planck2018I}. Many attempts have been made to
examine this tension, in terms of different systematics \citep{Yamamoto2022,Wright2020,Yao2020,Yao2017,Kannawadi2019,Pujol2020,Mead2021,DESY3model,Amon2022,Fong2019}, different statistics \citep{Asgari2021,Joachimi2021,Lin2017b,Harnois-Deraps2021,Shan2018,Sanchez2021,Leauthaud2022,Chang2019}, and possible new physics \citep{Jedamzik2021}. We also refer to recent reviews for the readers' references \citep{Perivolaropoulos2021,Mandelbaum2018}.
To fully understand the physics behind this so-called ``$S_8$'' tension, different cosmological probes are required, as their sensitivities to the systematics are different. Many new observations are also needed, to explore different redshift ranges, sky patches, and even equipment properties. Among the many proposed stage IV galaxy surveys like Dark Energy Spectroscopic Instrument (DESI \cite{DESI2016a,DESI2016b}), Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST, \citealt{LSST2009}), Euclid \citep{Euclid2011}, Roman Space Telescope (or WFIRST, \citealt{WFIRST2015}) and China Space Station Telescope (CSST, \citealt{Gong2019}), DESI is the only one currently operating {and
has measured more than 7.5 million redshifts so far}.
DESI itself will provide tremendous constraining power in studying the expansion history of the Universe as well as the large-scale structure \citep{DESI2016a}. Its cross-correlations with other lensing surveys (referred to as galaxy-galaxy lensing or g-g lensing) will provide not only more, but also independent cosmological information \citep{Prat2021,Joudaki2018,Sanchez2021}, while it can be used to study the galaxy-matter relation \citep{Leauthaud2022,Leauthaud2017}, test gravity \citep{Zhang2007,Jullo2019,Blake2020}, and study the systematics \citep{Yao2020,Yao2017,SC2008,Zhang2010photoz,Giblin2021}. However, stage III surveys like DES (Dark Energy Survey, \citealt{DESY3cosmo}), KiDS (Kilo-Degree Survey, \citealt{Heymans2021}), and HSC (Hyper-Suprime Cam, \citealt{HSC_Hikage2019}) do not offer extremely large overlap with DESI, while the stage IV surveys mentioned previously will require many years of observations before reaching their full overlap with DESI. In short, the sky overlap will limit the cross-correlation studies with DESI in the near future.
In this work, we study the cross-correlations between galaxy shear measured from DECaLS (Dark Energy Camera Legacy Survey) DR8 and galaxies from the DESI $1\%$ (SV3) survey, and compare those with the overlapped data from KiDS and HSC. We measure the g-g lensing signals of the different weak lensing surveys with DESI 1\% survey and estimate their S/N (signal-to-noise ratio) that can be achieved with full DESI in the future. We explore the advantages of DECaLS, and exhibit the measurements of shear-ratio and cosmic magnification as two promising tools in using the great constraining power of DECaLS $\times$ DESI. Additionally, to achieve the expected precision, we propose requirements on the DECaLS data, in terms of the shear calibration and the redshift distribution calibration.
This work is organized as follows. In Section\,\ref{sec theory} we briefly introduce the observables and their theoretical predictions. In Section\,\ref{sec data} we describe the DESI, DECaLS, KiDS, and HSC data we use. In Section\,\ref{sec results} we show the g-g lensing measurements for different DESI density tracers and different lensing surveys, and the measurements of shear-ratio and cosmic magnification. We summarize our findings from DESI$\times$DECaLS for the 1\% survey in Section.\,\ref{sec conclusions}.
\section{Theory} \label{sec theory}
In this section, we briefly review the theory of the g-g lensing observables. We assume spacial curvature $\Omega_k=0$ so that the comoving radial distance equals the comoving angular diameter distance.
\subsection{Galaxy-galaxy lensing}
\label{sec g-g lensing}
Since the foreground gravitational field can distort the shape of the background galaxy, there will be a correlation between the background galaxies' gravitational shear $\gamma^{\rm G}$ and the foreground galaxies' number density $\delta_{\rm g}$. {The correlation of $\left<\delta_{\rm g}\gamma^{\rm G}\right>$ (or $w^{\rm gG}$) will probe the clustering of the underlying matter field $\left<\delta_{\rm m}\delta_{\rm m}\right>$ (or the matter power spectrum $P_{\rm \delta}(k)$), the galaxy bias $b_g(k,z)$, and the redshift-distance relation, which are sensitive to the cosmological model and gravitational theory.} We recall the g-g lensing angular power spectrum \citep{Prat2021}:
\begin{equation}
C^{g\kappa}(\ell)=\int_{0}^{\chi_{\rm max}}\frac{n_{\rm l}(\chi)q_{\rm s}(\chi)}{\chi^2} b_{\rm g}(k,z) P_{\rm \delta}\left(k=\frac{\ell+1/2}{\chi},z\right)d\chi, \label{eq C^gG}
\end{equation}
which is a weighted projection from the 3D {non-linear} matter power spectrum $P_{\rm \delta}(k,z)$ to the 2D galaxy-lensing convergence angular power spectrum $C^{g\kappa}(\ell)$. It will also depend on the galaxy bias $b_{\rm g}=\delta_{\rm g}/\delta_{\rm m}$, the comoving distance $\chi$, the redshift distribution of the lens galaxies $n_{\rm l}(\chi)=n_{\rm l}(z)dz/d\chi$, and the lensing efficiency as a function of the lens position (given the distribution of the source galaxies) $q_{\rm s}(\chi)$, which is written as
\begin{equation}
q_{\rm s}(\chi_{\rm l}) = \frac{3}{2}\Omega_{\rm m}\frac{H_0^2}{c^2}(1+z_{\rm l})
\int_{\chi_{\rm l}}^\infty
n_{\rm s}(\chi_{\rm s})\frac{(\chi_{\rm s}-\chi_{\rm l})\chi_{\rm l}}{\chi_{\rm s}}d\chi_{\rm s}, \label{eq q}
\end{equation}
where $n_{\rm s}(\chi_{
\rm s})$ denotes the distribution of the source galaxies as a function of comoving distance, while $\chi_{\rm s}$ and $\chi_{\rm l}$ denote the comoving distance to the source and the lens, respectively.
The real-space galaxy-shear correlation function can be obtained through the Hankel transformation
\begin{equation}
w^{\rm gG}(\theta) = \frac{1}{2\pi}\int_{0}^{\infty}d\ell \ell C^{g\kappa}(\ell) J_2(\ell\theta) \label{eq w Hankel},
\end{equation}
where $J_2(x)$ is the Bessel function of the first kind with order 2. The ``G'' represents the gravitational lensing shear $\gamma^{\rm G}$, which is conventionally used to separate from the intrinsic alignment $\gamma^{\rm I}$, whose contribution is ignored in this work due to the photo-$z$ separation shown later.
Therefore, by observing the correlation of $w^{\rm gG}$, we can derive the constraints on the cosmological parameters through Eq.\,\eqref{eq C^gG}, $P_{\rm \delta}(k)$ and $\chi(z)$. In order to get the precise cosmology, many systematics need to be considered, for example, the shear calibration error that can shift the measurement of $w^{\rm gG}$, the inaccurate estimation of redshift distribution for the source $n_{\rm s}(\chi_{\rm s}(z_{\rm s}))$ which can bias the theoretical estimation of Eq.\,\eqref{eq C^gG}, the massive neutrino effects and the baryonic effects that can bias the matter power spectrum $P_{\rm \delta}(k,z)$, {and the non-linear galaxy bias $b_g(k,z)$}\footnote{In this work we use the mathematical classification of linear/non-linear bias as a matched filter, however, for more physical modeling, this is normally expressed as 1-halo/2-halo terms and HOD (halo occupation distribution) descriptions such as central/satellite fractions \citep{Leauthaud2017}}. In this work, we mainly focus on the statistical significance for DESI$\times$DECaLS, rather than the systematics. The current statistical error for the $1\%$ survey is expected to be more dominant, but for cautious reasons, we will not give final estimations on the cosmological parameters.
\subsection{Shear-ratio} \label{sec shear-ratio}
The g-g lensing two-point statistics normally contain stronger detection significance at the small-scale than at the large-scale, due to a stronger tidal gravitational field and more galaxy pairs (throughout the whole sky, not around a particular galaxy). However, due to the inaccurate modeling of small-scale effects, such as the non-linear galaxy bias $b_{\rm g}(k,z)$, suppression in the matter power spectrum $P_{\rm \delta}(k)$ due to massive neutrino and baryonic effects, etc., the small-scale information is conventionally abandoned \citep{Heymans2021,DESY3cosmo,Lee2022}. However, by choosing the same lens galaxies with source galaxies at different redshifts, i.e. with the same redshift distribution $n_u(z)$ for the lens while different redshift distribution $n_v(z)$ and $n_w(z)$ for the sources, the ratio between the angular power spectra $C^{g\kappa}_{uv}$ and $C^{g\kappa}_{uw}$ (or the correlation functions $w^{\rm gG}_{uv}$ and $w^{\rm gG}_{uw}$) will mainly base on the two lensing efficiency functions as in Eq.\,\eqref{eq q} for the $v$-th and $w$-th source bins. This ratio does not suffer strongly from the modeling of the galaxy bias $b_{\rm g}$ or the matter power spectrum $P_{\rm \delta}(k)$, as they share the same lens sample according to Eq.\,\eqref{eq C^gG}. {The shear-ratio (or lensing-ratio) has been used to improve cosmological constraints \citep{Sanchez2021}, as it is sensitive to the $\chi(z)$ relation in Eq.\,\eqref{eq q} and the nuisance parameters for the systematics,} or to study the shear bias \citep{Giblin2021}. In this work, we will show the great potential of measuring shear-ratio with DESI$\times$DECaLS.
To account for the full covariance in measuring shear-ratio $R=w_2/w_1$, and to prevent possible singular values when taking the ratio (when $w_1\sim0$), we construct the following data vector \begin{equation}
V=w_1R-w_2, \label{eq constructed vector}
\end{equation}
which is designed to be $0$ when $R$ is correctly predicted from the two data sets $w_1$ and $w_2$ that we want to take the ratio. The resulting covariance for the data vector $V$ is
\begin{equation}
C' = R^2 C_{11} + C_{22} - R(C_{12}+C_{21}), \label{eq constructed cov}
\end{equation}
where $C_{ij}$ is the covariance between $w_i$ and $w_j$. The likelihood of $-2{\rm ln}\mathscr{L}=V^{\rm T}C'^{-1}V$ will give the posterior of the shear-ratio $R$. To account for the covariance is $R$-dependent, normalization is done thereafter {so that its PDF satisfies $\int P(R)dR=1$}. An alternative way is to marginalize over the theoretical predictions $w_i$, similar to \cite{Sun2022,Dong2022}, which we leave for future studies.
\subsection{Cosmic magnification}
\label{sec mag theory}
The observed galaxy number density is affected by its foreground lensing signals, leading to an extra fluctuation besides the intrinsic clustering of galaxies, namely,
\begin{equation}
\delta_{\rm g}^{\rm L} = \delta_{\rm g} + g_{\mu}\kappa, \label{eq magnification}
\end{equation}
where $\delta_{\rm g}^{\rm L}$ denotes the observed lensed galaxy overdensity, $\delta_{\rm g}$ denotes the intrinsic overdensity of galaxies due to gravitational clustering, $\kappa$ is the lensing convergence affecting the flux and the positions of the foreground galaxy sample, and due to the foreground inhomogeneities. For a {complete and} flux-limited sample, the magnification amplitude $g_\mu=2(\alpha-1)$. In that case, the magnification amplitude is sensitive to the galaxy flux function $N(F)$, denoting the number of galaxies brighter than flux limit $F$, with $\alpha=-d{\rm ln}N/d{\rm ln}F$.
According to Eq.\,\eqref{eq magnification}, for a given galaxy sample at $z=z_1$, it not only contains clustering information of $\delta_{\rm g}(z=z_1)$, but also has lensing information of $\kappa$ from the matter at $z<z_1$, which is normally treated as a contamination to the clustering signals \citep{vonWietersheim-Kramsta2021,Deshpande2020,Kitanidis2021}. Meanwhile, attempts have been made to directly measure the cosmic magnification as a source of cosmological information \citep{Liu2021,Gonzalez-Nuevo2020,Yang2017}.
We follow the method of \cite{Liu2021} and correlate the shear galaxies at lower redshift (bin $i$) and the number density galaxies at higher redshift (bin $j$),
\begin{equation}
C^{\kappa\mu}_{ij}(\ell)=g_\mu \int_{0}^{\chi_{\rm max}}\frac{q_i(\chi)q_j(\chi)}{\chi^2} P_{\rm \delta}\left(k=\frac{\ell+1/2}{\chi},z\right)d\chi, \label{eq C^muG}
\end{equation}
which requires the redshift distribution of $n_i(z)$ being significantly separated from $n_j(z)$, so that the intrinsic clustering $\times$ lensing shear signal vanishes. The corresponding correlation function from the Hankel transformation is similar to Eq.\,\eqref{eq w Hankel}.
\subsection{Signal-to-noise definition}
\label{sec S/N}
The S/N definition in this work uses amplitude fitting. For a given measurement $w_{\rm data}$ and an assumed theoretical model $w_{\rm model}$, we fit an amplitude $A$ to the likelihood:
\begin{equation}
-2{\rm ln}\mathscr{L}=\left(w_{\rm data}-Aw_{\rm model}\right){\rm Cov}^{-1}\left(w_{\rm data}-Aw_{\rm model}\right),
\end{equation}
so that a posterior of $A^{+\sigma_A}_{-\sigma_A}$ can be obtained, {where $\sigma_A$ is the Gaussian standard deviation}. Then the corresponding S/N is $A/\sigma_A$.
We note that, if $w_{\rm data}$ is a single value rather than a data vector, this S/N defined by amplitude fitting is identical to the S/N of the data itself, namely $A/\sigma_A=w_{\rm data}/\sigma_{w_{\rm data}}$. This is the case for most of the S/N calculated in this work, when there is one single measurement at small-scale and one at large-scale, and the small-scale and large-scale data correspond to different (nonlinear/linear) galaxy biases so they should be treated separately.
\section{Data} \label{sec data}
In this section, we introduce the DESI spectroscopic data and the shear catalogs from DECaLS/KiDS/HSC. We note even though the DES-Y3 catalog can have an overlap with full DESI for $\sim1264$ deg$^2$, its overlap with DESI SV3 catalog is $0$. We, therefore, do not present any analysis for DES.
\subsection{DESI} \label{sec DESI}
DESI is the only operating Stage IV galaxy survey. It is designed to cover 14,000 deg$^2$ of the sky, with 5,000 fibers collecting spectra simultaneously \citep{DESI2016b,Silber2022,Miller2022}. DESI aims to observe density tracers such as BGS (Bright Galaxy Survey, \citealt{RuizMacias2020}), LRG (luminous red galaxies, \citealt{Zhou2020}), ELG (emission line galaxies, \citealt{Raichoor2020}), and QSO (quasi-stellar objects, \citealt{Yeche2020}), with generally increasing redshift. Other supporting papers on target selections and validations can be find in \cite{AllendePrieto2020,Alexander2022,Lan2022,Cooper2022,Hahn2022,Zhou2022,Chaussidon2022}. DESI plans to use these tracers to study cosmology, especially in BAO (baryonic acoustic oscillations) and RSD (redshift-space distortions) \citep{DESI2016a,Levi2013}. It is located on the 4-meter Mayall telescope in Kitt Peak, Arizona \citep{DESI2022a}. From 2021 till now, DESI has finished its ``SV3'' \citep{DESIsv} and ``DA0.2'' catalogs, which will be included in the coming Early Data Release (EDR, \citealt{DESIdr}). The Siena Galaxy Atlas \citep{DESIsga} is also expected soon.
The DESI experiment is based on the DESI Legacy Imaing Surveys \citep{Zou2017,Dey2019,Schlegel2022}, with multiple supporting pipelines in spectroscopic reduction \citep{Guy2022}, derivation of classifications and redshifts \citep{Bailey2022}, fiber assigement \citep{Raichoor2022}, survey optimization \citep{Schlafly2022}, spectroscopic target selection \citep{Myers2022}
In this work, we use the DESI SV3 catalog, which is also known as the $1\%$ survey (with a sky coverage of $\sim140$ deg$^2$), for the g-g lensing study. We consider the DESI BGS, LRGs, and ELGs, while ignoring the QSOs as the available number is relatively low. {In SV3, each galaxy is assigned a weight to account for the survey completeness and redshift failure.} Since the purpose of this paper is not a precise measurement of cosmology, we assume the linear galaxy biases follow $b_{\rm BGS}(z)D(z)=1.34$, $b_{\rm LRG}(z)D(z)=1.7$, and $b_{\rm ELG}(z)D(z)=0.84$, where $D(z)$ is the linear growth factor normalized to $D(z=0)=1$ \citep{DESI2016a}. The number of galaxies used will be informed later in the paper, as the overlap between the DESI $1\%$ survey and the lensing surveys are different.
\subsection{DECaLS} \label{sec DECaLS}
We use lensing shear measurement from DECaLS DR8, which contains galaxy images in $g-$, $r-$, and $z-$bands \citep{Dey2019}. DECaLS DR8 galaxies are processed by Tractor \citep{Meisner2017,Lang2014} and divided into five types according to their morphologies: PSF, SIMP, DEV, EXP, and COMP \citep{Phriksee2020,Yao2020,Zu2021,Xu2021}. The galaxy ellipticities $e_{1,2}$ are measured ---- except for the PSF type ---- with a joint fit on the $g-$, $r-$, and $z-$bands. A conventional shear calibration \citep{Heymans2012,Miller2013,Hildebrandt2017} is applied as in
\begin{equation} \label{eq shear calib}
\gamma^{\rm obs} = (1+m)\gamma^{\rm true}+c,
\end{equation}
with a multiplicative bias $m$ and additive bias $c$, to account for possible residual bias from PSF modeling, measurement method, blending and crowding \citep{Mandelbaum2015,Martinet2019}. This calibration is obtained by comparing with Canada–France–Hawaii Telescope (CFHT) Stripe 82 observed galaxies and Obiwan simulated galaxies \citep{Phriksee2020,Kong2020}.
Several versions of the photometric redshift for the DECaLS galaxies have been estimated \citep{Zou2019,Zhou2021,Duncan2022}. We apply the most widely used one \citep{Zhou2021}, which uses the $g$, $r$, and $z$ optical bands from DECaLS while borrowing $W1$ and $W2$ infrared bands from WISE (Wide-field Infrared Survey Explorer, \citealt{Wright2010}). The photo-$z$ algorithm is trained based on a decision tree, with training samples constructed from a wide selection of spectroscopic redshift surveys and deep photo-$z$ surveys. We additionally require $z<21$ to select galaxies with better photo-$z$. {We use the photo-z distribution to represent the true-z distribution $n(z)$, while allowing a systematic bias of $\Delta z$ in the form $n(z-\Delta z)$, to pass its effect to Eq.\,\eqref{eq q} then Eq.\,\eqref{eq C^gG}. This is appropriate as weak lensing is mainly biased due to the mean redshift but slightly affected by the redshift scatter.}
Overall, the DR8 shear catalog has $\sim 9,000$ deg$^2$ sky coverage ---- which will be the final overlap with full DESI ---- with an average galaxy number density of $\sim1.9$ gal/arcmin$^2$. The overlapped area with DESI $1\%$ survey is $\sim106$ deg$^2$, which is significantly larger than the other stage III lensing surveys.
We note that the current DECaLS DR8 shear catalog can have some residual multiplicative bias $|m|\sim0.05$ \citep{Yao2020,Phriksee2020}, {possibly due to the selections in observational data while making the comparison \citep{Li2020,Jarvis2016}.} This will prevent us from getting reliable cosmology for measurements with $S/N>\sim20$. Also, there exists a possible bias in the redshift distribution $n(z)$, which will require a galaxy color-based algorithm \citep{Hildebrandt2017,Buchs2019,Wright2020} or a galaxy clustering-based algorithm \citep{Peng2022,Zhang2010photoz,vandenBusch2020} to get the correction. For these two reasons, we choose not to extend this study to the precision cosmology level. A future version of the DECaLS DR9 shear catalog is under development, with improved data reduction and survey procedures\footnote{https://www.legacysurvey.org/dr9/description/}, with more advanced shear calibration {for a pure Obiwan image simulation-based algorithm} (Yao et al. in preparation) and redshift calibration (Xu et al. in preparation).
\subsection{KiDS}
The Kilo-Degree Survey is run by the European Southern Observatory and is designed for weak lensing studies in $ugri$ optical bands. The KiDS data are processed by THELI \citep{Erben2013} and Astro-WISE \citep{deJong2015,Begeman2013}. The galaxy shear measurements are obtained by $lens$fit \citep{Conti2017,Miller2013}, and the photo-$z$s are measured by BPZ \citep{Benitez2000,Benitez2004} using the KiDS $ugri$ optical bands and the $ZYJHK_{\rm s}$ infrared bands from VIKING \citep{Wright2019}. The KiDS shears are calibrated following the same equation as Eq.\,\eqref{eq shear calib} with image simulation \cite{Kannawadi2019}.
We use the KiDS-1000 shear catalog \citep{Giblin2021,Asgari2021} in this work. The overlapped area with DESI SV3 is $\sim55$ deg$^2$. The expected overlapped area between the full DESI footprint and KiDS-1000 is $\sim456$ deg$^2$.
\subsection{HSC}
The Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP, or HSC) is a Japanese lensing survey using the powerful Subaru telescope. It covers five photometric bands $grizy$. Compared with KiDS and DES, HSC has its unique advantage in the galaxy number density and high-z galaxies (but with a smaller footprint). The HSC shears are calibrated similarly to Eq.\,\eqref{eq shear calib} \citep{Mandelbaum2018HSC} but with an additional shear responsivity \citep{HSC_Hamana2019}.
We use the HSC-Y1 shear catalog \citep{HSC_Hikage2019,HSC_Hamana2019}, which overlaps with DESI SV3 for $\sim48$ deg$^2$. The expected overlap between HSC-Y3 data and full DESI is $\sim733$ deg$^2$.
\begin{figure}
\includegraphics[width=\columnwidth]{figure/nz_BGS_ANY.png}
\caption{The galaxy redshift distributions for the DESI BGS with $0<z<0.5$ and photo-$z$ distributions for the lensing surveys with $0.6<z_p<1.5$. The numbers in the labels are the number of galaxies in the overlapped region.}
\label{fig: nz BGS}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{figure/wgG_BGS_ANY.png}
\caption{The galaxy-galaxy lensing angular correlation functions, corresponding to the galaxies samples in Fig.\,\ref{fig: nz BGS}. In the upper panel, the theoretical curves are given by the fiducial cosmology and the assumed galaxy bias model. The \{small-scale, large-scale\} detection significances are \{9.1, 5.8\} for BGS$\times$DECaLS, \{10.2, 3.9\} for BGS$\times$KiDS , and \{16.1, 4.3\} for BGS$\times$HSC. In the lower panel, we show the ratio between our measurements and the corresponding theoretical model, with the latter re-weighted using the number of pairs and lensing weights to account for the band power problem with wide angular bins. The DECaLS and HSC results are slightly shifted horizontally.}
\label{fig: wgG BGS}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{figure/wgG_BGS_DECaLS.png}
\caption{The galaxy-galaxy lensing angular correlation function $w^{\rm gG}$ (upper panel) and its $45\deg$-rotation test $w^{\rm gX}$ (lower panel) for the BGS$\times$DECaLS g-g lensing only, with the same distribution as in Fig.\,\ref{fig: nz BGS} but with more angular bins with 50 jackknife sub-regions. In the upper panel, the theoretical curves are given by the fiducial cosmology and the assumed galaxy bias model. The detection significance for the 5 angular bins are \{6.5, 6.6, 8.4, 4.7, 3.2\}, with the 4 large-scale bins well-agreed with the prediction from fiducial cosmology and the linear bias assumption. {The total S/N using amplitude fitting (as described in Sec.\,\ref{sec S/N}) is $8.9\sigma$ ($A=1.03^{+0.12}_{-0.11}$) for the right three large-scale dots, and is $10.0\sigma$ ($A=1.0^{+0.1}_{-0.1}$) for the right four large-scale dots.} In the lower panel where the shear are rotated for $45\deg$, the results are consistent with 0, with reduced-$\chi^2\sim3/5$.}
\label{fig: wgG BGS DECaLS}
\end{figure}
\section{Results} \label{sec results}
In this section, we show the measurements of different galaxy-shear correlation functions. The estimator for the galaxy-shear correlation is:
\begin{equation} \label{eq gG estimator}
w^{\rm gG }(\theta)=\frac{\sum_{\rm ED}\textsc{w}_{\rm E}\gamma^+_{\rm E}\textsc{w}_{\rm D}}{\sum_{\rm ER}(1+m_{\rm E})\textsc{w}_{\rm E}\textsc{w}_{\rm R}}
-\frac{\sum_{\rm ER}\textsc{w}_{\rm E}\gamma^+_{\rm E}\textsc{w}_{\rm R}}{\sum_{\rm ER}(1+m_{\rm E})\textsc{w}_{\rm E}\textsc{w}_{\rm R}}\ ,
\end{equation}
where $\textsc{w}_{\rm E}$, $m_{\rm E}$ and $\gamma^+_{\rm E}$ denotes the lensing weight (inverse-variance weight for DECaLS \citealt{Phriksee2020} and HSC \citealt{HSC_Hikage2019}, an adjusted version for KiDS \citealt{Miller2013}), the multiplicative bias correction (for HSC there is an extra shear responsivity included), and the tangential shear of the source galaxy, with respect to the given lens galaxy with weight $\textsc{w}_{\rm D}$ or $\textsc{w}_{\rm R}$. The $\Sigma$-summations are calculated for all the ellipticity-density (ED) pairs and the ellipticity-random (ER) pairs. We note Eq.\,\eqref{eq gG estimator} already includes the correction for boost factor \citep{Mandelbaum2005boostfactor,Amon2018}, {and this equation is adequate for the multiplicative bias $m_{\rm E}$ defined either per galaxy or per sample.} The correlation uses DESI official random catalogs to simultaneously correct for the additive bias in the presence of a mask and reduce the shape noise. We will show the measurements with different lens samples and source catalogs using the above estimator.
\subsection{DESI $w^{\rm gG}$}
\label{sec wgG}
We first show the g-g lensing measurements for DESI BGS and the three shear catalogs. The normalized redshift distributions $n(z)$ are shown in Fig.\,\ref{fig: nz BGS}, with the number of galaxies being used in the labels. We use BGS with $0<z<0.5$, and require the photo-$z$ of the source galaxies located at $0.6<z_p<1.5$, so that the overlap in redshift is very small even considering the inaccuracy of photo-$z$. We see that DECaLS has the most available BGS lenses, while HSC has the most available sources and the highest redshift. We notice there are unexpected spikes for the photo-z distribution of KiDS, which is probably due to cosmic variance as the overlapped area is much smaller than the full KiDS data.
\begin{figure}
\includegraphics[width=\columnwidth]{figure/nz_LRG.png}
\caption{The galaxy redshift distributions for the DESI LRGs with $0<z<0.6$ and photo-$z$ distributions for the lensing surveys with $0.7<z_p<1.5$. The numbers in the labels are the number of galaxies in the overlapped region.}
\label{fig: nz LRG}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{figure/wgG_LRG.png}
\caption{The galaxy-galaxy lensing angular correlation functions, corresponding to the galaxies samples in Fig.\,\ref{fig: nz LRG}. In the upper panel, the theoretical curves are given by the fiducial cosmology and the assumed galaxy bias model. The \{small-scale, large-scale\} detection significances are \{3.5, 1.9\} for LRG$\times$DECaLS, \{8.7, 2.2\} for LRG$\times$KiDS, and \{10.6, 2.4\} for LRG$\times$HSC. }
\label{fig: wgG LRG}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{figure/nz_ELG.png}
\caption{The galaxy redshift distributions for the DESI ELGs with $0<z<0.7$ and photo-$z$ distributions for the lensing surveys with $0.8<z_p<1.5$. The numbers in the labels are the number of galaxies in the overlapped region.}
\label{fig: nz ELG}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{figure/wgG_ELG.png}
\caption{The galaxy-galaxy lensing angular correlation functions, corresponding to the galaxies samples in Fig.\,\ref{fig: nz ELG}. The theoretical curves are given by the fiducial cosmology and the assumed galaxy bias model. The \{small-scale, large-scale\} detection significance are \{-0.3, 1.4\} for ELG$\times$DECaLS, \{-1.1, 1.4\} for ELG$\times$KiDS, and \{2.5, 2.6\} for ELG$\times$HSC. The negative values at small-scale represent negative measurements, which might be due to the non-linear galaxy bias, satellite fraction, or shot noise.}
\label{fig: wgG ELG}
\end{figure}
We show the measured correlation functions for the DESI BGS g-g lensing in Fig.\,\ref{fig: wgG BGS}. The correlations are measured in 2 logarithmic bins in $0.5<\theta<80$ arcmin, with the statistical uncertainties calculated using jackknife re-sampling. We find that all three lensing surveys have strong g-g lensing signals, even for the current 1\% DESI data. The measurements are shown in blue dots (DECaLS), orange triangles (KiDS), and green squares (HSC), while the corresponding theoretical comparisons are shown in the blue solid curve, the orange dash-dotted curve, and the green dotted curve. From this figure, we find that the advantage of DECaLS is its large-scale cosmological information, with the highest S/N $\sim5.8$. This is due to DECaLS's significantly large overlap with DESI, reducing the cosmic variance. On the other hand, KiDS and HSC has larger S/N than DECaLS at small-scale, due to their higher source galaxy number density, which lowers the shape noise.
In this work we choose not to estimate the best-fit cosmology, as for DECaLS, there are some unaddressed potential systematics (as discussed in Sec\,\ref{sec DECaLS}), while for KiDS and HSC we do not want to harm the ongoing blinding efforts in the DESI collaboration (although for a larger catalog with the larger overlapped area). The theoretical estimations in Fig.\,\ref{fig: wgG BGS} and all the other similar figures in this work are based on the KiDS-1000 COSEBI $\Lambda$CDM cosmology with maximum posterior of the full multivariate distribution (MAP, \cite{Asgari2021}), which has $h=0.727$, $\Omega_{\rm b} h^2 =0.023$, $\Omega_{\rm c} h^2 =0.105$, $n_{\rm s} =0.949$ and $\sigma_8 =0.772$. We note the choice of other fiducial cosmology \citep{Planck2018I,Asgari2021,DESY3cosmo,HSC_Hamana2019} will give similar results for the current stage with DESI SV3. The linear galaxy biases are assumed following the descriptions of difference density tracers in Sec\,\ref{sec DESI}.
We note that the choice of 2 log-bins is limited by the 20 jackknife sub-regions \citep{Yao2020,Mandelbaum2006}, which is limited by: (1) the requirement of each jackknife sub-region is independent up to the largest scale we use (80 arcmin), and (2) the size of the overlapped region for KiDS and HSC ($\sim50$ deg$^2$). As the DESI survey expands, the available overlapped region will increase accordingly, resulting in increases in both the available number of sub-regions and the maximum angular scale we can measure. {Alternatively, we can use an analytical covariance (similar to Appendix \ref{sec apdx cov} but more tests need to be done) or simulation based covariance for future DESI data.} We also note in this work the inverses of the covariances are corrected \citep{Hartlap2007,Wang2020} due to the limited number of sub-regions.
As a demonstration of more angular binning, we use BGS$\times$DECaLS data to show the choice of 50 jackknife sub-regions and 5 angular bins, as in Fig.\,\ref{fig: wgG BGS DECaLS}. We show that with proper binning, more cosmological information can be extracted. The $\theta>\sim2$ arcmin measurements (the right 4 large-scale dots) agree with the linear bias assumption very well. In the future, with a larger overlapped footprint, more jackknife sub-regions can be used, so that more angular bins can be measured, either to increase the total S/N or to address any scale-dependent systematics.
We do see great potential for DECaLS from the above results, {although measurements will ultimately be limited by systematic errors.}
We show the redshift distribution of the DESI LRGs and the three lensing surveys in Fig.\,\ref{fig: nz LRG}, requiring $z<0.6$ for the spec-$z$ LRGs and $0.7<z_p<1.5$ for the source galaxies. Similar to the BGS, more LRGs can be used when overlapping with DECaLS, while the available DECaLS source galaxies are less than in the other surveys. Since LRGs are generally distributed at higher $z$ than the BGS, we choose to increase the $z$-cut of the LRGs and the $z_p$-cut of the sources, resulting in reduced source galaxies compared with Fig.\,\ref{fig: nz BGS}.
This figure shows the DECaLS source galaxies are more reduced (from 133k to 78k) as it is shallower than the other two.
The correlation measurements for the LRGs are presented in Fig.\,\ref{fig: wgG LRG}. At large-scale, the DECaLS signal is weaker than KiDS and HSC, but it still offers comparable S/N. At the small-scale, the S/N is dominated by deep surveys. The small-scale measurements are significantly higher than the theoretical predictions, due to LRGs being generally more massive than BGS, with stronger non-linear galaxy bias at such separations.
Furthermore, we study the g-g lensing measurements of the DESI ELGs. We show the redshift distribution of the DESI ELGs and the three lensing surveys in Fig.\,\ref{fig: nz ELG}, requiring $z<0.7$ for the spec-$z$ ELGs and $0.8<z_p<1.5$ for the source galaxies. The available number of galaxies is further reduced compared to BGS and LRGs, due to DESI ELGs being mainly distributed at $z>0.7$. And the high-z sources for DECaLS are significantly less than KiDS and HSC.
The correlation measurements of the ELGs are shown in Fig.\,\ref{fig: wgG ELG}. HSC appears to have the largest S/N at both large-scale and small-scale, and the S/N of DECaLS at large-scale is comparable to KiDS.
{All three lensing surveys have small-scale measurements lower than the theoretical predictions, suggesting the low measurement is not a systematics of DECaLS. We suspect this might be due to shape noise, sample variance, or possibly non-linear galaxy bias. As when we go from large-scale to small-scale, the non-linear halo bias for less massive halos (for example the host halos for ELGs, see Fig.\,\ref{fig: wgG ELG}) tends to drop compared with its linear bias, while the non-linear halo bias tends to increase for the more massive halos (for example the host halos for the LRGs, see Fig.\,\ref{fig: wgG LRG}) according to Fig.\,1 of \cite{Fong2021}. The satellite galaxy fraction in the ELGs could also lead to a low amplitude at small-scale \citep{Niemiec2017,Favole2016,Gao2022}. These will require a higher S/N to test in the future. In this work, we only focus on large-scale ELGs measurement.}
\begin{table*}
\centering
\caption{We summarize the S/N of the DESI 1\% survey (SV3) g-g lensing results in Fig.\,\ref{fig: wgG BGS}, \ref{fig: wgG LRG} and \ref{fig: wgG ELG}, and forecast the {ideal} final S/N with full DESI, by rescaling the covariance based on the overlapped area, {and assuming DECaLS data can be well calibrated}. We note that the ELG measurements become negative sometimes, and therefore decide not to predict its final S/N. From this figure, we see that the advantage of DECaLS is at low-z (with BGS) and large-scale. We additionally present the possible bias in the forecasted S/N, namely $\Delta$S/N. It includes the contribution from the statistical error of the current measurement, and residual systematical bias from the data calibration. We use multiplicative bias $|m|\sim0.05$ \citep{Yao2020,Phriksee2020} and redshift bias $|\Delta z|\sim0.02$ \citep{Zhou2021} for DECaLS DR8, $|m|\leq0.015$ and $|\Delta z|\leq0.013$ for KiDS \citep{Asgari2021}, and $|m|\leq0.03$ and $|\Delta z|\leq0.038$ for HSC \citep{HSC_Hikage2019}, to predict their systematical error in the forecasted S/N. We note the statistical contribution of $\Delta$S/N results from rescaling the $1\sigma$ error from Fig.\,\ref{fig: wgG BGS}, \ref{fig: wgG LRG} and \ref{fig: wgG ELG}, and is scale-independent and redshift-independent. The contribution from multiplicative bias $m$ is also scale-independent, while the contribution from redshift bias $\Delta z$ is weakly scale-dependent and redshift-dependent. In the table, we only show the $\Delta$S/N($\Delta z$) values corresponding to the BGS results at the large-scale. }
\label{tab forecast}
\begin{tabular}{ c c c c c | c c c c | c c }
\hline
survey & SV3 overlap & \multicolumn{3}{|c|}{SV3 S/N [small-scale, large-scale]} & full overlap & \multicolumn{3}{|c|}{{ideal} forecast S/N [small-scale, large-scale]} &
\multicolumn{2}{|c|}{forecast {potential bias} $\Delta$S/N} \\
& [deg$^2$] & BGS & LRG & ELG & [deg$^2$] & BGS & LRG & ELG & statistical & systematical \\
\hline
DECaLS & 106 & [9.1, 5.8] & [3.5, 1.9] & [-0.3, 1.4] & $\sim9000$ & [83.8, 53.4] & [32.2, 17.5] & [N/A, 12.9] & $\pm9.2$ & $\pm5\%(m)\pm1.4\%(\Delta z)$ \\
KiDS & 55 & [10.2, 3.9] & [8.7, 2.2] & [-1.1, 1.4] & 456 (DR4) & [29.3, 11.2] & [25.1, 6.3] & [N/A, 4.0] & $\pm2.9$ & $\pm1.5\%(m)\pm0.8\%(\Delta z)$\\
HSC & 48 & [16.1, 4.3] & [10.6, 2.4] & [2.5, 2.6] & 733 (Y3) & [62.9, 16.8] & [41.4, 9.4] & [9.8, 10.2] & $\pm3.9$ & $\pm3\%(m)\pm1.6\%(\Delta z)$\\
\hline
\end{tabular}
\end{table*}
\subsection{Forecasts and Systematics}
We summarize our findings for the g-g lensing measurements from BGS (Fig.\,\ref{fig: wgG BGS}), LRGs (Fig.\,\ref{fig: wgG LRG}), and ELGs (Fig.\,\ref{fig: wgG ELG}) in Table\,\ref{tab forecast}. We see that DECaLS has its unique advantage in extracting cosmological information at large-scale and at lower redshift (when correlating with the DESI BGS). {Neglecting systematic errors for the moment, which will be dominant in practice, we give the forecast of the S/N with the complete DESI survey by re-scaling the covariance according to the overlapped area. This re-scaling assumes the covariance of the g-g lensing signal is dominated by the Gaussian covariance. Since we are extrapolating from small regions with significant boundary effects in our large-scale bin, this is only an approximation.}
We theoretically test the different components of the covariance in Appendix\,\ref{sec apdx cov} for your interest. The large-scale information of future DECaLS$\times$BGS can reach $>50\sigma$, which is stronger than most of the current g-g lensing data,
and will be very promising in studying the current $S_8$ tension \citep{Hildebrandt2017,HSC_Hamana2019,HSC_Hikage2019,Asgari2021,Heymans2021,DESY3cosmo,DESY3model,DESY3data,Planck2018I}.
The contribution from LRGs and ELGs, and possibly QSOs in the future, can also offer independent cosmological information.
\begin{figure}
\includegraphics[width=\columnwidth]{figure/sys_bias.png}
\caption{The impact of the residual shear multiplicative bias $m$ and the bias in the redshift distribution $\Delta z$. For different $m$ and $\Delta z$, we evaluate the resulting $w_{\rm bias}/w_{\rm true}$ at the large-scale of Fig.\,\ref{fig: wgG BGS}, \ref{fig: wgG LRG} and \ref{fig: wgG ELG} ($\theta\sim51$ arcmin) and show the ratio as the color map. The effect of $m$ is totally scale-independent, while the effect of $\Delta z$ is weakly scale-dependent, which can bring an additional $\sim20\%$ difference at maximum. We also show where the bias from $m$ and $\Delta z$ perfectly cancel each other (black solid curve), and the location where the net bias reaches $\pm0.01$ (blue dashed curve) and $\pm0.02$ (orange dotted curve).}
\label{fig: sys bias}
\end{figure}
We note that the S/N predictions in Table\,\ref{tab forecast} ignored the potential bias from systematics, such as residual shear multiplicative bias $m$ and redshift distribution $n(z)$. The existence of the shear multiplicative bias $m$ will change the lensing efficiency from $q_{\rm s}$ to $(1+m)q_{\rm s}$ in Eq.\,\eqref{eq C^gG} and \eqref{eq q}. The bias in redshift distribution $\Delta z$ will change the redshift distribution for the source galaxies from $n_{\rm s}(\chi_{\rm s}(z_{\rm s}))$ to $n_{\rm s}(\chi_{\rm s}(z_{\rm s}-\Delta z))$ in Eq.\,\eqref{eq q}, {so that the whole redshift distribution is shifted towards higher-z direction by $\Delta z$}. For example, if we assume the residual multiplicative bias is $|m|\sim0.05$ (which is found for some DECaLS galaxy sub-samples as in \cite{Phriksee2020,Yao2020}), and enlarge the covariance to account for this potential bias, then the S/N of DECaLS$\times$BGS at large-scale will be reduced from $>50\sigma$ to $\sim20\sigma$. This is a huge loss of cosmological information, although $\sim20\sigma$ is still comparable to the $\sim11\sigma$ of KiDS-DR4 and $\sim 17\sigma$ of HSC-Y3. Therefore, we emphasize the importance of calibrating DECaLS data in a more precise way in the future for reliable cosmological measurements. We note the current measurements with DESI 1\% survey have S/N$\ll20\sigma$, therefore the impacts from such biases are still within the error budget. {The assumed systematics can enlarge the large(small)-scale uncertainties from $\sim17\%(\sim10\%)$ to $\sim18\%(\sim12\%)$.}
We further estimate the requirements on the DECaLS calibrations for precision cosmology. {We evaluate the fractional bias in the measured correlation function $w^{\rm gG}$, considering some residual multiplicative bias $m$ and redshift bias $\Delta z$, and present the results in Fig.\,\ref{fig: sys bias}.} To safely use the $\sim50\sigma$ data from the large-scale of DECaLS$\times$BGS, the residual multiplicative bias alone need to be controlled within $|m|<0.02$, and the mean of the redshift distribution of the source galaxies $\left<z\right>$ need to be controlled within $|\Delta z|<0.03$ on its own. {The net bias considering both $m$ and $\Delta z$ should be controlled in between the orange dotted curves in Fig.\,\ref{fig: sys bias}.} To safely use the cosmological information in both the large-scale and the small-scale, with overall S/N$\sim100\sigma$, we require the calibrations to have $|m|<0.01$ and $|\Delta z|<0.015$ individually, {while the net bias considering both $m$ and $\Delta z$ should be controlled in between the blue dashed curves in Fig.\,\ref{fig: sys bias}.}
We note that using tomography and combining g-g lensing measurements from different density tracers (BGS, LRGs, ELGs, and possibly QSOs in the future) can bring stronger S/N, so the requirements on the calibration terms will be more strict. However, these studies will require a much larger covariance, thus more jackknife sub-regions and much larger overlapped regions, which are beyond the ability of the current data size. We leave this study to future works.
\subsection{Shear-ratio}
\begin{figure}
\includegraphics[width=\columnwidth]{figure/R.png}
\caption{The {MCMC posterior PDF of the} shear-ratio measurements for BGS$\times$DECaLS using Eq.\,\eqref{eq constructed vector} and \eqref{eq constructed cov}. The galaxies are distributed as in Fig.\,\ref{fig: nz BGS}, with source galaxies split into $0.6<z_p<0.9$ and $0.9<z_p<1.5$. The constraint on the shear-ratio uses the two small-scale angular bins ($\theta<\sim5$ arcmin) as in Fig.\,\ref{fig: wgG BGS DECaLS}. The resulting $R=1.21^{+0.42}_{-0.35}$ agrees with the theoretical prediction between $1.13$ and $1.18$. When re-scaling the covariance to the final overlap of DESI$\times$DECaLS, the shear-ratio can be constrained as good as $\sigma_R\sim0.04$ when using the small-scale information, and $\sigma_R\sim0.03$ when using the full-scale.}
\label{fig: R}
\end{figure}
Shear-ratio is a powerful tool to probe cosmology or test systematics \citep{Sanchez2021,Giblin2021}, and it is {insensitive} to many small-scale physics. As shown in Table\,\ref{tab forecast}, DECaLS$\times$DESI, especially for the BGS and LRGs, can offer very high S/N measurements at the small-scale. We take the BGS from the DESI 1\% survey as an example to study this topic.
The galaxy samples are distributed similarly to the BGS$\times$DECaLS $n(z)$ as in Fig.\,\ref{fig: nz BGS}, but in addition, the source galaxies are further split into two groups: $0.6<z_p<0.9$, and $0.9<z_p<1.5$. We calculated the corresponding correlations $w^{\rm gG}_1$ and $w^{\rm gG}_2$, and their ratio with $R=w^{\rm gG}_2 / w^{\rm gG}_1$, {following Eq.\,\eqref{eq constructed vector}, \eqref{eq constructed cov} and the description in Sec.\,\ref{sec shear-ratio}.}
The shear-ratio results are shown in Fig.\,\ref{fig: R}. Following the same angular binning as in Fig.\,\ref{fig: wgG BGS DECaLS} for the correlation calculations, we use the two small-scale angular bins with $\theta<\sim5$ arcmin, since the three large-scale bins are expected in the {direct 2-point cosmology} study, as described in Sec.\,\ref{sec wgG}. The current small-scale information can constrain shear-ratio at $R=1.21^{+0.42}_{-0.35}$, which is consistent with our theoretical prediction (using $R=w^{\rm gG}_2 / w^{\rm gG}_1$, Eq.\,\eqref{eq C^gG} and \eqref{eq w Hankel}) between $1.13$ and $1.18$. This small angular variation is due to the angular dependence in $P(k=\frac{\ell+1/2}{\chi},z)$ in Eq.\,\eqref{eq C^gG}, which is not fully canceled when taking the ratio using correlation functions. We note this weak angular dependence is small and can be easily taken into account in the theoretical predictions.
To predict the constraining power when full DESI finishes, we rescaled the covariance based on the overlapped area as in Table\,\ref{tab forecast}, and find the shear-ratio can be constrained at $\sigma_R=0.04$ with the small-scale information, which is not used in getting the $S_8$ constraint. Considering full information for the shear-ratio study, we can obtain $\sigma_R=0.03$. These statistical errors are comparable with the shear-ratio studies in \citep{Sanchez2021} with DES-Y3 data, {showing a promising future in using shear-ratio to improve cosmological constraint
and/or to further constrain the systematics \citep{Giblin2021}. }
\subsection{Cosmic magnification}
\label{sec mag}
We discussed that the ELG$\times$DECaLS results have low S/N in Fig.\,\ref{fig: nz ELG}, \ref{fig: wgG ELG} and Table\,\ref{tab forecast}, as the ELGs are mainly distributed at large-$z$, while the advantage of DECaLS is at low-$z$. On the other hand, this opens a window to the study of cosmic magnification by putting the ELGs at high-z and using shear from low-z DECaLS galaxies. We follow the methodology in \cite{Liu2021} and use galaxy samples distributed as in Fig.\,\ref{fig: nz ELG mag}. The DECaLS galaxies are located at a much lower photo-$z$ compared with the ELGs, as in the targeted shear-magnification correlation, the shear-density correlation exists as a source of systematics when even a small fraction of shear galaxies appear at higher-$z$ than the ELGs.
The measurements are shown in Fig.\,\ref{fig: wgG ELG mag}. We find positive signals at the small-scale, and {null detections} at the large-scale, for all DECaLS, KiDS, and HSC. We tested the 45-deg rotation of the shear, resulting in consistency with 0 on all scales for all the source samples. Considering the similar calculation with eBOSS ELGs \footnote{\url{https://www.sdss.org/surveys/eboss/}} and DECaLS sources as a reference, we found the measurements are consistent with 0 on all scales, see Appendix\,\ref{sec apdx eBOSS} for details. In the measurements of Fig.\,\ref{fig: wgG ELG mag}, the {null detections} at the large-scale could be due to cosmic variance or some negative systematics such as intrinsic alignment. The positive measurements at the small-scale could be due to the targeted magnification signals, the cosmic variance, or photo-$z$ errors. We note to separate these different signals, either a stronger signal with clear angular dependencies or additional observables are needed to break the degeneracy.
As a further step, we present an effective amplitude fitting of $g_{\mu,{\rm eff}}$ for the magnification signals, following Eq.\,\eqref{eq C^muG}, in Table\,\ref{tab mag}. We find $\sim1\sigma$ {measurement} for KiDS and $\sim2\sigma$ {measurement} for DECaLS and HSC. Considering the ELG samples are quite similar as shown in Fig.\,\ref{fig: nz ELG mag}, and the three best-fit $g_{\mu,{\rm eff}}$-amplitudes are consistent, we evaluated the combined best-fit, achieving $\sim3\sigma$ significance. The covariance between different surveys is ignored for the combined estimation, as shot noise is more dominant in this case than the cosmic variance. Additionally, we find that by including shear galaxies from $0<z_p<0.4$, the significance of magnification detection drops, due to the low-z data having much weaker lensing efficiency as in Eq.\,\eqref{eq q}, and is mainly contributing noise.
The fitting goodness of the reduced-$\chi^2$ (defined by the $\chi^2$ between the best-fit and the data, divided by the degree of freedom) is generally close to $\sim1$ for each case. This shows no significant deviation between the model and the data. The detected $\sim3\sigma$ positive signal can be either due to the cosmic magnification, or very similar stochastic photo-z outliers between the three lensing surveys. As DECaLS, KiDS and HSC have totally different photometric bands, photo-z algorithms, and training samples, we think the detected signals are less likely due to the similar photo-z outliers,
and more likely to be the cosmic magnification signal. Therefore, by assuming the combined best-fit of $g_{\mu,{\rm eff}}\sim6.1$ as the true value
and rescaling the covariance similar to Table\,\ref{tab forecast}, we expect $\sim10\sigma$ detection for DECaLS DR9,
which is very promising for a stage III lensing survey. By then, with a better understanding of the systematics such as IA and photo-$z$ outlier, these cross-correlations can bring very promising constraining power in studying cosmic magnification. {We can choose to: (1) cut a complete and flux-limited sample and compare it with the flux function; (2) try to use the given DESI completeness and flux function to find a relation of $g_{\mu,{\rm eff}}(\alpha)$ rather than $g_\mu=2(\alpha-1)$; (3) compare with realistic mocks to infer $g_{\mu,{\rm eff}}$; (4) add an artificial lensing signal $\kappa$ to real data and infer $g_{\mu,{\rm eff}}$ as a response $\partial\delta^{\rm L}_{\rm g}/\partial\kappa$, similar to MetaCalibration \citep{Sheldon2017,Huff2017}.}
\begin{figure}
\includegraphics[width=\columnwidth]{figure/nz_ELG_mag.png}
\caption{The redshift distribution for high-z ELGs ($1<z<1.6$) and low-z source galaxies ($0.4<z_p<0.7$) for magnification study. The choice of such a large redshift gap is to prevent potential leakage due to photo-$z$ inaccuracy. The numbers in the labels are the number of galaxies in the overlapped region.}
\label{fig: nz ELG mag}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{figure/wgG_ELG_mag.png}
\caption{The magnification(ELGs)-shear correlation measurements, corresponding to the galaxy samples in Fig.\,\ref{fig: nz ELG mag}. The theoretical curves are based on Eq.\,\eqref{eq magnification}, assuming $g_{\mu,{\rm eff}}=1$ as a reference. The \{small-scale, large-scale\} detection significance for ELG$\times$DECaLS are \{2.2, 0.3\}, for ELG$\times$KiDS are \{1.2, -0.3\}, and for ELG$\times$HSC are \{2.8, -0.3\}. The negative values at the large-scale represent negative measurements, which might be due to shot noise, sample variance, or impact from systematics with negative values, like intrinsic alignment if there exists some photo-z outlier.}
\label{fig: wgG ELG mag}
\end{figure}
\begin{table}
\centering
\caption{This table shows the best-fit amplitude $g_{\mu,{\rm eff}}$ for the cosmic magnification. The upper part corresponds to the results in Fig.\,\ref{fig: wgG ELG mag} for DECaLS, KiDS, HSC, and the combination of them (the ``all'' case). We find with the DESI 1\% survey, we can already detect cosmic magnification at $\sim3.1\sigma$ for the shear galaxies distributed at $0.4<z_p<0.7$, while the $z_p<0.4$ galaxies are mainly contributing noise as it corresponding lensing efficiency (Eq.\,\eqref{eq q}) is low. The degree of freedom is calculated as $dof=N_{\rm data}-N_{\rm para}$. We see no significant deviation between data and model as $\chi^2/dof\sim1$.
}
\label{tab mag}
\begin{tabular}{cccc}
\hline
Case & $g_{\mu,{\rm eff}}$ & S/N & $\chi^2/dof$ \\
\hline
DECaLS $0.4<z_p<0.7$ & $10.6^{+5.2}_{-5.8}
$ & $1.8\sigma$ & 0.6/1 \\
KiDS $0.4<z_p<0.7$ & $4.2^{+6.0}_{-5.7}
$ & $0.7\sigma$ & 1.3/1 \\
HSC $0.4<z_p<0.7$ & $5.6^{+2.3}_{-2.3}$ & $2.4\sigma$ & 1.1/1 \\
all $0.4<z_p<0.7$ & $6.1^{+1.9}_{-2.0}
$ & $3.1\sigma$ & 3.9/5 \\
all $0<z_p<0.7$ & $5.3^{+2.0}_{-2.0}
$ & $2.7\sigma$ & 12.5/11 \\
\hline
\end{tabular}
\end{table}
\section{Conclusions}
\label{sec conclusions}
In this work, we study the cross-correlations between DESI 1\% survey galaxies and shear measured from DECaLS, one of the imaging surveys for DESI target selection. For the 1\% DESI data, DECaLS can have comparable performances compared with the main stage-III lensing surveys KiDS and HSC. More specifically, we measure the cross-correlations of DESI BGS/LRGs/ELGs $\times$ different shear catalog, shown in Fig.\,\ref{fig: wgG BGS}, \ref{fig: wgG LRG} and \ref{fig: wgG ELG}. We forecast the level of significance with full DESI data in Table\,\ref{tab forecast}. {Assuming systematic errors can be cleaned with high precision in the future,} we find the large-scale S/N could reach $>50 \sigma $ for DECaLS$\times$BGS, $>15\sigma$ for DECaLS$\times$LRG, and $>10\sigma$ for DECaLS$\times$ELG, which are very promising before the stage IV surveys come out.
We point out that the main difficulty in obtaining DECaLS cosmology is the calibrations for the systematics. In order to safely use the large-scale $\sim50\sigma$ information of BGS$\times$DECaLS, we need to achieve the minimum requirements on: (1) the multiplicative bias of $|m|<0.02$ and (2) the mean of redshift distribution $|\Delta z|<0.03$. To safely use the full-scale $\sim100\sigma$ data, we required $|m|<0.01$ and $|\Delta z|<0.015$ for future calibrations. The requirement could be even higher when combining different observables, but it will require a larger footprint than the 1\% survey for the study. These requirements are essential guides for future calibrations and studies on cosmology.
To fully use the advantage of DECaLS, we further explored two promising observables, the shear-ratio, and the cosmic magnification. We show the current 1\% BGS data can constrain shear-ratio with $\sigma_R\sim0.4$, while the full DESI BGS can give $\sigma_R\sim0.04$ using only the small-scale information, as shown in Fig.\,\ref{fig: R}. Furthermore, weak detections of potential cosmic magnification are shown in Fig.\,\ref{fig: wgG ELG mag} and Table\,\ref{tab mag}. We discussed how the possible systematics can affect this signal in Sec.\,\ref{sec mag}. We also expect DECaLS to have a strong contribution ($\sim10\sigma$ detection) to future magnification studies, if the observed signals in this work are not due to fluctuations.
To summarize, DECaLS lensing is a very promising tool that can enrich the cosmological output of DESI. It will bring new cosmological information with its huge footprint. It has great advantages in the large-scale and the low-$z$ information, {after carefully addressing the systematics}. It will offer strong S/N for shear-ratio study, and good potential in measuring cosmic magnification. Careful calibrations of the shear and redshift distribution can result in very promising outcomes.
\section*{Acknowledgements}
We thank Xiangkun Liu, Weiwei Xu, and Jun Zhang for their helpful discussions. We thank Chris Blake, Daniel Gruen, and Benjamin Joachimi for their contribution during the DESI collaboration-wide review.
HYS acknowledges the support from NSFC of China under grant 11973070, the Shanghai Committee of Science and Technology grant No.19ZR1466600 and Key Research Program of Frontier Sciences, CAS, Grant No. ZDBS-LY-7013. PZ acknowledges the support of NSFC No. 11621303, the National Key R\&D Program of China 2020YFC22016. JY acknowledges the support from NSFC Grant No.12203084, the China Postdoctoral Science Foundation Grant No. 2021T140451, and the Shanghai Post-doctoral Excellence Program Grant No. 2021419.
We acknowledge the support from the science research grants from the China Manned Space Project with NO. CMS-CSST-2021-A01, CMS-CSST-2021-A02 and NO. CMS-CSST-2021-B01.
We acknowledge the usage of the following packages pyccl\footnote{\url{https://github.com/LSSTDESC/CCL}, \citep{Chisari2019CCL}},
treecorr\footnote{\url{https://github.com/rmjarvis/TreeCorr}, \citep{Jarvis2004}},
healpy\footnote{\url{https://github.com/healpy/healpy}, \citep{Healpy_Gorski2005,Healpy_Zonca2019}},
matplotlib\footnote{\url{https://github.com/matplotlib/matplotlib}, \citep{Hunter2007}},
emcee\footnote{\url{https://github.com/dfm/emcee}, \citep{emcee}},
corner\footnote{\url{https://github.com/dfm/corner.py}, \citep{corner}},
astropy\footnote{\url{https://github.com/astropy/astropy}, \citep{astropy}},
pandas\footnote{\url{https://github.com/pandas-dev/pandas}},
scipy\footnote{\url{https://github.com/scipy/scipy}, \citep{scipy}},
dsigma\footnote{\url{https://github.com/johannesulf/dsigma}}
for their accurate and fast performance and all their contributed authors.
This research is supported by the Director, Office of Science, Office of High Energy Physics of the U.S. Department of Energy under Contract No. DE–AC02–05CH11231, and by the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility under the same contract; additional support for DESI is provided by the U.S. National Science Foundation, Division of Astronomical Sciences under Contract No. AST-0950945 to the NSF's National Optical-Infrared Astronomy Research Laboratory; the Science and Technologies Facilities Council of the United Kingdom; the Gordon and Betty Moore Foundation; the Heising-Simons Foundation; the French Alternative Energies and Atomic Energy Commission (CEA); the National Council of Science and Technology of Mexico (CONACYT); the Ministry of Science and Innovation of Spain (MICINN), and by the DESI Member Institutions: \url{https://www.desi.lbl.gov/collaborating-institutions}.
The DESI Legacy Imaging Surveys consist of three individual and complementary projects: the Dark Energy Camera Legacy Survey (DECaLS), the Beijing-Arizona Sky Survey (BASS), and the Mayall z-band Legacy Survey (MzLS). DECaLS, BASS and MzLS together include data obtained, respectively, at the Blanco telescope, Cerro Tololo Inter-American Observatory, NSF's NOIRLab; the Bok telescope, Steward Observatory, University of Arizona; and the Mayall telescope, Kitt Peak National Observatory, NOIRLab. NOIRLab is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. Pipeline processing and analyses of the data were supported by NOIRLab and the Lawrence Berkeley National Laboratory. Legacy Surveys also uses data products from the Near-Earth Object Wide-field Infrared Survey Explorer (NEOWISE), a project of the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration. Legacy Surveys was supported by: the Director, Office of Science, Office of High Energy Physics of the U.S. Department of Energy; the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility; the U.S. National Science Foundation, Division of Astronomical Sciences; the National Astronomical Observatories of China, the Chinese Academy of Sciences and the Chinese National Natural Science Foundation. LBNL is managed by the Regents of the University of California under contract to the U.S. Department of Energy. The complete acknowledgments can be found at \url{https://www.legacysurvey.org/}.
The authors are honored to be permitted to conduct scientific research on Iolkam Du'ag (Kitt Peak), a mountain with particular significance to the Tohono O'odham Nation.
\section*{Data Availability}
The data used to produce the figures in this work are available through \url{https://doi.org/10.5281/zenodo.7322710} following DESI Data Management Plan.
The inclusion of a Data Availability Statement is a requirement for articles published in MNRAS. Data Availability Statements provide a standardized format for readers to understand the availability of data underlying the research results described in the article. The statement may refer to original data generated in the course of the study or to third-party data analyzed in the article. The statement should describe and provide means of access, where possible, by linking to the data or providing the required accession numbers for the relevant databases or DOIs.
\bibliographystyle{mnras}
\section{Introduction}
Weak gravitational lensing is one of the most promising cosmological probes in studying the nature of dark matter, dark energy, and gravity \citep{Refregier2003,Mandelbaum2018}. The combination between different probes can be even more powerful, due to more constraining power and breaking the degeneracy between the parameters \citep{Planck2018I,DESY3cosmo}. However, possibly due to residual systematics or new physics beyond the standard $\Lambda$CDM model, the tension between CMB (cosmic microwave background) at redshift $z\sim1100$ and the late-time galaxy surveys at $z<\sim1$ {troubles us when using their synergy} \citep{Hildebrandt2017,HSC_Hamana2019,HSC_Hikage2019,Asgari2021,Heymans2021,DESY3cosmo,DESY3model,DESY3data,Planck2018I}. Many attempts have been made to
examine this tension, in terms of different systematics \citep{Yamamoto2022,Wright2020,Yao2020,Yao2017,Kannawadi2019,Pujol2020,Mead2021,DESY3model,Amon2022,Fong2019}, different statistics \citep{Asgari2021,Joachimi2021,Lin2017b,Harnois-Deraps2021,Shan2018,Sanchez2021,Leauthaud2022,Chang2019}, and possible new physics \citep{Jedamzik2021}. We also refer to recent reviews for the readers' references \citep{Perivolaropoulos2021,Mandelbaum2018}.
To fully understand the physics behind this so-called ``$S_8$'' tension, different cosmological probes are required, as their sensitivities to the systematics are different. Many new observations are also needed, to explore different redshift ranges, sky patches, and even equipment properties. Among the many proposed stage IV galaxy surveys like Dark Energy Spectroscopic Instrument (DESI \cite{DESI2016a,DESI2016b}), Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST, \citealt{LSST2009}), Euclid \citep{Euclid2011}, Roman Space Telescope (or WFIRST, \citealt{WFIRST2015}) and China Space Station Telescope (CSST, \citealt{Gong2019}), DESI is the only one currently operating {and
has measured more than 7.5 million redshifts so far}.
DESI itself will provide tremendous constraining power in studying the expansion history of the Universe as well as the large-scale structure \citep{DESI2016a}. Its cross-correlations with other lensing surveys (referred to as galaxy-galaxy lensing or g-g lensing) will provide not only more, but also independent cosmological information \citep{Prat2021,Joudaki2018,Sanchez2021}, while it can be used to study the galaxy-matter relation \citep{Leauthaud2022,Leauthaud2017}, test gravity \citep{Zhang2007,Jullo2019,Blake2020}, and study the systematics \citep{Yao2020,Yao2017,SC2008,Zhang2010photoz,Giblin2021}. However, stage III surveys like DES (Dark Energy Survey, \citealt{DESY3cosmo}), KiDS (Kilo-Degree Survey, \citealt{Heymans2021}), and HSC (Hyper-Suprime Cam, \citealt{HSC_Hikage2019}) do not offer extremely large overlap with DESI, while the stage IV surveys mentioned previously will require many years of observations before reaching their full overlap with DESI. In short, the sky overlap will limit the cross-correlation studies with DESI in the near future.
In this work, we study the cross-correlations between galaxy shear measured from DECaLS (Dark Energy Camera Legacy Survey) DR8 and galaxies from the DESI $1\%$ (SV3) survey, and compare those with the overlapped data from KiDS and HSC. We measure the g-g lensing signals of the different weak lensing surveys with DESI 1\% survey and estimate their S/N (signal-to-noise ratio) that can be achieved with full DESI in the future. We explore the advantages of DECaLS, and exhibit the measurements of shear-ratio and cosmic magnification as two promising tools in using the great constraining power of DECaLS $\times$ DESI. Additionally, to achieve the expected precision, we propose requirements on the DECaLS data, in terms of the shear calibration and the redshift distribution calibration.
This work is organized as follows. In Section\,\ref{sec theory} we briefly introduce the observables and their theoretical predictions. In Section\,\ref{sec data} we describe the DESI, DECaLS, KiDS, and HSC data we use. In Section\,\ref{sec results} we show the g-g lensing measurements for different DESI density tracers and different lensing surveys, and the measurements of shear-ratio and cosmic magnification. We summarize our findings from DESI$\times$DECaLS for the 1\% survey in Section.\,\ref{sec conclusions}.
\section{Theory} \label{sec theory}
In this section, we briefly review the theory of the g-g lensing observables. We assume spacial curvature $\Omega_k=0$ so that the comoving radial distance equals the comoving angular diameter distance.
\subsection{Galaxy-galaxy lensing}
\label{sec g-g lensing}
Since the foreground gravitational field can distort the shape of the background galaxy, there will be a correlation between the background galaxies' gravitational shear $\gamma^{\rm G}$ and the foreground galaxies' number density $\delta_{\rm g}$. {The correlation of $\left<\delta_{\rm g}\gamma^{\rm G}\right>$ (or $w^{\rm gG}$) will probe the clustering of the underlying matter field $\left<\delta_{\rm m}\delta_{\rm m}\right>$ (or the matter power spectrum $P_{\rm \delta}(k)$), the galaxy bias $b_g(k,z)$, and the redshift-distance relation, which are sensitive to the cosmological model and gravitational theory.} We recall the g-g lensing angular power spectrum \citep{Prat2021}:
\begin{equation}
C^{g\kappa}(\ell)=\int_{0}^{\chi_{\rm max}}\frac{n_{\rm l}(\chi)q_{\rm s}(\chi)}{\chi^2} b_{\rm g}(k,z) P_{\rm \delta}\left(k=\frac{\ell+1/2}{\chi},z\right)d\chi, \label{eq C^gG}
\end{equation}
which is a weighted projection from the 3D {non-linear} matter power spectrum $P_{\rm \delta}(k,z)$ to the 2D galaxy-lensing convergence angular power spectrum $C^{g\kappa}(\ell)$. It will also depend on the galaxy bias $b_{\rm g}=\delta_{\rm g}/\delta_{\rm m}$, the comoving distance $\chi$, the redshift distribution of the lens galaxies $n_{\rm l}(\chi)=n_{\rm l}(z)dz/d\chi$, and the lensing efficiency as a function of the lens position (given the distribution of the source galaxies) $q_{\rm s}(\chi)$, which is written as
\begin{equation}
q_{\rm s}(\chi_{\rm l}) = \frac{3}{2}\Omega_{\rm m}\frac{H_0^2}{c^2}(1+z_{\rm l})
\int_{\chi_{\rm l}}^\infty
n_{\rm s}(\chi_{\rm s})\frac{(\chi_{\rm s}-\chi_{\rm l})\chi_{\rm l}}{\chi_{\rm s}}d\chi_{\rm s}, \label{eq q}
\end{equation}
where $n_{\rm s}(\chi_{
\rm s})$ denotes the distribution of the source galaxies as a function of comoving distance, while $\chi_{\rm s}$ and $\chi_{\rm l}$ denote the comoving distance to the source and the lens, respectively.
The real-space galaxy-shear correlation function can be obtained through the Hankel transformation
\begin{equation}
w^{\rm gG}(\theta) = \frac{1}{2\pi}\int_{0}^{\infty}d\ell \ell C^{g\kappa}(\ell) J_2(\ell\theta) \label{eq w Hankel},
\end{equation}
where $J_2(x)$ is the Bessel function of the first kind with order 2. The ``G'' represents the gravitational lensing shear $\gamma^{\rm G}$, which is conventionally used to separate from the intrinsic alignment $\gamma^{\rm I}$, whose contribution is ignored in this work due to the photo-$z$ separation shown later.
Therefore, by observing the correlation of $w^{\rm gG}$, we can derive the constraints on the cosmological parameters through Eq.\,\eqref{eq C^gG}, $P_{\rm \delta}(k)$ and $\chi(z)$. In order to get the precise cosmology, many systematics need to be considered, for example, the shear calibration error that can shift the measurement of $w^{\rm gG}$, the inaccurate estimation of redshift distribution for the source $n_{\rm s}(\chi_{\rm s}(z_{\rm s}))$ which can bias the theoretical estimation of Eq.\,\eqref{eq C^gG}, the massive neutrino effects and the baryonic effects that can bias the matter power spectrum $P_{\rm \delta}(k,z)$, {and the non-linear galaxy bias $b_g(k,z)$}\footnote{In this work we use the mathematical classification of linear/non-linear bias as a matched filter, however, for more physical modeling, this is normally expressed as 1-halo/2-halo terms and HOD (halo occupation distribution) descriptions such as central/satellite fractions \citep{Leauthaud2017}}. In this work, we mainly focus on the statistical significance for DESI$\times$DECaLS, rather than the systematics. The current statistical error for the $1\%$ survey is expected to be more dominant, but for cautious reasons, we will not give final estimations on the cosmological parameters.
\subsection{Shear-ratio} \label{sec shear-ratio}
The g-g lensing two-point statistics normally contain stronger detection significance at the small-scale than at the large-scale, due to a stronger tidal gravitational field and more galaxy pairs (throughout the whole sky, not around a particular galaxy). However, due to the inaccurate modeling of small-scale effects, such as the non-linear galaxy bias $b_{\rm g}(k,z)$, suppression in the matter power spectrum $P_{\rm \delta}(k)$ due to massive neutrino and baryonic effects, etc., the small-scale information is conventionally abandoned \citep{Heymans2021,DESY3cosmo,Lee2022}. However, by choosing the same lens galaxies with source galaxies at different redshifts, i.e. with the same redshift distribution $n_u(z)$ for the lens while different redshift distribution $n_v(z)$ and $n_w(z)$ for the sources, the ratio between the angular power spectra $C^{g\kappa}_{uv}$ and $C^{g\kappa}_{uw}$ (or the correlation functions $w^{\rm gG}_{uv}$ and $w^{\rm gG}_{uw}$) will mainly base on the two lensing efficiency functions as in Eq.\,\eqref{eq q} for the $v$-th and $w$-th source bins. This ratio does not suffer strongly from the modeling of the galaxy bias $b_{\rm g}$ or the matter power spectrum $P_{\rm \delta}(k)$, as they share the same lens sample according to Eq.\,\eqref{eq C^gG}. {The shear-ratio (or lensing-ratio) has been used to improve cosmological constraints \citep{Sanchez2021}, as it is sensitive to the $\chi(z)$ relation in Eq.\,\eqref{eq q} and the nuisance parameters for the systematics,} or to study the shear bias \citep{Giblin2021}. In this work, we will show the great potential of measuring shear-ratio with DESI$\times$DECaLS.
To account for the full covariance in measuring shear-ratio $R=w_2/w_1$, and to prevent possible singular values when taking the ratio (when $w_1\sim0$), we construct the following data vector \begin{equation}
V=w_1R-w_2, \label{eq constructed vector}
\end{equation}
which is designed to be $0$ when $R$ is correctly predicted from the two data sets $w_1$ and $w_2$ that we want to take the ratio. The resulting covariance for the data vector $V$ is
\begin{equation}
C' = R^2 C_{11} + C_{22} - R(C_{12}+C_{21}), \label{eq constructed cov}
\end{equation}
where $C_{ij}$ is the covariance between $w_i$ and $w_j$. The likelihood of $-2{\rm ln}\mathscr{L}=V^{\rm T}C'^{-1}V$ will give the posterior of the shear-ratio $R$. To account for the covariance is $R$-dependent, normalization is done thereafter {so that its PDF satisfies $\int P(R)dR=1$}. An alternative way is to marginalize over the theoretical predictions $w_i$, similar to \cite{Sun2022,Dong2022}, which we leave for future studies.
\subsection{Cosmic magnification}
\label{sec mag theory}
The observed galaxy number density is affected by its foreground lensing signals, leading to an extra fluctuation besides the intrinsic clustering of galaxies, namely,
\begin{equation}
\delta_{\rm g}^{\rm L} = \delta_{\rm g} + g_{\mu}\kappa, \label{eq magnification}
\end{equation}
where $\delta_{\rm g}^{\rm L}$ denotes the observed lensed galaxy overdensity, $\delta_{\rm g}$ denotes the intrinsic overdensity of galaxies due to gravitational clustering, $\kappa$ is the lensing convergence affecting the flux and the positions of the foreground galaxy sample, and due to the foreground inhomogeneities. For a {complete and} flux-limited sample, the magnification amplitude $g_\mu=2(\alpha-1)$. In that case, the magnification amplitude is sensitive to the galaxy flux function $N(F)$, denoting the number of galaxies brighter than flux limit $F$, with $\alpha=-d{\rm ln}N/d{\rm ln}F$.
According to Eq.\,\eqref{eq magnification}, for a given galaxy sample at $z=z_1$, it not only contains clustering information of $\delta_{\rm g}(z=z_1)$, but also has lensing information of $\kappa$ from the matter at $z<z_1$, which is normally treated as a contamination to the clustering signals \citep{vonWietersheim-Kramsta2021,Deshpande2020,Kitanidis2021}. Meanwhile, attempts have been made to directly measure the cosmic magnification as a source of cosmological information \citep{Liu2021,Gonzalez-Nuevo2020,Yang2017}.
We follow the method of \cite{Liu2021} and correlate the shear galaxies at lower redshift (bin $i$) and the number density galaxies at higher redshift (bin $j$),
\begin{equation}
C^{\kappa\mu}_{ij}(\ell)=g_\mu \int_{0}^{\chi_{\rm max}}\frac{q_i(\chi)q_j(\chi)}{\chi^2} P_{\rm \delta}\left(k=\frac{\ell+1/2}{\chi},z\right)d\chi, \label{eq C^muG}
\end{equation}
which requires the redshift distribution of $n_i(z)$ being significantly separated from $n_j(z)$, so that the intrinsic clustering $\times$ lensing shear signal vanishes. The corresponding correlation function from the Hankel transformation is similar to Eq.\,\eqref{eq w Hankel}.
\subsection{Signal-to-noise definition}
\label{sec S/N}
The S/N definition in this work uses amplitude fitting. For a given measurement $w_{\rm data}$ and an assumed theoretical model $w_{\rm model}$, we fit an amplitude $A$ to the likelihood:
\begin{equation}
-2{\rm ln}\mathscr{L}=\left(w_{\rm data}-Aw_{\rm model}\right){\rm Cov}^{-1}\left(w_{\rm data}-Aw_{\rm model}\right),
\end{equation}
so that a posterior of $A^{+\sigma_A}_{-\sigma_A}$ can be obtained, {where $\sigma_A$ is the Gaussian standard deviation}. Then the corresponding S/N is $A/\sigma_A$.
We note that, if $w_{\rm data}$ is a single value rather than a data vector, this S/N defined by amplitude fitting is identical to the S/N of the data itself, namely $A/\sigma_A=w_{\rm data}/\sigma_{w_{\rm data}}$. This is the case for most of the S/N calculated in this work, when there is one single measurement at small-scale and one at large-scale, and the small-scale and large-scale data correspond to different (nonlinear/linear) galaxy biases so they should be treated separately.
\section{Data} \label{sec data}
In this section, we introduce the DESI spectroscopic data and the shear catalogs from DECaLS/KiDS/HSC. We note even though the DES-Y3 catalog can have an overlap with full DESI for $\sim1264$ deg$^2$, its overlap with DESI SV3 catalog is $0$. We, therefore, do not present any analysis for DES.
\subsection{DESI} \label{sec DESI}
DESI is the only operating Stage IV galaxy survey. It is designed to cover 14,000 deg$^2$ of the sky, with 5,000 fibers collecting spectra simultaneously \citep{DESI2016b,Silber2022,Miller2022}. DESI aims to observe density tracers such as BGS (Bright Galaxy Survey, \citealt{RuizMacias2020}), LRG (luminous red galaxies, \citealt{Zhou2020}), ELG (emission line galaxies, \citealt{Raichoor2020}), and QSO (quasi-stellar objects, \citealt{Yeche2020}), with generally increasing redshift. Other supporting papers on target selections and validations can be find in \cite{AllendePrieto2020,Alexander2022,Lan2022,Cooper2022,Hahn2022,Zhou2022,Chaussidon2022}. DESI plans to use these tracers to study cosmology, especially in BAO (baryonic acoustic oscillations) and RSD (redshift-space distortions) \citep{DESI2016a,Levi2013}. It is located on the 4-meter Mayall telescope in Kitt Peak, Arizona \citep{DESI2022a}. From 2021 till now, DESI has finished its ``SV3'' \citep{DESIsv} and ``DA0.2'' catalogs, which will be included in the coming Early Data Release (EDR, \citealt{DESIdr}). The Siena Galaxy Atlas \citep{DESIsga} is also expected soon.
The DESI experiment is based on the DESI Legacy Imaing Surveys \citep{Zou2017,Dey2019,Schlegel2022}, with multiple supporting pipelines in spectroscopic reduction \citep{Guy2022}, derivation of classifications and redshifts \citep{Bailey2022}, fiber assigement \citep{Raichoor2022}, survey optimization \citep{Schlafly2022}, spectroscopic target selection \citep{Myers2022}
In this work, we use the DESI SV3 catalog, which is also known as the $1\%$ survey (with a sky coverage of $\sim140$ deg$^2$), for the g-g lensing study. We consider the DESI BGS, LRGs, and ELGs, while ignoring the QSOs as the available number is relatively low. {In SV3, each galaxy is assigned a weight to account for the survey completeness and redshift failure.} Since the purpose of this paper is not a precise measurement of cosmology, we assume the linear galaxy biases follow $b_{\rm BGS}(z)D(z)=1.34$, $b_{\rm LRG}(z)D(z)=1.7$, and $b_{\rm ELG}(z)D(z)=0.84$, where $D(z)$ is the linear growth factor normalized to $D(z=0)=1$ \citep{DESI2016a}. The number of galaxies used will be informed later in the paper, as the overlap between the DESI $1\%$ survey and the lensing surveys are different.
\subsection{DECaLS} \label{sec DECaLS}
We use lensing shear measurement from DECaLS DR8, which contains galaxy images in $g-$, $r-$, and $z-$bands \citep{Dey2019}. DECaLS DR8 galaxies are processed by Tractor \citep{Meisner2017,Lang2014} and divided into five types according to their morphologies: PSF, SIMP, DEV, EXP, and COMP \citep{Phriksee2020,Yao2020,Zu2021,Xu2021}. The galaxy ellipticities $e_{1,2}$ are measured ---- except for the PSF type ---- with a joint fit on the $g-$, $r-$, and $z-$bands. A conventional shear calibration \citep{Heymans2012,Miller2013,Hildebrandt2017} is applied as in
\begin{equation} \label{eq shear calib}
\gamma^{\rm obs} = (1+m)\gamma^{\rm true}+c,
\end{equation}
with a multiplicative bias $m$ and additive bias $c$, to account for possible residual bias from PSF modeling, measurement method, blending and crowding \citep{Mandelbaum2015,Martinet2019}. This calibration is obtained by comparing with Canada–France–Hawaii Telescope (CFHT) Stripe 82 observed galaxies and Obiwan simulated galaxies \citep{Phriksee2020,Kong2020}.
Several versions of the photometric redshift for the DECaLS galaxies have been estimated \citep{Zou2019,Zhou2021,Duncan2022}. We apply the most widely used one \citep{Zhou2021}, which uses the $g$, $r$, and $z$ optical bands from DECaLS while borrowing $W1$ and $W2$ infrared bands from WISE (Wide-field Infrared Survey Explorer, \citealt{Wright2010}). The photo-$z$ algorithm is trained based on a decision tree, with training samples constructed from a wide selection of spectroscopic redshift surveys and deep photo-$z$ surveys. We additionally require $z<21$ to select galaxies with better photo-$z$. {We use the photo-z distribution to represent the true-z distribution $n(z)$, while allowing a systematic bias of $\Delta z$ in the form $n(z-\Delta z)$, to pass its effect to Eq.\,\eqref{eq q} then Eq.\,\eqref{eq C^gG}. This is appropriate as weak lensing is mainly biased due to the mean redshift but slightly affected by the redshift scatter.}
Overall, the DR8 shear catalog has $\sim 9,000$ deg$^2$ sky coverage ---- which will be the final overlap with full DESI ---- with an average galaxy number density of $\sim1.9$ gal/arcmin$^2$. The overlapped area with DESI $1\%$ survey is $\sim106$ deg$^2$, which is significantly larger than the other stage III lensing surveys.
We note that the current DECaLS DR8 shear catalog can have some residual multiplicative bias $|m|\sim0.05$ \citep{Yao2020,Phriksee2020}, {possibly due to the selections in observational data while making the comparison \citep{Li2020,Jarvis2016}.} This will prevent us from getting reliable cosmology for measurements with $S/N>\sim20$. Also, there exists a possible bias in the redshift distribution $n(z)$, which will require a galaxy color-based algorithm \citep{Hildebrandt2017,Buchs2019,Wright2020} or a galaxy clustering-based algorithm \citep{Peng2022,Zhang2010photoz,vandenBusch2020} to get the correction. For these two reasons, we choose not to extend this study to the precision cosmology level. A future version of the DECaLS DR9 shear catalog is under development, with improved data reduction and survey procedures\footnote{https://www.legacysurvey.org/dr9/description/}, with more advanced shear calibration {for a pure Obiwan image simulation-based algorithm} (Yao et al. in preparation) and redshift calibration (Xu et al. in preparation).
\subsection{KiDS}
The Kilo-Degree Survey is run by the European Southern Observatory and is designed for weak lensing studies in $ugri$ optical bands. The KiDS data are processed by THELI \citep{Erben2013} and Astro-WISE \citep{deJong2015,Begeman2013}. The galaxy shear measurements are obtained by $lens$fit \citep{Conti2017,Miller2013}, and the photo-$z$s are measured by BPZ \citep{Benitez2000,Benitez2004} using the KiDS $ugri$ optical bands and the $ZYJHK_{\rm s}$ infrared bands from VIKING \citep{Wright2019}. The KiDS shears are calibrated following the same equation as Eq.\,\eqref{eq shear calib} with image simulation \cite{Kannawadi2019}.
We use the KiDS-1000 shear catalog \citep{Giblin2021,Asgari2021} in this work. The overlapped area with DESI SV3 is $\sim55$ deg$^2$. The expected overlapped area between the full DESI footprint and KiDS-1000 is $\sim456$ deg$^2$.
\subsection{HSC}
The Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP, or HSC) is a Japanese lensing survey using the powerful Subaru telescope. It covers five photometric bands $grizy$. Compared with KiDS and DES, HSC has its unique advantage in the galaxy number density and high-z galaxies (but with a smaller footprint). The HSC shears are calibrated similarly to Eq.\,\eqref{eq shear calib} \citep{Mandelbaum2018HSC} but with an additional shear responsivity \citep{HSC_Hamana2019}.
We use the HSC-Y1 shear catalog \citep{HSC_Hikage2019,HSC_Hamana2019}, which overlaps with DESI SV3 for $\sim48$ deg$^2$. The expected overlap between HSC-Y3 data and full DESI is $\sim733$ deg$^2$.
\begin{figure}
\includegraphics[width=\columnwidth]{figure/nz_BGS_ANY.png}
\caption{The galaxy redshift distributions for the DESI BGS with $0<z<0.5$ and photo-$z$ distributions for the lensing surveys with $0.6<z_p<1.5$. The numbers in the labels are the number of galaxies in the overlapped region.}
\label{fig: nz BGS}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{figure/wgG_BGS_ANY.png}
\caption{The galaxy-galaxy lensing angular correlation functions, corresponding to the galaxies samples in Fig.\,\ref{fig: nz BGS}. In the upper panel, the theoretical curves are given by the fiducial cosmology and the assumed galaxy bias model. The \{small-scale, large-scale\} detection significances are \{9.1, 5.8\} for BGS$\times$DECaLS, \{10.2, 3.9\} for BGS$\times$KiDS , and \{16.1, 4.3\} for BGS$\times$HSC. In the lower panel, we show the ratio between our measurements and the corresponding theoretical model, with the latter re-weighted using the number of pairs and lensing weights to account for the band power problem with wide angular bins. The DECaLS and HSC results are slightly shifted horizontally.}
\label{fig: wgG BGS}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{figure/wgG_BGS_DECaLS.png}
\caption{The galaxy-galaxy lensing angular correlation function $w^{\rm gG}$ (upper panel) and its $45\deg$-rotation test $w^{\rm gX}$ (lower panel) for the BGS$\times$DECaLS g-g lensing only, with the same distribution as in Fig.\,\ref{fig: nz BGS} but with more angular bins with 50 jackknife sub-regions. In the upper panel, the theoretical curves are given by the fiducial cosmology and the assumed galaxy bias model. The detection significance for the 5 angular bins are \{6.5, 6.6, 8.4, 4.7, 3.2\}, with the 4 large-scale bins well-agreed with the prediction from fiducial cosmology and the linear bias assumption. {The total S/N using amplitude fitting (as described in Sec.\,\ref{sec S/N}) is $8.9\sigma$ ($A=1.03^{+0.12}_{-0.11}$) for the right three large-scale dots, and is $10.0\sigma$ ($A=1.0^{+0.1}_{-0.1}$) for the right four large-scale dots.} In the lower panel where the shear are rotated for $45\deg$, the results are consistent with 0, with reduced-$\chi^2\sim3/5$.}
\label{fig: wgG BGS DECaLS}
\end{figure}
\section{Results} \label{sec results}
In this section, we show the measurements of different galaxy-shear correlation functions. The estimator for the galaxy-shear correlation is:
\begin{equation} \label{eq gG estimator}
w^{\rm gG }(\theta)=\frac{\sum_{\rm ED}\textsc{w}_{\rm E}\gamma^+_{\rm E}\textsc{w}_{\rm D}}{\sum_{\rm ER}(1+m_{\rm E})\textsc{w}_{\rm E}\textsc{w}_{\rm R}}
-\frac{\sum_{\rm ER}\textsc{w}_{\rm E}\gamma^+_{\rm E}\textsc{w}_{\rm R}}{\sum_{\rm ER}(1+m_{\rm E})\textsc{w}_{\rm E}\textsc{w}_{\rm R}}\ ,
\end{equation}
where $\textsc{w}_{\rm E}$, $m_{\rm E}$ and $\gamma^+_{\rm E}$ denotes the lensing weight (inverse-variance weight for DECaLS \citealt{Phriksee2020} and HSC \citealt{HSC_Hikage2019}, an adjusted version for KiDS \citealt{Miller2013}), the multiplicative bias correction (for HSC there is an extra shear responsivity included), and the tangential shear of the source galaxy, with respect to the given lens galaxy with weight $\textsc{w}_{\rm D}$ or $\textsc{w}_{\rm R}$. The $\Sigma$-summations are calculated for all the ellipticity-density (ED) pairs and the ellipticity-random (ER) pairs. We note Eq.\,\eqref{eq gG estimator} already includes the correction for boost factor \citep{Mandelbaum2005boostfactor,Amon2018}, {and this equation is adequate for the multiplicative bias $m_{\rm E}$ defined either per galaxy or per sample.} The correlation uses DESI official random catalogs to simultaneously correct for the additive bias in the presence of a mask and reduce the shape noise. We will show the measurements with different lens samples and source catalogs using the above estimator.
\subsection{DESI $w^{\rm gG}$}
\label{sec wgG}
We first show the g-g lensing measurements for DESI BGS and the three shear catalogs. The normalized redshift distributions $n(z)$ are shown in Fig.\,\ref{fig: nz BGS}, with the number of galaxies being used in the labels. We use BGS with $0<z<0.5$, and require the photo-$z$ of the source galaxies located at $0.6<z_p<1.5$, so that the overlap in redshift is very small even considering the inaccuracy of photo-$z$. We see that DECaLS has the most available BGS lenses, while HSC has the most available sources and the highest redshift. We notice there are unexpected spikes for the photo-z distribution of KiDS, which is probably due to cosmic variance as the overlapped area is much smaller than the full KiDS data.
\begin{figure}
\includegraphics[width=\columnwidth]{figure/nz_LRG.png}
\caption{The galaxy redshift distributions for the DESI LRGs with $0<z<0.6$ and photo-$z$ distributions for the lensing surveys with $0.7<z_p<1.5$. The numbers in the labels are the number of galaxies in the overlapped region.}
\label{fig: nz LRG}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{figure/wgG_LRG.png}
\caption{The galaxy-galaxy lensing angular correlation functions, corresponding to the galaxies samples in Fig.\,\ref{fig: nz LRG}. In the upper panel, the theoretical curves are given by the fiducial cosmology and the assumed galaxy bias model. The \{small-scale, large-scale\} detection significances are \{3.5, 1.9\} for LRG$\times$DECaLS, \{8.7, 2.2\} for LRG$\times$KiDS, and \{10.6, 2.4\} for LRG$\times$HSC. }
\label{fig: wgG LRG}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{figure/nz_ELG.png}
\caption{The galaxy redshift distributions for the DESI ELGs with $0<z<0.7$ and photo-$z$ distributions for the lensing surveys with $0.8<z_p<1.5$. The numbers in the labels are the number of galaxies in the overlapped region.}
\label{fig: nz ELG}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{figure/wgG_ELG.png}
\caption{The galaxy-galaxy lensing angular correlation functions, corresponding to the galaxies samples in Fig.\,\ref{fig: nz ELG}. The theoretical curves are given by the fiducial cosmology and the assumed galaxy bias model. The \{small-scale, large-scale\} detection significance are \{-0.3, 1.4\} for ELG$\times$DECaLS, \{-1.1, 1.4\} for ELG$\times$KiDS, and \{2.5, 2.6\} for ELG$\times$HSC. The negative values at small-scale represent negative measurements, which might be due to the non-linear galaxy bias, satellite fraction, or shot noise.}
\label{fig: wgG ELG}
\end{figure}
We show the measured correlation functions for the DESI BGS g-g lensing in Fig.\,\ref{fig: wgG BGS}. The correlations are measured in 2 logarithmic bins in $0.5<\theta<80$ arcmin, with the statistical uncertainties calculated using jackknife re-sampling. We find that all three lensing surveys have strong g-g lensing signals, even for the current 1\% DESI data. The measurements are shown in blue dots (DECaLS), orange triangles (KiDS), and green squares (HSC), while the corresponding theoretical comparisons are shown in the blue solid curve, the orange dash-dotted curve, and the green dotted curve. From this figure, we find that the advantage of DECaLS is its large-scale cosmological information, with the highest S/N $\sim5.8$. This is due to DECaLS's significantly large overlap with DESI, reducing the cosmic variance. On the other hand, KiDS and HSC has larger S/N than DECaLS at small-scale, due to their higher source galaxy number density, which lowers the shape noise.
In this work we choose not to estimate the best-fit cosmology, as for DECaLS, there are some unaddressed potential systematics (as discussed in Sec\,\ref{sec DECaLS}), while for KiDS and HSC we do not want to harm the ongoing blinding efforts in the DESI collaboration (although for a larger catalog with the larger overlapped area). The theoretical estimations in Fig.\,\ref{fig: wgG BGS} and all the other similar figures in this work are based on the KiDS-1000 COSEBI $\Lambda$CDM cosmology with maximum posterior of the full multivariate distribution (MAP, \cite{Asgari2021}), which has $h=0.727$, $\Omega_{\rm b} h^2 =0.023$, $\Omega_{\rm c} h^2 =0.105$, $n_{\rm s} =0.949$ and $\sigma_8 =0.772$. We note the choice of other fiducial cosmology \citep{Planck2018I,Asgari2021,DESY3cosmo,HSC_Hamana2019} will give similar results for the current stage with DESI SV3. The linear galaxy biases are assumed following the descriptions of difference density tracers in Sec\,\ref{sec DESI}.
We note that the choice of 2 log-bins is limited by the 20 jackknife sub-regions \citep{Yao2020,Mandelbaum2006}, which is limited by: (1) the requirement of each jackknife sub-region is independent up to the largest scale we use (80 arcmin), and (2) the size of the overlapped region for KiDS and HSC ($\sim50$ deg$^2$). As the DESI survey expands, the available overlapped region will increase accordingly, resulting in increases in both the available number of sub-regions and the maximum angular scale we can measure. {Alternatively, we can use an analytical covariance (similar to Appendix \ref{sec apdx cov} but more tests need to be done) or simulation based covariance for future DESI data.} We also note in this work the inverses of the covariances are corrected \citep{Hartlap2007,Wang2020} due to the limited number of sub-regions.
As a demonstration of more angular binning, we use BGS$\times$DECaLS data to show the choice of 50 jackknife sub-regions and 5 angular bins, as in Fig.\,\ref{fig: wgG BGS DECaLS}. We show that with proper binning, more cosmological information can be extracted. The $\theta>\sim2$ arcmin measurements (the right 4 large-scale dots) agree with the linear bias assumption very well. In the future, with a larger overlapped footprint, more jackknife sub-regions can be used, so that more angular bins can be measured, either to increase the total S/N or to address any scale-dependent systematics.
We do see great potential for DECaLS from the above results, {although measurements will ultimately be limited by systematic errors.}
We show the redshift distribution of the DESI LRGs and the three lensing surveys in Fig.\,\ref{fig: nz LRG}, requiring $z<0.6$ for the spec-$z$ LRGs and $0.7<z_p<1.5$ for the source galaxies. Similar to the BGS, more LRGs can be used when overlapping with DECaLS, while the available DECaLS source galaxies are less than in the other surveys. Since LRGs are generally distributed at higher $z$ than the BGS, we choose to increase the $z$-cut of the LRGs and the $z_p$-cut of the sources, resulting in reduced source galaxies compared with Fig.\,\ref{fig: nz BGS}.
This figure shows the DECaLS source galaxies are more reduced (from 133k to 78k) as it is shallower than the other two.
The correlation measurements for the LRGs are presented in Fig.\,\ref{fig: wgG LRG}. At large-scale, the DECaLS signal is weaker than KiDS and HSC, but it still offers comparable S/N. At the small-scale, the S/N is dominated by deep surveys. The small-scale measurements are significantly higher than the theoretical predictions, due to LRGs being generally more massive than BGS, with stronger non-linear galaxy bias at such separations.
Furthermore, we study the g-g lensing measurements of the DESI ELGs. We show the redshift distribution of the DESI ELGs and the three lensing surveys in Fig.\,\ref{fig: nz ELG}, requiring $z<0.7$ for the spec-$z$ ELGs and $0.8<z_p<1.5$ for the source galaxies. The available number of galaxies is further reduced compared to BGS and LRGs, due to DESI ELGs being mainly distributed at $z>0.7$. And the high-z sources for DECaLS are significantly less than KiDS and HSC.
The correlation measurements of the ELGs are shown in Fig.\,\ref{fig: wgG ELG}. HSC appears to have the largest S/N at both large-scale and small-scale, and the S/N of DECaLS at large-scale is comparable to KiDS.
{All three lensing surveys have small-scale measurements lower than the theoretical predictions, suggesting the low measurement is not a systematics of DECaLS. We suspect this might be due to shape noise, sample variance, or possibly non-linear galaxy bias. As when we go from large-scale to small-scale, the non-linear halo bias for less massive halos (for example the host halos for ELGs, see Fig.\,\ref{fig: wgG ELG}) tends to drop compared with its linear bias, while the non-linear halo bias tends to increase for the more massive halos (for example the host halos for the LRGs, see Fig.\,\ref{fig: wgG LRG}) according to Fig.\,1 of \cite{Fong2021}. The satellite galaxy fraction in the ELGs could also lead to a low amplitude at small-scale \citep{Niemiec2017,Favole2016,Gao2022}. These will require a higher S/N to test in the future. In this work, we only focus on large-scale ELGs measurement.}
\begin{table*}
\centering
\caption{We summarize the S/N of the DESI 1\% survey (SV3) g-g lensing results in Fig.\,\ref{fig: wgG BGS}, \ref{fig: wgG LRG} and \ref{fig: wgG ELG}, and forecast the {ideal} final S/N with full DESI, by rescaling the covariance based on the overlapped area, {and assuming DECaLS data can be well calibrated}. We note that the ELG measurements become negative sometimes, and therefore decide not to predict its final S/N. From this figure, we see that the advantage of DECaLS is at low-z (with BGS) and large-scale. We additionally present the possible bias in the forecasted S/N, namely $\Delta$S/N. It includes the contribution from the statistical error of the current measurement, and residual systematical bias from the data calibration. We use multiplicative bias $|m|\sim0.05$ \citep{Yao2020,Phriksee2020} and redshift bias $|\Delta z|\sim0.02$ \citep{Zhou2021} for DECaLS DR8, $|m|\leq0.015$ and $|\Delta z|\leq0.013$ for KiDS \citep{Asgari2021}, and $|m|\leq0.03$ and $|\Delta z|\leq0.038$ for HSC \citep{HSC_Hikage2019}, to predict their systematical error in the forecasted S/N. We note the statistical contribution of $\Delta$S/N results from rescaling the $1\sigma$ error from Fig.\,\ref{fig: wgG BGS}, \ref{fig: wgG LRG} and \ref{fig: wgG ELG}, and is scale-independent and redshift-independent. The contribution from multiplicative bias $m$ is also scale-independent, while the contribution from redshift bias $\Delta z$ is weakly scale-dependent and redshift-dependent. In the table, we only show the $\Delta$S/N($\Delta z$) values corresponding to the BGS results at the large-scale. }
\label{tab forecast}
\begin{tabular}{ c c c c c | c c c c | c c }
\hline
survey & SV3 overlap & \multicolumn{3}{|c|}{SV3 S/N [small-scale, large-scale]} & full overlap & \multicolumn{3}{|c|}{{ideal} forecast S/N [small-scale, large-scale]} &
\multicolumn{2}{|c|}{forecast {potential bias} $\Delta$S/N} \\
& [deg$^2$] & BGS & LRG & ELG & [deg$^2$] & BGS & LRG & ELG & statistical & systematical \\
\hline
DECaLS & 106 & [9.1, 5.8] & [3.5, 1.9] & [-0.3, 1.4] & $\sim9000$ & [83.8, 53.4] & [32.2, 17.5] & [N/A, 12.9] & $\pm9.2$ & $\pm5\%(m)\pm1.4\%(\Delta z)$ \\
KiDS & 55 & [10.2, 3.9] & [8.7, 2.2] & [-1.1, 1.4] & 456 (DR4) & [29.3, 11.2] & [25.1, 6.3] & [N/A, 4.0] & $\pm2.9$ & $\pm1.5\%(m)\pm0.8\%(\Delta z)$\\
HSC & 48 & [16.1, 4.3] & [10.6, 2.4] & [2.5, 2.6] & 733 (Y3) & [62.9, 16.8] & [41.4, 9.4] & [9.8, 10.2] & $\pm3.9$ & $\pm3\%(m)\pm1.6\%(\Delta z)$\\
\hline
\end{tabular}
\end{table*}
\subsection{Forecasts and Systematics}
We summarize our findings for the g-g lensing measurements from BGS (Fig.\,\ref{fig: wgG BGS}), LRGs (Fig.\,\ref{fig: wgG LRG}), and ELGs (Fig.\,\ref{fig: wgG ELG}) in Table\,\ref{tab forecast}. We see that DECaLS has its unique advantage in extracting cosmological information at large-scale and at lower redshift (when correlating with the DESI BGS). {Neglecting systematic errors for the moment, which will be dominant in practice, we give the forecast of the S/N with the complete DESI survey by re-scaling the covariance according to the overlapped area. This re-scaling assumes the covariance of the g-g lensing signal is dominated by the Gaussian covariance. Since we are extrapolating from small regions with significant boundary effects in our large-scale bin, this is only an approximation.}
We theoretically test the different components of the covariance in Appendix\,\ref{sec apdx cov} for your interest. The large-scale information of future DECaLS$\times$BGS can reach $>50\sigma$, which is stronger than most of the current g-g lensing data,
and will be very promising in studying the current $S_8$ tension \citep{Hildebrandt2017,HSC_Hamana2019,HSC_Hikage2019,Asgari2021,Heymans2021,DESY3cosmo,DESY3model,DESY3data,Planck2018I}.
The contribution from LRGs and ELGs, and possibly QSOs in the future, can also offer independent cosmological information.
\begin{figure}
\includegraphics[width=\columnwidth]{figure/sys_bias.png}
\caption{The impact of the residual shear multiplicative bias $m$ and the bias in the redshift distribution $\Delta z$. For different $m$ and $\Delta z$, we evaluate the resulting $w_{\rm bias}/w_{\rm true}$ at the large-scale of Fig.\,\ref{fig: wgG BGS}, \ref{fig: wgG LRG} and \ref{fig: wgG ELG} ($\theta\sim51$ arcmin) and show the ratio as the color map. The effect of $m$ is totally scale-independent, while the effect of $\Delta z$ is weakly scale-dependent, which can bring an additional $\sim20\%$ difference at maximum. We also show where the bias from $m$ and $\Delta z$ perfectly cancel each other (black solid curve), and the location where the net bias reaches $\pm0.01$ (blue dashed curve) and $\pm0.02$ (orange dotted curve).}
\label{fig: sys bias}
\end{figure}
We note that the S/N predictions in Table\,\ref{tab forecast} ignored the potential bias from systematics, such as residual shear multiplicative bias $m$ and redshift distribution $n(z)$. The existence of the shear multiplicative bias $m$ will change the lensing efficiency from $q_{\rm s}$ to $(1+m)q_{\rm s}$ in Eq.\,\eqref{eq C^gG} and \eqref{eq q}. The bias in redshift distribution $\Delta z$ will change the redshift distribution for the source galaxies from $n_{\rm s}(\chi_{\rm s}(z_{\rm s}))$ to $n_{\rm s}(\chi_{\rm s}(z_{\rm s}-\Delta z))$ in Eq.\,\eqref{eq q}, {so that the whole redshift distribution is shifted towards higher-z direction by $\Delta z$}. For example, if we assume the residual multiplicative bias is $|m|\sim0.05$ (which is found for some DECaLS galaxy sub-samples as in \cite{Phriksee2020,Yao2020}), and enlarge the covariance to account for this potential bias, then the S/N of DECaLS$\times$BGS at large-scale will be reduced from $>50\sigma$ to $\sim20\sigma$. This is a huge loss of cosmological information, although $\sim20\sigma$ is still comparable to the $\sim11\sigma$ of KiDS-DR4 and $\sim 17\sigma$ of HSC-Y3. Therefore, we emphasize the importance of calibrating DECaLS data in a more precise way in the future for reliable cosmological measurements. We note the current measurements with DESI 1\% survey have S/N$\ll20\sigma$, therefore the impacts from such biases are still within the error budget. {The assumed systematics can enlarge the large(small)-scale uncertainties from $\sim17\%(\sim10\%)$ to $\sim18\%(\sim12\%)$.}
We further estimate the requirements on the DECaLS calibrations for precision cosmology. {We evaluate the fractional bias in the measured correlation function $w^{\rm gG}$, considering some residual multiplicative bias $m$ and redshift bias $\Delta z$, and present the results in Fig.\,\ref{fig: sys bias}.} To safely use the $\sim50\sigma$ data from the large-scale of DECaLS$\times$BGS, the residual multiplicative bias alone need to be controlled within $|m|<0.02$, and the mean of the redshift distribution of the source galaxies $\left<z\right>$ need to be controlled within $|\Delta z|<0.03$ on its own. {The net bias considering both $m$ and $\Delta z$ should be controlled in between the orange dotted curves in Fig.\,\ref{fig: sys bias}.} To safely use the cosmological information in both the large-scale and the small-scale, with overall S/N$\sim100\sigma$, we require the calibrations to have $|m|<0.01$ and $|\Delta z|<0.015$ individually, {while the net bias considering both $m$ and $\Delta z$ should be controlled in between the blue dashed curves in Fig.\,\ref{fig: sys bias}.}
We note that using tomography and combining g-g lensing measurements from different density tracers (BGS, LRGs, ELGs, and possibly QSOs in the future) can bring stronger S/N, so the requirements on the calibration terms will be more strict. However, these studies will require a much larger covariance, thus more jackknife sub-regions and much larger overlapped regions, which are beyond the ability of the current data size. We leave this study to future works.
\subsection{Shear-ratio}
\begin{figure}
\includegraphics[width=\columnwidth]{figure/R.png}
\caption{The {MCMC posterior PDF of the} shear-ratio measurements for BGS$\times$DECaLS using Eq.\,\eqref{eq constructed vector} and \eqref{eq constructed cov}. The galaxies are distributed as in Fig.\,\ref{fig: nz BGS}, with source galaxies split into $0.6<z_p<0.9$ and $0.9<z_p<1.5$. The constraint on the shear-ratio uses the two small-scale angular bins ($\theta<\sim5$ arcmin) as in Fig.\,\ref{fig: wgG BGS DECaLS}. The resulting $R=1.21^{+0.42}_{-0.35}$ agrees with the theoretical prediction between $1.13$ and $1.18$. When re-scaling the covariance to the final overlap of DESI$\times$DECaLS, the shear-ratio can be constrained as good as $\sigma_R\sim0.04$ when using the small-scale information, and $\sigma_R\sim0.03$ when using the full-scale.}
\label{fig: R}
\end{figure}
Shear-ratio is a powerful tool to probe cosmology or test systematics \citep{Sanchez2021,Giblin2021}, and it is {insensitive} to many small-scale physics. As shown in Table\,\ref{tab forecast}, DECaLS$\times$DESI, especially for the BGS and LRGs, can offer very high S/N measurements at the small-scale. We take the BGS from the DESI 1\% survey as an example to study this topic.
The galaxy samples are distributed similarly to the BGS$\times$DECaLS $n(z)$ as in Fig.\,\ref{fig: nz BGS}, but in addition, the source galaxies are further split into two groups: $0.6<z_p<0.9$, and $0.9<z_p<1.5$. We calculated the corresponding correlations $w^{\rm gG}_1$ and $w^{\rm gG}_2$, and their ratio with $R=w^{\rm gG}_2 / w^{\rm gG}_1$, {following Eq.\,\eqref{eq constructed vector}, \eqref{eq constructed cov} and the description in Sec.\,\ref{sec shear-ratio}.}
The shear-ratio results are shown in Fig.\,\ref{fig: R}. Following the same angular binning as in Fig.\,\ref{fig: wgG BGS DECaLS} for the correlation calculations, we use the two small-scale angular bins with $\theta<\sim5$ arcmin, since the three large-scale bins are expected in the {direct 2-point cosmology} study, as described in Sec.\,\ref{sec wgG}. The current small-scale information can constrain shear-ratio at $R=1.21^{+0.42}_{-0.35}$, which is consistent with our theoretical prediction (using $R=w^{\rm gG}_2 / w^{\rm gG}_1$, Eq.\,\eqref{eq C^gG} and \eqref{eq w Hankel}) between $1.13$ and $1.18$. This small angular variation is due to the angular dependence in $P(k=\frac{\ell+1/2}{\chi},z)$ in Eq.\,\eqref{eq C^gG}, which is not fully canceled when taking the ratio using correlation functions. We note this weak angular dependence is small and can be easily taken into account in the theoretical predictions.
To predict the constraining power when full DESI finishes, we rescaled the covariance based on the overlapped area as in Table\,\ref{tab forecast}, and find the shear-ratio can be constrained at $\sigma_R=0.04$ with the small-scale information, which is not used in getting the $S_8$ constraint. Considering full information for the shear-ratio study, we can obtain $\sigma_R=0.03$. These statistical errors are comparable with the shear-ratio studies in \citep{Sanchez2021} with DES-Y3 data, {showing a promising future in using shear-ratio to improve cosmological constraint
and/or to further constrain the systematics \citep{Giblin2021}. }
\subsection{Cosmic magnification}
\label{sec mag}
We discussed that the ELG$\times$DECaLS results have low S/N in Fig.\,\ref{fig: nz ELG}, \ref{fig: wgG ELG} and Table\,\ref{tab forecast}, as the ELGs are mainly distributed at large-$z$, while the advantage of DECaLS is at low-$z$. On the other hand, this opens a window to the study of cosmic magnification by putting the ELGs at high-z and using shear from low-z DECaLS galaxies. We follow the methodology in \cite{Liu2021} and use galaxy samples distributed as in Fig.\,\ref{fig: nz ELG mag}. The DECaLS galaxies are located at a much lower photo-$z$ compared with the ELGs, as in the targeted shear-magnification correlation, the shear-density correlation exists as a source of systematics when even a small fraction of shear galaxies appear at higher-$z$ than the ELGs.
The measurements are shown in Fig.\,\ref{fig: wgG ELG mag}. We find positive signals at the small-scale, and {null detections} at the large-scale, for all DECaLS, KiDS, and HSC. We tested the 45-deg rotation of the shear, resulting in consistency with 0 on all scales for all the source samples. Considering the similar calculation with eBOSS ELGs \footnote{\url{https://www.sdss.org/surveys/eboss/}} and DECaLS sources as a reference, we found the measurements are consistent with 0 on all scales, see Appendix\,\ref{sec apdx eBOSS} for details. In the measurements of Fig.\,\ref{fig: wgG ELG mag}, the {null detections} at the large-scale could be due to cosmic variance or some negative systematics such as intrinsic alignment. The positive measurements at the small-scale could be due to the targeted magnification signals, the cosmic variance, or photo-$z$ errors. We note to separate these different signals, either a stronger signal with clear angular dependencies or additional observables are needed to break the degeneracy.
As a further step, we present an effective amplitude fitting of $g_{\mu,{\rm eff}}$ for the magnification signals, following Eq.\,\eqref{eq C^muG}, in Table\,\ref{tab mag}. We find $\sim1\sigma$ {measurement} for KiDS and $\sim2\sigma$ {measurement} for DECaLS and HSC. Considering the ELG samples are quite similar as shown in Fig.\,\ref{fig: nz ELG mag}, and the three best-fit $g_{\mu,{\rm eff}}$-amplitudes are consistent, we evaluated the combined best-fit, achieving $\sim3\sigma$ significance. The covariance between different surveys is ignored for the combined estimation, as shot noise is more dominant in this case than the cosmic variance. Additionally, we find that by including shear galaxies from $0<z_p<0.4$, the significance of magnification detection drops, due to the low-z data having much weaker lensing efficiency as in Eq.\,\eqref{eq q}, and is mainly contributing noise.
The fitting goodness of the reduced-$\chi^2$ (defined by the $\chi^2$ between the best-fit and the data, divided by the degree of freedom) is generally close to $\sim1$ for each case. This shows no significant deviation between the model and the data. The detected $\sim3\sigma$ positive signal can be either due to the cosmic magnification, or very similar stochastic photo-z outliers between the three lensing surveys. As DECaLS, KiDS and HSC have totally different photometric bands, photo-z algorithms, and training samples, we think the detected signals are less likely due to the similar photo-z outliers,
and more likely to be the cosmic magnification signal. Therefore, by assuming the combined best-fit of $g_{\mu,{\rm eff}}\sim6.1$ as the true value
and rescaling the covariance similar to Table\,\ref{tab forecast}, we expect $\sim10\sigma$ detection for DECaLS DR9,
which is very promising for a stage III lensing survey. By then, with a better understanding of the systematics such as IA and photo-$z$ outlier, these cross-correlations can bring very promising constraining power in studying cosmic magnification. {We can choose to: (1) cut a complete and flux-limited sample and compare it with the flux function; (2) try to use the given DESI completeness and flux function to find a relation of $g_{\mu,{\rm eff}}(\alpha)$ rather than $g_\mu=2(\alpha-1)$; (3) compare with realistic mocks to infer $g_{\mu,{\rm eff}}$; (4) add an artificial lensing signal $\kappa$ to real data and infer $g_{\mu,{\rm eff}}$ as a response $\partial\delta^{\rm L}_{\rm g}/\partial\kappa$, similar to MetaCalibration \citep{Sheldon2017,Huff2017}.}
\begin{figure}
\includegraphics[width=\columnwidth]{figure/nz_ELG_mag.png}
\caption{The redshift distribution for high-z ELGs ($1<z<1.6$) and low-z source galaxies ($0.4<z_p<0.7$) for magnification study. The choice of such a large redshift gap is to prevent potential leakage due to photo-$z$ inaccuracy. The numbers in the labels are the number of galaxies in the overlapped region.}
\label{fig: nz ELG mag}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{figure/wgG_ELG_mag.png}
\caption{The magnification(ELGs)-shear correlation measurements, corresponding to the galaxy samples in Fig.\,\ref{fig: nz ELG mag}. The theoretical curves are based on Eq.\,\eqref{eq magnification}, assuming $g_{\mu,{\rm eff}}=1$ as a reference. The \{small-scale, large-scale\} detection significance for ELG$\times$DECaLS are \{2.2, 0.3\}, for ELG$\times$KiDS are \{1.2, -0.3\}, and for ELG$\times$HSC are \{2.8, -0.3\}. The negative values at the large-scale represent negative measurements, which might be due to shot noise, sample variance, or impact from systematics with negative values, like intrinsic alignment if there exists some photo-z outlier.}
\label{fig: wgG ELG mag}
\end{figure}
\begin{table}
\centering
\caption{This table shows the best-fit amplitude $g_{\mu,{\rm eff}}$ for the cosmic magnification. The upper part corresponds to the results in Fig.\,\ref{fig: wgG ELG mag} for DECaLS, KiDS, HSC, and the combination of them (the ``all'' case). We find with the DESI 1\% survey, we can already detect cosmic magnification at $\sim3.1\sigma$ for the shear galaxies distributed at $0.4<z_p<0.7$, while the $z_p<0.4$ galaxies are mainly contributing noise as it corresponding lensing efficiency (Eq.\,\eqref{eq q}) is low. The degree of freedom is calculated as $dof=N_{\rm data}-N_{\rm para}$. We see no significant deviation between data and model as $\chi^2/dof\sim1$.
}
\label{tab mag}
\begin{tabular}{cccc}
\hline
Case & $g_{\mu,{\rm eff}}$ & S/N & $\chi^2/dof$ \\
\hline
DECaLS $0.4<z_p<0.7$ & $10.6^{+5.2}_{-5.8}
$ & $1.8\sigma$ & 0.6/1 \\
KiDS $0.4<z_p<0.7$ & $4.2^{+6.0}_{-5.7}
$ & $0.7\sigma$ & 1.3/1 \\
HSC $0.4<z_p<0.7$ & $5.6^{+2.3}_{-2.3}$ & $2.4\sigma$ & 1.1/1 \\
all $0.4<z_p<0.7$ & $6.1^{+1.9}_{-2.0}
$ & $3.1\sigma$ & 3.9/5 \\
all $0<z_p<0.7$ & $5.3^{+2.0}_{-2.0}
$ & $2.7\sigma$ & 12.5/11 \\
\hline
\end{tabular}
\end{table}
\section{Conclusions}
\label{sec conclusions}
In this work, we study the cross-correlations between DESI 1\% survey galaxies and shear measured from DECaLS, one of the imaging surveys for DESI target selection. For the 1\% DESI data, DECaLS can have comparable performances compared with the main stage-III lensing surveys KiDS and HSC. More specifically, we measure the cross-correlations of DESI BGS/LRGs/ELGs $\times$ different shear catalog, shown in Fig.\,\ref{fig: wgG BGS}, \ref{fig: wgG LRG} and \ref{fig: wgG ELG}. We forecast the level of significance with full DESI data in Table\,\ref{tab forecast}. {Assuming systematic errors can be cleaned with high precision in the future,} we find the large-scale S/N could reach $>50 \sigma $ for DECaLS$\times$BGS, $>15\sigma$ for DECaLS$\times$LRG, and $>10\sigma$ for DECaLS$\times$ELG, which are very promising before the stage IV surveys come out.
We point out that the main difficulty in obtaining DECaLS cosmology is the calibrations for the systematics. In order to safely use the large-scale $\sim50\sigma$ information of BGS$\times$DECaLS, we need to achieve the minimum requirements on: (1) the multiplicative bias of $|m|<0.02$ and (2) the mean of redshift distribution $|\Delta z|<0.03$. To safely use the full-scale $\sim100\sigma$ data, we required $|m|<0.01$ and $|\Delta z|<0.015$ for future calibrations. The requirement could be even higher when combining different observables, but it will require a larger footprint than the 1\% survey for the study. These requirements are essential guides for future calibrations and studies on cosmology.
To fully use the advantage of DECaLS, we further explored two promising observables, the shear-ratio, and the cosmic magnification. We show the current 1\% BGS data can constrain shear-ratio with $\sigma_R\sim0.4$, while the full DESI BGS can give $\sigma_R\sim0.04$ using only the small-scale information, as shown in Fig.\,\ref{fig: R}. Furthermore, weak detections of potential cosmic magnification are shown in Fig.\,\ref{fig: wgG ELG mag} and Table\,\ref{tab mag}. We discussed how the possible systematics can affect this signal in Sec.\,\ref{sec mag}. We also expect DECaLS to have a strong contribution ($\sim10\sigma$ detection) to future magnification studies, if the observed signals in this work are not due to fluctuations.
To summarize, DECaLS lensing is a very promising tool that can enrich the cosmological output of DESI. It will bring new cosmological information with its huge footprint. It has great advantages in the large-scale and the low-$z$ information, {after carefully addressing the systematics}. It will offer strong S/N for shear-ratio study, and good potential in measuring cosmic magnification. Careful calibrations of the shear and redshift distribution can result in very promising outcomes.
\section*{Acknowledgements}
We thank Xiangkun Liu, Weiwei Xu, and Jun Zhang for their helpful discussions. We thank Chris Blake, Daniel Gruen, and Benjamin Joachimi for their contribution during the DESI collaboration-wide review.
HYS acknowledges the support from NSFC of China under grant 11973070, the Shanghai Committee of Science and Technology grant No.19ZR1466600 and Key Research Program of Frontier Sciences, CAS, Grant No. ZDBS-LY-7013. PZ acknowledges the support of NSFC No. 11621303, the National Key R\&D Program of China 2020YFC22016. JY acknowledges the support from NSFC Grant No.12203084, the China Postdoctoral Science Foundation Grant No. 2021T140451, and the Shanghai Post-doctoral Excellence Program Grant No. 2021419.
We acknowledge the support from the science research grants from the China Manned Space Project with NO. CMS-CSST-2021-A01, CMS-CSST-2021-A02 and NO. CMS-CSST-2021-B01.
We acknowledge the usage of the following packages pyccl\footnote{\url{https://github.com/LSSTDESC/CCL}, \citep{Chisari2019CCL}},
treecorr\footnote{\url{https://github.com/rmjarvis/TreeCorr}, \citep{Jarvis2004}},
healpy\footnote{\url{https://github.com/healpy/healpy}, \citep{Healpy_Gorski2005,Healpy_Zonca2019}},
matplotlib\footnote{\url{https://github.com/matplotlib/matplotlib}, \citep{Hunter2007}},
emcee\footnote{\url{https://github.com/dfm/emcee}, \citep{emcee}},
corner\footnote{\url{https://github.com/dfm/corner.py}, \citep{corner}},
astropy\footnote{\url{https://github.com/astropy/astropy}, \citep{astropy}},
pandas\footnote{\url{https://github.com/pandas-dev/pandas}},
scipy\footnote{\url{https://github.com/scipy/scipy}, \citep{scipy}},
dsigma\footnote{\url{https://github.com/johannesulf/dsigma}}
for their accurate and fast performance and all their contributed authors.
This research is supported by the Director, Office of Science, Office of High Energy Physics of the U.S. Department of Energy under Contract No. DE–AC02–05CH11231, and by the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility under the same contract; additional support for DESI is provided by the U.S. National Science Foundation, Division of Astronomical Sciences under Contract No. AST-0950945 to the NSF's National Optical-Infrared Astronomy Research Laboratory; the Science and Technologies Facilities Council of the United Kingdom; the Gordon and Betty Moore Foundation; the Heising-Simons Foundation; the French Alternative Energies and Atomic Energy Commission (CEA); the National Council of Science and Technology of Mexico (CONACYT); the Ministry of Science and Innovation of Spain (MICINN), and by the DESI Member Institutions: \url{https://www.desi.lbl.gov/collaborating-institutions}.
The DESI Legacy Imaging Surveys consist of three individual and complementary projects: the Dark Energy Camera Legacy Survey (DECaLS), the Beijing-Arizona Sky Survey (BASS), and the Mayall z-band Legacy Survey (MzLS). DECaLS, BASS and MzLS together include data obtained, respectively, at the Blanco telescope, Cerro Tololo Inter-American Observatory, NSF's NOIRLab; the Bok telescope, Steward Observatory, University of Arizona; and the Mayall telescope, Kitt Peak National Observatory, NOIRLab. NOIRLab is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. Pipeline processing and analyses of the data were supported by NOIRLab and the Lawrence Berkeley National Laboratory. Legacy Surveys also uses data products from the Near-Earth Object Wide-field Infrared Survey Explorer (NEOWISE), a project of the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration. Legacy Surveys was supported by: the Director, Office of Science, Office of High Energy Physics of the U.S. Department of Energy; the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility; the U.S. National Science Foundation, Division of Astronomical Sciences; the National Astronomical Observatories of China, the Chinese Academy of Sciences and the Chinese National Natural Science Foundation. LBNL is managed by the Regents of the University of California under contract to the U.S. Department of Energy. The complete acknowledgments can be found at \url{https://www.legacysurvey.org/}.
The authors are honored to be permitted to conduct scientific research on Iolkam Du'ag (Kitt Peak), a mountain with particular significance to the Tohono O'odham Nation.
\section*{Data Availability}
The data used to produce the figures in this work are available through \url{https://doi.org/10.5281/zenodo.7322710} following DESI Data Management Plan.
The inclusion of a Data Availability Statement is a requirement for articles published in MNRAS. Data Availability Statements provide a standardized format for readers to understand the availability of data underlying the research results described in the article. The statement may refer to original data generated in the course of the study or to third-party data analyzed in the article. The statement should describe and provide means of access, where possible, by linking to the data or providing the required accession numbers for the relevant databases or DOIs.
\bibliographystyle{mnras}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,282 |
Q: Creating a AntiCheat for minecraft, and trying to access a list from another class in java I am trying to code a very simple, yet effective anticheat. Whenever I put an ArrayList in one of my classes, and try to access it elsewhere, it doesn't say there is anything in the List.
public List<String> map = new ArrayList<String>();
public List<String> getMap() {
return map;
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public AimA() {
super("Aim", "A");
AntiCheat.getInstance().addReset("aimVlA");
}
This is the part of the aim check code that creates the ArrayList in AimA.java.
public List<String> map = new AimA().getMap();
And this is where I am trying to access it, in InfoCommand.java.
I am getting no errors, just this:
[21:05:28 INFO]: MajesticMagician issued server command: /menu info
Thank you for your time. If there is anything I haven't provided, please tell me.
I don't know if this is it or not, but here.
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| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,025 |
Q: How to wrap long lines into label control? I have content of 50-60 words in label and it goes beyond my groupbox where I put it, so I need to wrap it so it can be accommodate within groupbox.
A: Just Set the AutoSize property of the label to False, then reposition then label to the size you need
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Why All Data is Not Created Equal
Although relational databases will continue to be used for high-speed online transaction processing, conventional relational databases have clearly exhausted their usefulness for business analytics. What's ahead for database technology?
By Charlie Silver, CEO, Algebraix Data Corp.
Every enterprise relies on data to make decisions, as evidenced by the fact that the business analytics software market is now over $30 billion annually and growing rapidly. Yet, today the business analytics systems of nearly every Global 2000 company still relies on outdated relational database technology from the 1970s. Despite the challenges the classic relational data model imposes on scalability, performance, and manageability in the face of modern data volumes and applications, it continues to be the de facto standard for enterprises worldwide.
Until recently, suppliers of relational databases were arguing that they could handle all the data needs of any enterprise, but that argument started to break down with the advent of XML and the proliferation of XML documents because the XML format doesn't fit well into the relational data model.
Today, the preponderance of electronic data -- in the form of computer-generated documents containing combinations of audio recordings, graphics, images, numeric data, text, and video recordings, which together constitute more than 85 percent of all enterprise data -- does not fit well into the relational data model. In fact, the Web is now the world's largest heterogeneous database of this so-called "unstructured" data. Think of all the unstructured data accessible via the public Internet and private intranets that cannot be readily analyzed because it's not "structured" in the time-honored relational-data format
As a result, at least 85 percent of the business analytics investments that are being made today analyze less than 15 percent of enterprise data. Although the way we use data is increasingly focused on analytics, relational databases have been maxed out in their usefulness as an analytics tool. Based on some estimates, current data growth rates suggest we'll produce nearly 10 trillion gigabytes of data within the next three years. That's enough to store nearly 70 trillion hours of Flash video. Moreover, this unstructured data is growing at more than twice the rate of structured data.
The Dirty Little Secret of the Relational Database Industry
The dirty little secret of the relational database industry is that before data can be processed by a conventional relational database, it must be pre-structured into "relational-data tables" comprised of rows and columns, much like spreadsheets. Unfortunately, the data stored in relational-data tables is not inherently searchable. Consequently, over the last 40 years, the conventional relational database has gone from an emerging technology to one that is rapidly becoming obsolete.
As the amount of enterprise data continues to grow exponentially, so do the sizes and numbers of relational-data tables required to manage it. Moreover, as relational-data tables become larger, queries from analytic applications must scan through an increasing number of rows and columns to find requested data. Today we've come to accept that large enterprises need teams of IT professionals to deal with the burden of managing relational-data tables -- creating, loading, and tuning them.
As a consequence of inherent problems stemming from the limitations of conventional relational databases, including the burdensome task of managing the ever-growing complexity and numbers of tables, vendors are being forced to hire increasing numbers of database administrators to rely upon a variety of workarounds as well.
As an example, for lack of better alternatives, many enterprises are being forced to embrace Hadoop, an open-source program inspired by Google's MapReduce. These are brutal, desperate attempts to gain control over mushrooming volumes of unstructured data or so-called "Big Data." It is a very painful and expensive process because there is no query language and there are no standards -- everything developed is application-specific. This is a clear indication that conventional relational databases simply can't cope with Big Data, and the industry is desperately looking for new and better tools.
In 1999, Internet pioneer Tim Berners-Lee together with the World Wide Web Consortium (W3C) unveiled the first Resource Description Framework (RDF) standard -- a radically new data model that was conceived as a way of facilitating access to any information available via the Web -- independently of its format. Since its inception, the U.S. government has been a leader in fostering development of the new tools required to develop data-management applications based on the RDF standard. As you can well imagine, the U.S. government faces huge obstacles when combating its overwhelming amounts of unstructured data.
Look no further than the U.S. intelligence community that must integrate information feeds from all over the world in a variety of disparate formats. RDF technology is also known as "triplestore" technology because the RDF data model is comprised of exactly three resource identifiers; this emerging technology is still in its infancy that many believe will ultimately replace relational database technology.
Relational Data Model vs. Triplestore Data Model
The relational data model was a breakthrough when it was conceived over 40 years ago. It provided conceptual means to manipulate data (e.g., sales transactions) retrieved from a computer database. When application performance became a problem (which happened frequently), its relational-data tables and queries were restructured, more server hardware was added, or both. Unfortunately, because it was often difficult or impossible to design a single database to handle multiple applications with acceptable performance, this application dependence led to rampant data "silos" with different table and query structures. As no thought was given to managing unstructured data when the relational data model was conceived, the relational data model was not designed to accommodate unstructured data and, to no one's surprise, it has proven to be highly ineffective for that task.
Unlike the relational data model which forces all data to be pre-structured into a two-dimensional, row-and-column tabular format, the triplestore data model was designed to embrace any logical data format. Thus, the triplestore data model was the first universal conceptual data model to be developed. By virtue of the W3C Consortium, the RDF became a worldwide standard in 1999. Although it has taken 12 years for it to begin to be employed in commercial data-management applications, and few companies are currently using it for commercial applications, the U.S. Department of Defense has decreed that, in the future, all of its data-management applications will be implemented using triplestore technology.
The triplestore data model is a vastly different data model than the relational data model with which database professionals have become so familiar. Decades of time and investment have made people slow to accept the fact that relational databases are not able to do all the things they would like them to do. Sometimes it takes, and unfortunately in this case it has taken, a long time for people to adjust to the realities. A typical enterprise is not going to go too far out on a limb for a technology that isn't embraced by major suppliers such as IBM, Oracle, and Microsoft.
Oracle does have a triplestore database product, but perhaps more promising is IBM's Watson system, an artificial intelligence system capable of answering questions posed in natural language. Many wouldn't know that Watson depends on triplestore technology for its predictive analytics capabilities. Enterprises are now beginning to develop commercial applications with triplestore technology. In IBM's case, it evidently believes that vertical applications such as financial analysis, evidence-based medicine, and government intelligence represent huge new business opportunities for its Watson systems -- i.e., for applications requiring triplestore databases.
Historically, those who came up the curve most rapidly on triplestore technology were people from the artificial intelligence (AI) community. The affinity between AI and triplestore technology is that triplestore technology enables people to make logical assertions and draw inferences from data -- which, of course, is what AI is all about. Triplestore technology gives enterprises a way to manage different types of data and structures andit enables them to draw inferences from the data. IBM is doing precisely that with its Watson systems thanks to a layer of predictive mathematics on top of a triplestore database.
Algebra: The Missing Link
What still is needed to enhance triplestore databases is a technology that can effortlessly handle management of unstructured data and query large amounts of data at greater speeds aswell as perform logical inferencing, the process of deriving logical conclusions from premises known or assumed to be true.
Mathematics is the key to unifying data management across different data structures. By using advanced algebra to define and manipulate the relationships between data in disparate formats, the mathematical approach eliminates the time-consuming maintenance and performance problems associated with pre-structuring, importing, cataloging, indexing, and storing data in relational-data tables. As the mathematical approach is completely compatible with the relational data model as well, it enables simultaneous access to both structured and unstructured data and provides commercial enterprises with a non-disruptive path forward.
Analyzing enormous and rapidly increasing volumes of data from different sources in different formats in time to make a difference in business operations, is practically impossible using conventional relational databases. Consequently, as data is collected over time, the gap between the amount of data collected and the amount of data that can be effectively analyzed continues to increase.
Although relational databases will continue to be used for high-speed online transaction processing, conventional relational databases have clearly exhausted their usefulness for business analytics. We're now on the precipice of a major breakthrough in enterprise data management, and advanced algebra will be what pushes analytics across the Big Data frontier.
Charles Silver is the CEO of Algebraix Data Corp., which provides mathematically based data-management technology across the entire spectrum of computer data-management applications. He has more than 25 years of experience as a successful entrepreneur and can be contacted at csilver@algebraixdata.com. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,910 |
\section{Introduction}
The ordering and recurrent structures of sequential data in many applications, ranging from robotics and finance to speech and biology, usually carry crucial information. The neural networks based approaches \citep{hochreiter1997long} deal with sequences by costly training on all input-output pairs, thus face obstacles in meta-learning tasks \citep{finn2017meta}. In addition, these models barely capture the propagating uncertainty across time. On the other hand, Gaussian Processes (GPs) \citep{williams2006_GPML}, as a Bayesian nonparametric approach, can model uncertainty flexibly by inferring the distribution over functions; however, it suffers from a high computational burden.
For real-world applications in robotics and autonomous vehicles that involve human interactions, it is essential to efficiently capture not only the representations of underlying temporal dynamics but also the propagating uncertainty from an agent.
Neural Processes (NPs)\citep{garnelo2018conditional,garnelo2018NP} approximate a stochastic process by modelling a distribution over regression functions with prediction complexity linear in the size of observed context set \citep{garnelo2018conditional}.
NPs estimate an order invariant predictive distribution of \textit{target} output conditioned on \textit{context} input-output pairs of arbitrary size.
NPs display some of the fundamental properties and capabilities of GPs, but have the weakness of underfitting. Attentive Neural Process (ANP) addressed this drawback by learning the relevant information among contexts and targets via attention mechanisms \citep{kim2019attentive}. As a generalization of NPs, ANP models a stochastic process leveraging on both uncertainty-awareness as Bayesian models and computation efficiency inherited from neural networks.
Recurrent models with long short-term memory (LSTM) \citep{hochreiter1997long} have been the leading approach for sequential structure modelling at present.
The LSTM is an efficient gradient-based method for training recurrent networks, which improves the learning process by stabilizing the flow of the back-propagated errors. It defines the state-of-the-art performance on sequential tasks such as speech and text data \citep{graves2013speech_lstm, sutskever2014sequence_text}. \par
In spite of the aforementioned appealing properties, neither NPs nor LSTM models could be solely utilized to properly learn the recurrent structures and propagating uncertainty in temporally ordered sequences. Moreover, given the fact that most real-world engineering problems involve temporal dynamics that controlled by underlining continuous functions (e.g., Partial Differential Equation (PDE) with time derivatives), the uncertainty also reveals important information such as human factor. It is essential to efficiently capture both the uncertainty and temporal order \citep{al2016gplstm}. While several models are proposed based on state-space models \citep{doerr2018PRSSM}, recurrent neural networks \citep{al2016gplstm}, and Gaussian Processes \citep{wilson2011GP_reg_net}, learning from sequential data remains to be an area of active research.
In this paper, we introduce Recurrent Attentive Neural Process (RANP), or alternatively, Attentive Neural Process Recurrent Neural Network (ANP-RNN) in order to better model continuous sequential data in real-world applications. The proposed ANP-RNN incorporates RNNs into ANP explicitly, thus can capture both the ordering sequential information as well as the propagating uncertainty.
Benefited by the meta-learning framework of NPs, ANP-RNN learns a stochastic process efficiently from limited observations for multiple tasks. At the same time, it captures the ordering and recurrent features from observed sequences as well.
We demonstrate the effectiveness of ANP-RNN with a 1D function regression task on synthetic data. We further demonstrate that ANP-RNN outperforms NPs, ANP, and LSTMs in trajectory prediction tasks for self-driving applications in terms of accuracy and expressiveness.
\begin{figure*}[t!]
\centering
\includegraphics[width=0.95\linewidth]{first_cherry.png}
\caption{The comparison of predictions given by a fully trained NP, ANP and ANP-RNN in 1D function regression. The contexts (large dots) are used to predict the target outputs ($y$-values of all $x \in [-4,4]$). It is noticeably that the RANP predictions capture both local behaviors from contexts and the global distribution, whereas NP only keeps the global shape of the function and ANP trends to be influenced by contexts dramatically.}
\label{fig_first_cherry}
\end{figure*}
\section{Background}
\label{background}
\paragraph{Attentive Neural Processes (ANPs)} The NP is a model for stochastic process realizations that maps an input $X \in \mathbb{R}^{d_x}$ to an output random variable $Y \in \mathbb{R}^{d_y}$. Specifically, NP is defined as a (infinite) family of conditional distributions, in which an arbitrary number of observed \textit{contexts} $(X_C, Y_C):= (x_i, y_i)_{i \in C}$ is used to model an arbitrary number of \textit{targets} $(X_T, Y_T):=(x_i, y_i)_{i \in T}$. Where $C$ depicts a set of $n$ \text{context} points and $T$ describes $m$ unobserved points. The generative process can be written as:
\begin{equation}
P(Y_T|X_T, X_C, Y_C) := \int p(Y_T | X_T, r^*_C, z)q(z | s_C) dz
\end{equation}
where $z$ is a global latent variable describing uncertainty in the predictions of $Y_T$ for a given observation $(X_C,Y_C)$, and is modelled by a factorized Gaussian parameterized by $s_C := s(X_C, Y_C)$, with $s$ being a MLP encoder which represents the \textit{context} $(X_C, Y_C)$ with permutation invariance.
Meanwhile, deterministic function $r^*_C$ aggregates \textit{contexts} by taking the mean of pair-wise \textit{context} representations in NPs. When in ANP, each target query $X_T$ attends to context by $r^*_C:=r^*(X_C,Y_C,X_T)$ to form query-specific representations. In particular, each context $(x,y)$ pair is passed through an multilayer perceptron (MLP) encoder followed by self-attention layers to form a pair-wise representations $r_i$, and these are processed in \textit{cross-attention} layers with $X_T$ attended. Under this setting, the global structure of the stochastic process realization is preserved since $z$ induces correlations in the marginal distribution of predictions $Y_T$ in the latent path, where as the fine-grained local structure is captured by the deterministic path. \par
The model parameters are learned via variational approximation by maximizing the following ELBO
\begin{equation}
\log p(Y_T|X_T, X_C,Y_C) \geq \mathbb{E}_{q(z|s_T)}[\log p(Y_T|X_T,r^*_C,z)] - D_{KL}(q(z|s_T) || q(z|s_C))
\end{equation}
using reparameterization trick \citep{kingma2013_AEVB}.
Note that since the conditional prior $p(z|s_T)$ is intractable, the variational posterior $q(z|s_T)$ is used for approximation, as the KL regularization term aligns the summary of \textit{contexts} and \textit{targets} closer to each other. It also reveals the underlying principle of ANPs who learns to infer the \textit{target} stochastic process by assuming that contexts and targets come from the same realization of the data-generating stochastic process, especially when targets contain contexts.
\par
\paragraph{Recurrent Neural Networks and LSTM} Long Short-Term Memory (LSTM) \citep{hochreiter1997long} is a special form of Recurrent Neural Networks (RNNs) and is one of the most successful ways to exploit sequential information of the data. LSTM places a \textit{memory cell} into each hidden unit and uses a few gate vectors to control the passing of information along the sequence, therefore improve the long-range dependencies and overcome the vanishing gradients problem in RNNs.
The gating mechanism not only improves the flow of errors through time, but also make the network be capable of decide whether to keep, erase, or overwrite memorized information, and therefore increase stability to the network's memory.
\begin{figure*}[t!]
\centering
\includegraphics[width=0.95\linewidth]{anp_lstm_graphical_model.png}
\caption{Graphical models of related models and of the ANP-LSTM. Gray shading indicates the observed variables. \textit{C} depicts context variables and \textit{T} for target variables to predict. The diamonds depict deterministic variables.}
\label{fig_graphical_model}
\end{figure*}
\section{Recurrent Attentive Neural Process}
\label{headings}
In this section, we proposed Attentive Neural Process - Recurrent Neural Network (ANP-RNN) in order to capture ordering and recurrent structures for modeling sequential data. The main idea is to combine the merits of RNNs and ANP.
\begin{figure*}[t!]
\centering
\includegraphics[width=\linewidth]{np_lstm.png}
\caption{Model architecture of ANP-RNN }
\label{fig_architecture}
\end{figure*}
\subsection{Model Construction}
We incorporate ANPs with recurrent structure by using an LSTM network to transform the original input space in which the generating stochastic process is modeled, as shown in Figure \ref{fig_architecture}. \par
The sequences of inputs are formally denoted as vectors of measurements $\Bar{x}_1 = [x^1]$, $\Bar{x}_2 = [x^1, x^2],...,\Bar{x}_n=[x^1,x^2,...,x^n]$, $x^t \in \mathcal{X}$, and the length of the sequences $\Bar{x}_n$ would grows. The collection of corresponding real-valued target vectors is $y = \{y_i\}^n_{i=1}$, where $y_i \in \mathbb{R}^d$. It is assumed that only the most recent $L$ steps of a sequence contribute to the prediction of the targets, and the sequences can be written as $\Bar{x}_i = [x^{i-L+1},x^{i-L+2},...,x^i],i=1,...,n$. Our goal is to model the distribution of functions (realization of stochastic process) $f: \mathcal{X}^L \mapsto \mathbb{R}^d$, which are assumed to be generated from a stochastic process, conditioned on observation data.
Here we first convert an input sequence $\Bar{x}_i$ to a latent representation $h_i \in \mathcal{H}$, and then learn the distribution of realizations that map $h_i$ to $y_i$. Since recurrent models are one of the most promising ways to exploit sequential structure of data. The mapping $f: \mathcal{X}^L \mapsto \mathbb{R}^d$ is represented by recurrent model as
\begin{equation}
\begin{split}
&y_i = \psi(h_i) + \epsilon^t \\
&h^t_i = \phi(h^{t-1}_i, x^{i-L+t}) + \delta^t \text{ , }t=1,...,L
\end{split}
\end{equation}
Let the recurrent model $\phi: \mathcal{X}^L \mapsto \mathcal{H}$ be the transformation mapping $\{ \Bar{x}_i \}^n_{i=1}$ to $\{h_i \}^n_{i=1}$, thus the sequential structure in $\{ \Bar{x}_i \}^n_{i=1}$ is integrated into the corresponding latent representations. Subsequently, the ANP is utilized to learn the condition distributions, where the transformed future targets information $(H_T(X), Y_T):=(H_i,Y_i)_{i\in T}=(\Phi(X_i),Y_i)_{i\in T}$ is modelled conditioned on the transformed information of past observed contexts $(H_C(X), Y_C):=(H_i,Y_i)_{i \in C}=(\Phi(X_i),Y_i)_{i \in C}$, in which we certainly have $C \subset T $ from the instinct of time series. Therefore, those conditional distributions are expressed as:
\begin{equation}
p(Y_T | X_T, X_C, Y_C):= \int p(Y_T|H_T, H_C,Y_C,r^*_C,z)q(z|H_C,Y_C) d z
\end{equation}
Here, the mapping from observed inputs to targets vectors is modelled as a stochastic process in a deterministic transferred space. The fact that ANPs treat samples as multiple realizations of a stochastic process enables our proposed model to enlighten the underlying ordering dynamics of sequential data.
\subsection{Learning and Inference}
We train the model using the evidence lower bound (ELBO) of the conditional log likelihood of $Y_T$ as follows
\begin{equation}
\log p(Y_T|X_T, X_C,Y_C) \geq \mathbb{E}_{q(z|s_T)}[\log p(Y_T|X_T,r^*_C,z)] - D_{KL}(q(z|s_T) || q(z|s_C))
\end{equation}
The inference is as follows. First, the input sequences $\{ \bar{x}_i\}^n_{i=1} \in \mathcal{X}^n$ is mapped into representations $\{ h_i\}^n_{i=1} \in \mathcal{H}^n$ using LSTM cells. For notation simplification, we denote $H_C=\Phi (X_C)$ and $H_T=\Phi (X_T)$. Then we can derive the lower bound as \citep{kim2019attentive}
\begin{equation}
\begin{split}
&\log\ p(Y_T|X_T,X_C,Y_C) \geq \\
& \mathbb{E}_{q(z|H_T,Y_T,H_C,Y_C)}[log\ p(Y_T|z,H_T,H_C,Y_C)+ \log\frac{q(z|H_C,Y_C)}{q(z|H_T,Y_T,H_C,Y_C)}]
\end{split}
\end{equation}
where $q(z|H_T,Y_T,H_C,Y_C)$ is represented in latent path as $q(z|s_T)$ and $q(z|H_C,Y_C)$ is represented as $q(z|s_C)$ with MLPs as shown in the graph above.
So we can rewrite the equation as
\begin{equation}
\begin{split}
\log\ p(Y_T|X_T,X_C,Y_C) &\geq \mathbb{E}_{q(z|s_T)}[\log\ p(Y_T|z,H_T,H_C,Y_C)+\log\frac{q(z|s_C)}{q(z|s_T)}]\\
&=\mathbb{E}_{q(z|s_T)}[\log\ p(Y_T|z,H_T,H_C,Y_C)]-D_{KL}(q(z|s_T)||q(z|s_C))
\end{split}
\end{equation}
Finally, we apply the deterministic path representation $r_C^*$ into the equation with $r_C^*:=r(H_C,Y_C)$ containing the information of $H_C$ and $Y_C$ and then get
\begin{equation}
\log\ p(Y_T|X_T,X_C,Y_C) \geq \mathbb{E}_{q(z|s_T)}[\log p(Y_T|H_T,r^*_C,z)] - D_{KL}(q(z|s_T) || q(z|s_C))
\end{equation}
Our model is constructed as simple as possible, meanwhile it is able to represent and quantify \textit{predictive uncertainty} in sequential data. This is achieved by: (1) First, the input sequence is transferred into a latent space by a deterministic LSTM network; (2) Second, the distribution over the functions that map latent sequences to outputs is learned via an ANP. The learning and inference of ANP-RNN/LSTM model is completely achieved by a probabilistic treatment. Thus, the parameters of our proposed model are learned by minimizing negative log-likelihood (NLL), and the prediction are expressed as finding the distribution of targets conditioned on observed contexts.
\par
\section{Related Works}
\label{others}
Recently, there has been a increasing interest in learning and inferring stochastic processes with neural networks. Condition Neural Processes (CNPs) \citep{garnelo2018conditional} model a stochastic process but lack a latent variable for global sampling. Neural Processes (NPs) \citep{garnelo2018NP} models the global uncertainty by introducing an explicit latent path. \citet{kim2019attentive} solved the under-fitting problem and improved the prediction accuracy of NPs by incorporating cross-attention into a latent path. Sequential Neural Processes (SNPs) \citep{singh2019snp} were proposed for modeling non-stationary stochastic process for 4D scene inference with Generative Query Networks (GQN). The Functional Neural Process (FNPs) \citep{louizos2019_FNP} learn the distribution of a function by building a graph of dependencies among local latent variables.
Generative Query Networks (GQNs) \citep{eslami2018_GQN,kumar2018_CGQN} model the prediction that renders a frame of scene conditioned on a viewpoint, and are regarded as a special case of NPs where $x$ are viewpoints and $y$ are frames.
\par
Learning from stochastic temporal sequence has been long regarded as a critical problem in the control and dynamical system literature. \textit{State-space models} (SSM) and generative \textit{autoregressive models} are usually applied to describe stochastic temporal processes \citep{van2012SSM_AR}. In the deep stochastic SSM domain, when \citet{chung2015VRNN} added an auto-regressive mechanism to the latent, Deep Kalman Filters (DKF) \citep{krishnan2016DKF} and Deep Variational Bayes Filters (DVBF) \citep{karl2016DVBF} adopted Markovian state transition models for latent states and emission models for observations respectively. Similarly, the above connections can be incorporated into either RNN or Stochastic RNN \citep{biswas2018SRNN}. Recurrent SSM have also been proposed \citep{doerr2018PRSSM} for learning long-term dependencies. Another approach to learn the latent topics in the sequence is developed by combining LSTM with a latent topic model \citep{jo2017_LDA_LSTM} or statistic. Other variants and inference approximations related to modeling stochastic sequences are proposed by \citet{fraccaro2017VAE_LG_SSM} and \citet{krishnan2017NSSM}. In addition, \citet{gemici2017memory_trans} and \citet{fraccaro2018generative_tempoal_model} attach a memory to transition models in order to capture the long-term nonlinear dependencies.
Gaussian Processes (GPs) \citep{williams2006_GPML} are also prevalent in time series modeling. GP-based SSM \citep{eleftheriadis2017_GP_SSM, wang2006_gp_ssm} are introduced in which GPs are adoped as either transition or observation functions. Recurrent GP \citep{mattos2015_RGP} extends the GP-SSM models by applying a recurrent architecture with GP-basd activation functions, however, this model suffers from a sophisticated approximation procedure. Furthermore, GP-LSTM \citep{al2016gplstm} was developed to learn GP kernels with recurrent structure, in which the kernels are learnt via joint optimization for deep networks \citep{wilson2016deepkernellearning, wilson2016stochastic_dkl} and dropout in order to pursue flexibility and scalability \citep{wilson2015_massive_gp}. \par
The most recent related work to our proposed model is GP-LSTM\citep{al2016gplstm}, in which the rare input is embedded by a recurrent neural network for a Gaussian Process regression. However, the sophisticated semi-stochastic block-gradient optimization procedure of GP-LSTM limits its usage. ANP-RNN/LSTM shares a similar philosophy with the GP-LSTM and can learn and predict efficiently due to the neural network structure inherited from NPs. The SNP mentioned above is capable of modeling a non-stationary stochastic process, whereas ANP-RNN/LSTM learns the distribution of a stochastic process by best utilizing the ordering and recurrent information in an observed continues sequence. Moreover, the SNP enhance the latent state $z_t$ by a recurrent structure, while ANP-RNN/LSTM preserves the global latent $z$, as well as the local representation $r^*$, and therefore can better capture the long and short term dependencies in the ordering of a time sequence.
\section{Experiments}
Since the ANP-RNN learns the stochastic process and is trained on multiple realizations of a stochastic process. At each training iteration, a batch of realizations is drawn from the data generating stochastic process. In order to investigate the ANP-RNN's ability to predict temporal dynamics, with the $x$ axis treated as time index, a sequence of these realizations are selected as contexts and targets.
The same decoder architecture is used for all experiments, and 8 heads are used for \textit{multihead} attention.
\begin{figure*}[t!]
\centering
\includegraphics[width=1.0\linewidth]{1D_regression.png}
\caption{Quantitative comparison between NP, ANP and ANP-LSTM for 1D function regression with random GP kernel hyperparameters. \textbf{Left:} Negative log-likelihood (NLL) for target points given contexts against training iterations for different model settings. \textbf{Right:} Sample predictive mean and variance conditioned on the same context from NP, ANP and ANP-LSTM of different attention mechanisms at iteration $t=400$. The true underlying function is shown in slim black dashed lines while the observed contexts are thick black lines. Best viewed in color.}
\label{1D_regression}
\end{figure*}
\paragraph{1D Function regression on synthetic stochastic process} The ANP-RNN/LSTM is first tested on data generated from a synthetic stochastic process. In order to illustrate ANP-RNN/LSTM's ability to predict ordered sequences, we construct the stochastic process by adding a Sine function to a Gaussian Process with a squared-exponential kernel and small likelihood noise, rather than just using data from a Gaussian Process. At each iteration, a sequence with fixed length and increment ($X = \{x_i\}^{50}_{i=1},x_{n}=x_0+0.1 \times n$) is chosen from the entire function domain $(\forall n, x_n \in [-4, 4])$ to serve as both contexts and targets. Although NP, ANP, and ANP-RNN/LSTM are all able to make a prediction from permutation invariance contexts\citep{garnelo2018conditional,kim2019attentive}, it is more straightforward to use ordered observations to predict a time series in real-world situations. Here only the cross-attention in the deterministic path is used for ANP and ANP-RNN/LSTM, and we use the same encoder/decoder architecture for NP, ANP, and ANP-RNN/LSTM except for the cross-attention.
\begin{figure}[t!]
\centering
\subfloat[Point-wise predictions of the ego-vehicle trajectory by Neural Process (NP) ]{\includegraphics[width=0.95\linewidth]{trajectories_np.png}%
\label{fig2a}}
\hfil
\subfloat[Point-wise prediction of the ego-vehicle trajectory by Attentive Neural Process (ANP)]{\includegraphics[width=0.95\linewidth]{trajectories_anp.png}%
\label{fig2b}}
\hfil
\subfloat[Point-wise prediction of the ego-vehicle trajectory by LSTM]{\includegraphics[width=0.95\linewidth]{trajectories_lstm.png}%
\label{fig2c}}
\hfil
\subfloat[Point-wise prediction of the ego-vehicle trajectory by ANP-LSTM ]{\includegraphics[width=0.9\linewidth]{trajectories_anplstm.png}%
\label{fig2d}}
\caption{Qualitative comparison of the NP, ANP, LSTM and ANP-LSTM predictions of the lane-changing behavior of autonomous vesicles. Slim dashed lines correspond to the ground truth, blue lines correspond to predictive mean and light blue area depicts the point-wise variance.}
\label{fig_lane_change}
\end{figure}
Figure \ref{1D_regression} (left) gives negative log-likelihood (NLL) of targets conditioned on giving contents $\frac{1}{|T|}\sum_{i \in T} \mathrm{E}_{q(z|S_C)[\log p(y_i|x_i, r ,z)]}$ for different models trained on a synthetic time series stochastic process. ANP-RNN/LSTM displays a more rapid decrease in NLL compared to (A)NP models, especially for the former with multi-head attention. More qualitative results are provided in Appendix A to demonstrate the performance of different models at different time step. Meanwhile, it can be seen that the multi-head attention mechanism performs better than Laplace attention. In Figure \ref{1D_regression} (right), the learned conditional distributions are shown for a qualitative comparison between different models with different attention mechanisms. The predictive mean of both the NP and ANP with multi-head attention underfits the context. NP attempts to capture the global information of data however results in learning a large likelihood noise, while ANP is sensitive to local dynamics in the data and trends to overfiting certain area. Both ANP-RNN/LSTM with Laplace and multi-head attention mechanism appear to give a good reconstruction of the contexts as well as prediction of contexts.
Laplace attention is parameter-free (keys and queries are x-coordinates) while the multi-head attention \citep{vaswani2017multihead_attention} makes the query to attend to different keys and thus give smoother query-values \citep{kim2019attentive}. As expected, ANP-RNN/LSTM with multi-head attention gives the best prediction by capture the underlying structure of the synthetic stochastic process.
\paragraph{Autonomous driving traffic scenarios}
In this section the ANP-LSTM is applied to an autonomous driving application along with, Neural Processes (NPs), Attentive Neural Processes (ANPs) and a plain LSTM. We look into the NGSIM dataset and specifically look for lane changing behaviors. In each lane changing scenarios, the target car is going to change its lane in the coming seconds and our goal is to predict its trajectory given the information of its surrounding vehicles. The trajectory of the target vehicle is regarded as a collection of real-value vectors $\mathbf{y}=\{ \mathbf{y_t} \}^n_{t=1} $, $\mathbf{y_t} \in \mathbb{R}^d$, where $n$ is the length of trajectory. The sequence of all surrounding vehicle positions are depicted as vectors of measurements $\boldsymbol{\bar{x}_1} = [\boldsymbol{x^1}] \text{ , } \boldsymbol{\bar{x}_2} = [\boldsymbol{x^1}, \boldsymbol{x^2}], \dots, \boldsymbol{\bar{x}_n} = [\boldsymbol{x^1}, \boldsymbol{x^2}, \dots,\boldsymbol{x^n}]$. Assuming only the most recent $L$ steps of surrounding vehicle positions carries crucial information for predicting target vehicle trajectory, and let $\boldsymbol{\bar{X}} = \{ {\boldsymbol{\bar{x}_t}} \}^n_{t=1}$ be a collection sequences $\boldsymbol{\bar{x}_i} = [\boldsymbol{x^{i-L+1}}, \boldsymbol{x^{i-L+2}},...,\boldsymbol{x^{i-L+L}}]$ with corresponding length $L$, where $\boldsymbol{x}^i \in \mathcal{X}$. Therefore, we can model and infer the trajectory of interactive vehicle lane changing by model the distribution of a mapping $f:\mathcal{X} \mapsto \mathbb{R}^d$. The difficulty of this tasks lays in the extremely complicated interaction between the target vehicle and surrounding vehicles. Considering that the longitudinal and lateral vehicle dynamics are usually treated separately\citep{rajamani2011_vehicle_dynamics}, our model is trained to predict the two longitudinal and lateral trajectory separately and then jointly predict the positions per frame of the target vehicle.
As attentive neural processes adopts a loss in the form of an approximation of Negative Log-likelihood (NLL), a normal distribution over our target position is given each frame instead of merely a mean prediction. From the Figure \ref{fig_lane_change} we can see that NP, ANP and LSTM cannot capture the hidden structure of the stochastic process and give poor predictions. NP and ANP tend to assign huge standard deviation because of the immense uncertainty of prediction. Thus, the trajectory distribution mean is far from the ground truth. LSTM, as it only predicts a single estimate using mean squared error (MSE), always falls into a local optimum which fails to capture the movement of the vehicle. As for ANP-LSTM, the predicted distribution captures the ground truth closely, indicates that our proposed ANP-LSTM(RNN) is capable of learning and predicting complicated sequential data.
the LSTM part models the time series information into the ANP and then the ANP infers the trajectory using the context information to get quite close prediction curves and velocity fields.
\begin{table}[t]
\centering
\begin{tabular}[b]{llllllll}
\toprule
\cmidrule(r){1-2}
& \text{ }
& 1s
& 2s
& 3s
& 4s
& MSE
& NLL\\
\midrule
\multirow{2}{*}{LSTM} & $\mu$ & 0.286 & -0.330 & -0.588 & -0.776 & 1.4500 & ---\\
& $\sigma$ & --- & --- & --- & --- & --- &--- \\[0.2cm]
\multirow{2}*{NP} & $\mu$ & --- & --- & --- & --- & 92778 & 203882 \\
& $\sigma$ & --- & --- & --- & --- & --- & ---\\[0.2cm]
\multirow{2}*{ANP} & $\mu$ & --- & --- & --- & --- & 7024.45 & 353693\\
& $\sigma$ & --- & --- & --- & --- & --- & --- \\[0.2cm]
\multirow{2}*{ANP-LSTM} & $\mu$ & \textbf{0.020} & \textbf{0.109} & \textbf{0.130} & \textbf{0.203} & \textbf{0.1673} & \textbf{-0.0229} \\
& $\sigma$ & \textbf{0.235} & \textbf{0.276} & \textbf{0.307} & \textbf{0.332} & --- & --- \\
\bottomrule
\end{tabular}
\caption{Absolute Mean Errors and Standard Deviation of the Trajectory Prediction Compared with the Ground-True $\boldsymbol{h}$ in the Lateral Direction. The Unit is in Meters except for the negative log likelihood (NLL). The predictive $\mu$ and $\sigma$ of NP and ANP are omitted since they completely failed model the target vehicle trajectory. }
\label{sample-table}
\end{table}
\section{Conclusion}
In this paper, Recurrent Attentive Neural Process, or alternatively, ANP-RNN is proposed to model a stochastic process from ordered sequential data. It is demonstrated that this model outperforms NPs, ANPS and LSTM models in terms of accuracy, NLL and qualitative comparison. The ANP-RNN expands the capability of Neural Processes based approaches of learning real-word time series. There exists a large scope of future research for ANP-RNN. Whereas \citet{singh2019snp} added a recurrent in the latent of Neural Process for capture non-stationary dynamics of a stochastic process, their structure could be combined with ANP-RNN in order to better model the complex sequential data from real-world scenarios. Last but the not least, the modest incorporation of NPs and LSTM models makes ANP-RNN open to different variants of recurrent neural networks \citep{oliva2017statisticalRNN} and neural process \citep{singh2019snp,louizos2019_FNP}, and thus bless ANP-RNN with huge potential to solve real-world problems.
\bibliographystyle{plainnat}
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"redpajama_set_name": "RedPajamaArXiv"
} | 1,183 |
Q: Algorithm : Find the least wastage in cutting the Trees? You are given n Trees with their heights in an array.
and you are given a value k units , that much wood you need to collect.
You can have an axe of any height you want but you can use only 1 axe when you choose.
tell the most optimum height of axe you should use and which trees you will cut so that you get the minimum wastage.
if you cut a tree of height H with an axe of height X.
If H>X you get H-X wood
else 0 wood
I tries this problem but i am not able to think apart from brute-force which is pretty bad complexity.
UPDATE to queries below
:-
If the axe height is 0 it is not ncessary that there will be 0 wastage
say the tree heights are 2,4 and k is 5. I hope this makes the query clear.
In the above case the height of axe is 0 and i need to cut 2 trees to obtain 5 units of wood.
and the wastage will be 1 units which we have to minimise and it is minimum here
There is no need of other parameters like force or anything else
A: Subset sum, an NP-complete problem, is reducible to the problem of selecting the best set of trees for a given axe height. That portion of your problem is NP-hard, and the best known algorithms have exponential complexity.
A: [EDIT 12/9/2013: Fixed formula in last sentence!]
It is always possible to choose an axe height such that chopping all trees above this height will result in zero waste.
To see this, just sort the trees in descending order of height, and consider moving the axe height gradually down from the top of the tallest tree. Suppose the tallest tree has height h. Notice that the function
f(x) = total amount of wood cut by using an axe of height h - x to
chop all trees of at least this height
starts at 0 when x = 0, and is an increasing piecewise linear function of x, with no discontinuities. Every time x increases past the point when one or more trees just start to become choppable, the rate of change of f(x) increases, but this doesn't cause problems. So for any desired level of wood y, just (conceptually) intersect a horizontal line of height y with the graph f(x), and drop a vertical line from this point down to the x axis to find its value. (How to actually do this in a program I leave as an exercise, but here's a hint: consider trees in decreasing height order to find the pair of adjacent x values x1, x2 such that chopping at h - x1 produces too little wood, and h - x2 produces too much.)
A: seems like eko question of spoj...
1)sort the height of the trees.
2)subtract the a[i](greater height)-a[j](lesser height tree) multipled by the total tree considered till yet to be cut...
for more detail how to work look through the code of
#define gu getchar();
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
inline int scan()
{
int n=0;
char ch=gu;
while(ch<48){ch=gu;}
while(ch>47){n=(n<<3)+(n<<1)+ch-'0';ch=gu;}
return n;
}
bool dec(ll i,ll j)
{
return (i>j);
}
ll a[1000000]={0};
int main()
{
int n,i;
ll l,m;
scanf("%d %lld",&n,&m);
for(int i=0;i<n;i++)
scanf("%lld",a+i);
sort(a,a+n,greater<ll>());
//for(int i=0;i<n;i++)
// printf("%lld ",a[i]);
ll k=a[0];
for(i=1;i<n;i++)
{
//printf("*%lld ",m);
if(a[i]==k)
continue;
if((m-((i)*(k-a[i])))<=0)
{
if((m-((i)*(k-a[i])))==0)
{printf("%d\n",a[i]);break;}
else
{
ll z=(ll)(m/(i+1));
m=m-z*(i);
if(m==0)
{printf("%lld\n",k-z);break;}
if(m-(i+1)<0)
{printf("%lld\n",k-z-1);break;}
}
printf("%lld ",m);
}
m=m-((i)*(k-a[i]));
k=a[i];
}
return 0;
}
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 9,198 |
How to Power the Automotive TFT-LCD Displays Future
With the rapid evolution of driver information technology, we can expect the automobile of the future to be equipped with multiple displays, possibly a dozen per car or even more (Fig. 1). These "infotainment" displays will include an instrument cluster, a central information display, mirror replacement displays, and optionally, multiple entertainment displays for the rear seats.
1. The typical smart car will have multiple displays.
While the size and resolution of automotive displays have grown, their electronics have become more complex yet limited in both PCB size and cost. One example of increasing complexity is found in the array of power rails that bias the TFT-LCD (thin-film transistor liquid-crystal display) panel and power its backlight. Another example is the stringent level of diagnostics required for display systems that relay safety-relevant information to the driver.
This article reviews the shortcomings of a typical power-management solution for evolving automotive infotainment clusters. It then provides a solution to the size problem while facilitating the dynamic orchestration of the complex protocol required to operate the display while meeting automotive safety levels.
TFT-LCD Display
The standard display used in automotive systems is the active-matrix color TFT-LCD, which has become ubiquitous due to its high brightness, high resolution, reasonable cost, and demonstrated reliability in the challenging automotive environment. Liquid crystals have the ability to change their transmissivity with applied voltage. Each sub-pixel in an active-matrix TFT-LCD display receives its bias voltage (which sets its transmissivity) through a TFT transistor that acts as a switch. A pixel is made up of three sub-pixels, one for each of the primary colors: red, green, and blue.
Figure 2 shows the main elements of the TFT-LCD display power system. A power-supply (PS) block, TFT_LCD PS, powers the source and gate drivers with all of the power sequencing driven by a microcontroller. The gate drivers are supplied with the voltages VPGVDD and VDGVEE, which are used to switch on and off the TFT switches in each sub-pixel.
2. A TFT-LCD display includes backlighting.
The source driver applies a voltage of between VPOS (+7 V) and VNEG (−7 V) to the sub-pixel (represented electrically by the capacitor, CPIX, and the storage capacitor, CS), thus setting its transmissivity. When the TFT is turned off (VDGVEE = -10V), the pixel retains its charge and "remembers" its transmissivity setting until updated during the next video frame.
To avoid display "burn-in" and improve the lifetime of the liquid crystal material, the crystals of active-matrix LCDs are driven by the inversion method, which alternates the polarity of the voltage applied to the sub-pixel with respect to a common backside electrode (shown as ground in Fig. 3).
3. TFT-LCD pixel voltage rails.
TFT-LCD Voltage Rails
A typical TFT-LCD power IC (Fig. 4) with VIN = 3.3 V generates VPOS (+7 V) with a boost converter and VNEG (−7 V) with an inverter. Two charge pumps generate the positive (VDGVDD) and negative (VDGVEE) gate-drive voltages. The four external diodes necessary for each charge pump are omitted for simplicity here, but they're included in the complete PCB layout (shown in Figure 7) as one pair of dual diodes for VDGVDD (D3, D6 and D7, D9) and one pair for VDGVEE (D5, D6 and D11, D12).
4. TFT-LCD voltage-rail generation.
Since LCDs are not emissive displays, a source of white light is required to render the color image visible. Modern displays use white LEDs (light-emitting diodes) as the light source. The LEDs are placed on one side or on multiple sides of the display and illuminate the display area with the help of diffusors. The LEDsare usually arranged in "strings" that consist of multiple LEDs in series.
Due to the high forward voltage of white LEDs (3 V to 4 V), the total voltage needed to drive each string usually necessitates the use of a boost converter. Multiple strings are used to attain the required total brightness to render the display sunlight-readable. In Figure 5, a typical boost-controller IC drives a matrix of LEDs for the TFT-LCD backlight.
5. LED backlight systems must drive multiple LEDs.
This low-integration solution adopts two separate integrated circuits and related passive components to power the TFT-LCD display and backlight, but this isn't optimal from the perspective of PCB space utilization and for complete control of all voltage rails. In LCD displays, control of all enable inputs of the various power-supply ICs is necessary to attain the desired sequence and timing for the supply rails. Such control in a low-integrated solution requires a lot of GPIO pins on the microcontroller and increases software overhead.
Integrated Solution
Figure 6 shows an integrated solution. Both the TFT-LCD rails and the LED backlight controller are integrated in a single PMIC for tight control and reduced PCB space.
6. TFT-LCD and LED backlight PMIC.
An integrated PMIC solution with a serial control interface can have individual bits to control each of the internal converters, thus freeing up many pins on the microcontroller. This allows for full control of the sequencing of the outputs and the timing between them by using an external microcontroller. Alternatively, the burden on the external microcontroller can be reduced further by providing internal preset sequences.
ASIL-B Compliance
Integration of the I2C communication capability into the PMIC facilitates control and diagnostics. Automotive systems require additional diagnostics to attain safety ratings, e.g., an instrument cluster display that provides safety-relevant information to the driver. Sample diagnostics include:
Overvoltage/undervoltage detection on outputs
Error correction on internal memory if present
Parity bit or CRC (cyclic redundancy check) on any interface for error detection/correction
The inclusion of these functions in a single integrated circuit enables the system to reach the ASIL-B level of integrity more easily.
7. Integrated TFT-LCD and LED backlight PMIC PCB (2.65 cm x 1.3 cm = 3.45 cm2).
TFT-LCD displays are ubiquitous in modern cars and will be even more so in the car of the future. The electronics needed to drive the displays must be reduced to a minimum to limit PCB size and cost. This includes the complex array of power rails that bias the TFT-LCD panel and power its backlight.
We reviewed the shortcomings of a power-management solution with low integration and introduced a single-chip PMIC solution that tightly integrates the various voltage rails and serial communication. This new solution easily performs the required diagnostics to meet stringent ASIL-B safety ratings while reducing the PCB space needed for tight automotive applications. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 5,945 |
{"url":"https:\/\/www.investopedia.com\/articles\/retirement\/08\/borrow-from-401k-loan.asp","text":"The financial media have coined a few pejorative phrases to describe the pitfalls of borrowing money from a 401(k) plan. Some\u2014including financial planning professionals\u2014would even have you believe that taking a loan from a 401(k) plan is an act of robbery committed against your retirement.\n\nBut a 401(k) loan can be appropriate in some situations. Let's take a look at how such a loan could be used sensibly and why it need not spell trouble for your retirement savings.\n\n### Key Takeaways\n\n\u2022 When done for the right reasons, taking a short-term 401(k) loan and paying it back on schedule isn\u2019t necessarily a bad idea.\n\u2022 Reasons to borrow from your 401(k) include speed and convenience, repayment flexibility, cost advantage, and potential benefits to your retirement savings in a down market.\n\u2022 Common arguments against taking a loan include a negative impact on investment performance, tax inefficiency, and that leaving a job with an unpaid loan will have undesirable consequences.\n\u2022 A weak stock market may be one of the best times to take a 401(k) loan.\n\n## When a 401(k) Loan Makes Sense\n\nWhen you must find the cash for a serious short-term liquidity need, a loan from your 401(k) plan probably is one of the first places you should look. Let's define short-term as being roughly a year or less. Let's define \"serious liquidity need\" as a serious one-time demand for funds or a lump-sum cash payment\u2014or, to state the obvious, a major crisis like the coronavirus outbreak that interrupts your regular income flow.\n\nKathryn B. Hauer, MBA, CFP\u00ae, a financial planner with Wilson David Investment Advisors and author of \"Financial Advice for Blue Collar America\" put it this way: \"Let\u2019s face it, in the real world, sometimes people need money. Borrowing from your 401(k) can be financially smarter than taking out a cripplingly high-interest title loan, pawn, or payday loan\u2014or even a more reasonable personal loan. It will cost you less in the long run.\"\n\nWhy is your 401(k) an attractive source for short-term loans? Because it can be the quickest, simplest, lowest-cost way to get the cash you need. Receiving a loan is not a taxable event unless the loan limits and repayment rules are violated, and it has no impact on your credit rating.\n\nAssuming you pay back a short-term loan on schedule, it usually will have little effect on your retirement savings progress. In fact, in some cases, it can even have a positive impact. Let's dig a little deeper to explain why.\n\n## 401(k) Loan Basics\n\nTechnically, 401(k) loans are not true loans, because they do not involve either a lender or an evaluation of your credit history. They are more accurately described as the ability to access a portion of your own retirement plan money\u2014usually up to $50,000 or 50% of the assets, whichever is less\u2014on a tax-free basis.\ufeff\ufeff You then must repay the money you have accessed under rules designed to restore your 401(k) plan to approximately its original state as if the transaction had not occurred. On March 27, 2020, President Trump signed\ufeff\ufeff a$2 trillion coronavirus emergency relief package. It doubled the amount of 401(k) money available as a loan to $100,000. Previously it was$50,000 or 50% of your vested account, whichever is less.\n\nAnother confusing concept in these transactions is the term interest. Any interest charged on the outstanding loan balance is repaid by the participant into the participant's own 401(k) account, so technically, this also is a transfer from one of your pockets to another, not a borrowing expense or loss. As such, the cost of a 401(k) loan on your retirement savings progress can be minimal, neutral, or even positive. But in most cases, it will be less than the cost of paying real interest on a bank or consumer loan.\n\n1:01\n\n## Top 4 Reasons to Borrow From Your 401(k)\n\nThe top four reasons to look to your 401(k) for serious short-term cash needs are:\n\n### 1. Speed and Convenience\n\nIn most 401(k) plans, requesting a loan is quick and easy, requiring no lengthy applications or credit checks. Normally, it does not generate an inquiry against your credit or affect your credit score.\n\nMany 401(k)s allow loan requests to be made with a few clicks on a website, and you can have funds in your hand in a few days, with total privacy. One innovation now being adopted by some plans is a debit card, through which multiple loans can be made instantly in small amounts.\n\n### 2. Repayment Flexibility\n\nAlthough regulations specify a five-year amortizing repayment schedule, for most 401(k) loans, you can repay the plan loan faster with no prepayment penalty.\ufeff\ufeff Most plans allow loan repayment to be made conveniently through payroll deductions\u2014using after-tax dollars, though, not the pre-tax ones funding your plan. Your plan statements show credits to your loan account and your remaining principal balance, just like a regular bank loan statement.\n\nThere is no cost (other than perhaps a modest loan origination or administration fee) to tap your own 401(k) money for short-term liquidity needs. Here's how it usually works:\n\nYou specify the investment account(s) from which you want to borrow money, and those investments are liquidated for the duration of the loan. Therefore, you lose any positive earnings that would have been produced by those investments for a short period. And if the market is down, you are selling these investments more cheaply than at other times. The upside is that you also avoid any further investment losses on this money.\n\nThe cost advantage of a 401(k) loan is the equivalent of the interest rate charged on a comparable consumer loan minus any lost investment earnings on the principal you borrowed. Here is a simple formula:\n\n\ufeff\\begin{aligned} \\text{Cost Advantage} = \\ &\\text{Cost of Consumer Loan Interest} \\ - \\\\ &\\text{Lost Investment Earnings} \\\\ \\end{aligned}\ufeff\n\nLet's say you could take out a bank personal loan or take a cash advance from a credit card at an 8% interest rate. Your 401(k) portfolio is generating a 5% return.\u00a0Your cost advantage for borrowing from the 401(k) plan would be 3% (8 \u2013 5 = 3).\n\nWhenever you can estimate that the cost advantage will be positive, a plan loan can be attractive. Keep in mind that this calculation ignores any tax impact, which can increase the plan loan's advantage because consumer loan interest is repaid with after-tax dollars.\n\n### 4. Retirement Savings Can Benefit\n\nAs you make loan repayments to your 401(k) account, they usually are allocated back into your portfolio's investments. You will repay the account a bit more than you borrowed from it, and the difference is called \"interest.\" The loan produces no (that is to say, neutral) impact on your retirement if any lost investment earnings match the \"interest\" paid in\u2014i.e., earnings opportunities are offset dollar-for-dollar by interest payments.\n\nIf the interest paid exceeds any lost investment earnings, taking a 401(k) loan can actually increase your retirement savings progress. Keep in mind, however, that this will proportionally reduce your personal (non-retirement) savings.\n\n## Stock Market Myths\n\nThe above discussion leads us to address another (erroneous) argument regarding 401(k) loans: by withdrawing funds, you'll drastically impede the performance of your portfolio and the building up of your retirement nest egg. That's not necessarily true. First of all, as noted above, you do repay the funds, and you start doing so fairly soon.\u00a0Given the long-term horizon of most 401(k)s, it's a pretty small (and financially irrelevant) interval.\ufeff\ufeff\n\n### 19%\n\nThe percentage of 401(k) participants with outstanding plan loans in 2016 (latest information), according to a study by the Employee Benefits Research Institute.\ufeff\ufeff\n\nThe other problem with the bad-impact-on-investments reasoning: It tends to assume the same rate of return over the years and\u2014as recent events have made stunningly clear\u2014the stock market doesn't work like that. A growth-oriented portfolio that's weighted toward equities will have ups and downs, especially in the short term.\n\nIf your 401(k) is invested in stocks, the real impact of short-term loans on your retirement progress will depend on the current market environment. The impact should be modestly negative in strong up markets, and it can be neutral, or even positive, in sideways or down markets.\n\nThe grim but good news: The best time to take a loan is when you feel the stock market is vulnerable or weakening, such as during recessions. Coincidentally, many people find that they need funds or to stay liquid during such periods.\n\n## Debunking Myths With Facts\n\nThere are two other common arguments against 401(k) loans: The loans are not tax-efficient and they create enormous headaches when participants can't pay them off before leaving work or retiring. Let's confront these myths with facts:\n\n### Tax Inefficiency\n\nThe claim is that 401(k) loans are tax-inefficient because they must be repaid with after-tax dollars, subjecting loan repayment to double taxation. Only the interest portion of the repayment is subject to such treatment. The media usually fail to note that the cost of double taxation on loan interest is often fairly small, compared with the cost of alternative ways to tap short-term liquidity.\n\nHere is a hypothetical situation that is too often very real: Suppose Jane makes steady retirement savings progress by deferring 7% of her salary into her 401(k). However, she will soon need to tap $10,000 to meet a college tuition bill. She anticipates that she can repay this money from her salary in about a year. She is in a 20% combined federal and state tax bracket. Here are three ways she can tap the cash: \u2022 Borrow from her 401(k) at an \"interest rate\" of 4%. Her cost of double-taxation on the interest is$80 ($10,000 loan x 4% interest x 20% tax rate). \u2022 Borrow from the bank at a real interest rate of 8%. Her interest cost will be$800.\n\n## The Bottom Line\n\nArguments that 401(k) loans \"rob\" or \"raid\" retirement accounts often include two flaws: They assume constantly strong stock market returns in the 401(k) portfolio, and they fail to consider the interest cost of borrowing similar amounts via a bank or other consumer loans (such as racking up credit card balances).\n\nDon't be scared away from a valuable liquidity option embedded in your 401(k) plan. When you lend\u00a0yourself appropriate amounts of money for the right short-term reasons, these transactions can be the simplest, most convenient, and lowest-cost source of cash available. Before taking any loan, you should always have a clear plan in mind for repaying these amounts on schedule or earlier.\n\nMike Loo, an investment advisor representative for\u00a0Trilogy Financial, puts it this way,\u00a0\"While one's circumstances in taking a 401(k) loan may vary, a way to avoid the downsides of taking one in the first place is preemptive. If you are able to take the time to preplan, set financial goals for yourself, and commit to saving some of your money both often and early, you may find that you have the funds available to you in an account other than your 401(k), thereby preventing the need to take a 401(k) loan.\"","date":"2021-01-25 19:35:55","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 1, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.3485070466995239, \"perplexity\": 3628.60869439906}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2021-04\/segments\/1610703644033.96\/warc\/CC-MAIN-20210125185643-20210125215643-00625.warc.gz\"}"} | null | null |
\section{Numerical Methods}
\subsection{The N-Body+SPH code:GASOLINE}
We have used the fully parallel, N-Body+smoothed particle hydrodynamics (SPH)
code GASOLINE to compute the evolution of both the collisionless and
dissipative component in the simulations. A detailed description of the code is available in the literature${\it(S1)}$.
Here we recall its essential features.
GASOLINE computes gravitational forces
using a tree--code${\it(S2)}$ that employs multipole expansions to approximate the gravitational
acceleration on each particle. A tree is built with each node storing
its multipole moments. Each node is recursively divided into smaller
subvolumes until the final leaf nodes are reached. Starting from the
root node and moving level by level toward the leaves of the tree, we
obtain a progressively more detailed representation of the underlying
mass distribution. In calculating the force on a particle, we can
tolerate a cruder representation of the more distant particles leading
to an $O(N \log{N})$ method. Since we only need a crude representation
for distant mass, the concept of ``computational locality'' translates
directly to spatial locality and leads to a natural domain decomposition.
Time integration is carried out using the leapfrog method, which is a
second-order symplectic integrator requiring only one costly force
evaluation per timestep and only one copy of the physical state of the system.
\begin{figure}
\vskip 9.0cm
{\special{psfile="fig3.eps" hscale=60 vscale=60 hoffset=40 voffset=-95}}
\smallskip {\small Figure S1. Rotation curve of the multi-component galaxy model used in the merger
simulation. The different lines represent the contribution of the different component of the galaxy to the total rotation curve (blue line) as indicated in the Figure.}
\end{figure}
SPH is a technique of using particles to integrate
fluid elements representing gas${\it(S3,S4)}$
GASOLINE is fully Lagrangian, spatially and temporally adaptive and efficient
for large $N$. It employs
radiative cooling in the galaxy merger simulation used as a starting point for the refined
simulations presented in this Report. We use a standard cooling
function for a primordial mixture of atomic hydrogen and helium. We shut off radiative
cooling at temperatures below $2 \times 10^{4}$ K that is
about a factor of $2$ higher than the temperature at which atomic radiative
cooling would drop sharply due to the adopted cooling function.
With this choice we take into account non-thermal, turbulent pressure to model
the warm ISM of a real galaxy${\it(S5)}$. Unless strong shocks occur (this will be
the case during the final stage of the merger) the gaseous disk evolves nearly isothermally
since radiative cooling is very efficient at these densities ($< 100$ atoms/cm$^3$) and
temperatures ($10^4$ K), and thus dissipates rapidly the compressional heating resulting
from the non-axisymmetric structures (spiral arms, bars) that soon develop in each
galaxy as a result of self-gravity and the tidal disturbance of the companion.
The cooling rate would increase with the inclusion of metal lines, but ${\it(S31)}$
have shown that the equation of state of gas at these densities is still nearly isothermal
($\gamma \sim 0.9-1.1$) for a range of metallicities (with $\gamma$ being lower for higher
metallicity), supporting the validity of simple choice for the cooling function.
Cooling by metals will surely be important below $10^4$ K, but this would be irrelevant
in our scheme since we have imposed a temperature floor of $2 \times 10^4$ K to account
for non-thermal pressure (see above). The specific internal
energy of the gas is integrated using the asymmetric formulation. With this formulation
the total energy is conserved exactly (unless physical dissipation due to cooling
processes is included) and entropy is closely conserved away from shocks,
which makes it similar to alternative entropy integration approaches${\it(S6)}$.
Dissipation in shocks is modeled using the
quadratic term of the standard Monaghan artificial viscosity${\it(S4)}$.
The Balsara correction term is used to reduce unwanted shear viscosity${\it(S7)}$.
The galaxy merger simulation${\it(S8)}$ includes star formation as well.
The star formation algorithm is such that gas particles in dense, cold Jeans unstable regions and in
convergent flows spawn star particles at a rate proportional to the local dynamical
time${\it(S9,S10)}$. The star formation efficiency was set to $0.1$,
which yields a star formation rate of $1-2 M_{\odot}$/yr for models in isolation that have a
disk gas mass and surface density comparable to those of the Milky Way.
\subsection{The simulations of galaxy mergers}
For the Report we performed a refined calculation of a galaxy merger simulation
between two identical galaxies.
The initial conditions of this and other similar merger simulations are described in a
previous paper${\it(S8)}$.
We employed a multicomponent galaxy model constructed using the technique originally developed
in ${\it(S11,S12)}$, its structural parameters being consistent with the $\Lambda$CDM paradigm for structure formation${\it(S13)}$.
The model comprises a spherical and isotropic Navarro-Frenk-and-White (NFW)
dark matter (DM) halo${\it(S14,S15)}$, an exponential disk, and
a spherical, non-rotating bulge. We adopted parameters
from the Milky Way model A1 of ${\it(S16)}$. Specifically, the DM
halo has a virial mass of $M_{\rm vir}=10^{12} M_{\odot}$, a
concentration parameter of $c=12$, and a dimensionless spin parameter
of $\lambda=0.031$. The mass, thickness and resulting scale length of the disk
are $M_{\rm d}=0.04 M_{\rm vir}$, $z_{0}=0.1 R_{\rm d}$, and $R_{\rm d}=3.5$ kpc,
respectively. The bulge mass and scale radius are $M_{\rm b}=0.008 M_{\rm vir}$
and $a=0.2 R_{\rm d}$, respectively. The DM halo was adiabatically contracted
to respond to the growth of the disk and bulge${\it(S17)}$ resulting
in a model with a central total density slope close to isothermal.
The galaxies are consistent with the stellar mass Tully-Fisher and size-mass relations.
To each of them we add a (softened) particle initially at rest at the center of the bulge
to represent a supermassive black hole (SMBH). We used a SMBH mass equal to
$M_{\rm BH}=2.6 \times 10^{6} M_{\odot}$, consistent with the $M_{BH}-\sigma$ relation${\it(S8)}$.
\begin{figure}
\vskip 9cm
{\special{psfile="fig4.eps" hscale=60 vscale=60 hoffset=40 voffset=-100}}
\smallskip {\small Figure S2. Cumulative gas mass profile (normalized to the total gas
mass) within the inner $100$ pc. Three simulations with $\gamma=7/5$ for three
different values of the gravitational softening are shown, $40$ pc (black solid line),
$10$ pc (red dot-dashed line) and $2$ pc (green dashed line).}
\end{figure}
The gas fraction, $f_{\rm g}$, is 10\% of the total disk mass.
The rotation curve of the model is shown in Figure S1.
Different encounter geometries were explored in the large suite of merger simulations
previously performed and published${\it(S15)}$: prograde or retrograde coplanar mergers
as well as mergers in which one of the disks was inclined with respect to the orbital plane.
The simulation
presented in this Report is the refined version of a coplanar prograde encounter. This
particular choice is by no means special for our purpose, except that the galaxies
merge slightly faster than in the other cases, thus minimizing the computational
time invested in the expensive refined simulation. We note that the existence
of a coherent nuclear disk after the merger is a general result that does not depend
on the details of the initial orbital configuration, including the initial relative inclination
of the two galaxies${\it(S15)}$. Similarly, gas masses and densities
in the nuclear region differ by less than a factor of 2 for runs having the same initial
gas mass fraction in the galaxy disks but different initial orbits.
The galaxies approach each other on parabolic orbits with pericentric distances
that were 20\% of the galaxy's virial radius, typical of cosmological
mergers${\it(S18)}$ . The initial separation of the halo centers was twice
their virial radii and their initial relative velocity was determined from the corresponding
Keplerian orbit of two point masses. Each galaxy consists of $10^5$
stellar disk particles, $10^5$ bulge particles, and $10^6$ DM particles.
The gas component was represented by $10^5$ particles.
We adopted a gravitational softening of $\epsilon = 0.1$ kpc
for both the DM and baryonic particles of the galaxy, and
for its SMBH $\epsilon=0.03$ kpc.
\subsection{The refined simulations of the nuclear region}
\subsubsection{Particle splitting}
In this Report we use the same technique of particle splitting that we have used before to study the formation
of a disk galaxy${\it(S19)}$.
Splitting has been already used to follow supermassive
black holes evolving in spherical gaseous backgrounds${\it(S20)}$ and to model the formation of primordial stars and black holes at high redshift${\it(S21)}$.Several schemes for particle splitting have been proposed
, both static and dynamic, and it has been shown that splitting gives robust
results even when simulating highly dynamical systems such as collapsing clouds${\it(S22)}$.
In dynamic splitting the mass resolution is increased during the simulation based on some criterion,
such as the local Jeans length of the system. This requires extreme care when calculating SPH density or pressure at the boundary between the fine grained and the coarse grained volumes. In static splitting the approach is much more conservative and one simply selects a subvolume to refine. The simulation is then restarted with increased mass resolution just in the region of interest.
We adopted the latter technique. By selecting a large enough volume for the fine grained region one can
avoid dealing with spurious effects at the coarse/fine boundary.
We select the volume of the fine-grained region large enough to guarantee that the dynamical timescale
of the entire coarse-grained region is much longer than the dynamical timescale of the refined region.
In other words, we make sure that gas particles from the coarse region will reach the
fine region on a timescale longer than the actual time span probed in this work. This is important because
the more massive gas particles from the coarse region can exchange energy with the lower mass particles
of the refined region via two-body encounters, artificially affecting their dynamics and thermodynamics${\it(S20,S23)}$.
Hence our choice to split in a volume of 30 kpc in radius, while the two galaxy cores are separated
by only $6$ kpc.
The new particles are randomly distributed according to the SPH smoothing kernel within a volume of size $\sim h_p^3$, where $h_p$ is the smoothing length of the parent particle. The velocities of the child particles are equal to those of their parent particle (ensuring momentum conservation)
and so is their temperature, while each child particle is assigned a mass equal to $1/N_{\rm split}$ the mass of the parent particle, where
$N_{\rm split}$ is the number of child particles per parent particle.
The mass resolution in the gas component was originally $2 \times 10^4 M_{\odot}$
and becomes $\sim 3000 M_{\odot}$ after splitting, for a total of 1.5 million SPH
particles.. The star and dark matter particles are not splitted
to limit the computational burden.
The softening of the gas particles is reduced to $2$ pc (it was $100$ pc in the low resolution simulations).
For the new mass resolution, the local Jeans length is always resolved by 10 or more SPH smoothing
kernels${\it(S24,S25)}$ in the highest density regions occurring in
the simulations. The softening of the black holes is also reduced from $30$ pc to $2$ pc.
The softening of dark matter and star particles remains $100$ pc because they are not splitted. Therefore
in the refined simulations stars and dark matter particles essentially provide a smooth background
potential to avoid spurious two-body heating against the much lighter gas particles, while the computation focuses on the gas component which dominates by mass in the nuclear region (see sections 2.1-2.3).
We have verified that, thanks to the fact that gas dominates the mass and dynamics of the
nuclear region, the large softening adopted for the dark matter particles does not affect
significantly the density profile of the inner dark halo that surrounds the nuclear disk.
We constructed an equilibrium gaseous disk embedded
in a dark halo choosing parameters as close as possible to the nuclear disk of the merger remnant
in our simulation. The mass ratio between the equilibrium disk and the dark halo is a factor of 2
lower than that in our simulation in order to facilitate the stability of the disk against
fragmentation in absence of turbulence (turbulence is a significant stabilizing factor in the
merger remnant of our standard simulation). We evolve the
system with different particle numbers and choosing a softening of the dark matter particles
as large as the disk radius, as in the refined simulations, or 30 times smaller, i.e. equal to that of
the gas particles. We compare the different runs after evolving the
gaseous disk for a few orbital times and we find that spurious effects are
seen in the profiles of the large dark matter softening simulation only at scales
as small as 3-4 times the softening of the gas particles (Figure S3).
At such distance from the center the density profile flattens out and is about a
factor of 3 lower than in the simulation with small dark matter softening.
The reason why a flattening of the density profile does not occur
at a much larger scale of order the dark matter softening
is because gas dominates the inner mass distribution, causing a contraction of the halo
that overwhelms the tendency to form a constant density core owing
to the large softening (the effect of halo contraction on the slope of
density profiles is recognized to be important in general and has been
widely studied and demonstrated, even in the context of mergers ${\it(S8)}$).
Moreover, the total density profile, including the gas component, is even less
affected (Figure S3). The total density profile is actually most relevant for the overall strength of dynamical friction. In summary, the effect of the
large dark matter softening is only manifest at scales that approach
the nominal resolution of the simulation set by the gas softening and therefore it hardly affects the
sinking of the black hole pair.
\subsubsection{Resolution tests}
In fluid systems for which gravity plays a major role, as it is the case here,
the effective spatial resolution is set by the largest between the gravitational softening and the
SPH smoothing length. These can be forced to be always equal, such as in experiments of molecular cloud
collapse${\it(S26)}$, but this requires introducing adaptive gravitational softening, which can cause
spurious fluctuations in the potential energy of the particles. Here we opt for a fixed gravitational
softening${\it(S8)}$ and we set it in such a way as to have a high force
resolution while being comparable or somewhat larger than the SPH smoothing length (or, more precisely, a spherical volume of radius equal to the softening always contains of order $2*N_{\rm sph}$ or more, where $N_{\rm sph}$ is the
number of neighboring particles used in the SPH calculation (=32 in GASOLINE).
\begin{figure}
\vskip 11.6cm
{\special{psfile="fig5a.eps" hscale=50 vscale=50 hoffset=50 voffset= 50}}
{\special{psfile="fig5b.eps" hscale=50 vscale=50 hoffset=50 voffset= -220}}
\vskip 5 cm
{\small Figure S3. Density profiles of the dark matter (top) and of the sum of the dark matter
and gaseous component (bottom) of an equilibrium nuclear gaseous disk embedded in a dark matter
halo ($R_{\rm disk}$ is the radius of the nuclear disk and the density is measured in
simulation units).
The tests were run to study the dependence of the profiles on the softening of
the dark matter component (see 1.3.1 for a description of the test). Different curves correspond to
different simulations. The solid line is used for a simulation with a dark matter softening
$=0.033 R_{\rm disk}$ and $50000$ particles in the halo, the dashed
line refers to a simulation with a dark matter softening equal to $R_{disk}$ and $50000$
halo particles, and the dot-dashed line is used for a simulation with a dark matter
softening equal to $R_{\rm disk}$ and $5000$ halo particles. In all simulations the softening
of the gas is $=0.033 R_{\rm disk}$. The curves are shown from two gas softening lengths outwards.}.
\end{figure}
The latter choice avoids spurious fragmentation${\it(S24,S25)}$.
During the late stage of the merger densities grow considerably, and locally the SPH smoothing lengths
can be appreciably smaller than the softening, with the result that the radial inflow of gas might
be suppressed, as in the analogous case of star forming clouds${\it(S24)}$.
We tested how the results depend on the choice of the gravitational softening of the gas by running the refined part
of the calculation with a softening of $40$ pc, $10$ pc, or $2$ pc (the latter is our
choice in the reference simulation used in the Report). We adopt an adiabatic equation of state with $\gamma=7/5$
(see next section). We find that the gas mass profile at scales smaller
than 100 pc, namely in the region of the nuclear disk, approaches convergence at a softening of about $10$ pc
(see Figure S2).
This means that the amount of gas that ends up in the nuclear disk, which ultimately determines the strength of
the drag, is a robust result (see also 2.2).
Likewise, the scale height and global structural properties of the nuclear disk,
such as average density, size, sound speed, velocity dispersion and rotational velocity are nearly equal
when comparing
the $10$ pc and the $2$ pc runs. This explains why the orbital decay rate is nearly identical until
the two SMBHs are separated by a distance resolved with both the $10$ pc an the $2$ pc simulation${\it(S27)}$.
On the other end, the non-axisymmetric features in the disk and
the gas inflow at the smallest scales become increasingly better resolved as the gravitational
softening is decreased, implying that an even higher resolution will be necessary to study the fueling of
the black holes in a robust way.
\subsection{Thermodynamics of the nuclear region: the model}
In the refined simulations the gas is ideal and each gas particle obeys $P=(\gamma - 1) \rho u$.
The specific internal energy $u$ evolves with time as a result of $PdV$ work and shock heating modeled via
the standard Monaghan artificial viscosity term (no explicit radiative cooling term is included). We refer
to section 1.1 for a description of the implementation.
The entropy of the system increases as a result of shocks. Including irreversible heating from shocks is
important in these simulations since the two galaxy cores undergo a violent collision.
Shocks are generated even later
as the nuclear, self-gravitating disk becomes non-axisymmetric, developing strong spiral arms.
Therefore the highly dynamical regime modeled here is much different from that considered by previous works
starting from an equilibrium disk model, which could be evolved using a polytropic equation of state and
neglecting shock heating${\it(S28-S30)}$.
Radiative cooling is not directly included in the refined simulations. Instead, the magnitude of the
adiabatic index, namely the ratio between specific heats, is changed in order to mimic different
degrees of dissipation in the gas component, thereby turning the equation of state of the
gas into an ``effective'' equation of state${\it(S26,S31,S32)}$.
Previous works${\it(S31)}$ have used a two-dimensional radiative transfer code to study the
effective equation of state of interstellar clouds exposed to the intense UV radiation field
expected in a starburst finding that the gas has an adiabatic index $\gamma$
in the range $1.3-1.4 (=7/5)$ for densities in the range $5 \times 10^3- 5 \times 10^4$ atoms/cm$^3$.
The latter density is comparable to the volume-weighted mean density in our simulated nuclear
disks. Such values of the adiabatic index are expected for quite a range of starburst intensities, from
$10$ $M_{\odot}$/yr to more than $100$ $M_{\odot}$/yr${\it(S32)}$, hence encompassing the peak star formation rate of
$\sim 40 M_{\odot}$/yr measured in the original galaxy merger simulations${\it(8)}$.
Hence under these conditions the nuclear gas is far from isothermal ($\gamma=1$),
which would correspond to radiative cooling being so efficient to balance heating coming from compression and/or radiative processes, as it happens in the first stage of the simulation.
The inefficient cooling is mostly due to a high optical depth which causes
trapping of H$_2$O lines. In addition the warm dust heated by the starburst continuously heats the gas
via dust-gas collisions, and the cosmic-rays also heat the gas substantially.
We adopt $\gamma = 7/5$ in the simulation described in the Report (we have
also run a case for $\gamma=1.3$ and found that the structure of the nuclear disk is substantially
unchanged). In essence, we treat the gas as a one-phase medium whose mean density and internal
energy (the sum of thermal and turbulent energy) will correspond to the mean density and line width
seen in observed nuclear disks${\it(S33)}$.
In section 2.2 we provide more details on
the structure of the nuclear disk. For
densities above $10^5$ atoms/cm$^3$ or below $10^3$ atoms/cm$^3$ cooling is more efficient and
$\gamma$ should drop even below 1${\it(S31)}$
Therefore, in reality the nuclear disks will have a complex multi-phase structure with temperatures
and densities spanning orders of magnitude, as shown by detailed numerical calculations${\it(S34,S35)}$.
In particular, the lowest density and highest density gas present in the refined simulation
would be characterized by have an effective sound speed, $v_s = \sqrt{\gamma
k_B T / \mu}$, lower than that in the simulation. A lower gas sound speed will yield
a faster decay of the black hole binary${\it(S28)}$.
This is because the
drag is more efficient in a supersonic rather than in a subsonic regime${\it(S36)}$. Since the
gas in the simulation is already transonic the sound speed need not be much lower for the gas
to become supersonic. A colder gas will also becomes denser, which again goes in the direction
of increasing the sinking rate of the black holes. Hence, if
anything we err on the side of underestimating the drag by using a constant, high $\gamma$ everywhere.
A faster decay will only strengthen our scenario.
We tested that the transition
between the thermodynamical scheme used in the low-res part of the simulation, which adopts the
cooling function described in section 1.1, and the second thermodynamical scheme with the effective
equation of state does not introduce large fluctuations
in the hydrodynamical variables. This was done by rerunning the refined stage of the simulation with the same cooling function
adopted in the low resolution part of the simulation. This new refined simulation was then compared with the standard $\gamma=7/5$
refined simulation before the merger, just
one crossing time of the inner region (calculated within a volume of $200$ pc around one of the cores) after refinement.
We recall that in the standard simulations we introduce the effective equation of state exactly when we apply the
refinement. The chosen time is shorter than the merging time of the two cores but
long enough to show eventual fluctuations resulting from switching to the
effective equation of state in our standard refined simulation.
We find that the density distributions are nearly identical in the cores, while they are slightly different
in the region of high compression between the two cores. Such differences are of the expected
sign, namely that a larger pressure gradient develops with the effective
equation of state compared to the cooling simulation as the two disks approach each other (indeed the refined simulation with cooling
behaves almost as an isothermal run, i.e. corresponds to a softer equation of state relative to the $\gamma=7/5$ run).
\begin{figure}
\vskip 11.6cm
{\special{psfile="fig6a.eps" hscale=50 vscale=50 hoffset=50 voffset=40}}
{\special{psfile="fig6b.eps" hscale=55 vscale=55 hoffset=40 voffset=-270}}
\vskip 7cm
{\small Figure S4.
Top: Orbital evolution of the binary supermassive black holes.
The blue line shows the relative distance as a function of time for the pair in
the $\gamma=7/5$ simulations, as in Figure 2 of the Report, while the red line
shows it for the $\gamma=5/3$ simulation (see section 2.1). Bottom: Evolution of the
eccentricity of the pair of SMBHs as a function of the number of orbits
performed in the nuclear disk in the $\gamma=7/5$ simulation.
The binary forms after about eight orbits.
The time spanned by the orbits corresponds to that in the inset of Figure 2 of the Report.}
\end{figure}
\section{Supporting Online Text}
\subsection{Effects of thermodynamics on the sinking of the SMBHs}
We tested how a smaller degree of dissipation affects the structure and dynamics of the
nuclear region by increasing $\gamma$ to $5/3$. This would correspond to a purely adiabatic gas,
or equivalently it corresponds to the assumption that radiative cooling is completely negligible.
The radiative feedback from
an active galactic nucleus (AGN) is a good candidate for a strong heating source that the models
on which we based our prescription for thermodynamics described in the previous section
do not take into account${\it(S31,S32)}$.
An AGN would not only act as an additional source of radiative
heating but would also increase the turbulence in the gas
by injecting kinetic energy in the surrounding medium, possibly suppressing gas cooling${\it(S37,S38)}$.
Even before the two galaxy cores merge, when they are still a few kpc away, a mild gas inflow
collects more than $10^8 M_{\odot}$
within a few hundred parsecs from the black holes. The gas is already arranged in a disk-like
structure, which is highly tidally distorted and presents inward radial motions.
Therefore, there is room to imagine that significant gas accretion might take place before
the merger is completed, turning one or both the two black holes into an AGN.
\begin{figure}
\vskip 7.0cm
{\special{psfile="fig7.eps" hscale=50 vscale=50 hoffset=50 voffset=-80}}
\smallskip
{\small Figure S5. Radial velocities within the nuclear disk ($\gamma = 7/5$)
starting at $t=5.1218$ Gyr (blue line), and then after another $10^5$ years
(red line) and $2 \times 10^5$ years (green line). Remarkable inflow and
outflow regions are the result of streaming motions within
the bar and spiral arms arising in the disk during the phase of
non-axisymmetric instability sustained by its self-gravity
At later times the instability saturates due to self-regulation and the radial motions also level
down (green line).}
\end{figure}
We have run another refined simulation with $\gamma=5/3$ to explore this
extreme situation. In this case we find that a turbulent, pressure supported cloud of a few hundred
parsecs arises from the merger rather than a disk. The mass of gas is lower within 100 pc relative to the
$\gamma=7/5$ case because of the adiabatic expansion following the final shock at the merging of the cores. The nuclear
region is still gas dominated, but the stars/gas ratio is $> 0.5$ in the inner $100$ pc.
The black hole pair does not form a binary due to inefficient orbital decay, and maintains a separation
of $\sim 100-150$ pc (Figure S4) well after they have formed a binary in the $\gamma=7/5$ case.
The gas is hotter and more turbulent; the sound speed $v_s \sim 100$ km/s and the turbulent velocity
$v_{\rm turb} \sim 300$ km/s become of the same order of $v_{\rm bh}$, the velocity of the black holes, and the density
around the black holes is $\sim 5$ times lower than in the $\gamma=7/5$ case. The lower density, and to a minor
extent the fact that the motion of the two black holes occurs in a transonic rather than in a supersonic regime
greatly reduce the drag due to the gas (see below).
A strong form of AGN feedback which can shut off cooling at galactic as well
as at cluster scales has been sometimes advocated to stop the cooling flow in clusters, create entropy cores
and, in general, reduce the overcooling problem at large scales${\it(S39,S40)}$.
Given the discovered sensitivity to the value of $\gamma$, it would appear that a scenario in which
black holes rapidly form a binary and eventually later coalesce owing to the drag provided by the
gas requires that models for AGN feedback be effective on the large scale and simultaneously have negligible thermodynamical effects at small scales. This might indeed be a more general requirement if one has
to preserve the ubiquitous nuclear disk-like structures seen in many merger remnants
(see below section 2.2). Indeed, previous works that included a prescription for AGN feedback
in galaxy merger simulations similar to ours${\it(S37,38)}$ find that feedback affects strongly
the thermodynamics of the gas in the nuclear region only $>10^8$ years after the merger is
completed.
As briefly mentioned in the Report, we have attempted a simple calculation of the accretion rate of the
black holes and of their released energy output assuming Bondi-Hoyle spherical accretion
of the gas within twice the softening of the black holes, following the scheme
adopted in ${\it(S37,S38)}$.
We have neglected the motion of the black holes relative to the surrounding gas since these
move on orbits corotating with the disk (hence there is nearly no net relative motion between
the gas and the holes). In addition, we have assumed that the radiative emission is Eddington limited and occurs with an efficiency of $10 \%$ (indeed we find that they can sustain a mean accretion rate of
$0.05 M_{\odot}$/yr, slightly below Eddington) and
would radiate an amount of energy nearly comparable to the internal energy of the gas (the sum of turbulent, rotational and
thermal energy) over the time comprised between the formation of the nuclear disk and the formation of the binary.
The latter result is obtained if all the radiated energy goes into heating the surrounding gas isotropically,
neglecting radiative losses or hydrodynamical instabilities at the interface between different phases, such as Kelvin-Helmoltz
or Rayleigh-Taylor instabilities, that can convert thermal energy into turbulent energy. Isotropic heating was
also assumed in ${\it(S37,S38)}$, who indeed matched the $M-\sigma$ relation by depositing only $5\%$ of
the emitted energy into heating of the gas. If we make the same assumption here then the total radiated
energy over the same timescale is smaller than the internal energy of the gas by more than a factor
of 50. This leads us to conclude that the radiative heating from the SMBHs should not affect significantly
the thermodynamics of the gas and thus its equation of state.
However, if the black holes begin accreting earlier on, when
the two galaxy cores have not merged yet, the integrated energy output until the binary forms can be much larger
and could affect the thermodynamics of the newly formed nuclear disk. Indeed once the black holes become active they
would be able to accrete and emit at the Eddington limit for at least a Salpeter time, which
is $4 \times 10^7$ yr, a timescale almost 100 times longer than the binary formation timescale (there is indeed
enough gas in the nuclear region to sustain an even more prolonged accretion, albeit below Eddington).
While gas accretion should be more effective, and thus the assumption that emission occurs
at the Eddington limit more sensible, when the nuclear disk has already formed
simply because the gas has larger inward radial motions and thus should feed the
black holes more efficiently (see also section 2.2)
only higher resolution calculations capable of studying in detail the dynamics of the gas near the holes will be able to address the issue of when accretion becomes significant, and if and when it
can produce a significant energetic feedback on the nuclear disk. Furthermore, additional test runs that we have performed (without
black holes) show that if the equation of state becomes stiffer ($\gamma=5/3$ instead of $\gamma=7/5$) only {\it after}
the merger is completed, the nuclear disk structure is barely
affected (this would correspond to the case in which the SMBHs become active only after the formation of the nuclear disk).
Therefore the timing of accretion during the merger is a crucial aspect that will have to be explored by future work. Section 2.2 will briefly discuss how the structure of the inner gaseous distribution in runs
with different values of $\gamma$ compares with the observations of the nuclear regions of
merger remnants.
In the $\gamma=5/3$ case the black holes could still decay and form a binary as a result of the
interaction with the stellar background. Since the resolution of the stellar background in
the simulations is likely inadequate to assess directly the effect of dynamical friction,
we calculated the dynamical friction timescale in a collisionless background analytically${\it(S41)}$
using
\begin{eqnarray}
{\tau_{DF}=1.2 {
V_{cir}r_{cir}^2
\over[GM_{bh}/{\rm{e}}]\ln(M_{sd}/M_{bh})}\,\varepsilon^{0.4}}
\end{eqnarray}
where $V_{\rm cir}$ and $r_{\rm cir}$ are, respectively, the initial
orbital velocity and the radius of the circular orbit with the
same energy of the orbit of the black holes in the simulation, and $\varepsilon$ is the circularity of the
orbit ($\varepsilon = J(E)/J_{cir}(E)$, where $J(E)$ is the angular momentum of the orbit
as a function of its orbital energy $E$ and $J_{circ}(E)$ is the angular momentum of a circular
orbit having the same orbital energy $E$, so that $\varepsilon =0$ corresponds to a radial orbit and
$\varepsilon =1$ corresponds to a circular orbit), $M_{sd}$ is the sum of the
dark matter and stellar mass within $r_{cir}$. We calculate the decay time
starting from when the two black holes are $100$ pc apart, namely at the
periphery of the nuclear disk, just after the merger. Drawing the numbers
from the simulation we set $r_{\rm cir} = 100$ pc, $V_{\rm circ}$= 200 km/s, $\varepsilon =0.5$,
$M_{\rm bh} = 2.4 \times 10^6 M_{\odot}$ and $M_{\rm sd} = 5 \times 10^8 M_{\odot}$.
We find that timescales for dynamical friction timescale in a collisionless background are
$5 \times 10^7$ yr and $3 \times 10^7$ in the $\gamma=5/3$ and $\gamma=7/5$ case, respectively
(the shorter timescale in the $\gamma=7/5$ case is due to the fact that the stars and halo adiabatically
contract more in response to the higher gas mass concentration, hence $M_{\rm sd}$ is higher).
In comparison, the binary formation timescale in the $\gamma=7/5$ simulation is only $5 \times
10^5$ years.
Equation 1 was derived for an isothermal sphere. The stellar and dark matter
distribution are indeed only mildly triaxial within a few hundred parsecs from the center ($c/a > 0.7$, where $c$ is the semi-minor axis and $a$ the semi-major axis of the mass distribution) and the total profile is extremely
close to that of an isothermal sphere${\it(S8)}$. The fact that the merger remnant
is not far from spherical confirms the predictions of larger-scale simulations regarding the effect of
gas cooling on the structure of the global potential${\it(S42,S43)}$.
Note that equation actually yields a lower limit to the dynamical friction timescale since close to parsec scales, as the binary becomes hard, evacuation of the stellar background due to three-body encounters
will begin, and the efficiency of the sinking process will be greatly reduced. Whether sinking will
continue and eventually lead to coalescence of the two holes is uncertain in this case given the fact
that the gas does not play an important role. Centrophilic orbits in triaxial systems would help in refilling the
loss cone, and could in principle bring the black holes down to the distance where gravitational waves
would take over${\it(S44)}$. However, as we just mentioned, the structure of the stellar core
is only mildly triaxial. Further investigation with simulations having higher resolution in the collisionless
component is needed. The $\gamma=5/3$ run was stopped $5 \times 10^6$ years after the merger of the gaseous cores
is completed. Once again, the fact that there is no evidence that the holes are sinking until the end is
likely due to insufficient mass and force resolution in the collisionless background that does
not allow to resolve dynamical friction properly${\it(S45)}$ (as we will explain in the remainder of this
section the gas contributes little to the drag in this case).
We also compared our results with the expected dynamical friction timescale due to the gaseous
background. In the run with $\gamma=7/5$ the gas is distributed in a disk rather than in
an isothermal sphere. Since the disk thickness is $> 10$ times the black hole gravitational
softening and owing to the fact that the density profile of the disk can be roughly
approximated with a power law
with an index close to 2 (except at the center where it becomes steeper) we are allowed to use
eq. (1) to obtain a rough estimate.
As previously shown${\it(S28)}$, analytical
predictions${(S36)}$ can overestimate the drag in the supersonic regime by a factor $\sim 1.5$.
In the $\gamma=7/5$ case the regime is mildly supersonic and the analytical formula should yield the
correct prediction. In this case the drag is $\sim 2.3$ time stronger than in the
corresponding collisionless case${\it(S28)}$. This is fairly consistent with our results. Indeed, formula (1) with a reduction of a factor of $2.3$ would give $2.3 \sim 10^6$ yr if we set $M_{gas}=M_{sd}$, the
gas mass being about 20 times more than the mass in stars. This timescale has to be compared with
that measured in the simulation, $5 \times 10^5$ yr (we recall that the gas profile is steeper
than $r^{-2}$ near the center, therefore it is not surprising that the decay is actually faster).
Despite the apparent agreement with the analytically estimated drag we note that the orbital dynamics
of the two black holes might be affected by more than just the gravitational wake. Indeed the
disks show strong , highly dynamical non-axisymmetric features such as spiral arms (see next section);
in the analogous, well-studied case of planet migration orbital decay is well described by torques
exerted onto the target body by the spiral modes and its efficiency depends on the location of resonances
between the orbital motion and the spiral pattern that extract or deposit angular momentum${\it(S46)}$.
The latter description of the orbital decay might be more appropriate here rather
than just considering the effect of the gravitational wake (see also the discussion on the orbital
eccentricity below)
The drag drops rapidly by an order of magnitude approaching the subsonic
regime${\it(S20)}$; this coupled with the fact that $M_{gas}$ is a factor of 5 lower in the $\gamma=5/3$ would give
a drag 50 times smaller in the latter case, explaining why the orbital decay provided by the gas is so
inefficient in such conditions.
In summary, in the $\gamma=7/5$ run the sinking timescale due to the
gas is much shorter than that due to the stellar background because of the combination
of (1) the fact that gas densities are much higher than stellar densities in the center and (2) the
fact that in the supersonic regime the drag in a gaseous background is stronger than that in a stellar
background with the same density. Adding star formation is unlikely to change this conclusion. In fact the
low-resolution galaxy mergers simulations yield a starburst timescale of $5 \times 10^7$ yr. During this
time, which is much longer than the binary formation timescale, half of the gas in the nuclear
disk is turned into stars. Instead, in the $\gamma=5/3$ stars and gas would
contribute to the drag in a comparable way as the black holes begin to sink
but since the sinking timescale is much longer and
comparable with the star formation timescale the overall orbital evolution will be dictated
by the stars rather than by the gas.
There are, however, some caveats in our argument regarding the role of star formation in the $\gamma=7/5$
case. First, the starburst timescale is based on the low resolution merger simulations. Had we included
star formation in the refined simulations we would have probably found shorter timescales locally
since these simulations are capable of resolving much higher densities and the star formation rate
depends on the local gas density. Second, one might wonder how the inclusion of feedback from star
formation, which was neglected in the low resolution merger simulations, would affect gas properties
and, eventually, the orbital decay of the black holes. As for the first issue, we can obtain a rough
estimate of how short the star formation timescale can be in the following way. We note that in the
nuclear disk most of the gas is at densities above $100$ atoms/cm$^3$. At these densities molecular
hydrogen formation is efficient ${\it(S47)}$.
Let us then make the rather extreme assumption that all the gas in the disk is molecular and
readily available for star formation. Then, let us simply assume that
molecular gas will be turned into stars on the local orbital timescale. Star formation in molecular clouds
is rather inefficient, and typically 30\% of the dense, molecular gas only is converted into stars, possibly
because internal turbulence in the clouds prevents them from collapsing altogether ${\it(S48)}$. Therefore let us
write the star formation rate in the nuclear disk as a whole as $dM_*/dt = 0.3 \times M_{gas}/T_{orb}$,
where $T_{orb} = 10^6$ years, the orbital time at the disk half mass radius, $25$ pc, and
$M_{gas} = 3 \times 10^9 M_{\odot}$.
The resulting star formation rate is $900 M_{\odot}$/yr , about 25 times higher than that estimated
in the low-res simulations. Nonetheless, even with such high star formation rate less than 1/5
of the gas in the disk, $4.5 \times 10^8 M_{\odot}$, would be converted into stars during the time
required for the black holes to sink and bind in the nuclear disk ($5 \times 10^5$ years).
Regarding the issue of feedback, radiative feedback from stars is implicitly included in our choice
of the equation of state in the $\gamma=7/5$ case (see above), but feedback from supernovae
explosions is not taken into account.
However, supernovae feedback would contribute to both heating the gas and increasing
its turbulence, which should go in the direction of decreasing the star formation rate and therefore
strengthening our previous argument concerning the role of star formation.
Moreover, while it will have remarkable effects on the
multi-phase structure of the gas $({\it S34-S35})$, it should not have a major impact on the
energetics of the disk in the $\gamma=7/5$ case. In fact, assuming
a star formation rate of $900 M_{\odot} / yr$ and a Miller-Scalo initial
stellar mass function we obtain that
supernovae should damp $\sim 4 \times 10^{51}$ erg/yr ($7 \times 10^{48}$ erg per solar mass of stars
formed) into the surrounding gas, corresponding to $\sim 2 \times 10^{57}$ erg damped
during the binary formation timescale, $5 \times 10^5$ yr.
This is about $50\%$ smaller than the internal energy of the gas in the nuclear disk
(the sum of turbulent, rotational and thermal energy).
However, since the decay of the black holes will be sensitive to changes in the local gas density along their orbit, only future calculations that incorporate directly the effects of star formation and
supernovae explosions will probably find quantitative differences relative to our simple thermodynamical
model.
We note the black holes sink on an eccentric orbit in the nuclear disk (see above). We tracked the
evolution of the eccentricity after the two cores merge and the holes are embedded in a single disk and
found that despite fluctuations the eccentricity $e$ after about $10^6$ yr is roughly identical to its initial value, $e \sim 0.5$ (Figure S4).
Only in the initial phase of the decay we do signs a tendency of circularization. This is different from
what found in ${\it(S30)}$, who measured fast circularization of for binaries of SMBHs evolving in equilibrium
nuclear disks. A caveat in the comparison is that we can only follow a few orbits once the binary is
formed in the refined simulations. Nevertheless, a tendency towards circularization is clear already
during the first few orbits in ${\it (S30)}$, contrary to what we find here. The reason for this difference
is not clear
but it is probably related to differences in the structure of the nuclear disk. The disk in the refined
simulation has a much stronger spiral pattern than that in ${\it(S30)}$ due to its much higher self-gravity,
having a mass $30$ times higher.
Analytic calculations of tidal torques in the context of planet migration ${\it(S49)}$ have shown
that a massive body moving in an eccentric
disk is characterized by an orbit whose eccentricity is comparable to the degree of non-axisymmetry of the disk.
Such calculations considered a simple m=1 spiral mode superimposed on the disk potential
as the source of the ``eccentricity'' of the disk (the mode is treated as a forcing term in the
equations of motion) but
the results should be quite general in a qualitative sense. The consequence is that a black hole in a strongly non-axisymmetric disk should move on a more eccentric orbit relative to the case of a mildly axisymmetric disk, and that this tendency
for the natural orbit (in the sense that it is the natural solution of the equations of motion)
to be eccentric should counteract the tendency of dynamical friction to circularize the orbit
as the black holes decay. The net outcome will depend on how the structure of the nuclear disk
evolves with time. This is an important issue that warrants further investigation
because the coalescence time of the binary in the gravitational radiation dominated phase
depends on its orbital eccentricity.
Finally, the last stage of the refined simulations provides the initial conditions for future
models that will eventually follow the hardening of the binary below parsec scales. These future calculations
will be able to show whether the last parsec problem can be overcome in the nuclei of merger
remnants with gas, as suggested by simulations of binary SMBHs embedded in equilibrium nuclear disks
${\it(S20, S28-S30)}$.
The binary should continue to sink as a result of gas drag . Its sinking rate, however,
will strongly
depend on the dynamics and thermodynamics of the disk at scales below the resolution of
the refined simulations. The properties of the gas below one parsec
will determine whether a gap will be opened by the binary, slowing down significantly albeit not
stopping its orbital decay, or whether the holes will sink at a faster rate as a result of torques
by the asymmetries in the mass distribution surrounding the two holes ${\it(S28-S30)}$.
Whether or not an appreciable fraction of the gas will be converted into stars by the
time the separation of the binary has fallen below a parsec will also have
an impact since, for instance, the conditions for gap formation will depend on the
local gas density and the overall sinking rate might have a non-negligible contribution
from the stars.
\subsection{Structure and kinematics of the nuclear disks}
The nuclear disk produced in the $\gamma=7/5$ case is highly turbulent. The source of turbulence
are the prominent shocks generated as the cores merge and the persistent non-axisymmetric structure
sustained by the self-gravity of the disks after the merger is completed${\it(S34,S35)}$.
The perturbation due to the binary black holes is a negligible effect since their mass is about $10^3$ times
smaller than the mass of the disk (we tested this by restarting a simulation after
removing the black holes once the merger is completed). The degree of turbulence,
of order $50-100$ km/s as measured by the radial velocity dispersion, is comparable to that of
observed circumnuclear disks${\it(S33,S47)}$.
The disk is composed by a very dense, compact region of size about 25 pc which contains
half of its mass (the mean density inside this region is $> 10^5$ atoms/cm$^3$). The
outer region instead, from 25 to 75-80 pc, has a density 10-100 times lower, and is surrounded
by even lower density rotating rings extending out to a few hundred parsecs. The disk scale
height also increases from inside out, ranging from 20 pc to nearly 40 pc.
The volume-weighted density within 100 pc is in the range $10^3-10^4$ atoms/cm$^3$, comparable to
that of observed nuclear disk ${(\it S33)}$.
This suggests that the degree of dissipation implied by our equation
of state is a reasonable assumption despite the simplicity of the thermodynamical scheme adopted.
The rotating, flattened cloud produced in the $\gamma=5/3$ is instead more turbulent and less
dense than observed circumnuclear disks in merger remnants. The mean velocity dispersion measured within
$100$ pc is about $300$ km/s, higher than the mean rotational velocity within the same radius,
which is $\sim 250$ km/s. This suggests that the $\gamma=5/3$ simulation does not describe the
typical nuclear structure resulting from a dissipative merger,
The strong spiral pattern in the disk produces remarkable radial velocities. Since spiral modes transfer angular momentum inwards and mass outwards${\it(S52,S53)}$
, strong inward radial velocities are present. The amplitude
of radial motions evolves with the amplitude of the spiral pattern, in the sense that radial motions
decline as the spiral arms weaken over time.
Just after the merger, when non-axisymmetry
is strongest, radial motions reach amplitudes of $\sim 100$ km/s (Figure S5).
This phase lasts only a couple of orbital
times, while later the disk becomes smoother as spiral shocks increase the internal energy which in turn
weakens the spiral pattern.
Inward radial velocities of order $30-50$ km/s are seen for the remaining few orbital times
during which we are able to follow the system (Figure S5). Such velocities are comparable to those recently
seen in high resolution observations of the nuclear disk of nearby Seyfert galaxies${\it(S54)}$.
As the gas reaches down to a few parsecs from the center
its radial velocity diminishes because one approaches the limits of the gravitational force resolution in the
simulation ($\sim 2$ pc). Therefore the fact that there is almost no net radial velocity within a
few parsecs from the center (Figure S5)
is an artifact of the limited resolution. In addition, in this innermost region the gas is so dense ($\rho
> 10^5$ cm$^{-3}$) that our equation of state breaks down, since a lower $\gamma$, close to the isothermal value,
would be more appropriate (see section 1.4). A higher dissipation rate likely means the gas inflow rate in the innermost region
of the disk will be higher than the one seen in the current simulations${\it(S55)}$. If we assume that speeds of
$30-50$ km/s can be sustained down
to scales of a few parsecs, $> 10^8 M_{\odot}$ of gas could reach parsec scales in about $10^5$ yr. The latter timescale is
much smaller than the duration of the starburst, and therefore such gas inflow should develop in a similar way even
when star formation is taken into account. The inflow is also marginally faster than the decay timescale of the binary SMBH measured in the simulations, which is $\sim 5 \times 10^5$ years. Presumably some of this gas
could be intercepted by the two SMBHs as they are spiraling down (the relative velocities between the gas and the
black holes are small since the SMBHs are always corotating with the nuclear disk), but the higher dissipation
rate expected near the central, denser regions
might increase the magnitude of the drag due to the gas in reality and bring the sinking time of the
binary very close to the gas inflow timescale. In the latter case the two SMBHs could undergo massive accretion,
and probably become active while they are sinking. Only future simulations that include a realistic treatment
of the gas thermodynamics at all scales will be able to study gas accretion and orbital decay simultaneously.
Our single-phase simulations seem to describe reasonably well the average properties of observed
nuclear disk because they capture the thermodynamics of the low density, pressurized
medium that has the largest volume filling factor ${\it(S33)}$.
Yet they do not model directly the molecular gas, which will have temperatures of order
$100$ K, much lower than the effective temperature produced by our equation of state,
and comprises most of the gas mass in observed nuclear disks ${\it(S33)}$.
The dense molecular phase would be better described
as an ideal gas with $\gamma=1$ or lower (see 1.4). While a model of the multi-phase interstellar
medium in the disk should be the ultimate goal for future simulations, one could also design an
intermediate scheme in which the equation of state (in particular $\gamma$) changes as a function of
density, as done in simulations of molecular cloud collapse ${\it(S26)}$.
If a large fraction of the gas has a much softer equation of state compared to the $\gamma=7/5$
runs a much denser and thinner disk will likely form. We performed a simulation that
adopts an isothermal equation of state ($\gamma = 1$) in the refined part of the calculation
and indeed the resulting disk has a mass comparable to that in the previous calculations
but a scale height of only $\sim 5$ pc,
which would probably shrink even further with a higher spatial resolution. The sound speed
is only $10$ km/s compared to $60$ km/s in the $\gamma=7/5$ case, and turbulence is also
much weaker. The disk is violently
gravitationally unstable, with dense rings and arms, which would likely fragment with a smaller
softening. The simulation was stopped after the merger because the very high densities at the center
prevented an efficient integration. However, the cores merged faster than in the $\gamma=7/5$ case
and we expect the black holes would also sink faster based on the results of previous work ${\it(S28)}$
that found how the orbital decay is faster when the gas has a higher density and/or
has a lower sound speed, even in the case in which the disk is significantly clumpy.
In reality the nuclear region will have the global properties, especially
the global energetics, of our $\gamma = 7/5$ simulation, while locally the densest gas
will have properties closer to that of the isothermal test run. Such a complex multi-phase
structure is predicted by simulations of self-gravitating turbulent disks ${\it(S34-S35)}$.
\bigskip
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JOHN ALFRED HEPWORTH was born in Pinjarra, Western Australia, in 1921 and attended Perth Modern School.
He served in the AIF in World War II, travelling to the Middle East, Ceylon and New Guinea. Australia's year-long struggle to take the northern coast of New Guinea informed _The Long Green Shore,_ which was commended in a 1949 _Sydney Morning Herald_ literary competition and compared to Mailer's _The Naked and the Dead_.
The manuscript was rejected by an English publisher who felt that there were too many war books. Hepworth turned to journalism, poetry and drama, though he occasionally tinkered with his novel.
In the 1960s a number of his plays were performed, and in the following decade he gained prominence through his 'Outsight' column in the _Nation Review_ , a magazine he edited for several years. Hepworth then penned columns for the controversial _Toorak Times_.
From the early 1980s onwards he wrote many books, some with Bob Ellis and others illustrated by Michael Leunig.
For two decades Hepworth worked at the ABC, where he was chief subeditor on the Radio Australia news desk. He lived in Melbourne, and had a long relationship with the playwright Oriel Gray—the couple had two sons—and later with his wife Margaret.
John Hepworth died in 1995, soon after learning that _The Long Green Shore_ would finally go into print. Ellis, who was instrumental in getting the book published, in an introduction put its closing soliloquy on par with the Gettysburg Address. Critics hailed it as a classic war novel, and for some time a film adaptation was to be Russell Crowe's directorial debut.
LLOYD JONES lives in Wellington. His best-known works include _Mister Pip_ , winner of the Commonwealth Writers' Prize and shortlisted for the Man Booker Prize, _The Book of Fame_ and _Hand Me Down World_. His acclaimed memoir _A History of Silence_ was published in 2013.
ALSO BY JOHN HEPWORTH
Non-fiction
_John Hepworth...His Book_ (edited by Morris Lurie, illustrated by Michael Leunig)
_Boozing Out in Melbourne Pubs_ (with John Hindle, illustrated by Bloo Souter)
_Around the Bend_ (with John Hindle, illustrated by Geoff Prior)
_The Little Australian Library_ (illustrated by Keith Brown)
Colonial Capers series
Fiction
_The Multitude of Tigers_ (illustrated by Michael Leunig)
For children
_Top Kid_ (with Bob Ellis)
_The Paper Boy_ (with Bob Ellis)
_The Big Wish_ (with Steve J. Spears)
_Looloobelle the Lizard_ (illustrated by Frank Hellard)
_Hunting the Not Fair_ (illustrated by Nick Donkin)
textclassics.com.au
textpublishing.com.au
The Text Publishing Company
Swann House
22 William Street
Melbourne Victoria 3000
Australia
Copyright © The Estate of John Hepworth 1995
Introduction copyright © Lloyd Jones 2014
The moral rights of the authors have been asserted.
All rights reserved. Without limiting the rights under copyright above, no part of this publication shall be reproduced, stored in or introduced into a retrieval system, or transmitted in any form or by any means (electronic, mechanical, photocopying, recording or otherwise), without the prior permission of both the copyright owner and the publisher of this book.
First published by Picador, Pan Macmillan Australia 1995
This edition published by The Text Publishing Company 2014
Cover design by WH Chong
Page design by Text
Typeset by Midland Typesetters
Printed in Australia by Griffin Press, an Accredited ISO AS/NZS 14001:2004
Environmental Management System printer
Primary print ISBN: 9781922147820
Ebook ISBN: 9781922148810
Author: Hepworth, John, 1921– author.
Title: The long green shore / by John Hepworth; introduced by Lloyd Jones.
Series: Text classics.
Subjects: World War, 1939–1945—Campaigns—New Guinea—Fiction.
Other Authors/Contributors: Jones, Lloyd.
Dewey Number: A823.3
CONTENTS
INTRODUCTION
[_Final Dispatches_
by Lloyd Jones](frontmatter06.xhtml)
_The Long Green Shore_
Final Dispatches
_by Lloyd Jones_
THE paths of two war novelists, John Hepworth and Norman Mailer, crossed in a geographical sense, as well as in literary fortune. Mailer spent a muggy Christmas Day in 1944 aboard an American troopship in Hollandia Bay, in Papua New Guinea. At the same time, Hepworth was ashore, dodging snipers, and wishing for a bath. Both Mailer's _The Naked and the Dead_ and Hepworth's _The Long Green Shore_ begin in the hold of a troopship. In Hepworth's account, 'There is always a stench, a slave smell.'
Fresh from the war both Mailer and Hepworth are told by publishers that the last thing anyone wishes to read is a book about the war. Mailer persists, shopping his manuscript around until it finds a willing publisher. _The Naked and the Dead_ will go on to occupy a spot on the _New York Times_ bestseller list for nearly a year, and provide the young writer and his new wife with enough money to sail to Paris and live the expat life at a dollar a day while attending the Sorbonne on the GI Bill.
Hepworth, back in Australia, is less fortunate. It seems he accepted the verdict of the one publisher he sent the manuscript to, Macmillan in London, as the final word on the matter. He shoves his manuscript in the drawer, where, according to Bob Ellis, a friend and colleague of Hepworth, it will remain for many decades, until its eventual publication by Picador in 1995—not long after the author's death.
In Ellis's preface to the first edition we learn that the 28-year-old Hepworth wrote the novel in response to a literary competition run by the _Sydney Morning Herald_. (It was highly commended in 1949.) It is hard to believe that a competition could have provided singular motivation for such an assured debut.
Fifty years on from the 1948 release of _The Naked and the Dead_ , writing in the preface to the anniversary edition, Mailer describes his novel as the work of an 'amateur'. He also refers to himself in the third person, as I suppose one might view one's callow youth from the distance of old age. But as Mailer notes, 'the book had vigour. That is the felicity of good books by amateurs.'
Hepworth's novel has none of the same defects; no lacing of nouns with adjectives, 'none of the bestseller style' that Mailer charges his own book with.
I think it is safe to say that neither novel would have been written without the authors' respective war experiences. But by temperament and literary ambition the two works fly in different directions.
The ambition behind _The Long Green Shore_ was never to 'out-write' others or to launch the author into the literary firmament. Hepworth's project is more modest, but no less serious for it. His aim was to transcribe an experience as truthfully as possible. And perhaps it is true to say of soldier-novelists that they have two audiences—those of us content to read from the armchair at home and those they went to war with. The second audience is bound to have a chastening effect on any exuberance or over-egging of the realities of war.
The tone of the young Hepworth's prose is entirely trustworthy. Undoubtedly some serious reading lies behind its understatedness. A hard-earned experience transcends its literary style. Hepworth's task is to speak honestly about the manner of a soldier's death: this often arrives without any warning, although the march along the long green shore might be regarded as one long rehearsal for such a moment; at times it is as though death already occupies a soldier's soul and he is simply waiting on his final dispatch.
Fear sits differently in soldiers. Hepworth seems well acquainted with its varying thresholds and black humour. Whispering John, one of the older characters, sniggers with satisfaction at his good luck to date. 'The young blokes crack up and the old soldier keeps on going, eh?' It is a false boast, as he well knows; his own end is simply forestalled.
Now and then the presiding eye of the narrative takes a step back, such as in the opening scene, declaring that this is no ordinary war novel.
We sailed that last night through the tail end of a hurricane sea. We came up and ran naked on the open canvas square of the battened hatches, standing taut and breathless against the ecstasy of cleanliness in the driving rain...There was a spirit of carnival, a revelry of cleanliness and nakedness in the rain, with the combed wind sweeping the open deck and voices shouting and laughing in the storm while the darkened ship plunged through the rolling seas.
Between moments of barbarity and banality are occasions of great beauty, and for much of the time _The Long Green Shore_ is a young soldier's paean to the puzzling thrill of being alive.
The most enduring novels about World War II turned out to be satirical—Joseph Heller's _Catch-22_ and, for capturing the vulgarity and absurdity of war, Kurt Vonnegut's _Slaughterhouse 5_ is in my view without peer.
The most talked-about war novel in recent times is _Yellow Birds_ by Kevin Powers, which draws on his experience as a marine in Iraq. The reader walks in the combatant's boots, and hears the dry rasp of his heart and mind. There is no attempt to draw big lessons. No geopolitical agenda, just one man's experience of being cast like chaff into a horror zone. At times, Powers is guilty of prettifying the experience, which is as problematic as the poet who surrenders genuine grief to poetic form. Perversely, art ends up destroying that which it wished to preserve. In the case of the broken-hearted poet, why write a poem? Why not jump off a bridge?
_The Long Green Shore_ is written from a different place. It is an act of remembering mates who died—and, as it happens, did so unnecessarily. The enemy which Command is so eager to engage with is less interested in the Australians. For all that the march mattered, the platoon might as well have found a place on the beach and played volleyball until the end of the war.
Towards the end of the novel, word of the catastrophic nuclear bombing of Hiroshima and Nagasaki filters down to this remote area of fighting in the South Pacific. The deaths of various mates and acquaintances have already been soberly accounted. The news from Japan creates a new frame for what we have learned so far.
It is a breathtaking moment in which the futility of everything the soldiers on the long green march have gone through is painfully clear. It is clear too that this novel has earned its place on the shelves. I hope it endures.
_The Long Green Shore_
## AUTHOR'S NOTE
From the last Christmas of the Second World War, until that war ended, two brigades of the Sixth Australian Infantry Division fought an obscure but at times bitter and bloody campaign along the savage north coast of New Guinea.
When the war ended, and the snakeskin drums sounded the word through the mountains, they were within sight of the deathly valley of the Sepik.
This campaign from Aitape to Wewak was an unnecessary one. The Japanese army in the area was isolated from the rest of the Pacific. They occupied no strategically important ground: they showed no aggressive intent.
This campaign was war in its classic wastefulness. It was fought for no apparent reason, other than that Australia might claim another Division in action; and, perhaps, strengthen her voice with their bodies at the Peace table.
To that end, a few hundred men died.
I know it is not such a great number in the millions of the dead—but it is bitter that they might have died in a better cause.
_The Long Green Shore_ is not, strictly, the story of this campaign. But I have chosen it as the framework because here the battle itself has no importance other than individual life and death, and this allows a sharper drawing of men's awareness of life and death. The victory of the Desert, the defeat in Greece, the drowning, gaunt agony of the Kokoda Trail would not have allowed quite the same delineation.
This is essentially a true book, though many of the incidents did not happen in this piece of war, but to other men in other campaigns. The men are true men, but none is one man entire—each is a synthesis of half a dozen or more.
This is the Australian soldier as he is...with something about him essentially national; but, at the same time, basically the same man at war as the legionnaires who crossed the world with Alexander, or the commando who marched with Xenophon through Asia Minor.
It is a long time ago, as our time goes. We who were young begin to grow old.
They have carried the dead out of the green and drifting sea of the rainforest and planted them row by row in domestic earth.
The world is not at peace. But it will be. Surely it will be. One day.
_J. H._
## 1
We sailed that last night through the tail end of a hurricane sea. We came up and ran naked on the open canvas square of the battened hatches, standing taut and breathless against the ecstasy of cleanliness in the driving rain.
We scooped water from the pools that gathered in the folds of canvas and lathered the fresh foam of soap on our salt-dry bodies. We lined up for the plunge under the showers where the rain guttered off the gun platforms and deck housing in fat shuddering streams.
It was the first freshwater bath we had had for a week. There was a spirit of carnival, a revelry of cleanliness and nakedness in the rain, with the combed wind sweeping the open deck and voices shouting and laughing in the storm while the darkened ship plunged through the rolling seas.
*
Pez and Janos came in naked from the rain bath on the deck, blundering through the double blackout curtains in the roll of the ship, and climbed gingerly down the thin steel stairway into the moist stench of the hold.
There is always a stench, a slave smell, in the hold of a troopship. The stink clings to your clothes and skin long after you climb up into the fresh air.
They picked their way through the crowded well of the hold, dodging the bawdy salutes of their mates to their nakedness, and entered into the maze of bunks massed in double tiers five high.
As they dried themselves on greasy towels in the cramped alleyway between the bunks, Janos wrinkled his nose: 'I can't stand this stink—you could cut it with a spoon.'
Janos was a tall, lean lad from the rich and rugged floodlands of the New South Wales north coast. He had a strong, bony face, a wry mouth and clear grey eyes. His nose was broken and crooked in a way that sundry women had found intriguing.
'Broke her that many times playing football,' he'd tell you, 'decided last time to let her stay broke and I've never had any trouble with her since.'
He came from Grafton where jacaranda blooms and strange tales are told of what happens when the blue flower bursts.
'It's the fever,' he said, 'the jacaranda fever. You can see it in the wenches when they walk the street—the way they swing their hips and carry their breasts proud and look sideways at you with that summer look in their eyes. You've got to step careful at night in the long grass down by the river. It's a great thing to be young and have your strength and be in Grafton when the jacaranda blooms.
'And there is a legend that any wench whose head you tilt to kiss beneath a jacaranda tree, who does not have the same colour shining in her eyes, then she, poor girl, will die a virgin.' He grins: 'The legend has been proved in part—concerning those whose eyes _do_ shine.'
As Janos dragged his jungle green shirt off the bed, the leather wallet fell out and dropped open on the floor. Pez picked it up and handed it back to him, glancing as he did so at the photo framed in the celluloid panel.
'Janice on top tonight,' he observed. 'Is little Mary out of favour?'
'No,' said Janos, 'Janice is on view tonight in memory of things lost but not forgotten. She was a sweet little thing and accommodating too, and it is my great regret that she had a husband.'
Janice had been a part of the jacaranda fever. A buxom lass, she was—a rich northern dish of milk and honey. That night he was in her room at the pub and her husband came home unexpectedly—well, maybe a husband wouldn't appreciate a perfectly reasonable explanation concerning the aphrodisiac effect of the blooming of a blue flower, so Janos went out the window—taking most of his clothes with him, but forgetting his hat. For weeks afterwards a brawny citizen haunted the pubs, tenderly enquiring if any of the AIF boys had lost a hat.
'Hell, that reminds me,' said Pez. 'I should write to Helen tonight—haven't written since we left Cairns.'
'Write tomorrow when we get ashore—she'll get it just as soon.'
'Yeah, tomorrow we're ashore,' said Pez, 'and maybe soon it won't matter whether I wrote or not.'
'Cheerful bastard, aren't you?' grinned Janos. 'I can't stand this stink—I'm going to sleep up on deck, rain or no rain.'
'I'll take a wander round and see what the troops are doing first,' said Pez. 'I'll be with you later.'
All the card players were gathered at the tables or on blankets spread in the open space in the well of the hold. Those who had money still played poker. Those who were broke, watched, or played bridge and five hundred. A few were already half-asleep on their bunks, the sweat streaming from them. Others, where the lights on their beds were good enough, read or wrote. Not many were writing letters—there was nothing much to say—but there was plenty of literature available.
We had received a comforts parcel the day before—you remember those parcels that a benevolent nation distributed for your cultural relaxation and entertainment on shipboard. There were a great number of inspired novelettes in gaudy paper covers with such titles as _The Corpse on Fifth Avenue_ and _The Corpse with the Missing Face_ and _Gunfire at Rustlers Gulch._ And they tried to tell us there was a paper shortage back home.
But these well-wishers thought of the physical as well as the spiritual man. There was also in each parcel a tin of very sticky lollies, a handkerchief, a pair of socks, a tube of toothpaste which was admirable for cleaning rifle barrels and polishing metal souvenirs, and, of course, a cake of soap.
A grateful country looks after its men when they are going into battle. 'Nothing,' as Dick the Barber remarked sourly when we opened the parcels, 'is too good for the Australian soldier.'
Pez made his way down the alleys between the bunks.
There was Regan lying on his bunk—the top one of the tier, with the luxury of direct lighting and an overhead air vent that roared gently in amplification of the sound that you heard when you were a kid and pressed a shell against your ear to hear the roar of the sea.
Regan lay in his bunk in fractional comfort, his body sticky and sweating and his face and throat bathed in the thick, cool jet of air. He was a thin lad in his twenties with a ragged thatch of black hair, a thin, swarthy, Irish face and close-set blue eyes.
He was holding a paper-backed novel, but he wasn't reading. He was lying there, staring at the blurred page and feeling fear in his heart. It had always been the same for him—this fear of being hurt and the greater fear of people knowing that he was afraid.
Pez passed on and paused to watch the poker game for a moment. He saw Cairo Fleming grin and bluff his last pound on a pair of deuces. And when old Whispering John called him on an ace-high blue, he laughed. He got up from the table broke, and he grinned: 'Hell, Mrs Kelly wouldn't let her little boy Ned play with you blokes.'
You can tell a lot from the way a man plays poker—especially the way he loses.
Old Whispering John always played his cards with elaborate cunning, close to the vest. Next hand he was first to bet.
'I'll make it a modest sixteen shillings,' he whispered.
Brogan's hand went into the pack and young Griffo made it twenty-four. Sunny and Ocker both threw in and it was up to John again.
'You can't make it twenty-four,' said Whispering John querulously. 'It was only a four-bob game.'
'I made it eight for cards,' said Griffo. 'You made it sixteen yourself, first bet.'
Whispering John looked hard at young Griffo and felt hatred for this youth who sat looking at him with elaborate unconcern and a womanish mouth.
'I wish to Christ I knew what you had in your hand,' John whined.
'There's one sure way to find out,' said Sunny.
'All right, all right!' snapped Whispering John. Anyone'd think I didn't have the guts to look.' He held his cards up between a bony thumb and forefinger. He was breathing unevenly.
Young Griffo laid down three queens.
'Six tits,' he said.
Whispering John slammed his cards down with petty viciousness on the table: 'I had three tens,' he complained. 'I get three tens and he has three queens. He's been got at, the bastard. He's been touched. Christ, I never seen such paper as I'm getting tonight.' He pushed the stool back and stood up, 'That finishes me—when your luck runs that way it's time to get out.'
Pez threaded his way back into the alleys between the bunks.
There was a group around the Laird, who swung gently in the hammock he had scrounged from the crew's quarters and slung between two iron stanchions so that it was in the cool spot right under the big ventilator shaft.
'Well, I don't know,' boomed the Laird, 'but I'll make a bet that fifty per cent of these skulls we've got get themselves killed or go troppo within a week.' He snarled with fine scorn: 'Duntroon boys! My God, what hoons! What drongos! After seeing their form it's my considered opinion that they couldn't lead their old grandmothers to the company latrine.
'You know that little bloke?' he said. 'You know, that smooth-faced snotty little bloke with the curly hair—what do they call him?—Billy the Kid, that's right...' His voice dropped to a horrified rumble: 'Do you know what he tried to make me do at Redlynch, just before we got on the boat? He tried to make me do rifle exercises by numbers! I've been in the army four years and that hairy-arsed schoolboy comes along and wants me to do rifle exercises by numbers. I told him what he could do with the rifle—by number, too, and bayonet end first.'
Said Dick the Barber: 'Well, I don't know, you can't always tell by the way a bloke looks—remember Bosker?'
'Who's he?' asked Bishie. 'Not that big major up at Brigade?'
'No,' said Dick the Barber. 'He was a lairy little bloke, Bosker, with a kind of Haw Haw voice and an absolute nut about having your buttons done up. He got killed at Sanananda—but he did a bloody good job.'
'Yeah,' said the Laird. 'He should have got a VC for that job—he earned it.'
Pez remembered that day. Three times Bosker had gone through that desolate waste of swamp and palms, where the shells were falling, to carry orders to 'A' Company, pinned down on the flank. The fourth time he died in the swamp.
'But I wouldn't worry too much about these apes of officers we've got,' Dick the Barber was saying. 'When you get down to it, who does the work? The poor old drack private and the corporal. The corporal—he's the leader—he's the one that actually takes the men in and does the job after all the brass hats have finished deciding what the job is. And we've got better corporals than any other army in the world.'
Said Bishie: 'If it comes to that, we can always shoot the skulls first and carry on from there.'
But Dick the Barber was talking: 'And you know there's men on this boat that aren't even getting their efficiency pay. Brass hats—brass bastards! They're going to send those men in and ask them to go forward scout and they won't even give them efficiency pay.
'Christ, it's an insult! They say to a man: "Now, if you're a good boy for six months, and you don't go ack-willie, and you know how to fire a Bren gun, and you can do your bloody gas drill that you'll never bloody need—then we'll open our great big brass hearts and give you an extra zac a day."
'Sixpence a day! A lousy zac! Christ, you'd think they were giving you gilt-edged security for life! Some of these blokes over-stayed their leave a couple of days—or else they shot into town and got drunk—so they took the lousy zac a day off them.'
His voice jumbled with bitterness and anger: 'So they reckon they're not efficient soldiers, but they're still going to send them into action. They ought to be cut up and their swags burnt!'
'Now, now, Dick,' grinned Bishie, 'don't get yourself excited.'
'Why the hell shouldn't I get excited?' snapped Dick the Barber. 'That's the trouble with the world—people don't get excited about these things.'
'Sure,' cut in Harry Drew quietly. 'But it's a waste of time and energy, getting excited and not doing anything. We'll fix a deputation to Slapsy Paint tomorrow and see if we can get anything done about it.'
The Laird heaved his bulk up in the hammock and leaned on one elbow as he chuckled reminiscently: 'You know, I had a mate once like that. If anything went wrong he'd scream and tear his hair and stamp around cursing and swearing better than any bullocky.
'He was with me when I was up the scrub—a little bloke, sandy hair, name of Samuels—and a bloody good mate, too. You might know his brother, Dick—he had a brother, Alec, I think his name was. He was a dentist down the 'Gong.'
Dick the Barber reflected. 'A thin dark-haired bloke with a bit of a twisty eye?'
'No,' said the Laird, 'he was a big fair-haired snodger—hell of a nice bloke but always getting into strife with married women.'
'I can't place him,' said Dick the Barber ruminatingly. 'Can't place him anywhere round the 'Gong.'
'Oh, well,' admitted the Laird, 'I wouldn't be certain it was down the south coast—might have been out Wagga way he lived.'
'Think I'll hit the cot,' said Harry Drew, rising and stretching. 'We'll be in tomorrow, I guess.'
'Yeah, we'll see her tomorrow.'
Bishie stared sombrely ahead. He was new to this mob, he'd come out of the militia. He was remembering the last time—a different time to the one they knew and he could not really share it with them.
He remembered the smell of smoke and blood. Behind them Rabaul was burning and they fled through the jungle and the swamp with the dry mouths of fear.
This time they wouldn't have to run.
Cairo Fleming stood hunched over the rail in the deeper shadow of a lifeboat and stared down at the boiling blue sparks of phosphorescence in the white foam furrowed from the ship's bow. He knew the feel of the sea—the wild, swift bucking of a small and slippery deck and the sting of the combed salt spray as the fishing smack butted jauntily into the long, grey rollers of the South Pacific. Toes, naked, gripping the smooth surging deck...The small comforting smell of oil and engines in the gulf of wind and sea...The nets running out, dropping out behind in the grey water...The squirming, heavy weight of them when they were hauled in and the slower, heavy bite of the boat in the running seas to home...
Cairo stared at the blue and boiling sparks and felt the surge of the deck as a memory. Inside the heavy army boots, his lean toes instinctively crooked and clung, as though his trousers were again rolled to his knees and his feet planted, balanced apart, gripping the small deck. And in the foam and the darkness of the sea and the hurricane-grey sky and the timeless surge, he felt his loneliness—that loneliness and nostalgic discontent he knew all his life.
He knew what they used to say: 'Cairo's always happy,' they used to say. 'You never see Cairo without a grin on his face.'
The Laird used to tell about him and Cairo in the Owen Stanley show: coming up the track from Popandetta, the Nips opened up with a mountain gun. Cairo dives for a hole and then props when he sees a considerably dead Nip sitting up in her. Then one lands a bit close and the shrap whistles through the trees. Cairo says to the dead Nip: 'Brother, I need that hole more than you,' and he leans down, grabs him by the collar, hauls most of him out and dives in just as another one bursts about five yards away.
No one ever knew whether Cairo was blown or jumped into that hole—Cairo himself thinks he maybe got some assistance.
And again at Sanananda, the Laird would tell: We were cut off for a bit and things looked sticky. Cairo says nothing to us, but goes quietly to Coulter—Captain Coulter, his third pip came through not long before and he had charge of the Company then—he got killed a couple of days later, remember—Cairo says to Coulter: 'Look, I don't mind seeing if I can get back to the battalion—we might get some help.'
And Coulter turned on him: 'Get back to your bloody section, Fleming,' he said. 'You're too good a bloody soldier to lose trying this VC stuff.'
Cairo shrugs, and says OK, and starts back. But he'd only gone a few steps when Coulter calls him: 'Thanks mate,' he says.
Poor old Coulter copped it two days later—shrapnel in the guts. He was a good man. He died hard.
Sure, he always had a grin, had Cairo. He was always happy—though sometimes when he grinned he wasn't happy.
It's bad, the loneliness of being apart from humanity when you want desperately to be part. It keeps you awake like a hunger in the night. And even when people do accept you, there is always that doubt, that fear in the mind that they may be doing it consciously out of pity, or condescendingly to flatter their own egos. It is a burning thing, that fear—it scorches the clean flesh of your pride.
'Hell,' thought Cairo. 'I'm being sorry for myself.'
He grinned wryly in the darkness and the twisting of his broad mouth showed strong white teeth. It was a strong face—a round, heavy jaw and broad mouth and nostrils, deep brow, soft brown eyes and crinkly black hair. His body was lean and hard and his hands slender, the fingers thin and strong.
'Hell,' he thought. 'What does it matter? Tomorrow we land and after that...'
A vague figure blundered a little, missing the roll of the boat, collided with the frame of a lifeboat derrick and cursed casually.
'That you, Log?' said Cairo.
'Yeah,' said the Log. 'Where are you?'
'Over here near the rail—watch the rope.'
Log groped his way to the rail, rested his elbows on it and hunched down beside Cairo.
'What are you doing, mate?' he asked.
'Just thinking,' said Cairo.
'Problems?'
'No—just thinking.'
They slouched there watching a drunken star that staggered on the northern horizon. They were comfortably silent for a long time. Cairo felt a strange contentment in the surging of the ship...
Deacon had been lying on his bunk, his eyes closed, the sticky trickle of sweat on his body, trying to sleep.
But instead of sleep he drifted back always into the dream—until in the end he was forcing himself to stay in the half-darkness of the mind and striving to re-create the look of her and the sound of her voice and the scenes they had moved through together.
The heat and stench and sweat of the hold, the throbbing of the ship and babble of voices from the Laird and Bishie and Dick the Barber talking down the alley, he forced away until they were resting thinly on the skin of his brain and he was burrowed deep into the warm darkness of his memory.
He felt a faint, pleasant stirring of the bowels as he conjured. They were lying in the long, sun-warm grass on the banks of the river. The wattles grew low over them and made a cool, thin cavern of shade. The golden pollen drifted down as a small breeze rustled the branches. Some of it had powdered the deep auburn of her hair and he noticed it as she turned to him.
Her cropped auburn hair, with the small curls clinging round her head like that sculpture of the Greek boy in the museum. Her eyes shining, her tip-tilted nose powdered with freckles and her rich mouth slightly open and wry with desire.
His arm was around her shoulders and she turned her soft, firm young body urgently to his. The feeling of the sun warming and the earth and green things growing and the sap singing...
His mind hinged on this sequence and he couldn't force the imagery on past that point. The memory of her turning to him blurred into the sun and the earth and the trees.
Three times he forced the image up and each time it blurred. With a small curse of frustration, he sat up suddenly. He reached under the pack and the illegal lifebelt which made up his pillow, and took out a leather wallet. He opened it and drew a folded letter from among the small pack of photographs in the celluloid-covered compartment. The letter was grimy on the edges from handling. Deacon leaned on one elbow, part way out of his bunk to catch the light, and read it again.
That young, flourishing, artificial script...
_Oh My Darling,_
_I cried all night after you had gone and next morning the girls at the office were very sticky about why my eyes were so red. But I wouldn't tell them. I couldn't tell anyone about us and how I feel for you._
_Everything has been black and miserable since you left me and the only thing that lets me go on living (the only thing that makes me want to go on living) is the thought that this time will be the last time that you will be away._
_I am jealous of all the other times you went away and it was not me that felt sick in the heart when you were gone. (Do you really think I am jealous of you, darling? I am! I'm terribly jealous! Do you think that is a bad thing?) I hate all those other women you have known. You are the first man I have ever truly loved and I wish I could be the first one for you, like you are for me._
_I know you will laugh at me, but perhaps men never feel the same way about these things as a woman. And I am a woman now, my darling—you made me that, even if you haven't made me an honest one yet. But you will, won't you? You do want to marry me, don't you?_
_It's different for a man, I know, but sometimes I get terrible black depressions and I am sure that you never truly loved me and I am so desolate and miserable and I could kill myself. Other times I just wake up in the morning and I am sure, for no good reason, that you do love me and you will come back._
_Oh, I'm a shameless woman, I know I am, my darling. I gave you my body and I suppose I really am a very immoral person and I ought to feel ashamed when I sit opposite Mummy at breakfast._
_But I don't, my darling, I don't! I feel very proud and very happy—that is, when I'm not feeling very small and very miserable and certain that you don't love me._
_Oh, come home soon, darling. Look after yourself and come home soon so that I can be an abandoned woman and be yours again._
_Goodbye for a while, a little while, my darling._
_Margaret_
Deacon finished reading, but stayed, leaning on one elbow, staring at, but not seeing, the written page. He could feel a pride of conquest and an egotistical glow at the extravagance of her abandonment. She was so young and theatrical, with such a young passion for being in love with love.
You told lies to a woman and tried to weave those lies into a pattern to make the whole affair a golden tapestry, a piece of artistry, a highly skilled game. You never found in your beloved Margaret that depth and sincerity of emotion you thought to find in love when you were young.
When you were young, Deacon! The romantic bitterness and weight of twenty-two years made you mourn for the time 'when you were young'.
This beloved Margaret had touched but never torn your heart. Everything you did or said had a cold shadow of calculation in it. 'It's got to stop,' Deacon thought. The labour of weaving patterns in words and keeping up the pretence was too great, the game was palling. But there must be some way to let her down easy—to break it up but leave her with the shine in her eyes and the warm, eager parting of her lips.
Oh, when we are arrogant enough to believe that we have created love in a woman, Deacon, we must condescend to handle her very gently. Even when we break her heart we must make sure that we find some pattern that relieves us of the burden, but provides that she still must love us. 'There must be some way that wouldn't hurt her,' was the way Deacon thought of it.
'Hey! What are you perving on?' said Fluffy, pausing by the bunk. 'Where'd you get the letter? Carrier pigeon service?'
'No,' said Deacon, folding it quickly but casually. 'It's an old one.'
'One from the steady, eh?' said Fluffy, grinning. 'It'll do you no good reading that sort of thing now, boy. It'll give you bad dreams. You'll be sleeping next to nothing warm or soft for the next year or so. Better forget her. Hank the Yank's probably in, anyway.' He grinned, and passed on down the alley.
Fluffy. A tough kid from Waterloo. A tough kid who talked tough, but mostly because he had seen too many films. He was a good lad. He was to die on the bank of a muddy river with machine-gun bullets stitched across his guts.
'Tomorrow,' thought Deacon, 'we'll land. We'll be able to post mail.' He dragged out his writing pad and scrawled his number, rank, name and unit across the top of the page. Then...'Beloved Margaret,' he wrote, with a little flourish.
He paused, chewing the top of his pencil. Down the alley he could hear Dick the Barber holding forth: 'Well, I wonder how Killer Connell's feeling tonight. He's been sweating for action ever since he came to us, and now it looks like he'll get it.'
Lieutenant-Colonel Connell, using only his right hand, levered the stopper out of the whisky bottle with his thumb and poured a stiff nobbler into his own and the Doctor's glasses. Killer Connell they called him, but the title did not derive from his exploits on the field.
It was that day on the Tablelands when we were practising for the Divisional parade. The battalion ground was a naked brown field shimmering in the burning sun.
As the platoons and companies broke off from the square and marched in a long battalion column round the field and past the saluting base, Connell stood under the shade of the trees, screaming: 'Swing your arms! Lengthen your step! Come on, "A" Company! Come on, Pioneers! Call yourselves soldiers—Jesus Christ, a mob of Palmer Street whores could march better than that!'
And the word was muttered round from mouth to mouth as they marched: 'The old boy didn't get home till five o'clock this morning—down on the nest with that nurse of his at Atherton.'
'Maybe she knocked him back,' someone suggested. 'Maybe that's what's wrong with him—he didn't get a bit last night.'
Two strays, shaggy friendly mongrels that had been straying round the camp for days, came running and yelping onto the parade ground in front of the column.
'Battalion, halt!' screamed Connell.
As the troops bunched up to the halt they could see him making his way across to the back of the parade ground and hear him yelling for the RPs.
'Sergeant Hino! Sergeant Hino!' he yelled. 'Where the bloody hell are you when you're bloody well called?'
'A nice way he talks to men,' muttered Janos satirically.
Hino, the fat little Regimental Provost, was coming at an agitated trot from where he had been stationed at the far corner of the field. Connell made towards him with long, angry strides. We couldn't hear what was being said but we could see Connell gesturing angrily and Hino standing there trembling and stammering, 'Yes, Sir! No, Sir!' and nearly knocking out what little brains he had, he saluted so hard when Connell dismissed him.
The troops stood relaxed, resting their rifle butts in the red dust, while Hino and a couple of other RPs tried to catch the frisky, yelping excited dogs.
There were surreptitious grins and muttered comments and a burst of laughter as the little ginger dog eluded the fat and despairing Sergeant Hino by diving between his legs. Then some officer, with an eye on Connell, would snap over his shoulder in his best Duntroon voice: 'Quiet, "A" Company! Stop that laughing!'
But Connell had walked back under the shade and was standing with his back to the parade. His hands clasped behind him, he stared with pale and unblinking eyes into the grey-green thickets of timber that stretched away to the left of the camp. His mouth was tight, his shoulders hunched, the fingers of his clasped right hand twitched and his breathing was ragged.
The RPs eventually caught the dogs and led them off. The Adjutant gave the order and the long column swung again into the march past. All the Company officers were rallying their men.
'Come on! Come on now, Fourteen Platoon!'
'Hansen, pick up that step!'
'Knight, straighten that rifle!'
'Johnson, swing that arm higher! Higher! Higher! Right up to the shoulders!'
Running up and down the flanks of their platoons: 'Lef, ri! Lef, ri!' Harrying them like sheepdogs—yapping like sheepdogs. But Connell still stood with his back to the parade, his hands clasped behind him, staring out through the trees.
They were halfway round for the second time when they heard the shots—two spaced reports echoing thinly from down the scrub—and heads twitched at the sound. 'What was it?' 'Not a rifle...' 'Revolver, I think.'
Connell turned back to the parade and started screaming again. Now there was a sort of satisfaction in his voice: 'Come on, march!' he bellowed. 'I'll stay here all day if necessary. I'll march you round and round and round this bloody square until you drop or do it right!'
Word filtered back through the grapevine of the marching men. 'It was the dogs. He had the dogs shot, the bastard!'
They marched stubbornly. You could feel their bitter silence through the thud of their heavy boots and the beating of the brass band. Round and round they went. Then Connell stopped them and abused them, and harangued and threatened them. Then they marched again—and again, and again. They marched. They swung their arms and moved their feet, but with a stubborn mediocrity. It could not be attacked as a deliberate and insolent slovenliness, but it was still quite obvious.
The strange duel went on. A clash between a sullen and savage man with the immense mumbo power of discipline and rank behind him, and the vast, silent, stubborn and tangible anger of a thousand men who would have forgiven him many worse things, but could not forgive him shooting two dogs.
And in the end, Connell was beaten and dismissed them. When they broke from their parades there was a strange feeling of triumph and elation through the camp. The lines were filled with voices louder than usual and wild carolling ho-ho-hos and laughter rang through the trees. And the voices and the laughter fell on Connell like a black rain and burned him like acid.
So they called him Killer Connell.
Young Rocky Bennet was foolish enough to write the story of the shooting of the dogs in a letter home. The officer censoring the mail—old Suck'n See Seaton—took it to Connell, who gave Rocky twenty-eight days field punishment.
Lieutenant-Colonel Connell splashed a small quantity of soda into the glass and tossed off the whisky. He and Doc Maguire were sitting at the small table in Connell's cabin—the whisky bottle was three-parts empty.
'They hate me, Doc,' said Connell. 'That's the way I want them to feel.'
He stared for a moment at the empty glass as he put it down on the table. There was a hard, thin, sensual line round his mouth and nostrils. His pale, harsh blue eyes were a trifle bloodshot and puffiness under the eyes and the nervous skin over the strong Gothic bone of his face showed dissipation and sleeplessness and nerves rubbed raw.
'Men who are happy and contented and well fed don't fight well, Doc,' he said. 'I want 'em lean and hungry and hating me and themselves and everyone else in the world. Then they'll fight! And these boys of mine are going to fight, by Jesus!'
He poured himself another drink and the Doc, who tossed his tot off at one gulp when Connell reached for the bottle, pushed his own glass over for a refill. The Doc never talked much when he was drinking.
'You know, Doc,' said Connell, 'I was bloody near a breakdown on the Tablelands. A man's a fool the way he gets hold of some slut and wears himself out on her...' He sneered at the memory. 'Christ! It doesn't make you feel good. It doesn't make you feel happy or forget. Whoring and drinking. What's the reason, Doc? Why does a man do it?'
'I don't know, Cliff,' said the Doc. 'I'm no psychologist.'
Connell looked at him and his mouth twisted: 'No, you're no psychologist. You're not even much of a doctor—a whisky soak—a drunken quack—the pox doctor's clerk.'
Doc Maguire looked at him steadily, a little blankly. The spirit was starting to work now and he felt the calmly sullen detachment of his drunkenness. He never got falling-down drunk, the Doc—his voice just got a bit slower and more considered and he would stare steadily. The tiny scarlet threads of veins in his cheeks grew brighter, and nothing mattered, nothing touched him.
'How do you reckon you'll go in action the first time, Doc?' sneered Connell. 'It'll be a bit harder than you're used to—harder than sitting in the mess all night soaking whisky and then getting up next morning to dish out a few cascara tablets and aspirin.'
Maguire contemplated Connell and licked his lips slowly. 'You watch your own guts, Cliff,' he said casually. 'I'll watch mine. I'll be all right. I'll be there when I'm wanted. You smash 'em up—I'll patch 'em up.'
Connell's face flushed and hardened: 'You'll address me by my rank, Captain Maguire,' he snapped. 'And remember that I'm your superior officer now.'
Maguire lumbered slowly to his feet, gathered himself half to attention and gave a casual imitation of a salute—looking all the time at Connell with an expression of blank derision. 'Goodnight, Lieutenant-Colonel Connell, DSO and Bar,' he said, and turned towards the door.
As he lifted the latch, Connell spoke. 'Come here, Mag,' he said gruffly.
With his hand still on the latch, Maguire turned slowly: 'Yes, Lieutenant-Colonel?'
'Come here, Mag, for Christ sake. Come and have a drink.'
Connell poured two healthy slugs into the glasses, concentrating his gaze on the measure as he did so. Maguire stayed still for a long moment, staring at Connell's bent head. Then he shrugged his shoulders slightly, let the latch drop and walked back to the table.
The mob round Harry Drew was urging him on, laughing and whooping: 'Rip it up her, boy! Bore it into her! Let her go!'
'All right, all right!' said Harry Drew. 'You think I talk for the sake of talking. But these flabby, time-serving politicians are getting up back home and telling us what we're thinking. Read the papers! The AIF thinks so-and-so. The AIF wants such-and-such. How the hell do they know what we want or think? They never ask us. According to these fat-arse opportunists we just love this war—we can't get enough of it! You know these boys will fight to hell and back, if necessary, and everyone does want to get in and get it over with. But what they really want—the old blokes anyway that have seen it before—is to get back home and stay. No one with any sense breaks his neck to get into a blue. No one really likes killing.'
Harry Drew smoked a stinking pipe and loved an argument. He knew the names of all the Cabinet Ministers and remembered who had sent scrap iron to Japan.
Hell, he was arguing about politics that night we stood on the start line at Tobruk. Full as a boot on army rum, he was, and laying down the law like he had a stand on the Domain. And he was still arguing—and willing to fight about it—when we moved into the attack.
The card game was breaking up and they were on a couple of rounds of show to finish—one draw and show for two bob a hand to finish the game.
'We'll have another round, eh?' invited Whispering John. He had insinuated himself back into the game—he never stayed out for long—and since he was winning a few shillings he played quickly, with suppressed eagerness and a small, cunning grin on his lips.
'I'll be in another round if you like,' said young Griffo. 'Another dozen if you like—I'm easy.'
'One more round will do me,' said Brogan. 'I'm two quid behind now and I can't see myself picking it up at this game.'
Sunny and Ocker grunted assent and old John flipped the cards round rapidly as they pushed their two bobs to the centre of the table.
'Come on,' he snickered confidentially. 'Put your money in the centre and play like scholars and gentlemen.' He was pleased with his catch-cry. 'This is where you make the money—you come here in motor cars and go home with the arse out of your pants,' he snickered.
'Come on, John,' said Brogan. 'Turn me over two broads—and not too many aces. Finish her quick—we land tomorrow and I want to get some sleep tonight.'
'Yes,' said John as he flipped the cards over, 'you need to sleep tonight—sleep as much as you can—you'll lose a lot from here on.'
*
Regan stirred uneasily in the thick, smothering sleep of the hold. The massed tiers of bunks around him were filled now and thick with heavy breathing and occasional snores. Curly Thomas, in the next bunk, had come up after Regan was asleep and turned the nozzle of the air vent over onto his bunk.
So Curly slept in the comparative comfort of the cool stream of air sucked down from the deck, while Regan sweated and tossed with bad dreams.
Bishie was threading his way through the sleeping tangle of the hold to fill his water bottle at the one tap, located over near the latrines.
The Laird was lying back, half asleep, his hands clasped behind his head, half listening to Dick the Barber.
'You know,' Dick was saying, 'a funny thing happened to a mate of mine once—a little bloke by the name of Spade Burns—you might know him if you worked out west any time.'
Deacon was falling—a slow, sickening fall into darkness—and there was a sudden shock as he threw himself back from the edge of the pit and jerked awake.
He was slouched over on his side and the pencil had fallen from his slackened fingers onto the pad. He looked at the sheet—his number, rank and name were on the top of the page, then: 'Beloved Margaret'. The rest of the page was a blank.
'Ah, hell,' he yawned. 'I'll finish her tomorrow when we get in.'
He put the pad and pencil under his lifebelt pillow and turned over heavily and uncomfortably to sleep. He could hear Dick the Barber's voice down the alley, and a grunted comment from the Laird.
Cairo Fleming put his toothbrush and paste back in the toilet holdall and slipped it back into his haversack. He kicked off his unlaced boots and climbed into the bunk.
'Night, Cairo,' said the Log drowsily from the next bunk.
Cairo closed his eyes. 'Night, mate,' he said.
Lieutenant-Colonel Connell poured the last of the whisky.
'Sluts,' he said. 'They're all sluts and she was as bad as any of them. I was glad to get away from her...'
Doc Maguire looked steadily at him with that same blank derision and made no comment.
Pez and Janos were bedded down in the shelter of a tarpaulin under the forward gun platform in the ship's smell of pitch and hemp. The sharp edge of the wind flicked at them and when the ship rolled it buffeted their shelter, whip-cracking the loose ends of the tarpaulin.
But they were wrapped in a warm cocoon of blankets—their own and some they had borrowed from the sweating sleepers in the hold—and had draped their ground sheets so the water would drain off down through the ropes and not collect underneath them.
They lay silent, rocked in the vast plunge of the ship, and heard the wind howling through the rigging. There is no sound like it on earth—the wind howling on the vast bowstrings of the mast and stays.
'We're riding out of the rain,' said Pez.
You could see the sky ahead was broken and a stormy moon was tossing in a streaming sky.
'Port tomorrow,' said Pez.
'Yeah,' said Janos: 'If the old tub holds together that long.'
Captain Dyall Jones, Master of the _City of Benong_ , patted the worn rail of the bridge as a rider pats the foaming neck of his horse after a hard run.
They were a pair, he thought, the ship and he. But for the brutal grace of war, both of them lay in Wreckers' Row.
Chicken farms in Surrey are a dream of the open sea, but when the fowls scratch under your window you dream of the sea again. Chicken farms and a war a-blowing?
He remembered getting out the good black suit and brushing it down—the smell of solid serge and mothballs. The trip to London—the polite disinterest of the Admiralty and the suggestion that this might be a younger man's war. The days and weeks spent sitting on hard wooden benches outside snugly closed office doors. A quiet, solid, stubbornly persistent figure in brushed black, twisting the hard-brimmed hat in his stubborn, ship-wise fingers.
Finally they got tired of his persistence and, in despair, had given him the _City of Benong—_ which itself was too old for a young ship's war.
They had been somewhere off the bloody beach of Dunkirk; the stukas had missed them when they ran for Alexandria after Greece fell; and the Son of Heaven had lost them in the darkness out of Malaya.
Captain Dyall Jones eyed the broken sky ahead.
'Keep her steady on that pattern, Mr Johnson. She'll do.'
'Aye, sir,' said Mr Johnson; and thought privately, with immense pride, what monstrous maritime things a man would take to sea in times of war.
Captain Dyall Jones left the bridge and the _City of Benong_ sailed out under a sky of streaming cloud and moon.
Pez lay trying to think of home.
He thought: 'I should be calling up pictures of how the fire would be burning in the front room at home on a night like this. And how it would be—coming in out of the rain to the warmth of the fire.'
But the images were all manufactured in words first and then forced into the brain. There was no real picture—no emotional memory.
Even in the thought of Helen there was no warmth—though God knows there had been enough fire between them when they lay together; and a deep, friendly warmth of peace and home on those calm evenings when they sat opposite each other, quietly reading or talking.
And then, of course, there was their problem—three people loving where only two could love. No good thinking about that—there could be no solution yet.
'When the war is over,' she had said. 'When you both come home.' There was loyalty in her—even if loyalty is not always sense. 'I can't write to Bob and tell him it's ended,' she said. 'And when he comes home and I know he's got to go again—I can't tell him then.' She had stared into the fire, her hands clasped against her temples, ruffling the shining brown of her hair. 'And I don't know whether it _has_ finished. I know how I feel about you, but I know he needs me. War and loneliness can twist things—you can't just grab what you think you want without thinking if other people have rights.'
The whole business seemed far away now. All you could do was say: 'Sometime—sometime I will again consider hotly the problems of life and love.'
But a man might never measure out that time, or know if it was coming to him.
Maybe that was the solution. If Bob was killed...
You couldn't wish him dead, but it would solve it. There would be no barriers then—no divided loyalties—no question except that answered by the hasty heart.
But there was no reality in that either. That was in the future, and a soldier has no future.
Suddenly he felt the great loneliness of himself upon the earth: the monstrous, lonely howling of the wind was in the rigging; he had lost his past—the future was uncertain; he was alone on a stormy-mooned ocean.
Pez settled back into the rough warmth of his blanket cocoon. He breathed the cold, clean air.
So there was no future—what the hell.
He slept.
## 2
Pez awoke in the first grey dawn, stretched his cramped body on the nest of ropes, crawled out of his blankets and went to the rail.
The _City of Benong_ was anchored in the lee of a small island that lay in the mouth of a broad, shallow bay. There was a great mass of shipping gathered in the calm waters of the bay—a war armada of rusty, sea-grey vessels. Invasion barges surged through the tangle. On the distant smooth black sands, a long line of barges were humped half on the beach, half in the water—their jaws flopping open on the sand like clumsy mechanical saurians.
At first glance the green bank of palms and jungle growth seemed solid. But as Pez gazed he saw the long palm-leaf buildings take shape under the camouflage of trees, the distant toy movements of men and trucks, the thin, hazel pennants of smoke from the cook-fires in the camps.
You could pick out ant swarms of activity where they were loading cases on trucks at the food dumps and the flow of movement in the marshalling yards on the beach where they were loading men and equipment into the barges.
Inland, the hazy, fanged, green mountains piled up into the mist of distance. Thick white cloud lay in the valleys and trailing scarves of it clung on the climbing jungle trees of the mountainside.
Pez turned to find where the sunglow was growing—got his bearings and turned to gaze down the long green shore.
This was the way they were going—down there where the trees and the foam and the beach faded into the perspective of sea and sky.
Down past there was Nip country...
Janos joined Pez at the rail.
He yawned: 'Christians awake and greet the happy morn!'
The order is to disembark at ten o'clock sharp. So at eight everyone has been herded up out of the hold and crushed into company lots on the deck with all their gear.
At twelve, we are still there in the open sun on the burning steel deck. At half past, word comes round: there will be no meal—we'll get that ashore—but there is a cup of tea down the galley for those who want it. There is a general scramble for chipped enamel mugs.
The troops are used to this old army habit: run like hell to the start point and then sit on your backside for two hours—move two paces and sit some more.
They are sprawled over the deck, some squatting on their packs playing cards, some reading paper-backed novels, a couple scrawling letters home.
Old Whispering John is still in the poker school. He is still winning and grins delightedly as he shuffles the greasy pack.
Some are slouched over the rails, checking up on landmarks and trying to establish the position of our troops and the Nips: 'Down there, just past that far headland—that's where the Fourth Battalion's holding them.'
Rumour and information—positive if not factual—comes scrambling aboard a troopship along the anchor chain as it drops into the shallows of a new harbour.
The young reinforcements are cocky and elated. They confidently pass on to each other the news that the Nip is starving and disorganised and half-armed. They make profound military assessments. They see this is going to be a snack, with all the glory and no danger. Some of them are condescending and almost sorry for the enemy. They begin to doubt, in their self-mesmerism, whether it is really worthwhile taking the trouble to defeat such a sorry foe. If they go on like this, they will be feeling offended that the brass hats have offered them such a menial glory.
But the old hands are not so complacent. Mud is mud and here they make mountains of it. And a starving animal or a starving man is fierce.
We hear that up the river the Fourth Battalion has struck some opposition from our 'unarmed' foe: three killed yesterday, a couple wounded.
It is the Yankee armada in the bay. They are leaving, sailing north, tomorrow.
We hear for the first time the legend of the nurses—the legend that goes with us down the long green shore. But it is always on a different track—over the other hill.
The Fourth Battalion brought out some Yankee nurses that the Nips had captured in the Philippines, we hear. The Nip officers brought them over with them and have been using them. One of these nurses is in a bad way—rotten with the pox. She begs them not to bring her back. She wants to shoot herself. She smashes a bottle and tries to cut the veins in her wrists. They're down at the hospital now, we are told. You can see it—that long native hut and those tents back behind that wooden tower—you can see the red cross through the trees.
God knows where this legend comes from, but every week or so it revives. Sometimes there are four nurses, sometimes seven. Sometimes the Fourth rescues them, sometimes the Fifth or First. But otherwise the story has the same theme each time—and lots of our blokes believe it and repeat it seriously each time they hear it.
These rumours and legends of the track and camp are the soldiers' literature and radio and vaudeville show. Rumours of peace, rumours of leave—legends of death and miracles of chance.
Most popular are the legends of the immorality and stupidity of officers—and a number of these are not rumours.
*
Finally, at three o'clock, disembarkation starts. A choppy swell has risen and we must go over the tall side of the ship and clamber down the wildly swaying scrambling nets, into the tossing barge below.
It is a heavy climb with the full weight of equipment on your back. Your arms creak in their sockets and the net bucks like a steer. And your mates still on deck, and those already safely down, jeer and cheer as you ride the wild ropes and stumble into the barge.
Dick the Barber is the last man down for our barge. We have to drag him off the net by force. He is white and shivering. Shells don't worry Dick so much, but heights terrify him. All the way over Kokoda he crossed those little vine and log bridges across the ravines on hands and knees, clinging like a koala.
The barge swings away from the ship's side and turns for the land amid ribald jeers from up top and obscene warnings of improbable fates in store for us ashore.
The section moves into the row of tents nearest the beach. The area had been a Yankee cemetery. The coffins were dug up only a few days before the battalion moved in and the area smoothed over with bulldozers.
Slapsy Paint, our Loot, appears and gives his usual vague directions about bedding arrangements and meal parade and wanders off again.
The heavy, leaden-grey casks of the Yankee dead are stacked over in one corner of the area. There are several hundred of them. A gang of American negroes, half-naked and glistening in the sweating sun, are loading them onto lorries.
Pez and Janos go down together to collect their bed boards from the dump near the temporary kitchen.
Jonesy, the thin cook, is idly inspecting the contents of blackened dixies ranged on the long trench fire. From time to time he pumps with his foot the roaring petrol burner that sprays a long, pent blue tongue of flame down the trench.
Pez sniffs hungrily: 'What's for dinner?'
'Stew,' says Jonesy. 'A good bully beef stew.'
'Well,' says Pez. 'If it's good you know what to do with it—a good thing never hurts you.'
They trudge home through the black sand with their bed boards and wooden support frames. Home...a word that means many things to a soldier. It can be a two-man tent in the scrub or a hole in the ground.
Those rows of tents in the naked square still have an unlived-in quality. The dirt on the floors is not even trodden down yet. There are none of the appurtenances of living that make a home—the food box in the corner, the water buckets outside the door, the blackened home-made billy for the inevitable brew of tea.
Everyone starts the business of settling down to a new home—according to taste, once the first scramble for a bed is over. Dick the Barber has the story of the coffins—Harry Drew has been to the 'I' section up the road and has the good guts about the Fourth Battalion—Laird has located food among the wreckage of the deserted American camp down the beach and has marked out a wire and sentry protected ration dump over the other side of the road for future reference.
The coffins belong to the Yanks who were killed taking this beach. They are taking them back down the coast and planting them until the war is over and then taking them back to the States.
'Why the hell don't they plant 'em and let 'em grow,' growls the Laird. 'Another piece of dirt's no different the way they are.'
'It's respect for the dead,' says Deacon. 'Don't you know the dead have to get more respect than the living?'
'Respect this bloke, then,' says Pez. 'He's through living.' Pez had been scraping the sand smooth underneath his bed and uncovered a thin-boned skull and a few frail ribs.
He tosses the skull into the middle of the tent and Fluffy grabs it and checks the teeth: 'No gold. The Yanks have cleaned him out before.' It was the first time Fluffy had ever handled a human skull. 'I'll take it home for me kid sister,' he says. He handles it gently as he passes it on.
Janos examines the rib bones: 'They're so thin.'
The Laird grunts: 'There's not much to a man when you get down to the bone.' Deacon made to pass him the skull. 'Don't give me that,' the Laird rumbles. 'I've seen too many.'
Deacon balances the skull delicately on his extended palm and addresses it with wry heroics: 'Alas, poor Yorick...'
'A swim! A swim!' the cry goes up. Clothes are flung off hurriedly and there is a dash for the tent flap.
Pez gathers the skull from Deacon's hand as he goes and tucks it under his arm. Fluffy tackles him as they race across the sand and Pez, as he falls, tosses the skull to Janos with a smooth rugby pass.
The bunch of lean, naked figures race, shouting, over the black sand to the surf. The bleached skull passes among them, tossed like a football.
Janos, on the fringe of the scrum as they near the water, misses a pass and the skull curves out in a slow arc—hits and rolls slowly until it fetches up against the shell-shredded stump of a coconut palm.
They leave it there and race on—poise for a moment on the firm, sea-washed sand of the beach—then rush down the shallow, shelving water of the ebbing wave and hurl themselves, yelling, over the white foaming wall of the incoming breaker into the deep, cool silk of ocean banked behind it.
Back in the tent Deacon drags out his airmail pad, sharpens a stump of pencil by slitting the wood away from the lead with a long thumbnail, lays tobacco, papers and matches handy, and disposes himself to write his letters.
'Come on down the Yank camp,' the Laird urges.
'I've got to write a letter,' objects Deacon.
'Hell, you can write any time,' the Laird argues. 'But if we don't scrounge through the Yanks early, all the best munga'll be gone.'
'I've got to write a letter,' insists Deacon. 'I've been trying to write it for a week.'
'Another day won't matter then,' reasons the Laird.
'But it's to my Queensland heeler—my Sheila—my best sort.'
'Then she's probably out with a Yank,' the Laird argues conclusively. 'Another two days won't matter.'
Deacon tosses the pad on his bed as he rises to go out.
'Beloved Margaret,' it opens with a little flourish.
The rest is blank.
It is a time of waiting and speculation, rumours and legends, old tales told of old campaigns, endless poker games with greasy, dog-eared packs of cards.
Discipline—the petty, stupid discipline of a base camp—largely disappears. The officers are not so insistent on being saluted at every turn—not that they got saluted at every turn when they did insist on it.
But still the daily bumble of routine orders harasses us.
For three days blankets must be folded in two to the centre and packs placed directly behind them on our beds. Then, for four days, webbing equipment must be laid out on the blankets with the bayonet pointing down. For six days after that the order is changed and bayonets must be laid diagonally across the webbing. Then the order is changed again: webbing equipment is moved down in front of the blanket and the pack must be placed in the centre of the blanket.
These ridiculous orders are an eternal mystery to the troops.
Dick the Barber supposes that the skulls must earn a living and justify their existence in some manner.
Every morning and afternoon there are route marches in the blazing sun with full packs.
They are brokenfoot marches. For a start our feet are tender from shipboard. And the air seems light in the tropics—it leaves empty aching spaces in your lungs after you have been marching a while. The pack straps cut deep into your shoulders as you march and after a few hundred yards you are panting like a fat poodle. The sweat squirts from your skin, saturating the jungle green shirt and slacks.
The only pleasure in it is to stumble in from the march and line up with your dixie at the cookhouse for a quart of tepid, sweet tea—you suck at it, blowing like a horse, and feel it soak down inside of you.
'I think you're being too hard on them right off,' Doc Maguire told Connell.
'Too hard, hell!' said Connell. 'I'm going to march them till they start to drop. Anyone that can't stand this pace won't stand the going further up. I don't want any weak sisters—I want them hard and tough and hungry when I take them in.'
'You can march them in the morning for one hour, Cliff,' said Maguire. 'There'll be no route march in the afternoon.'
They were standing beside the table in the RAP tent. There was no one else in the tent; but young Cliffie, the orderly, who was painting the dermatitis on Brogan's backside in the adjoining tent, heard what was said.
Connell stopped for a moment as though he wasn't sure what he'd heard.
'What the hell do you mean?' he said.
'An hour in the morning, Cliff, no marching in the afternoon,' said Maguire calmly. 'You'll break those men if you keep on running them like you are—you won't harden them, you'll break them.'
'I'll march them how I want.'
'Not while I'm the Doc, Cliff.'
'Keep to your lousy pills—that's your job—mine is to make these men ready for the track.'
'That's my job too, Cliff.'
'I'm the Colonel!'
'I'm the Doc, Colonel.'
'Not when I'm through with you, you won't be,' snarled Connell.
The thin red veins had sprung into a scarlet web on his white face. He picked up a thin glass beaker and smashed it on the table: 'Like that you'll be—from tomorrow!'
Connell was on his way out of the tent. He couldn't have heard, but the Doc murmured to himself, almost with a quiet certainty and satisfaction: 'An hour in the morning—none in the afternoon.'
After a while the Doc came into the tent where young Cliffie was practising his impressionist art on Brogan's haunches.
'How are you, lad?' he asked. 'How are you feeling?'
There was something new in the Doc's voice—he really sounded as though he cared how a buck private was feeling with the island itch around his backside.
'Not bad, Doc,' said Brogan.
Brogan had never before called Maguire anything but 'Sir'—with politeness as insolent as was safe.
Next day we marched for an hour in the morning—there was no march in the afternoon.
A good deal of the day we surf and sunbake naked on the sand. Soon we are nearly as brown as the native boys.
Equipment is checked and issued. We line up at the grindstone in the pioneer tent and sharpen our bayonets—they're handy for opening tins.
Rations are pretty light on at our cookhouse but we live well by scavenging on the Yankee rubbish dumps down at the old camp and by raids on the ration dump through the barbed wire.
The Yanks always seem to have too much of everything—compared to us—and they always seem to leave half their gear behind them when they go.
Down past the point there are hundreds of jeeps and trucks and amphibious craft rusting in the Yank car park. One company dumped twenty good jeeps in forty fathoms of water out past the reef because they had no one to hand them over to and they didn't want to take them with them.
There is good scrounging down at the old Yank camp. Rubbish is piled up in the deserted mess huts and kitchens—shattered crates and boxes seem to have been hurled together in a pile in the middle of the floor. Some of the tins have busted and are rotten, but most of them are quite good. Anyway we always listen when we puncture the tin to make sure the air sucks in and the vacuum seal still holds.
Scratching around the camp one afternoon, Pez and Janos found themselves caught between sundown and darkness in the mess hut. It was a strange feeling—suddenly the light was grey and the beach was desolate. Everything seemed very silent, as though there were watchers in the fringe of the scrub and in the shadows of the sand dunes.
The flywire door, torn off its hinges, flapped mournfully against the wall. It was some distance down the beach to their own camp—the tents were out of sight. No one was visible on the beach—it might have been the end of the world.
'What the hell are you running for?' grinned Janos as they went back down the beach quicker than was really necessary.
'That place didn't feel as though it liked having me there,' said Pez.
The Yank rations are so good that even their rubbish dumps have better food than we've got in our kitchens. Every tent is crowded now with tins of pineapple and peanut butter and assorted stews and hashes. In some of the field rations there are cigarettes and glucose lollies. At night we drink American coffee and munch American-issue chocolate (made in Australia, but not for us) and puff American cigarettes.
There is a deal of discussion about the Yanks. They are all right—they fight well, when they can throw a couple of hundred tonnes of high explosive into a position. They live too well—compared with us, that is. They get too much money—compared with us. They talk as though no one else was fighting the war. They take our girls. 'Over-dressed, over-paid, over-sexed and over here.'
All that's left of them here now is the sustaining rubbish dump of their food, and after a few days the Laird passes the general judgment on that: 'It's all right,' he says, lifting his nose from a dixie of American corned beef hash and baked beans. 'It's all right for a change, but it's too sweet and too soft. For the track—for the hard road—give me our old bully and biscuits. You'd go further on a tin of bully and a packet of dog biscuits than you'd go on a hundredweight of this stuff.'
Things are pretty quiet here.
Only one night Regan gets frightened by the shadows on the beach during his guard. Dick the Barber comes on as his relief. Dick comes up softly through the sand without him hearing and when Regan looks up and sees this figure standing beside him he drops his rifle and runs screaming along the beach.
We found him a couple of hundred yards along where he had fallen in the sand and couldn't rise again for terror.
We got him back to the tent and Pez feeds him the quick cup of coffee Brogan put on. The Laird and Harry Drew are quietly recalling how frightened they've been from time to time by shadows: 'I would have screamed then,' the Laird recalls, 'but I couldn't.'
Doc Maguire walked into the tent. There was a moment's silence and no one seemed to know what to say.
'I heard someone,' said the Doc. 'Young Cliffie told me it was down here—I thought somebody might be hurt.'
'No,' said Pez. 'Just one of our blokes got a bit of a scare and gave a bit of a yell—he's not hurt.'
The Doc was looking at Regan where he sat huddled on the bed: 'Fear can hurt, too. Are you feeling all right, lad?'
There was silence in the tent and all eyes turned to Regan—some things a man has to say for himself.
'Yeah, I'll be OK, Doc,' managed Regan.
'I thought maybe he should come up to RAP for the night. We could send him to sleep, make sure he got a good rest.'
'I think he's better here, Doc,' said Pez. 'I think he's better with us.'
The Doc looked round the tent: 'Yes—maybe you're right.'
There was a long pause. The Doc didn't offer to go. A decision was made and approved by all without a word being spoken.
'Would you like a cup of coffee, Doc?' said Pez. 'We just made a quick brew.'
'Sure,' said the Doc. 'Thanks.'
'Here's a mug,' said Bishie, emptying the dregs of his coffee.
Pez sloshed some water from the bucket and washed the grounds out. The Laird had the billy ready and filled the chipped enamel mug generously.
'Milk?' said Pez, reaching for the condensed milk tin.
'No thanks, Pez,' said the Doc. He sat on the edge of the bed beside Regan and ladled sugar from the biscuit tin container that Pez presented to him with the air of a host.
Medals and strips of ribbon are hard-won things and you can wear them proudly if you have that sort of pride. But there are other things—more common, more generously given, but harder to win—particularly for officers, harder to win. We are brothers, we are men. Our words will never say the things we mean—but living we will drink to you. Dead—our hearts will weep for you.
The Doc sat on the edge of the bed and sipped from Bishie's chipped enamel mug.
'Bloody good coffee,' he said.
The Nip was down the road too far to do any damage to us but you could get the scent of him—that rotten-sweet incense smell he left behind him in the jungle.
His burned, shrapnel-pocked trucks stood along the side of the road—under some of them a crumbling skeleton. Rusting iron push-carts, jungle carts, were scattered round in the undergrowth with pieces of rotting webbing equipment. There were scores of Nip rifles—mostly broken and half-burned—and clips of ammunition half-buried in the sand.
There seemed to be a strange foreign significance to all this junk. You never actually thought it, but you felt: 'This was the enemy; he lived here; he used these things. This rising sun laid out in wood, with the heart burned black and dead—this was his cook-fire.'
The enemy is always strange and there is a faint awfulness about the place where he has been. For you can never imagine the enemy as just a man—if you could, perhaps you would never kill him.
The poker game was going one afternoon; Laird was darning a pair of socks and Deacon was contemplating his letter to Margaret, when Dick the Barber stuck his head in the flap and announced:
'They ate the bookie from the Fourth Batallion.'
He was a nice bloke, the Fourth Battalion bookie. He laid fair odds and you could always be sure of the dough come settling day. Not like Scottie of the Second who welshed on a good book and went through sooner than pay—even though he had plenty socked away at home, money that he'd made from the game. A loud-mouthed alec, Scottie had always been. But the bookie from the Fourth—he was a quiet sort of a guy; he'd done a bit of pencilling before the war and set up in business for himself when he enlisted.
A patrol had gone out across the river and run into an ambush. They had two killed and hadn't been able to get the bodies out with them when they withdrew. Next day they attacked and recovered the bodies; but when they got them they found the brains, kidneys and liver had been cut out and slices of flesh cut from the buttocks.
Harry Drew sucked strenuously at the gurgling bowl of his pipe: 'Yes. We struck that last time in the Owen Stanleys—about Templeton's Crossing—up above the Crossing I think it was. We found the bodies with the flesh cut off the backsides and we found fresh meat in the dixies round their cook-fires later on. But whether they were eating it themselves or feeding it to their dogs—they had a lot of dogs with them—we never really found out.'
'I don't think I'd fancy being eaten,' says Janos. 'Not that it matters when a man's dead—but somehow I don't think I'd fancy it.'
'No,' grinned Pez. 'It's sort of undignified.'
Deacon, lounging back on his bed, head propped up on his webbing pack, flicked a cigarette butt through the flap of the tent with careful concentration before he spoke: 'That's a question—how hungry would you have to be before you'd eat human flesh? A question. Myself, I reckon I came pretty close to it that last time. They say it tastes like pork.'
'How would Selby go?' asked Pez. Selby was the fat cook. 'Old long-pig Selby—the man I'd sooner be shipwrecked with.'
'That bookie from the Fourth had a wife and kid, didn't he?' rumbled the Laird from the corner.
'Yeah,' said Pez. 'Two kids.'
The mail finally caught up with us and most had two or three letters. Some of the literary boys had as many as a dozen, but most of us didn't have the stamina to write to that extent.
Janos had two letters—one from his mother and one from Mary. The one from Mary was quite short. He had opened it first. He read it and then put it aside while he opened his mother's letter and read that slowly.
Things were not good at home. His younger brother had been staying out at night. The landlord had been trying to get them out of the house. There was not much money, but his allotment was helping greatly. Where was he? Was there anything he needed? When would he be home? When would the dreadful war finish?
His mother—she was a woman whom he felt he only vaguely knew. Older than she should have been. Sick and broken and defeated. Always on the verge of tears and infuriating in her ineffectual passion to be possessive of her children. They had never known her. They had been alien to her all their lives, although they kissed her goodbye and fled her tears when they went to the wars, and bothered to half-lie to her when they had been out all night.
Janos turned back to Mary's letter and read it through twice more.
Pez looked up from Helen's letter on the other bed: 'Get one from the Queensland?'
'Yeah, I got one,' admitted Janos.
'I'll get the sporting page off you later,' said Pez.
'Ain't gonna be no sporting page,' said Janos. He tossed the letter across to Pez. 'A Yankee marine—she wants to live in Idaho—she sends her love and hopes I'll understand.'
'You understand?' asked Pez.
'Sure! Elementary, dear Watson! A Yankee marine—she wants to live in Idaho—she sends her love—sure, I understand!'
'Snap out of it,' says Pez. 'Helen sends her love.'
'Tell her thanks,' said Janos. 'But the phrase is distasteful to me just this once.'
Helen knew Janos though she had never seen him. Our wives and sweethearts knew our comrades whom they never saw—sometimes they knew them better than we did.
'You weren't banking on her, were you?' Pez asked after a while.
'No,' said Janos. 'I don't bank on anything.'
'There'll be time to look around when we get back—you can do better. To hell with her.'
'It's a long way to go just to look around,' said Janos. 'Even when you know nothing will come of it, it's good, while you're away, to know that there's a door that you can knock on first when you get home. So long as you've got a contact you can feel you're not all soldier—you can be half a man still.'
Janos was still carrying this black mood around with him when he ran foul of Connell in a dirty temper.
Connell hauled Janos out in front of the section and abused him: 'You're not even a soldier's bootlace,' he told him.
Janos was standing very stiff and straight and he answered Connell back though his voice was so low we could hardly hear him: 'We'll see about that after we've been up the track a bit,' he told Connell.
We thought Janos was a moral to go along for answering back but Connell just sneered at him: 'We'll see,' he said.
Janos was still taut with anger when he fell in again beside Pez: 'I'll show him—I'll show the rotten bastard.'
'Take it easy, boy,' muttered Pez.
Later, they lay on the beach, baking in the sun.
'You won't show anyone anything unless you relax and watch where you're going,' said Pez. He was worried. It's bad for a man to be caught up in anger with one idea. He doesn't watch where he's going or what he's doing—he walks into things on the track.
'Sure, I know,' grinned Janos. 'I'm having a tough trot. I'm feeling sorry for myself. In the words of the classics: "Dear Bill—What a bastard!" '
He lay for a moment and then he said quietly and earnestly: 'I will show him though—and to hell with her.'
The natives were coming back from the hills now, where they had fled when the Nips struck this coast. The poorest refugees in the world—refugees in the jungle.
Pez and Janos watched them come down the wide dusty road that curved round the bay.
A tribe moving camp, or on the march, moves in order—the women, bowed against their loads, laughing and chattering—that shrill island laughter—the men striding out and the children running and laughing beside them. Going to work in the mornings or coming home in the evenings, there is laughter and chatter and they will sing—they are together, there is community among them as they move.
But these people moved silently and slowly. Pez and Janos stood on the side of the road and watched them come.
There were about forty of them strung out down the road—incredible skeletons, their black skins tinged grey with sickness and starvation. They were naked except for strings round their middles holding a piece of rough bark or rough-woven grasses to hide their genitals. They carried nothing but sticks to help their walking and a few clutched leaf-wrapped fragments of food.
They were not moving together. Each one walked as he could and the few children, their bellies swollen with hunger, kept close beside their parents and their heads hung down. There was no talk and no laughter.
'The poor bastards,' said Pez. Janos was silent.
At the end of the line was a man. As bone-thin as the rest, he yet walked with a stubborn, savage strength about him and his sunken eyes burned in the hawk-like skull of his face. He carried a thick hollow bamboo stick. He looked up, straight at them, as he came abreast.
'What have you got there, mate?' said Janos.
The native stopped and tapped the bamboo enquiringly, as he looked at them. Janos nodded.
The man squatted in the dust, keeping at a distance from them. He up-ended the bamboo and shook it, watching them all the while. A tight bundle of gold and white feathers shook out. He caught it in one hand and held it up to them, expressionless.
'Bird of paradise,' said Pez. They came closer to see it. 'And Christ, she stinks.'
The skin had not been properly cleaned and was rotten—putrid flesh and long, slender, gold and white feathers.
'How much do you want for it?' asked Pez.
'One and six,' said the native carefully. He pronounced it _one and sick'ss._
Pez dug into his pocket, pulled out some coins, and offered him a shilling, a threepence and three pennies. The native shook his head: 'One and sick'ss.'
'He wants the right coin, I suppose,' said Janos. He pulled out a zac and tossed it to Pez.
Pez showed the man the coins—the shilling and sixpence. He nodded and proffered the bird.
'Wait a bit,' said Pez. He went and plucked a large green leaf and took the bird on it. The native picked up his bamboo and set off after the others with long, stubbornly strong strides. He clutched the coins tightly in one hand.
Janos cursed and abandoned his attempt to knock a green coconut from the palm by hurling stones at it.
'Hey!' he said to the big bronzed native boy who had watched his efforts for some time with a quizzically philosophical look. 'Hey, what about shooting up the tree and getting a coconut for me, mate?'
The boy looked at him and grinned without answering. He was a big fellow with a graceful, proud body, a spotless scarlet lap-lap twisted around his waist and a scarlet hibiscus tucked in his crinkly black hair.
'Hmm,' thought Janos. 'Doesn't speak English, eh.' He tried to recall what little pidgin he'd picked up from conversations.
'You fellow,' he began, uncertainly but beguilingly. 'Catchem coconut belongem me.'
He paused expectantly. But the boy just grinned at him.
Janos gestured dramatically to the boy, the tree and himself and tried again: 'You fellow catchem coconut belongem me—me fellow givem cigarette. One cigarette—two cigarette—three cigarette,' he coaxed, carefully raising three fingers in turn. 'Go up along tree, catchem coconut bringem me.'
But the boy just grinned.
Then, just as Janos, desperately, was about to try again, the boy spoke. Perfect colloquial English, with a slight American accent: 'I really wouldn't eat them yet—they're too goddam green,' he said. And walked away.
'Christ,' said Janos, retailing the story with great delight. 'I could have belted him in the teeth! There's me battling with the pidgin—trying to get him up the tree after the coconuts and after all that, he turns to me and says, "I really wouldn't eat them yet—they're too goddam green." '
Nearly six weeks we had been here now...six weeks of nerve-tightening expectancy and subtle shaping of the mind for battle and hardening of the body for the track.
We crowded round the sand table with the country sculpted out in miniature and the 'I' Officer gave us the disposition of our own and the enemy forces—reports brought in by native patrols from deep in Nip territory. There were patches of prophetic red on some of the features along the toy shore. We were to know them in time—Bayonet Ridge and that dark gulch where Slapsy Paint would lie dying in front of us through the long agony of a dying day.
We attended lectures on malaria control, hygiene in the jungle, scrub typhus.
Over the road, 'A' Company showed they had learned their lessons well and were prepared.
They had a new sergeant major—a pukka, spit-and-polish type—who had decided to come and get himself a bit of combat glory before the war ended after spending the first four years of it at Duntroon frightening would-be officers.
He tried to pull his Duntroon stuff on 'A' Company. They warned him several times, but he took no notice. Then one night they caught him in the dark and beat him up. They knocked him down and then kicked him about a bit.
Not very pretty—but it showed that the boys were ready for the trail. This wasn't a pretty business.
Connell called a battalion parade.
When all the companies were drawn up on the sandy square he took over without ceremony and stood them easy.
'Now keep quiet and listen,' he said.
They slouched, leaning on their rifles, and tipped their hats forward to shield their eyes from the glare of the sun. Connell walked slowly up and down in front of the slouched jungle green ranks—turning a little from side to side to include them all as he spoke.
'I want to talk to you, men,' he said. 'This is the last time I will talk to you all together before we go into action. It will be the last time I'll talk to some of you—before we finish this show, a lot of you will be dead.'
'Cheerful bastard,' grunted the Laird.
'There have been a lot of rumours around that the Nip was starving, that he was disorganised, that he had no arms or ammunition.
'I have instructed my officers to tell you, and I give you my own word now, that such is not the case. Some scattered members of his force may be starving and unarmed; but the great mass of his army is intact, well fed and well armed. They have nowhere to retreat to except the jungle and you will find them a desperate and skilful and completely savage foe.
'We are going to search out this enemy and destroy him! And, in order to do that, we must be more cunning, more skilful, more enduring and more savage than he is himself.
'I don't know what you have been taught in the past, but as far as I am concerned, you can forget what they call the "rules of war". The little yellow bastard knows no laws of decency, or humanity. We'll have no time to take prisoners—destroy them where you find them in any way you can.
'This is going to be no picnic. You are fighting through some of the worst terrain in the world and fighting the most savage foe in the world. A lot of you are going to die, but this battalion, if I have anything to do with it, is going to be the best battalion in the divvy.
'I think it's the best battalion in the divvy at the moment—and it's going to stay that way if I have to kill three-quarters of you to do it.
'This is a hard game and you've got to be bloody hard to play it. I won't ask any man to go anywhere I won't go and I expect every man to follow me to the end.
'Any man who hasn't the guts to go the full distance can take his pack and go now—I don't want him with me.
'The only thing I can promise you is blood and guts—and I want to see more of the Nips' than your own. I can promise, too, that you will eat more regularly this time than you did in the Owen Stanley campaign—there'll be no ten men to a tin of bully beef a day this time.
'That's all I've got to say—except to wish you Good Hunting.'
Janos' voice fell clear and casual through the parade: 'When do we go, sir?'
Connell looked straight at Janos a moment. 'I don't know—but it won't be long.'
A challenge had been noted and remembered.
As we marched back to our tents, Deacon was murmuring with mild inanity: 'Before our wedding day, which is not long...'
'What the hell's that?' says Fluffy.
' _Prothalamion._ I think.'
'What?'
'Sweet Thames run softly till I end my song...'
## 3
Remember, we played poker a lot—hour after hour the greasy broads fluttered over the blanket. You could lose yourself. There was no need to think and the money didn't matter much, whether you won or lost—this was no time to think about money.
The brain could not be shaken with vague fears—you could lose yourself in the calculation of two pairs with the chance of filling or the chance of buying a gutzer straight.
'Never try and buy the middle pin to a straight,' Dick the Barber used to say. 'There's men walking around today with the arse out of their strides through trying to buy a gutzer.'
You could sit for hour after hour in the mechanic oblivion and mechanic excitement of the falling cards—even the cramped and aching muscles from uncomfortable positions became part of the pattern—you became reluctant to ease your aching back and legs because that meant leaving the security, the refuge, of this cave of cards—and outside the night is empty.
Soldiers' talk is casually blasphemous and obscene but there's no real offence in it—it doesn't mean what it says, mostly.
They talk about women, of course. They tell lies about their conquests and amorous adventures in Alexandria and Athens—some rapacious Egyptian trollop can become a Cleopatra in retrospect, and an Athenian shop girl is touched with the immortal fire of Helen—or are you sure she was not your Helen? They sacked and plundered more than Troy to tear her from your arms, and she wept when you were leaving, and I doubt if Helen's ancient tears made such bright and bitter rain.
But the fierce sexual torments that the popular novelists attribute to the soldier on the tropic isle are not for us. You don't find them so much in the infantry—not when there's a blue brewing anyway. Those placid, safe and deadly monotonous base jobs are where such fiery worms breed in the brain and bowels.
In the infantry there is the compensation of that strong comradeship that you never get in a base job. There is the simple animal necessity for subjugating all other desires and instincts to the track—the earth is our lover; its dangers and its refuge. There is the strong emotional and physical catharsis of fear and battle.
We think of women, sure; we talk of women; we desire them; but of way back and of way ahead.
The Laird spoke nearer the truth than the novelists when he stretched back from the lantern one night, tossed aside the letter he had been reading, and sighed prodigiously: 'Ah, I wish I was back home with Mumma—I wouldn't complain, even if she put her cold feet on my back.'
There was the usual outburst of bawdy clichés and variations on the theme.
'It's a great sport,' said Whispering John, licking his lips in lascivious travesty. 'The old indoor sport, the horizontal game.'
'Don't tell me you still indulge, John?' said Deacon.
'Why,' said Fluffy with delight, 'a good sweat and a green apple would just about finish you, John.'
'Don't you worry,' sniggered John confidentially. 'I've had my days—I've done the stations of the cross in Paris and had my nose rubbed in the Bowery. I'll warn you: if ever you get to the Bowery don't go putting your head through any trapdoors you might see—you'll get your nose rubbed if you do.'
'Were you ever married, John?' asked Fluffy seriously. 'If you don't object to a personal question, like?'
'I've got an Irish wife in Liverpool,' said John. 'And that's why I've never gone back. I've got a fat white wench in Panama who looks for me still. And I'd have married a brown girl in Manila—but her husband turned up first.'
The Laird stretched back on his bed and boomed to the world at large: 'Time for a brew! Who's putting the brew on?'
'I'll light the fire,' said Bishie. He swung his feet down off the bed, tossed his paper-backed thriller, _Death in the Dog House_ , into the appropriate trash box in the middle of the tent and yawned.
'Best go up and scrounge some petrol from transport,' said the Laird. 'Scorp will give you some—say I sent you.'
'Is there any wood?' Bishie wanted to know.
'No wood,' said the Laird. 'We'll get some petrol and make a dirt fire.'
'Someone get the water,' said Bishie as he went out. He tripped, as he always did, over the fly rope of the tent, and his good-natured curses faded down the line.
Dick the Barber looked up for a moment from the poker hand he was studying in the corner of the poker game: 'I've got the supper: tinned snags from the Yanks and Selby gave me a loaf of bread—you'll just have to cut the mildew away from the edges.'
'I'll get the water,' said Regan. He laid down a letter he had been writing, crouched over a stump of candle on a box in the middle of the tent. 'Where's the billy?'
'The william can,' directed the Laird from his relaxed position on the bed, 'is under Pez's bed. There's no water here, but there's a bucketful under the flap of the first Mortar tent at this end—if you go up quietly they'll never know you took it.
'And now,' said the Laird. 'We want someone to make the toast and heat the snags—a reliable man we want. What about you, Cairo?'
Cairo left the card game he was watching in the corner: 'Yeah, I'll make it,' he said. 'Where's the stuff?'
'Outside in the box the bread and snags,' the Laird issued his communiqué. 'And there's some margarine in the tent next door—ask Ocker for it if you can't get it without him seeing you.'
Cairo paused at the flap of the tent and looked at the Laird: 'What the hell are you doing in all this?' he asked.
'Me?' boomed the Laird. 'Good God, if it wasn't for me there wouldn't be any supper—I organised it.' He settled back on his pillow.
The card game went on. The table was a blanket spread on two cases of .303 ammunition. The lamps were two empty jam tins filled with rifle oil scrounged from the Q store, with pieces of tent rope threaded through the centre of the lids for wicks. They had been made under the Laird's directions and gave a fitful yellow light and a thick curling tongue of black smoke. All the card players spat black for a month after they got rid of those lanterns of the Laird's.
Notes and silver were scattered on the blanket in front of the players and they sat crouched on boxes and buckets. Dick the Barber shuffled the cards with swift, neat flicking movements of his well-kept fingers so that they whispered and rippled as he ran them. It was a smooth shuffle, of long practice—a gambler's shuffle, a cardsharp shuffle—and pretty to watch.
Not that Dick the Barber ever cheated at cards, but he'd learned the art when he was a young bloke and used to play with the crowd from Clancy's gym out in the old back room behind the stadium. Banker Orville taught him, and Banker knew more about shuffling cards, but Banker never took money from a sucker—unless the sucker thought he was smart, and then he took it off him just for the good of his soul and to teach him a lesson.
Old John had left the game once already tonight after being beaten three good hands running by young Griffo. He had taken himself for a walk up around the orderly room. His stomach and back were aching from the discomfort of his box seat and his mouth was stale and bitter with nicotine from the constant, nervous smoking.
He had felt an impotent fury at himself, for losing the bets and for showing his anger. Old John wanted to be liked—he had a great hunger for friendship and affection. But his small soul could only ape the words and gestures of it.
They were probably talking about him now. 'Old John always squeals when he loses,' they'd be saying.
Young Griffo would be counting his winnings and saying in that calmly sarcastic voice of his: 'Hell! If I'd known he was going to whinge so much I'd have given him a quid to stop the game from breaking up. I've a good mind not to play with him again. I don't like a man that can't lose.'
Old John couldn't stay away long. He wandered back to where the remnants of the game were playing cribbage. He wandered up, carefully casual, and watched their play for a while with a small slavey grin. The brown leather of his face was drawn tight over the gaunt bone and his forehead was bald to the top of his head—a skull face.
There came a break in the play and old John moved back into his seat and sat grinning in what he meant to be a pleasant fashion but which had something of the quality of a dog that has been kicked but still wants to be friendly.
He grinned, showing dirty teeth, and said in a hurried, confidential whisper: 'I borrowed a few shilling up the road—what about we go back to poker again, eh?'
'I'll run 'em round for deal,' says young Griffo, flicking the broad around face up to each player. 'First jack.'
The Laird finished his last bite of toast and rich, greasy pork sausage.
'Yeah,' he said. 'This bloke had gone away and here's this orchard heavy with fruit. Well, we think. It's a pity to see those poor citizens in the city deprived of their vitamins. So we borrow a horse and dray and slave for a fortnight—taking the stuff by night and casing it up and freighting it away.
'About ten days later we get a letter from the Market Board. There's no cheque, but a little note that says, "Dear Sir," it says, "We have disposed of your consignment of apples but the return was insufficient to cover the cost of freight and we enclose a bill for ninepence which represents the balance of the freight charge. Trusting you will forward this amount by return mail, we remain, yours faithfully..."
'Yeah, we worked for a fortnight for less ninepence.'
The Laird was remembering that shed at Ginty's place where they stacked the fruit—working by the flickering yellow light of a hurricane lamp which stained the warm, sweet darkness of the shed.
He sank gently, and aware, into the warm flood of memory...the thin, sappy smell of sawn pine from the boxes and the mellow, ripe smell of the apples, and Ginty giving them a hand—his slow, amorous voice, a voice that licked its lips and savoured the words with earthy lasciviousness—as he told the story, the long anatomically detailed story of a generous-bodied French prostitute he had lived with for a week in Paris during the last war. It was Ginty's only story and he had been telling it every night—any time Ginty talked for more than five minutes he started to tell the story or else started to complain about his wife who was tall and thin and mean with herself.
Ginty was dead now—a tree had fallen too soon under his axe.
Regan held up his book but he wasn't reading.
This would be his first time in action. It had always been the same for him—this fear of being hurt and fear of people knowing...
When he was only a kid, his father was trying to teach him to swim out to the reef where it ringed out about fifty yards from the shore, making a smooth pool in the surf. The 'Blue Hole' they used to call it.
'I'm going to teach you to swim, son,' he said. 'The same way as my old man taught me.'
He picked young Regan up and threw him as far as he could out into the smooth water. And when the child came to the surface choking and crying:
'Go on! Swim! Swim!'
But the child floundered in terror, choking and crying, and was half-drowned when the father finally dragged him in. And later, when they got home, old Regan gave the kid a thrashing, a cold-blooded thrashing, for being a coward. Old man Regan had fear in his heart, too.
So Regan lay very still and thought of all tomorrows. Desperately he wanted to be accepted as one of these casual, hard-bitten men—as they appeared to him. But all the time the fear was gnawing at his bowels and he was afraid it must show in his face.
That was why he gambled and lost all his money. He wanted them to say: 'He's a good gambler, Regan!' And he talked big and casual about rackets and brawls. He wanted them to say: 'Regan knows how to take care of himself—he's been around.'
He tried to imagine himself in action—tried to imagine what it would be like from what he'd heard...
'We're cut off,' the Captain says. 'Someone's got to try and get back through the valley, but I'll say it straight—it's a hundred to one shot if you get through. Anyone take it?'
No one in the battered little group stirs. Then Regan gets slowly to his feet and settles the sling of his Owen on his shoulder. He draws deep on the stub of his cigarette and flicks it away deliberately. He rubs the back of his hand across his bristly chin.
'I'll go,' he says casually.
He tried to imagine himself on a lone patrol...or leading a bayonet charge on a hill...
But always in these imaginings there came the moment of pain. And although he couldn't conjure the feel of lead or steel biting into his flesh, he felt the numbing terror in his bowels—the same dazed, blind terror he had felt when he was a child smothering in the smooth water.
And he thought desperately: 'What will I do? How will I know what to do?'
He tried to wipe the dreams away and concentrate on his book. But after he had read a few lines the print blurred again and the pattern began to weave over.
An odd line kept turning in his brain: 'That was a long time ago and in another country...'
It was a line he had read somewhere, or a line Deacon had used, but he couldn't remember—at school, maybe...
Young Snowy from the orderly room stuck his head in the tent. He was wearing a large mysterious grin. 'Sergeant Pennyquick, your presence is requested at the Company orderly room...but quickly.'
There was a babble of questioning: 'What's on? What's doing, Snowy? What the hell is it this time? Is it the move?'
Whispering John tossed down his hand: 'Deal me out until I find out what's up.'
Snowy lingered a moment after John was gone: 'This is it,' he said, grinning significantly. 'I'll drum you—pack your bags—this is it—that's all I'm at liberty to divulge.'
'This is it—this'll be it,' said Bishie. 'Now's the time to say your prayers.'
'Praying'll do you no good,' said the Laird. 'If your number's up, it's up—that's all there is to it.'
'Oh, I wouldn't altogether disbelieve in the power of prayer,' said Dick the Barber.
'I remember a lass called Bertha—a big lass, beef to the ankles, but a hell of a nice kid. Her father used to run the Four Square pub down the 'Gong. "Big Bertha" we used to call her.
'She was always good for a round of drinks on the cuff if you ran short of change and she was always good for a bite if you were short of a quid. Her old man had a couple of dogs and used to train them down on the back track where we ran ours.
'Well, this night Bertha and I went out to the dogs at the Park and there was a dog called Poppies Pride in the fourth that she reckoned was a moral. She had a bad trot in the first three races and up comes this Poppies Pride event. She slaps every cracker she's got on this Poppies Pride and borrows a quid off me and slaps it on the terrier as well.
'Well—the red light's showing and away they go. A broken-down hound that hadn't won a race since Christ was in short pants—a hound by the name of Bigfoot Bill—scarps to the front. And, as they come to the straight and down the field, there's Bigfoot Bill looking a cert and about ten lengths behind him Poppies Pride flat to the boards and the rest of the field nowhere.
'Well, Bertha, she's jumping up and down and screaming for this Poppies Pride to come on! Come on!
'Then, of a sudden, she stops and sits down quiet and clasps her hands and looks at Bigfoot Bill and says in a gentle voice, sort of reverently: "Fall, you bastard, fall."
'And the next hurdle Bigfoot Bill runs slap bang into it, falls arse over head and breaks his neck. Poppies Pride romps home and Bertha collects and I get my quid back.
'So, I wouldn't altogether disbelieve in the power of prayer.'
Cairo, the Log and Fluffy sat together on the edge of the end bed, facing into the darkness towards the sea.
'You won't find it so bad,' the Log was saying, quietly. 'You'll be frightened—everyone is—but you'll get through it. You go through it with your mates, you rely on them, they rely on you. The worst is the loneliness—not so bad in the jungle, but down the desert—when you're moving forward under fire, strung out in a thin line five yards apart, you get awful lonely. You find yourself edging over to the bloke next to you—it makes you feel better to be close to someone. But that's a bad thing—keep scattered, keep apart all the time, then if they get you they only get one—if you're together, the whole group cops it.'
He nodded his head towards the crowded tent: 'They'll fight well, these boys...'
'Hell, there'll always be wars, Harry,' said Janos for argument. 'It's in the nature of man.'
'Then change his nature,' said Pez.
'Is it the nature of man?' demands Harry Drew. 'Or is it the nature of those who lead him, of those who sell and buy?
'Is it man's nature to destroy himself? To shut himself away from all the comfort of the world? Think! Think! While ever there are a hundred million people in the world who parrot like you that war is man's nature—that wars will always be—then there's no hope for us. There's enough blindness and treachery in the high places without ordinary people turning to hatred and stupid cant.
'There's probably not one of you really knows what he's fighting for. You never think! All you can do is parrot that there'll always be wars. It's only by chance that you are fighting this time on the right side. It's just that man is really good at heart, that injustice stirs him to anger of itself, that he will fight for liberty by instinct. Man progresses despite himself—out of a thousand, million blundering years...'
'But we progress,' insisted Pez. 'We progress.'
'Sure, we progress,' said Harry. 'We have done wonders! We have conjured new life, new states, new miracles of machines from the earth and air since the century turned. But how much faster, how much further, could we go if you and all the other millions like you realised your power and fought for that?'
'But you can't do without the moneyed man,' said young Bishie evilly.
'Can't do without the moneyed man!' snarled Harry Drew in disgust. 'How long will it take you mugs to realise that the moneyed man can't do without you?'
'Now, now,' said Janos soothingly. 'Don't do the nana. Take it easy. Keep your shirt on.'
'I'm not doing the nana!' yelled Harry Drew. 'I'm trying to drum some sense into your bloody thick skulls.'
'Gentlemen!' said Whispering John, ducking in under the tent flap.
There was a sudden silence and he looked at them with an important malignant grin: 'Now you new blokes are going to get your feet in the mud. It's on—we're moving tomorrow.'
Everyone felt that faint thrill of coolness in their hearts. No fear, but a tightening of the nerves, a tension of the breath.
'Is it the right drum?' asks the Laird.
John gave his cunning little wink: 'It's on all right; we move to the river, relieve the Fourth and then push on.'
Deacon slowly closed his pad. The page had his number, rank, name and unit at the top. Then 'Beloved Margaret,' and the rest was blank. It was a hell of a hard job to write, that letter.
Everyone was very casual about it—carefully laconic. For the old soldiers it was another move—there had been plenty like this before, they knew what was coming.
But the new men could sense the breath of the unknown and mysterious enemy—the shadows of the long green shore—and violence and death they did not know but had often dreamed about.
Everyone was very careful—the cards fluttered over the spread blanket—there was time for a hand or two of poker yet, and it was not till tomorrow that they started down the long green shore.
## 4
We took over from the fourth battalion and camped that night on the banks of the river. The sections were ringed out in perimeter.
We cut poles and erected our tiny two-man doover tents—straight, strong poles for the stretchers we carried, and these frames lashed onto the bearers with jungle vines.
'These are the best damn thing the army ever got out,' said Dick the Barber. 'Remember how it was the last time—sleeping on the ground in the rain?'
'Yeah,' said the Log. 'That first night at Templeton's Crossing I slept sitting up in a hole with my groundsheet wrapped around me. It rained all night and the water was up to my waist. And my Christ, I was hungry.'
It was a complete blackout that night, of course—no fires, no smoking, no talking after dark. Though you could get a smoke by crouching under a blanket to light the match and you could puff away safely if you shielded the glow of the cigarette at the bottom of the slit trench.
We stood to in the shallow, hastily dug weapon pits at sunset—stand down half an hour after dark. Fifty per cent security—two hours on guard, two hours off.
In the two hours in the pit your eyes ache from the strain of darkness. The night is alive with nerve-sharpening rustlings and cracklings and a million cicada voices of insects, whistling and chirruping and strumming.
There was a sudden, terrifying flapping of leathern wings from the branches above.
'Flying fox,' whispered Harry Drew to young Griffo who was on guard with him. 'Pigs!' he whispered a moment later as there came a steady, stealthy crackling from the bushes in front. 'You've got no chance of really seeing or hearing anything unless they walk right on top of you.'
Occasionally, during the night, there was a shot from further down the line. 'Just nerves,' Cairo Fleming reassured Regan who crouched beside him.
Once there was the heavy boom of a grenade and a long burst of machine-gun fire.
About two o'clock the rain started dredging down. Some of us had not yet learned the tricks of making a dry bed in the jungle. The rain came in and filled up the canvas of our beds like a bath.
The Log squelched as he turned over in his bed. 'Christ,' he said. 'I'll be glad when it's day and a man can get up out of this.'
'Tomorrow we go over the river,' whispered Regan from the bottom bed. 'The Nips are on that side. I don't care if it never breaks day myself.'
'Forget it till tomorrow,' said the Log. 'Get your sleep in, boy—you'll be needing it.'
It was that night after the rain started, remember, that young Darky was killed over in 'B' Company—his mate, Big Brown, killed him.
Big was on guard and Darky, coming to relieve him, missed his way in the darkness and came up on the wrong side.
Big was taken by surprise and swung the bayonet before Darky could speak. It took Darky in the throat and he was dead in a couple of minutes.
They had to tie Big Brown with ropes to keep him down—he was crying and screaming all night—and next day they had to pump him full of morphine before they could move him back.
Four days we stopped there—expecting every morning to cross the river. We learned a number of things in those four days. We learned to fix our doover tents so that the rain stayed out—or most of it, anyway. We learned what saplings were best for bed poles and which would crack suddenly in the middle of the night and flop you into the mud. We knew now for certain the sounds of the flying fox and the pig in the darkness. We learned to wake the instant a comrade's hand touched our shoulder to take over guard. We learned to drop back to sleep immediately we crawled back into bed.
On the second day the sniper fired from across the river.
It was such a matter-of-fact thing—just a flat report from the trees across the river and half an ounce of lead smacking into the trunk of a sago palm near Captain Baird's head.
Such a small thing, but its effect was swift and vast and subtle. It was the final catalyst that changed the chemistry of our brains.
All their drill and preparation had turned to this—all the hours spent round the sand table and Connell's plain words and lectures on malaria and typhus and booby traps and cover and concealment all fused now into a tangible thing. The jungle became hostilely neutral—we couldn't see where the Nip was. This ground, these trees, this river, was no longer our encampment and our home. We were here on sufferance only—we walked only where we could, by chance or force of arms. Without any words being spoken we were drawn together and became brothers against this first shot fired on us—we were on the trail.
Pez and Janos were sitting beside their doover tent on the lip of the river bank when the shot was fired. They rolled into their weapon pit—instinct throwing them there before reason—and in that same scrambling moment all other movement along the bank was gone. Not a man was to be seen—but the jungle held its breath and the leaves of the trees had a thousand eyes.
'I think I know where he is,' said Janos after a bit. 'See that small light green bush against the dark green? He's somewhere about there.'
'Seemed about there,' agreed Pez. 'You can't see him?'
'Think I'll go and get him,' said Janos after a while.
'They'll send out a patrol,' said Pez. 'Don't be a fool.'
'I'll go by myself,' said Janos. 'I got reasons.'
Pez turned to him: 'You haven't got any ideas...because of Mary?'
'Hell, no,' grinned Janos. 'She's not troubling me—it's the other reason.'
'I'll come with you.'
'Because of the reason, I want to go alone.'
'Greta bloody Garbo,' said Pez. He thought for a moment. 'OK. But be careful, boy.'
'Sure,' said Janos. 'I'll be careful.'
They wriggled back out of the pit and slipped round the back of their doover, squatting near the head of their beds.
'We'll move this doover back a few yards, later on,' said Janos. 'She's too open. Lend me your rifle, will you? An Owen might be too short for this job.'
He took up Pez's rifle, snapped the bolt and checked the loading of the magazine. He tied a cloth bandolier of ammunition round his waist and picked up a couple of primed grenades. He straightened the pins so they could be pulled more easily and stuck the grenades in his belt.
'I'll cut down the back and around to cross the river,' he said. 'Give me three minutes and then tell Bairdie I've gone. He'll tell Company and Battalion so they'll know I'm over there.'
'Good luck, boy—you bloody fool. Be careful,' said Pez.
'Sure, I'll be back,' said Janos.
He moved away through the trees. The rifle was tucked under his arm as though he was going duck shooting. Pez watched until the trees hid him, then went and told Bairdie. Bairdie cursed and rang Battalion.
For three-quarters of an hour Pez lay in the shallow weapon pit where he had lain with Janos. Janos' Owen gun, loaded and cocked, lay in his hand; its nose poked through the bamboo camouflage. He watched the other bank, as two hundred other pairs of eyes watched through the leaves.
His eyes were fixed on the light green bush—but the jungle was blind and still. His ears were tuned to catch impossible sounds—a jungle boot cat-stalking five hundred yards away, or a green shoulder brushing like a shadow through the green tracery of the undergrowth.
It came suddenly and the sound of it was anti-climatic to the drama: a single heavy report and then, a few seconds later, as though the hunter had paused to take careful aim, another report from the same rifle.
'That was ours,' said the Laird.
'Both of them,' said Dick the Barber. 'Both ours.'
'I'll lay a spin that was Janos,' said Regan, as though his wager could intimidate the gods of chance and his own fear. 'A spin that was Janos—I'll bet he gets back without a scratch, even.'
Twenty minutes later Janos re-crossed the river. They were all there to give him a hand up the slippery bank. Pez could only say: 'You bastard—you silly, dumb bastard!' over and over again.
'I'll be back in a minute,' said Janos.
Pez went with him down the track to Battalion.
Lieutenant-Colonel Connell was standing near his tent talking to the Egg Eater—the red-headed Major, and the Adjutant—Winnie the War Winner. Pez stopped on the edge of the clearing and Janos went on. Winnie and the Egg Eater seemed to withdraw as Janos walked casually across the clearing and it was as though he and Connell met alone.
'There was a sniper across the river,' said Janos quietly. 'I got him.' There was the faintest possible emphasis on the 'I'.
Connell looked at him for a long time. 'Good!' he said.
Janos turned and walked back to Pez and they went together down the track to their Company.
Later when they were gathered around Janos, talking it over, Regan looked at him with admiration.
'Jeez, you're a cool customer,' he says. 'Doesn't anything frighten you?'
Janos grinned. 'I was shit-scared every step of the way,' he said.
We went forward on the fifth morning. We knocked down our tents and loaded our packs. We were to leave them at the 'Q' Store before we crossed the river.
'They'll be bunged up to you tonight,' they told us.
'Yeah,' says Dick the Barber. 'If we're still around to need 'em.'
Pez folded his tent in half and strapped it on the back of his pack. Janos had his gear ready and was sitting on his pack reading a greasy, much-thumbed edition of _Huckleberry Finn_ —a Yankee service pocketbook edition that he had found down at the first camp. Pez checked round the doover to make sure nothing was left behind.
'This your shirt?' he asked Janos, holding up a piece of muddy green.
'Yeah,' said Janos. 'But throw it away. I've got one and that's enough for any man on this trip.'
Pez bundled the shirt up and tossed it away out of sight in the bushes. Suddenly he felt a twinge of irritation.
'I dunno—I think you ought to carry it—means you haven't got a dry change.'
Janos looked up slowly from his book. 'How many shirts have you got?'
'One,' said Pez.
'Well, what the hell's all the excitement about?'
'Jesus,' muttered Pez, half to himself. 'The stuff we throw away—you could outfit three armies on it. Someone's got to pay for it.'
'Well, take it easy, boy,' says Janos. 'Take it easy—no need to snap my head off.'
'Sorry,' grunted Pez.
He struggled into his equipment and pack and lay down on the comparatively dry ground that had been sheltered by the tent. The pack slid high up on his shoulders, under his head, to make a pillow. His rifle was lying across his body and the brim of his hat was pulled down covering his face.
When you slide down on your pack like that you can feel all the weariness and the small aches of your body settle down into comfortable leaden sediment in your bones and it would be good to lie like that forever.
Pez's eyes drooped, half-closed under the hat brim. They were heavy, burning a little, and pebbly from sleeplessness. He could feel his lips hot and dry—there was a taste of blood on them—and he could feel how the skin had tightened over his cheekbones.
But these things helped too, he realised. They were somehow in character, part of the rhythm, and they helped you to play the part of a soldier. That is the only way—to try and identify yourself with the jungle and the pattern of war. To become the animal that steps quietly and is sensitive to the flutter of movement or the whisper of alien sound, that can sleep in the rain and suck enough strength from an hour of sun. Withdraw, conserve yourself. There is no yesterday and no tomorrow. Time is the time of war or the time of peace. Gather your strength for the job in hand and keep just one small core of your brain where you can remember, without urgency and without despair.
There was still Helen and this problem.
Bob should be home on leave now. Would she tell him this time? Would she change her mind about waiting till the war was over, and tell him? How would you tell him? Would you just say: 'Oh, by the way, Bob, I've been bouncing around with Pez while you've been away. I love him. I've decided to divorce you and marry him.'
And what would Bob say about it?
'Oh, all right, dear, I'll have my things out by tomorrow night.'
Maybe that would be the way if people were intelligent and civilised—or if they were peculiarly inhuman in their emotions, and decadent. But there is nothing inhuman in the way you feel for Helen—it seems right that you should love and be together.
It's hard to imagine how Bob feels about Helen. Could he feel the same way you do? It always seems impossible that other people's blood should run as warm as ours and their hearts ache as deeply.
Did a man have a right to take another man's wife away from him? Or maybe you're forgetting that, theoretically anyway, wives don't belong to husbands any more. Maybe it was up to Helen—it was up to her to say yes or no—not for you or him to wonder if you had a right.
Funny thing—you'd known her for years before it happened—never thought of her that way before. It started that leave—she'd been unhappy and lonely and you'd been bored—too much grog and not enough to do. You'd known her since she was a kid—always been good friends—never thought of her like that before.
It started off as just a roll in the hay—and a damned good one, too—but it soon changed. It soon became...Hell! It was hard to put into words, except that it seemed good and right and proper to be together.
Well, the problem was still there and still unanswered. But there was an unreality about it from here—from this angle of the jungle slanting under the brim of a slouch hat—you couldn't work it out from here...
Janos was shaking him heavily by the shoulder.
'Come on, boy, come on...Time to move—it's on for young and old.'
Half-asleep, Pez scrambled clumsily to his feet under the weight of his gear—shrugged the weight of the pack into a more comfortable position, slung his rifle on his shoulder and climbed into line behind Janos. Janos turned and grinned.
'How you feeling, mate?'
Pez grinned back. 'Better,' he said. 'You know, it's a good thing we don't both get dirt on the liver at the same time.'
'Right, three!' called Harry Drew. 'Drop your packs at the "Q" Store as we pass.'
The section filed out and slogged down into the mud of the track.
You lie beside the track and watch them go. You lie with head and shoulders resting on your muddy pack, rifle resting across your body and your legs sprawled—the soldier rests where he can. (See the little red book.)
They come up tall and brush past you in a swish of green as they go. You see them from the dramatic perspective of the ground beneath their feet—the brass studs shining in the soles of the heavy jungle boots—the Yankee gaiters laced round the calf of the leg—the stained jungle-green slacks and shirt open at the neck—the rain-battered slouch hats slanting over one eye.
They come with their rifles slung over the shoulder, their Owens cradled under the arm. They lean slightly forward—their shoulders hooded against the weight of the pack—a cloth bandolier of ammunition slung round their waists—a couple of primed grenades stuck in their belts—a tin of bully beef and a packet of hard biscuits in their pouches.
Identification discs are tied round their throats with old bootlaces or pieces of cord and dangle on their breasts like crucifixes. A soldier's crucifix—meat tickets they call them: dead meat tickets.
They move along the track in single file, dumping their packs in the clearing on the bend, and pass on, stripped down for the trail.
Cairo Fleming, as he comes up level with you, grins and says: 'Get off your back, you bludger.'
And you just grin back and say: 'Good luck, mate—I'll be right behind you.'
'Get one for me, too, Fluffy,' says young Onnie Smith, who is cleaning a Bren gun in the pit beside you.
'Get one yourself,' says Fluffy. 'There'll be plenty to go around.'
They go past and on—down to the river...
The river should have been clear. We had patrolled it every day.
But you can't trust the jungle—comb through it if you like, it is clean and safe, you say—but even as you pass, ambush may be gathering behind you, or in the trees above you.
They let the scouts go through and the head of the section reach the bank. They opened up when the body of the section was strung across the river.
Brogan died swiftly in the middle of the stream. He fell and his body was dragged away by the current. Young Griffo, acting stretcher bearer, forgot the bullets, as a man will do, and went to do his job—which was to help Brogan now he was hit.
But the current, as it twisted Brogan's body around, let his shattered head drift to the surface for a second. Griffo could see there was nothing for him but burying. The time for that was later. He bent again for the bank.
It was a solitary machine gun. The bullets came pattering over the water like recurrent bursts of hail. There was a horrible dream quality about it. You couldn't, in that moment, imagine that these drops falling in the river, skipping like stones, were really deadly. You couldn't tie them up with a phantom gun that was beating—stopping—beating somewhere a thousand miles away.
Oh, this is death and fear and ecstasy—and the lungs, and eyes and ears are filled enormous with the colour of it. The drill books don't provide for this. The instinct for the earth and cover is helpless here. We are caught in the horrible grey catalepsy of the rushing river.
There, on the bank, a thousand miles away, is life—there is the earth, our Mother, that we can embrace her—the sweet mud; the sheltering furrow; the strong protecting arm of trunks and trees.
Here we are naked in the empty plain of the river. This is no home—the earth we know, but here we are alien, rejected and exposed to the black rain. Our limbs are held in a leaden dream—we hurl ourselves for the other bank but we go with the horrible slow motion of a dream—and all the time the bright deadly rain is pattering around us in the river.
And yet we are not afraid.
This has been too sudden, too monstrously improbable, for fear to develop. All the chemistry of fear is working for our salvation—the adrenalin of fear shoots in our blood, firing a tremendous strength to fling us to the shore.
Before you feel true fear you must realise, you must be aware. The protecting dream-film disappears and you are seared with the burning brand that sends you screaming and helpless, fleeing—or with the corruption of fear that numbs you and leaves you helpless, trembling, transfixed.
Suddenly this obscenity flops on Regan's brain and he starts plunging through the water with a horrible bucking motion—like a terrified horse trying to drag itself from a bog.
It's funny in a way. It's almost funny.
Fluffy is laughing at him—a shrill, unnatural sound in all this roaring soundless tumult.
Harry Drew is yelling from the bank: 'Come on! Come on! Come on!'
The innocent, pattering rain runs across the water and patters over Fluffy's body. He is still laughing—he drops his rifle—it splashes into the river—he is holding his stomach with both hands—laughing or screaming—he staggers on—laughing or screaming. He falls as he tries to run up the muddy bank—his hands still under him, holding his stomach—he twists his head sideways out of the mud—the mud is in his mouth, but he is still laughing—or screaming...it goes on and on. The sound goes on and on for a thousand years and we are caught in the grey nightmare of the river—we are shod with lead and clothed with iron...
Regan has fallen near the bank and Harry Drew is dragging him up from the river. Regan is crying—sobbing. Harry throws him into shelter against the trunk of a tree and turns for Fluffy. But Griffo reaches him first.
He is lying as he fell—his legs dredging in the water, his arms under him, his head turned sideways—laughing out of the mud that mires his mouth. The bank is running red under him—the blood runs down and is licked away in the foam of the current.
Young Griffo is tearing open the first-aid pack as he hurls himself through the water. He seems to move faster than any of us—he is doing a job for someone else.
He turns Fluffy over.
The kid's still sort of laughing and hanging on to his stomach—his fingers are spread wide and stiff but it's coming through them—his hands are muddy and bloody—his eyes are open. His face is still sort of laughing but his eyes are open and wide—and they know.
Griffo tears Fluffy's shirt down and the wounds lie open.
'Oh, Christ, Christ, Christ,' Griffo is saying over and over. He scrapes the mud away from Fluffy's mouth.
'You can't do anything for him,' snarls Harry Drew.
Fluffy's laughing turns to moaning and soon he will be screaming.
'Knock him out!' snarls Harry Drew. 'Hook him! Hit him! He's finished—put him out! He'll die before he comes to—don't let him suffer.'
Griffo looks up. He is white.
'I can't,' he says, 'I can't hit him.'
Harry scrambles over, snarling at him, but he groans when he looks at Fluffy.
'Poor bastard—' he says. 'Poor kid.'
He smashes his fist against Fluffy's jaw. The jaw snaps shut. Fluffy's body slumps. He is silent.
The blood still runs from him, staining the jungle green of his trousers black. It is running into the hostile river—licked up and flicked away in the alien current.
We should all have died in that river but, by the normal miracle of war, we survive.
Brogan is dead. Fluffy is dying. Young Sunny, the drag man, turned back and made the other bank, though with three bullets in one thigh. The Log has a bullet burn across his shoulders—Griffo goes to him.
All the others are safe. They have vanished—blended and gone into the silence and the jungle and the dripping leaf.
Old Whispering John is there, crouching against a stump, his eyes fixed on Bishie crouching ahead of him. Old John's dirty teeth are showing in a fixed little grin. The webbing pouches on his chest are riddled, and there are even bullet burns on his shirt. Later he is going to show them and boast about them: 'How's that, eh? The old soldier gets through, eh?'
'Funny,' he'll say with ill-concealed gloating. 'Young Fluffy, his first up and he cops it, and me, the old soldier, I walk right through it with not a scratch. Funny, eh?'
Harry Drew sends a swift whisper into the silence of the trees: 'Laird, take over for a while—watch Pez and Janos.'
The whisper goes from tongue to tongue in leaf and branch and fern.
Harry Drew slides round the tree and flops down beside Regan: 'How are you feeling?'
'OK,' shivers Regan.
Harry puts his arm around the kid's shoulders—thin shoulders.
'Come on, kid—everyone feels as bad first time. Will you come with me—stick with me?'
'Sure, Harry,' says Regan.
Sure, Harry! You are God, here on this muddy track, if you can beat these wasps of wrath away—if you can walk like Christ and unafraid—if you can keep me from death—or, better still, if you can keep me from fear of it showing in my eyes. Sure, Harry!
Harry Drew leaves the tree in the peculiar crouching crab-like run of the soldier under fire. He pauses by a tree, dodges on and falls into the shadows of the shrub. A few seconds later Regan follows him with a valiant imitation of that same run. He pauses faithfully by the same tree, dodges on and falls panting heavily in the shadow of the same bush a few feet from Harry Drew.
'OK, kid?' says Harry.
Regan manages to grin through his parched lips.
'Sure, Harry.'
## 5
But we must be inconstant to the earth—there's the pity and the terror of it. We must rise—and never more reluctant from a lover's bed. A red cross is drawn on a map and we must go there. The sky is grey and the jungle crouches, bland and waiting. The wet drips incessantly, implacably, imperturbably from the leaf—charting the passage of eternity.
Pez and Janos crouch against the bole of a tree and talk it over. They crouch on their haunches, crouch on their toes—ready. They do not look at each other—they watch the jungle. They whisper from the corners of their mouths. The rifle and the Owen are held loosely in their hands—ready.
'They might open with mortars,' insists Pez. 'It'd be a hell of a thing to walk into your own mortars.'
'They won't,' says Janos. 'They'd wait for us to call for them—and we've got no line back across the river. They know we're here somewhere. They wouldn't use mortars unless we called for them. We've got to get that gun.'
'They might just open up.'
'The longer we wait the less chance we've got!'
'Where do you reckon the gun is?'
'About three or four hundred yards down—can't be far from the bank.'
'They might be strong.'
'Probably just a gun crew.'
'They'll know we're here.'
'We know they're there.'
'Wait a while—we might get mortar support.'
'If it doesn't come in thirty seconds, it won't come till we call,' says Janos.
He turns his wrist and glances briefly at the second hand of his watch. He keeps his wrist turned and his gaze goes back steadily to the jungle. Thirty seconds. The leaf drips fifteen grains of eternity.
'OK,' he says. 'Bring them forward, not too close. When I give the hand, get them down and let them keep down—less movement the better. They'll probably have a cover man out—you watch him—I'll try for the gun.'
Janos glides away. Pez follows—his hand conjures the patrol from the earth—they materialise, drifting through the grey-green of the undergrowth. Harry Drew leads again, Regan is close behind him.
Here is a ballet and a symphony—here is a dance whose name is Death—whose overture is silence—waiting on the cue for savage strings, the bowel-plucking whine of the bullets. All the earth and yesterday and tomorrow are blotted out in this fierce, relaxed concentration that narrows a burning spotlight on this rain-soaked stretch of mud and jungle. The earth is suspect, save where we stand—the trees are treacherous—the leaves slant like eyes.
Janos drifts...the Owen in his hands loses the stock of metal and plastic and becomes an instinct of life, shifting and probing like mantis antennae...
Pez's hand beats imperatively towards the earth and the furtive life behind him returns to the earth.
Janos drifts on. Pez follows—his dominant hand keeps the earth still and unbreathing behind him...
Janos was right. They had a cover man out. Pez killed him as he fired at Janos, and Janos sprang towards the pit where the two Nips were trying to swing the gun around against him.
He killed them both in the pit. One fell forward over the gun. The other—a big fellow with a square face—was trying to clamber out, trying to run. He fell against the edge of the pit, his crucified arms stretched up over the mounded earth, his fingers clawing, and he was biting in agony into the red clay of the edge of the pit when Janos fired again—and passed swiftly on, to drop, crouching, into the shelter of a further tree, his eyes swift and steady on the jungle as he snapped another clip into his Owen.
In a few moments Pez joined him.
'I went through these two Nips in the hole,' said Pez. 'Nothing on mine at all. Three pens, a watch and a bundle of yen notes—take what you want.'
'Not for me,' said Janos. 'Thanks for getting that first one—he'd have got me.'
'I didn't,' said Pez. 'I just nicked him. He tried again when I came up to him. I brained him with the butt.'
The lobe of Janos' right ear was a bloody smudge. Pez saw it as he rose. 'I'll fix that for you,' he said.
Janos rubbed a quick hand against it; stared for a moment at the smudge of blood on his palm; then rubbed it off on his trouser leg.
'She'll do,' he said. 'Let's wander on.' He took two short steps, vomited briefly and spat with a wry mouth. He glided off into the trees.
Pez looked for a moment at his loot from the bodies. He stuck the watch in his pocket, tossed the notes and fountain pens back into the pit and followed Janos.
Behind him, the patrol materialised through the trees.
The rest of that day we see nothing of the enemy—but that is no safety when with every step he may appear. We pass down the track. We reach a spot on the map, marked with a cross in red. We camp.
We eat a mouthful of bully before dark. Our water bottles we have filled on the way. The rest of the Company is following behind us, spread in a thin line down the track back to the river. We dig ourselves in before dark and a quick patrol clears our front without finding anything. We make ourselves beds of grass and branches, and huddle under the thin shelter of our waterproof capes—but the rain comes through. It is impossible to stay dry or get warm. Hour on, hour off, we are on guard. When your turn comes, your mate nudges you and you open your stinging eyes, hold your rifle a bit closer and crouch, listening for sounds you could never hear. It is impossible to see. No one sleeps much that night—or the next—or the next.
That first night, before dark, Connell had come up the track to see us in our forward position.
Janos stepped deliberately onto the track in front of him.
He held up two fingers. 'Two more makes three,' he said.
'Good,' said Connell. But he paused before he said it.
'Good work, boys,' he said to the rest of us. 'Damn good show. I'll try to get you up a hot meal sometime tomorrow.'
He went back down the track.
Janos stood by the side of the track, his arms folded, and watched him go.
Days and weeks followed—quietly enough, but never with peace. The enemy is unpredictable. For days we probe through country where a handful could hold up an army—but never a hostile shot is fired against us. Then, suddenly, we will stumble on a machine-gun nest, or a sniper in some hopeless position where the only retreat is death.
But always, whether we are forward or in reserve, there is that small fraying—continuous and never ceasing—on the nerves.
You who know war in a romantic dream, or in the sob stories of newspapers, might imagine that it is only the thunder of bombardment or the terrors of the charge which breaks a soldier's will and manhood; but the slow-burning acid of monotony and sterile days can be as bad, or worse. You live constantly with a small fear that can never be spoken, and never become real, but can never be dispelled.
You might know you are safe—you are behind the lines—there are no Nips within a quarter of a mile. You might know that, but the knowledge can never fully soothe the nerves or stop them from trembling as antennae to probe the blind bank of the jungle to the side of you, and the edges of the clearing where the jungle path turns. Too often, death has come out of the silence and the unliving jungle. Though you might know there is no danger, it is no use telling your body and your nerves and the dark places of your brain so long schooled and skilled for the task of being ready for death and violence, when all is still.
So you have no rest. The shadow and the smell and the texture of death is always real and tangible about you. Walk ten yards into the scrub and the nightmare closes around you.
All seems still and silent. Then, as you stand, you are aware of interminable life—a vast, corrupt writhing as of slimy sea-flowers and forest washed forever by a drifting ocean. Nothing is still. Every leaf and twig and branch and bud writhes and quivers with some secret, malignant life of its own. Everything crawls and curls on the stem. Nothing is silent; that hush you heard when you stopped you now find is made up of ten million tiny, rasping, whittling, evil sounds—all of deadly portent if you listen—
Did the twig break, or was it broken? Did the bush rustle, or did the stealthy footfall brush it?
There is an eternal smell of death and decay. The silt of centuries of corruption is trodden moss-like underfoot. You grasp a branch and it crumbles in your hand like mushroom. The leaf and the plant and the limb are always dying and are swiftly eaten by the savage and unhealthy organisms that live.
The earth itself is vile and stinks with the essence of corruption long distilled into it. And for this desolate and savage and unwholesome earth, men died...their blood stained it and the sickly sweet smell stained its vileness deeper.
'Why are we fighting for this?' the Laird boomed. 'For my part, let the Nips keep it—serve the bastards right!'
Deacon asked Connell one day when he met him, ploughing down a track ankle-deep in mud.
'I was here before the war,' said Connell. 'There's an old saying—where there's mud there's money.'
There is only the time of war and the time of peace—this is the time of war.
We are forward section for days. We drop back and another platoon moves forward through us to take up the spearhead. We go forward again.
There is a rhythm about the track—a material music about the ache of the pack on your shoulders and in the pulsing muscles that go on labouring long after they are exhausted beyond the point of normal human endeavour.
There is poetry in the feeling of the rifle stock under your hand, or the Owen cradled over your arm. There is kinship between you and these finely machined pieces of walnut and steel; there is strength in them. A man who, unarmed, would scratch the earth, can face the enemy like a knight of old with a lance couched on his arm. As a musketeer felt for his sword, so we feel for our guns. Not that we love them as individuals—one gun is just like another—it's just the feeling they give you.
You get sensitive to the feeling of the earth under your feet. There is the slide and dragging weight of the muddy track and the lightness of firm, sun-baked earth when you strike a hard patch.
Your skin runs oily with the drenching sweat of your body and there are those incredible moments when, by chance, passing through a glade or coming out on the side of a hill, a blessed breeze comes for a moment and the sweat freezes on your body in ecstasy.
The body is a good machine and will keep going. The knees are the worst. They tremble violently—'laughing knees' we call them. When you are moving it's not so bad; but when you stop you find your knees are giggling and you stand under your pack, shivering like a beaten animal...
So the days go on. We march—the dull slog through the mud or sand, when the only horizon is the earth and the heels of the man in front of you, and the weight of the pack bows you down as a load of sorrows. We carry—returning swiftly and lightly over the track we have taken and dragging crates of ammunition and cases of food back with us to the front. We advance—stripped down to the ultimate burden of hard rations, ammunition and weapons—armoured with the sensitivity of fear—holding chance as a talisman against mortality. We fight—occasionally the scattered or the single shots—the body falling, the scream of pain or the frightened whimper; sometimes under the thunder of big guns, locked in combat on a savage hill.
Old Whispering John gets thinner and darker each day. His little bright blue eyes burn deeper into his skull-like face. He never loses his little grin—but it seems fixed, as something apart from himself.
Younger men and tougher men physically than old John have cracked up and been sent back sick, but old John goes on. Each one that goes, he sniggers with evil satisfaction: 'Another one gone, eh? Another of the young colts cracked up and the old soldier still going, eh?'
Sometimes he hobbles and falls back a bit on a long march—but he always catches up. He's never in the front, he never leads, but he's never exactly behind; and all the time he sniggers with satisfaction: 'The old soldier keeps on going, eh? The young blokes crack up and the old soldier keeps on going, eh?'
John's darkening complexion doesn't come altogether from the sun. He gave up washing the day we moved up to relieve the Fourth and the nearest he's come to it since we crossed the river is when it rains extra heavy. John gave up cleaning his teeth, also, and it gets so that we avoid him when he comes up and tries to buttonhole us confidentially.
'Stinking Jesus,' Deacon calls him privately.
'Even his best friends won't tell him,' says Dick the Barber.
*
Our Company was spread along half a mile of beach that ran from a small river to the edge of a large clearing. On one side was the pebble-white, sharply shelving beach; on the other, a grey stretch of swamp. The wood sprouted between and the main body of our troops were sprawled through the thicket. Most of them lay in the hot shade, with head and shoulders propped up on sweat-stained packs, rifles lying close at hand and legs sprawled ungainly.
About ten-thirty the Nips opened up with a barrage from their mountain guns in the hills. The Log prodded the sleeping Cairo Fleming as the splintering explosions of the shells strode on long legs down the fringe of the wooded strip, probing into the blindness of the trees. These ordinary contact shells couldn't do much harm, but occasionally the Nips sent over a timed fuse that burst in the air and the shrap smacked down through the trees. They were nasty.
Cairo yawned and slid down into the hole beside the Log. They crouched, listening for a moment as the shell bursts strode past them down the beach.
Cairo's head drooped and he was about to drift into sleep again when a shrill, moaning scream swelled up from down the beach—swelled and rang on and on—and the cry was flung from mouth to mouth along the beach: 'Stretcher bearers! Stretcher bearers!'
The scream of the wounded is the loudest sound of battle—even through distance you can feel the minute texture of its agony sliding like ice in the veins and the pity of it like a strong hand twisting your bowels.
Doc Maguire passed them, going towards the screaming, ploughing through the sand on the fringe of the trees.
'Who was it, Doc?' called Cairo.
'Don't know. Don Company, I think,' he replied without looking or pausing.
The line of shells was creeping back down the beach now. You could see the burst of them in the sand and the violent, lopped convulsion of branches where they struck among the trees. Maguire walked straight into them without slackening.
'A good man,' said Cairo.
'Yeah,' said the Log.
A few minutes later the grapevine whisper ran down through the line: Rocky Bennet—burst right on top of him—dead.
'He was a good little bloke,' said Cairo. 'Remember that time in Cairns he took on the three provosts? He did three months in Groverley for that lot. Remember, he always used to say: "Three months'll do me, I'll do it on my head. A month for each of the bastards is fair enough." '
'Was he married?' asked the Log.
'Yeah, I think he had a wife,' said Cairo. 'I think he got married on that last leave.'
They sat for a long time in silence. The Log crouched there—his head sunk on his breast, but his eyes wide and steady with memory.
'What are you thinking about, mate?' asked Cairo.
'Nothing. Just thinking,' said the Log.
'Anything worrying you?'
'No,' said the Log. 'I was just thinking that if my son had lived he'd be about ten months old now.'
Cairo looked quickly away and there was silence in the pit.
All day long we huddle in the trees. We are waiting for our guns to come up within range.
Way back behind us, the Gunners and the Fourth Battalion, which is in reserve, are bringing up the guns. They tie ropes and chains to the twenty-five pounders and drag them along by animal force...straining and groaning inch by inch through the treacherous soft places—cheering and laughing breathlessly as she rumbles slowly but steadily behind them on the good going. Chanting the Volga Boat Song breathlessly. The Volga, not so Vulgar.
The old catch-cry is raised, of course. The old vulgar suggestion is made: 'If you're going to work like a horse, you might as well look like one!' A couple of clowns carry the idea further. They expose their genitals and prance against the ropes, neighing and pawing like stallions.
It doesn't make the drag any easier, but it gives a laugh. It helps keep the men on their feet long after they should have fallen.
Janos heard the plane first. The whisper sped and the fringe of trees between the swamp and the sand came swiftly to furtive life—crouched, concentrating on the sky.
The Nips had been shelling us desultorily all day. Rocky Bennet had been killed and Doc Maguire had three or four wounded bedded down under a bank at the bottom edge of the beach.
The Wirraway came cruising casually down the beach, about four hundred feet up, and dipped its wings in salute to us in the trees as it swung inland. We could see the saluting gloved hand of the observer and his hooded, goggled face peering down as he waved.
'Those blokes are mad, you know,' said Dick the Barber, 'plain mad. Fancy going up in the air when there's good solid ground to crawl on.'
The Wirraway circled the hill where the Nip battery was set up. The plane buzzed up and down, casually skimming the trees, and occasionally darting down viciously and peck-peck-pecking at some target. Then she climbed up and circled, waiting, above and back of the hill.
There was a swift, high rushing and whining in the air, and halfway down the Nip hillside the trees exploded and a big mushroom of dirty white smoke puffed out.
The plane came skimming over the hill and banked through the smoke.
A few minutes later, another smoke shell landed higher up the hill. Then another burst, right on the ridge—then another and another, tracing the contour along. We cheered.
'They never miss, those boys,' said the Laird. 'They snipe at five miles.'
The Wirraway dived in again, strafing along the ridge—peck-peck-pecking viciously along the hill—like a willie wagtail attacking an elephant. Then she turned and came sweeping over our trees again, her wings dipping in salute, and sped back down the beach.
'He'll be sleeping warm and eating well tonight,' said Pez. 'We should have joined the Air Force.'
Janos grinned: 'We should have stayed home,' he said. 'Here, have some bully.'
'I'll have just a trifle more of the _pâté de foie_ , me good man,' says the Deacon to Bishie.
Deacon is lounging in his pit, his feet propped up on the edge, his hat carefully tucked at the back of his neck to stop the sand trickling down where his head and shoulders rest against the other wall.
'Certainly, old cock,' says Bishie, who is reclining on one elbow beside the pit.
He digs a knob of pink and white bully out of the tin with a spoon and proffers it to Deacon: 'More _foie gras_ , me Lord—and would your Lordship care for an iced vovo to go with it?'
'Thank you,' says the Deacon, taking the knob of bully delicately in his fingers. 'But if you refer to the dog biscuits, me good man—stick 'em! I believe I lost my second-last filling on one this morning and my dentist's three thousand miles away.'
'Anything else, old cock?' enquires Bishie servilely.
'Just a sip of the Veuve Clicquot.'
Bishie passes the water bottle.
'And tell Lady Jane to bath well before she goes to bed,' continues the Deacon. 'Last time, me good man, you were a little careless behind the ears—scrub her thoroughly all over this time.'
'Oh, sure, old cock—all over!' leers Bishie.
'And tell the second chambermaid I'll see her in the dunny later,' says the Deacon.
The sun is dying. We are packed and ready.
The barrage opens with a single whine and explosion on the enemy hill.
Then the shells fall—one-two...one-two-three...
And now the air is full to the black sky with the rushing whine, the shuttling, zipping, heart-swelling pattern of shells plucking the heartstrings of the earth and sky. In the gathering darkness we can see the constant flashes running along the enemy ridge and the crown of the hill is smothered in smoke and flame and thunder. The hill top seems to heave and we can almost see dark things tossing and falling...
We move out of our little wood and, in single file, cross swiftly under cover of the first darkness and our sheltering guns. That quarter-mile of waste sand and kunai into the broad shelter of the trees seems as wide as the earth. For the music of the guns—whether they are our own or the enemy's—makes your heart enormous. We are lost for ever with shadows before us and shadows behind us and the sweet foul music of hell above and around us and the naked, sterile and unfriendly earth beneath our undestined feet.
We make the shelter of the trees.
By whisper and touch and instinct we break up into our little groups and bed down in the darkness—huddled closer together for comfort in this strange place.
After a while our barrage eases. But at irregular intervals during the night, one or two shells will burst over on the hill.
'That's just to keep 'em awake and make 'em nervous,' Harry Drew whispers to Regan.
The Fifth Battalion, who are travelling further inland, are coming up to the hill. They are to put on an attack in the morning and the barrage from our twenty-fives opens up again with the first smudge of grey.
Then, quite suddenly, the shells stop. Everybody is listening in that silence. Then it comes—the swift, thin clatter of the Brens and Owens, the heavier beat of the Nip woodpeckers, the spaced reports of rifles and, smacking through them all, the slamming explosion of mortars and grenades.
'They're into it,' says the Laird.
All day long the firing continues on the hill, dying away for a while into silence spaced by single sniping shots, then flaring up again in the swift rattle of automatics and the slam of grenades.
We hear it, fading a little behind us, as we advance that day, and it is still with us when we camp that night.
We lost a man that night.
Early in the afternoon we passed along the beach where the trees were twisted with the mighty winds sweeping in from the depths of the Pacific. They were things of violence—with great roots widespread, clutching the earth, and limbs twisted paralytically to withstand the storm.
Charley Company was along the beach, Don Company was across the track, and we swung inland, into the fringe of the dripping rainforest, to make the other side of the perimeter.
We had a bit of time before dark and we made ourselves comfortable. We put up our tents carefully and made our beds strong. They sent us up a meal in dixies from the kitchen back down the track—bully stew and dehydrated spuds boiled up. It was fairly hot, it tasted good, and there was even some fairly fresh bread that had been dropped by the bully beef bombers back in the clearing.
It looked like being a quiet night, but the rain and the wind started about a quarter of an hour after dark. The rain came dredging down through the thick curtain of trees. The wind could not touch us, but we could hear it beating gigantically against the treetops.
It was an old, dead tree, shaken and felled by the fist of this wind that, in the middle of the night, crashed onto the doover tent where the Deacon and Bishie dossed with the Log and Cairo Fleming.
Another four feet to the right and they would all have copped it. As it happened, Bishie was sitting up near the head of his bunk to keep himself awake for his guard. The tree missed him, smashed the end of his bed and, falling at an angle, killed the Deacon as he slept.
Most us didn't know what had happened. Some of us, near enough, heard the crash. We heard the sound of chopping—axes beating on solid, dead wood—but in this blind world of wind and darkness and drumming, ceaseless rain you can't tell where things are. You can only sit tight and watch and listen. What happens in your own tight circle of rain and darkness is all that concerns you—the rest can wait.
It took an hour to cut the tree away from the Deacon. It had crushed him across the chest and stomach. He couldn't have felt a thing, he must have died straightaway. They had to lift carefully to get him onto the blanket.
The Log and Cairo and Bishie dug his grave. Bishie wept while he dug. They buried him just after dawn.
A soldier leaves so little when he dies—a watch they gave him when he left the office to enlist—a small pack of faded photographs—some old letters in a mildewed wallet—stained with the sweat of his skin when he was living and the blood of him when he died.
As we passed out on our way down the track that morning, the grave was by the side of the path, the fresh-mounded earth with a sealed, inverted bottle stuck neck down in the soft soil. Bishie had lashed together two small broken branches from the tree that killed him, to make a cross.
Oh, Deacon, who sought love and never found it! If I had paused beside you as you dreamed, as Fluffy did that night on the boat...I wonder did the ancient mark burn on your brow then, even as you dreamed? Oh, Deacon—to life you should have been so great a lover—but the embrace of the earth is cold and wet where you lie under the rain trees on that little hill.
The telegram that went back home said: 'Killed in action.'
Deacon had carried a battered writing pad in his webbing pouch. Bishie found it as he went through his things and tossed it away. As we passed on, it lay under the bushes in the rain, not far from where he lay.
His number, rank, name and unit were scrawled across the top of the page. Then 'Beloved Margaret,' with a little flourish. The rest was blank.
You get used to the colour and the smell of death—the blood from the mouth, the destroyed flesh, the small black scuttling things that infest the corpse in the jungle.
You get used to the colour of death in the living—the grey jungle-pallor on the faces—the bright, blind weariness of eyes—the bones showing up white and hard under the skin.
After the first time, you get used to a man going crazy beside you—you watch for it. Usually you can pick them—they get very quiet for a day or so—their eyes get an absent sort of look, as though they were thinking back. Then a madness boils up in them like a curse of Job and they will scream and sing with it. They will fight you with the strength of it—clawing with teeth, and boots, and nails—cursing and praying.
And sometimes after you have overpowered them and your blood and their blood is on their hands with the violence of trying not to hurt them, the madness will suddenly leave their savage flesh. They will collapse in your arms like a child and weep with gentle despair while you carry them to Doc Maguire.
Usually when you get them there, the madness comes again and they will shriek for you not to leave them. You will have to hold them while the Doc presses the bright needle into their arm, crooning the while with a gentleness no woman ever heard from him. The strong grey medicine soothes the fever of their blood and abates the wildness of their heart and brains.
We call it 'going troppo'.
Our Company was forward most of the time down this stretch of the shore. Sodden, desolate country it was—desolate jungle. Every afternoon about four the rain would start—you could see it come sweeping down the hills—and it would drench down solidly all night.
Our section was point section most of the time. Janos was point scout and he made himself a legend that sped back down the shore and flew inland to our troops cutting through the hills. He saved us all many times with his skill and swiftness. Ten Nips he had killed, and each time he bailed Connell up on the track and added the score.
'Eight,' he told Connell as we held the marsh on the river.
'Nine,' he said the day after Deacon died. He walked into Connell's tent at the edge of the abandoned aerodrome, overgrown with kunai—'Ten,' he said.
Connell said nothing, but he boasted to others of what his battalion and his men could do.
It was at that 'drome, remember, we had a fine grog party. There was a lot of junk, plane wrecks and equipment scattered through the tall kunai grass. I don't remember who it was first lighted on the compasses filled with alcohol, but everyone was in it. Out came the chipped enamel mugs and the dixies and there's everyone busy cracking compasses, like you'd crack an egg, and draining the spirit.
It tasted fine over the tongue—smooth, like a good Scotch whisky—but about six inches down it started to expand and burn—vodka was mother's milk to it!
Our mob retired for the night as full as bulls. There was considerable indiscriminate firing at an imaginary enemy, and Janos had to be restrained from a project to shoot through the centre pole of Connell's tent so that it would collapse on top of him.
'You remember that time in Syria,' recalled the Laird, 'when big Johnno from Don Company was going to shoot Boomerang Billy. You remember, he staggers along to the Officers' Mess and bellows—"Boomerang Billy, I want you!" And old Boomerang shoots out, ready to fly right up to him. "Boomerang Billy, you bastard," says big Johnno, very solemn-like, "Boomerang Billy, I'm going to shoot you." And Boomerang Billy takes off up the hill, with big Johnno staggering after him, letting go a burst every now and then from the hip. He couldn't have hit him in a year, but Boomerang went up that hill like a mountain goat.'
Good old Boomerang. He had a completely misplaced confidence in his ability to steer a course by the stars.
You remember, too, that day he was drilling us at Kilo 69. You know how officers pick up clichés—esprit stuff—'This is it, chaps,' kind of thing. Well, Billy's was, 'One man spoilt the whole show!' Whenever he was drilling, you could rely on having to do it over half a dozen times because 'One man spoilt the whole show!' This day we'd gone round and round and every time it was the same complaint. When he stopped us again—it was as hot as hell—and he bellowed: 'One man spoilt the whole show!' a weary voice pipes up from the back row—'Yes, it was you, you silly old bastard!'
Slapsy Paint, our Platoon Officer, rejoined us at the 'drome before we went on to Drogula Bay.
Slapsy had been fairly new to us when we sailed and we hadn't seen much of him since. He was a funny sort of bloke. A big ox-like man whom you'd take to be either lazy or stupid—he was lazy.
He'd been a Duntroon officer for most of the war—but he wasn't the usual pukka-wallah type. He told us once, in a moment of rare confidence, that he'd joined the permanent army long before the war because he was looking for a job. He had been a carpenter, but he reckoned that was too hard and too uncertain, so he joined the army. They had shot him out to us—he didn't want to come. He had been quite happy where he was at Duntroon and quite prepared to finish the war there; but there was some trouble about a major he hooked one night he was drunk in the mess and he finished up with us. He made no pretence—he didn't want to fight. He left the show to Harry Drew and old John and Janos—he just wanted to keep out of trouble.
But he was always running into trouble with Connell. Orders were that sleeves were to be rolled down at sunset and the face and hands smeared with mosquito repellent to discourage the malarial anopheles. Officers were supposed to enforce this order rigidly, but Slapsy himself would be wandering round half the night naked except for a grimy towel round his middle. Connell would come through in his jeep on inspection and Slapsy would wander out on the track to meet him, naked except for the towel round his middle, his big feet squelching in the mud.
Slapsy carried a flute with him and when we were back a bit he'd sit for hours on the edge of the bunk in his doover, the grimy towel round his waist, his muddy feet sticking out in the rain, trying to play the Brahms Lullaby.
It was the only tune he knew, and soon we all knew it—every wrong note as Slapsy played it, every uncertain pause where he started a passage over again. We would grin at one another as the sweet, quavering notes floated up through the trees and rain.
'Jesus, he's at it again,' Pez would crow delightedly.
'I wish he'd get another tune,' Janos would complain.
Slapsy might be pretty drack as an officer, but there was a certain pride and delight in him. We used to boast about him to other platoons and invite them up to hear him playing.
There had been some doubt about the illness that prevented Slapsy from joining us when first we started up the long green shore. But after he'd been back with us a few days, we sort of forgot about that. There was that time they struck the booby traps on the beach—Jimmy Mollison walked into one and had both his legs blown off. They called on Slapsy to come down and delouse the area. He borrowed a makings off Pez—he was constantly running out of tobacco—rolled himself a smoke, borrowed a match, hauled up his pants. 'I'll be back in about half an hour,' he said. 'If you hear a loud bang, I won't be back.'
Slapsy was all right. There are a number of good officers, of course, and a great number of poor ones. The ones that came up through the ranks on the field are generally the best—they know what it's about. Most of the blokes that haven't been in a blue before aren't worth a bumper. We've all got to learn, of course, but most of this batch of Duntroon boys imagine that they know it already—just because they read a book. They're all right in standing camp—they bellow very nicely and impressively on the parade ground and know the regulations backwards—but in a blue they're dangerous with their regulations—you've got to tell them to get the hell out of the way and not make nuisances of themselves.
So we didn't mind Slapsy—he didn't try to interfere—and he's a character.
It was a heavy march to the bay. Not that we struck much opposition on the way there—only one Nip, dug in like a weasel between the twisting roots of a big tree.
Snowy Myers' platoon were ahead that morning and big Tomo had got this Nip with a hand grenade. From what we could see of him in the hole, he was a mess—we didn't search him for souvenirs.
We were carrying full packs, and ammunition besides—mortar bombs and .303. It was just a matter of marching—clambering and sliding and slogging, until your mind is black with exhaustion, and your body aching with the weight of your pack, and your chest burning.
When the word came to halt, Pez stumbled off the edge of the track—dragging Janos and the case of mortar bombs they carried between them. He dropped his end of the case and fell backwards on his pack, sliding down it until his head and shoulders rested.
Gradually...the heart's thunder ceases—the breath eases its labour—the red blood fades from behind the eyes.
Pez sat up, dragged out his makings and rolled a cigarette. He stuck the weed between his dry lips and scratched a wax match on the serrated bottom of the tin. These tins were usually made too smooth, so that the match wouldn't strike—or too sharp, so that they tore the head off. The head tore off Pez's match.
'Here,' says Janos, whose cigarette is going. 'Ignite yourself, my friend.'
Pez leans across painfully and lights his cigarette from Janos' bumper.
'All those as have tobacco may smoke,' says Regan. 'All those as haven't can go through the motions.'
Old Whispering John is talking about the girl he knew in Panama and describing her amorous powers with detailed relish.
Young Griffo is sceptical: 'You tell me that? You think I'm a bunny because I come out of a hole?'
'Man came up out of the mud,' declaims Harry Drew. 'He makes and destroys a thousand cities; and now he flies through the air, drives ships under the sea and has touched the stars! And where does it get us?' His gesture embraces the jungle and the track: 'Back in the mud!'
Somewhere up ahead a heavy machine gun starts beating. There is a momentary silence down the line.
'Woodpecker,' says Janos.
Then comes the smaller, stinging rattle of the Bren and the Jap gun beats again in a long, heavy burst.
There is always someone firing up near the front, but you can never get quite used to the sound of the enemy—a tightness bands around the chest and stomach and the nerves and brain become light and sharp and clear.
After the guns stop, old Whispering John forgets to resume his amorous tale and Harry Drew leaves his philosophising.
'Wonder if they got anyone?' says the Laird. 'That Bren gun didn't fire again—only rifles and Owens.'
'Big Tomo would be scouting,' says Janos. 'He'd be awake.'
'I got a feeling we're going to strike trouble at this bay,' says the Laird. 'It's been too quiet.'
No one disagrees with him.
Myers' platoon had reached the edge of the bay when they struck the woodpecker. Janos was half wrong about big Tomo—he was point scout, but he wasn't awake. They killed him as he slipped from the shadow of a tree and waved his section on.
Five are wounded and we've got to get them back. The barges can't come into the beach until dark, and that's too long. The obstacle is the river about four hundred yards ahead of us. It is not very wide but it's armpit deep and fast, ripping straight through the beach and smashing into the sea. We can't take them any other way—they've got to come over that river. We can't bridge it, but the Laird sends word back and some empty four-gallon drums and some long ropes are rushed up to us. Some of us cross the river—it tears at you like you were chained to horses.
They bring the first of the wounded down the beach. Young Sad Saunders, it is. He's copped it somewhere in the legs. His rifle lies between his thighs and his legs are strapped to it to keep him straight.
'It's OK,' he says. 'It's not too bad—poor old Tomo copped the lot.'
We lash an empty drum at each corner of the stretcher to float it and tie the long ropes, two at each end. We take the two front ropes across the river and the men on that side haul as the others pay out. Some of them go with the stretcher. We manage to keep it fairly straight, but the current drags at it and bucks it against the ropes. The men in the water are fighting against the current themselves all the way and can't help much except to steady the raft. 'It's a rough trip,' Sad groans once, but says quickly: 'She's right, keep her going.'
The black stubble of his chin shows up against the deadly yellow-white of his skin when we lift him up on the other side. He's a bit wet, but all right. The relief stretcher bearers take him over and continue down the beach.
Maguire arrives just as they are taking Sad. He examines him swiftly and lightly: 'You'll be all right, lad—I'll be back by the time they get you on a bed.'
He comes up to the river: 'How is it?'
'Oh, bloody lovely,' says Harry Drew. He shows the Doc our ferry. 'Two hundred Yankee ducks rotting down at the camp there, but when we want one here to ferry casualties we don't get it...we've got to drag them across the river like this.'
'Yes, I know,' says the Doc. 'I know how it is.'
He crosses the river—goes up along the beach to check the wounded they are bringing down and comes back before the next case arrives at our ferry.
'They'll all be pretty right if we can get on to them tonight,' he says. 'Be gentle as you can with them.'
He goes back down the beach with long strides.
So we cursed and struggled across the river with the wounded. Cursing our own inevitable clumsiness with them, cursing the river, cursing the goddamned, bumble-headed brass hats that let amphibious craft rust down on the shore so that we had to hurt these men, already hurt, dragging them across the river.
We get them across. Darby Munro is the last. In the face and chest he's copped it. We can't see much of the face for pads, but his eyes are shining bright with pain and drugs and he tries to grin at us: 'I never did like that nose of mine much, anyway,' he mumbles.
We nearly lost him crossing the river. The stretcher bucked and he rolled half into the water. Pez and Janos were on that side and they got their hands under him. For long, long seconds they struggled, cursing and panting and praying, against the fierce drag of the current—while Harry Drew snarled savage, impotent curses from the bank and the Laird bellowed prayerfully: 'Hold him! Hold him! For Christ's sake, hold him!'
Pez had Darby by the shoulders and he could feel him sort of laughing: 'Ride her, ride her,' he was mumbling through the bandages. 'Drop me and I'll bloody sue you.'
They lifted him back and went on to the other bank.
*
The Nips were dug in solidly at the bay.
For a week we were locked in battle with them on the hill—close, bloody fighting filled with steel and thunder.
The first three days our guns were still too far behind to support us. The fourth day the guns opened up and the moaning they wove into the sky and the shattering explosions in front of us that shook the earth were sweet music. But ammunition was light on—our attack failed—we had to wait another day for the full strength of our guns.
It was about this time we noticed that Slapsy was going a bit odd. He came crawling round the pits. He seemed to want to talk about something—and seemed to have forgotten exactly what it was. He asked odd questions—how we got our nicknames, were our mothers living—and when we asked him how things were going—when the guns could be expected, whether food was coming up to us—he didn't know.
Pez and Harry Drew talked it over.
'I think old Slapsy's going a bit queer,' said Pez. 'Have you noticed him?'
'Might be,' agreed Harry Drew. 'We'd best watch him. He's a big man—it could be awkward here if he got violent.'
'What can you do, Harry, if he goes off his nut?' enquired Regan, who was hunkered down beside him in the pit.
Harry Drew looked at the thin, battered, grimy kid and grinned: 'Stop him the best way you can. If you happen to be around, kid, you'd best use a rifle butt to make sure.'
So we watched him. But it didn't make any difference—it was so odd, so unexpected, the way it happened—it was funny, almost.
Things had been quiet most of that morning—both the Nip and us locked in the earth on that hillside—an occasional sniping shot or burst of automatic fire sweeping the ground. And suddenly, incredibly, the sound of a flute broke the baleful air—sweet and off-key, as always, the Brahms Lullaby. And, fantastically, Slapsy Paint rose up out of the earth—naked except for the grimy towel round his middle—walking in some calm nightmare of faraway—earnestly and absently playing on his flute.
None us saw him until it was too late. It was so unreal, so incredible—he walked calmly up the hillside, playing his flute—up towards the Nips, playing his flute—pausing and starting over again, as he always did, on that piece in the second bar.
Only one of us found a voice. The Laird was shouting: 'Get down! Get down!' when they fired and we saw Slapsy fall—and you could feel the shock, the incredulous surprise in him, as he fell.
The earth saved him—the solid Mother Earth. He fell into her shelter as a drunk can fall safely down the stairs. We could see he was hit—it looked pretty bad—in the legs and somewhere in the jaw or throat.
The Nips swept a curtain of fire down the hill, and we answered back—it was something to do—it was the only thing we could do. The Nips couldn't get to him, but neither could we—there was too much open ground. We could only wait for dark.
Slapsy Paint just lay there, as though he had woken in a strange room after being sick a long while—or being out on the grog. He just seemed to be lying there.
His flute had fallen in the open and a Nip sniper amused himself smashing it. We could see the little pockmarks springing in the ground around it. One—two—three—four—five—six—the seventh shot smashed it. There was a _Banzai!_ from up the hill.
Through that long afternoon he lay there. He either couldn't, or had sense enough not to, move. From some of the pits we could see him—from others, as the afternoon deepened, we could hear him.
There is nothing more horrible...to be locked into the earth by lead and steel, and hear, through the agony of a dying afternoon, the moans and cries of a man you know. To hear him, to see him, and not be able to move—to know that no heroism and no millionth chance could take you across that burning gulch to bring him to safety.
He moaned and cried...on and on it went...you couldn't shut your ears to that sound—it seemed to swell somewhere from inside you, yourself, and ring on and on, horribly, insanely, and for ever.
In the pit, Regan shivered with pity and shook his head, trying to writhe away from this evil dream: 'Oh, no!—No!—No!'
'Don't listen!' said Harry Drew. 'Don't listen, kid!'
'Christ, I could hit him from here,' said Janos. 'I can finish him with one bullet. Quick—he'd never know.'
'Might be best,' said Harry Drew. 'He looks bad. It might be best.'
'Oh, no...no...no.'
'You can't do it,' said Pez. 'He might live. We can get him after dark. Put the mortars on and we can get him at dark. He might live.'
Mostly he moaned or cried. The only words we could understand were every now and then he would call out, over and over: 'Leave me—leave me—leave me—' over and over and on and on through that long afternoon.
Pez and Janos and the Laird nominated as three to go and get him when darkness came.
'I know where he is,' said Janos. 'I can find him in the dark—I'd best go.'
'I'll tag along with you,' said Pez.
'He's a big bloke,' said the Laird. 'I guess I'd better make one to carry him.'
'I want to go, Harry,' said Regan.
'Don't be silly, kid,' said Harry Drew. 'There's plenty more to go than you.'
'Harry, I've got to go.'
'He's a big man, kid. It needs more weight than you've got to carry him.'
'I'll carry my end—please, Harry, I've got to go.'
Harry took him by the shoulders—thin shoulders: 'Don't try and play it big, kid—a man can only do as much as he can do—that's all that's wanted of you. You don't have to go.'
'I have to go—I want to, Harry.'
'OK, kid—if you're sure.'
'I'm sure.'
Slapsy's cries stopped just before sundown.
'He might be dead,' said Harry Drew. 'I'm not going to risk men to get out a dead 'un.'
'We've got to go, Harry,' said Pez.
'He's alive—he must be alive,' Regan wanted to say, but he didn't say it.
'We'll go,' said Janos.
The mortars threw everything they had against the Nip emplacements on the hill. The sharp, splitting explosions of their bombs beat along the ridge like hail, until the hill was thick with the thunder of it. From the pits we opened with everything we had—firing on fixed lines to leave a narrow lane of safety for the carrying party to reach Slapsy.
It was nothing, really.
Janos and Pez and the Laird and Regan just climbed up out of the pit. Crouching, they followed Janos, who led them swiftly and surely to Slapsy.
They lifted him onto the stretcher. He moaned a little. They carried him back. He was alive.
It was nothing—to walk in the darkness of that fiery furnace. Just that it was uncomfortable, the trip back—a man seems heavier lying on a stretcher and Slapsy was a big man, anyway. You can't crouch to gain the false security of worshipping the earth when you are carrying a stretcher—you can scramble on all fours, lumping the stretcher between you, but that takes longer and is more awkward in the dark. So they stood up—trusting to Janos to lead them straight back—and stumbled as quickly as they could down the hillside to their own pits.
Harry Drew clasped Regan to him like a lost son: 'Good kid!' he said. 'Good kid!'
So we lay in the earth and waited for our guns to be fed.
We got word back that Slapsy would be right. Doc Maguire had patched him up fine before sending him back down the line. On the table Slapsy hadn't come to properly, but from time to time he muttered: 'Leave me...leave me... leave me...'
We lost Bishie here, too. He had been wounded with a grenade on the second day. There were half a dozen pieces of shrap in his back, but he kept quiet and refused to go down to the RAP for treatment. But after the third day he was so stiff and sore he could hardly move.
Doc Maguire got to hear of it and came crawling up to the platoon. 'Where's Bishop?' he said with a grin.
He went to him: 'What the devil do you think you're doing, still here?'
'I'm all right, Doc,' said Bishie. 'Honest I am.'
'We'll have a look,' said the Doc. He lifted Bishie's shirt gently—it stuck to his back in places. The wounds were shallow, but angry-looking and their blurry mouths cried out.
'Three days ago you got hit?' asked the Doc.
'Yeah, I think it was about three days ago,' said Bishie.
'You know, I ought to put you in on a self-inflicted—you should have come to me when you got hit.'
'I'll be all right here, Doc,' said Bishie. 'Just patch me up now and I'll be all right here.'
'No,' said the Doc. 'You're coming with me, boy—you've had it for a while.'
'Let me stay, Doc.'
'Come on, boy.'
Bishie looked as though he was about to burst into tears when he said goodbye—or maybe it was just not sleeping for three nights. The Nip machine gun was beating over on the left flank. Bishie went to pick up his rifle.
'Leave it, boy,' said the Doc. 'You won't need it for a while—with any luck you won't need it again.'
They crawled out back to the track and the Doc's hand rested lightly on Bishie's shoulder as they went together down the road.
After dark that night, Bishie hobbled down to the beach, round past the headland, to meet the barge that was to take him to hospital. He remembered the last time he had waited on such a beach. A long time ago now it seemed...
After the terror and the flight through the jungle, the terror of waiting—the fear that after all that monstrous effort they should be taken. And then the nightmare journey in the small boat—hugging the shadows of the shore by day—eyes burning and blistered from staring at the sky—watching, watching for the treacherous wings.
And now his wounds were aching—he was tired—deadly tired. 'But at least, this time,' he thought, 'we didn't run.'
On the fifth day our guns opened in strength and the hill flamed and roared and trembled under their barrage. They blasted it like a quarry face—you would have sworn that no thing living could survive in that desolation. We ourselves, when we came up from our safe earth, were blinded and deafened with the insanity of it.
But there were some left. We used the bayonet—it was a savage, swift, unwholesome fray—we won the hill.
We took no prisoners. Only one Nip cried surrender—he came out with both hands raised high, crying something in his native tongue.
The Log killed him with a savage thrust, and kept on stabbing long after the Nip was dead. We had to drag him away.
Of course, the Log had a reason—that dazed scatter of shots from the battered hilltop when we started our attack had killed Cairo Fleming...
The Log sat hunched against a tree on what had been a Nip hillside. He sat with his head cradled in his arms between his knees—his forehead pressed against the rifle in his hands...
'I remember the day that Cairo Fleming died...sure, other men died that day and had died in the days before—but Cairo was my friend.'
Cairo's dead, Log—no ghost will rise to speak for him.
'It's hard to tell you...in my own heart I know my friend, but the things I can put into words maybe won't sound important or impressive—there's no drama, no hero stuff in them. Just that we marched and slept and fought together—were broke together and cashed-up together.
'We got our share of strife and we raised our share of merry hell in Alex and Jerusalem and Haifa and Tel Aviv. Remember that leave in Cairo? That's where he got his name—we acquired a Wog donkey and stormed the front steps of Shepherd's Hotel, demanding accommodation for man and beast as the law provides!
'Maybe we never saw the pyramids, but we saw plenty else—lights and shadows—alleys and arak. Anything can happen in Cairo—and when you're young—and a soldier—and the world's your oyster—it usually does.
'Then came the desert—Cairo and I were there—then Greece...We were there when they tried to hold the Hun on the river at Larissa. But he broke us and the cry was: "Get out as best you can!" Cairo and I took to the hills together.
'After a long time, a dangerous time—through dark nights, by small ships threading through the islands of the Dodecanese—we came out of Greece together.
'Maybe you can imagine what those words mean— _We came out of Greece together._
'Then we came home—came Kokoda and the Trail—came the long rest—came this.'
We know him, Log. We know him. They pinned no medals on him, they made no speeches—we need no medals or speeches—we know him and remember. He was just a good, ordinary bloke—that's a point—that's an important thing—he was an ordinary bloke like you or me—maybe a bit better than you or me.
Because, you see, Cairo was an Australian—a blue-blood—an Australian of the oldest, proudest stock. His ancestors didn't step ashore with Phillip; nor were they chained below decks in the prison hulks. They were here before Cook—before de Quiros—before the ancient eyes of Polynesian and Egyptian mariners may have seen these shores.
'Cairo was my friend.'
Come, Log. That stinging of your eyes comes from the long weariness of battle—it nestles beneath all our heavy lids. Come, Log. We will bury him on the hill he died for. Come, Log. Let us lay our black brother in the black earth. Mourn not the dead—but always remember: He was black—he fought and died—he was a good man—he was an Australian.
So we possessed the bay.
As we took our hill, the barrage had lifted onto the next. Another Company passed through us and they in turn took their hill and so on.
We possessed the bay.
## 6
Connell was on the phone: 'But my boys don't want it, sir,' he said. 'We can push on tomorrow—they're in the pink of condition.'
'Listen, Connell,' said the Brig. 'We're not in that much of a hurry. They're going to rest whether they want it or not. You'll be relieved tomorrow.'
Connell slammed the handset down and strode outside his tent. He stood glaring around for a moment and then yelled: 'Sergeant Hino! Sergeant Hino!'
The little fat RP Sergeant came scrambling up through the trees and stood saluting agitatedly: 'Yes sir! Yes sir!'
'Get a party and clean the scrub away from around my tent,' said Connell. 'It looks like a brothel.'
'Of course,' Tubby Hino tells us later, 'I thought of an answer to that one—it was on the tip of my tongue to say it too...'
The Second Battalion came through and relieved us. We rested ten days at the bay.
Sickness and battle had thinned us down. That hill had cost our own group Slapsy Paint, Bishie, Cairo—young Griffo with a smashed leg, Dick the Barber with a stomach wound. Old Whispering John had a long, shallow knife slash down his back from the attack on the hill—but it was only a scratch. He sniggered about it with great satisfaction: 'The old soldier gets through, eh?'
Once we stopped the malaria struck us. The Atebrin hadn't stopped it much, though we took the little yellow tablets faithfully twice a day. Harry Drew went down, Regan followed him. We met the Log one afternoon coming down from the hill—he was shivering violently from cold and the sweat was beaded on his brow. Back he went.
The surf was good and Pez and the Laird swam slowly about a mile out to catch a big shoot.
'You're mad,' Janos said. 'I wouldn't go out there for a thousand pounds—it's too dangerous.'
Pez and the Laird swam slowly—climbing up the great, long swells and bursting through the smother of foam at the top. Every now and then when the wave carried too much white on top they duck-dived under it and were dragged down—pounded and smothered joyously under the broken waters.
Out in the deep swell they lay rolling slowly with porpoise delight in the great depth of cool, clean water. There is an odd sense of comfort mixed with loneliness, swimming so far out. It is as though a man drifts in an alien—but not hostile—environment and really only a small grey ghost of fear and loneliness can rise in his mind.
The Laird called softly: 'Hey, Pez! Look over there—do you see what I see?'
A shark was cruising slowly about fifty yards away—the triangular fin cutting smoothly towards them—tacking away—then cutting back.
'Nothing we can do,' whispered the Laird. 'Keep still—and if it comes, splash like hell.'
They watched and waited—the fin cutting away and tacking back—then it disappeared.
They waited—it seemed a long time...
'Come on, boy,' said the Laird. 'Let's catch a shoot in.'
They swam with painful slowness back into the line of breakers. They waited three or four waves until they caught one that broke at the right time.
Like seals on that foaming crest—the wild exultation of speed and foam and spray—the swift rush of swimming to catch the weight of the wave—the gradual balancing of power as you reined on to it and the swelling, roaring rush; flung a long age down the cooling, soaring breast of the wave—closer and closer and closer to the shore where it destroys itself on the broken mouth of the rock—they slide off before the thunder.
Connell went down to the RAP and found Maguire. 'Come for a walk with me, Mag,' he said.
'Just a minute,' said the Doc. 'Try the sulpha on that one,' he told his orderly, 'and make sure he gets back early in the morning to have it dressed again.'
He came out of the tent. 'Where do you plan to take this constitutional?' he asked.
'Let's go along the beach,' said Connell. 'I want to get away from it.'
'From what?' enquired Maguire mildly.
'From this—from everything!' said Connell.
They went down the track through the trees and onto the white sand of the beach.
'This damned sitting still gets on my tit,' said Connell. 'Brig's orders—silly old bastard.'
'Relax, Cliff,' said Maguire. 'You can't keep going all the time—why, anyway? What makes you want to run all the time?'
'We're here to do a job—let's get on with the bloody thing!'
'You're not fighting the war by yourself. Something troubling you, or are you just leading up for me to prescribe a mild sedative?'
'I don't want your pills!'
'What are you afraid of, Cliff?'
'What the hell do you mean?'
'I mean what's worrying you—what's the trouble?'
'Nothing.'
They walked on some distance over the sand in silence.
'What do you want from life, Cliff?' asked the Doc.
'I don't know, Mag,' said Connell after a moment.
The Doc nodded his head and murmured aloud, but to himself—'Sad people.'
When you are sitting still you have time to think—when you think your brain rusts and sheds flakes of despair. It is blind ahead—discontent and self-disgust—run, run—it's no fiend that close behind you treads—it's yourself.
'Most people,' said the Doc, 'are running from something—from the past, the present or the future.'
'I don't need a psychiatrist,' said Connell. 'Save it for a thesis.'
Remember how the old house had stood back deep in the grounds, and the long, gravelled drive that had been a coachway when the house was built? A wonderful drive where a boy could come in through the big iron gates coming home from school at the end of term—drop the suitcase on the grass and run—a long wonderful way with the gravel crunching and splattering under his flying feet—wonderful running with the wind in his face—and there would be Mother standing on the porch waiting, as she always was for him when he came home, laughing and crying and holding her arms out to him as he ran...
There was that soft, secret thing between them—something that instinctively was hidden from Father. Remember those slow solemn walks around the grounds, with Father all sober black and gold watch chain—the Sunday morning walks after Church—with Father discoursing ponderously on Life and Responsibility and the Things a Man Did and Did Not Do. He would talk interminably overhead—pausing now and then to snip a dead flowerhead or pinch off a withering twig. And always during the walk Father would pick a single bloom, the most perfect he could find, and at the end of the walk he would take it in and present it to Mother with the same ritual phrase every Sunday morning, year after year: 'For you, my dear. Clifford and I have been talking.'
Father was inordinately proud of the two elms that grew at the entrance of the drive—they had been planted by his father before him and he often spoke to the boy about how he must care for them—as though in some way they were the living symbol of the House and the Family, and Life and Responsibility and the Things a Man Did and Did Not Do. The elms had begun to die in the year that he died...It was raining when he died—the Melbourne skies had wept for many days before he died. The boy had had to walk down the long stairs in the grey light of the afternoon and stand beside the open coffin and look at the terrible loneliness of the dead.
And then it was found that things were never quite the same after—Father's Responsibility had not carried on beyond his death. The elms died and the House died...
'That's a sunset,' said the Doc.
'What?' said Connell. 'Oh, yes.' The gravelled drive was gone and the white sand was heavy underfoot. The elms were dead and the jungle trees grew savagely.
Still, influence and tradition were enough to get some scraps of preferment. Outposts of the empire—life in the islands—heat, boredom and sterile lives—the wide-verandahed house—the natives in white—keeping up appearances and squabbling privately about money. He remembered the day he had come back from Moresby—a day earlier than he had told Phyllis...
'Where belongim missus?' he asked his headboy.
The boy, grinning, had held up the newborn kitten. 'Picaninny belongim cat come up along kai kai time.'
'To hell with the cat,' snarled Connell. 'Where belongim missus?'
'Catchim lik lik walk longa Boss Rannerson.'
Drinking—drinking alone and heavily—and then on the impulse striding out of the house—through the frangipanis and across the little board bridge across the creek and up towards the hill where Rannerson's house stood. Standing in the shadows watching the darkened house and listening to the smothered laughter and breathless murmuring and small cries. Life is savagery and despair.
'Look at that,' said the Doc. He held a scarlet branch of coral, curiously smooth and shaped like a stag's antler. Antlers, horns—the cuckold horns.
'What?' said Connell. 'Oh, yes.'
He could remember Rannerson coming to see him. Rannerson—big, brutally sensual and coarse with joviality.
'Look here, Connell, you're being a fool. What do you want to do: challenge me to a duel? Look, it's your own damn fault, coming home a day early—never come back home unexpected up here. It's the heat—they all get arse-end itchy—they go looking for it. On the other hand, you do the same thing—or wouldn't you care for me to mention Mae Thompson? You see, I'm not a gentleman, Connell—I'm not public school, or officer-and-gentleman or anything like you—I don't mind mentioning a woman's name in the mess. Look, come off it—we've all got to do something to fill in time here. I've had her, you've had her—and very nice too. Only we three know about it. Forget about it. Have a drink.'
Rannerson had called the boy himself and ordered the whisky. And Connell had drunk with him and hated himself. He and Phyllis had been together for a year after that, before the war separated them.
Lots of people try to run—from the past, the present or the future. What is the future? Thought rusts the brain and it sheds flakes of despair.
'As a matter of fact, I've got a flask of brandy,' said the Doc as they went back up the jungle path from the beach to the RAP. 'It's supply—I'll prescribe you a dose.'
'I'll take it, Mag,' said Connell. 'And after that—I will take a couple of your bloody pills, too.'
Pez and Janos and the Laird were lounging beside the muddy road at the bay when the General's jeep got bogged. She swung, roaring along the track, and came to rest belly-deep in mud. Pez and Janos and the Laird disappeared into the bushes instantly.
They saw the brass hats get out and walk around the stranded vehicle pontifically.
'Watch this,' whispered Pez. 'This'll be good.'
The General made a masterly military assessment of the problem. 'I think we'll have to dig it out,' he pronounced.
The Colonel pondered this gravely. 'What we need is a shovel,' he decided finally.
The Captain went and got the shovel—and gave it to the driver and he started to dig.
'That's the way of it,' rumbled the Laird. 'Right through the goddam army—everyone else makes the decisions, the poor bloody private does the job.'
Later, on their way back to the doover, they passed Connell on the track. He was looking particularly pleased with himself.
'I know what that means,' grunted the Laird. 'We'll be on the move again in a day or two. He's only happy when he's in a blue.'
We got ourselves a new lieutenant before we set out. Minnie, his name was—Minnie the Mouse. He'd been a Q bloke mostly and we'd left him at our base camp down the shore. But we'd lost so many officers they dragged him out and shot him up to us.
He was a funny little bloke—physically slight and extremely timid. He'd won his pips by passing brilliantly in theoretical work at an officers' school—if they'd left him at a desk job somewhere around Victoria Barracks he'd probably have given good and valuable service during the war.
It was his own fault, of course. He wanted to be a soldier—a fighting soldier—but he lacked all the equipment except that desire. It had got him as far as a commission in an infantry battalion and now it had finally got him a fighting platoon—but the job was not for him.
Minnie was an only child and he had a fond mother and father. Pez met his old man in town one leave...
He was strolling down Pitt Street and this old bloke in civvies pulled him up.
'I saw your colour patch,' he said. 'My son's in the same battalion as you—I thought you might know him—Sullivan's the name—Lieutenant Sullivan.'
Pez scratched his head—Sullivan—Sullivan—suddenly he remembered: 'Oh, God yes! I remember but mostly we call him...Oh, you know, we've got nicknames for all the officers.'
Near as dammit he'd said Minnie the Mouse. The old bloke probably wouldn't have liked that—he seemed proud as hell of Minnie being a Loot. A nice old bloke he was, too, but with those kind of soft rabbity eyes, just like Minnie.
The old bloke wanted to know what we called him and that had Pez worried for a bit.
'Munga,' he told him finally. 'That's what we call him—Munga—it's an old one from the Middle East.'
The old boy was pleased and proud.
'Oh yes, he was there, too,' he said. 'He was in the Middle East.'
Minnie had been a good son. He'd never whored around or got drunk and he'd lived all his life in timid frustration. He had paid court to a respectable young lady in a perfectly respectable fashion for years—the theatre on Thursdays, a dance on Saturdays, and a salad and cold meat dinner at her mother's place every Sunday. Her mother thought he was a nice boy and it was generally understood that they would marry when his bank balance and clerkly salary reached the proportions thought respectable.
The nearest Minnie got to respect as an officer was when the men said he 'wasn't a bad poor bastard'. The other skulls laughed at him behind his back—but managed to get him to do a good deal of their paperwork for them back in standing camp.
So this was our new officer. First Slapsy and then Minnie—we could certainly draw the crow.
They told us this might be the last show we would do before going home. We were to take over from the Second Battalion for a while—then they would come through us and finish the stretch.
We were hearing rumours of another war, too. The second front had opened in Europe. We heard the news in whispers down the line—in occasional wireless news—in reports of men coming back from hospital.
While we marched along the long green shore men died in the steel ring of Cherbourg—the earth was stained more red at Arnhem—the Russian guns thundered as they rolled in the East. Something was happening north of us in the Pacific—there was a place called Iwo Jima.
So we went on—what was left of us. We struck good weather. The road was broad and hard. We were second platoon. The only Nips we saw were the dead ones that the sections in front left for us.
One day we halted near the body of a young Nip lying by the side of the track. It was smoko. Janos walked over and flopped down next to the body: 'Come on,' he invited Pez. 'It's all right, he doesn't stink. He's fresh.'
The Nip was only a lad—it's hard to tell with them, but he looked about eighteen. He had fallen forward on his face, his head was turned to the right and his legs sprawled. He had died swiftly, without struggle, and looked as though he had fallen in exhausted sleep. There were three bullet holes in his back, smudged black with blood around the edges—quite neat and seeming to bear no relationship to death. A trickle of blood had dried in the corner of his mouth. One hand was outflung and he still clutched a fresh bundle of plucked grasses—another bundle was tucked into his back pocket.
'Wonder why he was picking grass?' said Janos. 'He doesn't look as though he was hungry.'
The grasses were thick and juicy looking.
'I think it's that koyu the natives use,' said Pez. 'They say it's a good vegetable.'
'A man should have green vegetables,' said Janos. He took the grasses out of the hand of the dead man. He had to use force to bend the fingers back.
'You're not going to eat it, are you?' asked the Laird.
'Why not? If it won't kill him, it won't kill me.'
Janos made the stew that night and stirred the grass into it. None of the others except Pez would eat it with him. Pez didn't quite understand: 'What is this? A sacrificial supper?'
Janos just grinned.
They had pitched their doover facing the beach and Janos had gone down to the fires to make the stew while Pez dug the weapon pit.
The sun was slanting down when Janos got back. They sat on the edge of the weapon pit and ate the stew. It was good and hot, with flour stirred into it to thicken it. The dead Nip's grass tasted something like spinach, but faintly bitter. Neither said anything more about it.
It was stand to before they finished. First Janos crouched down in the pit and smoked, then Pez. They sat together, talking in low voices.
It was a safe billet and time to get a good rest. We were camped in a little belt of trees on the edge of the white sands. In front of us was the sea—behind us a broad dirt road. Other platoons were camped across the road, ahead and behind us.
Pez and Janos sat together on the edge of the weapon pit. The moon had risen before stand to ended and it was shining bright and silver on the sand and mottled on the road and left us in black shadows in the trees.
'It's been a long time, Pez,' said Janos. 'This is a hell of a business...'
'Yeah,' said Pez. 'It's been a long time—a lot of men...'
'I don't know what I go back to when it ends—if I'm left when it ends,' said Janos. 'Sometimes it bothers me.'
'Don't worry, boy,' said Pez. 'We're near enough to the end now—you're home and hosed—we'll drink a gallon of beer in Ma Maloney's yet.'
'When we first went away, home was close,' reflected Janos. 'You could remember it, and what you would do when you got back was clear.
'But it's been a long time now and things have changed. When you go back on leave the children you left behind—the kids next door—are men and women and you walk like a stranger in the street. People say hullo to you in the street and drink with you in the pubs and ask you how it was—but you don't really belong there—you're a wanderer, a blow-in, a ghost. They treat you with politeness, but not too lavishly. They spread themselves the first time you went away—they seem to resent it a bit now every time you come home again—they sent you away like a hero—they seem to expect that you should have done the decent thing and died like one—then they could feel satisfied they'd done right by you.
'If the war ended tomorrow, we'd be lost and lonely—we're lost and lonely now, so where's the beginning and the ending...?'
Pez made no answer—there was none to make. But it's a bad thing when a man starts talking about the future at times like this. In the rambling philosophy of a camp, that sort of thing is all right. But it's not a good thing to start thinking on those lines when you're on the track.
The whisper to stand down came floating through the trees.
'Come on, boy, let's sleep,' said Pez.
They were comfortable bunks in the clean sand that night—you could still feel the warmth of the sun on the earth through the blanket. Pez and Janos lay silent side by side under their tent flaps for a while. Then Janos said goodnight and rolled over. He was asleep in a few moments.
Pez lay awake and listened. There was a calm brooding silence on the beach. The hard, comforting feeling of his rifle lay beside him—the muzzle resting on the pack that made his pillow—a strange beloved to lie abed with. 'But I have known women who could be less cold, yet not so comforting,' he thought.
'Oh no, it couldn't be, Janos my brother—while we live we are not lost. All your courage and skill and wisdom cannot go for nothing. While we live we are not lost.'
Pez found himself thinking, for no reason, of the Deacon. He remembered one morning they had come up the track and on top of a sharp rise there was the body of a Nip ludicrously dead. His body made an arch, resting on head and feet, his naked backside poking up in the air. We ran right into him as we topped the rise. The body was swollen and the skin had that tight, waxy look that they get. He was crawling.
The Deacon had paused in mock surprise—stepped back, sweeping his hat off, and bowed low to that backside: 'And good morning to you, sir,' said Deacon. 'The face is familiar but I'm afraid I can't quite place where I've met you.'
Why the hell should he remember Deacon...?
While we live we are not lost...
The Laird woke Pez for guard at two o'clock. He rolled out into the pit and sat there smoking a covered cigarette to wake himself properly.
Just before he was due to wake Janos, there were shots up the beach and a man came running down the sand. In the bright moonlight you could see he was a Nip. Pez fired, but it seemed he missed. Then an Owen opened up from further down. You could see the spurts of sand running across the beach towards him and then his body shuddered as the bullets struck him.
He started shrieking—a terrible, animal noise, and, turning, he rushed into the sea and was lost—though for long minutes afterwards you imagined you could hear the screams coming, pounded through the thunder of the surf.
Janos was behind Pez in the pit by now.
'Silly time for a bloke to go for a swim,' he said.
When we went forward that morning we ran into a Nip mountain gun. That was the finish of Minnie. It was the first time he had been under fire and he just ran around in circles. 'Like a chook with no head,' the Laird described it. He had no idea what to do. Whispering John and Harry Drew took charge. Minnie just crawled into a hole and stopped there.
A couple of days after that they sent Minnie back down the coast to the base camp. He was sent back as a neurosis case—an officer is entitled to get neurosis a damn sight quicker than a private.
It was that morning, too, that the Indians were shot. They'd escaped from the Nips and tried to get into our lines. They came down the track, waving bits of rag.
Young 'Squizzy' Taylor from Charley Company shot them down as they came. He was a bit nervous and Connell's orders were to take no prisoners. He didn't realise until he'd done it that they were our own men.
Two of them were dead when they got to them. The third they carried in and Doc Maguire worked over him all day—but he died.
The next day we took our objective—this was to be the end of the trail for us, they assured us.
We passed through a stretch of country that had been lived in once and was now overgrown. The roads were sunken but still definable. Everywhere was the ghostly smell and sign of the enemy—piles of rusting ammunition dumped along the side of the track—foxholes, weapon pits and dugouts burrowed in between the writhing octopus roots of the trees. For here, again, gnarled thick-limbed nightmare trees grew twisted into violent still life. Dozens of burned and rusting trucks were entangled in the jungle growth at the side of the roads—most of them had the skeleton of the driver underneath and the steel cabins were punched full of holes where the planes had strafed them.
At intervals were stacks of boxes with Japanese lettering burned on the sides. The boxes had rotted in the rain and burst with the weight of their contents—ammunition and equipment, but never food or clothing.
Our objective was a clearing a little inland. There was nothing to it. We went carefully along the track and reached the clearing without any trouble. There was a native hut in the centre. We riddled it from the edge of the clearing and then ran up to it.
Old Whispering John it was that kicked open the door. Janos and Pez and the Laird went on to clear the other side. Young Sunny covered old John. The rest of the platoon took ground.
Old John told the story later. He leaned his chin affectionately on Janos' shoulder and sniggered confidentially: 'There's this Nip there,' he whispered. 'He's lying on the bed and when I kick the door in he staggers to his feet. So I let him have a burst in the guts.' He sniggered. 'He walks round the room for a while holding his guts—and then he goes and lies on the bed.'
'Maybe he was tired!' snarled Janos—twisting his head to avoid old John's foul breath.
The war in Europe ended.
Young Sunny came running along the track: 'They've tossed it in—the Huns have tossed it in!' he yelled.
'Take it easy,' growled the Laird.
No one danced on the long green shore because the war in Europe had ended. A big shoal of fish had come in near the beach that morning—in close enough for our grenades. We had fresh fish for breakfast and that was more important just for the moment.
It was something to talk about, sure. But what the hell! Europe was a long way from us—our war was still going—it would take time to swing armies and air force men from Europe to the Pacific—our job was still to do, and time was the deadly factor.
It is a simple equation—the old blokes are the most worried—matter-of-factly worried. A soldier may have a thousand lives—no more. You can stand up just so many times and after that, no more. The longer you go, the higher the odds pile up. These old blokes have bowed to death so often—they know their time is running out.
It was that day, too, that Pez went back to hospital. He had been up all night with vomiting and diarrhoea. He was a pale shivering shell in the morning.
'You've got the wog all right, boy,' said Janos.
'Feels like it,' chattered Pez. His eyes were swimming, his skin burning, he was deadly cold inside.
Janos carried his pack for him down to the RAP.
'Don't worry about it, boy,' he said. 'This looks like the end of it. They reckon we're finished now. The Second's taken over and our next trip will be home. If we get home, the way things are shaping, we'll never go away again—she'll be all over before that.'
Doc Maguire took a look at Pez.
'Looks like a touch of the wog,' he said cheerfully. 'But even if it's not we'll send you back for a bit of rest—fatten you up a bit. Have you been eating all right?'
'Oh, not badly, on and off, Doc,' shivered Pez.
'Thought so,' said the Doc. 'A bit of starvation is what's wrong with you.'
'I'll make sure they send your letters back,' said Janos. 'Look after yourself, boy.'
Pez lay down on a stretcher with a couple of blankets over him while he waited for the ambulance. He could keep nothing in his stomach. They gave him a cup of tea—he brought it up. They gave him a dose of quinine—it came up immediately and the bitter sting of it remained at the back of his nose.
All the world is dazed and pitched off-key. The body loses substance.
There is only one other patient in the three-tonner ambulance truck with him—a young lad from the Second Battalion with a leg wound. He grunts a little as the truck bumps and sways down the road. His eyes are a little hysterical—too much white showing in them—and his voice rambles...
'I cut their throats,' he is saying. 'We never took any prisoners in our mob—I cut their throats—even the dead ones. After it's finished I go around and cut their throats—even the dead ones.'
He falls silent and groans between his teeth as the truck grinds and bumps down in a rough pinch.
'My brother was in Malaya,' he says. 'They killed my brother in Malaya—some blokes who were with him told me—they cut his throat like a pig...'
They waited half an hour at the ambulance station at the 'drome for the plane to come in. There are other cases there—stretcher cases mostly that have been carried down from the hills.
From where Pez sits he can see across into the hospital itself—a casualty clearing station. The sides of one of the tents is drawn back for the light. Three or four white robed figures move around the table, bending over it. Red flesh is showing on the naked figure strapped to the table.
The plane comes.
On the trip down he crouches near a window and with hot, heavy eyes stares at the meaningless drift of jungle and shore that flows beneath him—the long green shore that so painfully and darkly they had fought and marched along. All the weary weeks it had taken them and now it passes in a brief twenty minutes.
The first thing you feel when you get into hospital is a sense of your own dirtiness—the grime that has been under your fingernails unnoticed for months suddenly seems gritty and itchy on the tips of your fingers.
There is no glory in the world like a hot shower—you come out purged and clean—your whole body is light as in a dream. It must be a thousand years since you were clean before.
There is a rare pleasure in the lightness and cleanliness of unaccustomed pyjamas and your feet are shod with air in slippers after the heavy jungle boots.
For the first week, Pez slept, mostly. Sleeping for a couple of hours and waking briefly to drift back again. It is an unreal world of polite voices and soups and sweets with meals and lights at night and music from the loudspeaker beating softly through the long palm-leafed ward. This is peace and rest—but somehow it is further away from home and reality than the weapon pit is. Here are books and morning tea with biscuits and women—brisk and professionally tender—so neatly starched in khaki, so sweet-smelling, so soft of face—how coolly warm their fingers are on your brow—but we are further from home, this is peaceful desolation.
Harry Drew and Regan visit Pez. They are on their way back to the battalion. He hears news of others. Some are dead, some have gone home, some are in hospital still, some have gone back up the track.
At the end of the first week they put a bloke with pleurisy into the end bed next to Pez. He was dying. For three days they fought for him. There was always a nurse by his side. Bottles of plasma and serum and glucose were suspended over his bed, the long red tubes snaking down. The life-liquids dripped into his veins hour after hour. The nurses sat by him and smoothed his brow and tried to calm him when he raved and brushed moist cotton wool on his parched lips when he begged and groaned for water.
The third night he called out a lot and the doctors came many times. When Pez woke in the morning the bed was empty and the bottles had been taken down. The little nurse called Bunty was sniffling and red-eyed as she remade the bed. She had been with him at the last. It must be hard to fight so long and passionately and skilfully and then have them die under your hands.
*
When Pez gets up and about again he makes way a bit with Bunty. They really got acquainted one day when he strolled into the storeroom out the back of the ward to get a fresh towel.
The linen cabinet was a dark little cubicle and Pez, groping his way in blindly from bright sunshine outside, ran bang into Bunty who was inside the cubicle doing a quick change act.
'Hell! I'm sorry,' said Pez, retreating hastily from that disturbing soft nakedness.
He leaned against the wall outside the cubicle and lifted his eyes ostentatiously to heaven: 'Why don't you hang out a sign—lady undressing?'
'What the devil are you doing here, anyway?' asked Bunty, amused. 'You're not supposed to be here.'
'I was after a clean towel,' confessed Pez. 'I missed out on the issue.'
A suggestively naked arm came out of the cubicle with a laundered towel: 'If a towel's all you're after, that's a change. Usually you blokes are after something else once you get on your feet.'
'Oh, I'm adaptable,' said Pez. 'I can turn my hand to practically anything.'
Bunty came out of the darkness, buttoning her jacket: 'In that case,' she said evilly, 'and on account of the embarrassment you've caused me, you can give me a hand to do some ironing.'
So Pez helped Bunty do the ironing and spent a lot of time talking to her casually and smoking her cigarettes as he worked. It was a very casual and comradely affair.
Once she did suggest that if he could dig up a bottle of whisky somewhere she was very partial to whisky and knew a very comfortable and private sandhill—but Pez couldn't lay hands on a bottle of whisky.
When he was leaving she kissed him in a friendly fashion and they made a date for a pub crawl in Sydney after the war.
The ward next door was the troppo ward. It was closed in with heavy cyclone wire and guarded by provosts. Odd cries and yells came from it at times.
There was one bloke Pez could see and hear through the wire. He was a big bloke. His left arm was smashed and in plaster.
He would stand for hours looking out through the wire—the fingers of his good hand hanging onto the wire above his head, his smashed hand held against his stomach, his face pressed against the mesh.
For a long time he would stand quietly. Then suddenly he would open his mouth wide and give vent to a long animal scream that went on and on—at the same time seeming quite detached from him. His calmly insane face was visible through the wire, the mouth wide open, and those agonised shrieks seemed to be coming from some other being locked inside him.
He escaped one day.
The first Pez knew was when he saw him running. He came with a peculiar loping run, his smashed hand, weighted with the plaster, swinging pendulum-like. He was crowing in a thin wailing voice as he ran and chuckling with childish triumph.
He came running into the ward and went straight to the little bald-headed bloke in the bed opposite Pez. He lay down on the bed, snuggled down.
'I got away from them, Eddie,' he chuckled with childish triumph. 'Look, see!' He was showing his dead meat tickets with a furtive, confidential air. 'Look, Eddie—you know me—I'm a Protestant—they're all Hindus in there—I'm a Protestant and they're trying to make me a Hindu—but I got away—' he shivered again with delighted childish laughter.
'Sure, sure, she'll be right, Happy,' said Eddie. 'You'll be all right here.'
Half a dozen provosts came running into the ward. Big, beefy blokes, panting from the run. They crowded round the bed but none of them seemed to be anxious to be first.
The man with the smashed arm cowered back on the bed, snarling. When they tried to grab him he kicked at them and beat at them with his plaster arm. He was shrieking incoherent filth at them, the teeth and red gums showing in his savage mouth.
Eddie had his arms around him.
'Get away from him! Get away!' Eddie was pleading. 'Leave him alone! He'll smash his arm again—he's smashed it three times already.'
There was an angry growl from the rest of the ward, a swift gathering anger: 'Provost! Provost! Let him alone!'
The little dark-eyed Sister was in the middle of the provosts suddenly, ordering them back: 'Get outside, boys,' she said. 'I'll handle this.'
'He's dangerous, Sister,' said one provost. 'He tried to use a knife.'
'Get outside,' she said.
The bloke with the smashed arm was still snarling—watching the provosts. They withdrew to the doorway.
The dark-eyed Sister walked calmly up to the bed and stood close to him. Everyone in the long ward held their breath. Slowly her hand went out and rested lightly on his forehead.
'Are you all right, lad?' she asked.
He looked at her a long moment—gradually the snarl faded, the distorted face relaxed. He looked at her with utter weariness—the tormented eyes finding rest in the cool and unpitying warmth of her.
'Yes, Sister, I'm all right—only make them go away—see, I'm a Protestant—see, I can show you my meat tickets—they're all Hindus—make them go away, Sister.'
She ordered the provosts away. They go reluctantly. She stayed quietly talking to him. 'How do you feel?' she asked.
'All right, Sister—I'm all right—just my head aches.'
She soothed his brow—oh, those hands had the sweetness of a benediction and like cool water soothed our fevers.
'I just want to stay here with my mates, Sister—I know they want to put me on a plane tonight—I'll go on the plane, Sister, but I just want to stop here with my mate until then—this is my mate, Eddie—I just want to stay here with him and sleep.'
The little bald-headed bloke, Eddie, had him in his arms, nursing him.
'He'll be all right, Sister,' said Eddie. 'I'll look after him—he'll be all right until the plane.'
The Sister asked will she bring another bed in for him, to put alongside Eddie's bed, but Eddie said no, he's comfortable—he'll look after him.
The little bald-headed bloke sat there holding the big bloke in his arms all the afternoon. Sometimes the big bloke slept, other times he talked in a swift confidential little whisper and showed Eddie his meat tickets.
He was calm in the evening but the provosts came in again and he kicked and screamed when he saw one of them with the morphia shining in his hand.
The dark-eyed little Sister came in again.
The provosts left him and the big bloke finally went quietly with Eddie.
'I know they want me on the plane,' he said. 'I'll go on the plane—just so long as they keep away from me.'
In the small bay of the island where the convalescent camp was, a rough wooden jetty jutted out from the shrill white sand. Draped over the rail of the jetty was a long, lean American. He stared morosely down into the clear water and, with backwoods accuracy, spat from time to time at the coral-coloured fish that drifted up to the surface and flicked away.
Another American came down onto the beach. 'Hey, Hank!' he yelled through cupped hands. 'The Cap'n warnts you!'
The tall, morose citizen spat into-the water. 'Go tell the Cap'n,' he yelled back, 'tuh take a flyin' fark at a gallopin' goose—I ain't a'comin'!'
This pleasantry so intrigued Pez that he sought further acquaintance: 'What's the matter, Yank?' he asked. 'You sound browned-off.'
'Man,' said the American, 'I been goosed and gart at—this here base ain't nothin' from beginnin' tuh end but hart cark!'
'What?' queried Pez.
'Cark!' said the American. 'C-O-C-K—cark!'
'Don't you think the Captain might be disturbed that you won't join him?' asked Pez.
The American spat again. 'He's a cark sarker from Fifth Avenoo—I know him frum way back—when I tell him I ain't a'comin' he knows I ain't a'comin'.'
'You've got your army organised properly,' admired Pez.
'We gart organisation,' said the American. 'We gart organisation like I gart a hole in the head—it takes a whole garddamn army to organise me so I set on my ass arn this gard forsaken pimple arn the ass end uv the world, while I gart a redhead waitin' for me back at Kings Crarss...man, she's hart and she's strong for me! She's gart legs like Grable and tits like you never saw in a dream. And I set here on my ass on a pimple on the ass end uv the world—and the Cap'n warnts to see me!'
'I got a girl up near the Cross myself,' said Pez. 'It's all right—she's not a redhead.' He pulled his wallet out and opened it at the photo of Helen.
'Say, she's sharp,' admired the American. 'She's gart class.'
He dug out his own wallet. 'No, nart that one—that's muh wife. This other one—that's muh Bella.'
'I see what you mean,' admired Pez.
'Oh man, she was hart,' mourned the American, 'and strong for me. Incidentally, my name's Hank.'
'Mine's Pez.'
'Look, I gart a case uv canned beer—tastes like parrot's piss—would you care to join me?'
'Never knocked one back yet,' said Pez.
'Well, carm on—we'll go arp round the back way—I wouldn't drink with any uv the cark sarkers here—they all like to play soldiers—so long as the garddamned war ain't too close, they like it fine.'
'Say, Pez,' said Hank, a couple of nights later. Whut's this garddamned swy—this two-arp you basstuds play?'
'Come and I'll show you,' offered Pez. As they struck off across the island to the swy school, he instructed Hank. 'Now, you've seen the game, haven't you?'
'Yes, uh've seen it,' admitted Hank, 'but I never gart close enough to it—looks like all cark to me.'
'Well, you see, you've got a ring—you've got a boxer, he holds the stake money—you've got a ringie, he hands the kip on and calls the bets—a spinner comes in with two pennies on the kip...'
'Whart's the garddamned kip?'
'A little piece of board that you rest the pennies on when you toss them. Then when the guts is set and you're set on the side...'
'Whart's this garddamned guts and side?'
'Well, the guts is the centre—the stake your spinner is spinning for. That's got to be set first and then any bets on the side are set. The spinner's usually for heads—if you're a tail better you set the centre or bet against another headie on the side. Then the ringie calls, "Set in the guts, all set on the side—come in spinner," and up go the pennies. You can bar them if they float or if you don't think it's a fair go—but you've got to bar them in the air. Down they come and the ringie calls the result—heads or tails—or ones, no result. If you're spinning for a head and you do them, she rides and you double up to the third, then the boxer takes his drag. On the fourth you can drag some yourself—but if you let her ride she doubles every time. If you can do a dozen in a big school you got a fortune.'
'Whart happens if you tail 'em?'
'You pass the kip—you've had it.'
The school was in some dead ground over at the back of the island. The ring was a canvas square lit with globes powered from truck batteries. There were thirty or forty at the game and the ringie, a short, villainous-looking character, was skipping around the canvas in his stockinged feet and bellowing hoarsely: 'Come on! We want another quid in the guts to see him go—just one more fiddly from you tailies—come on, he's done 'em five—I want a tailie for a quid to see him go!'
'Why, I guess I'll accommodate you for that,' said Hank.
The ringie looked up at the accent as though his favourite and long-lost brother had just walked in. He took Hank's pound and tossed it to the boxer, who was crouched on a kerosene case at the edge of the ring, with the centre money laid out in little heaps of individual bets in front of him. The boxer covered Hank's pound and the ringie shouted with renewed enthusiasm, 'Come on, get set on the side—any more bets on the side—he's done five already—any money for a head, any money for a tail. Right! Set in the centre, set on the side—it's a fair go—come in spinner!'
The ringie eased to the side of the ring and muttered to the boxer out of the corner of his mouth, 'Did you cop the septic tank just walked in? We might make wages yet tonight.'
The spinner weighed the pennies carefully on the kip and looked up to measure his objective or seek help from God...
'Ring out!' bellowed the ringie hoarsely. 'Ring out, he's a high spinner.'
'Whart the garddamned hell does he warnt now?' demanded Hank.
'Give him room, he throws them high,' said Pez.
The spinner tossed the pennies up high and back over his head, giving a little hop for luck as he did so. The coins rang together in the air and the ringie shouted with unconvincing playfulness: 'Jingles for joy! Ring back—I'll call them!' The coins slapped and rolled on the canvas—heads craned—the Lady glared up in two places. 'He's micked 'em,' announced the ringie morosely. 'Pay the tails—and what about a bit of a sling from you headies!'
'Man,' said Hank as he got his two pounds back. 'This here's a game! I can work out a system.'
A quarter of an hour later, and twenty pounds lighter, he and Pez trudged back across the island. 'Jesse James,' said Hank, 'Dillinger, Capone—we've had them back in the States—but never nothin' like that game.'
Hank poked his head into the tent as Pez was packing to go back to the mainland. 'Here, Pez,' he said, 'I gart you two cartons uv cigarettes. Couldn't get you any garddarmned Luckies—these here are made out uv shag shit—but they burn.'
Pez dragged a Nip flag out of his pack. 'I got you the flag, Hank. She's genu-wine—my mate finished making her this morning. I shot the holes in it myself and when the tomato sauce dries you won't be able to tell it from blood.'
'Thanks Pez,' said Hank.
'And apart from that, I got you a story to go with it,' said Pez. He struck a pose. 'This here flag, my friends, was captured in the bloody fighting before we took the Nip headquarters at Booma Ridge. Defended it was by a company of Nip Royal Marines—all six feet high and fighting fools who had sworn a Shinto, Banzai, Kamikaze oath that the flag would not fall into the hands of the enemy while one of them remained alive.'
With an expression of awe, Hank sat down on the bed.
'For two days and two nights we were locked in mortal combat on that hill, friends—it was tough, mighty tough—until the only man of the Nip guard remaining alive was Captain Sake Sake. He draped the flag around his body, drew his sword and charged down the hill, till he fell in the face of withering fire. Here are the holes, you see, my friends—these same holes are where the bullets pierced the flag and struck mortally into the body of Major Sake Sake.'
'He gart quick promotion,' said Hank.
'And these same ominous stains, friends, are where his lifeblood flowed as he died to honour his oath!'
'Jee-sus Christ!' said Hank reverently. 'That's hart, man. That sure is the hartest kind uv cark!'
'I'd have got his sword for you too,' apologised Pez, 'but my mate over at workshops hasn't quite finished making it. She'll be right, though—made out of the best quality jeep spring and with Colonel Sake Sake's family history tastefully engraved on the blade—gen-u-wine Samurai. He'll bring it over the day after tomorrow.'
'That'll be fine, Pez,' said Hank. 'I'll trade it to some uv these new cark sarkers that are comin' out. They admire to get somethin' with bullet holes and blood so they can tell the folks back home how they waded knee deep in it—and just what fightin'est sons uv bitches they really are. I'll sock 'em plenty.'
They walked to the barge together.
'Say, Pez,' said Hank. 'If you happen to be in Noo Yark after the war, remember two thousan' one hunnerd and thirty-five on Thirty-Fifth Street. You'll find it easy—anyone'll tell you.'
'Yeah,' said Pez. 'Well, don't forget what I told you: the back bar at the Imperial at the Cross, any time after five. Ask Eileen.'
As the barge drew out from the jetty, Hank leaned over the rail, 'See you after the war, man. Don't forget.' He was calling across the water: 'Two thousan' one hunnerd and thirty-five on Thirty-Fifth Street—Noo Yark.' A thought struck him, he bellowed: 'City!'
There were only a handful of men at the base camp, but rations were still light on and the main source of supply was still the Yank rubbish dumps.
Pez struck the Log at the camp and they met the blokes left behind when we went up the long green shore, and caught up on all the gossip. Sergeant Buney, the Vickers sergeant, who had developed bad feet mysteriously just before we moved, had been making a pretty penny selling stuff belonging to blokes who had been killed—stuff left behind in their kitbags in the battalion store. There were a few mutterings among the boys about it, but nothing was ever done about him—no complaint was made. The dead can't complain.
On their way down to the mess, Minnie the Mouse stuck his head out of a tent. He seemed surprised and grateful when Pez hailed him.
'Coming down to eat?' asked Pez.
'No, thanks,' said Minnie. He seemed shy of something. 'No—as a matter of fact I'm writing a letter.'
Pez glanced into the tent. There was a small deal table set for the light, a writing pad, pen and ink, and an inch-thick pile of what looked like manuscript. 'Looks like some letter,' Pez said. 'You nearly finished it?'
'Well, no,' said Minnie. He seemed a bit embarrassed, but pleased to talk to someone. 'As a matter of fact, it's a very difficult letter to write.'
It appears Minnie had been hanging around the base camp for some time. They were going to board him south with some honourable and comfortable neurosis of the type reserved for officers. Then he got a letter from his girl—the one he'd wooed respectably for going on nine years.
It wasn't a very long letter. In fact, pretty near everyone around the base knew it by heart. It was just two lines, announcing that Dorothy was going to marry a British commando named Bruce. It was signed, with rather unhappy formality, 'Yours faithfully'.
A couple of nights after he received the letter, Minnie attended the open-air picture show down at the hospital area. While a faithless lady on the screen was entertaining her lover, he rose babbling incoherently and emptied his revolver into the screen.
They took his revolver off him, but decided later that he was not really dangerous and let him go back to the unit base camp to wait for a plane south.
Now he sat in his tent all day and wrote. He wouldn't attend the normal mess parade, but it was suspected that he used to sneak down to the kitchen at night and get tinned stuff.
All day long he would sit writing. There was a great wad of manuscript when Pez last saw it. He asked Minnie if he'd like it posted, but Minnie said it wasn't finished yet.
Pez's mail finally caught up with him. There were half-a-dozen letters from Helen—the last ones written after the war in Europe ended. 'Come home,' she said. 'Be careful and come home to me.'
He felt warm and benevolent on the strength of it and went to talk to Minnie for a while to try and cheer him up. Then later he got to thinking about it.
'Come home,' she said. Sure, she said that—but he had to go home to the problem—that still stood—there were still three where only two could go.
A woman might write a thing like that—and mean it for the moment—but when he did get home...
The last night at the camp, Pez got very drunk on home-distilled gin and sat very late in his tent writing to Helen.
_My Darling, My Dearest, My Honey,_
_I'm on my way back to the unit after Con Camp. Your letters caught up with me today. I've read them all through many times and I feel there's something tremendously important I've got to say. The only trouble is, I don't know what it is—I've sat here for hours trying to think what it is I want to say._
_Possibly this is complicated by the fact that I'm drunk on gin made fresh this afternoon by Bill Abdou (you remember him) from Workshops. In fact, I am as drunk as Chloe—full as a bull—or a boot, or a goog—molo—pissed as a newt or (if you prefer it) to the eyebrows._
_Or maybe it's the thought—the impossible, fantastic thought that the war might some time, soon now, be over. What that will mean to us, I don't know._
_I suppose that is what troubles me, really—I am looking for a meaning. That's it—the wonder of the world. The meaning of living—the meaning of death—the meaning of love. Is living being alive and death ceasing to be alive and loving tumbling on a bed? I ask this question without notice of the Honourable Minister for Human Affairs._
_Helen, my dearest, I am drunk and I love you. I am coming back—and to you. I don't care what arguments there are against it—I am coming back to take you. I am drunk and I love you. I love you even more, sober, but not so poetical. Goodnight my love, my dearest. You are the Song of Songs, which is Solomon's, and if your belly is not quite a heap of wheat set about with lilies, it will do until a heap of wheat set about with lilies comes along._
_I am drunk and biblical and bedevilled and damned... and I want a meaning. I look up at the sky and wonder—and I look down at the earth and wonder—and I dream on you and wonder. The wonder of the world._
_I am drunk—and Christ I miss you and I need you._
The word came suddenly. Everyone except base personnel to move that evening.
'I don't like the look of this, Pez,' grumbled the Log. 'Why do they want everyone in such a damn hurry?'
They tumbled onto a barge just before dark and after a beaten-iron voyage, the monstrous, clanging, stinking creature flopped its jaw up on the sand next morning and they stumbled from its crowded throat.
The doover tents were knocked down in the battalion area and the packs loaded for the track.
Janos grinned when he saw Pez slogging up the hill. 'How are you, boy? Ready for the track? The bastards have pulled us in again.'
It seemed the Second had struck a bit of trouble down the shore and we were to cut inland and come in on the Nips' flank.
It was a hell of a thing to have to do. To start over again when we thought we were finished—when we thought the war might have ended for us.
A couple of the older blokes are left behind—ones who have been in it since practically the first day. The Log is one and the Laird another. But old Whispering John comes. 'The old soldier'll see it through,' he cackles.
The Log and the Laird stand by the side of the track and wave to us as we go—they look kind of naked and lonely standing there in just shirts and slacks while we slog down the track armoured in webbing equipment and packs.
Harry Drew had been supposed to stay. Regan had said goodbye to him: 'You're not coming, Harry, I'll see you when she's all over.'
But Harry came with us.
Young Regan walked behind him as he led us down the track.
## 7
We struck into the hills—savage tracks that scrambled up and slithered down. It is the old story—patrolling, probing, killing. We are all apprehensive about it, I think—we are all afraid of it this time—we had been so near the end.
There are frequent clashes with Connell over the native boys who come with us into the hills. We talk to them and give them an occasional cigarette, they're good boys—but Connell objects.
'You don't understand them,' he says, 'they're just like children. Planters have got to work these boys again after the war's finished and you're ruining them.'
'Yeah, we're ruining them,' snarls Harry Drew later. 'They'll want an extra bob a day after the war—we're ruining them—cutting down the profits.'
There was that day in the hills that Harry Drew came up laughing like hell. He'd just heard the best story of the year—Watson, that Angau bloke had told him.
It seemed this happened before the First World War. One of the mission stations along the coast had a fine coconut plantation. The missionaries had done a splendid job of the joss and had so impressed the natives with their hellfire that they one and all became devout Christians.
The missionaries had been very careful to explain to the converted heathen that they were working for the Lord now—everything belonged to the Big Pfella Jesus and the copra had to be carefully gathered and shipped away to the same Big Pfella Jesus.
Well, one time when the missionaries were away on tour, leaving the mission to their head boy, a trader calls in and tries to buy some copra. But the head and all the other boys explain to him that they can't sell any copra, that it all belongs to the Big Pfella Jesus, and they bring out little coloured Sunday School cards of Jesus to show just who the big boss is.
Well, the trader, who is a man of imagination, goes back to his schooner and drinks a square bottle of gin with his raffish mate and has a long think. As a result of this he goes for a little trip around the islands, waiting for his beard to grow nice and long. Then he comes back and waits until he gets word that the missionaries are away on tour again.
He dresses himself and his mate in robes of blasphemous white and, with a bunch of black heathens dancing and waving palm leaves before him, he strides into the mission yard, raises his hand and declares in a voice of the mountains, 'I am Big Pfella Jesus and I have come for my copra!'
And the faithful mission boys worked like slaves to get the copra onto the boat for him. When it was all loaded, the trader called them all together and prayed over them fervently and blasphemously in pidgin: "You pfella boys, good boys—supposim you catchim longa me Heaven—plenty kai kai, number one—plenty pom pom, number one..." and he went around as they knelt in the dust and laid a godless paw devoutly on each woolly head and sprinkled his own special brand of holy water from a gin bottle with the label carefully washed off. Then he presents the head boy with the bottle and the little bit of holy water left in it for his own use and tells him he's a number one good boy. Back he goes to his ship, with his own heathen crew dancing and waving palm leaves before him, and away he sails.
We asked Tamal, the big police boy, what he thought of the missionaries.
Tamal grinned sourly: 'Too much Jesus, not enough kai kai,' he declared.
So we gave him a tin of bully.
Janos kills two more Nips as forward scout, but when Connell passes on the track Janos doesn't move to add up the score for him.
It was the morning after we took the last village on the western ridge that the Indian came in.
A youngish man, he was, but he looked ancient and bone-thin with the dirty-grey pallor of starvation shining through the Punjab copper of his skin. He had crouched all night in the rain outside the sentry lines and came in half an hour after dawn, waving a piece of cloth and crying:
'Master! Master! Don't shoot—Indian! Indian!'
He kept up his shrill, quavering cry until he was well inside the perimeter. Then, when he saw he was safe, he suddenly stopped and was shaken with a fierce, cold fit of shivering.
'Tired—tired—hungry,' he told Pez and Janos who were taking him back to Company headquarters.
He tried to tell them of the years of starvation and death that had passed since his capture and of the great fear that possessed him when he walked towards the sentry crying shrilly: 'Don't shoot! Don't shoot!' The Nips had told them that the Australians would shoot on sight and there had been rumours about the other Indians who tried to give themselves up down the shore and had been shot waving the white flag.
He had escaped the previous day and crept in terror through the bush to the Australian lines. In the afternoon, at a hidden waterhole, he had carefully washed the piece of cloth he had used as a white flag. As he waited, an Australian patrol had drifted swiftly and silently along the ridge above him. He had wanted to call out to them, but he had been afraid.
Then, as it grew dark, he had crawled as close as he dared to the Australian perimeter and crouched there all night. In the morning he had walked in—expecting every minute to feel the numbing sting of bullets punching into his flesh—with the great agony of freedom so near, swelling in his breast—and then the terrible flood of weakness and fierce shuddering that took him when he realised he was free, he was safe...
He tried to tell them all about it, but all he could do was to look at Pez and Janos with a pathetic grin, gesturing round the camp and then to himself and chanting softly: 'Good—good—good.'
Pez reported him in to headquarters.
'Bloke here by the name of Ranjit,' he said. 'Been ack-willie for three years—reporting back for duty.'
Captain Baird talked to Ranjit, then told him to wait while he contacted Battalion, back down the track.
'What about giving him a feed, Cap?' said Janos. 'Looks as though tucker's been a bit light on for him.'
'Sure,' said Baird, 'take him over to your kitchen.'
So Pez and Janos took him over to the kitchen and the mob gathered round to try and talk to Ranjit. They gathered he had been taken in Singapore and had been a slave of the Nips ever since. Of the company of ninety of his countrymen that they had brought to New Guinea with him, only fifteen were now left alive.
You could almost see the strength and life flowing back into his body and his eyes as he tried to tell them where the Nips were and how strong they were and what had happened to him.
And the mob grinned with delight as they watched him put away the biggest issue of bully beef stew that any one man ever put away. 'Good on you, mate,' they said, and grinned at him. He grinned back as he ate and smoked the cigarettes they rolled for him.
As he passed through the Company on his way back down the track to Battalion, Ranjit wore a huge grin and greeted every single person he passed with a salute and a bow. The privates grinned at him with delight and returned his salute and said, 'Good on you, mate!' but some of the officers were uncomfortable and seemed uncertain whether to return his salute or smile benignly.
'Good morning, sah—good morning, sah,' said Ranjit, on his triumphal way. He got well to the top of the first hill then collapsed quite suddenly.
Old Doc Barnes, the medical orderly from Don Company, cursed the bloody fools who had let him stuff so much bully beef into himself and called for the stretcher bearers.
So Ranjit was carried back in triumph—suffering from malnutrition and over-eating.
It was about this time we found what had apparently been a big Nip base camp—crumbling buildings and piles of incense and rotting junk. We salvaged some postcards out of the mess—miracles of exquisite fragility in design.
Pez and Janos found the door to the big cave-like room dug out at the back of the store room. Pez kicked the rotting door away and Janos twisted a bunch of dried cane into a torch and lit it. By the flaring, smoky light they could see that the room was crammed with shelves all filled with small metal containers, each bearing numbers and symbols. Pez took one down and opened it. Inside was a handful of ashes.
'Ashes,' said Janos. 'Ashes of the dead. They're names and numbers on those boxes. Christ, there are thousands of them. This was an army.'
In the smoky red flare of the cane torch, thousands of metal containers crouched on the shelves of that cave-like room, each bearing a name and a number, each containing its handful of ashes.
This was an army.
The fantastic news came through the day before we attacked the final hill.
We got it from the sig wires, up from the beach—it sounded like: 'They dropped one bomb and a city was destroyed.' The sig wires kept repeating something about an atomic bomb—atomic bomb. As we were waiting to go down the valley to that hill, everyone was talking about it.
'It sounds fantastic,' said Harry Drew, 'but these are days when fantastic things happen—they've been splitting the atom for years, of course...'
'Drop another one,' said Pez. 'Drop a dozen and finish this bloody business quick.'
'I don't know,' said Harry Drew. 'I don't know if it's the sort of thing that should be used—a whole city—women and children.'
'Is one big bomb any different to ten thousand small ones?' demanded Pez. 'They kill women and children just the same.'
'It sounds horrible,' said Janos. 'It sounds frightening.'
'Yes,' agreed Pez, after a pause. 'It's frightening—but it might save a lot more lives in the long run.'
*
'B' Company were ahead of us and we had to pass through them. Their headquarters were set on a little flat knoll at the junction of three tracks. The Sally tent was set up on the highway and the coffee urns were out and smoking. We stopped for coffee and biscuits and the talk was all of an atom bomb—'One bomb, one city!' They were incredulous, and yet it seemed right.
There was a small graveyard to the right of the track, opposite the Sally tent. There were three crosses and one open pit. As we finished our coffee, and filed away from the tent we could see the Don Company boys bringing the body up from down the valley.
It was a bad track to the left—knee-deep in black, slimy mud. They had the corpse, wrapped in a grey blanket, lashed to a litter and they had tied themselves to it with ropes.
The leader would give a shout and they would all fling themselves against the ropes, grunting and plunging against the thick, clinging mud and dragging the corpse and the four men who were carrying and steadying the litter, half a dozen wild staggering yards at a time—until they stopped exhausted and bogged down. All of them—the men on the ropes and the carriers and the corpse on the blanket—were plastered from head to foot in stinking black mud.
It was young Jimmy Travers—that little fair-haired bloke who came out from doing three months in Groverley only a week before we sailed.
We are pinned down.
Right at the foot of the track that clambers crazily up the hillside to the ridge we must win, we are pinned down under fire from the Nip weapon pits that are dotted left to right up the slope—deadly pockmarks on each side of the track.
We are bound in terror to the earth under their fire. We will never rise.
But Janos is calling for grenades—and suddenly, incredibly, he is standing—black hail is falling and he is standing! And, incredibly, we are standing, too—and he is screaming: 'Come on, you bastards! Do you want to live forever?'
We are running—we are charging—we are shouting! We are gods and madmen! Janos standing and his screaming of that terrible, fatal cry of battle that has been flung down the centuries—it drags us from the earth and storms us—laughing, yelling, screaming, stabbing, snarling, firing—it hurls us up the hill.
We win the ridge. The enemy is dead behind us, but ahead he still lives. Again we are driven to the earth, and this time we cannot rise. We are bound naked to the earth. Darkness falls, but still we cannot move. We must lie till dawn, clasping the earth in the agony of fear. Until dawn, when our comrades can attack on that other hill.
It had been dark and filled with death a long, long time. The Nips had been tossing grenades—blast grenades—must have been all they had. There was no shrap, but the concussion beat like a mighty hammer blow on the earth, which shuddered and trembled in your embrace—it smacked like a fist at the nape of your neck.
Pez could hear Janos' voice—a long way away, it seemed—small and frightened, whispering: 'Pez...Pez... Where are you...? Pez... Pez...'
Pez dragged himself inches into the darkness towards a vague shape that whispered.
'Here, boy, what's wrong?'
Janos wriggled swiftly to him: 'I'm frightened, Pez—it's getting me—I'm frightened.'
A blast grenade landed in front of them and crushed them between the earth and sky.
Janos almost started up. Pez slammed an arm across his shoulders and pinned him back to the earth. 'Keep still, boy,' he pleaded. 'For Christ sake, keep still. We can't move. We've got to wait till morning. We're in a fold here—we're safe if we keep still.'
Janos' breath was shuddering and his body trembled violently under Pez's arm. 'It's got me, Pez,' he whispered. 'I'm frightened.'
And so, through the long nightmare of darkness, Pez held him to the earth—whispering, pleading with him, and holding his trembling body to the earth.
We are saved.
'B' Company attacks with the first light and springs us from the trap. We are haggard and grimed and grey—our eyes burn red in gaunt faces—our hands tremble.
Pez has to lift Janos to his feet.
'I'm through, boy,' he whispers. 'Never again—I can never go again.'
*
But we didn't have to go again.
Word came through that we were to stay put—patrol our front, but keep out of trouble.
We built our doover tents on the ridge and on the lip of the gully. We corded the muddy track with scrub timber. The Sally tent moved up to us on the ridge and there was the Sally bloke dishing out hot coffee and biscuits.
Strange how you grow accustomed to a piece of earth and it is home. This hostile ridge we stormed foam-flanked became familiar in a day—our land—won with blood. Behind that hummock there, the old soldier, Whispering John, had died; the fixed little grin had snarled back when we found him, showing his stained yellow teeth. Near that pit there, young Regan fell with a bullet in his spine—they say he may never walk again.
We wait.
There is a swift wing unbeating in the sky; there is a high wind that never stirs a leaf, blowing without a ripple over the Pacific and the whole world—a waiting wind. There is a strange and soundless bugle call frozen like a curlew's call midway between the earth and stars.
And at night we lie in our doovers and young Snowy Miller from Don Company up the hill sings the songs—the old songs. He has a choir-boy voice, untrained but sweet and true, and the old songs float down the hill, drifting through the trees...'I Dream of Jeanie' and 'Waken for Me'...
'She's over,' the sig wires said. 'I tell you she's all wrapped up—she's buggerup finish—she's ridge!'
But nobody really believed it.
Then Bairdie came up the track and called us together and read it out to us. A personal letter from the General, almost; assuring us that we had won—innings declared.
And the drums began beating in the hills—they throbbed and boomed through the hills all day and into the night—telling the Kanaka boys with the Nips in the mountains, that it was over—no more hide and seek—time to come home for dinner.
And when the police boys and the carrying parties passed, the boys grinned hugely and stamped their splayed feet in the joyful mud: 'War bin pfinis—bagerup pfinis—Japan man pfinis—hihihihihihi—plenty kai kai, plenty pom pom—war bagerup—pfinis!'
Surely one should dance and sing and pound a comrade on the back—we won! But we feel lost and lonely and there's a breathless wind in the high air. We sit about in our doovers and speak quietly and casually—and it's only when you look at a man's eyes that you realise he is seeing something beyond the mountains and the trees—a vast, slow, broken wheel is turning in the sky—and in some strange way he is unbelieving and afraid of what he sees.
Pez chopped the side out of a biscuit tin and found some black paint somewhere. THE ROAD BACK, he daubed in bold letters and planted it beside their doover, with an arrow pointing back down the track to the sea.
He spent a deal of time outlining to Janos an ambitiously alcoholic project for the first civilised pub they encountered.
It was almost dark on the night of the day the war ended when Janos rose to take the first trick at guard.
'How are you feeling, mate?' asked Pez. 'I'll take it if you like.'
'No, I'm all right.'
'You sure?'
'Yeah,' said Janos with a grin. 'I'm a big boy again now—I'm not afraid of the dark any more.'
He went down to Harry Drew's doover to get the Owen for guard.
Those of us further down the hill heard the single, flat explosion of the shot from the crest of the ridge, and the long cry—stretcher bearers! stretcher bearers!—came pelting down the hill.
We heard their shod feet thudding on the corded track as they ran up the hill and, after a while, we heard them returning—the careful, dragging trample of their feet, as though they carried something heavy.
'What happened?' someone called from the darkness beside the track.
'Owen went off accidentally.'
'Anyone hurt?'
'Yes, Janos.'
'Is he bad?'
'He's dead.'
And the earth stood open to receive its dead.
This man born of woman, who had but a little time of life, lay shrouded in a grey blanket. To lie in cold corruption in the black earth—in the alien earth where the leaves weep for ever for the rainforest.
Pez and Harry Drew and Sunny dug his grave—narrow and not too deep—and the cross is painted that says, NX13686 Private W. E. Janner.
The rest of the platoon, loaded ready for the track, stand bareheaded in the rain. Connell, who came up that morning and had waited for the burial, stands behind Pez.
And when it is done, except for the earth heavy on him, Pez steps forward, and scraping a handful of sticky clay, casts it on him. And Connell steps forward and throws a handful of earth into the pit himself—then walks hurriedly away back down the track.
The platoon moves off and Pez and Harry Drew and Sunny shovel the thick earth furiously and silently into the pit, smooth the mound and plant the cross at the head.
They climb into their packs and Pez picks up the ROAD BACK sign that had stood outside their doover.
He walks to the grave and, bending over awkwardly under the weight of his pack, plants it firmly at the foot, with the arrow pointing away down the track towards the sea.
Harry Drew leads off the track, with Sunny after him.
Pez follows.
The drums are beating in the hills.
Pez sat in his tent at the new camp on the beach, writing a letter.
_Dear Mrs Janner,_
_I am writing this on behalf of the platoon._
_Your son died saving some of our lives._
_We were cut off and surrounded and there was a break made through our lines. Bill stopped that breakthrough and saved us. But he was killed doing it._
_We will never be able to tell you how we felt about him. All we can say is that he died most bravely and he was our friend..._
What the hell! He _could_ have died like that a thousand times—instead of the monstrously stupid chance of a gun going off accidentally.
Private W. E. Janner...used to know a man once of that name...Janos we called him—the God that looks forward and back.
Why shouldn't he write a lie like that to her—it could have been the truth. What the hell would she care, anyway? She never really knew him. All she'd want to do would be to cry over him a little.
Not that _we_ weep... _our_ hearts are dry—but our brother Janos is dead.
Pez walked out of the tent and, in the rich moonlight, ploughed across the unfamiliar sand of the new camp to the beach.
There was a wind blowing high that did not blow. A broken wheel was turning in the sky. There was a bugle call transfixed by the spear of stars, pinned like a curlew call between the earth and sky.
The bay was empty and the seas stretched barren far away. But soon the seas would bring ships and there would be a coming home and a heart singing. We must go on down a long, long track. But at least when he got home there was a door to knock on—even if an uncertain door.
God, there must be a meaning. Fiercely he was certain that there must be a meaning.
Surely, while we live we are not lost.
Oh Janos, Janos my brother!
Surely we are not lost—while we live.
Dancing on Coral
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Introduced by Susan Wyndham
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Introduced by Peter Conrad
Sydney Bridge Upside Down
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Bush Studies
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Introduced by Helen Garner
The Cardboard Crown
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Introduced by Brenda Niall
A Difficult Young Man
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Introduced by Sonya Hartnett
Outbreak of Love
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Introduced by Chris Womersley
The Australian Ugliness
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Introduced by Christos Tsiolkas
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Introduced by Michael McGirr
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Introduced by John Marsden
The Even More Complete
Book of Australian Verse
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Diary of a Bad Year
J. M. Coetzee
Introduced by Peter Goldsworthy
Wake in Fright
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Introduced by Peter Temple
The Dying Trade
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The Songs of a Sentimental Bloke
C. J. Dennis
Introduced by Jack Thompson
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Sumner Locke Elliott
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Fairyland
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The Explorers
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The Fringe Dwellers
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The Long Prospect
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The Watch Tower
Elizabeth Harrower
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The Long Green Shore
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The Unknown Industrial Prisoner
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The Glass Canoe
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A Woman of the Future
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The Young Desire It
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The Middle Parts of Fortune
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Selected Stories
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Amy's Children
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The Scarecrow
Ronald Hugh Morrieson
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The Dig Tree
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textclassics.com.au
| {
"redpajama_set_name": "RedPajamaBook"
} | 4,453 |
\section{INTRODUCTION}
\label{sec:intro}
The Swift gamma-ray burst satellite~\cite{gehrels} was successfully launched
on 2004 November 20. Since then, it has provided observations and positions of
GRBs and their afterglows to observers and robotic telescopes typically within
a minute, thanks to its three instruments: the wide-field Burst Alert
Telescope~\cite{Barthelmy} and the two narrow-field instruments, X-Ray
Telescope~\cite{Burrows} and UV/Optical Telescope~\cite{Roming}\,. When a GRB
is detected by the BAT and a slew is possible, Swift automatically re-points
to bring the burst within the field of view of the XRT and the UVOT.
The XRT uses a grazing incidence Wolter-1 telescope consisting of a thermally
controlled carbon fibre telescope tube, an X-ray mirror system of 12
concentric gold-coated electroformed Ni shells with a 3.5m focal length, and a
Focal Plane Camera Assembly (FPCA) housing an e2v CCD-22 with $600\times 602$
image pixels, located behind an optical blocking filter with an optical
transmission of about $0.25\%$. The CCD is mounted on a thermoelectric cooler
connected via a heat pipe to an external radiator. The FPCA also includes an
autonomous Sun shutter, four $^{55}$Fe calibration sources and a substantial
mass of Al proton shielding (which also reduces thermal variations). To avoid
the effects of pile-up, the XRT is able to autonomously select one of the
three following readout modes~\cite{Hill} according to the source brightness:
Photo-diode (PD) mode at highest count rates with a 0.14 ms time resolution
and no spatial information; Windowed Timing (WT) mode at moderate count rates
with a 1.8 ms time resolution and 1-D spatial information; at lower count
rates Photon Counting mode (PC) with a 2.5 s time resolution and 2-D spatial
information.
During the first year in orbit two major incidents occurred which required
modification of the instrument's operation, although they have not affected
its scientific productivity. First, before the CCD was cooled to its nominal
operating temperature of $-100^{\circ}$C, the XRT thermo-cooler (TEC) power
supply system apparently failed, and therefore the XRT has to rely on passive
cooling via the heat pipe and radiator in combination with enhanced management
of the spacecraft orientation to reduce the radiator view of the sunlit earth.
In flight the XRT is nowadays operated with CCD temperatures of -75 to
-52$^{\circ}$C (see Kennea et al.~\cite{kennea} for more details). Secondly,
on 2005 May 27 the XRT was hit by a particle (micro-meteoroid) which scattered
off the mirror system to hit several CCD pixels, causing new bright pixels,
one bright column and two bright column segments~\cite{Abbey}\,. Charge
leakage from the top of the bright column affects its immediate neighbours.
The evolution of charge leakage depends on the CCD temperature which can now
only be controlled by orientation of the spacecraft. After this event, the
optical filter showed no sign of damage. Similar events were also observed in
the XMM-Newton EPIC MOS CCDs. The bright pixels and columns have been vetoed
on-board for the PC and WT modes. This is impossible in PD mode so that mode
is no longer used, which had the beneficial effect of reducing the CCD
temperature.
These two incidents had no direct impact on the spectroscopic performance of
the XRT, or its ability to image and locate new GRBs. Indeed, the XRT
routinely measures the early X-ray light-curves and spectra of all the GRB
afterglows at which it is promptly pointed (hence $95\%$ of the 183 GRBs
detected by the BAT for which a spacecraft slew was possible within 5 minutes
after the BAT trigger were detected by the XRT up until the middle of July 2007;
the BAT has detected a total of 243 GRBs up until the middle of July 2007). These
observations have revealed previously unexpected multiple
breaks~\cite{Zhang,Nousek} and flares in the early X-ray
light-curves~\cite{Zhang,Burrows07,King,Proga,Perna} suggesting extended
activity of the central engine up to $10^5$ s after the trigger for long and
short GRBs; which challenges the current progenitor models. Essential spectral
and temporal information was also obtained with the XRT for the peculiar event
GRB 060218 showing for the first time the rise of a
supernova~\cite{Campana06}\,. The XRT has also discovered the first short
burst afterglow~\cite{gehrels2} and provided accurate locations of several
short GRBs, which are associated with elliptical galaxies or star-forming
galaxies, the burst being located in the outskirts of the galaxy in the latter
case; these results tend to indicate that short GRBs are likely to be due to
binary compact object spiral-in and collision~\cite{Eichler,Rosswog}\,. The
XRT also provides essential information for non-GRB targets, for example with
the follow-up of the recurrent nova RS Ophiuchi~\cite{Bode} or the
micro-quasar GRO J1655-40~\cite{Brocksopp}\,. The fraction of time spent on
non-GRB targets (excluding the calibration targets) is $\sim 39.4\%$ since the
launch, and this is expected to increase over time.
In this paper, we concentrate on the XRT CCD in-flight spectral calibration,
and describe recent improvements to the response model made available as
response matrices through the HEASARC caldb (RMF version
009~\cite{Campana07}). The results obtained during the pre-flight calibration
were covered in Osborne et al.~\cite{Osborne}\,.
\section{IN-FLIGHT CALIBRATIONS}
\begin{table}[h]
\caption{Summary of the in-flight calibration targets used up to July 2007.}
\label{tab1}
\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
Object & Type & Mode & Purpose & Exposure (ks) \\
\hline
RXJ 1856.5-3754 & Neutron star & PC/WT & Low energy response & 55/47 \\
\hline
PKS 0745-19 & Cluster of & PC & Effective area & 61 \\
& galaxies & & & \\
\hline
2E 0102-7217 & SNR & PC & Gain, energy resolution and & 76\\
& & WT & shoulder & 55 \\
\hline
Cas A & SNR & PC & Energy scale offset, gain, shoulder, & 144 \\
& & WT & CTI and energy resolution & 51 \\
\hline
3C 273 & Quasar & WT & Effective area and cross-calibration& 18 \\
& & & with XMM-Newton & \\
\hline
PSR 0540-69 & Pulsar & PC/WT & Effective area & 56/26 \\
\hline
PKS 2155-304 & Blazar & WT & Effective area (cross-calibration & 13\\
& & & with XMM-Newton) &\\
\hline
NGC 7172 & Seyfert 2 & PC & Redistribution & 15 \\
\hline
G21.5 & SNR & PC & High-energy shelf & 40 \\
\hline
Mkn 421 & Blazar & WT & Effective area and cross-calibration & 33 \\
& & & with XMM-Newton & \\
\hline
Crab & Pulsar & WT & Effective area & 46 \\
\hline
\end{tabular}
\end{center}
\end{table}
Since the FPCA front door was opened, spectroscopic calibrations have been
only performed using a set of well known celestial objects observed every six
months in order to monitor the change in the spectral response (see
Table~\ref{tab1}). The fraction of time spent on calibration targets is $\sim
7.5\%$ since the launch. Many of our calibration targets are also used by
other X-ray observatories. This allows us to perform cross-calibration
campaigns with different X-ray instruments (e.g. the XMM-Newton EPIC MOS
cameras for the quasar 3C 273 and the blazar Mkn 421). In addition, we make
use of four $^{55}$Fe calibration sources permanently illuminating the non-imaging
area of the CCD. In order to optimise and facilitate the scheduling of the
calibration targets, a new state was implemented on-board the XRT in 2007 May.
This new state allows us, for instance, to control the observation mode while
the XRT is still in auto-state depending on the purpose of the observations.
\section{RESPONSE MODEL DEVELOPMENTS FROM JANUARY 2006 to JUNE 2007}
When an X-ray photon interacts within the CCD, it generates a charge cloud
which is collected in the depletion region after spreading in the bulk of the
detector. The charge cloud may spread into more than one pixel depending on
its energy and location of interaction. To compute the response matrices we
stack simulated spectra of monochromatic X-rays. We use the grade recognition
process used in the analysis software (for PC mode this is a $3\times 3$ pixel
matrix centred on the highest pixel). To avoid noise being included in the
charge summation and excessive telemetry usage, a threshold is set on-board
below which pixels are not considered.
The X-ray spectrum resulting from monochromatic radiation significantly
differs from a simple Gaussian, it consists of six components: a Gaussian peak
with a shoulder on the low energy side of the peak, an escape peak and a Si
K$\alpha$ fluorescence peak if the photon energy is above the Si K-shell edge,
a shelf extending to low energies, and at the very lowest energies a noise
peak (of which only the high energy side may be seen above threshold).
Below 1.5 keV, the shoulder and shelf are mainly produced by the charge losses
at the interface between the SiO$_2$ layer and the active silicon volume of
the open electrode, possibly due to a local inversion of the electric field
near the detector surface. Above 1.5 keV, the shoulder and the shelf are
produced by several processes: (i) sub-threshold losses; (ii) recombination
and trapping in the bulk of the detector; (iii) inhomogeneity of the electric
field in the depletion depth, in addition to the surface losses. Their exact
shapes depend on the readout mode, and hence they are different for the PC and
WT modes. Both above and below 1.5 keV, the main peak broadens with time due
to the degradation of the charge transfer efficiency, producing a larger
shoulder at lower energies (see Section~\ref{CTI}).
Changes in our spectral response code have been made in order to better
reproduce the different components mentioned above. The recent improvements
described below have been released as new spectral response files (version
v009~\cite{Campana07}).
\subsection{The shelf from photons above $\sim 2$ keV}
\label{sec:shelf}
The new response matrice files (v009 RMFs) include an empirical rescaling of
the low energy shelf made by X-rays above 2\,keV, which significantly improve
the quality of spectral fits to the calibration sources (see
Fig.~\ref{fig_shelf}). This was previously incompletely modelled for either PC
or WT modes, resulting in an underestimation of the modelled redistributed
counts when fitting spectra of heavily absorbed sources (e.g. $N_H \ge
10^{22}$ cm$^{-2}$).
\begin{figure}[h]
\begin{center}
\begin{tabular}{cc}
\includegraphics[height=5.8cm]{spec_PC_ngc7172} & \includegraphics[height=5.8cm]{spec_WT_g0-2_4U1608_RMF_v009}\\
\end{tabular}
\end{center}
\caption[]{Left:
XRT PC grade 0-12 spectrum of NGC 7172 using the new v009 (red) and previous
v008 (black) response files. The use of a {\scriptsize WABS*POWERLAW} model
gives a value of $N_H \sim 7.3 \times 10^{22}$ cm$^{-2}$. Right: XRT
WT grade 0-2 spectrum of the X-ray binary 4U 1608 using the new v009 (red)
and previous v008 (black) response files. The use of a {\scriptsize
WABS*(POWERLAW+DISKBB)} model gives a value of $N_H \sim 10^{22}$
cm$^{-2}$.}
\label{fig_shelf}
\end{figure}
\subsection{The shoulder from photons above $\sim 1.5$ keV}
Before the v009 release of the calibration files, the shoulder, which was
modelled by artificially increasing the event split threshold in order to
increase the sub-threshold losses, was not reproduced well (see Fig. 6a in
Osborne et al.~\cite{Osborne}). We showed that modification of the shape of
the charge cloud formed in the field-free region using the formalism described
in Pavlov \& Nousek~\cite{Pavlov} can lead to a more physical modelling of the
shoulder (see Fig. 6b in Osborne et al.~\cite{Osborne}), the shape being no
longer a 2-D Gaussian (although a 2-D Gaussian remains sufficient in the
depletion region). Fig.~\ref{fig_shoulder} shows the relatively good
agreement of the model with the very complicated spectrum of the SNR Cas A
(the North knot as noted in Fig.~\ref{fig_shoulder}).
\begin{figure}[h]
\begin{center}
\begin{tabular}{cc}
\includegraphics[height=4.4cm]{Cas_pc_image} & \includegraphics[height=4.8cm,angle=0]{casa_spie1}\\
\end{tabular}
\end{center}
\caption[]{Left: PC grade 0 image of the SNR Cas A. Right: PC grade 0 spectrum
of the North knot of the SNR Cas A (see the image on the left). The data
were taken in 2005 February 17. The spectrum is fit using a {\scriptsize
PHABS(VNEI+VNEI)} model (see Willingale et al.~\cite{Willingale}). }
\label{fig_shoulder}
\end{figure}
\section{THE RESIDUALS AROUND AND BELOW THE OXYGEN EDGE}
\label{residual}
The fits of several continuum sources reveal negative (less than 20\%)
residuals around the Oxygen edge (0.54 eV) using v008 and v009 RMFs.
Recently, observational evidence has shown that the CCD bias level can
significantly vary during the timescale of an orbital snapshot on an
astrophysical target. The bias level is mode-dependent and is subtracted
on-board during the XRT observations. Bias variations during a snap-shot can
occur due to changes in the CCD temperature and/or scattered optical light
from the sunlit Earth\cite{Beardmore}\,. This can result in energy scale
offsets, which give rise to residuals when fitting spectra, especially at low
energies (e.g. around the Oxygen edge). Energy scale offsets can be seen in
both PC and WT modes. A new command option was implemented in the 2.6 XRT
software ({\scriptsize WTBIASDIFF}) in order to correct the WT data for this
effect. A tool {\scriptsize XRTPCBIAS} included in the 2.7 XRT
software\,\footnote{see the following URL:
http://heasarc.gsfc.nasa.gov/docs/software/lheasoft/release$_{-}$notes.html}
has been released in July 2007 by the XRT software team, which corrects the PC
data. The use of these contemporary time-dependent bias estimators can
significantly improve the energies of low energy events (see
Fig.~\ref{fig_scale}).
Charge transfer inefficiency due to accumulating proton damage also results in
a slow change in the energy scale. This is discussed in Section~\ref{CTI}.
\begin{figure}[h]
\begin{center}
\begin{tabular}{cc}
\includegraphics[height=5.6cm]{CasA_pcbias} & \includegraphics[height=5.3cm]{RSOph_offset}\\
\end{tabular}
\end{center}
\caption[]{Left: Comparison of the energy centroid of the Si and S lines in
the North (N) and South East (SE) knots of the SNR Cas A as observed by the
XMM MOS cameras (N: black; SE: red) and the XRT (N: green, cyan; SE: blue,
magenta). The green and blue crosses correspond to XRT/PC grade 0 data for
which the bias was contaminated by optical light from the sunlit Earth. The
data were processed with the CALDB2.6 software which does not allow to bias
corrections. In this case, an energy scale offset is observed when compared
with the XMM MOS curves. The cyan and magenta crosses correspond to the same
data processed with the new CALDB2.7 software including the tool
{\scriptsize XRTPCBIAS}, which corrects the data. Right: XRT WT grade 0-2
spectrum of RS Ophiuchi: ({\it black}) the data not corrected to the bias
problem and ({\it red and blue}) the data corrected using the new command
option {\scriptsize WTBIASDIFF}.}
\label{fig_scale}
\end{figure}
Cross-calibration performed with other X-ray instruments in orbit such as {\it
XMM-Newton} and {\it Suzaku} on the supernova remnant 2E 0102-7217 reveals
that at least these CCD cameras seem to suffer from an overestimation of the
model with respect to the data around the Oxygen edge. Recently, the MOS
calibration team has decided to apply an {\it ad hoc} correction to their
quantum efficiency (QE) by decreasing the QE below the Oxygen edge by 10-15\%,
in order to correct the residuals. We are investigating whether a similar
approach could work in the case of the XRT, once the effects of energy scale
offset have been corrected.
\section{CHARGE TRANSFER INEFFICIENCY}
\label{CTI}
CCD detectors provide good X-ray imaging and spectroscopic performance.
However, the CCD energy resolution and gain degrade with time due to the
increase of the CTI. The main origin of CTI is the increase of charge traps,
which are mainly due to the irradiation of high-energy protons on the CCD
passing through the shielding. Although the low-Earth orbit of {\it Swift} and
the thick Al shielding around the CCD detector reduce the proton flux, the
frequent passages of the spacecraft through the South Atlantic Anomaly (SAA)
can cause formation of charge traps, and hence an increase of CTI. Since the
launch, the FWHM measured using the four $^{55}$Fe calibration sources
(located in each corner of the CCD; the area of the detector covered by these
corner sources being small and outside the imaging area) increased from 146 eV
at 5.9 keV in Feb 2005 to 210 eV in March 2007 when using the {\it bad and
good columns} (i.e. columns with and without significant traps),
respectively. The broadening of the line is due to the energy scale shifting
effect of traps in the pixels through which the charge has to be transported.
The increase of traps in the CCD imaging area, the serial register and the
frame-store area also causes energy scale offset as shown in the left panel in
Fig.~\ref{fig_CTI}. In this Figure, the data were processed with a gain file
not corrected from the CTI increase.
\begin{figure}[h]
\begin{center}
\begin{tabular}{cc}
\includegraphics[height=5.8cm]{spec_WT_CasA_line_CTI}&\includegraphics[height=6.3cm,width=9cm]{CTI_June2007}\\
\end{tabular}
\end{center}
\caption[]{Left: WT grade 0-2 spectrum of the SNR Cas A in the energy band of
the Si and S lines at different epochs since the launch showing the
degradation of the energy resolution and the gain due to the increase of
traps in the CCD. The WT data were processed with the command option
{\scriptsize WTBIASDIFF} correcting the bias level if corrupted (see
Section~\ref{residual}). The measurements of the energy centroid of the Si
and S lines imply an energy shift of about -50\,eV from February 2005 to
June 2007, when the increase of CTI over time is not taking into account in
the gain file. The FWHM of the Si line increases from 105\,eV in February
2005 to about $131$\,eV in June 2007. Right: Evolution of the serial (blue)
and parallel (red) CTI with time since the launch as measured using the four
corner source data. The CTI values were computed vetoing the columns with
significant traps.}
\label{fig_CTI}
\end{figure}
Since we do not have any on-board calibration source illuminating the imaging
area, we use four $^{55}$Fe (5.9 keV) calibration sources to track the
temporal evolution of CTI. We define a parallel and serial CTI as follows:
$$\mathrm{CTI}_{p,s} = \frac{E_i-E_{p,s}}{n\times E_i}$$ where
$\mathrm{CTI}_{p,s}$ corresponds to the parallel and serial CTI respectively,
and $E_i$ is the measured energy centroid of the corner source CS3 closest to
the output amplifier (bottom left of the imaging area), which does not suffer
from the CTI loss in the imaging area. $E_{p,s}$ is the measured energy
centroid of the source located in the top left and bottom right corner of the
imaging area, respectively. $n$ is the number of pixels that the charge has
to pass through in being readout (i.e. transfered down the CCD and then along
the readout strip). Note that we used only the columns with no significant
traps to do the computation, hence the CTI values derived are free from the
effects of the traps. The computed parallel and serial CTI values (see the
right panel Fig.~\ref{fig_CTI}) as well as the gain values of the corner
source CS3 closest to the output amplifier are used to generate an
epoch-dependent gain file. The gain variations measured from the corner source
CS3 are due to the CTI increase over time in the store-frame area (in which no
CTI measurements can be performed since no calibration sources illuminate this
part of the CCD) and/or possible gain variations of the output FET (Field
Effect Transistor) with time. Up until July 2007, the gain of the corner
source CS3 increased by about $1\%$. While the parallel CTI increased
relatively steadily since the launch from $5\times 10^{-6}$ to $3.5\times
10^{-5}$ in June 2007 (see Fig.~\ref{fig_CTI}), the serial CTI increased
rapidly in a short period of time around November 2005 and stayed relatively
constant around $2.5\times 10^{-5}$ from December 2005 up to March 2007. An
updated v007 gain file in PC and WT modes will be soon released.
In order to correct the data from the effects of traps, we plan to determine
the location and depth of the largest traps and implement a correction in the
data processing software. We need to use a stable, sufficiently extended and
emission line-dominated source to map the central imaging area (a $200\times
600$ pixel window in PC mode and a 200 pixel window in WT). Supernova
remnants (SNRs) are the best astrophysical sources. We plan to use the SNR
Cas A which has intense Silicon and Sulphur lines. Although the energy
centroids show an energy variation of less than $\pm 10$ eV (at the energy of
the Si and S lines) across the remnant~\cite{Willingale}\,, the energy
variation due to traps that we want to measure are much larger. The only
drawback of this method is that we cannot map all the imaging area ($600\times
602$ pixels) due to the excessive exposure time that would be needed.
A more efficient and simpler approach would be to use the charge injection
technique~\cite{Prigozhin} to measure the CTI for each column, as it has been
done for the Soft X-ray cameras on-board {\it Suzaku}~\cite{Nakajima}\,, since
we can then correct all the CCD imaging area without long calibration
exposures. We are undertaking further work to verify the feasibility of this
technique in the case of the e2v CCD-22 used in the XRT.
\section{REDUCTION OF NOISE BY SUBSTRATE VOLTAGE CHANGE}
The loss of the active cooling causes the XRT to operate at higher than
expected temperatures (see Section 1); this generates significant
thermally-induced noise appearing as low energy events. Raising the substrate
voltage as described in Osborne et al.~\cite{Osborne} will allow a reduction
of this noise and the use of lower energy X-ray events, since the volume of
Silicon in which carriers are generated is reduced.
Osborne et al.~\cite{Osborne} have shown that raising the substrate voltage
will cause a decrease of the depletion depth, resulting in a migration of
events to higher grades (hence, an increase of the sub-threshold losses) and a
slight decrease of the QE. We performed observations of Cas A (2.2\,ks in PC
and 0.8\,ks in WT) and the Crab (0.6\,ks in WT) with raised substrate voltage
($V_{\rm ss} = 6$ V instead of 0 V). Fig.~\ref{fig_substrate} shows that the
changes in the effective area are small between $V_{\rm ss} = 6$ V and 0 V
(i.e. less than 15\% at 6 keV). The gain will also change when the substrate
voltage settings are modified, because the gain of the output FET, which works
in a source follower configuration, will slightly change in this new
configuration.
\begin{figure}[h]
\begin{center}
\begin{tabular}{cc}
\includegraphics[height=5.3cm]{CasA_gain_Vss6} & \includegraphics[height=5.8cm]{spec_CRAB_Vss}\\
\end{tabular}
\end{center}
\caption[]{Left: WT grade 0-2 spectra of Cas A with the substrate voltage
$V_{\rm ss} = 6$ V (red crosses) and $V_{\rm ss} = 0$ V (black crosses). Note that
the gain changed between the two configurations, since the gain of the
output FET slightly changed between the two configurations (see
text). Right: WT grade 0-2 off-pulse spectra of the Crab with $V_{\rm ss} = 6$
V (red crosses) and $V_{\rm ss} = 0$ V (black crosses). The two plots show that
the changes in the effective area, hence the QE, are minimal between the two
configurations. }
\label{fig_substrate}
\end{figure}
\section{CONCLUSION}
We showed that our Monte-Carlo code computing the PC and WT RMFs allows us to
describe the CCD response well. Thus, the v009 RMF files release in July 2007
allow a better modelling of the low-energy shelf of heavily absorbed sources
and a better physical description of the origin of the shoulder from photons
above 1.5 keV. We also showed that energy scale offsets due to corruption of
the bias level in both PC and WT modes can limit the improvements of the
instrument spectral response, especially at low energies. New tool
{\scriptsize XRTPCBIAS} and the new command option {\scriptsize WTBIASDIFF}
have been provided by the XRT software team to correct the bias level in both
PC and WT mode, and hence suppress energy scale offset. These tools are
included in the 2.7 XRT software package recently released.
We are working on a more complete trap characterisation. To do so, the XRT
began observing the SNR Cas A for 80\,ks in PC mode and 50\,ks for WT. Because
of the development of traps with time in the CCD detector, we also outline the
importance to use an on-board calibration source which fully illuminates the
focal plane, for instance as used on-board XMM-Newton, for future X-ray CCD
instruments.
Finally, in order to improve further the XRT spectral performance, we plan
to raise permanently the substrate voltage to $V_{\rm ss}=6$\,V on-board before
the end of 2007. An intense phase of re-calibration of the instrument will
shortly follow to update the spectral response files, the gain file and the
ground data processing software.
\subsection{Acknowledgements}
OG, APB, AFA, KLP, JPO, LT, PE, RS gratefully acknowledge PPARC funding. This
work is supported in Italy by ASI grant I/R/039/04 and the Ministry of
Universiy and Research of Italy (PRIN 2005025417), and at Penn State by NASA
contract NAS5-0136.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,493 |
from __future__ import absolute_import
from __future__ import print_function
from zerver.lib.alert_words import (
add_user_alert_words,
alert_words_in_realm,
remove_user_alert_words,
user_alert_words,
)
from zerver.lib.test_helpers import (
most_recent_message,
most_recent_usermessage,
)
from zerver.lib.test_classes import (
ZulipTestCase,
)
from zerver.models import (
Recipient,
UserProfile,
)
from typing import Text
import ujson
class AlertWordTests(ZulipTestCase):
interesting_alert_word_list = ['alert', 'multi-word word', u'☃']
def test_internal_endpoint(self):
# type: () -> None
user_name = "cordelia"
email = self.example_email(user_name)
self.login(email)
params = {
'alert_words': ujson.dumps(['milk', 'cookies'])
}
result = self.client_post('/json/users/me/alert_words', params)
self.assert_json_success(result)
user = self.example_user(user_name)
words = user_alert_words(user)
self.assertEqual(words, ['milk', 'cookies'])
def test_default_no_words(self):
# type: () -> None
"""
Users start out with no alert words.
"""
user = self.example_user('cordelia')
words = user_alert_words(user)
self.assertEqual(words, [])
def test_add_word(self):
# type: () -> None
"""
add_user_alert_words can add multiple alert words at once.
"""
user = self.example_user('cordelia')
# Add several words, including multi-word and non-ascii words.
add_user_alert_words(user, self.interesting_alert_word_list)
words = user_alert_words(user)
self.assertEqual(words, self.interesting_alert_word_list)
def test_remove_word(self):
# type: () -> None
"""
Removing alert words works via remove_user_alert_words, even
for multi-word and non-ascii words.
"""
user = self.example_user('cordelia')
add_user_alert_words(user, self.interesting_alert_word_list)
theoretical_remaining_alerts = self.interesting_alert_word_list[:]
for alert_word in self.interesting_alert_word_list:
remove_user_alert_words(user, alert_word)
theoretical_remaining_alerts.remove(alert_word)
actual_remaining_alerts = user_alert_words(user)
self.assertEqual(actual_remaining_alerts,
theoretical_remaining_alerts)
def test_realm_words(self):
# type: () -> None
"""
We can gather alert words for an entire realm via
alert_words_in_realm. Alerts added for one user do not impact other
users.
"""
user1 = self.example_user('cordelia')
add_user_alert_words(user1, self.interesting_alert_word_list)
user2 = self.example_user('othello')
add_user_alert_words(user2, ['another'])
realm_words = alert_words_in_realm(user2.realm)
self.assertEqual(len(realm_words), 2)
self.assertEqual(list(realm_words.keys()), [user1.id, user2.id])
self.assertEqual(realm_words[user1.id],
self.interesting_alert_word_list)
self.assertEqual(realm_words[user2.id], ['another'])
def test_json_list_default(self):
# type: () -> None
self.login(self.example_email("hamlet"))
result = self.client_get('/json/users/me/alert_words')
self.assert_json_success(result)
self.assertEqual(result.json()['alert_words'], [])
def test_json_list_add(self):
# type: () -> None
self.login(self.example_email("hamlet"))
result = self.client_post('/json/users/me/alert_words', {'alert_words': ujson.dumps(['one ', '\n two', 'three'])})
self.assert_json_success(result)
result = self.client_get('/json/users/me/alert_words')
self.assert_json_success(result)
self.assertEqual(result.json()['alert_words'], ['one', 'two', 'three'])
def test_json_list_remove(self):
# type: () -> None
self.login(self.example_email("hamlet"))
result = self.client_post('/json/users/me/alert_words', {'alert_words': ujson.dumps(['one', 'two', 'three'])})
self.assert_json_success(result)
result = self.client_delete('/json/users/me/alert_words', {'alert_words': ujson.dumps(['one'])})
self.assert_json_success(result)
result = self.client_get('/json/users/me/alert_words')
self.assert_json_success(result)
self.assertEqual(result.json()['alert_words'], ['two', 'three'])
def message_does_alert(self, user_profile, message):
# type: (UserProfile, Text) -> bool
"""Send a bunch of messages as othello, so Hamlet is notified"""
self.send_message(self.example_email("othello"), "Denmark", Recipient.STREAM, message)
user_message = most_recent_usermessage(user_profile)
return 'has_alert_word' in user_message.flags_list()
def test_alert_flags(self):
# type: () -> None
self.login(self.example_email("hamlet"))
user_profile_hamlet = self.example_user('hamlet')
result = self.client_post('/json/users/me/alert_words', {'alert_words': ujson.dumps(['one', 'two', 'three'])})
self.assert_json_success(result)
result = self.client_get('/json/users/me/alert_words')
self.assert_json_success(result)
self.assertEqual(result.json()['alert_words'], ['one', 'two', 'three'])
# Alerts in the middle of messages work.
self.assertTrue(self.message_does_alert(user_profile_hamlet, "Normal alert one time"))
# Alerts at the end of messages work.
self.assertTrue(self.message_does_alert(user_profile_hamlet, "Normal alert one"))
# Alerts at the beginning of messages work.
self.assertTrue(self.message_does_alert(user_profile_hamlet, "two normal alerts"))
# Alerts with surrounding punctuation work.
self.assertTrue(self.message_does_alert(user_profile_hamlet, "This one? should alert"))
self.assertTrue(self.message_does_alert(user_profile_hamlet, "Definitely time for three."))
# Multiple alerts in a message work.
self.assertTrue(self.message_does_alert(user_profile_hamlet, "One two three o'clock"))
# Alerts are case-insensitive.
self.assertTrue(self.message_does_alert(user_profile_hamlet, "One o'clock"))
self.assertTrue(self.message_does_alert(user_profile_hamlet, "Case of ONE, won't stop me"))
# We don't cause alerts for matches in URLs.
self.assertFalse(self.message_does_alert(user_profile_hamlet, "Don't alert on http://t.co/one/ urls"))
self.assertFalse(self.message_does_alert(user_profile_hamlet, "Don't alert on http://t.co/one urls"))
def test_update_alert_words(self):
# type: () -> None
user_profile = self.example_user('hamlet')
me_email = user_profile.email
self.login(me_email)
result = self.client_post('/json/users/me/alert_words', {'alert_words': ujson.dumps(['ALERT'])})
content = 'this is an ALERT for you'
self.send_message(me_email, "Denmark", Recipient.STREAM, content)
self.assert_json_success(result)
original_message = most_recent_message(user_profile)
user_message = most_recent_usermessage(user_profile)
self.assertIn('has_alert_word', user_message.flags_list())
result = self.client_patch("/json/messages/" + str(original_message.id), {
'message_id': original_message.id,
'content': 'new ALERT for you',
})
self.assert_json_success(result)
user_message = most_recent_usermessage(user_profile)
self.assertEqual(user_message.message.content, 'new ALERT for you')
self.assertIn('has_alert_word', user_message.flags_list())
result = self.client_patch("/json/messages/" + str(original_message.id), {
'message_id': original_message.id,
'content': 'sorry false alarm',
})
self.assert_json_success(result)
user_message = most_recent_usermessage(user_profile)
self.assertEqual(user_message.message.content, 'sorry false alarm')
self.assertNotIn('has_alert_word', user_message.flags_list())
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,475 |
\section{Introduction and preliminaries}
The purpose of this paper is to study
the fixed-point set of an element of a CAT(0) group in its boundary.
We say that a metric space $(X,d)$ is a {\it geodesic space} if
for each $x,y \in X$,
there exists an isometric embedding $\xi:[0,d(x,y)] \rightarrow X$ such that
$\xi(0)=x$ and $\xi(d(x,y))=y$ (such $\xi$ is called a {\it geodesic}).
Also a metric space $(X,d)$ is said to be {\it proper}
if every closed metric ball is compact.
Let $(X,d)$ be a geodesic space and
let $T$ be a geodesic triangle in $X$.
A {\it comparison triangle} for $T$ is
a geodesic triangle $\overline{T}$ in the Euclidean plane ${\Bbb R}^2$
with same edge lengths as $T$.
Choose two points $x$ and $y$ in $T$.
Let $\bar{x}$ and $\bar{y}$ denote
the corresponding points in $\overline{T}$.
Then the inequality $$d(x,y) \le d_{{\Bbb R}^2}(\bar{x},\bar{y})$$
is called the {\it CAT(0)-inequality},
where $d_{{\Bbb R}^2}$ is the natural metric on ${\Bbb R}^2$.
A geodesic space $(X,d)$ is called a {\it CAT(0) space}
if the CAT(0)-inequality holds
for all geodesic triangles $T$ and for all choices of two points $x$ and
$y$ in $T$.
Let $X$ be a proper CAT(0) space and $x_0 \in X$.
The {\it boundary of $X$ with respect to $x_0$},
denoted by $\partial_{x_0}X$, is defined as
the set of all geodesic rays issuing from $x_0$.
Then we define a topology on $X \cup \partial_{x_0}X$
by the following conditions:
\begin{enumerate}
\item[(1)] $X$ is an open subspace of $X \cup \partial_{x_0}X$.
\item[(2)] For $\alpha \in \partial_{x_0}X$ and $r, \epsilon >0$, let
$$ U_{x_0}(\alpha;r,\epsilon)=
\{ x \in X \cup \partial_{x_0} X \,|\,
x \not\in B(x_0,r),\ d(\alpha(r),\xi_{x}(r))<\epsilon \}, $$
where $\xi_{x}:[0,d(x_0,x)]\rightarrow X$ is the geodesic from $x_0$ to $x$
($\xi_{x}=x$ if $x \in \partial_{x_0} X$).
Then for each $\epsilon_0>0$,
the set
$$\{U_{x_0}(\alpha;r,\epsilon_0)\,|\, r>0\}$$
is a neighborhood basis for $\alpha$ in $X \cup \partial_{x_0}X$.
\end{enumerate}
This is called the {\it cone topology} on $X \cup \partial_{x_0} X$.
It is known that
$X \cup \partial_{x_0} X$ is
a metrizable compactification of $X$ (\cite{BH}, \cite{GH}).
Let $X$ be a geodesic space.
Two geodesic rays $\xi, \zeta:[0,\infty) \rightarrow X$ are
said to be {\it asymptotic} if there exists a constant $N$ such that
$d(\xi(t),\zeta(t)) \le N$ for each $t \ge 0$.
It is known that
for each geodesic ray $\xi$ in $X$ and
each point $x \in X$,
there exists a unique geodesic ray $\xi'$ issuing from $x$
such that $\xi$ and $\xi'$ are asymptotic.
Let $x_0$ and $x_1$ be two points of a proper CAT(0) space $X$.
Then there exists a unique bijection
$\Phi:\partial_{x_0}X \rightarrow \partial_{x_1}X$
such that $\xi$ and $\Phi(\xi)$ are asymptotic
for each $\xi \in \partial_{x_0}X$.
It is known that $\Phi:\partial_{x_0}X\rightarrow \partial_{x_1}X$
is a homeomorphism (\cite{BH}, \cite{GH}).
Let $X$ be a proper CAT(0) space.
The asymptotic relation is an equivalence relation
in the set of all geodesic rays in $X$.
The {\it boundary of} $X$, denoted by $\partial X$,
is defined as the set of asymptotic equivalence classes of geodesic rays.
The equivalence class of a geodesic ray $\xi$ is denoted by $\xi(\infty)$.
For each $x_0 \in X$ and each $\alpha \in \partial X$,
there exists a unique element $\xi \in \partial_{x_0}X$
with $\xi(\infty)=\alpha$.
Thus we may identify $\partial X$ with $\partial_{x_0}X$ for each $x_0 \in X$.
Let $X$ be a proper CAT(0) space
and $G$ a group which acts on $X$ by isometries.
For each element $g \in G$ and
each geodesic ray $\xi:[0,\infty)\rightarrow X$,
a map $g \xi:[0,\infty)\rightarrow X$
defined by $(g\xi)(t):=g(\xi(t))$ is also a geodesic ray.
If geodesic rays $\xi$ and $\xi'$ are asymptotic,
then $g\xi$ and $g\xi'$ are also asymptotic.
Thus $g$ induces a homeomorphism of $\partial X$ and
$G$ acts on $\partial X$.
A {\it geometric} action on a CAT(0) space
is an action by isometries which is proper (\cite[p.131]{BH})
and cocompact.
We note that every CAT(0) space
on which a group acts
geometrically is a proper space (\cite[p.132]{BH}).
Details of CAT(0) spaces and their boundaries are found in
\cite{BH} and \cite{GH}.
Suppose that a group $G$ acts geometrically on a CAT(0) space $X$.
For a subset $A\subset G$,
the limit set $L(A)$ of $A$ is defined as
$L(A)=\overline{Ax_0}\cap \partial X$,
where $x_0\in X$ and
$\overline{Ax_0}$ is the closure
of the orbit $Ax_0$ in $X\cup \partial X$.
We note that
the limit set $L(A)$ is determined by $A$ and not depend on the point $x_0$.
For $g\in G$,
we define $F_g$ and $\mathcal{F}_g$
as the fixed-point sets of $g$ in $X$ and $\partial X$ respectively,
that is,
$F_g=\{x\in X|\, gx=x\}$ and
$\mathcal{F}_g=\{\alpha\in\partial X|\, g\alpha=\alpha\}$.
By \cite[Corollary~II.2.8~(1)]{BH},
we see that $F_g\neq\emptyset$ if and only if
the order $o(g)$ of $g$ is finite,
since the action of $G$ on $X$ is proper.
In this paper, we investigate $\mathcal{F}_g$.
We prove the following theorem in Section~2.
\begin{Theorem}\label{Thm1}
Suppose that a group $G$ acts geometrically on a CAT(0) space $X$.
For $g\in G$,
$\mathcal{F}_g=L(Z_g)$,
where $Z_g$ is the centralizer of $g$, i.e.,
$Z_g=\{v\in G|\, gv=vg\}$.
\end{Theorem}
For a subset $A\subset G$,
$L(A)\neq\emptyset$ if and only if $A$ is infinite.
Hence Theorem~\ref{Thm1} implies the following corollary.
\begin{Corollary}\label{Cor1}
Suppose that a group $G$ acts geometrically on a CAT(0) space $X$.
For $g\in G$,
$\mathcal{F}_g\neq\emptyset$ if and only if $Z_g$ is infinite.
\end{Corollary}
We can obtain the following corollary from Corollary~\ref{Cor1}.
\begin{Corollary}\label{Cor2}
Suppose that a group $G$ acts geometrically on CAT(0) spaces $X$ and $X'$.
For $g\in G$,
$\mathcal{F}_g\neq\emptyset$ if and only if $\mathcal{F}'_g\neq\emptyset$,
where $\mathcal{F}_g$ and $\mathcal{F}'_g$ are
the fixed-point sets of $g$ in $\partial X$ and $\partial X'$ respectively.
\end{Corollary}
Let $X$ be a CAT(0) space and let $g$ be an isometry of $X$.
The {\it translation length} of $g$ is the number
$|g|:=\inf\{d(x,gx)\,|\,x\in X\}$, and
the {\it minimal set} of $g$ is defined as
$\operatorname{Min}(g):=\{x\in X\,|\,d(x,gx)=|g|\}$.
An isometry $g$ of $X$ is said to be {\it hyperbolic},
if $\operatorname{Min}(g)\neq\emptyset$ and $|g|>0$ (cf.\ \cite{BH}).
We also prove the following theorem in Section~2.
\begin{Theorem}\label{Thm2}
Let $g$ be a hyperbolic isometry of a proper CAT(0) space $X$.
Then the fixed-point set of $g$ in $\partial X$ is
$\mathcal{F}_g=\partial\operatorname{Min}(g)$,
where $\partial\operatorname{Min}(g)$ is
the boundary of the minimal set $\operatorname{Min}(g)$ of $g$.
\end{Theorem}
For a hyperbolic isometry $g$ of a CAT(0) space $X$,
$\operatorname{Min}(g)$ is the union of the axes of $g$ and
$\operatorname{Min}(g)$ splits as a product $Y_1\times \operatorname{Im}\sigma$,
where $\sigma:{\Bbb R}\rightarrow X$ is an axis of $g$ (\cite[p.231]{BH}).
Hence
$\partial\operatorname{Min}(g)$ is the suspension $\partial Y_1*\{g^{-\infty},g^{\infty}\}$.
Theorem~\ref{Thm2} implies that
the fixed-point set $\mathcal{F}_g$ has a suspension form.
Let $\mathcal{P}_g$ be the periodic-point set of $g$ in $\partial X$.
Then
$$\mathcal{P}_g=\bigcup_{n\in{\Bbb N}}\mathcal{F}_{g^n}
=\bigcup_{n\in{\Bbb N}}\partial\operatorname{Min}(g^n).$$
Hence the periodic-point set $\mathcal{P}_g$ of $g$
is also a suspension form.
We obtain the following corollary from Theorems~\ref{Thm1} and \ref{Thm2}.
\begin{Corollary}\label{Cor3}
Suppose that a group $G$ acts geometrically on a CAT(0) space $X$.
For $g\in G$ such that $o(g)=\infty$,
$\mathcal{F}_g=L(Z_g)=\partial\operatorname{Min}(g)$.
\end{Corollary}
\section{Proof of the main theorems}
We first prove Theorem~\ref{Thm1}.
\begin{proof}[Proof of Theorem~\ref{Thm1}]
Suppose that a group $G$ acts geometrically on a CAT(0) space $X$.
Let $g\in G$ and let $x_0\in X$.
We first show that
$\mathcal{F}_g\subset L(Z_g)$.
Let $\alpha\in \mathcal{F}_g$ and
let $\xi:[0,\infty)\rightarrow X$ be the geodesic ray
such that $\xi(0)=x_0$ and $\xi(\infty)=\alpha$.
Since $\alpha\in \mathcal{F}_g$, $g\alpha=\alpha$.
Hence the geodesic rays $\xi$ and $g\xi$ are asymptotic,
and there exists a number $M>0$
such that $d(\xi(t),g\xi(t))\le M$ for any $t\ge 0$.
Since the action of $G$ on $X$ is cocompact and $X$ is proper,
$GB(x_0,N)=X$ for some $N>0$.
For each $i\in{\Bbb N}$,
there exists $v_i\in G$ such that $d(\xi(i),v_ix_0)\le N$.
Then
\begin{align*}
d(x_0,v_i^{-1}gv_ix_0)&=d(v_ix_0,gv_ix_0) \\
&\le d(v_ix_0,\xi(i))+d(\xi(i),g\xi(i))+d(g\xi(i),gv_ix_0) \\
&\le 2N+M,
\end{align*}
because $d(v_ix_0,\xi(i))\le N$ and $d(\xi(i),g\xi(i))\le M$.
Since the action of $G$ on $X$ is proper,
the set $\{h\in G|\, d(x_0,hx_0)\le 2N+M\}$ is finite.
Hence there exists $g'\in G$
such that $\{i\in {\Bbb N}|\,v_i^{-1}gv_i=g'\}$ is infinite.
Let $\{i_j|\,j\in {\Bbb N}\}=\{i\in {\Bbb N}|\,v_i^{-1}gv_i=g'\}$.
Then $v_{i_j}^{-1}gv_{i_j}=g'$ for each $j\in{\Bbb N}$, and
$$ v_{i_j}^{-1}gv_{i_j}=g'=v_{i_1}^{-1}gv_{i_1}. $$
Hence $g=(v_{i_j}v_{i_1}^{-1})g(v_{i_1}v_{i_j}^{-1})$.
Thus $v_{i_j}v_{i_1}\in Z_g$ for each $j\in{\Bbb N}$.
Here we note that
$v_{i_j}v_{i_1}^{-1}\neq v_{i_{j'}}v_{i_1}^{-1}$
if $j\neq j'$.
Since $\{v_{i_j}x_0|\,j\in{\Bbb N}\}$ converges to $\alpha$ in $X\cup\partial X$,
$\{v_{i_j}v_{i_1}^{-1}x_0|\,j\in{\Bbb N}\}$ converges to $\alpha$.
Hence $\alpha\in L(\{v_{i_j}v_{i_1}^{-1}|\,j\in{\Bbb N}\})\subset L(Z_g)$.
Thus $\mathcal{F}_g\subset L(Z_g)$.
Next, we show that
$\mathcal{F}_g\supset L(Z_g)$.
Let $\alpha\in L(Z_g)$.
There exists a sequence $\{v_i|\,i\in{\Bbb N}\}\subset Z_g$
such that $\{v_ix_0|\,i\in{\Bbb N}\}$ converges to $\alpha$ in $X\cup\partial X$.
For each $i\in{\Bbb N}$, $gv_i=v_ig$.
Here the sequence $\{gv_ix_0|\,i\in{\Bbb N}\}$ converges to $g\alpha$
and $\{v_igx_0|\,i\in{\Bbb N}\}$ converges to $\alpha$.
Thus $g\alpha=\alpha$, i.e.,
$\alpha\in\mathcal{F}_g$.
Therefore $\mathcal{F}_g=L(Z_g)$.
\end{proof}
Next we prove Theorem~\ref{Thm2}.
\begin{proof}[Proof of Theorem~\ref{Thm2}]
Let $g$ be a hyperbolic isometry of a proper CAT(0) space $X$
and let $x_0\in \operatorname{Min}(g)$.
We first show that $\mathcal{F}_g\subset\partial\operatorname{Min}(g)$.
Let $\alpha\in \mathcal{F}_g$ and
let $\xi:[0,\infty)\rightarrow X$ be the geodesic ray
such that $\xi(0)=x_0$ and $\xi(\infty)=\alpha$.
Since $\alpha\in \mathcal{F}_g$, $g\alpha=\alpha$.
Hence the geodesic rays $\xi$ and $g\xi$ are asymptotic.
Now $d(x_0,gx_0)=|g|$ because $x_0\in \operatorname{Min}(g)$.
Hence
$$d(\xi(t),g\xi(t))\le d(\xi(0),g\xi(0))=d(x_0,gx_0)=|g|.$$
This means that $d(\xi(t),g\xi(t))=|g|$ and $\xi(t)\in \operatorname{Min}(g)$
for each $t\ge 0$.
Hence $\operatorname{Im}\xi\subset\operatorname{Min}(g)$ and $\alpha\in\partial\operatorname{Min}(g)$.
Thus $\mathcal{F}_g\subset\partial\operatorname{Min}(g)$.
Next we show that $\mathcal{F}_g\supset\partial\operatorname{Min}(g)$.
Let $\alpha\in \partial\operatorname{Min}(g)$ and
let $\xi:[0,\infty)\rightarrow X$ be the geodesic ray
such that $\xi(0)=x_0$ and $\xi(\infty)=\alpha$.
Then $\operatorname{Im}\xi\subset\operatorname{Min}(g)$,
since $\alpha\in\partial\operatorname{Min}(g)$ and $\operatorname{Min}(g)$ is convex.
Hence $\xi(t)\in\operatorname{Min}(g)$ and $d(\xi(t),g\xi(t))=|g|$ for any $t\ge0$.
This means that $\xi$ and $g\xi$ are asymptotic and $\alpha=g\alpha$,
i.e., $\alpha\in\mathcal{F}_g$.
Thus $\mathcal{F}_g\supset\partial\operatorname{Min}(g)$.
Therefore $\mathcal{F}_g=\partial\operatorname{Min}(g)$.
\end{proof}
\section{Remarks}
Let $g$ be a hyperbolic isometry of a proper CAT(0) space $X$.
For each $n\in {\Bbb N}$,
$\mathcal{F}_{g^n}=\partial\operatorname{Min}(g^n)$ by Theorem~\ref{Thm2}.
We note that an axis of $g$ is also an axis of $g^n$ for each $n\in{\Bbb N}$.
Then the minimal set $\operatorname{Min}(g^n)$ of $g^n$
splits as a product $\operatorname{Min}(g^n)=Y_n\times \operatorname{Im}\sigma$,
where $\sigma:{\Bbb R}\rightarrow X$ is an axis of $g$ (cf.\ \cite{BH}).
Here $Y_n\subset Y_{kn}$ for each $n,k\in{\Bbb N}$.
The fixed-point set of $g$ in $\partial X$ is
$$ \mathcal{F}_{g}=\partial\operatorname{Min}(g)=\partial(Y_1\times\operatorname{Im}\sigma)
=\partial Y_1*\{g^{\infty},g^{-\infty}\}.$$
Also the periodic-point set of $g$ is
\begin{align*}
\mathcal{P}_g&=\bigcup_{n\in{\Bbb N}}\mathcal{F}_{g^n}=\bigcup_{n\in{\Bbb N}}\partial\operatorname{Min}(g^n)\\
&=\bigcup_{n\in{\Bbb N}}\partial(Y_n\times\operatorname{Im}\sigma)
=(\bigcup_{n\in{\Bbb N}}\partial Y_n)*\{g^{\infty},g^{-\infty}\}.
\end{align*}
Thus the fixed-point set and the periodic-point set of $g$ have
suspension forms.
Let $A$ be the union of geodesic lines
which are parallel to an axis $\sigma$ of $g$.
Then $A$ splits as a product $Y\times\operatorname{Im}\sigma$.
By the above argument,
$\mathcal{P}_g=\bigcup_{n\in{\Bbb N}}\partial\operatorname{Min}(g^n)\subset \partial A$ and
$\bigcup_{n\in{\Bbb N}}\partial Y_n\subset \partial Y$.
Here the following problem arises.
\begin{Problem}
Is it always the case that
$\mathcal{P}_g=\partial A$
(i.e.\ $\bigcup_{n\in{\Bbb N}}\partial Y_n=\partial Y$)?
\end{Problem}
Let $g$ be a hyperbolic isometry of a Gromov hyperbolic space $X$.
By an easy argument,
we see that
the fixed-point set $\mathcal{F}_g$
of $g$ in the boundary $\partial X$ is
the two-points set $\{g^{\infty},g^{-\infty}\}$.
Also for each $\alpha\in\partial X\setminus\{g^{-\infty}\}$,
the sequence $\{g^i\alpha\,|\,i\in{\Bbb N}\}$ converges to $g^\infty$ in $\partial X$.
Here the following problem arises.
\begin{Problem}
Let $g$ be a hyperbolic isometry of a proper CAT(0) space $X$ and
let $A$ be the union of geodesic lines
which are parallel to an axis $\sigma$ of $g$.
Is it the case that
for each $\alpha\in\partial X\setminus\partial A$,
the sequence $\{g^i\alpha\,|\,i\in{\Bbb N}\}$ converges to $g^\infty$
in $\partial X$?
\end{Problem}
Also the following problem arises.
\begin{Problem}
Suppose that a group $G$ acts geometrically on a CAT(0) space $X$.
Is it always the case that
there do not exist $g\in G$ and $\alpha,\beta\in\partial X$
such that
${\limsup}_{n\rightarrow\infty}d_{\partial X}(g^n\alpha,g^n\beta)>0$
and
${\liminf}_{n\rightarrow\infty}d_{\partial X}(g^n\alpha,g^n\beta)=0$?
\end{Problem}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,662 |
package db
import (
"database/sql"
"fmt"
_ "github.com/lib/pq"
"github.com/thcyron/sqlbuilder"
"github.com/thcyron/tracklog/pkg/models"
)
type Postgres struct {
db *sql.DB
}
func (d *Postgres) Open(dsn string) error {
db, err := sql.Open("postgres", dsn)
if err != nil {
return err
}
if err := db.Ping(); err != nil {
return err
}
d.db = db
return nil
}
func (d *Postgres) UserByID(id int) (*models.User, error) {
user := new(models.User)
query, args, dest := sqlbuilder.Select().
Dialect(sqlbuilder.Postgres).
From(`"user"`).
Map(`"id"`, &user.ID).
Map(`"username"`, &user.Username).
Map(`"password"`, &user.Password).
Map(`"password_version"`, &user.PasswordVersion).
Where(`"id" = ?`, id).
Build()
err := d.db.QueryRow(query, args...).Scan(dest...)
if err == sql.ErrNoRows {
return nil, nil
}
if err != nil {
return nil, err
}
return user, nil
}
func (d *Postgres) UserByUsername(username string) (*models.User, error) {
user := new(models.User)
query, args, dest := sqlbuilder.Select().
Dialect(sqlbuilder.Postgres).
From(`"user"`).
Map(`"id"`, &user.ID).
Map(`"username"`, &user.Username).
Map(`"password"`, &user.Password).
Map(`"password_version"`, &user.PasswordVersion).
Where(`"username" = ?`, username).
Build()
err := d.db.QueryRow(query, args...).Scan(dest...)
if err == sql.ErrNoRows {
return nil, nil
}
if err != nil {
return nil, err
}
return user, nil
}
func (d *Postgres) AddUser(user *models.User) error {
var id int
query, args, dest := sqlbuilder.Insert().
Dialect(sqlbuilder.Postgres).
Into(`"user"`).
Set(`"username"`, user.Username).
Set(`"password"`, user.Password).
Return(`"id"`, &id).
Build()
err := d.db.QueryRow(query, args...).Scan(dest...)
if err != nil {
return err
}
user.ID = id
return nil
}
func (d *Postgres) UpdateUser(user *models.User) error {
query, args := sqlbuilder.Update().
Dialect(sqlbuilder.Postgres).
Table(`"user"`).
Set(`"username"`, user.Username).
Set(`"password"`, user.Password).
Set(`"password_version"`, user.PasswordVersion).
Build()
_, err := d.db.Exec(query, args...)
return err
}
func (d *Postgres) DeleteUser(user *models.User) error {
_, err := d.db.Exec(`DELETE FROM "user" WHERE "id" = $1`, user.ID)
return err
}
func (d *Postgres) RecentUserLogs(user *models.User, count int) ([]*models.Log, error) {
tx, err := d.db.Begin()
if err != nil {
return nil, err
}
defer tx.Rollback() // read-only transaction
var (
log models.Log
logs []*models.Log
)
query, args, dest := sqlbuilder.Select().
Dialect(sqlbuilder.Postgres).
From(`"log"`).
Map(`"id"`, &log.ID).
Map(`"user_id"`, &log.UserID).
Map(`"name"`, &log.Name).
Map(`"start"`, &log.Start).
Map(`"end"`, &log.End).
Map(`"duration"`, &log.Duration).
Map(`"distance"`, &log.Distance).
Where(`"user_id" = ?`, user.ID).
Order(`"created" DESC`).
Limit(count).
Build()
rows, err := tx.Query(query, args...)
if err != nil {
return nil, err
}
for rows.Next() {
if err := rows.Scan(dest...); err != nil {
return nil, err
}
l := new(models.Log)
*l = log
logs = append(logs, l)
}
if err := rows.Err(); err != nil {
return nil, err
}
for _, log := range logs {
if err := d.getLogTags(tx, log); err != nil {
return nil, err
}
}
return logs, nil
}
func (d *Postgres) UserLogYears(user *models.User) ([]int, error) {
var (
years []int
year int
)
query, args, dest := sqlbuilder.Select().
Dialect(sqlbuilder.Postgres).
From(`"log"`).
Map(`DISTINCT EXTRACT(YEAR FROM "start")`, &year).
Where(`"user_id" = ?`, user.ID).
Order(`EXTRACT(YEAR FROM "start") ASC`).
Build()
rows, err := d.db.Query(query, args...)
if err != nil {
return nil, err
}
for rows.Next() {
if err := rows.Scan(dest...); err != nil {
return nil, err
}
years = append(years, year)
}
if err := rows.Err(); err != nil {
return nil, err
}
return years, nil
}
func (d *Postgres) UserLogByID(user *models.User, id int) (*models.Log, error) {
tx, err := d.db.Begin()
if err != nil {
return nil, err
}
defer tx.Rollback() // read-only transaction
log := new(models.Log)
query, args, dest := sqlbuilder.Select().
Dialect(sqlbuilder.Postgres).
From(`"log"`).
Map(`"id"`, &log.ID).
Map(`"user_id"`, &log.UserID).
Map(`"name"`, &log.Name).
Map(`"start"`, &log.Start).
Map(`"end"`, &log.End).
Map(`"duration"`, &log.Duration).
Map(`"distance"`, &log.Distance).
Map(`"gpx"`, &log.GPX).
Where(`"id" = ?`, id).
Build()
err = tx.QueryRow(query, args...).Scan(dest...)
if err == sql.ErrNoRows {
return nil, nil
}
if err != nil {
return nil, err
}
if err := d.getLogTracks(tx, log); err != nil {
return nil, err
}
if err := d.getLogTags(tx, log); err != nil {
return nil, err
}
return log, nil
}
func (d *Postgres) getLogTracks(tx *sql.Tx, log *models.Log) error {
var (
track models.Track
tracks []*models.Track
)
query, args, dest := sqlbuilder.Select().
Dialect(sqlbuilder.Postgres).
From(`"track"`).
Map(`"id"`, &track.ID).
Map(`"log_id"`, &track.LogID).
Map(`COALESCE("name", '')`, &track.Name).
Map(`"start"`, &track.Start).
Map(`"end"`, &track.End).
Map(`"duration"`, &track.Duration).
Map(`"distance"`, &track.Distance).
Where(`"log_id" = ?`, log.ID).
Build()
rows, err := tx.Query(query, args...)
if err != nil {
return err
}
for rows.Next() {
if err := rows.Scan(dest...); err != nil {
return err
}
t := new(models.Track)
*t = track
tracks = append(tracks, t)
}
if err := rows.Err(); err != nil {
return err
}
for _, track := range tracks {
if err := d.getTrackPoints(tx, track); err != nil {
return err
}
}
log.Tracks = tracks
return nil
}
func (d *Postgres) getTrackPoints(tx *sql.Tx, track *models.Track) error {
var (
point models.Point
points []*models.Point
)
query, args, dest := sqlbuilder.Select().
Dialect(sqlbuilder.Postgres).
From(`"trackpoint"`).
Map(`"id"`, &point.ID).
Map(`"track_id"`, &point.TrackID).
Map(`"point"[0]`, &point.Longitude).
Map(`"point"[1]`, &point.Latitude).
Map(`"time"`, &point.Time).
Map(`"elevation"`, &point.Elevation).
Map(`"heartrate"`, &point.Heartrate).
Where(`"track_id" = ?`, track.ID).
Build()
rows, err := tx.Query(query, args...)
if err != nil {
return err
}
for rows.Next() {
if err := rows.Scan(dest...); err != nil {
return err
}
p := new(models.Point)
*p = point
points = append(points, p)
}
if err := rows.Err(); err != nil {
return err
}
track.Points = points
return nil
}
func (d *Postgres) getLogTags(tx *sql.Tx, log *models.Log) error {
var (
tag string
tags []string
)
query, args, dest := sqlbuilder.Select().
Dialect(sqlbuilder.Postgres).
From(`"log_tag"`).
Map(`"tag"`, &tag).
Where(`"log_id" = ?`, log.ID).
Build()
rows, err := tx.Query(query, args...)
if err != nil {
return err
}
for rows.Next() {
if err := rows.Scan(dest...); err != nil {
return err
}
tags = append(tags, tag)
}
if err := rows.Err(); err != nil {
return err
}
log.Tags = tags
return nil
}
func (d *Postgres) UserLogsByYear(user *models.User, year int) ([]*models.Log, error) {
tx, err := d.db.Begin()
if err != nil {
return nil, err
}
defer tx.Rollback() // read-only transaction
var (
log models.Log
logs []*models.Log
)
query, args, dest := sqlbuilder.Select().
Dialect(sqlbuilder.Postgres).
From(`"log"`).
Map(`"id"`, &log.ID).
Map(`"name"`, &log.Name).
Map(`"start"`, &log.Start).
Map(`"end"`, &log.End).
Map(`"duration"`, &log.Duration).
Map(`"distance"`, &log.Distance).
Map(`"gpx"`, &log.GPX).
Where(`"user_id" = ?`, user.ID).
Where(`EXTRACT(YEAR FROM "start") = ?`, year).
Order(`"start" DESC`).
Build()
rows, err := tx.Query(query, args...)
if err != nil {
return nil, err
}
for rows.Next() {
if err := rows.Scan(dest...); err != nil {
rows.Close()
return nil, err
}
l := new(models.Log)
*l = log
logs = append(logs, l)
}
if err := rows.Err(); err != nil {
return nil, err
}
for _, log := range logs {
if err := d.getLogTags(tx, log); err != nil {
return nil, err
}
}
return logs, nil
}
func (d *Postgres) AddUserLog(user *models.User, log *models.Log) error {
tx, err := d.db.Begin()
if err != nil {
return err
}
query, args, dest := sqlbuilder.Insert().
Dialect(sqlbuilder.Postgres).
Into(`"log"`).
Set(`"user_id"`, user.ID).
Set(`"start"`, log.Start).
Set(`"end"`, log.End).
Set(`"duration"`, log.Duration).
Set(`"distance"`, log.Distance).
Set(`"name"`, log.Name).
Set(`"gpx"`, log.GPX).
Return(`"id"`, &log.ID).
Build()
if err := tx.QueryRow(query, args...).Scan(dest...); err != nil {
tx.Rollback()
return err
}
for _, track := range log.Tracks {
if err := d.addLogTrack(tx, log, track); err != nil {
tx.Rollback()
return err
}
}
return tx.Commit()
}
func (d *Postgres) addLogTrack(tx *sql.Tx, log *models.Log, track *models.Track) error {
var name *string
if track.Name != "" {
name = &track.Name
}
query, args, dest := sqlbuilder.Insert().
Dialect(sqlbuilder.Postgres).
Into(`"track"`).
Set(`"log_id"`, log.ID).
Set(`"name"`, name).
Set(`"start"`, track.Start).
Set(`"end"`, track.End).
Set(`"duration"`, track.Duration).
Set(`"distance"`, track.Distance).
Return(`"id"`, &track.ID).
Build()
if err := tx.QueryRow(query, args...).Scan(dest...); err != nil {
return err
}
for _, point := range track.Points {
if err := d.addTrackPoint(tx, track, point); err != nil {
return err
}
}
return nil
}
func (d *Postgres) addTrackPoint(tx *sql.Tx, track *models.Track, point *models.Point) error {
query, args, dest := sqlbuilder.Insert().
Dialect(sqlbuilder.Postgres).
Into(`"trackpoint"`).
Set(`"track_id"`, track.ID).
SetSQL(`"point"`, fmt.Sprintf("point(%f,%f)", point.Longitude, point.Latitude)).
Set(`"time"`, point.Time).
Set(`"elevation"`, point.Elevation).
Set(`"heartrate"`, point.Heartrate).
Return(`"id"`, &point.ID).
Build()
if err := tx.QueryRow(query, args...).Scan(dest...); err != nil {
return err
}
return nil
}
func (d *Postgres) UpdateLog(log *models.Log) error {
tx, err := d.db.Begin()
if err != nil {
return nil
}
query, args := sqlbuilder.Update().
Dialect(sqlbuilder.Postgres).
Table(`"log"`).
Set(`"name"`, log.Name).
Where(`"id" = ?`, log.ID).
Build()
_, err = tx.Exec(query, args...)
if err != nil {
return err
}
if err := d.replaceLogTags(tx, log); err != nil {
tx.Rollback()
return err
}
return tx.Commit()
}
func (d *Postgres) replaceLogTags(tx *sql.Tx, log *models.Log) error {
_, err := tx.Exec(`DELETE FROM "log_tag" WHERE "log_id" = $1`, log.ID)
if err != nil {
return err
}
for _, tag := range log.Tags {
query, args, _ := sqlbuilder.Insert().
Dialect(sqlbuilder.Postgres).
Into(`"log_tag"`).
Set(`"log_id"`, log.ID).
Set(`"tag"`, tag).
Build()
_, err = tx.Exec(query, args...)
if err != nil {
return err
}
}
return nil
}
func (d *Postgres) DeleteLog(log *models.Log) error {
tx, err := d.db.Begin()
if err != nil {
return err
}
_, err = tx.Exec(`DELETE FROM "log" WHERE "id" = $1`, log.ID)
if err != nil {
return err
}
return tx.Commit()
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,029 |
<component name="libraryTable">
<library name="Gradle: org.springframework.amqp:spring-rabbit:1.2.0.RELEASE">
<CLASSES>
<root url="jar://$MAVEN_REPOSITORY$/org/springframework/amqp/spring-rabbit/1.2.0.RELEASE/spring-rabbit-1.2.0.RELEASE.jar!/" />
</CLASSES>
<JAVADOC />
<SOURCES>
<root url="jar://$MAVEN_REPOSITORY$/org/springframework/amqp/spring-rabbit/1.2.0.RELEASE/spring-rabbit-1.2.0.RELEASE-sources.jar!/" />
</SOURCES>
</library>
</component> | {
"redpajama_set_name": "RedPajamaGithub"
} | 7,237 |
{"url":"https:\/\/stemcie.com\/view\/91","text":"$\\require{\\cancel}$ $\\require{\\stix[upint]}$\n\n### MATHEMATICS 9709\n\n#### Cambridge International AS and A Level\n\n Name of student Date Adm. number Year\/grade Stream Subject Pure Mathematics 1 (P1) Variant(s) P11, P12, P13 Start time Duration Stop time\n\nQtn No. 1 2 3 4 5 6 7 8 9 10 11 12 Total\nMarks 4 6 5 7 7 7 7 9 8 11 9 10 90\nScore\n\nGet Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt all the 12 questions Question 1 Code: 9709\/13\/O\/N\/20\/1, Topic: Quadratics$\\text{(a)}$Express$x^{2}+6 x+5$in the form$(x+a)^{2}+b$, where$a$and$b$are constants.$[2]\\text{(b)}$The curve with equation$y=x^{2}$is transformed to the curve with equation$y=x^{2}+6 x+5$. Describe fully the transformation(s) involved.$[2]$Question 2 Code: 9709\/12\/O\/N\/17\/2, Topic: Functions A function$\\mathrm{f}$is defined by$\\mathrm{f}: x \\mapsto 4-5 x$for$x \\in \\mathbb{R}$.$\\text{(i)}$Find an expression for$\\mathrm{f}^{-1}(x)$and find the point of intersection of the graphs of$y=\\mathrm{f}(x)$and$y=\\mathrm{f}^{-1}(x)$.$[3]\\text{(ii)}$Sketch, on the same diagram, the graphs of$y=\\mathrm{f}(x)$and$y=\\mathrm{f}^{-1}(x)$, making clear the relationship between the graphs.$[3]$Question 3 Code: 9709\/11\/O\/N\/19\/4, Topic: Series A runner who is training for a long-distance race plans to run increasing distances each day for 21 days. She will run$x \\mathrm{~km}$on day 1 , and on each subsequent day she will increase the distance by$10 \\%$of the previous day's distance. On day 21 she will run$20 \\mathrm{~km}$.$\\text{(i)}$Find the distance she must run on day 1 in order to achieve this. Give your answer in$\\mathrm{km}$correct to 1 decimal place.$[3]\\text{(ii)}$Find the total distance she runs over the 21 days.$[2]$Question 4 Code: 9709\/12\/O\/N\/17\/5, Topic: Trigonometry$\\text{(i)}$Show that the equation$\\cos 2 x\\left(\\tan ^{2} 2 x+3\\right)+3=0$can be expressed as$[3]$$$2 \\cos ^{2} 2 x+3 \\cos 2 x+1=0$$$\\text{(ii)}$Hence solve the equation$\\cos 2 x\\left(\\tan ^{2} 2 x+3\\right)+3=0$for$0^{\\circ} \\leqslant x \\leqslant 180^{\\circ}$.$[4]$Question 5 Code: 9709\/11\/M\/J\/18\/5, Topic: Coordinate geometry The diagram shows a kite$O A B C$in which$A C$is the line of symmetry. The coordinates of$A$and$C$are$(0,4)$and$(8,0)$respectively and$O$is the origin.$\\text{(i)}$Find the equations of$A C$and$O B$.$[4]\\text{(ii)}$Find, by calculation, the coordinates of$B$.$[3]$Question 6 Code: 9709\/13\/M\/J\/17\/7, Topic: Circular measure The diagram shows two circles with centres$A$and$B$having radii$8 \\mathrm{~cm}$and$10 \\mathrm{~cm}$respectively. The two circles intersect at$C$and$D$where$C A D$is a straight line and$A B$is perpendicular to$C D$.$\\text{(i)}$Find angle$A B C$in radians.$[1]\\text{(ii)}$Find the area of the shaded region.$[6]$Question 7 Code: 9709\/12\/M\/J\/18\/7, Topic: Functions The function$\\mathrm{f}$is defined by$\\mathrm{f}: x \\mapsto 7-2 x^{2}-12 x$for$x \\in \\mathbb{R}$.$\\text{(i)}$Express$7-2 x^{2}-12 x$in the form$a-2(x+b)^{2}$, where$a$and$b$are constants.$[2]\\text{(ii)}$State the coordinates of the stationary point on the curve$\\mathrm{y = f}(x)$.$[1]$The function$\\mathrm{g}$is defined by$\\mathrm{g}: x \\mapsto 7-2 x^{2}-12 x$for$x \\geqslant k$.$\\text{(iii)}$State the smallest value of$k$for which$\\mathrm{g}$has an inverse.$[1]\\text{(iv)}$For this value of$k$, find$\\mathrm{g}^{-1}(x)$.$[3]$Question 8 Code: 9709\/11\/M\/J\/18\/8, Topic: Series$\\text{(a)}$A geometric progression has a second term of 12 and a sum to infinity of 54. Find the possible values of the first term of the progression.$[4]\\text{(b)}$The$n$th term of a progression is$p+q n$, where$p$and$q$are constants, and$S_{n}$is the sum of the first$n$terms.$\\text{(i)}$Find an expression, in terms of$p, q$and$n$, for$S_{n}$.$[3]\\text{(ii)}$Given that$S_{4}=40$and$S_{6}=72$, find the values of$p$and$q$.$[2]$Question 9 Code: 9709\/13\/O\/N\/20\/8, Topic: Differentiation The equation of a curve is$\\displaystyle y=2 x+1+\\frac{1}{2 x+1}$for$x>-\\frac{1}{2}$.$\\text{(a)}$Find$\\displaystyle\\frac{\\mathrm{d} y}{\\mathrm{~d} x}$and$\\displaystyle\\frac{\\mathrm{d}^{2} y}{\\mathrm{~d} x^{2}}$.$[3]\\text{(b)}$Find the coordinates of the stationary point and determine the nature of the stationary point.$[5]$Question 10 Code: 9709\/12\/M\/J\/17\/10, Topic: Functions The function$\\mathrm{f}$is defined by$\\mathrm{f}(x)=3 \\tan \\left(\\frac{1}{2} x\\right)-2$, for$-\\frac{1}{2} \\pi \\leqslant x \\leqslant \\frac{1}{2} \\pi$.$\\text{(i)}$Solve the equation$\\mathrm{f}(x)+4=0$, giving your answer correct to 1 decimal place.$[3]\\text{(ii)}$Find an expression for$\\mathrm{f}^{-1}(x)$and find the domain of$\\mathrm{f}^{-1}$.$[5]\\text{(iii)}$Sketch, on the same diagram, the graphs of$y=\\mathrm{f}(x)$and$y=\\mathrm{f}^{-1}(x)$.$[3]$Question 11 Code: 9709\/12\/M\/J\/20\/10, Topic: Differentiation The equation of a curve is$y=54 x-(2 x-7)^{3}$.$\\text{(a)}$Find$\\displaystyle\\frac{\\mathrm{d} y}{\\mathrm{~d} x}$and$\\displaystyle\\frac{\\mathrm{d}^{2} y}{\\mathrm{~d} x^{2}}$.$[4]\\text{(b)}$Find the coordinates of each of the stationary points on the curve.$[3]\\text{(c)}$Determine the nature of each of the stationary points.$[2]$Question 12 Code: 9709\/13\/M\/J\/21\/10, Topic: Coordinate geometry Points$A(-2,3), B(3,0)$and$C(6,5)$lie on the circumference of a circle with centre$D$.$\\text{(a)}$Show that angle$A B C=90^{\\circ}$.$[2]\\text{(b)}$Hence state the coordinates of$D$.$[1]\\text{(c)}$Find an equation of the circle.$[2]$The point$E$lies on the circumference of the circle such that$BE$is a diameter.$\\text{(d)}$Find an equation of the tangent to the circle at$E$.$[5]\\$\n\nWorked solutions: P1, P3 & P6 (S1)\n\nIf you need worked solutions for P1, P3 & P6 (S1), contact us @ [email\u00a0protected] | +254 721 301 418.\n\n1. Send us the link to these questions ( https:\/\/stemcie.com\/view\/91 ).\n2. We will solve the questions and provide you with the step by step worked solutions.\n3. We will then schedule a one to one online session to take you through the solutions (optional).","date":"2022-05-22 20:01:55","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7561339139938354, \"perplexity\": 3418.6259821168405}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-21\/segments\/1652662546071.13\/warc\/CC-MAIN-20220522190453-20220522220453-00332.warc.gz\"}"} | null | null |
{"url":"http:\/\/www.physicsforums.com\/showthread.php?s=cd71ec94bc846e1a7e7c8e38bf78ad84&p=4603576","text":"# Heisenberg's Uncertainty Principle\n\nby eehiram\nTags: heisenberg, principle, uncertainty\n P: 121 My source is the high school chemistry textbook: General Chemistry, 2nd Edition, by Donald A. McQuarrie and Peter A. Rock, published 1987 (This is not for a high school homework assignment.) According to Heisenberg's Uncertainty Principle, the product of the uncertainty in the momentum measurement \u0394p and the uncertainty in the position measurement \u0394q of a particle is greater than or equal to Planck's constant h divided by 4$\\pi$: \u0394p \u0394q \u2265 h \/ (4$\\pi$) This is not due to poor measurement or poor experimental technique, as is sometimes supposed: that bouncing waves or particles affects the location of the particle being measured, like in a billiard collision. (The measurement waves or particles are presumed to be of comparable size to the particle being measured.) Heisenberg's Uncertainty Principle is usually limited to only small particles. Does this mean that particles do not have a physical location unless and until we observe them? (I do not want to make a broad question, but rather a narrow question.) Does Heisenberg's Uncertainty Principle necessarily pit Classical physics (and Logic and common sense and billiards) against the Copenhagen School? Has Heisenberg's Uncertainty Principle agreed with the majority of experimental laboratory results?\n PF Gold P: 6,283 The HUP is trivially easy to demonstrate experimentally and there are no results that disagree with it. If there were, it would have been invalidated. That's how science works. There are MANY discussions about HUP on this forum if you want more details. You are correct about it being a fundamental fact of nature, not having anything to do with our measurement capabilities.","date":"2014-08-22 03:57:31","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.3247874081134796, \"perplexity\": 669.0263760759856}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2014-35\/segments\/1408500822560.65\/warc\/CC-MAIN-20140820021342-00313-ip-10-180-136-8.ec2.internal.warc.gz\"}"} | null | null |
"""This file implements the chaffing algorithm.
Winnowing and chaffing is a technique for enhancing privacy without requiring
strong encryption. In short, the technique takes a set of authenticated
message blocks (the wheat) and adds a number of chaff blocks which have
randomly chosen data and MAC fields. This means that to an adversary, the
chaff blocks look as valid as the wheat blocks, and so the authentication
would have to be performed on every block. By tailoring the number of chaff
blocks added to the message, the sender can make breaking the message
computationally infeasible. There are many other interesting properties of
the winnow/chaff technique.
For example, say Alice is sending a message to Bob. She packetizes the
message and performs an all-or-nothing transformation on the packets. Then
she authenticates each packet with a message authentication code (MAC). The
MAC is a hash of the data packet, and there is a secret key which she must
share with Bob (key distribution is an exercise left to the reader). She then
adds a serial number to each packet, and sends the packets to Bob.
Bob receives the packets, and using the shared secret authentication key,
authenticates the MACs for each packet. Those packets that have bad MACs are
simply discarded. The remainder are sorted by serial number, and passed
through the reverse all-or-nothing transform. The transform means that an
eavesdropper (say Eve) must acquire all the packets before any of the data can
be read. If even one packet is missing, the data is useless.
There's one twist: by adding chaff packets, Alice and Bob can make Eve's job
much harder, since Eve now has to break the shared secret key, or try every
combination of wheat and chaff packet to read any of the message. The cool
thing is that Bob doesn't need to add any additional code; the chaff packets
are already filtered out because their MACs don't match (in all likelihood --
since the data and MACs for the chaff packets are randomly chosen it is
possible, but very unlikely that a chaff MAC will match the chaff data). And
Alice need not even be the party adding the chaff! She could be completely
unaware that a third party, say Charles, is adding chaff packets to her
messages as they are transmitted.
For more information on winnowing and chaffing see this paper:
Ronald L. Rivest, "Chaffing and Winnowing: Confidentiality without Encryption"
http://theory.lcs.mit.edu/~rivest/chaffing.txt
"""
__revision__ = "$Id: Chaffing.py,v 1.7 2003/02/28 15:23:21 akuchling Exp $"
from Crypto.Util.number import bytes_to_long
class Chaff:
"""Class implementing the chaff adding algorithm.
Methods for subclasses:
_randnum(size):
Returns a randomly generated number with a byte-length equal
to size. Subclasses can use this to implement better random
data and MAC generating algorithms. The default algorithm is
probably not very cryptographically secure. It is most
important that the chaff data does not contain any patterns
that can be used to discern it from wheat data without running
the MAC.
"""
def __init__(self, factor=1.0, blocksper=1):
"""Chaff(factor:float, blocksper:int)
factor is the number of message blocks to add chaff to,
expressed as a percentage between 0.0 and 1.0. blocksper is
the number of chaff blocks to include for each block being
chaffed. Thus the defaults add one chaff block to every
message block. By changing the defaults, you can adjust how
computationally difficult it could be for an adversary to
brute-force crack the message. The difficulty is expressed
as:
pow(blocksper, int(factor * number-of-blocks))
For ease of implementation, when factor < 1.0, only the first
int(factor*number-of-blocks) message blocks are chaffed.
"""
if not (0.0<=factor<=1.0):
raise ValueError, "'factor' must be between 0.0 and 1.0"
if blocksper < 0:
raise ValueError, "'blocksper' must be zero or more"
self.__factor = factor
self.__blocksper = blocksper
def chaff(self, blocks):
"""chaff( [(serial-number:int, data:string, MAC:string)] )
: [(int, string, string)]
Add chaff to message blocks. blocks is a list of 3-tuples of the
form (serial-number, data, MAC).
Chaff is created by choosing a random number of the same
byte-length as data, and another random number of the same
byte-length as MAC. The message block's serial number is
placed on the chaff block and all the packet's chaff blocks
are randomly interspersed with the single wheat block. This
method then returns a list of 3-tuples of the same form.
Chaffed blocks will contain multiple instances of 3-tuples
with the same serial number, but the only way to figure out
which blocks are wheat and which are chaff is to perform the
MAC hash and compare values.
"""
chaffedblocks = []
# count is the number of blocks to add chaff to. blocksper is the
# number of chaff blocks to add per message block that is being
# chaffed.
count = len(blocks) * self.__factor
blocksper = range(self.__blocksper)
for i, wheat in map(None, range(len(blocks)), blocks):
# it shouldn't matter which of the n blocks we add chaff to, so for
# ease of implementation, we'll just add them to the first count
# blocks
if i < count:
serial, data, mac = wheat
datasize = len(data)
macsize = len(mac)
addwheat = 1
# add chaff to this block
for j in blocksper:
import sys
chaffdata = self._randnum(datasize)
chaffmac = self._randnum(macsize)
chaff = (serial, chaffdata, chaffmac)
# mix up the order, if the 5th bit is on then put the
# wheat on the list
if addwheat and bytes_to_long(self._randnum(16)) & 0x40:
chaffedblocks.append(wheat)
addwheat = 0
chaffedblocks.append(chaff)
if addwheat:
chaffedblocks.append(wheat)
else:
# just add the wheat
chaffedblocks.append(wheat)
return chaffedblocks
def _randnum(self, size):
# TBD: Not a very secure algorithm.
# TBD: size * 2 to work around possible bug in RandomPool
from Crypto.Util import randpool
import time
pool = randpool.RandomPool(size * 2)
while size > pool.entropy:
pass
# we now have enough entropy in the pool to get size bytes of random
# data... well, probably
return pool.get_bytes(size)
if __name__ == '__main__':
text = """\
We hold these truths to be self-evident, that all men are created equal, that
they are endowed by their Creator with certain unalienable Rights, that among
these are Life, Liberty, and the pursuit of Happiness. That to secure these
rights, Governments are instituted among Men, deriving their just powers from
the consent of the governed. That whenever any Form of Government becomes
destructive of these ends, it is the Right of the People to alter or to
abolish it, and to institute new Government, laying its foundation on such
principles and organizing its powers in such form, as to them shall seem most
likely to effect their Safety and Happiness.
"""
print 'Original text:\n=========='
print text
print '=========='
# first transform the text into packets
blocks = [] ; size = 40
for i in range(0, len(text), size):
blocks.append( text[i:i+size] )
# now get MACs for all the text blocks. The key is obvious...
print 'Calculating MACs...'
from Crypto.Hash import HMAC, SHA
key = 'Jefferson'
macs = [HMAC.new(key, block, digestmod=SHA).digest()
for block in blocks]
assert len(blocks) == len(macs)
# put these into a form acceptable as input to the chaffing procedure
source = []
m = map(None, range(len(blocks)), blocks, macs)
print m
for i, data, mac in m:
source.append((i, data, mac))
# now chaff these
print 'Adding chaff...'
c = Chaff(factor=0.5, blocksper=2)
chaffed = c.chaff(source)
from base64 import encodestring
# print the chaffed message blocks. meanwhile, separate the wheat from
# the chaff
wheat = []
print 'chaffed message blocks:'
for i, data, mac in chaffed:
# do the authentication
h = HMAC.new(key, data, digestmod=SHA)
pmac = h.digest()
if pmac == mac:
tag = '-->'
wheat.append(data)
else:
tag = ' '
# base64 adds a trailing newline
print tag, '%3d' % i, \
repr(data), encodestring(mac)[:-1]
# now decode the message packets and check it against the original text
print 'Undigesting wheat...'
newtext = "".join(wheat)
if newtext == text:
print 'They match!'
else:
print 'They differ!'
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,944 |
\section{Introduction}
The specific heat of solids is one of the most fundamental thermodynamic quantities. Its temperature dependence reveals important information about the energy scales of electronic, magnetic and lattice degrees of freedom. It is thus an inherently sensitive tool to detect phase transitions which involve one or more of the above-mentioned degrees of freedom. Consequently, various techniques \cite{Stewart83} to measure specific heat in calorimetric experiments at ambient pressure and low temperatures are well established and nowadays even commercially available \cite{Lashley03,acoption}. Typically, these techniques require adiabatic conditions, i.e., an almost ideal decoupling of the sample from the environment, so as to achieve high accuracy in the determination of absolute values of the specific heat. Among these techniques, the relaxation method \cite{Bachmann72} is considered as the standard method in which a heat pulse is given to the sample of interest and the relaxation time towards the initial temperature after switching off the pulse is directly related to the size of the specific heat. Alternatively, in particular in cases where the sample mass is very small, is the AC technique \cite{Sullivan68,Eichler79,Kraftmakher02}, in which the sample is heated by an oscillatory heat source and the resulting temperature oscillation can be used to infer the specific heat, preferred.
As a matter of fact, AC specific heat measurements have proven to be particularly suited for measurements under pressure \cite{Bonilla74,Baloga77,Eichler79,Chen93,Bouquet00,Demuer00,Wilhelm03,Kubota08,Umeo17}. In general, pressure $p$ represents an essential parameter for tuning phase transitions in solids \cite{Jayaraman72,Lorenz05,Imada98,Brando16}. To perform measurements under pressure, the sample has to be embedded into a pressure medium inside a pressure cell. This typically provides a stronger coupling between the sample and the bath (i.e., the oustide of the pressure cell), compared to ambient-pressure experiments performed in vacuum. Whereas the analysis of data taken under pressure with the relaxation method suffers from the huge addenda contribution from pressure cell and medium, the AC technique has a second major advantage in addition to its sensitivity for samples with small masses: the choice of the measurement frequency allows for the measurement on a different timescale than the one determined by the relaxation time to the bath. This can result, to first approximation, in a decoupling of the sample from the bath, thereby paving the way to extraction of absolute values of the specific heat on a semi-quantitative level \cite{Eichler79}.
Typically, in order to perform AC calorimetric experiments in piston-pressure cells up to $p\,\approx\,2\,-\,3\,$GPa, either small ruthenium oxide (RuO$_2$) thermometers \cite{Kubota08,Chen93,Baloga77} or thermocouples \cite{Bonilla74,Wilhelm03,Bouquet00,Demuer00} have been used to detect the temperature oscillations. On one hand, RuO$_2$ thermometers are inherently sensitive only at low temperatures due to their insulating nature; on the other hand they are easy to handle. Thermocouples cover a wider temperature range, but come along with obstacles in their handling. The reliable use of thermocouples requires a firm contact to the sample which often can be only realized by spot-welding of the thermocouple to the sample. Spot-welding is not possible in case of non-metallic samples, but also is often found to be problematic for metallic (and often brittle) samples. In addition, obtaining absolute values of temperature changes with high accuracy can only be guaranteed when the thermal contact to a reference temperature is good which can be challenging in the pressure-cell environment.
In this work, we present another option: using Cernox\cite{Cernox} thermometers as temperature sensors. Cernox sensors combine the advantages of RuO$_2$ thermometers and thermocouples. They are well established at ambient pressure in most low-temperature laboratories, as they provide a high sensitivity over a wide temperature range, as well as short thermal response times. In addition, they can easily be attached to any sample without the need of spot-welding. This being said, it is surprising that, to the best of our knowledge, the properties of Cernox thermometers have not been studied under pressure so far. Our results show that the sensitivity of Cernox thermometers remains large over the entire investigated pressure range up to 2\,GPa and temperature range up to at least 150\,K. We demonstrate that this high sensitivity of the sensors allows us to study the specific heat of solids under pressure (including various types of phase transitions) at a semi-quantitative level. The wide temperature range covered by this setup will allow for the study of larger regions of phase diagrams by specific heat under pressure, with the convenience of using commercially-available temperature sensors.
This paper is organized as follows. First, we describe details of the experimental setup (Sec. \ref{sec:setup}) used in this work to determine the resistance behavior of the Cernox thermometers under pressure, as well as the specific heat of solids under pressure. In the next section (Sec. \ref{sec:Cernoxresistance}), we show one of the main results of this work, namely that the resistance change of the Cernox thermometers under pressures up to 2\,GPa is very modest and readily describable. Following this, we turn to our description of the AC specific heat data obtained using these Cernox thermometers. Therefore we first provide some theoretical background information on AC specific heat measurements and illustrate our measurement protocol in Sec. \ref{sec:ACtheory}. In Sec. \ref{sec:specheatresults} we discuss the results of specific heat under pressure measurements on three different test cases each of which undergoes a different type of phase transition. These systems were chosen to cover a wide range of phase transition temperatures (7 K up to 130 K) as well as removed entropies, thereby demonstrating the versatility of Cernox thermometers for measurements of specific heat under pressure.
\section{Experimental Setup}
\label{sec:setup}
To perform AC calorimetric measurements, the sample of interest is placed between a heater and a thermometer (see Fig.\,\ref{fig:schematicsetup} (a)). In our setup, we use bare Cernox-chip thermometers \cite{Cernox} (type CX-1070 or type CX-1080) as thermometers. The bare chips have dimensions of 0.965\,$\times\,0.762\,\times\,0.203$\,mm$^3$ and are thus ideally suited to fit into standard piston-pressure cells (see Figs.\,\ref{fig:schematicsetup} (b) and (c) for schematic drawings). In addition, they are deposited on a sapphire substrate with low mass (\,$\le\,3\,$mg), thus have themselves a small specific heat, and short response times (1.5\,ms at 4.2\,K). As a heater, we use strain gauges\cite{straingauges} (type FLG-02-23, Tokyo Sokki Kenkyujo Co., Ltd.) which have an active heater area of $\approx\,1\,\times\,1.4$\,mm$^2$. They show an almost temperature-independent resistance as a function of temperature ($R(T,p)\,\approx\,$120\,$\Omega$) and are enclosed in a very thin layer of plastic coating giving rise to a low thermal mass. The samples, with typical masses $\,\sim\,2\,$mg, are cut into plates with dimensions as close as possible to the active heater area dimensions. The thermometer and heater are attached to the sample by using Devcon 5 Minute epoxy (No. 14250) to improve the thermal contact between the individual components and to guarantee sufficient mechanical stability in the pressure cell (shown schematically in Figs.\,\ref{fig:schematicsetup} (a) and (c)). A photograph of the assembly is shown in Fig.\,\ref{fig:schematicsetup}\,(d). The wires of the thermometer and heater are soldered to the wires passing the pressure-cell feedthrough. The thermometer is connected in a pseudo-four-point configuration in which the four wires for current and voltage are reduced to two wires inside the pressure cell. In addition, a Pb sample is mounted on the feedthrough in a four-point configuration for determining its critical temperature, $T_c$, via resistance measurements. The $T_c$ value can be used to determine the pressure, $p$, at low temperature as $T_c(p)$ is well characterized in literature \cite{Bireckoven88}.
The sample end of the feedthrough is placed in a Teflon-cup (see Figs.\,\ref{fig:schematicsetup}\,(b) and (c)) which is filled with the pressure-transmitting medium. In all the experiments presented here, a mixture of 4:6 mixture of light mineral oil:n-pentane \cite{Budko84,Kim11} is used as a pressure-transmitting medium. It solidifies at $p\,\approx\,3-4\,$GPa at room temperature, thus ensuring hydrostatic pressure conditions in the available pressure range. Two anti-extrusion rings made out of phosphor-bronze are used to prevent the teflon from flowing through the interstices when pressurized. The outer cell body is made out of Grade 5 titanium alloy (Ti 6Al-4V) and the inner cylinder out of Ni-Cr-Al alloy. Its design is similar to the one described in Ref. \citen{Budko84}. As Ti 6Al-4V alloy turns superconducting \cite{Ridgeon17} below $\approx\,$5\,K and as a consequence, its thermal conductivity becomes significantly reduced, the sample inside the cell cannot be cooled below 5\,K. Therefore, the use of this particular cell is restricted to temperatures above 5\,K. This issue can be circumvented by using cells made out of a different material, such as CuBe/Ni-Cr-Al.
Pressure is applied by applying a load to the piston at room temperature by a hydraulic press and locked by tightening the lock nut. All measurements shown in this manuscript were performed inside the pressure cell. At the beginning of each pressure cycle the pressure cell was closed hand-tight. Whereas this procedure typically results in a small, but finite pressure at room temperature \cite{Thompson84} ($p\,\lesssim\,0.3\,$GPa), the pressure at low temperature inferred from $T_c$ of Pb is usually very close to 0\,GPa ($p\,\lesssim\,0.04\,$GPa). We refer to this situation in the manuscript as ``ambient-pressure'' condition ($p\,=\,0\,$GPa). All data shown were obtained by increasing pressure to the measured value.
\begin{figure}
\includegraphics[width=0.9\textwidth]{setup-schematics.pdf}
\caption{(a) Schematic diagram of the sample arrangement with heater and thermometer. The heater is supplied with an AC voltage with frequency $\omega/2$ which results in an oscillation of the temperature of the sample with frequency $\omega$; (b) Schematic diagram of the piston-pressure cell used in the present work; (c) Schematic diagram of the sample assembly and Pb sensor inside the teflon cup; (d) Photograph of the heater, sample and thermometer mounted on the pressure-cell feedthrough. The Pb sensor for the determination of the pressure value near 7\,K is also mounted on the feedthrough.}
\label{fig:schematicsetup}
\end{figure}
The measurements were carried out in a cryogen-free cryostat (Janis SHI-950 with a base temperature of $\approx\,3.5\,$K). The probe, used in this cryostat, is wired with phosphor-bronze wires (QT-36, LakeShore Inc.) to ensure low heat flow through the wires. The temperature was controlled continuously between base and room temperature by a LakeShore 336 controller. Temperature was monitored by a calibrated temperature sensor (Cernox-1030) which was placed directly outside the pressure cell by inserting it into a copper bracket. The Cernox thermometer inside the pressure cell was supplied by a DC current (Model CS580, Stanford Research Systems). The size of the DC current was adjusted with temperature such that the voltage limit ($<\,100\,$mV) of the thermometer is not exceeded. The voltage oscillations of the thermometer which result from the AC heating were pre-amplified and filtered (Model SR560, Stanford Research Systems) and then measured with a Lock-In Amplifier (Model SR860, Stanford Research Systems) the internal oscillator of which was used to provide the heating voltage. The heating power was chosen such that the amplitude of the induced temperature oscillation $T_{AC,0}$ (see Fig.\,\ref{fig:schematicsetup} (a)) was typically smaller than 20\,mK. To measure frequency responses (i.e., measurements as a function of frequency, see below), we used the built-in frequency option of this particular Lock-In Amplifier which allows to change the frequency within user-defined frequency limits and sweep rates. The DC resistance of the bare Cernox chips inside the pressure cell was read out simultaneously to each specific heat measurement by a Digital Voltmeter (SIM970, Stanford Research Systems). The resistance of the Pb sensor was measured with a LakeShore AC Resistance Bridge (Model 370). All data are recorded using a custom LabView Program.
\section{Results: Cernox resistance under pressure}
\label{sec:Cernoxresistance}
Figure \ref{fig:Cernoxresistance} (a) summarizes our main result on the behavior of the Cernox (type CX-1080) resistance, $R$, as a function of temperature, $T$, at three selected pressures up to $p\,\approx\,$2\,GPa. These data were taken without any applied heat to the heater inside the pressure cell. At ambient pressure, the resistance shows a typical behavior for Cernox thermometers: the resistance increases with decreasing temperature and the slope d$R$/d$T$ is finite over the entire temperature range which guarantees a sufficient sensitivity of this thermometer from low temperatures ($T\,\approx\,$5\,K) up to high temperatures ($T\,\approx\,$150\,K). Upon increasing pressure, the resistance at a fixed temperature is reduced by $\approx\,$28\% at 5\,K ($\approx\,10\,$\% at 150\,K) at 2\,GPa (see Fig.\,\ref{fig:Cernoxresistance} (b) for change of resistance as a function of pressure at different temperatures). However, the overall behavior as a function of temperature is nearly unchanged. To quantify the sensitivity of the thermometer, one can refer to the dimensionless quantity (d$R$/d$T$)/($R/T$) which is displayed as a function of $T$ in the inset of Fig. \ref{fig:Cernoxresistance} (a) for the same pressure values as the ones depicted in the main panel. This representation shows that this type of Cernox thermometer has an almost temperature- and pressure-independent sensitivity factor of 1.25. Only at low temperatures ($T\,<\,25\,$K), an increased sensitivity up to 1.5 is observed for all pressures. Thus, our measurements clearly show that Cernox thermometers keep their high sensitivity across a wide temperature range up to 2\,GPa. Note that even though we restrict ourselves in this study to temperatures below 150\,K, it is known that (d$R$/d$T$)/($R/T$) of the Cernox thermometers remains almost unchanged at ambient pressure up to room temperature \cite{Cernox}. Based on our results, it is therefore likely that the Cernox thermometers are very sensitive up to room temperature, even under pressure. Moreover, we did not find any indications of changes in the thermometer behavior from one pressure cycle to the next or strong deviations in the behavior of different chips (see Fig.\,\ref{fig:Cernoxresistance} (b)). Nevertheless, the minor differences in the resistance behavior of different chips depicted in Fig.\,\ref{fig:Cernoxresistance} (b) requires a calibration of each chip for each pressure run, as will be described below. All in all, our results show the Cernox chips can be used as temperature sensors in pressure experiments with high reliability and reproducibility.
\begin{figure}
\includegraphics[width=0.9\textwidth]{Cernox-pressure-110518.pdf}
\caption{(a) Resistance, $R$, of a Cernox thermometer, type CX-1080, as a function of temperature, $T$, at three different pressures $p$, ranging from 0\,GPa to 2.05\,GPa; Inset: Sensitivity, defined as $|$d$R/$d$T/(R/T)|$, as a function of temperature for the same pressure values, as depicted in the main panel. The step at $T\,\approx\,$50\,K in the data at 0\,GPa and 2.05\,GPa is likely an artifact associated with changing of thermometer current; (b) Resistance of a Cernox thermometer, type CX-1080, normalized to its ambient-pressure value, $R/R(p\,=\,0)$ at different temperatures between 5\,K and 150\,K. Open and closed symbols represent measurements on two different chips of the same type.}
\label{fig:Cernoxresistance}
\end{figure}
\section{AC Specific heat: Theoretical background and Measurement Protocol}
\label{sec:ACtheory}
In the following, we want to focus on one possible application for which it is essential to determine temperatures with high sensitivity inside the pressure cell, namely when performing measurements of the specific heat of solids under pressure. As we employ here the method of AC calorimetry, this section will provide theoretical background information \cite{Sullivan68,Eichler79} on the AC calorimetric technique which is essential for understanding our measurement protocol.
To extract absolute specific heat values from an AC calorimetry experiment, an understanding of the heat flow from the heater to the various components in the system is needed. On one hand, the heat is transferred from the heater (specific heat $C_H$) through the sample ($C_S$) to the thermometer ($C_{\Theta}$) which are connected via finite thermal conductances. In the following, the thermal conductances between sample and heater as well as thermometer and sample which govern the heat transfer are denoted as $\lambda_{HS}$ and $\lambda_{\Theta S}$, respectively. On the other hand, each component is also coupled to a bath with temperature $T_B$ (which corresponds to the temperature on the outside of the pressure cell) by finite thermal conductances, denoted by $\lambda_H$, $\lambda_S$ and $\lambda_\Theta$. A block diagram of this arrangement is shown in Fig.\,\ref{fig:frequencydependence} (a). Note that the couplings $\lambda_H$, $\lambda_S$ and $\lambda_{\Theta}$ are non-negligible in the present case, as the sample has to be embedded in a pressure medium inside the pressure cell for measurements under pressure. This, in general, means that the absolute values of the specific heat cannot be determined under pressure with high accuracy. Nonetheless, we will show below that the AC technique implemented in this work allows for a determination of specific heat value under pressure at a semi-quantitative level by choosing the right measurement frequency.
When the heater is supplied with an AC voltage $U(t)\,=\,U_0 \sin(\frac{\omega}{2} t)$, it gives rise to an AC heating power $P(t)\,=\,P_0 \sin^2(\frac{\omega}{2}t)$ and the temperature of the sample will respond in the following manner:
\begin{equation}
T(t) \,=\, T_{DC} + T_{AC}(t).
\end{equation}
$T_{DC}$ refers here to the time-independent increase of the sample temperature with respect to the bath, which is determined by the heating power as well as the coupling to the bath via $T_{DC}\,=\,T_B+\frac{P_0}{2\lambda_S}$. The second term $T_{AC}(t)\,=\,T_{AC,0} \sin(\omega t + \phi)$ describes the temperature oscillation of the sample which oscillates with twice the driving frequency of the heater. The amplitude of this oscillation $T_{AC,0}$ contains the information about the specific heat of the sample $C_S$. The sensitivity of an AC specific heat setup is particularly high for small samples (i.e. with small $C_S$), as $T_{AC,0}$ is inversely proportional to $C_S$. In detail, the relation of $T_{AC,0}$ to $C_S$ for a realistic model with finite thermal conductances was discussed in the works of Sullivan and Seidel (Ref. \citen{Sullivan68}), as well as Eichler (Ref. \citen{Eichler79}), and reads as
\begin{eqnarray}
T_{AC,0} \,&=&\, \frac{P_0}{2\omega C}\,\cdot\,F(\omega) \label{eq:frequency-response} \\
\textnormal{with\ } F(\omega)\,&=&\,[1+2\,\cdot\,(\frac{\lambda_H}{\lambda_{HS}}+\frac{\lambda_\Theta}{\lambda_{\Theta S}})+\frac{1}{(\omega \tau_1)^2}+(\omega \tau_2)^2]^{-1/2} \label{eq:frequency-response2}\\
\textnormal{and\ } C &=& C_H + C_\Theta + C_S, \tau_1=\frac{C}{\lambda_S}, \\
\tau_2 &=& \sqrt{\tau_H^2+\tau_\Theta^2} \textnormal{\ with \ } \tau_H\,=\,C_H/\lambda_{HS} \textnormal{\ and \ } \tau_\Theta = C_\Theta/\lambda_{\Theta S}.
\end{eqnarray}
Thus, whenever the measurement frequency is choosen such that $(\omega \tau_1)^2\,\gg\,1$ and $(\omega \tau_2)^2\,\ll\,1$, with $\tau_1$ and $\tau_2$ corresponding to the thermal relaxation times to the bath and within the assembly of heater, sample and thermometer, respectively, then $F(\omega)\,\approx\,[1+2\,\cdot\,(\frac{\lambda_H}{\lambda_{HS}}+\frac{\lambda_\Theta}{\lambda_{\Theta S}})]^{-1/2}$. The error in determination of absolute values then is mainly determined by the ratios $\frac{\lambda_H}{\lambda_{HS}}$ and $\frac{\lambda_\Theta}{\lambda_{\Theta S}}$. However, sample, heater and thermometer are in intimate contact, whereas the heat path to the bath (i.e., the outside of the pressure cell) is long. This implies due to the geometrical arrangement that, to a first approximation, $\lambda_H\,\ll\,\lambda_{HS}$ and $\lambda_\Theta\,\ll\,\lambda_{\Theta S}$ (and we will show below that this assumption is verified in our setup), and therefore $F(\omega)\,\approx\,1$. It then follows that $T_{AC,0}\,=\,\frac{P_0}{2\omega C}$.
The frequency which meets these criteria is called the optimal measurement frequency $\omega_{opt}$. As $\tau_1$ and $\tau_2$ depend on the specific heat of the sample, as well as on thermal conductances $\lambda_{HS}, \lambda_S$ and $\lambda_{\Theta S}$, $\omega_{opt}$ will in general be a function of temperature and pressure, and will differ from sample assembly to sample assembly. Correspondingly, $\omega_{opt}$ has to be determined experimentally for each sample, temperature and pressure individually, prior to each measurement of the specific heat. It can be shown that $\omega_{opt}$ is the frequency at which $F(\omega)$ is maximal. As suggested by eq. \ref{eq:frequency-response}, direct experimental access to $F(\omega)$ is provided by measuring the frequency dependence of the quantity $\omega\,\cdot\,T_{AC,0}$ (called frequency response hereafter). In Figs. \ref{fig:frequencydependence} (b) and (c) we show examples of the frequency responses, normalized to their respective maximum, recorded with our setup when measuring the specific heat of elemental Pb (The specific heat results on Pb will be discussed in Sec.\,\ref{sec:specheatresults} in more detail.). First, we compare in Fig.\,\ref{fig:frequencydependence}\,(b) the frequency response, taken at $T\,=\,6$\,K at two different pressures ($p\,=\,0\,$GPa and 1.97\,GPa). Each frequency response (normalized to its maximum value) reveals a broad maximum at $\approx\,100\,$Hz and 300\,Hz, respectively, which we assign to the optimal measurement frequencies $\omega_{opt}$. Note that a broad maximum (or even a wide plateau) suggests that $(\omega \tau_1)^2\,\gg\,1$ and $(\omega \tau_2)^2\,\ll\,1$ across a wide frequency range which minimizes errors in the determination of absolute values of the specific heat. The observation of a broad maximum is therefore crucial for the determination of absolute values of the specific heat under pressure on a semi-quantitative level, as achieved with our setup. At the same time, at a fixed pressure, as shown in Fig.\,\ref{fig:frequencydependence}\,(c) for $p\,=\,$1.97\,GPa, we find that the broad maximum in the frequency response and thereby $\omega_{opt}$ shifts to lower frequencies with increasing temperature. The evolution of $\omega_{opt}$, determined from the numerical derivation of the frequency response data, with $T$ and $p$ is summarized in Fig.\,\ref{fig:frequencydependence}\,(d).
The knowledge of the frequency response allows us to extract the relaxation times $\tau_1$ and $\tau_2$ of this particular assembly at different pressures. The solid lines in Fig.\,\ref{fig:frequencydependence}\,(b) show a fit of eq.\,\ref{eq:frequency-response2} to our experimental data, taken at 6\,K. The fits, which were performed with keeping $(\frac{\lambda_H}{\lambda_{HS}}+\frac{\lambda_\Theta}{\lambda_{\Theta S}})$ fixed to 0, are in very good agreement with our experimental data set. They yield $\tau_1\,=\,(0.047\,\pm\,0.001)\,$s and $\tau_2\,=\,(0.0016\,\pm\,0.0001)\,$s at ambient pressure and $\tau_1\,=\,(0.015\,\pm\,0.001)\,$s and $\tau_2\,=\,(0.0009\,\pm\,0.0001)\,$s at $p\,=\,1.97\,$GPa. Thus, the optimal measurement frequencies $\omega_{opt}$ fulfill the criteria mentioned above as $(\omega_{opt} \tau_1)^2\,\approx\,22\,\gg\,1$ and $(\omega_{opt} \tau_2)^2\,\approx\,0.02\,\ll\,1$ at $p\,=\,0\,$GPa and $(\omega_{opt} \tau_1)^2\,\approx\,20\,\gg\,1$ and $(\omega_{opt} \tau_2)^2\,\approx\,0.07\,\ll\,1$ at $p\,=\,1.97\,$GPa. Our fitting results indicate that both relaxation times decrease with increasing pressure. This tendency is naturally expected, as the coupling to the bath, but also the coupling within the assembly likely increase under compression. Therefore, the increased optimal frequency $\omega_{opt}$ with applied $p$ is directly a consequence of the decreased relaxation times. The temperature dependence of $\omega_{opt}$ is less intuitive to understand as it depends on the temperature-dependent changes of specific heat as well as thermal conductivity of sample, heater as well as thermometer.
It should be noted that the error in the determination of the absolute value of the specific heat can be estimated from the knowledge of $\tau_1$ and $\tau_2$. Equations \ref{eq:frequency-response} and \ref{eq:frequency-response2} suggest that any finite $\tau_1$ as well as any non-zero $\tau_2$ will give rise to an overestimation of the specific heat value by the factor $[1+\frac{1}{(\omega \tau_1)^2}+(\omega \tau_2)^2]^{1/2}$, if $\frac{\lambda_H}{\lambda_{HS}}+\frac{\lambda_\Theta}{\lambda_{\Theta S}}\,\approx\,$0. Our results of $\tau_1$ and $\tau_2$ correspond to an overestimate of specific heat by $\approx\,$3\,\% at ambient pressure, and $\approx\,$5\,\% at 1.97 GPa by our setup. This estimate shows that our setup can, in principle, deliver absolute values on a semi-quantitative level, despite a non-negligible coupling to the bath. Importantly, the analysis performed here shows that the overestimation of specific heat does not significantly change with pressure. This allows for the determination of changes (especially relative changes) of specific heat under pressure with higher accuracy. We confirm these conclusions from the analysis of the frequency response in Sec. \ref{sec:specheatresults}, where we present specific heat under pressure data on three different test cases and compare with ambient-pressure literature data taken under adiabatic conditions.
The theoretical background information given here explains the measurement protocol which we follow to determine the specific heat of a sample using the AC technique. It includes in total three separate, sequential temperature sweeps. First, we need to calibrate the Cernox thermometers inside the pressure cell at a specific pressure to quantify the DC temperature increase $T_{DC}$ of the sample which results from applying heat to the heater inside the cell. To this end, we place a calibrated thermometer outside on the pressure cell and record the resistance of the Cernox thermometer inside the pressure cell upon slow warming with a rate of $\approx\,0.25\,$K/min without any voltage applied to the heater inside the cell (see Sec.\,\ref{sec:Cernoxresistance}). In the second temperature sweep, we record the frequency response $\omega\,\cdot\,T_{AC,0}$ vs. $\omega$ as a function of temperature for the same, specific pressure. From this data, we extract $\omega_{opt}$ as a function of $T$ and typically fit this smooth data set with an exponential function $\omega_{opt}\,=\,\omega_0+A\exp(-T/t_1)$ with free parameters $\omega_0$, $A$ and $t_1$ (see grey lines in Fig.\,\ref{fig:frequencydependence} (d)). Within our measurement program, we adjust the measurement frequency continuously with temperature according to this exponential function during the third temperature sweep for a specific pressure. This ensures that the AC temperature oscillation $T_{AC,0}$ as a function of $T$ is always measured at the optimal measurement frequency which then allows us to infer the specific heat on a semi-quantitative level.
\begin{figure}
\includegraphics[width=0.9\textwidth]{Pb_optimalfrequency_090518.pdf}
\caption{(a) Schematic diagram illustrating heat flows from the sample to the heater (governed by the thermal conductivity $\lambda_{HS}$), from the sample to the thermometer ($\lambda_{\Theta S}$), and from sample, heater and thermometer to the bath ($\lambda_S$, $\lambda_H$ and $\lambda_\Theta$); (b) Normalized frequency response, i.e., the product of frequency $\omega$ and oscillation amplitude $T_{AC,0}$ normalized to its maximum value $(\omega T_{AC,0})_{max}$ vs. $\omega$, for a Pb sample at $T\,=\,6$\,K and $p\,=\,0\,$GPa and 1.97\,GPa; (c) Normalized frequency response for a Pb sample at different temperatures between 5\,K and 9\,K at $p\,=\,1.97\,$GPa; (d) Evolution of the optimal measurement frequency $\omega_{opt}$ as a function of temperature and pressure, obtained from the data presented in (b) and (c) (for details, see main text). Grey lines represent exponential fits to the $\omega_{opt}$ vs. $p$ data sets.}
\label{fig:frequencydependence}
\end{figure}
\section{Specific heat under pressure: Results}
\label{sec:specheatresults}
In the following, we demonstrate the wide applicability of the Cernox thermometers in measurements of specific heat under pressure by examining three test cases with very different transition temperatures, ranging from $T\,\approx\,7\,$K (superconducting transition in Pb) up to $T\,\approx\,130\,$K (magnetostructural transition in BaFe$_2$As$_2$), as well as very different amounts of entropy change.
\subsubsection{Superconducting phase transition in elemental Pb}
The first sample for a study of specific heat under pressure chosen here is elemental lead (Pb) which undergoes an ambient-pressure superconducting transition at a critial temperature $T_c\,=\,7.2\,$K. The shift of $T_c$ with pressure is well characterized in literature \cite{Bireckoven88} and therefore often utilized as a manometer at low temperatures.
\begin{figure}
\includegraphics[width=0.8\textwidth]{Pb-050918.pdf}
\caption{(a) Molar specific heat $C_{molar}$ of elemental Pb as a function of temperature $T$ at four different pressures up to 1.97\,GPa; (b,c) Comparison of $C_{molar}(T)$ of Pb and the resistance $R_{Pb}(T)$ of the Pb pressure sensor at a pressure of 0 GPa (b) and 1.97\,GPa (c).}
\label{fig:Pb}
\end{figure}
Figure \ref{fig:Pb} (a) shows our results of the specific heat, $C_{molar}$, of Pb at different pressures up to 1.97\,GPa. At all pressures, we find a jump-like change of $C_{molar}$ at a critical temperature $T_c$. This feature is characteristic for the mean-field type phase transition into the superconducting state in BCS superconductors. The critical temperature, extracted from our $C_{molar}$ data, is suppressed with increasing $p$, consistent with literature results \cite{Bireckoven88}. In addition, the overall specific heat is reduced upon pressurization, likely due to a combination of changes in the electronic density of states as well as lattice stiffening (see below for more details).
To demonstrate the high accuracy in the determination of phase transition temperatures from our specific heat data, we compare in Figs. \ref{fig:Pb} (b) and (c) the specific heat of the Pb sample, placed between heater and thermometer, with the resistance of the Pb manometer, $R_{Pb}$, at lowest pressure ($p_1\,=\,0\,$GPa) and highest pressure ($p_4\,=\,1.97\,$GPa) of our experiment. At both pressures, the midpoint of the jump in $C_{molar}$ occurs at the same temperature at which the resistance clearly shows a jump-like change into the superconducting state. This also demonstrates that there are no significant pressure gradients in our pressure cell.
Next, we want to discuss to which extent our setup delivers a semi-quantitative determination of the specific heat of solids by comparing our results to literature results \cite{Shiffman63} on Pb (see Fig. \ref{fig:Pb-analysis}). Our data overestimates the absolute specific heat value by $\approx\,12\,\%$, compared to the literature results from Ref. \citen{Shiffman63}. As outlined in Sec.\,\ref{sec:ACtheory}, an overestimate of absolute specific heat values determined with the AC technique is a consequence of finite relaxation times $\tau_1$ and $\tau_2$. The overestimation factor of about 3\,\%, estimated from an analysis of the frequency responses in Sec. \,\ref{sec:ACtheory}, is of similar size as the overestimation found here from the comparison with literature data on Pb. Note that we did not correct our data for the specific heat of the addenda, i.e., of thermometer, heater and the tiny layers of glue. These additional contributions to the measured specific heat, which can be as large as 50\,\% of the total measured specific heat depending on the specific sample, its size, mass and shape (estimated by measuring the size of the addenda at ambient pressure using the relaxation-time method), likely give rise to the slightly larger overestimation of 12\,\% found empirically here. Clearly, despite the strong coupling to the bath due to the pressure medium and uncertainties in the size of the addenda, our data resembles literature results on a semi-quantitative level, i.e., within less than approximately a factor of 2. This upper limit was estimated empirically in the study of the three different test cases presented in this manuscript. The superconducting jump size extracted from our data at ambient pressure amounts to $\Delta C_{sc}\,\approx\,(44.6\,\pm\,0.5)\,$mJ/mol/K \cite{Shiffman63,Clement52}. This value is slightly smaller than reported values in literature ($\Delta C_{sc}\,=\,$52.9\,mJ/mol/K up to 57.5\,mJ/mol/K), but nevertheless matches on the same semi-quantitative level.
Upon pressurization, we find a significant reduction of $\Delta C_{sc}$ with increasing $p$ down to $\approx\,(29.0\,\pm\,0.5)\,$mJ/mol/K at 1.97\,GPa (see Fig.\,\ref{fig:Pb-analysis} (b)). For superconductors, the change in $\Delta C_{sc}$ is related on the one hand to a change in $T_c$ as well as to a change in the density of states at the Fermi level $N(E_F)$ \cite{Carbotte90}. Figure \ref{fig:Pb-analysis} (b) also includes a plot of $\Delta C_{sc}/T_c$ as a function of $T_c$. The strong change of $\Delta C_{sc}/T_c$ with $p$ by $\approx\,-\,25\,\%$ indicates that most of the change of $\Delta C_{sc}$ with $p$ can be attributed to changes of $N(E_F)$ with $p$, rather than to changes of $T_c$. Unfortunately, no literature data on the change of $N(E_F)$ in Pb with $p$ is available. Also the determination of the change of $N(E_F)$ under $p$ by extracting the Sommerfeld coefficient $\gamma$ from our specific heat data turns out to be not reliable due to the relatively high $T_c$ of Pb combined with a relatively low Debye temperature $\Theta_D\,\approx\,100\,$K at ambient pressure. Thus, we performed density-functional theory (DFT) calculations \cite{Hohenberg64,Kohn65} of the band structure of Pb up to 2\,GPa using PBEsol as exchange-correlation functional with spin-orbit coupling (SOC) effect as implemented in VASP \cite{Kresse96,Kresse96b}. At zero pressure, the theoretical lattice constant of 4.934\,\AA\ agrees very well with the experimental values of 4.95\,\AA. At 2 GPa, the lattice constant is reduced to 4.872\,\AA. We find a decrease of $N(E_F)$ from 0.5303\,states/eV/cell to 0.5121 \,states/eV/cell by 2\,GPa which corresponds to $\approx\,-\,3.5$\,\%. Even though this value is smaller than the one inferred from our specific heat measurements, both results are consistent in inferring a decrease of $N(E_F)$ with pressure. This supports our conclusion that in case of Pb changes of the specific heat anomaly $\Delta C_{sc}$ under $p$ result from a decrease of $N(E_F)$ with pressure.
\begin{figure}
\includegraphics[width=0.8\textwidth]{Pb_analysis-050918.pdf}
\caption{(a) Comparison of ambient-pressure literature data \cite{Shiffman63} on the specific heat $C_{molar}$ of elemental Pb (grey symbols) and the specific heat obtained in the present work in the pressure cell at ambient pressure (black solid line); (b) Evolution of the superconducting jump size in the specific heat $\Delta C_{sc}$, as well as the jump size normalized to the critical temperature, $\Delta C_{sc}/T_c$, with $T_c$.}
\label{fig:Pb-analysis}
\end{figure}
\subsubsection{Antiferromagnetic transition in the rare-earth compound GdNiGe$_3$}
The specific heat anomaly at the superconducting transition in Pb as well as the transition temperature respond strongly to application of external pressure. In addition, the amount of entropy change is relatively small. For the next system, we chose GdNiGe$_3$ anticipating a weak response to pressure and a large change in entropy ($\approx\,R \ln(8)$) \cite{Mun10}. This allows us to show that changes of the absolute values of specific heat under pressure are not a result of an artifact due to modified coupling to the bath or within the assembly of sample, heater and thermometer, i.e., due to changing $\tau_1$ and $\tau_2$. This in turn allows us to establish a high accuracy in the determination of \textit{changes} of the specific heat under pressure. At the same time, a system with a phase transition occurring at higher transition temperature compared to the superconducting transition in elemental Pb is desired to prove high sensitivity of our setup at even higher temperatures.
The rare-earth based GdNiGe$_3$ system has a single antiferromagnetic (afm) transition\cite{Mun10} at $T_N\,\approx\,$26\,K. Importantly, as the moment-carrying Gd is trivalent in this compound and therefore has a Hund's rule $J\,=\,S\,=\,7/2$ ground state ($L\,=\,0$), the compound lacks any magneto-crystalline anisotropy or splitting of the Hund's rule ground state multiplet. Experiments \cite{Mun10} confirmed that GdNiGe$_3$ shows an almost isotropic susceptibility in the paramagnetic state with an effective moment $\mu_{eff}\,=\,8.0\,\mu_B$/Gd$^{3+}$, close to the free-ion value of 7.94\,$\mu_B$/Gd$^{3+}$. Correspondingly, specific heat measurements \cite{Mun10} showed a single $\lambda$-shaped peak at $T_N$ (see grey symbols in Fig.\,\ref{fig:GdNiGe3} for a reproduction of these data). The magnetic entropy, $S$, extracted from measurements of the specific heat was found to be almost constant at $T\,>\,T_N$ with $S\,=\,$17\,J/(mol$\cdot$K), i.e., close to the expected value of $R \ln(8)$. This result is fully consistent with the absence of crystal-field effects in this compound. As the magnetism of this compound can be well understood in terms of localized 4f moments which interact via RKKY (Ruderman-Kittel-Kasuya-Yosida) interaction \cite{Ruderman54}, the response to hydrostatic pressure is expected to be relatively weak. This, together with the well-defined entropy in the paramagnetic state and a high transition temperature, makes this system a suitable reference system for a study of the specific heat under pressure.
\begin{figure}
\includegraphics[width=0.8\textwidth]{GdNiGe3-050918.pdf}
\caption{Molar specific heat divided by temperature $C_{molar}/T$ as a function of temperature $T$ of GdNiGe$_3$ at different pressures up to 1.2 GPa. For comparison, literature data at ambient pressure \cite{Mun10} on this compound are shown in grey. The arrow indicates exemplary the jump size at the antiferromagnetic transition, $\Delta C_{molar}/T$, at lowest pressure $p\,\sim\,0.2$\,GPa (for a definition of criterion and evolution with pressure, see main text). }
\label{fig:GdNiGe3}
\end{figure}
The results of our specific heat study on GdNiGe$_3$ under pressure are shown in Fig.\,\ref{fig:GdNiGe3} in a $C_{molar}/T$ vs. $T$ representation. For comparison, we included the literature specific heat data on this compound at ambient pressure, taken from Ref. \citen{Mun10}. At all measured pressures, our data nicely reveal the $\lambda$-shaped phase transition anomaly at $T\,\approx\,26\,$K. In addition, we also find a small hump in the specific heat below 10\,K. Such a hump in the specific heat at temperatures well below the ordering temperatures was found in various Gd-based systems \cite{Kong14} and was explained by modelling the specific heat of a $(2J+1)$ multiplet in a mean-field approach \cite{Bouvier91,Blanco91}. The comparison of our specific heat data with literature in terms of absolute values indicates an $\approx\,$10\% to 40\% overestimation of the specific heat for $T\,>\,15\,$K. For $T\,<\,15\,$K, we find an underestimate of $C_{molar}/T$. The reason for this behavior is unclear at present, as eqs.\,\ref{eq:frequency-response} and \ref{eq:frequency-response2} do not allow an underestimate. However, this additional data set on GdNiGe$_3$ also confirms that we are not only highly sensitive in tracing phase transitions even at higher temperatures, but also that we can determine absolute specific heat values within less than a factor of 2 deviation from literature.
\begin{figure}
\includegraphics[width=0.8\textwidth]{GdNiGe3-analysis-050918.pdf}
\caption{(a) Change of jump size in specific heat at $T_N$, $\Delta C_{molar}/T$, and $T_N$ (inset) with pressure; (b) Comparison of estimated magnetic entropy at 0.2 GPa (present experiment, black circles) with literature results\cite{Mun10} at ambient pressure (grey squares). Inset: Estimated magnetic entropy at different pressures up to 1.2\,GPa.}
\label{fig:GdNiGe3-analysis}
\end{figure}
In the following, we focus on the relative evolution of the specific heat with pressure. The overall specific heat values at each temperature are reduced upon applying pressure. Similar to the case of Pb, we assign this reduction to changes of the lattice and electronic specific heat. More importantly, however, we find that the $\lambda$-shaped peak, as well as the low-temperature hump are almost unaffected by pressure. This relates to the position of the anomalies as well as the size and shape of the anomaly. To quantify this statement, we show in Fig.\,\ref{fig:GdNiGe3-analysis} (a) the evolution of the jump size of the $\lambda$-shaped anomaly, $\Delta C_{molar}/T$, as well as the transition temperature $T_N$ (inset) with pressure. Whereas $T_N$ is extracted from the minimum in the derivative of the $C_{molar}/T$ data, $\Delta C_{molar}/T$ is calculated by the difference of $C_{molar}/T$ values at those temperatures at which d($C_{molar}/T$)/d$T$\,=\,0.1\,(d($C_{molar}/T$)/d$T$)$_{T_N}$ (see arrow in Fig.\,\ref{fig:GdNiGe3}). We find a slight decrease of $\Delta C_{molar}/T$ with pressure by $\approx\,-\,$6\,\% and a small increase of $T_N$ by less than 1\,\% within a pressure range of $\approx\,$1\,GPa. We want to emphasize that the relative change in $\Delta C_{molar}/T$ is tiny compared to the specific heat changes observed under pressure in elemental Pb. At present, this tiny change of the specific heat features in GdNiGe$_3$ cannot unequivocally be assigned to a single origin: Either the change is indeed related to changes of physical properties under pressure (see Refs. \citen{Bouvier91,Blanco91} for theoretical discussions of specific heat features in Gd-based compounds on a mean-field level), or the change is an artifact arising from uncertainties in the absolute values determined with the AC calorimetric technique related to changes in the relaxation times $\tau_1$ and $\tau_2$ with pressure. Most likely, both factors actually play a role here, but more importantly none of them gives rise to changes in the specific heat beyond $\approx\,$6\,\% when changing pressure by 1\,GPa. Thus, we can conclude from our specific heat measurements on GdNiGe$_3$ that changes in the specific heat of more than $\approx\,$6\,\% within 1\,GPa, in particular at phase transitions, can reliably be attributed to changes of physical properties, rather than to instrumental artifacts. We also note that in principle the addenda contribution can change with pressure. This change is explicitly included in the error bar given above. However, in general it is reasonable to assume that in first approximation the specific heat of the addenda does not change with pressure.
To extract the magnetic entropy and changes of this quantity with pressure from the present data set, non-magnetic (phononic and electronic) contributions need to be subtracted. These contributions are typically obtained by measuring the specific heat of a non-magnetic reference sample if available. In this case, YNiGe$_3$ serves as a suitable non-magnetic reference system the ambient-pressure specific heat of which was reported in Ref. \citen{Mun10}. As an independent measurement of YNiGe$_3$ with our AC calorimetric setup would require a new assembly with different relaxation times $\tau_1$ and $\tau_2$ which likely give rise to different error in the determination of absolute specific heat values compared to our values on GdNiGe$_3$, this approach to determine the non-magnetic contributions is not suitable in the present case. However, assuming that the overestimation factor is, in first approximation, temperature-independent and contributions from heater and thermometer to our measured specific heat are comparably negligible, we can rescale the reported ambient-pressure data on YNiGe$_3$ such that it almost matches our specific heat data on GdNiGe$_3$ at $T\,\gg\,T_N$ and $p\,\sim\,0.2\,$GPa. This procedure allows us to provide an estimate on the magnetic entropy from our data set (see Fig.\,\ref{fig:GdNiGe3-analysis} (b)). Our estimate of the magnetic entropy yields $S\,\sim\,15.7\,$J/mol/K at $T\,=\,T_N$ which corresponds to 90\% of the expected $S\,=\,R\,\ln(8)$. Even if this analysis can only provide a rough estimate of the entropy due to the uncertainties involved in the determination of the non-magnetic contributions, it confirms that we can determine not only specific heat, but also entropies on the same semi-quantitative level. When now discussing changes of the entropy as a function of pressure, we have to make further assumptions on how the non-magnetic contributions are affected by pressure. The change of the non-magnetic contributions reveals itself e.g. in the measured specific heat at $T\,\gg\,T_N$ which indicates a sizable reduction of $C_{molar}/T$ with $p$. To account for this change, we make the reasonable assumption that changes in the Sommerfeld coefficient $\gamma$ as well as the Debye lattice constant $\beta$ give rise to changes in the non-magnetic specific heat via $C_{molar}/T\,\propto\,\gamma + \beta T^2$. We now apply a temperature-independent as well as a quadratic correction to the $C_{molar}/T$ data of YNiGe$_3$ such that it matches our specific heat data on GdNiGe$_3$ at $T\,\gg\,T_N$ for $p_2$ and $p_3$ individually and subtract the so-derived non-magnetic contributions from our experimental data on GdNiGe$_3$. These estimates of the magnetic entropy are shown in the inset of Fig.\,\ref{fig:GdNiGe3-analysis}. We do not find any significant changes of the estimated magnetic entropy with pressure. This result is consistent with the almost unchanged size of specific heat anomaly $\Delta C_{molar}/T$ with $p$ and provides further evidence that changes of specific heat and entropies with pressure can be estimated with comparably high accuracy.
\subsubsection{Structural/magnetic transition in the iron-pnictide BaFe$_2$As$_2$}
Finally, to further demonstrate the sensitivity of our setup at even higher temperatures (above 100\,K), we present specific heat measurements under pressure on BaFe$_2$As$_2$. This material undergoes a structural and antiferromagnetic transition at $T_{s,N}\,\approx\,130\,$K from a tetragonal-paramagnetic to an orthorhombic-antiferromagnetic state \cite{Rotter08}. In the BaFe$_2$As$_2$ system either chemical substitution (e.g. of Fe by Co) \cite{Ni08,Canfield10,Sefat08} or pressure \cite{Colombier09} suppress this structural-magnetic transition and unconventional superconductivity, with critical temperatures up to $\approx\,22\,$K, emerges.
\begin{figure}
\includegraphics[width=0.8\textwidth]{Ba122-050918.pdf}
\caption{Molar specific heat divided by temperature, $C_{molar}/T$, as a function of temperature $T$ of BaFe$_2$As$_2$ at ambient pressure as well as at $p\,=\,2.05$\,GPa; Inset: Specific heat, $C_{molar}$, of BaFe$_2$As$_2$ at ambient pressure on expanded scale.}
\label{fig:Ba122}
\end{figure}
Figure \ref{fig:Ba122} shows our results for the specific heat of BaFe$_2$As$_2$ in the pressure cell at ambient pressure as well as at $p\,=\,$2.05\,GPa. Our ambient-pressure data show a very sharp peak at the structural-magnetic transition at $T\,\approx\,132\,$K. Even if the size of the phase transition is strongly reduced by the application of $p\,=\,2.05\,$GPa, indicating a strongly reduced entropy change at the phase transition with pressure, we can still clearly resolve the phase transition at a lower temperature $T\,\approx\,112\,$K. The decrease in the phase transition temperature by $\approx\,-10\,$K/GPa agrees very well with earlier reports of the pressure dependence of $T_{s,N}$ based on resistance data \cite{Colombier09}. More importantly, not only can we resolve the high-temperature anomaly, but we can also measure the specific heat across the entire temperature range 5\,K$\,\le\,T\,\le\,$150\,K by using a single thermometer (see inset of Fig.\,\ref{fig:Ba122}). This is a clear advantage of using the Cernox thermometers as temperature sensors for AC specific heat measurements rather than RuO$_2$ thermometers which are inherently sensitive only in a much more limited, low-temperature range. The setup presented here will therefore allow in the future to measure the specific heat under pressure of systems which show a cascade of phase transitions at very different temperatures, such as e.g. the superconducting as well as magnetic-structural transition in Co-doped BaFe$_2$As$_2$.
\section{Summary}
In conclusion, we studied the response of Cernox thermometers to external pressure in piston-pressure cells up to 2\,GPa. These thermometers are frequently used in low-temperature experiments due to their high sensitivity. We find that the sensitivity of the Cernox thermometers remains high under pressures up to 2\,GPa. In addition, they are mechanically robust and survive numerous pressure cycles. Thus, our study shows that these temperature sensors can be used to measure temperatures inside the pressure cell with high accuracy. As a possible application, for which this high sensitivity is essential, we present in detail the use of these thermometers in measuring the specific heat of solids under pressure. By studying three different test cases (elemental Pb, GdNiGe$_3$ and BaFe$_2$As$_2$), we show that the high sensitivity of the Cernox thermometers allows to measure specific heat of solids under pressure across a wide temperature range as well as wide range of entropy changes. Therefore, by using Cernox thermometers, it will be possible in the future to study systems which show a cascade of phase transition across a wide temperature range by specific heat under pressure in a piston-pressure cell, possibly even up to room temperature. In addition, we demonstrate that our setup does not only allow to trace phase transitions, but is also very accurate in determining changes of the specific heat as a function of pressure.
\begin{acknowledgments}
We thank E. Mun and N. Ni for growing the GdNiGe$_3$ and BaFe$_2$As$_2$ crystals used in the study. This work was carried out at Iowa State University and supported by Ames Laboratory, US DOE, under Contract No. DE-AC02-07CH11358. G.D.'s efforts were partially funded by the Gordon and Betty Moore Foundation's EPiQS Initiative through Grant No. GBMF4411. L.X. was supported, in part, by the W. M. Keck Foundation.
\end{acknowledgments}
\bibliographystyle{modaps}
\section{Introduction}
The specific heat of solids is one of the most fundamental thermodynamic quantities. Its temperature dependence reveals important information about the energy scales of electronic, magnetic and lattice degrees of freedom. It is thus an inherently sensitive tool to detect phase transitions which involve one or more of the above-mentioned degrees of freedom. Consequently, various techniques \cite{Stewart83} to measure specific heat in calorimetric experiments at ambient pressure and low temperatures are well established and nowadays even commercially available \cite{Lashley03,acoption}. Typically, these techniques require adiabatic conditions, i.e., an almost ideal decoupling of the sample from the environment, so as to achieve high accuracy in the determination of absolute values of the specific heat. Among these techniques, the relaxation method \cite{Bachmann72} is considered as the standard method in which a heat pulse is given to the sample of interest and the relaxation time towards the initial temperature after switching off the pulse is directly related to the size of the specific heat. Alternatively, in particular in cases where the sample mass is very small, is the AC technique \cite{Sullivan68,Eichler79,Kraftmakher02}, in which the sample is heated by an oscillatory heat source and the resulting temperature oscillation can be used to infer the specific heat, preferred.
As a matter of fact, AC specific heat measurements have proven to be particularly suited for measurements under pressure \cite{Bonilla74,Baloga77,Eichler79,Chen93,Bouquet00,Demuer00,Wilhelm03,Kubota08,Umeo17}. In general, pressure $p$ represents an essential parameter for tuning phase transitions in solids \cite{Jayaraman72,Lorenz05,Imada98,Brando16}. To perform measurements under pressure, the sample has to be embedded into a pressure medium inside a pressure cell. This typically provides a stronger coupling between the sample and the bath (i.e., the oustide of the pressure cell), compared to ambient-pressure experiments performed in vacuum. Whereas the analysis of data taken under pressure with the relaxation method suffers from the huge addenda contribution from pressure cell and medium, the AC technique has a second major advantage in addition to its sensitivity for samples with small masses: the choice of the measurement frequency allows for the measurement on a different timescale than the one determined by the relaxation time to the bath. This can result, to first approximation, in a decoupling of the sample from the bath, thereby paving the way to extraction of absolute values of the specific heat on a semi-quantitative level \cite{Eichler79}.
Typically, in order to perform AC calorimetric experiments in piston-pressure cells up to $p\,\approx\,2\,-\,3\,$GPa, either small ruthenium oxide (RuO$_2$) thermometers \cite{Kubota08,Chen93,Baloga77} or thermocouples \cite{Bonilla74,Wilhelm03,Bouquet00,Demuer00} have been used to detect the temperature oscillations. On one hand, RuO$_2$ thermometers are inherently sensitive only at low temperatures due to their insulating nature; on the other hand they are easy to handle. Thermocouples cover a wider temperature range, but come along with obstacles in their handling. The reliable use of thermocouples requires a firm contact to the sample which often can be only realized by spot-welding of the thermocouple to the sample. Spot-welding is not possible in case of non-metallic samples, but also is often found to be problematic for metallic (and often brittle) samples. In addition, obtaining absolute values of temperature changes with high accuracy can only be guaranteed when the thermal contact to a reference temperature is good which can be challenging in the pressure-cell environment.
In this work, we present another option: using Cernox\cite{Cernox} thermometers as temperature sensors. Cernox sensors combine the advantages of RuO$_2$ thermometers and thermocouples. They are well established at ambient pressure in most low-temperature laboratories, as they provide a high sensitivity over a wide temperature range, as well as short thermal response times. In addition, they can easily be attached to any sample without the need of spot-welding. This being said, it is surprising that, to the best of our knowledge, the properties of Cernox thermometers have not been studied under pressure so far. Our results show that the sensitivity of Cernox thermometers remains large over the entire investigated pressure range up to 2\,GPa and temperature range up to at least 150\,K. We demonstrate that this high sensitivity of the sensors allows us to study the specific heat of solids under pressure (including various types of phase transitions) at a semi-quantitative level. The wide temperature range covered by this setup will allow for the study of larger regions of phase diagrams by specific heat under pressure, with the convenience of using commercially-available temperature sensors.
This paper is organized as follows. First, we describe details of the experimental setup (Sec. \ref{sec:setup}) used in this work to determine the resistance behavior of the Cernox thermometers under pressure, as well as the specific heat of solids under pressure. In the next section (Sec. \ref{sec:Cernoxresistance}), we show one of the main results of this work, namely that the resistance change of the Cernox thermometers under pressures up to 2\,GPa is very modest and readily describable. Following this, we turn to our description of the AC specific heat data obtained using these Cernox thermometers. Therefore we first provide some theoretical background information on AC specific heat measurements and illustrate our measurement protocol in Sec. \ref{sec:ACtheory}. In Sec. \ref{sec:specheatresults} we discuss the results of specific heat under pressure measurements on three different test cases each of which undergoes a different type of phase transition. These systems were chosen to cover a wide range of phase transition temperatures (7 K up to 130 K) as well as removed entropies, thereby demonstrating the versatility of Cernox thermometers for measurements of specific heat under pressure.
\section{Experimental Setup}
\label{sec:setup}
To perform AC calorimetric measurements, the sample of interest is placed between a heater and a thermometer (see Fig.\,\ref{fig:schematicsetup} (a)). In our setup, we use bare Cernox-chip thermometers \cite{Cernox} (type CX-1070 or type CX-1080) as thermometers. The bare chips have dimensions of 0.965\,$\times\,0.762\,\times\,0.203$\,mm$^3$ and are thus ideally suited to fit into standard piston-pressure cells (see Figs.\,\ref{fig:schematicsetup} (b) and (c) for schematic drawings). In addition, they are deposited on a sapphire substrate with low mass (\,$\le\,3\,$mg), thus have themselves a small specific heat, and short response times (1.5\,ms at 4.2\,K). As a heater, we use strain gauges\cite{straingauges} (type FLG-02-23, Tokyo Sokki Kenkyujo Co., Ltd.) which have an active heater area of $\approx\,1\,\times\,1.4$\,mm$^2$. They show an almost temperature-independent resistance as a function of temperature ($R(T,p)\,\approx\,$120\,$\Omega$) and are enclosed in a very thin layer of plastic coating giving rise to a low thermal mass. The samples, with typical masses $\,\sim\,2\,$mg, are cut into plates with dimensions as close as possible to the active heater area dimensions. The thermometer and heater are attached to the sample by using Devcon 5 Minute epoxy (No. 14250) to improve the thermal contact between the individual components and to guarantee sufficient mechanical stability in the pressure cell (shown schematically in Figs.\,\ref{fig:schematicsetup} (a) and (c)). A photograph of the assembly is shown in Fig.\,\ref{fig:schematicsetup}\,(d). The wires of the thermometer and heater are soldered to the wires passing the pressure-cell feedthrough. The thermometer is connected in a pseudo-four-point configuration in which the four wires for current and voltage are reduced to two wires inside the pressure cell. In addition, a Pb sample is mounted on the feedthrough in a four-point configuration for determining its critical temperature, $T_c$, via resistance measurements. The $T_c$ value can be used to determine the pressure, $p$, at low temperature as $T_c(p)$ is well characterized in literature \cite{Bireckoven88}.
The sample end of the feedthrough is placed in a Teflon-cup (see Figs.\,\ref{fig:schematicsetup}\,(b) and (c)) which is filled with the pressure-transmitting medium. In all the experiments presented here, a mixture of 4:6 mixture of light mineral oil:n-pentane \cite{Budko84,Kim11} is used as a pressure-transmitting medium. It solidifies at $p\,\approx\,3-4\,$GPa at room temperature, thus ensuring hydrostatic pressure conditions in the available pressure range. Two anti-extrusion rings made out of phosphor-bronze are used to prevent the teflon from flowing through the interstices when pressurized. The outer cell body is made out of Grade 5 titanium alloy (Ti 6Al-4V) and the inner cylinder out of Ni-Cr-Al alloy. Its design is similar to the one described in Ref. \citen{Budko84}. As Ti 6Al-4V alloy turns superconducting \cite{Ridgeon17} below $\approx\,$5\,K and as a consequence, its thermal conductivity becomes significantly reduced, the sample inside the cell cannot be cooled below 5\,K. Therefore, the use of this particular cell is restricted to temperatures above 5\,K. This issue can be circumvented by using cells made out of a different material, such as CuBe/Ni-Cr-Al.
Pressure is applied by applying a load to the piston at room temperature by a hydraulic press and locked by tightening the lock nut. All measurements shown in this manuscript were performed inside the pressure cell. At the beginning of each pressure cycle the pressure cell was closed hand-tight. Whereas this procedure typically results in a small, but finite pressure at room temperature \cite{Thompson84} ($p\,\lesssim\,0.3\,$GPa), the pressure at low temperature inferred from $T_c$ of Pb is usually very close to 0\,GPa ($p\,\lesssim\,0.04\,$GPa). We refer to this situation in the manuscript as ``ambient-pressure'' condition ($p\,=\,0\,$GPa). All data shown were obtained by increasing pressure to the measured value.
\begin{figure}
\includegraphics[width=0.9\textwidth]{figures/setup-schematics.pdf}
\caption{(a) Schematic diagram of the sample arrangement with heater and thermometer. The heater is supplied with an AC voltage with frequency $\omega/2$ which results in an oscillation of the temperature of the sample with frequency $\omega$; (b) Schematic diagram of the piston-pressure cell used in the present work; (c) Schematic diagram of the sample assembly and Pb sensor inside the teflon cup; (d) Photograph of the heater, sample and thermometer mounted on the pressure-cell feedthrough. The Pb sensor for the determination of the pressure value near 7\,K is also mounted on the feedthrough.}
\label{fig:schematicsetup}
\end{figure}
The measurements were carried out in a cryogen-free cryostat (Janis SHI-950 with a base temperature of $\approx\,3.5\,$K). The probe, used in this cryostat, is wired with phosphor-bronze wires (QT-36, LakeShore Inc.) to ensure low heat flow through the wires. The temperature was controlled continuously between base and room temperature by a LakeShore 336 controller. Temperature was monitored by a calibrated temperature sensor (Cernox-1030) which was placed directly outside the pressure cell by inserting it into a copper bracket. The Cernox thermometer inside the pressure cell was supplied by a DC current (Model CS580, Stanford Research Systems). The size of the DC current was adjusted with temperature such that the voltage limit ($<\,100\,$mV) of the thermometer is not exceeded. The voltage oscillations of the thermometer which result from the AC heating were pre-amplified and filtered (Model SR560, Stanford Research Systems) and then measured with a Lock-In Amplifier (Model SR860, Stanford Research Systems) the internal oscillator of which was used to provide the heating voltage. The heating power was chosen such that the amplitude of the induced temperature oscillation $T_{AC,0}$ (see Fig.\,\ref{fig:schematicsetup} (a)) was typically smaller than 20\,mK. To measure frequency responses (i.e., measurements as a function of frequency, see below), we used the built-in frequency option of this particular Lock-In Amplifier which allows to change the frequency within user-defined frequency limits and sweep rates. The DC resistance of the bare Cernox chips inside the pressure cell was read out simultaneously to each specific heat measurement by a Digital Voltmeter (SIM970, Stanford Research Systems). The resistance of the Pb sensor was measured with a LakeShore AC Resistance Bridge (Model 370). All data are recorded using a custom LabView Program.
\section{Results: Cernox resistance under pressure}
\label{sec:Cernoxresistance}
Figure \ref{fig:Cernoxresistance} (a) summarizes our main result on the behavior of the Cernox (type CX-1080) resistance, $R$, as a function of temperature, $T$, at three selected pressures up to $p\,\approx\,$2\,GPa. These data were taken without any applied heat to the heater inside the pressure cell. At ambient pressure, the resistance shows a typical behavior for Cernox thermometers: the resistance increases with decreasing temperature and the slope d$R$/d$T$ is finite over the entire temperature range which guarantees a sufficient sensitivity of this thermometer from low temperatures ($T\,\approx\,$5\,K) up to high temperatures ($T\,\approx\,$150\,K). Upon increasing pressure, the resistance at a fixed temperature is reduced by $\approx\,$28\% at 5\,K ($\approx\,10\,$\% at 150\,K) at 2\,GPa (see Fig.\,\ref{fig:Cernoxresistance} (b) for change of resistance as a function of pressure at different temperatures). However, the overall behavior as a function of temperature is nearly unchanged. To quantify the sensitivity of the thermometer, one can refer to the dimensionless quantity (d$R$/d$T$)/($R/T$) which is displayed as a function of $T$ in the inset of Fig. \ref{fig:Cernoxresistance} (a) for the same pressure values as the ones depicted in the main panel. This representation shows that this type of Cernox thermometer has an almost temperature- and pressure-independent sensitivity factor of 1.25. Only at low temperatures ($T\,<\,25\,$K), an increased sensitivity up to 1.5 is observed for all pressures. Thus, our measurements clearly show that Cernox thermometers keep their high sensitivity across a wide temperature range up to 2\,GPa. Note that even though we restrict ourselves in this study to temperatures below 150\,K, it is known that (d$R$/d$T$)/($R/T$) of the Cernox thermometers remains almost unchanged at ambient pressure up to room temperature \cite{Cernox}. Based on our results, it is therefore likely that the Cernox thermometers are very sensitive up to room temperature, even under pressure. Moreover, we did not find any indications of changes in the thermometer behavior from one pressure cycle to the next or strong deviations in the behavior of different chips (see Fig.\,\ref{fig:Cernoxresistance} (b)). Nevertheless, the minor differences in the resistance behavior of different chips depicted in Fig.\,\ref{fig:Cernoxresistance} (b) requires a calibration of each chip for each pressure run, as will be described below. All in all, our results show the Cernox chips can be used as temperature sensors in pressure experiments with high reliability and reproducibility.
\begin{figure}
\includegraphics[width=0.9\textwidth]{figures/Cernox-pressure-110518.pdf}
\caption{(a) Resistance, $R$, of a Cernox thermometer, type CX-1080, as a function of temperature, $T$, at three different pressures $p$, ranging from 0\,GPa to 2.05\,GPa; Inset: Sensitivity, defined as $|$d$R/$d$T/(R/T)|$, as a function of temperature for the same pressure values, as depicted in the main panel. The step at $T\,\approx\,$50\,K in the data at 0\,GPa and 2.05\,GPa is likely an artifact associated with changing of thermometer current; (b) Resistance of a Cernox thermometer, type CX-1080, normalized to its ambient-pressure value, $R/R(p\,=\,0)$ at different temperatures between 5\,K and 150\,K. Open and closed symbols represent measurements on two different chips of the same type.}
\label{fig:Cernoxresistance}
\end{figure}
\section{AC Specific heat: Theoretical background and Measurement Protocol}
\label{sec:ACtheory}
In the following, we want to focus on one possible application for which it is essential to determine temperatures with high sensitivity inside the pressure cell, namely when performing measurements of the specific heat of solids under pressure. As we employ here the method of AC calorimetry, this section will provide theoretical background information \cite{Sullivan68,Eichler79} on the AC calorimetric technique which is essential for understanding our measurement protocol.
To extract absolute specific heat values from an AC calorimetry experiment, an understanding of the heat flow from the heater to the various components in the system is needed. On one hand, the heat is transferred from the heater (specific heat $C_H$) through the sample ($C_S$) to the thermometer ($C_{\Theta}$) which are connected via finite thermal conductances. In the following, the thermal conductances between sample and heater as well as thermometer and sample which govern the heat transfer are denoted as $\lambda_{HS}$ and $\lambda_{\Theta S}$, respectively. On the other hand, each component is also coupled to a bath with temperature $T_B$ (which corresponds to the temperature on the outside of the pressure cell) by finite thermal conductances, denoted by $\lambda_H$, $\lambda_S$ and $\lambda_\Theta$. A block diagram of this arrangement is shown in Fig.\,\ref{fig:frequencydependence} (a). Note that the couplings $\lambda_H$, $\lambda_S$ and $\lambda_{\Theta}$ are non-negligible in the present case, as the sample has to be embedded in a pressure medium inside the pressure cell for measurements under pressure. This, in general, means that the absolute values of the specific heat cannot be determined under pressure with high accuracy. Nonetheless, we will show below that the AC technique implemented in this work allows for a determination of specific heat value under pressure at a semi-quantitative level by choosing the right measurement frequency.
When the heater is supplied with an AC voltage $U(t)\,=\,U_0 \sin(\frac{\omega}{2} t)$, it gives rise to an AC heating power $P(t)\,=\,P_0 \sin^2(\frac{\omega}{2}t)$ and the temperature of the sample will respond in the following manner:
\begin{equation}
T(t) \,=\, T_{DC} + T_{AC}(t).
\end{equation}
$T_{DC}$ refers here to the time-independent increase of the sample temperature with respect to the bath, which is determined by the heating power as well as the coupling to the bath via $T_{DC}\,=\,T_B+\frac{P_0}{2\lambda_S}$. The second term $T_{AC}(t)\,=\,T_{AC,0} \sin(\omega t + \phi)$ describes the temperature oscillation of the sample which oscillates with twice the driving frequency of the heater. The amplitude of this oscillation $T_{AC,0}$ contains the information about the specific heat of the sample $C_S$. The sensitivity of an AC specific heat setup is particularly high for small samples (i.e. with small $C_S$), as $T_{AC,0}$ is inversely proportional to $C_S$. In detail, the relation of $T_{AC,0}$ to $C_S$ for a realistic model with finite thermal conductances was discussed in the works of Sullivan and Seidel (Ref. \citen{Sullivan68}), as well as Eichler (Ref. \citen{Eichler79}), and reads as
\begin{eqnarray}
T_{AC,0} \,&=&\, \frac{P_0}{2\omega C}\,\cdot\,F(\omega) \label{eq:frequency-response} \\
\textnormal{with\ } F(\omega)\,&=&\,[1+2\,\cdot\,(\frac{\lambda_H}{\lambda_{HS}}+\frac{\lambda_\Theta}{\lambda_{\Theta S}})+\frac{1}{(\omega \tau_1)^2}+(\omega \tau_2)^2]^{-1/2} \label{eq:frequency-response2}\\
\textnormal{and\ } C &=& C_H + C_\Theta + C_S, \tau_1=\frac{C}{\lambda_S}, \\
\tau_2 &=& \sqrt{\tau_H^2+\tau_\Theta^2} \textnormal{\ with \ } \tau_H\,=\,C_H/\lambda_{HS} \textnormal{\ and \ } \tau_\Theta = C_\Theta/\lambda_{\Theta S}.
\end{eqnarray}
Thus, whenever the measurement frequency is choosen such that $(\omega \tau_1)^2\,\gg\,1$ and $(\omega \tau_2)^2\,\ll\,1$, with $\tau_1$ and $\tau_2$ corresponding to the thermal relaxation times to the bath and within the assembly of heater, sample and thermometer, respectively, then $F(\omega)\,\approx\,[1+2\,\cdot\,(\frac{\lambda_H}{\lambda_{HS}}+\frac{\lambda_\Theta}{\lambda_{\Theta S}})]^{-1/2}$. The error in determination of absolute values then is mainly determined by the ratios $\frac{\lambda_H}{\lambda_{HS}}$ and $\frac{\lambda_\Theta}{\lambda_{\Theta S}}$. However, sample, heater and thermometer are in intimate contact, whereas the heat path to the bath (i.e., the outside of the pressure cell) is long. This implies due to the geometrical arrangement that, to a first approximation, $\lambda_H\,\ll\,\lambda_{HS}$ and $\lambda_\Theta\,\ll\,\lambda_{\Theta S}$ (and we will show below that this assumption is verified in our setup), and therefore $F(\omega)\,\approx\,1$. It then follows that $T_{AC,0}\,=\,\frac{P_0}{2\omega C}$.
The frequency which meets these criteria is called the optimal measurement frequency $\omega_{opt}$. As $\tau_1$ and $\tau_2$ depend on the specific heat of the sample, as well as on thermal conductances $\lambda_{HS}, \lambda_S$ and $\lambda_{\Theta S}$, $\omega_{opt}$ will in general be a function of temperature and pressure, and will differ from sample assembly to sample assembly. Correspondingly, $\omega_{opt}$ has to be determined experimentally for each sample, temperature and pressure individually, prior to each measurement of the specific heat. It can be shown that $\omega_{opt}$ is the frequency at which $F(\omega)$ is maximal. As suggested by eq. \ref{eq:frequency-response}, direct experimental access to $F(\omega)$ is provided by measuring the frequency dependence of the quantity $\omega\,\cdot\,T_{AC,0}$ (called frequency response hereafter). In Figs. \ref{fig:frequencydependence} (b) and (c) we show examples of the frequency responses, normalized to their respective maximum, recorded with our setup when measuring the specific heat of elemental Pb (The specific heat results on Pb will be discussed in Sec.\,\ref{sec:specheatresults} in more detail.). First, we compare in Fig.\,\ref{fig:frequencydependence}\,(b) the frequency response, taken at $T\,=\,6$\,K at two different pressures ($p\,=\,0\,$GPa and 1.97\,GPa). Each frequency response (normalized to its maximum value) reveals a broad maximum at $\approx\,100\,$Hz and 300\,Hz, respectively, which we assign to the optimal measurement frequencies $\omega_{opt}$. Note that a broad maximum (or even a wide plateau) suggests that $(\omega \tau_1)^2\,\gg\,1$ and $(\omega \tau_2)^2\,\ll\,1$ across a wide frequency range which minimizes errors in the determination of absolute values of the specific heat. The observation of a broad maximum is therefore crucial for the determination of absolute values of the specific heat under pressure on a semi-quantitative level, as achieved with our setup. At the same time, at a fixed pressure, as shown in Fig.\,\ref{fig:frequencydependence}\,(c) for $p\,=\,$1.97\,GPa, we find that the broad maximum in the frequency response and thereby $\omega_{opt}$ shifts to lower frequencies with increasing temperature. The evolution of $\omega_{opt}$, determined from the numerical derivation of the frequency response data, with $T$ and $p$ is summarized in Fig.\,\ref{fig:frequencydependence}\,(d).
The knowledge of the frequency response allows us to extract the relaxation times $\tau_1$ and $\tau_2$ of this particular assembly at different pressures. The solid lines in Fig.\,\ref{fig:frequencydependence}\,(b) show a fit of eq.\,\ref{eq:frequency-response2} to our experimental data, taken at 6\,K. The fits, which were performed with keeping $(\frac{\lambda_H}{\lambda_{HS}}+\frac{\lambda_\Theta}{\lambda_{\Theta S}})$ fixed to 0, are in very good agreement with our experimental data set. They yield $\tau_1\,=\,(0.047\,\pm\,0.001)\,$s and $\tau_2\,=\,(0.0016\,\pm\,0.0001)\,$s at ambient pressure and $\tau_1\,=\,(0.015\,\pm\,0.001)\,$s and $\tau_2\,=\,(0.0009\,\pm\,0.0001)\,$s at $p\,=\,1.97\,$GPa. Thus, the optimal measurement frequencies $\omega_{opt}$ fulfill the criteria mentioned above as $(\omega_{opt} \tau_1)^2\,\approx\,22\,\gg\,1$ and $(\omega_{opt} \tau_2)^2\,\approx\,0.02\,\ll\,1$ at $p\,=\,0\,$GPa and $(\omega_{opt} \tau_1)^2\,\approx\,20\,\gg\,1$ and $(\omega_{opt} \tau_2)^2\,\approx\,0.07\,\ll\,1$ at $p\,=\,1.97\,$GPa. Our fitting results indicate that both relaxation times decrease with increasing pressure. This tendency is naturally expected, as the coupling to the bath, but also the coupling within the assembly likely increase under compression. Therefore, the increased optimal frequency $\omega_{opt}$ with applied $p$ is directly a consequence of the decreased relaxation times. The temperature dependence of $\omega_{opt}$ is less intuitive to understand as it depends on the temperature-dependent changes of specific heat as well as thermal conductivity of sample, heater as well as thermometer.
It should be noted that the error in the determination of the absolute value of the specific heat can be estimated from the knowledge of $\tau_1$ and $\tau_2$. Equations \ref{eq:frequency-response} and \ref{eq:frequency-response2} suggest that any finite $\tau_1$ as well as any non-zero $\tau_2$ will give rise to an overestimation of the specific heat value by the factor $[1+\frac{1}{(\omega \tau_1)^2}+(\omega \tau_2)^2]^{1/2}$, if $\frac{\lambda_H}{\lambda_{HS}}+\frac{\lambda_\Theta}{\lambda_{\Theta S}}\,\approx\,$0. Our results of $\tau_1$ and $\tau_2$ correspond to an overestimate of specific heat by $\approx\,$3\,\% at ambient pressure, and $\approx\,$5\,\% at 1.97 GPa by our setup. This estimate shows that our setup can, in principle, deliver absolute values on a semi-quantitative level, despite a non-negligible coupling to the bath. Importantly, the analysis performed here shows that the overestimation of specific heat does not significantly change with pressure. This allows for the determination of changes (especially relative changes) of specific heat under pressure with higher accuracy. We confirm these conclusions from the analysis of the frequency response in Sec. \ref{sec:specheatresults}, where we present specific heat under pressure data on three different test cases and compare with ambient-pressure literature data taken under adiabatic conditions.
The theoretical background information given here explains the measurement protocol which we follow to determine the specific heat of a sample using the AC technique. It includes in total three separate, sequential temperature sweeps. First, we need to calibrate the Cernox thermometers inside the pressure cell at a specific pressure to quantify the DC temperature increase $T_{DC}$ of the sample which results from applying heat to the heater inside the cell. To this end, we place a calibrated thermometer outside on the pressure cell and record the resistance of the Cernox thermometer inside the pressure cell upon slow warming with a rate of $\approx\,0.25\,$K/min without any voltage applied to the heater inside the cell (see Sec.\,\ref{sec:Cernoxresistance}). In the second temperature sweep, we record the frequency response $\omega\,\cdot\,T_{AC,0}$ vs. $\omega$ as a function of temperature for the same, specific pressure. From this data, we extract $\omega_{opt}$ as a function of $T$ and typically fit this smooth data set with an exponential function $\omega_{opt}\,=\,\omega_0+A\exp(-T/t_1)$ with free parameters $\omega_0$, $A$ and $t_1$ (see grey lines in Fig.\,\ref{fig:frequencydependence} (d)). Within our measurement program, we adjust the measurement frequency continuously with temperature according to this exponential function during the third temperature sweep for a specific pressure. This ensures that the AC temperature oscillation $T_{AC,0}$ as a function of $T$ is always measured at the optimal measurement frequency which then allows us to infer the specific heat on a semi-quantitative level.
\begin{figure}
\includegraphics[width=0.9\textwidth]{figures/Pb_optimalfrequency_090518.pdf}
\caption{(a) Schematic diagram illustrating heat flows from the sample to the heater (governed by the thermal conductivity $\lambda_{HS}$), from the sample to the thermometer ($\lambda_{\Theta S}$), and from sample, heater and thermometer to the bath ($\lambda_S$, $\lambda_H$ and $\lambda_\Theta$); (b) Normalized frequency response, i.e., the product of frequency $\omega$ and oscillation amplitude $T_{AC,0}$ normalized to its maximum value $(\omega T_{AC,0})_{max}$ vs. $\omega$, for a Pb sample at $T\,=\,6$\,K and $p\,=\,0\,$GPa and 1.97\,GPa; (c) Normalized frequency response for a Pb sample at different temperatures between 5\,K and 9\,K at $p\,=\,1.97\,$GPa; (d) Evolution of the optimal measurement frequency $\omega_{opt}$ as a function of temperature and pressure, obtained from the data presented in (b) and (c) (for details, see main text). Grey lines represent exponential fits to the $\omega_{opt}$ vs. $p$ data sets.}
\label{fig:frequencydependence}
\end{figure}
\section{Specific heat under pressure: Results}
\label{sec:specheatresults}
In the following, we demonstrate the wide applicability of the Cernox thermometers in measurements of specific heat under pressure by examining three test cases with very different transition temperatures, ranging from $T\,\approx\,7\,$K (superconducting transition in Pb) up to $T\,\approx\,130\,$K (magnetostructural transition in BaFe$_2$As$_2$), as well as very different amounts of entropy change.
\subsubsection{Superconducting phase transition in elemental Pb}
The first sample for a study of specific heat under pressure chosen here is elemental lead (Pb) which undergoes an ambient-pressure superconducting transition at a critial temperature $T_c\,=\,7.2\,$K. The shift of $T_c$ with pressure is well characterized in literature \cite{Bireckoven88} and therefore often utilized as a manometer at low temperatures.
\begin{figure}
\includegraphics[width=0.8\textwidth]{figures/Pb-050918.pdf}
\caption{(a) Molar specific heat $C_{molar}$ of elemental Pb as a function of temperature $T$ at four different pressures up to 1.97\,GPa; (b,c) Comparison of $C_{molar}(T)$ of Pb and the resistance $R_{Pb}(T)$ of the Pb pressure sensor at a pressure of 0 GPa (b) and 1.97\,GPa (c).}
\label{fig:Pb}
\end{figure}
Figure \ref{fig:Pb} (a) shows our results of the specific heat, $C_{molar}$, of Pb at different pressures up to 1.97\,GPa. At all pressures, we find a jump-like change of $C_{molar}$ at a critical temperature $T_c$. This feature is characteristic for the mean-field type phase transition into the superconducting state in BCS superconductors. The critical temperature, extracted from our $C_{molar}$ data, is suppressed with increasing $p$, consistent with literature results \cite{Bireckoven88}. In addition, the overall specific heat is reduced upon pressurization, likely due to a combination of changes in the electronic density of states as well as lattice stiffening (see below for more details).
To demonstrate the high accuracy in the determination of phase transition temperatures from our specific heat data, we compare in Figs. \ref{fig:Pb} (b) and (c) the specific heat of the Pb sample, placed between heater and thermometer, with the resistance of the Pb manometer, $R_{Pb}$, at lowest pressure ($p_1\,=\,0\,$GPa) and highest pressure ($p_4\,=\,1.97\,$GPa) of our experiment. At both pressures, the midpoint of the jump in $C_{molar}$ occurs at the same temperature at which the resistance clearly shows a jump-like change into the superconducting state. This also demonstrates that there are no significant pressure gradients in our pressure cell.
Next, we want to discuss to which extent our setup delivers a semi-quantitative determination of the specific heat of solids by comparing our results to literature results \cite{Shiffman63} on Pb (see Fig. \ref{fig:Pb-analysis}). Our data overestimates the absolute specific heat value by $\approx\,12\,\%$, compared to the literature results from Ref. \citen{Shiffman63}. As outlined in Sec.\,\ref{sec:ACtheory}, an overestimate of absolute specific heat values determined with the AC technique is a consequence of finite relaxation times $\tau_1$ and $\tau_2$. The overestimation factor of about 3\,\%, estimated from an analysis of the frequency responses in Sec. \,\ref{sec:ACtheory}, is of similar size as the overestimation found here from the comparison with literature data on Pb. Note that we did not correct our data for the specific heat of the addenda, i.e., of thermometer, heater and the tiny layers of glue. These additional contributions to the measured specific heat, which can be as large as 50\,\% of the total measured specific heat depending on the specific sample, its size, mass and shape (estimated by measuring the size of the addenda at ambient pressure using the relaxation-time method), likely give rise to the slightly larger overestimation of 12\,\% found empirically here. Clearly, despite the strong coupling to the bath due to the pressure medium and uncertainties in the size of the addenda, our data resembles literature results on a semi-quantitative level, i.e., within less than approximately a factor of 2. This upper limit was estimated empirically in the study of the three different test cases presented in this manuscript. The superconducting jump size extracted from our data at ambient pressure amounts to $\Delta C_{sc}\,\approx\,(44.6\,\pm\,0.5)\,$mJ/mol/K \cite{Shiffman63,Clement52}. This value is slightly smaller than reported values in literature ($\Delta C_{sc}\,=\,$52.9\,mJ/mol/K up to 57.5\,mJ/mol/K), but nevertheless matches on the same semi-quantitative level.
Upon pressurization, we find a significant reduction of $\Delta C_{sc}$ with increasing $p$ down to $\approx\,(29.0\,\pm\,0.5)\,$mJ/mol/K at 1.97\,GPa (see Fig.\,\ref{fig:Pb-analysis} (b)). For superconductors, the change in $\Delta C_{sc}$ is related on the one hand to a change in $T_c$ as well as to a change in the density of states at the Fermi level $N(E_F)$ \cite{Carbotte90}. Figure \ref{fig:Pb-analysis} (b) also includes a plot of $\Delta C_{sc}/T_c$ as a function of $T_c$. The strong change of $\Delta C_{sc}/T_c$ with $p$ by $\approx\,-\,25\,\%$ indicates that most of the change of $\Delta C_{sc}$ with $p$ can be attributed to changes of $N(E_F)$ with $p$, rather than to changes of $T_c$. Unfortunately, no literature data on the change of $N(E_F)$ in Pb with $p$ is available. Also the determination of the change of $N(E_F)$ under $p$ by extracting the Sommerfeld coefficient $\gamma$ from our specific heat data turns out to be not reliable due to the relatively high $T_c$ of Pb combined with a relatively low Debye temperature $\Theta_D\,\approx\,100\,$K at ambient pressure. Thus, we performed density-functional theory (DFT) calculations \cite{Hohenberg64,Kohn65} of the band structure of Pb up to 2\,GPa using PBEsol as exchange-correlation functional with spin-orbit coupling (SOC) effect as implemented in VASP \cite{Kresse96,Kresse96b}. At zero pressure, the theoretical lattice constant of 4.934\,\AA\ agrees very well with the experimental values of 4.95\,\AA. At 2 GPa, the lattice constant is reduced to 4.872\,\AA. We find a decrease of $N(E_F)$ from 0.5303\,states/eV/cell to 0.5121 \,states/eV/cell by 2\,GPa which corresponds to $\approx\,-\,3.5$\,\%. Even though this value is smaller than the one inferred from our specific heat measurements, both results are consistent in inferring a decrease of $N(E_F)$ with pressure. This supports our conclusion that in case of Pb changes of the specific heat anomaly $\Delta C_{sc}$ under $p$ result from a decrease of $N(E_F)$ with pressure.
\begin{figure}
\includegraphics[width=0.8\textwidth]{figures/Pb_analysis-050918.pdf}
\caption{(a) Comparison of ambient-pressure literature data \cite{Shiffman63} on the specific heat $C_{molar}$ of elemental Pb (grey symbols) and the specific heat obtained in the present work in the pressure cell at ambient pressure (black solid line); (b) Evolution of the superconducting jump size in the specific heat $\Delta C_{sc}$, as well as the jump size normalized to the critical temperature, $\Delta C_{sc}/T_c$, with $T_c$.}
\label{fig:Pb-analysis}
\end{figure}
\subsubsection{Antiferromagnetic transition in the rare-earth compound GdNiGe$_3$}
The specific heat anomaly at the superconducting transition in Pb as well as the transition temperature respond strongly to application of external pressure. In addition, the amount of entropy change is relatively small. For the next system, we chose GdNiGe$_3$ anticipating a weak response to pressure and a large change in entropy ($\approx\,R \ln(8)$) \cite{Mun10}. This allows us to show that changes of the absolute values of specific heat under pressure are not a result of an artifact due to modified coupling to the bath or within the assembly of sample, heater and thermometer, i.e., due to changing $\tau_1$ and $\tau_2$. This in turn allows us to establish a high accuracy in the determination of \textit{changes} of the specific heat under pressure. At the same time, a system with a phase transition occurring at higher transition temperature compared to the superconducting transition in elemental Pb is desired to prove high sensitivity of our setup at even higher temperatures.
The rare-earth based GdNiGe$_3$ system has a single antiferromagnetic (afm) transition\cite{Mun10} at $T_N\,\approx\,$26\,K. Importantly, as the moment-carrying Gd is trivalent in this compound and therefore has a Hund's rule $J\,=\,S\,=\,7/2$ ground state ($L\,=\,0$), the compound lacks any magneto-crystalline anisotropy or splitting of the Hund's rule ground state multiplet. Experiments \cite{Mun10} confirmed that GdNiGe$_3$ shows an almost isotropic susceptibility in the paramagnetic state with an effective moment $\mu_{eff}\,=\,8.0\,\mu_B$/Gd$^{3+}$, close to the free-ion value of 7.94\,$\mu_B$/Gd$^{3+}$. Correspondingly, specific heat measurements \cite{Mun10} showed a single $\lambda$-shaped peak at $T_N$ (see grey symbols in Fig.\,\ref{fig:GdNiGe3} for a reproduction of these data). The magnetic entropy, $S$, extracted from measurements of the specific heat was found to be almost constant at $T\,>\,T_N$ with $S\,=\,$17\,J/(mol$\cdot$K), i.e., close to the expected value of $R \ln(8)$. This result is fully consistent with the absence of crystal-field effects in this compound. As the magnetism of this compound can be well understood in terms of localized 4f moments which interact via RKKY (Ruderman-Kittel-Kasuya-Yosida) interaction \cite{Ruderman54}, the response to hydrostatic pressure is expected to be relatively weak. This, together with the well-defined entropy in the paramagnetic state and a high transition temperature, makes this system a suitable reference system for a study of the specific heat under pressure.
\begin{figure}
\includegraphics[width=0.8\textwidth]{figures/GdNiGe3-050918.pdf}
\caption{Molar specific heat divided by temperature $C_{molar}/T$ as a function of temperature $T$ of GdNiGe$_3$ at different pressures up to 1.2 GPa. For comparison, literature data at ambient pressure \cite{Mun10} on this compound are shown in grey. The arrow indicates exemplary the jump size at the antiferromagnetic transition, $\Delta C_{molar}/T$, at lowest pressure $p\,\sim\,0.2$\,GPa (for a definition of criterion and evolution with pressure, see main text). }
\label{fig:GdNiGe3}
\end{figure}
The results of our specific heat study on GdNiGe$_3$ under pressure are shown in Fig.\,\ref{fig:GdNiGe3} in a $C_{molar}/T$ vs. $T$ representation. For comparison, we included the literature specific heat data on this compound at ambient pressure, taken from Ref. \citen{Mun10}. At all measured pressures, our data nicely reveal the $\lambda$-shaped phase transition anomaly at $T\,\approx\,26\,$K. In addition, we also find a small hump in the specific heat below 10\,K. Such a hump in the specific heat at temperatures well below the ordering temperatures was found in various Gd-based systems \cite{Kong14} and was explained by modelling the specific heat of a $(2J+1)$ multiplet in a mean-field approach \cite{Bouvier91,Blanco91}. The comparison of our specific heat data with literature in terms of absolute values indicates an $\approx\,$10\% to 40\% overestimation of the specific heat for $T\,>\,15\,$K. For $T\,<\,15\,$K, we find an underestimate of $C_{molar}/T$. The reason for this behavior is unclear at present, as eqs.\,\ref{eq:frequency-response} and \ref{eq:frequency-response2} do not allow an underestimate. However, this additional data set on GdNiGe$_3$ also confirms that we are not only highly sensitive in tracing phase transitions even at higher temperatures, but also that we can determine absolute specific heat values within less than a factor of 2 deviation from literature.
\begin{figure}
\includegraphics[width=0.8\textwidth]{figures/GdNiGe3-analysis-050918.pdf}
\caption{(a) Change of jump size in specific heat at $T_N$, $\Delta C_{molar}/T$, and $T_N$ (inset) with pressure; (b) Comparison of estimated magnetic entropy at 0.2 GPa (present experiment, black circles) with literature results\cite{Mun10} at ambient pressure (grey squares). Inset: Estimated magnetic entropy at different pressures up to 1.2\,GPa.}
\label{fig:GdNiGe3-analysis}
\end{figure}
In the following, we focus on the relative evolution of the specific heat with pressure. The overall specific heat values at each temperature are reduced upon applying pressure. Similar to the case of Pb, we assign this reduction to changes of the lattice and electronic specific heat. More importantly, however, we find that the $\lambda$-shaped peak, as well as the low-temperature hump are almost unaffected by pressure. This relates to the position of the anomalies as well as the size and shape of the anomaly. To quantify this statement, we show in Fig.\,\ref{fig:GdNiGe3-analysis} (a) the evolution of the jump size of the $\lambda$-shaped anomaly, $\Delta C_{molar}/T$, as well as the transition temperature $T_N$ (inset) with pressure. Whereas $T_N$ is extracted from the minimum in the derivative of the $C_{molar}/T$ data, $\Delta C_{molar}/T$ is calculated by the difference of $C_{molar}/T$ values at those temperatures at which d($C_{molar}/T$)/d$T$\,=\,0.1\,(d($C_{molar}/T$)/d$T$)$_{T_N}$ (see arrow in Fig.\,\ref{fig:GdNiGe3}). We find a slight decrease of $\Delta C_{molar}/T$ with pressure by $\approx\,-\,$6\,\% and a small increase of $T_N$ by less than 1\,\% within a pressure range of $\approx\,$1\,GPa. We want to emphasize that the relative change in $\Delta C_{molar}/T$ is tiny compared to the specific heat changes observed under pressure in elemental Pb. At present, this tiny change of the specific heat features in GdNiGe$_3$ cannot unequivocally be assigned to a single origin: Either the change is indeed related to changes of physical properties under pressure (see Refs. \citen{Bouvier91,Blanco91} for theoretical discussions of specific heat features in Gd-based compounds on a mean-field level), or the change is an artifact arising from uncertainties in the absolute values determined with the AC calorimetric technique related to changes in the relaxation times $\tau_1$ and $\tau_2$ with pressure. Most likely, both factors actually play a role here, but more importantly none of them gives rise to changes in the specific heat beyond $\approx\,$6\,\% when changing pressure by 1\,GPa. Thus, we can conclude from our specific heat measurements on GdNiGe$_3$ that changes in the specific heat of more than $\approx\,$6\,\% within 1\,GPa, in particular at phase transitions, can reliably be attributed to changes of physical properties, rather than to instrumental artifacts. We also note that in principle the addenda contribution can change with pressure. This change is explicitly included in the error bar given above. However, in general it is reasonable to assume that in first approximation the specific heat of the addenda does not change with pressure.
To extract the magnetic entropy and changes of this quantity with pressure from the present data set, non-magnetic (phononic and electronic) contributions need to be subtracted. These contributions are typically obtained by measuring the specific heat of a non-magnetic reference sample if available. In this case, YNiGe$_3$ serves as a suitable non-magnetic reference system the ambient-pressure specific heat of which was reported in Ref. \citen{Mun10}. As an independent measurement of YNiGe$_3$ with our AC calorimetric setup would require a new assembly with different relaxation times $\tau_1$ and $\tau_2$ which likely give rise to different error in the determination of absolute specific heat values compared to our values on GdNiGe$_3$, this approach to determine the non-magnetic contributions is not suitable in the present case. However, assuming that the overestimation factor is, in first approximation, temperature-independent and contributions from heater and thermometer to our measured specific heat are comparably negligible, we can rescale the reported ambient-pressure data on YNiGe$_3$ such that it almost matches our specific heat data on GdNiGe$_3$ at $T\,\gg\,T_N$ and $p\,\sim\,0.2\,$GPa. This procedure allows us to provide an estimate on the magnetic entropy from our data set (see Fig.\,\ref{fig:GdNiGe3-analysis} (b)). Our estimate of the magnetic entropy yields $S\,\sim\,15.7\,$J/mol/K at $T\,=\,T_N$ which corresponds to 90\% of the expected $S\,=\,R\,\ln(8)$. Even if this analysis can only provide a rough estimate of the entropy due to the uncertainties involved in the determination of the non-magnetic contributions, it confirms that we can determine not only specific heat, but also entropies on the same semi-quantitative level. When now discussing changes of the entropy as a function of pressure, we have to make further assumptions on how the non-magnetic contributions are affected by pressure. The change of the non-magnetic contributions reveals itself e.g. in the measured specific heat at $T\,\gg\,T_N$ which indicates a sizable reduction of $C_{molar}/T$ with $p$. To account for this change, we make the reasonable assumption that changes in the Sommerfeld coefficient $\gamma$ as well as the Debye lattice constant $\beta$ give rise to changes in the non-magnetic specific heat via $C_{molar}/T\,\propto\,\gamma + \beta T^2$. We now apply a temperature-independent as well as a quadratic correction to the $C_{molar}/T$ data of YNiGe$_3$ such that it matches our specific heat data on GdNiGe$_3$ at $T\,\gg\,T_N$ for $p_2$ and $p_3$ individually and subtract the so-derived non-magnetic contributions from our experimental data on GdNiGe$_3$. These estimates of the magnetic entropy are shown in the inset of Fig.\,\ref{fig:GdNiGe3-analysis}. We do not find any significant changes of the estimated magnetic entropy with pressure. This result is consistent with the almost unchanged size of specific heat anomaly $\Delta C_{molar}/T$ with $p$ and provides further evidence that changes of specific heat and entropies with pressure can be estimated with comparably high accuracy.
\subsubsection{Structural/magnetic transition in the iron-pnictide BaFe$_2$As$_2$}
Finally, to further demonstrate the sensitivity of our setup at even higher temperatures (above 100\,K), we present specific heat measurements under pressure on BaFe$_2$As$_2$. This material undergoes a structural and antiferromagnetic transition at $T_{s,N}\,\approx\,130\,$K from a tetragonal-paramagnetic to an orthorhombic-antiferromagnetic state \cite{Rotter08}. In the BaFe$_2$As$_2$ system either chemical substitution (e.g. of Fe by Co) \cite{Ni08,Canfield10,Sefat08} or pressure \cite{Colombier09} suppress this structural-magnetic transition and unconventional superconductivity, with critical temperatures up to $\approx\,22\,$K, emerges.
\begin{figure}
\includegraphics[width=0.8\textwidth]{figures/Ba122-050918.pdf}
\caption{Molar specific heat divided by temperature, $C_{molar}/T$, as a function of temperature $T$ of BaFe$_2$As$_2$ at ambient pressure as well as at $p\,=\,2.05$\,GPa; Inset: Specific heat, $C_{molar}$, of BaFe$_2$As$_2$ at ambient pressure on expanded scale.}
\label{fig:Ba122}
\end{figure}
Figure \ref{fig:Ba122} shows our results for the specific heat of BaFe$_2$As$_2$ in the pressure cell at ambient pressure as well as at $p\,=\,$2.05\,GPa. Our ambient-pressure data show a very sharp peak at the structural-magnetic transition at $T\,\approx\,132\,$K. Even if the size of the phase transition is strongly reduced by the application of $p\,=\,2.05\,$GPa, indicating a strongly reduced entropy change at the phase transition with pressure, we can still clearly resolve the phase transition at a lower temperature $T\,\approx\,112\,$K. The decrease in the phase transition temperature by $\approx\,-10\,$K/GPa agrees very well with earlier reports of the pressure dependence of $T_{s,N}$ based on resistance data \cite{Colombier09}. More importantly, not only can we resolve the high-temperature anomaly, but we can also measure the specific heat across the entire temperature range 5\,K$\,\le\,T\,\le\,$150\,K by using a single thermometer (see inset of Fig.\,\ref{fig:Ba122}). This is a clear advantage of using the Cernox thermometers as temperature sensors for AC specific heat measurements rather than RuO$_2$ thermometers which are inherently sensitive only in a much more limited, low-temperature range. The setup presented here will therefore allow in the future to measure the specific heat under pressure of systems which show a cascade of phase transitions at very different temperatures, such as e.g. the superconducting as well as magnetic-structural transition in Co-doped BaFe$_2$As$_2$.
\section{Summary}
In conclusion, we studied the response of Cernox thermometers to external pressure in piston-pressure cells up to 2\,GPa. These thermometers are frequently used in low-temperature experiments due to their high sensitivity. We find that the sensitivity of the Cernox thermometers remains high under pressures up to 2\,GPa. In addition, they are mechanically robust and survive numerous pressure cycles. Thus, our study shows that these temperature sensors can be used to measure temperatures inside the pressure cell with high accuracy. As a possible application, for which this high sensitivity is essential, we present in detail the use of these thermometers in measuring the specific heat of solids under pressure. By studying three different test cases (elemental Pb, GdNiGe$_3$ and BaFe$_2$As$_2$), we show that the high sensitivity of the Cernox thermometers allows to measure specific heat of solids under pressure across a wide temperature range as well as wide range of entropy changes. Therefore, by using Cernox thermometers, it will be possible in the future to study systems which show a cascade of phase transition across a wide temperature range by specific heat under pressure in a piston-pressure cell, possibly even up to room temperature. In addition, we demonstrate that our setup does not only allow to trace phase transitions, but is also very accurate in determining changes of the specific heat as a function of pressure.
\begin{acknowledgments}
We thank E. Mun and N. Ni for growing the GdNiGe$_3$ and BaFe$_2$As$_2$ crystals used in the study. This work was carried out at Iowa State University and supported by Ames Laboratory, US DOE, under Contract No. DE-AC02-07CH11358. G.D.'s efforts were partially funded by the Gordon and Betty Moore Foundation's EPiQS Initiative through Grant No. GBMF4411. L.X. was supported, in part, by the W. M. Keck Foundation.
\end{acknowledgments}
\bibliographystyle{modaps}
\section{Introduction}
The specific heat of solids is one of the most fundamental thermodynamic quantities. Its temperature dependence reveals important information about the energy scales of electronic, magnetic and lattice degrees of freedom. It is thus an inherently sensitive tool to detect phase transitions which involve one or more of the above-mentioned degrees of freedom. Consequently, various techniques \cite{Stewart83} to measure specific heat in calorimetric experiments at ambient pressure and low temperatures are well established and nowadays even commercially available \cite{Lashley03,acoption}. Typically, these techniques require adiabatic conditions, i.e., an almost ideal decoupling of the sample from the environment, so as to achieve high accuracy in the determination of absolute values of the specific heat. Among these techniques, the relaxation method \cite{Bachmann72} is considered as the standard method in which a heat pulse is given to the sample of interest and the relaxation time towards the initial temperature after switching off the pulse is directly related to the size of the specific heat. Alternatively, in particular in cases where the sample mass is very small, is the AC technique \cite{Sullivan68,Eichler79,Kraftmakher02}, in which the sample is heated by an oscillatory heat source and the resulting temperature oscillation can be used to infer the specific heat, preferred.
As a matter of fact, AC specific heat measurements have proven to be particularly suited for measurements under pressure \cite{Bonilla74,Baloga77,Eichler79,Chen93,Bouquet00,Demuer00,Wilhelm03,Kubota08,Umeo17}. In general, pressure $p$ represents an essential parameter for tuning phase transitions in solids \cite{Jayaraman72,Lorenz05,Imada98,Brando16}. To perform measurements under pressure, the sample has to be embedded into a pressure medium inside a pressure cell. This typically provides a stronger coupling between the sample and the bath (i.e., the oustide of the pressure cell), compared to ambient-pressure experiments performed in vacuum. Whereas the analysis of data taken under pressure with the relaxation method suffers from the huge addenda contribution from pressure cell and medium, the AC technique has a second major advantage in addition to its sensitivity for samples with small masses: the choice of the measurement frequency allows for the measurement on a different timescale than the one determined by the relaxation time to the bath. This can result, to first approximation, in a decoupling of the sample from the bath, thereby paving the way to extraction of absolute values of the specific heat on a semi-quantitative level \cite{Eichler79}.
Typically, in order to perform AC calorimetric experiments in piston-pressure cells up to $p\,\approx\,2\,-\,3\,$GPa, either small ruthenium oxide (RuO$_2$) thermometers \cite{Kubota08,Chen93,Baloga77} or thermocouples \cite{Bonilla74,Wilhelm03,Bouquet00,Demuer00} have been used to detect the temperature oscillations. On one hand, RuO$_2$ thermometers are inherently sensitive only at low temperatures due to their insulating nature; on the other hand they are easy to handle. Thermocouples cover a wider temperature range, but come along with obstacles in their handling. The reliable use of thermocouples requires a firm contact to the sample which often can be only realized by spot-welding of the thermocouple to the sample. Spot-welding is not possible in case of non-metallic samples, but also is often found to be problematic for metallic (and often brittle) samples. In addition, obtaining absolute values of temperature changes with high accuracy can only be guaranteed when the thermal contact to a reference temperature is good which can be challenging in the pressure-cell environment.
In this work, we present another option: using Cernox\cite{Cernox} thermometers as temperature sensors. Cernox sensors combine the advantages of RuO$_2$ thermometers and thermocouples. They are well established at ambient pressure in most low-temperature laboratories, as they provide a high sensitivity over a wide temperature range, as well as short thermal response times. In addition, they can easily be attached to any sample without the need of spot-welding. This being said, it is surprising that, to the best of our knowledge, the properties of Cernox thermometers have not been studied under pressure so far. Our results show that the sensitivity of Cernox thermometers remains large over the entire investigated pressure range up to 2\,GPa and temperature range up to at least 150\,K. We demonstrate that this high sensitivity of the sensors allows us to study the specific heat of solids under pressure (including various types of phase transitions) at a semi-quantitative level. The wide temperature range covered by this setup will allow for the study of larger regions of phase diagrams by specific heat under pressure, with the convenience of using commercially-available temperature sensors.
This paper is organized as follows. First, we describe details of the experimental setup (Sec. \ref{sec:setup}) used in this work to determine the resistance behavior of the Cernox thermometers under pressure, as well as the specific heat of solids under pressure. In the next section (Sec. \ref{sec:Cernoxresistance}), we show one of the main results of this work, namely that the resistance change of the Cernox thermometers under pressures up to 2\,GPa is very modest and readily describable. Following this, we turn to our description of the AC specific heat data obtained using these Cernox thermometers. Therefore we first provide some theoretical background information on AC specific heat measurements and illustrate our measurement protocol in Sec. \ref{sec:ACtheory}. In Sec. \ref{sec:specheatresults} we discuss the results of specific heat under pressure measurements on three different test cases each of which undergoes a different type of phase transition. These systems were chosen to cover a wide range of phase transition temperatures (7 K up to 130 K) as well as removed entropies, thereby demonstrating the versatility of Cernox thermometers for measurements of specific heat under pressure.
\section{Experimental Setup}
\label{sec:setup}
To perform AC calorimetric measurements, the sample of interest is placed between a heater and a thermometer (see Fig.\,\ref{fig:schematicsetup} (a)). In our setup, we use bare Cernox-chip thermometers \cite{Cernox} (type CX-1070 or type CX-1080) as thermometers. The bare chips have dimensions of 0.965\,$\times\,0.762\,\times\,0.203$\,mm$^3$ and are thus ideally suited to fit into standard piston-pressure cells (see Figs.\,\ref{fig:schematicsetup} (b) and (c) for schematic drawings). In addition, they are deposited on a sapphire substrate with low mass (\,$\le\,3\,$mg), thus have themselves a small specific heat, and short response times (1.5\,ms at 4.2\,K). As a heater, we use strain gauges\cite{straingauges} (type FLG-02-23, Tokyo Sokki Kenkyujo Co., Ltd.) which have an active heater area of $\approx\,1\,\times\,1.4$\,mm$^2$. They show an almost temperature-independent resistance as a function of temperature ($R(T,p)\,\approx\,$120\,$\Omega$) and are enclosed in a very thin layer of plastic coating giving rise to a low thermal mass. The samples, with typical masses $\,\sim\,2\,$mg, are cut into plates with dimensions as close as possible to the active heater area dimensions. The thermometer and heater are attached to the sample by using Devcon 5 Minute epoxy (No. 14250) to improve the thermal contact between the individual components and to guarantee sufficient mechanical stability in the pressure cell (shown schematically in Figs.\,\ref{fig:schematicsetup} (a) and (c)). A photograph of the assembly is shown in Fig.\,\ref{fig:schematicsetup}\,(d). The wires of the thermometer and heater are soldered to the wires passing the pressure-cell feedthrough. The thermometer is connected in a pseudo-four-point configuration in which the four wires for current and voltage are reduced to two wires inside the pressure cell. In addition, a Pb sample is mounted on the feedthrough in a four-point configuration for determining its critical temperature, $T_c$, via resistance measurements. The $T_c$ value can be used to determine the pressure, $p$, at low temperature as $T_c(p)$ is well characterized in literature \cite{Bireckoven88}.
The sample end of the feedthrough is placed in a Teflon-cup (see Figs.\,\ref{fig:schematicsetup}\,(b) and (c)) which is filled with the pressure-transmitting medium. In all the experiments presented here, a mixture of 4:6 mixture of light mineral oil:n-pentane \cite{Budko84,Kim11} is used as a pressure-transmitting medium. It solidifies at $p\,\approx\,3-4\,$GPa at room temperature, thus ensuring hydrostatic pressure conditions in the available pressure range. Two anti-extrusion rings made out of phosphor-bronze are used to prevent the teflon from flowing through the interstices when pressurized. The outer cell body is made out of Grade 5 titanium alloy (Ti 6Al-4V) and the inner cylinder out of Ni-Cr-Al alloy. Its design is similar to the one described in Ref. \citen{Budko84}. As Ti 6Al-4V alloy turns superconducting \cite{Ridgeon17} below $\approx\,$5\,K and as a consequence, its thermal conductivity becomes significantly reduced, the sample inside the cell cannot be cooled below 5\,K. Therefore, the use of this particular cell is restricted to temperatures above 5\,K. This issue can be circumvented by using cells made out of a different material, such as CuBe/Ni-Cr-Al.
Pressure is applied by applying a load to the piston at room temperature by a hydraulic press and locked by tightening the lock nut. All measurements shown in this manuscript were performed inside the pressure cell. At the beginning of each pressure cycle the pressure cell was closed hand-tight. Whereas this procedure typically results in a small, but finite pressure at room temperature \cite{Thompson84} ($p\,\lesssim\,0.3\,$GPa), the pressure at low temperature inferred from $T_c$ of Pb is usually very close to 0\,GPa ($p\,\lesssim\,0.04\,$GPa). We refer to this situation in the manuscript as ``ambient-pressure'' condition ($p\,=\,0\,$GPa). All data shown were obtained by increasing pressure to the measured value.
\begin{figure}
\includegraphics[width=0.9\textwidth]{setup-schematics.pdf}
\caption{(a) Schematic diagram of the sample arrangement with heater and thermometer. The heater is supplied with an AC voltage with frequency $\omega/2$ which results in an oscillation of the temperature of the sample with frequency $\omega$; (b) Schematic diagram of the piston-pressure cell used in the present work; (c) Schematic diagram of the sample assembly and Pb sensor inside the teflon cup; (d) Photograph of the heater, sample and thermometer mounted on the pressure-cell feedthrough. The Pb sensor for the determination of the pressure value near 7\,K is also mounted on the feedthrough.}
\label{fig:schematicsetup}
\end{figure}
The measurements were carried out in a cryogen-free cryostat (Janis SHI-950 with a base temperature of $\approx\,3.5\,$K). The probe, used in this cryostat, is wired with phosphor-bronze wires (QT-36, LakeShore Inc.) to ensure low heat flow through the wires. The temperature was controlled continuously between base and room temperature by a LakeShore 336 controller. Temperature was monitored by a calibrated temperature sensor (Cernox-1030) which was placed directly outside the pressure cell by inserting it into a copper bracket. The Cernox thermometer inside the pressure cell was supplied by a DC current (Model CS580, Stanford Research Systems). The size of the DC current was adjusted with temperature such that the voltage limit ($<\,100\,$mV) of the thermometer is not exceeded. The voltage oscillations of the thermometer which result from the AC heating were pre-amplified and filtered (Model SR560, Stanford Research Systems) and then measured with a Lock-In Amplifier (Model SR860, Stanford Research Systems) the internal oscillator of which was used to provide the heating voltage. The heating power was chosen such that the amplitude of the induced temperature oscillation $T_{AC,0}$ (see Fig.\,\ref{fig:schematicsetup} (a)) was typically smaller than 20\,mK. To measure frequency responses (i.e., measurements as a function of frequency, see below), we used the built-in frequency option of this particular Lock-In Amplifier which allows to change the frequency within user-defined frequency limits and sweep rates. The DC resistance of the bare Cernox chips inside the pressure cell was read out simultaneously to each specific heat measurement by a Digital Voltmeter (SIM970, Stanford Research Systems). The resistance of the Pb sensor was measured with a LakeShore AC Resistance Bridge (Model 370). All data are recorded using a custom LabView Program.
\section{Results: Cernox resistance under pressure}
\label{sec:Cernoxresistance}
Figure \ref{fig:Cernoxresistance} (a) summarizes our main result on the behavior of the Cernox (type CX-1080) resistance, $R$, as a function of temperature, $T$, at three selected pressures up to $p\,\approx\,$2\,GPa. These data were taken without any applied heat to the heater inside the pressure cell. At ambient pressure, the resistance shows a typical behavior for Cernox thermometers: the resistance increases with decreasing temperature and the slope d$R$/d$T$ is finite over the entire temperature range which guarantees a sufficient sensitivity of this thermometer from low temperatures ($T\,\approx\,$5\,K) up to high temperatures ($T\,\approx\,$150\,K). Upon increasing pressure, the resistance at a fixed temperature is reduced by $\approx\,$28\% at 5\,K ($\approx\,10\,$\% at 150\,K) at 2\,GPa (see Fig.\,\ref{fig:Cernoxresistance} (b) for change of resistance as a function of pressure at different temperatures). However, the overall behavior as a function of temperature is nearly unchanged. To quantify the sensitivity of the thermometer, one can refer to the dimensionless quantity (d$R$/d$T$)/($R/T$) which is displayed as a function of $T$ in the inset of Fig. \ref{fig:Cernoxresistance} (a) for the same pressure values as the ones depicted in the main panel. This representation shows that this type of Cernox thermometer has an almost temperature- and pressure-independent sensitivity factor of 1.25. Only at low temperatures ($T\,<\,25\,$K), an increased sensitivity up to 1.5 is observed for all pressures. Thus, our measurements clearly show that Cernox thermometers keep their high sensitivity across a wide temperature range up to 2\,GPa. Note that even though we restrict ourselves in this study to temperatures below 150\,K, it is known that (d$R$/d$T$)/($R/T$) of the Cernox thermometers remains almost unchanged at ambient pressure up to room temperature \cite{Cernox}. Based on our results, it is therefore likely that the Cernox thermometers are very sensitive up to room temperature, even under pressure. Moreover, we did not find any indications of changes in the thermometer behavior from one pressure cycle to the next or strong deviations in the behavior of different chips (see Fig.\,\ref{fig:Cernoxresistance} (b)). Nevertheless, the minor differences in the resistance behavior of different chips depicted in Fig.\,\ref{fig:Cernoxresistance} (b) requires a calibration of each chip for each pressure run, as will be described below. All in all, our results show the Cernox chips can be used as temperature sensors in pressure experiments with high reliability and reproducibility.
\begin{figure}
\includegraphics[width=0.9\textwidth]{Cernox-pressure-110518.pdf}
\caption{(a) Resistance, $R$, of a Cernox thermometer, type CX-1080, as a function of temperature, $T$, at three different pressures $p$, ranging from 0\,GPa to 2.05\,GPa; Inset: Sensitivity, defined as $|$d$R/$d$T/(R/T)|$, as a function of temperature for the same pressure values, as depicted in the main panel. The step at $T\,\approx\,$50\,K in the data at 0\,GPa and 2.05\,GPa is likely an artifact associated with changing of thermometer current; (b) Resistance of a Cernox thermometer, type CX-1080, normalized to its ambient-pressure value, $R/R(p\,=\,0)$ at different temperatures between 5\,K and 150\,K. Open and closed symbols represent measurements on two different chips of the same type.}
\label{fig:Cernoxresistance}
\end{figure}
\section{AC Specific heat: Theoretical background and Measurement Protocol}
\label{sec:ACtheory}
In the following, we want to focus on one possible application for which it is essential to determine temperatures with high sensitivity inside the pressure cell, namely when performing measurements of the specific heat of solids under pressure. As we employ here the method of AC calorimetry, this section will provide theoretical background information \cite{Sullivan68,Eichler79} on the AC calorimetric technique which is essential for understanding our measurement protocol.
To extract absolute specific heat values from an AC calorimetry experiment, an understanding of the heat flow from the heater to the various components in the system is needed. On one hand, the heat is transferred from the heater (specific heat $C_H$) through the sample ($C_S$) to the thermometer ($C_{\Theta}$) which are connected via finite thermal conductances. In the following, the thermal conductances between sample and heater as well as thermometer and sample which govern the heat transfer are denoted as $\lambda_{HS}$ and $\lambda_{\Theta S}$, respectively. On the other hand, each component is also coupled to a bath with temperature $T_B$ (which corresponds to the temperature on the outside of the pressure cell) by finite thermal conductances, denoted by $\lambda_H$, $\lambda_S$ and $\lambda_\Theta$. A block diagram of this arrangement is shown in Fig.\,\ref{fig:frequencydependence} (a). Note that the couplings $\lambda_H$, $\lambda_S$ and $\lambda_{\Theta}$ are non-negligible in the present case, as the sample has to be embedded in a pressure medium inside the pressure cell for measurements under pressure. This, in general, means that the absolute values of the specific heat cannot be determined under pressure with high accuracy. Nonetheless, we will show below that the AC technique implemented in this work allows for a determination of specific heat value under pressure at a semi-quantitative level by choosing the right measurement frequency.
When the heater is supplied with an AC voltage $U(t)\,=\,U_0 \sin(\frac{\omega}{2} t)$, it gives rise to an AC heating power $P(t)\,=\,P_0 \sin^2(\frac{\omega}{2}t)$ and the temperature of the sample will respond in the following manner:
\begin{equation}
T(t) \,=\, T_{DC} + T_{AC}(t).
\end{equation}
$T_{DC}$ refers here to the time-independent increase of the sample temperature with respect to the bath, which is determined by the heating power as well as the coupling to the bath via $T_{DC}\,=\,T_B+\frac{P_0}{2\lambda_S}$. The second term $T_{AC}(t)\,=\,T_{AC,0} \sin(\omega t + \phi)$ describes the temperature oscillation of the sample which oscillates with twice the driving frequency of the heater. The amplitude of this oscillation $T_{AC,0}$ contains the information about the specific heat of the sample $C_S$. The sensitivity of an AC specific heat setup is particularly high for small samples (i.e. with small $C_S$), as $T_{AC,0}$ is inversely proportional to $C_S$. In detail, the relation of $T_{AC,0}$ to $C_S$ for a realistic model with finite thermal conductances was discussed in the works of Sullivan and Seidel (Ref. \citen{Sullivan68}), as well as Eichler (Ref. \citen{Eichler79}), and reads as
\begin{eqnarray}
T_{AC,0} \,&=&\, \frac{P_0}{2\omega C}\,\cdot\,F(\omega) \label{eq:frequency-response} \\
\textnormal{with\ } F(\omega)\,&=&\,[1+2\,\cdot\,(\frac{\lambda_H}{\lambda_{HS}}+\frac{\lambda_\Theta}{\lambda_{\Theta S}})+\frac{1}{(\omega \tau_1)^2}+(\omega \tau_2)^2]^{-1/2} \label{eq:frequency-response2}\\
\textnormal{and\ } C &=& C_H + C_\Theta + C_S, \tau_1=\frac{C}{\lambda_S}, \\
\tau_2 &=& \sqrt{\tau_H^2+\tau_\Theta^2} \textnormal{\ with \ } \tau_H\,=\,C_H/\lambda_{HS} \textnormal{\ and \ } \tau_\Theta = C_\Theta/\lambda_{\Theta S}.
\end{eqnarray}
Thus, whenever the measurement frequency is choosen such that $(\omega \tau_1)^2\,\gg\,1$ and $(\omega \tau_2)^2\,\ll\,1$, with $\tau_1$ and $\tau_2$ corresponding to the thermal relaxation times to the bath and within the assembly of heater, sample and thermometer, respectively, then $F(\omega)\,\approx\,[1+2\,\cdot\,(\frac{\lambda_H}{\lambda_{HS}}+\frac{\lambda_\Theta}{\lambda_{\Theta S}})]^{-1/2}$. The error in determination of absolute values then is mainly determined by the ratios $\frac{\lambda_H}{\lambda_{HS}}$ and $\frac{\lambda_\Theta}{\lambda_{\Theta S}}$. However, sample, heater and thermometer are in intimate contact, whereas the heat path to the bath (i.e., the outside of the pressure cell) is long. This implies due to the geometrical arrangement that, to a first approximation, $\lambda_H\,\ll\,\lambda_{HS}$ and $\lambda_\Theta\,\ll\,\lambda_{\Theta S}$ (and we will show below that this assumption is verified in our setup), and therefore $F(\omega)\,\approx\,1$. It then follows that $T_{AC,0}\,=\,\frac{P_0}{2\omega C}$.
The frequency which meets these criteria is called the optimal measurement frequency $\omega_{opt}$. As $\tau_1$ and $\tau_2$ depend on the specific heat of the sample, as well as on thermal conductances $\lambda_{HS}, \lambda_S$ and $\lambda_{\Theta S}$, $\omega_{opt}$ will in general be a function of temperature and pressure, and will differ from sample assembly to sample assembly. Correspondingly, $\omega_{opt}$ has to be determined experimentally for each sample, temperature and pressure individually, prior to each measurement of the specific heat. It can be shown that $\omega_{opt}$ is the frequency at which $F(\omega)$ is maximal. As suggested by eq. \ref{eq:frequency-response}, direct experimental access to $F(\omega)$ is provided by measuring the frequency dependence of the quantity $\omega\,\cdot\,T_{AC,0}$ (called frequency response hereafter). In Figs. \ref{fig:frequencydependence} (b) and (c) we show examples of the frequency responses, normalized to their respective maximum, recorded with our setup when measuring the specific heat of elemental Pb (The specific heat results on Pb will be discussed in Sec.\,\ref{sec:specheatresults} in more detail.). First, we compare in Fig.\,\ref{fig:frequencydependence}\,(b) the frequency response, taken at $T\,=\,6$\,K at two different pressures ($p\,=\,0\,$GPa and 1.97\,GPa). Each frequency response (normalized to its maximum value) reveals a broad maximum at $\approx\,100\,$Hz and 300\,Hz, respectively, which we assign to the optimal measurement frequencies $\omega_{opt}$. Note that a broad maximum (or even a wide plateau) suggests that $(\omega \tau_1)^2\,\gg\,1$ and $(\omega \tau_2)^2\,\ll\,1$ across a wide frequency range which minimizes errors in the determination of absolute values of the specific heat. The observation of a broad maximum is therefore crucial for the determination of absolute values of the specific heat under pressure on a semi-quantitative level, as achieved with our setup. At the same time, at a fixed pressure, as shown in Fig.\,\ref{fig:frequencydependence}\,(c) for $p\,=\,$1.97\,GPa, we find that the broad maximum in the frequency response and thereby $\omega_{opt}$ shifts to lower frequencies with increasing temperature. The evolution of $\omega_{opt}$, determined from the numerical derivation of the frequency response data, with $T$ and $p$ is summarized in Fig.\,\ref{fig:frequencydependence}\,(d).
The knowledge of the frequency response allows us to extract the relaxation times $\tau_1$ and $\tau_2$ of this particular assembly at different pressures. The solid lines in Fig.\,\ref{fig:frequencydependence}\,(b) show a fit of eq.\,\ref{eq:frequency-response2} to our experimental data, taken at 6\,K. The fits, which were performed with keeping $(\frac{\lambda_H}{\lambda_{HS}}+\frac{\lambda_\Theta}{\lambda_{\Theta S}})$ fixed to 0, are in very good agreement with our experimental data set. They yield $\tau_1\,=\,(0.047\,\pm\,0.001)\,$s and $\tau_2\,=\,(0.0016\,\pm\,0.0001)\,$s at ambient pressure and $\tau_1\,=\,(0.015\,\pm\,0.001)\,$s and $\tau_2\,=\,(0.0009\,\pm\,0.0001)\,$s at $p\,=\,1.97\,$GPa. Thus, the optimal measurement frequencies $\omega_{opt}$ fulfill the criteria mentioned above as $(\omega_{opt} \tau_1)^2\,\approx\,22\,\gg\,1$ and $(\omega_{opt} \tau_2)^2\,\approx\,0.02\,\ll\,1$ at $p\,=\,0\,$GPa and $(\omega_{opt} \tau_1)^2\,\approx\,20\,\gg\,1$ and $(\omega_{opt} \tau_2)^2\,\approx\,0.07\,\ll\,1$ at $p\,=\,1.97\,$GPa. Our fitting results indicate that both relaxation times decrease with increasing pressure. This tendency is naturally expected, as the coupling to the bath, but also the coupling within the assembly likely increase under compression. Therefore, the increased optimal frequency $\omega_{opt}$ with applied $p$ is directly a consequence of the decreased relaxation times. The temperature dependence of $\omega_{opt}$ is less intuitive to understand as it depends on the temperature-dependent changes of specific heat as well as thermal conductivity of sample, heater as well as thermometer.
It should be noted that the error in the determination of the absolute value of the specific heat can be estimated from the knowledge of $\tau_1$ and $\tau_2$. Equations \ref{eq:frequency-response} and \ref{eq:frequency-response2} suggest that any finite $\tau_1$ as well as any non-zero $\tau_2$ will give rise to an overestimation of the specific heat value by the factor $[1+\frac{1}{(\omega \tau_1)^2}+(\omega \tau_2)^2]^{1/2}$, if $\frac{\lambda_H}{\lambda_{HS}}+\frac{\lambda_\Theta}{\lambda_{\Theta S}}\,\approx\,$0. Our results of $\tau_1$ and $\tau_2$ correspond to an overestimate of specific heat by $\approx\,$3\,\% at ambient pressure, and $\approx\,$5\,\% at 1.97 GPa by our setup. This estimate shows that our setup can, in principle, deliver absolute values on a semi-quantitative level, despite a non-negligible coupling to the bath. Importantly, the analysis performed here shows that the overestimation of specific heat does not significantly change with pressure. This allows for the determination of changes (especially relative changes) of specific heat under pressure with higher accuracy. We confirm these conclusions from the analysis of the frequency response in Sec. \ref{sec:specheatresults}, where we present specific heat under pressure data on three different test cases and compare with ambient-pressure literature data taken under adiabatic conditions.
The theoretical background information given here explains the measurement protocol which we follow to determine the specific heat of a sample using the AC technique. It includes in total three separate, sequential temperature sweeps. First, we need to calibrate the Cernox thermometers inside the pressure cell at a specific pressure to quantify the DC temperature increase $T_{DC}$ of the sample which results from applying heat to the heater inside the cell. To this end, we place a calibrated thermometer outside on the pressure cell and record the resistance of the Cernox thermometer inside the pressure cell upon slow warming with a rate of $\approx\,0.25\,$K/min without any voltage applied to the heater inside the cell (see Sec.\,\ref{sec:Cernoxresistance}). In the second temperature sweep, we record the frequency response $\omega\,\cdot\,T_{AC,0}$ vs. $\omega$ as a function of temperature for the same, specific pressure. From this data, we extract $\omega_{opt}$ as a function of $T$ and typically fit this smooth data set with an exponential function $\omega_{opt}\,=\,\omega_0+A\exp(-T/t_1)$ with free parameters $\omega_0$, $A$ and $t_1$ (see grey lines in Fig.\,\ref{fig:frequencydependence} (d)). Within our measurement program, we adjust the measurement frequency continuously with temperature according to this exponential function during the third temperature sweep for a specific pressure. This ensures that the AC temperature oscillation $T_{AC,0}$ as a function of $T$ is always measured at the optimal measurement frequency which then allows us to infer the specific heat on a semi-quantitative level.
\begin{figure}
\includegraphics[width=0.9\textwidth]{Pb_optimalfrequency_090518.pdf}
\caption{(a) Schematic diagram illustrating heat flows from the sample to the heater (governed by the thermal conductivity $\lambda_{HS}$), from the sample to the thermometer ($\lambda_{\Theta S}$), and from sample, heater and thermometer to the bath ($\lambda_S$, $\lambda_H$ and $\lambda_\Theta$); (b) Normalized frequency response, i.e., the product of frequency $\omega$ and oscillation amplitude $T_{AC,0}$ normalized to its maximum value $(\omega T_{AC,0})_{max}$ vs. $\omega$, for a Pb sample at $T\,=\,6$\,K and $p\,=\,0\,$GPa and 1.97\,GPa; (c) Normalized frequency response for a Pb sample at different temperatures between 5\,K and 9\,K at $p\,=\,1.97\,$GPa; (d) Evolution of the optimal measurement frequency $\omega_{opt}$ as a function of temperature and pressure, obtained from the data presented in (b) and (c) (for details, see main text). Grey lines represent exponential fits to the $\omega_{opt}$ vs. $p$ data sets.}
\label{fig:frequencydependence}
\end{figure}
\section{Specific heat under pressure: Results}
\label{sec:specheatresults}
In the following, we demonstrate the wide applicability of the Cernox thermometers in measurements of specific heat under pressure by examining three test cases with very different transition temperatures, ranging from $T\,\approx\,7\,$K (superconducting transition in Pb) up to $T\,\approx\,130\,$K (magnetostructural transition in BaFe$_2$As$_2$), as well as very different amounts of entropy change.
\subsubsection{Superconducting phase transition in elemental Pb}
The first sample for a study of specific heat under pressure chosen here is elemental lead (Pb) which undergoes an ambient-pressure superconducting transition at a critial temperature $T_c\,=\,7.2\,$K. The shift of $T_c$ with pressure is well characterized in literature \cite{Bireckoven88} and therefore often utilized as a manometer at low temperatures.
\begin{figure}
\includegraphics[width=0.8\textwidth]{Pb-050918.pdf}
\caption{(a) Molar specific heat $C_{molar}$ of elemental Pb as a function of temperature $T$ at four different pressures up to 1.97\,GPa; (b,c) Comparison of $C_{molar}(T)$ of Pb and the resistance $R_{Pb}(T)$ of the Pb pressure sensor at a pressure of 0 GPa (b) and 1.97\,GPa (c).}
\label{fig:Pb}
\end{figure}
Figure \ref{fig:Pb} (a) shows our results of the specific heat, $C_{molar}$, of Pb at different pressures up to 1.97\,GPa. At all pressures, we find a jump-like change of $C_{molar}$ at a critical temperature $T_c$. This feature is characteristic for the mean-field type phase transition into the superconducting state in BCS superconductors. The critical temperature, extracted from our $C_{molar}$ data, is suppressed with increasing $p$, consistent with literature results \cite{Bireckoven88}. In addition, the overall specific heat is reduced upon pressurization, likely due to a combination of changes in the electronic density of states as well as lattice stiffening (see below for more details).
To demonstrate the high accuracy in the determination of phase transition temperatures from our specific heat data, we compare in Figs. \ref{fig:Pb} (b) and (c) the specific heat of the Pb sample, placed between heater and thermometer, with the resistance of the Pb manometer, $R_{Pb}$, at lowest pressure ($p_1\,=\,0\,$GPa) and highest pressure ($p_4\,=\,1.97\,$GPa) of our experiment. At both pressures, the midpoint of the jump in $C_{molar}$ occurs at the same temperature at which the resistance clearly shows a jump-like change into the superconducting state. This also demonstrates that there are no significant pressure gradients in our pressure cell.
Next, we want to discuss to which extent our setup delivers a semi-quantitative determination of the specific heat of solids by comparing our results to literature results \cite{Shiffman63} on Pb (see Fig. \ref{fig:Pb-analysis}). Our data overestimates the absolute specific heat value by $\approx\,12\,\%$, compared to the literature results from Ref. \citen{Shiffman63}. As outlined in Sec.\,\ref{sec:ACtheory}, an overestimate of absolute specific heat values determined with the AC technique is a consequence of finite relaxation times $\tau_1$ and $\tau_2$. The overestimation factor of about 3\,\%, estimated from an analysis of the frequency responses in Sec. \,\ref{sec:ACtheory}, is of similar size as the overestimation found here from the comparison with literature data on Pb. Note that we did not correct our data for the specific heat of the addenda, i.e., of thermometer, heater and the tiny layers of glue. These additional contributions to the measured specific heat, which can be as large as 50\,\% of the total measured specific heat depending on the specific sample, its size, mass and shape (estimated by measuring the size of the addenda at ambient pressure using the relaxation-time method), likely give rise to the slightly larger overestimation of 12\,\% found empirically here. Clearly, despite the strong coupling to the bath due to the pressure medium and uncertainties in the size of the addenda, our data resembles literature results on a semi-quantitative level, i.e., within less than approximately a factor of 2. This upper limit was estimated empirically in the study of the three different test cases presented in this manuscript. The superconducting jump size extracted from our data at ambient pressure amounts to $\Delta C_{sc}\,\approx\,(44.6\,\pm\,0.5)\,$mJ/mol/K \cite{Shiffman63,Clement52}. This value is slightly smaller than reported values in literature ($\Delta C_{sc}\,=\,$52.9\,mJ/mol/K up to 57.5\,mJ/mol/K), but nevertheless matches on the same semi-quantitative level.
Upon pressurization, we find a significant reduction of $\Delta C_{sc}$ with increasing $p$ down to $\approx\,(29.0\,\pm\,0.5)\,$mJ/mol/K at 1.97\,GPa (see Fig.\,\ref{fig:Pb-analysis} (b)). For superconductors, the change in $\Delta C_{sc}$ is related on the one hand to a change in $T_c$ as well as to a change in the density of states at the Fermi level $N(E_F)$ \cite{Carbotte90}. Figure \ref{fig:Pb-analysis} (b) also includes a plot of $\Delta C_{sc}/T_c$ as a function of $T_c$. The strong change of $\Delta C_{sc}/T_c$ with $p$ by $\approx\,-\,25\,\%$ indicates that most of the change of $\Delta C_{sc}$ with $p$ can be attributed to changes of $N(E_F)$ with $p$, rather than to changes of $T_c$. Unfortunately, no literature data on the change of $N(E_F)$ in Pb with $p$ is available. Also the determination of the change of $N(E_F)$ under $p$ by extracting the Sommerfeld coefficient $\gamma$ from our specific heat data turns out to be not reliable due to the relatively high $T_c$ of Pb combined with a relatively low Debye temperature $\Theta_D\,\approx\,100\,$K at ambient pressure. Thus, we performed density-functional theory (DFT) calculations \cite{Hohenberg64,Kohn65} of the band structure of Pb up to 2\,GPa using PBEsol as exchange-correlation functional with spin-orbit coupling (SOC) effect as implemented in VASP \cite{Kresse96,Kresse96b}. At zero pressure, the theoretical lattice constant of 4.934\,\AA\ agrees very well with the experimental values of 4.95\,\AA. At 2 GPa, the lattice constant is reduced to 4.872\,\AA. We find a decrease of $N(E_F)$ from 0.5303\,states/eV/cell to 0.5121 \,states/eV/cell by 2\,GPa which corresponds to $\approx\,-\,3.5$\,\%. Even though this value is smaller than the one inferred from our specific heat measurements, both results are consistent in inferring a decrease of $N(E_F)$ with pressure. This supports our conclusion that in case of Pb changes of the specific heat anomaly $\Delta C_{sc}$ under $p$ result from a decrease of $N(E_F)$ with pressure.
\begin{figure}
\includegraphics[width=0.8\textwidth]{Pb_analysis-050918.pdf}
\caption{(a) Comparison of ambient-pressure literature data \cite{Shiffman63} on the specific heat $C_{molar}$ of elemental Pb (grey symbols) and the specific heat obtained in the present work in the pressure cell at ambient pressure (black solid line); (b) Evolution of the superconducting jump size in the specific heat $\Delta C_{sc}$, as well as the jump size normalized to the critical temperature, $\Delta C_{sc}/T_c$, with $T_c$.}
\label{fig:Pb-analysis}
\end{figure}
\subsubsection{Antiferromagnetic transition in the rare-earth compound GdNiGe$_3$}
The specific heat anomaly at the superconducting transition in Pb as well as the transition temperature respond strongly to application of external pressure. In addition, the amount of entropy change is relatively small. For the next system, we chose GdNiGe$_3$ anticipating a weak response to pressure and a large change in entropy ($\approx\,R \ln(8)$) \cite{Mun10}. This allows us to show that changes of the absolute values of specific heat under pressure are not a result of an artifact due to modified coupling to the bath or within the assembly of sample, heater and thermometer, i.e., due to changing $\tau_1$ and $\tau_2$. This in turn allows us to establish a high accuracy in the determination of \textit{changes} of the specific heat under pressure. At the same time, a system with a phase transition occurring at higher transition temperature compared to the superconducting transition in elemental Pb is desired to prove high sensitivity of our setup at even higher temperatures.
The rare-earth based GdNiGe$_3$ system has a single antiferromagnetic (afm) transition\cite{Mun10} at $T_N\,\approx\,$26\,K. Importantly, as the moment-carrying Gd is trivalent in this compound and therefore has a Hund's rule $J\,=\,S\,=\,7/2$ ground state ($L\,=\,0$), the compound lacks any magneto-crystalline anisotropy or splitting of the Hund's rule ground state multiplet. Experiments \cite{Mun10} confirmed that GdNiGe$_3$ shows an almost isotropic susceptibility in the paramagnetic state with an effective moment $\mu_{eff}\,=\,8.0\,\mu_B$/Gd$^{3+}$, close to the free-ion value of 7.94\,$\mu_B$/Gd$^{3+}$. Correspondingly, specific heat measurements \cite{Mun10} showed a single $\lambda$-shaped peak at $T_N$ (see grey symbols in Fig.\,\ref{fig:GdNiGe3} for a reproduction of these data). The magnetic entropy, $S$, extracted from measurements of the specific heat was found to be almost constant at $T\,>\,T_N$ with $S\,=\,$17\,J/(mol$\cdot$K), i.e., close to the expected value of $R \ln(8)$. This result is fully consistent with the absence of crystal-field effects in this compound. As the magnetism of this compound can be well understood in terms of localized 4f moments which interact via RKKY (Ruderman-Kittel-Kasuya-Yosida) interaction \cite{Ruderman54}, the response to hydrostatic pressure is expected to be relatively weak. This, together with the well-defined entropy in the paramagnetic state and a high transition temperature, makes this system a suitable reference system for a study of the specific heat under pressure.
\begin{figure}
\includegraphics[width=0.8\textwidth]{GdNiGe3-050918.pdf}
\caption{Molar specific heat divided by temperature $C_{molar}/T$ as a function of temperature $T$ of GdNiGe$_3$ at different pressures up to 1.2 GPa. For comparison, literature data at ambient pressure \cite{Mun10} on this compound are shown in grey. The arrow indicates exemplary the jump size at the antiferromagnetic transition, $\Delta C_{molar}/T$, at lowest pressure $p\,\sim\,0.2$\,GPa (for a definition of criterion and evolution with pressure, see main text). }
\label{fig:GdNiGe3}
\end{figure}
The results of our specific heat study on GdNiGe$_3$ under pressure are shown in Fig.\,\ref{fig:GdNiGe3} in a $C_{molar}/T$ vs. $T$ representation. For comparison, we included the literature specific heat data on this compound at ambient pressure, taken from Ref. \citen{Mun10}. At all measured pressures, our data nicely reveal the $\lambda$-shaped phase transition anomaly at $T\,\approx\,26\,$K. In addition, we also find a small hump in the specific heat below 10\,K. Such a hump in the specific heat at temperatures well below the ordering temperatures was found in various Gd-based systems \cite{Kong14} and was explained by modelling the specific heat of a $(2J+1)$ multiplet in a mean-field approach \cite{Bouvier91,Blanco91}. The comparison of our specific heat data with literature in terms of absolute values indicates an $\approx\,$10\% to 40\% overestimation of the specific heat for $T\,>\,15\,$K. For $T\,<\,15\,$K, we find an underestimate of $C_{molar}/T$. The reason for this behavior is unclear at present, as eqs.\,\ref{eq:frequency-response} and \ref{eq:frequency-response2} do not allow an underestimate. However, this additional data set on GdNiGe$_3$ also confirms that we are not only highly sensitive in tracing phase transitions even at higher temperatures, but also that we can determine absolute specific heat values within less than a factor of 2 deviation from literature.
\begin{figure}
\includegraphics[width=0.8\textwidth]{GdNiGe3-analysis-050918.pdf}
\caption{(a) Change of jump size in specific heat at $T_N$, $\Delta C_{molar}/T$, and $T_N$ (inset) with pressure; (b) Comparison of estimated magnetic entropy at 0.2 GPa (present experiment, black circles) with literature results\cite{Mun10} at ambient pressure (grey squares). Inset: Estimated magnetic entropy at different pressures up to 1.2\,GPa.}
\label{fig:GdNiGe3-analysis}
\end{figure}
In the following, we focus on the relative evolution of the specific heat with pressure. The overall specific heat values at each temperature are reduced upon applying pressure. Similar to the case of Pb, we assign this reduction to changes of the lattice and electronic specific heat. More importantly, however, we find that the $\lambda$-shaped peak, as well as the low-temperature hump are almost unaffected by pressure. This relates to the position of the anomalies as well as the size and shape of the anomaly. To quantify this statement, we show in Fig.\,\ref{fig:GdNiGe3-analysis} (a) the evolution of the jump size of the $\lambda$-shaped anomaly, $\Delta C_{molar}/T$, as well as the transition temperature $T_N$ (inset) with pressure. Whereas $T_N$ is extracted from the minimum in the derivative of the $C_{molar}/T$ data, $\Delta C_{molar}/T$ is calculated by the difference of $C_{molar}/T$ values at those temperatures at which d($C_{molar}/T$)/d$T$\,=\,0.1\,(d($C_{molar}/T$)/d$T$)$_{T_N}$ (see arrow in Fig.\,\ref{fig:GdNiGe3}). We find a slight decrease of $\Delta C_{molar}/T$ with pressure by $\approx\,-\,$6\,\% and a small increase of $T_N$ by less than 1\,\% within a pressure range of $\approx\,$1\,GPa. We want to emphasize that the relative change in $\Delta C_{molar}/T$ is tiny compared to the specific heat changes observed under pressure in elemental Pb. At present, this tiny change of the specific heat features in GdNiGe$_3$ cannot unequivocally be assigned to a single origin: Either the change is indeed related to changes of physical properties under pressure (see Refs. \citen{Bouvier91,Blanco91} for theoretical discussions of specific heat features in Gd-based compounds on a mean-field level), or the change is an artifact arising from uncertainties in the absolute values determined with the AC calorimetric technique related to changes in the relaxation times $\tau_1$ and $\tau_2$ with pressure. Most likely, both factors actually play a role here, but more importantly none of them gives rise to changes in the specific heat beyond $\approx\,$6\,\% when changing pressure by 1\,GPa. Thus, we can conclude from our specific heat measurements on GdNiGe$_3$ that changes in the specific heat of more than $\approx\,$6\,\% within 1\,GPa, in particular at phase transitions, can reliably be attributed to changes of physical properties, rather than to instrumental artifacts. We also note that in principle the addenda contribution can change with pressure. This change is explicitly included in the error bar given above. However, in general it is reasonable to assume that in first approximation the specific heat of the addenda does not change with pressure.
To extract the magnetic entropy and changes of this quantity with pressure from the present data set, non-magnetic (phononic and electronic) contributions need to be subtracted. These contributions are typically obtained by measuring the specific heat of a non-magnetic reference sample if available. In this case, YNiGe$_3$ serves as a suitable non-magnetic reference system the ambient-pressure specific heat of which was reported in Ref. \citen{Mun10}. As an independent measurement of YNiGe$_3$ with our AC calorimetric setup would require a new assembly with different relaxation times $\tau_1$ and $\tau_2$ which likely give rise to different error in the determination of absolute specific heat values compared to our values on GdNiGe$_3$, this approach to determine the non-magnetic contributions is not suitable in the present case. However, assuming that the overestimation factor is, in first approximation, temperature-independent and contributions from heater and thermometer to our measured specific heat are comparably negligible, we can rescale the reported ambient-pressure data on YNiGe$_3$ such that it almost matches our specific heat data on GdNiGe$_3$ at $T\,\gg\,T_N$ and $p\,\sim\,0.2\,$GPa. This procedure allows us to provide an estimate on the magnetic entropy from our data set (see Fig.\,\ref{fig:GdNiGe3-analysis} (b)). Our estimate of the magnetic entropy yields $S\,\sim\,15.7\,$J/mol/K at $T\,=\,T_N$ which corresponds to 90\% of the expected $S\,=\,R\,\ln(8)$. Even if this analysis can only provide a rough estimate of the entropy due to the uncertainties involved in the determination of the non-magnetic contributions, it confirms that we can determine not only specific heat, but also entropies on the same semi-quantitative level. When now discussing changes of the entropy as a function of pressure, we have to make further assumptions on how the non-magnetic contributions are affected by pressure. The change of the non-magnetic contributions reveals itself e.g. in the measured specific heat at $T\,\gg\,T_N$ which indicates a sizable reduction of $C_{molar}/T$ with $p$. To account for this change, we make the reasonable assumption that changes in the Sommerfeld coefficient $\gamma$ as well as the Debye lattice constant $\beta$ give rise to changes in the non-magnetic specific heat via $C_{molar}/T\,\propto\,\gamma + \beta T^2$. We now apply a temperature-independent as well as a quadratic correction to the $C_{molar}/T$ data of YNiGe$_3$ such that it matches our specific heat data on GdNiGe$_3$ at $T\,\gg\,T_N$ for $p_2$ and $p_3$ individually and subtract the so-derived non-magnetic contributions from our experimental data on GdNiGe$_3$. These estimates of the magnetic entropy are shown in the inset of Fig.\,\ref{fig:GdNiGe3-analysis}. We do not find any significant changes of the estimated magnetic entropy with pressure. This result is consistent with the almost unchanged size of specific heat anomaly $\Delta C_{molar}/T$ with $p$ and provides further evidence that changes of specific heat and entropies with pressure can be estimated with comparably high accuracy.
\subsubsection{Structural/magnetic transition in the iron-pnictide BaFe$_2$As$_2$}
Finally, to further demonstrate the sensitivity of our setup at even higher temperatures (above 100\,K), we present specific heat measurements under pressure on BaFe$_2$As$_2$. This material undergoes a structural and antiferromagnetic transition at $T_{s,N}\,\approx\,130\,$K from a tetragonal-paramagnetic to an orthorhombic-antiferromagnetic state \cite{Rotter08}. In the BaFe$_2$As$_2$ system either chemical substitution (e.g. of Fe by Co) \cite{Ni08,Canfield10,Sefat08} or pressure \cite{Colombier09} suppress this structural-magnetic transition and unconventional superconductivity, with critical temperatures up to $\approx\,22\,$K, emerges.
\begin{figure}
\includegraphics[width=0.8\textwidth]{Ba122-050918.pdf}
\caption{Molar specific heat divided by temperature, $C_{molar}/T$, as a function of temperature $T$ of BaFe$_2$As$_2$ at ambient pressure as well as at $p\,=\,2.05$\,GPa; Inset: Specific heat, $C_{molar}$, of BaFe$_2$As$_2$ at ambient pressure on expanded scale.}
\label{fig:Ba122}
\end{figure}
Figure \ref{fig:Ba122} shows our results for the specific heat of BaFe$_2$As$_2$ in the pressure cell at ambient pressure as well as at $p\,=\,$2.05\,GPa. Our ambient-pressure data show a very sharp peak at the structural-magnetic transition at $T\,\approx\,132\,$K. Even if the size of the phase transition is strongly reduced by the application of $p\,=\,2.05\,$GPa, indicating a strongly reduced entropy change at the phase transition with pressure, we can still clearly resolve the phase transition at a lower temperature $T\,\approx\,112\,$K. The decrease in the phase transition temperature by $\approx\,-10\,$K/GPa agrees very well with earlier reports of the pressure dependence of $T_{s,N}$ based on resistance data \cite{Colombier09}. More importantly, not only can we resolve the high-temperature anomaly, but we can also measure the specific heat across the entire temperature range 5\,K$\,\le\,T\,\le\,$150\,K by using a single thermometer (see inset of Fig.\,\ref{fig:Ba122}). This is a clear advantage of using the Cernox thermometers as temperature sensors for AC specific heat measurements rather than RuO$_2$ thermometers which are inherently sensitive only in a much more limited, low-temperature range. The setup presented here will therefore allow in the future to measure the specific heat under pressure of systems which show a cascade of phase transitions at very different temperatures, such as e.g. the superconducting as well as magnetic-structural transition in Co-doped BaFe$_2$As$_2$.
\section{Summary}
In conclusion, we studied the response of Cernox thermometers to external pressure in piston-pressure cells up to 2\,GPa. These thermometers are frequently used in low-temperature experiments due to their high sensitivity. We find that the sensitivity of the Cernox thermometers remains high under pressures up to 2\,GPa. In addition, they are mechanically robust and survive numerous pressure cycles. Thus, our study shows that these temperature sensors can be used to measure temperatures inside the pressure cell with high accuracy. As a possible application, for which this high sensitivity is essential, we present in detail the use of these thermometers in measuring the specific heat of solids under pressure. By studying three different test cases (elemental Pb, GdNiGe$_3$ and BaFe$_2$As$_2$), we show that the high sensitivity of the Cernox thermometers allows to measure specific heat of solids under pressure across a wide temperature range as well as wide range of entropy changes. Therefore, by using Cernox thermometers, it will be possible in the future to study systems which show a cascade of phase transition across a wide temperature range by specific heat under pressure in a piston-pressure cell, possibly even up to room temperature. In addition, we demonstrate that our setup does not only allow to trace phase transitions, but is also very accurate in determining changes of the specific heat as a function of pressure.
\begin{acknowledgments}
We thank E. Mun and N. Ni for growing the GdNiGe$_3$ and BaFe$_2$As$_2$ crystals used in the study. This work was carried out at Iowa State University and supported by Ames Laboratory, US DOE, under Contract No. DE-AC02-07CH11358. G.D.'s efforts were partially funded by the Gordon and Betty Moore Foundation's EPiQS Initiative through Grant No. GBMF4411. L.X. was supported, in part, by the W. M. Keck Foundation.
\end{acknowledgments}
\bibliographystyle{modaps}
\section{Introduction}
The specific heat of solids is one of the most fundamental thermodynamic quantities. Its temperature dependence reveals important information about the energy scales of electronic, magnetic and lattice degrees of freedom. It is thus an inherently sensitive tool to detect phase transitions which involve one or more of the above-mentioned degrees of freedom. Consequently, various techniques \cite{Stewart83} to measure specific heat in calorimetric experiments at ambient pressure and low temperatures are well established and nowadays even commercially available \cite{Lashley03,acoption}. Typically, these techniques require adiabatic conditions, i.e., an almost ideal decoupling of the sample from the environment, so as to achieve high accuracy in the determination of absolute values of the specific heat. Among these techniques, the relaxation method \cite{Bachmann72} is considered as the standard method in which a heat pulse is given to the sample of interest and the relaxation time towards the initial temperature after switching off the pulse is directly related to the size of the specific heat. Alternatively, in particular in cases where the sample mass is very small, is the AC technique \cite{Sullivan68,Eichler79,Kraftmakher02}, in which the sample is heated by an oscillatory heat source and the resulting temperature oscillation can be used to infer the specific heat, preferred.
As a matter of fact, AC specific heat measurements have proven to be particularly suited for measurements under pressure \cite{Bonilla74,Baloga77,Eichler79,Chen93,Bouquet00,Demuer00,Wilhelm03,Kubota08,Umeo17}. In general, pressure $p$ represents an essential parameter for tuning phase transitions in solids \cite{Jayaraman72,Lorenz05,Imada98,Brando16}. To perform measurements under pressure, the sample has to be embedded into a pressure medium inside a pressure cell. This typically provides a stronger coupling between the sample and the bath (i.e., the oustide of the pressure cell), compared to ambient-pressure experiments performed in vacuum. Whereas the analysis of data taken under pressure with the relaxation method suffers from the huge addenda contribution from pressure cell and medium, the AC technique has a second major advantage in addition to its sensitivity for samples with small masses: the choice of the measurement frequency allows for the measurement on a different timescale than the one determined by the relaxation time to the bath. This can result, to first approximation, in a decoupling of the sample from the bath, thereby paving the way to extraction of absolute values of the specific heat on a semi-quantitative level \cite{Eichler79}.
Typically, in order to perform AC calorimetric experiments in piston-pressure cells up to $p\,\approx\,2\,-\,3\,$GPa, either small ruthenium oxide (RuO$_2$) thermometers \cite{Kubota08,Chen93,Baloga77} or thermocouples \cite{Bonilla74,Wilhelm03,Bouquet00,Demuer00} have been used to detect the temperature oscillations. On one hand, RuO$_2$ thermometers are inherently sensitive only at low temperatures due to their insulating nature; on the other hand they are easy to handle. Thermocouples cover a wider temperature range, but come along with obstacles in their handling. The reliable use of thermocouples requires a firm contact to the sample which often can be only realized by spot-welding of the thermocouple to the sample. Spot-welding is not possible in case of non-metallic samples, but also is often found to be problematic for metallic (and often brittle) samples. In addition, obtaining absolute values of temperature changes with high accuracy can only be guaranteed when the thermal contact to a reference temperature is good which can be challenging in the pressure-cell environment.
In this work, we present another option: using Cernox\cite{Cernox} thermometers as temperature sensors. Cernox sensors combine the advantages of RuO$_2$ thermometers and thermocouples. They are well established at ambient pressure in most low-temperature laboratories, as they provide a high sensitivity over a wide temperature range, as well as short thermal response times. In addition, they can easily be attached to any sample without the need of spot-welding. This being said, it is surprising that, to the best of our knowledge, the properties of Cernox thermometers have not been studied under pressure so far. Our results show that the sensitivity of Cernox thermometers remains large over the entire investigated pressure range up to 2\,GPa and temperature range up to at least 150\,K. We demonstrate that this high sensitivity of the sensors allows us to study the specific heat of solids under pressure (including various types of phase transitions) at a semi-quantitative level. The wide temperature range covered by this setup will allow for the study of larger regions of phase diagrams by specific heat under pressure, with the convenience of using commercially-available temperature sensors.
This paper is organized as follows. First, we describe details of the experimental setup (Sec. \ref{sec:setup}) used in this work to determine the resistance behavior of the Cernox thermometers under pressure, as well as the specific heat of solids under pressure. In the next section (Sec. \ref{sec:Cernoxresistance}), we show one of the main results of this work, namely that the resistance change of the Cernox thermometers under pressures up to 2\,GPa is very modest and readily describable. Following this, we turn to our description of the AC specific heat data obtained using these Cernox thermometers. Therefore we first provide some theoretical background information on AC specific heat measurements and illustrate our measurement protocol in Sec. \ref{sec:ACtheory}. In Sec. \ref{sec:specheatresults} we discuss the results of specific heat under pressure measurements on three different test cases each of which undergoes a different type of phase transition. These systems were chosen to cover a wide range of phase transition temperatures (7 K up to 130 K) as well as removed entropies, thereby demonstrating the versatility of Cernox thermometers for measurements of specific heat under pressure.
\section{Experimental Setup}
\label{sec:setup}
To perform AC calorimetric measurements, the sample of interest is placed between a heater and a thermometer (see Fig.\,\ref{fig:schematicsetup} (a)). In our setup, we use bare Cernox-chip thermometers \cite{Cernox} (type CX-1070 or type CX-1080) as thermometers. The bare chips have dimensions of 0.965\,$\times\,0.762\,\times\,0.203$\,mm$^3$ and are thus ideally suited to fit into standard piston-pressure cells (see Figs.\,\ref{fig:schematicsetup} (b) and (c) for schematic drawings). In addition, they are deposited on a sapphire substrate with low mass (\,$\le\,3\,$mg), thus have themselves a small specific heat, and short response times (1.5\,ms at 4.2\,K). As a heater, we use strain gauges\cite{straingauges} (type FLG-02-23, Tokyo Sokki Kenkyujo Co., Ltd.) which have an active heater area of $\approx\,1\,\times\,1.4$\,mm$^2$. They show an almost temperature-independent resistance as a function of temperature ($R(T,p)\,\approx\,$120\,$\Omega$) and are enclosed in a very thin layer of plastic coating giving rise to a low thermal mass. The samples, with typical masses $\,\sim\,2\,$mg, are cut into plates with dimensions as close as possible to the active heater area dimensions. The thermometer and heater are attached to the sample by using Devcon 5 Minute epoxy (No. 14250) to improve the thermal contact between the individual components and to guarantee sufficient mechanical stability in the pressure cell (shown schematically in Figs.\,\ref{fig:schematicsetup} (a) and (c)). A photograph of the assembly is shown in Fig.\,\ref{fig:schematicsetup}\,(d). The wires of the thermometer and heater are soldered to the wires passing the pressure-cell feedthrough. The thermometer is connected in a pseudo-four-point configuration in which the four wires for current and voltage are reduced to two wires inside the pressure cell. In addition, a Pb sample is mounted on the feedthrough in a four-point configuration for determining its critical temperature, $T_c$, via resistance measurements. The $T_c$ value can be used to determine the pressure, $p$, at low temperature as $T_c(p)$ is well characterized in literature \cite{Bireckoven88}.
The sample end of the feedthrough is placed in a Teflon-cup (see Figs.\,\ref{fig:schematicsetup}\,(b) and (c)) which is filled with the pressure-transmitting medium. In all the experiments presented here, a mixture of 4:6 mixture of light mineral oil:n-pentane \cite{Budko84,Kim11} is used as a pressure-transmitting medium. It solidifies at $p\,\approx\,3-4\,$GPa at room temperature, thus ensuring hydrostatic pressure conditions in the available pressure range. Two anti-extrusion rings made out of phosphor-bronze are used to prevent the teflon from flowing through the interstices when pressurized. The outer cell body is made out of Grade 5 titanium alloy (Ti 6Al-4V) and the inner cylinder out of Ni-Cr-Al alloy. Its design is similar to the one described in Ref. \citen{Budko84}. As Ti 6Al-4V alloy turns superconducting \cite{Ridgeon17} below $\approx\,$5\,K and as a consequence, its thermal conductivity becomes significantly reduced, the sample inside the cell cannot be cooled below 5\,K. Therefore, the use of this particular cell is restricted to temperatures above 5\,K. This issue can be circumvented by using cells made out of a different material, such as CuBe/Ni-Cr-Al.
Pressure is applied by applying a load to the piston at room temperature by a hydraulic press and locked by tightening the lock nut. All measurements shown in this manuscript were performed inside the pressure cell. At the beginning of each pressure cycle the pressure cell was closed hand-tight. Whereas this procedure typically results in a small, but finite pressure at room temperature \cite{Thompson84} ($p\,\lesssim\,0.3\,$GPa), the pressure at low temperature inferred from $T_c$ of Pb is usually very close to 0\,GPa ($p\,\lesssim\,0.04\,$GPa). We refer to this situation in the manuscript as ``ambient-pressure'' condition ($p\,=\,0\,$GPa). All data shown were obtained by increasing pressure to the measured value.
\begin{figure}
\includegraphics[width=0.9\textwidth]{figures/setup-schematics.pdf}
\caption{(a) Schematic diagram of the sample arrangement with heater and thermometer. The heater is supplied with an AC voltage with frequency $\omega/2$ which results in an oscillation of the temperature of the sample with frequency $\omega$; (b) Schematic diagram of the piston-pressure cell used in the present work; (c) Schematic diagram of the sample assembly and Pb sensor inside the teflon cup; (d) Photograph of the heater, sample and thermometer mounted on the pressure-cell feedthrough. The Pb sensor for the determination of the pressure value near 7\,K is also mounted on the feedthrough.}
\label{fig:schematicsetup}
\end{figure}
The measurements were carried out in a cryogen-free cryostat (Janis SHI-950 with a base temperature of $\approx\,3.5\,$K). The probe, used in this cryostat, is wired with phosphor-bronze wires (QT-36, LakeShore Inc.) to ensure low heat flow through the wires. The temperature was controlled continuously between base and room temperature by a LakeShore 336 controller. Temperature was monitored by a calibrated temperature sensor (Cernox-1030) which was placed directly outside the pressure cell by inserting it into a copper bracket. The Cernox thermometer inside the pressure cell was supplied by a DC current (Model CS580, Stanford Research Systems). The size of the DC current was adjusted with temperature such that the voltage limit ($<\,100\,$mV) of the thermometer is not exceeded. The voltage oscillations of the thermometer which result from the AC heating were pre-amplified and filtered (Model SR560, Stanford Research Systems) and then measured with a Lock-In Amplifier (Model SR860, Stanford Research Systems) the internal oscillator of which was used to provide the heating voltage. The heating power was chosen such that the amplitude of the induced temperature oscillation $T_{AC,0}$ (see Fig.\,\ref{fig:schematicsetup} (a)) was typically smaller than 20\,mK. To measure frequency responses (i.e., measurements as a function of frequency, see below), we used the built-in frequency option of this particular Lock-In Amplifier which allows to change the frequency within user-defined frequency limits and sweep rates. The DC resistance of the bare Cernox chips inside the pressure cell was read out simultaneously to each specific heat measurement by a Digital Voltmeter (SIM970, Stanford Research Systems). The resistance of the Pb sensor was measured with a LakeShore AC Resistance Bridge (Model 370). All data are recorded using a custom LabView Program.
\section{Results: Cernox resistance under pressure}
\label{sec:Cernoxresistance}
Figure \ref{fig:Cernoxresistance} (a) summarizes our main result on the behavior of the Cernox (type CX-1080) resistance, $R$, as a function of temperature, $T$, at three selected pressures up to $p\,\approx\,$2\,GPa. These data were taken without any applied heat to the heater inside the pressure cell. At ambient pressure, the resistance shows a typical behavior for Cernox thermometers: the resistance increases with decreasing temperature and the slope d$R$/d$T$ is finite over the entire temperature range which guarantees a sufficient sensitivity of this thermometer from low temperatures ($T\,\approx\,$5\,K) up to high temperatures ($T\,\approx\,$150\,K). Upon increasing pressure, the resistance at a fixed temperature is reduced by $\approx\,$28\% at 5\,K ($\approx\,10\,$\% at 150\,K) at 2\,GPa (see Fig.\,\ref{fig:Cernoxresistance} (b) for change of resistance as a function of pressure at different temperatures). However, the overall behavior as a function of temperature is nearly unchanged. To quantify the sensitivity of the thermometer, one can refer to the dimensionless quantity (d$R$/d$T$)/($R/T$) which is displayed as a function of $T$ in the inset of Fig. \ref{fig:Cernoxresistance} (a) for the same pressure values as the ones depicted in the main panel. This representation shows that this type of Cernox thermometer has an almost temperature- and pressure-independent sensitivity factor of 1.25. Only at low temperatures ($T\,<\,25\,$K), an increased sensitivity up to 1.5 is observed for all pressures. Thus, our measurements clearly show that Cernox thermometers keep their high sensitivity across a wide temperature range up to 2\,GPa. Note that even though we restrict ourselves in this study to temperatures below 150\,K, it is known that (d$R$/d$T$)/($R/T$) of the Cernox thermometers remains almost unchanged at ambient pressure up to room temperature \cite{Cernox}. Based on our results, it is therefore likely that the Cernox thermometers are very sensitive up to room temperature, even under pressure. Moreover, we did not find any indications of changes in the thermometer behavior from one pressure cycle to the next or strong deviations in the behavior of different chips (see Fig.\,\ref{fig:Cernoxresistance} (b)). Nevertheless, the minor differences in the resistance behavior of different chips depicted in Fig.\,\ref{fig:Cernoxresistance} (b) requires a calibration of each chip for each pressure run, as will be described below. All in all, our results show the Cernox chips can be used as temperature sensors in pressure experiments with high reliability and reproducibility.
\begin{figure}
\includegraphics[width=0.9\textwidth]{figures/Cernox-pressure-110518.pdf}
\caption{(a) Resistance, $R$, of a Cernox thermometer, type CX-1080, as a function of temperature, $T$, at three different pressures $p$, ranging from 0\,GPa to 2.05\,GPa; Inset: Sensitivity, defined as $|$d$R/$d$T/(R/T)|$, as a function of temperature for the same pressure values, as depicted in the main panel. The step at $T\,\approx\,$50\,K in the data at 0\,GPa and 2.05\,GPa is likely an artifact associated with changing of thermometer current; (b) Resistance of a Cernox thermometer, type CX-1080, normalized to its ambient-pressure value, $R/R(p\,=\,0)$ at different temperatures between 5\,K and 150\,K. Open and closed symbols represent measurements on two different chips of the same type.}
\label{fig:Cernoxresistance}
\end{figure}
\section{AC Specific heat: Theoretical background and Measurement Protocol}
\label{sec:ACtheory}
In the following, we want to focus on one possible application for which it is essential to determine temperatures with high sensitivity inside the pressure cell, namely when performing measurements of the specific heat of solids under pressure. As we employ here the method of AC calorimetry, this section will provide theoretical background information \cite{Sullivan68,Eichler79} on the AC calorimetric technique which is essential for understanding our measurement protocol.
To extract absolute specific heat values from an AC calorimetry experiment, an understanding of the heat flow from the heater to the various components in the system is needed. On one hand, the heat is transferred from the heater (specific heat $C_H$) through the sample ($C_S$) to the thermometer ($C_{\Theta}$) which are connected via finite thermal conductances. In the following, the thermal conductances between sample and heater as well as thermometer and sample which govern the heat transfer are denoted as $\lambda_{HS}$ and $\lambda_{\Theta S}$, respectively. On the other hand, each component is also coupled to a bath with temperature $T_B$ (which corresponds to the temperature on the outside of the pressure cell) by finite thermal conductances, denoted by $\lambda_H$, $\lambda_S$ and $\lambda_\Theta$. A block diagram of this arrangement is shown in Fig.\,\ref{fig:frequencydependence} (a). Note that the couplings $\lambda_H$, $\lambda_S$ and $\lambda_{\Theta}$ are non-negligible in the present case, as the sample has to be embedded in a pressure medium inside the pressure cell for measurements under pressure. This, in general, means that the absolute values of the specific heat cannot be determined under pressure with high accuracy. Nonetheless, we will show below that the AC technique implemented in this work allows for a determination of specific heat value under pressure at a semi-quantitative level by choosing the right measurement frequency.
When the heater is supplied with an AC voltage $U(t)\,=\,U_0 \sin(\frac{\omega}{2} t)$, it gives rise to an AC heating power $P(t)\,=\,P_0 \sin^2(\frac{\omega}{2}t)$ and the temperature of the sample will respond in the following manner:
\begin{equation}
T(t) \,=\, T_{DC} + T_{AC}(t).
\end{equation}
$T_{DC}$ refers here to the time-independent increase of the sample temperature with respect to the bath, which is determined by the heating power as well as the coupling to the bath via $T_{DC}\,=\,T_B+\frac{P_0}{2\lambda_S}$. The second term $T_{AC}(t)\,=\,T_{AC,0} \sin(\omega t + \phi)$ describes the temperature oscillation of the sample which oscillates with twice the driving frequency of the heater. The amplitude of this oscillation $T_{AC,0}$ contains the information about the specific heat of the sample $C_S$. The sensitivity of an AC specific heat setup is particularly high for small samples (i.e. with small $C_S$), as $T_{AC,0}$ is inversely proportional to $C_S$. In detail, the relation of $T_{AC,0}$ to $C_S$ for a realistic model with finite thermal conductances was discussed in the works of Sullivan and Seidel (Ref. \citen{Sullivan68}), as well as Eichler (Ref. \citen{Eichler79}), and reads as
\begin{eqnarray}
T_{AC,0} \,&=&\, \frac{P_0}{2\omega C}\,\cdot\,F(\omega) \label{eq:frequency-response} \\
\textnormal{with\ } F(\omega)\,&=&\,[1+2\,\cdot\,(\frac{\lambda_H}{\lambda_{HS}}+\frac{\lambda_\Theta}{\lambda_{\Theta S}})+\frac{1}{(\omega \tau_1)^2}+(\omega \tau_2)^2]^{-1/2} \label{eq:frequency-response2}\\
\textnormal{and\ } C &=& C_H + C_\Theta + C_S, \tau_1=\frac{C}{\lambda_S}, \\
\tau_2 &=& \sqrt{\tau_H^2+\tau_\Theta^2} \textnormal{\ with \ } \tau_H\,=\,C_H/\lambda_{HS} \textnormal{\ and \ } \tau_\Theta = C_\Theta/\lambda_{\Theta S}.
\end{eqnarray}
Thus, whenever the measurement frequency is choosen such that $(\omega \tau_1)^2\,\gg\,1$ and $(\omega \tau_2)^2\,\ll\,1$, with $\tau_1$ and $\tau_2$ corresponding to the thermal relaxation times to the bath and within the assembly of heater, sample and thermometer, respectively, then $F(\omega)\,\approx\,[1+2\,\cdot\,(\frac{\lambda_H}{\lambda_{HS}}+\frac{\lambda_\Theta}{\lambda_{\Theta S}})]^{-1/2}$. The error in determination of absolute values then is mainly determined by the ratios $\frac{\lambda_H}{\lambda_{HS}}$ and $\frac{\lambda_\Theta}{\lambda_{\Theta S}}$. However, sample, heater and thermometer are in intimate contact, whereas the heat path to the bath (i.e., the outside of the pressure cell) is long. This implies due to the geometrical arrangement that, to a first approximation, $\lambda_H\,\ll\,\lambda_{HS}$ and $\lambda_\Theta\,\ll\,\lambda_{\Theta S}$ (and we will show below that this assumption is verified in our setup), and therefore $F(\omega)\,\approx\,1$. It then follows that $T_{AC,0}\,=\,\frac{P_0}{2\omega C}$.
The frequency which meets these criteria is called the optimal measurement frequency $\omega_{opt}$. As $\tau_1$ and $\tau_2$ depend on the specific heat of the sample, as well as on thermal conductances $\lambda_{HS}, \lambda_S$ and $\lambda_{\Theta S}$, $\omega_{opt}$ will in general be a function of temperature and pressure, and will differ from sample assembly to sample assembly. Correspondingly, $\omega_{opt}$ has to be determined experimentally for each sample, temperature and pressure individually, prior to each measurement of the specific heat. It can be shown that $\omega_{opt}$ is the frequency at which $F(\omega)$ is maximal. As suggested by eq. \ref{eq:frequency-response}, direct experimental access to $F(\omega)$ is provided by measuring the frequency dependence of the quantity $\omega\,\cdot\,T_{AC,0}$ (called frequency response hereafter). In Figs. \ref{fig:frequencydependence} (b) and (c) we show examples of the frequency responses, normalized to their respective maximum, recorded with our setup when measuring the specific heat of elemental Pb (The specific heat results on Pb will be discussed in Sec.\,\ref{sec:specheatresults} in more detail.). First, we compare in Fig.\,\ref{fig:frequencydependence}\,(b) the frequency response, taken at $T\,=\,6$\,K at two different pressures ($p\,=\,0\,$GPa and 1.97\,GPa). Each frequency response (normalized to its maximum value) reveals a broad maximum at $\approx\,100\,$Hz and 300\,Hz, respectively, which we assign to the optimal measurement frequencies $\omega_{opt}$. Note that a broad maximum (or even a wide plateau) suggests that $(\omega \tau_1)^2\,\gg\,1$ and $(\omega \tau_2)^2\,\ll\,1$ across a wide frequency range which minimizes errors in the determination of absolute values of the specific heat. The observation of a broad maximum is therefore crucial for the determination of absolute values of the specific heat under pressure on a semi-quantitative level, as achieved with our setup. At the same time, at a fixed pressure, as shown in Fig.\,\ref{fig:frequencydependence}\,(c) for $p\,=\,$1.97\,GPa, we find that the broad maximum in the frequency response and thereby $\omega_{opt}$ shifts to lower frequencies with increasing temperature. The evolution of $\omega_{opt}$, determined from the numerical derivation of the frequency response data, with $T$ and $p$ is summarized in Fig.\,\ref{fig:frequencydependence}\,(d).
The knowledge of the frequency response allows us to extract the relaxation times $\tau_1$ and $\tau_2$ of this particular assembly at different pressures. The solid lines in Fig.\,\ref{fig:frequencydependence}\,(b) show a fit of eq.\,\ref{eq:frequency-response2} to our experimental data, taken at 6\,K. The fits, which were performed with keeping $(\frac{\lambda_H}{\lambda_{HS}}+\frac{\lambda_\Theta}{\lambda_{\Theta S}})$ fixed to 0, are in very good agreement with our experimental data set. They yield $\tau_1\,=\,(0.047\,\pm\,0.001)\,$s and $\tau_2\,=\,(0.0016\,\pm\,0.0001)\,$s at ambient pressure and $\tau_1\,=\,(0.015\,\pm\,0.001)\,$s and $\tau_2\,=\,(0.0009\,\pm\,0.0001)\,$s at $p\,=\,1.97\,$GPa. Thus, the optimal measurement frequencies $\omega_{opt}$ fulfill the criteria mentioned above as $(\omega_{opt} \tau_1)^2\,\approx\,22\,\gg\,1$ and $(\omega_{opt} \tau_2)^2\,\approx\,0.02\,\ll\,1$ at $p\,=\,0\,$GPa and $(\omega_{opt} \tau_1)^2\,\approx\,20\,\gg\,1$ and $(\omega_{opt} \tau_2)^2\,\approx\,0.07\,\ll\,1$ at $p\,=\,1.97\,$GPa. Our fitting results indicate that both relaxation times decrease with increasing pressure. This tendency is naturally expected, as the coupling to the bath, but also the coupling within the assembly likely increase under compression. Therefore, the increased optimal frequency $\omega_{opt}$ with applied $p$ is directly a consequence of the decreased relaxation times. The temperature dependence of $\omega_{opt}$ is less intuitive to understand as it depends on the temperature-dependent changes of specific heat as well as thermal conductivity of sample, heater as well as thermometer.
It should be noted that the error in the determination of the absolute value of the specific heat can be estimated from the knowledge of $\tau_1$ and $\tau_2$. Equations \ref{eq:frequency-response} and \ref{eq:frequency-response2} suggest that any finite $\tau_1$ as well as any non-zero $\tau_2$ will give rise to an overestimation of the specific heat value by the factor $[1+\frac{1}{(\omega \tau_1)^2}+(\omega \tau_2)^2]^{1/2}$, if $\frac{\lambda_H}{\lambda_{HS}}+\frac{\lambda_\Theta}{\lambda_{\Theta S}}\,\approx\,$0. Our results of $\tau_1$ and $\tau_2$ correspond to an overestimate of specific heat by $\approx\,$3\,\% at ambient pressure, and $\approx\,$5\,\% at 1.97 GPa by our setup. This estimate shows that our setup can, in principle, deliver absolute values on a semi-quantitative level, despite a non-negligible coupling to the bath. Importantly, the analysis performed here shows that the overestimation of specific heat does not significantly change with pressure. This allows for the determination of changes (especially relative changes) of specific heat under pressure with higher accuracy. We confirm these conclusions from the analysis of the frequency response in Sec. \ref{sec:specheatresults}, where we present specific heat under pressure data on three different test cases and compare with ambient-pressure literature data taken under adiabatic conditions.
The theoretical background information given here explains the measurement protocol which we follow to determine the specific heat of a sample using the AC technique. It includes in total three separate, sequential temperature sweeps. First, we need to calibrate the Cernox thermometers inside the pressure cell at a specific pressure to quantify the DC temperature increase $T_{DC}$ of the sample which results from applying heat to the heater inside the cell. To this end, we place a calibrated thermometer outside on the pressure cell and record the resistance of the Cernox thermometer inside the pressure cell upon slow warming with a rate of $\approx\,0.25\,$K/min without any voltage applied to the heater inside the cell (see Sec.\,\ref{sec:Cernoxresistance}). In the second temperature sweep, we record the frequency response $\omega\,\cdot\,T_{AC,0}$ vs. $\omega$ as a function of temperature for the same, specific pressure. From this data, we extract $\omega_{opt}$ as a function of $T$ and typically fit this smooth data set with an exponential function $\omega_{opt}\,=\,\omega_0+A\exp(-T/t_1)$ with free parameters $\omega_0$, $A$ and $t_1$ (see grey lines in Fig.\,\ref{fig:frequencydependence} (d)). Within our measurement program, we adjust the measurement frequency continuously with temperature according to this exponential function during the third temperature sweep for a specific pressure. This ensures that the AC temperature oscillation $T_{AC,0}$ as a function of $T$ is always measured at the optimal measurement frequency which then allows us to infer the specific heat on a semi-quantitative level.
\begin{figure}
\includegraphics[width=0.9\textwidth]{figures/Pb_optimalfrequency_090518.pdf}
\caption{(a) Schematic diagram illustrating heat flows from the sample to the heater (governed by the thermal conductivity $\lambda_{HS}$), from the sample to the thermometer ($\lambda_{\Theta S}$), and from sample, heater and thermometer to the bath ($\lambda_S$, $\lambda_H$ and $\lambda_\Theta$); (b) Normalized frequency response, i.e., the product of frequency $\omega$ and oscillation amplitude $T_{AC,0}$ normalized to its maximum value $(\omega T_{AC,0})_{max}$ vs. $\omega$, for a Pb sample at $T\,=\,6$\,K and $p\,=\,0\,$GPa and 1.97\,GPa; (c) Normalized frequency response for a Pb sample at different temperatures between 5\,K and 9\,K at $p\,=\,1.97\,$GPa; (d) Evolution of the optimal measurement frequency $\omega_{opt}$ as a function of temperature and pressure, obtained from the data presented in (b) and (c) (for details, see main text). Grey lines represent exponential fits to the $\omega_{opt}$ vs. $p$ data sets.}
\label{fig:frequencydependence}
\end{figure}
\section{Specific heat under pressure: Results}
\label{sec:specheatresults}
In the following, we demonstrate the wide applicability of the Cernox thermometers in measurements of specific heat under pressure by examining three test cases with very different transition temperatures, ranging from $T\,\approx\,7\,$K (superconducting transition in Pb) up to $T\,\approx\,130\,$K (magnetostructural transition in BaFe$_2$As$_2$), as well as very different amounts of entropy change.
\subsubsection{Superconducting phase transition in elemental Pb}
The first sample for a study of specific heat under pressure chosen here is elemental lead (Pb) which undergoes an ambient-pressure superconducting transition at a critial temperature $T_c\,=\,7.2\,$K. The shift of $T_c$ with pressure is well characterized in literature \cite{Bireckoven88} and therefore often utilized as a manometer at low temperatures.
\begin{figure}
\includegraphics[width=0.8\textwidth]{figures/Pb-050918.pdf}
\caption{(a) Molar specific heat $C_{molar}$ of elemental Pb as a function of temperature $T$ at four different pressures up to 1.97\,GPa; (b,c) Comparison of $C_{molar}(T)$ of Pb and the resistance $R_{Pb}(T)$ of the Pb pressure sensor at a pressure of 0 GPa (b) and 1.97\,GPa (c).}
\label{fig:Pb}
\end{figure}
Figure \ref{fig:Pb} (a) shows our results of the specific heat, $C_{molar}$, of Pb at different pressures up to 1.97\,GPa. At all pressures, we find a jump-like change of $C_{molar}$ at a critical temperature $T_c$. This feature is characteristic for the mean-field type phase transition into the superconducting state in BCS superconductors. The critical temperature, extracted from our $C_{molar}$ data, is suppressed with increasing $p$, consistent with literature results \cite{Bireckoven88}. In addition, the overall specific heat is reduced upon pressurization, likely due to a combination of changes in the electronic density of states as well as lattice stiffening (see below for more details).
To demonstrate the high accuracy in the determination of phase transition temperatures from our specific heat data, we compare in Figs. \ref{fig:Pb} (b) and (c) the specific heat of the Pb sample, placed between heater and thermometer, with the resistance of the Pb manometer, $R_{Pb}$, at lowest pressure ($p_1\,=\,0\,$GPa) and highest pressure ($p_4\,=\,1.97\,$GPa) of our experiment. At both pressures, the midpoint of the jump in $C_{molar}$ occurs at the same temperature at which the resistance clearly shows a jump-like change into the superconducting state. This also demonstrates that there are no significant pressure gradients in our pressure cell.
Next, we want to discuss to which extent our setup delivers a semi-quantitative determination of the specific heat of solids by comparing our results to literature results \cite{Shiffman63} on Pb (see Fig. \ref{fig:Pb-analysis}). Our data overestimates the absolute specific heat value by $\approx\,12\,\%$, compared to the literature results from Ref. \citen{Shiffman63}. As outlined in Sec.\,\ref{sec:ACtheory}, an overestimate of absolute specific heat values determined with the AC technique is a consequence of finite relaxation times $\tau_1$ and $\tau_2$. The overestimation factor of about 3\,\%, estimated from an analysis of the frequency responses in Sec. \,\ref{sec:ACtheory}, is of similar size as the overestimation found here from the comparison with literature data on Pb. Note that we did not correct our data for the specific heat of the addenda, i.e., of thermometer, heater and the tiny layers of glue. These additional contributions to the measured specific heat, which can be as large as 50\,\% of the total measured specific heat depending on the specific sample, its size, mass and shape (estimated by measuring the size of the addenda at ambient pressure using the relaxation-time method), likely give rise to the slightly larger overestimation of 12\,\% found empirically here. Clearly, despite the strong coupling to the bath due to the pressure medium and uncertainties in the size of the addenda, our data resembles literature results on a semi-quantitative level, i.e., within less than approximately a factor of 2. This upper limit was estimated empirically in the study of the three different test cases presented in this manuscript. The superconducting jump size extracted from our data at ambient pressure amounts to $\Delta C_{sc}\,\approx\,(44.6\,\pm\,0.5)\,$mJ/mol/K \cite{Shiffman63,Clement52}. This value is slightly smaller than reported values in literature ($\Delta C_{sc}\,=\,$52.9\,mJ/mol/K up to 57.5\,mJ/mol/K), but nevertheless matches on the same semi-quantitative level.
Upon pressurization, we find a significant reduction of $\Delta C_{sc}$ with increasing $p$ down to $\approx\,(29.0\,\pm\,0.5)\,$mJ/mol/K at 1.97\,GPa (see Fig.\,\ref{fig:Pb-analysis} (b)). For superconductors, the change in $\Delta C_{sc}$ is related on the one hand to a change in $T_c$ as well as to a change in the density of states at the Fermi level $N(E_F)$ \cite{Carbotte90}. Figure \ref{fig:Pb-analysis} (b) also includes a plot of $\Delta C_{sc}/T_c$ as a function of $T_c$. The strong change of $\Delta C_{sc}/T_c$ with $p$ by $\approx\,-\,25\,\%$ indicates that most of the change of $\Delta C_{sc}$ with $p$ can be attributed to changes of $N(E_F)$ with $p$, rather than to changes of $T_c$. Unfortunately, no literature data on the change of $N(E_F)$ in Pb with $p$ is available. Also the determination of the change of $N(E_F)$ under $p$ by extracting the Sommerfeld coefficient $\gamma$ from our specific heat data turns out to be not reliable due to the relatively high $T_c$ of Pb combined with a relatively low Debye temperature $\Theta_D\,\approx\,100\,$K at ambient pressure. Thus, we performed density-functional theory (DFT) calculations \cite{Hohenberg64,Kohn65} of the band structure of Pb up to 2\,GPa using PBEsol as exchange-correlation functional with spin-orbit coupling (SOC) effect as implemented in VASP \cite{Kresse96,Kresse96b}. At zero pressure, the theoretical lattice constant of 4.934\,\AA\ agrees very well with the experimental values of 4.95\,\AA. At 2 GPa, the lattice constant is reduced to 4.872\,\AA. We find a decrease of $N(E_F)$ from 0.5303\,states/eV/cell to 0.5121 \,states/eV/cell by 2\,GPa which corresponds to $\approx\,-\,3.5$\,\%. Even though this value is smaller than the one inferred from our specific heat measurements, both results are consistent in inferring a decrease of $N(E_F)$ with pressure. This supports our conclusion that in case of Pb changes of the specific heat anomaly $\Delta C_{sc}$ under $p$ result from a decrease of $N(E_F)$ with pressure.
\begin{figure}
\includegraphics[width=0.8\textwidth]{figures/Pb_analysis-050918.pdf}
\caption{(a) Comparison of ambient-pressure literature data \cite{Shiffman63} on the specific heat $C_{molar}$ of elemental Pb (grey symbols) and the specific heat obtained in the present work in the pressure cell at ambient pressure (black solid line); (b) Evolution of the superconducting jump size in the specific heat $\Delta C_{sc}$, as well as the jump size normalized to the critical temperature, $\Delta C_{sc}/T_c$, with $T_c$.}
\label{fig:Pb-analysis}
\end{figure}
\subsubsection{Antiferromagnetic transition in the rare-earth compound GdNiGe$_3$}
The specific heat anomaly at the superconducting transition in Pb as well as the transition temperature respond strongly to application of external pressure. In addition, the amount of entropy change is relatively small. For the next system, we chose GdNiGe$_3$ anticipating a weak response to pressure and a large change in entropy ($\approx\,R \ln(8)$) \cite{Mun10}. This allows us to show that changes of the absolute values of specific heat under pressure are not a result of an artifact due to modified coupling to the bath or within the assembly of sample, heater and thermometer, i.e., due to changing $\tau_1$ and $\tau_2$. This in turn allows us to establish a high accuracy in the determination of \textit{changes} of the specific heat under pressure. At the same time, a system with a phase transition occurring at higher transition temperature compared to the superconducting transition in elemental Pb is desired to prove high sensitivity of our setup at even higher temperatures.
The rare-earth based GdNiGe$_3$ system has a single antiferromagnetic (afm) transition\cite{Mun10} at $T_N\,\approx\,$26\,K. Importantly, as the moment-carrying Gd is trivalent in this compound and therefore has a Hund's rule $J\,=\,S\,=\,7/2$ ground state ($L\,=\,0$), the compound lacks any magneto-crystalline anisotropy or splitting of the Hund's rule ground state multiplet. Experiments \cite{Mun10} confirmed that GdNiGe$_3$ shows an almost isotropic susceptibility in the paramagnetic state with an effective moment $\mu_{eff}\,=\,8.0\,\mu_B$/Gd$^{3+}$, close to the free-ion value of 7.94\,$\mu_B$/Gd$^{3+}$. Correspondingly, specific heat measurements \cite{Mun10} showed a single $\lambda$-shaped peak at $T_N$ (see grey symbols in Fig.\,\ref{fig:GdNiGe3} for a reproduction of these data). The magnetic entropy, $S$, extracted from measurements of the specific heat was found to be almost constant at $T\,>\,T_N$ with $S\,=\,$17\,J/(mol$\cdot$K), i.e., close to the expected value of $R \ln(8)$. This result is fully consistent with the absence of crystal-field effects in this compound. As the magnetism of this compound can be well understood in terms of localized 4f moments which interact via RKKY (Ruderman-Kittel-Kasuya-Yosida) interaction \cite{Ruderman54}, the response to hydrostatic pressure is expected to be relatively weak. This, together with the well-defined entropy in the paramagnetic state and a high transition temperature, makes this system a suitable reference system for a study of the specific heat under pressure.
\begin{figure}
\includegraphics[width=0.8\textwidth]{figures/GdNiGe3-050918.pdf}
\caption{Molar specific heat divided by temperature $C_{molar}/T$ as a function of temperature $T$ of GdNiGe$_3$ at different pressures up to 1.2 GPa. For comparison, literature data at ambient pressure \cite{Mun10} on this compound are shown in grey. The arrow indicates exemplary the jump size at the antiferromagnetic transition, $\Delta C_{molar}/T$, at lowest pressure $p\,\sim\,0.2$\,GPa (for a definition of criterion and evolution with pressure, see main text). }
\label{fig:GdNiGe3}
\end{figure}
The results of our specific heat study on GdNiGe$_3$ under pressure are shown in Fig.\,\ref{fig:GdNiGe3} in a $C_{molar}/T$ vs. $T$ representation. For comparison, we included the literature specific heat data on this compound at ambient pressure, taken from Ref. \citen{Mun10}. At all measured pressures, our data nicely reveal the $\lambda$-shaped phase transition anomaly at $T\,\approx\,26\,$K. In addition, we also find a small hump in the specific heat below 10\,K. Such a hump in the specific heat at temperatures well below the ordering temperatures was found in various Gd-based systems \cite{Kong14} and was explained by modelling the specific heat of a $(2J+1)$ multiplet in a mean-field approach \cite{Bouvier91,Blanco91}. The comparison of our specific heat data with literature in terms of absolute values indicates an $\approx\,$10\% to 40\% overestimation of the specific heat for $T\,>\,15\,$K. For $T\,<\,15\,$K, we find an underestimate of $C_{molar}/T$. The reason for this behavior is unclear at present, as eqs.\,\ref{eq:frequency-response} and \ref{eq:frequency-response2} do not allow an underestimate. However, this additional data set on GdNiGe$_3$ also confirms that we are not only highly sensitive in tracing phase transitions even at higher temperatures, but also that we can determine absolute specific heat values within less than a factor of 2 deviation from literature.
\begin{figure}
\includegraphics[width=0.8\textwidth]{figures/GdNiGe3-analysis-050918.pdf}
\caption{(a) Change of jump size in specific heat at $T_N$, $\Delta C_{molar}/T$, and $T_N$ (inset) with pressure; (b) Comparison of estimated magnetic entropy at 0.2 GPa (present experiment, black circles) with literature results\cite{Mun10} at ambient pressure (grey squares). Inset: Estimated magnetic entropy at different pressures up to 1.2\,GPa.}
\label{fig:GdNiGe3-analysis}
\end{figure}
In the following, we focus on the relative evolution of the specific heat with pressure. The overall specific heat values at each temperature are reduced upon applying pressure. Similar to the case of Pb, we assign this reduction to changes of the lattice and electronic specific heat. More importantly, however, we find that the $\lambda$-shaped peak, as well as the low-temperature hump are almost unaffected by pressure. This relates to the position of the anomalies as well as the size and shape of the anomaly. To quantify this statement, we show in Fig.\,\ref{fig:GdNiGe3-analysis} (a) the evolution of the jump size of the $\lambda$-shaped anomaly, $\Delta C_{molar}/T$, as well as the transition temperature $T_N$ (inset) with pressure. Whereas $T_N$ is extracted from the minimum in the derivative of the $C_{molar}/T$ data, $\Delta C_{molar}/T$ is calculated by the difference of $C_{molar}/T$ values at those temperatures at which d($C_{molar}/T$)/d$T$\,=\,0.1\,(d($C_{molar}/T$)/d$T$)$_{T_N}$ (see arrow in Fig.\,\ref{fig:GdNiGe3}). We find a slight decrease of $\Delta C_{molar}/T$ with pressure by $\approx\,-\,$6\,\% and a small increase of $T_N$ by less than 1\,\% within a pressure range of $\approx\,$1\,GPa. We want to emphasize that the relative change in $\Delta C_{molar}/T$ is tiny compared to the specific heat changes observed under pressure in elemental Pb. At present, this tiny change of the specific heat features in GdNiGe$_3$ cannot unequivocally be assigned to a single origin: Either the change is indeed related to changes of physical properties under pressure (see Refs. \citen{Bouvier91,Blanco91} for theoretical discussions of specific heat features in Gd-based compounds on a mean-field level), or the change is an artifact arising from uncertainties in the absolute values determined with the AC calorimetric technique related to changes in the relaxation times $\tau_1$ and $\tau_2$ with pressure. Most likely, both factors actually play a role here, but more importantly none of them gives rise to changes in the specific heat beyond $\approx\,$6\,\% when changing pressure by 1\,GPa. Thus, we can conclude from our specific heat measurements on GdNiGe$_3$ that changes in the specific heat of more than $\approx\,$6\,\% within 1\,GPa, in particular at phase transitions, can reliably be attributed to changes of physical properties, rather than to instrumental artifacts. We also note that in principle the addenda contribution can change with pressure. This change is explicitly included in the error bar given above. However, in general it is reasonable to assume that in first approximation the specific heat of the addenda does not change with pressure.
To extract the magnetic entropy and changes of this quantity with pressure from the present data set, non-magnetic (phononic and electronic) contributions need to be subtracted. These contributions are typically obtained by measuring the specific heat of a non-magnetic reference sample if available. In this case, YNiGe$_3$ serves as a suitable non-magnetic reference system the ambient-pressure specific heat of which was reported in Ref. \citen{Mun10}. As an independent measurement of YNiGe$_3$ with our AC calorimetric setup would require a new assembly with different relaxation times $\tau_1$ and $\tau_2$ which likely give rise to different error in the determination of absolute specific heat values compared to our values on GdNiGe$_3$, this approach to determine the non-magnetic contributions is not suitable in the present case. However, assuming that the overestimation factor is, in first approximation, temperature-independent and contributions from heater and thermometer to our measured specific heat are comparably negligible, we can rescale the reported ambient-pressure data on YNiGe$_3$ such that it almost matches our specific heat data on GdNiGe$_3$ at $T\,\gg\,T_N$ and $p\,\sim\,0.2\,$GPa. This procedure allows us to provide an estimate on the magnetic entropy from our data set (see Fig.\,\ref{fig:GdNiGe3-analysis} (b)). Our estimate of the magnetic entropy yields $S\,\sim\,15.7\,$J/mol/K at $T\,=\,T_N$ which corresponds to 90\% of the expected $S\,=\,R\,\ln(8)$. Even if this analysis can only provide a rough estimate of the entropy due to the uncertainties involved in the determination of the non-magnetic contributions, it confirms that we can determine not only specific heat, but also entropies on the same semi-quantitative level. When now discussing changes of the entropy as a function of pressure, we have to make further assumptions on how the non-magnetic contributions are affected by pressure. The change of the non-magnetic contributions reveals itself e.g. in the measured specific heat at $T\,\gg\,T_N$ which indicates a sizable reduction of $C_{molar}/T$ with $p$. To account for this change, we make the reasonable assumption that changes in the Sommerfeld coefficient $\gamma$ as well as the Debye lattice constant $\beta$ give rise to changes in the non-magnetic specific heat via $C_{molar}/T\,\propto\,\gamma + \beta T^2$. We now apply a temperature-independent as well as a quadratic correction to the $C_{molar}/T$ data of YNiGe$_3$ such that it matches our specific heat data on GdNiGe$_3$ at $T\,\gg\,T_N$ for $p_2$ and $p_3$ individually and subtract the so-derived non-magnetic contributions from our experimental data on GdNiGe$_3$. These estimates of the magnetic entropy are shown in the inset of Fig.\,\ref{fig:GdNiGe3-analysis}. We do not find any significant changes of the estimated magnetic entropy with pressure. This result is consistent with the almost unchanged size of specific heat anomaly $\Delta C_{molar}/T$ with $p$ and provides further evidence that changes of specific heat and entropies with pressure can be estimated with comparably high accuracy.
\subsubsection{Structural/magnetic transition in the iron-pnictide BaFe$_2$As$_2$}
Finally, to further demonstrate the sensitivity of our setup at even higher temperatures (above 100\,K), we present specific heat measurements under pressure on BaFe$_2$As$_2$. This material undergoes a structural and antiferromagnetic transition at $T_{s,N}\,\approx\,130\,$K from a tetragonal-paramagnetic to an orthorhombic-antiferromagnetic state \cite{Rotter08}. In the BaFe$_2$As$_2$ system either chemical substitution (e.g. of Fe by Co) \cite{Ni08,Canfield10,Sefat08} or pressure \cite{Colombier09} suppress this structural-magnetic transition and unconventional superconductivity, with critical temperatures up to $\approx\,22\,$K, emerges.
\begin{figure}
\includegraphics[width=0.8\textwidth]{figures/Ba122-050918.pdf}
\caption{Molar specific heat divided by temperature, $C_{molar}/T$, as a function of temperature $T$ of BaFe$_2$As$_2$ at ambient pressure as well as at $p\,=\,2.05$\,GPa; Inset: Specific heat, $C_{molar}$, of BaFe$_2$As$_2$ at ambient pressure on expanded scale.}
\label{fig:Ba122}
\end{figure}
Figure \ref{fig:Ba122} shows our results for the specific heat of BaFe$_2$As$_2$ in the pressure cell at ambient pressure as well as at $p\,=\,$2.05\,GPa. Our ambient-pressure data show a very sharp peak at the structural-magnetic transition at $T\,\approx\,132\,$K. Even if the size of the phase transition is strongly reduced by the application of $p\,=\,2.05\,$GPa, indicating a strongly reduced entropy change at the phase transition with pressure, we can still clearly resolve the phase transition at a lower temperature $T\,\approx\,112\,$K. The decrease in the phase transition temperature by $\approx\,-10\,$K/GPa agrees very well with earlier reports of the pressure dependence of $T_{s,N}$ based on resistance data \cite{Colombier09}. More importantly, not only can we resolve the high-temperature anomaly, but we can also measure the specific heat across the entire temperature range 5\,K$\,\le\,T\,\le\,$150\,K by using a single thermometer (see inset of Fig.\,\ref{fig:Ba122}). This is a clear advantage of using the Cernox thermometers as temperature sensors for AC specific heat measurements rather than RuO$_2$ thermometers which are inherently sensitive only in a much more limited, low-temperature range. The setup presented here will therefore allow in the future to measure the specific heat under pressure of systems which show a cascade of phase transitions at very different temperatures, such as e.g. the superconducting as well as magnetic-structural transition in Co-doped BaFe$_2$As$_2$.
\section{Summary}
In conclusion, we studied the response of Cernox thermometers to external pressure in piston-pressure cells up to 2\,GPa. These thermometers are frequently used in low-temperature experiments due to their high sensitivity. We find that the sensitivity of the Cernox thermometers remains high under pressures up to 2\,GPa. In addition, they are mechanically robust and survive numerous pressure cycles. Thus, our study shows that these temperature sensors can be used to measure temperatures inside the pressure cell with high accuracy. As a possible application, for which this high sensitivity is essential, we present in detail the use of these thermometers in measuring the specific heat of solids under pressure. By studying three different test cases (elemental Pb, GdNiGe$_3$ and BaFe$_2$As$_2$), we show that the high sensitivity of the Cernox thermometers allows to measure specific heat of solids under pressure across a wide temperature range as well as wide range of entropy changes. Therefore, by using Cernox thermometers, it will be possible in the future to study systems which show a cascade of phase transition across a wide temperature range by specific heat under pressure in a piston-pressure cell, possibly even up to room temperature. In addition, we demonstrate that our setup does not only allow to trace phase transitions, but is also very accurate in determining changes of the specific heat as a function of pressure.
\begin{acknowledgments}
We thank E. Mun and N. Ni for growing the GdNiGe$_3$ and BaFe$_2$As$_2$ crystals used in the study. This work was carried out at Iowa State University and supported by Ames Laboratory, US DOE, under Contract No. DE-AC02-07CH11358. G.D.'s efforts were partially funded by the Gordon and Betty Moore Foundation's EPiQS Initiative through Grant No. GBMF4411. L.X. was supported, in part, by the W. M. Keck Foundation.
\end{acknowledgments}
\bibliographystyle{modaps}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,471 |
Formula 1Opinion
OPINION: Why the 2012 Brazilian Grand Prix is the best world championship grand prix of all
by Jake Nichol April 11, 2019
written by Jake Nichol April 11, 2019
The 2012 Brazilian Grand Prix had many subplots, but Sebastian Vettel took his third world championship in one of the most remarkable sporting events of all time. Photo by Clive Mason/Getty Images/Red Bull Content Pool)
Let's clear one thing up from the off. This weekend's event at the Shanghai International Circuit is not the 1000th Formula 1 race. Nor is it the 1000th grand prix. It is the 1000th event to count towards the world championship in F1's history, but even this is caveated.
In the first eleven seasons of the fledgeling series, America's most famed open-cockpit race, the Indianapolis 500 had a slot on the calendar. This was to put the 'world' in the world championship, in a championship otherwise dominated by visits to European circuits. These eleven races are something of an anomaly as F1 drivers routinely ignored the bother of a trip stateside to rural Indiana. But in the index of F1's annals, they stand, as worthy and important as the other 988 races to date.
Indeed, there's also the case of the 1952 and 1953 seasons where the F1 world championship was run to Formula 2 regulations; the legacy of a shortage of appropriate machinery following Alfa Romeo's withdrawal after cleaning house in '51, as Juan Manuel Fangio took the first of his five drivers' crowns.
But, like the Indy 500s, the races of these two campaigns stand in the count towards 1,000, meaning that China will hold the accolade of staging the milestone race in the planet's premier racing series.
So, with 999 races to chose from, there is plenty of competition to select one of them to be proclaimed as the best world championship grand prix. Such a debate is rightly hotly contested with Brazil 2008 and Canada 2011 having strong claims to having the honour bestowed. But there is one race, some eight seasons ago, that stands head and shoulders above the rest: the 2012 Brazilian Grand Prix.
Such a question as to which race can be proclaimed the best is, of course, rooted, like an old Oak, in the grounds of subjectivity. There are myriad reasons why one would have a single grand prix entrenched in their mind as the best.
Your chosen race might have fallen on your birthday or that of a loved one; you could have got married or met the love of your life the very day that the race took place; perhaps your favourite driver stormed through the field from the back to claim an unlikely points finish or race win, or maybe even the drivers' championship. Or maybe a backmarker did something memorable, truly unexpected given the limitations of their equipment that hooked you in and made a lifelong F1 fan out of you.
Whatever your reasoning for selecting the race you have, it is based in the subjectivity of your circumstance. 'But isn't this article then just your own opinion?', you might be asking while reading this. In a word: yes, it is. However, the mechanisms of objectivity and social media allow a non-biased conclusion to be reached, that, by whatever criteria you use to measure, leads back to the 878th world championship grand prix taking its place on the pedestal as the best race of all.
What makes a good grand prix?
The recipe of what makes good grand prix is non-fluid and something which most fans can coalesce around, often doing so by sharing their opinions via the Deep Blue of social media. The first ingredient of which is tension. A tense Sunday afternoon spent chuntering from a sedentary position at your TV as the drama plays out is one of the thrills of watching and reacting to live, elite sport, where such fine margins mean the difference between winning and the first of the losers. And the afternoon/early evening (for UK viewers) of 25 November 2012 had tension and drama rarely seen in F1.
The race was a season-finale title decider between the blue corner of the reigning double world champion, unquenchable in his thirst to shatter all the records held by his compatriot, the retiring 91-time race winner, and to-date, only septuple world champion, Michael Schumacher. And in the red corner, the Spanish matador who had man-handled his recalcitrant Cavallino Rampante to the cusp of joining the elite band of triple world champions. This was Sebastian Vettel vs Fernando Alonso played out in the amphitheatre of the Autodromo Jose Carlos Pace.
Fernando Alonso had dragged an uncompetitive Ferrari to the cusp of the world championship in 2012.
Credit: (Octane Photographic Ltd.)
As the crowds began to enter the Interlagos circuit, the atmosphere grew thicker and heavier. Expectations of a gladiatorial fight were carried on the Brazilian winds, swirling through the paddock, scented by the carnival-like beat of the drums and local delicacies. These two men were about to enter the Colosseum to take the field of play for the biggest fight of their lives: to join the gods of their chosen profession.
And while we're on the subject of a deity greater than humankind, the race also had another vital ingredient: rain. Now, it is not a prerequisite for the wet stuff to make an appearance for grands prix to be considered a classic, far from it. Cast your mind back to the 2014 Bahrain Grand Prix, (incidentally the 900th race) or at Monza in 1971, where the top five finishers were separated by just 0.061s at the flag. But when another variable is added to the complicated mix of a grand prix, the excitement level builds. All the greats have destroyed the rest in the wet, and there have been some eye-catching performances – chiefly Vittorio Brambilla in Austria 1975. To quote former US Defence Secretary Donald Rumsfeld, rain is a "known unknown."
As the storm brewed above Sao Paulo, it was just a matter of time, before the rain joined the party, thus presenting Alonso with the slither of hope he was longing for.
Vettel was fourth on the grid, behind the McLaren's of Lewis Hamilton and Jenson Button and also his Red Bull team-mate, Mark Webber. Alonso languished in eighth after qualifying but was promoted to seventh on the starting grid after a penalty for Williams' Pastor Maldonado. As the cars sat waiting for the lights to go out, Vettel held a 13-point advantage over Alonso, meaning the Ferrari driver had to take a podium finish and hope Vettel finished tenth or lower. In a fundamentally slower car than the RB12, Alonso needed a miracle.
A slow start for Vettel and being crowded out by Webber at Turn 1 left him mired in midfield of the 24-strong pack as it charged down the back-straight toward Turn 4, Descida do Lago. Turning into the left-hander, Vettel was clattered into by the Williams of Bruno Senna and was lucky not to retire on the spot with the damage sustained to the floor, radiators, and aerodynamics on the left-hand side of the chassis. Rolling gently down the hill, Vettel, stone-dead last, regrouped and set about the charge that would claim him a third world championship.
Meanwhile, at Turn 1 on the second lap, Alonso's rear-gunner, team-mate Felipe Massa, hung Webber out to dry, allowing the wily Spaniard to slip through into third place. Championship winning territory, just as Vettel was beginning to catch the backmarkers. By the end of lap five, the German had risen to thirteenth place, despite Red Bull chief technical officer Adrian Newey's concerns about the long-term lifespan of the crippled car.
This was the ultimate game of cat-and-mouse. The cat was severely handicapped, but you always felt would succeed in its mission, while the mouse had stolen an early advantage, but coming with the caveat that a mistake was fairly predictable. When it came, on Lap 5, it was the decisive blow. Alonso ran slightly wide into the braking zone of Turn 1, allowing Force India's Nico Hulkenberg through to inherit third place. Never again would Alonso be in a title-winning position despite the many twists to come.
What about Brazil 2008?
Now, at this point, a legitimate question you might be asking is: 'What makes this any different from Brazil 2008?' – or some variant thereof. Both races were held at the same venue, both final race showdowns for the title, and both influenced the weather. The answer is very simple: Hulkenberg. Not the driver, himself, but more what he represented during the race in question.
Fans clamour for a driver in a midfield team, with no real likeliness of continued success, to take it to the big boys, and bloody their noses, a la Vettel himself, while at Toro Rosso, in the torrential conditions of the 2008 trip to Italy. In today's F1, such a performance is, of course, unlikely, much before the 2021 regulations reset. But Hulkenberg's endeavours that day, some 121 races ago, was the last occasion a genuine midfield team had a shot at claiming victory.
The very nature a David taking it to Goliath is one of the feelgood factors of elite sport. An example in another sport would be when Leicester City confounded 5,000-1 expectations to win the 2015-16 Premier League title. Claudio Ranieri's side captured the hearts of neutrals and completed the most unlikely of successes; indeed, it was The Foxes' first-ever top-flight title.
This is an advantage 2012 has over 2008. In the latter, Massa comfortably won from pole, doing all he could to try and snatch the title from Hamilton, whose exploits that afternoon are well-documented. There was no midfield interloper to affect the race, and 2008 falls slightly short as a result.
In the event, Hulkenberg's performance should have come as no shock. Prior to the race, Force India was confident of a strong result in Brazil for drivers Hulkenberg and Paul di Resta. It was at Interlagos in 2010 that German Hulkenberg (then at Williams) annexed the first pole of his career in wet/dry conditions – similar to race day two years later. He had qualified in sixth, among the front runners, on merit and was well poised to take a shock result.
Nico Hulkenberg's performance in the race was outstanding, and the last time a midfield team had a genuine shot at victory.
Credit: Octane Photographic Ltd.
After slipping by Alonso, he set off after the two McLaren's, who were having their own private duel up-front having checked out. As Hamilton pitted for intermediates as the drizzle intensified, Hulkenberg made the same inspired call as Button, who as often shone in the tricky conditions, and opted to carry on with the slicks. It was inspired as the drizzle stopped seconds after Hamilton stopped, leaving Button and Hulkenberg with a 20-second plus advantage over the pack of Hamilton, Alonso, Kamui Kobayashi and Vettel.
On Lap 19, having carved chunks out of Button's lead, Hulkenberg dived to the inside of the Senna S and snatched the lead. The next tour around, Alonso – always thinking two steps ahead – in championship-losing position in fourth, called for the safety car to clear (limited debris.)
Seven laps circulating behind the safety car later, Hulkenberg floored it and opened up a big gap to Hamilton, who had jumped Button, suffering from graining, on the second lap after the restart. In complete control, and driving serenely, at Turn 8, he drifted wide and half-spun the VJM05, dropping behind Hamilton.
Amid Lap 54 drama in the pits for Vettel, who, not being able to communicate with his pitwall due to radio problems, had come in for slicks, just as another rain shower arrived overhead. He came in again, to the surprise of the team a lap later for the correct intermediates – Winning a world championship was never meant to be simple, Hulkenberg attempted an inside lunge on Hamilton, his final race for McLaren before moving to Mercedes for 2013, at Turn 1.
Complicating matters was the presence of a gaggle of backmarkers. Hulkenberg got out of shape, and slid into the McLaren's front suspension, destroying it, while being rewarding for the clumsy move by the stewards with a drive-through that would drop him to fifth. Button sailed through, to take a lead he would never lose, for the fifteenth, and final victory of his career.
Not over yet
So near, yet so far for Hulkenberg as the drama was still not over. As well as the battle for the world championship up front, a fight for survival was raging at the back, as Marussia and Caterham fought desperately over tenth in the constructors', that would unlock precious prize money for 2013.
By virtue of Timo Glock's twelfth place finish in Singapore for Marussia, Caterham needed eleventh or better to move ahead of their rivals, as both had failed to score a point in the previous 19 grands prix. In the dying laps, Charles Pic was holding the prized position for the former, (Pic would be moving from Marussia to Caterham for 2013), but Vitaly Petrov, dropped for the following campaign, sliced by the Frenchman to nab the most coveted eleventh place in F1 history and secure tenth in the constructors' for Caterham – all the good it did them.
Meanwhile, Schumacher, the old regenmeister, himself had worked the Mercedes W03 up to sixth, the position Vettel would need if Alonso (now second after the Hamilton/Hulkenberg incident) won the race. In a handing over of the baton, Schumacher waved his countryman through with a handful of laps left in his career to secure Vettel a deserved world title.
Like every football match can't be a 3-3 thriller, not every grand prix will be brilliant. That is why, when grands prix explode and all hell breaks loose, they are cherished and revered decades later.
The combination of events of the 2012 Brazilian Grand Prix has not been seen before or since. Only two final race deciders have been needed since 2012, in '14 and '16 when Hamilton and Nico Rosberg fought for the crown in the Abu Dhabi desert (each picking up a title apiece). And downpours of a nature to unduly disrupt a grand prix aren't as frequent in the middle-east as in a country sitting on the equator. That is a shame, as the extra unpredictable climatic nature of the Brazilian weather was another factor the teams to cope with.
Vettel's car suffered from radio problems, which led to confusion at the final round of pitstops.
Credit: Clive Mason/Getty Images/ Red Bull Content Pool)
Moreover, the route F1 has travelled since 2012, when there were seven different winners from five different teams in the first seven races, makes a performance of Hulkenberg's virtually impossible. Yes, a midfield team can sneak a podium on an off-day for four of the top six, but with the relative reliability of today's 1.6l V6 turbo-hybrids, that happens but once a season at best.
Quite simply, the events of the 2012 Brazilian Grand Prix produced one of the most remarkable sporting events of all time, and quite objectively, the best Formula 1 world championship grand prix of them all. So far.
1000th Formula 1 grand prix2012 FIA Formula 1 World ChampionshipAutodromo Jose Carlos PaceCharles PicFernando AlonsoFormula 1Jenson ButtonLewis HamiltonMichael SchumacherNico HülkenbergSebastian Vettel
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Jake Nichol
Jake Nichol is a motorsport journalist writing about the Formula 1 world championship for The Checkered Flag. He is currently freelancing for Autosport, where his work includes IndyCar, NASCAR and UK-wide national race meetings.
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\section{Introduction}
Among statistical approaches to modeling neural networks, the Ising model, beside other binary models, has received a lot of attention as a maximum entropy pairwise model. An instance of such binary models is a Boltzmann machine which is a Monte Carlo version of the Hopfield network. The Potts model \cite{Potts52} is essentially the generalization of the Ising model to more than two state network units and, like the Ising model, it first caught attention for its richness in physical applications \cite{Wu82}. Kanter was among the first who generalized the application of the Ising model in neural networks with features of learning and associative memory \cite{Amit85-2, Amit85-1} to Potts model \cite{Kanter88}. Some recent efforts have been dedicated to estimating the storage capacity of Potts model for associative memory \cite{Xiong10, Kropff05, Lowe07, Bolle93}. Ising models constructed based on recorded data from cultured cortical neurons have proven successful in providing a good description of the real data \cite{Schneidman06}. Although the quality and limitations of this model concerning pairwise correlations in larger networks are still under investigation \cite{Roudi09}, the Ising and Potts models are potentially capable of incorporating higher order correlations. Recently, these models with specific energy functions are found useful at many levels of image processing, including segmentation of an image into its constituent regions and multi-scale analysis of image data \cite{Mumford10}.
In their 2002 article, Hauser \etal suggested that a computational mechanism for recursion, which provides a capacity to generate an infinite range of expressions from a finite set of elements, is the only uniquely human component of the faculty of language \cite{Hauser02}. This argument, beside considerations about the local and global circuitry of the neocortex, is the basis of Treves and Roudi's proposal for a Potts model with a hopping behavior among global network states, given the discrete nature of these attractor states. ``The trajectory \ldots will essentially include periods close to attracting states \ldots and rapid transitions between them. The system \emph{latches} between attractors'', as these authors describe it \cite{Treves05,ofTheEvol}. The dynamics of their model comprises sets of differential equations that determine the activation and adaptation behavior of network units \cite{ofTheEvol}. Other reports have studied the structure of latching transitions \cite{Kropff07-2, Russo08} as well as the issue of storing correlated patterns in such networks \cite{Kropff07-1}.
Interestingly, the latching problem in memory-based analyses bears a likeness to multi-stability problems, such as perceptual bi-stability: a phenomenon in which perception alternates between two distinct interpretations of an ambiguous stimulus. Moreno-Bote \etal challenge in their study the mainstream models that ascribe alternations between dominance of two or more competing neural populations to some form of slow adaptation acting on the dominant population, that leads to a switch in dominance to the competing population (\emph{oscillator models}). They propose noise as the main cause of alternations in their \emph{noise-driven attractor models} and construct a neurally plausible and experimentally consistent attractor model \cite{Moreno-Bote07}. There is a parallelism between the stochastic nature of dynamics in our model and noise in attractor models, as both models predict that alternations would cease in the hypothetical absence of noise: by \{eliminating noise/approaching zero temperature\} the system would \{settle down/freeze\} in one of the \{two percepts/several stored patterns\} and stay there indefinitely.
The model we present here is an alternative to the published approach by Treves \cite{Treves05}, with the major distinction of enjoying a stochastic dynamics traditionally present in physical Ising and Potts models. In fact, we have used the Markov chain Monte Carlo algorithm for a network with the Gibbs probability measure. Additionally, thanks to an adaptive potential function the network maintains the adaptive quality of neuronal activity. The combination of these features results in a latching behavior, driven by both noise and adaptation with corresponding adjustable parameters--temperature and adaptation time constant, respectively. The latching we observe here is consistently qualified as a temporary retrieval of one stored pattern, followed by subsequent abandonment of that pattern and retrieval of another pattern.
In theory, given the two parameters of temperature (noise) and adaptation, it is not evident at all how the latching behavior would be observed in different regions of the parameter space. A key finding here (from simulations) is that this hopping behavior is limited to a particular region of adaptation versus noise, beyond which the system either locks in a specific attractor state, or disorderedly fluctuates over various configurations without any pattern retrieval at all. Even within the very area where latching behavior is observed, a privileged critical temperature ($T_\mathrm{c}=1$) inferred from statistical analysis suggests another preference, allowing us to distinguish an optimal region of activity. A comparison of the latching ``quality'' at such an optimal point with other sample points will also confirm our expectation of an optimal region.
The emergence of a sharply distinct region of activity is by and large nontrivial, and a theoretical description of various network states in terms of analytic solution to the dynamics equations in our stochastic multi-state (Potts) network might be a difficult task. Instead, we will endeavor in our current report to identify and demonstrate various network states using simulations of networks with various scales and characteristic parameters. We will establish the robustness of the observed latching region in networks of various size scales in terms of various order parameters; examine the effect of simulation run time; corroborate the independence of the results from initial conditions and cue patterns; study the interplay of noise and adaptation in the near-optimal region; and propose an optimality criterion and identify its region.
\section{Overview of model}
A \emph{Potts} network is a collection of $M$ interacting \emph{units}, each of which may be in one of multiple discrete states. It is actually a generalization of the \emph{Ising Model} with units having more than two possible states. A unit may represent a single neuron or a neural population, having multiple states of activity (action potential, firing rate, etc.) modeled as multiple Potts states.
In the model presented here, each unit may be in one of $S+1$ possible states\footnote{A more generalized (and realistic) condition is an inhomogeneous network in which $S$ might be different among units. We will not deal with such conditions here.}
\[
s \in \{0,\ldots,S\}
\]
consisting of $1$ ``null'' state ($s=0$), and $S$ ``genuine'' states ($s = 1, \ldots, S$). \footnote{Terminlogy borrowed from \cite{Treves05}.}
\subsection{Interaction of units}
The following energy function is defined for the network\footnote{For convenience, we omit the negative sign common in physical notations.}:
\begin{equation}\label{hamiltonian}
E= \frac{1}{2(S+1)^2}\sum_{i=1}^M{h_i^{s_i}}
\end{equation}
, where
\begin{equation}\label{h}
h_{i}^{s}=\sum_{j\neq i}\sum_{k,l=0}^{S} w_{ij}^{kl}u_{sk}u_{s_{j}l}
\end{equation}
describes the energy associated with unit $i$ being in an arbitrary state $s$, and $s_j$ denotes the \emph{current} state of the $j$th unit. $u_{sk}$ is defined based on the following modification of the Kronecker's delta function is defined:
\begin{equation}\label{u}
u_{sk}=(S+1)\delta_{sk}-1
\end{equation}
which serves comparing two selected states of activity, $s$ and $k$. It assumes a value of $S$ if $s=k$, and $-1$ otherwise, thus the total summation over $k=0,\ldots,S$ adds up to zero. (Examine the case of $S=1$ -- the Ising model.)
There is also a \emph{weights matrix}, $w_{ij}^{kl}$, defined in section \ref{learningRule} which determines the relative preference of units $i$ and $j$ being in states $k$ and $l$, respectively.
\subsection{Learning rule}\label{learningRule}
A number of $p$ patterns are stored in the network with the weights matrix defined as follows:
\begin{equation}\label{w}
w_{ij}^{kl}=\frac{1}{(S+1)^2 M p}\sum_{\mu=1}^{p} u_{{\xi_i^\mu}k} u_{{\xi_j^\mu}l} (1-\delta_{k0})(1-\delta_{l0})
\end{equation}
in which $\xi_i^\mu$ represents the state of unit $i$ in pattern $\mu$. Notice that a weight of zero is associated with null states.
Substituting (\ref{w}) in (\ref{h}) shows that if a unit takes up a state which is defined in a stored pattern, the energy associated with that unit will be locally maximized. We will use this feature in section \ref{dynamics} to implement a higher rate of occurrence for our stored patterns via an appropriate distribution function.
\subsection{Dynamics}\label{dynamics}
To define a stochastic, while adaptive, dynamics for the system, we set the common Boltzmann rate, $e^{\beta h_i^s}$ ($\beta>0$), for the occurrence of state $s$ in unit $i$, and adaptively manipulate the ``attractiveness'' of a local attractor by virtually altering the energy function, $h_i^s$, based on the recent activity of each unit-state.
To accomplish this using a Monte-Carlo method of simulation, we randomly select a unit $i$ (which is in state $s_i$) in each iteration of the program, then choose a random state $r$ as a candidate for transition from $s_i$ to $r$. The transition occurs with the following probability (the Metropolis algorithm):
\begin{equation}\label{dynamics}
P(s_i \rightarrow r) =
\cases{
1 & if $\tilde{h}_i^r \geq \tilde{h}_i^{s_i}$ \cr
\exp{\lbrack\beta(\tilde{h}_i^r-\tilde{h}_i^{s_i})\rbrack} & otherwise \cr
}
\end{equation}
where
\begin{equation*}
\tilde{h}_i^k := h_i^k - {h^T}_i^k
\end{equation*}
represents an adapting potential, with $h_i^k$ coming from (\ref{h}) and ${h^T}_i^k$ being some adapting threshold with the following dynamics:
\begin{equation} \label{adapt}
\eqalign{
\tau\dot{h^T}_i^k &= u_{s_{i}k}-{h^T}_i^k \qquad k=1,\ldots,S \cr
{h^T}_i^0 &= 0 . \cr}
\end{equation}
Notice that there is no adaptation mechanism for null states.
The inverse of parameters $\tau$ (adaptation time constant) and $\beta$ (inverse temperature) represent the levels of \emph{noise} and \emph{adaptation} in the system respectively.
\section{Simulation and analysis}
Networks of various scales ($M=100$, $300$, $600$ and $900$) with $S=10$ were simulated over a domain of noise-adaptation combinations. Throughout this study, the value $S=10$ is used, unless otherwise stated. A number of $p\approx \frac{1}{30}M$ patterns were stored in each network. Patterns were generated following the method described in \cite{Treves05} which is capable of producing non- to highly-correlated patterns with desired levels of complexity and common units. In each pattern, a fraction of $a=0.5$ units were set to be in genuine states, with others being in null state. For the following studies, the correlation determinant factor ($\zeta$) was set to zero to produce uncorrelated patterns. For more details see the supplementary material.
\subsection{Overlaps behavior}
A primary quantity of interest, $O_\mu$, is the pattern retrieval reflected in the overlap (similarity) of the current state of the network with the stored pattern \(\mu\). It is simply measured by counting the number of common genuine unit-states between the current configuration of the network and each stored pattern, and then normalizing the result:
\begin{equation}\label{overlapsDef}
O_\mu = \frac{1}{M a}\sum_{i=1}^M \delta_{s_i \xi^\mu_i}(1-\delta_{0 s_i}).
\end{equation}
The resulting variations of overlaps, $O_\mu$, over time are depicted in figure~\ref{probesAHD} for three different pairs of $\beta$ and \(\tau\) selections. With proper selection of noise ($\beta^{-1}$) and adaptation ($\tau^{-1}$) parameters, a \emph{latching} behavior is observed in overlaps diagrams as the system hops from one retrieved pattern to another (figure~\ref{probesAHD}, middle.) Other types of behavior were also identified, in which the system is either underactive and frozen in a single pattern (figure~\ref{probesAHD}, top,) or overactive with no pattern retrieval (figure~\ref{probesAHD}, bottom.)
\begin{figure}
\begin{center}
\includegraphics{probes/figure1_probesAHD}
\end{center}
\caption{Overlaps between the network status and the ten stored patterns in a network of $300$ units change over time. Notice that a pattern ($\mu=0$) is used as an initial cue in each run of the program. $P=(x, y)$ in each title means $\beta=10^{-x}$ and $\tau = 10^{-y}$. You can find the corresponding labels in figure~\ref{s10m300p10_OELand_top}. \label{probesAHD}}
\end{figure}
\subsection{Fluctuations landscape}
To investigate the overall behavior of the network for each possible combination of noise and adaptation parameters, the averages of overlaps variations
\begin{equation*}\label{overlapsVariance}
{\sigma_O}^2 = \frac{1}{p}\sum_{\mu=1}^p (<{O_\mu}^2>_t - {<O_\mu>_t}^2)
\end{equation*}
were measured over a wide grid of noise-adaptation sample points, where $<\dots>_t$ denotes averaging over a sufficiently long period of time at each point. The result is depicted in figure~\ref{s10m300p10_OELand_top} (top) for a network of size $M=300$ units, with $S=10$ for each unit.
\begin{figure}
\begin{center}
\includegraphics{landscapes/figure2a_s10m300p10_overlapsLand_top}
\includegraphics{landscapes/figure2b_s10m300p10_energyLand_top}
\end{center}
\caption{Overlaps (top) and energy (bottom) fluctuations suggest a limited region of latching activity within the domain of noise ($-\log \beta$) and adaptation ($-\log \tau$) parameters. \label{s10m300p10_OELand_top}}
\end{figure}
Fluctuations of the total energy $E$ (see equation~(\ref{hamiltonian})), another order parameter, were also measured over the same grid points using the variance
\begin{equation*}
{\sigma_E}^2 = <E^2>_t - {<E>_t}^2 .
\end{equation*}
The result is plotted in figure~\ref{s10m300p10_OELand_top} (bottom.)
As shown in figure~\ref{s10m300p10_OELand_top} the confined region of maximum fluctuations is the region that latching behavior occurs. Looking at sample points $A$,$H$ and $D$ studied in figure~\ref{probesAHD} confirms our expectation that the lower left section of the plot is in fact a \emph{frozen} region of activity if considered in a sufficiently short period of time compared to the adaptation time constant (see section~\ref{sectScaling}). The rest of the landscape belongs to an overactive or \emph{dead} region of pattern retrieval. At all three points $C$, $D$, and $E$, the behavior of overlaps diagram is similar, at least in appearance (see figures~\ref{probesAHD} and \ref{probesEFG}, the graph for point $C$ looks similar hence not shown for brevity). In this region, the system is too active in terms of unit-state fluctuations ($q_\mathrm{EA}$ parameter, section~\ref{sectScaling}) for any patterns to be retrieved, which means ironically dead in terms of pattern retrieval.
To reveal more details about the behavior of the network with various combinations of noise-adaptation parameters, several other sample points were labeled in figure~\ref{s10m300p10_OELand_top} and their overlaps graphs were sketched. The points were chosen to be cases with minimal noise, figures~\ref{probesIBJ}, or very slow adaptation, figure~\ref{probesEFG}.
\begin{figure}
\begin{center}
\includegraphics{probes/figure3_probesIBJ}
\end{center}
\caption{Overlaps between the network status and the ten stored patterns in a network of $300$ units change over time. These graphs show three cases with a common, relatively low noise value. Adaptation, though, is different, decreasing from the top panel to the bottom. $P=(x, y)$ in each title means $\beta=10^{-x}$ and $\tau = 10^{-y}$. You can find the corresponding labels in figure~\ref{s10m300p10_OELand_top}. \label{probesIBJ}}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics{probes/figure4_probesEGF}
\end{center}
\caption{Overlaps between the network status and the ten stored patterns in a network of $300$ units change over time. These graphs show three cases with a common, relatively slow adaptation. Noise, however, is different, decreasing from the top panel to the bottom. At these points no latching behavior is observed. $P=(x, y)$ in each title means $\beta=10^{-x}$ and $\tau = 10^{-y}$. You can find the corresponding labels in figure~\ref{s10m300p10_OELand_top}. \label{probesEFG}}
\end{figure}
\section{Size scaling, run time and initial conditions} \label{sectScaling}
The overall behavior of the system is invariant with respect to various network sizes: Several sections of figure~\ref{s10m300p10_OELand_top} were selected and replotted for different network sizes, $M = 100$, $300$, $900$. Some of these sections are depicted in figure~\ref{scalings}. The corresponding regions of activity evidently match in different size scales.
At this stage of the study, a third order parameter besides $\sigma_O$ and $\sigma_E$ was also examined, which provided a better understanding of the observed regions of activity. The Edwards-Anderson order parameter defined as
\begin{equation}\label{q_EA}
q_\mathrm{EA}=\frac{1}{MS(S+1)}\sum_{i,k}{{\left\langle u_{s_{i}k}\right\rangle}_t}^2
\end{equation}
is also plotted in figures~\ref{beta31_6_q} and \ref{tau63_q} for various sizes of the network in sections passing through different regions. The figures reveal that in the region of high $\sigma_\mathrm{O}$ and high $\sigma_\mathrm{E}$, the parameter $q_\mathrm{EA}$ varies gradually from its maximum to minimum value. To see what $q_\mathrm{EA}$ measures, notice that $\sum_{k}{{\left\langle u_{s_{i}k}\right\rangle}_t}^2$ in equation~(\ref{q_EA}) is the average state of a unit $i$ in time, which takes the value $S^2+S$ if the unit is in a fixed state $s_i$, and vanishes if the unit is randomly and uniformly fluctuating between all states (cf the definition of $u_{sk}$ in~(\ref{u})). Averaging this for all units and normalizing such that the maximum value is $1$ yields equation~(\ref{q_EA}). This quantity is hence a better indicator of overall network activity as it clearly distinguishes between active and silent network states. Therefore, it is the high value of $q_\mathrm{EA}$ more than the low value of $\sigma_\mathrm{O}$ that indicates the frozen region.
\begin{figure}
\begin{center}
\subfloat[$\sigma_O$ for $-\log{\beta}=-0.25$]{\includegraphics[width=0.5\textwidth]{scales/s10m100_300_900p10_beta1_7_O}\label{beta1_7_O}}
\subfloat[$\sigma_O$ for $-\log{\tau}=-2.7$]{\includegraphics[width=0.5\textwidth]{scales/s10m100_300_900p10_tau501_O}\label{tau501_O}}\\
\subfloat[$\sigma_E$ for $-\log{\beta}=-0.25$]{\includegraphics[width=0.5\textwidth]{scales/s10m100_300_900p10_beta1_7_E}\label{beta1_7_E}}
\subfloat[$\sigma_E$ for $-\log{\tau}=-2.7$]{\includegraphics[width=0.5\textwidth]{scales/s10m100_300_900p10_tau501_E}\label{tau501_E}}\\
\subfloat[$q_\mathrm{EA}$ for $-\log{\beta}=-1.5$]{\includegraphics[width=0.5\textwidth]{scales/s10m100_300_900p10_beta31_6_q}\label{beta31_6_q}}
\subfloat[$q_\mathrm{EA}$ for $-\log{\tau}=-1.8$]{\includegraphics[width=0.5\textwidth]{scales/s10m100_300_900p10_tau63_q}\label{tau63_q}}
\end{center}
\caption{Several order parameters in various sections of the noise-adaptation landscape (inset, see figure~\ref{s10m300p10_OELand_top}) are examined for different network sizes. Panels (a), (c), and (e) are vertical sections with a fixed value of $\beta$ (varying adaptation). Panels (b), (d), and (f) are horizontal sections with a fixed adaptation (varying noise). A perfect consistency is observed. \label{scalings}}.
\end{figure}
Figures~\ref{beta31_6_q} and \ref{tau63_q} suggest that the shape and extent of the regions are robustly preserved under size scaling in the limited-sized networks that were studied. However, changing the simulation run time has a totally different effect on the extent of some regions. Figure~\ref{longland} shows a selection of the same landscape as figure~\ref{s10m300p10_OELand_top}, which is obtained through a much longer run time at each point. All the figures so far were obtained with a run time of $300$ ``steps,'' with each step here being $M$ single iterations of the program. Figure~\ref{longland}, however, is the result of $5000$ steps at each point. In the left panels, the data from the initial $1500$ steps of the simulation was ignored. The right panels where created using the full $5000$ steps. Not much difference is observed. The landscape view of $q_\mathrm{EA}$ was also plotted this time.
\begin{figure}
\begin{center}
\subfloat[$\sigma_O$ for $t = 1500$ to $5000$]{\includegraphics[width=0.5\textwidth]{longLand/s10m300p10g100LongLandO_top}\label{longland_O}}
\subfloat[$\sigma_O$ for $t = 1$ to $5000$]{\includegraphics[width=0.5\textwidth]{longLand/s10m300p10g100LongLandO_top_IK}\label{longland_O_IK}}\\
\subfloat[$\sigma_E$ for $t = 1500$ to $5000$]{\includegraphics[width=0.5\textwidth]{longLand/s10m300p10g100LongLandE_top}\label{longland_E}}
\subfloat[$\sigma_E$ for $t = 1$ to $5000$]{\includegraphics[width=0.5\textwidth]{longLand/s10m300p10g100LongLandE_top_IK}\label{longland_O_IK}}\\
\subfloat[$q_\mathrm{EA}$ for $t = 1500$ to $5000$]{\includegraphics[width=0.5\textwidth]{longLand/s10m300p10g100LongLandq_top}\label{longland_q}}
\subfloat[$q_\mathrm{EA}$ for $t = 1$ to $5000$]{\includegraphics[width=0.5\textwidth]{longLand/s10m300p10g100LongLandq_top_IK}\label{longland_O_IK_IK}}
\end{center}
\caption{The noise-adaptation landscape for $5000$ steps. In the left panels, some initial portion of the data is ignored. Compare with figure~\ref{s10m300p10_OELand_top} where the run time is $300$ steps. \label{longland}}
\end{figure}
A noticeable difference between the short and the long simulation runs is observed. In the long runs, the region in which overlap fluctuations is observed extends more downwards, towards slower adaptations, or longer adaptation time constant. In other words, as we decrease the adaptation, the effect of small adaptation is still significant in the total overlap and energy fluctuations, because, although the retrieved patterns last for longer times, they finally switch to other patterns (non-optimal latching). The value of $q_\mathrm{EA}$ also increases more gradually in the long runs.
Consequently, one can argue that in reality there are no distinct phases or phase transitions if we look at the system in a sufficiently long time window, just a dynamics that slows down as the adaptation slows down. However, the maximum actual specific time scale of a real neural system sets an upper limit to the adaptation time constant, above which the system may be ``effectively'' frozen, or overactive, depending on the noise value. Moreover, an increase occurring in all the order parameters begins at around $-\log{\tau} = -1.7$, which is independent of the run time and network size. This also may be considered as a phase change phenomena. In fact, at around this point the dynamics is extremely sensitive to $\tau$ variations. With slow enough adaptation the system will have enough time to fully retrieve patterns. However, the lower limit for adaptation time constant (upper limit for adaptation speed) is, once again, systematically determined. If $\tau$ gets too small, the life time of retrieved patterns tends towards a time ``step.'' This means the adaptation is so fast that some parts of a pattern de-adapt before the whole pattern is retrieved, thus giving no time for the attractor state to rise. This ``step'' is an intrinsic property of real systems.
To ensure that our results are independent of various initial conditions and cue patterns, a section of figure~\ref{s10m300p10_OELand_top} was reexamined using a run period of $9000$ steps, with various random initial conditions and cue patterns. We also threw away the data from the first $3000$ steps of the total $9000$ steps. Four different cue patterns with two random initial conditions for each pattern were tried at each point (8 trials). The resulting standard deviations are shown in figures~\ref{initsOE} and \ref{initsq} with error bars. The inset graphs show the corresponding section of study in figure~\ref{s10m300p10_OELand_top}.
\begin{figure}
\begin{center}
\includegraphics{inits/s10m300p10_beta31_6_O}\\
\includegraphics{inits/s10m300p10_beta31_6_E}
\end{center}
\caption{Reliability check: deviations from mean values over various initial conditions
and various cue patterns are shown with error bars. The run period is $9000$ steps compared to 300 in figures~\ref{scalings} and \ref{s10m300p10_OELand_top} (the inset). Also, the initial $3000$ steps of each run is ignored. In these sections, the peak in the inset graph is extended more towards slower adaptations because in the longer runs, the non-optimal latching will still be observed with slower adaptations.
\label{initsOE}}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics{inits/s10m300p10_beta31_6_q}
\end{center}
\caption{Continued from figure~\ref{initsOE}.
\label{initsq}}
\end{figure}
The behavior of the error bars in the lower panel of figure~\ref{initsOE} seems very interesting. In our effort to understand the large variations in the error bars, especially the sudden change from $-3.7$ to $-3.85$, we simulated again and examined our data for energies and overlaps at these points. The usual behavior of the system at these points is shown in figures~\ref{errorbarProbes_O} and \ref{errorbarProbes_E}, top and middle panels, for randomly selected trials (initial conditions). The apparent behavior of the graphs does not show much of a difference. However, we noticed that the huge error bars are the result of few occurrences of a behavior that appeared in some trials, like in figures~\ref{errorbarProbes_O} and \ref{errorbarProbes_E}, bottom. It appears that the system virtually ``nulls out" sometimes. By the definition of overlaps, equation~(\ref{overlapsDef}), the null states are excluded from overlap calculation. So, the overlaps should vanish if all the units are in null states. To understand the behavior of the energy graph, notice that equations~(\ref{hamiltonian}) to (\ref{w}) tell us that the energies assigned to the null states are zero. However, the $-1$ values of $u_{sk}$ that appear in the sum in equation~(\ref{h}) make a nominal contribution to the total energy, making it slightly off zero. The system gets out of this ``resting state'' merely due to de-adaptation of other states and noise. The null-out did not occur in our trials at $-\log{\tau} \le 7.85$ in figure~\ref{initsOE}, hence minimal error bars. It occurs more frequently, and lasts for shorter periods of time as $-\log{\tau}$ gets larger, hence the decreasing error bars to the right.
\begin{figure}
\begin{center}
\includegraphics{errorBarsProbes/errorbarProbes_O_brief}
\end{center}
\caption{Overlaps behavior over time at points where the error bars in figure~\ref{initsOE} change suddenly. Typical behaviors are shown in the top and middle panels. In the bottom panel, a null-out effect is observed. \label{errorbarProbes_O}}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics{errorBarsProbes/errorbarProbes_E_brief}
\end{center}
\caption{Energy behavior over time at points where the error bars in figure~\ref{initsOE} change suddenly. Typical behaviors are shown in the top and middle panels. In the bottom panel, a null-out effect is observed. \label{errorbarProbes_E}}
\end{figure}
Another interesting feature of figure~\ref{initsOE} is the difference between the energy and overlaps peaks, or rather bumps. While the rise in both graphs begins at about the same point on the right extreme of the panels for the reason that was explained before, the $\sigma_\mathrm{O}$ graph drops a bit later than the $\sigma_\mathrm{E}$ graph on the left. It is also much smoother than the $\sigma_\mathrm{E}$ graph. This behavior can again be understood by referring to figures~\ref{errorbarProbes_O} and \ref{errorbarProbes_E}. In these figures we see several transitions between patterns with very close energies. Such transition make up a significant portion of $\sigma_\mathrm{O}$, while in terms of energy, they mean little fluctuations.
\section{Behavior at around $\beta = 1$}\label{beta1}
Two different horizontal sections of figure~\ref{longland} (left panels) were selected for more detailed study in the region where noise has a considerable effect (figure~\ref{horizSections}). The section at $-\log{\tau} = -4.65$ is where adaptation is relatively slow, and the section at $-\log{\tau} = -2.25$ is where both noise and adaptation play a critical role in the behavior of the system (at around point $H$ in figure~\ref{longland}). More specific parameters are explained in the figure captions.
\begin{figure}
\begin{center}
\subfloat[$\sigma_O$ for $-\log{\tau} = -2.25$]{\includegraphics[width=0.5\textwidth]{horizSections/s10m300p10Longt177_O}\label{t177_O}}
\subfloat[$\sigma_O$ for $-\log{\tau} = -4.65$]{\includegraphics[width=0.5\textwidth]{horizSections/s10m300p10Longt44668_O}\label{t44668_O}}\\
\subfloat[$\sigma_E$ for $-\log{\tau} = -2.25$]{\includegraphics[width=0.5\textwidth]{horizSections/s10m300p10Longt177_E}\label{t177_E}}
\subfloat[$\sigma_E$ for $-\log{\tau} = -4.65$]{\includegraphics[width=0.5\textwidth]{horizSections/s10m300p10Longt44668_E}\label{t44668_E}}\\
\subfloat[$q_\mathrm{EA}$ for $-\log{\tau} = -2.25$]{\includegraphics[width=0.5\textwidth]{horizSections/s10m300p10Longt177_q}\label{t177_q}}
\subfloat[$q_\mathrm{EA}$ for $-\log{\tau} = -4.65$]{\includegraphics[width=0.5\textwidth]{horizSections/s10m300p10Longt44668_q}\label{t44668_q}}
\end{center}
\caption{Two horizontal sections of figure~\ref{longland} (insets). In the left panels, the run time is $9000$ steps, with the first $3000$ steps ignored. In the right panels, the run time is $5000$ with the first $1500$ steps ignored. All the inset graphs are from figure~\ref{longland} (left panels) with $5000$ steps run and $1500$ ignored. The right panels in the above figure completely match the inset graphs. The error bars here are calculated in the same fashion as figures~\ref{initsOE} and \ref{initsq}, i.e. 8 trials with different initial conditions/cue patterns. \label{horizSections}}.
\end{figure}
To understand the behavior of the graphs in the right panels of figure~\ref{horizSections}, we choose to explain the overlap behavior in panel~\ref{t44668_O} as $-\log{\beta}$ decreases. At around $-\log{\beta}=0.1$ the noise is so strong that it does not allow any patterns to show up (figure~\ref{b1probes_1}, top). A phase transition at around $\beta =1$ is a characteristic of an Ising models. A classical two-dimensional $q$-state Potts model also exhibits phase transition when $\exp({\beta})-1=\sqrt{q}$ \cite{Baxter73}. The phase transition beginning at around $\beta = 1$ is not surprising. At around $-\log{\beta}=-0.05$ some jittering begins to show up (figure~\ref{b1probes_1}, middle). Notice that we are still close to the high-noise border, and the adaptation is slow but not zero, so it facilitates transitions induced by noise. This results in the first peak at around $0$. At around $-0.2$ the temperature is low enough for the retrieved patterns to stabilize (figure~\ref{b1probes_1}, bottom). Thus the overlap fluctuations decrease again at this point. However, a glance at the $q_\mathrm{EA}$ graph in panel~\ref{t44668_q} reveals that although a number of about $aM$($=0.5\cdot300$) units are fixed in the primary retrieved pattern, the rest of them are still fluctuating freely between various states. This can be seen better when the rest of the system is attracted to secondary patterns that are partially retrieved as shown in figure~\ref{b1probes_2}, top. This pattern retrieval needs a slightly lower temperature to occur, and the partially retrieved patterns are, like in the first peak, jittery and transient. This results in a smaller peak at around $-0.35$. As we further decrease the temperature, both partial and full pattern retrievals get solid and stable (figure~\ref{b1probes_2}, middle), resulting in low $\sigma_\mathrm{O}$ and $\sigma_\mathrm{E}$ values again. Here, we notice a ``life-shortening'' effect of noise on pattern retrievals. It can be observed in all of our data (including those not presented herein) that increasing noise alone results in a higher probability of pattern transitions, hence shorter retrieval lifetimes.
\begin{figure}
\begin{center}
\includegraphics{b1probes/b1probes_1}
\end{center}
\caption{Overlaps behavior at some select points in figure~\ref{horizSections} right panels. The top panel shows a dead/overactive dynamics. As $-\log{\beta}$ decreases, pattern retrieval begins (middle) and the retrieved patterns solidify as we further decrease the noise (bottom).\label{b1probes_1}}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics{b1probes/b1probes_2}
\end{center}
\caption{Overlaps behavior at some select points in figure~\ref{horizSections}. The top panel shows a secondary pattern retrieval that occurs when noise is low enough. The primary and secondary retrieved patterns solidify as we further decrease the noise (middle). In the bottom panel, the interplay between noise and adaptation is high, and the latching behavior is close to optimal. \label{b1probes_2}}
\end{figure}
Now, we turn our attention to the other selected section, where $-\log{\tau}= -2.25$ (figure~\ref{horizSections}, left panels). Adaptation is faster in this section, so with decreasing temperature the first patterns show up in a lower temperature. The ascents in the $\sigma_\mathrm{O}$ and $q_\mathrm{EA}$ graphs look quite simple. The $\sigma_\mathrm{E}$ graph, however, shows an interesting peak immediately after the rise. Recalling that close-energy pattern transitions can account for overlaps activity with little energy fluctuations, we conclude that this peak signifies the most diverse pattern activity in terms of energy fluctuations. An instance of overlaps activity at $(-0.25, -2.34)$ is shown in figure~\ref{b1probes_2}, bottom. If we look back at figure~\ref{probesIBJ} we can see what happens if we further decrease the noise. We see that although pattern fluctuations may be fast due to fast adaptation, several patterns may rise at a time, that is, secondary and higher order pattern retrievals are observed in low temperatures. This ``purifying'' effect of noise was also observed in our study of the section $-\log{\tau} = -4.65$. Here, our results confirm that for a pure, distinct pattern retrieval we need $\beta$ close enough to~$1$.
We are now ready to articulate our optimality criterion and specify its region. We define a \emph{utility function} such that optimal latching corresponds to maximal utility function. Among various possiblities, we take our utility function $U(\beta, \tau, T)$ to be the number of \emph{transitions} between \emph{uniquely} retrieved patterns over a given rum time $T$. A pattern $\mu$ is ``uniquely'' retrieved when for some high and low thresholds $T_\mathrm{H}$ and $T_\mathrm{L} \in [0,1]$, we have $O_\mu > T_\mathrm{H}$ and $O_{\nu} < T_\mathrm{L}$ for all $\nu \neq \mu$. A ``transition'' occurs when a uniquely retrieved pattern is replaced by another. We calculate $U$ by counting the number of transitions.
The above utility function immediately excludes the dead/overactive region as not optimal. It also demands for the fastest latching dynamics. By ``fast'' we mean the life span of retrieved patterns and the transition time between retrievals are short. This requires that adaptation be maximal. The uniqueness condition for retrievals makes the noise maximal, too. With proper selection of $T_\mathrm{H}$ and $T_\mathrm{L}$, and a fixed $T$, the optimal region should get confined to around point $H$, or the bottom panel in figure~\ref{b1probes_2}.
Other optimality criteria are also possible to suggest. One can simply take $\sigma_\mathrm{E}$ as the utility function since it has an absolute maximum at around $(-0.1, -3)$ (cf figure~\ref{longland}). The overlaps and energy behavior at this point are plotted in figure~\ref{maxEnergyProbe}. Interestingly, we see that the retrieval periods are short, and the system spends considerable time in overactive/dead state (not null-out, compare with figures~\ref{errorbarProbes_O} and \ref{errorbarProbes_E}, bottom) during transitions where the average energy is almost zero.
As yet another option, one may look for the most ``diverse'' transitions as being optimal. By diverse, we mean having maximum randomness in terms of maximum entropy rate (assuming a stationary distribution):
\begin{equation*}
H = - \sum_{\mu \nu} p_\mu P_{\mu \nu} \log P_{\mu \nu}
\end{equation*}
where $p_\mu$ is the retrieval rate of pattern $\mu$, and $P_{\mu \nu}$ is the transition matrix. The search for this region shall be done in future studies.
\begin{figure}
\begin{center}
\includegraphics{maxEnergyProbe/maxEnergyProbe}
\end{center}
\caption{Overlaps (top) and energy (bottom) behavior when $\sigma_\mathrm{E}$ is at maximum. Overactive periods separate the retrievals.\label{maxEnergyProbe}}
\end{figure}
\section{Discussion}
In this work, we have constructed a model combining two major characteristics from apparently separate disciplines. Our model possesses two major components: a temperature parameter and an adaptation one. The former is a primary constituent of a thermodynamical and statistical-physics framework, while the latter represents a major quality of real neural networks and plays an important role in the dynamics of realistic models suggested to date for the study of numerous phenomena in the brain. Figure~\ref{s10m300p10_OELand_top} reveals how these two basic components are joined to form a novel perspective - a latching behavior confined to a limited region of the parameter space.
A construction of Ising networks based on data from real retinal neurons suggests a preferred working temperature at around $\beta = 1$ \cite{Tkacik08}. A phase transition at this point is also observed in our model. The other basic parameter in our model, adaptation time-constant, also plays a key role in determining the type of network activity. The region where latching behavior occurs is limited in terms of noise and adaptation. However, more specific optimal criteria can be suggested to limit the desired area. The joint analysis of the two basic components, temperature and adaptation, singles out a critical region of optimal activity at around point $H$ in figure~\ref{s10m300p10_OELand_top}. A comparison of the latching behavior at a sample point in this zone, such as $H$ (figure~\ref{probesAHD}, or \ref{b1probes_2} bottm), with several other points of latching possibility, such as $I$, $B$ or $J$ (figure~\ref{probesIBJ}), reveals how indeed the optimal region is privileged: the retrieval sequence at $H$ exhibits fast and pure emergence of distinct patterns with regular periods, in contrast to co-occurring retrievals and indistinct, irregular transitions at other sample points. The findings here suggest that in the realistic models that incorporate adaptation mechanism, the respective time constants and the amount of noise might need to be limited to permitted ranges that comply well with the overall functionality of the network.
A rich variety of dynamical states are observed in different regions of the phase diagram. From a grammatical point of view, a traditional latching behavior occurs when a retrieval is cued by its previous retrieval, like in figure~\ref{probesIBJ}. However, with a sufficient presence of noise in the system, the network tends toward a spontaneous activity in which pattern retrievals are more or less cued by noise. This is most noticeable in figure~\ref{maxEnergyProbe}. In cases like point $H$, figure~\ref{probesAHD} middle, the transitions are highly noise driven, though the chain is not totally memory-less given the exponential recovery of adapted unit-states. Hence a deeper understanding of the boundaries and grammatical characteristics of these two types of behavior is definitely needed in future works.
Moreover, there are two types of dynamical states observed so far that can separate retrieval chains: overactive states (figure~\ref{maxEnergyProbe}) and null-outs (figure~\ref{errorbarProbes_E} bottom). The former is typical of the overactive/dead region where unit-states fluctuate too rapidly to form patterns. The latter occurs when noise is low enough for units to settle in null states, when the system is ``tired'' of recently retrieved patterns. This is, however, not a favorable state compared to pattern energy levels, hence it is a temporary state even though the null states do not adapt. Further work is required to verify these speculations and determine the rate and lifetime of such states.
Another interesting dynamical state is the `hierarchical' pattern retrieval exemplified in figures~\ref{b1probes_2} top, and \ref{probesIBJ}. In this sort of dynamics, ``one state is retrieved, serving as a framework for other states to be partially retrieved one after the other in the meantime,'' as described by a referee for this article. This as well seems very promising in terms of grammatical significance. Though further analysis falls out of the context of this article and remains for future studies.
As shown in section~\ref{beta1}, noise has a shortening effect on retrieval lifetime, or, an increasing effect on the rate of transitions. In fact, noise is an essential constituent of the dynamics and unit-state transitions stop shortly as $\beta \to \infty$ (cf equation~(\ref{dynamics})). This accords well with the recent models \cite{Moreno-Bote07} in which alternations in dominant patterns of neural activity is induced by noise, while adaptation would not lead to alternations in the absence of noise. What is important in this scenario is that instead of an ad hoc assumption about the presence of noise, it is the interplay between adaptation and noise which sets the timescale of alternations. The fact is that the transition probabilities between different attractor states need not be at the scale of biophysical noise source characterized by fast timescales. This, indeed, would be too unrealistic given that the latching state of the network is meant to support transition states corresponding to highest cognitive states. In terms of the state-space and energy landscape, the noise-adaptation interplay will shift the boundary line between basin of attractors as well as reducing the depth of the minimum associated with dominant patterns \cite{Moreno-Bote07}. Given the optimal region in the noise-adaptation state space for maximum rate of transition probabilities there is room for realistic rate of alternations by varying noise and adaptation rates in the appropriate domain. In a similar vain, Kumar \etal \cite{Kumar10} have emphasized the rate of noise in shifting the dynamics in favor of spiking activity propagation in neural networks. The idea of a feed-forward network embedded in a recurrent network and hence the possibility of alternating patterns of activity in the form of a packet of synchronous neural activity bears a close resemblance to the hopping behavior of different attractor states in the Potts model. It will be interesting to see how the noise-adaptation interplay may play a similar role in controlling different activity modes in such embedded feed-forward networks.
The ``Potts'' virtue of this model, which lies in the multiplicity of states of each unit, plays a dramatic role in determining the shape and extent of latching region(s). The parameter $S$ was kept to be $10$ throughout this study. However, the effect of its alteration remains to be a target of future studies. Moreover, a thorough analysis of transition structure in the retrieval sequence is required to illuminate the potentials of the network for grammatical association and sequence generation. Any such analysis shall be preferably performed around the optimal region where the retrievals are unique, with high signal-to-noise quality, and frequent enough.
\ack{}
The authors would like to thank Yasser Roudi for his insightful comments and critical assessment, and Mohammad Reza Razvan for helpful suggestions at the early stage of this work. We also appreciate the critical comments and suggestions by the referees for this article, which spurred deeper analyses and new findings. The computation was carried out at Math. Computing Center of IPM (\url{http://math.ipm.ac.ir/mcc}).
\include{bibl}
\end{document}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,552 |
Q: Using HtmlAgilityPack to parse HTML with Headers, Tables, Rows, Cells I'm trying to use HtmlAgilityPack to parse through a webpage's HTML to parse out the rows/cells of tables.
The code sample almost works, except I get an exception on the Table collection. I presume this might have something to do with Header not formatted as a collection (and I cannot modify the source of the HTML).
Please help with the code, or please suggest alternatives or workarounds.
The structure is:
Header -> Table -> Row -> Cell
There are a collection of Headers (which contain the date), that contain collection of Tables, which contain a collection of Rows, and Rows contain a collection of Cells.
string html = @"
<html>
<body>
<h3>February 8, 2014</h3>
<table>
<tr>
<td><b>Site</b></td>
<td><b>ColumnA</b></td>
<td><b>ColumnB</b></td>
<td><b>ColumnC</b></td>
</tr>
<tr>
<td>SiteA</td>
<td>3</td>
<td>6</td>
<td>3</td>
</tr>
<tr>
<td>SiteB</td>
<td>4</td>
<td>6</td>
<td>2</td>
</tr>
<tr>
<td>SiteC</td>
<td>4</td>
<td>9</td>
<td>4</td>
</tr>
</table>
<h3>February 7, 2014</h3>
<table>
<tr>
<td><b>Site </b></td>
<td><b>ColumnA</b></td>
<td><b>ColumnB</b></td>
<td><b>ColumnC</b></td>
</tr>
<tr>
<td>SiteA</td>
<td>2</td>
<td>4</td>
<td>1</td>
</tr>
<tr>
<td>SiteB</td>
<td>1</td>
<td>1</td>
<td>2</td>
</tr>
<tr>
<td>SiteC</td>
<td>2</td>
<td>6</td>
<td>1</td>
</tr>
</table>
</body>
</html>
";
HtmlDocument doc = new HtmlDocument();
doc.LoadHtml(html);
foreach (HtmlNode header in doc.DocumentNode.SelectNodes("//h3"))
{
string headerDate = header.InnerText;
foreach (HtmlNode table in header.SelectNodes("table")) //System.NullReferenceException
{
foreach (HtmlNode row in table.SelectNodes("tr"))
{
Console.Write(headerDate);
foreach (HtmlNode cell in row.SelectNodes("td"))
{
Console.Write("\t" + cell.InnerText);
}
Console.WriteLine();
}
}
}
Expected Results:
February 8, 2014 Site ColumnA ColumnB ColumnC
February 8, 2014 SiteA 3 6 3
February 8, 2014 SiteB 4 6 2
February 8, 2014 SiteC 4 9 4
February 7, 2014 Site ColumnA ColumnB ColumnC
February 7, 2014 SiteA 2 4 1
February 7, 2014 SiteB 1 1 2
February 7, 2014 SiteC 2 6 1
Thank you. Jake.
A: You're iterating over the headers as if you're expecting the tables to be within the header tags, but the tables are not within the header tags, despite what the misleading indentation appears to suggest. The header tags are siblings of the tables, not parents.
<h3>February 8, 2014</h3> <-- </h3> closes the header tag
<table> <-- this is the next element at the same level, not a child
<tr>
<td><b>Site</b></td>
<td><b>ColumnA</b></td>
<td><b>ColumnB</b></td>
<td><b>ColumnC</b></td>
</tr>
</table>
Keep in mind that indentation/whitespace is meaningless in html. It's the tags that rule all.
| {
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} | 5,727 |
{"url":"https:\/\/www.physicsforums.com\/threads\/physics-problem-with-frequency.61174\/","text":"# Physics Problem (with frequency)\n\n1. Jan 25, 2005\n\n### Drey0287\n\nA sound wave has a frequency of 700 Hz in air and a wavelength of .50m. What is the temperature of the air?\n\nspeed of sound in air = 345 m\/s.\n\n2. Jan 25, 2005\n\n### Parth Dave\n\nI believe the mistake you made was to assume that the spped of sound in air is 345 m\/s. You can tell just based on the information you are given in the question. If the frequency is 700 Hz and the wavelength is 0.5 m, then what MUST the speed of sound be?\n\nThere is actually a formula that relates speed of sound in air with temperature. Find that and you shall find the answer you desire.\n\n3. Jan 25, 2005\n\n### futb0l\n\nYupp, remember when the air molecules are heated up, it moves faster.\n\n4. Jan 25, 2005\n\n### Sirus\n\n$$v\\approx 331\\mbox{m\/s}+0.6\\mbox{T}$$\n\nwhere $v$ is the speed of sound in air, and $\\mbox{T}$ is the temperature in degrees Celsius.","date":"2017-05-23 18:35:44","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.7946881651878357, \"perplexity\": 528.2760200683858}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-22\/segments\/1495463607649.26\/warc\/CC-MAIN-20170523183134-20170523203134-00611.warc.gz\"}"} | null | null |
Vlade Guigni
Vlade Guigni Trio
Vlade Guigni is a Drummer, Producer/Engineer and Educator originally from The Dominican Republic based in Boston MA, USA. He has worked with an extensive list of artists from the Jazz, Gospel, Fusion an Studio music scene from his native country, The Dominican Republic and the international scene. The list includes Danilo Montero, Lucia Parker, Lilly Goodman, Johan Paulino, Marcos Yaroide, Isabelle Valdez, Egleyda Belliard, Oscar Micheli, Josean Jacobo, Eliacim, Tribu Del Sol, Grupo Lega2, Minns Quintet, David Vasquez, Gerald Clayton, David Gilmore, Phil Wilson, Darcy James Argue, Elisa Smith, Simona Minns, Jireh Calo, Shea Rose, Marlon Saunders, Enrique Gonzalez Müller, Bill Banfield, Totó La Momposina, just to name a few.
In 2012 Vlade was awarded with a Scholarship for the prestigious Berklee College of Music after auditioned for the "Michel Camilo Endowed Scholarship Fund". Since then he has studied with world renowned musicians such as Neal Smiht, Terri Lyne Carrington, Ralph Peterson, John Hazilla, Henrique De Almeida, Ian Froman, Larry Finn, Billy Kilson, Leo Blanco, Ed Tomassi, Tia Fuller, Greg Hopkins. Prince Charles Alexander, Enrique Gonzalez Muller, John Whynot, Leanne Ungar, Mark Wessel and many others.
In 2015 Vlade was accepted on the world renowned Berklee Global Jazz Institute, an elite organization that is composed by top Jazz Players in the world. The Global Jazz consists in a program for the social change with the music. We travel the world and play in top Jazz festivals like the Panama Jazz Festival, Monterrey Jazz Festival, Toronto Jazz Festival, Dominican Republic Jazz Festival, along with many other places. The Global Jazz not only plays at these festivals but also teaches workshops and clinics. The Faculty Includes Danilo Perez, Terri Lyne Carrington, George Garzone, John Patitucci, Alan Pascua, Ben Street, Brian Blade, Joe Lovano and many other guest artists.
Also in 2015 he played Drums on the Berklee Online/Coursera course called: "Producción Musical y su efecto en la Composición" leaded by the Latin Grammy Award Winner Producer/Engineer and Berklee Faculty Enrique Gonzalez Müller. This course is about is the first one completely taught in spanish and is about music production. The course is available completely free and worldwide and has reached thousands of students all over the world in less than a year.
Currently, Vlade keeps himself busy playing with artists from all different styles in the Boston area. He Endorses Canopus Drums, Meinl Cymbals, Vic Firth Drumsticks and Ahead Armor Cases.
http://www.vladeguigni.com/ https://www.instagram.com/vladeguignimusic/ https://twitter.com/VladeGuigni https://www.youtube.com/user/vladywarrior https://www.facebook.com/vladeguigni17
14×16.5" Silver Sparkle
10×8" Rack Tom
14×14" Floor Tom
20×14" Bass Drum
Black Sparkle
Vlade Guigni 関連ニュース | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,872 |
Q: Show ZF2 request execution time I want to print in every page of my site, which is in ZF2, the request execution time.
I have already defined a constant within the index.php (which is the first file the request access) with the request initial microtime(true).
Now, where should I get the request final microtime(true)?
My plan is to have something like this:
$executionTime = ($finalTime - $initialTime) / 1000000; // in seconds
$executionTime = number_format($executionTime, 2);
A: The problem is that you probably want to add this information to the view (so the user can see it) which would mean adding the time before you render the view (before MvcEvent::EVENT_RENDER). The problem is though that the view is rendered way before MvcEvent::EVENT_FINISH is triggered so the time would not be accurate. This won't be easy to solve...
You could consider adding some time related header inside your response.
Here an interesting related question about adding your custom headers.
*
*There is for example a $request_time variable for NGinx which you could use out-of-the-box:
$request_time
request processing time in seconds with a milliseconds resolution (1.3.9, 1.2.6); time elapsed since the first bytes were read from the client
add_header X-Request-Time $request_time always;
*There is also an Age response header field. You can find it here in the Header Field Definitions section 14.6 in RFC2616.
The Age response-header field conveys the sender's estimate of the
amount of time since the response (or its revalidation) was
generated at the origin server. A cached response is "fresh" if
its age does not exceed its freshness lifetime. Age values are
calculated as specified in section 13.2.3.
Maybe you could use it to calculate the time it took to process the request on the server.
You could also add a custom header in your ZF2 application by adding some code to your Module.php like this:
function onBootstrap(MvcEvent $event) {
$application = $event->getApplication();
$eventManager = $application->getEventManager();
$eventManager->attach(MvcEvent::EVENT_FINISH, [$this, 'addTimeHeader']);
//...
}
function addTimeHeader(MvcEvent $event) {
$time = // get your time value
$response = $event->getResponse();
$response->getHeaders()->addHeaderLine('X-Request-Time', $time);
}
The issue will still be to get this data inside your view. If you use an AJAX request it will be easy to get the header from the response, but if you don't use AJAX it is a whole different story. Read more here in this answer.
A: To achieve what you ask, and some more, in a development environment, you could use the Zend Developer Tools modules, which will automatically give you some informations regarding your application.
In a production environment, you could instead listen to the MvcEvent::EVENT_FINISH, that is the last event emitted by the Zend framework MVC
A: If you want to be a really dirty, add in your index.php file at beginning:
$_GET['the_time'] = round(microtime(true) * 1000);
Wherever you want in the view or layout print:
echo round(microtime(true) * 1000) - $_GET['the_time'];
// Use $_GET as global variable
Note: The rest of developers will probably hate you.
A: My solution is based on this answer.
Every view of mine has a footer.phtml attached to it, so if I print it there, there will be no need to change many files.
To print the time there, first I wrote something specific to that footer.phtml, for example Execution time:
Than in module/Application/Module.php I added this code to onBootstrap()
$eventManager->attach(\Zend\Mvc\MvcEvent::EVENT_FINISH, function($e) {
$time = microtime(true) - REQUEST_MICROTIME;
// formatting time to be more friendly
if ($time <= 60) {
$timeF = number_format($time, 2, ',', '.').'s'; // conversion to seconds
} else {
$resto = fmod($time, 60);
$minuto = number_format($time / 60, 0);
$timeF = sprintf('%dm%02ds', $minuto, $resto); // conversion to minutes and seconds
}
// Search static content and replace for execution time
$response = $e->getResponse();
$response->setContent(str_replace(
'Execution time:', 'Execution time: '.$timeF, $response->getContent()));
}, 100000);
A: You can capture time to variable in index.php and then use register_shutdown_function to print time difference between:
index.php
define('APP_START_TIME', microtime(true));
register_shutdown_function(function(){
echo 'Request time(sec): ' . number_format(microtime(true) - APP_START_TIME, 3);
});
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,771 |
{"url":"https:\/\/idontknowbut.blogspot.com\/2013\/08\/","text":"## Thursday, August 29, 2013\n\n### A professional writer's problems\n\nJohn C Wright is a SF writer, and on his blog he describes a problem I hadn't heard about before:\nIt (word limit) is established by the bookstores, who limit the number of inches a binding can occupy on the shelf. Any author whose books do not sell through finds his name not on the list of books the stores are willing to buy from the publisher. Nowadays, now that bookstores are large conglomerates, the calculation is done by computer with no human judgment involved, so if a midlist author with a fine record of book sales suffers one book that was bought in too large a number or which made too small a sale, suddenly his books are not bought in as large of numbers by the distributors, and therefore his sales drop again, and therefore his books are bought in even fewer numbers, and therefore his career is over unless he changes his name and writes under a pan name. This has happened to a friend of mine, John Hemry\/Jack Campbell who writes the LOST FLEET series.\n\nWhat happened to me with THE HERMETIC MILLENNIA is that a staffer made a mistake and over-ordered the production \u2014 whether it was too many units or the manuscript was too long was not clear \u2014 and so I cannot make my numbers unless I sell out every single copy of the book. That is why I am pathetically begging my readers to go out and buy them all, because I have been informed the publisher will not buy the rest of the series. If the book sells through, I have some hope that they may reverse that decision.\n\nScott Adams wrote of \"Powerpoint poisoning\" and this smells like Excel bookstore management. Just plug in the numbers and you're guaranteed success.\n\nI've read several of his books and enjoyed them, btw.\n\nUPDATE: Changed the title. Professional as in makes money from it. I liked the ambiguity of real writer\/real problem, but it doesn't work well.\n\n## Tuesday, August 27, 2013\n\n### Syria\n\nOn a grimmer note, I try to figure out what's going on in international affairs by looking at what people say and do and trying to estimate what's not getting reported. (Reporters, by and large, don't seem to be a very well-informed lot.)\n\nBenghazi had some Syria connection, and maybe some Egypt connection as well, and the US administration has been lying like a rug since the get-go. Maybe they have some good reasons for that; trying to cover up weapons shipments to Syrian insurgents. Although some of them ask for US help, I'd suspect most wouldn't be eager to stain their good Islamic credentials by too much public fraternizing with the Great Satan. So to first order I conclude that we've been shipping arms and other goodies to one or more insurgent groups--and if prior experience is any guide we've sent stuff to enemy groups more than once.\n\nSo now there's another poison episode, that seems to kill 1\/10 of the victims. Other attacks seem to have killed about 1\/3, making this seem more like the Bhopal disaster (1\/20 killed). Which suggests that the attack, if it was the government using chemical weapons, wasn't well executed. If rebel groups had the weapons they might not know how to use them effectively. Or somebody might be stirring the pot with something that wasn't completely weaponized. Or this was an accident with stolen weapons.\n\nAlthough the foreign policy of this administration seems to be managed via Ouija board, I still try to see if there's any sense to this. As plenty of people have already pointed out, we're better off if both groups lose. So there's no sense to intervening unless there's some vital interest at stake. And there is one, that isn't talked about: seizing control of loose chemical weapons. \"Punishing\" or \"sending a signal\" makes no sense. We know he had weapons already, and we know he already used them. So where's the urgency? Is something slipping? (And do you trust \u2205 to keep his eye on the ball?)\n\nYou may not have seen the BBC story reporting that all 25,000 students taking the entrance exam failed. \"The students lacked enthusiasm and did not have a basic grasp of English, a university official told the BBC.\" For those interested, tuition seems minimal: about \\$1.27 per credit for undergraduates.\nFrom BBC: University spokesman Momodu Getaweh told Focus on Africa that the university stood by its decision, and it would not be swayed by \"emotion\".\n\n\"In English, the mechanics of the language, they didn't know anything about it. So the government has to do something,\" he said.\n\n\"The war has ended 10 years ago now. We have to put that behind us and become realistic.\"\n\nThe school apparently was a bit embarrassed and changed their minds, admitting 1,626 after all, as the story below shows, and also the BBC followup.\n\nMs (President of Liberia) Sirleaf did not say why the university, based in the capital Monrovia, had agreed to admit 1,800 students after discussions with her.\n\nWhat happened? I can't quite tell from the test numbers: 50% score in English and 40% in Math seems pretty low, but that's because I'm used to normalized tests. (Usually: Quantitative Chemistry back at SIU had passing set at 40%: it was the flunk-out course for chemistry students, and quite rough.)\n\nI think the 100% failure was due to two effects: one explicit and one that I'm just guessing at. They say they were trying to increase admissions standards. So they based the thresholds on the test averages from the previous year: 49% English and 33% Math. (i.e. 70% and 50% respectively). That should have cut the pool down by about a factor of 20, using WAG numbers for the standard deviation (10). But it cut it down to 0. And when they used 50% English (=last year's average) OR 40% Math (about last year's average), they only got 1600 passing--it should have been closer to 12,000 if students this year were like students last year.\n\nMy guess is that somebody took a little extra care about security of the exams this year, and a lot of students weren't able to cheat as usual. I can't prove that, but it seems likely.\n\nHEADLINE: UL TO CONSIDER ONLY 1,626 CANDIDATES\nDATE: 22 AUGUST 2013\nSOURCE: All Africa\n(c) 2013 AllAfrica\nAug 22, 2013 (The Inquirer) -- The University of Liberia (UL)\nsays it will enroll 1,626 candidates who took the university's\nentrance barely a day following reports that all 25,000\ncandidates who sat the test failed massively.\n\nHowever, at a news conference yesterday, the head of the UL Relations, Dr. S. Momolu Getaweh said the UL Senate reviewed several other scenarios below the benchmarks and thereupon recommended for admission 1,626 candidates who scored either at least 40% in Math or 50% in English in the Undergraduate Programs.\n\nHe also disclosed that those to be admitted include 25 for the College of General Studies (Continuing Education), 93 in the six (6) graduate programs, thirty seven (37) for the Law School and 24 for the School of Pharmacy for Academic 2013\/2014.\n\nDr. Getaweh giving the official result of the recent UL Entrance Examinations which were administered in June and July 2013 said the results indicate that no candidate out-rightly earned the scores of 50% in Math and 70% in English previously set by the Faculty Senate of the University as the passing scores for the Undergraduate Examinations.\n\nDr. Getaweh said, \"Similarly, no candidate who sat for the Graduate Programs, Law School and School of Pharmacy Exams earned the score of 70% also set by the UL Senate as passing.\"\n\nThe UL Relations head said holding these results constant, no candidate would have otherwise been admitted to the University for Academic 2013\/2014 in the above programs.\n\nHowever, he noted that in the case of the A. M Dogliotti College of Medicine, where the score of 70% is passing, 47 candidates made 70% and above.\n\nDr. Getaweh said in view of the above, the Faculty Senate of UL met in two separate and special sessions on Wednesday, August 14 and Tuesday, August 20, 2013, respectively, to deliberate on the outcome of the examinations, and as a result of the two meetings\nand several hours of discussions, the UL Senate reviewed several other scenarios below the benchmarks.\n\nHe also disclosed that the recommendations of the Faculty Senate have been endorsed by the University as presented with the recommendations that candidates in the Undergraduate division will be required to take two transitional courses one in Mathematics and the other in English. He said both courses will be administered for six hours a week without academic credit.\n\nDr. Getaweh said, \"Candidates admitted in this category will also be permitted to take an additional three (3) credit hour course which shall be determined by their respective Colleges. However, the total hours of academic work for the first semester of\n2013\/2014 shall not exceed 9 hours a week. The students MUST pass the transitional courses within two semesters, if they wish to continue at the University.\"\n\nHe also said upon admission to the University, the rules governing poor academic performance shall apply and these rules shall be provided the candidates during the matriculation exercises following registration for first semester 2013\/2014.\n\nDr. Getaweh also said the final decision for admission to the Graduate Programs, Law School, School of Pharmacy and Medical School shall be made following the fulfillment of other criteria set out by the Admission Committees of the respective programs and colleges as indicated.\n\nHe disclosed that the names of the candidates in all programs will be published shortly in the UL Campus Review Newsletter.\n\nLast academic year 2012\/2013, the University of Liberia admitted nearly 7,500 candidates in the Undergraduate Programs because the criteria used for those admissions were quite different from this year. The average scores of 49% and 33% for English and Mathematics respectively were used as the basis for passing.\n\nThe university commended all those who participated in administering this year's Entrance Examinations and extended sincere apology to the candidates, parents and the general public\nfor any inconveniences they may have experienced during the administration of these examinations.\n\nWhen on the observation raft over the Kitch-iti-kipi (turn the wheel and it slowly rides back and forth along the cable) one vacationing teacher joked that men don't ask for directions. I suddenly realized that it was her fault. We're carefully taught to do the problems first before looking up the answers in the back of the book.\n\n## Sunday, August 25, 2013\n\n### I don't understand beauty\n\nOne tree is symmetrical and beautiful, another twisted and ugly, and another twisted and beautiful. Beauty isn't invested in only the symmetric or the useful, it just is. Somehow.\n\nSometimes I don't appreciate it at first, but then when I look at it right I discover it was there all along. Like math--you don't invent math, you discover it.\n\n### Abstracting conversation\n\nWhen we \"chat\" or blog we abstract our communication to just words, and I'll bet that there are a few formulaic aspects to the words that we aren't conscious of.\n\nSo when you meet the other face to face for the first time, I suppose you might recognize them, but there would be new channels open for the first time.\n\nIt couldn't be the same, unless the communication was one sided. Would it seem the same?\n\nWith Skype you hear the inflections and pauses that make up one of the missing channels, so it would be more nearly the same.\n\nI've been in phone conferences with colleagues that I only met in person later. They sounded the same, and their gestures did not surprise me, but there was something more to being with them in person. Something that made it easier to interact, ask favors, make suggestions--much easier than by phone or by email.\n\n### Power in ordinary people\n\nYoungest Daughter, having read a number of James Bond one-liners, decided to watch a few of the movies. All at once. (School starts tomorrow. No, I was at work and didn't watch any.)\n\nOne of the things that makes Bond interesting is watching a lone man run through a deadly puzzle, squeaking through where he must and turning his enemies' weapons against them where he can, and leaving destruction behind. The destruction is needed to stop worse destruction, so he's one of the good guys(*), but we're fascinated see how much influence a single man can have without being bitten by a radioactive spider or becoming a monster. (Wish fulfillment: I'm not Superman, but maybe I could be . . . well, with some training . . . )\n\nThere are other ways of having influence too, though I don't think they'll make a lucrative series of movies on her. I remember reading her song when I was young and thinking it too stupid for words. I read the whole poem as an adult and have liked it ever since. (**) In a world of disasters, just a distant touch-and-go and people changed.\n\nAmelie was a little like that, but with Amelie planning her changes (not always with good results). Unfortunately most of the personal problems I know about aren't as easily tweaked--so much for wish fulfillment.\n\nI wonder how extensive an ordinary person's influence actually runs. Maybe more than they expect, and less than they fantasize.\n\n(*) and Bond has good taste, which is a stand-in for being a \"good guy.\"\n\n(**) You probably know a few people this describes:\n\n\"... used that smile,\nThat hateful smirk of boundless self-conceit\nWhich seems to take possession of this world\nAnd make of God their tame confederate.\nPurveyor to their appetites . . . you know ! \"\n\n## Thursday, August 22, 2013\n\n### Cheer up and have a spot of tea\n\nBaking helps treat depression? I like the idea of self-medicating with chocolate chip cookies or a hot buttered baguette.\n\nWe can appeal to some famous names to expand the idea even farther:\n\n\u2022 \"And, as there is nothing like housework for the troubled soul of a woman, so a general clean-up is good for sailors. I had this from a general petty officer who had also passed through deep waters\" (Kipling, Sea Warfare)\n\u2022 \"There is nothing like housework for calming the nerves\" (Miss Bianca in The Rescuers by Margary Sharp)\n\nTo be serious about the matter, I'm not a psychiatrist but I suspect that we slap clinical labels on things that don't deserve it. \"Theodore Dalrymple\" wrote that many people labeled \"depressed\" are merely unhappy and don't require sophisticated intervention. Not all; I know some who do need help. (I'm not talking about professional judgment but the common language.(*)) I think quite a few of us use medical paradigms, and seek medical help, when older and simpler rules will suffice. IIRC followup work with people who survived 9\/11 found that catharsis didn't make for a healthier outcome, but denial and repression seemed to work OK. (There may have been a link to it here, but it is gone now, though Schneiderman discusses the matter. He's a life coach, not a therapist.)\n\nUnfortunately too much sugar isn't good for me. Maybe I need to take up cabinetry.\n\n(*)The common language drives me nuts sometimes when people invoke \"quantum leaps\" or \"energy flows\" with no notion of what they're talking about.\n\n## Wednesday, August 21, 2013\n\n### Copper\n\n\"Copper linked to Alzheimer's disease\" says the BBC headline. The story says that while one study suggests copper might contribute to Alzheimer's, others suggest that it might help protect the brain. The headline is a trifle misleading... Technically protecting the brain is a kind of link too, but it strains the usual use of words.\n\nBy the way, does anybody remember when aluminum was the culprit, and we were all supposed to worry about our cookware?\n\nAluminum isn't terribly good for you, and while we need some copper that can be bad too. And maybe Alzheimer's has more than one cause. The phrase \"second childhood\" is a lot older than aluminum pots.\n\n## Tuesday, August 20, 2013\n\n### Culture changing\n\nAn exhibit in the Museum of Ojibwa Culture said that one technology they rejected instead of adapting was the grain mill, which made flour too fine for traditional recipes. In Africa there were problems with famine relief Bulgar wheat--none of the traditional cooking methods gave a palatable result and many people wouldn't eat it. We're used to variety--we search for it--but I guess food is tradition, food is family, food is comfort.\n\nAnd yet a cuisine can move to a new land and use new ingredients and still be recognizably the old cuisine. (One Korean restaurant served thinly sliced hot-dogs in sauce--not quite traditional but it fit anyway.) So what makes changing foods hard? Is there a difference between a traditional set of recipes and a cuisine?\n\nRobin at the counter said an interesting upcoming event was a women's drum circle. Up until quite recently they'd not been allowed to do that. I thought it a little odd that they should be working so hard to retain the old culture, complaining about Pere Marquette et al for \"denouncing native spirituality and traditions\" and trying to replace the old religious practices--and yet be willing to introduce innovations that flatly contradicted the old ways. No skin off my nose--I'm not Ojibwa and have no dog in this hunt.\n\nBut on consideration I think the only thing they're guilty of is hypocrisy, not of being unfaithful to their culture.\n\nA culture comes from the religion a people share, the technologies and roles they share, the language they use to define their shared values, and a family history--and maybe something more.\n\nThe Jesuits tried to change the Ojibwa religion. That would have inevitably changed the culture. The shared values would also differ, and the language defining them would include new concepts. They would not change into Europeans, but many practices would change or vanish, and new ones take their place. The same thing is happening in this case--they have absorbed (from Christianity or the bastardized Christianity that is post-Enlightenment liberalism) a new value, and their culture changed accordingly.\n\nI have no sense for what role drumming played in their culture, and so can't guess what \"other things\" will come along with the change or already happened behind the scenes. Presumably there's been some change in what it means to be an Ojibwa man or Ojibwa woman: a change in their place in the universe. Just as Christianity would do.\n\nI remember reading an Indian legend in Twain. It was tightly compressed and obviously assumed a lot of cultural knowledge (a woman doing X is odd and means Y is likely). The same story was retold recently at 20 times the length with more explanation and using tropes from the Anglo understanding of Indian culture. I wonder how common it is for Indian story tellers to take the Anglo interpretation and use that in their own descriptions and self-understanding.\n\nOK, an example: living in harmony with the world. Praying to the spirit of the deer for \"forgiveness.\" The oldest stories I've read seem less like the Disney Pocahontas (\"I know every rock and tree and creature\") and more of a nervous animism. You never know what spirit you have disturbed; best to be on the safe side and placate them. Maybe I just read the wrong stories. I've been wrong before. But I notice that many of the descriptions of Indian spiritual life are recent and are not isolated from cultural interplay. It is much nicer to think that your ancestors lived in harmony with nature than to think that they were afraid of malign spirits and living on the hairy edge of disaster. The language to frame it is available, you'd be tempted to use the new narrative. (I do not question that philosophies of harmony existed, especially of harmony between people.)\n\nWe seem to try to characterize Indian culture by their technologies. They are the weavers of baskets, bakers of pots, chippers of arrowheads, silent stalkers of deer: whatever. At camp Runamucka you got an Indian name, learned to weave beads, and learned somewhat garbled traditional greetings: \"ozhaawashkonaagozi vai!\" \"miskonaagozi vai!\"\n\nOf course the real tribes adopted new technologies when they could. Some mastered the horse and proceeded to master and terrorize the other tribes. (Even horseless groups were perfectly capable of organizing empires and mounting 500-mile campaigns to chase down and annihilate their enemies.) That technology radically changed their culture. I don't know of any tribes that mastered the manufacture of guns or iron (maybe the Cherokee?) and were dependent on Europeans for powder and iron stock. That doesn't seem intrinsically different from trading to distant tribes for flint or copper, but it changed the relative values of different jobs in a very short time. No more autarky--bit by bit you get integrated into a wide-flung market economy. When blankets from the trader are warmer, more durable, and easier to sew and repair than your old hide garments, how can you keep valuing the hide seamstress? Nice to be able to know how to do it in a pinch, but I'd rather use an iron axe than make my own stone axe. Now the fur trapper, he's important.\n\nIt seems to be received wisdom in some circles that when women's work was devalued, women's worth was devalued. I'm not acquainted with any examples of this theory, and in any event \"mother\" is an irreducibly valuable office, but the general idea has some plausibility. We do often have utilitarian attitudes towards each other. I'd expect the social order to change with new technologies.\n\nI wonder what is going to emerge from our chaos. Even setting the idol of multiculturalism to one side, we sling new technologies in the mix as fast as our wallets will stand (despite the complaints of our betters who want to be tribal elders able to forbid sweet sodas and other corrupting influences). Our elite have largely abandoned the traditional religion and acquired some new ones. The legal machinery seems designed to mangle families--not much way to convey tradition that way. The stories are shared, sometimes even between groups, but there have to be new stories every season. Even the shared values I'm not sure are shared that broadly anymore.\n\n## Monday, August 19, 2013\n\n### People and Peoples followup\n\nI said I would check Psalms to see how it read from a peoples\/family perspective, as opposed to an individual perspective. So here goes.\n\nIf I were repeating this exercise, I might come up with a slightly different partitioning--not everything is clear cut. But the first distinction is a grammatical one: is this an \"I\" or a \"we\" song or does it not appear in English (NASB) or obviously refer to the Messiah?\n\n\u2022 I\n\n1, 3, 4, 5, 6, 7, 9, 11, 13, 15, 16, 17, 18, 22, 23, 25, 26, 27, 28, 30, 31, 32, 34, 35, 38, 39, 40, 41, 42, 43, 49, 51, 52, 54, 55, 56, 57, 59, 61, 62, 63, 64, 66, 69, 70, 71, 73, 77, 84, 86, 88, 89, 91, 92, 94, 101, 102, 108, 109, 111, 116, 119, 120, 121, 122, 130, 131, 135, 139, 140, 141, 142, 143, 144, 145, 146\n\n\u2022 WE\n\n8, 12, 14, 20, 44, 47, 48, 60, 74, 75, 79, 80, 85, 90, 100, 103, 105, 106, 107, 123, 124, 126, 128, 129, 137\n\n\u2022 Neither or clearly messianic (not me)\n\n2, 8, 10, 19, 21, 24, 29, 33, 36, 37, 45, 46, 50, 53, 58, 65, 67, 68, 72, 76, 78, 81, 82, 83, 87, 93, 96, 97, 98, 99, 104, 110, 112, 113, 114, 115, 117, 118, 125, 127, 132, 133, 134, 135, 136, 147, 148, 149, 150\n\nThe next question is whether the song is best understood as an individual talking to God, or it sort-of could-be a group, or it works both individual or group, or it is definitely \"we\", or not really applicable to this scheme.\n\n\u2022 Individual\n\n18, 27, 38, 39, 41, 42, 43, 49, 51, 55, 62, 63, 88, 131, 139\n\n\u2022 Sort-of group but mostly individual\n\n16, 17, 22, 26, 35, 40, 52, 57, 69, 71, 86, 89, 91, 94, 101, 111, 112, 116, 119, 125, 131, 141, 144\n\n\u2022 Individual or Group both work\n\n1, 3, 4, 5, 6, 7, 9, 10, 11, 13, 19, 23, 25, 28, 30, 31, 32, 54, 56, 59, 61, 64, 70, 73, 84, 90, 92, 100, 102, 107, 109, 121, 124, 126, 127, 128, 130, 138, 140, 142\n\n\u2022 Clearly Us\n\n12, 14, 15, 20, 33, 34, 37, 44, 47, 60, 65, 66, 68, 74, 77, 78, 79, 80, 81, 83, 85, 87, 95, 96, 97, 98, 103, 105, 106, 122, 123, 133, 137, 143, 147\n\n\u2022 Not applicable to this scheme\n\n2, 8, 21, 24, 29, 36, 45, 46, 48, 50, 53, 58, 67, 72, 75, 76, 82, 93, 99, 104, 108, 110, 113, 114, 115, 117, 118, 120, 129, 132, 134, 135, 136, 145, 146, 148, 149, 150\n\nReviewing the Psalms this way suggests that this isn't as clear a study as I hoped. Though a great many psalms are (and of course have been) used by groups, the themes of group suffering, group longing, group repentance, and so on don't dominate. They're there if you want them.\n\nAnd as AVI pointed out, identity was thought of differently then.\n\nUPDATE: I left out one little detail: the church is the new Israel, and it could suffer in the same ways as the Jews did, for the same kinds of reasons.\n\n### Using money\n\nI know that 19 times out of 20 money I give to one of the homeless guys (almost all men), will promptly be wasted on drugs, alcohol, smokes by the cigarette--wasted at best, harmful most of the time.\n\nThat by itself isn't obviously such a great reason not to give--if I don't, will I spend it on a fattening lunch or book I won't get around to reading? Wasted either way, possibly damaging either way.(*)\n\nEncouraging the homeless to hang around and beg isn't good for them or the rest of us, and turning charity into an anonymous financial transaction shrivels it. So there's that. But there they are, and there's Jesus strong words...\n\nI used to give McD tickets (they're not on the Square anymore)--still kind of anonymous, and maybe even a little insulting, but less harmful. Though McD's might have their own ideas about customers who sit in a booth all day.\n\nThe one thing I have trouble prying loose is time.\n\n(*)Actually, reviewing the receipt ledger suggests that most of the cash goes to groceries and gasoline.\n\n### Expedition\n\n\"We get more done before breakfast than most people get done all day.\" (US Army ad)\n\nIt seemed as though Pere Marquette memorials were all over the place in the UP, though that's probably sampling bias: the crossroads are more interesting places. Reading about all the places he'd been, and missions he'd founded, and records he'd made, I noticed that the marker for his grave said he died at the age of 38. He asked for the assignment when he was 28.\n\nWhen I was 38 I mumble mumble mumble\n\n## Sunday, August 18, 2013\n\n### Another \"why not\"\n\nThe North American Indian tribes, with the possible exception of Calusa Indians of southwestern Florida, didn't use sails on their boats. Which seems a little odd; there are plenty of lakes which would be easier to get around on if you had a sail you could unfurl when the wind was right. The Egyptians used them to go up the Nile, and I presume sails would be equally useful going up the Mississippi or the Missouri. (You'd have to learn tacking, but that shouldn't take too long.) Maybe Superior isn't the best place to learn about sailing, but there are other lakes.\n\nBut the most famous Indian water vehicle (hardly the only one, though) was the birchbark canoe, which while nice and light for portaging isn't ideal for hooking a mast on. That would require a heavier frame, making the result a lake-only vehicle.\n\nMy Better Half pointed out that the Indian fishing methods were shallow water technology, and so there'd be no great need to go out far and deep, where sails would be most helpful. While they made plenty of fishing nets, I don't find any reference to long and deep nets for deep water fishing. If the populations were low enough that shallow water fishing was adequate to provide the supply (but Cahokia or Aztalan?), then the additional effort wouldn't have been worth it. So why bother with sails.\n\n### Vacations and recreation\n\nDriving through the Upper Peninsula drives home how central recreation is to the place. Without it most of the place would be subsistence hunting\/fishing, since the ore and big trees are mostly gone and most of the soil is pretty lousy. Most boats aren't for professional fishing or transport, but for visitors.\n\nSo what do people go to do? Fish. Hunt. Travel around in boats. Walk long distances. Live in primitive conditions for a while.\n\nMaking a living by hunting or fishing isn't all that easy, as the older Yoopers and the Ojibwe before them could testify. It was hard work, and even with modern tools it takes time and effort (unless you bait the deer). So tens of thousands of us take a vacation from our hard jobs by doing a different hard job.\n\nNot all our recreations are like that: some are \"sit and watch\" recreations (watching the boats roll in, watching the Brewers lose, watching reality shows or watching an opera), and others are contests (business league softball games and so on). But sometimes we try to relax by doing completely different work--as in the dude ranches.\n\nNot just any kind of work, but either something exotic (cowboy or astronaut) or something that we can point to afterwards and say \"I did that\". Sweeping floors is not going to attract vacationers, nor the inhuman job of bolting the rear flange on pump after pump after pump.\n\nBut there's probably room (and maybe even a thriving market I haven't heard about) for people paying to spend a week in a woodshop or machinist shop with some pros helping them make something. I do kludge carpentry--better since I invested in a second-hand table saw, but nowhere near what I could do with the space and proper tools (and that wouldn't be as good as the pros). But I haven't the budget or space for a good setup. I don't think I'd shell out for a week with good advisers and use of a good rig, but then I'm not that interested in spending big bucks on a good fishing boat either--but somebody's buying them.\n\n### The Soo\n\n\"I love work. I can sit and watch it all day.\"\n\nThat came to mind while we watched a 1000-foot ship slowly slide into the Poe lock(*). The giant machine needs only a crew of 25 or so, according to the boat watcher and former ship engineer beside me (and the captain's job isn't all that well paid these days). Hard work, and dully unromantic for those who have to do it; but amazing to the rest of us. Watching it is even rather peaceful to those of us who don't have to worry about 2 1\/2 foot clearances.\n(*)\n\nI heard the obvious joke a half a dozen times\n\n## Sunday, August 11, 2013\n\n### People and Peoples\n\nThere are many things I don't quite understand about how God works. One is what was the meaning of the centuries spent as slaves in Egypt, or the centuries without prophets, or the decades of trouble without any sign.\n\nSome saints experience a dark night of the soul, including such famous saints as Mother Theresa. They say the experience reshapes them and brings them closer to God.\n\nBut what about a \"dark century of the soul\" for a people? God can be interested in peoples as well as people; on the relationships among peers and along the generations. Without losing sight of people an infinite God can also care about tribes.\n\nIt is risky to try to explain what we call good and bad in a person's life (see Job), and it has to be even harder to understand God's purposes in something bigger than a single person. What would God be looking for?\n\nI need to go through Psalms and see how it relates to \"families:\" I always read it from the point of view of individuals.\n\n### Not-quite universal hymns\n\nWe sang Immortal, Invisible this morning. Have you noticed that a Jew, or even a Muslim could sing it without qualms (provided they didn't know its provenance)? It sings about God's transcendence and power, which all three religions affirm. (Not so Rejoice, the Lord is King, of course.) I don't think a Hindu would, though; since it implicitly denies the existence of any other gods, and emphasizes His invisibility and inaccessibility. It would require some serious mental gymnastics about the atman or else a who-cares attitude.\n\nEven the things we think we can all agree on, aren't always universal.\n\n## Saturday, August 10, 2013\n\n### Amazing mosquitoes--but I still hate them\n\nFrench researchers figured a way to get microscopic video(*) of mosquitoes biting mice. The mosquito probe wiggles around inside trying to stab a capillary. And the probe is quite complicated, including stabbing blades that latch on inside as anchors, and a dual pipe system with blood getting sucked one way and saliva going the other.\n\nAnd it seems that people who are \"immune\" to mosquito bites really aren't. Their systems respond to the bite, trying to clog up the bite hole with white blood cells, but the mosquito just wiggled the probe around to hit a bigger blood vessel.\n\nGo read the article, and watch a video or three.\nThanks to Texan99 \"We had a rule for the kids: bugs in the house get stomped; bugs outside you leave alone.\" Mosquitoes were the exception.\n\n(*)They peeled up a thin flap of skin and took the video through it while the mosquito drank.\n\n### Lucky kids\n\nSome 3rd year students at Niels Bohr got time on the Nordic Optical Telescope as part of their course, and the first night they saw emission lines from a quasar--gravitationally lensed in 3 other places. There's a picture here.\n\nA good instructor can give his students a project that is both within their competence and still in undiscovered country, but this group lucked out with something nice and spectacular. The fellow who originally found that quasar, when he heard about the students' findings, got excited and went back and found 3 more images.\n\nThis is quite a rich find.\n\nIn addition to the quasar itself, you also get other interesting information. A quasar varies in brightness and you can measure that there is a different arrival time for the light from the different observations, because the light paths are not of equal length. In this way you can calculate the geometric model of the light\u2019s path. You can also calculate the mass of the galaxy cluster and you can calculate what is called the Hubble parameter, which tells us about the expansion of the universe.\n\nIt has been an incredible experience for the students. \u201cIt is amazing to be allowed to participate in something that is relevant to research so early in our education,\u201d says Thejs Brinckmann, whose appetite for a future as a researcher has been whetted even more.\n\nI spent a couple of months on an undergrad project too, but only came up with some minor results in compartmental analysis.\n\n## Thursday, August 08, 2013\n\n### EAA correction\n\nI spoke to a pilot friend who helped with the pyrotechnics at EAA, and he said they used dynamite, detcord, and gasoline. Three gallons would make a good 2-story-house sized flame that we could feel from half a mile away.\n\nI should have asked how to join the team. Although maybe it is better if I don't. The director is retiring this year--and that may be a good thing. My friend had to put out a few small fires that fell near the setup for the next blasts. A bit too close for comfort.\n\n### Mondegreen wisdom\n\nWhen singers don't have good articulation or when the mix is too instrument-heavy I find when I reassemble the babble into something nearly intelligible it doesn't seem quite relevant to the rest of the song. (I often must look up lyrics online, and I find that songs that seemed muddy back in the 60-70's are still muddy today--it wasn't just the static-y radio.)\n\nI did the same with speech when young and unfamiliar with exotic uses of words, and do the same now that I'm older and people mumble more.\n\nSometimes the revision is better than the original. A line from the religious controversies of a few centuries ago ran something like: \"Confess a man against his will; he's of the same opinion still.\" Perfectly true; compelling somebody to recite a creed doesn't make him believe it. But when I was 10 I'd not heard the word confess used that way, and I reconstructed the lines as \"Convince a man against his will; he's of the same opinion still.\" That is an unpleasant indictment--and every day we run across that kind of stubborn refusal to see.\n\nA rattle of dishes disguised \"self deluded\" as \"self diluted,\" which is a polite way to describe lives that should have overflowed with works of grace and kindness--but instead drip self-absorption.\n\nMaybe there are advantages--but I wish people wouldn't mumble.\n\n## Tuesday, August 06, 2013\n\n### Courtesy as teacher\n\nI've written at more length on the topic of courtesy before here and here and here.\n\nI've heard it said that if you want to hate a man, do him an injury. Conversely, if you want to learn to love a man, do him a kindness.\n\nIf courtesy is a kind of attenuated love, then the everyday practice of it should train me to appreciate a bond, however faint, between me and my neighbor. The everyday absence of courtesy will also teach me something. Will it cultivate dislike for my neighbors, or merely callousness?\n\n## Monday, August 05, 2013\n\n### A \"light\" at the end of the tunnel\n\nI looked in the windows of the new library this morning on the way to work. It isn't quite ready yet. There's something lonely and disquieting about looking through shelf after empty shelf after empty shelf. Where there should be thoughts and joys there's nothing.\n\nBut, 2\/3 of the way across the building through a \"tunnel\" of empty shelves, a splash of different colors said a bridgehead was established.\n\n### Kidnapped\n\nI don't remember how old I was when I read Treasure Island, but I remember enjoying it once I got past the obscure references in the first few chapters. I thought a squire worked for a knight, and I didn't understand the social structure the story was embedded in, but the book was fun. When I re-read it a few months ago, I noticed things I hadn't seen the first three times. Fortunately I've not had experiences with pirates, but I knew the environment much better than when a young boy.\n\nMy parents, presumably gratified by my interest in the story, bought Kidnapped. Screeching halt. I tried twice to get into the book, but the dialect was too alien and Stevenson assumed that the reader understood a wealth of different things about Scotland and its relations with England. (Only 1\/4 Campbell: I don't keep track of clan leaders)\n\nFor an adult, the book is worth the time. David isn't the same kind of resourceful hero (as witness his time on the island), and is fairly prickly, but the story works.\n\nI don't know if the picture of the Highlanders is true to life, but it is crisp and lively. If you haven't read it, you'll probably like it.\n\nOnce I got past Margaret Wise Brown (I wish I had her wordsmith skills), there seemed to be three classes of books: Winnie-the-Pooh class, Green Smoke-class, and Gulliver's Travels class. (We tended to get more British children's book authors, possibly because it was easier to get them from James Thin than from New York.) For some reason I never was very enthusiastic about Winnie (and Paddington was only a little better) myself, and never read them with our kids. But Wind in the Willows I can still read for fun. Odd that the sophisticated stories and the ultra-simple ones are the ones with better staying power. (There was a bit of a furor when the library pitched Mary Poppins, but when I went back to read it as an adult I realized why nobody had taken it off the shelf in years--it isn't really very good.)\n\nWith no TV (only a few hours at night), and radio broadcasts more static-y than I cared to put up with, I browsed the eclectic mix lying around at home. I wasn't Christian and eschewed the obviously Christian books, but Gabriel and the Creatures was nicely offbeat and Manson's Tropical Diseases endlessly fascinating; there was Ayesha, Rabelais... but funny thing: when I started reading Ian Fleming all the James Bond books suddenly and permanently vanished.\n\n## Saturday, August 03, 2013\n\n### EAA 2013\n\nThe Oshkosh EAA week is fun. We went today, with a couple of friends (thanks to the generous donation of someone with extra tickets). We stayed until after Yves Rossy flew.\n\nMy favorite part of the place was the innovation hall and environs. I wouldn't have thought that compressed natural gas would have enough power to compensate for the overhead of the heavy tank, but apparently at these pressures it has 38% higher octane than aviation fuel. And there was an ultra-high altitude glider, a display of heads-up display, the new Orion project exhibit (I wonder how often names are reused), and others. I spent quite a while talking with a fellow with a 40-pound electronics crate, used to plug in avionics modules for rocket guidance. That beast was solid. I'd seen how light everything had to be in a rocket, and hadn't realized how rugged some components had to be (outside of the nozzle).\n\nTrue to its origins, the show offers a thousand ways to buy\/build\/rent and equip your own airplane. Proud owners show off their accomplishments, hobbyist groups maintain old military craft (including the only DC-3 to actually drop its men in the right spot at Ste Mere-Eglise). Larger tents hosted talks about safety, construction, regulatory nuances, and dozens of specialized topics as well. The big manufacturers were there, and so were a couple of mission groups looking for pilots. (Meanwhile back at the museum, a man who'd spent 13 years in prison after his spy plane was shot down over the USSR gave a talk on spying during the Cold War. I couldn't stay for it all, and English was not his first language so he was reading his PowerPoints. Did you know that spying is the second oldest profession, and the only one enjoined in the Bible? Actually farming is mandated too...)\n\nThe aviation show starts with the military bird show; a few overflights and then a re-enactment of Pearl Harbor (Zeros piloted by Americans, and dynamite\/gasoline blasts or so we were told; the black smoke suggested heavier oil; maybe FAE). Later airplanes sometimes made \"bomb\" runs too, including (rather incongruously) a trainer with no bomb bay or weapon mounts.\n\nThe volunteer pilots practiced long and hard with their birds, and it showed in the tight formations they achieved. The announcer mentioned their long hours, and it occurred to me that these men had more flight time than the lads who flew them to war. Though of course the latter had to master the art of not getting killed by alert enemies, which is a whole different set of skills.\n\nThe acrobats did amazing things with their planes. Some snide cynic said that we go to auto races in hopes of seeing a crash, but that's not so. We want the acrobats to overcome the danger and do the apparently impossible. The danger has to be there, but we want the victory.\n\nYves rode the side of the helicopter to 6500 feet, and tried to get all the engine lights OK. They finally lit up and he fell off, and after enough of a dive he started his pulse jets. It took me a while to spot him, and I lost sight regularly. The jumbotrons showed the view from a camera on his wing, and when he reached his flight limit of 2000 feet he opened his chute. Which means we could hear the man flying his jets, and see the on-again\/off-again contrails, but we couldn't get a good look at him until he reached the ground. He's not a daredevil--developing that kind of rig he'd have been dead already if he was.\n\nTomorrow the sunburns will be annoying, but today we had a good time.\n\n## Friday, August 02, 2013\n\n### St GKC?\n\nA post on a tweet about an announcement that doesn't appear online: an interesting idea if true--opening the case for canonization for G.K.Chesterton.\n\nIIRC candidates for sainthood are supposed to exemplify \"heroic virtue.\" Working as a writer and exercising gifts in the life of the mind while enjoying marriage and the pleasures of the table isn't quite the image surrounding most saints of the calendar. Martyrdom, yes. Spending years trying to guide monks or nuns, yes. Fasts, working with the poor, becoming pope; those seem to be more traditional. But recently I gather they've been trying to include more married saints, to emphasize that marriage can be a sanctifying vocation too. (About time)\n\nThere's some dispute about the role of saints in the church, but all factions agree that saints can be examples for the rest of us. I could do worse than imitate GKC.\n\nDoing a little tracking: From Facebook\nHere is the exact wording from Dale's announcement at the conference:\n\n\"Martin Thompson says that Bishop Peter Doyle 'has given me permission to report that the Bishop of Northampton is sympathetic to our wishes and is seeking a suitable cleric to begin an investigation into the potential for opening a cause for Chesterton.'\"","date":"2023-01-29 12:05:14","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.25960567593574524, \"perplexity\": 2292.681329361943}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2023-06\/segments\/1674764499713.50\/warc\/CC-MAIN-20230129112153-20230129142153-00062.warc.gz\"}"} | null | null |
from django.core.management.base import BaseCommand
from ... import models
class Command(BaseCommand):
args = ''
help = u"Clean SessionTicket and ProxyGrantingTicket linked to expired sessions"
def handle(self, *args, **options):
models.ProxyGrantingTicket.clean_deleted_sessions()
models.SessionTicket.clean_deleted_sessions()
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,712 |
The altar of incense is first mentioned in Exodus chapter 30 as one of the items inside the Holy Place of the tabernacle. The top of the altar was square—one cubit per side—and the whole altar was two cubits high. A cubit was about twenty inches, or just under two feet. The altar of incense was made of acacia wood and overlaid with gold. It had four "horns," one at each corner, similar to the altar of sacrifice in the courtyard (Exodus 27:2). Rings of gold were built into the altar so that it could be carried with acacia wood poles that were slipped through the rings. The altar of incense was placed before the veil that separated the Holy Place from the Holy of Holies. On the other side of the veil was the Ark of the Testimony, where the presence of God was (Exodus 25:22).
Aaron was instructed to burn incense on the altar each morning and at twilight, every day, as a regular offering to the Lord (Exodus 30:7–8). God gave the recipe for making the incense and stipulated that no other incense ever be burned on the altar (verses 34–38). The fire used to burn the incense was always taken from the altar of burnt offering outside the sanctuary (Leviticus 16:12). Never was the altar of incense to be used for a burnt offering, a grain offering, or a drink offering (Exodus 30:9). Once a year, on the Day of Atonement, the high priest was to put blood on the horns of the altar of incense to cleanse it. The altar of incense was called "most holy to the Lord" (verse 10).
Of course, God's primary desire for His people is that they be holy. Simply going through the rituals required by the Law—including the burning of incense on the altar of incense—was not enough to make the Israelites right with God. The Lord wanted their hearts and lives to be right, not just their formalities. During Isaiah's time, the people were disobedient to God, yet they still maintained the temple rites, and that's why God said through the prophet, "Stop bringing meaningless offerings! Your incense is detestable to me" (Isaiah 1:13). More important than burning the proper incense at the proper time with the proper fire with the proper implements was having a proper heart before God.
The altar of incense, then, can be seen as a symbol of the prayers of God's people. Our prayers ascend to God as the smoke of the incense ascended in the sanctuary. As the incense was burned with fire from the altar of burnt offering, our prayers must be kindled with heaven's grace. The fact that the incense was always burning means that we should always pray (Luke 18:1; 1 Thessalonians 5:17). The altar of incense was holy to the Lord and was atoned for with the blood of the sacrifice; it is the blood of Christ applied to our hearts that makes our prayers acceptable. Our prayers are holy because of Jesus' sacrifice, and therefore they are pleasing to God.
The altar of incense can also be seen as a picture of the intercession of Christ. Just as the altar of sacrifice in the courtyard was a type of Christ's death on our behalf, the altar of incense in the Holy Place was a type of Christ's mediation on our behalf—Christ's work on earth and in heaven. The altar of incense was situated before the mercy-seat of the Ark—a picture of our Advocate's standing in the presence of the Father (Hebrews 7:25; 9:24). The incense was to be burning continually on the altar of incense, which shows the perpetual nature of Christ's mediation. Christ's intercession on our behalf is a sweet-smelling savor to God.
It is beautiful to know that God considers the prayers of believers to be like a sweet smell of incense. Because of Christ, we can now enter God's holy presence by faith, with full assurance (Mark 15:38; Hebrews 4:16). We offer our prayers upon the altar, trusting in Jesus, our eternal, perfect, and faithful High Priest (Hebrews 10:19–23). | {
"redpajama_set_name": "RedPajamaC4"
} | 7,523 |
A BWB Holster or Below WaistBand Holster is a type of handgun holster worn inside the waistband of the wearers pants and rests below the belt line. A BWB holster offers deeper concealment when compared to the traditional IWB (Inside WaistBand) holster, which results in more noticeable comfort. Because a BWB Holster is worn inside the pants and below the belt it is often the most concealed type of holster available that works with most clothing options.
Advantages and Disadvantages
The primary benefit of a BWB holster is deep concealment ensuring the firearm is securely and discreetly concealed at all times. Many types of IWB, OWB (Outside WaistBand) and SOB (Small Of Back) holsters can expose the firearm when the shirt becomes lodged between or if the wearers top is too short or snug; with a BWB this is not an issue because the firearm is completely concealed within the pants, shorts, slacks or skirt.
Another benefit of the BWB holster it that it is designed to flow naturally with the body creating flexibility at the pivot points resulting in easy wearability and all day comfort. Holsters that are worn at the waistband and belt, or sometimes even around the shoulders, can often restrict movement causing pinching or rubbing of the skin and general discomfort.
When carrying a firearm retention ability is always a consideration and the BWB holster excels in this area as well. Due to its deep concealment the BWB holster is less likely to be accessed by another person. The caveat to this is that the BWB holsters higher level of retention and deep concealment can cause the firearm to be more difficult to retrieve, especially while seated, putting it at a slight disadvantage. Most often choosing the correct size BWB holster for the firearm can often help overcome this issue and commonly leaning back with a BWB holster gains better access to the firearm from a seated position.
Materials
Options for a BWB holster materials vary with leather and denim being the two most common found. Leather and denim are both breathable and attractive in appearance. While denim is often less expensive, leather is more durable and can be dyed in many colors; leather will also take the form of the firearm and a quality leather is thick enough to provide protection from perspiration and other elements.
Common Types and Styles
Holster designs for firearms cover a wide variety of shapes, sizes, and materials. Holsters are generally designed to offer protection to the firearm, secure retention, and provide access to it. The most popular options of BWB holsters resemble fanny packs or a pouch type of concealment for the firearm. As an added safety feature a few of the BWB holsters ensure the trigger is inaccessible in the holster until the firearm is drawn. Concealment holsters are designed to easily conceal sub-compact and compact firearms while a few even offer options for full-sized firearms. Because BWB Holsters are designed to be worn below the waistband, under clothing and held close to the body, comfort is important.
See also
Handgun holster
Paddle holster
References
Handgun holsters | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,034 |
package org.apache.spark.sql.connector.expressions.aggregate;
import org.apache.spark.annotation.Evolving;
/**
* An aggregate function that returns the number of rows in a group.
*
* @since 3.2.0
*/
@Evolving
public final class CountStar implements AggregateFunc {
public CountStar() {
}
@Override
public String toString() { return "COUNT(*)"; }
@Override
public String describe() { return this.toString(); }
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,339 |
{"url":"https:\/\/www.doubtnut.com\/question-answer\/the-equation-of-the-plane-through-the-intersection-of-the-planes-x-y-z1-and-2x-3y-z-4-0-and-parallel-642981072","text":"Home\n\n>\n\nEnglish\n\n>\n\nClass 12\n\n>\n\nMaths\n\n>\n\nChapter\n\n>\n\nPlane\n\n>\n\nThe equation of the plane thr...\n\nThe equation of the plane through the intersection of the planes<br> x+y+z=1 and 2x+3y-z+4 = 0 and parallel to x-axis is\n\nUpdated On: 27-06-2022\n\n(a) y-3z-6=0(b) y-3z+6=0(c) y-z-1=0(d) y-z+1=0","date":"2022-12-07 20:21:34","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.22759006917476654, \"perplexity\": 13348.21166138961}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-49\/segments\/1669446711218.21\/warc\/CC-MAIN-20221207185519-20221207215519-00721.warc.gz\"}"} | null | null |
> [Yeoman](http://yeoman.io) generator
## Getting Started
### What is Yeoman?
Trick question. It's not a thing. It's this guy:
Basically, he wears a top hat, lives in your computer, and waits for you to tell him what kind of application you wish to create.
Not every new computer comes with a Yeoman pre-installed. He lives in the [npm](https://npmjs.org) package repository. You only have to ask for him once, then he packs up and moves into your hard drive. *Make sure you clean up, he likes new and shiny things.*
```bash
npm install -g yo
```
### Install and run the generator
1. checkout this repository
2. open a console (cmd, bash, terminal, etc)
3. call:
```bash
npm link
npm install
```
4. create a directory for your new project
5. go to that directory in your console
6. initiate Yeoman:
```bash
yo microservice
```
7. answer all the questions
8. start coding with your new microservice
## License
MIT
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,282 |
\section{Introduction}
The knowledge of the complex evolution of the stellar component in high redshift galaxies relies on how detailed is our understanding of the history
of stars in nearby galaxies. The best way to trace back the star formation episodes in a galaxy is to study resolved stars. However, this is possible
only for few nearby objects, tipically using the best observational facilities to date, and only for the brightest stars in the population.
Given such limitations several techniques have been proposed to disentangle the properties of unresolved stellar systems, one of these is the Surface
Brightness Fluctuations method \citep[SBF hereafter]{ts88}. The SBF technique was introduced as a distance indicator for elliptical galaxies within
$\sim$1-20 Mpc. After more than two decades of systematic applications it is now recognized that the SBF method works in a much larger distance
interval, and can be applied to a wider class of objects: ellipticals, bulges of spirals, dwarf ellipticals, globular clusters, etc. In addition, it
is well accepted that SBF magnitudes and colors represent a potential tool to analyze in details the physical and chemical properties of unresolved
and resolved stellar systems.
In this paper we will briefly discuss some applications of the SBF method done at the INAF-Observatory of Teramo by the SPoT\footnote{Teramo--Stellar
POpulations Tools group website: www.oa-teramo.inaf.it/SPoT} group.
\section{SBF by the SPoT Group}
\subsection{Models}
To derive distances from measured SBF magnitudes one needs a calibration of absolute SBF versus one integrated color \citep{tal90}. The calibration
is usually derived following an {\it empirical} approach \citep{tonry01}, which suffers for the usual drawbacks: one needs to know in advance the
distance of few objects in order to derive the zeropoint of the calibration; the calibration can be obtained for one filter at a time, etc. To avoid
these problems one can derive {\it theoretical} calibrations by means of stellar population models.
Taking advantage of the expertise by members of our group in the numerical sinthesys of stellar populations \citep[e.g.][]{brocato99,brocato00}, we
derived SBF models for stellar systems in the age range $\sim$50 Myr - 15 Gyr, for metallicity [Fe/H] from $\sim -2.3$ to 0.3 dex, for standard
UBVRIJHK photometric bands and HST filters (ACS, WFPC2 and NICMOS).
The reliability of the SBF models proposed by our group has been tested against various observational data \citep{c03,r05}. As an example the
optical calibrations derived in V, I, and $z'$ using the SPoT models agree nicely with the empirical ones \citep[e.g.][]{biscardi08}. Also, the
comparison of near--IR models with available data has shown that the general behaviour of observations is well reproduced.
It is worth to emphasize that our approach to derive SBF models is original with respect to other methods. Our technique, in fact, is based on the
synthesis of Simple Stellar Populations (SSP) and it has two main advantages (see \citet{r05}, Sect. 3). First, multi-band Color-Magnitude Diagrams,
integrated colors and luminosity functions are available in addition to SBF models. Thus, models are tested against the observed SBF magnitudes {\it
and} also versus other astronomical observables of resolved and unresolved systems. Second, the SPoT code allows the user to set many different input
parameters (stellar tracks, mass loss, IMF, atmosphere models, etc.). As a consequence, the sensitivity of SBF to various properties of the stellar
population can be analyzed.
As an example, in our first release of SBF models we showed that the properties of hot evolved stars in old stellar systems (HB, Hot-HB, Post-AGB)
can be explored using SBF magnitudes in bands like B, or U. The future class of detectors with increased efficiency in the blue bands - like WFC3 on
board of HST, or the WSO satellite \citep{pagano07} - will be of great interest for SBF applications to the wavelength interval below 5000 $\AA$.
\begin{figure*}[t]
\centering \resizebox{6.5cm}{6.5cm}{\includegraphics[clip=true]{cantiello.fig1.eps}}
\resizebox{6.5cm}{6.5cm}{\includegraphics[clip=true]{cantiello.fig2.eps}} \caption{\footnotesize Upper panel: Color-color diagram obtained using the
optical-to-near--IR {\it integrated} colors V-K and I-K. The metallicity is color coded - [Fe/H]=$-1.8$, $-1.3$, $-0.7$, $-0.3$, $0.0$, $+0.3$ dex
are shown in black, blue, cyan, green, red and magenta, respectively. For each metallicity ages between 1.5 and 14 Gyr are shown (larger symbols size
means older ages). The SPoT models used are from \citet{r05}. Lower panel: As upper panel (same symbols, same models) except that SBF colors are
taken into account. Differently from upper panel, models with different chemical compositions are well separated from each other. Note that the
magnitude interval span by the x-- and y--axis is the same in both panels.} \label{colors}
\end{figure*}
\subsection{Measurements}
As mentioned above the SBF was proposed as a method to measure distances. To estimate the distance of a galaxy the SBF magnitude and, usually, the
integrated $(V-I)_0$ color are obtained in one single annulus. However, it is reasonable to expect that SBF variations can be observed within a
single galaxy.
In 2003 we started a campaign aimed at the detection and study of SBF gradients in galaxies. For this purpose we have developed a procedure optimized
to reveal radial variations of SBF magnitudes. In our first study of SBF gradients - based on I-band images of eight ellipticals observed with ACS -
we found that the presence of SBF gradients seems to be correlated with the mass of the galaxy. In particular, less massive objects do not show
significant gradients \citep{c05}.
The presence of SBF gradients, though not unexpected, represents a further piece of information to study the evolutionary path of galaxies. Moreover,
gradients do not depend on the distance of the object, so any comparison with models is free from this heavy uncertainty. Comparing data with SPoT
models we have pointed out that the amplitude of the SBF versus color gradient seems to be dominated by a [Fe/H] variation along the radius of the
galaxy, rather than to age variations. Such result appears even more meaningful if one considers that the only galaxy in our sample with a gradient
likely dominated by age variations is NGC 1344, a galaxy that shows morphological irregularities possibly related to a recent gravitational
interaction.
This study has been recently extended, again using ACS data, both in the I- and V-band \citep{c07}. The study comprises 14 galaxies spanning a large
interval of total magnitudes ($\sim$10 mag), and with very different properties. The new data confirm the results found in our previous study, and
suggest that a larger database of SBF measurements will provide a valuable tool to analyze stars in galaxies.
In general, our study on the use of SBF as a tracer of stellar population properties - via SBF gradients, absolute SBF magnitudes, or optical SBF
colors - demonstrated that the metallicity of the dominant stellar component can be better confined with respect to age, unless optical to near--IR
SBF magnitudes are coupled (see next section).
Besides the exploration of the properties of unresolved stellar populations, we have also taken into account the chance to measure SBF for the study
of resolved stellar systems, and galaxies at large distances. In the first case we have carried out a dedicated study on star clusters in the
Magellanic Clouds, providing the first optical SBF measurements for different MC star clusters, and analysing in details their optical and near--IR
SBF properties through data to models comparisons \citep{r05}. More recently, we measured SBF magnitudes for four distant ellipticals observed with
ACS. The large distances of the objects observed allowed us to estimate H$_0$ - see Biscardi et al.'s article in this volume, and references therein.
\subsection{SBF--colors }
To date the study of unresolved stellar populations using SBF has been carried out using three different approaches: $i$) absolute SBF magnitudes;
$ii$) optical SBF colors; $iii$) SBF gradients. However, since the main application of SBF is to derive distances, none of the applications existing
in literature is optimized for stellar population studies.
In Fig.~\ref{colors} we show two color-color panels, both obtained using the SPoT models for ages between 1.5 and 14 Gyr, and metallicity [Fe/H] from
$-1.8$ to 0.3 dex. The upper panel of the figure shows the integrated optical-to-near--IR colors I-K and V-K, the lower panel uses the same I-K and
V-K colors but SBF magnitudes are taken into account. It is easy to recognize in the upper panel that the age-metallicity degeneracy strongly
affects models. On the contrary, the lower panel shows that optical-to-near--IR SBF color models in the age and metallicity regimes considered are
well separated, and a data to models comparison will help to put substantial constraints to the metallicity of the system. At the same time, thanks
to the large separation between models at fixed [Fe/H], these SBF-color panels can also be used to constrain the age of the dominant stellar
component within an interval better confined with respect to, e.g., integrated colors.
The applications of the SBF-color technique described above are to date limited to optical colors, or refer to inhomogeneous sets of optical and
near--IR SBF measurements \citep[e.g.][]{jensen03}. In all present applications, however, the comparison of data with models confirm the reliability
of the technique proposed and of models, and supports the potential of SBF colors to explore the physical and chemical properties of unresolved
stellar populations.
\section{Conclusions and Future perspectives}
The SBF technique is to date one of the most reliable distance indicators for elliptical galaxies. However, to our point of view, this technique is
underestimated with respect to its real potentiality.
Concerning distance measurements, the SBF method is able to provide distances from few Kpc up to $\sim$150 Mpc with present observing facilities, and
possibly to much larger distances with future instrumentations. Such unique characteristic gives the SBF the potential to cover the distance scale
ladder from local to low redshift ($z\leq0.05$) distances. Thus, SBF measurements, coupled with a reliable calibration of absolute SBF magnitudes,
provide a great opportunity to substantially reduce the systematic uncertainty that affects the cosmological distance scale.
With regard to stellar population analysis, there are only few studies dedicated to this topic based on the SBF method. However, it is now evident
that SBF can greatly improve our understanding of the properties of unresolved stellar systems. We presented SPoT models in a specific SBF
optical-to-near--IR color plane showing the potential of SBF colors to substantially remove the age-metallicity degeneracy. Future application of
this technique - possibly coupled with the measure SBF-color gradients attainable with the next generation optical and near--IR large FoV detectors -
will provide significant constraints to the knowledge on the formation and evolution of the stellar component in low-redshift galaxies.
\begin{acknowledgements}
It is a pleasure to aknowledge J. P. Blakeslee and S. Mei for their helpful contribution to the topic of SBF and SBF gradients measurements.
\end{acknowledgements}
\bibliographystyle{aa}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,426 |
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{"url":"http:\/\/mathhelpforum.com\/advanced-algebra\/188597-irreducible-gl-2-module.html","text":"1. ## irreducible gl(2)-module\n\ni was wondering what the irreducible $gl(2)$-module $V((\\lambda_1, \\lambda_2))$ is?\n\n2. ## Re: irreducible gl(2)-module\n\nOriginally Posted by wik_chick88\ni was wondering what the irreducible $gl(2)$-module $V((\\lambda_1, \\lambda_2))$ is?\nwhen posting a question, you need to explain your notation clearly so we know what you're talking about. we are not inside your head!!\nanyway, i guess you're talking about modules over Lie algebras? you didn't say anything as if we were your classmates!!\n\"irreducible\" means simple, i.e. your module has no non-trivial submodule.\n\n3. ## Re: irreducible gl(2)-module\n\nyes modules over Lie Algebras\n$gl(2)$ has basis $\\{a^1_1, a^1_2, a^2_1, a^2_2\\}$\n\ni have to find constraints $\\lambda_1$ and $\\lambda_2$ such that the irreducible $gl(2)$-module $V((\\lambda_1, \\lambda_2))$ has dimension $n$...any ideas?","date":"2017-09-26 20:44:36","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 11, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9293577075004578, \"perplexity\": 1252.0251843486685}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-39\/segments\/1505818696681.94\/warc\/CC-MAIN-20170926193955-20170926213955-00237.warc.gz\"}"} | null | null |
{"url":"https:\/\/cs.stackexchange.com\/tags\/backtracking\/hot?filter=all","text":"# Tag Info\n\n7\n\nHere's the relevant paragraph from the MiniSAT paper: The decision phase will continue until either all variables have been assigned, in which case we have a model, or a conflict has occurred. On conflicts, the learning procedure will be invoked and a conflict clause producted. The trail will be used to undo decision, one level at a time, until ...\n\n6\n\nOverview of the problem If you takes teenagers as vertices of a graph, and have an edge whenever the two teenagers are compatible. This gives you an undirected graph, and what you need is a Hamiltonian path in this graph (a path that contains every node exactly once). Maybe searching the web on this abstract version of the problem will yield more ...\n\n6\n\nBacktracking is a general algorithm \"that incrementally builds candidates to the solutions, and abandons each partial candidate (\"backtracks\") as soon as it determines that the candidate cannot possibly be completed to a valid solution.\" (Wikipedia). So, basically, what you do is build incrementally all permutations. As soon as as you build a single ...\n\n6\n\n(Throughout this answer I use $\\phi = \\frac{1+\\sqrt{5}}{2}$, which is the Golden Ratio.) Solution: If $s\\leq n$, the attackers can win in one day. If $s+dpw<\\phi^2n$ and $s<2n$, the attackers can win in $2+\\max(k,0)$ days, where $$k=\\left\\lceil\\frac{\\log_\\phi{\\left(\\frac{n+(dpw+s-2n)\\phi^{-1}}{n-(dpw+s-2n)\\phi}\\right)}}{4}\\right\\rceil.$$ If $dpw<n$...\n\n6\n\nYou described the simplest case of the neural network, where the center neuron has only one output $a$, which is connected to the final loss function. In general, there can be several outputs and the total error signal coming to this node equals the sum over all output connections. Plus the error messages across these connections are different. And the ...\n\n5\n\nYes, these two heuristics does sound like inconsistent. Most Constrained Variable (MCV) (also called MRV for Minimum Remaining Values) tries to reduce the size of the next branch to search while Least Constraining Values tries to enlarge the size of the next branch to branch. However, if you take a close a look, they both serve the same goal, which is, given ...\n\n5\n\nThe idea of the backtracking algorithm is simple, though somewhat cumbersome to express. Perhaps it's easiest to explain it working through the example in the question. We start by putting $T_1$ on chair 1. We then put $T_2$ on chair 2. Then we put $T_3$ on chair 3, and we discover a conflict. So we backtrack, replacing $T_3$ with the next available student. ...\n\n5\n\nThis answer begins with a first section explaining the problem in more general terms. The direct answer to the question for the example given by the OP is then given in a second section that illustrate the discussion in the first. You may well want to skip the first section and go direcly to the second one, depending on whether you like to start with basic ...\n\n5\n\nOne of the best solution is likely based on a linear programming relaxation or direct integer programming. For the latter, the branching and backtracking will be implicit, and you won't have to manage it yourself. I have seen it solved in two ways using this technique. We can slightly improve your bounding algorithm as well. The textbook method Using ...\n\n4\n\nIntroduce a new variable $Q$, whose domain is $\\{0000,0001,0010,\\dots,1111\\}$. It represents the value of $C1,C2,C3,P$. For instance, if $Q=0001$, that means that $C1=0$, $C2=0$, $C3=1$, $P=0$. Then, you add a constraint that the first bit of $Q$ is equal to $C1$ (that's a binary constraint), a constraint that the second bit of $Q$ is equal to $C2$ (...\n\n4\n\nYour optimal alignment seems to be an optimal local alignment, the best substring match. Needleman-Wunsch is for global alignment. With the simple program by Eddy that you can find on the internet I have determined a global score of 0. This is better than the gobal score you get: -5 (for 10 gaps and 5 matches). Sequence X: GCATGCU Sequence Y: GATTACA ...\n\n3\n\nThis is a classic Dynamic Programming problem. Basically, dynamic programming is a way of turning a recursive algorithm into an iterative one with better runtime, by saving previous results that we might need again. In this case, we can write the problem as two recursive functions: maxSumSubtractFirst(startIndex): if startIndex is past the end of the ...\n\n3\n\nThe idea here is to implement the following recursive definition of the set $A_n$ of all binary strings of length $n$: $$A_0 = \\{\\epsilon\\}, \\qquad A_n = \\{x0 : x \\in A_{n-1}\\} \\cup \\{x1 : x \\in A_{n-1}\\}.$$ Here $\\epsilon$ is the empty string. You can also start at $A_1 = \\{0,1\\}$, but your program actually has $0$ as a base case. Starting with this ...\n\n3\n\nHere's an idea for generating instances with a non-unique solution that will be difficult to solve by backtracking but actually are quite easy to solve: Let $M$ be $h$ tall and $2w$ wide. Take the integers ${1, 2, ... w}$ and fill $M$ with them randomly. For $i = 1$ to $w$, replace column $w + i$ to be the column with only the value $i$. We know that $M$ ...\n\n3\n\nConsider that there might be something wrong with your experimental setup. The theoretical running time of an algorithm is based on an ideal model of a computer, but in practice there are lots of non-ideal behaviours. The running time of an experiment can vary based on lots of factors, and will be different from run-to-run. You should repeat the experiment ...\n\n3\n\nThe problem is strongly $NP$-complete by reduction from 3-Partition. Given a set of $3n$ integers with total sum $3M$, we want to determine whether they can be partitioned into $n$ triples, each having sum $M$. Note that we can assume that no four integers have sum $\\leq M$. Suppose a day is $3M+n-1$ units of time long. We want to visit $n-1$ museums $m_1,\\... 2 The obvious answer is: take a snapshot (checkpoint) of your state before applying the arc consistency inferences; recursively explore that option; and then if it is a failure, restore the state back to your snapshot. Whether this is efficient depends upon the size of the state and the amount of work done during the recursive call. For this particular ... 2 for example 1 and 2 relative to 3 are placed correctly, but 1 relative to 2 is placed incorrectly? You have already tested that 1 and 2 are placed correctly, otherwise you wouldn't call backtrack(3). Recall that sol[i] = j means that the queen in column$i$is put at row$j$. By calling backtrack(k+1) you have already verified that every queen in$1 \\dots ...\n\n2\n\nIf it were me, I would encode this as an instance of ILP (integer linear programming) and let an off-the-shelf ILP solver deal with the backtracking and pruning. Introduce $n$ variables $x_1,\\dots,x_n$, where $x_i=1$ means that you include the $i$th circle in the subset and $x_i=0$ means you don't include it. Add the following constraints: $0 \\le x_i \\le ... 2 Your analysis would be reasonable for rooks, but not for queens. For example, in the second row there are not n-1 possible positions, but n-2 in two cases and n-3 in most cases. Now big-O provides an upper bound, but it is an upper bound that vastly overestimates the effort needed. 2 The intervening assignments between the current assignment and the backjump point might have been arrived at via considerable backtracking and backjumping themselves and it would be wasteful to repeat all that work. But in the context of a modern solver that work may not need to be repeated, because: Any conflicts that occurred during the intervening ... 2 I will try to give a solution. Tell me if I am mistaking anywhere. First observation : When we have equal number of chairs and persons the solution is trivial.Ask all the people from 1st gate to fill chairs from start. then next gate starts where 1st gate stopped. I leave it to you to check that this is the optimal solution. Second observation : We can use ... 2 Yes, it is common for a SAT solver to combine several techniques, e.g., random restarts with smart backtracking or other tricks. More generally, nothing stops you from throwing everything and anything at a problem you want to solve. (The reason a book might talk very specifically about say \"probabilistic algorithms\" instead of \"here's how you solve problem X ... 2 The problem is NP-hard, by a straightforward reduction from the partition problem. Therefore, you should not expect any efficient algorithm. However, there is a pseudo-polynomial-time algorithm using dynamic programming (see pseudo-polynomial-time algorithm for the partition problem for inspiration). 2 Why did it fail? Look at the code cache = new int[size+1][volume+1];. Suppose size is 1 and volume is$10^9$. One int uses 4 bytes. So this cache will use$4 \\times 2 \\times 10^9$bytes, which is about 8G, which is way much bigger than the limit, 32768K. So the online judge will show you out-of-memory error. Could a DP solution without backtracking be ... 2 Integer linear programming can potentially be more efficient. 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\section{Introduction}
This note concerns the conjecture of M.~Auslander that a direct summand of a covariant $\mathrm{Ext}$-functor is again of that form. More precisely, suppose $\mathscr{A}$ is an abelian category with enough projectives, $A$ is an object of $\mathscr{A}$, and $F$ is a direct summand of the functor $\mathrm{Ext}^{1}(A,-)$. Then the question is whether $F$ is of the form $\mathrm{Ext}^{1}(B,-)$ for some object $B$ of $\mathscr{A}$. The motivation for this problem comes from Auslander's foundational work~\cite{Aus66} on coherent functors from abelian categories to the category of abelian groups. It is an immediate consequence of
Yoneda's lemma and the left-exactness of the $\mathrm{Hom}$ functor that each coherent functor gives rise (non-uniquely) to an exact sequence $X \to Y \to Z \to 0$ in the original abelian category. Specializing to such exact sequences which are short exact, one is naturally led to consider the corresponding subcategory $\mathscr{A}_{0}$ of coherent functors. Thus the objects of this subcategory are coherent functors whose projective resolutions are images of short exact sequences in $\mathscr{A}$ under the Yoneda embedding. An immediate example of such a functor is $\mathrm{Ext}^{1}(A,-)$.
As Auslander showed~\cite[Prop. 4.3]{Aus66}, if the answer to the above question is in the affirmative for any $A \in \mathscr{A}$ and any $F$, then the functors of the form
$\mathrm{Ext}^{1}(B,-)$ are the only injectives in $\mathscr{A}_{0}$. He also
showed~\cite[Prop.~4.7]{Aus66} that the answer is positive assuming that $A$ is of finite projective dimension. P.~Freyd \cite{Fr66} showed the same in the case $\mathscr{A}$ has countable sums. In \cite{Aus69} Auslander undertook a more systematic study of this problem and gave a unifying proof of the above two results. In addition, he provided a detailed analysis in the case when $\mathscr{A}$ was a category of modules over a ring. Among other things, he showed that, in general, a direct summand of the functor
$\mathrm{Ext}^{1}(A,-)$, where $A$ is a finitely generated module over a ring $R$, need not be of the form $\mathrm{Ext}^{1}(B,-)$ for some finitely generated $R$-module $B$, even when $R$ is noetherian.
In this note, we return to general abelian categories and show that the answer to the above question is still positive if $A$ is noetherian and satisfies the descending chain condition on images of nested endomorphisms.
In fact, this result is proved in greater generality -- it holds for any additive functor of the form $G(A,-)$ (resp., $G(-,A)$), provided natural endo-transformations of such a functor are induced from endomorphisms of its fixed argument, see Theorem~\ref{main} for details.
A preliminary result, establishing the Fitting lemma for objects of finite length in an abelian category, is recalled in the next section. In the section following the proof of Theorem~\ref{main}, we apply this theorem to the functors covariant
$\mathrm{Ext}$, covariant
$\mathrm{Hom}$ modulo projectives, and $\mathrm{Tor}$.
\section{Preliminaries}
This section contains preliminary results, all of which are well-known. For the convenience of the reader, their proofs are included in the case of a general abelian category, since the author could not find them in the literature.
Let $\mathscr{A}$ be an abelian category and $A$ an object of $\mathscr{A}$. Recall that the intersection of two subobjects of $A$ always exists and can be defined as the pullback of the corresponding monomorphisms \cite[Prop. 4.2.3]{B1}. Furthermore, the union of two subobjects of $A$ always exists and can be defined as the pushout over their intersection \cite[Prop. 1.7.4]{B2}. In particular, for any endomorphism
$f : A \to A$, the intersection $\mathrm{Ker}\, f^{n} \cap \mathrm{Im}\, f^{n}$ and the union
$\mathrm{Ker}\, f^{n} + \mathrm{Im}\, f^{n}$ are defined as subobjects of $A$ for any natural~$n$.
The commutative diagram
\[
\xymatrix
{
A \ar@{=}[d] \ar[r]^{f} & A \ar[d]^{f}\\
A \ar[r]^{f^{2}} & A
}
\]
shows that $\mathrm{Ker}\, f$ is a subobject of $\mathrm{Ker}\, f^{2}$ and, likewise, $\mathrm{Ker}\, f^{n}$ is a subobject of $\mathrm{Ker}\, f^{n+1}$. It also shows that $f$ induces an epimorphism
$\mathrm{Im}\, f \to \mathrm{Im}\, f^{2}$ and, likewise, an epimorphism $\mathrm{Im}\, f^{n} \to \mathrm{Im}\, f^{n+1}$.
The commutative diagram
\[
\xymatrix
{
A \ar[d]^{f} \ar[r]^{f^{2}} & A \ar@{=}[d]\\
A \ar[r]^{f} & A
}
\]
shows that $\mathrm{Im}\, f^{2}$ is a subobject of $\mathrm{Im}\, f$ and, likewise, $\mathrm{Im}\, f^{n+1}$ is a subobject of $\mathrm{Im}\, f^{n}$.
The object $A$ is said to be of finite length if it has both the descending chain condition (DCC) and the ascending chain condition (ACC). This is equivalent to saying that there exists a finite chain of subobjects
\[
0 = A_{0} \subset A_{1} \subset \ldots \subset A_{s} = A
\]
whose successive quotients are simple objects. The next lemma is elementary and well-known, at least for modules. For completeness, we give a categorical proof.
\begin{lemma}\label{pushout}
Let
\[
\xymatrix
{
0 \ar[r] & A \ar[r]^{a} \ar[d]^{b} & B \ar[r]^{r} \ar[d]^{d} & C \ar[r] \ar@{=}[d] & 0 \\
0 \ar[r] & D \ar[r]^{c} & E \ar[r]^{t} & C \ar[r] & 0
}
\]
be a commutative diagram in $\mathscr{A}$ with exact rows. Then $(c,d)$ is a pushout of~$(a,b)$.
\end{lemma}
\begin{proof}
Let $(x,y)$ be a pushout of $(a,b)$. We then have a commutative diagram
\[
\xymatrix
{
A \ar[dd]^{b} \ar@{>->}[drr]_{a} & & & & \\
& & B \ar[ld]_{y} \ar@{->>}[drr]^{r} \ar [dd]_<<<<<<{d} & & \\
D \ar@{>->}[r]^{x} \ar@{=}[dd] & Z \ar@{..>}[dr]_{u} \ar@{->>} '[r] [rrr]^{s} & & &C \\
& & E \ar@{->>}[urr]^{t} & & \\
D \ar@{>->}[urr]^{c} & & & &
}
\]
of solid arrows, where the horizontal and the two slanted sequences are short exact. Since $da = cb$, the universal property of pushouts yields a map $u : Z \to E$ with $uy = d$ and $ux = c$. We claim that $s = tu$. Since $ra = 0 = tcb$, there is a unique morphism $q : Z \to C$ such that $qy = r$ and $qx = tc$. But both~$s$ and~$tu$ have this property, and therefore $s = tu$. Clearly, $u$ is an isomorphism. It now follows that $(c,d)$ is also a pushout.
\end{proof}
Now we recall the Fitting lemma in an abelian category.
\begin{lemma}\label{Fitting}
In the above notation, let $f : A \to A$ be an endomorphism.
\begin{enumerate}
\item If $A$ has the ACC, then $0 \simeq \mathrm{Ker}\, f^{n} \cap \mathrm{Im}\, f^{n}$ for all $n$ large enough. If $f$ is an epimorphism, then it is an isomorphism.
\smallskip
\item If $A$ has the DCC, then the inclusion of $\mathrm{Ker}\, f^{n} + \mathrm{Im}\, f^{n}$ in $A$ is an isomorphism for all $n$ large enough. If $f$ is a monomorphism, then it is an isomorphism.
\smallskip
\item (The Fitting Lemma) If $A$ is of finite length, then $A \simeq \mathrm{Ker}\, f^{n} \oplus \mathrm{Im}\, f^{n}$ for all $n$ large enough. The morphism $f$ is nilpotent on $\mathrm{Ker}\, f^{n}$ for all $n$ and is an isomorphism on $\mathrm{Im}\, f^{n}$ for all $n$ large enough. Also, $f$ is an isomorphism whenever it is a monomorphism or an epimorphism.
\end{enumerate}
\end{lemma}
\begin{proof}
(1) Since $A$ has ACC, the commutative diagram with exact rows
\[
\xymatrix
{
0 \ar[r] & \mathrm{Ker}\, f^{n} \ar[r] \ar@{>->}[dd] & A \ar[rr]^{f^{n}} \ar@{=}[dd] \ar[dr] & & A \ar[r] \ar[dd]^{f} & \mathrm{Coker}\, f^{n} \ar[r] \ar[dd] & 0\\
&&& \mathrm{Im}\, f^{n} \ar[ur] \ar@{->>} [dd] && \\
0 \ar[r] & \mathrm{Ker}\, f^{n+1} \ar[r] & A \ar '[r] [rr]^{f^{n+1}} \ar[dr] & & A \ar[r] & \mathrm{Coker}\, f^{n+1} \ar[r] & 0\\
&&& \mathrm{Im}\, f^{n+1} \ar[ur] &&
}
\]
shows that the leftmost vertical morphism is an isomorphism for all $n \geq p$ for
some~$p$. By the snake lemma\footnote{For a proof of the snake lemma in a general abelian category, see~\cite{Fay}.}, the vertical morphism in the middle is also an isomorphism. The right-hand side of the diagram shows that this map is induced by $f$. In other words, the restriction of $f$ to $\mathrm{Im}\, f^{n}$ is an isomorphism for all $n \geq p$. This implies that $f$ is an isomorphism whenever it is an epimorphism. Since the images of powers of $f$ form a descending chain, the restriction of any power of $f$ to $\mathrm{Im}\, f^{n}$ is also an isomorphism for all $n \geq p$. In particular, this is true for $f^{n}$. On the other hand, the restriction of $f^{n}$ to $\mathrm{Ker}\, f^{n}$ is zero. It now follows immediately that $\mathrm{Ker}\, f^{n} \cap \mathrm{Im}\, f^{n} \simeq 0$.
\medskip
(2) Since $A$ has the DCC, the inclusion $\mathrm{Im}\, f^{n+1} \to \mathrm{Im}\, f^{n}$
is an isomorphism for all $n \geq p$ for some~$p$. Therefore the inclusion
$\mathrm{Im}\, f^{2n} \to \mathrm{Im}\, f^{n}$ is also an isomorphism. Thus in the commutative diagram
\[
\xymatrix
{
0 \ar[r] & K \ar[r] \ar[d] & \mathrm{Im}\, f^{n} \ar[r]^{f^{n}} \ar@{>->}[d] & \mathrm{Im}\, f^{2n} \ar[r]
\ar[d]^{\simeq} & 0 \\
0 \ar[r] & \mathrm{Ker}\, f^{n} \ar[r] & A \ar[r]^{f^{n}} & \mathrm{Im}\, f^{n} \ar[r] & 0
}
\]
with exact rows, the rightmost vertical map is an isomorphism. It now follows from Lemma~\ref{pushout} that the inclusion of $\mathrm{Ker}\, f^{n} + \mathrm{Im}\, f^{n} $ in $A$ is an isomorphism. In particular, when $f$ is a monomorphism, it is also an epimorphism, and hence and isomorphism.
\medskip
(3) The union $\mathrm{Ker}\, f^{n} + \mathrm{Im}\, f^{n}$ is the image of the morphism
\[
q: \mathrm{Ker}\, f^{n} \oplus \mathrm{Im}\, f^{n} \to A
\]
induced by the inclusions of the summands in $A$. By (2), $q$ is an epimorphism. The kernel of $q$ is isomorphic (as an object, but not necessarily as a subobject) to $\mathrm{Ker}\, f^{n} \cap \mathrm{Im}\, f^{n}$ \cite[p.~27]{B2}, which is isomorphic to $0$ by~(1). Since $q$ is an epimorphism and a monomorphism, it is an isomorphism. The rest has already been established.
\end{proof}
\section{Direct summands of functors}
Suppose $\mathscr{A}$ is an abelian category and $A$ an object of $\mathscr{A}$. We say that $A$ satisfies the \texttt{descending chain condition on images of nested endomorphisms} (DCC on INE) if any descending chain
\[
A = A_{0} \supset A_{1} \supset A_{2} \supset \ldots
\]
of subobjects, where each $A_{i+1}$ is the image of some endomorphism of $A_{i}$, stabilizes (as a chain of subobjects). Apparently, any artinian object satisfies this condition.
Let $G : \mathscr{A}^{op} \times \mathscr{A} \to \mathtt{Ab}$ an additive (covariant) bifunctor with values in abelian groups. We make a further assumption that, for any object $A$, the map
\[
(A,A) \to \mathrm{Nat}\big{(}G(A,-), G(A,-)\big{)} : f \mapsto G(f,-),
\]
sending a morphism to the corresponding natural transformation, is a surjection.
\begin{theorem}\label{main}
Under the above assumptions, let $A$ be a noetherian object of
$\mathscr{A}$ satisfying the DCC on INE. If $F$ is a direct summand of the functor $G(A,-)$, then there is a subobject $B$ of
$A$ such that $F \simeq G(B,-)$.
\end{theorem}
\begin{proof}
Let
\[
\xymatrix
{
F \ar[r]^<<<<<{\iota} & G(A,-) \ar[r]^>>>>>{\pi} & F
}
\]
be a factorization of the identity map. Then the composition
\[
\xymatrix
{
G(A,-) \ar[r]^<<<<<{\pi} & F \ar[r]^>>>>>{\iota} & G(A,-)
}
\]
is an idempotent endomorphism of $G(A,-)$ and, by the assumption on $G$, $\iota \pi = G(f,-)$ for some endomorphism $f : A \to A$. If $f$ is an epimorphism in $\mathscr{A}$, then by Lemma~\ref{Fitting}, it is an isomorphism. In such a case, since both $\iota \pi$ and $1 = \pi \iota$ are isomorphisms, $F$ and $G(A,-)$ become isomorphic, and we are done. Thus we may assume that $f : A \to A$ is not an epimorphism.
For an epi-mono factorization of $f$ (in $\mathscr{A}$)
\[
\xymatrix
{
A \ar@{->>}[r]^{\alpha} & \mathrm{Im}\, f \ar@{>->}[r]^{\beta} & A
}
\]
through its image, we have $G(f,-) = G(\alpha,-) G(\beta,-)$. Postcomposing
$\iota \pi = G(f,-)$ with $\iota$, we have $\iota = G(f,-) \iota$. Setting $\delta := G(\beta,-) \iota$, we have a commutative diagram
\[
\xymatrix
{
& F \ar[dl]_{\iota} \ar '[d] [dd]_{\delta}\ar[dr]^{\iota} &\\
G(A,-) \ar[rr]^>>>>>>>>>>{G(f,-)} \ar[dr]_{G(\beta, -)}& & G(A,-)\\
& G(\mathrm{Im}\, f, -) \ar[ur]_{G(\alpha,-)}&
}
\]
Since $G(\alpha,-)\delta = \iota$ and $\iota$ is a split monomorphism, the same is true for $\delta$. This shows that $F$ is a direct summand of $G(A_{1},-)$, where $A_{1} :=\mathrm{Im}\, f$ is a proper subobject of $A$ and at the same time an image of $A$ under an endomorphism. Repeating the foregoing argument with $A_{1}$ in place of $A$, etc., we have a descending chain $A \supset A_{1} \supset A_{2} \supset \ldots$ such that each term is the image of an endomorphism of the previous term and $F$ is a direct summand of each $G(A_{i},-)$. Since this chain must stabilize, the last endomorphism $A_{n} \to A_{n}$ must be an epimorphism, hence an isomorphism. But then, as we saw in the beginning of the proof,
$F \simeq G(A_{n},-)$.
\end{proof}
Recall that $\mathscr{A}$ is called a \texttt{length} category if all of its objects have finite length.
\begin{theorem}
Suppose $\mathscr{A}$ is an abelian length category and $G : \mathscr{A}^{op} \times \mathscr{A} \to \mathtt{Ab}$ an additive (covariant) bifunctor with values in abelian groups. Suppose that for any object $A$ any natural transformation
$G(A,-) \to G(A,-)$ is induced by a suitable endomorphism of $A$. If $F$ is a direct summand of $G(A,-)$, then there is a subobject $B$ of $A$ such that
$F \simeq G(B,-)$. \qed
\end{theorem}
\begin{remark}\label{covariant}
The above theorem and corollary remain true, with obvious modifications, for the functor $G(A,-)$ if $G$ is an additive (covariant) functor on $\mathscr{A} \times \mathscr{A}$.
\end{remark}
\section{Direct summands of some homological functors}
In this section, we shall give some immediate applications of Theorem~\ref{main}. We begin with the covariant $\mathrm{Ext}$ functors. The relevant result concerning natural transformations between such functors is due to Hilton-Rees~\cite{HR} and says that such transformations are in one-to-one, arrow-reversing correspondence with projective equivalence classes of homomorphisms between the corresponding contravariant arguments. This means that, by assigning to each object the corresponding covariant $\mathrm{Ext}$ functor, one has a full contravariant embedding of the category modulo projectives in the abelian category of additive functors on the original category with values in abelian groups, where the morphisms between such functors are natural transformations.\footnote{Strictly speaking, for this statement one has to assume that the class of objects of the original category is a set, otherwise the resulting ``category'' need not be a category. The reader should notice, however, that in the proof of the forthcoming Theorem~\ref{HR} we do use categorical concepts. To justify this, we have two options. The first one is to switch from categories to quasicategories,
see~\cite[3.49-3.51]{AHS}. The other option is to notice that, in the proof of the theorem, we do all arguments componentwise. Accordingly, the formal definition of a functor category is not needed. The details are left to the reader.} We shall now give a short and straightforward proof of this result.
\begin{theorem}[Hilton-Rees]\label{HR}
Assume that the abelian category $\mathscr{A}$ has enough projectives and let $A$ and $B$ be objects of $\mathscr{A}$. Then the correspondence
\[
(B,A) \to \big{(}\mathrm{Ext}^{1}(A,-), \mathrm{Ext}^{1}(B,-)\big{)} : f \mapsto \mathrm{Ext}^{1}(f,-)
\]
induces an isomorphism
\[
(\underline{B,A}) \to \mathrm{Next}^{1,1}(A,B)
\]
between the group $(\underline{B,A})$ of morphisms from $B$ to $A$ modulo the morphisms factoring through projectives and the group $\mathrm{Next}^{1,1}(A,B)$ of natural transformations from $\mathrm{Ext}^{1}(A,-)$ to $\mathrm{Ext}^{1}(B,-)$.
\end{theorem}
\begin{proof}
An exact sequence
\[
\xymatrix
{
\theta : & 0 \ar[r] & \Omega A \ar[r] & P \ar[r] & A \ar[r] & 0
}
\]
with $P$ projective gives rise to an exact sequence of functors
\[
\xymatrix
{
0 \ar[r] & (A,-) \ar[r] & (P,-) \ar[r] & (\Omega A, -) \ar[r] & \mathrm{Ext}^{1}(A,-) \ar[r] & 0.
}
\]
Taking functor morphisms into $\mathrm{Ext}^{1}(B,-)$ and applying Yoneda's lemma yields a commutative diagram with an exact top row
\[
\xymatrix
{
0 \ar[r] & \mathrm{Next}^{1,1}(A,B) \ar[r] & \big{(}(\Omega A, -), \mathrm{Ext}^{1}(B,-)\big{)} \ar[d]^{\simeq} \ar[r] & \big{(}(P, -), \mathrm{Ext}^{1}(B,-)\big{)} \ar[d]^{\simeq}\\
& & \mathrm{Ext}^{1}(B, \Omega A) \ar[r] & \mathrm{Ext}^{1}(B, P)
}
\]
In particular, we see that $\mathrm{Next}^{1,1}(A,B)$ is a set. The horizontal morphism on the bottom is part of a long exact sequence and therefore its kernel is isomorphic to $\mathrm{Coker}\, ((B,P) \to (B,A))$, which is $(\underline{B,A})$. Now, $\mathrm{Ext}^{1}(f, -) \in \mathrm{Next}^{1,1}(A,B)$ is mapped by the horizontal homomorphism to the right multiplication by $\theta f$. Under the Yoneda isomorphism, this transformation is sent to $\theta f$, which is also the image of $f \in (B,A)$ in $\mathrm{Ext}^{1}(B, \Omega A)$. Thus, the inverse of the constructed isomorphism is precisely
$[f] \mapsto \mathrm{Ext}^{1}(f,-)$.
\end{proof}
The above proof also works for natural transformations between contravariant $\mathrm{Ext}$-functors. In that case however, one needs to replace $\mathrm{Hom}$ modulo projectives by
$\mathrm{Hom}$ modulo injectives, denoted by $(\overline{A,B})$. We thus have the Hilton-Rees theorem for the contravariant Ext functor.
\begin{theorem}\label{HRprime}
Assume that the abelian category $\mathscr{A}$ has enough injectives and let $A$ and $B$ be objects of $\mathscr{A}$. Then the correspondence
\[
(A,B) \to \big{(}\mathrm{Ext}^{1}(-, A), \mathrm{Ext}^{1}(-, B)\big{)} : f \mapsto \mathrm{Ext}^{1}(-, f)
\]
induces an isomorphism
\[
(\overline{A,B}) \to \mathrm{Next}(A,B)^{1,1}
\]
between the group $(\overline{A, B})$ of morphisms from $A$ to $B$ modulo the morphisms factoring through injectives and the group $\mathrm{Next}(A,B)^{1,1}$ of natural transformations from $\mathrm{Ext}^{1}(-, A)$ to $\mathrm{Ext}^{1}(-, B)$. \qed
\end{theorem}
Combining Theorem~\ref{HR} with Theorem~\ref{main}, we have
\begin{proposition}
Let $A$ be a noetherian object satisfying the DCC on INE in an abelian category
$\mathscr{A}$ with enough projectives. If $F$ is a direct summand of the functor $\mathrm{Ext}^{1}(A,-)$, then there is a subobject $B$ of $A$ such that $F \simeq \mathrm{Ext}^{1}(B,-)$. In particular, the result is true when $A$ is of finite length. \qed
\end{proposition}
\begin{corollary}
Let $\Lambda$ be an artin algebra, $\Lambda$-$\mathrm{mod}$ the category of finitely generated (left) $\Lambda$-modules, and
$F : \Lambda$-$\mathrm{mod} \longrightarrow \mathtt{Ab}$ an additive functor. If $F$ is a direct summand of $\mathrm{Ext}^{1}(A, -)$, where $A \in \Lambda$-$\mathrm{mod}$, then there exists a submodule $B$ of~$A$
such that $F \simeq \mathrm{Ext}^{1}(B, -)$. \qed
\end{corollary}
\begin{remark}
As we mentioned in the introduction, the last corollary implies that the covariant Ext functors are the only injectives in the category of finitely presented functors
$\Lambda$-$\mathrm{mod} \longrightarrow \mathtt{Ab}$ determined by short exact sequences. On the other hand, in general, these functors need not be injective in the ambient category of all finitely presented functors. It is not difficult to prove that if $\Lambda$ is (left) hereditary, then the functors $\mathrm{Ext}^{1}(B, -)$ are injective in the category of all finitely presented functors. However, even in that case, there must be injectives not of the form $\mathrm{Ext}^{1}(B, -)$. To see that,
recall~\cite{G} that the category of finitely presented functors on an abelian category with enough projectives has enough injectives. Assuming that all injectives in f.p.$(\Lambda$-$\mathrm{mod} , \mathtt{Ab})$ are the Ext functors,
for any nonzero module $\Lambda$-module $A$ we have a monomorphism
$(A,-) \longrightarrow \mathrm{Ext}^{1}(B, -)$ into a suitable injective. Evaluating it on the injective envelope of $A$, we then have a zero map with a nonzero domain, a contradiction.\footnote{The same argument shows that the category of finitely presented functors determined by short exact sequences does not have enough injectives. In fact this is always true: just use the fact that any injective is a direct summand of a suitable Ext functor~\cite{Aus66} and run the above argument.}
\end{remark}
\medskip
In the case when the endomorphism ring of $A$ is artinian as an abelian group, the assumption that $\mathscr{A}$ have enough projectives can be dropped. To this end, recall the following result of Oort~\cite[p. 561]{O63}:
\begin{theorem}
Let $\mathscr{A}$ be an abelian category all of whose objects are artinian. If
\[
\lambda : \mathrm{Ext}^{1} (B,-) \to \mathrm{Ext}^{1} (A,-)
\]
is a natural map and $\mathrm{Hom}(A,B)$ is an artinian group, then there exists a morphism
$\alpha \in \mathrm{Hom}(A,B)$ which induces $\lambda$. \qed
\end{theorem}
Combining this result with Theorem~\ref{main}, we have
\begin{corollary}
Suppose $\mathscr{A}$ is an abelian length category and and $A$ is an object whose endomorphism ring is artinian as an abelian group. If $F$ is a direct summand of the functor $\mathrm{Ext}^{1}(A,-)$, then there is a subobject $B$ of $A$ such that $F \simeq \mathrm{Ext}^{1}(B,-)$. \qed
\end{corollary}
Combining Theorem~\ref{HRprime} with Theorem~\ref{main}, we have
\begin{proposition}
Let $A$ be an object of finite length in an abelian category $\mathscr{A}$ with enough injectives. If $F$ is a direct summand of the functor $\mathrm{Ext}^{1}(-,A)$, then there is a subobject $B$ of $A$ such that $F \simeq \mathrm{Ext}^{1}(-,B)$. \qed
\end{proposition}
\bigskip
We now turn our attention to the covariant $\mathrm{Hom}$ modulo projectives functor. By Yoneda's lemma, natural transformations from $(\underline{A^{\prime},-})$ to $(\underline{A,-})$ are in a functorial bijection with $(\underline{A,A^{\prime}})$. Thus, Theorem~\ref{main} yields
\begin{proposition}
Let $A$ be an object of finite length in an abelian category $\mathscr{A}$ with enough projectives. If $F$ is a direct summand of the functor $(\underline{A,-})$, then there is a subobject $B$ of $A$ such that $F \simeq (\underline{B,-})$. \qed
\end{proposition}
\bigskip
Next, we look at direct summands of the functor $\mathrm{Tor}_{1}(A,-)$. For that, we fix a ring $\Lambda$ and view $\mathrm{Tor}_{1}^{\Lambda}(-,-)$ as a bifunctor f.p.\,($\mathrm{mod}$-$\Lambda$) $\times$ $\Lambda$-$\mathrm{mod}$ $\to \mathtt{Ab}$, whose first argument is taken from the category of finitely presented right $\Lambda$-modules. It is well-known (and is not difficult to prove) that, for any finitely presented right $\Lambda$-module $A$, we have a functor isomorphism $\mathrm{Tor}_{1}(A,-) \simeq (\underline{\mathrm{Tr}\, A, -})$, where $\mathrm{Tr}\, A$ denotes the transpose of $A$. If $A^{\prime}$ is another finitely presented right $\Lambda$-module, then, by Yoneda's lemma applied to the category of modules modulo projectives,
\[
\mathrm{Nat}\big{(}\mathrm{Tor}_{1}(A,-), \mathrm{Tor}_{1}(A^{\prime},-)\big{)}
\simeq \big{(}(\underline{\mathrm{Tr}\, A, -}), (\underline{\mathrm{Tr}\, A^{\prime}, -})\big{)}
\simeq (\underline{\mathrm{Tr}\, A^{\prime}, \mathrm{Tr}\, A}),
\]
But the transpose, viewed as a functor on the category of finitely presented modules modulo projectives, is a duality, and therefore the latter is isomorphic to
$(\underline{A, A^{\prime}})$. We now have, in view of Remark~\ref{covariant}, the following
\begin{proposition}
Let $A$ be a finitely presented right $\Lambda$-module of finite length. If~$F$ is a direct summand of the functor $\mathrm{Tor}_{1}(A,-)$, then there is a finitely presented submodule
$B$ of $A$ (automatically of finite length) such that $F \simeq \mathrm{Tor}_{1}(B,-)$.
\end{proposition}
\begin{proof}
The proof of Theorem~\ref{main} produces a module $B = A_{n}$, where
\[
A = A_{0} \supset A_{1} \supset \ldots \supset A_{n} = B
\]
is a sequence of submodules of $A$ such that each $A_{i+1}$ is a homomorphic image of $A_{i}$. We cannot immediately use this theorem, because the category of finitely presented modules does not, in general, have kernels and is not therefore abelian. But the proof would still work if we show that each $A_{i}$ is finitely presented. Since for each $i$ the kernel of the epimorphism $A_{i} \to A_{i+1}$, being a submodule of a module of finite length, is finitely generated, $A_{i+1}$ is finitely presented whenever $A_{i}$ is. But $A = A_{0}$ is finitely presented, and an induction argument finishes the proof.
\end{proof}
\begin{remark}
The above result is also true, with obvious modifications, for left finitely presented modules.
\end{remark}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,224 |
Q: Find and update in nested json object without changing the same key-pair value in different child path This is an update to my previous question Find and update in nested json object
Sample Data
TestObj = {
"Categories": [{
"Products": [{
"id": "a01",
"name": "Pine",
"description": "Short description of pine."
},
{
"id": "a02",
"name": "Pine",
"description": "Short description of pine."
},
{
"id": "a03",
"name": "Poplar",
"description": "Short description of poplar."
}],
"id": "A",
"title": "Cheap",
"description": "Short description of category A."
},
{
"Product": [{
"id": "b01",
"name": "Maple",
"description": "Short description of maple."
},
{
"id": "b02",
"name": "Oak",
"description": "Short description of oak."
},
{
"id": "b03",
"name": "Bamboo",
"description": "Short description of bamboo."
}],
"id": "B",
"title": "Moderate",
"description": "Short description of category B."
}]
};
My Function
function getObjects(obj, key, val, newVal) {
var newValue = newVal;
var objects = [];
for (var i in obj) {
if (!obj.hasOwnProperty(i)) continue;
if (typeof obj[i] == 'object') {
objects = objects.concat(getObjects(obj[i], key, val, newValue));
} else if (i == key && obj[key] == val) {
obj[key] = newValue;
}
}
return obj;
}
called as
getObjects(TestObj, 'id', 'A', 'B');
It works fine if I'm going to update id; since id don't have duplicates. But if I'm updating name all data matching key value pair is updated. But how to constrain it into a particular key-pair value.
What shall i provide to the function to constrain the update scope and how to implement it. Please help me.
Note: The json that I will b manipulating will be dynamically generated so I can't have any hard coded value in the function
A: I think you can somehow use a path to locate the value and then do the update. I got the idea from this post. (answered by @shesek)
var getPath = function (obj, path, newValue) {
var parts = path.split('.');
while (parts.length > 1 && (obj = obj[parts.shift()]));
obj[parts.shift()] = newValue;
return obj;
}
console.log(getPath(TestObj, 'Categories.0.Products.1.id', 'AAA'))
console.log(TestObj)
So you can pass in the path to the object, for example, if you want to update the id of the following object to "AAA", you can pass in Categories.0.Products.1.id
{
"id": "a02",
"name": "Pine",
"description": "Short description of pine."
}
then, the object will become
{
"id": "AAA",
"name": "Pine",
"description": "Short description of pine."
}
Hope it can shed some light on!
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,354 |
Q: tolower function of the corpus package throws an error I trying to do some text mining using twitter data. I do the following:
#connect to twitter API
setup_twitter_oauth(consumer_key, consumer_secret, access_token, access_secret)
#set radius and amount of requests
N=200 # tweets to request from each query
S=200 # radius in miles
lats=c(38.9,40.7)
lons=c(-77,-74)
roger=do.call(rbind,lapply(1:length(lats), function(i) searchTwitter('Roger+Federer',
lang="en",n=N,resultType="recent",
geocode=paste(lats[i],lons[i],paste0(S,"mi"),sep=","))))
This all works fine but when I want to use the tolower function of the corpus package like this:
data=as.data.frame(cbind(tweet=rogertext))
corpus=Corpus(VectorSource(data$tweet))
corpus=tm_map(corpus,tolower)
It trows this error:
> corpus=tm_map(corpus,tolower)
Error in FUN(X[[i]], ...) :
invalid input 'RT @Federerism: Roger Federer reaches 5 million followers on twitter Love You Roger í ½í¸˜ í ½í¸ í ½í¸˜ í ½í¸ #Roger #Federer # Federerism #Maestro https:/…' in 'utf8towcs'
Any thought on what goes wrong?
A: base::tolower chokes on special characters. This is often a problem when mining tweets. You could try catching errors or just use stringi's tolower pendant:
# tw <- searchTwitter('Roger Federer reaches 5 million followers on twitter Love You Roger', n=1)
download.file("https://www.dropbox.com/s/33ilhcu2v82nwuq/twitter_tolower.rda?dl=1", tf <- tempfile(fileext = ".rda"), mode="wb")
load(tf)
tw[[1]]$getText()
# [1] "RT @Federerism: Roger Federer reaches 5 million followers on twitter Love You Roger \xed��\xed�\u0098 \xed��\xed�\u008d \xed��\xed�\u0098 \xed��\xed�\u008d #Roger #Federer # Federerism #Maestro https:/…"
## Does not work:
tolower(tw[[1]]$getText())
# Error in tolower(tw[[1]]$getText()) :
# invalid input 'RT @Federerism: Roger Federer reaches 5 million followers on twitter Love You Roger í ½í¸˜ í ½í¸ í ½í¸˜ í ½í¸ #Roger #Federer # Federerism #Maestro https:/…' in 'utf8towcs'
## Works:
stringi::stri_trans_tolower(tw[[1]]$getText())
# [1] "rt @federerism: roger federer reaches 5 million followers on twitter love you roger \xed��\xed�\u0098 \xed��\xed�\u008d \xed��\xed�\u0098 \xed��\xed�\u008d #roger #federer # federerism #maestro https:/…"
## Works, too:
library(tm)
corp <- Corpus(VectorSource(tw[[1]]$getText()))
corp <- tm_map(corp, content_transformer(stringi::stri_trans_tolower))
content(corp[[1]])
# [1] "rt @federerism: roger federer reaches 5 million followers on twitter love you roger \xed��\xed�\u0098 \xed��\xed�\u008d \xed��\xed�\u0098 \xed��\xed�\u008d #roger #federer # federerism #maestro https:/…"
A: Try the following:
corpus <- tm_map(corpus, content_transformer(tolower))
There has been a change of syntax in the tm package a few years ago. Hope this solves the problem.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,232 |
Christine Joyce Dradidi Ondoa is a physician and medical administrator who is regarded as one of Uganda's finest leaders especially in ensuring that the quality of health service delivery in Uganda is improved, and discipline and ethical code of conduct among health workers is observed. She is a Ugandan paediatrician and Christian Leader. She currently serves as the Director General of the Uganda AIDS Commission. She was appointed to that position by the President of Uganda in February 2014. Prior to that, she served as a Senior Presidential Advisor to President Yoweri Kaguta Museveni on Public Health. She was a member of the board of directors of the Global Alliance for Vaccines and Immunization (GAVI). She was Minister of Health in the Ugandan Cabinet from 2011 to 2013. She was appointed to that position on 27 May 2011, but was replaced by Ruhakana Rugunda on 23 May 2013. On account of being a cabinet minister she was a member of the Ugandan Parliament, in an ex officio capacity. Prior to that, she was the Executive Director of Mbarara Regional Referral Hospital, one of the fourteen regional referral hospitals in Uganda.
Background
She was born in Moyo District on 21 October 1968.
Education
Christine Ondoa attended Mount Saint Mary's College Namagunga for her high school studies. She holds the degree of Bachelor of Medicine and Bachelor of Surgery (MBChB), obtained in 1994, from Makerere University Medical School (MUMS), the oldest medical school in East Africa. She also holds the degree of Master of Medicine in Pediatrics (MMed), obtained in 2000, also from MUMS. In March 2011, she graduated from the Uganda Management Institute with the postgraduate Diploma in Public Administration & Management (Dip.PA&M). In 2012 she graduated from the same institution with the degree of Master of Management Studies (MMS) She has now enrolled in the Institute of National Transformation for her PhD. She did her internship at St. Francis Hospital Nsambya from 1994 until 1995. She stayed on at Nsambya from 1995 until 1997, when she went back to Makerere University Medical School for her postgraduate training in pediatrics. Between 2000 and 2009, she worked in Arua Regional Referral Hospital as a consultant pediatrician. Between 2009 and 2010, she worked at Jinja Regional Referral Hospital as Senior Pediatrician and later promoted to Hospital Director and senior consultant pediatrician. She also served as the chairperson of the governing council for Jinja School of Nursing and Midwifery. From January 2011 until May 2011, she worked as the Executive Director at Mbarara Regional Referral Hospital, the teaching hospital of Mbarara University of Science and Technology (MUST). Then from May 2011 to May 2013, she was Uganda's Minister of Health.
Personal details
Dr. Ondoa is the mother of one son named Reuben Azi, born in 1996. She is a Born-again Christian, and was ordained as Pastor, on 23 April 2011, by Bishop Julius Peter Oyet in LifeLine Ministries at Mbuya, Nakawa Division, in Kampala, the capital of Uganda and the largest city in that country. On 28 January 2012, Dr. Christine Ondoa was married to Mr. Thomas Udong P'ongona at Church of the Resurrection, Bugolobi, followed by a reception ceremony held at the Speke Resort and Conference Center at Munyonyo.
See also
Parliament of Uganda
Cabinet of Uganda
Ministry of Health (Uganda)
Uganda AIDS Commission
References
External links
Website of the Parliament of Uganda
Full List of Ugandan Cabinet Mininisters, 27 May 2011
Website of LifeLine Ministries
European Times
1968 births
Living people
Makerere University alumni
Uganda Management Institute alumni
Ugandan pediatricians
Ugandan Christians
People from Adjumani District
Madi people
People from West Nile sub-region
Government ministers of Uganda
21st-century Ugandan women politicians
21st-century Ugandan politicians
Ugandan healthcare managers
Women government ministers of Uganda
People educated at Mount Saint Mary's College Namagunga | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,333 |
{"url":"https:\/\/www.physicsforums.com\/threads\/volume-integration-using-washermethod.259708\/","text":"# Homework Help: Volume integration using washermethod\n\n1. Sep 27, 2008\n\n### peercortsa\n\nvolume integration using \"washer method\"\n\n1. The problem statement, all variables and given\/known data\nThe region R bounded by y = x$$^{2}$$, y = 0, x = 1 and x = 4 is rotated about x = \u22121\n\n2. Relevant equations\ni know that these equations take on the form of $$\\pi\\int_a^b \\\\((outer radius)^{2} - (inner radius)^{2})\\\\,dx$$\n\n3. The attempt at a solution\nso i set the problem up like this and still cant get the correct answer which is $$339\\pi\/2$$\n\n-for the bounds i know that the integral i want to evaluate is between 0 and 16 based on the line y=0 and the function $$y=x^{2}$$ evaluated at x=4.\n\n-the outer radius is $$1+\\sqrt{y}$$ and the inner radius is just 1\n\n$$\\pi\\int_0^{16}\\\\ (1+\\sqrt{y})^2-(1)^2\\\\,dy$$\n\nLast edited: Sep 27, 2008\n2. Sep 27, 2008\n\n### tiny-tim\n\nWelcome to PF!\n\nHi peercortsa! Welcome to PF!\n\nThat's right \u2026 but then your thickness is dx, so that's what you must integrate over \u2026\n\n\u222b(blah blah) dx, where blah blah is entirely a function of x.\n\n3. Sep 27, 2008\n\n### peercortsa\n\nso..... did i even set up the equation correctly cuz i still cant seem to get the right answer no matter what i try\n\n4. Sep 27, 2008\n\n### tiny-tim\n\nYour \u03c0\u222b\u2026dx is correct for the area\n\nbut you still need to put the height inside the \u222b to make the volume.\n\nHave a go!","date":"2018-05-22 18:02:35","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 1, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8545050024986267, \"perplexity\": 810.9396935875678}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-22\/segments\/1526794864837.40\/warc\/CC-MAIN-20180522170703-20180522190703-00106.warc.gz\"}"} | null | null |
\section{Introduction}\label{sec:intro}
Highly unsaturated molecules account for a large portion of the known interstellar species \cite{mcguire2018census}.
For instance, the presence of several carbon-chain molecules is one of the most characteristic features of the chemical composition of starless cores, such as the Taurus Molecular Cloud (TMC-1), one of the brightest source of carbon-chain species \cite{yamamoto2017book}.
Among the unsaturated molecular species, cyanopolyynes, i.e., linear molecules of general chemical formula \ce{HC_{2n+1}N}, are widespread in the interstellar medium (ISM) and all members up to \ce{HC11N} have been detected to date \cite{Loomis2020}.
Cyanoacetylene (\ce{HC3N}, IUPAC name prop-2-ynenitrile), the simplest member of the cyanopolyynes family, was found to be an abundant species in a large variety of astronomical objects: starless cores \cite{suzuki1992dark}, post-AGB objects \cite{wyrowski2003crl}, carbon-rich circumstellar envelopes \cite{decin2010warm}, massive star-forming regions \cite{li2011large}, protoplanetary disks \cite{chapillon2012proto}, solar-type protostars \cite{al2017iras}, external galaxies \cite{rico2020super}, and Galactic Center molecular clouds \cite{zeng2018complex}.
The deuterated form of cyanoacetylene (\ce{DC3N}) has been detected in the ISM as well.
The first astronomical observation of \ce{DC3N} has been reported towards TMC-1 \cite{langer1980tmc} by the detection of the $J=5\rightarrow4$ emission rotational transition around 42\,GHz.
Consecutively, \ce{DC3N} has tentatively been detected in the high-mass star-forming regions Orion KL \cite{esplugues2013orion} and Sagittarius B2 \cite{belloche2016emoca}. In these regions, deuterium fractionation is not as effective as in dark clouds, thus preventing a strong enhancement above the deuterium cosmic abundance.
Recently, \ce{DC3N} has been detected in some low-mass cores (see e.g., Refs.\cite{al2017iras},\cite{bianchi2019astrochemistry}) and in a sample of 15 high-mass star-forming cores \cite{rivilla2020dc3n}. The latter work, based on the spectroscopic results presented in this paper, suggests that \ce{DC3N} is enhanced in the cold and outer regions of star-forming regions, likely indicating the initial deuteration level of the large-scale molecular cloud within which star formation takes place. Rivilla \emph{et al.} \cite{rivilla2020dc3n} also summarize all the astronomical observations of \ce{DC3N} so far.
Microwave (MW) transitions of \ce{DC3N} were first reported for the ground and the four lowest singly-excited states during the course of an extensive study of cyanoacetylene isotopologues \cite{mallinson1978microwave}.
A larger number of vibrationally excited states was re-examined in depth some years later and a rigorous determination of the effective molecular parameters was attained \cite{plummer1988excited}.
Recently, the laboratory investigation of the rotational spectrum of \ce{DC3N} has been extended to the THz regime for the ground and the $v_7=1$ states \cite{spahn2008thz}. In the same paper, the authors revised the \ce{^{14}N} and \ce{D} hyperfine-structure constants derived in Refs.~\cite{fliege1983hfs,tack1983beam} from supersonic-jet Fourier-Transform Microwave (FT-MW) spectroscopy.
As far as its infrared (IR) spectrum is concerned, the experimental position and intensity of all fundamentals but the weak $\nu_4$ mode have been determined from low resolution (0.5\,\wn) studies \cite{uyemura1982ir,benilan2006ir}. Some combination and overtone bands were also observed in the same works.
In addition, two medium resolution (0.025--0.050\,\wn) IR studies were performed by Mallinson \& Fayt \cite{mallinson1976high} and Coveliers \emph{et al.} \cite{coveliers1992far}. In the former, the band center of the three stretching modes of \ce{DC3N} ($\nu_1$, $\nu_2$, and $\nu_3$) has been determined; in the latter, the far-infrared (FIR) spectrum was recorded between 200 and 365\,\wn and the $\nu_7$ fundamental was analyzed together with the bands $\nu_6 - \nu_7$, $\nu_5 - \nu_7$, and $\nu_4 - \nu_6$, and their hot-bands.
In this work, a detailed investigation of both millimeter/submillimeter-wave and infrared spectra of \ce{DC3N} is reported.
Pure rotational transitions within all the vibrational states with energy lower than 1015\,\wn have been detected and 27 fundamental, overtone, combination, and hot ro-vibrational bands have been analyzed at high resolution (0.001--0.01\,\wn).
The new measurements have been combined in a fit containing almost 6700 distinct transition frequencies, thus allowing the determination of a consistent set of spectroscopic parameters.
This work represents the most exhaustive spectroscopic characterization of \ce{DC3N} so far and provides a robust line catalog useful for astronomical applications. Moreover, the large number of vibrational excited states are of interest for harmonic/anharmonic force field computations.
The paper is structured as follows. First, the synthesis of the sample and the spectrometers used for spectral recording are described (\S\ref{sec:exp}). Then, the effective Hamiltonian employed for the energy levels description is given (\S\ref{sec:theory}). Successively, the general features of the spectra and their analysis are discussed (\S\ref{sec:analysis}).
Finally, the results are summarized and the conclusions are presented (\S\ref{sec:concl}).
\section{Experimental details}\label{sec:exp}
\subsection{Synthesis of deuterocyanoacetylene}
Methyl propiolate (\ce{HC+CCOOCH3}) was purchased from TCI-Europe and used without further purification.
The \ce{DC3N} sample was synthesized in Rennes following the procedure described in Ref.~\cite{benilan2006ir}.
Briefly, \ce{HC+CCOOCH3} was added dropwise to liquid ammonia resulting in a 100\,\% conversion into \ce{HC+CCONH2}.
The propiolamide was then mixed with phosphorous anhydride (\ce{P4O10}) and calcined white sand; the whole system was heated up to 470\,K over 2\,h while connected to a liquid nitrogen-cooled trap where pure cyanoacetylene was collected.
Cyanoacetylene (3\,g), heavy water (\ce{D2O}, 4\,mL) and potassium carbonate (\ce{K2CO3}, 50\,mg) were mixed together in an inert atmosphere. The biphasic mixture was then stirred for about 20\,min at room temperature.
Subsequently, on a vacuum line, partially deuterated cyanoacetylene was condensed in a 77\,K cooled trap, while water was blocked in a first 220\,K trap. The operation was repeated 3 times by addition of \ce{D2O} and \ce{K2CO3} to the partially deuterated cyanoacetylene. The residual \ce{D2O} was removed by vaporisation on \ce{P4O10} and \ce{DC3N} was finally condensed in a trap cooled to 150\,K.
Deuterocyanoacetylene with an isotopic purity greater than 98\,\% was obtained in a 67\,\% yield. The sample can be stored indefinitely at 250\,K without decomposition.
\subsection{Infrared spectrometers}
The FIR spectrum of \ce{DC3N} was recorded at the AILES beamline of the SOLEIL synchrotron facility using a Bruker IFS 125 FT interferometer \cite{Brubach2010} and a white-type multipass absorption cell whose optics were adjusted to obtain a 150\,m optical path length \cite{Pirali2012,Pirali2013}.
For the present experiment, we used the far-IR synchrotron radiation continuum extracted by the AILES beamline.
The interferometer was equipped with a 6\,\textmu m Mylar-composite beamsplitter and a 4\,K cooled \ce{Si}-bolometer.
Two 50\,\textmu m-thick polypropylene windows isolated the cell from the interferometer, which was continuously evacuated to 0.01\,Pa limiting the absorption of atmospheric water. Vapor of \ce{DC3N} was injected into the absorption cell at a 25\,Pa pressure. The spectrum covers the range 70--500\,\wn and consists of the co-addition of 380 scans recorded at 0.00102\,\wn resolution.
IR spectra in the 450--1600\,\wn range were recorded in Bologna using a Bomem DA3.002 Fourier-Transform spectrometer \cite{tamassia2020tfe}.
It was equipped with a Globar source, a \ce{KBr} beamsplitter, and a liquid nitrogen-cooled \ce{HgCdTe} detector. A multi-pass cell with absorption-lengths from 4 to 8\,m was employed for the measurements.
Sample pressures ranging between 25 and 650\,Pa were used to record the spectra.
The resolution was generally 0.004\,\wn, except for the very weak $\nu_4$ band, which was recorded at a lower
resolution of 0.012\,\wn.
Several hundreds of scans, typically 800, were co-added in order to improve the signal-to-noise ratio (S/N) of the spectra.
All the spectra have been calibrated using residual water or \ce{CO2} absorption lines whose reference wavenumbers were taken from Refs.~\cite{MatsushimaCalibrationH2O,Horneman2005} and from \texttt{HITRAN} \cite{gordon2017hitran2016}, respectively.
No apodization functions were applied to the interferograms.
\subsection{Millimeter and submillimeter spectrometers}
Rotational spectra have been recorded using two frequency-modulation (FM) millimeter/submillimeter spectrometers located in Bologna and in Garching.
The Bologna spectrometer has been described in details elsewhere \cite{degli2019determination,melosso2019sub}.
Briefly, a Gunn diode oscillator operating in the W band (80--115\,GHz) was used as primary source
of radiation, whose frequency and phase stability are ensured by a Phase-Lock Loop (PLL).
Spectral coverage at higher frequencies was obtained by coupling the Gunn diode to passive frequency
multipliers in cascade (doublers and triplers, Virginia Diodes, Inc.).
The output radiation, sine-wave modulated in frequency ($f=48$\,kHz), was fed to the glass absorption cell
containing \ce{DC3N} vapors at a pressure between 1 and 15\,Pa, depending on the
intensity of the lines under consideration.
The outcoming signal was detected by a Schottky barrier diode and sent to a Lock-in amplifier
set at twice the modulation-frequency ($2f$ scheme); the demodulated signal is then filtered into a
resistor-capacitor (RC) system before data acquisition.
In Garching the CASAC spectrometer developed at the Max-Planck-Institut f\"ur extraterrestrische Physik was used.
Full details on the experimental set-up are given in Ref.~\cite{bizzocchi2017accurate}; here, we report only a few key details
which apply to the present investigation.
The instrument is equipped with an active multiplier chain (Virginia Diodes) as a source of radiation in the
82--125\,GHz band.
Further multiplier stages in cascade allow to extend the frequency coverage up to $\sim 1.1$\,THz with an
available power of 2--20\,\textmu W.
The primary millimeter radiation stage is driven by a cm-wave synthesizer (Keysight E8257D) operating in the
18-28\,GHz band, which is locked to a \ce{Rb} atomic clock to achieve accurate frequency and phase stabilisation.
A closed-cycle \ce{He}-cooled \ce{InSb} hot-electron bolometer operating at 4\,K (QMC) is used as a detector.
As in Bologna, frequency ($f=50$\,kHz) modulation technique is employed and the second derivative of the actual
absorption profile is thus recorded by the computer-controlled acquisition system after lock-in demodulation at $2f$\@.
The absorption cell is a plain Pyrex tube (3\,m long and 5\,cm in diameter) fitted with high-density polyethylene
windows.
The measurement were performed using gaseous samples at pressure of a few Pa.
In this condition, \ce{DC3N} is stable for ca.~2\,h without significant decomposition due to hydrogen exchange.
The spectra were recorded in the frequency ranges 80--115\,GHz and 920--1070\,GHz in Garching, and in the window 240--440\,GHz in Bologna.
\begin{table}[htb!]
\centering
\caption{Energy and intensity of all fundamental modes of \ce{DC3N}.}
\label{tab:dc3n_modes}
\scalebox{0.99}{
\begin{threeparttable}
\begin{tabular}{clccc}
\hline\hline \\[-0.5ex]
Modes & Description & Energy & Reference & \multicolumn{1}{c}{Abs. intensity} \\[0.5ex]
& & (\wn) & & \multicolumn{1}{c}{(atm$^{-1}$cm$^{-2}$)} \\[0.5ex]
\hline \\[-1.5ex]
$\nu_1$ & \ce{C-D} stretching & 2608.520(3) & \cite{mallinson1976high} & $81.3\pm5.7$\tnote{a} \\[0.5ex]
$\nu_2$ & \ce{C+C} stretching & 2252.155(3) & \cite{mallinson1976high} & $50.5\pm2.4$\tnote{a} \\[0.5ex]
$\nu_3$ & \ce{C+N} stretching & 1968.329(3) & \cite{mallinson1976high} & $38.7\pm4.0$\tnote{a} \\[0.5ex]
$\nu_4$ & \ce{C-C} stretching & 867.60(6) & This Work & $<0.1$\tnote{b} \\[0.5ex]
$\nu_5$ & \ce{CCD} bending & 522.263933(7) & This Work & $83.8\pm4.7$\tnote{a} \\[0.5ex]
$\nu_6$ & \ce{CCC} bending & 492.759896(7) & This Work & $106.\pm8$\tnote{a} \\[0.5ex]
$\nu_7$ & \ce{CCN} bending & 211.550293(5) & This Work & $0.89\pm0.11$\tnote{b} \\[0.5ex]
\hline\hline \\[-1ex]
\end{tabular}
\begin{tablenotes}
\item \flushleft \textbf{[a]} From low-resolution integrated band-intensity measurements at 296\,K (Ref.~\cite{benilan2006ir}). \textbf{[b]} From low-resolution integrated band-intensity measurements at 293\,K (Ref.~\cite{uyemura1982ir}).
\end{tablenotes}
\end{threeparttable}
}
\end{table}
\section{Theoretical background}\label{sec:theory}
From a spectroscopic point of view, \ce{DC3N} is a closed-shell linear rotor.
It has 7 vibrational modes: 4 stretchings ($\nu_1$--$\nu_4$; $\Sigma$ symmetry) and 3 doubly-degenerated bendings ($\nu_5$--$\nu_7$; $\Pi$ symmetry). They are summarized in Table~\ref{tab:dc3n_modes}.
In the present work, only the low-lying vibrational states ($v_4$, $v_5$, $v_6$, and $v_7$, with one of multiple quanta of excitation) have been investigated for two main reasons:
(i) transitions associated to the lower energy states are of astrophysical interest, and (ii) some of the vibrational states are connected by a network of anharmonic resonances fully described within our chosen energy threshold of 1015\,\wn; above this limit the states are either unperturbed or involved in higher-order resonances.
Therefore, the stretching modes $\nu_1$, $\nu_2$, and $\nu_3$, lying above this threshold, have not been investigated.
Conventionally, we labelled a given vibrational state with the notation $(v_4,v_5^{l_5},v_6^{l_6},v_7^{l_7})_{e/f}$,
where $l_t$ is the vibrational angular momentum quantum number associated to the bending mode $t$
and the $e/f$ subscripts indicate the parity of the symmetrized wave functions \cite{brown1975labeling}.
When the $l_t$ and $e/f$ labels are not indicated, we refer to all the possible sub-levels of a state.
The full ro-vibrational wave-function is then given by the ket $\ket[e/f]{v_4,v_5^{l_5},v_6^{l_6},v_7^{l_7};J,k}$.
The vibrational part of the wave-function is expressed as combination of one- or two-dimensional harmonic
oscillators, whereas the rotational part is the symmetric-top wave-function
whose quantum number $k$ is given by
$k = l_5 + l_6 + l_7$\@.
A substate is denoted as $\Sigma$ when $k=0$, $\Pi$ for $\lvert k \rvert =1$, $\Delta$ for $\lvert k \rvert =2$, and so on.
The following Wang-type linear combinations \cite{yamada1985effective} lead to symmetry-adapted basis functions:
\begin{subequations} \label{eq:Wang}
\begin{align}
\left\lvert v_4,v_5^{l_5}\right.,&\left.v_6^{l_6},v_7^{l_7};J,k\right\rangle_{e/f}
= \frac{1}{\sqrt{2}} \left\{
\ket{v_4,v_5^{l_5},v_6^{l_6},v_7^{l_7};J,k} \pm (-1)^k
\ket{v_4,v_5^{-l_5},v_6^{-l_6},v_7^{-l_7};J,-k}
\right\} \,, \\
\left\lvert v_4,0^0\right.,&\left.0^0,0^0;J,0\right\rangle_{e} = \ket{v_4,0^0,0^0,0^0;J,0} \,.
\end{align}
\end{subequations}
The upper and lower signs ($\pm$) correspond to $e$ and $f$ wave-functions, respectively.
For $\Sigma$ states ($k = 0$), the first non-zero $l_t$ is chosen positive.
Here, the omission of the $e/f$ label indicates unsymmetrised wave-functions.
The Hamiltonian used to reproduce the ro-vibrational energy levels is equivalent to the one used for \ce{HC3N} \cite{bizzocchi2017hc3n}:
\begin{equation} \label{eq:hamdc3n}
\mathscr{H} = \mathscr{H}_\mrm{rv} + \mathscr{H}_\mrm{\textit{l}-type} + \mathscr{H}_\mrm{res} \,,
\end{equation}
\noindent
where $\mathscr{H}_\mrm{rv}$ is the ro-vibrational energy including centrifugal
distortion corrections, $\mathscr{H}_\mrm{\textit{l}-type}$ represents the $l$-type interaction between the $l$
sub-levels of the excited bending states, and $\mathscr{H}_\mrm{res}$ accounts for
resonances among accidentally quasi-degenerate ro-vibrational states.
The resonance network active in \ce{DC3N} resembles the one found for \ce{HC3N} and will be described later.
The Hamiltonian matrix is built by using unsymmetrised ro-vibrational functions.
It is subsequently factorized and symmetrized using Eqs.~\eqref{eq:Wang}.
The matrix elements of the effective Hamiltonian are expressed using the formalism
already employed for the analysis of \ce{HC3N} \cite{bizzocchi2017hc3n}.
\section{General features and analysis}\label{sec:analysis}
\subsection{Vibrational spectra}
Although infrared spectra were recorded up to 1600\,\wn in this study, our analysis is limited to the portion of the electromagnetic spectrum below $\sim$ 1040\,\wn. This is because the highest energy state within our threshold of 1015\,\wn is the (0110) state, whose combination band falls in the region 999--1035\,\wn.
In total, 27 ro-vibrational bands have been observed at high resolution for the first time and successfully analyzed. They include fundamental, overtone, combination, and hot-bands, and are listed in Table~\ref{tab:dc3n_vibdata} along with the observed sub-bands, frequency and $J$ ranges, number of data used in the analysis, and the root-mean-square (\textit{rms}) error of the final fit.
All the observed bands are also graphically displayed in Figure~\ref{fig:dc3n_levels}.
\begin{table}[htb!]
\centering
\caption{Ro-vibrational bands recorded and analyzed in this work.}
\label{tab:dc3n_vibdata}
\begin{threeparttable}
\begin{tabular}{llcccc}
\hline\hline \\[-1ex]
Band & Sub-bands & Freq. range & $J$ range & No. of lines & $rms \times 10^{4}$ \\[0.5ex]
& & (\wn) & & & (\wn) \\[0.5ex]
\hline\ \\[-1.5ex]
$\nu_7$ & $\Pi - \Sigma^+$ & 190-240 & 1-93 & 258 & 0.5 \\[0.5ex]
$\nu_6$ & $\Pi - \Sigma^+$ & 466-522 & 2-109 & 267 & 3.6 \\[0.5ex]
$\nu_5$ & $\Pi - \Sigma^+$ & 500-557 & 0-117 & 255 & 3.7 \\[0.5ex]
$\nu_4$ & $\Sigma^+ - \Sigma^+$ & 830-865 & 0-61 & 109 & 9.6 \\[0.5ex]
$2\nu_7$ & $\Sigma^+ - \Sigma^+$ & 405-445 & 2-78 & 136 & 1.0 \\[0.5ex]
$2\nu_6$ & $\Sigma^+ - \Sigma^+$ & 975-1018 & 2-101 & 141 & 5.2 \\[0.5ex]
$\nu_6+\nu_7$ & $\Sigma^+ - \Sigma^+$ & 686-736 & 1-89 & 166 & 2.5 \\[0.5ex]
$\nu_5+\nu_7$ & $\Sigma^+ - \Sigma^+$ & 715-769 & 1-105 & 170 & 3.0 \\[0.5ex]
$\nu_5+\nu_6$ & $\Sigma^+ - \Sigma^+$ & 999-1035 & 3-63 & 102 & 3.8 \\[0.5ex]
$\nu_6 - \nu_7$ & $\Pi - \Pi$ & 257-306 & 1-89 & 309 & 0.6 \\[0.5ex]
$\nu_5 - \nu_7$ & $\Pi - \Pi$ & 288-333 & 1-86 & 291 & 0.7 \\[0.5ex]
$\nu_4 - \nu_6$ & $\Sigma^+ - \Pi$ & 329-375 & 1-79 & 222 & 0.6 \\[0.5ex]
$4\nu_7 - \nu_6$ & $\Sigma^+ - \Pi$ & 351-352 & 59-60 & 2 & 0.4 \\[0.5ex]
$2\nu_7 - \nu_7$ & $\Sigma - \Pi$ & 193-236 & 1-78 & 391 & 0.8 \\[0.5ex]
$3\nu_7 - 2\nu_7$ & $\Pi - \Sigma^+$ & 191-235 & 4-77 & 178 & 0.7 \\[0.5ex]
$4\nu_7 - 3\nu_7$ & $\Sigma^+ - \Pi$ & 193-219 & 10-58 & 89 & 0.9 \\[0.5ex]
$3\nu_7 - \nu_7$ & $\Pi - \Pi$ & 405-441 & 4-68 & 208 & 1.0 \\[0.5ex]
$\nu_6+\nu_7 - \nu_7$ & $(\Sigma, \Delta) - \Pi$ & 478-508 & 5-56 & 329 & 6.9 \\[0.5ex]
$\nu_6+2\nu_7 - 2\nu_7$ & $\Pi - (\Sigma^{+}, \Delta)$ & 476-512 & 12-65 & 93 & 5.2 \\[0.5ex]
$2\nu_6 - \nu_6$ & $\Sigma - \Pi$ & 500-519 & 10-68 & 43 & 7.0 \\[0.5ex]
$\nu_5+\nu_7 - \nu_7$ & $(\Sigma^{+}, \Delta) - \Pi$ & 505-545 & 2-75 & 464 & 4.5 \\[0.5ex]
$\nu_5+2\nu_7 - 2\nu_7$ & $\Pi - (\Sigma, \Delta)$ & 505-542 & 2-82 & 106 & 3.5 \\[0.5ex]
$\nu_6+2\nu_7 - \nu_7$ & $\Pi - \Pi$ & 690-718 & 4-53 & 153 & 4.7 \\[0.5ex]
$\nu_5+2\nu_7 - \nu_7$ & $\Pi - \Pi$ & 721-748 & 2-45 & 296 & 4.1 \\[0.5ex]
$\nu_5+\nu_7 - 2\nu_7$ & $(\Sigma^{+}, \Delta) - (\Sigma^{+}, \Delta)$ & 290-330 & 2-81 & 261 & 0.9 \\[0.5ex]
$\nu_6+\nu_7 - 2\nu_7$ & $(\Sigma^{+}, \Delta) - (\Sigma^{+}, \Delta)$ & 256-306 & 2-84 & 402 & 0.9 \\[0.5ex]
$4\nu_7 - 2\nu_7$ & $(\Sigma^{+}, \Delta) - (\Sigma^{+}, \Delta)$ & 406-437 & 5-67 & 302 & 1.0 \\[0.5ex]
\hline\hline
\end{tabular}
\end{threeparttable}
\end{table}
\begin{figure}[htb!]
\centering
\includegraphics[width=0.9\textwidth]{scheme-eps-converted-to.pdf}
\caption{Vibrational energy-level diagram of \ce{DC3N} up to 1015\,\wn, where the arrows represent the 27 IR bands analyzed in this work. Red and blue arrows indicate the bands observed at SOLEIL and in Bologna, respectively.}
\label{fig:dc3n_levels}
\end{figure}
\begin{figure}[p!]
\centering
\includegraphics[width=0.95\textwidth]{fir-eps-converted-to.pdf}
\includegraphics[width=0.95\textwidth]{mir-eps-converted-to.pdf}
\caption{Portions of the FIR (upper panel) and MIR (lower panel) spectra of $d$-cyanoacetylene (black traces). A simulation spectrum of the most intense bands is also reported for both \ce{DC3N} (red) and \ce{HC3N} (grey). Lines belonging to \ce{CO} and various \ce{H2O} isotopologues were removed from the spectra.}
\label{fig:dc3n_ir}
\end{figure}
Figure~\ref{fig:dc3n_ir} shows a general overview of portions of the FIR (180--460\,\wn range, upper panel) and mid-infrared (MIR, 450--800\,\wn range, bottom panel) spectra recorded in this work.
The most prominent bands in the FIR region are the $\nu_7$ fundamental, $\nu_6 - \nu_7$, $\nu_5 - \nu_7$, $\nu_4 - \nu_6$, and $2\nu_7$ overtone bands.
The MIR region is dominated by the very strong fundamentals $\nu_6$ and $\nu_5$. The low-frequency side of the spectrum is particularly crowded due to the proximity of the two fundamentals, the presence of their associated hot-bands, and of the $\nu_6$ of \ce{HC3N} centered at 500\,\wn.
\ce{HC3N} is present in the sample as result of the H/D exchange in the cell.
Having a medium IR intensity, the combination bands $\nu_6+\nu_7$ and $\nu_5+\nu_7$ are well visible in the high-frequency part of the MIR spectrum as seen in the bottom panel of Figure~\ref{fig:dc3n_ir}.
Although not displayed in Figure~\ref{fig:dc3n_ir}, the overtone $2\nu_6$ and the combination $\nu_5+\nu_6$ bands centered around 975--1018\,\wn and 999--1035\,\wn, respectively, are clearly detectable as well, despite the presence of strong absorption lines due to \ce{HDO}.
The very weak ($< 0.1$ atm$^{-1}$ cm$^{-2}$) $\nu_4$ fundamental at 830--865\,\wn had to be recorded at higher pressure (400\,Pa) and lower resolution (0.012\,\wn). In this case, up to 2600 scans were co-added to improve the S/N of the spectrum.
\subsection{Rotational spectra}
Rotational spectra were recorded for all the 14 states whose vibrational energy do not exceed our threshold of 1015 \wn.
Literature data were available for some of these states, as pointed out in Section~\ref{sec:intro}.
However, line positions of some millimeter-wave transitions from Ref.~\cite{mallinson1978microwave} are affected by large uncertainties (up to 300\,kHz) and many data are limited to low frequencies.
For these reasons, we decided to re-investigate and extend the spectrum for all these vibrational states.
The largest improvements have been realized for the states (1000), (0110), (0020), and (0004) involved in a network of anharmonic resonances, for which extended data-sets were obtained.
In particular, the (0110) state, not included in the analysis of Ref.~\cite{plummer1988excited},
has been assigned for the first time in this study and its interaction with the (1000) state has been identified and properly accounted for.
Table~\ref{tab:dc3n_rotdata} summarizes the set of rotational data used in the analysis, specifying the observed sub-levels, $J$ and frequency ranges, number of distinct fitted frequencies, the \textit{rms} error of the final fit, and the corresponding references used.
\begin{table}[htb!]
\centering
\caption{Summary of the rotational data used in the analysis.}
\label{tab:dc3n_rotdata}
\begin{threeparttable}
\begin{tabular}{lcccccl}
\hline\hline \\[-1ex]
State & $\left|k\right|$ & $J$ range & Freq. range & No. of lines & $rms$ & Reference \\[0.5ex]
& & & (GHz) & & (kHz) & \\[0.5ex]
\hline\hline \\[-1.5ex]
Ground state & 0 & 3-126 & 33-1069 & 52 & 13.2 & TW, Ma78, Pl88, Sp08 \\[0.5ex]
$v_7 = 1$ & 1$_{\mrm{e,f}}$ & 5-105 & 50-896 & 67 & 10.9 & TW, Ma78, Pl88, Sp08 \\[0.5ex]
$v_6 = 1$ & 1$_{\mrm{e,f}}$ & 7-44 & 67-381 & 42 & 17.0 & TW, Pl88 \\[0.5ex]
$v_5 = 1$ & 1$_{\mrm{e,f}}$ & 7-44 & 67-381 & 42 & 13.7 & TW, Pl88 \\[0.5ex]
$v_4 = 1$ & 0 & 7-51 & 67-439 & 32 & 23.6 & TW, Pl88 \\[0.5ex]
$v_7 = 2$ & 0, 2$_{\mrm{e,f}}$ & 7-44 & 67-383 & 61 & 24.0 & TW, Ma78, Pl88 \\[0.5ex]
$v_7 = 3$ & (1, 3)$_{\mrm{e,f}}$ & 7-44 & 68-384 & 77 & 20.0 & TW, Ma78, Pl88 \\[0.5ex]
$v_7 = 4$ & 0,(2, 4)$_{\mrm{e,f}}$ & 7-48 & 68-419 & 85 & 19.8 & TW, Pl88 \\[0.5ex]
$v_6 = 2$ & 0, 2$_{\mrm{e,f}}$ & 7-44 & 67-382 & 54 & 44.7 & TW, Pl88 \\[0.5ex]
$v_6 = v_7 = 1$ & (0, 2)$_{\mrm{e,f}}$ & 7-44 & 67-382 & 93 & 30.8 & TW, Ma78, Pl88 \\[0.5ex]
$v_5 = v_7 = 1$ & (0, 2)$_{\mrm{e,f}}$ & 7-44 & 67-382 & 78 & 20.8 & TW, Pl88 \\[0.5ex]
$v_5 = v_6 = 1$ & (0, 2)$_{\mrm{e,f}}$ & 9-44 & 84-381 & 63 & 14.6 & TW \\[0.5ex]
$v_6 = 1, v_7 = 2$ & $(\pm1, 3)_{\mrm{e,f}}$ & 7-46 & 68-400 & 95 & 21.9 & TW, Pl88 \\[0.5ex]
$v_5 = 1, v_7 = 2$ & $(\pm1, 3)_{\mrm{e,f}}$ & 9-44 & 85-383 & 97 & 17.4 & TW \\[0.5ex]
interstate\tnote{a} & & 44-49 & 364-429 & 10 & 19.7 & TW \\[0.5ex]
\hline\hline
\end{tabular}
\begin{tablenotes}
\item \flushleft Abbreviations are used as follow: \textbf{TW} This work, \textbf{Ma78} Mallinson \& De Zafra (1978) \cite{mallinson1978microwave}, \textbf{Pl88} Plummer \emph{et al.} (1988) \cite{plummer1988excited}, \textbf{Sp08} Spahn \emph{et al.} (2008) \cite{spahn2008thz}. [a] Transitions between the interacting states (1000) and (0004).
\end{tablenotes}
\end{threeparttable}
\end{table}
With the exception of $v_4 = 1$, all the states possess a rotational constant $B$ greater than that of the ground state and therefore their rotational lines lie at frequencies higher than those of the corresponding ground state transition.
This can be seen in Figure~\ref{fig:dc3n_long}, where the broad scan covers the $J=13 \leftarrow 12$ transitions for many vibrational satellites.
In this excerpt, the $l$-type resonance patterns of all the excited bending states analyzed are visible.
From a visual inspection, it is easy to associate some of these patterns to the pertaining state: the ground and $v_4=1$ exhibit a single line, while each bending state has $\sum=\prod_{t}(l_t+1)$ lines (even though not always resolvable).
\begin{figure}[htb!]
\centering
\includegraphics[width=\textwidth]{dc3n_rot-eps-converted-to.pdf}
\caption{A 2\,GHz broad scan of the $J = 13\leftarrow 12$ rotational transition of \ce{DC3N} around 110\,GHz. The spectrum was recorded at room temperature, with \ce{DC3N} at a pressure of 0.05\,Pa, RC= 3\,ms, frequency step 50\,kHz, FM = 120\,kHz, scan speed = 0.4\,MHz/s, 2 scans. The arbitrary units of the $y$-axis are set so that the intensity of the ground state (GS) transition, out of scale in the figure, is 1.}
\label{fig:dc3n_long}
\end{figure}
\subsection{Analysis of the spectra}
The sample of pure rotational and ro-vibrational data contains 6691 distinct frequencies involving 14 vibrational states of \ce{DC3N}. This work represents the first-ever investigation of its ro-vibrational spectrum in the region between 365 and 1040\,\wn.
Moreover, the FIR spectrum has been thoroughly re-investigated at higher resolution with an accuracy two or three orders of magnitude better than Ref.~\cite{coveliers1992far}.
As far as the rotational spectrum is concerned, this work extends the observation of excited states transitions to the submillimeter-wave region.
In addition, rotational transitions with $J$ up to 126 were recorded at THz frequencies (1.069\,THz) although only for the ground state.
In the combined fit, a different weight was given to each datum in order to take into account the different measurements precision.
Uncertainties spanning from 0.0004 to 0.00075\,\wn were used for the infrared measurements performed in Bologna; the weak $\nu_4$ band being the only exception, for which an uncertainty of 0.001\,\wn was assumed. FIR data recorded at higher resolution with the FT-IR spectrometer of the AILES beamline have been given uncertainties between 0.00005 and 0.0001\,\wn, based on calibration residuals and the S/N of spectral lines.
As far as pure rotational transitions are concerned, we assumed a typical experimental error of 10--20\,kHz for our new millimeter/submillimeter measurements. Data from literature were used with the uncertainty stated in the original papers \cite{mallinson1978microwave,plummer1988excited,spahn2008thz}.
Only few lines from Ref.~\cite{mallinson1978microwave}, whose residuals were far off their declared errors, were not used in the fit.
\begin{table}[htb!]
\centering
\caption{Spectroscopic constants derived for \ce{DC3N} in the ground and $v_4 = 1$ states.}
\label{tab:dc3n_gs}
\begin{threeparttable}
\begin{tabular}{ll..}
\hline\hline \\[-1ex]
Constant & Unit & \multicolumn{1}{c}{Ground state} & \multicolumn{1}{c}{$v_4 = 1$} \\[0.5ex]
\hline \\[-1.5ex]
$G_v$ & \wn & 0.0 & 867.594(75) \\[0.5ex]
$B_v$ & MHz & 4221.580853(37) & 4212.271(16) \\[0.5ex]
$D_v$ & kHz & 0.4517857(89) & 0.45312(11) \\[0.5ex]
$H_v$ & mHz & 0.03949(78) & 0.03949\tnote{a} \\[0.5ex]
$L_v$ & nHz & -0.154(23) & -0.154\tnote{a} \\[0.5ex]
\hline\hline
\end{tabular}
\begin{tablenotes}
\item \flushleft Number in parenthesis are one standard deviation in units of the last quoted digit. [a] Kept fixed to ground state value.
\end{tablenotes}
\end{threeparttable}
\end{table}
\begin{table}[htb!]
\centering
\caption{Spectroscopic constants derived for \ce{DC3N} in singly-excited bending states.}
\label{tab:dc3n_singly}
\begin{threeparttable}
\begin{tabular}{ll...}
\hline\hline \\[-1ex]
Constant & Unit & \multicolumn{1}{c}{$v_7 = 1$} & \multicolumn{1}{c}{$v_6 = 1$} & \multicolumn{1}{c}{$v_5 = 1$} \\[0.5ex]
\hline \\[-1.5ex]
$G_v$ & \wn & 211.5502859(33) & 492.7605681(48) & 522.2639331(49) \\[0.5ex]
$X_{\mrm{L}_\mrm{(tt)}}$ & GHz & 19.5125\tnote{a} & 56.39\tnote{a} & ... \\[0.5ex]
$B_v$ & MHz & 4234.519466(31) & 4229.25208(11) & 4225.835835(71) \\[0.5ex]
$D_v$ & kHz & 0.4718865(60) & 0.462123(45) & 0.452490(14) \\[0.5ex]
$H_v$ & mHz & 0.08240(30) & 0.0637(45) & 0.03949\tnote{b} \\[0.5ex]
$L_v$ & nHz & -0.154\tnote{b} & -0.154\tnote{b} & -0.154\tnote{b} \\[0.5ex]
$d_{\mrm{JL}_\mrm{(tt)}}$ & kHz & -9.971\tnote{a} & 141.5\tnote{a} & ... \\[0.5ex]
$q_{\mrm{t}}$ & MHz & 5.907823(56) & 3.15095(11) & 2.68903(13) \\[0.5ex]
$q_{\mrm{tJ}}$ & Hz & -13.646(11) & -1.572(22) & -1.627(27) \\[0.5ex]
$q_{\mrm{tJJ}}$ & \textmu Hz & 43.37(57) & ... & ... \\[0.5ex]
\hline\hline
\end{tabular}
\begin{tablenotes}
\item \flushleft Number in parenthesis are one standard deviation in units of the last quoted digit. [a] Constrained value, see text. [b] Kept fixed to ground state value.
\end{tablenotes}
\end{threeparttable}
\end{table}
\begin{table}[htb!]
\centering
\caption{Spectroscopic constants derived for \ce{DC3N} in overtone states.}
\label{tab:dc3n_over}
\begin{threeparttable}
\begin{tabular}{llmmmm}
\hline\hline \\[-1ex]
Constant & Unit & \multicolumn{1}{c}{$v_7 = 2$} & \multicolumn{1}{c}{$v_7 = 3$} & \multicolumn{1}{c}{$v_7 = 4$} & \multicolumn{1}{c}{$v_6 = 2$} \\[0.5ex]
\hline \\[-1.5ex]
$G_v$ & \wn & 422.3753581(61) & 632.510162(64) & 841.9860892(95) & 983.021(78) \\[0.5ex]
$X_{\mrm{L}_\mrm{(tt)}}$ & GHz & 19.354043(62) & 19.1988(19) & 19.03874(52) & 56.39(58) \\[0.5ex]
$y_{\mrm{L}_\mrm{(tt)}}$ & MHz & ... & ... & 1.82(12) & ... \\[0.5ex]
$B_v$ & MHz & 4247.45224(11) & 4260.38118(15) & 4273.30576(21) & 4236.558(16) \\[0.5ex]
$D_v$ & kHz & 0.491827(21) & 0.512469(34) & 0.53448(11) & 0.471993(61) \\[0.5ex]
$H_v$ & mHz & 0.03949\tnote{b} & 0.03949\tnote{b} & 0.176(21) & 0.03949\tnote{b} \\[0.5ex]
$L_v$ & nHz & -0.154\tnote{b} & -0.154\tnote{b} & -0.154\tnote{b} & -0.154\tnote{b} \\[0.5ex]
$d_{\mrm{JL}_\mrm{(tt)}}$ & kHz & -10.426(30) & -10.947(24) & -11.368(21) & 141.6(39) \\[0.5ex]
$h_{\mrm{JL}_\mrm{(tt)}}$ & Hz & ... & ... & -0.0552(64) & ... \\[0.5ex]
$q_{\mrm{t}}$ & MHz & 5.93258(10) & 5.95888(12) & 5.98281(15) & 3.15095\tnote{a} \\[0.5ex]
$q_{\mrm{tJ}}$ & Hz & -13.897\tnote{a} & -14.149(36) & -14.288(46) & -1.571\tnote{a} \\[0.5ex]
$q_{\mrm{tJJ}}$ & \textmu Hz & 43.37\tnote{a} & 43.37\tnote{a} & 43.37\tnote{a} & ... \\[0.5ex]
\hline\hline
\end{tabular}
\begin{tablenotes}
\item \flushleft Number in parenthesis are one standard deviation in units of the last quoted digit. [a] Constrained value, see text. [b] Kept fixed to ground state value.
\end{tablenotes}
\end{threeparttable}
\end{table}
\begin{sidewaystable}[ph!]
\centering
\caption{Spectroscopic constants derived for \ce{DC3N} in combination states.}
\label{tab:dc3n_comb}
\begin{threeparttable}
\begin{tabular}{llmmmmm}
\hline\hline \\[-1ex]
Constant & Unit & \multicolumn{1}{c}{$v_6 = v_7 = 1$} & \multicolumn{1}{c}{$v_5 = v_7 = 1$} & \multicolumn{1}{c}{$v_5 = v_6 = 1$} & \multicolumn{1}{c}{$v_6 = 1, v_7 = 2$} & \multicolumn{1}{c}{$v_5 = 1, v_7 = 2$} \\[0.5ex]
\hline \\[-1.5ex]
$G_v$ & \wn & 703.8550157(95) & 734.058721(13) & 1014.2947(11) & 914.21137(23) & 945.143633(32) \\[0.5ex]
$X_{\mrm{L}_\mrm{(aa)}}$ & GHz & 56.39\tnote{a} & ... & ... & 56.39\tnote{a} & ... \\[0.5ex]
$X_{\mrm{L}_\mrm{(bb)}}$ & GHz & 19.3189\tnote{a} & 19.5125\tnote{a} & 56.39\tnote{a} & 19.1254(87) & 19.3142(16) \\[0.5ex]
$X_{\mrm{L}_\mrm{(ab)}}$ & GHz & 16.16651(21) & 23.13131(38) & 40.245(33) & 16.2848(57) & 23.0216(30) \\[0.5ex]
$r_{\mrm{ab}}$ & GHz & -17.04625(41) & 0.32219(69) & -63.498(67) & -16.6526(81) & 0.87043(34) \\[0.5ex]
$r_{\mrm{abJ}}$ & kHz & -5.784(70) & -65.965(72) & ... & -12.0(12) & -64.05(11) \\[0.5ex]
$B_v$ & MHz & 4242.274182(83) & 4238.741823(94) & 4233.55575(16) & 4255.2987(20) & 4251.64459(18) \\[0.5ex]
$D_v$ & kHz & 0.481887(24) & 0.472594(28) & 0.463447(40) & 0.502237(37) & 0.492993(33) \\[0.5ex]
$H_v$ & mHz & 0.03949\tnote{b} & 0.03949\tnote{b} & 0.03949\tnote{b} & 0.03949\tnote{b} & 0.03949\tnote{b} \\[0.5ex]
$L_v$ & nHz & -0.154\tnote{b} & -0.154\tnote{b} & -0.154\tnote{b} & -0.154\tnote{b} & -0.154\tnote{b} \\[0.5ex]
$d_{\mrm{JL}_\mrm{(aa)}}$ & kHz & -11.254\tnote{a} & ... & ... & 141.5\tnote{a} & ... \\[0.5ex]
$d_{\mrm{JL}_\mrm{(bb)}}$ & kHz & 141.5\tnote{a} & -9.971\tnote{a} & 141.5\tnote{a} & -12.54(76) & -10.482(55) \\[0.5ex]
$d_{\mrm{JL}_\mrm{(ab)}}$ & kHz & 43.88(12) & -5.08(13) & 80.35(29) & 43.75(46) & -6.810(46) \\[0.5ex]
$q_{\mrm{a}}$ & MHz & 3.17827(15) & 2.70634(31) & 2.69091(31) & 3.19092(20) & 2.72654(16) \\[0.5ex]
$q_{\mrm{aJ}}$ & Hz & -1.571\tnote{a} & -1.626\tnote{a} & -1.626\tnote{a} & -1.517\tnote{a} & -1.626\tnote{a} \\[0.5ex]
$q_{\mrm{b}}$ & MHz & 5.94427(18) & 5.90943(73) & 3.15095\tnote{a} & 5.9489(16) & 5.93169(23) \\[0.5ex]
$q_{\mrm{bJ}}$ & Hz & -13.646\tnote{a} & -13.738(98) & -1.571\tnote{a} & -14.17(33) & -13.646\tnote{a} \\[0.5ex]
$q_{\mrm{bJJ}}$ & \textmu Hz & 43.37\tnote{a} & 43.37\tnote{a} & ... & 43.37\tnote{a} & 43.37\tnote{a} \\[0.5ex]
$u_{\mrm{ab}}$ & Hz & ... & ... & -1.641(74) & ... & ... \\[0.5ex]
\hline\hline
\end{tabular}
\begin{tablenotes}
\item \flushleft Number in parenthesis are one standard deviation in units of the last quoted digit. [a] Constrained value, see text. [b] Kept fixed to ground state value.
\end{tablenotes}
\end{threeparttable}
\end{sidewaystable}
The spectral analysis was performed using a custom \texttt{PYTHON} code that employs the \texttt{SPFIT} program \cite{pickett1991} as computational core (see Ref.~\cite{bizzocchi2017hc3n} for further details about the code).
The data were fitted to the Hamiltonian of Eq.~\eqref{eq:hamdc3n} and its coefficients optimized in an iterative least-squares procedure.
Some spectroscopic parameters could not be determined from the available experimental data.
In these cases, the constant of a given vibrational level were derived from the corresponding optimized values obtained for other levels belonging to the same vibrational manifold considering, whenever feasible, a vibrational dependence.
In other cases, they were simply fixed to zero.
The spectroscopic parameters obtained from the combined fit procedure are collected in Tables~\ref{tab:dc3n_gs}-\ref{tab:dc3n_comb}.
As anticipated, the analysis of \ce{DC3N} follows the approach successfully adopted for \ce{HC3N} \cite{bizzocchi2017hc3n}.
The main difference is the set-up of the anharmonic resonances network, which arises from the different energy of some vibrational levels due to the isotopic substitution. In particular, the $\nu_5$ vibrational energy, 663.36848(3)\,\wn in \ce{HC3N}, drops to 522.26378(2)\,\wn in \ce{DC3N}. For \ce{HC3N}, two resonant systems were described: (i) $v_5=1 \sim v_7=3$ and ii) $v_4=1 \sim v_5=v_7=1 \sim v_6=2 \sim v_7=4$. Of the two systems, the former is not present in \ce{DC3N} while the latter is almost the same, except for $v_5=v_7=1$, replaced by $v_5=v_6=1$. The treatment of such perturbations led to the determination of the corresponding interaction parameters, $C_{30}$ for the cubic terms, ($v_4=1$)--($v_6=2$) and ($v_4=1$)--($v_5=v_6=1$), and $C_{50}$ for the quintic term ($v_4=1$)--($v_7=4$). Moreover, a centrifugal distortion parameter $C_{50}^J$ was included in the analysis.
For the states involved in this resonance system, many experimental data are available.
In the MIR region, we recorded the $\nu_4$, $\nu_5+\nu_6$, and $2\nu_6$ bands that provide the energy position
for most of the interacting levels.
The energy of the $v_7=4$ was determined through the FIR spectrum, where the $4\nu_7 \leftarrow 3\nu_7$ hot-band and the $4\nu_7 \leftarrow \nu_6$ band were detected.
A large pure rotational data-set is also available for the polyad of interacting states.
Besides several rotational transitions observed within the vibrational states, a small set of interstate transitions between the (1000) and (0004) states were identified.
The coefficients $C_{mn}$ of the resonance Hamiltonian are given in Table~\ref{tab:dc3n_reso}.
\begin{table}[htb!]
\centering
\caption{Resonance parameters.}
\label{tab:dc3n_reso}
\begin{threeparttable}
\begin{tabular}{lcl.}
\hline\hline \\[-1ex]
Interacting states & Parameter & Unit & \multicolumn{1}{c}{Value} \\[0.5ex]
\hline \\[-1.5ex]
($v_4 = 1$) -- ($v_6 = 2$) & $C_{\mrm{30}}$ & \wn & 17.422(33) \\[0.5ex]
($v_4 = 1$) -- ($v_5 = v_6 = 1$) & $C_{\mrm{30}}$ & \wn & -6.527(13) \\[0.5ex]
($v_4 = 1$) -- ($v_7 = 4$) & $C_{\mrm{50}}$ & GHz & 2.70065(76) \\[0.5ex]
& $C_{\mrm{50}}^J$ & kHz & 9.807(35) \\[0.5ex]
\hline\hline
\end{tabular}
\begin{tablenotes}
\item \flushleft Number in parenthesis are one standard deviation in units of the last quoted digit.
\end{tablenotes}
\end{threeparttable}
\end{table}
\section{Conclusions}\label{sec:concl}
In this work, a large set of high-resolution rotational and ro-vibrational data of \ce{DC3N} has been recorded and analyzed in order to achieve a detailed knowledge of all the vibrational states approximately below 1000\,\wn of energy.
To reach this goal, infrared spectra of \ce{DC3N} have been recorded in the range 150--1600\,\wn at high resolution (0.001--0.004\,\wn). In this region, 27 fundamental, overtone, combination, and hot-bands have been observed and analyzed.
Notably, the very weak $\nu_4$ fundamental has also been detected, even though at lower resolution (0.012\,\wn).
Also, pure rotational transitions for 14 states have been recorded to extend the investigation of the spectrum to the submillimeter-wave region up to \emph{ca.} 500\,GHz.
Almost 6700 experimental transitions were included in a least-squares fit procedure thanks to which a large number of rotational and ro-vibrational spectroscopic parameters have been determined for 14 different vibrational states. The whole set of data has been fitted with an overall weighted standard deviation $\sigma$ of 0.95, meaning that on average all data are well-reproduced within their given uncertainties.
The vibrational energies were determined experimentally for all the investigated states, without any assumption.
The combination of both high-resolution ro-vibrational data and pure rotational measurements allowed an accurate modeling of the spectrum of \ce{DC3N}, including perturbations produced by the observed anharmonic resonances.
The interaction between the (1000) and (0110) states has been introduced for the first time, with the effect to eliminate the residual discrepancies described in Refs.~\cite{plummer1988excited,coveliers1992far}.
The present work shows once again the success of a combined analysis of data from different spectral regions, like infrared and millimeter-wave fields. The results are generally more coherent and fewer assumptions are needed, if not any. Also, a more extended set of spectroscopic parameters can be obtained with reliability.
This study provides an extensive line catalog (deposited as Supplementary Material) which can be used to assist future astronomical observations of \ce{DC3N} and is suitable for modeling both cold and hot regions of the interstellar medium.
\section{Acknowledgement}
This study was supported by Bologna University (RFO funds) and by MIUR (Project PRIN 2015: STARS in the CAOS, Grant Number 2015F59J3R). This work has been performed under the SOLEIL proposal \#20190128; we acknowledge the SOLEIL facility for provision of synchrotron radiation and would like to thank the AILES beamline staff for their assistance.
L.B., P.C., and B.M.G. acknowledge the support by the Max Planck Society.
V.M.R. has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk\l{}odowska-Curie grant agreement No 664931. LC acknowledges support from the Italian Ministero dell'Istruzione, Universit\`a e Ricerca through the grant Progetti Premiali 2012 - iALMA (CUP C52I13000140001).
J.-C.G. thanks the Centre National d'Etudes Spatiales (CNES) for a grant.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 346 |
/* $NetBSD: ufsmount.h,v 1.7 1998/03/18 15:57:29 bouyer Exp $ */
/*
* Copyright (c) 1982, 1986, 1989, 1993
* The Regents of the University of California. All rights reserved.
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* This product includes software developed by the University of
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* 4. Neither the name of the University nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
* @(#)ufsmount.h 8.6 (Berkeley) 3/30/95
*/
/*
* Arguments to mount UFS-based filesystems
*/
struct ufs_args {
char *fspec; /* block special device to mount */
struct export_args export; /* network export information */
};
/*
* Arguments to mount MFS
*/
struct mfs_args {
char *fspec; /* name to export for statfs */
struct export_args export; /* if exported MFSes are supported */
caddr_t base; /* base of file system in memory */
u_long size; /* size of file system */
};
#ifdef _KERNEL
struct buf;
struct inode;
struct nameidata;
struct timeval;
struct ucred;
struct uio;
struct vnode;
struct netexport;
/* This structure describes the UFS specific mount structure data. */
struct ufsmount {
struct mount *um_mountp; /* filesystem vfs structure */
dev_t um_dev; /* device mounted */
struct vnode *um_devvp; /* block device mounted vnode */
u_int32_t um_flags; /* UFS-specific flags - see below */
union { /* pointer to superblock */
struct fs *fs; /* FFS */
struct lfs *lfs; /* LFS */
struct m_ext2fs *e2fs; /* EXT2FS */
} ufsmount_u;
#define um_fs ufsmount_u.fs
#define um_lfs ufsmount_u.lfs
#define um_e2fs ufsmount_u.e2fs
#define um_e2fsb ufsmount_u.e2fs->s_es
struct vnode *um_quotas[MAXQUOTAS]; /* pointer to quota files */
struct ucred *um_cred[MAXQUOTAS]; /* quota file access cred */
u_long um_nindir; /* indirect ptrs per block */
u_long um_bptrtodb; /* indir ptr to disk block */
u_long um_seqinc; /* inc between seq blocks */
time_t um_btime[MAXQUOTAS]; /* block quota time limit */
time_t um_itime[MAXQUOTAS]; /* inode quota time limit */
char um_qflags[MAXQUOTAS]; /* quota specific flags */
struct netexport um_export; /* export information */
u_int64_t um_savedmaxfilesize; /* XXX - limit maxfilesize */
};
/* UFS-specific flags */
#define UFS_NEEDSWAP 0x01 /* filesystem metadata need byte-swapping */
/*
* Flags describing the state of quotas.
*/
#define QTF_OPENING 0x01 /* Q_QUOTAON in progress */
#define QTF_CLOSING 0x02 /* Q_QUOTAOFF in progress */
/* Convert mount ptr to ufsmount ptr. */
#define VFSTOUFS(mp) ((struct ufsmount *)((mp)->mnt_data))
/*
* Macros to access file system parameters in the ufsmount structure.
* Used by ufs_bmap.
*/
#define MNINDIR(ump) ((ump)->um_nindir)
#define blkptrtodb(ump, b) ((b) << (ump)->um_bptrtodb)
#define is_sequential(ump, a, b) ((b) == (a) + ump->um_seqinc)
#endif /* _KERNEL */
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,657 |
Check these Limo vehicles from 14 companies in Angeles, Pampanga* and send us request to compare rates!
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} | 3,032 |
De Hoogbrugstraat (Maastrichts: Hoegbrögkstraot) is een straat in het stadsdeel Wyck, in het centrum van de Nederlandse stad Maastricht. De straat is van middeleeuwse, mogelijk vroegmiddeleeuwse oorsprong. Vanaf de veertiende eeuw was het een van de drukste straten van Maastricht, waar zich veel kooplieden en neringdoenden vestigden. Tegenwoordig is het een vrij rustige woon-, winkel- en horecastraat met een overwegend zeventiende en achttiende-eeuwse bebouwing. De straat telt 60 rijksmonumenten en 16 gemeentelijke monumenten.
Naamgeving
De straatnaam Hoogbrugstraat (vroeger Hoogebrugstraat of Hoogbruggestraat) dateert mogelijk uit de middeleeuwen en verwijst naar de Hoogebrug of Hoogbrugge, de (letterlijk) hoge brug over de verdwenen Maasarm buiten de Hoogbruggepoort. Deze poort werd later aangeduid als Duitse of Aker Poort. De naam Hoogbrugge wordt voor het eerst genoemd in 1296. Op plattegronden uit de eerste helft van de negentiende eeuw staat de straatnaam meestal in het Frans aangegeven: Rue haut pont. Mogelijk heette de straat eerder Oude Straat (Aw Straot).
Er zijn meer straatnamen in Maastricht die verwijzen naar bruggen. In het verlengde van de Sint Servaasbrug bevindt zich op de linker Maasoever de Maastrichter Brugstraat. Op de rechter Maasoever ligt de Wycker Brugstraat. De Hoge Brug uit 2003 heeft niets met de historische Hoogbrugge of Hoogbrugstraat te maken. Evenmin is er een verband met Hoge Barakken, waarbij het bijvoeglijk naamwoord betrekking heeft op de ligging nabij de Hoge Maaspunt.
Ligging
De Hoogbrugstraat ligt in het stadsdeel Wyck op de rechter Maasoever van het Maastrichtse centrum. De straat loopt min of meer van oost naar west tussen Hoogbrugplein en (nu) Waterpoort. Oorspronkelijk zette de Hoogbrugstraat zich in westelijke richting voort tot aan de Maasoever. Omdat de straat aan het (west)einde enigszins afbuigt naar het noorden, verloopt de aansluiting met de zuid-noord lopende Rechtstraat via een flauwe bocht. Er zijn vijf zijstraten, waarvan drie aan de noordzijde. Van oost naar west: Lage Barakken, Wycker Grachtstraat en Rechtstraat. Ook is hier een voetgangerspassage naar het Bourgogneplein, waarvan de ingang gevormd wordt door een poort in het pand Hoogbrugstraat 28. Aan de zuidzijde liggen twee zijstraten: Hoge Barakken en Ruiterij. Daarnaast is er een doorgang voor voetgangers naar de Hoge Barakken, bereikbaar via een poort in Hoogbrugstraat 15. De Hoogbrugstraat is ongeveer 250 m lang en varieert sterk in breedte: van circa 5 m bij de bocht naar de Rechtstraat, tot 25 m bij de aansluiting op het Hoogbrugplein.
Verkeer en inrichting
In de gehele straat is gemotoriseerd verkeer toegestaan in beide richtingen. Door zijn afzijdige ligging ten opzichte van de Maasbruggen heeft de straat geen functie voor het doorgaand verkeer en rijden er geen lijnbussen. Parkeren is uitsluitend toegestaan in de aangegeven parkeervakken, tegen betaling (via parkeerautomaten). Door de wisselende breedte is de straat niet uniform ingericht; wel is er over de gehele lengte één rijbaan (niet gescheiden en zonder fietsstroken) en zijn er aan beide zijden trottoirs. Door de onregelmatige rooilijn varieert de stoepbreedte aanzienlijk. Op het smalste punt bedraagt deze nauwelijks een meter; elders bevinden zich pleinachtige ruimtes tussen de rijweg en de huizen. Waar de breedte het toelaat, zijn parkeervakken aangegeven (voor langs- of dwarsparkeren). Op diverse plaatsen, onder andere bij in- en uitritten, zijn anti-parkeerpaaltjes geplaatst. Verder is er ruimte gereserveerd voor fietsenrekken, bomen en zitbanken. Met uitzondering van het westelijk deel, is de rijweg geasfalteerd en zijn de parkeervakken en trottoirs geplaveid met kasseien (bij de trottoirs diagonaal gelegd). Het gedeelte van de straat ten westen van Wycker Grachtstraat heeft een afwijkende (tijdelijke?) inrichting met betonstraatsteen (rijweg) en ruitvormig gelegde natuurstenen tegels. Parkeervakken zijn hier onderdeel van het trottoir, gemarkeerd door een afwijkende bestrating en stoeptegels met de letter P.
Geschiedenis
De geschiedenis van het gebied rond de Hoogbrugstraat wordt voor een deel bepaald door de ligging tussen de historische Maasbruggen en de belangrijkste stadspoort van Wyck. Door de aanleg van de 'Percée' in de late negentiende eeuw, verloor de straat die functie en verpauperde ze. In de tweede helft van de twintigste eeuw werden veel monumentale panden opgeknapt en kreeg de straat een deel van zijn oude glorie terug.
Romeinse tijd en middeleeuwen: ontstaansgeschiedenis
Archeologische waarnemingen in de omgeving van het kruispunt Hoogbrugstraat/Ruiterij/Waterpoort/Rechtstraat tonen aan dat dit gebied in de Romeinse tijd en in de vroege middeleeuwen bewoond was. De aard en omvang van de Romeinse nederzetting op de rechter Maasoever zijn nog nauwelijks onderzocht. Wel is duidelijk dat de bewoning in dit gebied direct gerelateerd was aan het bestaan van de Romeinse brug, die op de rechteroever aanlandde ter hoogte van Stenenwal 15 (alwaar een gedenksteen in het plaveisel is ingemetseld). De aanlanding lag echter ergens in het midden van de huidige stroomdraad, omdat de Wycker oever door riviererosie – en door afgraving – in de loop der eeuwen is opgeschoven naar het oosten. De Romeinse hoofdweg van Boulogne-sur-Mer naar Keulen, pas sinds het einde van de twintigste eeuw Via Belgica genoemd, boog na de brug af naar het noorden, waarbij halverwege de latere Rechtstraat werd gekruist, om via het Geuldal zijn weg verder oostwaarts te vervolgen. Een zuidelijke aftakking vanaf de brug richting Aken, in later eeuwen aangeduid als Oude Akerweg, ontstond waarschijnlijk in de zevende of achtste eeuw. Deze volgde het tracé van de Hoogbrugstraat, waarna ook verder van de rivier vandaan bewoning zal zijn ontstaan.
De voorstad Wyck is in de middeleeuwen altijd veel kleiner gebleven dan het stadsdeel op de linker Maasoever. In feite bestond Wyck uit twee hoofdstraten: de min of meer parallel aan de Maas lopende Rechtstraat en de dwars daarop gepositioneerde Hoogbrugstraat. Volgens de Maastrichtse stadsarcheoloog Titus Panhuysen werd deze kleine woonkern al aan het einde van de twaalfde eeuw beschermd door een aarden verdedigingswal met palissaden en een gracht. De vestingdeskundige Louis Morreau houdt het op de dertiende eeuw als ontstaansperiode van de eerste verdedigingsgordel, waaraan de namen Wycker Grachtstraat en Wycker Grachtje herinneren. Een groot deel van de huidige Hoogbrugstraat lag buiten deze omwalling, inclusief het Sint-Gillishospitaal, dat al in 1286 wordt genoemd als bezit van het Onze-Lieve-Vrouwekapittel. In de veertiende eeuw verloor de aarden wal zijn functie door de bouw van de verder oostwaarts gelegen Wycker stadsmuur. De nieuwe muur volgde ongeveer het tracé van de Hoge en Lage Barakken, waardoor het stadsdeel iets meer ruimte kreeg en de Hoogbrugstraat in zijn geheel binnen de ommuurde stad kwam te liggen. De stadsmuur van Wyck had een lengte van ca. 1500 m en telde twaalf muurtorens, twee veldpoorten en enkele kleinere waterpoorten.
In het noorden van Wyck lag de Sint-Maartenspoort, maar de voornaamste poort was de Hoogbruggepoort, vanaf de achttiende eeuw Wycker-, Aker- of Duitse Poort ("Poort Almagne") genoemd. Het was een rechthoekig bouwwerk met een hoog zadeldak en een ruim vijf meter hoge poortdoorgang met een gotisch gewelf en voorzien van een valhek. Waarschijnlijk werd de poort in de vijftiende eeuw uitgebreid met twee ronde, in de gracht uitgebouwde muurtorens, die door zware muren met het bestaande bouwwerk werden verbonden. Rondom de Wycker stadsmuur lag een Maasarm, die het gehele stadsdeel omspoelde. Na het Beleg van 1407-1408, waarbij de Luikenaren het vooral op Wyck gemunt hadden, werd in 1412 de brug over de Maasarm bij de Hoogbruggepoort herbouwd in steen. De stenen Hoogbrugge, met zijn tien bogen, werd gerekend tot de drie Maasbruggen van Maastricht, en was met zijn steile helling met recht een 'hoge brug'.
Ancien régime: hoofdverkeersweg en handelsstraat
In de stedenatlas Civitates orbis terrarum van Braun en Hogenberg is zowel een plattegrond als een vogelvluchtperspectief van Maastricht afgedrukt, beide omstreeks 1575 ontstaan. Ze laten zien dat de Hoogbrugstraat, hoewel niet direct aansluitend op de Maasbrug, toch gunstig gelegen was tussen die brug en de belangrijkste stadspoort van Wyck, de Hoogbruggepoort, die in 1543 was gemoderniseerd. Al het verkeer vanuit of in de richting van Aken, Keulen, Mainz of Frankfurt am Main moest gebruik maken van die poort, en dus ook van de Hoogbrugstraat, om zonder omwegen de brug te bereiken of de stad te verlaten.
Een pentekening van de Hoogbrugstraat uit 1669, toegeschreven aan Valentijn Klotz, verschaft veel informatie. De tekenaar staat met zijn rug naar de Hoogbruggepoort en kijkt naar het westen. De vele luifels en uitgestalde waren geven aan dat hier ambachtslieden en handelaren gevestigd waren. Het bredere deel van de straat, vlak bij de poort, was tevens in gebruik als moesmarkt. De tekening geeft tegelijkertijd inzicht in de transformatie van houtskeletbouw naar steen, die de straat in deze periode onderging. Rechts, aan de noordzijde, zijn nog diverse vakwerkgevels te zien. Aan de overkant heeft de verstening al plaatsgevonden en is een rijtje 'moderne' krul- en trapgevels te zien. Verderop zijn aan de zuidzijde het Sint-Gillishospitaal (met klokkentoren) en de hoge puntgevel van de Poort van Beusdael te herkennen, en de torens van de Onze Lieve Vrouwekerk op de linker Maasoever.
Het middeleeuwse hospitaal of gasthuis van Sint-Gillis had in de zeventiende een militaire bestemming, wat op de tekening te zien is aan het huisje van de schildwacht. Het pand fungeerde als de hoofdwacht voor Wyck. In 1757 werd het gebouw teruggegeven aan het Onze-Lieve-Vrouwekapittel en werd er een oudevrouwenhuis in gevestigd. De Poort van Beusdael was in de zestiende eeuw de stadsresidentie van de heren van Beusdael. In 1669, ten tijde van de tekening, was het huis eigendom van het Akense magistratengeslacht Colyn. In 1686 werd het verkocht aan de Eijsdenaar Michiel Peerboom, een rijke koopman, die in Wyck onder andere de bierbrouwerij De Vels bezat. Mogelijk is achter het meeste linkse huis op de tekening een ander poorthuis te zien, de Poort van Gulpen, waarover verder geen gegevens bekend zijn.
Ook in de achttiende eeuw was de Hoogbrugstraat een drukke verkeersstraat, die leidde naar de uitvalswegen naar Aken, het Land van Dalhem en Luik. De Hoogbruggepoort verwerkte meer verkeer dan welke andere stadspoort in Maastricht. Samen met de Rechtstraat, de Muntstraat en de Grote Staat, had de Hoogbrugstraat de grootste winkeldichtheid in Maastricht. Anderzijds hadden de winkels in Wyck lange tijd minder prestige dan bijvoorbeeld die in de Grote Staat of op het Vrijthof; de huurwaarde lag er namelijk een stuk lager. Hetzelfde kan ook geconcludeerd worden uit het feit dat omstreeks 1800 slechts één winkel in de Hoogbrugstraat niet-eigen personeel in dienst had (in de Rechtstraat waren dat er vijf; in de Grote Staat zeven).
Op achttiende-eeuwse plattegronden – en meer nog op de omstreeks 1750 vervaardigde Franse Maquette van Maastricht – is een groot deel van de huidige bebouwing van de Hoogbrugstraat te herkennen. Achter de aaneengesloten huizenrijen liggen voornamelijk tuinen en boomgaarden. Ten zuiden van de straat ligt een kazernecomplex, de Hoge Barakken. Dat zich in deze tijd veranderingen aankondigden, illustreert het voorbeeld van de ondernemersfamilie Rouffaer. Begin achttiende eeuw bezaten de Rouffaers een handel in granen, brandewijn, haring, kaas en specerijen aan de Rechtstraat, later aangevuld met een jeneverstokerij aan de Kaleminkstraat en een oliemolen en gistfabriekje aan de Ruiterij. Arnold Rouffaer (1748-1818) liet in 1790 drie huizen in de Hoogbrugstraat afbreken en bouwde er een groot handelshuis voor in de plaats, het Huis Rouffaer. Achter het huis lag een bedrijfsterrein met diverse opstallen, dat doorliep tot aan de Wycker Grachtstraat.
Na de inname van de stad door Kléber in 1794 was Maastricht twintig jaar lang een Franse stad. De anti-klerikale politiek van de Fransen betekende het einde van alle kloosters en kerkelijke liefdadigheidsinstellingen, waardoor ook het Sint-Gillishospitaal een burgerlijk bestuur kreeg. Anderzijds bood de Franse Tijd nieuwe kansen aan een kleine groep ondernemers.
Negentiende eeuw: industrialisatie en verpaupering
In de loop van de negentiende eeuw veranderde het karakter van de straat, eerst door de vestiging van industrieën in de directe omgeving, later door de sloop van stadsmuren en vestingwerken en de daarmee samenhangende verschuiving van verkeersstromen.
Op de kadastrale minuutkaart van circa 1823 zijn alle percelen aan de Hoogbrugstraat nauwkeurig ingetekend. Uit een vergelijking met de kadastergegevens van 1842 valt op te maken welke percelen toen in gebruik waren als bedrijfsterrein. Te zien is dat het grote perceel van de handelsonderneming Rouffaer eigendom is van de kinderen van Johan Rouffaer (1780-1834), maar in werkelijkheid was de onderneming een jaar eerder, in 1841, verkocht. Blijkbaar was er geen opvolger binnen de familie te vinden. In 1887 vestigden zich hier de Zusters Missionarissen van Onze Lieve Vrouw van Afrika, een Franse missiecongregatie, die echter in 1893 alweer vertrokken. Aan de overkant van de straat lagen het wijnpakhuis en de "suikerijmolen" van Noël Gregoire Lallemand en de brouwerij van Jan Dolmans. Verderop, eveneens aan de zuidzijde, lag de brouwerij annex herberg "De Prince van Luijck", lange tijd in bezit van de familie Gilissen. In de negentiende eeuw was de brouwerij eigendom van Alexander Coenegracht. Aan het einde van die eeuw werd het bedrijf overgenomen door J. Zintzen. De groothandelaar Alexander Coenegracht bezat rond 1800 tevens een zoutziederij annex zeepfabriek op de hoek Hoogbrugstraat-Hoge Barakken, gedeeltelijk grenzend aan de brouwerij. In 1842 waren beide bedrijven volgens de kadasterkaart in handen van zijn weduwe.
Een andere zout- en zeepziederij werd in 1835 opgericht door twee dynamische entrepreneurs: Nicolaas Antoon Bosch (1797-1857) en Wijnand Nicolaas Clermont (1802-1879). Bosch bezat al een aantal bedrijven in Wyck, waaronder de brouwerij De Keyzer; voor Clermont was het waarschijnlijk de eerste onderneming. Het bedrijf werd gevestigd op het achterterrein van de Poort van Beusdael, waar van 1834 tot circa 1850 tevens het glas-in-loodatelier van de Franse broers Toussaint en Antoine Cartisser gevestigd was. Blijkbaar was het pand, met een perceelsgrootte van 930 m², ruim genoeg om twee bedrijven te huisvesten. De samenwerking tussen Bosch en Clermont eindigde waarschijnlijk in 1851, toen laatstgenoemde met een andere zakenpartner een aardewerkfabriek begon, pal naast de zout- en zeepziederij (ongeveer ter plekke van de huidige Ruiterij). Uit dit bedrijf kwam in 1863 de Société Céramique voort, die in korte tijd uitgroeide tot verreweg de grootste werkgever in Wyck. Het is bekend dat Wyck-zuid omstreeks 1900 het armere deel van Wyck was, met relatief veel 'huurkazernes'. Hoewel nooit onderzocht, mag worden aangenomen dat er een verband bestaat met de aanwezigheid van de Société Céramique en enkele kleinere fabrieken in deze omgeving.
In 1867 werd de vestingstatus van Maastricht opgeheven, waarna grote delen van de middeleeuwse stadsmuren en buitenwerken werden afgebroken. Oorspronkelijk was het de bedoeling dat de Aker Poort als historisch monument behouden zou blijven, maar enkele ondernemers van de Hoogbrugstraat waren het daar niet mee eens en begonnen in september 1868 eigenhandig met de sloop, waarna de autoriteiten besloten dat de bouwvallig geworden poort dan maar afgebroken moest worden. De Maasarm werd in de jaren daarna gedempt en de Hoogbrugge, net buiten de Duitse Poort gelegen, werd gesloopt. De sloop van de vestingwerken maakte in de jaren 1880 de aanleg mogelijk van de Percée (Frans: doorbraak), die de Maasbrug (Sint Servaasbrug) in rechte lijn zou verbinden met het (toekomstige) station, een plan dat al vóór 1867 bestond. De nieuwe straat nam binnen de kortste keren de verkeersfunctie van de Hoogbrugstraat vrijwel geheel over. Als gevolg daarvan verhuisden veel winkels naar de Percée; er voor in de plaats kwamen cafés. In de statige huizen woonden arbeidersgezinnen in een- en tweekamerwoningen. De sloop van de vestingwerken betekende dus indirect de devaluatie van de Hoogbrugstraat van hoofdstraat naar achterafstraat, waardoor er weinig geïnvesteerd werd. Enerzijds werkte dat de verkrotting in de hand, anderzijds betekende het het behoud van relatief veel monumentale panden.
Na 1900: herstel en herwaardering
Na de bouw van het nieuwe Station Maastricht (1913-1915) in de as van de Percée verplaatste het verkeer zich naar de reeds langer bestaande spoorwegovergang aan de Akerstraat, in het verlengde van de Hoogbrugstraat. Het verkeer bleef echter de smalle Hoogbrugstraat mijden en maakte nu gebruik van de Wilhelminasingel om de spoorwegovergang te bereiken, meer nog na het gereedkomen van de Wilhelminabrug in 1932.
Omdat grote delen van Wyck in het winterbed van de Maas lagen, deden zich geregeld overstromingen voor, zoals op een foto uit 1926 is te zien. Door de kanalisatie van de rivier en de demping van de Oude Maasarm in het Wyckerveld gedurende de werkverschaffing in de jaren 1930, is in het centrum van de stad de kans op hoogwater aanzienlijk afgenomen.
De Tweede Wereldoorlog liet ook in de Hoogbrugstraat sporen achter. Al op 10 mei 1940, tijdens de kortdurende Slag om Maastricht, trokken de Duitse tanks door de straat, op weg naar de inderhaast aangelegde noodbrug over de Maas (de bestaande bruggen waren door Nederlandse springcommando's onklaar gemaakt). Weerstand werd tevergeefs geboden door een sectie van het grensbataljon van het 13e Regiment Infanterie, waaraan een plaquette aan de gevel van Hoogbrugstraat 9 herinnert. Op de hoek van de Wycker Grachtstraat sloeg op 11 mei 1940 een geallieerde bom in, die waarschijnlijk bedoeld was voor de Duitse noodbrug. Het pand werd geheel verwoest. De Joodse bewoners van nr. 39 overleefden de oorlog niet. De ongehuwde zussen Mathilde Esther (1884-1942) en Irma Hélène Beesman (1886-1942) werden beiden op 31 augustus 1942 vermoord in Auschwitz. Hun inwonende neef, Karel Dahl (1910-1945), werd na een verblijf in diverse Silezische werkkampen op 11 maart 1945 vermoord in het buitenkamp Bad-Warmbrunn.<ref>[https://www.struikelsteentjes-maastricht.nl/uimg/struikelsteentjes/b68048_att-8.-karel-dahl-en-dames-beesman-2.pdf ] op struikelsteentjes-maastricht.nl.</ref> Sinds 2018 houden drie struikelsteentjes op de stoep voor hun woning de herinnering levend.
In 1959 werd het Sint-Martinushuis geopend, een katholiek wijkcentrum gevestigd in het pand Hoogbrugstraat 42. Het was het eerste 'categoriale' buurthuis in Nederland, bedoeld voor het 'onmaatschappelijke' deel van de Sint-Martinusparochie in Wyck-zuid. Het wijkgebouw was tevens de thuisbasis van de in 1957 opgerichte Wieker Fanfare Sint Franciscus. Vanwege het feit dat de bevolking van Wyck zich vernieuwd had – veel 'onmaatschappelijken' waren verhuisd naar de buitenwijken – en omdat na een renovatie de huur te hoog werd, verhuisde het buurthuis in 1992 naar de Ambachtsschool aan de Sint Maartenslaan.
In 1971 eiste een brand in het monumentale cafépand Hoogbrugstraat 41 twee levens. In 1978 woedde een grote brand in hotel-café 't Brandpunt op de hoek van de Lage Barakken.
Eind jaren 1970 leidde de stadsvernieuwing in Oud-Wyck tot het opknappen van meerdere vervallen panden in de Hoogbrugstraat. De opening van Hotel Maastricht in 1977 betekende een impuls voor de verpauperde zuidwesthoek van Wyck. Aanvankelijk behoorde ook het rijksmonument Hoogbrugstraat 69 tot het hotel. In 1982 ging de stadsvernieuwing van start op het terrein tussen Hoogbrugstraat, Wycker Grachtstraat, Bourgognestraat en Lage Barakken, destijds aangeduid als 'Stadsvernieuwingsplan Wyck C-2', vanaf 1986 Bourgogneplein genoemd. De bestaande inrijpoort van het rijksmonument Hoogbrugstraat 28 werd aangepast ten behoeve van een voetgangerspassage naar het nieuwe woongebied. In 1983 werd de Hoogstraat heringericht, waarbij de rijweg werd opgeschoven om plaats te maken voor vijftig parkeerplaatsen en bredere stoepen. Er kwamen enkele zitbanken en aan de zijde van de Akerstraat werden bomen geplant.
In de jaren 1990 werd ten zuiden van de Hoogbrugstraat de wijk Céramique aangelegd op de voormalige fabrieksterreinen van de Société Céramique. Achter de bebouwing aan de Hoogbrugstraat werd een nieuwe straat aangelegd met een oude naam, Hoge Barakken. De inrijpoort van het rijksmonument Hoogbrugstraat 15 werd aangepast en fungeert thans als doorgang naar de nieuwe straat. Het relatief brede deel van de Akerstraat tussen Wilhelminasingel en Hoogbrugstraat, dat stedenbouwkundig eerder bij de Hoogbrugstraat hoort, kreeg de naam Hoogbrugplein. Ook de omgeving van de Ruiterij kreeg een opknapbeurt.
Door de sterke groei van het toerisme in Nederland – en met name door de populariteit van stedentrips en 'funshoppen' – werd ook het stadsdeel Wyck ontdekt als 'best bewaarde geheim van Maastricht'. Het leidde in de eerste plaats tot een herwaardering van de Rechtstraat als populaire winkel- en uitgaansstraat, maar ook de Hoogbrugstraat heeft daar, in iets mindere mate, van geprofiteerd. De vestiging van enkele coffeeshops zorgde voor een vorm van toerisme, waar niet iedereen blij mee was. Anno 2021 zijn vrijwel alle monumentale gebouwen gerestaureerd en is er weinig leegstand van winkels, waarbij moet worden aangetekend dat veel winkelpanden in de loop van de twintigste eeuw zijn verbouwd tot horecagelegenheden of woningen.
Architectuur en beeldhouwkunst
De bebouwing aan de Hoogbrugstraat bestaat grotendeels uit woonhuizen uit de zeventiende en achttiende eeuw, veelal in de traditionele stijl van de Maaslandse renaissance, soms in een van de Lodewijkstijlen. Zestig panden zijn rijksmonumenten, waarmee de straat op vier na de meest monumentrijke straat van Maastricht is. Daarnaast telt de straat zestien gemeentelijke monumenten. Vrijwel alle huizen zijn opgetrokken in rode of bruine baksteen, vaak met horizontale banden en lijsten van natuursteen (meestal Naamse steen), soms met verticale pilasters of lisenen, soms ook met versierde sluitstenen boven de segmentbogige vensters, in een enkel geval met een hoofdgestel met gebeeldhouwde consoles. Een groot aantal huizen bezit een gevelsteen. Van veel huizen is de begane grond in de negentiende of twintigste eeuw gewijzigd door moderne winkelpuien.
Noordelijke straatwand (even nummers)
In het oostelijk deel van de noordelijke straatwand bevinden zich diverse gave panden. Nr. 6, volgens de gevelsteen uit 1764 en "IN HET CASTEEL VAN LIMBORG" genaamd, is een huis met een hoge lijstgevel, voorzien van segmentboogvensters in Naamse steen. De pui is geheel van Naamse steen. In het interieur bevinden zich enkele schoorsteenmantels in Lodewijk XVI-stijl. De gevel van nr. 10 is veel smaller en lager, maar heeft eveneens een pui van Naamse steen. De muurvlakken daarboven zijn wit geschilderd. De nrs. 14 en 18 hebben beide ovale, met hardsteen omlijste vensters op de zolderverdieping. Laatstgenoemd pand heeft een zeventiende-eeuwse achtergevel; de voorgevel is in 1765 vernieuwd en voorzien van een gevelsteen, "IN DEN WITTEN ENGEL".
Een fraai voorbeeld van een zeventiende-eeuwse gevel is te zien op nr. 26, ondanks het feit dat de pui is gewijzigd en de kruiskozijnen zijn uitgebroken. De gevel is opgebouwd uit veldbrandsteen, Limburgse mergel en Naamse steen en eindigt in een hoofdgestel met geprofileerde consoles. Het naastgelegen pand nr. 28 was vroeger een herberg, "A la clef d'or" geheten, waaraan de gouden sleutel in het snijraam boven de voordeur herinnert. Het brede pand heeft een lijstgevel met horizontale banden en kozijnen van Naamse steen. Links bevindt zich een koetspoort met een omlijsting van Naamse steen en een sluitsteen met het jaartal 1711. De poort geeft toegang tot het Bourgogneplein, waaraan een achterbouw uit 1705 grenst. In het interieur bleven onder andere een Lodewijk XV- en een empireschoorsteenmantel bewaard.
Ook de nummers 30 t/m 36 hebben fraaie achttiende-eeuwse lijstgevels, hoewel nr. 32 een vernieuwde pui heeft. De gevel van nr. 36 in Lodewijk XVI-stijl is van dit rijtje de meest sierlijke. Deze bestaat geheel uit Naamse steen en bezit onder andere gebeeldhouwde pilasters met trofeeën, boven de ingang een gebeeldhouwde bovendorpel, onder de Franse ramen gebeeldhouwde panelen met guirlandes en gekruiste looftakken, op de eerste verdieping een gebogen fronton met een profielkop in een medaillon, en een hoofdgestel met eierlijst. Ook inwendig zijn plafonds en schoorsteenmantels uit de Lodewijk XVI-periode bewaard gebleven.Van den Boogard/Minis (2001), p. 131. De lijstgevel van nr. 42 bestaat uit twee smalle en drie bredere traveeën, en is mogelijk in de achttiende eeuw ontstaan door samenvoeging van twee panden. De kap met dakkapellen dateren uit het tweede kwart van de negentiende eeuw. Ernaast ligt op nr. 44 een pand uit de late achttiende eeuw met een gave lijstgevel, die geheel uit Naamse steen is opgetrokken, en een mansardedak. Bijzondere details zijn de geblokte hoekdammen, de gekoppelde deur- en vensteromlijstingen, en de panelen op de begane grond en in de attiek.
De nummers 46 t/m 56 vormen een rijtje van relatief smalle en hoge panden met lijstgevels van baksteen en Naamse steen, alle voorzien van een gevelsteen. Bij de laatste drie panden (52 t/m 56) zijn de muurvlakken van baksteen wit geschilderd, waardoor het constrast met de natuurstenen geveldelen wordt vergroot. De laat-achttiende-eeuwse gevel van nr. 58 is geheel van Naamse steen en is versierd met geblokte muur- en hoekdammen, gebeeldhouwde sluitstenen (bij het centrale venster met een masker), op de begane grond panelen met diamantkoppen, en een attiek met een rozet. In het interieur bevindt zich een trap, enkele schoorsteenmantels en een alkoofomlijsting in Lodewijk XVI-stijl. Het hoekpand Hoogbrugstraat 62, op de hoek van de Wycker Grachtstraat, werd in mei 1940 bij een luchtbombardement verwoest en een jaar later in historiserende stijl herbouwd.
Het tegenoverliggende hoekhuis op nr. 64 heeft aan de kant van de Hoogbrugstraat een lijstgevel met horizontale en verticale banden van Naamse steen. De pui bestaat geheel uit Naamse steen. De centrale ingang wordt geflankeerd door vensters, alle met segmentbogen, en met paneelwerk onder de vensters. Boven de entree is een grote gevelsteen geplaatst met een zonnewijzer en de tekst "17 IN DE SONWIJSER 86". De zijgevel aan de Wycker Grachtstraat is zeventiende-eeuws met later toegevoegde vensteropeningen. Door het egaal wit schilderen van de gevel is het contrast tussen de (incomplete) mergelstenen banden en de bakstenen muurdelen verloren gegaan. De natuurstenen vensteromlijstingen van de twee benedenvensters zijn niet mee geschilderd, net zo min als de talrijke muurankers.
Voor een beschrijving van het indrukwekkende koopmanshuis op nr. 72, zie: Huis Rouffaer. De smalle gevels ter linker- en ter rechterzijde hebben allemaal vernieuwde puien. Min of meer origineel is de wit geschilderde gevel van nr. 78, in feite de zijgevel van Rechtstraat 83, met onder andere drie segmentboogvormige vensters, omlijst met Naamse steen, waarvan het meest rechtse is gekoppeld met een ingang, en diverse muurankers.
Zuidelijke straatwand (oneven nummers)
In het negentiende-eeuwse hoekpand met de Hoge Barakken was vroeger Café Céramique gevestigd. Voor een beschrijving zie aldaar. Het pand ernaast (nr. 3) heeft een achttiende-eeuwse lijstgevel met gevelsteen "17 IN HET GROEN HUIS 68", maar de vakwerkgevel aan de oostzijde toont aan dat het huis veel ouder is. Hoogbrugstraat 9 heeft een eenvoudige baksteengevel met hardstenen deur- en venster omlijstingen en een gedenksteen die herinnert aan de gevechten die hier op 10 mei 1940 plaatsvonden. Het naastgelegen pand op nr. 11 domineert door zijn hoogte en breedte dit deel van de zuidelijke straatwand. Het betreft het brouwershuis annex herberg "De Prince van Luijck". De gevel is zes traveeën breed en drie verdiepingen hoog. Het pand bezit bovendien een hoge kap. De twee middentraveeën vormen een risaliet met een frontonachtige bekroning, waarin een oculusvenster is aangebracht, versierd met een festoen. Eveneens onderdeel van de middenrisaliet is de grote, rondbogige koetspoort in een omlijsting van Naamse steen. In de poortomlijsting is een gevelsteen met een fruitboom en de tekst "IN DEN KEERSSE / 17 BOEM 52" geplaatst. De regelmatig over de gevel verdeelde segmentboogvensters zijn omlijst met Naamse steen. In het interieur zijn nog een Lodewijk XV-trappenhuis en Lodewijk XVI-tegelschouwen aanwezig..
Ook de twee aansluitende panden (nrs. 13 en 15) zijn met vijf traveeën breder dan de meeste huizen in de straat, maar minder breed en ook minder hoog dan nr. 11. Beide huizen hebben een grote, met Naamse steen omlijste poort, die bij het eerste pand rechts in de gevel, bij het tweede links geplaatst is. Die laatste poort geeft sinds circa 1995 toegang tot de achtergelegen straat Hoge Barakken. Bij het linkerpand is de poort tevens de entree; het rechterpand heeft een extra deur ten behoeve van het daar gevestigde restaurant. Opvallend bij nr. 13 is de zeer hoge kap waarin drie extra woonlagen zijn ondergebracht. De regelmatig geplaatste vensters zijn bij beide panden omlijst met Naamse steen. De bakstenen geveldelen zijn bij het rechterpand wit geverfd. Dit pand bezit tevens enkele interieurelementen in Lodewijk XVI-stijl..
Na nr. 15 volgt een rijtje kleinere huizen waarvan de rooilijn bovendien enkele meters naar voren springt. De meeste gevels zijn slechts twee traveeën breed en twee verdiepingen hoog, wel met hoog opgaande daken. Nr. 19 springt het meest in het oog met de enige rolwerkgevel in Wyck. Bijzonder is dat deze gevel zich verheft boven een deels doorbroken hoofdgestel in typisch Maaslandse renaissancestijl. De mergelstenen delen van de gevel zijn niet als zodanig herkenbaar door de egaal witte verflaag. Wel zijn bij een recente restauratie de delen van Naamse steen ontdaan van de verflagen. De gevelsteen vermeldt slechts het jaartal 1694.
Na deze reeks zeventiende en achttiende-eeuwse panden volgt een dubbel woonhuis in eclectische stijl, dat hier enigszins uit de toon valt. De huizen zijn in 1902 gebouwd in opdracht van de Société Céramique. Meest opvallend zijn de tegeltableaus van de plateelschilder Henri Breetvelt onder de vensters van de eerste verdieping, met voorstellingen van 'Hollandse' landschappen. De tegels van nr. 33 zijn in Delfts blauwe stijl, die van nr. 35 in sepiatinten. Onder de goot is een over de twee panden doorlopende strook met decoratieve tegels aangebracht, hier met kleurrijke florale motieven. Breetveld was van 1902 tot 1906 (1909?) in dienst van de Société Céramique.
Het Sint-Gillishospitaal (nr. 37) en de Poort van Beusdael (nr. 43), beide van (laat)middeleeuwse oorsprong, worden elders uitgebreid beschreven. De tussengelegen panden op nr. 39 en 41 zijn redelijk gave achttiende-eeuwse woonhuizen, die met hun lage, wit geschilderde lijstgevels haast gespiegeld lijken. De deuren en vensters zijn met Naamse steen omlijst, bij het linkerpand alleen op de begane grond. Vóór dit pand liggen drie stolpersteine'' (zie hierboven). Het rechterpand bezit een jaarsteen met het jaartal 1784.
Hoogbrugstraat 45 is een opvallend bouwwerk, niet alleen door zijn ligging, bijna in de as van de straat, maar ook door zijn hoogte en opvallende architectuur. Het hoekpand dateert uit 1903 en is gebouwd in historiserende stijl met elementen van de chaletstijl. Het pand heeft drie bouwlagen en een zolderverdieping onder een mansardedak. De noordoostelijke hoek wordt gemarkeerd door een vierkante toren met een overkragend tentdak, bekroond door een piron. De hoek wordt naar beneden toe tweemaal afgeschuind. De daardoor ontstane overstekken, evenals de pseudo-vakwerkgevels boven de pui, geven het gebouw een 'middeleeuws' aanzien. De pui bestaat uit een hoge zandstenen plint met daarboven rode baksteen. De vensters zijn voorzien van meerruits bovenlichten. De ingang bevindt zich in de hoektravee, waar tevens een vroegtwintigste-eeuwse stadsklok is aangebracht.
Tussen de grote, vooruitspringende panden nr. 45 en 69 staat een tiental kleinere, meest achttiende en negentiende-eeuwse woonhuizen, die hun oorspronkelijke uiterlijk in wisselende mate bewaard hebben. De nrs. 49, 53, 55 en 67 behoren tot de slechts zes panden in de straat die noch rijks-, noch gemeentemonument zijn. Van de meeste panden zijn de puien gewijzigd. Vermeldenswaard is de fraaie, laatnegentiende-eeuwse winkelpui, alsmede de sgraffitolijst onder de dakrand, van nr. 63.
Het laatste pand aan de zuidzijde van Hoogbrugstraat (nr. 69) is een bijna geheel vrijstaand hoekhuis, waarvan de oostzijde naar de Hoogbrugstraat is gericht, de noordzijde aan Waterpoort grenst, en de westzijde en een gedeelte van de zuidzijde aan de Ruiterij liggen. Het is een groot huis van baksteen met een uitkragend schilddak dat aan drie zijden een dakkapel geeft. De gevel aan Hoogbrugstraat telt drie bouwlagen en vijf traveeën. De plint en de hoekblokken zijn van Naamse steen, maar de laatste reiken niet verder dan halverwege de eerste verdieping. De segmentbogige ingang en de veertien vensters zijn volkomen symmetrisch geplaatst, maar nemen naar boven toe in hoogte af. De sluitstenen in de omlijstingen van Naamse steen zijn versierd met diamantkoppen. De gevel wordt verstevigd en versierd door zestien symmetrisch aangebrachte muurankers.
Gevelstenen
De straat telt zeventien gevelstenen, waarbij de diverse jaarstenen, de oorlogsplaquette op nr. 9 en de struikelsteentjes bij nr. 39 niet zijn meegerekend. Op twee na dateren ze allemaal uit de achttiende eeuw. De wapensteen van de hierboven beschreven Poort van Beusdael is de oudst bewaard geblevene en dateert uit 1690. De gevelsteen van Hoogbrugstraat 15 is een replica uit 2002. De steen op nr. 70 is afkomstig van een afgebroken pand in het voormalige Ruiterstraatje, tegenwoordig Ruiterij. Hieronder een selectie.
Straat in Maastricht-Centrum
Wyck | {
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You may decide to take out private health insurance in the UK or take out insurance in your home country before arriving in the UK. There are a vast range of companies providing this service via the internet.
University employees have access to health care cash plans and a discounted private medical scheme, which aim to provide health care at more affordable rates. Please see the University health benefits webpage for further information. | {
"redpajama_set_name": "RedPajamaC4"
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Easter is just around the corner and our neighbours at Haddon Hall will be opening their doors in time for the Easter celebrations!
Haddon Hall opens its doors this Easter and celebrations will begin with a guitar ensemble on Saturday 26th of March, led by Richard Haslam, a student at Royal Northern College of Music. On Sunday 27th and Monday 28th of March the fun continues with Easter crafts and an Easter Trail – you can even wear your Easter bonnet! If you visit Haddon Hall on Sunday 27th you can also have your face painted to complement your bonnet and spring outfit.
Haddon Hall has many exciting events in the diary as the warmer months approach – from May Day celebrations, to a flower exhibition and fun with archery. Take a look at their upcoming events for more information, and plan your next adventure.
If you would like to preview the historic delights of Haddon Haddon Hall as you enjoy a cup of tea at home, take a look at this virtual tour of the medieval manor. Just a few miles from Haddon Hall, we look forward to welcoming you to The Peacock this Spring. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,119 |
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